T /^/(o PARTIAL REFERENCE INDEX Tables of Quantities of Materials for Concrete and Mortar. . .213-215 Tables of Quantities of Materials for Rubble Concrete 216-217 Tables and Diagrams of Compressive Strength of Concrete. . .312-316 Laws of Proportioning Concrete 194 Working Stresses in Reinforced Concrete 573 Tables for Rectangular Beam Design 576-578 Tables for T-beam Design . 586-588 Tables for Beams with Steel in Top and Bo'ttom 589-592 Tables for Number and Spacing of Stirrups 585 Tables for Slab Design 579-584 Tables of Constants for Beam Design 596-598 Tables for Column Design 599-603 Diagrams for Beams with Steel in Top and Bottom 593-595 Bending Moment Diagrams 505-508, 604-606 Beam and Slab Design 481-496 Flat Slabs 540-551 Column Design 558-565 Example of Floor Design 553 Example of Beam Bridge Design 696 Example of Arch Design 733 Specifications for Reinforced Concrete 28 Specifications and Methods of Testing Cement 62 Tests of Aggregates 115 Feret's Tests of Strength of Mortars 146 Surface Finish 262 Note. — The attention of those who are not especially familiar with concrete construction is called to Chanter T. nng^ t in -.>.:-i- ' ■■'- — ^=-i- -t^ .fa . — <■'- ■ ^ j out and the Chapter II Cornell inntverstt^ Xibrar^ OF THE mew l^orJ^ State Colleae of agriculture .^xi '7 •) 1 Cornell University Library TA 439.T25 1916 A treatise on concrete, plain and reinfor 3 1924 003 647 355 The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924003647355 1^%^ b > O C- a^ A TREATISE ON CONCRETE PLAIN AND REINFORCED MATERIALS, CONSTRUCTION, AND DESIGN OF CONCRETE AND REINFORCED CONCRETE WITH CHAPTERS BY R. FERET, WILLIAM B. FULLER, FRANK P. McKIBBEN AND SPENCER B. NEWBERRY COMPLEMENTARY BOOKS BY THE SAME AUTHORS CONCRETE COSTS AND (IN PREPARATION) EARTHWORK BY HAND AND MACHINE BV FREDERICK W. TAYLOR, M.E.. Sc.D. SANFORD E. THOMPSON, S.B. M.Am.Soc.C.E. Consulting Engineer THIRD EDITION TOTAL ISSUE, NINETEEN THOUSAND NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL, Limited 1916 CopintlGHT, 1905, IQOg, BY FREDERICK W. TAYLOR Copyright, 1916, by Estate of FREDERICK W. TAYLOR and'SANFORD E. THOMPSON All rights resened COMPOSED AND PRINTED AT THE WAVERLY PRESS By the Williams & Wilkins Company Baltimoei:, Md., U. S. A. PREFACE TO FIRST EDITION This treatise is designed for practicing engineers and contractors, and a I.St) for a text and reference book on concrete for engineering students. To broaden the scope of the work and avoid personal inaccuracies, each chapter has been submitted f3r critcism to at least one, and, in some cases, to three or four specialists in the particular line treated. We have aimed to refer by name to all authorities quoted, and where the data is taken from 1 ooks or periodicals, to give the original publication, so that- each subjecT may be mvestigafed further. Proof clippings have also been submitted for approval to those whose names are mentioned. Numerous cross refer- ences will be found as well as many repetitions, inserted for the purpose of -:mphasizing important facts. The chapters are arranged for convenience in reference, and therefore are not always in logical order. The Concrete Data in Chapter I presents a list- of definitions of words and terms relating distinctively to cement and concrete; a summary of the most important facts and conclusions, with references to the pages discuss- ing them; data on concrete labor, and conversion ratios. The Elementary Outline of the Process of Concreting, Chapter II, is de- signed, not for the civil engineer, but for those seeking simple directions as to the exact procedure in laying a small quantity of concrete. Most of the subjects there treated are discussed at length in subsequent chapters. The Specifications for Cement in Chapter III include the latest recom- mendations of committees of our national societies, with incidental changes to adapt them for direct use in purchase specifications. The Concrete Specifications have been prepared by the authors to represent standard practice. Specifications for First-class or High Steel, drawn up by Mr. Taylor, are, we believe, the first recommendations which have been rnade to safely adapt this important material to reinforced concrete construction. In Chapter IV the Choice of Cement is considered in an elementary fashion, which will serve as a guide to the constructor. Classification of Cements, Chapter V, distinguishes the various cements and limes manu- factured in the United States and Europe. W PREFACE Mr. Spencer B. Newberry, an international authority on the subject treated, has very kindly written for us Chapter VI on the Chemistry of Hydraulic Cement, discussing this complex subject in such a clear and prac- tical manner that it will be of interest not only to the scientist, but also to the general reader and to the cement manufacturer. Mr. Newberry has also criticised Chapter V. Chapters VII and VIII give the latest information on the testing of ce- ment. Chapter IX presents practical rules for selecting sand for mortar, and the effect of different sands and of foreign ingredients upon its quality. Characteristics of the Aggregate are further treated, and practical data in regard to it are given in Chapter X. The subject of Proportioning Concrete has been treated, at our request, by Mr. William B. Fuller, the concrete expert, and his practical use of mechanical analysis is fully discussed. The tables of Quantities of Materials for Concrete and Mortar, in Chapter XII, and the diagram of curves, will be found useful in estimating materials. The Strength of Concrete, Chapter XX, is taken up from a practical standpoint so that the data may be directly employed in design. The theory and design of reinforced concrete are as yet in an elementary stage, but the rules and tables in Chapter XXI represent the most ad- vanced knowledge on the subject. Practical methods of Mixing and Laying Concrete are treated in Chap- ters XIII, XIV and XV. Mr. Ren6 Feret, of Boulogne-sur-Mer, France, whose extended researches enable him to speak with authority, has kindly written for us Chapter XVI, entitled The Effect of Sea Water. Chapters XVII, XVIII and XIX, on Freezing, Fire and Rust Protection, and Water- Tightness are of practical interest to the contracting engineer. Plain and Reinforced Concrete Structures are treated in as much detail as space permits in Chapters XXIII to XXVIII inclusive. The designs are taken mostly from original drawings redrawn by the authors. They have been selected, not as extraordinary productions, but because the data in regard to them may be of use in designing similar structures. Methods of Cement Manufacture in its modern types are described in detail in Chapter XXX. The References in Chapter XXXI will be found especially valuable to one pursuing more extended investigations than can be presented in a volume of tbis size. They have been selected from the large number contained in the authors' index, as those which it may be to the advantage of the reader to consult. Note: The chapter numbers have been changed to agree with the Second Edition. PREFACE V The articles are usually described by their subject-matter rather than by their titles verbatim. Appendix I gives the method of chemically analyzing cement and cement materials according to the recommendations of the American Chemical Socle- 7. Additional formulas for reinforced concrete beams, too complicated for insertion in the body of the book, are given in Appendix II, these having been kindly compiled by Prof. Frank P. McKibben for this treatise. The authors desire to express their sincere appreciation of the various kindnesses extended to them while compiling the work. It has been neces- sary, because of the lack of authoritative information on many fundamental questions, not only to conduct numerous original investigations, but also to correspond with the most prominient engineers in this country, and with experts in England, France, and Austria. Mr. Feret, besides writing the chapter on The Effect of Sea Water, has kindly criticised Chapter IX, and made numerous suggestions which have been incorporated. Mr. Fuller has examined and criticised all the chapters on practical con- struction, and Prof. McKibben has rendered material assistance in the hne of investigations and criticisms relating to the theories of reinforced con- crete. The authors are indebted to many gentlemen for careful criticism of chapters or portions of chapters, for drawings, or for replies to questions, and take this opportunity to express their sincere appreciation of all such assistance. Among those to whom especial acknowledgment is due are the following: Messrs. Earle C. Bacon, David B. Butler (England), Harry T. Buttolph, Howard A. Carson, Edwin C. Eckel, William E. Foss, George B. Francis, John R. Freeman, Charles S. Gowen, Allen Hazen, Rudolph Hering, James E. Howard, Richard L. Humphrey, A. L. Johnson, George A. Kim- ball, Robert W. Lesley, Alfred Noble, William Barclay Parsons, Henry H. Quimby, George W. Rafter, Ernest L. Ransome, Clifford Richard- son, Thomas F. Richardson, A. E. Schutt6, W. Purves Taylor, Edwin Thacher, Leonard C. Wason, George S. Webster, Robert Spurr Weston, Joseph R. Worcester; and Professors Ira O. Baker, Lewis J. Johnson, Edgar B. Kay, Gaetano Lanza, Charles L. Norton, Charles M. Spofford, George F. Swain, Arthur N. Talbot. Cuts have kindly been furnished by Allis-Chalmers Co., Austin Manu- facturing Co., Automatic Weighing Machine Co., Bonnot Co., Bradley Pulverizer Co., Clyde Iron Works, Contractors Plant Co.. Drake Standard VI PREFACE Machine Works, Fairbanks Co., Falkenau-Sinclair Machine Co., Farre] Foundry and Machine Co., Iroquois Iron Works, Kent Mill Co., Link-Belt Engineering Co,, McKelvey Concrete Machinery Co., W. F. Mosher & Son, Tinius Olsen and Co., Philadelphia Pneumatic Tool Co , Thos. Prosser and Son, Ransome Concrete Machinery Co., Riehle Bros. Testing Machine Co., Robins Conveying Belt Co., Sherburne and Co., T. L, Smith, Henry Troemner, Tucker and Vinton. FREDERICK W. TAYLOR. SANFORD E. THOMPSON. February, 1905. The writer wishes to state that the investigation and study necessary for the writing of this book were done by his colleague, Mr. Thompson, and desires that full credit for this should be given to him. Frederick W. T.a,ylor. • PREFACE TO THIRD EDITION . Developments in reinforced concrete as a result; of tests and experi- ence since the issue of the Second Edition have made it necessary to greatly enlarge the treatment of design and construction. As in previous editions, the aim has been to give to the construction engineer, the architect, and the contractor^ data for design and for build- ing, and to the student a compreherisive and practical text and reference book useful not inerely for the, study of theory at college, but to pre- serve and iise in practice. The comprehensive treatment of both plain and reinforced concrete in a single volume — for reinforced concrete can- not be made satisfactorily unless the laws and best practice in plain concrete are followed— give it a peculiar value for the* practicing engineer. The entire volume has been revised and largely rewritten. The most important changes, as indicated, are in the portion of the book treating of reinforced concrete. Instead of a single chapter, three chapters are presented: Chapter XX on Tlieory, giving the derivation of formulas; Chapter XXI on Tests, selected from experiments in this couijtry and abroad that give a definite basis for theory and practice; and Cliapter XXII on Design, with working formulas and methods of design.. As important features of reinforced concrete. Chapter XXIII on Build- ing Construction has been rewritten and enl3,rged, giving, as illustrations, drawings of tj^ical structures and , many details showing rciethods of handling the design in the drafting rooms of the architect and the en- gineer; an entirely new chapter, XXV, on Beam Bridges, lias been writ- ten with examples worked out for .different types of design; Chapters XXVII to XXXI have bqen revised. ' ..,...',... , . ■, The Arch chapter kindly prepared by Prof. Frank P. McK^ibben for the second edition remains substantially the same; the material on stress distribution has been rewritten and transferred to Chaptier XX. Prominent among^ the additions in the first part of the book are the Specifications for Reinforced Concrete written by the author for the construction of' the Massachusetts Institute of, Technology buildings; tlie new^ cenie'nt specifications presented by the Joint Conferences and adopted, in' 1916;' and the .revised chapter on Chemistry of Hy- drauhc Cements by Mr. Spencer B. Newberry. Chapters XIII and XIV, Mixing and Depositing, have been rewritten. viii PREFACE Chapter XV on the Effect of Sea Water has been submitted to the author, Mr. R. Feret, who has approved it with certain revisions. The effect of various agencies upon concrete is treated in Chapters XVI and XVII. Water-tightness, Chapter XVIII, and Strength of Plain Concrete, Chapter XIX, particularly the latter, have been changed so as to give results of recent tests and the conclusions derived from them. In the Preface to the Second Edition acknowledgment was made to Messrs. E. D. Boyer, R. D. Bradbury, WilHam B. Fuller, Frank P. McKibben, Spencer B. Newberry, George F. Swain, Arthur N. Talbot, Joseph R. Worcester, and Edward Smulski. In the Third Edition thanks are due Messrs. Duff A. Abrams, Earnest Ashton, P. H. Bates, Edward D. Boyer, Lewis R. Ferguson, William B. Fuller, Robert W. Lesley, Spencer B. Newbury, Henry H. Quimby, Henry J. Seaman, Henry S. Spackman, Charles M. Spofford, Stone & Webster Engineering Corporation, George F. Swain, Arthur N. Talbot, George S. Webster, Rudolph J. Wig, Joseph R. Worcester. Special acknowledgment is due to Mr. Edward Smulski for his most valuable assistance and collaboration in the preparation of Chapters XX, XXI and XXII on Reinforced Concrete; to Mr. Royall D. Brad- bury for assistance in connection with Chapter XXV on Beam Bridges; and to Mr. Harold M. Davis for thorough work of analysis of material and in preparing the book for publication. Acknowledgment for cuts is made to Aberthaw Construction Co., Ambursen Co., American Concrete Institute, American Luxfer-Prism Company, Atlas Portland Cement Co., Austin Manufacturing Co., Burchartz Fireproofing Co., Inc.,Condron Co., Dayton Malleable Iron Co., Engineering Record, Fairbanks Co., Farrell Foundry & Machine Co., Howard & Morse, Lakewood Engineering Co., Special Committees on Cement Testing, Tinius Olsen Co., Ohio State Highway Department, Ransome Concrete Machinery Co., Raymond Concrete Pile Co., Simp- son Bros. Corp., Sterhng Wheelbarrow Co., Stone & Webster Engineer- ing Corporation, G. L. Stuebner Iron Works, Trussed Concrete Steel Co., U. S. Bureau of Standards, University of Illinois. Since the issue of the Second Edition a great loss has been suffered in the death of the senior author, Dr. Frederick W. Taylor, whose coun- sel and definite requirements were so instrumental in making the book an accepted authority. In the present revision an endeavor has been made to follow the principles laid down by our beloved colleague. SANFORD E. THOMPSON. Boston. November, 1916. CONTENTS • CHAPTER I Essential Elements in Concrete Construction Essential Elements, Summary of Important Facts, and Conclusions. . Data on Handling Concrete Labor Costs of Hand Mixing Weights and Volumes Definitions CHAPTER II ^ Elekentary Outline of the Process of Concreting Where Concrete may be Used Selection of Materials Proportions Quantities of Material Tools and Apparatus required for Concrete Work Construction of Forms Mixing and Laying Concrete Approximate Cost of Concrete Strength of Concrete CHAPTER III Specipications for Reinforced Concretb Materials and Tests Proportions Mixing and Placing Concrete Joints Splicing Reinforcement '. Principles of Design of Reinforced Concrete Columns Working Stresses CHAPTER IV Classification of Cements Portland Cement Natural Cement ix f X CONTENTS 1 PAGE Puzzolan or Slag Cement 44 Hydraulic Lime 45 Common Lime 45 ,'.- CHAPTER V , Chemistry or Hydraulic Cements. — By Spencer B. Newberry Introduction '. 48 Chemical Constitutents of Cement 49 Materials ■. . . /;■,''.■.'■'..■ ..'..,'.:.. .' 52 Proportion of Ingredients 53 Effect of Composition on Quality 59 CHAPTER VI Specifications and Tests of Cements Specifications and Methods of Tests for Portland Cement 62 Proposed Tentative Specifications and' Methods of Test for Compressive Strength of Portland Cement Mortar : , 80 Full Specifications for the Purchase of Natural Cement ' • 82 Apparatus for a Cement Testing Laboratory 83 ■ Specific Gravity of Cements ' 84 AdVa,ntages of Fine Grinding , ; . . 87 Quantity of Water for Neat Paste and Mortar 88 Tests for Setting .■ : 90 European Methods for Determining Set 90 Test of Rise in Temperature While Setting '. 93 American and European Standard Sands Compared 94 Form of Briquette for Tensile Tests , 96 Machines for Testing Tensile Strength 96 Tensile Tests of Neat Cement and Mortar; 98 Compressive Tests of Cement and Mortar. 100 Transverse Tests of Cement ......'..!' 102 Adhesion Tests of Cement 102 Soundness or Constancy of Volume 103 Color of Cement ,. ^ 112 Weight of Cement. . , 113 Microscopical Examination of Portland Cement Clinker 114 CHAPTER VII v.,- Tests of Aggregates Sampling and Shipping Sand 115 Test of Strength of Mortar ■...'.■ '. .'. J nfi Mechanical Analysis .-...,... 117 Test for Organic Impurities ....'. 118 Chemical Tests.-. :. .-. . 118 Hardness and Strength of Particles '. 119 Color Tests 119 CONTENTS 3a CHAPTER VIII Voids and Other eHASACTEEisiics op Concrete Aggregates PAGE Laws of Volumes and Voids 120 Classification of Broken Stone 121 Average Specific Gravity of Sand and Stone ; : . i2i Method of Determining Specific Gravity '. . . . . 1 24 Determination of Voids ^. 126 Voids and Density of Mixtures of Different Sized Materials 129 CHAPTER IX Strength and Composition as Cement Mortars Strength of Similar Mortars Subjected to Different Tests 145 Relation of Density to Strength ..,.,.,. 145 Granulometric Composition of Sand — Feret's Three-Screen Method of Analysis.. 155 Effect of Size of Sand upon the Strength of Mortar 160 Tests of Density and Strength of Mortars of Coarse vs. Fine Sand. 162 Practical Applications of the Laws of Density '. 163 Conversion of Mechanical Analysis to Granulometric Composition. ...... '. 164 Effect of Quantity Of Water upon the Strength of Mortar 165 Effect of Gaging with Sea Water .- 166 Limestone Sand and Screenings 166 Sand vs. Broken Stone Screenings 1 166 Sharpness of Sand 167 Effect of Natural Impurities in the Sand upon the Strength of Mortar 167 Effect of Mica in the Sand upon the Strength of Mortar 169 Effect of Lime upon the Strength of Mortar 170 Ground Terra-Cotta or Brick as a Substitute for Sand 172 Effect of Regaging Mortar ..,....,.........;..'.. 173 CHAPTER X ' ■' Proportioning Concrete — By William B. Fuxler !&nportance of Proper Proportioning^ : 175 Methods of Proportioning 176 Principles of Proper Proportioning '. > '.-. 177 Determination of the Proportion of Cement , ,. . 178 Proportioning by Arbitrary Selection of Volumes i/9 Proportioning by Void Determination - • 181 Rafter's Method of Proportioning '. '. . ' 184 French Method of Proportioning '........'..■.'. i 184 Mechanical Analysis '....'..'.'.'..'.... .':' .'.'..'... 183 Studies of the Density of Concrete .• '. '. . :'. .'. '■"■ : :' 19b Relation of Density to Strength : .".- .....'..'... 194 Laws of Proportioning : . . . . 194 Application of Mechanical Analysis Diagrams toProporfionmg. r; 1 . 196 Proportioning by Trial Mixtures '..'... ■. :' A'\ ;..'... . . ... 260 Proportions of Concrete in Practice .....'..;.. 202 xii CONTENTS CHAPTER XI Tables of Quantities or Materials for Concrete and Mortar PAGE Expressing the Proportions 205 Theory of a Concrete Mixture 207 Fonnulas for Quantities of Materials and Volumes 208 Tables of Quantities of Materials and Volumes 212 CHAPTER XII Preparations op Materials for Concrete Storing Cement 219 Screening Sand and Gravel 219 Stone Crushing 221 Washing, Sand and Stone 228 CHAPTER XIII Mixing Concrete Mixing Concrete by Hand 231 Mixing by Machinery 234 Concrete Plants 241 CHAPTER XIV Depositing Concrete Consistency of Concrete 350 Handling and Transporting Concrete 352 Depositing Concrete on Land 353 Ramming or Puddling 257 Bonding Old and New Concrete 258 Contraction Joints 259 Facing Concrete Walls 262 Depositing Concrete under Water 267 Concrete in Sea Water 268 CHAPTER XV Effect of Sea Water upon Concrete and Mortar. — By R. Feret External Phenomena 371 Action of Sulphate Waters 373 Chemical Processes of Decomposition 373 Search for Binding Materials Capable of Resisting the Action of Sea Water 374 Method of Determining the AbiUty of a Binding Material to Resist the Chemi- cal Action of Sulphate Waters 276 Mechanical Processes of Disintegration 377 Proportions for Mortars and Concretes 378 Mixtures of Puzzolan and Slag with Cements 379 Various Plasters and Coatings 380 CONTENTS xiii CHAPTER XVI Laying Concrete and Mortar m Freezing Weather PAGE Effect of Cold or Freezing 281 Construction in Freezing Weather 284 CHAPTER XVII Desiructiv,e Agencies Fire Protection 289 Theory of Fire Protection ^go Tests of Fire Resistance 291 Conductivity of Concrete and Imbedded Steel 291 Protection of Steel from Rusting 292 Effect of Acids 293 Effect of Alkalies '. . . 294 Effect of Oils 294 Electrolytic Action 29s CHAPTER XVIII Water-Tightness Concrete for Water-Tight Work 296 Special Methods for Waterproofing 1 299 Surface Treatment 299 Integral Waterproofing 301 Membrane Coatings and Asphalt 302 Laws of Permeability 304 Tests of Permeability 306 Results of Tests of Permeability 307 CHAPTER XDC Strength of Plain Concrete Compressive Strength of Concrete 310 Formula for Strengthof Concrete 313 Compressive Strength of Concrete in Practice 315 Maximum Strengths Recommended by the Joint Committee , 316 Relation of Percentage of Cement to the Strength of the Concrete 316 Effect of Consistency 317 Machine Versus Hand Mixed Concrete 319 Effect of Curing on Strength 320 Growth in Strength of Concrete 322 Effect of Aggregates upon the Strength of Concrete 322 Effect of Size of Coarse Aggregate 322 Effect of Quality of Stone 3^3 Slag 326 Cinders ,. •. 3^7 XIV CONTENTS PACE Coke Breeze 329 Effect of Concentrate^ Loading 330 Tensile Strength of Concrete 332 Transverse Strength of Concrete 332 Formula for Transverse or Bending Stress in Plain Concrete 333 Strength of Concrete in Shear 337 Fatigue of Cement . ', 338 Plasticity of Concrete 339 Determining Proportions of Old Concrete 339 Machines for CompresEive Tests r. . . . . . 340 Sawing Test Specimens 341 Microphotography of Concrete 342 Methods of Testing Concrete •.'...• '. 343 Specimens for Compressive Tests 343 CHAPTER XX Theory of Reinforced Concrete General Principles of Reinforced Concrete Beams 350 Assumptions ■■■■.■■. 3Si Analysis of Rectangular Beams 352 Bending Moment and Moment of Resistance. . . , 352 Straight Line Formula 352 Formulas for Rectangular Beams .' 353 Formulas for T-Beams . 355 Reinforced Concrete Beams with Steel in Top and Bottom 358 Steel in Bottom of Beam, Concrete Bearing Tension 360 Shearing Stresses in a Beam or Slab 362 Diagonal Tension in Simply Supported Beams ; 366 Diagonal Tension in Continuous Beams '.....' 366 Formulas for Shearing Stresses and Diagonal Tension . . .'. 366 Distribution of Diagonal Tension tp Concrete and Stirrups 370 Area and Spacing of Vertical Stirrups 371 Usefulness of Web Reinforcement; .'. 374 Web Reinforcement for Continuous Beams 374 Web Reinforcement for Cantilevers ' 375 Column Formulas • ■ • • . 375 Members under Flexure and Direct Stress. 377 Plain Concrete Section Under Direct Stress an<}, Bending Moment ^ 377 Distribution of Stresses in Reinforced Concrete Sections 380 Reinforced Concrete Rectangular Sections . .^ 381 Formulas for Reinforced Concrete Chimney and Hollow Circiilar Beam De- signs '390 CHAPTER XXI . . , , Tests of Reinforced CbHrCRfeTE'' • • ■ Modulus of Elasticity of Steel 400 Modulus of Elasticity of Concrete 400 Tests of Rectangular Beams 465 CONTENTS XV PACE PKenomena of Loading Rectangular Beams 405 Appearance of First Crack and Corresponding Stretch in Concrete 407 Professor Bach's Tests 408 Position of Neutral Axis 410 Stresses in Steel for Varying Intensity of Load , 411 Compressive Stresses in Conprete , 414 Tests with Compressive Failure 414 Tests of T-Beams 415 Tensile Failures of T-Beams 415 Tests of T-Beams to Determine the Effective Width of Flange 416 Tests of Beams to Determine Effect of Diagonal Tension 418 Behavior of Beams Failing by Diagonal Tension Under Load 425 Beams. Without Shear Reinforcement 426 Beams Reinforced for Tension and Compression 427 Tests of Bond Between Concrete and Steel 429 Pull-Out Tests 430 Bond Stresses in Beams 434 Hooks as End Anchorage 438 Action of Hooks in Beams 438 Splices of Tensile Reinforcement in Beams at Points of Maximum Stress. . . . 439 Deflection 44° Tests of Continuous Beams 441 Tests of Slabs to Determine Distribution of Load to Joists 447 Tests of Plain Concrete Columns 450 Concrete vs. Brick Columns 45^ Tests of Columns Reinforced with Vertical Steel 4S3 Tests of Spiral Columns 45^ Tests of Square Columns with Rectangular Bands 460 Tests of Columns with Structural Steel Reinforcement 461 Recommendations for the Design of Fireproof ed Columns 466 Tests of Long Columns 466 Resistance of Concrete and Reinforced Concrete to Twisting 466 Tests of Reinforced Concrete Buildings Under Load 468 Wenalden Building Test 47° Turner-Carter Building Test 47i Tests of Octagonal Cantilever Flat Slabs 472 CHAPTER XXn Reinforced Concrete Design Ratio of Moduli of Elasticity 477 Modulus of Elasticity in Tension 47? Quality of Reinforcing Steel • 478 Bending Test for Steel ■ 480 Formulas for Design of Rectangular Beams 481 Depths and Loads for Different Bending Moments 483 Formulas to Review a Beam Already Designed 483 Design of Slabs 484 xvi CONTENTS PAGE Reinforcement over Girders 486 Square and Oblong Slabs Supported by Four Beams 486 Design of T-Beam 487 Design of Beams with Steel in Top and Bottom 492 Details of Continuous Beams at the Support 496 Effect of Varying Moment of Inertia upon Bending Moment 499 Span of a Continuous Beam or Slab 5°° Distribution of Slab Load to Supporting Beams 500 Distribution of Beam and Slab Loads to\jirders 501 Bending Moments and Shears 502 Shear and Bending Moment Diagrams 504 Bending Moments to use in Design of Reinforced Beams 5^° Design of Wall Columns and End Beams 513 Vertical and Horizontal Shearing Stresses 515 Diagonal Tension 516 Area and Spacing of Vertical Stirrups 517 Uniformly Distributed Loading 518 Bent-up Bars and Inclined Stirrups 519 Web Reinforcement for Continuous Beams 520 Types of Shear Reinforcement 522 Design of Web Reinforcement 522 Diameter of Stirrups 525 Graphical Method of Spacing Stirrups 526 Stirrups for Moving Loads S31 Bond of Steel to Concrete in a Beam 533 Points to Bend Horizontal Reinforcement. 535 Lateral Spacing of Tension Bars 537 Depth of Concrete Below Steel 538 Length of Bar to Prevent SUpping 539 Recommendations as to the Size and Shape of Hook 540 Flat Slabs 54° Action of Flat Slabs S44 Design of Flat Slabs 546 Formulas for Bending Moments for Flat Slabs S47 Flat Slab End Panels 548 Reinforcement for Flat Slabs 549 Punching Shear and Diagonal Tension 549 Column Heads 551 Drop Panel 551 Thickness of Slab 551 Example of Beam and Slab Design 552 Miscellaneous Examples of Beam and Slab Design 557 Concrete Columns 55S Design of Reinforced Concrete Columns 559 Column Examples 564 Reinforcement for Temperature and Shrinkage Stresses 565 Systems of Reinforcement 570 CONTENTS xvii PAGB Working Unit Stresses 573 Table i. Areas, Weights and Circumferences of Bars 574 Tables 2 to 10. Besign of Beams and Slabs 576 Tables 11 to 13. T-Beams 586 Table 14. Beams with Compression Steel 589 Diagrams i to 3. Beams with Compression Steel 593 Tables 15 and 16. Tables for Constant, C 596 Table 17. Proportional Depth of Neutral Axis S98 Tables 18 to 21. Column Tables 599 Diagrams 4 to 6. Bending Moments for Different Spans and Loads. 604 CHAPTER XXIII Building Construction Relative Costs of Buildings of Different Materials 608 Actual Cost of Reinforced Concrete Buildings 611 Building Design and Construction 612 Typical Layouts 616 Floor Loads 617 Materials for Building Construction 620 Cinder Concrete 620 Concrete Blocks; Ornamental Stone 623 Concrete Floor Systems 624 Shafting Hangers and Inserts 630 Concrete Coluimis 631 Granolithic Floors 635 Brief Specifications for Lajmig Granolithic Finish on a Set Concrete Floor 637 Grinding Granolithic Surface 638 Concrete Stairs 639 Concrete Roofs 642 Concrete Walls , 643 Walls of Mortar Plastered upon Metal Lath 645 Unit Building Construction 646 Forms for Building Construction 646 Steel vs. Lumber ^ 647 Removal of Forms 648 Column Forms • 631 Beam and Girder Forms 651 Slab Forms 653 Wall Forms 656 Construction Methods 658 Bending Steel 6S9 Reinforced Concrete Chimneys 660 Design of Reinforced Concrete Chimneys 662 Summary of Essentials in Designs and Construction 664 Example of Chimney Design 6^6 xviii CONTENTS CHAPTER XXIV Foundation and Piers PACE Bearing Power of Soil and Rock , , 669 Concrete Capping for Piles , 670 Plain Concrete Footings 672 Reinforced Concrete Footings 673 Independent Column Footings 673 Combined Footings 678 Spread Footings , 684 Foundation Bolts 684 Concrete Piles 685 Sheet Piling '. 688 Bridge Piers 689 Foundations Under Water 6go CHAPTER XXV Beam Bridges Slab Bridges 693 Girder Bridges , 694 Loads 695 Design for a Slab Bridge 696 Design for a Girder Bridge 698 Through Girder Bridges 704 Continuous Girder Bridges '. 704 CHAPTER XXVI Arches. — By Frank P. McKibben Concrete versus Steel Bridges 708 Use of Steel Reinforcement 709 History of Concrete Arch Bridges 710 Classification of Arches 710 Arrangement of Spandrels and Rings 712 Hinges 713 Shape of the Arch Ring 714 Thickness of Riag at Crown 714 Live Loads for Highway Bridges ! 715 Live Loads for Railroad Bridges 717 Dead Loads and Earth Pressure . . 718 Outline of Discussion on Arch Design ; . . . 718 Relation between Outer Loads and Reactions at Supports 719 Notation 719 Three-Hinged Arch , 720 Two-Hinged Arch ., : . • 721 "Fixed" or "Continuous" Arches 722 CONTENTS xJx T» • I'ACE Relation between Outer Forces and the Thrust, Shear and Bending Moment for the Fixed Arch _2, Thrust, Shear and* Moment at the Crown -25 Graphical Method for Finding Constant - -2g Line of Pressure ' ,..;,,..;.. - 720 Effect of Temperature and Thrust ...,,...'«.: ." 720 Effect of Rib Shortening Due toThrust ..,.'. 7,2 Distribution of Stress over Cross Section ^,2 Method of Procedure for the Design 6i an Arch 7,3 Loadings to Use in Computations. . . .-. 738 Allowable Unit Stresses 74 1 Design of Abutment 741 Erection 744 Examples of Arch Bridges 748 CHAPTER XXVII Dams and Retaining Walls Retaining Walls 751 Foundations 753 Design of Retaining Walls of Gravity Section 754 Weight of Earth; Backing 756 Earth Pressure 757 Design of Reinforced Retaining Walls 760 Ejsample of Retaining Wall of T-Type 762 Example of Retaining Wall with Counterforts 765 Copings 768 Dams 768 Design of Dams 770 Core Walls 774 Temperature Changes in Concrete Dams 775 CHAPTER XXVIII Conduits and Tunnels Conduits -. 777 Moments and Pressures 781 Methods of Construction and Forms 786 Tunnels 788 Subways 789 CHAPTER XXIX Reservoirs and Tanks Open Reservoirs ' 791 Covered Reservoirs 792 Standpipes 794 Small Tanks 796 XX CONTEXTS CHAPTER XXX - Concrete Pavements and SroEWALKS , ^ PAGE Design of Pavements 79q One-course vs. Two-course 799 Proportions and Materials 799 Consistency 8oo Joints .- Sod Reinforcement 801 Construction , Sot Mixing and Placing 8or Finishing and Curing 8or Method of Laying Sidewalks 803 Cost and Time of Sidewalk Construction 808 Driveways ^ 810 Quantities of Materials for Sidewalks 811 CHAPTER XXXI Cement Manupacture Historical 813 Production of Cement 814 Portland Cement Manufacture 815 Natural Cement Manufacture 824 Puzzolan Cement Manufacture 825 CHAPTER XXXII Miscellaneous Structures , 827 CHAPTER XXXIII References to Concrete Literature 830 APPENDIX I Method of Combining Mechanical Analysis Curves 855 A Treatise on Concrete CHAPTER I ESSENTIAL ELEMENTS IN CONCRETE CONSTRUCTION The forming of concrete structures is essentially a manufacturing op- eration, and requires more close attention to detail both in the design and the building than most other classes of construction. For the benefit of those who are not thoroughly experienced, a number of the most essential elements are recorded below with references to pages upon which more detailed information may be obtained. An outline of the process of concreting, in elementary form, is given in Chapter II, page ii. CEMENT PAGE Cement should be sampled and tested in a laboratory except for imimportant structures 6i Cement should be purchased, even if not tested, with the require- ment that it must pass the specification of the American So- ciety for Testing Materials 28, 6i Portland cement is the only cement that can be used for all kinds of concrete work 12 SAND Tests of the sand, unless it come from a bank which has been pre- viously tested, are as necessary as tests of the cement 115 Vegetable matter in sand, even in small amount prohibits its use. . 168 Clay or Loam in sand is sometimes iajurious to mortars because introducing too much fine material, while in other cases it may be beneficial because the fine material is needed 167 Sharpness of grain is not necessary. 167 QuaJity of sand is chiefly dependent upon the coarseness and rela- tive coarseness of its grains 160 Fine sand, even if free from vegetable matter, makes a much weaker concrete than coarse sand. For imimportant work, if clean, it may sometimes be used, but it is usually cheaper to import a coarse sand and use leaner proportions 117, i46» 162 2 A TREATISE ON CONCRETE PAGE Nearly double the cement must be used, for equal strength with an equally clean sand if the grains are mostly less than ^-inch diameter, than if the grains are mixed rimning up to J-inch More water is needed in mortar of fine sand i6o Mixed Sand usually weighs more and contains a smaller volume of voids than coarse or fine sand 132 Voids in sand can not be accurately determined by pouring water into it, but can be found by weighing the sand and finding its moisture 126 Comparison of Sands can not be made by a study of voids because of the effect of varying degrees of moisture 138 Moist Sand measured loose is lighter in weight than loose dry sand 137 Specific Gravity of dry sand may be taken at 2.65 123 COARSE AGGREGATE Maximum size of stones should be such that the concrete is readily placed around the steel reinforcement and into the corners of the forms. For reinforced concrete a maximum size of one inch is sometimes specified 29 Soft stone should be avoided in important structures 323 Gravel, if used, must be clean; that is, the particles must be free from, coatrag of vegetable matter or clay which wUl retard the setting or prevent the cement from sticking to the pebbles. . 29, 326 Gravel can be washed satisfactorily only with special apparatus ... 228 Gravel, because of its rounded grains, contains fewer voids than broken stone even when the particles in each have passed through and been caught by the same screens 135 Smallest Percentage of Voids occurs in a mixture of sizes so graded that the voids of each size are filled with the largest particles which will enter them 132 Density of a mixture of coarse stones and sand is greater than that of the sand alone 133 Fuller and Thompson's Experiments show that the perfect grada- tion of sizes of aggregate appears to occur when the percent- ages of the mixed aggregate passing different sizes of sieves are defined by a curve which is a combination of an ellipse and a straight line 192 ESSENTIAL ELEMENTS 3 STRENGTH OF CONCRETE AND MORTAR PAOE With the same Aggregate the strength and water-tightness of a con- crete or mortar increases as the percentage of cement in a unit volume of mortar or concrete is increased 144 With the same Percentage of Cement the strength and the water- tightness of a concrete or mortar usually increases with the density 144 Concrete may often be increased in strength and made more water- tight by substituting more stone for a portion of the sand . 134 Strongest Mortar for any given proportions of cement to dry sand by weight is obtained from sand which produces the smallest volume of plastic mortar 164 Sharp Sand pro4uces but sUghtly stronger mortar than rounded sand 167 Coarse Sand produces stronger and usually more impervious mortar than fine sand 160 Mixed Sand, i.e., sand containing fine and coarse grains, in mortars leaner than i : 2 usually produces stronger and more impervi- ous mortars than coarse sand 165 Fine Sand always produces mortars of lower strength than coarse sand 160 Screenings from broken stone usually produce stronger mortar than sand 166 Mixtures of fine and coarse sand or of sand and screenings (or crusher dust) often produce better mortar than either material alone 163 Variation of Sand in different portions of the same bank may be util- ized by requiring the contractor to mix two sizes without exact measurement, so that the material as delivered shall contain not less than a definite percentage of sand coarse enough to be retained on a certain sieve 163 Form of Sand Grains and mineralogical nature of sand have but little effect upon the strength of the mortar 167 Clay or Loam in the sand is apt to weaken rich mortars and strengthen lean mortars 169 Gravel vs. Broken Stone Concrete. The difference in quality is so slight that usually the cheaper material may be selected. Gravel concrete, because of the smooth, rounded surfaces, ap- pears from tests to be weaker than broken stone concrete if 4 A TREATISE ON CONCRETE PAGE the sizes of particles in the two cases are alike, but a gravel mixture may require less cement because of better gradation of sizes of particles 324 Wet vs. Dry Concrete. A medium wet quaking mixture gives the most uniformly strong concrete. Dry mixed concrete may be strongest at very short periods 251 Excess of Water decomposes the cement and is very detrimental.. . 318 PROPORTIONING, MIXING AND PLACING Proportions must be accurately measured 231 Mixing must be thorough; concrete is improved by long mixing — 231 Machine mixing is better than hand mixing 231, 320 Enough water must be used in reinforced concrete so the mass will just flow sluggishly around the steel to thoroughly imbed it. 31, 251 For foundations of mass concrete, a jelly-like mass which will shake when being rammed is best 251 If concrete stiffens in barrows or in mixer it indicates that the cement has a "flash" set and it should not be used 92 If cement with a flash set has, been. used inadvertently the concrete must be soaked with water until it hardens 93 Old and new concrete must be bonded for tight work 258, 297 Joints in floor construction should be made in center of span 32, 259, 284 Surface treatment must be skillful, roughening is usually best 262 Plastering on external surfaces should be avoided 262 FORMS Forms must be braced securely to avoid being thrown out of line by the concrete or by the workmen 19, 658 Struts and braces supporting the forms must be strong enough to withstand the weight of the concrete above it and also a con- struction load of 50 to 75 pounds per square foot 658 Boards and planks need but few nails unless the forms are built so that the pressure tends to separate them from the cleats 65 8 Forms should be cleaned of all dirt and chips before laying con- crete. A steam hose is effective for this purpose 31 Column forms should be made with cleanout opening in lower end. 651 Forms cannot be straightened or lined up after concrete is placed.. 658 Wall forms usually may be removed in 24 to 48 hours 648 ESSENTIAL ELEMENTS ^ 7AGE Forms supporting reinforced members should be left in place until the concrete rings sound and is not readily chipped by a blow from a pick. In mild weather i to 4 weeks is usually sufficient, according to the character of ths member 648 In cold weather great caution must be used, as concrete sets slowly; sometimes the forms must remain until warm weather 648 If dead load, that is, weight of the concrete itself, is large, the forms must be left longer for concrete to attain sufficient strength. . . 648 Earth backfill must not be placed against a wall until it is 3 to 4 weeks old unless forms are left in place and braced 644 WATER- TIGHTNESS OF CONCRETE AND MORTAR Excess of Cement increases water-tightness 298 Aggregates should be caref uUy proportioned and graded 298 Clean Gravel is better than broken stone for water-tight concrete . . 304 Quaking or Wet Consistency produces best results 298 Lay Concrete in one continuous operation 296 Layers of Waterproof Material are sometimes necessary 302 Sea- water use requires special precautions 271 EFFECT OF FREEZING Setting and Hardening of Portland cement in concrete or mortar may be retarded for several months by cold or freezing 281 Ultimate Strength of Portland cement concrete and mortar appears to be but slightly, if at all, affected by freezing 281 Thin Scale is apt to crack from the surface of walks or waUs which have been frozen 282 Heating the Materials hastens setting and retards the action of frost 285 Salt Lowers the freezing pomt 287 FIRE AND RUST PROTECTION Mix Concrete Wet to render it impervious 292 Protection of Steel requires | inch to 2 inches of concrete ' 289 Cinders do not corrode metal 292 REINFORCEMENT All steel should be subject to the bending test 48c Steel must be placed in exact position called for on plans and fixed in place during process 'of concreting to prevent displacement . 658 6 A TREATISE ON CONCRETE PAGE Round steel can be safely used in reinforced concrete since with proper imbedment the concrete adheres to it with sufficient bond to develop the full strength of the steel at its elastic limit 430 Square and flat bars do not bond as well as round 432 Deformed bars, and bars with small diameters, are especially useful where the stress falls oH rapidly, as in footings 673 Deformed bars are also advantageous for temperature reinforcement 566 Structural steel, Uke T-bars and I-beams, are not so good for rein- forcement as plain round or deformed steel bars 432 Structural steel may be used in columns either to take the entire load with concrete aroimd it for protection, or else to act with the concrete. Although generally less economical than plain bars, it may permit smaller sized columns 563 Hi^h carbon steel, if of satisfactory quahty and thoroughly tested, may be used with a higher working stress than mild steel 479 High carbon steel, unless of special quahty, is apt to be brittle, and should not receive higher working stress than mild steel 480 Steel will not rust if completely surrounded with concrete of a wet consistency 292 Changes in temperature will not cause separation of steel from the concrete 261 Bars should always be lapped for continuous reinforcement 497 DESIGN Reinforced concrete, should be designed by experienced engineers. . 608 Bending moments must be selected for individual conditions.. . 502, 510 Neither steel nor concrete must be overstressed in any part. . . 482, 484 T-beams must be deep enough to prevent overstressing concrete in the flange 489 Width of flange of T-beam is limited by span and thickness of slab.. 488 Steel across the top of a girder is necessary 486 Continuous beams or slabs must be designed at support to resist negative bending moment. This requires as much steel at top over support as at bottom in the center 498 Compression in the bottom of a continuous beam or slab at the support must be provided for 496 Shear in a T-beam must be studied to see that stem is large enough 488 Vertical or inclined steel is necessary to resist diagonal tension.. .. 516 Bars must be small enough to resist the bond stress S33 ESSENTIAL ELEMENTS 1 PAOI Ends of bars must be imbedded or lapped far enough to provide bond sufficient to prevent danger of pulling out 539 Columns may be reduced in size by using rich proportions, vertical reinforcement, hooping, or a combination of these 559 Hooping serves to increase the toughness of the column 560 Working strength of a hooped column, however, must not be based on its ultimate crushing strength 560 ESTIMATING Cost of Materials is readily estimated from the quantity used . . 24, 214 Cost of Labor of mixing, and placing concrete can be estimated with close approximation 24, 25 Cost of forms and any incidental expense are the most difficult items to correctly estimate and vary largely with surrounding condi- tions. For this reason, estimates for reinforced concrete must be based upon very accurate data and large experience 26 For complete tables of costs under all kinds of conditions with dis- cussion of economical methods of design and construction see Con- crete Costs by the same author. DATA ON HANDLING CONCRETE Large load of broken stone or gravel for iron wheelbarrow on short haul in concrete work 3.0 cu. ft. Large load of sand for iron wheelbarrow on short haul in concrete work 3.5 " " Average load of ordinary concrete* for iron wheelbarrow . . 1.9" " Large " " " " " " " ... 2.2 " " Nimiber of shovelfuls of concrete per barrow in average load 13 " " " " " " " " large " 15 Average net time of one man filling wheelbarrow with con- crete if niin. Quick net time of one man fiUing wheelbarrow with con- crete I Average quantity concrete* mixed, wheeled 50 ft., and rammed, per man, per day of 10 hourst 2. 2 cu. yd. Large quantity concrete* mixed, wheeled 50 ft. and rammed, per man, per day of 10 hoursf 3 * All measurements of concrete are reduced to terms of quantity in place after ramming. tNote that the leveling and ramming, but not the labor on forms, are included in this item. 8 .1 TREATISE ON CONCRETE Average quantity concrete* laid as above with a gang of 15 men per day of 10 hoursf 33 cu. yd. Large quantity concrete* laid as above with a gang of 15 men per day of 10 hoursf 47 " " Approximate average quantity of concrete* leveled and rammed in 6-inch layers, per man, per day of 10 hours.. 11 " " Approximate large quantity of concrete* leveled and rammed ill 6-inch layers, per man, per day of 10 hours 16 " " Approximate average surface of rough braced plank form built and removed by one carpenter per day of 10 hours 25 sq. " LABOR COSTS OF HAND MIXING. | Values apply to 1:2:4, i:2|:5, and 1:3:6 proportions, and approximately to other ordinary proportions. Wages of labor 20 cents per hour with allowance included for foremen, superintendence, miscellaneous job expenses, and small tools. Liability insurance, home office expense, and profit are not included. Labor Cost per Cu. Yd. of Concrete. Mixing and placing :§ ^pl-1^,^?" Sand and cement spread dry on stone $1.05 Stone dumped on sand and cement 1.03 Sand-cement mortar spread on stone 1.08 Add to base cost per cubic yard: For wheeHng sand each additional 50 feet fo.oi stone 0.02 loading and hauhng sand and gravel 100 feet .... 0.41 Add for each 100 feet, up to one mile. . . . o.oi loading and hauliag sand and gravel one or more miles, per mile. 1.03 screening gravel to separate sand 0.36 carrying concrete on shovels 14 feet 0.16 wheeling " 100 feet 0.16 Add for each 100 feet 0.07 " wheeling very wet' concrete 100 feet 0.22 Add for each 100 feet o. 10 hauling concrete in single carts 100 feet 0.18 Add for each 100 feet . . 0.03 •All measurements of concrete are reduced to terms of quantity in place after ramming. tNote that the leveling and ramming, but not the labor on forms are included in this item. t Summarized from Concrete Costs, Table 56, page 318. § Includes measurihg aggregates (and wheeling 25 feet if measured in barrows), wetting stone, getting and emptying cement, wetting and mixing, shoveling to place or to barrows or buckets, leveling and tamping and miscellaneous work. Number of turns: dry sand and cement, 3 turns; saad 1 Silica Si O2 21.31 21-93 .18.38 20.42 25.48 22.60 26.S 28.95 21.70 1 .03 1. 12 Alumina AI2 O3 6.89 5. 98 1 4.76 10.30 8-90 2-5 11.40 319 f c.ea Iron Oxide Fe2 O3 2-S3 2.35 ^5.20 340 7.44 5-30 l-S 0.54 0.66 H Calcium Oxide Ca O 62.89 62.92 35.84 46.64 44-54 52.69 63-0 50.29 60.70 97.02 5S.5' Magnesian Oxide Mg 2.64 1. 10 14.02 12.00 2-92 I-15 l-o 2.96 0.8s 0.68 39.Si Sulphuric Acid S O3 1-34 1-54 0.93 2.S7 2.61 3-25 o.S 1.37 0.6b Loss on Ignition 1-39 2.91 3-73 6.7s 3.68 6.11 5-0 3-39 12.20 Other constituents 0.7S 11.46 3-74 1.46 0.30 O.IO m. F. HiUebrand, Society of Chemical Industry, 1902, Vol. XXI. 2W. F. Hiilebrand, Journal American Chemical Society, 1903, 25, 1180. ^Clifford Richardson, Brickbuilder, 1897, p. 229. ^Stanger& Blount, Mineral Industry, Vol. V, p. 69. ^andlot, Ciments et Chaux Hydrauliques, 1898, p. 174. ^Le Chatelier, Annales des Mines, September and October, 1893, p. 36. ^Report of the Board of U. S. Army Engineers on Steel Portland Cement, 1900, p. 52. sCandlot, Ciments et Chaux HydrauUques, 1898, p. 24. ^Rockland-Rock port Lime Co. i^Western Lime and Cement Co- CLASSIFICATION OF CEMENTS ■ 41 PORTLAND CEMENT Portland cement is defined by Mr. Edwin C. Eckel, formerly of the U. S. Geological Survey, as follows: "By the term Portland cement is to be understood the material obtained by finely pulverizing clinker produced by burning to semi-fusion an intimate artificial mixture of finely ground calcareous and argillaceous materials, this mixture con- sisting approximately of 3 parts of lime carbonate to i part of silica, alumina and iron oxide." The definition is often further limited by specifying that the finished product must contain at least 1.7 times as much lime, by weight, as of silica, alumina, and iron oxide together. The only surely distinguishing test of Portland cement is its chemical analysis and its specific gravity. Portland cement should always be used in reinforced concrete con- struction and in any construction liable to shocks or vibration or stresses other than direct compression. White Portland Cement is manufactured for surface finish and ornamental work. It contains relatively high alumina, with only i per cent or less of iron oxide. Iron Portland Cement has been made with a view to its use in sea and alkaline waters. It contains relatively high iron, with less than 2 per cent of alumina. It is slow setting, with high tensile strength in long time tests. The term Natural Portland Cement arose from the discovery in Boulogne-sur-Mer, France, as early as 1846, of a natural rock of suitable composition for Portland cement. A similar discovery in Pennsylvania gave rise to the same term in America, but the manufacturers soon found it necessary to add to the, cement rock a small percentage of purer limestone. Since the chemical composition of Portland cement, as defined above, is substantially uniform regardless of the materials from which it is made, in the United States the terms "natural" and "artificial" are meaningless. In France, cements intermediate between Roman and Portland are caUed "natural Portlands."* Sand Cement. Sand or silica cement is a mechanical mixture of Portland cement and mineral matter, ground together very finely in a tube mill or other suitable machine. Tests by the U. S. Reclamation Service! indicate that the action of this matter on the cement when *Candiol's Ciments et Cbaux Hydrauliques, iSpS, p. 164. t Rapier R. Coghlan, Engineering Acn'i, June 19, 1913. P- I27<:, and ^- E. Sale, Engineering Con- Iracting, December 3, 1913, p. 623. 42 A TREATISE ON CONCRETE mixed with water is chemical, and to produce a satisfactory sand, a rock, such as sandstone or certain igneous rocks, which contains solu- ble or colloidal silica, must be employed. Silica in this form appears to act as a weak acid so as to form an insoluble compound with the hydrated lime set free from the Portland cement when mixed with water. The proportion of sand that the Portland cement will carry depends on the amount of colloidal silica in the rock to be used. Usually the proportions are equal parts. The production of sand cement is economical only in regions where the cost of Portland cement is very high because of long transportation. The U. S. Reclamation Service has used it on large dams throughout the West at a cost about two-thirds that of Portland cement, in spite of the necessity of building a mill at each job. The properties of sand cement are satisfactory. It sets slower but its strength at all ages is as high or higher than Portland. It is, more- over, less Uable to injury from the action of the alkalies that are abundant in the western soils and waters. Tufa Cement. A cement that partakes of the nature of both sand and puzzolan cement (see p. 44) is the tufa cement employed on the Los Angeles Aqueduct and other work in California. Tufa cement as there used is a mechanical mixture in equal parts of commercial Port- land cement and tufa rock formed from volcanic puzzolanic powder which occurs in stratified beds 100 feet or more in thickness along the line of the Aqueduct. The table below shows typical chemical analyses of Monolith tufa cement (Monolith Portland and ground Typical Analyses of Porlland Cement, Tufa Cement, and Tufa Rock Constituents. Portland Cement. Tufa Cement. 3S Tufa and Similar Rocks. aHM •rtE-i« Silica SiO Iron Oxide Fe203 . . . Alumina AI2O3 Lime CaO Magnesia MgO Sulphuric Acid SO3. Loss Other constituents. . 21.31 2 -53 6.89 62.89 i:.64 1-34 .1-39 0-7S 25.02 2.72 S-S8 62.70 ..76 1. 14 35-34 II . 41 OS 3 -04 8.52 69.46 2.52 11-37 1.80 ^-95 0-43 6.28 SI 42.36 28.3s 9-15 0-S4 0.56 13-68 4S-68 30-09 "•9S 3-76 0.56 6.30 68.49 .27 •83 •OS .67 .06 •25 ♦ W. F. Hillebrand, Society of Chemical Industry, 1Q02, Vol. XXI. t J. B. Lippincott, TransactioN American Society of Civil Engineers, Vol. LXXVI, igta, p. 526. CLASSIFICATION OF CEMENTS 43 tufa), a Lehigh Valley Portland cement, Monolith Portland cement, and several puzzolanic materials. The tufa cement mortar as tested by the Los Angeles engineers* showed higher tensile strength after ten days than straight Portland cement mortar, while the leaner the mortar the greater the ratio. The growth in strength, as shown by five year tests, is steady. In compres- sion, 1:2:4 tufa cement concrete averaged about 20 per cent, weaker than 1:2:4 Portland cement concrete at ages up to 3 months, while 1:3:6 mixes were of substantially equal strength. The slow-harden- ing property of tufa cement requires the forms to be left in place longer than is ordinarily the practice. Special care also, is necessary in pro- tecting the concrete from low temperatures and from drying out and cracking. NATURAL CEMENT Natural cement is "made by calcining natural rock at a heat below incipient fusion, and grinding the product to powder." I Natural cement contains a larger proportion of clay than hydraulic lime, and is consequently more strongly hydraulic. Its composition is extremely variable on account of the difference in the rock used in manufacture. Natural cements in the United States in numerous instances bear the names of the localities where first manufactured. For example, Rosendale cement, a term heard in New York and New England more frequently than Natural cement, was originally manufactu'red in Rosendale, Ulster County, N. Y. Louisville cement first came from Louisville, Ky. The James River, Milwaukee, Utica, and Akron are other Natural cements named for localities. In England the best known Natural cement is called Roman cement. Occasionally one hears the term Parker's Cement, so called from the name of the discoverer in England. Natural cement may be substituted for Portland in concrete, if economy demands it, for dry unexposed work where the load in com- pression can never exceed, say, 75 pounds per square inch (5 tons per square foot) and will not be imposed until three months after placing. In mortar Natural cement is adapted for ordinary brickwork not sub- jected to high water pressure or to contact with water untU, say, one month after laying, and for ordinary stone masonry where the chief requisite is weight and mass. Natural cement concrete or mortar should never be allowed to freeze, * See paper by J. B. Lippincott, Transactions American Society of Civil Engineers, Vol. LXXVI, 191.1. p. S20- t Professional Papers, No. 28, U. S. Army Engineers, p. 33- 44 A TREATISE ON CONCRETE should never be laid under water, in exposed situations, in columns beams, floors or building walls, or in marine construction. LE CHATELIER'S CLASSIFICATION OF NATURAL CEMENTS In France there are several classes of Natural cement. Mr. H. Le Chatelier* classifies Natural cements as those obtained "by the heating of limestone less rich in lime than the limestone for hydraulic lime. They may be divided into three classes: | "Quick-setting cements, such as Vassy and Roman (Ciments a prise rapide, Vassy, romain) ; "Slow-setting cements (Ciments a prise demi-lente); " Grappiers cement (Ciments de grappiers). PUZZOLAN OR SLAG CEMENT Puzzolan cement is the product resulting from mixing and grinding together in definite proportions slaked lime and granulated blast furnace slag or natural puzzolanic matter (such as puzzolan, santorin earth, or trass obtained from volcanic tufa). The ancieiit Roman cements belonged to the class of Puzzolans. Blast furnace slag is essentially an artificial puzzolana, formed by the combustion in a blast furnace, and Puzzolan or slag cements, formerly made in the United States, are ground mixtures of granulated blast furnace slag, of special composition, and slaked lime. The cement is of light lilac color, of low specific gravity (2.6 to 2.8), very finely ground, and characterized h-y an intense bluish green color in a fresh fracture after long submersion in water. Puzzolan cements must not be con- founded with true Portlands made from blast furnace slag and lime. Puzzolan or slag , cements have been limited to certain possible uses by the engineer ofiicers of the U. S. Armyf as follows: Puzzolan cement never becomes extremely hard like Portland, but Puzzolan mortars and concretes are tougher or less brittle than Portland. The cement is well adapted for use in sea water, § and generally in all positions where constantly exposed to moisture, such as in foundations of buildings, sewers, and drains, and underground works generally, and in the interior of heavy masses of masonry or concrete. It is unfit for use when subjected to mechanical wear, attrition, or blows. It should never be used where it may be exposed for long periods to dry air, even after it has well set. It will turn white and disintegrate, due to the oxidation of its sulphides at the surface under such exposure. • Proc^dfe d'Essai des Mat^riaux HydrauUques, Annales des Mines, 1893. t For description of these classes see and edition " Concrete Plain and Reinforced" pp. 49 and 50. X Professional Papers No. 28. § See Cfiapter XV, by R. Feret. CLASSIFICATION OF CEMENTS 45 Puzzolanic material has been suggested by Dr. Michaelis, of Germany, and Mr. R. Feret, of France (see Chapter XV), as a valuable addition to Portland cement designed for use in sea water. HYDRAULIC LIME The hydraulic properties of a lime — its ability to harden under water — are due to the presence of clay, or, more correctly, to the sihca in the clay. Hydraulic Ume, although not manufactured in the United States, is still used to a certain extent in Europe as a substitute for ceriient. The celebrated lime-of-Teil of France is a hydraulic lime. Beton- Coignet is a mixture of hydraulic lime with cement and sand. Hydraulic lime is made up artificially in localities where labor is very cheap, as in the British dependencies, by grinding together balls of clay and lime hydrated for the purpose. A large dam* was built in 1914 in Mexico, of one-man stone laid in mortar of hydrauhc lime made up on the job. It set very slowly, but eventually became extremely hard. Regular tests were carried on during construction. Mr. Edwin C. Eckel states f chat "theoretically the proper composition for a hydraulic limestone should be calcium carbonate 86.8%, silica 13.2%. The hydraulic limestones in actual use, however, usually carry a much higher silica percentage, reaching at times to 25%; while alumina and iron are commonly present in quantities which may be as high as 6%. The lime content of the limestones commonly used varies from 55% to 65%." Although the chemical composition of hydraulic lime is similar to Port- land cement, its specific gravity is much lower, lying between 2.5 and 2.8.| In the manufacture of hydraulic lime the limestone of the required com- position is burned, generally in continuous kilns, and then sufiicient wntet is added to slake the free lime produced so as to form a powder without crushing. COMMON LDVIE Common lime is not suitable for a principal ingredient in concrete. It will not set in contact with water, sustain heavy loads, or resist wear. The use of lime mortar, in the building laws of some cities, is limited to chimney construction in frame buildings, while other cities permit its use in walls of all except fireproof buildings. The stresses on brick laid in lime mortar should be limited to 7 tons per square foot, •Authority of William B. Fuller. \ American Geologist, March, 1002, p. 152. t Candlot's Ciments et Chaux Hydrauliques, 189S, p. 26. 46 A TREATISE ON CONCRETE Lime and Natural cement mortar is suitable for ordinary building brickwork, for light rubble foundations and for building walls. Lime and Portland cement mortar is adapted for the same purposes as mortars of lime and Natural cement, but is of superior quality and strength. The commercial lime of the United States is "quicklime," which is chiefly calcium oxide (CaO). Lime is now manufactured oy a continuous process. Limestone of a rather soft texture, so as to be as free as possible from silica, iron and alumina, is charged into the top of a kiln which may be, say, 40 ft. high by 10 ft. in diameter. The fuel is introduced into combustion chambers near the foot of the shaft, and the finished product is drawn out from time to time through another opening in the bottom of the shaft. The tempera- ture of calcination may range from 1400° Fahr. (760° Cent.) to, at times, 2,000° Fahr. (1,090° Cent.) The product (see analysis, p. 40), in ordi- nary lime of the best quality, is nearly pure calcium oxide (CaO). Upon the addition of water the lime slakes, forming calcium hydrate (CaH202), and, with the continued addition of water, increases in bulk to twice to three times the original loose and dry \-olume of the lump lime as measured in the cask. In this plastic condition it is termed by plasterers "putty" or "paste." The setting of lime mortar is the result of three distinct processes which, however, maj' all go on more or less simultaneously. First, it dries out and becomes firm. Second, during this operation, the calcic hydrate, which is in solution in the water of which the mortar is made, crystallizes and binds the mass together. Hydrate of lime is soluble in 831 parts of water at 78° Fahr; in 759 parts at 32° and in 1136 parts at 140°. Third, as the per cent, of water in the mortar is reduced and reaches five per cent., carbonic acid begins to be absorbed from the atmosphere. If the mortar contains more than five per cent, this absorption does not go on. While the mortar contains as much as 0.7 per cent, the absorption continues. The resulting carbonate probably unites with the hydrate of lime to form a sub-carbonate, which causes the mortar to attain a harder set, and this may finally be converted to carbonate. The mere drying out of mortar, our tests have shown, is sufficient to enable it to resist the pressure of masonry, while the further hardening furnishes the neces- sary bond.* Magnesian Limes evolve less heat when slaking, expand less, and set more rapidly than pure lime. A typical analysis is given on page 40. • The authors are indebted to Mr. Clifford Richardson for this paragraph. CLASSIFICATION OF CEMENTS 47 Hydrated Lime is the powdered product formed by slaking quick lime with the requisite amount of water. The material as it comes into commerce is a very finely divided white powder, and if properly pre- pared contains no unhydrated particles of lime. For this reason it is preferable to common lime paste or putty for use with Portland cement, because if properly manufactured it is more thoroughly slaked and is easily handled and measured.* • See S. Y. Brigham in Engineering News, Aug. 27, 1903, p. 177, and Charles Warner in Rock Products, Feb. 1004, p. 26. 48 A TREATISE ON CONCRETE CHAPTER V CHEMISTRY OF HYDRAULIC CEMENTS* By Spencer B. Newberry INTRODUCTION Hydraulic cements are compounds consisting chiefly of lime, silica, and alumina, which have the property, when mixed with water to a paste, of hardening to a stone-like mass. They may be classified as follows: 1. Portland cement, made by calcining at high heat an artificial mixture of carbonate of lime with clay, shale or slag, in certain exact proportions, and grinding the resulting cHnker to powder. 2. Natural cement, made by burning at low heat limestone contain- ing excess of clay and usually much magnesia, and grinding the product. 3. Hydraulic Ume, obtained by burning limestone containing a small percentage of clay, slaking by sprinkling with water, and sifting the product. 4. Fuzzolan or slag cement, made by mixing and grinding slaked lime with certain kinds of volcanic scoria or blast-furnace slag. It will be noted that Portland cement. Natural cement and hy- draulic lime are all made by calcining mixtures of carbonate of lime with argillaceous material such as clay, shale or slag, the differences being in the proportions and temperatures of burning. It is well known that pure lime, while it hardens slowly in air, remains soft if kept con- stantly wet. Smeaton, .the engineer of the Eddystone lighthouse, in 1756, experimented with various kinds of lime, and discovered that only those containing a considerable proportion of clay would harden under water. He was thus the first to show the important part played by the insoluble constituents of impure limestone in conferring hydraulic properties on the lime burned from such stone. Limestones containing varying proportions of argillaceous matter are of frequent occurrence. It is found that if the clay substance con- tained is only 10 or 12 per cent., the product will heat and slake on sprinkling with water, and a hydraulic lime will result. On the other • The authors are indebted to Mr. Newberry for this chapter, which has been especially prepared by him for this Treatise. CHEMISTRY OF HYDRAULIC CEMENTS 49 hand, if the clay substance is 30 per cent, or more, and the stone is burned at high heat, it will fuse to a slag having no hydraulic properties; but if burned at low heat, just sufficient to drive off the carbon dioxide, a soft product is obtained which does not heat or slake with water. On grinding this to powder a quick-setting Natural cement is produced. Between these two extremes lies a certain proportion of hme and clay substance which stands a very high heat without fusing, does not slake or expand with water, and on grinding yields a material far superior to hydraulic lime or Natural cement in strength and promptness of harden- ing. This is known as Portland cement. CHEMICAL CONSTITUENTS OF CEMENT The nature of the compounds formed in the burning and hardening of cement remained obscure for a long period after Portland cement had been made and used on a large scale. Le Chatelier, in his epoch- making work in 1887, showed that cement clinker consists essentially of tri-calcium silicate, 3 CaO . Si02, and tri-calcium aluminate, 3 CaO.AliOs, and that on hardening with water the tri-calcium silicd,te is converted into crystalline calcium hydrate and hydrated mono-calcium silicate, as follows: 3CaO.Si02 + Aq. = 2Ca(OH)2 + CaO.SiO2.2l H2O. The aluminate also hydrates to hydrated tri-calcium aluminate. Subsequent investigators denied the existence of tri-calcium siUcate, as they failed to obtain this compound by fusing lime and siHca, a mix- ture of di-calcium silicate and free lime being obtained in all cases. For many years the question of the constitution of clinker was investigated by Clifford Richardson, E. D. Campbell, and others, and especially by E. S. Shepherd and G. A. Rankin of the Geophysical Laboratory of the Carnegie Institute, and P. H. Bates, A. A. Klein and A. J. Phillips of the Bureau of Standards. These investigators found that tri-calcium silicate is readily obtained if a very small percentage of alumina or magnesia is present in the mixture of lime and siHca; they thus have fully confirmed Le Chatelier's observations of twenty-eight years ago. The whole of our present knowledge of the chemistry of cement is admirably summed up in a paper by G. A. Rankin on "The Constituents of Portland Cement Clinker" (Journal Industrial and Engineering Chemistry, June, 1915. This paper should be read by all who are interested in the subject The important conclusions stated are im- perfectly summarized as follows: so A TREATISE ON CONCRETE The essential components of well-burned Portland cement clinker are Tri-calcium silicate, 3 CaO.Si02 Di-calcium silicate, 2 CaO.Si02 Tri-calcium aluminate, 3 CaO.AlaOs If the clinker is not well burned, so that practically complete equilibrium is not reached, there will be present also free lime, CaO, and an alumi- nate of the formula, 5 CaO . 3AI2O3 The other substances present, magnesia, iron oxide and alkalies, are useful in forming a flux, from which during the burning the tri- and di-silicate and tri-aluminate crystallize out. Fineness of grinding of the raw material and temperature and time of burning are factors in reaching equilibrium. Commercial gray cement clinker, containing 6.7 per cent, of fluxes, requires a temperature of about i425°Cent. White cement clinker, containing 2.4 per cent, fluxes, requires i525°Cent., while a mixture of pure lime, silica and alumina requires i65o°Cent. Tri-calcium siHcate, 3 CaO.Si02, is formed by prolonged heating of the constituents at a temperature somewhat below the fusing point of the compound, which is i9oo°Cent. If heated to fusion it is decomposed into a mixture of free lime and di-calcium silicate. It is this behavior which caused the existence of the compound to be so long denied. Di-calcium silicate, 2 CaO . Si02, exists in four forms. Of these, the beta form changes to the gamma form on cooling down to 67s°Cent., and in this transformation expands in volume about 10 per cent. ; this causes the crystals to fall to powder, a phenomenon often seen in the cooling of overclayed clinker and known as "dusting." Tri-calcium aluminate, 3 CaO.AUOs, is formed by heating the con- stituents for a long time at about i4oo°Cent. If heated to the melting point, i535°Cent., it is largely decomposed into free lime and fusible low-lime aluminates. In the burning of cHnker, the changes which take place may be briefly stated as follows: Carbon dioxide is driven ofi, and the resulting lime begins to com- bine with the silica, alumina, etc. present,- forming first the fusible aluminate, 5 CaO. AI2O3, and di-calcium silicate. These two compounds unite with more Hme to form tri-calcium silicate and tri-calcium alumi- nate. The formation of these substances is greatly aided by the pres- ence of a certain amount of liquid flux, which begins to form at i335°Cent. If held at about i42S°Cent. for some time, the 5 : 3 alumi- nate and the free lime will disappear, and the clinker will consist of tri- CHEMISTRY OF HYDRAULIC CEMENTS 51 calcium silicate, di-calcium silicate, tri-cakium aluminate and flux of indefinite composition. Professor Edward D. Campbell has published a most interesting account of the mechanical separation of the soUd and liquid constitu- ents of clinker at the burning temperature. Discs of clinker were pre- pared, placed between discs of pure magnesia" and exposed for 3 hours or longer to temperatures of 1475° to 1575° Cent. The fused portion of the clinker, corresponding to the "celite" of Tornebohm, was ab- sorbed by the magnesia discs, leaving the "alite" or crystalline portion in comparatively pure condition. This alite proves to be a calcium silicate, containing 2.8 to 3 molecules of lime to one of siUca, according to the basicity of the cHnker, with little alumina and very little iron oxide. The celite or liquid portion is essentially a calcium aluminate, containing httle silica but most of the alumina and iron oxide. These results accord with those stated by Rankin, the temperatures having been high enough to hold most of the tri-calcium aluminate in fused condition. The writer has permission to quote the following from a letter from Mr. P. H. Bates of the Bureau of Standards, referring to certain investi- gations not yet published: I am at present engaged on a paper which reports the results which we have obtained, with both neat and sand briquettes, made of the very pure constituents which are found in cement. We have been able to obtain tri-calcium silicate, containing in one case about 90 per cent, and in another 95 per cent, of this material. The di-calcium silicate has been prepared with much greater purity and also the tri-calcium aluminate in a very pure condition. We have followed the tensile specimens of these three compounds for a year, obtaining both the strengths and the amount of hydration determined by ignition loss as well as by micro- scopical examination. We have also mixed these three compounds in various proportions, by simply grinding together, and have obtained the same kind of data from these. The results have been very striking indeed. We found that the tri-calcium silicate of this purity, and containing only a few tenths of one per cent, of alumina, has all the properties of Portland cement, especially rate of setting and strength developed. The tri-calcium aluminate hydrates as rapidly as quick lime, and in 24 hours has as much strength as it will ever obtain, about 100 pounds per square inch. The di-calcium silicate hydrates very slowly and can hardly be removed from the molds before the end of a week. At the end of a year the neat specimens will have a strength very close to 600 pounds, but even with this strength it will have only about 5I per cent, water of hydration as compared with the tri-calcium silicate which has a little over 13 per cent, water of hydration but not much more strength. 52 A TREATISE ON CONCRETE MATERIALS As above stated, hydraulic lime is made by burning natural lime- stone containing a small amount of clay substance, while Natural cements are made by burning at low heat natural limestones containing a rela- tively large proportion of clay substance. Portland cement, on the other hand, is made by burning at high heat a mixture of materials of exactly correct composition, usually containing approximately 75 per cent, of carbonate of lime and 20 of anhydrous clay substance. A vari- ation of even one per cent, in the carbonate of lime, from the percentage found correct for given materials, will injuriously affect the quality of the cement obtained. If stone containing exactly the right amount of clay and of perfectly uniform composition could be found, Portland cement could be made from it simply by burning and grinding. No deposits of such stone are however known or likely to be discovered. The only way, therefore, that the necessary exact composition can be obtained is by making an artificial mixture of materials in correct pro- portions. Materials for Portland cement may be divided into two groups: Calcareous materials, containing excess of lime over that required for the mixture, and Argillaceous materials, containing excess of clay substance. The calcareous materials generally used are limestone, chalk or marl. These consist chiefly of carbonate of lime, and are found abundantly in nearly all sections of the country. The argillaceous materials in ordinary use are clay, shale, blast- furnace slag, and cement rock. The latter is a limestone containing more clay substance than is required. It occurs in extensive deposits in the Lehigh Valley region in Pennsylvania and New Jersey, and is used on a very large scale for cement manufacture, requiring the addi- tion of only a small amount of purer limestone to give a correct mixture. At some factories in that section it is necessary only to mix different layers from the same quarry in proper proportions. Magnesia, beyond a small percentage, has generally been considered objectionable, and liable to cause expansion and loss of strength at long periods. Authorities differ greatly in regard to the percentage of mag- nesia which may safely be present. This question is of great conse- quence in view of the wide-spread occurrence of deposits of more or less magnesian hmestone in all parts of the country. The standard 1 91 7 specifications of the United States and also the German official standard allow 5 per cent, magnesia in Portland cement. In a recent investiga- CHEMISTRY OF HYDRAULIC CEMENTS S3 tion by the United States Bureau of Standards, the highest strengths were obtained with cement containing 5 per cent, magnesia; cements opntaining 7.5 per cent, magnesia also gave strengths that were satisfac- tory. No bad effect in accelerated tests or normal tests for constancy of volume up to 28 days were noted with a magnesia content up to 18.98 per cent. All recent investigations indicate that magnesia in moderate amounts does not cause unsoundness as shown by ordinary tests, so that the allowance of 5 per cent, is certainly entirely safe. Cements with more than 7 or 8 per cent, magnesia, however, are inferior in strength, and appear to show increased expansion as shown by measurements of bars of concrete kept in air or water. This last point needs further exact investigation. Clay or shale for Portland cement manufacture should be silicious, ^nd practically free from coarse sand. It is desirable that the siUca in the mixture shall be from 2.5 to 3.5 times the sum of alumina and iron oxide. This figure is often called the silica ratio. More aluminous mixtures, with silica ratio of 2.0 or less, give fusible cUnker and quick- setting cement unless the lime is carried as high as is consistent with good soundness. High siKca ratio permits greater latitude in propor- tions, and allows the lime to be carried somewhat lower without danger of quick-setting. PROPORTION OF INGREDIENTS Experience has shown that with given materials there is a certain definite proportion of carbonate of lime to clay substance which gives beat results, and that a variation from this definite proportion, even to the amount of one-half per cent, of the carbonate of lime present, has a noticeably bad effect on the resulting product. This of course holds good only for fixed conditions of fineness of raw material and tempera- ture and time of burning, since extreme raw fineness and thorough burn- ing make it possible to carry the lime slightly higher, without danger of unsoundness, than would be practicable with coarser raw grinding and less perfect burning. Even with this qualification, however, the limit of proportions is exceedingly sharp and distinct,, and the interval between unsoundness, due to too high hme, and low strength or quick- setting, due to excess of clay, is very narrow. Generally speaking, the higher the hme, up to the limit of soundness as shown by the boiling test, the better the quality of the resulting cement. The recognized, existence of a definite proportion which will give best resultshas led to many attempts toestablish a definite formula by which, 54 A TREATISE ON CONCRETE from the analysis of the materials, the correct proportion could be cal- culated. In Germany it has been customary to so adjust the ingredi- ents, as proposed by Michaelis, that the "hydraulic modulus," the ratio by weight of lime to siUca, alumina and iron oxide, shall be from 1.8 to 2.2. These limits are of course much too far apart to be of practi- cal use. It has also become generally recognized by cement chemists ihit much more lime combines with silica than with alumina or iron oxide. The "hydrauhc modulus" is therefore a variable, and must be much higher in the case of silicious materials than with those high in alumina and iron. Le Cha teller stated in 1887 that the lime and magnesia in Portland cement should not exceed a maximum, CaO -I- MgO ^ SiOa + AI2O3 ~ ^ nor be less than a minimum CaO -f MgO ^^ SiOa-AlA-FezOa These formulas represent chemical equivalents and not weights. The best brands of modern Portland cement approach closely to the above maximum formula, while a cement corresponding to the minimum formula would be so greatly over-clayed as to be practically useless. These limits are therefore too far apart to be of value. Another serious defect in the formulas is the inclusion of magnesia with lime. All investi- gations show that magnesia is practically inert so far as the proportion of lime to clay is concerned. That is, an over-clayed mixture is not corrected by the addition of magnesia, and the proportions must be calculated on the basis of lime to silica, alumina, and iron oxide, leaving the magnesia out of account. Unfortunately, the recent scientific investigations on the constitution of cement clinker, described on preceding pages, while they identify the constituents of clinker, fail to establish the proportion in which these constituents should be present. The clinkers studied by Rankin were, in fact, much lower in proportion of lime than the best modem brands of cement, in spite of their having been burned in an electric furnace and thus not being contaminated with fuel ash. These clinkers showed tri-calcium sihcate, di-calcium sihcate and tri-calcium alumi- nate. It is an interesting question whether the di-calcium silicate would have disappeared if suf&cient Hme had been present to convert it into CHEMISTRY OF HYDRAULIC CEMENTS 55 tri-calcium silicate, and thus to bring the composition to that of Le Chatelier's maximum formula. Practically, it is certain that sound cement corresponding to Le Chatelier's maximum formula can be made, provided the raw materials are ground sufficiently iine and burned for the necessary time at suit- able temperature. There is also no doubt that cement of highest quality results from the highest practicable proportion of lime, pro- vided the raw grinding and burning are so conducted as to develop the full benefits of this high proportion. Some years ago tlie writer published a paper* containing an account of experiments based on the work of Le Chatelier. It was found that under ordinary conditions of raw grinding and burning, the maximum of lime which could be brought into combination to produce a sound cement is three equivalents for each equivalent of silica and two equiva- lents for each equivalent of alumina present. The composition of cement containing the maximum of lime would therefore be expressed by the formula X (sCaOSiOo) -I- Y (2CaO-Al203) It is understood that this formula is merely empirical, representing the relative proportions present, since the aluminate remains for the most part in the magma in combination with the iron oxide and part of the silica. The formula is also not in accordance with the latest re- searches, since these show tri-calcium aluminate instead of di-calcium aluminate, and part of the lime and silica combined as di-calcium sili- cate. However, we are not yet in position to construct an accurate formula based upon these researches, since we do not know how much Hme it is desirable to have in the form of di-calcium silicate, or what proportions of lime and alumina are or should be present in the magma from which the crystalline silicates and aluminate separate. If we assume that all the lime, silica and alumina are in the form of tri-calcium silicate and tri-calcium aluminate, the formula will be X (aCaO.SiOs) + Y (3CaO.Al.O3) This is Le Chatelier's maximum formula, eliminating the magnesia from the calculation. With the ordmary temperature and time of burning this would give too much lime, and would produce unsound cement. In order to approach actual working conditions we may assume that •Journal Society of Chemical Industry, Xovember 30, 1897. 56 .4 TREATISE ON CONCRETE four-fifths of the sUicate is tri-calcium and one-fifth di-calcium silicate. We shall then have X (2.8CaO.Si02) + Y (jCaO.AljOs) Substituting weights for equivalents, Lime = silica X 2.6 -|- alumina X i-6 Applied to ordinary cement materials, this gives almost exactly the same proportions as the original formula proposed by the writer. It is to be preferred to the latter, however, as it is more nearly in accord- ance with the latest and most exact experiment. It should be remembered that this formula represents the maximum of lime which a Portland cement, burned in the usual manner, may contain without showing unsoundness. This maximum can be reached only by extremely fine grinding of the raw material. This formula, also, by no means represents the composition of finished cement, since the ash of the fuel lowers the lime and raises the siHca and alumina, above that calculated from the raw material, by at least 2 per cent. In the laboratory, using gas as fuel, it will be found practicable to prepare sound cements corresponding to the above formula. In actual manufacture it is safer to reduce the lime slightly, to counterbalance possible defective grinding of raw material or unavoidable variations in composition. It will be found that the raw mixture at factories where the best Portland cements are made rarely falls below the com- position. Lime = silica X 2.5 -|- alumina X 1.6 This may be taken as a safe practical formula for commercial use. With fine grinding of the raw material it invariably will yield sound cements, while the use of a lower proportion of lime will be likely to produce quicksetting cement, low in tensile strength. As already ex- plained, commercial cements are usually considerably lower in lime, owing to change in composition produced by the fuel-ash. The writer's experiments have shown that magnesia forms with clay no products having hydraulic properties. It should be disregarded, therefore, in calculating cement mixtures, the composition of which should be calculated on the basis of the siHca, alumina and lime only, without regard to the magnesia present. Iron oxide, also, in the quantities usually met with in ordinary clays, plays an insignificant part so far CHEMISTRY OF HYDRAULIC CEMENTS 57 as the proportions of the constituents are concerned, and may be disre- garded in the calculation. As a practical example of the use of the above formula, let us suppose that we wish to make cement from limestone and clay of the following ' composition. Limestone. Clay. Lime 52.6 0.7 3-2 I.O 0-3 42.2 Magnesia 1.9 654 16. s 6 1 Silica Alumina Iron Oxide .' Loss on ignition, etc '. 7-9 100. 100.0 The silica and alumina in the limestone will require 3.2 X 2.5 + 1.6 = 9.6 per cent, lime, leaving 52.6 — 9.6 = 43.0 per cent, lime available for combination with clay. The sihca and alumina in 100 parts clay will require 65.4 X 2.5 + 16.5 X 1.6 = 189.9 parts lime. Subtracting the lime contained in the clay we have 189.9 ~ 2.2 = 187.7 parts lime required for loo.parts clay. As the 100 parts stone contain 43 parts available lime, that amount of stone will require 43 X 100 187.7 = 22.9 parts clay. The composition of the charge and of the resulting cement may be tabulated as follows: ^ 100 stone. 22.9 Clay. 122.9 Mix. 78.89 Cement. 100 Cement. 52.60 0.70 3-20 1. 00 0.30 42.20 0.50 0.43 14.98 3.78 1.40 I. 81 S3- 10 i-i3 18.18 4.78 1.70 44.01 S3 10 113 18.18 4.78 1.70 67.31 1 .46 ATaenesia Silica, 23.04 6.0s Alumina 2 IS 100.00 22 .90 1 2 2. go 78.89 100.00 58 A TREATISE ON CONCRETE As stated above the ash of the fuel will change the composition of the resulting cement materially; analysis of the product, burned with coal, will probably show about 65 per cent lime and perhaps 24 per cent silica. This fuel-ash is, however, not uniformly distributed through the product, but attaches itself chiefly to the surfaces of the clinker. It is not, therefore, found practicable to materially raise the proportion of lime to counterbalance the silica and alumina of the ash. It will be noted that in the above calculated analysis of raw mixture and cement the Lime — 1.6 alumina silica = 2.5 The writer proposes to call this figure the lime factor of the mixture. Adoption of this factor will give cements of practically maximum quality with any materials, whether silicious or aluminous, provided the mix is finely ground and properly burned. Owing to the influence of the ash of the fuel, as above explained, the factor of finished cements will usually be found about 0.2 lower than that of the raw material. Com- mercial cements generally show a factor of 2.3 to 2.4, though made from mixtures with a factor of 2.5 to 2.6. The following analyses, taken from a paper by the writer in Cement and Engineering News, November, 1901, show the influence of the fuel-ash on the composition of the clinker. The samples of clinker were taken one hour later than those of raw material, since the passage through the kiln required about one hour. Lehigh Portland Cement Company, Allentoum, Pa. Mix. Clinker, calculated from mix. Clinker found. SiOa 14.33 4-32 1 .46 42.69 1,81 35 14 22, l8 6.68 ^.26 66.08 2.80 22.96 6.78 2-54 63-95 2-94 AI2O3 Fe203 CaO... MgO and SO2 Lime-i.6 Alumina Factor — = 99-75 100.00 2.50 99,17 2.31 silica CHEMISTRY OF HYDRAULIC CEMENTS Sandusky Portland Cement Company, Syracuse, Ind. 59 ^ Mix. Clinker calculated from mix. Clinker found. SiOs .- 13-50 3-43 1.27 40.76 3-27 38.30 22.02 5.60 2.07 66. 4g 3-82 22.33 S-S3 3-28. 64.40 3-6i A1203 FeaOs ■ .. CaO MgO and SO. Loss Lime-i.6 Alumina Factor = =...... 100.53 100.00 2.61 99-15 2.48 silica Comparison of the above analyses of mix and clinker shows how greatly the ash of the fuel affects the composition. In commercial cement a still further reduction in the proportion of lime is caused by the addition of gypsum and the absorption of moisture and carbonic acid from the air. It will be readily seen, therefore, that analysis of finished cement gives but little indication of the true proportion of ingredients or of the quality of the product. EFFECT OF COMPOSITION ON QUALITY Too high proportion of lime (lime factor of mix above 2.6) will give a slow-setting cement which may fail in the steam test. If the excess of lime is great, pats of cement kept in cold water will show radial expansion cracks at the edges after a certain time, perhaps even within a few days. The same defects result from imperfect grinding of the raw material, and are far more often due to this cause than to excess of lime. Cement which is unsound and shows expansion from either cause may be improved and perhaps made sound by storage or by exposure to air. It is not, however, safe to rely greatly on this remedy. Lack of soundness is in all cases due to faulty manufacture, since well-burned cement made from suitably prepared raw materials will invariably pass all soundness tests when fresh from the grinding mills. Consumers are advised to accept no cement which fails to pass a reasonable steam test, as they will thus err, if at all, on the safe side, and will influence careless manufacturers to improve their methods. Too low proportion of lime, giving an over-clayed mixture, produces a fusible clinker, liable to overburning. This is especially the case with aluminous materials. If hard-burned, such mixtures give a fused clinker 6o A TREATISE ON CONCRETE liable to fall to dust on cooling, hard to grind, and yielding slow-setting cement of poor hardening properties. If light-burned, an over-clayed mixture yields soft brownish clinker, grinding to a brownish, quick- setting cement of inferior strength. Overburning rarely occurs except with over-clayed mixtures or in consequence of the fluxing action of the fuel-ash or the brick lining of the kiln. Properly proportioned mixtures stand a very high heat with- out injury. Underburning, as stated above, in the case of an over-clayed mixture, yields quick-setting and weak cement. Normal mixtures, when under- burned, usually give cement which fails in soundness tests. Light burning is generally indicated by heating of the cement on mixing with water. This behavior generally accompanies quick-setting, and may be so marked as to be quite apparent to the touch of the fingers. Some cements, though slow-setting when first made, become very quick- setting on storage. Cases are on record in which this change has taken place within a few days. After longer periods the original slow-setting quality may return. Cements which have become quick-setting may often be restored to normal set by the addition of i or 2 per cent, of hydrated lime. SPECIFICATIONS AND TESTS OF CEMENTS 6i CHAPTER VI SPECIFICATIONS AND TESTS OF CEMENTS In this chapter is presented the recent report on Standard Tests of Cement together with detailed information on testing. The tests which are regarded as most suitable for the selection and acceptance of cement for important concrete construction are as follows: Chemical analysis. Specific gravity. Fineness. Soundness or constancy of volume. Activity, or time of setting. Tensile or compressive strength of sand mortars. The French Commission* in 1893, in addition to these tests, gave standard rules for testing weight, homogeneity (with the microscope), compressive strength, bending strength, yield of paste and mortar (rendement) , porosity, permeability, decomposition, and adhesion, one or more of which tests may be desirable under certain conditions. As these are usually unimportant, only a brief description is given. In unimportant construction it is sometimes safe to use a first-class American Portland cement without testing, and in other cases the test for soundness is the only one which need be actually made. Under almost aU circumstances, however, when purchasing cement, fuU specifications are advisable, so that if the cement does not work satisfactorily it may be more carefully examined and unused portions rejected. In this chapter are presented, in addition to the description of the methods of making cement tests, complete lists of apparatus for a large and a small laboratory (p. 83), formulas and tables for determining the quantity of water in cement mortars (p. 8g), comparisons of American and European practice in cement testing, a discussion of the causes of unsoundness and the results of soundness tests (p. 103), curves showing the growth in strength of typical cements and cement mortars (p. 100), and other information with reference to the qualities and testing of Port- land cement. • Commission des ^lithodes d'Essai des Materiaux de Construction, 1894, Vol. I, p. 235. 62 A TREATISE ON CONCRETE The following specifications and methods of tests for Portland cement were adopted in it)i6 by the American Society for Testing Materials as a result of the recommendation of Committee C-i of that Society acting in cooperation with special committees representing the Board of Direction of the American Society of Civil Engineers and the Govern- ment Departmental Committee. A few comments by the authors are inserted. SPECIFICATIONS AND METHODS OF TESTS FOR PORTLAND CEMENT SPECIFICATIONS Definition. I. Portland cement is the product obtained by finely pulverizing clinker pro- duced by calcining to incipient fusion, an intimate and properly proportioned mix- ture of argillaceous and calcareous materials, with no additions subsequent to calci- nation excepting water and calcined or uncalcined gypsum. I. Chemical Prox'erties Cliemical 2. The following limits shall not be exceeded: Limits. Lggg gu ignitloH, per cent 4.00 Insoluble residue, per cent o. 85 Sulfuric anhydride (SO3), per cent 2 . 00 Magnesia (MgO), per cent S .00 II. Physical Properties and Tests Specific Gravity. 3. The specific gravity of cement shall be not less than 3.10 (3.07 for White Port- land) . Should the test of cement as received fall below this requirement, a second test may be made upon an ignited sample. The specific gravity test will not be made unless specifically ordered. Fineness. 4. The residue on a standard No. 200 sieve shall not exceed 22 per cent, by weight. Soundness. $• A pat of neat cement shall remain firm and hard, and show no signs of distor- tion, cracking, checking, or disintegration in the steam test for soundness. Time of Setting. 6. The cement shall not develop initial set in less than 45 minutes when the Vicat needle is used or 60 minutes when the Gillmore needle is used. Final set shall be attained within 10 hours. •Tensile Strengtli. 7. The average tensile strength in pounds per square inch of not less than three standard mortar briquettes (see Par. 51) composed of one part cement and three parts standard sand, by weight, shall be equal to or higher than the following: * See p. 80 for compressive strength recommendations. SPECIFICATIONS AND TESTS OF CEMENTS 63 Age at Test, days. Stonige of Test Pieces. Tensile Strength, lb. per sq. in. 28 I day in moist air, 27 days in water 300 8. The average tensile strength of standard mortar at 28 days shall be higher than the strength at 7 days. Strength requirements for neat cement are omitted in these specifi- cations because the committee decided them to be unnecessary. III. Packages, Marking and Storage 9. The cement shall be delivered in suitable bags or barrels with the brand and Packages and name of the manufacturer plainly marked thereon, unless shipped in bulk. A bag Markup, shall contain 94 lb. net. A barrel shall contain 376 lb. net. 10. The cement shall be stored in such a manner as to permit easy access for proper storage, inspection and identification of each shipment, and in a suitable weather-tight build- ing which will protect the cement from dampness. IV. Inspection 11. Every facility shall be provided the purchaser for careful sampling and in- Inspection, spection at either the mill or at the site of the work, as may be specified. .-Vt least 10 days from the time of sampling shall be allowed for the completion of the 7-day test, and at least 31 days shall be allowed for the completion of the 2S-day test. The cement shall be tested in accordance with the methods hereinafter prescribed. The 28-day test shall be waived only when specifically ordered. V. Rejection 12. The cement may be rejected if it fails to meet any of the requirements of these Rejection, specifications. 13. Cement shall not be rejected on account of failure to meet the fineness require- ment if upon retest after drying at ioo°C. for one hour it meets this requirement. 14. Cement failing to meet the test for soundness in steam may be accepted if it passes a retest using a new sample at an\- time within 28 dajs thereafter. 15. Packages varying more than 5 per cent, from the specified weight may be re- jected; and if the average weight of packages in any shipment, as shown by weighing 50 packages taken at random, is less than tliat specified, the entire shipment may be rejected. METHODS OF TESTS VI. Sampling 16. Tests may be made on individual or composite samples as may be ordered. Number of Each test sample should weigh at least (8) pounds. Samples. 64 A TREATISE ON CONCRETE Method of I?, (a) Individual Sample. — If sampled in cars one test sample shall be taken from Sampling, each 50 bbl. or fraction thereof. If sampled in bins one sample shall be taken from each 100 bbl. 17. (6) Composite Sample. — If sampled in cars one sample shall be taken from one sack in each 40 sacks (or i bbl. in each 10 bbl.) and combined to form one test sample. If sampled in bins or warehouses one test sample shall represent not more than 200 bbl. 18. Cement may be sampled at the mill by any of the following methods that may be practicable, as ordered: (a) From the Conveyor Delivering to the Bin. — At least 8 lb. of cement shall be taken from approximately each 100 bbl. passing over the conveyor. (6) From Filled Bins by Means of Proper Sampling Tubes. — Tubes in- B serted vertically may be used for sampling cement to a maximum depth of 10 ft. Tubes inserted horizontally may be used where the construction of the bin permits. Samples shall be taken from points well distributed over the face of the bin. (c) From Filled Bins at Points of U/scAarge.— Sufficient cement shall be drawn from the discharge openings to obtain samples representative of the cement contained in the bin, as determined by the appearance at the discharge openings of indicators placed on the surface of the cement directly above these openings before drawing of the cement is started. Treatment of " I9- Samples preferably shall be shipped and stored in air-tight containers. Sample. jTjq, g_ Samples shall be passed through a sieve having 20 meshes per linear inch Sampling iii order to thoroughly mix the sample, break up lumps and remove Iron, foreign materials. ■ eep. 4. ^ sampling iron is illustrated in Fig. 8. VII. Chemical Analysis Loss on Ignition Method. 20. One gram of cement shall be heated in a weighed covered platinum. crucible, of 20 to 25 cc. capacity, as follows, using either method (a) or (6) as ordered: (o) The crucible shall be placed in a hole in an asbestos board, clamped horizontally so that about three-fifths of the crucible projects below, and blasted at a full red heat for 15 minutes with an inclined flame; the loss in weight shall be checked by a second blasting for 5 minutes. Care shall be taken to wipe off particles of asbestos that may adhere to the crucible when withdrawn from the hole in the board. Greater neatness and shortening of the time of heating are secured by making a hole to fit the crucible in a circular disk of sheet platinum and placing this disk over a somewhat larger hole in an asbestos board. (6) The crucible shall be placed in a muffle at any temperature between 900 and iooo°C. for IS minutes and the loss in weight shall be checked by a second heating for s minutes. 21. A' permissible variation of 0.25 per cent will be allowed and all results in excess of the specified limit but within this permissible variation shall be reported as 4 pel cent. Permissible Variation. SPECIFICATIONS AND TESTS OF CEMENTS 65 Insoluble Residue 22. To a i-g, sample of cement shall be added 10 cc. of water and 5 cc. of concen- Method, trated hydrochloric acid; the liquid is warmed until effervescence ceases. The solu- tion shall be diluted to 50 cc. and digested on a steam bath or hot plate until it is evi- dent that decomposition of the cement is complete. The residue shall be filtered, washed with cold water, and the filter paper and contents digested in about 30 cc.of a s-per-cent solution of sodium carbonate, the liquid being held at a temperature just short of boiling for rs minutes. The remaining residue shall be filtered, washed with cold water, then with a few drops of hot hydrochloric acid, 1:9, and finally with hot water, and then ignited at a red heat and weighed as the insoluble residue. 23. A permissible variation of 0.15 per cent will be allowed and all results in permissible excess of the specified limit but within this permissible variation shall be reported as Variation. 0.85 per cent. Sulfuric Anhydride 24. One gram of the cement shaU be dissolved in 5 cc. of concentrated hydrochloric Method, acid diluted with 5 cc. of water, with gentle warming; when solution is complete 40 cc. of water shall be added, the solution filtered, and the residue washed thoroughly with water. The solution shall be diluted to 250 cc, heated to boiling and 10 cc. of a hot lo-per-cent solution of barium chloride shall be added slowly, drop by drop, from a pipette and the boiling continued until the precipitate is well formed. The solution shaU be digested on the steam bath until the precipitate has settled. The precipitate shall be filtered, washed, and the paper and contents shall be placed in a weighed platinum crucible and the paper slowly charred and consumed without flaming. The barium sulfate shall be then ignited and weighed. The weight ob- tained multipKed by 34.3 gives the percentage of sulfuric anhydride. The acid filtrate obtained in the determination of the insoluble residue may be used for the estima- tion of sulfuric anhydride instead of using a separate sample. 25. A permissible variation of o.io per cent will be allowed and all results in Permissible excess of the specified limit but within this permissible variation shall be reported as Variation. 2.00 per cent. Magnesia 26. To 0.5 g. of the cement in an evaporating dish shall be added 10 cc. of water Method, to prevent lumping and then 10 cc. of concentrated hydrochloric acid. The liquid shall be gently heated and agitated until attack is complete. The solution shall be then evaporated to complete dryness on a steam or water bath. To hasten dehydration the residue may be heated to 150 or even 2oo°C. for one-half to one hour. The residue shall be treated with 10 cc. of concentrated hydrochloric acid diluted with an equal amount of water. The dish shall be covered and the solution digested for ten minutes on a steam bath or water bath. The diluted solution shall be filtered and the separated siUca washed thoroughly with water.* Five cubic centimeters of concentrated hydrochloric acid and sufficient bromine water to precipitate any manganese which may be present, shall be added to the filtrate (about 250 cc). This is made alkaUne with ammonium hydroxide, boiled until there is but a faint odor of ammonia and the precipitate iron and aluminum hydroxides, after settling, are washed with hot water, once by decantation and slightly on the filter. Setting aside the filtrate, the precipitate shall be transferred by a jet of hot * Since this procedure does not involve the determination of silica, a second evaporation is unnecessary. 66 A TREATISE ON CONCRETE water to the precipitating vessel and dissolved in lo cc. of hot hydrochlpric acid. The paper shall be extracted with acid, the solution and washings being added to the main solution. The aluminum and iron shall be then reprecipitated at boiling heat by ammonium hydroxide and bromine water in a volume of about loo cc, and the second precipitate shall be collected and washed on the filter used in the first instance if this is still intact. To the combined filtrates from the hydroxides of iron and aluminum, reduced in volume if need be, i cc. of ammonium hydroxide shall be added, the solution is brought to boiling, 25 cc. of a saturated solution of boiling ammonium oxalate added, and the boiling continued until the precipitated calcium oxalate has assumed a. well-defined granular form. The precipitate after one hour shall be filtered and washed, then with the filter is placed wet in a platinum crucible, and the paper burned oil over a smaJI flame of a Bunsen burner; after ignition it is redissolved in hydrochloric acid and the solution diluted to 100 cc. Ammonia shall be added in slight excess, and the liquid boiled. The lime shall be then reprecipi- tated by ammonium oxalate, allowed to stand until settled, filtered and washed. The combined filtrates from the calcium precipitates shall be acidified with hydro- chloric acid, concentrated on the steam bath to about 150 cc, and made slightly alkaUne with ammonium hydroxide, boiled and filtered (to remove a little alumi- num and iron and perhaps calcium). When cool, 10 cc. of saturated solution of sodium-ammonium-hydrogen phosphate shall be added with constant stirring. When the crystallin ammonium-magnesium orthophosphate has formed, arrmionia shall be added in moderate excess. The solution shall be set aside for several hours in a. cool place, filtered and washed with water containing 2.5 per cent of NH3. The precipitate shall be dissolved in a small quantity of hot hydrochloric acid, the solu- tion diluted to about 100 cc, i cc. of a saturated' solution of sodium-ammonium- hydrogen phosphate added, and ammonia drop by drop, with constant stirring, until the precipitate is again formed as described and the ammonia is in moderate excess. The precipitate shall be then allowed to stand about two hours, filtered and washed as before. The paper and contents shall be placed in a weighed platinum crucible, the paper slowly charred and the resulting carbon carefully burned off. The precipitate shall be then ignited to constant weight over a Meker burner, or a blast not strong enough to soften or melt the pyrophosphate. The weight of mag- nesium pyrophosphate obtained multiplied by 72.5 gives the percentage of .magnesia. The precipitate so obtained always contains some calcium and usually small quan- tities iron, aluminum, and manganese as phosphates. Permissible 27. A permissible variation of 0.4 per cent will be allowed and all results in excess Variation. q{ ^.jjg specified limit but within this permissible variation shall be reported as 5.00 per cent. A simple test which sometimes may determine adulteration with raw or partially burned rock, is the purity test* with muriatic acid. It does not furnish the percentage of foreign ingredients, but the black precipi- tation of the adulterant darkens the color of the yellow jelly to a degree depending upon the quantity of adulteration. * Described in "Concrete Plain and Reinforced" 2nd edition, p. 4. SPECIFICATIONS AND TESTS OF CEMENT 67 SPECIFIC GRAVITY FLASK CAPHCITY OF APPROX. 250 Q C Fig. 9. Le Chatelier's Specific-Gravity Apparatus. {See p. 68) 68 A TREATISE ON CONCRETE Vlll. Determination of Specific Gravity Apparatus. 28. The determination of specific gravity shall be made with a standardized Le Chatelier apparatus which conforms to requirements as illustrated in figure g. This apparatus is standardized by the United States Bureau of Standards. Kerosene free from water or benzine not lighter than 62° Baume, shall be used in making this determination. Method. 29. The flask shall be filled with either of these liquids to a point on the stem between zero and one cc, and 64 g. of cement cooled to the temperature of the liquid shall be slowly introduced, taking care that the cement does not adhere to the inside of the flask above the liquid and to free the cement from air by rolling the fiask in an inclined position. After all the cement is introduced, the level of the h'quid will rise to some division of the graduated neck; the difference between readings is the volume displaced by 64 g. of the cement. The specific gravity shall be then obtained from the formula: „ . ^ . Weight of cement (g.) Specific gravity = Displaced volume, (cc.) 30. The flask, during the operation shall be kept immersed in water, in order to avoid variations in the temperature of the liquid in the flask which shall not exceed o.s°C. The results of repeated tests should agree within 0,01. 31. The determination of specific gravity shall be made on the cement as received; if it should fall below 3.10, a second determination shall be made after igniting the sample as described in section 20. Mr. Daniel D. Jackson has more recently devised an apparatus with which temperature corrections can be made more readily than with the older t)^es. This is described on page 85. IX. Determination of Fineness Apparatus. 32- Wire cloth for standard sieves tor cement shall be woven (not twilled) from brass, bronze, or other suitable wire, and mounted without distortion on frames not less than ij in. below the top of the frame. The sieve frames shall be circular, approximately 8 in. in diameter, and may be provided with a pan and cover. 33. A standard No. 200 sieve is one having nominally an 0.0029-in. opening and 200 wires per in., standardized by the U. S. Bureau of Standards, and conforming to the following requirements: The No. 200 sieve should have 200 wires per inch, and the number of wires in any whole inch shall not be outside the limits of 192 to 208. No opening between adjacent parallel wires shall be more than 0.0050 in. in width. The diameter of the wire should be 0.0021 in. and the average diameter shall not be outside the limits 0.0019 in. to 0.0023 in. The value of the sieve as determined by sieving tests made in con- formity with the standard specification for these tests on a standardized cement which gives a residue of 25 to 20 per cent on the No. 200 sieve, or on other similarly graded material, shall not show a variation of more than 1.5 per cent above or below the standards maintained at the Bureau of Standards. Method. 34. The test shall be made with 50 g. of cement. The sieve shall be thoroughly clean and dry. The cement shall be placed on the No. 200 sieve, with pan and cover SPECIFICATIONS AND TESTS OF CEMENTS 69 attached, if desired, and shall be held in one hand in a. slightly inclined position so that the sample will be well distributed over the sieve, at the same time gently strik- ing the side about 150 times per minute against the palm of the other hand on the up stroke. The sieve shall be turned every 25 strokes about one-sixth of a revolution in the same direction. The operation shall continue until not more than 0.05 g. passes through in one minute of continuous sieving. The fineness shah be deter- mined from the weight of the residue on the sieve expressed as a percentage of the weight of the original sample. 35. Mechanical sieving devices may be used, but the cement shall not be rejected if it meets the fineness requirement when tested by the hand method. 36. A permissible variation of i per cent, is allowed, and aU results in excess of the Permissibl specified Umit, but within this shall be reported as 22 per cent. Variation. Laboratory scales for weighing the samples and the residue are illus- trated in Fig. 10. Fig. 10. — Delicate Laboratory Scales. {See p. 6g.) Fine grinding has a number of advantages, chief among which is the increased strength of sand mortars. This is further discussed on page 87. It is impracticable to sift cement through a sieve finer than 200 meshes per linear inch. The particles which will just pass a No. 200 sieve are about o.io millimeter (0.004 inches) in diameter.*. ■ For separating the grains still finer than the No. 200 sieve, air analysis may be employed. . This is briefly described on page 88. X. Mixing Cement Pastes and Mortars 37. The quamtity of dry material to be mixed at one time shall not exceed 1000 Method, g. nor be less than 500 g. The proportions of cement or cement and sand shall be stated by weight in grams of the dry materials; the quantity of water shall be expressed in cubic centimeters (i g. = i cc). The dry materials shall be weighed, placed upon a non-absorbent surface, thoroughly mixed dry if sand be used, and a crater formed in the center, into which the proper percentage of clean water shall be poured; the material on the outer edge shall be turned into the crater by the aid of a trowel. After an interval of f minute for the absorption of the water the oper- ation shall be completed by continuous, vigorous mixing, squeezing and kneading * Allen Hazen in Report MassachusetU State Board of Health. 1892. : 70 A TREATISE ON CONCRETE with the hands for at least one minute.* During the operation of mixing, the hands should be protected by rubber gloves. 38. The temperature of the room and the mixing water shall be maintained as nearly as practicable at 2i°C. (7o°F.). The apparatus required for mixing briquettes consists of a piece of i-inch plate glass at least 24 inches square, counter scales (preferably metric system), recording from -^ gram to i| kilograms, a 250 cubic centimeter graduated measuring glass, rubber gloves, one 8-inch mason's trowel, one 4-inch pointing trowel. Fig. 11, and a ther- mometer. Fig. II. European standards specify mixing five minutes in- (Seep.jo.) stead of one minute. This difference in time is due to the methods of manipulation, in Europe the materials being mixed with a trowel or spoon. Experiments by the authors tend to show that a denser mixture can 'be obtained by kneading one minute than by mixing five minutes with a trowel, so that the American method is both quicker and better. XI. NoKMAL Consistency Apparatus. 39- The Vicat apparatus consists of a frame (A ) (Fig. 12) bearing a movable rod (B,) weighing 300 g., one end (C) being i cm. indiameterfor a distance of 6 cm., the other having a removable needle (D), i mm. in diameter, 6 cm. long. The rod is reversible, and can be held in any desired position by a screw (E)^ and has midway between the ends a mark (F) which moves under a scale (graduated to miUimeters) attached to the frame (A). The paste is held in a conical, hard-rubber ring (G), 7 cm. in diameter at the base, 4 cm. high, resting on a glass plate (.H) about 10 cm. square. Method, 40. In making the determination, 500 g. of cement, with a measured quantity of water, shall be kneaded into a paste, as described in Section 3 7, and quickly formed into • a ball with the hands, completing the operation by tossing it six times from one hand to the other, maintained about 6 in. apart; the ball resting in the palm of one hand shall be pressed into the larger end of the rubber ring held in the other hand, completely filling the ring with paste; the excess at the larger end shall be then removed by a single movement of the palm of the hand; the ring shall be then placed on its larger end on a glass plate and the excess paste at the smaller end sliced off at the top of the ring by a, single oblique stroke of a trowel held at a slight angle with the top of the ring. During these operations care shall be taken not to compress the paste. The paste confined in the ring, resting on the plate, shall be placed under the rod, the larger end of which shall be brought in contact with the surface of the paste ; the scale shall be then read, and the rod quickly released. The paste shall be of normal consistency when the cylinder * In order to secure uniformity in the results of tests for the time of setting and tensile strength the manner of mixing above described should be carefully followed. At least one minute is necessary to obtain the desired plasticity which is not appreciably affected by continuing the mixing for several min- utes. The exact time necessary is dependent upon the personal equation of the operator. The error in mixing should be on the side of over mixing. SPECIFICATIONS AND TESTS OF CEMENTS 71 settles to a point i o mm. below the original surface in J minute after being released. The apparatus shall be free from all vibrations during the test. Trial pastes shall be made with varying percentages of water until the normal consistency is obtained. The amount of water required shall be expressed in percentage by weight of the dry cement. 41 . The consistency of standard mortar shaJl depend on the amount of water requir- ed to produce a paste of normal consistency from the same sample of cement. Having determined the normal consistency of the sample, the consistency of standard mortar made from the same sample shall be as indicated in Table I, the values being in percentage of the combined dry weights of the cement and standard sand. Table I. — Percentage oe Water for Standard Mortars Percentage of Water for Neat Cement Paste of Normal Consistency. Percentage of Water for One Cement, Three Standard Ottawa Sand . Percentage of Water for Neat Cement Paste of Normal Consistency. Percentage of Water for One Cement, Three Standard Ottawa Sand. IS 9.0 23 10.3 16 9.2 24 10. s 17 9-3 2S 10.7 18 9-S 26 10.8 19 9-7 27 II. 20 9.8 28 II .2 21 10^0 29 II-3 22 10.2 30 ii-S Formulas of Mr. Feret for determining the percentage of water for sand mortars, and a table formerly used, are presented on page 89. The Boulogne Method for determining the proper consistency of neat paste was formerly in general use in France, and is still the best guide for determining the correct consistency of paste when the Vicat apparatus is not available. The Vicat apparatus, however, should be included in every well equipped cement laboratory, experiments by Messrs. P. Alexandre and R. Feret for the French Cornmission* showing that it gives much more imiform results than the Boulogne method. The Boulogne method requires that the paste shall be firm but well bonded, shining and plastic, and shall satisfy the following conditions: 1. The consistency shall not change if it is worked 3 minutes longer than the original 5 minutes, t 2. If dropped 50 centimeters (20 in.) from a trowel, it should leave the trowel clean, and fall without losing its shape or cracking. 3. Light pressure in the hand should bring water to the surface, and the paste should not stick to the hand. If a ball thus formed falls from * Commission des M6thodes d'Essai des Mat€riau2 de Construction, 1895, Vol. IV, p. 49. tXhe original working for the U. S. Standard tests is one minute (see paragraph 37.) 72 .1 TREATISE ON CONCRETE a height of about 50 centimeters (20 in.) it should retain its rounded form without sliowing cracks. 4. The proportion of water should be such that more or less will produce opposite effects from those of the proper consistency. I Fig. 12. — Vicat Apparatus. {See p. 70.) XII. Determination or Soundness* Apparatus. 42- A steam apparatus, which can be maintained at a temperature between 98 and ioo°C., or one similar to that shown in Fig. 13 is recommended.t The capacity * Unsoundness is usually manifested by change in volume which causes distortion, cracking, checkmg or disintegration. Pats improperly made or exposed to drj' ing may develop what are known as shrinkage cracks within the first 24 hours and are not an indication oE unsoundness. These conditions are illustrated in Figure 14. The failure of the pats to remain on the glass or the cracking of the glass to which the pats are at- tached does not necessarily indicate unsoundness. t A loosely covered vessel gives good results. Authors. SPECIFICATIONS AND TESTS OF CEMENTS n to v_ u U 13 ci 3 o c/3 8W "2 Si "2 nS «S flj- o;=! o jjooo HO"! j-jJ-j. 74 A TREATISE ON CONCRETE Pi Co CI 3 o C4 1^ s SPECIFICATIONS AND TESTS OF CEMENTS 75 of this apparatus may be increased by using a rack for holding the pats in a vertical or inclined position. 43. A pat from cement paste of normal consistency about 3 in. in diameter, \ in. Method, thick at the center, and tapering to a thin edge, shall be made on clean glass plates about 4 in. square, and stored in moist air for 24 hours. In molding the pat, the cement paste shall first be flattened on the glass and the pat then formed by drawing the trowel from the outer edge toward the center. 44. The pat shall then be placed in an atmosphere of steam at a temperature be- tween 98 and ioo°C. upon a suitable support i in. above boiling water for five hours. 45. Should the pat leave the plate, distortion may be detected best with a straight edge applied to the surface which was in contact with the plate. XIII. Determination of Time of Setting ' 46. The following are alternate methods, either of which may be used as ordered: 47. The time of setting shall be determined with the Vicat apparatus described in Vicat Apparatus. Section 39. (See figure 12.) 48. A paste of normal consistency shall be molded in the hard-rubber ring {G) as de- Vicat Method, scribed in Section 40, and placed under the rod (5), the smaller end of which shall be then carefully brought in contact with the surface of the paste, and the rod quickly re- leased. The initial set shall be said to have occurred when the needle ceases to pass a point s mm. above the glass plate in one-half minute after being released; and the final set, when the needle does not sink visibly into the paste. The test pieces shall be kept in moist air during the test. This may be accomplished by placing them on a rack over water contained in a pan and covered by a damp doth, kept from contact with them by means of a wire screen; or they may be stored in a moist closet. Care shall be taken to keep the needle clean, as the col- lection- of cement on the sides of the needle retards the penetration, while cement on the point may increase the penetration. The time of setting is affected not only by the percentage and temperature of the water used and the amount of kneading the paste receives, but by the temperature and humidity of the air, and its determination is therefore only approximate. 49. The time of setting shall be determined by the Gillmore needles. The GiUmore Gillmore needles should preferably be mounted as shown in Fig. 15 (J). Apparatus. 50. The time of setting shall be determined as follows : A pat of neat cement paste Gillmore Method, about 3 in. in diameter and J in. in thickness with a flat top (Fig. 15 (o) ), mixed to a normal consistency, shall be kept in moist air, at a temperature maintained as nearly as practicable at 2i°C. (70° F.). The cement is considered to have acquired its initial set when the pat will bear, without appreciable indentation, the Gillmore needle 3^ i"- i" diameter, loaded to weigh \ lb. The final set has been acquired when the pat will bear without appreciable indentation, the Gillmore needle -^-^ in. in diameter, loaded to weigh i lb. In making the test, the needles should be held in a vertical position, and applied lightly to the surface of the pat. For practical purposes in ordinary construction where laboratory apparatus is unavailable, the setting qualities of a cement or mortar may often be examined by making up pats from a number of the pack- 76 A TREATISE ON CONCRETE ages and trying their hardening by pressure of the thumb. When the thumb nail fails to indent the surface the paste or mortar may be considered to have reached its final set. C Soundness Pat with Top Surface Flattened. For Determining Time of Setting. (a) (i) Fig. 15. — Gillmore Needles and Pat. {See p. 75.) XIV. Tension Tests ' H ■ ^ ' ' Form of JSJ^LThe form of test piece shown in Fig. 16 shall be used. The molds shall Test Piece, bamade of non-corroding metal and have sufficient material in the sides to prevent spkeading: during molding. Gang molds when used shall be of the type shown in Fig-.'.i-y'.I- Molds shall be wiped with an oily cloth before using. I :. : c' ; ■.-.•: : The German standard briquette is sketched on page 96. standard Sand. 52. The sarid'to be used shall be natural sand from Ottawa, 111., screened to pass a No. -20 sieve and retaine'd on-a No. 30 sieve. This sand may be obtained from the Ottawa Silica.'CS).,-at'a?c6stof two cents per pound, f. o. b. cars, Ottawa, 111. 53. .This s^iicj hayiBgjpasssdtJje No, 20 sieve shall be considered standard when not SPECIFICATIONS AND TESTS OF CEMENTS 77 more than s g., pass the No. 30 sieve after one minute of continuous sieving of a soo-g. sample. 54. The sieves shall conform to the following specifications: The No. 20 sieve shall have between 19.5 and 20.5 wires per whole inch of the warp wires and between 19 and 21 wires per whole inch of the shoot wires. The diameter Fig. 16. — Details for Briquette. (See p. 76.) of the wire should be 0.0165 m. and the average measured diameter shall not fall outside the limits of 0.0160 and 0.0170 in. The No. 30 sieve shall have between 29.5 and 30.5 wires per whole inch of the warp wires and between 28.5 and 31.5 wires per whole inch of the shoot wires. The diameter of the wire should be o.oiio in. and the average diameter shall not be outside the limits 0.0105 to 0.0115 in- Photographs of the grains of Ottawa and of crushed quartz sand are shown on page 136. 78 A TREATISE ON CONCRETE European is compared with U. S. standard sand on p. 94. Molding. 55. Immediately after mixing, the standard mortar shall be placed in the molds, pressed in firmly with the thumbs and smoothed off with a trowel without ramming. Additional mortar shall be heaped above the mold and smoothed off with a trowel; the trowel shall be drawn over the mold in such a manner as to exert a moderate pressure on the material. The mold shall then be turned over and the operation of heaping, thumbing and smoothing off repeated. Testing. 56. Tests shall be made with any standard machine. The briquettes shall be broken as soon as they are removed from the water. The bearing surfaces of the clips and briquettes shall be free from grains of sand or dirt. The briquettes shall, be carefully centered and the load applied continuously at the rate of 600 lb. per minute. 57. Testing machines should be frequently calibrated in order to determine their accuracy. Fig. ly.^Details for Gang Molds {See p. 76.) Faulty 58. Briquettes that are manifestly faulty, or which give strengths differing more Briquettes, than IS per cent from the average value of all test pieces made from the same sample and broken at the same period shall not be considered in determining the tensile strength. XV. Storage of Test Specimens Apparatus. SQ. A moist closet shall consist of a soapstone, slate or concrete box, or a wooden box lined with metal, the interior surface being covered with felt or broad wicking kept wet, the bottom of the box being covered with water. The interior of the closet should be provided with non-absorbent shelves on which to place the test pieces, the shelves being so arranged that they may be withdrawn readily. Methods. 60. Unless otherwise specified all test specimens, immediately after molding, shall be placed in the moist closet for from 20 to 24 hours. 61. The briquettes shall be kept in molds on glass plates in the moist closet for at least 20 hours. After 24 hours in moist air the briquettes shall be immersed in clean water in storage tanks of non-corroding material. 62. The air and water shall be maintained as nearly as practicable at a tempera- ture of 2i°C. (70° F.). A moist closet and storage pans designed by Mr. Richard L. Hum- phrey are shown in Figs. 18 and 19, page 79. SPECIFICATIONS AND TESTS OF CEMENTS 79 ^ ELEVATION FRONT VIEW ■ QSOAPSTONE ji SECTION END SECTION Fig. 18.— Moist pioset. (See p. 78) SETAtL OF OVERFLOW QUriET PIPE FRONT VIEW Fig. 19.— Immersion Tanks. (See p. 78) 8o A TREATISE ON CONCRETE PROPOSED TENTATIVE SPECIFICATIONS AND METHODS OF TESTS FOR COMPRESSIVE STRENGTH OF PORTLAND CEMENT MORTAR* Specifications Compressive i. (a) A test piece of standard mortar composed of one part cement and three Strength, parts Standard sand, by weight, shall give compressive strengths equal to or higher than the following; Age at Test, days. Storage of Test Pieces. Compressive Strength, lb. per sq. in. 7 28 I day in moist air, 6 days in water I day in moist air, 27 days in water 1200 2000 (i) Each value shall be the average of the results of tests from not less than three test pieces. The compressive strength of standard mortar at the age of 28 days shall be higher than the strength determined at the age of 7 days. Methods of Tests -ng standard 2. The requirements governing the preparation of standard sand mortars for Mortar, tension test pieces shall apply to compression test pieces. Form of 3. A cylindrical test piece 2 in. in diameter and 4 in. in length is recommended Test Piece, f^^ jjgg jj^ making compression tests of standard mortars. The molds shall be made of non-corroding metal. A satisfactory form of mold is shown in Fig. 20. The ends of the mold shall be parallel. The tubing used in the molds shall be of suf- ficient thickness to prevent appreciable distortion. The molds shall be oiled before using. During the molding of the test piece, the mold shall rest on a clean, plane surface (preferably a piece of plate glass which is allowed to remain in place until the mold is removed). Molding. 4. The mortarf shall be placed in the mold in layers about i in. in thickness each layer being tamped by means of the steel tamper shown in Fig. 21. The weight of tamper is approximately | lb. In finishing the test piece, the mortar shall be heaped above the mold and smoothed off with a trowel. As soon as the test pieces from one sample are molded, the top of each test piece shall be covered with a piece of glass which is brought to a firm bearing on the fresh mortar. The cover glasses shall remain in place until the molds are removed. The compression test pieces shall be stored in the same manner as the tension test pieces. Testing. 5. Tests of standard-mortar cyhnders may be made in any testing machine which is adapted to meet the specified requirements. The test pieces shall be tested as soon as removed from the water. The ends of the test cylinders shall be smooth, plane surfaces. The metal bearing plates of the testing machine shall be * Accepted by the American Society for Testing Materials as tentative specifications, June, igi6. t If sufficient raortar for six 2 by 4 in. cylinders is to be mixed in a single batch, approximately 3000 g. of material will be required. In this case the mixing shall be continued for ij minutes. SPECIFICATIONS AND TESTS OF CEMENTS 8i placed in direct contact with the ends of the test piece. During the test a spherical bearing block shall be used on top of the cylinder. In order to secure a uniform distribution of the load over the test cylinder the spherical bearing block must be accurately centered. The diameter of the spherical bearing block should be only a little greater than that of the test piece. The test piece shall be loaded con- tinuously to failure. The moving head of the testing machine shall travel at the rate of not less than 0.05 or more than o.io in. per minute. Steel Clamp - ..... ,"....^ M 1 1 1 '*^ 1 ^ 1 ^ 1 ° ^ I^^^ i<|>l. 1 ! ■-IM V- 2- I- IC ->l Note ■■ Form may be Made of Seamless Brass Tubing of 2i"0uhide Diameter, No. 12 B. W.G.,with ^"Slot along one Element. Fig. 20. — Details for 2 by 4-in. Cylinder Form (See p. 80.) dux.. Fig. 21. — Details for Stetl Tamper [See p. 80.) Testing machines should be frequently calibrated in order to determine their accuracy. Cylinders that are manifestly faulty, or which give strengths differing more than IS per cent, from the average value of all test pieces tested at the same period and made from the same sample, shall not be considered in determining the com- pressive strength. 82 A TREATISE ON CONCRETE FULL SPECIFICATIONS FOR THE PURCHASE OF NATURAL CEMENT 1. Packages. Cement shall be packed in strong cloth or canvas sacks."}" Each package shall have printed upon it the brand or the name of the manufacturer. Packages received in broken or damaged condition may be rejected or accepted as fractional packages. 2. Weight. Three bags shall constitute a barrel, and the average net weight of the cement contained in one bag shall be not less than 94 lb., or 282 lb. net per barrel. A cement bag may be assumed to weigh one pound. The weights of the separate packages shall be uniform. 3. Requirements. =*= Cement failing to meet the seven-day requirements may be held awaiting the results of the twenty-eight day tests before re- jection. 4. Tests.* All tests shall be made in accordance with the methods pro- posed by the Committee on Uniform Tests of Cement of the American Society of Civil Engineers, presented to the Society January 21, 1903, and amended January 20, 1904, with all subsequent amendments thereto. (See Chapter VI, p. 63.) 5. Sampling. Samples shall be taken at random from sound packages, and the cement from each package shall be tested separately. 6.* The acceptance or rejection shall be based on the following require- ments: 7. Definition of Natural Cement.* This term shall be applied to the finely pulverized product resulting from the calcination of an argillaceous limestone at a temperature only sufficient to drive off the carbonic acid gas. 8. Fineness.* It shall leave by weight a residue of not more than 10% on the No. 100, and 30% on the No. 200 sieve. 9. Time of Setting.* It shall not develop initial set in less than ten minutes, and shall not develop hard set in less than thirty minutes, or in more than three hours. 10. Tensile Strength.* The minimum requirements for tensile strength for briquettes one square inch in cro;s section shall be as fol- lows, and the cement shall show no retrogression in strength within the periods specified: ♦Paragraphs designated by an asterisk are quoted from th» Standard Specifications of the American Society for Testing Materials. flf the cement is to be stored in a damp place or near the sea, it must be packed in well-macie u^ooden barrels lined with paper. SPECIFICATIONS AND TESTS OF CEMENTS 83 Neat Cement. Age Strength 24 hours in moist air 75 lb. 7 days (i day in air, 6 days in water) 150 " 28 days (x " ". 27 " " ) 250" One Part Cement, Three Parts Standard Ottawa Sand. Age _ Strength 7 days (i day in air, 6 days in water) 5° lb. 28 days (i " " 27 " " ) 125" II. Constancy of Volume.* Pats of neat cement about 3 inches in diameter, one-half inch thick at the center, and tapering to a thin edge, shall be kept in moist air for a period of 24 hours. (a) A pat is then kept in air at normal temperature. (6) Another pat is kept in water maintained as near 70° Fahr. as practicable. These pats are observed at intervals for at least 28 days, and, to satisfac- torily pass the tests, shall remain firm and hard and show no signs of distortion, checking, cracking, or disintegrating. APPARATUS FOR A CEMENT TESTING LABORATORYf (The apparatus is designed for one experimenter. Where the number of pieces is not stated, their number depends upon the quantity of cement to be tested.) *One piece plate glass, one inch thick, 24 by 24 inches square; *Four or more gangs of 3 or 4 molds each — A. S. C. E. standard (see Fig. 17, p. 78); *One metric counter scale recording from 10 grams to i| kilograms. *One No. 200 sieve (200 meshes to the linear inch), about 8 inches in diameter, and made of woven brass wire cloth, with wires 0.0021 inch, diameter (see p. 68) ; *One measuring glass graduated to 250 cubic centimeters; *One 8-inch mason's trowel; *One 4-inch pointing trowel (see Fig. 11, p. 70); *One-half dozen pairs rubber gloves; *Pieces of thick window glass 4 inches square for soundness tests; *One tensile testing machine (see Figs. 26 and 27, pp. 97 and 98); *Air thermometer; *Standard sand; •An asterisk designates the apparatus required for a temporary laboratory on construction work fThis list has been criticised and approved by Mr, Richard L. Humphrey. 84 A TREATISE ON. CONCRETE Two or more gangs of 3 molds each for 2-inch cubes; or, twelve 2 by 4 inch cylinders (see Fig. 20, p. 81); lo-pound tin cans with tight covers for holding samples; One special scale for weighing cement in ascertaining fineness (see Fig. 10, p. 69); One pan of same diameter as the sieves and 5 centimeters (1.97 in.) deep, with cover, for holding sieve when shaking it; One measuring glass graduated to 100 cubic centimeters; One cement sampler 24 inches long (see Fig. 8, p. 64) ; One minute sand glass; One' moist closet (see Fig. 18, p. 79); Galvanized iron waste cans; Apparatus for steaming and boiling specimens (see Fig. 13, p. 73); Tanks for immersing specimens (see Fig. 19, p. 79); Vicat needle apparatus (see Fig. 12, p. 72); One compression testing machine (adapted also to transverse tests), capacity at least 50 000 pound (see Figs. 94 and 95, pp. 340 and 341); Chemical thermometer; Specific gravity apparatus (see Fig. 9, p. 67); Microscope with ij inch objective; Set of sieves, about 8-inch diameter, for analyzing sands, sizes 0.25 inch diameter holes, No. 7, 12, 20, 30, 50, 90 (the number corresponds to the number of meshes to the linear inch, see p. 118); Mechanical shaker for sifting sand (see Fig. 54, p. 186). SPECIFIC GRAVITY OF CEMENTS The specific gravity test, by determining whether a cement is thor- oughly burned, supplements the chemical analysis, since the latter does not indicate the degree of calcination. The specific gravity of a true Portland cement ranges from 3.05 to 3.15. The adulteration of Portland cement lowers its specific gravity, because the substances used, — ^pow- dered sand, limestone, trass or slag, — are lighter than particles of pure cement. The test will not detect a small adulteration nor adulteration with a material of high specific gravity. Natural cement usually has a specific gravity above 2.75, ranging from this sometimes as high as 3.1,* thus overlapping the inferior limit given *Tests of Metals, U. S. A., 1901, p. 476. SPECIFICATIONS AND TESTS OF CEMENTS 85 for Portland cement. Puzzolan cement usually has a specific gravity of 2.7 to 2.9. The specific gravity of cement is lowered by exposure, because of the absorption of water and carbonic acid, hence the necessity of drying it at 100° Cent. (212° Fahr.) or igniting at low red heat (see p. 64) before determining. Even this temperature may not always be sufficient to restore old cements to their original condition.* Jackson Specific Gravity Apparatus. Mr. Daniel D. Jackson has devised an apparatus that gives satisfactory results for cement or fine aggregate. The graduations are made to read directly in terms of specific gravity and temperature variations are corrected by a table instead of attempting to prevent such variations. The glass tube is made of much smaller bore than in the Le Chatelier apparatus so that more accurate readings may be made. The method of finding the specific gravity which applies to cement or fine aggregate, is specified by Mr. Jackson as follows :t 1. Weigh out accurately to the tenths' place of decimals 50 grams of the dry sample of cement. 2. Fill the bulb and burette with kerosene, leaving just space enough to take the temperature by introducing a thermometer through the neck. Remove the thermometer and add sufiicient kerosene to fill exactly to the mark on the neck, drawing off any excess by means of the burette. 3. Run into the unstoppered Ehrlenmeyer flask about one-half of the kerosene in the bulb. Then pour in slowly the 50 grams of cement and revolve to remove air bubbles. Run in more kerosene until any adhering cement is carefully washed from the neck of the flask, and the kerosene is just below the ground glass. 4. Place the hollow ground-glass stopper in position, and turn it to fit tightly. Run in kerosene exactly to the 200 cubic centimeter gradu- ation on the neck, making sure that no air bubbles remain in the flask. 5. Read the specific gravity from the graduation on the burette and then the temperature of the oil in the flask, noting the difference between the temperature of the oil in the bulb before the determination and the temperature of the oil in the flask after the determination. 6. Make a temperature correction to the reading of the specific grav- ity by the use of the accompanying tables. •See experiments in Tests of Metals, U.,S. A., igoi, p. 476, and Dr. H. Kupfender ia Thonindus- triezeitung, translated in Cement, March, 1903, p. 23. t Daniel D. Jackson in Engineering Record, July 16, 1904, p. 83. 86 A TREATISE ON CONCRETE Temperature Correction for Jackson Specific Gravity Flask. {See p. 85.) Read temperature of oil in bulb before determination and of oil in flask after determination. Add correction if temperature of oil increases, and subtract it if it decreases. Change in Uncorrected Reading. Temperature Centigrade. 2.50 to 2.60 2.60 to 2.70 2.70 to 2.80 2.80 to 2. go 2. go to 3.00 3.00 to 3.IO 3.10 to 3.20 320 to 3.30 3.30 to 3.40 3.40 to 3.50 dee. 0.2 0.00 O.OI O.OI O.OI O.OI O.OI O.OI u.OI O.OI O.OI 0.4 O.OI O.OI O.OI O.OI O.OI O.OI O.OI O.OI 0.02 0.02 0.6 O.OI 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.8 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 i-.O 0.02 0.03 U.03 0.03 U.03 0.03 0.03 0.04 0.04 0.04 1.2 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.05 O.OS 1-4 0.03 0.04 0.04 0.04 0.04 0.0s 0.05 O.OS 0.06 u.06 1.6 0.04 0.04 0.04 0.05 0.05 0.0s 0.05 0.06 0.06 0.07 1.8 0.04 0.05 0.05 0.05 U.06 0.06 o.oS o'.ofi 0.07 0.07 2.0 0.05 0.05 U.05 0.06 0.06 0.06 U.07 0.07 0.08 0.08 .i.2 u.OJ 0.06 0.06 0.06 0.07 0.07 0.08 0.08 0.09 0.09 2.4 0.06 0.06 0.06 0.07 0.07 0.08 0.08 0.09 O.IO O.IO 2.6 0.06 0.07 0.07 0.07 0.08 0.08 0.09 0.09 0. 10 O.II 2.8 0.07 0.07 0.08 0.08 0.09 0.09 .0. 10 0. 10 O.II 0.12 30 0.07 0.08 0.08 0.09 u.09 O.IO O.IO O.II 0. 12 0.12 3-2 0.07 0.08 U.09 0.09 u.IO 0. 10 U.II 0.12 0.13 0.13 3-4 U.08 0.09 IJ.09 O.IO O.IO O.II 0.12 u. 12 0.13 0.14 3-6 U.08 0.09 O.IO 0. 10 O.II 0.12 0.12 0.13 0.14 O.IS 3-8 0.09 O.IO O.IO o.)'i 0.12 0.12 0.13 0.14 O.IS 0.16 4.0 0.09 O.IO O.II 0.12 0. 12 0.13 0.14 0.14 0. 16 0.17 4-2 0. 10 O.II 0. II 0.12 0-I3 0. 14 0.14 O.IS 0.17 0.17 4-4 , 0.10 0. II 0.12 .0.13 ^^•13 0. 14 U.I5 0. 16 0.17 0.18 4.6 O.II 0. 12 U.I2 0-13 u. 14 o.iS 0.16 U.I7 0.18 o.ig 4.8 D.II 0.12 0.13 0.14 "■IS 0.16 0. 16 0.17 0.19 0.20 50 1J.I2 0.13 0.14 0. 14 o-iS 0.16 0.17 0.18 0. 20 0.21 A neat little device for dropping fine material into a specific gravity apparatus so as to prevent the entraining of air has been devised by Mr. Thomas H. Wiggin. A thin wooden board with a circular hole in it is placed above the apparatus and a paper funnel fitted into the hole and filled with dry cement. An electro-magnet, such as is used with an ordinary electric door-bell, is connected with its storage battery and ar- ranged so that the clapper, instead of striking a bell, strikes a metal plate attached to the corner of the board. The constant tapping jars the funnel so that the grains fall slowly into the apparatus without re- quiring the attention of the operator. SPECIFICATIONS AND TESTS OF CEMENTS 87 ADVANTAGES OF FINE GRINDING The effects of fineness of grinding upon cements are to make them, — Stronger when tested with sand; Weaker when tested neat; Quicker setting; Capable of producing a larger volume of paste; Less affected by free lime. Fineness is expressed by the percentage of the total weight of the cement retained on each sieve.* A recognition of the value of extreme fineness has led to the adoption of higher standards than formerly, and manufacturers have accordingly improved the quality of their product in this respect. Strength Affected by Fineness. With the same proportions of sand, higher tensile and compressive strength is obtained from finely ground than coarsely ground cements. Conversely, a larger porportion of sand can be used with fine ground than with coarse ground cement, with the same resulting strength. The chief cementing value of a cement lies in the grains which are fine enough to pass a sieve having 200 meshes per linear inch. Phot- ographs of thin sections of sand briquets several years old made by Mr. E. W. Lazell show very clearly the coarser grains of cement which have never been penetrated and chemically changed by- the water. Tested neat, a coarse cement may give higher strength than the same cement after regrinding. This is chiefly due, in the opinion of the authors, to the fact that the fine cement requires more water in gaging to produce the same consistency of paste, so that the same weight of cement produces a larger volume of paste, which therefore has less density and consequently lower, strength. When sand is added, on the other hand, less influence is exerted by the water, because in any case a smaller volume of it is required in proportion to the dry materials, and besides this the very fine grains, Afhich also have higher cementing qualities, fit more readily into the voids in the sand. The relation of the density of a mortar to its strength is dis- cussed in Chapter IX, page 143. The efifect of the fineness of cement upon its strength was brought to general notice by Mr. John Grantf in 1880, who quotes experiments made in Germany by Dykerhoff. In 1883 Mr. I. J. MannJ illustrated * Sizes of American vs. European sieves are given in Concrete Plain and Reinforced, 2nd edition, pp. 84 and 85. * t Proceedings, Institution of Civil Engineers, Vol. LXII, p. 149. X Proceedings, Institution of Civil Engineers, Vol. LXXI, p. 254. 88 A TREATISE ON CONCRETE the small cementing value of the coarse particles by substituting for them grains of sand of the same size, with but little reduction in the resulting strength. Mr. D. B. Butler* in England made extended tests to determine the value of coarse particles in cement and the effect of regrinding. The cement was reground and sand of the same size as the coarse particles in the original was substituted for them, producing a cement nearly as strong as the cement before regrinding. The fine grinding of commercial cements has been one of the causes, by the acceleration of the setting, for the necessity of adding gypsum or plaster during manufacture. Separating Material Passing No. 200 Mesh Sieve. The high cement- ing value of the grains of cement passing a No. 200 sieve necessitates, for elaborate tests, still finer apparatus. The coarsest particles passing a No. 200 sieve are approximately 0.004 inch in diameter. A device developed by the Bureau of Standards! separates this material into four parts, the limiting sizes being 0.004 inch, 0.003 inch, 0.002 inch, and o.ooi inch. Beginning with the smallest particles the successive sizes to be separated are carried off one after the other through small open- ings in the analyzing chamber- by means of a steady stream of air under a low pressure. The residue is weighed after each separation and in this way the proportion of each size is determined. QUANTITY OF WATER FOE NEAT PASTE AND MORTAR The quantity of water used in gaging affects the results of tests, es- pecially in the determination of the time of setting and of the strength. (See p. 165.) Different cements even of the same class require different proportions of water to produce the same consistency, chiefly because of differing degrees of fineness, the cement containing the largest propor- tion of fine particles requiring the largest percentage of water by weight. For chemical combinations alone about 8 per cent, of water to the weight of the cement is customarilly assumed to be required, but in practice the percentage must be much greater. Percentage of Water for Mortar of Normal Consistency. The table of percentage of water for standard mortar quoted on page 71 from the report of the American Committee is based on Mr. Feret's formulaj •Proceedings, Institution of Civil Engineere, Vol. CXXXII, p. 343, and Butler's Portland Cement, iSpg.p. i6g. * t An Air Analyzer for Determining the Fineness of Cement, by J. C. Pearson and W. H. Sligh, Tech- nologic Papers of the Bureau of Standards, No. 48, 1915. X Commission des M^thodes d'Essai des Mat^riaux, 1895, \'ol. IV, p. 103. SPECIFICATIONS AND TESTS OF CEMENTS 89 evolved from an interesting series of experiments.* He found that it was impracticable to determine with the Vicat needle the proper consistency of a mortar of cement and sand, and therefore based his determination upon the average judgment of several operators, plotting tiie consistencies designated by them upon cross-section paper. The formula as used by the American Committee, expressing the values for convenience in percentages instead of in grams, isf W = f— ^+6.5 Where W = percentage of water for mortar in terms of weight of the mixture of dry materials; P = percentage of water required for neat cement of normal consistency; 5 = parts of sand by weight to one part cement. The following table gives percentages of water for dififerent proportions of mortar. It must be remembered that these percentages are for standard sand only, the percentages required for natural sand varying with the coarseness of its grain. Percentage of Water for Cement Mortars of Normal Consistency. Percentage of Water to Cement Plus Standard Ottawa Sand. it Percentage of Water to Cement Plus Standard Ottawa Sand. Proportions cement to sand by wei::lit. Proportions cement to sand by weight. l>" 1:1 1:2 1:3 1:4 1:5 1:1 1:2 1:3 1:4 1:5 18 19 20 21 22 23 24 2S 26 12. S 12.8 13.2 13.5 13.8 14.2 14.5 14.8 15.2 10.5 10.7 10.9 II .2 II. 4 II. 6 II. 8 12.1 12.3 9-5 9.7 9.8 10. 10. 2 10.3 lO-S 10.7 10.8 8.9 9.0 9.2 9-3 9-4 9.6 9-7 9.8 10. 8.5 8.6 8.7 8.8 8.9 9.0 9.^ 9-3 9.4 27 28 29 30 31 32 33 34 35 15.5 15-8 16.2 16.5 16.8 17.2 17.5 17.8 18.2 12.5 12.7 13.0 13.2 13.4 13-6 13-8 14. 1 14-3 II .u II. 2 II-3 II. 5 11. 7 11. 8 12.0 12. i! 12.3 10. 1 10.2 10.4 10.5 10.6 10.8 10.9 II. u 11. 2 9-5 9.6 9-7 9.8 9.9 10. 10. 1 10.2 10.4 French Consistency of Neat Paste. The Vitat needle (see p. 72) has been adopted in England and France as well as in the United States. In France a softer consistency is adopted requiring a penetration of 34 millimeters instead of 10 rhillimeters. * Methods of Mr. Fei:et's investigations are described and illustrated in an article by the authors on "Quantity of Water to Use in Gaging Mortars" vn Cement and Engineering News (Chicago), November, 1903. t Mr. Feret gives for the last term in the formula 6.0 for mortars of plastic consistency and 4.5 for mortars of dry consistency. 9° A TREATISE ON CONCRETE TESTS OF SETTING The methods employed in mixing and depositing the mortar or concrete and the character of the construction form a guide to the necessary re- quirements for the time of setting of the cement. The setting of cement is due to chemical reaction, as described by Mr. Spencer B. Newberry on page 49. The process is a gradual one, but may be arbitrarily divided into three periods: Initial set. Final set. Hardening. The dividing line betvi^een these periods is arbitrary, but the division is based upon the fact that after water is added the paste remains plastic for a certain period, and then commences to "stiffen" or crystallize. This is called the time of initial set. The setting process continues rapidly, and when a point is reached that the paste will withstand a certain pressure, arbitrarily fixed in practice, it is said to have reached its final set. I'he process of hardening now continues more slowly, and proceeds with in- creasing slowness- for an indefinite period. Those unfamiliar with cement construction must bear in mind that a cement which has reached its final "set" is not hard nor is it capable of bearing a load. Natural cement, for example, usually reaches its initial and its final set much earlier than Portland cement, but it hardens more slowly, and Natural cement masonry will not bear loading nearly so quickly as Portland cement masonry. EUROPEAN METHODS FOR DETERMINING SET The French and German requirements are similar to the American Vicat needle (p. 75) except that in them the commencement of the set is taken as the time when the needle can no longer penetrate entirely to the bottom of the box instead of limiting it to a penetration to a depth of 5 millimeters above the bottom surface. For sand mortars the French Commission designate the final set as the moment when thesurfaceof the mortar can support pressure of the thumb without indentation. As an alternate method, they use the Vicat ap- paratus with a needle one centimeter (0.39 in.) in diameter and weighing 5 kilograms (11.02 lb.). The preliminary reports of Mr. R. Feret and Mr. P. Alexander in Commission des Methodes d'Essai des Materiaux de Construction, 1895, Vol. IV, pp. in and 139, describe experiments with different apparatus. SPECIFICATIONS AND TESTS OF CEMENTS EUROPEAN Setting Requirements 91 Country. Germany. . . Switzerland Austria Denmark. . . England France Italy Russia Time of Initial Set. hr. None required Quick — 10 min. Medium — ^30 min. ihr. Quick — 2 to 10 min. Medium — 10 to 20 min. Slow — 20 min. ihr. Time of Final Set. Not required Quick — Max. 30 m. Slow — ^Min. 3 hr. None required None required. / Min. 2 hr. \ Max. IS hr. Min. 2 hr. Max. 12 hr. / Min. 2 hr. Max. 12 hr. Min. s hr. Max. 12 hr. Min. I hr. \ Max. 12 hr. } Method. Vicat Vicat Vicat Vicat Vicat Vicat Vicat Vicat Comparison of Vicat and GiUmore Needles. The Gillmore needles were first used by General Totten in 1830.* By these needles the initial set of neat cement is the time at which a wire one-twelfth-inch diameter, loaded to a j pound, is just supported by the mass without appreciable indentation. The final set is taken as the time when a wire one-twenty-fourth-inch diameter, loaded to weigh one pound, is supported without appreciable indentation. The diagram in Fig. 22, page 92, from experiments made at the Watertown Arsenalf upon various cements (designated by letters) shows the difference in the nominal time of setting when measured by the Gillmore needle and the Vicat needle, employing with the latter the German method. (See above.) The diagram also shows the variation in time of set of Portland cement occasioned by varying the proportion of water, and the effect of leaving out the usual "restrainer" of plaster of Paris or gypsum. The Rate of Setting. The rateof setting of cement, that is, the process of hardening, has been studied by the French Commission^ in France and by Prof. Edgar B. Kay in the United States. The diagram Fig. • Gillmoic's Treatise on Limes, Hydraulic Cements and Mortars, p. 80. t Tests of metaLj, U. S. A. , 1901 , p. 492 X Commission des MIthodes d'Essai des MatSriaux de Construction, 189S. Vol. IV, p. III. 92 A TREATISE ON CONCRETE 24, page 95, shows curves of setting made with a machine of Prof. Kay's design and the corresponding tensile strength of briquettes of the same cement. Prof. Kay calls attention to the positive change from the plastic to the granular or crystalline structure which in the cement shown occurred between the periods of 35 and 40 minutes. The elongation of the briquette when being broken gradually changed from f inch at the 5-minutes period to 0.15 inch at 40 minutes, while at 200 minutes, or one hour before the initial set was completed, the elongation was not measurable. PORTLAND CEMENTS VATER PER CENT TIME OF SETTINQ-HOURS NATURAL CEMENTS VATER TIME OF SETTING -HOURS 2 4 6 8 2 '^ B 8 - 20 0- _ -.-. 30 0- if A 25 0- ... ._ _. L 35 L._ .- -. 30 c. — _ - 40 . L.- -. 20 _.. . 30 . ... B 25 ... M 35 _ _.. 30 .- 40 h '-. L._ .- . 20 ._. .0 30 • 25 0- ..J N 35 r- -\ WITH P LASTE R 30 .._ 40 „- L. 20 =, 30 ... .J ..„ »n C 25 0. — — — 35 ,- _.J ,._ ... HOUT PLAS FER 30 .0 40 .- -. L. _ - - 20 = .- -. 35 .. D 25 ... ... P 40 _. ... -, 30 _. _J . 45 =-. ... .. 20 0. _.J .J .-. -» 40 J L. . E 25 o_. .._ -0 R 45 30 _. 50 NOTP — FULL LINPR RUnvt TIMF np SPTTlwn HV VlfJAT NPFHI E - - DO I-
  • / iSli p,t*0 CEM ENT l;SAND 1. ^7- ______ bO 40 / V — ■ --^ :=:=: === /' --^ d ^- ^ PC 3RTL AND 1:2 — ^ ?n POBTLAN f.-rs -- ._f iJATURALCE MENT lNEAT 20 10 ■v*=^ FOB TLA ^D 1 4" — — — 2 4 6 8 10 12 14 16 TIME, HOURS. 20 22 24 26 28 30 32 34 36 38 40 Fig. 23.— Rise in Temperature in 1 2-inch Cubes of Cement and Mortar. (Tests of Metals, U. S. A., igoi.) {See p. 93.) temperature was largely dependent upon the size of the specimen, small cubes showing very slight increase. He therefore made a series of tests upon 1 2-inch cubes to determine the temperature acquired by different • Commission des Methodes d'Essai des Matfaiaux de Construction, iSgs, Vol. IV, p. 133. . t Tests of Metals, U. S. A., 1901, p. 403. 94 A TREATISE ON CONCRETE brands of cement and mortars during setting, and plotted his volumes in a series of curves. The curves for a first-cln.ss brand of American Port- land cement with and without sand, and for a typical Natural (Rosen- dale) cement, are shown in Fig. 23. Mr. Howard found that while first-class American brands of neat Portland cement often reached a maximum temperature of 100° Cent. (212° Fahr.); the maximum temperature of the various brands of Ameri- can Natural cement was generally from 35° to 40° Cent. (95° to 104° Fahr.), and was reached at a shorter time than the Portland cements. The rise in temperature of the German brands of Portland cements was in general less than that of the American Portlands. The rise in temperature in Portland cement concrete is less than in neat Portland cement, but in the interior of a large mass like a dam may reach nearly 100° Fahrenheit. AMERICAN AND EUROPEAN STANDARD SANDS COMPARED The character of the sand has so great an effect upon the strength of a mortar that for comparing different brands of cement or specifying re- quirements of strength a sand of standard size and quality is essential. The U. S. Standard Sand recommended by the Committee of the Amer- ican Society of Civil Engineers, as specified on page 76, is a natural sand from Ottawa, 111., screened to pass a sieve having 20 meshes per linear inch, and retained on a sieve having 30 meshes per linear inch. The English Standard Sand is obtained from a pit at Leighton Buzzard,* and the screens are the same as in the United States. The German Standard Sand is a natural quartz retained between sieves having respectively 20 and 28 meshes per linear inch. The French Standard Sand, a natural sand from Leucate, France, is simple or compound. Simple standard sand must pass a screen having holes 1.5 millimeters (0.059 ™-) i"' diameter, and be retained on a screen, having holes one millimeter (0.039 in.) in diameter. Compound stand- ard sand is made by forming a mixture of equal weights of the following: (i) Grains passing holes of 2 mm. (0.079 i^-) and retained by 1.5 mm. (0.059 in.). (2) Grains passing holes of 1.5 mm. (0.059 ii.) and retained by i mm. (0.039- in.) (3) Grains passing holes of i mm. (0.039 in-) and retained by 0.5 mm. (0.020 in. • Butler's Portland Cement, 1899, p. 200, •NI 'OS U3d '91 HlBN3aiS 31ISN3J. \ \ ■^ ^ L_ — ■ r:=^ \^- ^ ^_, — -_ BNIHS '■itJ'o,, -9 ■ > i3s~^ ^ ^ ^ > ■^ T5~ \ ^*c s ^0 \s l? ^ I V- ^ V X V V N ] < N % to tu _l o -•>■^m "^ J6 - ■ i > *:>'' y p' >* ' '%. Fig. 31.— Examples of Unsound Pats at 4 months which were sound at 28 days. (See p. log.) practice. He gives as the probable reason for this that the test for sound- ness is generally made immediately upon the receipt of a shipment, while the cement used in construction haS opportunity to season, and upon the fact "that the disintegrating action of a cement is always far greater when mixed neat than when mixed with an aggregate, and the greater the amount of the aggregate the less the tendency to unsoundness." It is often good policy before rejecting a cement which fails to pass the hot test to hold it for a week or two so that it may further season and then retest it. Methods of Making Accelerated Tests. The methods of conducting accelerated tests are numerous, the object of all of them bein^ to hasten • ^ D Clh ^ > ^ ^ xf •t: ci 1 i^ iis iiTj ii-o s^ >.'i i's J3 a a Q M .5 -2 M .2 2 p M 1"^ 11 XJ Kd 4j b J3 6 U O u -g-s ■^-i -a i-d ii-a" ii-a S-o S^ ii-a 1^ l-y 1^ g g .S " .S " .s - ^1 •-H M • ^ tl ■-H ^ ■^ l-l •—1 )-l ^^ " Ih T fl M p M Q w> P OO P t^ p >=« -s^ 1-a ^-a 1^ 1 w§ Mg mg M§ ui wi „ ^ ^ ^ „ ^ ^ „ 1 U) m r5 M M W t^ !^ M «■ 1^ 00 2 2 d d d d d d d d ^ <-fH t^^ Mh «+-< M-( MH <-M o O O o O o O O w « « wl c/l m en U] tn w ■i)".^ 43"^^ -b"i> •i"^ -b"^ ■d"^ 43"^ ■d-i^ ■d"^ 2 -C S ii s ^ o ^ ■xJ OJ ^ (L> ,J=t CJ ^ OJ JD (U J3 *-o >^TJ >^T3 13 t-^-o >,-o >^t3 x-o :>,T3 >iT3 1§ 1§ 1§ 1§ ^s !§ IS 1§ ^§ < PP m m p pq pq pq pq pq pq nj Td -a t3 X) T3 T3 jj -, >-, >i >^ ^ >-, >-, "^j wi Tl wi 4-j (/j +3 wi +3 yj +3 u5 "h^ ci rJ^ E2 -^ ^ -c IS -« S (/> m j3 ^ -^3 « -2 2 yi 00 IN :i3 bD T 60 bOjS J ^ bpi5 bO =^ P3 bo m CO en " ^ 'bb 'bb w 4-> yi li &'2 fc-s fc'l £^S i! 4^ fc-S c^S fc-'S > > > a p > > > p 1 w t- OS ^ r^ r^ to CO M lO ^ IH On ro ^ t^ vO On o g IH *-• H M ■* 1 ^ ri r^ Os H r^ w !>. M r^ On M ■a U-) CO rO w LO Tf ^ H CO 11 ■s w N . CO 0) 00 O 00 i^ 00 w On On l>- On N (H '"' '"' w M M 0) )H H z 3£ H ^ i-d i-6 i^-d 1 01 . \o o ro t^ O CO 01 •O Ov OO o S M 01 -* 01 c PI £ 00 i>- to t^ t^ vO t-* t^ u w 2; 1 (/I §■ CO w N M r^ fO ■^ On 4 o\ r^ o U-) N 00 ^O 01 r^ 00 f^ t-* ^ 00 00 00 :z; :z; ft « SP CO j^ CO 01 lO 01 ■o N Ov 01 o On (O M lO m Tf Tf «o Tj- to to SPECIFICATIONS AND TESTS OF CEMENTS iii the hardening of the cement so as to produce in a few hours results which under ordinary conditions require weeks or months. Boiling the speci- mens, instead of steaming them as recommended by the Committee of the American Society of Civil Engineers, while more common, is more severe. Other methods are employed in Europe. The Steam Test, recommended by the Committee of the American So- ciety of Civil Engineers, requires, as already described (p. 72), that the pat after twenty-four hours in moist air shall be placed in an atmosphere of steam above boiling water. The Boiling Test was originated by Prof. Tetmajer in Germany. After twenty-four hours in moist air, or until it is thoroughly set, the specimen is placed in cold water, which is raised to and then maintained at the boiling point for several hours. Three or four hours is the time specified by Mr. W. Purves Taylor, and often used in the United States, although some cement factories boil for twenty-four hours. Dr. Michaehs ad- vocates six hours' boiling, and this period is specified by the French Commission. Combined Boiling and Tensile Test. A regular test at many Portland cement factories consists in testing the tensile strength of briquettes which have been subjected to the hot test. A briquette of neat cement after twenty-four hours under a damp cloth is placed in an atmosphere of steam over boihng water for an hour or two, and then immersed in water at about the boiling point and boiled for about twenty-four hours, when it must show a certain tensile strength. The Hot Water Test, as adopted by Mr. Henry Faija in England, and advocated there by Mr. David B. Butler, consists in subjecting a newly mixed pat to a moist heat of 100° to 105° Fahr. (38° to 40° Cent.) for six or seven hours, or until thoroughly set, and then placing it in warm water at a temperature of 115° to 120° Fahr. (46° to 49° Cent.) for the re- mainder of the twenty-four hours. Mr. Deval in France employed a temperature of 176° Fahr. (80° Cent.) for a period of six days. Other Accelerated Tests which have been employed in Europe are oven tests, where the specimen is heated in an oven; glow tests, where a ball is heated over a gas flame, and Prussing disc tests, where discs are formed under heavy pressure and then exposed to hot water. Measurement of Expansion. AppUances have been devised for testing the soundness of cement by measuring the amount of expansion or def- ormation which it undergoes in different periods of time. The principal of these are the long bar apparatus, devised by Messrs. Durand-Claye and ii» A TREATISE ON CONCRETE Debray, which was recommended by the French Commission, Bauschin- ger's caliper apparatus, and Le Chatelier's tongs.* The Chimney Expansion Test, in which a small quantity of neat cement is solidly pressed into a straight lamp chimney with the idea that an un- sound cement will break the glass, is worthless, as all first-class cements expand to a greater or less degree. Autoclave Test. Mr. H. J. Forcef has brought out in the United States an accelerated test of cement formerly used to a slight extent in Europe. I Three neat briquets and an "expansion bar" i inch square and 6 inches long are made up, stored in moist closet for 24 hours, and after the measurement of the bar placed in the autoclave apparatus, where the pressure is raised to 295 pounds in not more than one hour and maintained at this pressure for one hour longer, then gradually reduced. The specimens are taken out, placed in the moist closet for one hour, and then measured or broken in the tensile machine. The prisms must not show greater expansion than 0.5 per cent, and the briquets must break at 500 pounds or more and must show at least 25 per cent, increase in strength over the ordinary 24 hour test in order to pass the test. To determine the real value of the autoclave test in comparison with the standard tests for unsoundness, the Bureau of Standards has in progress a comprehensive series of compression tests of concrete. § The results indicate that the autoclave test provides no definite indi- cation of the action of the cement when made into concrete. COLOR OF CEMENT The color of a cement bears but slight relation to its quality, but a vari- ation of color in the same brand is sometimes an indication of inferioriiy. Natural cements made in different localities may often be distinguished from each other and from Portland cements by their color. Portland Cement. The chemical composition of Portland cements made by different processes is so uniform that the color of different brands varies less than that of Natural cements. The color of Portland cement is described as a cold blue gray. In England the term "foxy" is applied to a Portland cement of a brownish *Desciibed in Spalding's Hydraulic Cement, 1903, p. 166. t See papers on results obtained on the autoclave test for cement, American Society for Testing Mate- rials, Vol. XIII, 1913, p. 746. X Dr. Erdmenger in Journal Society of Chemical Industries, Vol. XII, p. 927. § See discussion by R. J. Wig, American Society for Testing Materials, Vol. XIV, 1914, p. 252. SPECIFICATIONS AND TESTS OF CEMENTS 113 color. According to Mr. David B. Butler* this denotes "insufficient cal- cination or the use of unsuitable clay or possibly excess of clay." He further states that if a Portland cement contains a large quantity of under- burned particles, on account of their lower specific gravity they tend to rise to the surface on troweling, thus forming a yellowish brown film which is noticeable in the section of the briquette after fracture. The dark color of the coarser particles of a Portland cement left as residue on a screen is due simply to the fact that cement clinker is black, and pieces which are not finely ground retain the color of the clinker. Natural Cement. The color of Natural cement varies with the character of the rock and consequently with the locality in which it is produced. It ranges from the light dcru of the Utica (111.) cement to the dark grayish brown of the Rosendale (N. Y.). Samples received by the authors from various manufactories show the James River cement to be a light yellowish brown, the Akron (N. Y.) cement, ^cru, the Milwaukee (Wis.) cement, drab, and the Louisville (Ky.) cement, a brownish gray. Certain other brands are similar in color to Portland. Fuzzolan Cement. Puzzolan cement made from slag is of a light lilac shade, much lighter than Portland. After being kept under water it assumes, when freshly fractured, a bluish green tint. This green tint, which according to Candlotf is due to sulphide of calcium present in the cement, is especially noticeable in a sample kept in sea water, and fades on exposure to dry air. WEIGHT OF CEMENT Weight is no indication of quality. Formerly, nearly all specifications required that a cement should reach a certain standard of weight per struck bushel or per cubic foot, on the principle that, other things being equal, a thoroughly burned cement is heavier than one which is under- burned. It soon developed, however, that the degree of fineness affected the weight much more than any difference in calcination, and the test for specific gravity was substituted. Method of Weighing Cement. The apparatus finally recommended by the French Commission, after a series of tests by Mr. P. Alexandre,! was a circular funnel with screen, as shown in Fig. 32. The cement placed upon the screen is stirred with a wooden spatula 4 cm. (if in.) wide, and 25 cm.. (10 in.) long, and falls through the screen into the cylindrical measure of one liter capacity (61 cu. in.). * Butler's Portland Cement, 1899, p. 255. 1 Candlot's Ciraents ct Chaux Hydrauliques, 1898, p. 159. t Commissioners dcs MSthodcs d'Essai des Mat^riaux de Construction, 189S, Vol. IV, p. 21. 114 A TREATISE ON CONCRETE MICROSCOPICAL EXAMI- NATION OF PORTLAND CEMENT CLINKER The structure of Port- land Cement clinker can be clearly discerned with the aid of the microscope and polarized b'ght by preparing thin sections of "''' it in the same way as those of rocks made by petrog- raphers. Le Chatelier, a French Fig. 32. Funnel Used in Weighing Cement. . , _ , , (See p. 113.) engineer, and iornebonn, a Swedish petrographer, some years ago identified two essential mineral entities, and tnree others oi less importance, as constituents of Portland cement clinker. Tornebohn denominated the two essen- tial constituents alite and celite. TESTS OF AGGREGATES 115 CHAPTER VII TESTS OF AGGREGATES It is as necessary to test the aggregate for mortar or concrete as it is to test the cement. This is particularly true of natural bank sand, since it is frequent- ly impossible even for the most expert engineer to determine by exami- nation whether or not a sand is fit to use for mortar and concrete. The experience of one of the authors during the last few years in the investigation of failures of concrete structures shows that the quality of the sand is more frequently to blame than the cement. Formerly sharpness of sand was considered its most important quality, but as discussed on page 167, it is now recognized that this has but little effect upon its use in mortar or concrete. The origin of the require- ment for sharpness was probably the appearance of sand in a pile. When a sand contains a large percentage of vegetable loam, which is one of the worst impurities, the pile when dried in the sun has a dirty or "dead" appearance, while a clean sand is bright and by its glistening appearance gives the effect of sharpness even although the grains are rounded. In this chapter are presented the important tests necessary for the acceptance of a given aggregate or for the comparison of different aggregates, also characteristics of aggregates under special conditions. These include tests of strength of mortar made from the sand in question (p. ri6); mechanical analysis or gradation of grains (p. 117); test for organic impurities (p. 118) ; chemical tests (p. 118) ; color tests (p. 119) ; hardness and strength of particles (p. 119). Voidsund characteristics of aggregates are treated in the following chapter. The effect of different characteristics and conditions on the strength of mortar, including the treatment of density and of granulometric composition, is treated in Chapter IX, on Strength and Composition of Cement Mortars. SAMPLING AND SHIPPING SAND To obtain a representative sample, cut into the natural bank or into the pile so as to use no sand which has fallen down from the surface. Make with the shovel a vertical face. Scrape vertically with the point ii6 A TREATISE ON CONCRETE of the shovel along this vertical face so as to form at the bottom a mixed pile of sand. Repeat in another place, if this one sample does not represent a fair average, and mix with the first sample. Send 20 pounds of sand to the laboratory packed so as to prevent drying out. TEST OF STRENGTH OF MORTAR The most positive method of determining the quality of a given sand or comparing the relative qualities of two or more different sands is to make up specimens with cement and find the actual strength in tension or compression. Frequently this is the only test needed. To eliminate the variation due to the quality of the cement and difference in manipulation of the specimen, the strength of the mortar from the sand in question always should be determined in comparison with that of mortar made with Standard sand from Ottawa, 111. The method of making up specimens should conform to standard requirements for testing cement, as given on pages 76 to 78. To avoid removal of any coating on the grains which may affect the strength, sand should not be dried before making into mortar, but should contain natural moisture, the weight of which may be corrected by deter- mination of percentage of moisture in a separate sample. The con- sistency of the mortar of Standard sand should be determined by the standard method described on page 89. The percentage of water to use with the sand in question should be such as to produce the same consistency as the Standard sand mortar. The specimens may be tensile briquets of standard shapes or, for compression, 2-inch cubes or 2 by 4 inch cylinders. Compression tests are much to be preferred. Sand Specifications. The requirement for the acceptance of fine aggregate is as follows: Fine aggregate shall consist of sand, crushed stone or gravel screen- ings, graded from fine to coarse and passing when dry a screen hav- ing j-inch diameter holes. It preferably should be a silicious material and not more than 30 per cent, by weight should pass a sieve having 50 meshes per lineal inch. It shall be clean and free from soft particles, lumps of clay, vegetable loam, and all other organic matter. Fine aggregate shall always be tested. Fine aggregates shall be of such quality that mortar composed of one part Portland cement and three parts fine aggregate by weight when made into briquets, or into prisms or cylinders, will show a tensile or compressive strength at an age not less than seven TESTS OF AGGREGATES 117 days at least equal to the strength of i : 3 mortar of the same con- sistency made with the same cement and standard Ottawa sand. If the aggregate be of poorer quality, the proportion of cement shall be increased in the mortar to secure the desired strength. If the strength developed by the aggregate in the i : 3 mortar is less than 70 per cent, of the strength of the Ottawa sand mortar, the material shall be rejected. To avoid the removal of any coating on the grains, which may affect the strength, bank sands shall not be dried before being made into mortar, but shall contain natural moisture. The percentage of moisture may be determined upon a separate sample for correcting weight. From 10 to 40 per cent, more water may be required in mixing bank or artificial sands than for Standard Ottawa sand to produce the same consistency. No requirement is made as to the age of specimens at time of test. Periods most convenient in practice are 3 days, 7 days, and 28 days. A sand passing the strength requirement at the age of 3 days may be accepted without serious question, since the ratio of strength to standard sand is apt to increase with age. On the other hand, if the strength is low at 3 days, the sand may be held for the later tests. MECHANICAL ANALYSIS If a fine aggregate is free from organic or other impurities and is of ordinary silica composition, the strength of the mortar is governed by the size and relative sizes of its grains. A coarse sand gives a stronger mortar than a fine one, and generally a gradation of grains from fine to coarse is advantageous. The effect of the coarseness of sand upon strength of mortar is illustrated by Feret's tests on page 159, and tests by the New York Bureau of Water Supply, page 162. Mechanical analysis alone will not determine the quality of a sand because impurities may affect the strength while not appreciably affecting the analysis. The relation of mechanical analysis to granulometric composition is discussed on page 164. The mechanical analysis of the coarse aggregate also has an important effect upon the strength of the concrete. Mechanical analysis methods are treated more fully in the chapter on Proportioning, pages 175 to 203. Sieves for Testing Sand. For the mechanical analysis of sand the following sieves are recommended.* • Selected from sieves in list accepted by Conference called by U. S. Bureau of Standards. ii8 A TREATISE ON CONCRETE 0.250 inch diameter holes.* No. 7 mesh holes 0.1 11 inch width 0.032 inch wire. No. 20 mesh holes 0.0335 iiich width 0.0165 i^^h wire. No. 50 mesh holes 0.0120 inch width 0.0080 inch wire. No. 90 mesh holes 0.0059 iiich width 0.0052 inch wire. If a larger number of sieves are desired No. 12 and No. 30 may be added (seep. 187). TEST FOR ORGANIC IMPURITIES To determine the percentage of organic impurities in a sand, the silt can be removed from the sand by placing it in a large bottle and wash- ing it with several waters. The wash water is evaporated, and the residue is screened through a No. 100 mesh sieve to remove coarse particles which do not affect the strength. The silt passing this sieve is weighed to obtain the percentage in the original sand, and then ignited in a platinum crucible to determine, after driving off the water, the percentage of combustible organic matter. Although data on the subject is incomplete, tests by Mr. Thompson tend to indicate that if the silt in a sand has more than 10 per cent, organic matter, and at the same time if the organic matter amounts to over 0.1 percent, of the total sand, the use of the sand may be danger- ous.f However, this is by no means a conclusive test, since the nature of the impurities governs their effect upon the mortar or concrete. The usual source of impurities is vegetable loam mixed with the sand by improper handhng or leaching down into it through the original ground. Mr. Thompson has found that this sometimes affects the sand to a depth of ID feet or more below the surface. Vegetable matter adhering to the grains of sand can sometimes be seen by examination under a glass. The so-called "dead" appearance of sand is usually due to vege- table impurities. Loam adhering to coarse gravel is apt to produce less serious effects. Its effect on mortar is discussed on page 168. CHEMICAL TESTS Complete chemical tests of sand are rarely necessary as the chemical composition does not usually affect the strength of the mortar or con- crete. However it is often necessary to distmguish a calcareous or * A No. 4 sieve, having 4 meslies per linear inch, passes approximately the same size grains as a sieve with 0.25 diameter holes, t See page 168. TESTS OF AGGREGATES 119 limestone sand. Limestone composition is determined by tests with dilute hydrochloric acid. If the material effervesces to a marked degree, it is either liihestone or magnesium composition and the percentage, may be obtained by quantitative analysis. The effect of hmestone com- position upon the strength of mortar is shown on page 166. COLOR TESTS The depth of color produced by digesting sand with a 3 per cent, solu- tion of sodium hydroxide has been found* to bear a relation to the compressive strength of mortar made with the sand. Eliminating other vfiriables, tests showed that sands giving high strengths in mortar gave a light colored solution when mixed with the hydroxide. Although not a test that can be used alone to indicate quality, it is likely to develop into an inexpensive test that can be employed to eliminate poor sands which are contaminated with vegetable impurities. HARDNESS AND STRENGTH OF PARTICLES The effect of aggregates of different hardness is shown in the table of concrete with different coarse aggregates on page 316. In general, it has been found that the harder the stone from which the concrete is made, the stronger is the concrete. The hardness of the grains of fine aggregate has less effect upon the strength. .In natural sand the strength of the particles seldom needs to be considered because if the grains are strong enough to have withstood the pulverizing effect of the elements, without becoming too fine for use, they are satisfactory for concrete. Furthermore, if the sand is tested for strength of mortar (see p. 116) any defect in strength will be apparent. Specific Gravity of Sand by Jackson Apparatus. Sand may be tested for specific gravity most accurately by a specific gravity apparatus. The Jackson flask when properly calibrated is a most convenient appa- ratus. (See p. 85). Further data on specific gravity of aggregates and methods of determining are treated in the following chapter. * 1916 Report of Committee C-g of the American Society for Testing Materials. 120 A TREATISE ON CONCRETE CHAPTER VIII VOIDS AND OTHER CHARACTERISTICS OF CONCRETE AGGREGATES In this chapter are given tables of the specific gravities and voids of different materials, and the method of determining them, also laws relating to the voids in concrete aggregates, and the effect of compacting such materials. LAWS OF VOLUMES AND VOIDS The most important of the general laws relating to volumes of different materials, and to their voids, may be stated as follows: (1) A mass of equal spheres, if symmetrically piled in the theoreti- cally most compact manner, would have 26% voids whatever the size of the spheres, but by experiment it is found that it is practically im- possible to get below 44% voids. (See p. 129.) (2) If a dry material having grains of uniform shape be separated by screens into grains of uniform dimensions, the separated sizes (except when finer than will pass a No. 74 screen) will contain a,pproximately equal percentages of voids; in other words, a dry substance consisting of large particles, all of similar size and shape, will contain practically the same percentage pf voids as a substance having grains of the same shape but of uniformly smaller size. (See p. 131.) (3) In any material the largest percentage of voids occur with grains of uniform size, and the smallest percentage of voids with a mixture of sizes so graded that the voids of each size are filled with the largest par- ticles that will enter them. (See p. 132.) (4) An aggregate consisting of a mixture of coarse stones and sand has greater density — that is, contains a smaller percentage of voids — than the sand alone. (See p. 133.) (5) By Fuller and Thompson's experiments, perfect gradation of sizes of the aggregate appears to occur when tiie percentages of the mixed ag- gregate passing diSerent sizes of sieves are defined by a curve which approaches a combination of an ellipse and straight line. (See p. 1£2.) (6) Materials with round grains, such as gravel, contain fewer voids than materials with angular grains, such as broken stone, even though VOIDS AND OTHER CHARACTERISTICS 121 the particles in both may have passed through and been caught by the same screens. (See p. 135.) (7) The mixture of a small amount of water with dry sand increases its bulk. In the case of most bank sands the maximum volume — and hence the smallest amount of solid matter per unit of volume, that is, the largest percentage of absolute voids — being reached with from 5% to 8% of water. (See p. 137.) CLASSIFICATION OF BROKEN STONE.* Rocks which are commonly employed for concrete or for road making are commercially classified as (a) traps, (b) granites, (c) limestones, (d) conglomerates, and (e) sandstones. The trade term "trap" includes dark green to black, heavy, close tex- tured, tough rocks of igneous origin, thus covering a variety of rock whose mineralogical names are diabase, norite, gabbro, etc. As shown in the table below, the traps usually, range in specific gravity from 2.80 to 3-oS- Granites, commercially so called, include the lighter colored, less dense rock, such as not only true granite, but syenite, diorite, gneiss, mica schist, and several other groups. Their specific gravities range from about 2.65 to 2.85, averaging close to 2.70. Although, as road metal, the traps are usually far superior to granites, for concrete there appears to be no great difference in the value of (he two classes. The distinction, however, is worth keeping because a concrete stone is often purchased from road metal quarries. Limestones of normal type range in specific gravity from 2.47 to 2.76, averaging about 2.60, although the very soft stones, which are not suitable for high class concrete, may fall below 2.0. Conglomerate, or pudding stone as it is often termed, is essentially a very coarse grained sandstone, ranging in specific gravity from 2.50 to 2.80. It makes a good concrete aggregate. Sandstones of compact texture, such as the Potsdam and Medina sand- stones, and the Hudson River bluestone, may run as high in specific gravity as 2.75, while the looser textured, more porous sandstones may fall as low as 2.10, a fair average being about 2.40. Shale and slate make poor concrete aggregates, because their crushing and shearing strength is low. *The authors are indebted to Mr. Edwin C. Eckel for the material under this heading, -which has been especially prepared by him for this Treatise. A TREATISE' ON CONCRETE Specific Gravity of Stone from Different Localities. Compiled by Edwin C. Eckel. Locality. Massachusetts Boston Minnesota Duluth Duluth Taylors Falls ..'.... New Jersey Jersey City Heights , Little Falls New York Staten Island , Specific Specific Gravity. Locality. Gravity. California . 2.78 Penrhyn 2.77 Rocklin 2.68 . 3.00 Connecticut . 2 .80 Greenwich 2 .84 3.00 New London 2.66 Georgia . 3.03 Stone Mt 2.69 . 2.99 Maine Hallowell 2.66 . 2.86 Maryland Port Deposit 2.72 Massachusetts Quincy 2.70 New Hampshire Keene 2.66 New York Ausable Forks 2. 76 Rhode Island Westerly 2.67 Vermont Barre 2.65 Wisconsin Amberg 2.71 Montello 2.6^ limestone. sandstone. Specific Gravity. Locality. Illinois Joliet 2,56 Lemont 2.51 Quincy 2.57 Indiana Bedford 2.48 Salem 2.51 Minnesota Frontenac 2.63 Winona 2.67 New York Canajoharie 2.68 Glens Falls 2.70 Kingston 2.69 Prospect 2.72 Sandy Hill 2.76 Williamsville 2.71 Soft Limestone France Caen . 1.84 ^Brownstone. ^Medina sandstone. "Potsdam sandstone. Specific Gravity Locality. Colorado Ft. Collins 2.4; Trinidad 2.3^ Connecticut Portland' 2 .6^ Massachusetts Longmeadow' 2 .4J Minnesota Fond du Lac 2.2^ New Jersey Belleville' 2.2( New York Albion* 2.6( Medina* 2 .4 Potsdam^ 2.61 Oxford* 2.7 Malden= 2.7 Oswego 2 .4 Ohio Berea° 2.1 Cleveland 2.2 Massillon 2.1 ■*Bluestone. ^Hudson River Bluestone. *^Berea grit. VOIDS AND OTHER CHARACTERISTICS 123 SPECIFIC GRAVITY OF SAND AND STONE The specific gravity of a substance is the ratio of the weight of a given volume to the weight of the same volume of distilled water at a tem- perature of 4° Cent. (39° Fahr.). For ordinary tests of stone and sand, the water need not be distilled and may be at ordinary temperature without materially affecting the result. A knowledge of the specific gravity of the particles of the sand and stone is important to the engineer in determining the percentages of voids in concrete aggregates. For accurate determinations of density the specific gravity of a natural sand must be determined. For ordinary purposes, such as the deter- mining of the percentage of voids, the specific gravity may be assumed as 2.65. This value has been determined as the usual specific gravity by experimenters in this country and abroad, except for calcareous sands which average about 2.69 by absolute determination, or about 2.55 if measured by the total volume of the particles having their pores filled with air. Gravels also have quite uniform specific gravity. According to Mr. A. E. Schutte, who has tested gravel from more than forty localities in the United States and Canada, an average value is 2.66. This uniformity in the specific gravity of different sands and of dif- ferent gravels is very convenient for calculation. For stones there is considerable variation. The following table gives average values of various concrete aggre- gates. In every case, the specific gravity is the ratio of the weight of an absolutely solid unit volume of each material to the weight of a unit volume of water. Specific gravities of stone from various localities are given on page 122. Average Specific Gravity of Various Aggregates. {See p. 123.) Material. Range. Sy ""^.l^^^ Average. Sand 2.62 to 2.68 2.65 165 Gravel 2 . 66 165 Conglomerate 2.6 162 Granite 2.65 to 2.85 2.7 168 Limestone 11.48 to 2.76 2.6 162 Trap. . ; 2.80 to 3.0s i! .9 180 Slate 2.7 168 Sandstone 2.10 to 2.75 2.4 150 Cinders (bituminous) j- ■ S 9S 124 A TREATISE ON CONCRETE METHOD OF DETERMINING SPECIFIC GRAVITY The specific gravity of a sample of material is determined by dividing its weight by the vi^eight of water which it displaces when immersed. The size of sample necessary for the accurate determination of a sand or stone of fairly uniform texture depends chiefly upon the delicacy of the apparatus employed. If scales reading to grams, and measures reading to cubic centimeters, are employed, a sample of 250 grams should give accurate results to two decimal places. With scales reading to J ounce, a sample of 4 lb. is necessary for similar accuracy. The water must be maintained at 68° Fahr. (20° Cent.). The sample should be taken by the method of quartering described on page 344- Before finding the specific gravity of siliceous sand, the sample should be dried in an oven at a temperature as high as 212° Fahr. (106° Cent.) until there is no further loss in weight. A porous stone, on the other hand, may be first moistened sufficiently to fill its pores, and then the surfaces of the particles dried by means of blotting paper. If this method is followed, the material should be in a similar condition when its voids are determined by the method given on page 126. The absolute specific gravity of the porous stone may be afterward found by drying in an oven and correcting for the moisture lost. The apparent specific gravity of sand or stone may be determined with an apparatus consisting of scales reading to ^ ounce or to 5 grams, and a tall glass vessel with a reference mark, such as a cylinder or a pharmacist's graduate. The method is as follows: Make a mark at any convenient place on the neck of the vessel; Fill the vessel with water at a temperature of 68° Fahr. (20° Cent.) up to this mark; Take a known weight in grams or ounces of the material; Pour material into vessel carefully, a few grains at a time, so that no bubbles of air are carried in with it; Pour out the clear water displaced by the material (leaving water in the vessel up to the level of the mark), and weigh the water poured out. Let ■9^ Weight of material placed in vessel. Ty=Weight of water displaced. Then Specific gravity of material = — - (i) VOIDS AND OTHER CHARACTERISTICS 125 It is essential that the weight of water displaced be weighed to within ±2%. If the scales are not sufficiently sensitive, more material must be taken and a larger vessel used. With balances sensitive to i gr. or 3^ oz. the displacement of more than 3 ounces of water is necessary. An alternate method, recommended by Committee D 4 of the Amer- ican Society for Testing Materials, for determining the apparent specific gravity of homogeneous coarse aggregates* is as follows: The apparent specific gravity shall be determined in the following manner: 1. A properly selected sample which will pass a 2.54 cm. (i-in.) circular opening and which will not pass a 1.27-cm. (|-in.) circular opening, and approximately cubical or spherical in shape, shall be dried to constant weight at a temperature between 100 and 110° C. (212 and 230° F.). 2. The dried sample shall be suspended in air by a fine wire or thread from a scale or balance and weighed in air to o.oi g., which weight shall be recorded as weight A. 3. It shall then be immersed, for not less than 10 minutes, in clear water having a temperature between 15 and 25° C. (60 and 77° F.) untU no air bubbles appear on the surface of the sample. 4. After all air bubbles shall have been removed from the surface and after the scales have been balanced, the sample shall be allowed to remain immersed for i minute, and if any change in weight takes place, the sample shall remain in water until the balance remains con- stant within 0.01 g. for i minute. This weight shall be recorded as weight B. 5. After weight B has been obtained, the sample shall be removed immediately from the water, the surface water shall be wiped off with a towel or filter paper, and the wet sample shall be promptly weighed in air. This shall be recorded as weight C. 6. The apparent specific gravity of the sample shall be calculated by dividing- the weight of the dry specimen {A) by the difference between the weights of the saturated specimen in air (C) and in water (-B) as follows: , Apparent specific gravity = — — C-B 7. The apparent specific gravity of the material shall be the aver- age of three determinations, made on three different samples, accord- ing to the method described above. * Attention is called to the distinction between apparent specific gravity and true specific gravity, Apparentspecificgravity includes the voids in the specimen and is therefore always less than or equal to but never greater than, the true specific gravity of a material. 126 A TREATISE ON CONCRETE DETERMINATION OF VOIDS The voids in sand, gravel, and broken stone may be obtained directly from the tables on pages 127 and 128. Special determinations may be made as described below. The percentage of voids in sand or iine broken stone cannot be accu- rately obtained by the ordinary method of placing in a measure and pour- ing in water, because it is physically impossible to drive out all the air. There may sometimes be enough of this held to amount to 10% of the volume of the sand, and thus cause a corresponding error in the per- centage of voids. The voids in coarse stone containing no particles under |-inch diame- ter may be determined by placing in a box or pail of known volume and poui:ing in water, but if the specific gravity is known the voids may be determined directly from the weight. This method can be used both for fine or coarse aggregate. The only apparatus required are scales of fair accuracy and an exact measure which contains not less than J cu. ft. If a cubic foot measure is not available a i6-quart pail will answer the purpose, although com- pactness of the sand is less easily adjusted because of the small diam- eter. Such a pail holds slightly over ^ cu. ft. and the exact measure is determined by weighing the pail, pouring in 31 lbs. 2 oz. of water, and marking the level of the surface. The pail up to this mark contains J cu. ft. of any material. The method of determining the voids is as follows: Weigh the measure ; Fill the measure to the required level with the material in the state in which the percentage of voids is required, that is, loose, shaken, or packed; Take a measure holding preferably not less than ^ cubic foot, weigh and fill with the material in the state in which the percentage of voids is required, that is loose, shaken, or packed. For use in propor- tioning, it is the authors' practice to weigh, deduct the weight of the measure, and figure the net weight of a cubic foot of the mate- rial, W. If the material consists of, or contains, sand or fine stone, correct for moisture by taking an exact weight, — about 10 lb., — drying in an oven at a temperature of at least 212° Fahr. (100° Cent.) until there is no further loss in weight, and after calculating the percentage of moisture in terms of the weight of the original moist sand or stone, express the percentage as a decimal, p. VOIDS AND OTHER CHARACTERISTICS In the following formula : Let W = weight of material per cubic foot; p = percentage of moisture; S = Specific gravity of material; 62.3 is the weight of a cubic foot of water. 127 Per cent, of absolute voids = ( i Wj-JVp 62.3 ?) (2) The air voids are determined, if desired, by deducting the volume of moisture (its weight divided by the weight of one cubic foot of water) Percentages of Voids Corresponding to Different Weights per Cubic Foot of Sand, Gravel, and Broken Stone Containing Various Percentages of Moisture. (See p. 129.) PERCENTAGES OF ABSOLUTE VOIDS IN MATERIAL CONTAINING MOISTURES BY WEIGHT.t 4% 6% 8% > S £ " o o £■ PERCENTAGES OF ABSOLUTE VOIDS IN MATERIAL CONTAINING MOISTURES BY WEIGHT, f 0% 4% 6% !&§ S' % % % % 70 57-6 58.4 59-3 60.1 75 54-5 55-4 56-4 57-3 80 81 51-5 S°-9 52-5 5^-9 53-4 52-9 54-4 53-9 82 83 84 50-3 49-7 49.1 Si-3 50-7 So.i 52-3 51-7 51-1 53-3 52-7 52.2 8S 86 87 48.5 47-9 47-3 49-5 48.9 48.3 50.6 50.0 49-4 S1.6 51.0 504 88 89 90 46.7 46.1 45-5 47-7 47.1 46.5 48.8 48.2 47.6 49.9 49-3 48.7 91 92 ?3 44.8 44.2 43-6 45-9 45-4 44.8 47.0 46-5 45-9 48.2 47.6 47.0 34 95 96 43-° 42.4 41.8 44.2 43-6 ^3'° 45-3 44-7 44.1 46-5 45-9 45-3 97 41.2 42.4 43-6 44-7 % 61.0 58.2 55-4 54.8 54-3 53-7 53-2 52.6 52.0 5 1 -5 5°-9 50-4 49.8 49.2 48.7 48.1 47.6 47 -o 46.4 % 1-3 1-3 1-3 1-3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 I -5 1-5 1-5 I -5 1-5 1-5 1.6 % % % % % 98 99 40.6 40.0 41.8 41.2 43 -o 42.4 44.2 43-6 45-3 44.8 100 lOI 102 39-4 38.8 38.2 40.6 40.0 39-4 41.8 41.2 40.7 43 -o 42.5 41.9 44.2 43-7 43-1 103 104 105 37-6 37-0 36-4 38.8 38.2 37-6 40.1 39-5 38.9 41-3 40.8 40.2 42.5 42.0 41.4 106 107 108 35-8 35-2 34-6 37 -o 36.4 35-9 38-3 37-7 37-2 39-6 39-0 38.5 40.9 40.3 39-7 109 IJO 33-9 33-3 35-3 34-7 36.6 36.0 37-9 37-3 39-2 38-7 115 30-3 31-7 33-1 34-5 35-9 120 27-3 28.7 30.2 31.6 33-1 125 24.2 25.8 27-3 28.8 3°-3 130 21.2 22.8 24.4 25-9 27-5 135 18.2 19.8 21.4 23-1 24.7 140 15-2 16.8 18.5 20.2 21.9 % 1.6 1.6 1.6 1.6 1.6 1.6 1-7 1-7 1-7 J^-7 1-7 1-7 1.8 1.8 1.9 2.2 2.2 •Also applicable to broken stones such as granite, conglomerate, and limestone, whose specific gravity jverages from 2.6 to 2.7. Table is based on specific gravity of 2.65. tThe per cent, of absolute voids given in the columns include the space occupied by both the air and the moisture. To determine the per cent, of air space, multiply the figure in the last column, opposite the weight of sand under consideration, by the per cent, of moisture by weight, and deduct result from the per cent, already found. 128 A TREATISE ON CONCRETE in a unit volume of the sand or stone, from the total voids. Expressed in percentages with notation same as above, Per cent, of air voids = Per cent, of absolute voids ■ Wp 62.3 (3) Example. — Given a sand whose loose weight per cubic foot is found to be 92 lb. and its moisture 3% by weight. Find the percentage of voids in the loose sand. Solution by formula. — Since from the example W = g2 and p = 0.03, and, from table on page 123, S = 2.65. T^ r 1 f -1 / 02 — 0.0^(02)^ Percentage of absolute voids = I i — ' — ^— \ 62.3 X 2.65 = 45-9% This percentage includes the space occupied by the moisture. The net percentage of voids occupied by air alone is the difference between the absolute voids and the percentage of moisture by volume. Moisture is 2.76 92 X 0.03 = 2.76 lb., or 7 — = 0.044 cu. ft., corresponding to 4.4% 02.3 voids by volume, hence air voids are 45.9% — 4.4 % = 41.5%. Percentages of Voids Corresponding to Different Weights per Cubic Foot Broken Stone of Various Specific Gravities. {See p. 129.) of Dry Weight one cu. ft. of PERCENTAGE OF ABSOLUTE VOIDS CORRESPONDING TO SPECIFIC GRAVITIES OF STONE Oi^ dry broken stone 2.4* 2.5 2.6t j 2,65} 2.75 2.8 2.911 % % % ! % ! % % % 70 80 S3-2 49.8 46. s S5-0 51.8 48.6 S6.8 ; 57-6 i 58.4 53-7 S4-S 55-4 50-6 5I-S : 52.4 S9-9 S7-0 S4.i 61.3 58.5 5S-7 8S go 95 43-2 39-8 36.S 45-4 42.2 39-0 47-5 44-5 41.4 48.S 4S-S 42.5 49-5 46.S 43- S S1.3 48.4 4S-S 53-0 50.2 47-4 100 no 33-1 29.8 26.4 35-8 32.6 29.4 38.3 3S-2 32.1 39-4 36.4 33-4 40.6 37-6 34-6 42.7 39-8 36.9 44-7 41.9 39-1 IIS 120 I2S 23.1 19.8 16.4 26.2 23.0 19.8 29.0 2S-9 22.8 3°-4 27-3 24-3 31-6 28.7 25-7 34.1 31.2 28.3 36-4 33-6 30.8 130 13s 140 I3-I 9-7 6.4 16.6 13-3 10. 1 19.8 16.7 13.6 21.2 18.2 15-2 22.7 19.7 16.7 2S-S 22.6 19.7 28.1 25-3 22.5 Note. — Average specific gravity of bituminous coal cinders may be taken as 1.5. * Sandstone. § Granite and slates, t Limestone and conglomerates. || Trap. t Sand. VOIDS AND OTHER CHARACTERISTICS 129 Solution by table (p. 127.) — Opposite 92 lb. per cu. ft., interpolating between 2% and 4% moisture, is 46.0% of absolute voids. From last column 3% by weiglit corresponds to 3% x 1.5 = 4.5% by volume. 46.0% — 4.5% = 41.5% air voids. Tables of Voids. From the tables on pages 127 and 128, the voids in sand, gravel, and broken stone may thus be determined simply by weighing the material and finding the percentage of moisture contained in it, as above described. Since the percentage of moisture by \olume is always greater than its percentage by weight, and the two are not pro- portional to each other, the final column is inserted in the first table for convenience in calculating the moisture by volume. VOIDS AND DENSITY OF MIXTURES OF DIFFERENT SIZED MATERIALS The term density as applied to mortar is defined on page 148. Similar!}', in a dry material, such as a concrete aggregate, it is represented by the total volume of the solid particles entering into a unit volume of the aggre- gate. In dry materials the density is the complement of the voids, since a material which has, say, 40% voids will have a density of 0.60; but density- is a more correct term to use than voids because it is applicable to con- cretes and mortars in which connection the term voids is somewhat ambiguous. The example on page 150 illustrates the method of de- termining the density of a concrete or mortar. The densities of dry aggregates of uniform specific gravity, or of mixtures in uniform proportions of materials with different specific gravities, are in direct proportion to their weights. For example, the densities of different dry sands may be compared by weight; or the densities of diiierent mix- tures of sand and broken trap in proportions, say, 2 parts sand to 4 parts trap may be compared by weight; but the density of sand and the densit}- of trap screenings cannot be compared by weights unless the differing specific gravities are taken into account. In the following discussion of the laws formulated on page 120, both the terms density and voids are used in relation to the dry materials. Voids in Masses of Similar Sized Particles, (i) The fact that the percentage of voids in a mass of equal spheres symmetrically piled in the theoretically most compact manner is independent of the actual diameter is simply a geometrical proposition, evident without demonstration by in- spection of Fig. 2iZ- In actual experiment it has b( jn found that while the percentage of voids is uniform regardless of the size of the spheres, it is impossible to 13° A TREATISE ON CONCRETE pour spheres into a measure so that they will arrange themselves sym- metrically, and the rather astonishing result has been reached by Mr. Fuller (see p. 177) that 44%, is the smallest percentage of voids which can be obtained with equal perfect spheres, no matter what may be their actual diameters or the size of the receptacle. The following simple demonstration,* which is of theoretical interest, proves that the percentage of voids in a mass of equal spheres symmetri- cally piled in the most compact manner is 26'7f , and that the radii (and consequently the diameters) of the two next smaller spheres which can Fig. 33. — Spheres of Equal Size. {See p. 129.) be inscribed between the larger ones are respectively 0.41 and 0.22 of the radius of the large spheres. The circles in Fig. 33 represent a horizontal plan of two layers of splieres. The centers Aj A3 Bj Di form a regular tetrahedron. Let edge be 2. Altitude = difierence between level of centers A, B, C, and level of centers D, E is — \/6~ 3 Let number of spheres in a layer be m, number of layers n. *For which the authors are indebted to Dr. Harry W. Tyler. VOIDS AND OTHER CHARACTERISTICS 13] Volume of one sphere is — — 3 Volume of spheres in a layer, ~ — ~ 3 Volume of all spheres, — (approx.) = Fj 3 Cross-section of including space is 2 \/J^ m (approx.) Volume of including space is 2 \/J'm X— -\/6" n (approx.) 3 = 4 -s/2" m n (approx.) = Fj D r Vi 4 111 flTT TT , , Katio — = —^ = —^ — 0.74 (approx.) corresponding to V, 3X4 '" « V2 3 V2 ■ about 26% voids. Inscribed Spheres. 1. Sphere inscribed between spheres A^ Aj Bj and D,: Distance from any vertex A^ of tetrahedron to center is J \/6" Radius of small sphere = ^ \/6~— i = 0-22 (approx.) or about — Qf the radius of the large spheres. ^°° 2. Sphere inscribed between A^ B^ Bj and Dj D2 Ej: Distance from A, to E, is 2\/~^ 41 Radius of small sphere = Va — i = 0.41 (approx.) or about of the radius of the large spheres. (2) The proposition that if a dry material such as sand, pebbles, or irregular broken stone, having grains of fairly uniform shapes, be separated by screens into grains of uniform dimensions, the separated sizes will con- tain approximately equal percentages of voids. Is not so self-evident, but experiment proves that in portions of the same material screened to uniform sizes the percentages of voids will be substantially alike until very fine sizes are reached, such as will pass a No. 74 sieve; below this degree of fineness the particles are entangled by air. The authors have found l)y experiments given in the following table, that different lots of broken stone from the same quarry, each screened to uniform size, will contain substantially the same percentages of voids, but that lots of stone from different quarries screened to the same size may differ because of the structure of the rock. Published records usually show slight variations in the weight per cubic foot of different sized broken stone, but it is noticeable that some authorities give the heaviest weight, 132 A TREATISE ON CONCRETE which corresponds to the smallest percentage of voids, for the larger sizes, while others give the reverse. The variation in results is due un- doubtedly to differences in methods of compacting and to the varia- tions in the sizes of the stones of each lot. Experiments by Mr. Feret in France, and Mr. Thomas F. Richardson in the United States, show that the percentages of voids in absolutely dry sand which has been screened to uniform size are almost identical. Mr. Feret, experimenting by shoveling dry sand loosely into a 5oliter (1.8 cu. ft.) box, — a measure large enough to eliminate errors of placing, — found that fine (F) medium (M) and coarse (G) sands each contained about 50% Voids ai d Compression of Broken Ti a-p and Gravel. {See p. 131.) Size of stone Class of Stone Crusher Size of Particles s .2 '0 > % MM .St. |i Is m. .s» ■a ° I % Si si a % -0 s s u .s M 13 I % No. 2 No. 3 Nos. 2, 3, 4 No. 2 No. 3 HardTrap Soft Trap Gravel Rotary Jaw 2i" to l" i" to i" 2i"to dust* 2" to J" 1" to r 2i" to i" S4-S 54-5 4S.O 51.2 51.2 36.S 14-3 14-5 11.9 14-3 I2.st 46.9 35-7 44.6 43-1 27.4 19.2 20.5 ''o.a 17.8 23 -9 ii.st Ail 42.8 30.6 40.6 350 28.2 IVariation is due to trap / breaking under rammer. Loose stone is as thrown by a laborer into a measuring box or barrel. Material rammed in 6-inch layers. voids, while mixing the sizes, which are defined on page 156, in the best proportions reduced the voids to 34%. Similar results were obtained by Mr. Richardson as a result of an extended series of tests made in. con- nection with the construction of the Wachusett Dam in Massachusetts. Densest Mixture of Sand and Stone. (3) The fact that the densest mixture occurs with particles of different sizes is so evident as to retjuirc no proof, and this being recognized, it follows that the least density and hence the largest percentage of voids occurs when the grains arc all of the same size. The converse of this proposition, that the smallest percentage of voids occurs in a mixture graded so that the voids of each size are filled with the largest particles which will enter them, is *Mixed'in proportions 44.4% No. 2, 33.3% No. 3, and 22.2% No. 4 (dust). t Another gravel tested, compressed, 8.5% on shaking, and ir.2% on hard ramming. VOIDS AND OTHER CHARACTERISTICS 133 illustrated in Figs. 34, 35, and 36, and is important in its application to the selection of materials for concrete. (4) The fact that an aggregate consisting of a mixture of stones and sand has greater density, that is, contains fewer voids than the sand alone. Fig. 34. — Large Stones with Voids filled with Sand. (See p. 133.) Fig. 35. — Large Stones with Voids filled with small Stones and Sand. (See p. 133.) is illustrated by comparison of Figs. 34 and 36. The voids of the large stone in Fig. 34 are filled with sand, while the voids in the same large stone in Fig. 36 are filled with mixed sand and stone, and the mass of the mixture is evidently denser, that is, it contains more solid material. This 134 A TREATISE ON CONCRETE law relates directly to the difference between mortar and concrete. The substitution of stones for small masses of sand reduces the voids and con- sequently the quantity of cement required. Extending the principle to the fixing of proportions of sand and stone, it is evident that for maximum Fig. 36. — Largo Stones, with Voids filled with medium sized Stones surrounded by smaller Stones and Sand so as to give Graded Mixture. (See p. 133.) economy and equal strength there should be used the largest possible quantity of stone in proportion to the sand, the strength of concrete being often actually increased simply by substituting more stone for a portion of the sand. In the following table this is illustrated by tests selected from Mr. Fuller's 6-inch beam experiments, which are given in full on page 334- Relation of Strength of Concrete to Relative Proportions of Sand and Stone. {See p. 134.) Proportions by weight of Proportions by weight of cement to total cement to sand and Modulus of Rupture aggregate. broken stone. lb. per sq. in. 6 1:1:5 5°4 6 1:2:4 439 6 1:3:3 355 6 1:4:2 210 6 i: 6:0 93 The total amount of aggregate in each case is the same, namely, one part cement to 6 parts sand and stone, but the strength varies with the relative proportions of each, from 93 lb. to 504 lb. The fine material must be small enough to enter the voids of the coarse, else the stones are merely thrust apart. Similarly, a mixture of coarse and fine sand (see p. 159) gives a denser mix than coarse, medium and fine. See also Chapter X. VOIDS AND OTHER CHARACTERISTICS 135 (s) The discussion of Fuller's experiments on the relation of the best practical mixture of sizes to a parabolic curve is given in Chapter X. Effect of Shape of Grain. (6) Aggregate with round grains, such as gravel, contains fewer voids than material with angular grains, such as broken stone, even if the particles in both are the same size, as is proved from experiments in America and France. Mr. Feret* gives the fol- lowing results of tests on the effect of the shape of the grain upon the density of sand, using in each case an artificial mixture of three sizes: Effect of Character of Sand Grains upon ihe Volume of the Sand. {See p. 135.) By R. Feeet. Nature of Sand. Shape of Grains. Actual solid volume per liter of sand Percentage of voids. Not shaken, liter. Shaken to refusal, liter. Not shaken. Shaken to refusal. Quartzite crushed in jaw Laminated Flat Angular Rounded "•525 0-SS7 0-S79 0.651 0.654 0.682 0.726 0.744 47-5 44-3 42.1 34-9 34-6 31.8 27.4 25.6 Ground quartzite Natural granitic sand The voids ia each case are the complements of the figures given. The conclusion to be drawn is that the density increases and the voids decrease as the sand approaches the round form. When experimenting upon gravels and broken stone Mr. Feretf sepa- rated each into three sizes which he called respectively: G (coarse) passing holes of 6 cm. (2.36 in.) diameter and retained by holes of 4 cm. (1.57 in.) diameter; M (medium) passing holes of 4 cm. (1.57 in.) diameter and retained by holes of 2 cm. (0.79 in.) diameter; F (fine) passing holes of 2 cm. (0.79 in.) diameter and retained by holes of I cm. (0.39 in.) diameter. Each size of broken stone loosely measured gave about 52% voids, and each size of gravel about 40% voids. The voids in the broken stone were reduced to 47%, the lowest result obtainable, by mixing G and F in about * Annates des Fonts et Chauss^es, i8g2, II, p. 32. t Annales dcs Fonts et Chauss^es, iSgz, II, p. 153- 136 A TREATISE ON CONCRETE equal parts with no M, and in the gravel to 34% with about 3^ parts of G to one part of F. These figures are applicable only to the materials Fig. 37. — Standard Ottawa Sand, dry.* No. 20 to No. 30 Sieves. (See p. 136.) Fig. 38. — Standard Ottawa Sand with 6% moisture* No. 20 to No. 30 Sieves. (See p. 136.) Fig. 39. — ^Natural Bank Sand.* No. 20 to No. 30 Sieves. (See p. 136.) Fig. 40. — Crushed Quartz.* No. 20 to No. 30 Sieves. (See p. 136.) studied, and do not apply to gravel or stone containing sand or dust. Photographs of Sand.f Photographs of three types of sand are shown in Figs. 37 to 40. Figures 37 and 38 are photographs of the Ottawa, * Magnified loj diameters. t Photograplis and tests of ten sands from different localities are given in '"Concrete Aggregates" Ijv Sanford E. Thompson before the International Engineering Congress, 1915. VOIDS AND OTHER CHARACTERISTICS 137 Illinois, bank sand screened to the size selected for the standard sand by the Committee of the American Society of Civil Engineers. They illustrate the efiiect of moisture upon the arrangement of the sand grains, which is more fully described below. Fig. 39 is an ordinary bank sand from Eastern Massachusetts which has passed through and been re- tained by the same screens as the Ottawa sand. Fig. 40 is a sample of crushed quartz sand, formerly the standard in the United States. The sands are all reduced by the same number of diameters. The Ottawa sand, Figs. 37 and 38, is apparently of finer grain than either the bank sand or the crushed quartz, but close inspection will show that its grains, very uniform in size, are of about the same diameter as the smallest grains in the other sands. In other words, all the grains cor- respond very closely to a No. 30 sieve, the lot of sand from which it was screened containing no larger particles. Effect of Moisture on Sand and Screenings. (7) Moist sand occupies more space and weighs less per cubic foot than dry sand. This is directly contrary to what one would naturally suppose. Indeed, it is almost in- credible that the addition of water can reduce the weight of any material. The statement is readily proved however, by shoveling a small quantity of natural sand as it comes from the bank with, say, 3% or 4% of moisture into a measure and drying it. The sand will settle, leaving the surface much below the level of the top of the measure. The explanation of this apparent anomaly lies in the fact that a film of water coats each particle of sand and separates it by surface tension from the grains surrounding it. This is illustrated in Figs. 37 and 38, page 136, the grains of the moist sand being separated from each other by the film of water. The moisture also causes the particles to adhere to each other in groups with the effect of less uniform distribution. Fine sand, having a larger number of grains, and consequently more surface area, is more increased in bulk by the addition of water than coarse sand. The volume of coarse broken stone and gravel is but slightly, if at all, changed by moisture, while small broken stone composed largely of particles of less than J-inch diameter is affected like sand. If a small quantity of water is poured into a vessel containing dry sand, the bulk is not increased because of the inertia of the particles, but if the sand after moistening is dumped out and then turned back into the vessel with a shovel or trowel, itsbulkwill be increased. On the same principle, a sand bank does not swell in bulk during a shower, but the effect of the moisture is shown in the excavated material as soon as it is loosened with the shovel, and therefore its loose measureiiient for concrete or mortar is afPected. 138 A TREATISE ON CONCRETE The diagram in Fig. 41, plotted by Mr. Fuller* from experiments upon a single sample of natural sand mixed by weight with varying per- centages of water, illustrates the effects of moisture upon the actual percent- ages of voids in sands loose and tamped. The volumes produced by varying degrees of compacting are located between the two ciurves. It is noticeable that both the loose and tamped sand increase in volume with the addition of water and reach a maximum with about 6% of water, then decrease, and finally, when saturated, return to slightly less than their original dry bulk. The same sand, it is seen, may contain from 27% to 44% of absolute voids, according to the percentage of water and the degree of compacting. The percentage of water by weight which wiU give the greatest bulk, — corresponding, of course, to the largest per- centage of absolute voids, — varies with different sands from 5% to 8%. The actual variation on dif- ferent days in the percentage of moisture in a natural bank sand was found by the authors, in a series of experiments, to range from ij% to 5^% of the total weight, or from 2j% to 7i% of the bulk of the moist sand. The sand, screened from a gravel bank in Eastern Massachusetts, ranged in coarseness from very fine to that which would pass a J-inch mesh screen. The moist sample was taken from the pile the day after a shower, and weighed 84^ lb. per cubic foot, while the dryer sample, taken after a period of dry weather, weighed 107 lb. per cubic foot. A sample of very fine sand which had been standing in a pile through the same shower contained 9^% of moisture by weight, corresponding to 13% by volume. Ordinary gravel, on the other hand, from which the sand'had been screened, was found after a heavy rain to contain only 1.8% of moisture by weight, this being apparently the maximum quantity which it would hold. ■^Engineering News, July 31, 1902, p. Si. 2 4 6 8 10 12 14 1618"' PERCENTAGE, (by WEIGHT) OF WATER TO SAND WHEN DRY Fig. 41. — Percentage of Absolute Voids in a Natural Bank Sand containing Varying Per- centages of Moisture. {See p. 138-) VOIDS AND OTHER CHARACTERISTICS 139 The maker of concrete is especially interested in the influence of moisture upon the bulk of sand and upon its voids (i) because of its effect upon the actual measurement of sand used in construction work, and (2) because of its effect upon his experimental determinations of proportions. Rather incomplete experiments of the authors tend to show that the actual effect of moisture upon the volume of sand used in concrete and mortar may often be less than would naturally be inferred from the various experiments cited, and depends largely upon the processes of handling the sand. For example, fairly dry sand (3% moisture) shoveled by laborers from the pile into the regular sand-measuring box weighed 454 lb., while after a rain, the sand (with 5% moisture) shoveled from the pile into the same box weighed 464 lb., that is, the moist sand was slightly heavier than the dry. Further handling reversed these relations, for on weighing these two sands in a half cubic foot measure, the moist sand, as we should ex- pect, was lighter than the dry. The explanation of this apparent discrepancy is undoubtedly due to the fact that as the rain which affected the moisture occurred after the sand had been excavated and piled near the mixing platform, its bulk, as suggested on page 137, was not affected. The laborers handhng the moist sand took large shovelfuls and the arrangement of the grains was not greatly disturbed. If the sand had been excavated after the rain, the handhng with shovels and dumping from the cart probably would have rearranged the grains so that the moist sand would have weighed less than the dry in the large measure as well as in the small box. Mr. Feret* calls attention to the fact that mortars of nominally the same proportions are richer in winter than in summer because of the greater amount of moisture in the sand, which, by increasing its bulk, reduces the absolute volume of the grains in a unit of measure. On the other hand, mortars are leaner in dry than in damp weather because the sand has greater density when dry. In the experimental study of sand for determining the proportions of cement to be used, the effect of moisture is exceedingly important. The voids in absolutely dry sand are certainly no criterion of its qualities for mortar, while a moist sand will give entirely different results on differ- ent days. The best that can be done, if the study can be pursued no further than void determination, is to select conditions as near as possible to the average, and after determining the voids, considered as air alone and also as space occupied by the air and moisture, to use the results as a basis for judgment, bearing in mind that the volume of paste made from 100 lb. *Annales des Fonts et Chauss^es, 1892, II, p. 16. I40 A TREATISE ON CONCRETE of neat Portland cement, while varying largely with different brands, averages about 0.86 cubic feet, and that the volume of the additional water required for the sand (see pages 160 and 209) actually occupies space in the resulting mortar. The most important conclusion to be drawn from the extreme variation in the same sand under different conditions is the impossibility of attaining results by the usual void experiments upon sand alone, which will be of accurate value in the consideration of mortar and concrete, and the prac- tical necessity of employing methods such as are described by the authors in Chapter IX, page 149, or by Mr. Fuller in Chapter X. In the preceding paragraphs we have referred chiefly to the variation in the condition of the same sand. The importance of studying mortars rather than the sand alone is still further emphasized by the varying effect of moisture upon sands of dif- ferent sizes. This is brought out very clearly in Mr. Feret's paper.* In studying the normal consistency of mortars he finds that not only every cement but also every sand has a definite percentage of water necessary Fig. 42. -Percentages of Water Re- to bring it to what may be called quired to Gage Ground Quartz Sand normal consistency. This he iUus- 01 all Granulometnc Compositions. . . , , • ,-.. (See p. 140.) trates in the triangle shown in Fig. 42 (constructed as described on page 156), giving the "proportions of water (by weight) required for ground quartz sands of all granulometric composition." It is evident from the diagram that coarse sands, f G, require 3% by weight of water, medium sands, M, 9%, and fine sands, F, 23%, while mixtures of the three sizes require intermediate percentages. Compacting of Broken Stone and Gravel. Since concrete is usually compacted by ramming or lubrication of semi-liquid mortar, the density or the percentage of voids in compacted material is an important function. The statement has been made frequently that the aggregate compacts more when rammed in concrete than when rammed dry or merely moistened with water, because the mortar acts as a lubricant. Experi- ments by the authors indicate that broken stone under the same ram- ♦Annales des Ponts et Chauss&s, 1892, II. +The sizRs of screens definin£ coarse, medium, and fine sands are given on page is6. VOIDS AXD OTHER CHARACTERISTICS 141 ming will compress on the average 1% more when it is moistened than when dry, and that an amount of mortar sufficient to lubricate without filling the voids produces no further reduction in volume. For example, a volume of broken stone mixed with 20% of mortar and rammed in 6-inch layers produced a volume exactly equal to that of the rammed broken stone which had been merely moistened. Further experiments, partially outlined in the table on page 132, upon gravel and also upon varying sizes and mixtures of trap rock from two quarries, the one producing a soft and the other an exceedingly hard stone, lead to the conclusion that with stones of the same general structure, the percentage of reduction in volume by similar ramming in 6-inch layers is quite uniform, irrespective- of the actual sizes of the particles, their relative sizes, the percentage of voids, and, within certain limits, the degree of hardness. On the other hand, the method of ramming the same stone will very largely affect the amount of compacting. Broken stone of the nature of trap, whether hard or soft, was found to compact when spread in 6-inch layers about 14% either under light ramming or shaking the measure, and about 21% under heavy ramming. In actual concrete work this large reduction of volume is of course seldom reached, because imperfect mixing and the necessary coating of the particles require a larger percentage of mortar than will just fill the voids of the rammed stone, and the bulk of concrete is usually greater than that of the original stone. Screened gravel spread in 6-inch layers and unconfined, compacted about 12% under either light or heavy ramming. These percentages of compacting are based upon the loose meas- urement of the material as thrown by a laborer into a barrel or box measure. Rehandling a material like broken stone as it comes from the crusher tends to mix particles of unequal size and therefore to compact it very slightly. In one case a screened stone fresh from the crusher compacted 1% when rehandled once, and an additional 1% when re- handled the second time. It is interesting to note that the method of shoveling broken stone into a measure has but slight effect upon its shrinkage; for example, a lot of stone thrown with force into an inclined barrel occupied a space scarcely appreciably less than when very carefully and lightly placed. On the other hand, dropping from a considerable height does affect the volume, for Mr. Desmond Fitzgerald* states that broken stone dropped 1 2 feet into a car shrank to a volume 7% less than when it was measured in a box. *TranSactions American Society of Civil Engineers, Vol. XXXI, p. 303. 142 A TREATISE OX CONCRETE Sand, unlike stone, is largely alTerled b}' the manner of slioveling and the size of the receptacle. Compacting of Sand. The degree of compacting of sand is largely dependent upon the percentage of moisture which it contains. The dry sand shown' in diagram in Fig. 41, page 138, when thoroughly tamped compacted from 34% to 27% voids or g.6% in volume,* the sand with 6% moisture from 44% to 31% voids or 18.8% in volume, and the saturated sand from ^3% to 26^% voids or 8.8% in volume. Attention is called by Mr. Feret to the fact that the measurement of the weight of a given sand depends not only upon the quantity of moisture in it, but also upon the depth of the box which is used for the measure, the quantity of sand introduced at a time, — that is, the size of a shovelful, — the height from which it falls, the amount of shaking, if any, given to the box during filling, the amount of compacting given to the mass when leveling it off, and the smoothness of the surface left. As an illustration of the difference due to the method of placing in the measure, the authors found that a certain coarse sand shoveled into a pail about as a laborer would fill a measure weighed 88.9 lb. per cubic foot, while the same sand carefully poured into the pail weighed 83.3 lb. per cubic foot. O.IA — 0.27 *Ratio of compacting = ^ = 0.090 1.00—0.27 STRENGTH OF CEMENT MORTARS 143 CHAPTER IX STRENGTH AND COMPOSITION OF CEMENT MORTARS The following are the important conclusions in this chapter: (1) The strength of a mortar depends primarily upon (a) percentage of cement in a unit of volume, and {b) density. (See p. 144.) (2) The strongest mortar for any given proportions, by weight, of cement to dry sand, is obtained from sand which with the given cement produces the smallest volume of plastic mortar. (See p. 162.) (3) The best sand is in general that which will produce the smallest volume of mortar of standard consistency when mixed with the given cement in the required proportions. (See pp. 144 and 163.) (4) The density of a mortar is determined by calculating the absolute volume of its ingredients. (See p. 149.) (5) The qualities of different sands may be studied by screening each into three sizes, and comparing their granulometric compositions with Feret's curves. (See p. 155.) (6) Sharpness of sand grains is of slight importance. (See p. 167.) (7) Coarse sand produces stronger mortar than fine sand. (See p. 160.) (8) Fine sand requires more water than coarse sand to produce a mortar of like consistency, and consequently its mortar is less dense. (See p. 160.) (9) Mixed sand, /. e., sand containing fine and coarse grains, in mor- tars leaner than 1 : 2, usually produces stronger and more impervious mortars than coarse sand. (See p. 159.) (10) Screenings from broken stone usually produce stronger mortars than sand because of their greater density. The relative value of screenings or sand may often be determined by comparing the densities or the densities of mortar made from them. (See pp. 163 and 166.) (11) Mixtures of fine and coarse sand or of sand and screenings often produce better mortar than either material alone. (See p. 163.) (12) The variation of the sand in different portions of the same bank maybe utilized by requiring the contractor to mix two sizes without exact measurement, so that material as delivered shall contain not less than a definite percentage of sand coarse enough to be retained on a certain sieve. (See p. 163.) 144 A TREATISE ON CONCRETE (13) Mineral impurities in sand, such as clay, in small quantities, may strengthen a lean mortar, and weaken a rich mortar. (See p. 168.) (14) Organic impurities in sand, such as vegetable loam, even in minute quantities may destroy the strength of the mortar or concrete. (See p. 168.) (15) Gaging with sea water does not affect the ultimate strength of mortars. (See p. 166.) (16) The unit fiber stress in a cement or mortar beam is about alike for prisms 4 cm. (1.6 in.) and 2 cm. (0.8 in.) on edge. (See p. 145.) (17) The unit fiber stress in bending is about 1.89 times the unit tensile strength of briquettes of 5 sq. cm. (See p. 145.) (18) The unit tensile strength of specimens decreases as the breaking area is enlarged. (See p. 145.) (19) The unit compressive strength of similar specimens of cement or mortar is not greatly affected by their size, (See p. 145.) Laws of Strength. There are two fundamental laws of strength which apply to mortars composed of the same cement with different proportions and sizes of sand. (1) With the same aggregate, the strongest and most impermeable mor- tar is that containing the largest percentage of cement in a given volume of the mortar. (2) With the same percentage of cement in a given volume of mortar, the strongest, and usually the most impermeable, mortar is that which has the greatest density,* that is, which in a unit volume has the largest per- centage of solid materials. The first of these rules is understood by ordinary users of cement, but the second rule states a fact which is appreciated only by experts. The value of a first-class cement is universally recognized, the effects of impurities have been studied in various ways, and the variations in strength of mortars made from different sands or broken stone screenings have been recorded, but the fundamental law of the relation of the density of a mor- tar to its strength, — a function nearly as important as the quality of the cement itself and explaining many of the seemingly paradoxical results of tests with different aggregates and different proportions of water, — is but vaguely comprehended by the majority of experimenters and most of the users of cement. The application of these laws to mortar is discussed in the following pages, and to concrete in Chapter XIX. •The meaning of density may be understood by referring to the figures on pp. 133 and 134. STRENGTH OF CEMENT MORTARS 145 STRENGTH OF SIMILAR MORTARS SUBJECTED TO DIFFERENT TESTS* Mr. Rend Feret, Chief of the l,aboratory of Bridges and Roads at Boulogne-sur-Mer, France, has made very extended tests of strength of mortars, studying his results scientifically, and in many cases formulating laws and formulas applicable to different conditions. The tests of one series in particular are of so wide a range in character and in proportions used that the authors have converted the values into English units, and reproduce the table in full on pages 146 and 147. After plotting the strengths in various ways, Mr. Feret reaches conclu' sions which may be summed up as follows: (a) The unit fiber stress for prisms 4 centimeters (1.6 in.) on an edge is about the same as for prisms 2 centimeters (0.8 in.) on edge. (b) The tensile strength per square centimeter of prisms having a break- ing area of 16 square centimeters (the strength of which he found to be similar to that of briquettes of the same section) is about two-thirds the strength per square centimeter of the normal briquettes which have an area of 5 square centimeters. This difference is attributed partly to the lack of homogeneity of the specimens, especially on their surfaces, but prin- cipally to the unequal distribution of the stress on the area of the section. (c) Resistance to flexion, that is, the unit fiber stress in bending, is about 1.89 times the tensile strength per unit of area of briquettes of 5 square centimeters. (d) The form and dimensions of the specimen do not greatly influence the strength per unit of area in compression when the height and width of the block are approximately equal. (e) Resistances to flexion and tension are proportional to each other, and resistances to compression, shearing, and punching are proportional to one another, but there is no constant relation between the resistance to compression and the resistance to tension or flexion. THE RELATION OF DENSITY TO STRENGTH In the same paper from which we have quoted, Mr. Feret treats of the density and elementary volumetric composition of mortars, using in his studies the results given in the table just described. He calls particular attention to the fact that the properties of hydraulic mortar, such as dura- bility, permeability, porosity, and ability to resist the decomposing action of sea water, depend not only upon the quality of the cement, but "in a measure greater than is generally believed, upon the granular physical * A valuable series of tests has also been made by Messrs. Humphrey ai'id Jordan at the U. S, G'n-ernnient Testing Laboratory at St. Louis, see Bulletin No. 331 U. S. 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O.OO OOO OOoO r- vo'Oo "^o <:> "^ o o lo lo O Ch CO O oo r^ ^^-^0 vo 000 OOO OOOO OOO ON O'O OOOOC7>I>-LOION ThNO\ 01 -. w O 0*00 J>»vO r^ \0 lo LO ■^ M M M w q o_ q q q q q q q 6 6 6 6 6 6 6 6 6 6 6 6 6 0*0 M OOO r^ 00 CO M M j>. ovoo o 't vo t^oo ooo\0 Mco'^^ coior^ r^ m rioioi o O "-I oi CO ^ w 00 ■+ O r^ COOO w lOiO'^ -t--fro fOOi 01 t^ On -^ O CO r^ NO lO •* OOO OOO OOOO OOO 00 r^oo On i-o -^ -^ O i-i NO cot^M loONCor^oiNO 01 OOm wmoi oicoco-^ OOO OOO OOOO 000 OnOO 01 NO O^OO OI O OI On rococo ^^lO On OnOnQn co iHOico-^u'/U^'Or^cO O oOOnooi^oioOOLOLo O«to O t~^ fONO MVOM lOMONTh LO"<^"^ N MCMOl coc'-j-^'^lo'^lonO'Ovo no COCOCOCOCOCOCOCOCOCO COCOCO CO LOOO lOOnCOOnOcoOnw r^Oco t^ '^ 01 On^ c*i Ot^iOI^'O'-O^O M 01 01 CO '^ lO lonO t^ h 01 CO 8(5 o * COOO i^ -^oq N vo CO CJ M ■ H CO o r^ LO y^ M 6 6 CO d q q q to CO 01 o CO o M M l-l H H H H M H H ^-v ^— N,.-N^— » ,-, ^^.-^^^ ,^ /— s 2 o S u SK B a ^ 5 I V. ° ° rt o ■ S i^ Ch '^ Ti- N •* o< cr ■* N « ^ O en I^ "' HI •PA TiD jad 00 o m - aDijd <* IT, a;uuiixoiddv " o O ■pK -no jad 1/5 ^ „ SJllSiSM ;2 00 w. 'i^ M g^-euiixojddv u " n ■ Ov .5-1 to Q H 4- Hm' 11 i^a, '' 's ^ - s. •■3-1 a « values of ( j from column (12) in the table on pages 146 and 147 for abscissas, and the average compressive strengths of the various mortars, from column (22), for ordinates. Since, in formula (i), K is equal to P divided by the square of the quantity in brackets, the value of K is the tangent of the straight line passing through the points. In Fig. 43 K = 1965, if the strength is in kg. per sq. cm. or iC = 28 000, if the strength is in lb. per sq. in. This particular value is applicable only to the cement used by Mr. Feret in his experiments and to specimens at the age of five months, but the principles involved are of general application. The most practical application of this formula is in the determination of the relative compressive strengths of various mortars made from the same cement, ■with sand in differing proportions and of different com- positions. Mr. Feret calls attention also to its possible use in laboratory experiments and specifications. A cement, for example, may be required to furnish, when mixed with any sand, a definite value of K, since the value of K is independent of the choice of the sand and of the composition of the mortar. Experiments by the authors tend to show that the formula does not apply strictly to specimens of different consistency, but that the general law of the increase of strength with the density is applicable except in ex- treme cases. The formula is inapplicable to tensile tests, although here, too, the general principle appears to hold good. This subject as related to concrete is discussed on pages 312 tu 314 GRANULOMETRIC COMPOSITION OF SAND Feret's Three-Screen Method of Analyzing Sand. The determination of the physical characteristics of the sand, which, mixed with a cement, will produce the densest mortar, has been the object iS6 A TREATISE ON CONCRETE of a large number of experiments by Mr. Feret, which are recorded in Annales des Fonts et Chaussfe, 1892. In America Messrs. William B. Fuller and Sanferd E. Thompson have extended the researches, by a different method, to the investigation of the properties of concrete. The mechanical analysis of saad and stone is discussed in Chapter X, and the results of earlier experiments are tabulated on page 334. Mr. Feret, in studying any sand, separates it by screening into three sizes. He then recombines these three sizes in \arying proportions, so as to obtain results which are applicable to any natural or artificially mixed sand. He distinguishes sand from gravel as consisting of grains which will pass through a screen having circular holes of 5 millimeters diameter (0.20 in.). The three sizes of sand he then calls G, M, and F, representing, respectively, the large (gros), medium (moyens), and fine (fins) particles as defined by sifting through metallic sieves with circular holes, or wire cloth of definite mesh, as follows: Large grains, G, passing circular holes 5 mm. (0.20 in.) diameter. Retained by circular holes 2 mm. (0.079 '"■) " Medium grains, M, passing circular holes 2 mm. (0.079 i"-) "■ Retained by circular holes 0.5 mm. (0.020 in.) " Fine grains, F, passing circular holes 0.5 mm. (0.020 in.) " These sizes, Mr. Feret states, are nearly equivalent to sand screened through sieves of wire cloth as follows: Large grains, G, passing screen of 4 meshes per sq. cm. ( 5 meshes per linear inch.) Retained on " 36 " " (15 " " " ) Medium grains, M, passing " 36 " " (15 " " " ) Retained on a " 324 " " (46 " " " ) Fine grains, F, passing " 324 " " (46 ' " " ) Sometimes, for experimental purposes, he divides each of the Sands, G, M, and F, into three intermediate sizes. The granulometric composition of any sand is represented by its relative proportions, expressed either in weights or absolute volumes, of G, M, and F. For example, a sand containing by weight 50% of the largest grains, 30% of the medium, and 20% of the fine grains, has a granulometric composition of g = 0.50, m = 0.30, f = 0.20. The granulometric composition of a sand which has been mechanically analyzed, and plotted on a diagram similar to that shown on page 190, may be ascertained readily by drawing three ordinates corresponding respec- tively to screens of 5, 15, and 46 meshes per linear inch, and deterrnining by the length or the difference in length of these ordinates the proportions which pass and which are retained by the screens of these three meshes. These three proportions or percentages represent the granulometric com- STRENGTH OF CEMENT MORTARS IS7 position. An illustration of this method of transforming mechanical analv lis to granulometric composition is shown in Fig. 51 on page 164- Feret's Triangles. To simplify the tabulation of results, and arrange them so that they may be understood at a glance, Mr. Feret has used a graphical arrangement which is exceedingly ingenious. In nearly all his writings we find little triangles with the apexes labeled G, M, and F. Curves or contours in these triangles, representing the various properties of the sands or mortars, are based on a system of three instead of two Fig. 44.— Feret's Three-Screen Method of Analyzing Sand. {See p. 157.) co-ordinates, that is, each curve is the loci of points measured from 3 axes placed at angles of 60° with each other. A full discussion of the theory of this is given in his paper " Sur la Compacitd des Mortiers Hydrauliques " in Annales des Fonts et Chaussees, 1892, II, but the principles may be un- derstoofl by reference to Fig. 44. The apexes of the triangle are labeled G, M, and F, corresponding to the three sizes of sand described on page 156- The granulometric composition of any sand is plotted as a single point in this triangle. The proportion of each of the three sizes in the sand is rep- resented by its perpendicular distance from the side opposite each apex. iS8 A TREATISE ON CONCRETE For example, exactly at the apex G, the granulometric composition is g = i.oo, m = o, f = o. A sand represented by the point "A" in the triangle has for its granulometric composition, g = 0.48, m = 0.35, f = 0.17. Sa;nd, B, whose point is on the line G M is a mixture of G and M with no fine particles. It can be readily proved by geometry that if the altitude of the triangle is i.oo, the sum of the three perpendicular distances from any given point in the triangle to the three sides equals i.oo. Also, that any combination of G, M, and F is contained in the triangle or else on one of its sides. To use Mr. Feret's language, "any sand will be repre- sented by a point in the triangle and by one alone, and, reciprocally, one granulometric composition of sand, and only one, will correspond to a given point on the interior or sides of the triangle." If the altitude of the triangle Fig. 45.— Absolute Volumes of Sand per Unit Volume of Sand not Shaken. (5ec p. i6o-) Fig. 46.— Absolute Volumes of Sand pei Unit Volume of Sand Shaken to Re fusal. {See p. 160.) is considered i.oo, any point, A, in the triangle is readily plotted by- locating it at perpendicular distances from each of the three sides corresponding to each component of its granulometric composition. For example, suppose that the granulometric composition of a sand, ^, is g = 0.48, m = 0.35, f = 0.17. As the apex G represents a sand containing only coarse grains, and the line opposite to it, M F, all sands containing no coarse grains, the locus of a sand containing coarse grains (g = 0.48) will lie somewhere upon a line parallel to M F and at a distance 0.48 from M F. B}' similar reason- ing it will also lie on a Kne parallel to G F and at a distance 0.35 from it. The intersection of these two lines is the locus of the sand A , and it will be seen that this intersection is at a perpendicular distance of 0.17 from the line M G (the side opposite F), which checks the plotting, since f = 0.17. For comparing a special property of different sands, or of mortars com- STRENGTH OF CEMENT MORTARS 159 posed of different sands, each sand employed in the tests is plotted and labeled with its value, — which may be in units of strength, weight, or volume, — and "contour lines" are sketched in by the eye, as one would draw contours from elevations on a topographical drawing. Any point on the same contour line represents a sand made up of the Fig. 47. — Absolute Volumes of Solid Ma- terials (c+s) per Unit Volume of Fresh Mortar in Proportions i : 3 (by Weight). (See p. i6o-) Fig. 49.— Compressive Strength in Pounds per Square Inch of Mortars with Various Mixtures of Sand, after One Year in Fresh Water. .Proportions 100 lb. Portland Cement to 3.2 cu. ft. Mixed Sand. {See p. 161.) Fig. 48. — Compressive Strength in Pounds per Square Inch of i : 3 (by Weight) Mortars with Different Mixtures ol Sand, after q Months in Air and 3 Months in Sea Water. (See p. 161.) Fig . 50.— Compressive Strength in Pounds per Square Inch of Mortars with Various Mixtures of Sand, after One Year in Air. Proportions 100 lb. Portland Cement to 3.2 cu. ft. Mixed Sand. (See p. 161.) different sizes, G, M, and F, in proportions corresponding to its perpen- dicular distances from the sides opposite each apex, but having the same strength, weight, volume, humidit}-, or whatever special function may be represented, as every other point on the same line. i6o A TREATISE ON CONCRETE Figs. 45 and 46, page 158, illustrate the use of tiie triangle for showing the volumes of sands composed of different sizes of grains. Any sand, for example, whose granulometric composition is represented by any point on the contour line labeled 0.575, in Fig- 45! ^^^.s, when measured loose, 0.575 of its volume, or 57^%, of absolutely solid matter, or, taking the complement, 42^% of voids. In Fig. 45 it will be seen that the greatest solid volume of loose sand is obtained by mixing G and F in proportions 60% G and 40% F by weight. The amount of solid matter in this mixture oi maximum density is 0.61 of the unit volume; in other words, the sand con- tains 39% voids. By interpolating between the contour Hnes we may see that a sand consisting of equal parts of the three sizes, which would be represented by a point at the geoQietrical center of the triangle, has about 0.597 solid matter, or 40.3% voids. In sands shaken to refusal. Fig. 46, the mixture of maximum density consists of sands G and F alone, in pro- portions about 55% G and 45% F, and the total solid matter, that is, the absolute volume of sand, in a unit volume of the shaken sand of maximum density, is 0.798, corresponding to 20.2% voids. EFFECT OF SIZE OF SAND UPON THE STRENGTH OF MORTAR As a matter of fact, the actual size of a sand, that is, the size of its grains, is subordinate, in its influence upon the strength and other quahties of a mortar, to the density of the mortar produced from it. One naturally ivould suppose that the densest sand, that is, the sand which contains, when dry, the fewest voids, when mixed with a given proportion of cement, would make, inevitably, the densest and therefore the strongest mortar. Such, however, is not necessarily the case, for the addition of both the cement and water change the mechanical composition. A mixture of fine sand and cement, for example, requires a larger percentage of water in gaging than a mixture of coarse sand and the same cement. The total volume of a mortar of plastic consistency is affected by the quantity of water used, as well as by the volumes of the dry materials. Hence, a mortar consisting of fine sand and cement will be less dense than one of coarse sand and the same cement, even though the fine and coarse sands, when weighed or measured dry, each contain the same proportions of solid matter and voids. Fine sand has more grains in a unit measure and therefore a greater number of points of contact of the grains. The water forms a film (see Fig. 38, p. 136,) and separates the grains by surface tension. The fact is graphically illustrated in Feret's triangle, Fig. 47, page 159, STRENGTH OF CEMENT MORTARS i6i in which the contour lines show the combined absolute volumes of the cement and sand in i : 3 mortar (proportioned by weight) made from sand of various compositions. It will be noticed that the point of maximum absolute volume, which is labeled 0.734, is much farther to the left than in Figs. 45 and 46, showing that for a mortar of maximum density, a sand is required containing more large particles, G, in proportion to the fine paii:icles, F, than for maximum density with the same sand in its dry state. From such experiments Mr. Feret* derives the law that: The plastic mortars, which, per unit of volume, contain the greatest abso- lute volume of solid materials (c + s), are those in which there are no medium grains, and in which coarse grains are found in a proportion double to that of fine grains, cement included. Figs. 48, 49, and 50, page 159, show the strength in compression, con- verted to pounds per square inch, of mortars made from various mixtures of the three sizes of sand. Comparing these with Fig. 47 it will be seen that the curves of strength follow the same general direction as the curves of density. This is in con- formity with the general laws stated at the commencement of the chapter and with the principles upon which Feret 's' formula (page 155) is based. There is one point which must be noticed when studying these and other similar triangles of Feret, namely, that his results, as shown by the curves on his triangles, apply exactly only to sands and cements, and not to mixtures of sand and coarse stone. In all the triangles, sands for maximum density are composed of a mixture of fine and coarse grains with no medium grains. It is shown on page 133 that a denser mixture can be obtained with stone and sand and cement, that is, v;ith three sizes of materials, than with sand and cement, and it is consequently probable that Feret could have obtained greater densities by making the size of G larger (that is, employing for G gravel or broken stone) and the size of F smaller, and that with' this arrangement a portion of the medium grains would have been absolutely necessary to obtain the maximum density. In this con- nection, however, it must be remembered that Feret's experiments were intended to cover, as far as possible, practical combinations of sizes of sand for mortar. It is noticeable, even with the sizes of sand which he uses, that the curves in Fig. 47 run sharply upward, and that mortars from mixtures of three sizes of sand are therefore very nearly as dense and strong as those made from. two sizes. Furthermore, when the three sizes *Annales des Fonts et Chaussdes, 1896, 11, p. 182. l63 A TREATISE ON CONCRETE G, M, and F are mixed together, a graded mixture is formed in which there are particles ranging from 0.2 inch down to fine dust. Experiments indicate, as stated on page 196, that sand for concrete requires for best results more fine material than mortar sand. TESTS OF DENSITY AND STRENGTH OF MORTARS OF COARSE VS. FINE SAND The application of Mr. Feret's tests is shown in the table on pages 146 and 147, and the following tables, to illustrate its practical use in Compressive Strength and Elementary Volumetric Composition of 2-inch Cubes of Portland Cement and Bank Sand. {See p. 162.) By Sanpord E. Thompson.* Propor- tions by Weight ll ■II c PERCENTAGES PASSING SAND SIEVES ELEMENTARY VOLUMES (l^.)' Hi < i»8 Sand Sieve No. 8 No. 20' No. 50 Sieve ! Sieve Sieve i No. 200 Sieve [ c 1 S 1 c + s S i» 2 (1) (2) (3) (1) ; (5) {' (6) (7) ! (8) (9) i (10) (11) (12) (13) (U) Coarse Fine Very Fine . 1:2.6 1:2.6 1:2.6 1:31 I03 I : 3 100 I : .3 100 84 62 28 ! 3 100 84 77 I 6 100 g2 84 ; 27 0. 171', 0. 5i8i 0. 08.9 0. i54| 0.466, 0.620 0. 149 0.45 I 0. 600 0. 126 0.083 0.074 71S 40S 330 3S30 232= 207; comparing the quality of different sands, are presented; the first giving the density and strength of three natural bank sands as tested by one Tests by New York Board of Water Supply E 1 ■1 1 1 1 /i I- ^ z ^ 75 1 ^ 1 / 1 ^ z ii 'f / I 1 / -1 r II cJ 1 Jf ^ II el -/■ 1 J II ^, iy 1 :- i.0 II Si ^, f 1 ] « 1 A ] H II + II f ^ ; 1 1 ;.5 / \ 1 / / ' ; 1 tQ / )f ] 1 ,/ > 1 1 ^ ♦^ 1 1 ] ¥ ! I \ 1 " 1'^ |c 25 i 0.0 50 olo 1 75 0,1 00 0, 26 0. 50 0.175 0200 Diameters of Particles in inchts. o o o o ZZ ZZ Fig. 51. — Conversion of Mechanical Analysis to Granulometric Composition. (5ce. p. 165-) CONVERSION OF MECHANICAL ANALYSIS TO GRANULOMETRIC COMPOSITION As an illustration of methods of contrasting two different sands and of making practical use of Feret's researches, we may compare tests made by Mr. R. L. Humphrey* in connection with the construction of the Pennsyl- vania Avenue Subway, Philadelphia. He found the tensile strength at the age of one year, of i : 3 mortar made with sand screened from gravel, to be about 50% stronger than that made with sand dredged from the Dela- ware River. The mechanical analysesf of the two sands are plotted by ♦Transactions American Society of Civil Engineers, Vol. XLVIII, p. 558. fMechanical Analysis Curves are described in Chapter X, page 182. STRENGTH OF CEMENT MORTARS 165 the authors in Fig. 51, page 164, from tables presented by Mr. Humphrey. To transform these mechanical analysis curves to Feret's granulometric composition, we may draw on the diagram, ordinates corresponding to the sizes of sieves used by him, namely, No. 5, No. 15, and No. 46. (See p. 156-) From inspection of the curve it is evident that the granulometric composition of the gravel sand is g = 0.56, m = 0.35, f = 0.09, and of the river sand is g = 0.00, m = 0.89, f = o.ii. Plotting these granulometric compositions as C and D on Feret's triangle. Fig. 49, and interpolating between contours, we find the relative compressive strengths of mortars made from the two sands to be, after one year in fresh water, about as 1775 is to 2550, or as i: 1.44, while Mr. Humphrey's ratio of tensile strength for the two mortars at the age of one year is as 304 is to 470, or as i: 1.53. These ratios are remarkably similar when the differences in conditions are considered. Numerous tests have been made in America* in proof of the general law that coarse sands are stronger than fine. Many experimenters have seemed to reach the result that coarse sand is stronger than mixed sand. In certain cases this is undoubtedly true, because of mixing the different sizes in wrong proportions, or because the mortar of coarse sand contains so large a proportion of cement that the voids are completely filled and the addition of fine sand decreaseSj instead of increasing, the density. Mortar, for example, as rich as i : 2 (i.e., one part cement to two parts sand) of Coarse sand is as strong as, and often stronger than, mortar of similar propor- tions made of almost any mixed sands, but with leaner mortars, a small admixture of from 10% to 25% of fine sand improves it. Natural sand, which in appearance is very coarse, almost invariably has a small percentage of very fine particles which, with the fine grains of cement, may assist, in the leaner mixture, in producing a dense mortar. The mechanical analysis curves of sand shown in Fig. 57, on page 190, are an illustration of the fine matter contained in all bank sands. EFFECT OF QUANTITY OF WATER UPON THE STRENGTH OF MORTARS An excess of water decreases the density of the mortar and there- fore the strength. Fine sands require more water than coarse to pro- duce the same consistency. Hence, the weakness of fine sand mortars. (See p. 160.) A large excess of water injures the cement. (See p. 318.) A deficiency of water may affect the permanent strength of a mortar. *E. S. Wheeler in Report Chief of Engineers, U. S. A., iSq?, p. 3013, A. S. Cooper in Journal Franklin Institute, Vol. CXL, p. 326, Ira O, Baker in Journal Western Society of Engineers, Vol. ^- P- 73 i66 A TREATISE ON CONCRETE Although dry mixed mortars usually test higher than wet, because they can be more densely compacted, more uniform results, in practice as weU as in experiment, can be obtained with plastic mixtures. EFFECT OF GAGING WITH SEA WATER Briquets gaged with sea water set much slower than those gaged with fresh water* but long time testsf show no difference in strength. Tests by the authors in 1909 on 3-inch cubes of 1:2:4 concrete 14 months old gave 4 070 pounds per square inch for the specimens mixed with sea water and 3 870 pounds per square inch for those mixed with fresh water. LIMESTONE SAND AND SCREENINGS Fine aggregates of limestone composition, either sand or screenings, usually produce a mortar of higher strength than common sand. Tests by the authors of natural Hmestone sands from Canada and northern New York show in certain cases as much as 50 per cent, to 100 per cent, greater strength than would be expected of ordinary sand of similar- mechanical analysis. The gain in strength is somewhat slower than with quartz sand. The higher strength of mortar of limestone aggre- gates probably is due to their chemical composition. Results similar to these have been reached abroad by Mr. P. Alexandre and Mr. R. Feret. SAND VS. BROKEN STONE SCREENINGS The relative strength of mortars made from sand and from screenings of broken stone or crusher dust has occasioned much discussion and dis- pute. It is probably dependent chiefly upon the relative density of the different mortars. Usually, a mortar from screenings will show higher tests, while occasionally mortar from sand will be superior, because of the difference in size or of the relative sizes of the particles or grains com- posing the two materials. In some cases the form of grain exerts an influence upon the strength of the mortar, but usually this is of less consideration than the mechani- cal composition, t *P. Alexandre in Annales des Fonts et Chaussees, i8qo, II, p. 332. jAlexandre and Feret in Commission des M6thodes d'Essai des Materiaux de Construction, 189S, Vol. IV, p. III. tEaumatenalieni^unde, V Jahrgang (1000,) p. 21, and Annales des Ponts et Chaussees, 1892, II, p. 124. STRENGTH OF CEMENT MORTARS 167 Dusty screenings are especially bad for granolithic surfacing for side- walks, and must not be used. SHARPNESS OF SAND In the past all specifications have called for clean, "sharp " sand in spite of the fact that in many parts of the country where sharp sand is not obtainable, sand with rounded grains is furnished and used with perfect satisfaction. Comparative laboratory tests under conditions as nearly as possible identical uphold the practice of using sand with rounded grains. They indicate, as may be inferred from the previous discussion in this chapter, that the chief difference in natural sands is due to the size of the grains, and while the sharpness of grain may exert a certain influence it is of so much less importance than the size of the grain that the requirement of sharpness for sand should be omitted from concrete specifications. Referring to columns (11) and (22) in the table on page 146, and to Fig. 43, page 154, it is evident that the difference in strength of nearly all the mortars made with the various sands is explained by the differing percentages of cement and densities without reference to the character of the grains. The only noticeable exception is with the artificial sand, M', which consists of mixed sizes of crushed quartz. Mr. Feret* believes that this exception may be due to chemical action produced by the large quan- tity {\ its weight) of impalpable quartz. Sand N', also crushed quartz, but containing none of this fine powder, produces a mortar similar in strength to Hke mortars of natural sand having rounded grains. Other tests of Mr. Feretf and comparative tests, in the United States, of mortar with crushed quartz and natural sands generally confirm the above conclusion. The variation in the shape of the grains of natural sands and crushed quartz is illustrated in Figs. 37, 39, and 40, page 136. EFFECT OF NATURAL IMPURITIES IN THE SAND UPON THE STRENGTH OF MORTAR A clause to the effect that a sand for mortar or concrete shall be "clean" is almost universally found in masonry specifications. The necessity for this requirement is often questioned by cement experimenters, because the results of tests of mortar to which percentages of loam or clay have been added, often give higher results than those of mortar made with cement and pure sand. 'Bulletin de la Societe d'Encouragement pour I'lndustrie Nationale, 1897, Vol. U. tAnnales des Fonts et Chaussees, 1892, 11, p. 124. x68 A TREATISE ON CONCRETE As a matter of fact, it is impossible to make a general statement either to the effect that natural impurities in sand are beneficial or that they are detrimental. In some cases fine material may be of actual benefit, while in ethers the contrary is true. The case is covered by three conditions: (i) the character of the impuri- ties; (2) the coarseness of the sand; (3) the richness of the mortar. Character of Impurities. If the fine material is of ordinary mineral composition, such as clay, the mortar is affected only mechanically, and the results depend upon the coarseness of the sand of which the fine ma- terial is a fiart and the richness of the mortar, as indicated in paragraphs which follow. One exception to this general rule is when the clay is in such condition as to "ball up" and stick together so as to remain in lumps in the finished concrete. On the other hand, a small percentage of clay weir distributed may be valuable for making the concrete or mortar work smooth, and especially for increasing its water-tightness (see p. 301.) Vegetable or Organic Impurities. When the impurities are of an organic nature, like vegetable loam, they frequently have been found to prevent the mortar or concrete from hardening or to retard the hardening for so long a period as to make the sands entirely unfit for use. A very minute quantity of vegetable matter may produce injury, so small a per- centage in fact that frequently a sand which has passed careful inspection fails in practice to set properly with any brand of cement; therefore a test is absolutely necessary for any sand which has a suspicion of organic matter. The following tests of i : 3 mortar made with sand satisfactory in appear- ance, but which nevertheless caused the fall of a concrete building, are given Effect of Vegetable Impurities in Sand By Sanford E. Thompson, 1908. (See p, 168,.) Sand. Tensilestrength of 1 ; 3 mortar at 7 daj^s. Lb. per sq. inch A* Bt B washed - Wt Standard Ottawa Tensile strength of 1: 3 mortar at 28 days. Lb. per sq. inch. 93 114 201 300 * Poorest portion of bank; reddish and d?tk in appearance, •j- Average sand from bank which passed inspection. i A medium good sand from another banV similar to B in appearance, mechanical analysis, and chemical composition except nearly free from vegetable impurity. STRENGTH OF CEMENT MORTARS 169 in the following table. They are averaged from different series and for con- venience in comparison the results are all converted to the basis of standard sand mortar, considered as 200 pounds in 7 days and 300 pounds in 28 days. The mortars were stored in air to conform to the actual conditions. Com- parative tests on mortars from the same sands stored in moist air and in water corroborated the results. The cause of the failure was traced in the expert investigation, to vege- table impurities in the sand which had washed down into the bank from the soil above. The poorest sand, A, showed by mechanical analysis only 4% by weight of fine material passing a No. 100 sieve and 1.61% silt by washing, but this silt was found to contain nearly 30% of vegetable matter corresponding however to only 0.5% in the total sand. The vegetable matter appeared to coat the grains of sand so as to prevent adhesion of the cement and also retarded the setting. ESect of Fine Material in Filling Voids. Lean mortars may be im- proved by small admixtures of pure clay or by substituting dirty for clean sand, provided it is free from vegetable matter, because the fine material increases the density. Rich mortars, on the other hand, do not require the addition of fine material, and it may be positively detrimental, because the . cement furnishes all the fine material required for maximum density. This is illustrated in experiments by Mr. Griesenauer* in which an admixture of even 2 per cent of clay (based on the weight of the sand) slightly reduced the strength of i : 2 mortar, while 20% of clay, added to the 2 parts of sand, reduced the strength about 30%. In i : 3 mortar, on the other hand, the addition of 2% slightly increased the strength, and there was no appre- ciable injury up to 20% addition. In experiments by Mr. E. S. Wheelerf clay reduced the strength of neat and I : i mortars, but improved leaner mixtures. In this connection, of course, it must be borne in mind that if the sand is composed largely of fine material, the strength of the mortar is com- paratively low, as indicated in preceding pages. EFFECT OF MICA IN THE SAND UPON THE STRENGTH OF MORTAR The effect of mica in screenings from stone of a micaceous nature has been the subject of considerable controversy. Tests by Mr. FeretJ in France indicated that the presence of 2% of mica has but slight influence upon the tensile strength of mortar, but a greater one upon its compressive * Engineering News, April 28, 1904, p. 413. f Report Chief of Engineers, U. S. A., 1895, p. 3004, and 1896, p. 2827. i Bulletin de la Society d'Encouraeement pour I'Industrie Nationale, 1897, Vol. II. lyo A TREATISE ON CONCRETE strength. More recent tests by Mr. W. N. Willis* in 1907 on mortars made with standard Ottawa sand into which mica was introduced are illustrated in Fig. 52. He found that the presence of mica increased the voids and decreased the strength. The sand used in tests, loosely shaken, contained 37% voids, but as mica was added, the voids increased rapidly until with 20% mica the voids were 67% with a corresponding, decrease in weight, and three times the amount of water was required for mixing. It is thus evident that the reduction in strength was largely due to the decrease in density and not entirely caused by the slippery character of the grains. In crushed stone screenings it is probable that the effect of the same percentage of mica in the natural state would be less marked. Black mica, with a different crystalline form, is not injurious to mortar. 7 DAYS 28 DAVS 3M0S. J. 280 2 260 b] 110 Nl ion . 280 ?R0 /" / 249 O220 (a ^ 0k ■"^ 200 180 160 140 120 100 U.2UU ^80 A vA --— ■ ^ _ ,^ — - r,% __^ 1 160 [^ / if^ 'k^— ■ 2 r^ H P^/ y\y ^JAJ^ DC 80 " fin y- /X _^. --' jo^L — / ^^ J " 111 n n 7 OAVS 28 OAYS 3 MOS AGE OF MORTAR Fig. 52. — Effect of the Addition of Mica upon i : 3 Mortar of Standard Sand. By W. N.Willis. {Zee p. 170.) EFFECT OF LIME UPON THE STRENGTH OF MORTAR As a principal constituent of mortar in masonry construction, lime is inferior to cement in durability and strength. However, not only because of its relative cheapness, but also because a small addition of slaked or hydrated lime may increase the density of the mortar and cause it to work easier under the trowel, a Hmited quantity often can be used to advantage in mortar which is to be subjected to high loading. For concrete, lime, see Chapter XVIII, is a suitable ingredient to fill the voids, rendering it more impermeable.- "^Cement Age, Mar. 1907, p. 172. STRENGTH OF CEMENT MORTARS 171 Although lime mixed with neat cement is apt to decrease its strength, in combination with sand for cement mortars, a small admixtm'e of lime may add to the strength of the mortar. The questions as to whether lime is beneficial, and as to the amount which can be used, are determined by the character of the cement, the coarseness of the sand, and the proportions in which the two are mixed. The effect of lime in cement mortar or concrete is chiefly mechanical. In a porous mortar or concrete a small quantity of it assists in filling the voids, and if it is thoroughly slaked so as to contain no quicklime, its expansion need not be feared. Since even a neat cement paste has 35% to 45% water plus air voids, the inference might be drawn that the addition of lime would increase its density, and thus that the lime would be valuable even in very rich mortars. However, it seems to be practically impossible, except under high pressure, to replace the water which occupies the voids in neat cement paste with Mme or any other fine powder. But it is evident that a lean morta.-, such as a 1 : 4, or even a i : 3, should be improved by the addition of lime, and that this is true is illustrated in the following tests by Mr. Louis C. Sabin.* In these experiments the addition of 10% of lime — based on the weight of the cement — increases the strength of i : 3 mortar, and as shovm by item (3) in the table, a i : 3J mortar vidth 10% of lime is stronger than a i : 3 mortar vnth no lime. Items (4) and (5) illustrate the reduction in strength when the lime becomes more nearly a principal ingredient. Each value is an average of five briquettes.f Effect of Lime Paste upon the Strength of Portland Cement Mortar. By L. C. Saein. {See p. lyi.) Proportions cement plus lime to sand by weight parts Proportions cement to sand by weight parts Cement grams Lime} grams Sand grams Average Tensile Strength. " at 28 dys. lb. per sq. in. at 3 mos lb. per sq. m. (l) (3) (4) I--3 1:3 i'-3 1:3 1:3 I ■•3 J 1:4 1:6 200 200 180 150 100 •' 20 20 s° 100 600 600 600 600 600 201 242 238 1 63 57 236 265 264 171 70 •Report Chief of Engineers, U. S. A , i8g6, p. 2823. t See tests by Dr. E. W. Lazell, Transactions American Society for Testing Materials, Vol. VIII. jgoS, p. 418. {The weight of the lime paste was 2.7 times the weights in this column. 173 A TREATISE ON CONCRETE With another brand of cement and sand of different coarseness the relative quantity of hme to produce similai results, will diSer, but the general principle will still hold. In determining the amount of lime to add without decreasing the strength of a certain mortar, tests should be made with the materials to be employed. In scientific experiments by Mr. Feret* the maximum strength of i : 4 mortar of Portland cement and sand from Saint Malof was reached with an addition of 4% or 5% by weight of hydrated lime powder. As the mortar became richer, the lime had less effect, until at proportions 1:2, the addition of lime reduced the density, and at proportions i:ij the strength was also lowered. A larger number of bricks can be laid in a given time with mortar con- taining lime than with a lean cement mortar because the lime fills the pores in the mortar so that it spreads more readily without crumbling and ad- heres better to the bricks in " buttering " them. Unslaked Lime. Unslaked hme mixed with cement either for mortar or concrete is liable to produce expansion in the masonry and it is therefore never permissible to use it under any circumstances. Builders recognize that lime, putty, or paste is much improved by standing for several days, or, better, for months, before being used, because all the small lumps are thus slaked. This thorough slaking is especially necessary when lime is to be used, even as a very small ingredient, in important concrete and masonry construction; an admixture of even 2% of ground quicklime may seriously reduce the strength of the mortar. J Weight and Volume of Lime. In proportioning lime to cement, the method of measurement must be clearly stated. The volume of common lime or quickhme increases in slaking to about 2J times its volume meas- ured loose in the lime cask, the exact increase varying with the chemical composition and the purity of the hme. The weight of lime paste is about 2J times the weight of the same lime before slaking. Hydrated lime powder also occupies more volume than quicklime from which it is made. GROUND TERRA-COTTA OR BRICK AS A SUBSTITUTE FOR SAND Experiments by Mr. Louis C. Sabin§ indicated that for a mortar of Ught weight terra-cotta may be ground and used instead of sand. ■ Tests * Chimie Appliquee, 1897, P- 481. fSee p. 147- {Report of Chief of Engineers, U. S. A., i8g5; p. 2999. § Report 6f Chief ot Engineers, U. S. A., I8g6, p. 2866. STRENGTH OF CEMENT MORTARS 173 with both Portland and Natural cement mixed with the ground terra- cotta in various proportions gave at the end of three months tensile strengths which are not appreciably different from the strengths obtained with standard crushed quartz. Red brick pulverized* may also be used for the same purpose with good results. EFFECT OF EEGAGING MORTAR Tests indicate that, up to the time of the initial set of the cement, mortar or concrete may be regaged without injury. Beyond this period the strength is reduced. The wetter the mix, the longer the time the mortar or concrete may stand without loss of strength on regaging, probably because of the slowness with which wet mortar sets and hardens. For example, testsf show that the setting time of neat ce- 3600r '0 2 4 6 8 10 12 14 16 18 20 22 24 Ellapsed Time Between Gaging and Regaging in Hours Fig. 53. — Influence of Regaging on Compressive Strength of Mortars.J {See p. 174.) ♦Report Chief of Engineers, U. S. A., i8g6. p. 2830. fBy Sanford E. Thompson. (Tests reported by H. Burchartz in Mitteilungen aus dem KSniglichen Materialprijfungsamt zu Gross- Lichterfelde West 1911, p. 164. 174 A TREATISE ON CONCRETE ment paste may be increased two and one-half times by doubling the amount of water ordinarily used in testing. In the tests shown in Fig- 53, P- 1 73, mortar mixed with 8% of water begins to lose strength if regaged at all, whereas mortar mixed with io% of water may stand for nearly eight hours before regaging, with no loss hi strength. In practice, regaging of mortar that has begun to stiffen should not be permitted. Under ordinary weather conditions using a medium or wet mix the time may be liniited to two hours. In hot weather or Tyhen, for other reasons the cement is quick setting, a shorter time must be required. When mortars and concretes are regaged, water must be added until normal consistency is reached. A mix, originally very wet, may re- quire no water for perhaps six hours, while a dry mix needs additional water at all ages. The leaner the mix the less extra water required at regaging. The tests in the figure show the effect on the strength of mortars of different consistencies regaged after various lengths of time up to 24 hours. The strength tests were made at 7 and 28 days. The follow- ing table shows the effect of different percentages of water on the set- ting time of the cement used. Setting Time of Neat Cement with Different Percentages of Water* {See p. 174.) PerceDtage of water by weight. 27% 32% 36% 40% Initial Set S hrs. 8f hrs. lh hrs. 16 hrs. 9 hrs. 17 hrs. 9j hrs. 185 hrs. Final Set. The results are in general confirmed by tests in this country and abroad. Mr. Candlotf, however, found that mortars regaged after 1 2 and 24 hours, while showing great loss in strength at 7 and 28 days, gave only a small loss on long time tests, but this does not affect the general restrictions against the use of regaged mortar because in prac- tice it is usually the strength up to 28 days that is critical. * Tests reported by H. Burchartz in Mitteilungen aus dem Kcinigliclien Materialprafungsamt zu Gross Lichterfelde West igir.p. 164. t E. Candiot, Ciments et Chaux Hydrauliques, 1898, p. 3 55-365 . PROPORTIONING CONCRETE 175 CHAPTER X PROPORTIONING CONCRETE By William B. Fuller* IMPORTANCE OF PROPER PROPORTIONING The proper proportioning of concrete materials increases the strength obtainable from any given amount of cement, and also the water-tightness. Conversely, it permits, for a given requirement of strength and water-tight- ness, a reduction in the amount of cement, thereby reducing the cost. Upon large or important structures it pays from an economic standpoint to make very thorough studies of the materials of the aggregates and their relative proportions. This fact has been seriously overlooked in the past, and thousands of dollars have sometimes been wasted on single jobs by neglecting laboratory studies or by errors in theory. Since cement is always the most expensive ingredient, the reduction of its quantity, which may very frequently be made by adjusting the proportions of the aggregate so as to use less cement and yet produce a concrete with the same density, strength and impermeability, is of the utmost importance. As an example of such saving, the ordinary mixture for water-tight con- crete is about 1:2: 4, which requires 1.51 barrels of cement per cubic yard of concrete. By carefully grading the materials by methods of mechanical analysis the writer has obtained water-tight work with a mixture of about 1:3:7, thus using only 0.97 barrels of cement per cubic yard of concrete. This saving of 0.54 barrels is equivalent, with Portland cement at $1.60 per barrel, to $0.86 per cubic yard of concrete. The added cost of labor for proportioning and mixing the concrete because of the use of five grades of aggregate instead of two was about $0.15 per cubic yard, thus effecting a net saving of $0.71 per cubic yard. On a piece of work involving, say, 20 000 cubic yards of concrete such a saving would amount to $14 200.00, ah amount well worth considerable study and effort on the part of those in responsible charge. Proper proportioning is also important for reinforced concrete so as to give the uniformity and homogeneity which cannot be obtained without careful attention to the proportions and grading of the aggregates. * The authors are indebted to Mr. Fuller for the material for this chapter. 176 A TREATISE ON CONCRETE METHODS OF PROPORTIONING It is recognized generally that for maximum strength a concrete should be as dense as possible, that is, that it should have the smallest practi- cable percentage of voids. The various methods of aiming toward this result have been outlined as follows:* (1) Arbitrary selection ; one arbitrary rule being to use half as much sand as stone, as 1 : 2 : 4 or 1 : 3 : 6; another, to use a volume of stone equivalent to the cement plus twice the volume of the sand, such as 1 : 2 : 5 or 1 : 3 : 7. (2) Determination of voids in the stone and in the sand, and propor- tioning of materials so that the volume of sand is equivalent to the vol- ume of voids in the stone and the volume of cement slightly in excess of the voids in the sand. (3) Determination of the voids in the stone, and, after selecting the proportions of cement to sand by test or judgment, proportioning the mortar to the stone so that the volume of mortar will be slightly in excess of the voids in the stone. (4) Mixing the sand and stone and providing such a proportion of cement that the paste will slightly more than fill the voids. (5) Making trial mixtures of dry materials in different proportions to determine the mixture giving the smallest percentage of voids, and then adding an arbitrary percentage of cement, or else one based on the voids in the mixed aggregate. (6) Mixing the aggregate and cement according to a given mechanical analysis curve. (7) Making volumfetric tests or trial mixtures of concrete with a given percentage of cement and different aggregates, and selecting the mixture producing the smallest volume of concrete; then varying the proportions thus found, by inspection of the concrete in the field. The most practical method known to the writer for accurately deter- mining the proportions of each material is by mechanical analysis of the aggregates, as described on page 201. Volumetric synthesis, or proportioning by trial mixtures (p. 196) is another method, sometimes useful, which produces fairly scientific results. Since in many cases the proportions for a concrete must be selected more or less arbitrarily, after outlining the principles of proper proportioning, some of the less exact methods which are frequently used in practice will be •From "Proportioning Concrete,'' by Sanford E. Thompson, Journal Association Engineering Societies, Vol. XXXVI, Apr. igo6, p. 185. PROPORTIONING CONCRETE 177 taken up before referring to the more scientific ones, and some of the causes for inaccuracies of these approximate methods discussed. PRINCIPLES OF PROPER PROPORTIONING The principles underlying the correct proportions of the materials of concrete are the same as those for mortar, namely, that the mass when compacted shall have the greatest possible density. In order, therefore, to obtain a knowledge of correct proportioning it will be best to first study the general conditions which are known to affect density. Perfect spheres of equal size piled in the most compact manner theoreti- cally possible leave but 26% voids. If the spaces between such a pile of equal-Fiized perfect spheres were filled vnth other perfect spheres of diameter just sufficient, to touch the larger spheres, it would take spheres having relative diameters of 0.414 and 0.222 of the larger spheres, and the voids in the total included mass would be reduced to 20%. Using in this same manner smaller and smaller perfect spheres, it is conceivable that the voids could be reduced to so low a per cent of the total mass and to a size so small as to be only in a capillary form, and thus prevent the passage of water. This is assuming that every particle is placed exactly in its assigned place, but it is inconceivable that such an arrangement should take place under practical conditions, and in fact numerous trials by the writer with large masses of equal-sized marbles have demonstrated that they cannot be poured or tamped into a vessel so as to give less than 44% voids. If equal quantities of spheres of, say, three sizes are mixed together, the per cent of voids in the total mass immediately increases, becoming about 65%, due probably to the smallest spheres getting between and forcing apart the largest. If, however, the containing vessel is continually shaken and the spheres stirred around, the smallest spheres will gradually all gravitate to the bottom and the largest to the top and the amount of voids in the total mass will again approach 44%. If a large number of different sized spheres are used, employing an increasingly large number of the smaller sizes so that each larger size may be said to be wholly surrounded by the next smaller size, the voids remain the same, no matter what the shaking, and will in some cases reach as low as 27%. With ordinary stones and sands the same law holds as with perfect spheres except that they do not compact as closely, and the percentage of voids under comparable conditions is larger, varying with the degree of roughness and other features of the stones and sands used for the ex- periments. When dry cement is added to a dry aggregate of stone and sand it acts 178 A TREATISE ON CONCRETE in the same manner as fine sand, and for obtaining the greatest density with dry cement, the cement must replace an equivalent amount of fine sand. The theory of a concrete mixture is well stated by Mr. Feret* as follows : The problem of making the best concrete is thus reduced to the selec- tion of a mixture "of materials whose granulometric compositionf corre- sponds to the maximum of density, since when this composition is known absolute volumes of cement may be substituted for equal absolute volumes of fine sand and vice versa, so as to vary the strength as desired while the density remains the same. In other words, having mixed dry, inert materials in proportions neces- sary for greatest density, a portion of the grains of the very finest aggregate (that is, the finest particles of sand or dust) may be replaced by a corre- sponding quantity of cement to the extent required for the desired strength. This is not strictly true for concrete mixtures, because, when water is added to dry cement, the cement particles are separ?,ted from each other by the surface tension of the film of water, and it is no longer possible to obtain as dense a mixture as is theoretically possible with the dry mixture. The density of concrete therefore has been found to depend upon the varying degree of roughness of the stone and sand, the relative sizes of the diameters of the stone, sand and cement, and the amount of water used. The fineness of the cement particles and the amount of water to be used are determined by questions discussed elsewhere, and we have to deal here only with the proportioning of the sand and stone. DETERMINATION OF THE PROPORTION OF CEMENT The most diflicult question to decide with accuracy in proportioning is the proportion of cement to use. This is to a considerable extent a matter of mature judgment, depending upon the nature of the construction, the degree of strength required within a certain limit of time, the required watertightness, the character of the aggregates, and many other matters which must be considered in direct connection v/ith the work to be done and the available materials. An engineer experienced in concrete con- struction and tests can estimate approximately the strength of concrete made with certain materials, and selsct the proportions accordingly. The surest plan after selecting and grading the aggregates is to make up speci- mens of concrete and test its crushing strength, but this is usually impracti- cable for lack of time. The next best plan is to have the tensile strength determined of mortar made from the sand to be used and by comparing *Chimie Appliquee 1897, p. 523. ■{■Proportioning of sizes. PROPORTIONING CONCRETE lyg this with the strength of the mortar of standard sand an idea can be formed of the proportion of cement to select. If a sand is fine, a richer mortar must be used, frequently instead of a i : 2 selecting a i : ij or even i • i, and the amount of coarse aggregate also reduced to accord with this. An experimental plan which has been followed to determine the minimum quantity of cement which will produce a concrete practically free from air voids is to mix the aggregates in the correct proportions as described in the pages which follow, compact them by ramming or hard shaking, and then determine their voids by weighing and correcting for specific gravity.* The sand should be in the natural state of moisture found in the interior of the bank, not because this is the condition in which it will be mixed in the con- crete, but because it may be assumed in the natural state to contain a quantity of moisture varying with its fineness. If gravel is used it may be taken in the same way, while coarse broken stone should be dry, and dry broken stone screenings may be mixed with about 4% of water by weight. Correction must be made for this moisture after weighing the mixed material, so that the voids calculated will be simply air voids. In determining the quantity of cement to fill these air voids it may be assumed without appreciable error that 100 lb. of cement will make i.o cu. ft. of neat paste. This is a larger volume than would result with ordi- nary plastic paste, but makes a slight allowance for the additional moisture required for the sand and stone. To the quantity of cement thus deter- mined 10% may be added, i. e., 10% of the cement, not of the total mix- ture, to provide for imperfect mixing. PROPORTIONING BY ARBITRARY SELECTION OF VOLUMES The common custom of specifying arbitrarily the proportions of cement, sand and stone in parts by volume, while convenient in construction, causes wide discrepancies in results because of different methods of measuring the materials. A concrete called a i : 2 : 4 mixture by one man may not con- tain any more cement than a concrete termed a i 13:6 mixture by another, t Notwithstanding this, if the units of measurement and the methods of measuring are stated definitely, arbitrary selection of proportions may give good results in practice, although necessitating a larger quantity of cement with consequently a greater net cost than more scientific proportioning would require. The percentage of volume of sand required for ordinary gravel or broken *See page 126. ■(■These variations aie discussed more fully by the authors on page ao6. i8o A TREATISE ON CONCRETE stone from which the finest material has been screened may be taken between the limits of 40% and 60% with an average, which is suitable under many conditions, of 50%. If the cement is taken as additional, which is not strictly correct, this ratio corresponds to proportions i : i^ : 3, 1:2:4, I : 2^ : 5, and 1:3:6, which are suggested by the authors in Chapter II as standard mixtures for the use of those who are inexperienced in concrete work. In cases where the coarse material contains a good many small particles, as does crusher run, broken stone or graded gravel, or the sand is so fine as to flow readily into the voids of the stone, the proportion of sand should be slightly less than half the volume of stone. Since the cement also increases the bulk of mortar and hence assists to fill the voids in the stone, it is sug- gested that with such aggregates the volume of the stone be made equal to the cement plus twice the volume of the sand. This would give propor- tions I : ij : 4, 1:2:5, I : 2^ : 6, and i : 3 : 7 for these special conditions. Proportions adopted by various authorities and tabulated on page 202 and 203 may serve as a guide to arbitrary selection. It is a good plan on work which will not warrant special tests and for which there is no choice of aggregates, to use at first twice as much stone or gravel as sand and then vary the relative proportions of the sand to the stone as the work progresses, governing this by the way the concrete works into place. Too much sand vidll be indicated by the harsh working of the concrete, while if there is too little sand, stone pockets are apt to occur on the surface of the concrete, and it will be difficult to fill the voids of the stone. Screened vs. Unscreened Gravel or Broken Stone. Unscreened gravel is often used alone for the aggregate, but there is scarcely any case where the cost of screening and re-mixing the materials will not be less than the saving in the cement by using screened aggregates. The quantity of sand in different parts of the same gravel bank always varies greatly and the run of the bank rarely contains sufficient coarse stone to make a dense concrete. If, as is sometimes the case, the quantity of material coarser than J inch is about the same as that which passes a J-inch sieve, then, if used without screening the same quantity of total aggregate must be used as would otherwise be specified for the coarse aggregate; that is, instead of i : 2 : 4 proportions, the unscreened gravel would require i : 4. Broken stone as it runs from the crusher will contain considerable dust, and may sometimes be used economically by simply adding sand without screening. However, there is apt to be a separation of the coarse particles from the fine as they roll down the pile so that less homogeneous propor- PROPORTIONING CONCRETE i8i tions can be attained. Consequently the writer is in favor of separating the aggregate into as many parts as is consistent with economy for the work in hand. Even on small work he believes it preferable to screen out the sand or dust and re-mix it in the specified proportions. PROPORTIONING BY VOID DETERMINATION The determination of proportions by finding the volume of water which may be poured into the voids of a unit volume of stone and selecting' a volume of sand equal to this volume of water is one which gives no better results in practice than arbitrary selection of the proportions, as described in the preceding paragraphs, and varying the relative proportions of sand to stone when placing. The determination of the proportion of cement to sand by void measurement is still more misleading; in fact, for reasons dis- cussed below, it is so inaccurate that no consideration will here be given to it. The theory of proportioning by voids is that if the stone or gravel contains, say, 40 per cent voids as measured by the contained volume of water, the required volume of sand is theoretically 40% of the volume of the stone, and supposing the ratio of cement to sand to be as i : 2, the relation of parts of sand to parts of the coarse aggregate would be as 2 : 5, thus making the proportions i : 2 : 5. Because of the inaccuracy of this method of proced- ure, as discussed below, it is necessary in most cases, even although the cement and water will still further increase the bulk, to take a volume of sand, say 5% to 10% in excess of the voids; that is, for gravel with 40% voids to use 45% to 50% of its volume of sand, thus making the proportions 1:2:4^. If the coarse material is screened broken stone of large size, say i J or 2-inch, the volume of sand may be taken equal to the volume of voids instead of in excess of them, because the particles of sand will all be small enough to fit into the voids of the stone without appre- ciably increasing its bulk. Such stone usually has about 45% to 50% voids, so that we should have proportions i : 2 : 4^^ or i : 2 : 4, the same as for the gravel concrete. The irregular distribution of the materials by imperfect mixing may usually be disregarded, because the volume of gaged mortar is always in excess of the volume of sand from which it is made. Care must be exercised in any case to guard against a larger excess of sand than is absolutely necessary, because the voids in a concrete are lessened by using stone in place of sand. Take, for instance, sand having 45% voids and stone having 40% voids. With the sand just filling the voids of the stone it is easily calculated that the resultant mass has 18% 1 82 A TREATISE ON CONCRETE voids; but supposing an excess of io% of sand, there would be io% of the material having 45% voids, which means there would be 2.5% more voids in the resultant mass.* Authorities differ as to whether the stone should be loose or shaken when determining the voids. Loose measurement is generally considered preferable because it corresponds more nearl)? to the final volume of the concrete, and more sand is always necessary than will just fill the voids of rammed stone, since the sand and cement separate the stones and prevent their lying close together in concrete. In determining, however, the quan- tity of cement required for the mixture of aggregates the materials should be compacted as described on page 201. The chief inaccuracy of this method of basing the proportions of the finer materials of a concrete mixture upon the water contents of the voids in the larger is due to the difference in compactness of the materials under varied methods of handling, and to the fact that the actual volume of voids in a coarse material may not and usually does not correspond to the quantity of sand required to fill the voids, and that therefore the com- mon method of proportioning by basing the volume of sand or of mortar upon the volume of water which can be poured into the broken stone leads to false conclusions. The reasons for this inaccuracy are chiefly because the grains of sand thrust apart the particles of stone, and because with most aggregates a portion of the particles of sand or fine screenings are too coarse to enter the voids of the coarsest material. Even in a mass of stones of uniform size many of the separate voids are much smaller than the particles. If we have, then, a mass of gravel rang- ing from fine to coarse or a mass of crusher-run broken stone, even with the finest sand or the dust screened out of them, the individual voids are many of them so small that a large number of the particles of natural bank sand will not fit into them, but will get between the stones and in- crease the bulk of the mass. On account of this increase in bulk, even with thorough mixing more sand is required than the actual volume of the voids in the coarse material. The separation of the particles of stone by the sand is illustrated in the mixture shown in Fig. 2, page 15. To illustrate this important principle, an extreme example may be cited. Suppose that we have a mixture in equal parts of i-inch stone and |-inch stone. By the usual method of reasoning employed in proportioning concrete, if the i-inch stone has 50% voids, we should require a volume of |-inch, equal to 50% of the volume of the i-inch stone, in order to fill * See discussion by the writer in Transactions American Society of Civil Engineers, Vol. XLII, D. i^. PROPORTIONING CONCRETE 183 the voids in the latter. The absurdity of this is apparent, because the two stones are so near a size that the smaller cannot fit into the voids of the latter, and the bulk of the mixture is inappreciably less than the sum of the separate volumes, that is, the mixture still has nearly 50% voids. The principle is just as true, although the total effect is less, if we consider it with reference to the finer particles of the gravel or the crusher-run broken stone and the sand or fine screenings which are to be introduced to fill the voids. The sizes of many of the particles of the latter are so nearly equal to the sizes of the smallest particles of the coarse material that they increase the total bulk instead of reducing the voids. They also get between the surfaces of the stone particles and prevent the stones touch- ing each other. We might conclude from the above that the best concrete can be made with a coarse stone of uniform size and a sand whose particles are all small enough to fit into its voids; in fact, this is the conclusion reached by the advocates of broken stone of uniform size in preference to crusher-run stone. Our experiments indicate that while this may be true in theory, in prac- tice in making concrete the graded materials give about the same density and work rather smoother in handling and placing. ' The point, however, which is to be emphasized is the inaccuracy of determining the exact volume of sand or mortar by simply measuring the water contents of the voids in the coarse aggregate. The selection of the proportion of cement by determination of the water contents of the voids in sand is even more inaccurate than the propor- tioning of sand to stone by void measurement. The varying effect of moisture on the sand so influences the volume of the voids that their deter- mination is chiefly important as an aid to the judgment; and as a matter of fact, although in practice the quantity of cement is supposed to depend upon the volume of voids in the sand, it is customary to select a definite relation of cement to sand varying according to the character of the con- struction from I : I to I : 3, recognizing, however, that fine sand — and fine sands in an ordinary state of moisture will almost always have the distin- guishing characteristic of a lighter weight per cubic foot than coarse sands and a consequently larger percentage of voids — requires more cement for equivalent strength. As already stated, if the work is too small to warrant a thorough study of the materials by mechanical analysis or volumetric synthesis, or some other scientific method, it is evident from the above discussion that it is nearly as accurate to determine the proportions by arbitrary selection (see p. 178) as by a study of voids. i84 A TREATISE ON CONCRETE RAFTER'S METHOD OF PROPORTIONING Mr. George W. Rafter* has called attention to the method of propor- tioning the mortar as a percentage of the volurne of the stone slightly shaken, the relation of cement to sand having been determined by the required strength of concrete. Quoting from specifications for the Genesee Dam, the concrete is pro- portioned as follows: In forming concrete such a proportion of mortar of the specified com- position will be used as may be found necessary by trial to a little more than fill the voids in the aggregate. Tests of the voids will be made from time to time under the direction of the engineer, and instructions given as to the per cent of mortar of the specified composition to be used. For the information of the contractor, in the way of computing the cost of concrete of the quality herein required, it may be stated that ordinarily the per cent of mortar will be about ^3 per cent of the measured volume of the aggregate. In case of the use of a certain proportion of gravel in the aggregate, the proportion of mortar may be reduced to somewhat less than 30 per cent. This method of proportioning is more accurate than the usual procedure, because there is less apt to be an excess of mortar. It does not, however, take account of the fact that with a coarse aggregate of varying sized particles some of the grains of sand are too large to fit into the voids of the stone, and that therefore the coarse and fine aggregates must be studied together. An examination of the analysis of the sand used by Mr. Rafter indicates that to its fineness was due the small proportion of mortar to stone which he was able to use. Ninety-two per cent of the sand passed a No. 30 sieve, so that the grains were small enough to enter the voids of the stone without appreciably increasing the bulk of the concrete. FRENCH METHOD OF PROPORTIONING In France, proportions are ordinarily stated in terms of the volume of mortar to the volume of stone, and the mortar is described by the number of kilograms of Portland cement to i cubic meter or liter of sand. The following table gives the nominal proportions in English measure based on a volume of 3.8 cubic feet corresponding to similar French pro- portions based on kilograms of cement to a cubic meter of sand. *"0n the Theory of Concrete'' Transactions American Society Civil Engineers, Vol. XLII, p. 104. PROPORTIONING CONCRETE 185 American Equivalents of French Proportions. {See p. 184.) French meas- Ampri<-»n-Tno!i / / A 1 i '^ 1 rt f/ :k / / ^^/ u' / V ,«> / =E. 'd / .« V tc 1 £ 1 . \ / ^ y. 3 so XlJ 1 ,*' ^h r< f-^ )c> < =" ' Wj "}' .J '/ i »>~ p.'^ 3^ 5,C w ^y' .0 / ^ s-' ■ i ,, k :^< / H ,?/ 1 ."i '' v ^ * e ,'/ 1 ^ ^* ""A ^ y * ■>' f' V s- 25 z r^ / / ,^ - / \\ '/ / ot / U\ / £ \-^ / ?. ^ . ' !^> .<■ V 0- n _2 ■>^-:' \ / y 0.7s 1.00 1.25 DIAMETERS OF STONE IN INCHES Fig. s6- — Typical Mechanical Analysis of Crushed Trap Rock Separated into Three Sizes by Revolving Screens having 3, ij, f and \ inch perforations. (See ■p. 189.) separated into stone of three sizes and dust, by a revolving screen 2 feet 6 inches in diameter and 12 feet long set On a slope of i foot 9 inches. This was made up of four sections having respectively 3, ij, | and \ inch per- forations. The curves not only show the sizes of trap rock which ordinarily pass through crusher screens of given diameter of hole, but also illustrate how inefficient the screening process may be. For example, if the sizes Of the particles had corresponded exactly to the diameters of the holes and the screening had been more perfectly done, we should have had curves whose general direction and location is shown by the dotted lines No. 2,, No. 3i, and No. 4,, that is, for example. No. 3, since it represents stone which passes a ij inch screen and which is retained on a finch screen, should occupy a position between the ordinates representing 1.50 and 190 A TREATISE ON CONCRETE 0.7 s diameters. If the stone had rumbled longer in the screen because of flatter slope or screen sections of greater length, the curves would have approached more nearly to these dotted lines. Typical curves of a fine, a medium well graded, and a coarse sand are shown in Fig. 57. For convenience in plotting, the horizontal scale is ten 1 ■M 1 - ^ - - _ - 5 .- = ^ - r n - - — n - — ~ " = = = =■ - -1 -= = ^ - = 1 > _^. — ^ -^ \/ ^ ^ — 1 \ "" , <^ ^ ^ '■ i / c/ ' 1 ^ 1 1 / =,vt. / 1 1 ^. 1 1 ?J 7' 0/ 1 ^ / 1 e b> RO 7 / =>«-. f;^ \ 1 "■•^ 1 - S,| / ;>- u./ / 1 t Ix / / 1 1. ^ f / I 'I ,„ IN „. u. d ^ ^ -' ' £ 2 9* / J- 1. « « « > fi . z f ii i i Jf > i ^ j; ~ m % ? '^ «, V ^ 0.075 0.100 0.125 DIAMETERS OF SAND IN INCHES Fig. 57. - -Typical Mechanical Analyses of Fine, Medium, Well Graded and Coarse Sands. {See p. igo.) times greater than that of Figs. 55 and 56, the diagram showing diameters ranging from o to 0.200 inches diameter. The " granulometric composi- tion" of these sands may be determined if desired by reference to page 162. The mechanical analysis of crusher dust is apt to vary between the curves of iine sand and medium sand which are shown in Fig. 57. STUDIES OF THE DENSITY OF CONCRETE In the year 1901 the writer, through the permission and assistance rf Mr. E. LeB. Gardiner, Vice-President, and Mr. J. Waldo Smith, Chi.f Engineer, of the East Jersey Water Company, was enabled to make an extended series of experiments on the comparative strengths of different proportions of concrete aggregate, ^ilany mixtures oi different propor- tions were, made up into beams, their curves of mechanical analyses drawn as explained above, and the strength of the beams determined by breaking tests.* These tests indicated that the strength of concrete varies with the per- centage of cement contained in a unit volume of the set concrete, also with * The results of these tests are presented in the table on pages 334 and 335. PROPORTIONING CONCRETE 191 the density of the specimen. With the same percentage of cement, the densest mixture, irrespective of the relative proportions of the sand and stone, was in general the strongest. These tests further indicated that for the materials used there was a certain mixture of sizes of grains of the aggregate which, with a given percentage by weight of cement to the total aggregate, gave the highest breaking strength. In practice also it was found that the concrete made with this mixture worked most smoothly in placing. These tests led to a still more extended series by the writer and Mr. Sanford E. Thompson at Jerome Park Reservoir, New York, in 1903 and 1904, under the authorization of the Aqueduct Commission of the city of New York, Mr. J. Waldo Smith, Chief Engineer. The method of procedure and the results of the tests are given in full in a paper on "The Laws of Proportioning Concrete," by WiOiam B. Fuller and Sanford E. Thompson, Transactions American Society Civil Engineers, Vol. LIX, p. 67, 1907. The experiments were begun with a series of tests on the density of different mixtures of aggregate and cement to determine the laws of proportioning for maximum density for different materials, and these density experiments were followed by the manufacture of con- crete specimens in the attempt to determine the relation between the laws of strength and the laws of density. The mechanical analysis diagram furnished a ready means of studying the effect of various sized particles on the density of concrete. For this purpose crusher-run stone and bank gravel were screened into twenty-one sizes ranging from 3 inches down to that passing a No. 100 sieve, having meshes 0.0027 inch in diameter. These sized materials were then re-com- bined- in a predetermined mechanical analysis curve by weighing out the necessary quantities of each size. ' This material was next thoroiighly mixed with a given weight of cement and the whole amount wet and mixed and tamped into a strong cylinder in which its volume could be measured. This batch was then thrown away and another batch made up according to another mechanical analysis curve and its volume recorded. In this way over 400 different mechanical analysis curves were tested as to volume for the purpose of determining the ideal curve corresponding to the densest concrete mixture. Both broken stone and gravel were used in the tests, and to reduce the number of variables, most of the experiments were made upon the same proportions, using 10 per cent by weight of cement to the total dry materials, corresponding to proportions i : 9 by weight. In all of the tests instead of following the more usual plan of testing the 192 A TREATISE ON CONCRETE aggregate separately, every experiment was performed with a mixture of the aggregate and cement gaged with the water necessary to produce the proper consistency. The water was found necessary both in theory and practice. The cement and water actually occupy space in the mass, since many of the voids are too small for the grains of cement to fit into them without expanding the volume and the water also occupies actual bulk in the concrete. Besides this, a concrete mixed up with water is easier and smoother to handle than a mixture of dry materials alone which tend to separate when being placed. Curve of Maximum Density. The Little Falls tests made by the writer indicated that the curve at greatest density was substantially a parabola. The Jerome Park tests based on a larger number of experiments define the curve still more accurately as a combination of an ellipse and a straight line.* One of the most interesting developments was that a curve of substan- tially the same form would fit different materials whatever the maximum size of the stone. The J-inch stone, for example, required but very slight change in curve equation from the 2i-inch stone. The maximum density curve then was found to consist of a combination of an ellipset and a straight line, the ellipse being first constructed with its *Mr. Fuller's method of proportioning the materials so that their mixture will form a smooth, clearly defined curve appears, on its face, to conflict with Mr. Feret's coaclusion (see p. i6o) that the best mixture of sand and cement for mortar is made up of coarse and fine grains only, with no inter- mediate grains. For sand mortars, Mr. Feret's methods are undoubtedly more exact than Mr. Fuller's, but for a concrete mixture the conditions are different, and, as we have stated on page 133, more than two sizes of materials are theoretically necessary for obtaining the densest mixture. In practice, too, all classes of materials are more or less varied, and experiments show that the particles will best fit into each other if the sizes are graded. The best proof of the practical efficiency of Mr. Fuller's method lies in the fact that he has employed it day after day for determining the proportions of the aggregate for concrete used in constructing thin, water-tight walls. The pro- portions used by him for such work are about 1:3:7, whereas for water-tight construction where the materials are not scientifically graded 1:2:4 mixtures are commonly used. The method is exact and scientific and not "rule-of-thumb.'' The nature of the materials and their variation from hour to hour makes great refinement unnecessary, so that an accuracy of, say, 2% or 3% in the percentages are all that is necessary in practice. Although further tests may show that for other materials the form of the curve varies from that indicated by Mr. Fuller, the general method of analyzing materials and combining the curves is undoubtedly applicable what- ever the form of the curve, so that Mr. Fuller's general principles and methods still hold. ■j- In practice ellipses may be most readily plotted graphically by the Trammelpoint method as follows: ' Plot the major and minor axes on the diagram. The major or horizontal axis in all cases is on a line 7% above the base. The minor or vertical axis is at a distance, u, to the right of the vertical zero ordinate of the diagram. Lay a strip of paper or a thin straight-edge upon the major or hori- zontal axis, and mark upon it two points to represent the length of the semi-major axis, calling one of these points — the point on the zero ordinate — 0, ind the other point A. Mark off on the strip or straight-edge, in the same direction from 0, the length of the semi-minor axis, calling this point B. Now, swing the strip of paper or straight-edge little by little so that the outline of the Curve may be marked off by the point 0, while the points A and B are kept at all times upon the axes b and a respectively. The straight lines to continue the curves are drawn as tangents to them, or may be readily plotted from the data on the following page. PROPORTIONING CONCRETE 193 major axis coinciding with 7 per cent line of percentages, and the equation V of the ellipse, using the zero coordinates of the diagram, being {y — 7)^ = — a' {2ax — x^). One of the ideal curves is illustrated in Fig. 58, page 197, showing the general form which it takes. In practice it was necessary to raise the curve somewhat higher, that is, to use more sand than the very careful laboratory tests would indicate as the ideal mix. The values of a and b for the different materials, including the cement for the Ideal Mix, based on the Jerome Park stone and Cowe Bay sand and gravel, which, as already stated, were fairly representative materials, are as follows: Data for Plotting Ellipses in Curves of Ideal Mix. Materials. Ideal Mix Axes of Ellipse. Crushed stone and sand . . . . Gravel and sand. Crushed stone and screen- 0.04 +0. 16D 0.04 +0. 16D 0.035 +0.14D 28. 5 + 1. 3D 26.4 +1.3D 29.4+ 2. 2D In this table, D = tlie maximum diameter of the stone, in inches. For the Practical Mix the values of b must be greater so as to give a higher curve with more of the finer material. A quick and sufficiently accurate method of drawing the curves for the practical mix is to draw a straight line from the point where the largest diameter stone reaches the 100% line to the point on the vertical ordinate at zero diameter given in Column (i) in the following table. Data for Plotting Curves of Practical Mix. Materials. Intersection of tangent with vertical at zero diameter (1) Height of tangent point (2) Axes of Ellipse. a (3) 6 + 7 (4) Crushed stone and sand. Gravel and sand Crushed stone and screen- 28.S 26.0 29,0 35-7 33-4 36.1 0.150D 0.164D 0.147D 37-4 35-6 37-8 194 A TREATISE ON CONCRETE Then mark the tangent point on this line where it is intersected by the vertical ordinate for one-tenth the maximum diameter stone. This mark should check with the values given in column (2) of above table. Then plot the location of minor axis of the ellipse from the values of a and b+7, given in columns (3) and (4) in the above table. This point, together with t,he tangent point and the point at + 7 on the vertical ordi- nate at zerp diameter where the curve begins, gives three points on the ellipse, which is usually sufficient for drawing the curve with the aid of an irregular curve. If more points are wanted, they may be plotted graphically by the trammel point method as given in the note on page 192. RELATION OF DENSITY TO STRENGTH Having determined the maximum density curve as just explained, it vs'as important to know if the greatest strength coincided with the greatest density, and for this purpose a large number of beams, six inches square and six feet long, were made up and tested for transverse and crushing strength, for permeability and modulus of elasticity. Some beams were made using the proportions determined by the maximum density curve and other beams according to higher and lower curves to note if there were any decrease in these properties as the maximum density curve was departed from. The full results of the tests are given in the paper referred to,* but in general it may be said that a departure from the maximum density curve represented a reduction in all these properties except that when the curve was modified so as to use a uniform size of coarse stone instead of the graded stone it gave practically the same results as the graded. Any curving above the straight line in the coarse material decreased the density, and also the strength, indicating that the coarse aggregate should not have an excess of medium particles. LAWS OF PROPORTIONING From these experiments, laws of proportioning and also laws relating to strength and permeability which are outlined in full in the paper by Messrs. Fuller and Thompson* were evolved. Those relating specifically to strength are given on page 323 and those relating definitely to permeability on page 304 and reference should be made to these for complete conclusions. The laws relating especially to the grading of the aggregates are: See page iqi. PROPORTIONING CONCRETE 195 1. — Aggregates in which particles have been specially graded in sizes so as to give, when water and cement are added, an artificial mixture of greatest density, produce concrete of higher strength than mixtures of cement and natural material in similar porportions. The average im- provement in strength by artificial grading under the conditions of the tests was about 14 per cent. Comparing the tests of strength of con- crete having different percentages of cement, it is found that for similar strength the best artificially graded aggregate would require about 12% less cement than like mixtures of natural materials. 2. — ^The strength and density of concrete is affected but slightly, if at all by decreasing the quantity of the medium size stone of the aggregate and increasing the quantity of the coarsest stone. An excess of stone of medium size, on the other hand, appreciably decreases the density and strength of the concrete. 3. — The strength and density of concrete is affected by the variation in the diameter of the particles of sand more than by variation in the diameters of the stone particles. 4. — 'An excess of fine or of medium sand decreases the density and also the strength of the concrete, as will also a deficiency of fine grains of sand in a lean concrete. 5. — The substitution of cement for fine sand does not affect the density of the mixture, but increases the strength, although in a slightly smaller ratio than the increase in the ratio of cement. 6. — It follows from the foregoing conclusions that the correct propor- tioning of concrete for strength consists in finding, with any percentage of cement, a concrete mixture of maximum density, and increasing or decreasing the cement by substituting it for the fine particles in the sand or vice versa."" 7. — In ordinary proportioning with a given sand and stone and a given percentage of cement, the densest and strongest mixture is attained when the volume of the mixture of sand, cement and water is so small as just to fill the voids in the stone. In other words, in practical con- struction, use as small a porportion of sand and as large a proportion of stone as is possible without producing visible voids in the concrete. 8. — The best mixture of cement and aggregate has a mechanical analysis curvef resembling a parabola, which is a combination of a curve approaching an ellipse for the sand and a tangent straight line for the * This very important law requires further tests for confirmation, outside of the limits of the present tests. tFor definition of mechaRical analysis, see page 185. 196 A TREATISE ON CONCRETE stone. The ellipse runs to a diameter one-tenth the diameter of the max- imum size of stone, and the stone from this point is uniformly graded. 9. — The ideal mechanical analysis curve, i.e., the best curve, is slightly different for different materials. Cowe Bay sand and gravel, for ex- ample, pack closer than Jerome Park stone and screenings, and therefore require less of the size of grain which the authors designate as sand. 10.— The form of the best analysis curve for any given material is nearly the same for all sizes of stone, that is, the curve for |-inch, 1-inch, and 2|-inch maximum stone may be described by an equation with the maximum diameter as the only variable. In other words, suppose a diagram in which the left ordinate is zero, and the extreme right ordinate corresponds to 2f-inch stone, with the best curve for this stone drawn upon it. If, now, on this diagram the vertical scale remains the same, but the horizontal scale is increased two and a quarter times, so that the diameter of 1-inch stone corresponds to the extreme right-hand ordinate the best curve for the 1-inch stone will be very nearly the one already drawn for the 2}-inch stone. The chief difference is that the larger size stone requires a slightly higher curve in the fine sand portion. 11. — It follows from this last conclusion that from a scientific stand- point the term sand is a relative one. With 2;-inch stone, the best sand would range in size from to 0.22 inch diameter, while the best sand for |-inch stone would range in size from to 0.05 inch diameter. AFFLICATION OF MECHANICAL ANALYSIS DIAGRAMS TO PRO- PORTIONING The mechanical analysis diagram offers a very exact method of determin- ing the proper proportions of any materials for concrete by sieving each of the materials, plotting their analyses and combining these curves so that the result is as near as possible similar to the maximum density curve. Plot on the diagram the maximum density curve for the given materials to be used; if the equation for this material is not known use the practical equation previously given. Make a mechanical analysis of all of the materials which it is desired to mix together in the right proportions and plot the result of each analysis on the diagram on which the maximum den- sity curve has been plotted. The aim is to find a new curve representing the mixture of the materials, but which will conform as nearly as possible to the curve of maximum density. The proportions of dififerent materials required to produce this curve will show the relative quantity of each which must be used in pro- portioning. The theorv of the combination and comolete discussion of thp PROPORTIONING CONCRETE 197 methods to be employed with different forms of curves are treated in Appendix I. A less exact method, but one which is convenient in practice, is by inspec- tion and trial of different percentages. To illustrate this trial plan, the method of forming a curve of a mixture of several materials in stated pro- portions such as I : 2 : 4 will be given, then the curve for the mixture of the same materials which corresponds nearest to the curve of maximum density, and finally the application will be made to material like run of the bank gravel which may be separated into two or three parts. In reading this discussion it must be borne in mind that the same prin- ciples will apply to mixtures of several aggregates, although for simplicity the principal part of the discussion refers to two aggregates. The same 0.05 0.10 0.16 0.20 0.25 0.30 0.35 0.40 0.46 0.60 0.65 0.60 DIAMETERS OF PARTICLES IN INCHES 0.65 0.70 0:73 Fig. 58. — Curves of Fine and Coarse Crushed Stone and Mixtures, (p. 197) approximate plan may be used for the larger number of aggregates or the more exact method in the Appendix may be adopted. Plotting Curve of Mix in Studying Proportions. In Fig. 58 we have f-inch Shawangunk grit as one aggregate and the same material rolled to ^inch maximum size as the other, giving the mechanical analysis curves shown in the diagram.* In this diagram a curve of cement is also plotted so that the 1:2:4 curve represents the combination of the three materials. The curve marked 1:2:4 then represents the analysis of the mixture of cement, screenings * This diagram and the ones which follow are made up from materials used in subsequent studies by the New York Board of Water Supply, and referred to m the Discussion by Ml. James L. Davis, Transactions American Society Civil Engineers, Vol. LIX, p. 144. igS A TREATISE ON CONCRETE and stone in these proportions. This curve is mads up by plotting various points and connecting these by a smooth curve. To find the point, for example, where the curve cuts the ordinate correrponding to the No. 20 sieve, the sums of the percentages of the individual materials at this same ordinate are taken in the proportion which they bear to the concrete mi/iture. All of the cement is finer than the No. 20 sieve, and since the cement is one part of the seven parts in the mixture, one-seventh of 100 per cent repre- sents the percentage of cement in the mixture at the given ordinate. Simi- larly, since there are two parts of sand in the seven parts, the sand percent- age at the No. 20 ordinate, 61 per cent, is multiplied by two-sevenths, and the stone percentage, 6 per cent, by four-sevenths, thus giving as the point on the No. 20 sieve ordinate in the combined curve: } X 100 percent = 14. 3 per cent for cement I X 61 percent = 1 7 . 4 per cent for sand f X 6 per cent = 3.4 per cent for stone Total 35 ■ i per cent for the point in the curve. The other points in the curves are found in a similar manner. Curve of Mix to Best Fit the Maximum Density Curve. Take the same two aggregates plotted in Fig. 58, but in this case disregard the cement or rather consider it a part of the sand. (Frequently the cement must be con- sidered in the trial mixtures in order to study the part of the curve repre- senting the fine material to see that the percentages of the finest particles are satisfactory). The slide rule is convenient for this proportioning. Averaging the f-inch stone by a straight line, we see that it crosses the 0.15 line at about 9%; we note also that the -J -inch sand crosses the same line at 98% and the maximum density curve crosses the line at 43%, that is, along this line it is 34% from the |-inch stone to the maximum density curve and 55% to the |-inch sand. The percentages to be used to obtain a 43% mixture would be an inverse ratio of these two numbers to their total, that is, ||- = 38% of fine material and ||- = 62% of the coarse material. With the slide rule take these percentages of each curve, add together and plot a new curve, and see if it conforms reasonably with the maximum den- sity curve. If it does not, make another trial of percentages, the plot of the curve indicating by inspection the new percentages. It must be remembered that the fine portion of the curve includes also the cement, so having decided on the amount of cement to use, say the equiva- lent of a I : 7 mix, which has 12^% of cement, the actual proportions would be 1 2 J parts cement to 38 — 12^ = 251 parts fine aggregate to 62 parts coarse aggregate, or translated into the usual nomenclature, 1:2.04 :4.9s, or practically 1:2:5, showing that the ordinary mixture with this particu- PROPORTIONING CONCRETE igg lar material is the best. Supposing, however, the equivalent of a richer mixture, say i : 2 : 4, is wanted. This would contain 1:6 = 14^% cement and the proportions would be 14J : 23^ : 62, or I : 1. 62 : 4.27, or practically I : if : 4i shovidng that for richer mixtures less fine materials is desirable. M.O.SaO SIEVE MO. bO SIEVE ipi. /^ ^^ \\\t\t / ^ 15 ^rs5 ^^ yso^ / r— ■ _^ r-.^ v/^/ t K- S ,4>. _^^^ --^ v.[ ^ m icojS; hrr>»' ojji;^ G7H \'% x- Usi^ ;.^'^ >^ 1^ / 1 ] ^"n^-^ -^ ^:^^*~ »« \v/ "1?^" r ^-' uu S \h/ / i^^.t :'V (0 ; [/I 1 / / *i.>*.H3 o>S-'\3 / V "^ \\ • ' / ^'' D^ » -/-■ '/' ' '''/ / / ll! i ''^ — -"1 . ' / |i '/^^ /,' / / ^ / 20,. if i ^ 1 bJ / n i / W. -i_j — 1 /! 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 l.SO 1.40 1.50 DIAMETERS OF PARTICLES IN INCHES Fig- 59- — Cortland Gravel Screened to Two Sizes, {see p. 200.) 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.4( DIAMETERS OF PARTICJ-liS IN INCHES Fig. 6o. — Cortland Gravel Screened to Three Sizes, {seep. 200.') ^c3o A TREATISE ON CONCRETE Run of Bank Gravel. Gravel as it is found in the natural bank almost always contains too much fine material. In many cases screening this into two sizes produces a good curve which fits very closely to the curve of maximum density.* Other gravels, especially where the sand is greatly in excess, require two screenings for the best result. Fig. 59 represents a common run of such gravel, showing that screening into two sizes will not permit a mixture fitting very near to the maximum density curve. The figure also shows how far away the original analysis of the run of the bank is from the ideal curve. In Fig. 60 the same sand is shown screened into three sizes, and illustrates the improvement that can be obtained in this case by the extra screening, the effect of which is to leave out some of the medium size particles which are too large to fill the voids of the coarse stones, and therefore decrease the density and the strength of the mixture. PROPORTIONING BY TRIAL MIXTURES The density tests at Jerome Park and the relation there found of the strength to the density indicate a method of proportioning by trial mix- tures which may be called volumetric synthesis. This may be used to compare the density of the same materials mixed in different pro- portions or different materials mixed in similar proportions. Having determined the particular sand and stone which are to be used on any piece of work, a simple and accurate way of determining proportions is by actual trial batches of fresh material. For this it is only necessary to have good scales and a strong and rigid cylinder, say, a piece of lo-inch wrought-iron pipe capped at one end. Carefully weigh out and mix together on a piece of sheet steel or other non-absorbent material all the ingredients, having the consistency the same as is intended to be used in the work. Place these in the pipe, carefully tamping all the time, and note the height to which the pipe is filled. Weigh the pipe before filling and after being filled, thus checking weight of material mixed. Throw this material away before it has time to set, and clean the pipe. Make up another batch, using the same weights of cement and water and the same total weight of sand and stone, but have the ratio of weights of the sand and stone slightly different from the first. Note whether, after placing, the height in the cylinder is less or more than was the height of the first batch, and this will be a guide to further similar mixes, until a proportion is found which gives the least height in the cylinder, and at the same time works *An illustration o^ this is given by Mr. James L. Davis, in Transactions American Society of Civil Engineers, Vol. LIX, p. 145. PROPORTIONING CONCRETE 201 well while mixing and looks well in the cylinder, all the stones being covered with mortar. This method, if carefully followed, will give very accurate results, but of course does not indicate, as does mechanical analysis, what other changes can be made in the physical sizes of the sand and stones so as to get the best available composition. Mr. A. E. Schutt^, in studying the proportions of materials for bitumi- nous ntiacadam pavement for the Warren Brothers Company, has very effectively developed the method of volumetric synthesis with dry materials. His experiments included various classes and sizes of stone, sand, and screenings ranging from 3 inches diameter down to that which passes a No. 200 sieve. He found that the best method for compacting dry materials, such as sand, gravel or broken stone, is to place them in a vessel the shape of a truncated cone, with the largest diameter at the bottom. The cone is filled with the coarsest material and taken by a laborer, who compacts it by repeatedly striking the cone against the ground, keeping the measure full by adding new material of the same kind. When it ceases to settle, the contents is emptied and mixed with a portion of g, finer material, replaced in the measure and compacted as before. By repeated trials the exact size and maximum volume of successive finer materials, which may be added without appreciably increasing the bulk of the coarsest after thoroughly compacting, are determined. Mr. Schutte has found that for different shapes of particles the proportions of each size must be varied, but having determined the required percentages for a certain stone, that is, for a stone from a certain quarry, the proportions of the sizes from day to day need be varied but little. Practical Proportioning During Progress of the Work. The above methods of mechanical analysis and volumetric synthesis are methods to be used in the office or laboratory in determining the relative values of all the aggregates available for the work. When the work is begun, however, and the same general character of aggregate is used day by day, it is only necessary to see that the material does not change or, if it does, simply to readjust the relation between the fine and coarse aggregate. To do this by the mechanical analysis method, it is only necessary to have a nest of about six 8-inch sieves: say, stone sieves with i inch, J-inch and ^-inch diameter holes and sand sieves No. 7, 20, 50 and go, together with a cover and pan. The shaking can be done by hand, and the sievings beginning with the finest emptied into a long glass tube. If a standard sample has been previously put in the tube in the same way and the points of division between the different sievings marked on a paper pasted on the outside of the tube, the difference between the standard and the sample under test can be quickly seen and modifications made in the mix accordingly. 202 A TREATISE Oi\ CONCRETE The test by volumetric synthesis is one easily made in a modified way in the field and with care gives good results. Procure a galvanized tin pail and a spring balance graduated to half pounds; take a representative sample of concrete, being careful that it contains no more stones or mortar than the regular concrete; tamp it into the pail until level full and weigh. Any variation from the standard weight will show a change in the character of material, and this change can usually be detected and corrected by observ- ing the materials and mixing. If not, then mechanical analysis methods will have to be used. PROPORTIONS OF CONCRETE IN PRACTICE The proportion of cement to aggregate depends upon the strength (see p. 311) and water-tightness (see p. 298) required, as well as upon the character of the inert materials, and, in general, relatively rich mix- tures are necessary for loaded columns and beams in building construc- tion, for thin walls subjected to water pressure, and for foundations laid under water. The following table has been compiled to show a few examples in practice. Proportions in Actual Structures Class. Structure. Proportions. Reference. Massachusetts Special Sanford E. Thomp- Institute of columns. . I : I : 2 son Technology < Superstruc- Cambridge, ture :ii:3 Mass. Foundations Special :2 :4 Sanford E. Thomp- Youth's Com- columns. . : I : 2 son Buildings panion, Bos- ■ Superstruc- ton, Mass. ture 12:4 , Foundations ■■2h:S McElwain Fac- tory, Man- chester, N.H. ' Special columns. . Superstruc- ture ii:3 2i : 4i Specifications Foundations 2\:sh Tunkhannock, Penn. Viaduct 3 :5 Eng. Cont.,Apr. 1, Arch Bridges ■ Fort Worth, Tex. Viaduct. . . I 2 :4 1914, p. 382. Trans. A. S. C. E., Vol.LXXVIII.p. 1206. PROPORTIONING CONCRETE Proportions in Actual Strucltires. 203 Class. Structure. Proportions. Reference. Kansas City, Mo. 12th St. Viaduct 1:2:4 Eng. News, Jan. 7, 191S, p. 10. Girder Bridges Portland Me. Harbor Via- duct T :2 :4 I : 2i : 5 J. R. Worcester. Retaining Wall and ■ Piers Fort Worth, Tex. Viaduct.. Tunkhannock, Penn. Via- Trans. A. S. C. E., Vol.LXXVIII.p. 1206. duct Piers 1:3:5* Eng. Cont., Apr. i, 1914, p. 382. Kensico, N. Y I :3 :6.t Trans. A. S. C. E., Vol. LXXIX, p. Dams Medina River, Tex I : 3i : 6i 248-251. Eng. News, ' Sept. II, 1913, p. S08. Arrowrock, Idaho I : 2i : 1 II U ll .11 Q Volume of cement per barrel Net weight of cement per barrel Weight per cubic foot 43 11 •s t U * a Oft fi'ft -a <2 J in .2? ft. ft. sq.ft. cu.ft. ft. cu.ft. cu. ft. CU. ft. cu. ft. lb. lb. lb. lb. lb. lb. lb. 5 A 2.12 1.437 1.622 3446 0.17 0.23s 3.21 3-75 3-432 377-4 376-9 117.S 100.5 109.4 90.6 2I.I 6 B 2.19 1.430 1.605 3-405 6.12 0.171 3.3s 4.17 381.0 1 13.8 91.4 29.0 3 C 2.07 1.412 I.S7I 3.249 0.07 0.096 3.1s 4.05 387.0 112.8 94.2 22.7 S D 2.01 1.407 I.S54 3.123 0.07 0.093 3.03 3-99 3-S22 373-2 371-4 123.2 93-2 105.5 2S.6 6 E 2.08 1.403 1.546 3.219 0.04 0.059 3.16 4.19 374-2 118.4 89.2 24.3 I F 2.1.3 1.38 1.496 3.186 0.03 0.039 3.15. 4.27 3.69s 378-0 378-0 I20.I 88.5 102.3 22.0 Final Av< G 2.01 1.46 1.662 3.327 o.io 0.148 3.21 4.06 3.598 370-7 370.2 115.7 91.4 102.9 80.3 23.3 rages 2.00 1.42 I.S7P 3.292 0.09 0.120 3.tS 4.07 3.S62t 377-4 374.1t ij8.8 92.6 105. it 85.4t 24.0 Note. — A and B are American Cements; C. D E and F are German Cements; G is a Danish Cement; Paper weighs about i lb. *Box rocked over bar. tPartial averages, to be compared only with like brands. measurement, on the other hand, is variously fixed at from 3.8 to 4.5 cu. ft. to the barrel, or 100 to 845 lb. per cubic foot. The extreme actual variation is therefore from 3.1 to 4.5 cu. ft. per barrel, or 123 to 84I lb. per cubic foot. Proportions 1:3:6 in the first case would require I bag cement to 2.3 cu. ft. of sand and 4.6 cu. ft. of gravel; in the last case, proportions 1:3:6 would stand for i bag cement to 3.4 cu. ft. of sand and 6.8 cu. ft. of gravel. In other words, concrete mixed 1:3:6 by one man may be called i : 45 : 85 by another. Weight of Cement. Experiments by Mr. Howard A. Carson, for Boston Transit Commission, upon 31 barrels of Portland cement of QUANTITIES OF MATERIALS 207 American and foreign brands, furnish an interesting illustration of the diEference in weight of the same cement in different stages of compact- ness. The results,* a summary of which is presented in the table en page 206, show a variation from 86 to ir8 lb. in the average weights of the same cement, according as it was weighed sifted, or packed in a barrel, while the actual weight of one brand, the average of 5 barrels, was as high as 123 lb. per cubic foot as it came from Germany packed in a barrel. From the experiments just described, the ratios of volume and weight of the same cements in different degrees of compactness are calculated by the authors as follows: Ratio of volume of packed cement to capacity of barrel between heads 0.97 Ratio of volume packed to volume loose 0.78 Ratio of volume packed to volume shaken 0.88 Ratio of volume loose to volume shaken 1.13 Ratio of v\feight packed to weight loose i .28 Ratio of vs^eight packed to weight shaken 1.13 Ratio of weight packed to weight sifted ji .37 From the table it is evident that the selection of the volume of a barrel is arbitrary. The adopted volume of 3.8 cu. ft. is convenient for calcula- tion because it assumes a cubic foot of cement to weigh approximately 100 lb. THEORY OF A CONCRETE MIXTURE The discussion and the formulas which follow relate to plastic mortars and plastic or medium concrete. While a small amount of water in mixing may result, with heavy ramming, in a concrete or mortar of less than average volume, in practice the volume is more apt to be in- creased by lack of water because of the less perfect mixture and the visible voids. The volume of set concrete or mortar produced by a very wet mixture is approximately the same as that of a plastic mixture, because nearly all of the surplus water is thrown to the surface and expelled by the settling of the solid materials. This the authors have repeatedly proved by experiment. The frequently repeated assertion that a very wet mixture contains visible air voids because of the drying out of the water is incorrect. This may be proved by carefully pouring neat cement grout into a rectangular mold, one of whose sides is formed by a piece of glass. The surplus water is expelled, and the specimen' after setting is dense and glassy with no visible voids. The large visible voids which sometimes occur in very wet ♦Tabulated by Sanford E. Thompson in Engineering News, Oct. 4. 1900, p. 229. 2o8 A TREATISE ON CONCRETE concrete, similar in appearance to visible voids in dry concrete, are due to the grout running away from the stones, or to too violent agitation in placing. The volume of fresh concrete or mortar produced by any mixture of cement and aggregate or aggregates is equal to the sum of the volumes oi the separate particles of the cement, the sand, and the other dry materials, the water contained in the aggregate and added in mixing, and the small volume of air entrained between the particles. The volume of set mor- tar or concrete is not appreciably different from its compacted volume when fresh or green, except in very wet mixtures, which expel a portion of the water. The volumes of the particles of dry materials are termed absolute volumes, and it is important to note the distinction between the absolute volumes and the apparent volumes determined by measuring the materials. Absolute volumes are discussed on pages 148 to 152. The fact that water actually occupies space in a mass of fresh concrete or mortar has been entirely ignored by many writers on the subject of concrete mixtures. As stated on page 204, the fineness of the sand and the moisture contained in it affect the volume ei the resulting concrete or mortar. Mr. Feret has proved by experiments (cited on page 140) that fine sands require more water for gaging than coarse. This extra volume of water produces a mortar of less density and consequently less strength ; even stones such as are found in gravel or coarse broken stone require a very small percentage of water. FORMULAS FOR QUANTITIES OF MATERIALS AND VOLUMES A concrete is therefore made up of solid grains of cement plus water required for the cement, plus soHd grains of sand plus water required for the sand, plus soUd stone particles plus water required for the stone, plus air voids. The last term, the air voids, represents the voids entrained by the sand, which may be considered as a function or percentage of the sand, and the voids due to imperfect mixing of the concrete materials, which may be considered a function or percentage of the stone. Accord- ingly the volume of a concrete mixture may be expressed as a rational formula, which is applicable to all concrete and mortar mixtures in which the voids of the coarse stone are filled with mortar. The formula (i) which follows is presented to illustrate the theory, but because of the variation in the coefficient with different sands and different proportions, formula (2), page 209, and formulas (3) to (8), which are based on aver- age conditions, are suggested for practical use as sufficiently accurate for most purposes. QUANTITIES OF MATERIALS 209 Let c = absolute volume* of cement. 5 = absolute volume* of sand. g = absolute volume* of stone, w = ratio of the absolute volume of the water plus air voids of the cement, to the absolute volume of cement. n = ratio of the absolute volume of the water coating the grains of sand plus the air entrained in gaging it, to the absolute volume of sand. p = ratio of the absolute volume of the water coating the stone particles plus the air voids due to imperfect mixing, to the absolute volume of stone. W — volume of concrete produced. In other words, these ratios, m, n, and p, represent the sum of the vol- umes occupied by the water required for the material in mixing plus the air, in terms of the respective volumes of cement, sand, and stone. Then W= c + mc + s + ns + g + pg or W -~== {1 + m) c+ (i + n) s+ (1 + p) g (i) The coefficient n is really composed of two variables, one depending upon the coarseness of the sand, and the other, upon the ratio of cement to sand, since a lean mortar contains more air voids. It is possible to ex- press this coefficient as a more complex term with this ratio as a factor, but by what appears to be a peculiar coincidence, experiments show that for ordinary bank sand the variation in voids caused by different propor- tions may be provided for by taking the cement and sand together; in other words, for different proportions of the same cement and sand, the sum of the water and the air voids in the mortar is approximately a con- stant. Where there is no sand, or where the stone and sand are mixed, formula (i) must be employed. The more practical formula may be expressed as follows, eniploying similar notation to that given above, and letting r = ratio of the absolute volume of the water plus the air entrained in gaging, to the absolute volume of cement plus sand, then W, = c+ s+ r(c+ s) + g+ pg or W,= (i + r){c + s)+ {1+ p)g (2) ♦Absolute volumes are defined on p., 148. 210 A TREATISE ON CONCRETE \ FOR CONCRETE WITH GOOD COARSE SAND Substituting in formula (2) average values for r and p, which the authors have selected by analyzing the results of a number of exact records in the United States and Europe of the volumes of concrete and mortar made with good coarse sand, the formula becomes W, = 1.34 (c + s) + 1.08 g (3) This formula may be readily reduced to a practical working form if may be expressed in pounds by substituting for the absolute volume, c, the number of pounds of cement divided by its specific gravity (which may be taken as 3.1) times the weight of a cubic foot of water (62.3 lb.). It may also be expressed in barrels by substituting for the absolute volume, c, the number of barrels, B, multiplied by the net weight per barrel, 376 pounds, and divided, as above, by the specific gravity times the weight of a cubic foot of water [see formula (4)]. The terms re- lating to sand and stone may be expressed in pounds in a way similar to that just shown for cement, or they may be expressed in measured volume by substituting for the absolute volume, s or g, the measured volume, 5 or C, multiplied by the proportion of solid material con- tained in it. Expressing this algebraically, if Q = quantity of concrete made with B barrels cement, Qi = quantity of concrete made with one barrel cement, B = number barrels cement, Bj = number barrels cement per cubic yard of concrete, 5 = volume of loose sand in cubic feet, 5j = volume of loose sand in cubic yards per cubic yard of concrete, G = volume of brokfen stone or gravel or cinders in cubic feet, V = absolute voids in sand determined by weight method (p. 127), v' = absolute voids in stone determined by weight method (p. 128), then from formula (3), since c = B — 3.1X62.3 Q=l:^^2SH^B + i.34 {i—v)S+i.oS (i—v')G 62.3X3-1 Q = 2.61 B+1.34 (i —v) 5+1.08 (i —v') G (4) The volume of concrete in cubic feet made by one barrel of cement, assuming that a cubic foot of average loose, moist sand contains 8g pounds of dry sand, and that its specific gravity dry is 2.65, is, Q,= 2.61-1-0.723 5-1- 1.08 (i—wOG (S) QUANTITIES OF MATERIALS 2H This formula is applicable to average concrete made with Portland cement of good quality, coarse bank sand measured loose and containing ordinary moisture, and any broken stone or gravel of known voids. For- mula (5) has been used in compiling tables on pages 215 and 217, except in the first twelve proportions, page 215, which contain no sand. If the volume of concrete made from a barrel of cement plus the sand and other aggregate which accompanies it is known, the number of barrels of cement per cubic yard is readily calculated. In formula (5), Qi represents the number of cubic feet of concrete made with one barrel cement, hence the number of barrels cement per cubic yard of concrete is 27 divided by Q^ Assuming a cubic foot of average sand to contain 89 pounds of dry sand produces the formula employed in calculating tables on pages 230 to 232, and substituting in formula (6) the value of Q^ from formula (s), 27 ■^' ^ 2.61 + 0.723 S + 1.08 (i —v') G ^''' The formulas may be expressed in parts by volume (such as 1:2:4) by multiplying the coefficient of 5 and G by the assumed volume of a barrel, say by 4.0. Knowing the number of barrels of cement, JSj, per cubic yard of concrete, the number of cubic yards of sand per cubic yard of concrete, S^, is evidently _ _ 5i X quantity sand in cubic feet per barrel of cement ;„. 27 The quantity of stone is similarly obtained. If two or more coarse materials, such as broken stone and gravel, are used, they must be mixed in the selected proportions, before weighing, to determine their voids. FOR CONCRETE WITH VERY FINE SAND In mortars of extremely fine sands the density (c + s) is apt to be about 0.60 (see Feret's table, sand C, p. 146) and the coefficient of first term of i.oo formula (3) becomes —7 - = 1.67 instead of 1.34- In plastic mortars 0.00 of standard Ottawa sand the density (c + s), by tests of the authors, averages about 0.71, hence the coefficient becomes -^ — =1.41 instead of 0.71 212 A TREATISE ON CONCRETE 1.34; Substituting these values, or any others which may be obtained by experiment, in formula (2), the working formulas which follow it may be readily deduced. It is evident from the variation in the coefficient with different sands, that the variation in volume of mortar and concrete ob- tained by different experimenters is due chiefly to the difference in the materials employed. The coefficient of (c + s) is also affected, though to a less degree, by the character of the cement, some cements requiring more water than others and therefore producing a greater bulk of paste for a given weight of cement. FOR CONCRETE OF CEMENT AND COARSE AGGREGATE In concrete mixtures of cement and coarse stone, with no sand or screen- ings, formulas (2) to (8) are inapplicable because apparently the air voids ,do not increase with the leanness of the mixture until the point is reached at which the paste fails to fill the voids in the stone. It is therefore necessary to go back to formula (i), page 209. Since s is zero, the formula becomes W,= (i + m)c+ (1 + p)g (9) An average value of (i -1- w) for a first-class American Portland cement has been found by experiment to be 1.65. It varies with the quantity of water required to gage the cement to such a consistency that the voids will be filled, but no free water will exist upon the surface. The selected value, assuming 1% voids in the paste, corresponds to 20% of water by weight. The value of (i — p) is usually 1.04 to 1.08. An average formula for a concrete of cement and coarse stone may thus be taken as W2 = 1.6SC + 1.08^ (10) which is readily reduced to practical forms by the method adopted in evolving formulas (4) to (8) from formula (3). If the stone is a mixture of sand and gravel, or broken stone and screen- ings, the coefficient of g must be increased and a figure selected whose value depends upon the relative proportion of fine and coarse material. TABLES OF QUANTITIES OF MATERIALS AND VOLUMES Tables on pages 213 to 217 are calculated from formulas (5), (6), (8), and (9). The quantities for rubble concrete are reduced in pro- poition'to the percentage of rubble stone used. These formulas are QUANTITIES OF MATERIALS 213 used not merely because of their theoretical worth, but because, as stated on pajges 204 and 218, the results from them agree with actual experiment. The values are average values of sufficient exactness for practical use, although, as already suggested, variations in the quahty of the materials largely affect the resulting volumes, especially of the mortar. VOLUMES OF MORTARS AND QUANTITIES OF MATERIALS Volume of Plastic Mortar and Quantity of Materials per Cubic Yard {see p. 212.) Based on Tests and Experience of the Authors Ordinary Coarse Bank Sand. Very Fine Sand. Proportion by parts. Volume Com- pacted Plastic Mortar. Materials for 1 Cu. Yd. of Plastic Mortar. Volume Compacted Plastic Mortar. Materials for 1 Cu. Yd. Plastic Mortar. d a c!3 From one bag (94 lb.) of Cement From one bbl (376 lb.) of Cement. One bag cement as- sumed as 1 cu. ft. From one bag (94 lb.) of Cement. From one bbl. (376 lb.) of Cement. One bag cement assumed as 1 cu. ft. Packed Cement. Loose Sand. Packed Cement. Loose Sand. cu. /(. cu. ft. bll. cu. yd. cu. ft. cu.fl. Ibl. cu. yd. U.80 3-2 8.31 1 2 J.. 02 4-1 6.61 0.49 i-iS 4.6 S-QI 0.44 I 1.38 S-S 4.88 0.72 I-5I 6.0 4.48 0.66 li 1-74 7.0 3.87 0.86 1.88 7-S 3-61 0.80 2 2.11 8.4 3.21 0-9S 2.24 8.9 3.02 0.90 2* 2.47 9.9 2.74 1. 01 2-SI 10.4 2.60 0.96 3 2.83 II-3 2-39 1.06 2.97 II. 8 2.28 1. 01 3i 3-19 12.8 2.12 1. 10 3-33 13-3 2.03 ..OS 4 3-SS 14.2 1.90 ^■13 3-70 14.8 1.83 1.08 4l 391 IS.6 1.72 i-iS 4.06 16.2 1.67 I. II S 4.28 17. 1 1.58 1. 17 4.43 17.7 I-S3 I 13 si 4.64 18. s 1.46 1.19 4-79 19. 1 1. 41 I -15 6 5.00 20.0 I-3S 1.20 S-IS 20.6 I-3I 1. 17 Note: — Variations in the fineness of the sand and the cement, and in the con- sistency of the mortar, may affect the values by 10 per cent, in either direction. All except the first item in the table on page 213 and the first- 12 items in tables on pages 214 and 215 are calculated from formulas (5), (6), and (8), pages 210 to 211, with the assumption there outlined. The broken stone in the first twelve items in the concrete tables, pages 214 and 215, except where the voids are 40% or over, is assumed to contain fine material, and the coefficient selected for g, formula (9), varies from 1.08 for 50%, 45%, and 40% voids to 1.14 for 20% voids. 214 Quantities of Material for One Cubic Yard of Rammed Concrete One Bag of Cement (94 lb.) is Assumed as One Cubic Foot. (See p.' 2 12) ■£•3 Broken Stone. Scientifically Graded Mixtures. H^ Gravel or Proport 'ons Proport ions g> . CRUSHER RUN. WO DUST.* 45 % VOIDS. Mixed Stone by Parts. by Volume. Screened to and Gravel. 13 "^ It One Size. 50 % Voids. 40 % Voids. 30 % Voids. 20 % Voids ^ 1 H a 1 a 55 -a c i1 = 0"^ 'o'o'o i 1 s :/: CU. yd. m bbl. . H P i K fe Parts. Volume. ■ol Cement. 5 a Broken Stone. Gravel or Mixed Stone Scien- 9 Screened . ".10 tifically Graded Mix- tures. 1 t 1 55 11 1' to One Size. crdshe: RUN. NO BUS' 45 % VOI] and Gravel. 40% Voids. bbl. cu. ft. cu. ft % cu. ft. cu. ft. cu. ft. cu. ft. u u en C/3 2 3 8 12 74 18.7 19.5 20.2 21.8 2 4 8 16 S6 21.4 22.4 23. 5 25.6 2 S 8 20 15 24.0 25.4 26.8 29.4 2 4 10 16 66 23.1 24.2 25.2 27.4 5««< '"w r im n i i. i i nfig i 'lif U^9A Fig. 80. — Bridge Abutment with Paneled Surface, Scrubbed. {See p. 264.) 266 A TREATISE ON CONCRETE should be done immediately after completion of scrubbing and the patches scrubbed as soon as they are sufficiently set. The cost of scrubbing is very low if done at the right time. A laborer can easily scrub and rinse as much as one hundred square feet in an hour. In case the concrete ,has hardened, as it may in hot weather if left over night, a wire brush is advantageous. If the surface is too hard for this, a brick or block of wood with sand and water will rub off the skin, but in such cases the resulting finish will be comparatively smooth and of a different texture. Carborundum and water give best results on hard concrete. In cold weather scrubbing is somewhat uncertain in results and econ- omy because of irregularity of the setting of the concrete and the diffi- culty in determining just when to remove the face forms, also if the con- crete is under load, as in columns, care is necessary to insure sufficient strength to prevent fall or flow of the soft concrete. When scrubbing is to be done on a large face where a day's pouring is only a portion of the whole height, the face planking is erected in courses, supported by cleats and nailed to the uprights or studs, which are set at several inches from the face, so that the courses of planks can be removed individually and re-set higher up for the next day's pouring. A much smaller amount of face planking is thus required, which offsets the labor in constructing. Tooling. A very satisfactory but somewhat more expensive process of finishing a concrete surface is tooling it — either axing, bush-hammer- ing or pointing — when the surface is too hard for scrubbing. When done by hand the cost will run from if to 5 cents per square foot, ac- cording to the efficiency of the workman and the wages paid him. The most that one man can be expected to do in one hour is ten square feet. A pneumatic tool should do two or three times as much. The photo- graph. Fig. 78, page 263, shows at the left a concreted surfaceand at the right the surface after picking. Acid. The hardened skin also can be removed by the use of muriatic acid diluted with six parts of water. A stronger solution is not more effective and is liable to stain the aggregate. The process is expensive and troublesome, particularly on vertical surfaces, for repeated appli- cations are required to obtain satisfactory results. The acid should be thoroughly washed off. Color. Color effects, as well as different textures, are obtained by selecting the aggregates and, at the same time, combinations of colors DEPOSITING CONCRETE 267 are produced as, for example, yellow pebbles in panels and black shale stone in borders. Plaster Forms. Perfectly smooth forms that will not leave imprints on the concrete face have been made by plastering metal mesh with plaster-of-paris to which the concrete will not adhere. Such forms have been made interchangeable and repeatedly used, the corners and other joints at each setting being filled and smoothed with the sarpe plaster. White Cement. White Portland Cement, of high strength and mixed with sand is used to good effect in surface treatment. Panels. In connection with any of these treatments, sunken or in- taglio panels, or, on the other hand, raised panels, i.e., built in relief by special form construction, may be used to relieve the plain even surface of the concrete. Tile and terrazzo panels are also used for ornamenta- tion, as, for example, in subway stations, and ornamental bridges. Mortar Facing. If a mortar surface is required, it is best obtained by depositing the mortar and concrete together, the mortar close to the form. To place it, a movable form, preferably of steel, is held one or two inches behind the face, to govern the thickness of the mortar, and gradually withdrawn as the mortar and concrete are deposited. DEPOSITING CONCRETE UNDER WATER Concrete is usually placed under water by pourijig through a tube or tremie in a continuous flow or by molding large blocks on land to be placed by machinery or floats after hardening. Derrick buckets are sometimes used for depositing but the results are less satisfactory. Cofferdams, not necessarily watertight, are usuuUy required to prevent the concrete from spreading and the cement from washing away. The consistency should be quite wet, wetter than is good practice for work above water. Dry concrete, dry materials mixed without water, should never be deposited under water. Depositing through Tremies. In using tremies it is absolutely essen- tial that the concrete shall not be allowed to wash; the pipe must be kept full of concrete at all times, and the bottom of the pipe moved slowly about to allow the concrete to run gradually out with a minimum dis- turbance of the water. In case the charge is lost and the pipe fills with water, extra cement should be used in the concrete until the pipe is once more full and in proper working order. Some sort of a traveler, scow, or derrick, is necessary to move the tremie about. The size of tremie depends a good deal upon the size of the plant. For small work with the concrete deposited from wheelbarrows a diam- ,268 A TREATISE ON CONCRETE eter of about one foot at the top is enough. On large jobs with large mixers larger pipes are required. The diameter at the lower end should be from J to | as large again as the top to avoid plugging and permit telescoping of the section. The use of tremies is referred to as long ago as 1863 by Gilmore in his "Treatise on Limes, Hydraulic Cement and Mortars." Depositing from Buckets. The best type of bucket for the depositing of concrete is a box open at the top with a bottom that can be dropped down for emptying. The ordinary construction bucket that dumps by tipping and allows the water to stir up the concrete and wash out the cement cannot be used. Usually the cost is greater than with tremies and the results much less satisfactory. Depositing in Bags. In the past bags varying in size from small paper or muslin bags to jute sacks containing 100 tons* sometimes have been used for holding concrete together as it passed through the water. In some cases the concrete has been placed in the bags dry.f This is bad practice because concrete, unless thoroughly mixed, does not attain satisfactory strength or density. Molded Blocks. The molded block method is especially practical in tidal water where concrete deposited in place would be liable to serious Wash unless expensive, water-tight cofferdams were used. Large blocks weighing many tons may be cast and then lowered to place. Refer- ences to work constructed in this manner are given in Chapter XXXIII. CONCRETE IN SEA WATER For concrete laid in cofferdams in sea water the essential require- ments of construction are : (1) Select materials adapted to sea water use (See Chapter XV by R. Feret). (2) Proportion for maximum density using a mix as rich as 1:2:4. (3) Employ a medium consistency scarcely soft enough to flow. (4) Make cofferdams tight to prevent flow of water through green con- crete. (5) Be sure that concrete is hard before it is subjected to sea water. (6) At joints between set or partly set and fresh concrete, clean sur- face and make a neat cement bond. (See p. 259.) .The disintegration of concrete by sea water occurs chiefly between low * Proceedings Institute of Civil Engineers, Vol. XXXIX, p. 126, and Vol. LXXXVII, pp. loi and 126. t Lt. Col. J. A. Smith, Engineering Record^ March 23, 1895. DEPOSITING CONCRETE 269 and high tide, and is produced by a combination of frost and of chemi- cal action. If laid with the best of workmanship by methods outlined above it should resist the elements. Special precautions are necessary to prevent the tide from rising and falling on or through the fresh concrete. A number of failures of sea water construction have been due to this cause alone. The water washes the cement out of the green concrete and leaves a porous mass readily acted on by the sea water so as to be completely disintegrated. It is interesting to note in this connection that in reinforced concrete the steel may not be affected. In one instance in Boston Harbor, where the repairs were made under the direction of one of the authors, the concrete in certain sections which had been injured during construction by the tide was soft enough in places to pick out with the fingers, but the steel, which had had no opportunity to dry out, was intact after two years' exposure. In soutljem waters and below low tide concrete is affected but slightly. The effect of frost is illustrated in the sea wall of a power house in Boston Harbor, where the wall washed by the cold salt water is badly disin- tegrated, while the portion reached by the warm water discharge is unaffected. Concrete blocks or piles thoroughly hardened before expos- ure to sea water resist sea water excellently. Materials. The characteristics of aggregates required are discussed in the following chapter. Density is of the utmost importance to pre- vent water flowing into or through the mass and thus affecting the cement. Tests by the authors using concentrated sea water, in con- nection with the construction of the South Boston power house of the Boston Elevated Railway Company indicate that the choice of the cement should be governed largely by a low percentage of aluminum. A maximum of 6J% alumina is specified by the Boston Transit Com- mission for cement in sea-water as a result of tests of pats of neat cement ranging in composition from 4^% to 8% alumina. The cements low in alumina in general resisted decomposition for a much longer time than those high in alumina.* DRILLING CONCRETE In factory construction concrete floors must be drilled for bolts to anchor machinery. On a larger scale drilling is required for the re- •Report of Boston Transit Commission, June 30, 1914. P- S3; June 30, 19:5, p. 53. 27° A TREATISE ON CONCRETE moval of old concrete. The equipment and the selection of hand or machine tools depends upon the amount of work to be done. An ordinary star brick hand drill will cut holes for machinery by striking light quick blows to avoid chipping or breaking through. Similar methods have been used on the Boston Subway by the line and grade parties in drilling holes for lead plugs. A light pneumatic drill is also used for such work. In drilling a large number of holes in r : 2| : 5 rubble concrete* ten months old for ij inch anchor bolts, hand drillers averaged 1.8 linear feet of hole per hour, or about 14 Hnear feet per 8-hour day, while the pneumatic drill, cut 4.7 linear feet per hour, or about 38 Hnear feet per 8-hour day, with a maximum of 54 linear feet. In concrete three months old the average progress was about 85 feet per day. Wet or damp concrete drilled badly. One sharpening of a drill was required per 8 feet of hole. A section of retaining wall at Newton Highlands was torn out to pro- vide room for an extension of the station platform. A large steam drill on a tripod with 2" drill was used. A time study showed the work to consist of four operations with average times as follows: (i) Getting ready to drill and starting hole, a constant per hole, 7.5 minutes; (2) Drilling, per linear foot of depth of hole, 2.1 minutes; (3) Moving drill from hole to hole, varying with spacing, per linear foot of distance, 0.5 minutes; (4) Lost time, in terms of (i), (2) and (3), /o- ' Holes were about 25 inches deep and about 3 linear feet of drilling were required per cubic yard of concrete. The gang consisted of 10 men, — foreman, blacksmith and helper, fireman, drill runner and 5 laborers. By using the times given, an approximate estimate can be made for various conditions. •J. R. Taft in Engineering Record, September 3, 1910, p. 260. EFFECT OF SEA WATER UPON CONCRETE 271 CHAPTER XV EFFECT OF SEA WATER UPON CONCRETE AND MORTAR* By R. Feret Chief of the Laboratory of Bridges and Roads, Boulogne-sur-Mer, France. The principal conclusions which have been reached by the author of this chapter, as discussed in the following pages, are as follows: (1) No cement or other hydraulic product has yet been found which presents absolute security against the decomposing action of sea water (See p. 271.) (2) The most injurious compound of sea water is the acid of the dis- solved sulphates, sulphuric acid being the principal agent in the decom- position of cement. (See p. 272.) (3) Portland cement for sea water should be low in aluminum (see p. 274), and as low as possible in lime. (See p. 273.) (4) Puzzolanic material is a valuable addition to cement for sea water construction. (See p. 279.) (5) As little gypsum as possible should be added, for regulating the time of setting, to cements to be used in sea water. (See p. 272.) (6) Sand containing a large proportion of fine grains must never be used in concrete or mortar for sea-water construction. (See p. 278.) (7) The proportions of the cement and aggregate for sea water con- struction must be such as will produce a dense and impervious con- crete. (See p. 278.) EXTERNAL PHENOMENA At present there is no hydraulic product which is known to be capable of resisting absolutely the decomposing influence of sea water. It is true that some concrete masonry has remained intact for a very long time in salt water, but with our present knowledge it is impossible to say why these structures have resisted so well, and there is little doubt that the cements from which they were made might have decomposed rapidly if they had been used under different conditions. In some cases, on the other hand, siniilar large structures subject to the action of sea water were *The authors are indebted to Mr. Feret for this chapter, which has been especially prepared by him for this Treatise. 272 A TREATISE ON CONCRETE ruined in a few years and were torn down and completely rebuilt. Notable instances of this kind are the failures which occurred in the ports of Aber- deen,* Dunkerque, and Ymuiden. Such occurrences have aroused great interest in the subject of the action of sea water upon mortars, and but few questions have received more careful study. In spite of this, however, it cannot be said that any sure means of preventing these failures have been found. The decomposition manifests itself in various ways: sometimes th? mortar softens, and little by little becomes disintegrated; sometimes the mortar becomes covered with a crust which finally cracks off; more often fine white veins develop on the surface of the mortar, these gradually grow large and open, the mortar swells, cracks, and falls off in small pieces or collapses in a pulp-like mass. Almost always the interior of the decom- posed mortar is found to contain a soft white material which ma}' be easily separated from it. The chemical composition of this substance is not, however, constant. f Generally, the more advanced the state of decom- position, the more readily the white material can be extracted from the mortar and the richer it is in magnesia. The proportion of sulphuric acid in it also increases with the degree of decomposition, though less uniformly. ACTION OF SULPHATE WATERS For several years the injurious action of sea water upon hydraulic com- pounds was attributed chiefly to the magnesia in the water. It is note- worthy, however, that chloride of magnesia is almost without action, while sulphate of magnesia acts very energetically upon cement, and it has now been ascertained that magnesia plays only a secondary part, while in fact it is the sulphuric acid combined as a soluble sulphate which is the real cause of the decomposition. This has been confirmed in practise by the destruction of masonry washed by water which has traversed earth containing gypsum, or built from mortar made with sand which has been extracted from strata con- taining sulphate of lime. J A consideration of this fact makes it apparent how dangerous it is to use, in concrete or masonry subject to the action of sea water, cements to which the gypsum has been added for the purpose of regulating the rate of their setting or of increasing their initial strength. § There are numerous instances in which brick masonry has rapidly de- *Sniith, Proceedings Institution Civil Engineers, Vol. CVII, 1891-92. ■j-Feret, Annales des Fonts et Chauss^es, 1892, II, p. 93. JBied, Annales des Fonts et Chauss^es, 1902, Til, p. 95, §Feret, Annales des Fonts ct Chauss^es, 1890, I. p. 375, EFFECT OF SEA WATER UPON CONCRETE 273 composed because the bricks, burned with coal, contained alkaline sul- phates which when drawn out by water attacked the mortar of the joints.* These practical observations combined with certain laboratory experi- ments intelligently conducted have demonstrated that sulphuric acid is the principal agent in causing decomposition. Indeed, we must attribute to dissolved sulphates most of the damage which many American writers have improperly explained as due to the action of "alkalies" on the cement. CHEMICAL PROCESSES OF DECOMPOSITION Messrs. Candlot,-]- Michaelis,| and Deval§ have discovered successively by different methods that aluminate of lime Alj O3 3 CaO, which exists in cements in company with other calcareous salts, such as silicates, possesses the property of combining with sulphate of lime so as to give a double salt AI2 O3 3 CaO, 3 (SO3 CaO) combined with a large quantity of water with great increase in volume. This substance, moreover, has no firm coherence. It is soluble in pure water, but insoluble in lime water, a fact that explains its existence in a solid state in mortars. On the other hand, even if the cements do not contain free lime when they are anhydrous, their setting under the action of water frees a part of the lime which was combined with the acid elements, principally with silica. If a soluble sulphate other than sulphate of lime is placed in con- tact with a hydraulic binding material during hardening or after having set, it produces, with the freed lime, sulphate of lime, which in turn com- bines with the aluminate, giving "sulpho-aluminate," and produces the swelling which causes the disintegration of the mortar. The same reac- tions would be produced, moreover, without the intervention of free lime as a result of the reaction of the sulphuric acid of the salt dissolved by the water upon a part of the lime of the binding material. Although the formation of the sulpho-aluminate of lime seems to be the principal cause of the decomposition of cement by sea water and sulphate waters, it may not be the only one: the setting and the hardening of the cement in contact with water result in the separation of compounds rich in lime, in salts less calcareous, and in free lime. According to the nature of the medium and the conditions affecting its preservation, this reaction may be modified or counteracted in such manner that the hardening cannot *Zamboni, Industria, October 15, 1899. fCiments et Chaux Hydrauliques, Paris, 1891, p. 257. jDer Cement-BacUlus, Berlin, 1892. §BuUetm de la Societe d'Encouragement pour I'lndustrie Nationale, 1900, I, p. 49. 274 • A TREATISE ON CONCRETE follow its regular course; likewise, the lime set at liberty may be aissolved little by little in the water which penetrates the mortars, and may disappear by exosmose, giving place to other more or less injarious compounds. These various phenomena are yet far from being satisfactorily explained, nevertheless, it appears that those cements which are richest in lime are the most quickly decomposed. SEARCH FOR BINDING MATERIALS CAPABLE OF RESISTING THE ACTION OF SEA WATER For a long time the efforts of experimenters have been directed toward finding a cement of such composition that it cannot be decomposed by sea water. Thinking at first that the destructive action of the water resulted from the substitution of the magnesia which it contained, for the lime of the cement, the idea was conceived of making cement by burning dolomitic limestone which consequently was composed largely of salts of magnesia. But it was found that the magnesia which this contained, since it was burned necessarily at a very high temperature, was slaked with great difficulty, and by its tardy hydration caused the mortar to swell. Cements were also made experimentally of baryta, a laboratory product whose high price does not permit its introduction into regular practice.* After the discovery of the sulpho-aluminate of lime, the question changed its aspect, and alumina was considered a dangerous element in cement, the proportion of which ought to be reduced as much as possible. At present the specifications adopted by the Administration of Public Works in France limit to 8% the maximum amount of alumina allowed in cement intended for use in sea water, and this limit would be placed much lower were it not for the fact that in many localities it would be very difficult to obtain products containing less alumina. On the other hand, the percen- tage of alumina cannot be greatly reduced without at the same time ren- dering more difficult the burning of the cement, in which operation this element acts as a flux. • Accordingly, it was suggested that the alumina be replaced by iron oxide. Cements have been made in the laboratory which were absolutely free from alumina and rich in iron, and these re- sisted sea water very well.f The various hydraulic cements and limes produced by the works of Teil, whose reputation is world-wide, contain not more than 2% of alumina, and some of them usually last much better * Le Chatelier, Annales des Mines, May and June, 1887. t Le Chatelier, Congris International des Maf^riaux de Construction, held at Paris in igoo. Vol. II. Part 2, p. SI- EFFECT OF SEA WATER UPON CONCRETE 275 in sea water than most of the Portland cements which contain between 7% and 8% of alumina. These too, however, become decomposed under certain conditions, but with this peculiarity — that their disintegration is not usually accompanied by any increase of volume. It has been noted that the cements which are the richest in lime decom- pose the most quickly in sea water. Based upon this observation, the experiment was also tried of making cements for marine use by burning mixtures less rich in carbonate of lime than the ordinary Portland cements. This diminished the strength uf the cement, but the falling off in strength was only of secondary importance. The principal difficulty lay in the process of manufacture. In burning cements of this class there was pro- duced in the kilns a considerable quantity of powder possessing only a comparatively feeble hydraulic power, which obstructed the draught. This difficulty was lessened by mixing ferruginous materials (ore, etc.), or even sulphate of lime,* with the raw materials before burning. Also, the use of rotary kilns prevents the choking of the draught. As has just been said, cements low in lime do not attain as great strength as the ordinary Portland Cements, but they generally resist the decomposing action of sea water better. When the proportion of limestone is small, the burning can be done only at a very low temperature, and the cement obtained sets very quickly. Some of these low lime cements appear to resist chemical decomposition satisfactorily, while others resist no better than most of the Portland ce- ments, a difference which has not yet been explained. In any case, on account of the rapidity of set, this class of cements cannot readily be used on large work, and, in fact, their use is mainly limited to special cases. Another means of neutralizing the bad effects of the excess of lime liber- ated by the setting of Portland cement consists in mixing with the latter, before using, materials capable of combining with this lime so as to pro- duce insoluble compounds. Puzzolans have been found to be the most useful material for this purpose. Laboratory tests, verified by experiments on a larger SGale,f have shown that mortars made in this way generally resist sea water better than if they had been made from similar cements without puzzolanic material. Sometimes, too, their strength is increased by this mixture. *CandIot, paper delivered at the meeting of the French and Belgian members of the Inter national Association of the Materials of Construction, on April 25, 1903. iFeret, Annales des Fonts et Chaussdes, 1901, IV, p. 191. 276 A TREATISE ON CONCRETE METHOD OF DETERMINING THE ABILITY OF A BINDING MATERIAL TO RESIST THE CHEMICAL ACTION OF SULPHATE WATERS One method is to gage the cement to be tested with sufficient water to obtain a plastic paste, spread this paste on glass plates so as to form caltes or pats with thin edges, immerse the pats in sea water, and observe them from time to time. But with this method the amount of deformation in the pats depends to a large extent upon the hardness of the paste at the time of. immersion, so that a cement which cracks when immersed before setting may stand a long time without showing any trace or alteration if the pat is not placed in contact with the water until twenty-four hours after gaging. Further, the surface of the pat is quickly covered by a crust more or less thick resulting from the partial carbonization of the freed lime, so that the substitution of magnesia for a part of this lime and the presence of this crust may influence the decomposition of the underlying cement. Another and more exact method consists in molding a block of cement or of mortar of a sufficient thickness; for example, a briquette such as is used for a tensile test. Allow this to harden in the usual way, say for twenty-eight days, then cut out from the center of this block a small solid parallelopiped with sharp edges, and immerse it in sea water or in a sulphate solution (saturated gypsum, sulphate of magnesia, etc.). In order to prevent all new superficial carbonization of the specimen, carbonic acid should not be allowed to come in contact with or be present in this liquid. When decomposition occurs in the cement it is indicated by cracks which appear at the edge of the parallelopiped after a lapse of a variable time. As a third test, sea water under pressure can be made to filter contin- uously through mortars made with fine sand. The author of the present chapter uses for this test mortars containing from 250 to 450 kilograms (551 to 991 lb.) of cement per cubic meter (35.3 cu. ft.) of sand (corre- sponding approximately to proportions 1:6 to 1:3 by weight) which he gages to a plastic consistency and molds into cubes 50 square centimeters (7.74 sq. in.) on a face, with a tube of brass penetrating to the center of the block. After a few days the brass tubes are attached with India rubber tubes to a vessel containing sea water under a head of 2 meters (6.52 ft.). The amount of water which flows through each cube in a given time is accurately measured from time to time, the cube being immersed in sea water in a glass receptacle, where the state of preservation of the mortar can be closely observed. Finally, the following quite rapid method is used in the laboratory at Boulogne. A mixture is made consisting of 100 parts of cement to be EFFECT OF SEA WATER UPON CONCRETE 277 tested and 300 parts marble ground to a fine powder. To this is added gypsum in the form of a very fine powder, varying progressively from 0% to 20% of the weight of the cement. Plastic mortars are then made from each of these mixtures, which are molded into prisms 2 by 2 by 12.5 centimeters (0.8 by 0.8 by 4.9 in.), allowed to harden for seven days in moist air, and then immersed in fresh water after the length of each has been exactly measured. The water is frequently renewed and at stated periods the lengths of the prisms are again measured, at which time their state of preservation is also examined. The ability of the cement to resist decomposition by sulphates is indi- cated by the time taken for the prisms to expand abnormally and to develop cracks, and also by the quantity of gypsum which the binding material is able to bear for a given time without deterioration. As a result of a long series of experiments, especially of those made by the last two methods, the conclusion has been reached that no binding material has as yet been found which will not be decomposed sooner or later when subjected to these tests, so that at present no cement can be looked upon as absolutely safe from the action of sea water. MECHANICAL PROCESSES OF DISINTEGRATION It seems possible to divide the phenomena of disintegration into two classes according as the destruction of the mortar is produced by a sort of progressive dissolution of its elements without appreciable change in volume, or as the products of decomposition, collecting in the pores, en- large them and produce a scaling off and a weakening of the mortar. Thfs second class of phenomena is much the more frequent and serious. In both cases decomposition may be produced when the mortar is simply immersed, because of the penetration of the water into its pores and its renewal by the double phenomenon of endosmose and exosmose. But when the masonry is subjected to different degrees of pressure upon its opposite faces, as is usually the case, this tends to establish a current of water through it and the replacement of the dissolving elements goes on more actively. However, disintegration may, under these conditions, pro- ceed more slowly if the current of water is strong enough to carry away the solid products of decomposition as they are formed. The writer has cited in a former paper* experiments which plainly show the difference between these two methods of decomposition: if lean mortars, made with the same cement and sands of different granulometric compositions, are kept in abso- lutely quiet sea water, those which disintegrate most rapidly are the ones ♦Annales des Fonts et Chauss&s, 1892, 11, pp. 106 to 116. 278 A TREATISE ON CONCRETE into whose composition there enters no fine sand, but only medium sand or, and above all, coarse sand. These latter are the mortars that contain the voids of largest size. On the contrary, if a series of similar mortars are subjected to a continuous filtration of sea water, those made from coarse sand remain intact, while decomposition is more and more active for mortars containing more and more fine sand. In practise this latter is the most frequent case, and, in fact, it has been verified that the destruction oj concrete or mortar by sea water has in most cases been due to the use oj too fine sands. This is a point which cannot be too strongly insisted upon, and experi- ments show that a rather lean mortar of coarse sand is much preferable to a mortar of fine sand, even when a very large quantity of cement is intro- duced into the latter. Fine sands ought to be banished relentlessly from sea water construction even when the cost of coarse sand is very high.* When stone is at hand, an excellent sand can be obtained economically by crushing it. PROPORTIONS FOR MORTARS AND CONCRETES From the preceding it is evident that the best means of fighting against sea water is to prevent as far as possible its penetration into the mortars and concretes, and accordingly to make these of great density. It has been suggested in a preceding chapter (Chapter IX) with what size of sand and what quantity of cement this result can best be attained in mortars : the author of the present chapter has ascertained that the maxi- mum density is obtained with a mortar composed of material having about two parts of very coarse grains to one of fine grains, including cement. Usually, natural sands, even the coarsest, contain a propor- tion of relatively fine sand sufiicient to make it useless to add more with the cement. If a sand is used from which the fine grains have been screened, and this is mixed with about one-half of its weight of cement, a mortar is obtained at once very dense and of great strength, but whose use would often be too costly. In such cases the cement can be replaced by a mixture of sand and cement prepared in advance, such as the product known as "sand-cement," for the making of which a few fac- tories have been built in Europe and also in America. It must be borne in mind, however, that this solution, excellent for mortars destined to remain in the air or to come in contact only with fresh water, would be poor to use in sea water, for very fine sand intimately mixed with cement separates its grains and increases the surface of attack, and various experiments have shown that this kind of mortar suffers severely in sea water. •See also, Feret, Baumaterialienkunde, 1896, p. 139, and "Le Ciment," 1896, p. tit. EFFECT OF SEA WATER UPON CONCRETE 279 For use in sea water, on the contrary, if a good puzzolanic material can be procured on favorable terms, it is advantageous to grind this with the cement to take the place of the^ne sand, so that in the mortar it may play both a mechanical and a chemical role, assuring to it a great density, and at the same time forming, with the lime freed by the setting, compounds which tend to harden the mortar and render it impermeable. For concretes it has not yet been possible to express a general law. However, maximum density appears to be attained, in general, when the fine grains, including the cement, constitute, according to conditions, from 25 per cent, to 40 per cent, of the total mixture, the remainder being made up chiefly of large aggregate with little or no medium sized mate- rials. In all cases it is necessary to see that the concrete does not con- .tain voids, and above all that the cement is not diluted by an excess of fine sand, which must always be considered as the greatest enemy of masonry in sea water. In every case the sea water should be prevented from coming in con- tact with the work for as long a time as possible, so that the setting of the cement may be already considerably advanced. Yet it must not be forgotten that when the mortar contains a puzzolanic material its hard- ening can be properly effected only in the presence of moisture. MIXTURES OF PUZZOLAN AND SLAG WITH CEMENTS Tests by M. Vetillart and the writer, described in detail in a paper pub- lished in Annales des Fonts et Chaussees, 1908, 1, page 121, indicate that Puzzolanic material may be of great value when mixed with Portland cement for concrete construction in sea-water, materially increasing the durability of the concrete without increasing its cost. The conclusions reached in these tests are as follows: The use of Puzzolan in hydraulic mortars in combination with the cement increases the strength, and in a great many cases appreciably retards disin- tegration by sea-water. It should be employed then, at least experiment- ally, in accordance with the following recommendations: Grind the Puzzolan to the fineness of Portland cement. Mix it mechanically with the cement so as to obtain an absolutely thor- ough mixture. For Portland cement and a good natural Puzzolan, take two parts by weight of cement to one part of Puzzolan. Select only Puzzolan of known good quality; the use of gaize slightly roasted is especially recommended. If other kinds of cement or limes are used with Puzzolan, or if the Puz- zolan is of doubtful quality,— especially if it is obtained from granulated slag or a similar industrial by-product, — determine the proportions of the mixture by means of preliminary trials based on tests of strength. 28o A TREATISE ON CONCRETE Add to the sand the mixture of cement and Puzzolan as pure cement would be added, and in the same proportions; mix and place the mortar in the usual manner. Always use for comparison with the Puzzolan mortar, specimens of mortar, of the same proportions and made under identical conditions, in which the mixture of cement and Puzzolan is replaced by the same weight of pure cement. Allow the Puzzolan mortar to harden in the presence of moisture. It is as yet impossible to suggest detail rules for the acceptance and con- trol of Puzzolan cements. The recommendation is made, however, that their ability to resist the decomposing action of the salts in sea-water be compared to the resistance of pure cements by means of the test with sul- phate magnesia already referred to.* VARIOUS PLASTERS AND COATINGS Various methods have been tried to prevent sea water from wetting masonry too soon, either by coating the work with materials designed to obstruct the pores, or by covering it with a layer more or less thick and more or less impermeable, consisting usually of a rich mortar, clay, bitu- minous materials, etc. This method of protecting the work is generally rather costly and is not applicable to all kinds of construction. Besides, it presents this disadvan- tage, that if by accident there is any break in the continuity of the cover- ing, the sea water finds a passage towards the heart of the masonry and creeps in from one place to another, so that often the coating offers only an illusory security. In certain cases, a coating is formed spontaneously by the carbonization of the lime in the parts of the mortar near the free surface, and this action is aided by the development of sea organisms such as sea-weed and shell- fish. This cause, together with the differences in the saltness and the temperature of the water, and the course of the ocean .currents, is the one which is most often called upon to explain why mortars decompose more quickly in some regions than in others. * .See also Annales des Ports et Chauss^es, 1908, I, p. 107- LAYING CONCRETE IN FREEZING WEATHER 281 CHAPTER XVI LAYING CONCRETE AND MORTAR IN COLD OR FREEZING WEATHER The results of practice and experiment with cement and concrete exposed to frost or cold, which are discussed in detail in the following pages, may be summarized as follows: (1) Concrete work in winter is more difficult and somewhat more expensive than in summer, but policy frequently makes winter work necessary and even economical, and with precautions to prevent freezing first-class work results. (2) The setting and hardening of Portland cement concrete, or mortar is retarded by the cold even if not frozen and the strength at early periods is low. (3) Concrete which has been frozen may attain eventually, after thaw- ing and hardening, an ultimate strength nearly as high as ordinary concrete. (4) A thin scale is apt to crack from the surface of concrete walks or walls which have frozen before thorough hardening. (See p. 282.) (5) Frost expands cement masonry or concrete and settlement results with the thawing. (See p. 282.) (6) Heating materials hastens setting and retards the action of frost. (See p. 286). (7) Salt and calcium chloride lower the freezing point of water and if used in small quantities do not appear to affect the ultimate strength of the concrete or mortar. (See p. 287.) EFFECT OF COLD OR FREEZING Cold, even if the temperature is not below freezing, retards the harden- ing of concrete and mortar. When also the cement or the sand possesses slow hardening properties, the concrete may remain soft enough to break with the fingers for several months after laying. This is particularly the case with concrete placed below ground, as in piles. On the other hand, concrete of Portland cement, even if actually frozen, will eventually attain after thawing fair ultimate strength with only slight surface injury, if moisture is present or applied to permit proper hydration of the cement. This freedom from much permanent injury from frost 282 A TREATISE ON CONCRETE may be due in part to the internal heat of crystalhzation, especially in the interior of a large mass. A thin crust about xs inch thick is apt to scale from the surface of granohthic or concrete pavements which have frozen, leaving a rough instead of a trowelled surface. A similar result occurs in walls. The settlement of masonry due to contraction from thawing is another factor that must be allowed for in case of freezing. This settlement occurs both in concrete and in stone or brick masonry. Failures of newly laid brick walls, for example, have occurred through the frozen mortar thawing out on the surface next to the sun, with a resulting settlement which causes the wall to topple over. If for any reason the concrete actually freezes during construction, care must be taken to be sure that any laitance or scum which had risen to the surface and which, when frozen, resembles good concrete, is chipped ofi. Freezing Experiments. An extensive series of tests of frozen mortars was conducted by Mr. Thomas F. Richardson during the construction of the Wachusett Dam in Massachusetts, indicating that Portland cement mortar is not permanently injured by freezing. The results of tests extending up to one year showed that although briquettes mixed one part cement and three parts sand, had less strength at the end of seven days than those which^had not been frozen, the frozen specimens after longer periods, especially at the end of one year, gave as high or higher strength than those kept at ordinary temperatures. Mr. Richardson describes* the tests which were made in the middle of winter as follows: During the progress of the masonry work on the Wachusett Dam briquettes were made each week and submitted to the same conditions as the masonry, the molds being filled with mortar and placed out of doors in the air, not in the water, immediately after filling. At the same time briquettes were made and kept in the laboratory, both in air and in water, those in the air approximating more closely the conditions which obtained on the masonry construction at the dam. About | of the briquettes out doors were exposed to temperatures as low as 9° above zero in the first 24 hours, and some of them to temperatures as low as 12° below zero in the first week. Salt was used in most of the experiments, the quantity ranging from 4 to 16 pounds per barrel of cement, the average being about 6 pounds or about 3% by weight of water. Our experiments indicate that 8 pounds of salt per barrel of cement is sufficient, even in the coldest weather, and the results from 4 pounds are very nearly as good; 16 pounds do not seem to give quite as good results. * Kindly furnished by Mr. Richardson for this Treatise. LAYING CONCRETE IN FREEZING WEATHER 283 The following table gives the average results of the experiments: Ejfect of Frost upon- Tensile Strength 0/1:3 Mortar. {See p. 282.) By Thomas F. Richardson. Briquettes Kept No. of Bri- quettes Tensile Strength, lb. per sq. in. 7d. 28 d. 3 mo. 6 mo. i yr, Water in laboratory Air in laboratory Out doors, below freezing-. 20 20 80 268 298 139 3°4 3S2 238 359 364 344 370 392 435 4wi 517 627 The briquettes were made in sets of S, consequently 4 experiments are shown for water and air in laboratory, and 16 fpr out doors. In France similar results have been reached by Mr. P. Alexandre* as to the effect of temperatures shghtly above freezing. Mr. Charles S. Gowenf also has concluded from his tests that "there is no indication that freezing reduces the ultimate strength of the mortar, although it delays the action of setting." AGE, DAYS Fig. 81. — Strength of Neat Portland Cement Mortar, 2-inch Cubes, Set in Air at Different Temperatures. {See p. 283.) The effect of different uniform temperatures upon neat cement mortar is illustrated in Fig. 81 by curves made up by the authors from a series of experiments by Mr. J. E. Howard| at the Watertown Arsenal. The results with sand mortars are similar to the neat cement. Specimens were stored for thirty days at temperatures of 70° Fahr. (21° Cent.) • Annales des Fonts et Chauss&s, iSgo, II, pp. 302 and 422- t Proceedings American Society for Testing Materials, 1903, p. 393. t Tests of Metals U. S. A. 1901, p. 530. 284 A TREATISE ON CONCRETE 38° Fahr. (3° Cent.) and 0° Fahr. (- 18° Cent.) Part were broken after setting one extra day at 70° Fahr. to thaw and the others were placed in a temperature of 70° Fahr. and broken one week and three weeks later. The balance were kept till 90 days old at the lower temperatures and then part broken and part placed at 70°. The curves show the low strengths even at the age of 90 days with the lower temperatures and the sharp increase as soon as the cubes were placed in warm air. Cold retards setting. Prof. Tetmajer* found, for example, that i : 3 Portland cement mortar which attains its initial set at 2f hours and its final set at 8| hours when mixed at 65° Fahr. (18° Cent.), at a tempera- ture of freezing reaches its initial and final set at 21 and 38 hours respectively. Effect of Temperature on Growth in Strength of Concrete . Tests at the University of Illinois! show that concrete stored at temperatures ranging from below freezing to about 90° Fahr. gains strength with age in proportion to the temperature. The lower the temperature the lower the strength at all ages, and the slower the growth in strength. Speci- mens subjected to alternate freezing and thawing disintegrated badly, but those maintained well below freezing gained slightly in strength. Fig. 82 indicates the effect of temperature on strength of concrete at different ages. The curves are drawn by the authors from the results of the tests, but are plotted to apply to concrete testing 2 000 poundsj per sq. in. at 28 days and 70° Fahr. (the common standard for i : 2 : 4 concrete). The diagrams may be used in practice to indicate approxi- mately the growth in strength of concrete in building construction. CONSTRUCTION IN FREEZING WEATHER It is frequently necessary to erect concrete structures in winter, not- withstanding the extra cost, because of the economic value of early use. In such cases full precautions should be taken to prevent freezing and, in fact, to guard against low temperatures, for temperatures slightly above freezing retard setting and hardening. Although the tests cited above indicate that concrete, frozen after mixing, attains some strength if allowed to remain long enough before subjected to alternate thawing and freezing, it is a dangerous proceeding to permit on account of the possibiHty of trouble and it should be avoided except under most extra- * Johnson's Materials of Construction, igo3, p. 6i6. t A. B. McDaniel. University of Illinois, Bulletin No. 8l, 2915. t The actual breaking strength in the 28 day tests was about 1365 pounds per square inch, a low strength even for soft limestone. LAYING CONCRETE IN FREEZING WEATHER 285 ordinary circumstances. If necessary to continue work through the winter, precautions must be taken by (i) careful selection of materials, (2) heating^of materials and (3) protection from the cold. Materials to Use in Cold Weather. Natural cement of ordinary composition, as is shown conclusively by tests and practice, never re- gains its strength after freezing, and therefore never should be used where liable to freeze. 2400 — 220C ^ ^ '' •- 2000 ST ^1800 y /" y #' ^ •^ lann 0^ -*? ^ '^ "Siuoo c f / ^ A V ^ /' ^4 >y ^ ---' " ^ 1200 / N ?> V? ^ ,'■ ^^ / '^^ -^ ^ ^ 1000 / Yi y \ ■»^ <> ^ / / / \ ^ r-' ^ 03 J i / / ^-^ ^ f 1^^ ^ ^ / / / > 1^ J^ ^ -— " a g 600 Q ■ / / ^^ ^^ r as ^ --- / / ^ y P 3, ^ ^ ^ -IflD / y'' ^5 ^ / y . -^ / ^- ^ 20 30 40 50 60 70 80 90 100 U lU CU OV/ «*U OU DU /U OU OU 1^ Average Temperature During Hardening in Degrees fbiir. Fig. 82.— Efifect of Temperature on Growth in Strength of Concrete. (5ee p. 284.) A slow hardening Portland cement (the hardening determined not by the set but by the tensile strength at early periods) should be avoided for cold weather use. Not only should the cement pass the Standard Specifications, but it is sometimes advisable to require a higher than usual strength (in the laboratory tests) at the 24 hour neat and 7 days sand mortar periods. It is frequently advisable to select a brand which normally gives high strength at these early periods. 286 A TREATISE ON CONCRETE Of equal importance with the selection of the cement is the choosing of the sand, especially should a fine sand or a sand containing even a minute quantity of vegetable loam be avoided, as the reduction in the early strength incident to this may even be a contributary cause for failure in cold weather. Heating Materials. At moderate temperatures of say 30° to 40° Fahr., heating of the materials is sufficient to prevent trouble, provided cement and sand are satisfactory. If a drop in temperature below freezing is liable, the concrete should be protected, as with canvas sup- ported so as to provide an air space, or with straw which is absolutely free from manure. The water, sand and stone should be heated and in extreme cases the reinforcement and the forms may be steamed just before placing the concrete and a steam jet may even be played into the mixer drum* to warm it up. To heat the sand and gravel or stone, steam pipes may be run as grids or flat coils through the bins or storage piles. It is possible to arrange the piles so that the material will drop through the grids when required for use so as to have a thorough and even heating. On small work, as for hand mixing, fires under boiler plates can be used but are inade- quate on large jobs.f If not too chilled, the steam from the sand and stone coils may be run to the water tank to be used there as a coil or a jet, the former being preferable. Water should be heated to 100° to 120° Fahr. Excessive heating should be avoided as it may accelerate too much the setting of the cement. Exhaust steam in any form, or live steam in a jet is of little use in heating concrete materials. Protection from Frost. Covering with straw or canvas is inadequate for low temperatures, say below 28° Fahr. unless artificial heat is used. In building construction in addition to heating the materials, which should be done in any case, it is customary in order to prevent freezing and maintain a temperature for proper hardening, to enclose in canvas as soon as the column forms are erected on a floor. Stoves or sala- manders are placed on the finished floor to keep the cold from the sur- face of the new slab, while on the newly laid work straw is spread, or better still, canvas supported so as to provide an air space which may be warmed by steam coils or by allowing warm air to come up from the floor below through holes left for the purpose. The number of stoves * See Engineerins Record March i6, 1912, p. 295. tA combined water, sand, and stone heater designed for easy transportation is illustrated in the second edition of this Treatise, p. 324. LAYING CONCRETE IN FREEZING WEATHER 287 or salamanders required depends upon the temperature. For low tem- peratures, say below zero, one stove for three hundred square feet* of area may be necessary, while ordinarily a stove for every six hundred square feet is sufficient. Care should be taken to prevent overheating, especially of granolithic surfaces, thus avoiding checking. Addition ol Salt. If the concrete is kept from freezing or from reach- ing too low a temperature, no further precautions are necessary. Salt, because it lowers the freezing point of water, permits the laying of con- crete at comparatively low temperatures. Glycerine and alcohol, have been experimented upon, but tend to lower the strength of the mortar. Salt should not be used where there is danger of electrolysis, nor in reinforced concrete where there is liable to be an excessive amount of moisture present. Rules have been formulated for varying the per- centage of salt with the temperature of the atmosphere. Prof. Tet- majer'st rule, for example, reduced to Fahrenheit units, requires 1% by weight of salt to the weight of the water for each degree Fahrenheit below freezing. A rule frequently cited in print, which practical tests by the authors have proved to be entirely inadequate, is to require one pound of salt to 18 gallons of water for a temperature of 32° Fahr. and an increase of one ounce for each degree of lower temperature. Since the temperature of the air usually cannot be determined in advance, an arbitrary quantity is as suitable as a variable one. In the New York Subway work in 1903, 9% of salt to the weight of the water was adopted! On the Wachusett Dam, during the winter of 1902, 4 pounds of salt were used to each barrel of cement. For i : 3 mortar this corresponded to about 2% of the weight of the water. Experiments show that ordinary "quaking" concrete in proportions I : 2| : 5 requires about 130 poupds of water per barrel of Portland cement, hence 10% of salt in average concrete is equivalent to 13 pounds per barrel of Portland cement. Ordinary i : 2| mortar requires about 120 pounds of water per barrel of Portland cement, hence 10% of salt in average mortar is equivalent to about 1 2 pounds salt per barrel of Port- land cement. Salt is sometimes added in sufl&cient quantity to "float a potato" or an egg. About 15% of salt to the weight of the water is required to float a potato, and about 11% to float an egg. * Turner Construction Company, Engineering News, September 24, 1914, p. 636 t Johnson's Materials of Construction, 1903, p. 615. 288 A TREATISE ON CONCRETE Recent experiments, by Mr. Gowen* and Mr. Richardson,! extending up to a period of one year, tend to show that salt in a quantity corre- sponding to at least io% of the weight of the water does not lower the ultimate strength of ordinary mortar. The time of setting, however, is considerably lengthened and the strength at short periods is lowered. The effect, at laboratory temperature, of io% salt with i : 3 Portland cement mortar is illustrated in the following table : Tensile Strength of 1 13 Mortars made with Fresh and Salted Water, By Charles S. Gowen. I week. I mo. 3 mos. 6 mos. 9 mos. 12 mos Fresh water used 112 183 26S 335 351 45^ Salted water used 68 131 215 266 301 413 In Mr. Richardson's experimentsj smaller percentages of salt proved beneficial. Portland cement mortar in proportions i: 3, mixed with 4 and 8 pounds of salt per barrel cement (corresponding respectively to about 2% and 4% of the weight of the water), gave slightly higher tensile strength, than the unsalted mortar at all periods from 7 days to one year. Experiments by Mr. E. S. Wheeler§ indicate that the use of 10% of salt tends to prevent the swelling of briquettes in the molds, even if the speci- mens freeze. Practical Proportion of Salt. Since, in practice it is impossible to tell how low the temperature' will fall before the concrete sets, Mr. Thomp- son has adopted the arbitrary rule of 2 pounds of salt to each bag of cement to be used when the temperature is expected to fall several degrees below freezing, and if experience shows this to be insufficient to pre- vent the frost catching the surfaces, 3 pounds of salt are to be used. The salt can be added most conveniently by putting it into the mixing water. To determine the amount of salt per barrel or per tankful of water, the quantity of water used per bag of cement must be noted and from this the amount can be readily figured. Calcium Chloride. Experiments indicate that calcium chloride added in quantities not exceeding 2% of the weight of the cement is an effective agent for lowering the freezing point of the concrete. It should be used with caution, however, since a larger quantity than this is likely to so hasten the set as to make the concrete diflScult to handle. ♦Proceedings American Society for Testing Materials, 1903, p. 393. ■j-Report Metropolitan Water and Sewerage Board, 1903, p. 112. JSee page 283. §Report Chief of Engineers, U. S. A., 189;, pp. 2963 to 2971. DESTRUCTIVE AGENCIES 289 CHAPTER XVII DESTRUCTIVE AGENCIES FIRE PROTECTION Tests and experience have proved reinforced concrete to be the best all-round building material in ability to resist fire. The surface of the concrete is apt to be injured, but the main body and the imbedded steel is amply protected against all but the worst fires. Hence, a proper thickness of concrete outside the steel, over and above the section re- quired to carry stress, acts as fireproofing during the fire and can be replaced or repaired if necessary, without endangering the structure. Just what constitutes a proper thickness depends upon conditions that vary from a small fire in an out-of-the-way passage to a conflagration. In members of little importance, Hable to low temperatures, only M inch of concrete is sufficient protection for the reinforcement; for main beams and columns, liable to ordinary fires, i]4 to 2 inches is needed; for slabs M to i inch is customary. Where there is a pos- sibility of such an intensely hot fire as that in the Edison plant at West Orange, N. J., in 1914, it is not economical to design with suffi- cient structural protection to insure against structural damage and an overhead sprinkler system and similar protective devices should be used. The question as to whether or not the protective covering in columns should be taken as a part of the section depends upon the conditions to which they are to be subjected. If the bmlding contents are liable to be inflammable, at least i3^ inches should be considered as protective covering and not included in the effective section. As for the concrete itself, the denser and richer it is, the more effective is its resistance. The character of the aggregate has a good deal of influ- ence; cinder concrete is a specially good non-conductor of heat, but too weak for important work. Of the stronger aggregates, trap is particu- larly good; any stone containing much quartz tends to spUt and cnmible, while limestone is more liable to disintegration. In the design certain precautions are feasible; columns can be built circular and sharp, pro- jecting corners avoided in all cases as far as possible, so that the flames cannot attack from two sides at once. Hooping will keep the vertical column steel from springing in case the concrete spalls off. 490 A TREATISE ON CONCRETE Repairs In Case of Fire. In ordinary cases the repairs to buildings injured by fire consist in removing all injured concrete and replacing with new mortar. To repair the unusually extensive damage done the Edison buildings* it was necessary to remove injured concrete, wind the reduced cross-sectional area with closely spaced spiral hooping — sup- ported by vertical spacing bars — ^place circular column forms, and £11 with mortar. In case the old vertical reinforcement had buckled with the heat, new bars were placed. Where complete collapse had occurred, the floor above was jacked up and a new column built. THEORY OF FIRE PROTECTION Mr. Spencer B. Newberry, in an address delivered before the Associated Expanded Metal Companies, Feb. 20, 1902,! gives the following explana- tion of the fire-proof qualities of Portland cement concrete: The two principal sources from which cement concrete derives its capacity to resist fire and prevent its transference to steel are its combined water and porosity. Portland cement takes up in hardening a variable amount of water, depending on surrounding conditions. In a dense briquette of neat cement the combined water may reach 12%. A mixture of cement with three parts sand will take up water to the amount of about 18% of the cement contained. This water is chemically combined, and not given o£E at the boiUng point. On heating, a part of the water goes off at about 500° Fahr., but the dehydration is not complete until goo° Fahr. is reached. This vaporization of water absorbs heat, and keeps the mass for a long time at comparatively low temperature. A steel beam or column embedded in concrete is thus cooled by the volatilization of water in the surrounding cement. The principle is the same as in the use of crystallized alum in the casings of fireproof safes; natural hydraulic cement is largely used in safes for the same purpose. The porosity of concrete also offers great resistance to the passage of heat. Air is a poor conductor, and it is well known that an air space is a most efficient protection against conduction. Porous substances, such as asbestos, mineral wool, etc., are always used as heat-insulating material. For the same reason cinder concrete, being highly porous, is a much better non-conductor than a dense concrete made of sand and gravel or stone, and has the added advantage of lightness. In a fire the outside of the concrete may reach a high temperature, but the heat only slowly and imperfectly penetrates the mass, and reaches the steel so gradually that it is carried off by the metal as fast as it is supplied. * Report on Fire of Edison Phonograpli Works, by the Natiooal Fire Protection Association and National Board of Fire Underwriters, January 30, 1915, p. 34. t Cement, May, igoi, p. e$. DESTRUCTIVE AGENCIES 291 TESTS OF FIRE RESISTANCE Prof. Ira H. Woolson of Columbia University has made several series of tests* to determine the effect of heat upon the strength and elastic proper- ties of the concrete and upon the thermal conductivity of the concrete and the imbedded steel. , Effect Upon Strength. Tests to determine the effect of heat treatment upon the strength and elastic properties of different mixtures showed that the trap concrete was least affected. Concrete two months old, in pro- portions I :,2 :4, the crushing strength of which before heating was about 2500 pounds per square inch tested in 7-inch cubes, after being subjected to a heat of 1500° Fahr. for two hours gave a strength of about 1000 pounds per square inch. However, since this reduction in strength was due at least in part to the reduction in the effective area because of the surface deterioration (if the surface was injured to a depth of i-J inches the effec- tive area would be reduced from 49 sq. in. to 20 sq. in.), it is probable that the interior of the blocks was affected very little. The concrete made with gravel, which in these tests was nearly pure quartz having a high coeflS- cient of expansion, was affected to a much greater extent. Cinder con- crete, which showed a normal crushing strength of about one-half that of the trap, after heat treatment gave a corresponding weakening. The modulus of elasticity of the concrete was always greatly reduced by heat treatment. CONDUCTIVITY OF CONCRETE AND IMBEDDED STEEL As a result of the conductivity tests, which were made upon specimens of trap, gravel and cinder concrete having thermo-couples for measuring heat transmission imbedded so as to indicate the temperature at points varying from ^ inch to 6 inches from the heated face, Prof. Woolson drew the following conclusions :f All concretes have a very low thermal conductivity, and herein lies their ability to resist fire. When the surface of a mass of concrete is exposed for hours to a high heat, the temperature of the concrete one inch or less beneath the surface will be several hundred degrees below the outside. A point 2 inches beneath the surface would stand an outside temperature of 1500° Fahrenheit for two hours, with a rise of only 500° to 700°, and points vnth three or more inches of protection would scarcely be heated above the boiling point of water. * Proceedings of American Society for Testing Materials, Vol. V, 1905, p. 335; VI, 1906, p. 433; VII, 1907, p. 404. + Proceedings American Society for Testing Materials, Vol. VTI, 1907. p. 408. 292 A TREATISE ON CONCRETE The fact that cinder concrete showed a higher thermal conductivity than the stone concrete would indicate that its well-known fire-resistive qualities are due, in part at least, to the incombustible quality of the cinder itself. The thermal conductivity of the gravel concrete* was fully as low as that of the trap, but the specimens of gravel concrete cracked and crumbled in many cases when the trap and cinder specimens under similar treatment remained firm and compact. In the tests on the conductivity of imbedded steel with the end project- ing from concrete. Prof. Woolson found practically the sanie results with concrete from all three aggregates. With the temperature of the end sur- face of the concrete and the projecting end of the bar 1 700° Fahrenheit, a point in the bar only 2 inches from the heated face of the concrete developed a temperature of only 1000° Fahrenheit, while at a point 5 inches in the concrete the temperature was only 400° to 500°, and at 8 inches the tem- perature reached only the heat of boiling water. From these results Prof. Woolson concludes that "where reinforcing metal is exposed in the progress of a fire, only so much of the metal as is actually bare to the fire is seriously affected by it." Tests by the National Fire Prote^ction Associationf in 1905 upon beams 8 inches by 11 J inches by 6 feet long, of different kinds of concrete, showed that the strength of rods imbedded i inch from the lower surface was reduced about 25 per cent after heating to a temperature of 2000° Fahren- heit for one hour. With rods imbedded 2 inches a similar reduction in strength occurred after 2 hours and 20 minutes heating, and the strength of the concrete was appreciably reduced to a depth of 4 inches from the sides and bottom. The hardest and densest mixtures were usually the poorest conductors of heat; the cinder concrete gave, however, a slower rise of temperature than the others. PROTECTION OF STEEL FROM RUSTING Concrete, if mixed wet, protects steel reinforcement from rusting. The wet concrete flows around the steel and forms a thin film of cement that prevents attack by impurities in the atmosphere or in the aggre- gates. If mixed dry, stone or cinder pockets will form along the steel in which rusting is liable to begin. Cracks due to load or to tempera-^ *As stated in connection with the tests on preceding page, this gravel was nearly pure quartz. In other tests, concrete with gravel containing a larger percent of slate or other similar material has given much better results. ^Cement, January, 1906, p. 173. DESTRUCTIVE AGENCIES 293 ture stresses are scarcely ever large enough at point of contract with the steel to afford the slightest danger. In razing buildings reinforcing and structural steel imbedded for many years in first-class dense concrete has been found in perfect condition. The structural steel in the Boston subway,* imbedded for twelve years in concrete or protected by the cement mortar joints of brick arches, was found upon examination during changes in the structure to be free from rust. The only exception to this was under the rather large base plates (21 by 24 inches) of columns, where a thin layer of rust frequently was found , having tubercles sometimes \ inch thick. This was evidently due to the settling of the finer parts of the concrete under the plates. The small base-plates were practically free from rust. It has been seriously questioned whether the minute cracks which open in a concrete beam and slab even under loads which are absolutely safe do not permit corrosion of the steel reinforcement. Tests by A. Probstf in Germany, in 1907, indicate very conclusively that steel in reinforced beams, laid in ordinary wet concrete used in practical construction, is in no danger of rusting through the cracks formed in the concrete under tension, until near the breaking point of the steel. The specimens, 34 beams, which contained both plain and deformed bars and rusted and unrusted steel, were subjected in loading to the action of a mixture of oxygen, carbon dioxide, and steam, for a period of from 3 to 12 days. Unprotected steel subjected to this mixture was badlyrustedintwohours. After breaking up the specimens of concrete no rust was found even on steel stressed to its elastic limit, although some was discovered on steel stressed nearly to its breaking point, which could be attributed to large cracks extending to the metal and uncovering it. EFFECT OF ACIDS Dilute acids will attack green concrete and prevent its hardening. Therefore, if concrete is to be laid under water the purity of the water both from acid and strong alkalis must be determined. The discharge of a pulp miU into a river may prevent the hardening of concrete bridge piers .built in the river below the mill, but concrete that is well cured win resist successfully such acids as those in sewage even if quite con- centrated. If acids from factory wastes are to be discharged direct to the concrete sewers, special investigations are necessary. • Personal correspondence with Mr. Howard A. Carson, Chief Engineer. t Report of the Royal Department of Testing Materials in Gross Lichtenfelde, West Prussia. 294 A TREATISE ON CONCRETE Manure has no effect on seasoned concrete, although it is Uable to injure green concrete. Strong, concentrated acids will attack nearly every material and con- crete is no exception, the acid acting on the carbonate of lime in the cement. Nevertheless, mortar is used either alone or in combination with tile as a lining for digesters in pulp mills, where sulphurous acid is present under high heat pressure, and also for lining acid tanks. An unlimited supply of ground water containing sulphuric acid will in time cause complete disintegration.* A dense rich concrete or mortar is essential in resisting acid action. The failure of sewage tanks in one or two cases has been traced to poor concrete. EFFECT OF ALKALIES There have been numerous failures in the West due to alkali in soil and ground water, but there can be no doubt that nearly all are due to failure to recognize the conditions and provide for them. A permeable concrete on the other hand allows ground water to filter through, de- positing salts that expand when crystallized and disintegrating the con- crete in a manner similar to the action of sea water described by Mr. Feret on page 272. EFFECT OF OILS Oils and fats — mineral, animal, and vegetable — can with few excep- tions be safely handled in buildings of first-class concrete that was properly set. Floors in soap factories and machine shops have shown no harmful injury in many years. In certain manufacturing processes, on the other hand, where animal fats are heated to high temperatures concrete has been badly disinte- grated. Concrete tanks are liable to attack in this manner and floor slabs above the tanks, if subjected to the steam or vapor from the tank. Cocoanut oil and olive oil have proved destructive in tests. Mineral oils usually have no effect. Cold lard oil has no effect. Mr. Tochf states that the action of fat or vegetable oil is due to expan- sion caused by the formation of crystals of sterate and oleate of lime. References to detailed accounts of the action of acids, alkalis, and oils, are given in Chapter XXXni. • New York Board of Water Supply, 8th Annual Report, 1913, p. 56. t Engineering News, April 20, igos, p. 419. DESTRUCTIVE AGENCIES 295 ELECTROLYTIC ACTION Injury to reinforced concrete from electrolysis is rare m practical construction, and much of the damage attributed to it has been due prob- ably to other causes. Plain concrete, as shovra by tests and experience, is never injured. The danger to structural steel, even if encased in con- crete, is greater than to reinforced concrete. In locations v/here electroly- sis is liable to be present, certain precautions should be taken, such as insulating electrical transmission and, since conduction is greatly acceler- ated by moisture, in making the concrete water-tight. Exhaustive tests by the Bureau of Standards* indicate two forms of injury from electrolysis; (i) When the reinforcement is positive, which occurs when the electricity flows from the steel to the concrete, rusting the steel with consequent splitting of the concrete; (2) When the rein- forcement is negative, the current flowing from the concrete to the steel, softening the concrete around the steel and destroying the bond. This softening of the concrete appears to be caused by the concentration along the steel, under the action of the current, of the sodium and potassium in the cement in sufficient quantities to attack the cement. High voltages (gradients of 60 volts or more per foot) are necessary to produce enough rusting to split the concrete; on the other hand with a negative current even low voltages may destroy the bond to the steel and this action is not easily detected until actual failure begins. In structures liable to electrolysis no salt or calcium chloride should be used in mixing the concrete, since the rate of corrosion is increased many hundreds of times by the presence of these materials and low volt- ages therefore may be dangerous. * Paper by E. B. Rosa, Burton McCollum and O. S. Peters; Journal-American Concrete Institute. November, 1(>I4. 296 A TREATISE ON CONCRETE CHAPTER XVIII WATER-TIGHTNESS Concrete with first-class workmanship may be made practically im- permeable on ordinary construction work by proper proportioning, mixing, and placing, and no other means, such as surface coatings, foreign ingredients, or membranes, need be used. Structures that are to be water-tight require special skill in design and construction; cracks must be prevented or at least controlled; proportions should be worked out for proper density; and the mixing and placing must be handled with care and skill. CONCRETE FOR WATERTIGHT WORK To secure water-tight work it is important to: (1) Adopt a fairly rich mix. (See p. 298.) (2) Proportion aggregates to secure a dense mixture. (See p. 298.) (3) Mix concrete to quaking or wet consistency. (See p. 298.) (4) Place concrete carefully to avoid stone pockets. (See p. 299.) (5) Lay entire structure if possible in one operation, without joints. (See p. 297.) (6) If joints are unavoidable, clean and roughen old surface, wet it thoroughly, and coat with a layer of neat cement paste. (See p. 297.) (7) Provide for contraction in long structures by special joints or by steel reinforcement. (See p. 297.) (8) For continuous structures or where poor workmanship is feared, introduce membrane waterproofing. (See p. 302.) If leakage occurs through concrete walls it is almost invariably through horizontal or vertical joints, through cracks caused by tem- perature contraction, or through porous stone pockets due to poor con- struction. Where these difficulties cannot be overcome or when the damage or inconvenience in case of leakage is liable to be considerable. it is economical to use some supplementary method. Of the three methods in general use mentioned above, textile or felt membranes coated with asphalt or tar pitch, although expensive, are most reliable, and are used to advantage on such structures as subways and bridges WATER-TIGHTNESS 297 where traffic must be maintained. (See p. 302.) The use of certain foreign ingredients is relatively cheap and in certain cases should re- ceive consideration. Nevertheless, the question should always be considered whether the ingredient should not be extra Portland cement. Surface coatings, with a few exceptions, are of doubtful value. A plas- ter coat mixed with some ingredient is likely to split off and is expensive to apply. Both integral waterproofing and plaster coatings fail in the event of cracks. Design and construction are of equal importance for structures that are to be water-tight. The special considerations are thickness of waU to prevent seepage, reinforcement to reduce effect of temperature contraction, and water-tight joints, proper proportioning, consistency, mixing, placing, and curing. Thickness of Wall. A wall properly designed to resist the stresses is generally thick enough to resist percolation of water. A minimum thickness under any condition may be considered as 6 inches, so as to give room for placing of reinforcement and proper placing of the con- crete around it. Examples are cited in Chapter XXXIII of a is-inch wall sustaining a head of 40 feet of water, and a 5^ foot wall, a head of 100 feet. Reinforcement. To avoid cracks in water-tight construction due to unequal settlement, shrinkage in setting, and temperature contraction, reinforcement always should be used except in mass work where special contraction joints are provided. The cross-sectional area of the steel should be at least f of 1% of the gross cross-section of the concrete. Where openings occur which reduce the cross-section, a httle more steel not simply in per cent, but in actual cross-section, should be used than in the sohd slab portion of the wall, because there is less concrete to assist in taking tension. At the point of reduction in height of a wall, additional reinforcement must be introduced because the stress at this point is governed by the cross-section of the higher wall. Expansion Joints. If cracks cannot be avoided entirely in reinforced concrete or if the construction is of mass concrete, expansion joints must be provided. To make the joints water-tight, copper or sheet lead flashing has been used in dams, subways, and walls. In reservoirs the joints have been filled with asphalt and the joint backed up by a reinforced beam or slab to prevent the water pressure forcing the asphalt out. Bonded Joints. To avoid percolation through horizontal joints be- tween two days' work, the surface of the old concrete must be absolutely 298 A TREATISE ON CONCRETE cleaned of all dirt, scum, and laitance, down into the true concrete. This surface must be thoroughly soaked and immediately before laying the fresh concrete a layer of neat cement paste (not dry cement) must be spread, using a thickness of at least | inch to J inch, and the new concrete placed before this has begun to stiffen. For vertical joints between two days' work, similar procedure is necessary in addition to the reinforcement, which should extend through the joint a sufficient distance for a complete bond. (See Chapter XXII.) ' Proportions. On important work it is advisable to make special laboratory tests for the determination of the best available materials and the proper proportioning and grading of the aggregates. Proportions for water-tight concrete range usually from 1:1:2 to i: 2§: 4^; the most common mixtures being i: ij: 3 and 1:2:4. With a small coarse aggregate up to, say, J inch, the concrete is not much better than a mortar, and rich proportions, such as 1:1:2 or i: i|: 3 are required; while with a coarser stone, up to say j^ inch, a i: 2:4 mix will be satisfactory. A stone larger than this, while theoretically better, requires more care in placing to avoid stone pockets. With accurate grading by scientific methods, such as are described in Chapter X, water-tight work has been obtained with proportions as lean as 1:3:7. (See p. 175.) In mass work, such as dam construc- tion, the authors have recommended, where fine crushed screenings are available, proportions as lean as i : 4: 7, using for the fine aggregate specially prepared screenings with a large proportion of dust. Lean proportions have the advantage over a richer mix of less shrinkage on setting and therefore less tendency to crack. A finer sand is permissible for water-tight construction than for maximum strength because in the former the size of the voids rather than the percentage of voids is one of the chief factors. Proportioning by mechanical analysis, as described in Chapter X, is the best way to produce a water-tight concrete with the leanest possible mixture. - Consistency. The maintaining of a proper consistency is one of the most important requirements for water-tight work. The sluggishly fiowing consistency, such as is recommended for reinforced concrete work (see p.. 251), is also best for water-tight construction. If mixed too dry, the mass is porous and will permit penetration of water and also the formation of stone pockets. If mixed too wet, the mortar will r-un away from the stones, leaving stone pockets, the cement will be v^j^eiiaicslly- effected (see p. 251), and there is a tendency to form laitance WATER-TIGHTNESS 299 on the surface of layers or even through the mass, which permits the penetration of water. Tests are given on page 319 showing the effect of different percentages of water on permeabihty, strength, and density. For maximum water- tightness a sUghtly softer consistency than medium quaking appears desirable. Mixing the Concrete. Care must be exercised to maintain the pro- portions accurately for every batch. Thorough mixing must be in- sisted upon. Much concrete is rushed through the mixer so rapidly that it is not thoroughly mixed, and an unnecessarily large part of the cement remains unhydrated and inert. Placing the Concrete. Special care must be exercised in transport- ing to avoid separation of the ingredients. Trowelhng, tamping, or' spading, which brings the cement to the surface (provided the mix is not wet enough to produce laitance) increases the surface tightness. The formation of water-tight joints has already been referred to (see p. 297). Caring Concrete. To avoid shrinkage and the formation of cracks, the surface should be protected for a period of at least a week or ten days. SPECIAL METHODS FOR WATERPROOFING If the concrete is made and placed in accordance with the recom- mendations on pages 296 to 299, no additional treatment or waterproof- ing is required except, as suggested, for very long structures where temperature cracks are unavoidable or in places where the importance of the structure or the danger of poor workmanship makes the extra cost of special methods permissible; also where an old structure made with poor concrete must be waterproof, special methods must be employed. SURFACE TREATMENT Surface Washes. Surface washes in general have been found in- effective.* Long time tests showed in certain cases fair results, but indicated the necessity of additional applications from time to time. Alum and lye wash has been used by the U. S. Army Engineers. C. B. Hegarbtf employed a mixture of one pound concentrated lye^ 2 to s pounds alum, and 2 pounds water. * See Report of Committee on Waterproofing MateriaJs, Proceedings American Society for Testing Materials, Vol. XIII, 1913, P- 4S9- t Report of Chief of Engineers, U. S. A., igo3, i>. 3483. 300 A TREATISE ON CONCRETE Grout. For a surface which is to come in contact with water and be kept wet a coating of cement grout spread on with a brush serves to fill surface voids and tends to assist in preventing penetration of water.* This is worthless if exposed to the air. Trowelled Surface. The water-tightness of horizontal or inclined layers can be greatly increased by troweUing the concrete. This brings the cement to the top and produces a hard dense surface. With proper precautions for bonding, a hard trowelled mortar may be applied also to set concrete, and if the concrete is not too porous may resist pressure even when placed on the back of the wall. Hydrolithic finish is a special treatment of this type. In experimenting upon the permeability of concretes, the authors have noticed that even the light joggling necessary to compact a wet concrete and the spading along the forms increases the impermeability of the surface. Even after chipping off the top of the specimen for a depth of I to J inch, the flow may be several times less than when the pressure is directed on the under surface of the concrete. Plastering. Ordinary plastering of the surface is usually ineffective unless it is placed on the back of a wall and an additional wall of brick or concrete built up against it. In any case it does not prevent the formation of contraction cracks. In constructing a subway station on the Hudson and Manhattan Railway under compressed air, a 2 -inch mortar coat of clay and cement, one part finely divided clay and one part Portland cement, was placed against the lagging and timbering of the tunnel and inside of this the concrete lining was built. The tunnel was water-tight under the high head of salt water. Granolithic Finish. On horizontal or inclined surfaces a granolithic finish of mortar may be laid and trowelled as in sidewalk construction, placing it immediately after the concrete is laid. Paraffin. Concrete has been effectively waterproofed by a coating of hot paraflSn. On the Strawberry Valley Projectf of the U. S. Recla- mation Service, concrete subject to a fluctuating head of water at a temperature of 50° Fahr. below zero, scaled badly and it was necessary to close the pores of the surface. The horizontal surfaces were cleaned and paraffin, boiled to drive off any water, was applied with a paint brush, and driven into the pores with a gasoUne torch. Alum and Soap. Vertical surfaces in this Reclamation work were •See J. W. Schwab, Transactions American Society of Civil Engineers, Vol. LI, 1903, p. 123; Enii- ntcrint News, Becember 5, 1912, p. io6i; and Zentralblatt der Bauverwaltung, October 2, 1912. \ Engineering News, April is, 1915, p. 707. WA TER- TIGHTNESS 301 water-proofed with successive applications of alum and soap solutions. The alum solution consisted of 2 ounces of alum per gallon of hot water, and the soap solution of | pound of castile soap per gallon of hot water. The alum solution was applied first and worked in with a stiff brush and immediately followed by the hot soap solution. The temperature of both washes was maintained at 100° Fahr. INTEGRAL WATERPROOFING While the addition of cement, that is, the use of rich proportions, is usually the cheapest kind of integral waterproofing, under certain conditions a mixture of foreign materials is beneficial from the stand- point of increased water-tightness or economy. One result of the intro- duction of foreign materials is the necessity of more thorough mixing than usual and part of the benefit may be attributed to this. The U. S. Bureau of Standards, after an extensive series of tests,* reports: "The addition of so-called 'integral' waterproofing compounds will not compensate for lean mixtures, nor for poor materials, nor for poor workmanship in the fabrication of the concrete. Since in practice the inert integral compounds (acting simply as void filling material) are added in such small quantities, they have very little or no effect on the permeability of the concrete. If the same care be taken in making the concrete impermeable without the addition of waterproofing materials, as is ordinarily taken when waterproofing materials are added, an imper- meable concrete can be obtained." Hydrated Lime. The addition of hydrated lime tends to reduce the size of the voids and increase the water-tightness of a comparatively lean mix. It also "greases" the mortar so as to make the concrete flow into place more readily. Whether it is economical to use, instead of additional cement, niust be determined in each individual case. The percentage of hydrated liine to use varies with the proportions of the concrete and the character of the materials. Permissible quantities in practice range from 5% to 15% of the weight of the cement.f Hy- drated lime paste occupies about 2^ times the "bulk of paste from the same weight of Portland cement. It is , therefore efficient in void filling. Unslaked lime must never be used under any circumstances. (See p. 172.) Pulverized Clay. Clay when finely powdered and free from any trace • Tests of Waterproofing Materials, by R. J. Wig and P. H. Bates, Technologic Paper No. 3, 1912. t "Permeability Tests of Concrete with the Addition of Hydrated Lime," by SanfordE. Thompson, Proceedings American Society for Testing Materials, Vol. VIII, 1908, p. soo. 302 A TREATISE ON CONCRETE of vegetable matter acts as a void filler. The proportion depends upon conditions, but about 5% of the weight of the sand is generally effective. Clay, acting as a colloid, in combination with an electrolyte such as alum sulphate, has been suggested* for increasing water-tightness. Pulverized Rock. For mortars i : 3 and leaner, the addition of finely pulverized rock increases water-tightness as well as strength, f Alum and Soap Solution. An integral mixture of alum and soap similar to the mixture described for surface treatment (p. 300) is terpied the Sylvester Process, and has been used with satisfaction in certain cases.f Mr. Albert Grittner of Budapest reports§ successful results in water- proofing concrete with an 8% solution of potash soap substituted for the mixing water. MEMBRANE COATINGS AND ASPHALT Membrane waterproofing, consisting of one or more layers of water- proof paper or textile material coated with tar or asphalt, is the most expensive treatment for waterproofing, but at the same time the most reliable where absolute security is required and especially where tem- perature cracks are apt to occur as in subways and other long structures. It has the advantage of being to some extent elastic and hence permits a certain amount of expansion and contraction without cracking. This is not true of surface and integral methods. On the other hand, leaks are liable to occur through poor workmanship or through failure under the action of impurities in the ground water and when this occurs the water may work along behind the lining and finally penetrate it, fre- quently at considerable distances from the original leak. Another disadvantage is that in subways and tunnels membrane waterproofing prevents the radiation of heat. This objection proved so great in New York subways 1 1 that it was decided to omit all waterproofing on the roof and the sides down to a point 2 feet above ground water line, taking special precautions to secure a good water-tight mix. The results have proved satisfactory. Brick laid in mastic are more durable than paper or fabrics in the presence of gas drip, organic matter, and other injuri- ous materials. * Richard H. Gaino in Transactions American Society of Civil Engineers, Vol. LIX, 1907, p. 159. t Sec Chimie Appliquie by R. Feret, 1897 pp. 477 and 493. tSee Report Cliief of Engineers, U. S. A., 1901, p. 918. i International Association for Testing Materials, 1912, XVj. II F. Lavis in Eniineerini Nms, November 5, 1914, pp. wo and IK7. WATER-TIGHTNESS 303 Much bridge work is waterproofed, to protect the steel and the traffic under the bridge, by one or more coats of asphalt alone or with fabric, or by asphaltic concrete. The vibration to which many bridges are subject, in addition to ordinary expansion and contraction, make the membrane method — relatively elastic — much to be preferred either to the surface or integral method. Expansion joints, where any material movement is to take place, should be filled with asphalt and covered with a copper plate; the asphalt and fabric will take care of small movements. The methods of placing and the properties of first-class materials are fully described in "General Specifications for Waterproofing Solid Floor Railroad Bridges," by Samuel T. Wagner in Transactions Ameri- can Society of Civil Engineers, Vol. LXXIX, 1915, p. 311. Tests of asphalts, felts, and fabrics, are appended to the specifications. Asphalt is generally to be preferred for structures subject to vibration or where ductility and adhesion are required. Coal tar pitch becomes brittle at 40° Fahr. and fluid in summer. In a general way pitch gives better results under water than asphalt, and asphalt is preferable to pitch when exposed to air. Method of Laying Paper or Felt. The waterproof layer of a floor may be laid directly upon the ground if the soil is fairly dry and firm, but is usually spread upon a layer of concrete from 4 to 8 inches thick. In the former case* the first layer consists of strips with a 2 to 6-inch lap ce- mented with asphalt, and the remaining layers are mopped on. Upon a concrete bass it is customary to first spread a layer of the asphalt or tar upon the concrete, although, if the concrete is damp, the bottom layer of paper or felt may be placed dry, as described above. The "ply" in waterproofing, — that is, the number of layers which cover aU parts of the surface, — varies from 2 -ply to lo-ply. It is con- sidered better practice to "shingle" the strips than to place each ply or layer independently. If the surface to be waterproofed is rough it may be leveled with cement mortar. It must be dry before applying the tar or asphalt. The asphalt is heated and brought, generally in buckets, to the work. Several roUs of paper are started consecutively. Ahead of each roll, as it is unrolled, the liquid asphalt is swabbed upon the concrete with a mop, so that the paper or felt is spread directly upon the fresh hot stuff. As soon as the first roll is started the second is placed to overlap the first, a width depending upon the number of ply to be laid. For example, if the felt is 32 inches wide and is laid • This method was followed in portions of the floor in the approaches to the East Boston Tunnel. 304 A. TREATISE ON CONCRETE 3-ply, the second roll is lapped upon the first about 22 inches. As this is unrolled (in the same general direction as the first roll) the surface ahead of it is mopped with asphalt, as described above. A third roll is immediately stafted, lapping both of the two others, and so on for the entire width of the surface to be covered. A waterproof course of this character always forms a distinct joint in the mass, thus destroying its cohesion upon that plane, and the strength of the concrete in bending on the two sides of the layer must be con- sidered independently. LAWS OF PERMEABILITY The following conclusions have been reached with reference to the permeability of concrete and mortar. Many of these are based on experiments of Messrs. William B. Fuller and Sanford E. Thompson as presented in the paper on "Laws of Proportioning Concrete"* and in the paper on "The Consistency of Concrete "f by Mr. Thompson. (1) The permeability or flow of water through concrete is less as the percentage of cement is increased, and in very much larger inverse ratio4 (2) The permeability is less as the maximum size of the stone is greater. Concrete with maximum size stone of 2}-inch diameter is, in general, less permeable than that with i-inch maximum diameter stone, and this is less permeable than that with |-inch stone. j: (3) Concrete of cement, sand and gravel, is less permeable than concrete of cement, screenings and broken stons; that is, for equal permeability, a slightly smaller quantity of cement is required with rounded aggregates like gravel than with sharp aggregates like broken stone.l (4) Concrete of mixed broken stone, sand and cement, is more per- meable than concrete of gravel, sand and cement, and less permeable than similar concrete of broken stone, screenings and cement; that is, for watertightness, less cement is required with rounded sand and gravel than with broken stone and screenings.:]: (5) Permeability decreases materially with age.| (6) Permeability increases nearly uniformly with the increase in pressure.! * Transactions American Society of Civil Engineers, Vol. LIX, igo?, p. 67. t Proceedings American Society for Testing Materlab, Vol. VI, 1906, p. 358. ■ J "Laws of Proportioning Concrete," by Fuller and Tiiompson, Transactions American Society Civil Engineers, \'oI. LTX. 1907, p. 72. , f WA TER- TIGHTNESS 30s (7) Permeability increases as the thickness of the concrete decreases, but in a much larger inverse ratio.* (8) Of mortars containing the same percentage of cement but of variable granulometric composition, the most impermeable are those containing equal parts of coarse grains, G, and fine grains, F (see p. 156), the latter including the cement, f (9) Decomposition by the passage of sea-water through mortars mixed in equal proportions by weight increases as the sand contains more fine grains.f (10) Medium and fairly wet consistencies produce concrete much more water-tight than dry consistencies, and slightly more water-tight than very wet consistencies.! (11) The surface of concrete as molded is much more water-tight than the bottom of a specimen, because of the fine material which rises to the top.t Fig. 83. — Permeability Specimen used by U. S. Bureau of Standards. (See p. 306.) * " Laws of Proportioning Concrete," by Fuller and Thompson, Transactions American Society Civil Engineers, Vol. LIX, 1907, p. 72. t R. Feret in .'innales de Fonts et Chaussfe, 1892, II, p. 109. t "The Consistency of Concrete," by Sanford E. Thompson, Proceedings American Society for Test- ing Materials, \'ol. VI, 1906, p. 358, 306 A TREATISE ON CONCRETE TESTS OF PERMEABILITY Permeability tests are made by forcing water under the desired head against one surface of a concrete block, the block being so confined that the only outlet for the water is through the block and out of the opposite side. A successful design used by the U. S. Bureau of Stand- ards is shown in Fig. 83, p. 305. The water is confined to the center of the face by rubber gaskets and the specimen itself remains in its cast iron form or mold during the test. Another less expensive apparatus designed by one of the authors is shown in Fig. 84. The pipe is enlarged to 4 inches diameter to give a good surface of concrete and to permit thoroughly chipping it, while at the same time the external pipe connections are small, so that tight joints can be made readily. The walls of the mold may be coated with neat cement as well as the bottom, if desired, the concrete being placed in any case before the neat cement has begun to stiffen.* CHIPPED SURFACE - ■'.■■■/^." 7 :o.:'o"/."oCbNOR,ET,E" ?.'£?■ O-r" W, v:''^-P:^''-'f- : ^.v ;.■ -«■"■■-; - ■:■■.!-- • ■ ■-., 1 j( [( :.:,CHlP,PE-D:3L^RFACE'^^_£^^fj:';4.x,3,'nE0UCINQ - ;,')/ h"P''U^'^" ^.^[ ^T^-~~- COUPLING . 3 CLOSE NIPPLE JOINT NOT MADE UP I CLOSE NIPPLE 3 HOLE THROUQH^^; ir^ 3 J^ t REDUCING COUPLING BOTTOM OF FORM ^."jji^ CONNECTED WITH CITY PRESSURE Fig. 84. — Detail of Specimen for Testing Permeability. (See p. 306.) In testing, allow no water to pass along the face of the specimen, between the concrete and the mold. Cut down the surfaces, through which the water enters and leaves the specimen, so that the effect of the more impermeable skin coating will not confuse the results. Make the mix uniform and to insure this govern the size of the specimen by the maximum size of aggregate and use enough water to give a medium wet mix that works easily. Use a shght excess of fine sand to prevent large voids; small voids are less Ukely to be continuous through the concrete. If a coating of neat Cement is used on the sides of the block to prevent • For example -of the method adopted in earlier experiments, see "Consistency of Concrete," ford E. Thompson, Proceedings American Society for Testing Materials, Vol. VI., 1906, p. 374. San- WA TER-TIGHTNESS 307 the escape of the water, the coat must be molded with the concrete or else the hardened concrete must be chipped rough and soaked with water before applying the paste. Soak the specimen 24 hours before testing. RESULTS OF TESTS OF PERMEABILITY The following tests bear out the foregoing discussion on the behaviour of concrete under water pressure. The first table given is a summary of tests carried out by the Bureau of Standards and shows the decreased permeability due to increase in thickness, rich proportions, and age. Ejfect of Age, Thickness, and Amount of Cement on PermeMlity of Concrete Summarized from tests by U. S. Bureau of Standards' {See p. 307.) Leakage given in grams per minute after 7 hours. Pressure about 20 pounds per square inch. Concrete mixed with river sand and broken limestone. Area of specimens about 20 sq. in. Specimens 2 inches thick. Specimens 3 inches thick. Proportions. Age in Weeks. Age in Weeks. ■I 8 26 4 8 26 1:2:4 1:3:6 1:4:8 grams 0.628 1. 140 2.160 grams 2.02 grams grams moist 0.2S5 10.280 grams a i.650 grams 12.040 •Technologic Paper No. 3, by Rudolph J. Wig and P. H. Bates, 1912, p. go. The foregoing results as regards richness check those obtained by Messrs. Fuller and Thompson at Jerome Park in 1906. These tests shown in the following table indicate that (i) Gravel and sand make a more water-tight mix than broken stone and sand, which in turn is better than broken stone and screenings; (2) Richness of mix increases very materially the water-tightness, especially in the case of broken Stone and screenings; (3) Flow increases with the increase in pressure and nearly in proportion to it. The flow in these tests remained nearly constant for four hours, but the water was pure and the surface of the concrete clean. In practice these conditions do not hold, and the seepage through concrete may be expected to decrease regularly as the pores silt up. Bfiect of Thickness of Concrete Upon Permeability. Other experi- 3o8 A TREATISE ON CONCRETE ments, not here recorded, indicate that the rate of flow increases as the thickness of the concrete decreases, but in a much larger inverse ratio. Specimens 17 inches in length in proportion i :6.5 by weight were prac- tically water-tight, whereas specimens of half that length were not. Effect on Permeability of Percentage of Cement, Character of Aggregate and Pressure, By Fuller and Thompson* (See p. 307.) Thickness of Specimens 18 inches. Area of contract 36 square inches. Maximum diameter of stone 2 J- inches. PBOPOR- TIONS BY PERCENTAGE OP CEMENT TO TOTAL DRY MATERIALS KIND OF MATERIAL TIME IN WHICH WATER APPEARS AFTER STARTING PRESSURE RATE OF FLOW OF WATER IN GRAMS PER MINUTE, AT 'THE FOL- LOWING PRESSURES, PER WEIGHT Stone Sand -% min. 20 1b. 40 1b. eo lb. SO lb. I : II. 5 8.0 Crushed stone Screenings 7 25 161 237 273 I : 9 10. II " 3 II 24 37 49 I : 7 12. 5 « 3 15 22 30 38 I 5.8 I5-0 „ " S-5 5 8 10 12 I : 8.8 10. 2 Crushed stone Sand 9 4 II 17 22 1:6.9 12.7 ^j 10 2 1 3 3 I : 5-S 15-6 ,1 " ^.7 1-4 I 10.8 I : 8.4 I : 6.5 8-S 10.6 13-0 Gravel Sand 3 17 100 15 I 25 3 38 5 43 6 I : S-3 15-9 98 i-4 Effect of Size of Stone on Permeability By Fuller and THOMPSONt (S^e p. 309.) Thickness of Specimens 18 inches. Area of contact 36 square inches. Aggregates, crushed stone and natural sand. PROPORTIONS BY WEIGHT PERCENTAGE OF CEMENT TO TOTAL DRY MATERIAL MAXIMUM SIZE OF STONE TIME IN WHICH WATER APPEARS RATE OF FLOW OP WATER IN GRAMS PER MINUTE AT THE FOLLOWING PRESSURES PER SQ. IN. % in. min. 201b. 401b. 601b. 801b. I 2.9 . 5.7 I : 2.9 : 5.7 I : 2.9 : 5.7 10. 2 10. i! 10. 2 2i I i .1 29 I 4 5 10 8 10 17 12 IS 20 • Transactions American Society Civil Engineers, Vol. LIX, 1907, p. 132. t Transactions American Society of Civil Engineers, Vol. LIX, igo?, p. 136. WA TER-TIGHTNESS 309 EflEect of Size of Stone upon Permeability. The foregoing table gives the comparative permeability of concrete in the same proportions mixed with stone of different maximum size. The difference in this case is evidently due to the greater density of the concrete composed of the large stone. Effect of Coarseness of Sand upon Permeability. The effect of size of sand is shown in the following table and shows, as do tests by Mr. Feret, that more fine sand is required for maximum water-tightness than for maximum strength. Tests to determine Relative Permeability of Concrete with Coarse and Fine Bank Sand By Sanford E. Thompson. {See p. 309.) Proportions 1 : 3 : 6 by Volume or i : 2.8 : 5.7 6.3; Weight. Age 32 days CHARACTER Or SAND DENSITY c + s + g W4TER PASSING IN GRAMS PER MINUTE (i) All coarse 0-853 0.846 0.843 0.813 I4S-I IO.4 43-0 3°-^ (2) 4 coarse, i fine (^) 4 coarse, h fine (4) All fine Analyses of Natural Bank Sand and Screened Gravel used in Tests TOTAL PER CENT PASSING SIEVES Coarse Sand Fine Sand Screened Gravel I inch % 100 88 77 32 3 % 100 96 27 % 100 50 No. K TnJo 40 References to permeability tests on concrete and patented compounds are given in Chapter XXXIII. 3IO A TREATISE ON CONCRETE CHAPTER XIX STRENGTH OF PLAIN CONCRETE The strength of plain concrete, that is, of concrete without steel reinforcement, is governed primarily by (i) The quahty of the cement. (2) The texture of the aggregate.* (3) The quantity of cement in a unit volume of concrete. (4) The density f of the concrete. (5) The thoroughness of mixing. (6) The consistency. The effect of the percentage of cement and the density of the concrete, which are of special importance to the user in determining the propor- tions of materials may be expressed more explicitly as follows: (1) With the same ag^egate the strongest concrete is that containing the largest percentage of cement in a given volume of concrete, the strength varying nearly in proportion to this percentage. (2) With the same percentage of cement but different arrangements of the aggregates, the strongest concrete usually is that in which the aggre- gate is proportioned so as to give a concrete of the greatest density, that is with the smallest percentage of voids. In many cases relative den- sities nearly correspond to relative weights. The amount of water is a most important factor. A very wet mix wiU give a concrete two-thirds or less as strong as a concrete of medium consistency made of the same materials. (See p. 315.) These various characteristics and others are discussed in this chapter, which takes up the compressive strength of plain concrete, the tensile, shearing, and transverse or bending strength of concrete, and the testing of concrete specimens. COMPRESSIVE STRENGTH OF CONCRETE A compressive strength of 2 000 pounds per square inch may be expected of first-class concrete of medium consistency, in proportions one part cement, 2 parts sand, 4 parts broken stone or gravel, at the age of 28 days; at 14 days about i 600 pounds may be expected, and • The word aggregate is defined on page 9. t The meaning of density ia illustrated on pages 133 and 134. STRENGTH OF PLAIN CONCRETE 311 at 7 days about i 300 pounds. At one year the strength increases to about 3 500 pounds and at two years to about 4 000 pounds, provided the conditions are such that moisture has access to the concrete. In dry atmosphere the increase after 28 days is comparatively small. The compressive strength of concrete is affected by the characteristics of the cement. Certain cements harden faster than others, giving higher strengths at early periods; while other cements harden slowly but eventually obtain strengths as high or higher than those reached by the quicker hardening cements. The strength of two concretes of different proportions made with the same cement is approximately proportional to the percentage of cement in the mixture and a rough idea of comparative strengths can be obtained from this rule. More exact methods of determination and the various conditions affecting the strength are discussed in the pages that follow. In considering the effect of the amount of cement upon the strength it must not be forgotten that the character of the aggregate and the relative sizes of particles affect the strength to a marked degree. Fre- quently, by proper selection and proportioning of aggregates the required strength can be obtained at much less cost than by increasing the amount of cement. Safe Strength of Concrete. Working unit stresses are discussed fully in the chapter on Design of Reinforced Concrete. The percen- tage of the ultimate strength that may be used varies with different kinds of stress and the character of the structure. For different pro- portions and conditions the discussion in the following pages may be used as an aid to the judgment. The importance of the structure governs to a certain extent the stresses to be used and relatively high values frequently may be used with conservatism. Many times, however, concrete that will ultimately carry very light loads must be strong enough to do so a short time after placing and a much richer mix and larger sections must be used than would otherwise be necessary. Strength of Proportions in Practice. In selecting proportions to use in any structure the strength which can be attained at the required age with the available materials must be considered. In some cases a high strength required at early ages, because of immediate loading or early removal of forms, may necessitate a richer concrete than would be selected for a similar structure which carries but little dead load and does not receive its load for a considerable period after placing. If a wet consistency is to be used because of certain conditions of economy 312 A TREATISE ON CONCRETE in construction due allowance must be made in determining proportions for the relative weakness of a wet mixture. The refinement to which proportioning of aggregatesshouldbecarried, in accordance with Chapter X, must be governed by practical consider- ations. It is wise in any case to give due consideration to the possi- bility and to figure the relative costs of different methods of treatment. S. ■a a 1.8 o 1.7 ^ 1.6 S. \B — — — — — — — — 1 "~" ' __- " 1 \-? F ■^ y F .= ^ ].IC " n,^:p IS Vi '-r, ^7.' fl' .=,- n" ,- ' ^ :|3- Li / c '•' O 1.0 "gos §05 -f z' y f? M^ r.3 5, r- / ' • 1 :4k ^ 4-7 "w 4 ott2 ■•go.1 § 1200 la 800 eoo 400 200 0i02 0O4. 006 008 0.10 ai2 0.14 ai6 0.18 0120 022 024 026 Ratio of Parts of Cementto Total Parts of all Materials Including Cement Proportions adopted on the dash line are those giving, eor average con- ditions, MIXTURES WITH VOIDS WELL PILLED. STRENGTHS ARE BASED ON author's FORMULA, CONPIRMED BY TESTS. Fig. 8s.— Approximate Crushing Strength of Concrete of the Same Materials in Different Proportions. {See p. 313.) Diagram for Compressive Strength. The approximate relative strength of concrete made with the same aggregates in different pro- portions is shown by the diagram, Fig. 85 page 312. The diagram may be read in terms of ultimate strength with 1:2:4 concrete considered as 2 000 pounds per square inch; also in ratios which may be used conveni- ently when the strength of the i : 2 : 4 concrete is more or less than this. Vertical Imes indicate the proportion of cement to total material in- cluding the cement. Thus the proportion or ratio of cement in the 1:2:4 mixture is \ or 0.143. The light line in the diagram indicates the strength for standard STRENGTH OF PLAIN CONCRETE 313 proportions, using approximately twice as much coarse as fine aggregate. For rich mixes the proportion of sand is slightly decreased and for lean mixes the proportion is increased, because the cement acts with the sand in filling the voids in the coarse aggregate. To find the compressive strength of concrete in any proportions or the ratio of strength to that of 1:2:4 concrete, select the proper point in the diagram, or else interpolate between values given, and foUow horizontally to the left. Formula for Strength of Concrete. The diagram described is made up from a formula which in turn is based on a large number of tests. The formula is useful in estimating the strength of other proportions than those covered in the diagram, and also for comparing the strength of special mixtures and materials with different percentages of voids. The formula is similar in a general way in form to Feret's formula for strength of mortar. (See p. 155.) Let P = compressive strength of concrete in lb. per sq. in. c = barrels of cement per cubic yard of concrete. s = cubic yards of sand per cubic yard of concrete. g = cubic yards of gravel, or stone, per cubic yard of concrete. 0.1 is an empirical constant. M =3. coefficient varying with the strength of the cement, the texture of the coarse aggregate, and the age of the speci- men, but constant for aU proportions of the same materials mixed and stored under similar conditions. A table of values of M is given on page 314. Oj = voids in sand. Vg = voids in gravel. 37(1 weight of a barrel of cement ""^ 62.3 X 3-1 weight of a cubic'foot of water X specific gravity of cement Then |_27- 1.9SC-27 [(i -Vs)s + (i- v^)g] °'^j (i) Assuming the specific gravity of cement to be 3.1, the specific gravity of sand and stone to be 2.65, and the voids in the sand and stone to be each 46%, the formula becomes ^= ^[13.85-^ -7.48 (. + g)-°"] (2) 314 A TREATISE ON CONCRETE The values of c, s, and g can be obtained from the tables of quantities of materials, page 214, or may be computed from the formulas on pages 210 to 212. The term in the large brackets, that is, without the M, may be used as a ratio. The values of the coefficient, M, which may be adopted for different conditions, are given in the table below, and when substituted in the formula give P in terms of pounds per square inch. It must be understood that the formula is only correct when the voids of the coarse aggregate are filled with fine aggregate and cement; thus the formula would not be correct for such proportions as i: i: 6, in which the voids of the coarse aggregate evidently are not filled. Approximate Values oj Coefficient, M , for Use in Formulas (j) and (2) {See p. 313) Note that these are not strength values VALUES OF COEFFICIENT M Age. Granite or Trap. Gravel or Hard Limestone. Soft Limestone or Sandstone. Cinders. Consistency. Consistency. Consistency. Consistency. Medium. Very Wet. Medium. Very Wet. Medium. Very Wet. Medium. Very Wet. 7d. 2 480 I 360 2 260 I 220 I 700 920 680 370 14 d. 3 020 I 780 2 740 I 610 2 060 I 210 830 490 I mo. 3 780 2 330 3 440 2 120 2 580 I 59° I 040 640 3 " S 130 2 790 4 660 2 54° 3 Soo I 900 I 410 760 6 " S 870 3 780 5 330 3 440 4 000 2 580 I 610 I 040 I yr. 6 700 S 030 6 080 4 570 4 55° 3 420 I 840 I 380 For small sized stone, say J inch maximum, the values should be reduced about 20%. Example: What approximate strength at the age of six months may be expected of a granite concrete of medium consistency in proportions 1:2:5 made with special aggregates, ths sand having 46% voids and the stone 40% voids ? The specific gravity of the cement is 3.1 and a barrel of 4 cubic feet weighs 376 pounds. Solution: From Quantity Tables on page 214 the proportions require 1.26 bar- reb cement ; 0.37 cuDic yards of sand ; and 0.93 cubic yards of stone. From the table on page 314 we find the value of the co-efficient, M, to be 5870. Substituting these values and also the voids in formula (i ) gives P = 5870 f 2 rr — L27- 2.46- 27 [(i- 2.46 0.46J 0.37 + (i — 0.40) 0.93] -...] ot P 2950. STRENGTH OF PLAIN CONCRETE 315 COMPRESSIVE STRENGTH OF CONCRETE IN PRACTICE From study of a large number of actual tests of concrete specimens, confirmed by numerous tests of concrete cut out of completed structures, it is possible to present approximate values for the strength that may be expected with different proportions of mixtures. These strengths are based on a fair quality of aggregateandcommercialPortlandcement. Strengths are given for two different consistencies: (i) medium, which may be assumed to include not only a plastic mix but a mix of a con- sistency of very thick pea soup in which the coarse aggregate will not separate from the mortar in handling or in flowing down a slope, in fact, a mix just wet enough to flow very sluggishly into the forms and around the steel in reinforced concrete construction; and (2) very wet, or sloppy consistency representing a very wet mixture in which the mor- tar readily separates from the stones. These of course are simply rela- tive terms, the strength gradually decreasing with the addition of water as soon as the sluggishly flowing consistency is passed. With accurate grading of the aggregates, as stated on page 310, the strength may be increased without additional cement. Relation of strength as affected by different coarse aggregates is indicated in the table on page 316. A dry mixed concrete is somewhat stronger at the age of one month, but approximately the same at the age of six months, as the medium con- sistency. Conditions of storage, as indicated on page 320, may appreci- ably affect the growth in strength. The following table presents the approximate strength that may be expected of first-class concrete of different proportions, ages, and consistencies, tested in cylinders 8 inches in diameter by 16 inches high. Instead of assiuning nominal proportions, where the volume of sand is Approximate Compressive Strength of Concrete With Coarse Aggregate sttch as Gravel, Granite, or Hard Limestone. (See p. 315.) Medium Consistency. Very Wet Consistency. Proportions by Volume. Age z mo. Age 6 mo. Age I mo. Age 6 mo. lb. per sq. in. lb. per sq. in. lb. per sq. in. lb. per sq. in. i: i: 2j 3 240 5 020 I 990 3 260 • i:iJ:3i 2 470 3 830 I 520 2 480 1:2:4 2 000 3 100 t 230 2 010 i:2|:4f 1 650 2 560 I 020 I 660 1:3:5 I 500 2 320 920 I 500 1:4:7 I 060 I 640 650 I 060 3i6 A TREATISE ON CONCRETE one-half that of the stone, more practical relations are chosen which allow for the effect of the cement and sand in filling the voids. The values agree with the formula given on page 313 and with Fig. 85, page 312. Maximum Strengths Recommended by the Joint Committee. The Joint Committee on Concrete and Reinforced Concrete, recommend the following maximum values for ultimate strength to be used in de- sign. To use for working stresses and to allow a sufficient factor of safety, these of course, must be multiplied by the required percent- ages. (See Chapter XXII.) Limiting Strengths of Different Mixtures of Cgncrete Suggested by Joint Committee (In Pounds per Square Inch) Aggregate. l:i;2 i:ii:3 1:2:4 i:2i:s 1:3:6 Granite, trap rock Gravel, hard limestone, and hard sandstone 3 300 3 °o° 2 aoo 800 2 800 ' Soo I 800 700 2 200 2 000 I SCO 600 I 800 I 600 I 200 500 I 400 I 300 I 000 400 Soft limestone and sandstone. . Cinders Relation of Percentage of Cement to the Strength of the Concrete. As already stated, the strength of a concrete varies approximately with Comparative Density and Strength of Similar Concrete with Different- Percentages of Cement and 2\-inch Stone Graded as an Ellipse and Straight Line Bv Fuller and Thompson. {See p. 316.) Materials. Density with Difh-ehent Percentages of Cement* Modulus of Rupture at 90 Days, Different Percentages or Cement.* Compressive Strength AT 140 Days, Dif- ferent Percentages OF Cement. Stone. 1 Sand. 8% 10% j 12i% 15% s% 10% iH i5% 8% 10% "i% iS% Crushed Screenings Sand 0.829 I i88 980 " 0.846 25o . I 129 148 " 0.832 24S " 0.839 326 I 634 " 0.871 163 990 Gravel 0.8S5 245 I 7i5 " 0.865 307 I 890 " 0.867 339 '.'.'.'.'.'. 2 040 Averages o.85o o.85o 176 176 248 220 276 275 332 330 98S 985 I 428 12 30 I 6S4 I 540 I 837 Strength centage 8%ceni jomputed as proportional to the per- of cement, based on strength with ent * In gravel and sand mixtures the percentage by weight of cement was increased in each case to balance the difference in specific gravity between this and the crushed material STRENGTH OF PLAIN CONCRETE 317 the percentage of the cement in the mass so that this relation may be used as a rough guide for practical purposes. The preceding tabie gives the results of the Jerome Park tests* by Messrs. Fuller and Thompson, where the density of the concrete was maintained nearly constant. The actual compressive strength and also the modulus of rupture is low because a very wet mixture was used in making up the specimens. In these tests, the strength of the concrete with screenings was less than with sand. I ... , 3 JisriO'- ^ { f 5" 1 -^VS^SiQ- "S ~/.t 4 Weijot- siPJSR-^ y h ( 5 cs 4000 5500 3000 2500 iS Z^iOOO I >, rsoo g" «> ^^1000 I 500 "0 7/42/26001/3 ZMo. 6M» /lye at Tim e of Breaking Fig. 86. — Growth in Strength of Concrete of Wet, Normal, and Dry Consistencies. {See p. 318.) Effect of Consistency. The reduction in strength of concrete by the use of an excess of water is very marked. Very wet concrete, such as is sometimes used in practice in order to flow down a chute of flat slope, never attains the strength secured by a more plastic mixture and should never be used where normal strength is required by the design. Tests and experience show that even for reinforced concrete building construc- tion it is possible to use a very slow flowing, sluggish consistency that will fill the forms and imbed the steel without being so sloppy as to affect appreciably the ultimate strength. (See p. 250.) Concrete made with a dry mixture attains higher early strength than medium consistency up to the age of, say 6 weeks, when it is apt to be overtaken and passed by the wetter mix. In scarcely any case, therefore, is it wise to use in practice a mixture in which the concrete requires appreciable tamping to bring the mortar to the surface. * Transactions American Society of Civil Engineers, \'ol. LIX, p. 67, 1907. 3i8 A TREATISE ON CONCRETE The relative strength of very wet, medium, and dry mixed concrete at different ages is shown in Fig. 86, page 317. These tests are based on experiments made by various laboratories under the direction of the Aggregate (^ommittee of the American Concrete Institute.* The curves in Fig. 87 are plotted from experiments by the authorsf upon the strength, density J, and permeability of the concrete mixed with different percentages of water. In the three curves the points of maximum density, strength and water-tightness all lie not far from the medium quaking con- sistency, although for maximum water-tightness a still softer consistency appears to be slightly more efficient. These tests further indicate that (i) the consistency which will pro- duce the densest concrete will result in the greatest ultimate strength pro- vided an excess of water is not employed; (2) dry mixtures attain highest strength at short periods, but mixtures of quaking consistency approach the dryer specimens after longer setting; (3) very wet mixtures, especially of lean proportions, may be chemically injured, by excess of water. Effect of "Laitance." Whenever concrete is laid under water, the water is likely to be clouded by what appear to be particles of cement floating up from the mass which is being laid. This whitish substance is generally termed "laitance." A similar formation occurs on the surface of concrete laid with too much water. The authors have found serious defects in structures in which the concrete was laid by chuting with a large excess of water. At the top of the basement columns in one completed six-story structure was found a thickness of laitance varying from J-inch to 4 inches, which had to be cut out and replaced. Chemical and microscopical analyses, which Mr. Clifford Richardson has very kindly made for us, show that this laitance has nearly the same chemical composition, § except for a large loss on ignition, as normal Port- land cements, but consists largely of amorphous material of an isotropic nature, — that is to say, it does not affect polarized light, and has almost no setting properties. It is evident, therefore, that when concrete or mortar is laid under water, or with a large excess of water, a portion of the cement is rendered incapable of setting, and the strength of the mass is consequently reduced in propor- tion to this loss. The conclusion is naturally reached that for concrete * Report of Commiltee on Specifications and Methods of Tests of Concrete Materials, Sanford E. Thompson, Chairman, Journal of American Concrete Institute, October-November, 1914, p. 422. t Proceedings of American Society for Testing Materials, Vol. VI, lgo6, p. 358. X See p. 10 for definition and p. 149 for method of determining density. 5 See p. 2SI- STRENGTH OF PLAIN CONCRETE 319 laid under water, or in locations where a large excess of water is required in mixing, a higher percentage of cement than usual, about one-sixth more, should be employed. A lean mixture has been found to be more seriously injured by an excess of water than a rich one, probably because the water has a greater oppor- tunity to penetrate the mass, and therefore to dissolve the cement. .700 S.4 5.4 6.9 9.2 11.0 PERCENT WATER TO TOTAL WEIGHT OF DRY MATERIAL Fig. 87. — Comparative Permeability, Strength and Density of t :2\:i\ Concrete, mixed with Different Percentages of Water, By Taylor and Thompson. {See p. 318.) Machine Versus Hand Mixed Concrete. Machine mixed concrete on actual work and, when properly handled, in the laboratory, may be 320 A TREATISE ON CONCRETE counted on for greater strength and uniformity than hand-mixed con- crete. In mixing laboratory specimens, however, it is difficult when ■a few specimens are made at a time to prevent the cement and mortar sticking to drum of mixer and thus influencing the proportions. Tests of a large number of 6-inch cubes of i : 2 : 4 concrete by the University of Illinois* gave an average of 2 200 pounds per square inch for hand- mixed specimens and 2 800 pounds per square inch for machine mixed specimens. Tests by the authors of laboratory-made specimens in comparison with specimens taken from the mixer on the job show that with first- class workmanship the laboratory specimens are representative of the job concrete made with the same material. Furthermore, specimens of concrete cut from actual structures usually show higher strength than specimens taken either in the field or mixed in the laboratory. Comparativ& Strength of Concrete at Different Ages and Consistencies Stored Under ; Different Conditions .'\ , Each Value is an Average of four 6 by 6-inch Cylinders. Proportions i : 2 : 4 by weight. Normal Consistency Tests at University of Illinois. Consistency. .9 .a storage. Compressive Strength at Different Ages, lb. per sq. in. Dry. . . . Normal Wet. , . . Normal, Normal Normal- Normal 8.4 9-3 [0.2 9-3 9-3 9-3 9-3 Damp sand Damp sand Damp sand Air Coa ted with paraf- fine Damp sand. , . . . . Damp sandj Airt 1751 1390 1 103 1481 2140 177s 1354 2061 2658 1816 1623 2126 2615 1820 1657 2116 2314 3056 3063 2410 2232 2521 2734 2208 3941 3431 3281 2049 3339 3433 1888 3700 3768 3760 2350 367s 394S 2000 4890 4042 3914 2189 423s Effect of Curing on Strength. Tests indicate a marked efioct on the strength of concrete by the manner of curing. If specimens are kept in the dry air of the laboratory, comparatively little gain in strength is evidenced after the age of 28 days. Results of tests at the Uni- * University of Illinois, Bulletin No. 71, p. 176. t Journal American Concrete Institute, October-November, 1914, p. 435. X Made from dry stone; for all other test pieces the stone had been thoroughly wet before mixing . 321 Ratio of Compressive S+rength to Strength at One Month _eigigS§ ijijiigg i S S i i g ^ -< (D Q ft [J 322 A TREATISE ON CONCRETE versity of Illinois with specimens cured under different conditions are indicated in the following table. Although such tests have not yet been carried far enough to determine the effect on actual structures, the results show that a dry atmosphere should be taken into account in the construction of any structure which is to be closed from the weather at an early period. Certain temporary properties are noticed in con- crete subjected alternately to wet and dry conditions. For example, a loss in strength is noted in air-cured specimens when first placed in water, but the strength is gradually regained after soaking,* GROWTH IN STRENGTH OF CONCRETE Long-time compressive tests of concrete indicate a fairly uniform growth in strength with no such falHng off with age as is frequently observed in tensile tests on neat cement and sometimes in mortar briquets. In Fig. 88, page 321, is plotted an average curve showing a growth in strength representing some fifteen series of tests carried out in the United States, France, and Germany. The curve extends to the age of 35 years, and tests as far as 9 years show a further slight increase. Important in practical construction is the fact that the strength at 3 years is more than twice the strength at 28 days. For laboratory tests, the ratio of strength at 7 and 14 days is of interest as forming a basis for short-time tests when such are necessary to obtain advance information on aggregates or on special conditions. Comparison of various tests indicate no marked variations in growth with different proportions and different aggregates. Variations due to consistencies are referred to on page 317, and the effect of storage on page 320. A weak aggregate (see page 323) may limit the ultimate strength. EFFECT OF AGGREGATES UPON THE STRENGTH OF CONCRETE Effect of Size of Coarse Aggregate. The larger the maximum size of coarse aggregate, the higher the strength, with other conditions similar. In Fig. 89, page 323, are shown the results of tests by Messrs. Fuller and Thompson,! which show the increase in strength as the stones increase from | to 25 inch, maximum size. These tests and other series show that this increase in strength is due primarily to increased •Prof, J. L, Van Orman in Transactions of American Society of Civil Engineers, Vol, XXVII, 1914, p, 438, t Transactions American Society of Civil Engineers, Vol. LIX, p. 67, 1907, STRENGTH OF PLAIN CONCRETE 323 density with the larger size stone. The tests show that with |-inch stone, one-third more cement is needed than when the maximum size of stone is 2j inch, and with 1-inch stone, one-sixth more cement is needed than with 2| inch, assuming in both cases similar grading. The selection of maximum size of particles is apt to be made from practical considerations rather than the strength of the concrete. For mass concrete, a maximum of 3-inch is customary, although 6 and even 8-inch stone has been put throughamixer with satisfactory results. For reinforced concrete, a limit of i to i|-inch maximum size is necessary in order to properly flow around the steel. For face walls, washed or picked, a better appearance is secured by limiting the maximum size to I -inch. 1500 1400 1300 1200 u a. 1100 < o>iooo (0 C£ Ul 0. g 300 z D O Q. 200 ■ ■ ■ ^,j0S^^^^ n^G^---'■'^ ^'^ PNSS^ 100 ^^^Si^^^ TRANSVERSE STRENGTH 1 ^ .B50 ■ dEnSITV Ul -Tcn c MAXIMUM SIZE STONE Fig. 89. — Comparative Density and Strength of Concrete made from Broken Stone of different Maximum Sizes. Proportions 1:3:6. Age, 140 Days. {See p. 322.) Effect of Quality of Stone. Weak aggregates eventually limit the ultimate strength of the concrete because a thoroughly hardened con- crete will break through the coarse aggregate instead of pulling out the stone. 324 A TREATISE ON CONCRETE It is evident, therefore, that the strength of the stone is an im- portant requirement and furnishes an indication of its value. In general, furthermore, the strength of the stone varies, at least to a par- tial degree, with its specific gravity. A stone of heavy specific gravity, therefore, can be expected to produce in general a stronger concrete. The compressive strength of stone varies from s ooo to 20 000 lb. per sq. in. according to the texture. The approximate strengths of con- crete with different coarse aggregates are given on page 316. Gravel Versus Broken Stone. Comparative tests of concrete made with broken stone and with gravel in the same proportions by volume show almost always that concrete made from hard broken stone such as trap gives higher compressive strength than concrete made with gravel. This appears to be the rule not only when the materials are mixed by measured volumes regardless of the percentage of voids, but also when the broken stone and gravel are each screened to substantially the same size. The choice, however, between the two aggregates is more often a matter of relative cost and availabiUty than of the actual strength value, because the difference in strength, which usually is not above 8% to 10%, is not likely to be enough to be the governing factor. Furthermore, gravel makes a smoother mix so that the stones slip into place without so much tendency to separate from the mortar. For this reason gravel is usually better for watertight work and in places whe^e it is especially necessary to eliminate surface voids. These conclusions are further confirmed by tests of the U. S. Geo- logical Survey at St. Louis* and by E. Candlot in Francef. Comparative tests of concrete with different coarse aggregates are shown in Fig. 90, p. 325, representing tests by Messrs. Wm. B. Fuller and Sanford E. Thompson at Jerome Park Reservoir, New York City.| Because of the greater density, the proportions by volume being the same, the specimens made with gravel and sand contain in the set con- crete a slightly larger percentage of cement, so that the strength of the gravel concrete is slightly greater than if allowance had been made for this. The relatively low strength of the concrete with broken stone and screenings may be due in part to the character of the screenings, which were of gneiss rock and of poorer quality than that produced from a true granite. • Bulletin 344 U. S. Geological Survey, igoS. t See Concrete, Plain and Reinforced, 2nd Edition, p. 38s. t Transactions American Society of Civil Engineers, Vol. LIX, 1907, p. 67. STRENGTH OF PLAIN CONCRETE 325 These tests show that a concrete with an angular coarse aggregate, such as broken stone, is stronger than one with a rounded coarse aggre- gate, like gravel, using the "Same sand and cement. The stronger ad- hesion of cement to broken stone outweighs the greater density of gravel concrete. BROKEN STONE AND SCREENINGS QRAVEL AND SAND 1600 BROKEN STONE AND SAND 2l" AVERAGE COMPRESSIVE STRENGTH 300 i" 2i" , 1 1:9 GRADED ^ c " 1 200 V _ — — — f l:3:S AVERAGE TRANSVERSE STRENGTH i. .850 h .800 ,750 2i' llj9GRADED -— -^ r^^^=::=n:r4 BROKEN STONE AND SCREENINGS GRAVEL AND SANO AVERAGE DENSITY BROKEN STONE AND SANO Fig. 90. — Comparative Density and Strength of Concrete made with Different Aggregates. (See p. 324.; Replacing the sand with screenings of the same size and using broken stone produces a weaker concrete than sand and gravel, probably be- cause of the low density. 326 A TREATISE ON CONCRETE The gravel must always be clean. In a bank it is frequently covered with a film of dirt or loam which it is naturally impossible to remove without thorough washing in a special plant. (See p. 228.) A dirty gravel may reduce the strength as much as 25%. The stone with the smaller percentage of voids if proportioned by volume gives the lower strength. To illustrate, a cubic foot of stone measured loose with 40% voids contains more solid material than stone with 50% voids, and hence makes a greater bulk of concrete with the same proportions by volume. This is further illustrated in the table on page 214. Consequently, there is less cement in a unit volume of the concrete when the stone has 40 per cent voids; and while the density is slightly greater, it is not enough greater to counterbalance the decrease in the percentage of cement. If the proportions had been altered so as to use less sand with the stone having 40 per cent voids, the concrete would have been stronger, with the same amount of cement per cubic yard of concrete, because of the greater density. From this it must not be inferred that the aggregate with the largest percentage of voids is best to use. As indicated above, it requires more cement to a given volume of concrete, and the concrete is apt to be slightly less dense than with an aggregate having fewer voids, so that the latter is usually the more economical even although it is sometimes slightly inferior in strength. From the standpoint of a contractor, therefore, gravel concrete is cheaper than broken stone concrete when proportioned by volume for the reason that gravel has a smaller per- centage of voids and therefore makes a larger volume of concrete with the same measured materials. It is almost always cheaper to screen bank gravel, recombining the sand and screened gravel in the desired proportions because (i) bank gravel seldom runs uniform enough to depend upon the right pro- portions of fine to coarse aggregate and (2) the sand is apt to be in excess, thus requiring more cement to the cubic yard. Ordinarily the cost of screening is more than balanced by the saving in cement. Slag. Slag, a by-product from blast furnaces producing pig iron, has proved a satisfactory coarse aggregate for concrete, but more care must be used in selecting it than is the case with gravel and broken stone. The important requirements are that it shall contain little sulphur, shall be tough, and dense, and shall have been cooled for six to twelve months on large slag heaps, on to which it flows from the furnaces in layers about 6 inches thick. The weight per cubic foot of first-class •See tests of Howard A. Carson, 7th Annual Report, Boston Transit Commission, igoi, p. 39. STRENGTH OF PLAIN CONCRETE 327 slag (assuming 45% voids) should be not less than 70 pounds per cubic foot. This is an important requirement because it eUminates the soft, porous material. ,Slag has been used in important concrete structures in the blast furnace regions for many years and its durabiUty is well established for mass concrete provided a first class quality is used. Its use for reinforced work is more questionable because of the diffi- culty of obtaining uniformly good material. Tests indicate that a first-class slag may be expected to show strengths at least as high as limestone and gravel.* Mr. W. A. Aikent reports a large series of tests on 6-inch cubes of 1:2:4 concrete ranging in age from 28 days to one year. At 28 days, 3 months, and 6 months, 100 specimens each were broken and at 9 months and one year 50 specimens each. There is a substantial growth in strength although the absolute strengths themselves are low, proba- bly, Mr. Aiken states, because of a fine sand. Compressive Strength of Slag Concrete Age 28 Days 3 Months 6 Months 9 Months One Year Strength i 561 i 952 2 589 2 841 2 797 Ratio 1 . 00 1 . 25 1 . 66 j. . 83 i . 79 Cinders. Cinders, usually from soft coal, are one of the most variable materials used as a concrete aggregate, and need special care in selection and mixing to secure satisfactory or even safe work. They can never be safely used in design without tests to determine the breaking strength of the concrete. The heavier the cinders, and the less the amount of material passing the quarter-inch sieve, the stronger the concrete. (See p. 328.) Cinders containing fine impalpable ash are unfit for use, and cinders from industrial plants must be investigated to insure freedom from all injurious acids and alkalies. Tests and experience in building construction prove that steel properly imbedded in cinder concrete of wet consistency is not liable to rust. (See p. 293.) The following tables of tests at the Massachusetts Institute of Tech- nology and at Columbia University show clearly the effect of coarseness and weight on compressive strength. They show also that specially selected cinders will produce concrete of higher strength than the values suggested by the Joint Committee (see p. 316). * Engineering News, August lo, igil, p. 185, and Engineering Contracting, April 30, 1913, p. 483. t Proceedings American Society for Testing Materials, Vol. XIV, 1914, p- 280. 328 Compressive Strength of Cinder Concrete* (See p. 327.) 8 by 8 by 16-inch Prisms. Proportions 1:2:$ Kind of Coal. Description. Mech. Analysis % Passing. Weight of Concrete. lb. per cu. ft. Compressive Strength. Age 28 Days 1" i" i" J" lb. per sq. in. Georges Creek, Cumberland Dirty, brown, soft, nearly all fine, some unburned coal 100 96 84 71 89 400 Bituminous Dirty dark brown, soft, traces of vitreous clinker, no unburned coal 100 93 78 6S 9S 492 Mixture : Anthra- cite, Coke screen- ings No. 2 buck- wheat, bitumi- nous Clean black, hard, con- siderable unburned coal 100 93 76 60 91 64s Variety of bitumi- nous coal Dirty black, not much gritty or hard, some slag and unburned coal and coke 100 89 63 43 97 812 New River Bitumi- nous coal Dirty light brown, soft, no unburned material 100 81 70 5° 104 828 Dominion coal Dirty black, very soft, some slag and un- burned coal and coke 100 84 S7 36 lOI 868 New River Bitum- inous coal Dirty gray, soft, small amount of unburned coal and coke 100 80 49 33 109 883 Nova Scotia coal poor gravel Black, gray, very heavy, very little unburned, large particles look like slag 100 66 53 26 113 1088 Pocohontas mixed with buckwheat Brown, hard, well graded, no dust, no unburned coal or coke 100 83 47 26 III 1246 i" broken stone coarse sand 145 1620 * Tests at Massachusetts Institute of Technology under the direction of Prqf. C. M. Spofford and Prof. H. W. Hayward. Published by permission. STRENGTH OF PLAIN CONCRETE 329 Compression Tests of Cinder Concrete S by 8 by 16-inch Prisms. Tests at Columbia University* Kind of Coal. Pioiwrtions. Descrip- tion. Mecli. Analysis. % Passing. Weiglit Con- crete, lb. per cu. ft. Compressive Strength, lb. per sq. in. il' 1' i' r r I mo. 2 mo. 6 mo. lyr. Anthracite. . . Anthracite. . . Anthracite. . . Anthracite . . . Anthracite. . . I-2-S i-i-St 1-2-5 I-2-S 1-2-5 1-2-5 98 100 94 98 97 98 96 93 93 80 88 86 76 57 6S 63 34 24 25 107 100 107 109 113 113 407 507 818 980 1533 1355 701 662 1254 1035 2066 933 754 1744 1478 913 813 1465 1475 2570 Anthracite. . . 100 94 90 81 74 • Harold Perrine and George E. Strehan in Transactions Am. Soc. C. E., Vol. LXXIX, 1915, p. 523 t Hand mixed — two turns. Coke Breeze. Coke Breeze, ordinary coke that drops through the tines of the loading forks and runs below i| or 2 inches in size, gives unexpectedly high strength when used as a concrete aggregate, attain- ing in one series of testsf about three-fourths the strength expected from broken stone concrete. This aggregate, weighing only about 30 pounds per cubic foot, may be useful where a concrete of extremely light weight is required; because of its combustible nature it cannot be used for fireproofing. Variations in Tests of Concrete Aggregates. Tests by the Bureau of Standards! tend to confirm the opinions indicated by the authors else- where that with our present methods of tests the only specification for either fine or coarse aggregate that can be considered final is the requirement for strength of specimens mixed in the proportions to be used. The Bureau reports tests on 18 limestones running from i 276 to 3 984 pounds per square inch; on 11 gravels running from 888 to 4 126 pounds per square inch; and 3 granites running from 2 376 to 3 054 pounds per square inch. Taking the low value as 100%, the range for limestone is 213%; for gravel, 354%; and for granite, 29%. Comparatively few granites were tested. One sample of cinder con- crete tested at i 647 pounds per square inch. All proportions were 1:2:4 and the age for the above strengths was 4 weeks. It is further shown, as is evident from the laws of mechanical analy- sis (see Chapter X) that the relative values of different sands for use in concrete cannot be estimated accurately unless tested in combina- tion with the coarse aggregate, because the grading of the total mix- ture is the determining factor. { Tests at Massachusetts Institute of Technology under the direction of Prof. C. M. Spofford and Prof. H. W. Hiyward. Referred to by permission. § Technologic Piiper No. 58, U. S. Bureau of Standards, June 20, 1916. 330 A TREATISE ON CONCRETE EFFECT OF CONCENTRATED LOADING In concrete foundations for piers and in concrete footings it is cus- tomary to load an area smaller than that of the surface of the concrete. The question at once arises whether the stress shall be based upon the load divided by the total area of the concrete footing or by the area of contact. Experiments made upon concrete and other materials show that neither of these methods is correct, but that an intermediate area should be selected for computation. --T-T--tr++T rrr tr Tl --T1 : :: : --r- ::::q: I -M i-n — :::: 00 T TTT~ n: ffi ::i 4 _J _ :: TESTS BY QE.O. A..K1MB«LL a TESTS BY PROF. F. P. MC KIBBEr . -_ . :>a^ ' Tf D": -4- J4J 4i 'T' :: "^oo 08 ^ RATIO 0.7 OF AR EAD 00 ESE ED SU .5 RFAC -TO T DTAL fliREA OF .3 OONCR ETE 0.2 0.1 Fig. 91. Concentrated vs. Distributed Leading. (See p. 330.) In connection with the designing of concrete footings for the Boston Elevated Railway, 12-inch cubes were crushed by concentrating the load upon plates 10 by 10 inches and 8 by 8| inches.* At Lehigh University in 1908 a set of experiments was made upon the strength of 6 by 6 inch cubes of 1 :2 :4 proportions where the compressed area varied from the entire area of the specimen down to 1.21 square inches. In the diagram. Fig. gi, both sets of valuesf are plotted. The two sets agree where they overlap, and also are similar in general direction, and, in fact, in actual values of the ordinates, to curves drawn by Prof. J.B. John- sonf illustrating Bauschinger's tests upon other materials than concrete. , * Tests of Metals, U. S. A., 1899, p. 740. f From data presented to the authors by Mr. George A. Kimball and by Prof. Frank P. McKibfaen. ~i Johnson's Materials of Construction, p. 35. STRENGTH OF PLAIN CONCRETE 331 In considering tne smaller areas, as indicated by the smaller ratios of area, the fact must be considered that the compressed surface deformSj that is, actually compresses under the load, and the amount of deforma- tion, which may be approximately estimated from the modulus of elas- ticity, may sometimes be the limiting consideration. Also, in the small areas the possibility of punching through must be considered. To use the curve for determining the additional strength gained by the enlarged area under a pedestal or column, find the ratio of the com- pressed area to the total area, and from the point on the curve corre- sponding to this ratio find from the values at the left the increased ratio of strength to be expected. Thus, if a compressed area is one-half or 0.5 of the total area, the strength is increased 1.29 times. The use -is further illustrated by the following examples. Example I. — What dimensions of pedestal would be required to safely sup- port a load of 40 tons concentrated upon a plate 10 inches square, assuming an allowable distributed stress upon the concrete of 650 lb. per square inch ? Solution. — Forty tons or 80 000 pounds on 100 square inches represents 800 lb. per square inch, and the ratio of pressure required under the con- Q centrated load to the allowable pressure is therefore — =1.23; hence 650 . 1 r • 100 sq. in. from the curve, the total area of concrete necessary is ^ = 182 0-S5 square inches. Example 2. — The breaking strength of a 12-inch cube of i 12:4 concrete having chamfered edges, so that the area of contact of the load is reduced to 9 by 9 inches, or 81 square inches, is 324 000 pounds. What may be con- sidered as the ultimate strength of the concrete when loaded over its full area? Solution. — The strength per square inch of the cube figured on its cham- fered surface is ■. — = 4 000 lb. per square inch. The ratio of the I 81 compressed surface to the total area is — = 0.56, and from the diagram we 144 find the ratio of strength to be 1.22. Dividing 4 000 pounds, the unit strength on the concentrated surface by this gives as the probable ultimate of the concrete when loaded over its full area, 3 280 lb. per square inch. TENSILE STRENGTH OF CONCRETE The tensile strength of concrete. is usually of little importance in design because even when the tensile value is taken into account it is a 332 A /TREATISE ON CONCRETE matter of cross bending or modulus of rupture rather than of pure tension. Furthermore, tensile tests producing accurate results are hard to make on account of the difficulty in making up the specimens and breaking them. The following table gives results for medium consistencies. Tensile Strength of Concrete* Tensile Strength at 28 Days. Compressive Strength at 28 Days. lb. per sq. in. per cent of compressive strength. lb. per sq. in. 1:1:2 i:2:4t 210 140 1 10 6.4 7-" 8.0 9.2 3290 2500 1750 1 190 * Tests at Massachusetts Institute of Technology under the direction of Prof. C. M. Spofiford and Prof. H. \V. Hayward. Published by permission. t The strengths of these proportions are abnormally low in compression and the tensile strengths may be assumed correspondingly low. The ratios, however, agree substantially with results from other tests. Comparing the tensUe strengths with Mr. Fuller's transverse tests of beams given on page 334, it will be seen that the tensUe strength is from one-half to one-quarter the transverse strength. Just how much of this is due to the difficulty in molding and testing tensile specimens cannot be estimated, but since Fuller's specimens were made from a wet mix, the values may be considered as conservative and more rep- resentative of practical conditions than the tensile tests. The true relation between tensile and compressive strength or flexure and compression are probably more accurately indicated b}- the mortar tests of Mr. R. Feret on pages 334 to 335. TRANSVERSE STRENGTH OF CONCRETE The strength of a beam of plain concrete is limited by the tensile strength of the concrete at the place of greatest strain, which, with vertical loading, is its lowest surface. The value of this; transverse "fiber" strength or modulus of rupture is of less importance than the crushing strength, be- cause, on account of the brittleness of concrete in tension, that is, its liability to crack from shrinkage or sudden loading, it is seldom safe, and usually is not economical, to construct beams or girders without metal STRENGTH OF PLAIN CONCRETE 333 reinforcement. Most formulas for reinforced design disregard the tensile strength of the concrete. In certain computations, however, the tensile strength must be considered. Since concrete beams can be broken with less powerful and less expensive apparatus than crushing specimens, this form of specimen is often convenient for comparing the relative strength of different mixtures or different materials, and while the ratios thus ob- tained will not exactly coincide with those for crushing strength, they wiU be sufficiently close for many purposes. Fuller's Beam Tests. The table* on page 334 gives the results of a comprehensive series of tests of 6 by 6 by 72-inch beams made by Mr. William B. Fuller at Little Falls, N. J. Although different materials than those used by Mr. Fuller will of course show slightly different strength, the table is sufficiently representative of average conditions to permit its use for comparisons of different proportions, and, with a proper factor of safety, as a working guide to the safe transverse strength of con- crete. The proportions are given by weight but can be transformed to volume measure by referring to the footnote. The various columns present valuable data on weights and volumes and voids. The curves in Fig. 92 are plotted from the results in the table, and illustrate also the proportions corresponding to maximum strength for a given per cent, of cement. Tests by other authorities are mentioned under Strength of Beams in References, Chapter XXXIII. Formula for Transverse or Bending Stress in Plain Concrete. The common formulas for representing the longitudinal forces of compression and tension upon a beam are usually expressed with the following notation: Let / = intensity of stress at any point in the beam. M = bending moment. I = moment of inertia about its neutral axis of section containing the point under consideration. y = distance of the point from the neutral axis. b = breadth of beam. h = height of beam. Then .My // / = / (3) also, M^J- (4) * Especially prepared for this treatise by Mr. Fuller 334 ttl o ■6 ^ C/3 m It, u tt) Ul s 2 J2 a . ^ ?,- ~ J;J ii o < ti K O -f^ g "^ OS"' en 55 •a a a .S a K H en a: ti rt O S3 ? -^ •c 3 o t 3 ■B - •3»BJ3AB JO J0JJ3 ajqB 1 9«! ■* H M N * WOO « « CO VO (p H COW q>*q q. WHO « M q « K* to N CA a I m d •93BJ3AV Ul ass \0 M t- 00 O "O M w 1> t^vO VO '^'O 00 O w (OoO w Tf to fO •rantu -F!JM ? >ocoo(t lO N-O o-o to -J- 't t^ ■OWN Tl-oo o> ■^ ■* »o Oi o ^ Ch ■* *o CO fO (M ■mntu n 00 N N Coo w r^ «oo TfOO « r^ a CO Cf CI H 'i- ■* »o >o\0 W N COG . JO jaqranj^i ■^ \o\oo ■O t^^ 'O'O'O \o\oo V0\0 H «0'0 m ■s/tE0 li p > ■I"loi ? a t^ «^ O. tTCO MOO 1^ to WOO »o -3- TT s-o-e. lO w lO ■aiT333j33v '5 000 -^ 8 q q Th rj- ro i/ll-. to q- q t^OO CO q q q 0.00 op's W*0 CO o^o -: qq COOO M lO »o t^ qqq ■JU3UI33 00 M lilOO '-00 fi'as lO CO O lO »0 CO 00 r^\0 qqq ■si iS 3« 1g 3 u •Pioi 1- O.00 o. 00 >-■ >o r-co o> Cx 0> O. O CO O. 0*0.^ Q r- CO OOOO-O o. o. o. ^ -< •tzg 'J3li!A\. ^ \o r- t^ 00 ■* O O lOlO r^ »o CO lOlO t^ lO tN O 000 IH KSS ■XlQ PlOX lO H^O Pi CO M M ^-oooo lOOO « (WW i? eg? t- t~-00 lO Ol t^ •OvOO ■3U0JS pUB pnug iTijox T '^ 1— ro 0>»n fO 000 Oi t- fo«o to tt ^o lO'O "O M M f* M ■* n t^ t^ lO vO w CO O-IOM •SHOJS ^ •+ NCO CO SI 00 t^ CS r^ tN*o -^lOlO ■pnvs ^ fO mio fo 00 NOO I— l-~ t-» M Tj- ■^ CO CO M 0> IM r- (o H w w p) •JU3UI33 ';;^ 1/100 o> 00 >nin 0> 1- fO M M CO ■* fOO TT Oi lO ^1- lO CO M tN x-00 >-" f- ^co vO <0 H a o g d ss en ^ •gm -S 1 1 1 uinuj -IXEH 'o' CO CJ^O 00 >0 N fO lOO aq t~. to 4vd 00 coco 4 d w M H a VI t^ IT) t^ too d t^ M ro fO oD q o 4 o. lo loro fO OvoO M 4 M to ■^in lo -rsq o. I- O (O lO'O to N M O. 6. lo to CO ■* »o Pj ^q sy S- q >o M COVO >A ■^ M lO to d <- lO lO'O M q CO ly^\0 to "CO ■q- f >0 CO d 4 6. -t lo »o CO PJOO •MJEM -^ M ■<}• O. N r^ CO CO COOO 1^00 o> or^ ■* ■«*•"*« "*in « H CMO « O. t- N « H l> i-^r^oo 3 00 00 CO Hs6 6v MOO r^ ■<1- w -^ »oo6 d •ooo o. >d « M co'-r lo 'tooo lo m m " " ■3no;g '^ HCO oq ■* CO 6i M O M Tf TT r^ 4 6 \o o CO CO O M - ^ q -a- r^vo fOlOt^ ■»a- to M dod lo 00 O •puES TT 5- q^ « t to CO &\q <> « wco to M VO 00 r^ d \o m to i^toq 5 o, in 4 CO CO -^uaraa^ 3 o ■* o. CO r^ 4 CO MvO q « >H t- i^ TT CO to u) ri CO Mvq CO 4o6 lo d M d oi vo to ej ^«0 Q w :-88 -S88 -nOO O lO ^ ■=*■ to CO 00 « CO 00 lO 0> 2|3 00 •" N W to M cot- in M 0, •0 W VO to W ^^cT a 10 M 00 ov* ■^ o> t- fO ^ fON CO W N N 0. fO N iO«vO R-as RR? a CO 10 JO w CO w ri M 0.0 M t- 00 to fo avo ^ ■^ to fO 00 ^O I^ Oir- 0. 10 Tt (O 1-100 O-cO r* 0. low COOO »0 CO ■It CO VD to w 1-w w o-O v> a coio n Th co-O TT tO« www N -^ W WWW CH W W W M M .„„ N to ro CO ro CO CO coco CO CO CO CO SSS (O to CO ■* COM- ■^ -* CO CO CO to fO to CO to CO CO to CO CO to CO to CO CO to CO to to ■?S?il \0 W CO CO CO Ml ►1 " N o.r^ SS| Sirs 10 to Oi -O ■^ 000 W 1- -r t- W \0 r?K-^ "" ' • 1 O to - o. H M H O r?? ?H r^ •+ M CMC HMO 00 f n§| M M Is? "^ 1 ^ss? MVO CO Q Q 000 J- CO M ■* Tj- ^ 000 cot- 10 000 000 tf tT CO cO\D *0 q Q q 00 M r- •r ^co coo ■>r t- M CO in m 000 ^^ 1 fO cs r^ -OOO « q-o-q q.aa »0 N CO §08 M w 8 9§ 00 §88 Q to 0. q atD. VOOO g=S8 8'%=S> o> M H H M H " ,-v\0 lOOO \0 0>»^ CO 00 -O N »o M r^O c*)io ^=g;2 CO to 0> \o -t M w w Ov to 00 I»0 CO m m ^ M 000 ^ ■ ; : : : ' _ : / i lO '+00 N CO 00 00 CO "*0 OOOQ 00 112 isS 5:^-8 CO to Oi 00 ■^ 0. 00 r- t- CO li-, o> 00 00 00 w SS.'R COOO "* W C^l \0 op op 00 m to rf 00 ■^ lO 00 i>- 1- M »n o 5^5 CO CO 00 00 vO c< 0> CO ■O lH^O J- 1^ ■S-Rcg 000 I- W W f to COOO 0000 m M rnt- M r- i-oo 00 00 ^ ■ ■ 1 CO ■* fO to M in rj- o. CO H CO CO r~ "o CO to CJ CO ■^ ^0 ■^ r^ CO R ? »0 N 0> CO CO ■* 10 0. VO in M MOO 00*0 to w cot 00 ,--,1-1 0> CO WOO ooo WOO 0> O i^-io S8S Ov f^OO moo « ■^ CO CO r- ■*Q0 WO 00 V) 10 to*- wxq -a- •* to to wvo m in Ov to 5:&R sis "^ ■ • ■ 1 e-xO -+ O «0 O.'T q qq ■oo to q t 00 N \0 MOO inoo 0> M 10 •o^o m q q q 00 vO q q q COOO to q q q 00 M CO '^CO t— q q q O t O Mvq CO O « lO CO q. -r w co-O A 4 6. Tt 10 »0 ^\q o* H W CO 00 t^ M el \0 ■* »o q-oo-q 00 Ov Pj 4sd t^ mmvo r-00 00 in d M >o ■* ■* ■d-coq ^ CO CO tT q CON V) to lo 00 00 CO q « CO t coo CO TT <0 0. M W N vO io»o *o t-oovq 00 CO ^ lOoq 606 >d inoq f r^ to w 00 q lo 000 cjoq 10 r- w hI CO M CO ^« ?o^ t>. H H Oi coi> »nq.rj N M 0> CO -* •* & q w M M >n dviod vow CO NO 000 i- M 0. Tt 10 10 \0 r- t- 06 M d m N CO 00 w t- tovd to ■V ■* m incq t 00 -d-o '■ "" """ 1 « q^q 00 o> q ^ 22 qsH ^ ^* CO M covOOO "O 1000 -t M CO q. t^ w »o ^ooo 0, VO M CO >n q w r^ cj invooo CO Ov ,^00 CO N ^ lO « -o6 fO vd 4 1^ ■^000 00 r^ M q (N M- VO d- IN m M ^!2 to 0 CO W M M •0 CMO ^J-OO-O COM d *? T •? 6. t^ 4 »o M d co.q q Ovm TT M CO _fO CO ^-^ t-l l-< r^ to CO « t? r? r?" M H H t^OD '4 4 4 2 q .to •^io JO >o f- q- in joio M r; 2.qo vcf.-^ ' STffTs "n"?)^ W N N 00 N « CO C^lo Tj- 10\C »0 CO CO t-OO o- PO tO^ '-'f* t ■* t co'^io *j- ■* «a- $M p. ^ o P Si o to-iD O o (U coS^3 "00 o G ^ « S C +j C w !S S - _ flj ■ .- s >.» o'S gasss ttJ (U H H ? o ^E "go a S « ^ " Si o ^ "" "■ .. o 00 *" f o a o" " - ,i rs8" C ri M c ^ -4 «JCO C N " O rtvo I u " M „- o « o 336 A TREATISE ON CONCRETE For rectangular sections, I = — and up to the elastic limit for beams 12 of homogeneous material (but not for reinforced beams), y = i h. Hence for rectangular beams of homogeneous material, 6M (5) also, M = — fbh^ 6 (6) In considering the strength of a beam, since the stress is greatest at one or the other of the surfaces, y is generally understood to represent the dis- tance of the most strained fiber from the neutral axis, and / the intensity of stress upon this fiber. I 2 34 S 6 7 8 9 10 II 12 13 14 5 e 7 PARTS OF STONE, BY WEIGHT Fig. 92. — Curves F.howing strength of beams in pounds per square inch for various prop ortions by weight of sand and stone to one part Portland cement. Age 34 days. (See p. 333.) The foregoing formula is based upon the assumption that the neutral axis passes through the center of gravity of the cross section. For unreinforced mortar and concrete this is true, only in the early stages of the loading. But, although it is not correct after the elastic limit is passed, the comparative results computed on different beams of similar materials are relatively correct. For convenience in designing, a table is given in Chapter XXII for bending moments caused by uniformly distributed loads and for loads concentrated at different points. Also, in the same chapter , the moments of inertia, I, for various sections are tabulated. These tables are appli- cable for the most part to both plain and reinforced beams. STRENGTH OF PLAIN CONCRETE 337 Relation of Compressive to Transverse Strength of Concrete. The com- pressive strength of concrete varies from 4 to 8 times the transverse strength. The ratio varies with different ages, for the growth of com- pressive strength appears to be faster than the growth of tensile and transverse. This is specially true of concrete mixed with weak aggre- gates such as cinder. There appears to be very Httle difference in these relations between different proportions of the same materials. Tests by the U. S. Geological Survey at 28 days showed limestone and gravel concrete to be six times as strong in compression as in the tensile fibre stress in bending. For granite, the ratio was 7.5. The average ratios for all materials were 6, 7.5, and 8, at 4, 13, and 26 weeks, respectively. The beams used in this series were full size and should therefore be more reliable than the small specimens used in other tests which have given somewhat lower ratios. The proportions were 1:2:4. Shearing Strength of Concrete By Prof. Charles M. Spofford. Massachusetts Institute of Technology. (See p. 337; Age of Concrete 24 to 32 days. Mixture. Method of Storing. Shearing Strength lb. per sq. inch. Average Compressive Strength in lb. per sq. inch. Ratio of Shear to Maximum. Minimum. Average. Compression I 2.4 1:2:4 1:3:5 1:3:5 I 3:6 1:3:6 Air Water Air Water Air Water 1630 2090 1590 1380 1450 1200 960 I180 890 840 950 1040 1310 1650 1240 II20 II80 II20 2070 2620 1310 1360 95° 1270 0.63 0. 63 °-9S 0.82 1.24 0.88 Average Ratic 5 for T : 2 : 4 and I : 5 . 5 Concr ite u. 76 STRENGTH OF CONCRETE IN SHEAR Tests indicate that the strength of concrete in direct shear ranges from 60 to 80 per cent, of the compressive strength. These ratios from tests by Prof. Spofford in the table just given agree substantially with experi- ments made by Prof. Arthur N. Talbot at the University of Illinois.* I'rof. Talbot concluded that the resistance to shear is dependent upon the strength of the stone as well as upon the strength of the mortar, and for the richer mixture the strength of the stone probably exerts the greater influence. • University oi Illinois, Bulletin No. 8, igo6 338 .4 TREATISE ON CONCRETE This direct shear must not be confused with shear in a beam involving diagonal tension where the concrete may break when the shearing unit stress is 10% of the crushing strength. It is difacult to determine satisfactorily the resistance of concrete to direct shear owing to the diiBculty of eliminating the efiect of bearing action, diagonal tension, and beam stresses in general. At the Institute the test specimens were cylinders s inches in diameter by 1 8 inches long, and in testing, the end thirds of the cylinders were held rigidly by cast iron yokes, the pressure being applied through a cast iron half cylinder bearing, fitting between the two yokes, so as to shear the concrete across two planes. To compare the compressive strength of the concrete with the shearing strength, six extra cyUnders of the same dimensions were crushed, ' ~T — — - - — - ~ — "~ " ~ '" _ _ - — I ~ - — ~ -- rs _ s'S a.'^m* ' i <^. '" 9"" ot s ■ L.1 W - s oi- s UlT O^ ■" ^ .^ \- •_ _ _- '^ - - ^ r - ._ - -- 11 "" -^ -- ■- - — - - - P= k - £5 lJi|-,.««t 20U0 3000 4000 NUMBER OF REPETITIONS PRODUCING FAILURE. Fig. 93.— Fatigue of Neat Cement under Compression. {See p. 338.) THE FATIGUE OF CEMENT The action of cement under repeated stresses has been shghtly investi- gated by Prof. J. L. Van Ornum* at Washington University. The ex- periments were made upon 2-inch neat Portland cement cubes four weeks old. The results of tests on 92 of these blocks are shown in the dia- gram Ln Fig. 93. * Transactions American Society of Civil Engineers, Vol. LI, p. 443. STRENGTH OF PLAIN CONCRETE 339 PLASTICITY OF CONCRETE Plasticity of concrete is the property of flowing, or yielding very slowly under the continued pressure of heavy loads. Under ordinary working loads, concrete deforms in accordance with Hooke's law, but if the load, after being applied, is left in place the deformation resulting from the plastic property may be from three to five times* as great as that immediately following the application of the load itself. Tests indicate that under a fixed load these progressive deformations continue for a more or less definite time and then cease. f Under a computed SCO-pound unit stress in i : 2 : 4 gravel concrete beams, this period was about two weeks, and under a i 000-pound stress a few days longer than two weeks. Poisson's Ratio, the ratio of the deformation at right angles to the stress, to the deformation in the direction of the stress, has been found by various experimenters to range from 0.05 to 0.20. All things con- sidered, a fair average appears to be about o.io, and this value may be taken in computations requiring its use. DETERMINING PROPORTIONS OF OLD CONCRETE The approximate ratio of cement plus fine aggregate to coarse aggre- gate in concrete already in place can be determined by cutting out a piece of the concrete, crushing it to destruction in a testing machine and separating out the stones with a small hammer. The ratio of cement to fine" aggregate can then be determined by dis- solving out the cement in a strong solution of muriatic acid provided the aggregates are themselves insoluble. If the sand contains lime- stone, as is frequently the case where the country rock is limestone, a sample must be subjected to a separate acid test in order to correct for the amount dissolved out with the cement. When the coarse aggre- gate is limestone and the amount of dust originally in it is unJcnown, exact determination cannot be made. Mr. Nathan C. Johnson, has suggested a methodf of determining the proportions of old concrete by making a microphotograph of a polished section of the surface and planimetering the areas of cement, sand, and stone. The method is said to give good results. ♦Tests by F. R. McMillan, Bulletin of the University of Minnesota, March, 1913. t Earl B. Smith, Engineering Record, March 4, 1916, p. 329. t Engineering Record, February 27, igrs, p. 263. 340 A TREATISE ON CONCRETE MACHINE FOR COMPRESSION TESTS. A convenient compression testing machine operated by a hydraulic jack is shown in Fig. 94, page 340, as designed by Mr. William 0. Fig. 94. — Hydraulic Compression Testing Machine. {See p. 340.) STRENGTH OF PLAIN CONCRETE 341 Lichtner* and instaUed in the laboratory of Sanford E. Thompson. It takes specimens up to 12 inches square and its capacity is 250 000 pounds. The screw type of testing machine, which may be used for both tensile and compressive tests, is shown in Fig. 95, page 341., The .10 000 000-pound compression testing machine of the U. S. Bureau of Standards, the largest in the world, is a screw machine. Fig. 95. — Motor Driven Screw TVpe Compression Testing Macliine. {See p. 341.) SAWING TEST SPECIMENS Concrete blocks cut from structures for compression tests usually must be shaped to the form of prisms, with two parallel bearing faces. • See description in paper by William O. Lichtner, Proceedings American Society for Testing Materials, Vol. XIV, Part II, igu, p. 535- 342 A TREATISE ON CONCRETE The saw shown in Fig. g6, page 342, is being used successfully in the author's laboratory for sawing the concrete. Two 30-inch discs |-inch thick, of soft Norway iron, are revolved at a speed of 70 revolutions per minute by a i| horse-power motor. No. 20 carborundum mixed with a medium grade of automobile grease and kerosene oil is fed on to the rims of the blades. The block is clamped down to a traveling table that feeds against the saw automatically as the cut deepens. The saws are held in place by nuts and the shaft is threaded the entire length so that the width between blades can be varied from 4 to 12 inches, according to the thickness of block required. Fio. 96. — Saw for ShapingConcrete Test Specimens. (See p. 342.) MICROPHOTOGRAPHY OF CONCRETE Mr. Nathan C. Johnson by the use of the microscope* has succeeded in photographing concrete surfaces enlarged to 200' diameters. The voids known to exist in concrete, are made visible to the eye and the action of the sea water and ground water salts that crystallize in these voids, sometimes disintegrating the concrete, has been demonstrated. ' Series of six articles in Engineering Record, starting January 23, igis, p. g8. STRENGTH OF PLAIN CONCRETE 343 METHODS OF TESTING CONCRETE The methods of testing concrete and the interpretation of results, as investigated by various individuals and by the American Concrete Institute, are discussed in the following pages. Specimens for Compressive Tests. A compression test specimen in the form of a cylinder with the height equal to twice the diameter is recommended by the Committee on Specifications and Methods of Tests for Concrete Materials of the American Concrete Institute.* The diameter of the cylinder should be at least equal to four times the maximum size of the particles of the coarse aggregate. Where possible, the 8 by 1 6-inch cyhnder should be used, but for small sto.ie 6 by 12- inch is satisfactory and, because of its lighter weight, more convenient for field specimens taken from such work as building construction. Cubes, provided the strength is corrected for length (see p. 344), or prisms, may be used, but cylinders are to be preferred on account of greater ease in securing homogeneous specimens. Cylinders and prisms of the same dimensions give substantially the same results in unit strength. The theoretical angle of crushing is about 60° with the horizontal and a prism, to allow for two such 60° pyramids, one upright and the other inverted, must be twice as high as it is wide. The specimen shown in the testing machine in Fig. 94, page 340, shows the way in which a cylinder breaks. Effect of Ratio of Height to Width. Tests by various laboratories under the direction of the American Concrete Institute show the vari- ation in strength as the ratio of the height to width of specimen changes. When the height is more than twice the diameter, that is, when the ratio is greater than 2, there is very little variation in strength, but when the height is less than twice the diameter, the strength increases rapidly with the shorter specimens. The curve in Fig. 97, page 344, shows the variation. By this curve, cubes and prisms of other than the standard dimensions may be used if unavoidable and the results corrected to allow for the standard specimen. Making Test Specimens. In making concrete specimens, if the nominal proportions are by volume, determine the weight of each material and correct to give the corresponding proportions by weight. Estimate and weigh up the amount of each material for the batch. Only experienced men should mix concrete for experimental specimens. There is a certain knack which can be acquired only by practice, in * Journal American Concrete Institute October-November 1914, p. 422. 344 A TREATISE ON CONCRETE properly turning the materials so as to mix them thoroughly, and the amount and manner of ramming or puddUng is so important that speci.nens may be rendered worthless by improper manipulation. Usually several specimens are made of the same proportions to secure a reliable average result. These specimens should be mixed one at a time from individual batches in order to avoid variations in pro- portions and consistency throughout the batch. This involves more labor but increases the value of the results. sz-a zm ■z zm > 230 £j2a2o PT, 2.10 §g2D0 >i:-> I.3D lOf. W O^ 17D r 1.60 £ .?! 150 g1 «! 1-40 W 1.30 .t D L20 ^C 100 o'> 030 =§0 080 (£^Q70 050075100 1.50 200 500 4,00 500 Ratio i of Height to Width of Prisms Fig. 97. — Comparative Strength of Concrete Prisms of Different Heights. {See p. 343.} Method of Quartering. To obtain an average sample from a pile of sand, gravel, or stone, the method of quartering is useful. Shovel- fuls of the material are taken from the various parts of the pile, mixed together and spread in a circle. The circle is quartered, as one would quarter a pie, two of the opposite quarters are shoveled away from the rest, and the remainder is thoroughly mixed, spread, and quartered as before. The operation is repeated until the quantity is reduced to that required for the sample. Weights and Voids. To determine weights per cubic foot, fill a measure having a capacity of J cubic foot or more with the sand or gravel; lift the measure 2 inches above the floor and drop it; repeat, raising and dropping five times; fill measure full; strike off with a straight-edge, and weigh. STRENGTH OF PLAIN CONCRETE 345 From the weights and the specific gravity (see pp. 123 and 124) the voids can be determined. Mixing. All mixing should be done on a surface of metal or other impervious material. For large specimens and batches, a sheet of ziac or sheet iron is convenient to use. A batch for a single 6 by 12-itich cylinder can be mixed in a galvanized iron pan about 24 inches square and ij inches deep, using a lo-inch bricklayer's trowel blunted by cutting off 2 inches of the point. If the mixing is done on a wooden platform or concrete floor, the surface should be thoroughly wet several minutes before mixing is begun. The procedure for hand mixing is as follows: Mix the cement and sand until a uniform color is obtained; this will require not less than seven turns. Spread out the dry mixture in a layer of uniform thickness and on this spread uniformly the coarse aggregate. (At this point, gravel should be dry; porous crushed stone should be dampened.) Mix these materials at least four times. Form a shallow crater and pour into it about two-thirds the required amount of water. Turn into the crater the dry material from the edges untU the water is absorbed, and turn the mass until the batch is of a uniform color and consistency throughout, adding, by sprinkUng, from time to time the remainder of the water used. The consistency of the concrete for the specimen in the laboratory, to obtain results comparable with the sluggishly flowing concrete recommended for reinforced concrete in practice, should be a Httle stiffer than this, — about like a thick oatmeal mush. About seven turns of the wet concrete are necessary. Making Specimens. Place cpncrete in the molds in layers 3 to 4 inches thick, using care to prevent pockets of stone against the form. Tamp the concrete to bring the mortar to the surface and imbed all stones. Level off the top of the specimen with a trowel, but avoid working longer than is necessary. Capping. The bottom of the specimen is sufficiently prepared by casting on a machined metal plate or piece of plate glass. The top of the specimen is apt to be irregular, and if the mold is not quite full after setting, the cylinder may be filled flush with mortar and leveled off with a piece of plate glass left in place until the mortar sets. Both ends are thus made parallel. In testing, pieces of blotting paper may be placed between the end of the cylinder and the heads of the machine. Plaster of Paris is also used to square up the ends of slightly irregular specimens or neat cement paste may be used if much out of true. 346 A TREATISE ON CONCRETE Molds. The most satisfactory molds are of cast iron with machined metal base plates. A less expensive metal mold than cast iron, although not so satisfac- tory, may be made with a piece of sheet metal or galvanized iron of i8 or 20 gage shaped to the proper diameter with two longitudinal flanges about an inch wide. The mold may be made tight with clamps on the flanges or by holding the flanges together and slipping them into saw cuts in 2 by 4-inch timbers held rigidly in a horizontal position at the proper heights. If machined metal bases are not provided, plate glass coated with oil is satisfactory. For mortar, cylinders 2 inches in diameter by 4 inches long are recom- mended tentatively by the American Society for Testing Material. (See p. 81.) Wood molds, although saturated with oil or coated with paraffine, are apt to absorb water. Storage of Specimens. Test specimens must be kept moist; if stored in dry air, the gain in strength is much below normal, and a series carried out by the University of Illinois for the American Concrete Institute showed no gain at all up to two years. (See p. 320) . Moisture may be supplied by burying in damp sand or by covering with cloths suspended so as to cover and surround the specimens without touching them, and kept wet. Specimens properly stored show little or no loss in weight after jremoval from forms up to time of testing. Method of Testing., Use a spherical bearing block on top of the speci- men, the diameter of the block at least as great as that of the specimen. Keep the upper section of the adjustable block in motion as the head is brought to a bearing on the specimen, thus insuring a central bearing and preventing the block from being pulled aside, as frequently happens when the block is allowed to adjust itself. The moving head of the testing machine should travel at a rate of from 0.04 to o.io inches per minute. Note the character of failure and appearance of specimen and its behavior during test. Specimens for Field Tests. On important work samples should be taken regularly for tests at 14 and 28 days. For beams, columns and girders the concrete may be taken from barrows just before depositing; but wherever possible it should be taken from place just after depos- iting. The following procedure gives good results: Shovel the con- crete into a 14-quart galvanized iron pail, carry to the molding yard and remix to eUminate segregation of materials due to carrying, and 347 Expt. No File Walikam Reservoir. Date 2/g/o6. Form for Recording Data on Concrete Specimens Item. (Figures in ( ) refer to Item Numbers.) 1. Nominal Propoftions j .• j.^ . 4.1 2. Car No .... .00 3. Kind of Cement Atlas 4. Kind of Sand f « c. \G S- Analysis No : ^q and 421 6. Kmd of Coarse Aggregate w. Gravel 7. Analysis No ■ ■ • ■ A22 8. Weight of Cement Used 3/2 9. Weight of Sand Used r.72 10. Weight of Coarse Aggregate Used i2.Sj 11. Weight of Water Used j.-rv 12. Per Cent Water to Weight of Cement plus Sand 20% 13. Temperature of Water (0° F. 14. Temperature of Laboratory 70° F 15. Total Weight of Material (8) + (9) + (10) + (11) -2^ a6 16. Weight of Mold Empty ign 17. Weight of Mold Filled 26.30 18. Weight of Concrete Net 2^.^o 19. Weight of Concrete Left Over o.oo 20. Weight Unaccounted for — Assumed as Solid Material* 0.16 21. Weight Unaccounted for — Assumed as Water 0.00 22. Volume of Fresh Specimen (cu. ft.) 0.1^27 23. Weight of Specimen — Mold Removed 22.7 24. Method of Storage Air 25. Weight of Specimen Before Testing 22. S 26. Measurements of Specimen Before Testing. . . ■'/.gg" X 8.02" X 4.12" 27. Date and Hour Specimen Made 2/9~3 p-'tn. 28. Date Tested 3/g-lo a.m. 29. Specific Gravity Cement ... .J./5 30. Sand. .. .2.65 31. Stone. .. .2.75 32. Weight of Cement in Fresh Concrete (8) X / o-, . / ~ YZul — ^ ■•■ • 3-<^9 33. Weight of Sand in Fresh Concrete (9) X (i^) + (19) + (20) •• ' -5-^^ 34. Weight of Coarse Aggregate in Fresh Concrete (18) (1°) X (jy) ^ (jg) ^ (^^) I2.J6 35. Weight of Water in Fresh Concrete (11) X ( q\ a_ t — x . , — n..../.7(5 36. Absolute Volume Cement in Fresh Concrete (assume i cu.ft.water, 62.4 lb.) (32) (22) X 62. 4X (29) o-^oj" ^7. Absolute Volume Sand in Fresh Concrete ^ iM (22) X 62.4X(3o) ■ °-^^S 58. Absolute Volume Coarse Aggregate in Fresh Concrete (34) ^ (22) X 62.4 X (31) °-W ^0. Absolute Volume Water in Fresh Concrete 7 — , ^' ,, r o.l8d •'^ (.22; X (02.4) T 40. Total Absolute Volume Materials (36) + (37) + (38) + (39) . .o.ggg 41. Density (36) + (37) + (38) 0.815 4^. Remarks Computed by G. B. Checked by S. E. T. ♦Adhering to Tools and Trays. Divide the Total Loss, (15) —[(18) + (19)], by Estimation into Items (20) and (21). 348 A TREATISE ON CONCRETE pour into iron molds set on an iron plate and imbedded in moist sand. Use 8 by 1 6-inch cylinders if the aggregate runs up to 2 inches or more, but 6 by 12-inch cyhnders will prove more convenient if the maximum size of stone is only i| inches. Tamp the concre.te with a 6-inch ice chopper, taking about the same precautions as are employed on reg- ular work. The time of dumping into the molds and tamping should never exceed 5 minutes. Trowel the top surface just previous to in- itial set. After 48 hours take the blocks out of the sand, remove from the molds and rebury in moist sand until the day before testing. Specimens for Bou^rh Tests. If the quality of sand is questioned and a laboratory is not available, a rough test may be made by mixing up a block of mortar or concrete, using the same aggregates mixed in the same proportion and to the same consistency that is to be employed in the work, and examining the specimens from day to day. If kept at a temperature of 65° to 70° Fahr. under a moist cloth, the mortar or concrete should harden after 24 hours so as to resist the pressure of the thumb, and at the end of a week in the air it should be hard and sound. Recording Test Data. Tests are so expensive to make that it is always worth a little extra trouble to record enough data to make them of general use to engineers. Through failure to do this, a large proportion of the tests that have been performed are of local value only. The form on page 347 is designed for recording data used while making specimens. To this may be added blanks for recording the properties of the materials used and for recording the results of the test. The form presented is designed to record not merely the informa- tion required for a compression specimen but also to include the data and to give the routine method of computing the density of the con- crete, (see p. 148) a matter of the greatest importance in studying the comparative qualities of different materials and mixtures. THEORY OF REINFORCED CONCRETE 349 CHAPTER XX THEORY OF REINFORCED CONCRETE Reinforced concrete is concrete in which steel or other reinforcing metal is imbedded to increase its strength. The reinforcement in gen- eral exercises an auxiliary function as it is not self-sustaining but re- quires the support of the concrete to develop its resistance. Thus most often reinforcement consists of small bars of little stiffness in them- selves but which, when uhbedded in concrete to secure lateral support and bond, are capable of developing tensile or compressive resistance equal to that of self-sustaining structural steel. An arch of the Melan type (see Chap. XXVI) may be considered a reinforced concrete struc- ture, provided the metal ribs, even if otherwise strong enough to carry all the load, are not connected by lateral bracing and therefore have insufficient stabihty without assistance of the concrete. A similar arch or a girder structure consisting of metal ribs connected laterally by metal bracing and strong enough to carry the entire load should not be considered as a reinforced concrete structure, since it is in reality a metal bridge encased in concrete, which serves, not for stress bearing purposes, but for the auxiUary purpose of protecting the steel against corrosion and giving the structure the appearance of a masonry structure. In a similar way concrete columns and other members may be reinforced with structural steel. When, however, as in steel frame structures fire- proofed with concrete, the steel is self-supporting, designed to take the whole or nearly the whole of the stresses with the concrete merely as an auxiliary for, or chiefly for, protection, the member is not reinforced concrete. The theory of the design of reinforced concrete is definitelyestablished. The action of combinations of steel and concrete in tension and compres- sion and shear has been analyzed so that a thoroughly rational treat- ment is possible. In practice, in beam design, the straight line theory, as it is termed (see p. 352), which was selected and adopted by the authors for the first edition of this Treatise, in 1905, has since that time been accepted as the simplest to employ in computation and as giving results which may be used in design with safety and economy. In this chapter is presented the analysis of this straight line theory of stresses for rectangular beams (p. 352) followed by the same theory 3SO A TREATISE ON CONCRETE applied to T-beams (p. 355). The analysis of a beam with steel in top and bottom is given on page 358, and the analysis of beams with the concrete assumed to bear tension on page 360. The analysis of shear and diagonal tension is on page 362. The theory of columns of reinforced concrete reinforced with verti- cal steel bars is treated on page 375, and that of columns reinforced with vertical steel bars and spirals on page 377. Analyses and formulas are presented for the distribution of stresses in reinforced concrete under combined thrust and bending moment (p. 377) for use in arch design and in the design of columns and beams with eccentric load or thrust. The theory of reinforced concrete chimney design is treated on p. 390. Formulas to use in practical design with illustrations of methods of treatment will be found in Chapter XXII. Tests of reinforced concrete covering all usual features of design are taken up in Chapter XXI. GENERAL PRINCIPLES OF REINFORCED CONCRETE BEAMS Concrete is very strong in compression but is brittle and unreliable in pull or tension. Therefore, it cannot be used economically where ten- sile stresses have to be resisted. Steel, on the other hand, being a com- paratively ductile material, is well adapted for resisting pull, but is more costly than concrete for resisting compression. The economy in the use of reinforced concrete is obtained by placing concrete where compressive stresses are to be resisted, and steel where tensile stresses are to be resisted. The high bond and shearing resistance of concrete holds the steel and concrete, together so that they act as one unit. Requirements for Formulas for Reinforced Concrete Beams. The behavior of reinforced concrete beams under load, as discussed on page 405, is different from that of homogeneous beams. The location of the neutral axis for varying intensities of load is not constant. The com- pression in the concrete is nearly proportional to the load but the pull in the steel is not proportional to the load because of the variable amount of pull resisted by concrete (see p. 407). Although it is thus impossible to make formulas which represent actual conditions during the whole process of loading, the common formulas for design of beams give safe and economical results. They must satisfy the requirements that: (i) The compressive stresses in concrete for working loads must not exceed the allowable unit stress. (2) The beam must have the required factor of safety based on ulti- mate loads and elastic limit of steel. THEORY OF REINFORCED CONCRETE 351 The first requirement fixes the unit stresses for concrete. Formulas satisfying these requirements produce a design having a larger factor of safety against compression failure than against tensile failure because concrete is less uniform in its qualities and also it may be caUed upon during construction to resist stresses before its full strength has been attained. To satisfy the second requirement, it is necessary in the analysis of beams to eliminate the variable amount of tensile stress carried by the concrete (see p. 405), and assume that all the tensile stresses are carried by steel. Analysis based on this assumption will not represent the actual conditions in a beam under working load because the actual stress in steel will be less than the computation will show, but it will give the required factor of safety and therefore be correct for design. On page 412 is given a comparison between actual stresses and stresses computed by the accepted formula for beams with different percentages of steel. It is seen that for earlier stages of loading, the actual stress is much less than the computed. The difference, which is due to the tensile resistance of concrete, decreases with the increase of the load. At the elastic limit of steel the computed stresses agree fairly well with the actual stresses. The action is shown by the tests, illustrated in Fig. 119, page 413, which give the deformations of concrete and steel at various loads. Stresses, of course, are proportional to the deformations. The elastic limit of the steel corresponds to the ultimate strength of the beam in tension. Therefore the factor of safety must be based on strength at the elastic limit and formulas must be used which give cor- rect results at this period of the loading. In analyzing the results of the tests in the early stages of the loading, it is sometimes necessary to consider the tensile stresses in concrete. Formulas for such a case are given on page 360. ASSUMPTIONS In the analysis of beams, the following assumptions will be made: (i) A plane section before bending remains plane after bending. (See p. 403.) (2) Tension is borne entirely by the steel. (See p. 351.) (3) Initial stresses are absent in the steel. (4) Adhesion of concrete to steel is perfect within the elastic limit of the steel. (5) Modulus of elasticity of concrete is constant. (See p. 400.) Reasons for selecting these assumptions are as follows: 352 A TREATISE ON CONCRETE (a) Beams designed by formulas based on them have the required factor of safety, (i) The method of design is the simplest, (c) Adoption by the highest authorities in America and Europe. ANALYSIS OF RECTANGULAR BEAMS* Bending Moment and Moment of Resistance. In a beam subjected to bending, the bending moment due to the external forces, or loads, is resisted by the moment of the internal resisting forces, which will be called stresses. Since by simple mechanics, the bending moment for equilibrium must be equal to the resisting moment of the internal forces, or stresses,' the unknown stresses in the materials may be found by equat- ing the known external bending moment to the internal resisting moment. Straight Line Formula. The stresses cause deformation in the mate- rial and the consequent deflection of the beam. At, any vertical section through this beam, the compressive stresses above the neutral axis cause shortening of the fibers, and the tensile stresses below the neutral axis cause lengthening of the fibers. Assuming that a plane section before bending is plane after bending, that is, that a plane section through a beam simply swings its position without warping when the beam is bent, the deformation, or change in length, in any fiber is proportional to its distance from the neutral axis, as shown in Fig. 98, page 353. With a constant modulus of elasticity (see p. 400), stress is always propor- tional to deformation; therefore, the variation of the resisting stresses from the neutral axis upward can be represented by a straight line, as seen from Fig. 98, page 353. The compressive stresses then form a triangle having for its base the stress in the extreme fiber, /c, and for its height the distance from the extreme fiber to the neutraL axis, kd. The total compression may be considered as concentrated at the center of gravity of the triangle, which is distant 5 kd from the extreme fiber. The tensile stresses may be considered as acting in the center of gravity of the steel, which for one layer of bars is at the center of the bar, and for more layers, at the center of gravity of the set of bars. For equilibrium, the sum of all forces must equal zero, or the total compression must be equal to the total pull. The total tension and total compression, which are equal and acting in opposite directions, form a couple with a moment arm equal to the distance between the center of steel and the center of gravity of the triangle of compressive stresses. *The formulas in this chapter were originally prepared by Prof. Frank P. McKibben. THEORY OF REINFORCED CONCRETE 353 The moment caused by this couple is the resisting moment. For equi- librium this must equal the bending moment due to exterior forces. FORMULAS FOR RECTANGULAR BEAMS For this and succeeding analyses, let = total depth of beam. = thickness of T-beam flange, i.e., thickness of slab. = breadth of rectangular beam or iDreadth of flange of T-beam. = breadth of web of T-beam. = area of cross-section of steel. = ratio of steel in tension to area of beam, bd. In beams with steel in top and bottom: pi — ratio of tensile steel to area of beam, bd; p = ratio of compressive steel to area of beam, bd. = compressive unit stress in outside fiber of concrete. = tensile unit stress in outside fiber of concrete. = tensile unit stress, or pull, in steel. = compressive unit stress in steel. ; = modulus of elasticity of concrete. . = modulus of elasticity of steel. Es "" =K d = depth from outside compressive fiber to center of gravity of stee^ a = ratio of depth of compressive steel to depth, d, of beam. k = ratio of depth of neutral axis to effective depth of beam, d. fs fs E, E. NEUTRAL AXtS Fig. 98. — Resisting Forces in a Reinforced Concrete Beam. (See p. 332.) kd = depth of neutral axis below the compressive surface in a beam. ;■ = ratio of lever arm of resisting couple to depth d. jd = distance between centers of tension and compression. e = thickness of concrete below center of gravity of tensile steel. M = moment of resistance or bending moment in general. C = constant in Table 15, page-sge. 354 A TREATISE ON CONCRETE Since it is assumed that a plane section before bending remains a plane section after bending, we have the proportion stretch in steel _d(i — k) deformation in outside compressive concrete fibers kd , . J , ^. stress per square inch , and since deformation = —. — , we have modulus of elasticity A E, d{i-k) f, I - k ■ 1 , — = or — = . (i) and k = (.2; fc_ kd nfc k Jj_ £. ' nfc Solving formula (i) for /^ Now, as stated above, for equilibrium the total tension in the steel must be equal and opposite to the total compression in the concrete. The total tension in the steel is its unit stress, /„ multiplied by the area of the steel, pbd, and the total compression in the concrete is rep- resented by the area of the pressure triangle, ^Jckd, times the breadth of the beam, b. Equating these two forces and canceling out the bd which occurs in both, If the value of k in formula (2) be substituted for the k in formula (4), we have I (S) For any given percentage of steel the values of /^ and /^ cannot be assumed independently, as they bear a constant ratio to each other. Substituting the value of /^ in formula (3) for/^ in formula (4) we have 2 » (i — ^) Solving this quadratic equation and adopting the positive sign before k= — ftp +'\2np + {npy (7) THEORY OF REINFORCED CONCRETE 355 From formula (7) the location of the neutral axis may be determined for any percentage of steel, p, and any assumed ratio of moduli of elas- ticity, n. Values for k are given in table on page 596. The center of gravity of the compressive stresses is distant | kd from the top of the beam so that jd = d — \kd = d{i —\k). Since the total compression equals the total tension, the moment of resistance of the beam may be obtained by multiplying either the total tension, phdf^, or the total compression, \fj}kd, by the moment arm, jd. M=pfjhd' (8) and U = ~^^ (9) M = hJ__ (,o) and /, = -^^ (XX) For a given quality of concrete and steel, the values olf;,f„ P, k, and y, are constant so that we may consider the terms pfsj=ifckj equal to a X constant ■j;:;^. This changes the formulas (8) and (xo) to M^^-^ and d=C^f (X2) C To obtain the total depth of beam, k, a value e (see Fig. 98) must be added to the theoretical depth, d. Then, h=d+e. For the use of these formulas in design, see pages 481 to 484. FORMULAS FOR T-BEAMS If a reinforced concrete beam is built monolithic with the slab, the beam may be considered as a T-beam in which a portion of the slab acts as a flange. The formulas for T-beams given below are based on the same assump- tions as for rectangular beams. Tension is considered as taken entirely by the steel and the variation of stresses in concrete is according to a straight line. Unless the slab is very thick the neutral axis is located below the flange. For notation see page 353. Case I. Neutral Axis Below Flange, kd > t Formulas Neglecting Compression Below Flange. Neglecting the slight amount of compression in the stem between the neutral axis and 3S6 A TREATISE ON CONCRETE the bottom of the slab and referring to Fig. 99, page 356, we have similarly as for rectangular beams: k = 1+^ (13) nfc The total tension is equal to the unit stress in steel, /j, multiplied by the area of steel, A^. The total compression in the concrete is repre- sented by a trapezoid, the sides of which are fc and /^ ; and kd the depth is equal to f. The total compression, therefore, equals , 2kd — t ,, Je ot. 2kd By equating total tension to total compression acting on the section (14) . , ^ 2kd — t ,. 2kd -f; kd-f kd ^ Steel t Cen t er Line o f Compression ±. Neutrql Axis Fig. 99. — Resisting Forces in T-shaped Section of Beam. (See p. 356.) Solving the two above equations for kd and eliminating fc and /j, we get Position of neutral axis kd = 2nd As + (is) 2nAs + 2bt The distance of the center of compression from upper surface of beam ^kd ~ 2t t 2kd — t 3 (16) THEORY OF REINFORCED CONCRETE 357 Arm of resisting couple jd = d — z Moment of resistance M = AJdf, (17) and ilf = ^-M^Mjdf, (17a) 2Ra Fiber stresses Ajd f = ^''^ _ fi ^ (j ) bt (kd — it) jd n 1 — k Area of steel As = (20) fsjd Formulas Considering Compression Below Flange. For large beams where the stem forms a large part of the compression area the above formulas do not give results accurate enough for practical purposes. For such cases formulas given below are recommended, which take into account the compressive stresses in the stem as well as in the flange. The following formulas are derived by the same principles used in deriva- tion of formulas in the previous analysis. Depth to neutral axis •> /..At /I T.l\ ±\'>. ..A \ 11. ■Lt\ 1 (21) (22) (23) Moment of resistance M = AJdJs (24) M==J^[{2kd-t)bt-\-{M-t)n']jd (25) 2kd Fiber stresses M , .-. , , ■ 2Mkd , s. /.= _ (26) and A=f(,,,_,)j,+ (,,_,).,,],., (^7) _ j2ndAs+{b-b')l-' .(nAs+{b-b')tV nAs + ^'^-^ b' +1 b' )~ (kdt' - f /') i + {kd - tY (t + \{kd- 0) {b - b') i b' b' t {2kd - t) b + {kd - t)H' Arm of resisting couple jd = d — z 35^ A TREATISE ON CONCRETE Case II. Neutral Axis in Flange or at Underside of Flange, kd< t In this case, which occurs only with slabs that are very thick in pro- portion to the depth of the beam, use the rectangular beam formula, considering the T-beam as a rectangular beam of the same depth, the breadth of which is the breadth of the flange. The percentage is then based on the total area bd. REINFORCED CONCRETE BEAMS WITH STEEL IN TOP AND BOTTOM In beams reinforced with steel placed both in the compressive and tensile portions of the beam, the steel in the compressive portion, as in columns (p. 375), may be considered as taking its share of compression according to the ratio of moduli of elasticity of steel to concrete (see P- 353)- Neglecting the tension in concrete, as in beams without com- pressive steel, all the tension may be considered as resisted by the bottom steel. Referring to Fig. 100, page 358, the total compression consists of the compressive stresses in concrete represented by a triangle and the compressive stress in steel. The compressive unit stress in steel equals the unit stress in concrete at the same level multiplied by the ratio of their moduH of elasticity. j^/^ Fig. 100. — Resisting Forces with Steel in Top and Bottom of Beam. {See p. 358.) The sum of all the horizontal stresses acting on a cross section must equal zero; therefore, the total tension in steel must be equal to the compression in concrete plus the compression in the top steel. The resisting moment, that is, the moment of the internal stresses, may be obtained either by multiplying the total tension or compression by the distance between center of tension and center of compression, or by taking moments about the center of tension steel, the center of compres- sion in concrete, or the center of compression in steel. The moments of resistance obtained by either of the four methods must be equal. To THEORY OF REINFORCED CONCRETE 359 find the stresses for a certain loading, the moment of resistance taken in any one of these ways is equated to the known bending moment. Formulas. Deformations, as iisual, are assumed to vary directly as distance from neutral axis, hence from Fig. 100, using notation on p. 353, A E^^di,-k)^r-k ^vhence^ = — ^ (.8) f^ dk k ^_^_4 By comparing the above equation for k with that given for simple beams, page 354, it is evident that for any ratio of—, the position of the neutral axis is the same irrespective of whether the beam is provided with compressive steel or not. By similarity of triangles in Fig. 100, page 358, the following relations between the unit stresses may be obtained: ^''^f'^:r~h ^^9) and f's=nfc^— (30) fs = nf.l^ (3X) and /. ^^ ^ (3^) The total tension in steel equals bdpif, and the total compression in steel and concrete is bd^-^+ bdpj: = bd {if,k + p'fi) Since the sum of all the stresses must equal zero, the total compression acting on the cross-section of the beam equals the total tension, or bd{lj- + p'f'}j=bdp,f, Whence /-. = i (^ + p' f) = 7 (^ ^ + P% '-^ ¥■ , ,k — a , , Hence pi = — + p' (33) 2n{i — k) I — « Solving equation (33) for k, = -^2 11 (pi + p'a)+nHpi + p')'-n{pi+p') (34) 36o A TREATISE ON CONCRETE Taking moments about the center of compressive stress in the steel we have or by eliminating /c pi (i-a) 2n (i - k) —k^(- — a) M=f,bcP From which 2n (i — k) (35) f = E 6^^ (^ - ^) (36) M2 6^ p^ (j _ ^) (i _ a) - /^2 (^ - 3a) By substituting this value of /, in equations for/^ and fs respectively, we get /^ = — 7—, ^-7 ^ TITT-, ^ (37) and bd" 6n pi (i - ~k)ii-a)- k' (k - 3a) M 6» (k — a) b(P 6n pi (i - - k)ii-a)~ ¥ (k - 3a) fs = f^ — - — ,rr r „., . (38) It may be noted that the denominator in the three above equations is the same. A simplified method of using the formulas in practical design is given in the chapter on design. STEEL IN BOTTOM OF BEAM, CONCRETE BEARING TENSION. It is often required to find the actual stresses in reinforced concrete beams during the first stage of loading, for instance, to determine the load at the first crack, or the tensile stress in concrete at the first crack. In the first stage, which, as explained on page 405, lasts tiU minute cracks open, concrete may be considered as bearing its share of ten- sion. Therefore, the formulas given below, considering tension in con- crete and based on straight line distribution of stress, may be used for the above purpose. These formulas must not be used, however, in designing reinforced concrete beams. E Formulas. Assimie that the ratios of moduli of elasticity, — = w, are equal for concrete in tension and compression. Since elongation of steel and concrete at the same point must be equal and the cross-sec- THEORY OF REINFORCED CONCRETE 361 tional planes are assumed to remain plane during bending, we have from Fig. loi the following equations using notation on page 353: E, d- kd , , .1 d — kd f^ h - kd hence /, = nf'. - kd fc=f'c kd fs = nf. (41) I - k also /,' = /, h—kd h-kd " -" ■"' kd Equating horizontal forces on the section, we have 2 2 Expressing /j and fl in terms of /^ and simplifying, we have, kd ^ i-k , (h-kd)^ — = p dn + -^ — 2 k 2kd (39) (40) (42) (43) (44) Fig. 101. — Resisting Forces with Concrete Bearing Tension. {See p. 361.) From which This solved for k gives \2w/ \d/ I 2k d + 2pn K 2 (4S) f46) +pi 362 A TREATISE ON CONCRETE Taking moments about the center of the steel and expressing /^ in terms of /^, we have, for the moment of resistance: M = _/c* kd' (l - _k\__(h-kdy/^_ kd 3/ kd \ 3 2h 3 . _ fcbh 2 2d—-\i+k — i-] k\ dl . (47) Taking moments about the resultant of the compression and expressing /j in terms of /^ (Formula (39) ) we have: M = i My, and /:= M i^-k) (3-k) _^h(h — — k 3(^' (48) bd' ,p{i-k) (s-k)+^('i-kY d \d I (49) Also by substituting for /^ the values from Formulas (43) and (39) .3* ^' bd' fs = M . np{i-k)i3-k)+^('^- d \d 3n (i - k) bd^ np (i -k){3-k) + d \d (so) (51) For a given bending moment, M, stresses may be found from the above formulas. Note that denominators in all equations are the same. SHEARING STRESSES IN A BEAM OR SLAB The bending of a beam produces a tendency of the particles to slide upon each other or shear. It is therefore necessary to study (i) Vertical shearing stresses. (2) Horizontal shearing stresses, Vertical and Horizontal Shearing Stresses. Concrete is strong in direct shear (see p. 337) and capable of standing a working shearing THEORY OF REINFORCED CONCRETE 363 stress of at least 200 pounds per square inch, so that a concrete girder or beam or slab always has sufficent area of section to withstand this direct shearing stress. However, since the direct shearing stress is a measure of the diagonal tension (see p. 365), which is excessive when the direct shearing stress is comparatively low, it must always be computed in a beam or girder for use in the computation of diagonal stresses, as described on page 367. The shear is a maximum at the support, where it is equal to the reac- tion. Maximum shears for various loads are given in the diagram (Fig. ^51) page 505), in terms of the loads. While with uniform or symmet- rical loading the reaction, and therefore the maximum shear, is one- half the total load upon the beam, it will be noticed from the diagram that where the end beams of continuous beams are freely supported, which is very nearly the case when a beam runs into a light wall girder, the shear at the first support away from the end may be 25 per cent greater than normal, and should be specially provided for in cases like a ware- house where the full live load is liable to be constantly maintained. A further study of the four diagrams (Figs. 151 to 154, pp. 505 and 508) will illustrate the cases where allowances should be made. In case the concrete in a beam or slab has cracked vertically next to the support because of accident or poor design, the bearing value of the horizontal rods may have to be estimated. < s C •} " B CI i A *— «— , A Fig. 102. — Section of a T Beam. (See p. 363.) Longitudinal Vertical Shear in Flange of T-Beam. Vertical shear in a longitudinal direction is present in the wings of a T-beam due to the load upon a beam being maximum next to the flange, as shown by lines BA in Fig. 102, page 363. Results of tests are given on page 416. The area of concrete in a solid horizontal floor slab is generally sufficient to take care of this shear, but the following method may be used for computing it if desired ; 364 A TREATISE ON CONCRETE Let v/, = imit horizontal shear at A A. Vy = unit vertical shear at BA. b' = breadth of stem. b = breadth of flange. / = thickness of flange. The shear along the two planes BA may be considered as caused by the external forces acting not on the whole breadth, but only on the project- ing flanges of the T-Beam BC. Then it is readily shown* that VH b' (b - b') 2tb (52) Although this vertical shear through the flanges is readily borne by the concrete, it is advisable, as stated on page 418, to place horizontal bars across the top of the beam, even if the bearing bars in the slab run paral- lel to the beam, in order to resist unequal bending moment which is liable to occur and to assure T-beam action. Fillets at the angles between the flange and the beam, that is, between the slab and the beam, are not theoretically necessary, but they may be used for appearance sake and as an additional security in a deep beam with relatively shallow flanges or slabs. Small fillets are also advisable to aid in the removal of forms. DIAGONAL TENSION In a beam, besides direct horizontal tension and compression and direct horizontal and vertical shearing stresses, there exist also stresses acting in diagonal directions. The maximum diagonal stress composed of the tension and the shearing stresses is called diagonal tension. In steel and other homogeneous beams diagonal stresses need no attention. In reinforced concrete, however, it has been shown in beams tested to destruction that, beside tensile cracks at the points of maximum moment, diagonal cracks, caused by diagonal tension, develop near the supports. (See tests on pp. 418 10427.) These cracks have been of ten the cause of failure, frequently without warning, especially in beams reinforced with straight bars only or provided with insufficient web reinforcement. The need of low working stresses and effective web reinforcement is discussed in paragraphs which follow. b-h' •The above principle may be expressed by the equation ti^ 2t= Vf^b' ~~^, which solved for v will give formula (52}. THEORY OF REINFORCED CONCRETE 365 Diagonal Tension in Homogeneous Beams. The magnitude and in- clination of the diagonal tension in homogeneous beams may be found from the following formula: Let fd = diagonal tensile unit stress. fc = horizontal tensile unit stress. V = horizontal or vertical shearing unit stress. Then* fi = if'c+^if> + ^ (S3) The direction of this diagonal tension makes an angle with the horizontal equal to one-half the angle whose co-tangent is ^ — • V From the formula it is evident, since the value of /^ and v vary in dif- ferent parts of the cross section of the beam, that the value of the diag- onal tension and its angle of inclination also vary. At the bottom of the section where v=o, fd=fc and acts horizontally. At the neutral axis the direct tension, /^ = o, which reduces the formula to/j = » and the angle of inclination to 45°. Measure of Diagonal Tension for Reinforced Concrete Beams. In homogeneous beams, the diagonal forces can be determined easily by means of formula (53) above. In reinforced concrete, however, the diag- onal stresses are indeterminate because, as seen from the formula, they depend upon the horizontal tensile stresses in concrete, /<;. The action of concrete in tension is not dependable. It varies, also, for different stages of loading because for larger loadings concrete cracks, thus decreas- ing the tensile stresses carried by concrete. The tensile strength of concrete, which may be disregarded in figuring the moment of resistance of the beam, affects the magnitude of the diagonal tension to a great extent especially near the ends of simply supported beams where the stresses due to the bending moment are low and the stresses in concrete may not exceed its breaking strength in tension. While the exact de- termination of diagonal tension is impossible, tests show that the shear- ing unit stress, figured as given on page 367, may be accepted as a con- venient measure of diagonal tension. That is, the diagonal tension may be assumed as proportional to the direct shearing stress so that, by adopting proper working stresses based on tests producing diagonal tension failures, formulas for shearing stresses may be used for diagonal tension. This measure has been universally accepted and, in aubse- * For derivation see Merriman's "Mechanics of Materials," 19.05 edition, p. 265. 366 A TREATISE ON CONCRETE quent discussion, diagonal tension is expressed in terms of shearing stresses. Diagonal Tension in Simply Supported Beams. In simply supported beams, diagonal tension cracks start at the bottom of the beam, not at the support where the shear is greatest, but far enough out for the ten- sile stresses due to the bending moment to break the concrete. Hence, the importance of using enough tensile steel, in addition to the web reinforcement, to keep these unit tensile stresses near the supports low. Tests of beams otherwise comparable in size, reinforcement, and load- ing, show that diagonal cracks that actually develop can be prevented by the use of an increased amount of horizontal steel near the support. Not more than two-thirds of the horizontal bars in simply supported beams should be bent up near the support. Diagonal Tension in Continuous Beams. In continuous beams it is ihe top of the beam near the support that is in tension instead of the bottom. Accordingly, to prevent cracks, the steel should run well out on each side of the support before being bent down to carry the tensile stresses in the bottom of the beam near the center of the span. The proportion of the bottom horizontal steel, therefore, that may be bent up in fixed and continuous beams is much larger than in simply supported beams and may even exceed two-thirds the total area of the steel in the center without increasing the danger of diagonal cracks. Enough must be left for all requirements of tension and compression produced by the bending moments. Formulas for Shearing Stresses and Diagonal Tension. A convenient and safe method of determining the diagonal tension is by accepting for its measure the unit shearing stress as discussed on page 365. et total shear at section considered. (Reaction minus the loads between the support and the section.) V = horizontal (or vertical) shearing unit stress at section considered. b = breadth of beam. b' = breadth of web of T-beam. jd = moment arm or distance between center of compression and center of tension (approximately, in a T-beam, distance between center of slab and steel). Z = total shearing stress or diagonal tension in a given length of • beam, s. s — length of the portion of the beam considered. THEORY OF REINFORCED CONCRETE 367 The following general principles and formulas are discussed in para- graphs which follow. (i) Horizontal (or vertical) shearing stress is zero at the top of the section and changes according to a parabola till it reaches its maximum at the neutral axis. (See Fig. 103). Distfibution of shearing stresses Fig. 103. — Horizontal and Vertical Shearing Stresses in Beam. {See p. 368.) (2) If tension in concrete is» neglected, the horizontal (or vertical) shearing stress is constant below the neutral axis. (3) Total amount of horizontal shearing stress developed at any hori- zontal plane below the neutral axis in a distance, s, is Vs (54) (4) Shearing unit stress, the measure of diagonal tension, is total horizontal shearing stress, Z, divided by the horizontal area, b y, s, Vs that is 2/ = -r^ -V- bs. jd Hence " = bfd ^''^ For T-beams, v —-rr^ jd (ssa) If the shear V changes in the distance, s, the same formulas may be used except that V in the formula is the average shear in that section. (5) Vertical shearing unit stress is equal to the horizontal shearing unit stress, and acts at right angle to the plane of horizontal shearing stress. The distribution of vertical shearing stress over a vertical sec- tion is shown in Fig. 103. 368 A TREATISE ON CONCRETE (6) Diagonal tension may be expressed in terms of the shearing stress and the above formulas may be accepted as its measure. (7) If the width of the section below the neutral axis is not constant, the shearing unit stress will vary with the width, b. The minimum b must be taken in figuring the maximum shearing unit stress and the maximum diagonal tension. (8) In continuous T-beams, near the support, the maximum shearing unit stress will be in the stem right under the flange. The shearing stress and diagonal tension in the plane of tensile steel is small because the width, b, being the total width of the flange, is large. The action of horizontal shearing stress is illustrated in Fig. 103. A portion of a beam between two vertical sections subject to bending stresses is represented. If the bending moment at the left is Mi, the shear, V, and the length of the section, s, then, from the principles of mechanics, the bending moment at the right is M, = Mi-\- Vs. Since the bending moment at the right is larger than the bending mo- ment at the left, the unit compressive and tensile stresses at the right sec- tion are larger than at the left. Consider an arbitrary longitudinal plane, ef, above the neutral axis. The compressive stresses above this plane represented by the shaded portions of tRe triangles are at the left equal to Cyi, and at the right, C,, = Cy + ACyj. The difference between the two forces Cyi and Cy„ which act in opposite directions, is ACyi. This tends to move the upper portion of the beam along the plane effiei, but is kept in equilibrium by the horizontal shearing resistance in the beam on that plane. The shearing unit stress is equal to ACyi divided by the area, bs, of the plane, effiei. At the top of the beam the value of ACyi and also the total shearing stress is zero and increases steadily according to a parabola till it reaches its maximum at the neutral axis. There its value equals the difference between the total compression on the right and the total compression on the left. From the ordinary beam formulas, page 355, we know that the total compression may be found by dividing the bending moment by Ml the moment arm; thus, at the left, the total compression is Q = -— -, and Jd ,,, .,,r ^' Mi.Vs at the right, C, = -rj = -rr + -^■ jd jd jd Vs The difference between C; and C^ is thus, -rr" Therefore, the total Jd amount of horizontal shearing stress at the neutral axis for the length, THEORY OF REINFORCED CONCRETE 369 Vs s, and width, 6, is Z = — ■ This has to be resisted by the horizontal plane of the beam, bs, so that the shearing unit stress, Vs V w is -rr divided by hs, or v = ■ — . (1:6) jd bjd ^ If there is no tension in concrete, the difference between the stresses acting above any plane located below the neutral axis is the same as the difference at the neutral axis. Consequently the total horizontal shear- ing stress is uniform at all planes below the neutral axis. As the shear- ing unit stress depends upon the width 6, it is constant for rectangular sections, but varies with variable b. At the plane of reinforcement the stresses in steel at the left are Ti= ~; and at the right, T, = ^ = — / + ^, and the difference, ]d jd jd jd Vs Ti— T, = -— . This shows that the total horizontal shear or the tend- Jd ency to move the upper portion of the beam is the same at the plane of the bars as at the neutral axis. If there is tension in concrete, the total horizontal shearing stress, Z,on. any plane below the neutral axis will be decreased by the difference in tension at the two vertical sections above that plane. Ys The increase in the stress in steel, equal to -rj, between the two sec- Jd tions considered, must be transferred from the steel to the beam. There- fore, bond must exist between steel and concrete or else the upper portion of the beam will slide on the steel instead of increasing its stress. Tests of bond or resistance to slipping of bars are treated on page 429. Siagonal Tension Acting on an Element of a Beam. Fig. 104 rep- resents the stresses to which any element of a be,am is subjected. In Fig. 104a is shown a rectangular element of the beam the sides of which are dx and dy. This element is kept in equilibrium by six forces: two forces f'^dy acting in opposite directions being either direct tension or compression; and four shearing stresses caused by the increment of the moment, as explained in the preceding paragraphs. The two hori- zontal shearing stresses form a couple, wliich is resisted by a vertical couple. The moments of the two couples are equal, wherefore the horizontal shearing unit stress must be equal to the vertical shearing unit stress. 37° A TREATISE ON CONCRETE If we consider any inclined plane by taking a triangle instead of a rectangle, as in Fig. 104b, we find that this triangle is kept in equilibrium by five forces: one of them is f'cdy; three forces are shearing stresses on the three surfaces; and the last force is the diagonal tension, f^dz. The magnitude of this force may be found from formula (53) , page 365 . For each case there is a certain inclination of the plane for which the diagonal tension is a maximum. Fig. 104c represents a case when there is no direct tension or compres- sion or /c = o and the length of sides are units. In this case, as is evident Fig. 104. — Stresses Acting on an Element of Beam. {See p. 369.) from the force polygon in Fig. io4d, the magnitude of the diagonal force isfd'^2. The hypothenuse is V2; consequently the diagonal unit force is V, or the diagonal unit tensile stress equals the shearing unit stress. For reinforced concrete beams, the shearing unit stress is considered as the measure of the diagonal tension as to the magnitude, but not as to the direction, as seen from Fig. 104& to 104^. Distribution of Diagonal Tension to Concrete and Stirrups. Tests prove that in beams with web reinforcement, both concrete and steel resist the diagonal tension found by formula (54), page 367. The relative portions of stress taken by the concrete and steel are somewhat in- determinate. Assumptions variously made are: THEORY OF REINFORCED CONCRETE 371 (i) Web reinforcement takes all the diagonal tension with no re- liance on concrete. The web reinforcement therefore resists m the length s; -— . Jd (2) Web reinforcement takes two-thirds of the diagonal tension and the concrete the remainder. Web reinforcement resists in the 2 Vs length, s, the force g j^. Where the shearing unit stress does not exceed the allowable unit, v', all stress is taken by the concrete. (3) Concrete resists a certain definite unit stress per square inch, !)', the whole length of the beam, and the stirrups resist the remainder. Then in a length, s, the concrete resists v'bs, and the web reinforcement resists, „ „ „ Vs ,. V-v'bjd Zi = Z — vbs = -— - — vbs = — -^ 5. jd jd The first assumption corresponds to that made in ordinary beam design where the tensile strength of the concrete is disregarded. Tests have shown, however, that the actual stresses in the stirrups are less than would be obtained with this assumption (see page 419). The second assumption, that the web reinforcement takes two-thirds of the diagonal tension stress and the concrete the remainder, more nearly corresponds to actual conditions in a beam, and is therefore recommended for adoption.* At first thought it seems irrational to assume that con- crete without stirrups is safe for, say 40 lb. per sq. in., whereas a stress of 45 lb. allows only 15 lb. for concrete, but it is recognized in reinforced concrete that as soon as the limit of safe strength of concrete is passed, a large proportion of the stress must be transferred immediately to the steel. Area and Spacing of Vertical Stirrups. The area of steel and the spacing of stirrups may be found by placing the force to be resisted, as given above, equal to the working strength of the stirrups in tension. Let X = distance in feet from left support to point at which required spacing is desired. xi = distance in feet from left support to point beyond which stirrups are imnecessary. I = span of beam in feet. w = uniform load in pounds per foot. * Also recommended by the Joint Committee on Concrete and Reinforced Concrete. 372 A TREATISE ON CONCRETE V = total vertical shear in pounds at section x feet from left support. V = total shearing unit stress at section in pounds per square inch. v' = allowable shearing unit stress (or diagonal tension) on concrete alone. A; = cross-sectional area of all legs of a vertical stirrup in square inches. (In a U-stirrup this is the sum of the area of the two legs.) /j = allowable unit stress in stirrups in pounds per square inch. jd '= distance in inches from center of compression to center of hori- zontal reinforcement. (In a T-beam, this may be taken as distance between center of slab and steel; in a rectangular beam, as 0.87 of the total depth to steel.) b = breadth of beam in inches. b' = breadth of web in T-beam in inches. .s = spacing of stirrups in inches at a place x feet from left support. Since A^ is the area of a stirrup resisting diagonal tension in a distance, s, and/j is the tensile strength of steel, the strength of the stirrup in pull is Asfs. The area of stirrups and the spacing for different assumptions of distribution of. diagonal tension between stirrups and concrete may be found as follows :* (i) Area and spacing if stirrups take all the diagonal tension. Vs Vs The diagonal tension to be resisted is -— . Hence AJ, = -rr , and ]d jd As = ^--s (s7) and s^^-A, (57a) (2) Area and spacing if stirrups take two-thirds of the diagonal tension. 2 Vs 2 T'''^ Diagonal tension to be resisted is — rr-. Hence Asfs= ■ , and Z jd 3 jd we get by solving for A j and s, A,^-J-s (58) and s = ^-l^A, (s8a) 3 fsjd 2 V Formulas (58) and (58a) are recommended by the authors. (3) Area and spacing if concrete takes a definite amount of shear, v', and the stirrups, the remainder. The stress resisted by concrete in the distance, s, equals v'- bs. As Vs the total stress is Z = — , the stirrups must carry the difference, * The numbers of the formulas are changed from the second edition. THEORY OF REINFORCED CONCRETE 373 Vs ,, V-v'bjd -— — v'bs, or —:i— s. jd jd Equating this to the resistance of the stirrup, AJ„ and solving for A, and s, we get A. = ^^^s (59) and s = ^^A. (spa) fsjd (F - v'bjd) In T-beams use width of web b' in place of b. Uniformly Distributed Loading.* For uniformly distributed loading of w per lin. ft., the shear involving diagonal tension at any point distant from the support is F = — — wx = — {l — 2x), which, sub- 2 2 stituted above, gives: (1) If stirrups take all the diagonal tension. A,= -s (60) and 5= /'■' A, (60a) 2j^id w{l— 2X) (2) If stirrups take two-thirds of the diagonal tension. A,=- -s (61) and 5 = y'-' A, (6ia) if, id w{l— 2X) Formulas (61) and (61a) are recommended by the authors. (3) // concrete takes definite amount of shear, v', and stirrups, the rest. w (I — 2x) — 2v'bjd ,, , J 'ifsjd , ,, . A, = — ^^ —s (62) and .y = — ^-^ A, (63) 2fsid w{l — 2x) — 2v'bjd In T-beams use width of web b' in place of b. Tables 9 and 10, made for case (2), where concrete is assumed to take one-third of the shear and stirrups two-thirds are given on page 585. These are recommended for general use. Stirrups should be spaced by equation (s8a) or (6ia) up to a section where unit shear equals working shearing strength of concrete, bearing in mind, however, that the maximum spacing should not exceed three- fourths the depth of the beam. The distance from the support to the point where no stirtups are required, for uniform loading isf * The numbers of the formulas are changed from the second edition. t The diagram of shearing unit stresses is a triangle (Fig. 159, p. 526.) from which the distance Xi may be obtained by the known rule --i- 1- — xA = v -i- v'. This equa- tion solved for Xi gives formula (64), page 374. 374 -4 TREATISE ON CONCRETE From the above formulas it is evident that the necessary spacing of stir- rups is inversely proportional to the total shear V at any point and there- fore is the smallest at the end of the beam and increases toward its middle. Many constructors advise the insertion of occasional stirrups through- out the entire length of the beam even if they are not theoretically neces- sary. For a small beam where the stirrups are spaced uniformly, for con- venience, only the minimum value of s needs to be figured. Usefulness of Weh Reinforcement. Numerous tests have demon- strated that a beam properly reinforced with stirrups or bent bars sus- tains three or four times as much load as the same beam without web reinforcement. The same tests, however, show that the web reinforce- ment retards the appearance of first diagonal cracks only very little and that the web reinforcement does not get any stress until the first crack appears. It has been noticed* also that under working loads (that is, before the diagonal tension exceeds the tensile strength of the concrete) the beam acts similarly to a homogeneous beam, and as would be expected, the stress in the stirrups is sometimes compressive instead of tensile. This is, nevertheless, no argument against the use of web reinforce- ment, because in beams without stirrups, final failure follows closely the appearance of the first crack, while with beams having web reinforce- ment, stirrups and bent bars represent a factor of safety which allows stressing of conci'ete in diagonal tension nearly to its ultimate strength without any danger to the stability of the structure. Under working loads the stirrups may not act, but in case of overstressing, due to faulty construction or to occasional excessive loading, the stirrups pre- vent the failure of the beam. The minute cracks that may open are not dangerous and in many cases are hardly visible. Weh Reinforcement for Continuous Beams. The formulas given above are based upon results obtained from the tests of simply supported beams. Their use for continuous beams is on the safe side. In continuous beams, several conditions tend to prevent or at least to retard the formation of diagonal cracks. The compressive force, due to the reaction, tends to close the developed cracks. There exists also almost invariably some arch action, which decreases the direct and * Bulletin No. 64, University of Illinois, January 13, 1913. THEORY OF REINFORCED CONCRETE 375 diagonal tension. In continuous T-beams, the horizontal shearing unit stress is zero at the bottom and increases till it reaches a maximum at the neutral axis. From there it is constant till it reaches the bottom of the flange. As the width of the flange is much larger than the width of the stem, the shearing unit stress in the flange is much smaller than in the stem. Diagonal cracks, therefore, tend to open in the portion be- tween the neutral axis and bottom of flange, and larger unit .stress is required to open them than in simply supported beams. As there have been comparatively few tests on continuous beams, the formulas for web reinforcement given above should be used. "Web Reinforcement for Cantilevers. The conditions affecting web reinforcement is the same for cantilevers as at the supports of con- tinuous beams. In cantilevers supporting vertical loads, vertical stir- rups must, therefore, be attached to the tension steel (at the top) and the free ends hooked in the compressive portion of the beam (at the bottom). In other cantilevers, the stirrups must be placed parallel to the direction of the force and attached in the manner suggested above. COLUMN FORMULAS. For reinforced concrete columns centrally loaded, the following formu- las may be developed: Let / = average compressive unit stress upon the reinforced column-, equal to the total load divided by the effective area. fc = average compressive unit stress upon the concrete of the column. /, = average compressive unit stress upon the vertical steel in the column. ; E n = — ^^ = ratio of modulus of elasticity of steel to modulus of elasticity of concrete. P = load to be sustained by the column. A = area of total effectiA'e cross-section of column (see pp. 289 and 558) . Ac= area of concrete in effective cross-section. As= area of steel in cross-section. * = _i = ratio of area of steel to total effective area of column. A Since, as is evident from tests, a reinforced concrete column under load acts as a unit, the deformation or shortening of steel in the column is the same as the deformation or shortening of the concrete. 376 A TREATISE ON CONCRETE „ , . stress per square inch •, j <■ i- u From mechanics, 2 — ; = unit deformation, hence modulus of elasticity — = unit deformation of steel and — = unit deformation of concrete. Es E, The deforrriation of steel in a reinforced column is the same as the deformation of concrete and since — ^ = n, we have : A = A and /: = nL The stress in steel is therefore equal to the stress in concrete multiplied by the ratio of the moduli of elasticity, n. If a column sustains a load P, stresses in steel and in concrete must be equal to the load. Hence: P=f^Ac+/sAs or P =fcA + nfcAs Since Ac=A — As, we have P=fc [{A—As)+nAs] Finally, P=fAA + in-i) A,] (6s) and /, =^^^^__ (6sa) A + in- I) As The area of steel, A^, may be expressed in terms of ^, by substituting As=pA, which changes the above formulas to P = fA [i + U - i) p] (66) and /, = — ^ — (66a) Knowing the stress, fc, and the percentage, p, we may find the required area from A = ~ (67) /, [i + (« - i) p] Knowing the stress, /c, and the total area, the required area of steel, A„ and the percentage may be found from A, = ^pM (68) and p = IfJA. (68a) The average unit stress which is the total force, P, divided by the effective area, ^, P P /■ = — and A — — A f THEORY OF REINFORCED CONCRETE 377 The relation between / and fc may be found by substituting for P in the above equation its value from formula (66), giving f = fc[i + (n-i)p] '(69) Values of / for different percentages of steel are given on page 599. Columns with Spiral Reinforcement. The ultimate strength of a column with spiral reinforcement depends upon (i) the amount of vertical steel, and (2) the amount of spirals. Therefore in formulas for the breaking strength of a spiral column the amount of spirals must be considered. In design, however, the elastic hmit and not the break- mg strength of the column is the determining value as explained on page 456. As this is not affected by the amount' of spiral reinforcement, but by the amount of vertical steel only, the formulas given above for columns with vertical steel can be used and the difference in the two types taken care of in the assumed working unit stresses in the concrete. (Seep. s6i.) MEMBERS UNDER FLEXURE AND DIRECT STRESS The following formulas apply to cases in which members are sub- jected: (i) simultaneously to a bending moment and a direct thrust; (2) to an eccentric thrust. The first condition takes place, among others, in wall columns, which besides 1 the vertical load must sustain a bending moment caused by a rigid connection between the beam and the column. The second condition occurs in arches when the line of pressure does not coincide with the neutral axis in which case the. thrust acts on an eccentricity (see p. 718). A central load and a bending moment may be replaced by an eccentric thrust in which the eccen- tricity equals the bending moment divided by the thrust, and in turn the eccentric thrust can be replaced by a central load and a bending moment equal to the thrust multiphed by the eccentricity. Therefore the two cases will be treated at the same time because the method of determining stresses is exactly the same in both cases. PLAIN CONCRETE SECTION UNDER DIRECT STRESS AND BENDING MOMENT General Formula. For members subjected to a central load and a bending moment (or to an eccentric thrust) the stresses may be ob- tained by computing separately the stresses caused by the central load and by the bending moment. The sum of the results then gives the actual stresses. 378 A TREATISE ON CONCRETE Notation Let R = resultant of all forces acting on any section. fg = maximum unit compression in concrete. fc = maximum unit tension in concrete or minimum compression. N = thrust, a component of the forces normal to the section. V = shear, the component of the force R parallel to the section. b = breadth of rectangular cross section. h = height of rectangular cross section. e = eccentricity, that is, the distance from gravity axis to the point of application 'of the thrust which is the intersection of the line of pressure with the plane of the section. M = bending moment on the section. y = perpendicular distance from gravity axis to any point in the section. 1 = moment of inertia of entire cross section of concrete about, the hori- zontal gravity axis. /j = moment of inertia of cross-section of steel about the horizontal grav- ity axis. A = total area of cross-section. .4j = total area of section of steel. yi = perpendicular distance from gravity axis of unsymmetrical section to outside fiber having maximum compression. y, = perpendicular distance from gravity axis of unsymmetrical section to outside liber having maximum tension or minimum compression. fn = maximum unit compression in the steel. /, = maximum unit tension or minimum unit compression in the steel. p =• ratio of steel to total area of section; for rectangular sections p = ratio of steel area to bh. Es . n =— = ratio of moduh of elasticity of steel and concrete. k = ratio of depth of neutral axis to depth of beam k. kh = distance from outside compressive surface to neutral axis. d' = depth of steel in compression. d = depth of steel in tension. a = distance from center of gravity of symmetrical section to steel. e^ = value of eccentricity which produces zero stress in concrete at outer edge of rectangular section opposite to that on which thrust acts, Co, Cj = constants. THEORY OF REINFORCED CONCRETE 379 The stresses produced by a central load are uniformly distributed and are equal to - . The stresses produced by the bending moment, M, at any point at a distance, y, from gravity axis, as found by mechanics, equals ± —^- The sign depends upon whether the point is above or below the axis. The combined stresses, therefore, at any distance, y, from the axis of gravity equals the sum of the two above ex- . N Mv pressions, i.e. — =t —^ • From the above, it is evident that the second term varies with the position of the point in relation to the axis of gravity. Therefore the stresses vary from a maximum at one edge to a minimum at the opposite edge. Formulas for Rectangular Sections. Since in a rectangular section, A = bh, and I = — , the above formula for stress at any point changes to /^ = ^ ± ' - ■ Since the bending moment, M, equals Ne, the on on' N { X'^£v\ above formula may also be written, f,= — ( 1 --: -^^ ). As a rule, ■^ ■' hh\ h^ / we are concerned with maximum and minimum stresses which occur for y ± -• After substituting the value for y, we get 2 Maximum compressive stress, fc — —' i + — I bh\ h/ (70) Mmimum stress, /^ = — 1 i — — 1 bh \ h/ (71) The maximum stress is always compression. The minimum stress from Formula (71) may be either compression when — is smaller than /' h unity, that is, when e is smaller than -■ For e = -, or, when the force acts at the edge of the middle third of the section, the minimum stress equals zero, and the maximum stress equals double the stress caused by a central load of equal intensity. (See Fig. 105, p. 380.) h When e is larger than -, that is, if the load acts outside of the middle third, then the minimum stress is negative, i.e. the section is subjected 38o A TREATISE ON CONCRETE to tension. In such a case, this formula can be applied only when the material is capable of carrying tensile stresses. If the material cannot resist tension, as in masonry foundations, or in concrete where tension exceeds the allowable stress, it is necessary Force Within the Middle Third Force at Edge of the Middle Third Force Outside the Middle Third Fig. 105. — Stresses Caused by Eccentrically Applied Thrust. {See p. 379.) to assume that the pressure is distributed only over a section equal to three times the distance of the point of application on the load from the nearest edge. (See Fig. 106.) If that distance is g, the total effective width of the section is 3g. Substituting in Formula (70), e =—, and h 2 3^1 we get for plain concrete and masonry fc = '-^ (72) 2N_ DISTRIBUTION OF STRESSES IN REINFORCED CONCRETE SECTIONS General Formulas. The distribution of stresses over a reinforced con- crete section caused by a central force and a bending moment can be determined by the following formulas. As in column design (p. 376), the area of steel may be replaced by an area of concrete obtained by multiplying the steel area by n, the ratio of the modulus of elasticity of steel to the modulus of elasticity of concrete. This concrete should be placed at the same distance from the neutral axis as the steel area. The area of the transformed section, then, is A-{-{n—j)As. The stresses may be obtained by deter- mining separately the stresses caused by the central thrust and by the bending moment. The sum of the two stresses gives the actual stress. The stress due to the central thrust equals the thrust divided by the THEORY OF REINFORCED CONCRETE N 381 ^^^^' ^"^ ^ + (n- i)A' '^^^ ^^'^^^^ caused by the bending moment equals — -, in which /» is the moment of inertia of the transformed •it Fig. 106. — Stresses Caused by a Force Acting Outside the Middle Third of Plain Concrete Section. (See p. 380.) section and is equal to I + {n— i)I,. Substituting in the above ex- pression the value for the bending moment, M = Ne; and the value for the moment of inertia, the stress produced by the bending moment Ney equals , rr- Therefore the unit stress in the concrete at any distance, y, from the gravity section is /.= iV Ney A+in-x)A, T+{n-i)I, (73) It is evident that the stress is a maximum in fibers for which y is a maximum. The stress may be compression over the entire section, or compression over a portion of it, and tension over the remaining por- tion, depending upon the relative magnitude of the two expressions. Stress in steel equals the stress in the concrete fiber, placed the same distance from the gravity axis as the steel, multiplied by n, the ratio of moduli of elasticity. REINFORCED CONCRETE RECTANGULAR SECTIONS Since in a rectangular section A = Ih, and A^ = pbh, and the moment of inertia of the composite b¥ section, I -\-{n— 1)!, = — + 12 i)pbha^, the unit stress in concrete at a distance, y, from the gravity axis is 382 A TREATISE ON CONCRETE fc N_ bh (r 1 2 ye \ 12 («— i) pa^J (74) ■. + {n-i)p h'' + The stress is compression when the result is positive, and tension when it is negative. Maximum and minimum stresses are for outside fibers, for which the h distance is y = — The above formulas, therefore, change to Maximum and minimum stresses in concrete, I , 6 he /, = -(- bh\i \i + {n— i)p h^ + i2{n- Maximum and minimum stresses in steel. i) pa-") NCe bh Is N I I hh\i + (n i)p /«■' + 12 (w— i) i) pay (7S) (76) Use Fig. 108, p. 383, to find the value of the parenthesis, or C„ in formula (75) for the conditions given in the diagram. H-1 v?t -f.-~\ r'^^=:l ^^^^l-'.y^^ n " M ^ 3 \f.VWx i b. Force Producing Compression upon tile Whole Reinforced Section Force Acting at a Distance Larger tlian eo from the Axis of Gravity of Reinforced Section Fig. 107. — Stresses in Reinforced Concrete Section Caused by Eccentrically Applied Thrust. {See p. 382.) ESect of Eccentricity. As in plain concrete sections, the location of the center of thrust determines the distribution of the stress, as evi- dent from the above equations. If the thrust acts at the center of gravity, there is uniform compression over the whole section. As the center of thrust lies farther and farther from the gravity axis, the compression at the opposite surface decreases until it finally becomes zero, and then tension. When the first term in the brackets of the above equation is greater THEORY OF REINFORCED CONCRETE 383 aoz 004 ao6 aos aio a.12 0.14 om-ais ozo azz oza aze ozs 030 Valine's of ■?■ Fig. 108. — Diagram for Determining Compression and Eccentricity. {Seep. 382.) 384 A TREATISE ON CONCRETE than the second, the minimum stress in the concrete will be compres- sion. When the two terms are equal, the stress is zero in the outer edge of the concrete on the opposite side to that on which the thrust acts. When the second term is greater than the first, the result from the formula will be negative and the minimum stress will be tension. If the tension determined by the above formula exceeds the allow- able tension on concrete, the above formulas are not applicable and the formulas given on page 386 should be employed. Thrust Applied So That the Compression at One Surface Becomes Zero. The eccentricity for which this occurs may be determined by equating the two terms in formula (75) and solving the resulting equa- tion for e. if.P^k QRAVITY AXIS Fig. 109. — Stresses Caused by a Force Acting at a Distance Larger Than Co from the Axis of Gravity of Reinforced Section. (See p. 384.) Using previous notation and also letting e„ = value of e, which makes the stress zero, then _ A^ + 12 (« — i) pa^ I I + (n-i) p 6h In the above case, the formula on page 382 changes to Maximum unit compression in concrete. /. 27V bh{i + {11 — 1) p) Maximum unit compression in steel, nN /; hhix + (» — i) p) (-1) (77) (78) (79) Minimum compression in concrete = o Minimum compression in steel is very small and does not need to be determined. THEORY OF REINFORCED CONCRETE 3&S Distribution of Stress When One Surface Is In Tension. When the thrust is appUed at a distance from the gravity axis greater than the eccentricity, Co, derived by Formula (77), page 384, and the concrete is assumed to be unable to carry any tension, then Formulas (78) and (79). page 384 are no longer applicable, and the following method may be used in determining the stresses. In this method, the steel on the side opposite to that on which the thrust acts is assumed to carry all the tension stresses. Referring to Figure no, page 385, and making the same assumptions as given in connection with simple flexure on page 351, we find the following relation between the stresses in steel and in concrete; if.pbK ^' Hp^T}, \. GRAVITY AXIS NEUTRAL AXIS Fig. no. — Stresses Caused by a Force Producing Compression and Tension upon a Reinforced Section, Tensile Strength of Concrete Neglected. {See p. 385.) Unit compressive stress in the upper steel is and the unit tension in the lower steel is Is = >'fc - kh kh (80) (81) The stresses may be determined from the principle that for equilibrium the sum of the stresses acting on a section must equal the thrust, and that the bending moment of the external forces (which is the thrust multiplied by the eccentricity) equals the moment of resistance of the internal stresses. From the first principle, we have, since each steel pbh 2 area is- iV f.pbh ^ f.bkh fsPt^h (82) 386 A TREATISE ON CONCRETE Substituting the values for /J and/, from (80) and (81), j^ ^fjbh k" + 2npk - np ^g^^ 2 k The moment of the stresses about the gravity axis, obtained by tak- ing the sum of the moments of all the stresses about the gravity axis, after eliminating /,' and/^ by the use of Equations (80) and (81), is M=fMi'^+---) (84) By equating the expressions in Formulas (83) and (84) to the known thrust and known bending moment, we get two equations from which the unknown values of k and /. may be determined. This would mean, however, solving equations with the third power. In practice, the use of the curves given on page 387 and 388 will be found convenient. Calling the quantity in brackets in Formula (84), C. = I — — + — I' we may write \¥k 4 6/ M = CJM' (8s) from which M C„bh'^ and (86) L = < ^ (87) The value of C^ is dependent upon the known dimensions of the sec- tion and eccentricity; therefore, curves in Fig. 112, page 388, have been drawn to simplify the determining of the stresses. Determining the Value of k. The value of k in Formula (80) or (81), page 385, can be obtained as follows: Since the moment, M, equals Ne, the thrust multiplied by the eccentricity. Equation (83) multipHed by e may be equated to the formula for bending moment (84). The resulting equation is as follows: k' + 3(r--)k'+(>npk'-=3nPj+^-^ (88) \« 2/ h h ¥ THEORY OF REINFORCED CONCRETE 385 Values of Eccentrici+y f- Q80 Q70 aeo Qso a4o 030 Values of EccentricitLj -^ -Diagram for Determining Depths of Neutral Axis for Different Eccen tricities. Based on » = 15 and 2a = —A. (See p. 389.) 388 A TREATISE ON CONCRETE ai az 05 04 as o.6 a? oa 0.9 k, Ratio o| Depth of Neutral Axis to Depth of Section Fig. 112. — Diagram for Determining Constants Ca to be used in Formula (86). Based on h = 15 and 2a = —h. (See p. 389.) THEORY OF REINFORCED CONCRETE 389 If the value of k must be determined directly, substitute k = z- \h~ ^) ^^^'^ Equation (88) takes the form z^ + pz + q = 0, and since by Cardan's formula, the value of k may be computed. This follows the method suggested by Professor Morsh in "Der Eisenbetonbau," 1906, page iii. Curves for Determining Values of k and C^. (Equations 86 and 88). The formulas for k and C^ are comphcated and not adaptable for prac- tice. To simplify the determining of the stresses, two sets of curves are given on pages 387 and 388: (i) curves in which the values of k can be found for given values of- and ratio of steel, p ; (2) curves from which ft values of C^ can be taken for any value of k and ratio of steel, p. The curves for values of k were obtained by solving Equation (88) € A for -, using « = 15 and 2a = -h. This gives « S e_ ^ -k' + W + i4-# ^g ^ h sl^^ + go pk - 45P From the above equation, curves for - are readily drawn for different h percentages of steel and varying values of k without solving the third power equation. Determining of Stresses by Use of Diagrams. In finding the unit stresses for a given section having an eccentricity greater than Co (see p. 384) and containing a known quantity of steel, the following quanti- ties-would be known: breadth, b; depth, h; ratio of steel, p; ratio of elasticity, n; eccentricity, e; and moment, M. The method of pro- cedure of finding stresses may then be as follows. Determine-- Enter the bottom of F'ig. iii, page 387, with this h value of - and find the k corresponding for the given percentage of h steel. Then with this value of k enter Fig. 112, page 388, and find Q. M Apply Formula (86), page 386, where/, = ^r^- Having found the unit stress in the concrete, the unit stresses in the steel may be determined from formulas (80) and (81), page 385. 390 A TREATISE ON CONCRETE FORMULAS FOR REINFORCED CONCRETE CHIMNEY AND HOLLOW CIRCULAR BEAM DESIGNS Reinforced concrete chimneys may be regarded as vertical canti- lever beams supported at the base. The loads to be provided for are (i) the weight of the chimney and (2) the wind pressure. Although the design is somewhat complicated by the fact that the beam is cir- cular and hollow, the treatment is nearly identical with that of ordi- nary rectangular beams. In fact, the analysis which follows is based upon the several fundamental assumptions adopted in reinforced con- crete beam design with only one additional assumption viz. : that, since the concrete is usually thin as compared to the diameter of the chim- ney, no appreciable error is involved in assuming all material as con- centrated on the mean circumference of the shell. An analysis for shear is given on page 397. An example of chimney design and review is given in Chapter XXIII. Although specially devised for a chimney, the formulas are appli- cable to any hollow beam. The principles involved in the demonstration of the thickness of steel and concrete are taken by permission from the analysis by Messrs. C. Percy Taylor, Charles Glenday, and Oscar Faber.* The principal formulas given below are quoted in the text, where the general subject of concrete chimneys is discussed, and tables are presented there with the values of constants for use in design. NOTATION W = weight in pounds of the chimney above the section under considera- tion. M = moment in inch pounds of the wind about that section. P = total compression in concrete. T = total tension in steel. n =■— = ratio of modulus of elasticity of steel to that of concrete fg = maximum compression in concrete in pounds per square inch (meas- ured at the mean circumference). f^ = maximum tension in the steel in pounds per square inch. D = mean diameter of shell in inches, r = mean radius of shell in inches. i = total thickness of shell in inches. i^ = thickness in inches of concrete only. • Engineering (LoadonJ , Mar. is, 1508 THEORY OF REINFORCED CONCRETE 391 ; = thickness in inches of an imaginary steel shell of mean radius r. and having a cross-sectional area equivalent to the total area of rein- forcing bars. = total cross-sectional area, in square inches, of reinforcing bars in the section under consideration. = ratio of distance of neutral axis, from mean circumference on com- pression side, to diameter D. Cp and CjT = constants for any given value of k. (Tables 1 and 2, pp. 665 and 666.) jD = distance between center of compression and centre of tension. zD = distance from center of compression to center of force due to weight. Referring to Fig. 113, if /^ is the maximum intensity of stress in the con- crete atthe mean circumference on the compression side, then the intensity of compression in the steel at that point is w/^. Since/g is the maximum intensity of stress in the steel at the mean circumference on the tension side, then the variation of the stress in the steel, across the section cd, is represented by the straight line ab which cuts the line cd at e, thus locat- ing the neutral axis or the line of zero stress. Having assumed a con- stant value for the modulus of elas- ticity of the concrete in compression, it therefore follows that, at any point of a given section, the stress in either the concrete or the steel is directly proportional to the distance of that point from the neutral axis. Calling kD the distance of the neutral axis from the mean circumference on compression side as shown in Fig. 113, we have by similar triangles Pig. 113. — Resisting Forces in a Re- inforced Chimney. {Seep, sgi.) kD "d whence k = 392 A TREATISE ON CONCRETE By this formula the position of the neutral axis may be determined for any combinations of /g, /,, and «. If now, as shown in Fig. 114, a represents half the angle subtended at the center by the portion in compression, we have cos a = (i — 2 ^) from which, for any given value of z, cos a becomes known as well as a and sin a. Thus having located the neutral axis for any given com- binations of /j, /, and n and bear- ing in mind that the stress at any point of the shell is proportional to the distance of that point from the neutral axis, it is now possible to determine the total force on the compression side, the total force on the tension side, and also the location of the center of compres- sion and the center of tension. Considering a small radial ele- ment subtending an angle dd, as shown in Fig. 114, we have in this element, since the length of an arc is its radius times the angle, CONCRETE^ IN COM- PRESSION STEEL IN COMPRESSION' Ftg. 114- — Distribution of Stresses in the Steel of a Reinforced Chimney. (See P- 392-) area of concrete = ij'dd area of steel = t/dd The distance of the element from the neutral axis is >'(cos d — cos a), while the distance from the neutral axis to the point of extreme stress /, is r\j — cos a). Therefore the intensity of stress on this elemental area is and r (cos d — cos a) . f m the concrete ° r (i — cos a) r (cos 6 — cos a) J n —p ^ in the steel. r (1 — cos a) THEORY OF REINFORCED CONCRETE 393 Assuming these intensities at the mean circumference to represent the average for the entire element, we have the total force on the elemental area (concrete and steel) /„ r (cos d — cos a) ^ " " r{i~ cos a) The total force P on the compression side of the section is therefore h+nQ^ ^ /, , ,N I f^r (co-i 6— COS a) (i 1- cos a) Integrating this expression, gives 2 P = fa ^ (J>c + '^ K) ', ; (sin a — a cos a) •^^ " ' (i — cosq) Since any given position of the neutral axis determines, a, as shown above, this equation may take the form P =Cp/,r(<,+ «y (91) in which Cp is a constant for a given position of the neutral axis. (See Table i, page 665.) Having determined the magnitude of P, its location, with respect to the neutral axis, may best be found by taking its moment about that axis and dividin" by P, thus giving the distance from the neutral axis to the center of compression /j, as shown in Fig. 114. As before, the compressive force on an elemental area is /, r (cos 6 — cos a) dP = (t. + nQrdd -. r ^ ■ ' r (i — cos a) The distance of this forc&from the neutral axis being r(cos 6 — cos a), we have as its moment about that axis /^f* (cos 6 — cos a)' dM, = (t,+ nQrd d , (, _ ,^3 ,) while the moment of the total compressive force P is fa /, r (cos 6 — cos ay M = (t + n t^ 2 ] ^ ; ^^ d c Vc ^ si J ^^ (j _ cos a) 394 A TREATISE ON CONCRETE (i — cos 2 / f' r f" — 2 COS Integrating, we have a \ cos Odd + cos' a I d i^ il/^ = (L + nL)Lr' r Ua cos' a. - | sin u: cos a + i a) " ' ° (i — cos a) Dividing M^ by P we have M , (a cos' a — f sin a cos a + -j a) ^1 = V = ^ r- ^ '■ ^92; P (sin a — a cos a) Following a similar method of procedure it is possible to determine the total tension and the location of the center of tension. In accordance with our assurtjption that the concrete is to take no tensile stress it is evident that in considering the forces on the tension side of the section we are concerned merely with the steel. On the tension side a small element therefore has an area = t^r d 8 The intensity of stress on this element, being proportional to its distance from the neutral axis, is r (cos 6 + cos a) r (i + cos a) while the total tension on the small element is (cos + cos a) dT =l,rdOf, V-^ T ' ' (i + cos a) The total force T on the tension side of the section is therefore ty Integrating, we have C't-a) (cos 6 + COS a) T=2 \ t^rf,—. — , r^dd ' ' •" (i + COS a) T = f,r t, -. ; : (sin a + (w — a) cos a) ■'' ' (1 + COS a) ^ ' Since, as before, any given position of the neutral axis determines a, this equation may take the form T = Cj,f, r t, (.92.) in which Cyis a constant for a given position of the neutral axis (see Table I, page 665). Bya method similar to that used in considering the force on THEORY OF REINFORCED CONCRETE 395 the compression side we may write the moment, about the neutral axis, of the force on a small element on the tension side as i M y =t^rd Of^ r (cos + cos a)' (i + cos a) while the moment of the total tensile force T about this axis is M, = . J (t-«) ;• (cos + cos af (i + cos a) id Integrating, we have Mm = t. r" f' (i: cos a) {{n — a) cos' a +f sin a cos a + i (^ — a)] Dividing Mj, by T we have as the distance of the center of tension from the neutral axis 4 = ( (^ - «) cos^ a + f sin TT cos a + ^ (tt a)) (94) TF" jD zD I (sin a -\- {k — a) cos a) From formulas (92) and (94) it is evident that the distance between the total force in compression and the total force in tension (i. e., h -\- h) may, for any given position of the neutral axis, be expressed as a con- stant times the diameter D. Thus ^1 + h = jD as shown in Fig. 115. Likewise, as shown in Fig. 115, zD may represent the distance of the center of compression from the center of the chimney, z also being a con- stant for any given position of the neutral axis. In a chimney the tensile and compres- sive stresses which we have beencour sidering are produced by a combina- tion of wind pressure and the weight of the chimney. Thus, on any horizontal section cd, as shown in Fig. ri5,the forces external to that sec- tion are: the horizontal pressure of the wind, causing a moment M about the section, and a central vertical load W representing the weight of that portion of the chimney above the section under consideration. These forces are resisted, and held in equilibrium, by the forces P and T which represent the compressive and tensile stresses in the concrete and steel. Fig. 115. — External and Internal Forces Acting upon a Chimney. (See p. 395.) 396 A TREATISE ON CONCRETE The system of forces as shown in Fig. 1 1 5 must be in equilibrium. Hence, taking moments about the force P, we may write TjD = M - WzD But T = CtUK Therefore CTf/iJD = M -WzD Whence M - WzD rt. = The total area of steel A„ = 2;:r/, Therefore _2t:{M - WzD) (^,) ' C^LJD From Table I, page 665, it may be seen that the constant j changes but slightly for a considerable variation in the position of the neutral axis. 2TZ Taking = 8 for all cases, equation (95) may be 1 While this formula is not exact, the error involved is inappreciable for almost any case so that formula (96) may always be used instead of formula (95) Applying now the condition that the summation of all vertical forces must be zero, we have p - r = PF Substituting values of P and T as previously found, the equation becomes Cp// (/, + nQ ~ C^f/h = W Transposing and solving for t^ we obtain Cpf/ The total thickness of the shell is whence _ W + (Cr/. - Cpf,n) rt, l — -I- / CpU THEORY OF REINFORCED CONCRETE 397 For convenience in use, after having determined A^ by the formula given D A above, by substituting r = - and «, = -f this formula for t may best be written '= ^;z^" '" +^ (97) In view of the fact that formulas (95), (96) and (97) contain the con- stants z,j, Ct and Cp, which, as has been shown, are dependent for their value solely upon the location of the neutral axis, it is evident that, for any specific values of /„ /„ and n, which in turn will determine the position of the neutral axis, the expressions for A^ and / will admit of a further simplification. For given values of /„ /j and n, the necessary thickness of shell and area of reinforcement may be expressed merely in terms of the moment of the wind M, the weight W, and the mean diameter D. The expressions, as given, however, seem best adapted to general use, and when supplemented by the tables given on pages 665 and 666, are rendered quite simple of solution for specific values. In Table 2, page 666, are given values of k, the location of the neutral axis, for various combinations of /^./j and « ; while Table 1 , page 665, gives the corresponding values of the constants Cp-Cr-z andj for various posi- tions of the neutral axis. Shear or Diagonal Tension. Having determined the necessary thickness of shell and vertical reinforcement, the size and spacing of the circular steel hoops must be considered. The external forces produce shear and diagonal tension which may be analyzed similarly to like stresses in rectangular beams, and the reinforcement necessary to resist the diagonal tension, which is a function of the vertical tension, may be determined. Usually this reinforce- ment is not so great as that which it is ad\'isable to insert for the proper dis- tribution of temperature stresses, but nevertheless it should be determined to be sure that it is sufficient in quantity. The concrete should never be relied upon to carry any tension or vertical shear because the expansion from the heat may cause vertical cracks in the concrete. These need not be considered dangerous if sufficient horizontal reinforcement is provided any more than the vertical cracks in a brick or tile chimney. Considering the stresses due to vertical shear, it may be easily shown that at any horizontal section of a chimney the vertical shear per inch of height is the total horizontal shear on that section divided by the distance between centers of tension and compression, jD. With this as a 39* A TREATISE ON CONCRETE basis there may be developed a formula for practical use in determining the necessary area and spacing of horizontal steel hoops at any given section. Thus let hi = height, in feet, of chimney above section under consideration. F = effective wind pressure against chimney in pounds per square foot, /s = allowable tensile stress in pounds per square inch in steel hoops. D — mean diameter of shell in inches. Pa = ratio of area of steel hoop to area of concrete. At any horizontal section of a chimney the total shear on that section is equal to — h,F 12 while the maximum shear per inch of height is therefore D hF 12 jD Having seen that for all positions of the neutral axis / remains practically constant, and giving / an average value of, say, 0.783, the expression for the maximum vertical shear per inch of height becomes 0.106 MF while the shear or diagonal tension in one foot of height is 12 X o. 106 hjF. The area of steel in one foot of height of chimney will be 1 2 bp^ and the stress the hoops in this height are capable of sustaining on their two sec- tions is 2X12 tpj. Equating these we have 12 X .106 A;F = 2 X 12 tpj^ whence hiF i8.8/.< This ratio of steel is for shear or diagonal tension only. To provide for temperature stresses or rather to distribute the strains so as to prevent the localization of cracks an additional amount of horizontal steel is needed. This may be provided for arbitrarily by assuming 0.25% steel or rather THEORY OF REINFORCED CONCRETE 399 0.0025 for temp^ature stress iii addition to the steel for shear. Express- ing this as a formula for ratio of steel gives hiF ^ ^ Small rods spaced 6 to 10 inches apart except in the upper part of the stack where the spacing may be greater are advised. The spacing of hoops in many of the chimneys already built has been 1 8 inches to 36 inches, but as such chimneys have frequently cracked quite seriously, more recent designs have called for 8 or g inch spacing through the entire stack. Design of Hollow Circular Beams. The analysis of a hollow circular reinforced concrete beam whose thickness, compared relatively with its diameter, is small, is similar in principle to that of a chimney. In this case the weight of the member acts in the same direction as the external forces., so that in formulas (96) and (97) W the weight in the axial direction, is zero. The forces of compression, P, and tension, T, are equal. The area of steel and the thickness of shell are therefore obtained from formulas (96) and (97), pages 396 and 397, by making W — o. Note on Slim Chimneys. Since, in designing a chimney the selection of certain allowable working stresses in the concrete and in the steel will fix the position of the neutral axis, it is evident that the ratio of these working stresses limits the compressive area of the section. Hence, for a very high chimney in which there is a large compression in the lower sections, it is possible that the selection of an ordinary working stress in the steel of 14000 or 16000 pounds per square inch together with the custom- ary working stress in the concrete of, say, 500 pounds per square inch, would locate the neutral axis so near the compression side of the section as to make it impossible to obtain sufficient compression area to with- stand the compressive forces without exceeding the allowable unit stress in the concrete. If, therefore, the thickness of shell as computed from formula (97), page 397, should work out materially larger than the assumed thickness, recomputation should be made on the basis of a smaller working stress in the steel, thus changing the position of the neutral axis so as to allow a larger proportion of the section to carry compression. In such a case it may be necessary to make a series of trials with different working stresses in the steel imtil the competed thickness checks with the assumed thickness. In high chimneys o'' - .nail diameter it may be impossible to utilize a working stress in the Si ttl greater e\ en than 7000 or 8000 pounds per square inch. 400 A TREATISE ON CONCRETE CHAPTER XXI TESTS OF REINFORCED CONCRETE The selected tests presented in this chapter were originally carried out to determine the principles of the theory and design of reinforced concrete. They are given here to illustrate the principles and con- clusions presented in the preceding and the following chapters. MODULUS OF ELASTICITY OF STEEL The modulus of elasticity of steel varies from 28 000 000 pounds per square inch to 31 000 000 pounds per square inch; 30 000 000 is custom- arily taken as an average value, and is the value adopted in this treatise. All Steel, irrespective of its Ultimate Strength, Elastic Limit or Chemi- cal Composition, has Substantially the Same Modulus of Elasticity. It follows therefore from the principles of elasticity that the stretch under a given pull is independent of the character of the steel. MODULUS OF ELASTICITY OF CONCRETE For practical design it is recommended that the ratio of the modulus of elasticity of steel to that of concrete be taken at 15, corresponding to a concrete modulus of 2 000 000, for the 1:2:4 concrete used in ordinary practice. Determination of Modulus of Elasticity. The modulus of elasticity, E, may be taken as the quotient of the stress per unit of area divided by the deformation (that is, the elongation or the shortening) in a unit length. In customary English units where the modulus is in pounds per square inch, stress per square inch deformation per linear inch It is determined in the laboratory by measuring the deformation for the loads successively applied and plotting them as shown in Fig. 116. The curves in the diagram represent the deformations, at different stages of the loading, for atypical cylinder 8 inches in diameter by 16 inches high of extra sti-qng 1:2:4 concrete, tested at the Structural Materials Testing Lab- oratories, United States Geological Survey, St. Louis, Mo., in 1907. TESTS OF REINFORCED CONCRETE 401 The set, which is the permanent deformation when the load is released, IS not indicated in the diagram because the total deformation is that which must be used in reinforced concrete analysis. The form of the deformation curve is approximately a parabola,* but the tests at St. Louisf indicate that for first-class concrete the modulus is 4000 3800 3600 3400 3200 3000 X o z 2BO0 lu ^ 2000 3 m 2400 tc u 0. 2200 CO i 2000 o "■ 1800 z S 1600 u H 1400 CO z 1200 3 1000 800 600 400 200 ■n^ *^' ^\ ^^ L*-*- / ^. /- f ^; r ^? /^ / / H£E vcs ) ^ If y ,^ / f / ■/ w / / /f / / ^ i / (1 / \f / 1 1 If f DEFORMATION PER UNIT OF LENQTH Fig. 116. — Stress Deformation Diagram, Limestone Concrete Cylinders of Medium Consistency and Extra Good Quality.! (See p. 400.) nearly constant for about one-third of the ultimate strength. The modulus at this point is , or 3 200 000 pounds per square inch, in the four 0.00025 weeks old concrete tested. •See discussion by Prof. Talbot in University of Illinois Bulletin, No. lo, Feb. i, igoj, p. 21. t Bulletin No. 344, U. S. Geological Survey, pp. 36-5.'- t Bulletin No. 3j4, U. S. Geological Survey, p. 33. 402 A TREATISE ON CONCRETE Results of Tests. Numerous tests have been made to determine the modulus of elasticity of concrete which indicate as large a range in results obtained by different experimenters, even vpith concrete of the same pro- portions of cement to aggregate, as from i 500 000 to 5 000 000 per square inch. The reasons for this are not yet fully determined; it has been conclusively proved, however, that the age of concrete, its richness and its density have undoubtedly a large influence on this variation. The following table, compiled from various tests, may be of value as suggesting approximate values of the modulus for different proportions of concrete based upon the total deformation at one-third the crushing strength of cylinders at an age of thirty days. Two columns are given, one for ordinary wet concrete of medium quality, and one for concrete very carefully made with a dense mixture of mushy consistency and kept wet during hardening. The "ordinary" values are slightly below those which should be expected in practice on construction work. The modulus of elasticity of concrete probably bears a definite relation to its ultimate strength, but the factors which enter into this relation probably viill never be determined exactly. Plotting the results of a large number of tests made at the Watertown Arsenal, at the Government Labora- tory at St. Louis, and at many of the colleges, indicates an approxi- mate ratio of i 300 between the modulus of elasticity and the ultimate strength. Moduli of Elasticity of Concrete of Different Proportions. Approximate Average Values. (See p. 402.) ORDINARY WET CONCRETE. PROPORTIONS. Broken stone or gravel concrete Crushing Strength at 30 days. lb. per sq.in. I : li 3 1:2:4 I : 2} : 5 1:3:6 1:4:8 1:2:5 2300 1700 1500 1300 900 700 Modulus of Elasticity lb. per sq. in. 2 500 000 2 000 000 i 800 000 I 600 000 I 300 000 900 000 EXCEPTIONALLY STRONG CONCRETE. Crushing Strength at 50 days. lb. per sq.in. 2800 2500 2200 1900 1500 1000 Modulus of Elasticity lb. persq. JQ. 3 600 000 3 200 000 2 800 000 2 500 000 2 000 000 I •?oo 000 Note— A modulus of 2 000000, corresponding to a ratio of is, is recommended for general use for 1:2:4 concrete and a ratio of 12 for 1:1^:3 concrete. TESTS OF REINFORCED CONCRETE 403 Tests of Mortar Prisms. Elastic properties of prisms of neat Portland cement and cement mortar, from tests made by Mr. Howard* at the Watertown Arsenal, are presented in the following table: Elastic Properties of Cement and Mortar Prisms 6 by 6 by i8 inches. Watertown Arsenal. (5ee^.4o3) Brjnd COMPOSITION Age MODULUS OF ELASTICITY BETWEEN LOADS PER SQUARE INCH OF Permanent sets after loads per square inch of of Cement J lOO and 6oo 100 and I ooo 1 000 and 2 000 600 1 000 2 000 til lb. 01 Days lb. lb. lb. Inch Inch Inch Alpha Neat o 7 7143000 5 000 000 8 333 000 0. 0. 0. 4783 7 4167 000 3 600 000 3 448 000 0. 0. .0002 5 000 Alpha I I IS 3125000 2 812 000 2 326 000 -.0002 -.0002 .0007 3846 3S 2 381 000 2 500 000 2 941 000 0. .0002 .0012 4763 30 2 632 000 2 727 000 3 030 000 .0001 .0002 .00 ro 4948 Alpha r 2 15 I 724 006 I 475 000 .0005 .0025 1376 3^ 227-5 000 2 T95 000 I 538 000 .000 r .0006 .0040 2 184 3^ 2 778 000 2 8r2 000 2 325 000 0. .0004 .0020 2 755 Gaged length, 10 incaes. Modiilus of Elasticity in Beams vs. Columns. The modulus of elasticity in beams as determined by measurements and computations by Professor Talbot is approximately the same or possibly slightly lower than in col- umns. Effect of Consistency of Concrete upon the Modulus of Elasticity. An excess of water in the concrete not only decreases the strength (see page 317), but also affects the deformation curve so as to show a more variable modulus near the beginning of the test. The moduli of con- crete of different consistencies and at different ages are shown in the tables from tests of the authors on following page. The specimens were 12-inch cubes. Relation of Stress Deformation Curve to the Theory of Beams. The theory of beams is worked out under the assumption that a section plane before bending remains plane after bending so that the deformation or stretch at any point in the compressive portion of the beam is proportional to the distance of this point from the neutral axis. According to this assumption the distribution of stresses is also proportional to the distance from the neutral axis so long as the modulus of elasticity is constant. This distribu- *Te6t8of Metals, U. S. A., I8q8. 404 A TREATISE ON CONCRETE tion may be then represented by a straight Une as shown in Fig. 98, p. 353. When, however, the modulus of elasticity changes, Hook's law — that stress is proportional to deformation — ^is no longer applicable, since the intensity of stress is no longer proportional to the distance from the neutral axis but changes according to the relation of the moduli of elasticity at different load- ings, and the line representing the distribution becomes a curve.* Modulus of Elasticity of Concrete of Different Consistencies. ■^ Proportions by Volume I : 2i : 4J By Taylor and Thompson. {See p. 403.) DRY. MEDIUM. VERY WET. Approximate age in 1 ^ • ultimate q. in. Strength, sq. in- ultimate q. in- ultimate q. in* months. « tJ -w '^ « 3 HM " » s Hn " 11 Modulus at strength. Pounds per Q Modulus at strength. Pounds per B d, c3 Modulus at strength. Pounds pel I 4370 4 050 000 i3(>° 4 500 000 2110 2 100 000 2 5430 4 050 000 3940 4 550 000 2770 3 400 000 6 5170 5 255 000 517° 3 760 000 335° 2 880 000 17 5510 3 920 000 4720 3 750 000 2430 2 080 000 Since the modulus is nearly constant within the working limits the authors have adopted the straight line theory of distribution of stress as simplest and most practical, t Formerly the parabolic distribution of pressure in concrete above the neutral axis was used in preference to the straight line theory because it corresponds somewhat more nearly to actual test. The two theories, however, require practically identical percentages of steel and the only difference is in the determination of the unit stress in the concrete. When using the parabola theory, about 15% lower compressive stress in the con- crete must be used than when figuring by the straight line theory to obtain similar results. For example, 650 pounds per square inch safe compres- sion by the straight line theory corresponds to about 565 pounds per square inch by the parabola theory. * A comprehensive analytical discussion of the effect of a varying modulus of elasticity upon the pressure in a beam under different loadings is presented by Prof. Talbot in Journal Western Society of Engineers, Aug. 1904. f "The Consistency of Concrete," by Sanf ord E. Thompson, American Society for Testing Materials. Vol. VI, 1906. 1 It is also recommended by the Joint Committee, 19 16, TESTS OF REINFORCED CONCRETE 405 TESTS OF RECTANGULAR BEAMS. The most important determinations from the tests of beams are: Stress at which first cracks appear and the corresponding stretch in concrete; Location of neutral axis; Relation of ultimate compressive fiber stress to strength of concrete in compression; Distribution of stresses; Relation of bending moment to moment of resistance based on stresses in steel; Effect of the percentage of reinforcement; Effect of mix of concrete and age. The results and conclusions are given on the following pages. Formulas for design based on the tests may be found in Chapter XXII, pages 481 to 484. Phenomena of Loading Rectangular Beams. During loading of rein- forced concrete beams, three stages can be distinguished: first stage, before the appearance of the first crack; second stage, after first crack is developed, but before either of the materials passes its elastic Hmit; third stage, after the elastic limit has been passed. First Stage. Before the appearance of the first crack, a reinforced concrete beam behaves similarly to a homogeneous beam. Compression is resisted by concrete and tension is resisted by concrete and steel in proportion to their moduli of elasticity. The position of the neutral axis nearly coincides with the center of gravity of the section obtained by replacing the steel by concrete of an area equal to the area of steel multiplied by the ratio of moduli of elasticity. At an elongation or stretch of concrete equal to the ultimate stretch of plain concrete, first cracks appear in the beam. At first they are not visible to the naked eye and do not extend up to the reinforcement. This is called the first stage. Second Stage. At increased loads the number of cracks increases. They widen and move up toward the center of the beam. The larger the amount of reinforcement, the larger the number of cracks and smaller their width, as illustrated in Figure ii7,page4o6. In this stage, tension is resisted by steel and by the portion of concrete between the end of the crack and the neutral axis. The cracks never extend way up to the neutral axis (which rises as the cracks develop), because, since the deformation increases from zero at the neutral axis to its maximum at the level of the steel, there must TESTS OF REINFORCED CONCRETE 407 be a portion of concrete where the deformation is smaller than the ulti- mate stretch for the concrete. There must be, therefore, a fiber which is just at the point of breaking and, above it, a portion of concrete carry- ing tensile stresses. The portion of the tensile stress carried by con- crete decreases with the increase in the load. For equal intensity of loading, the stress carried by concrete is larger for smaller percentages of steel. For large loads and large percentages of steel, the amount of this stress in concrete is negligible, and as explained in the chapter on Theory, page 351, it is disregarded in designing reinforced concrete beams. In analyzing tests, however, it is necessary to take the tension in concrete into account since its existence explains why the moment of re- sistance, based on the stress in steel and figured by formula M = AJ^jd, is smaller than the bending moment, and why the actual stresses in steel obtained from deformations are smaller than the theoretical stresses. (See Fig. ng, page 413.) The amount of tension carried by the con- crete may be estimated by comparing the moment of resistance, based on the actual stresses in steel, with the bending moment. Third Stage. Beams Failing by Tension in Steel. When the steel reaches its elastic limit, one or two of the cracks, which were small up to this point, begin to open and extend towards the top. This is shown by the loads underlined in Figure 117, page 406. The deflection increases appreciably as the cracks widen and extend toward the top (the neutral axis rising), the compressive area becomes smaller, and finally the beam fails by totally destroying the compressive area. This condition is brought about by a small addition to the load at which the steel passes the elastic limit. The passing of the elastic limit of steel marks, there- fore , the failure of the beam. Ultimate strength of steel is never reached, and is, therefore, of no consequence in reinforced concrete design. Beams Failing by Compression. For beams failing by crushing of concrete, the third stage is marked by cracks in the top of the beam which appear after the elastic limit of the concrete in compression has been reached. At increased load, wedge-shaped pieces of concrete spall off and the beam fails. Appearance of First Crack and Corresponding Stretch in Concrete. Numerous tests prove that the appearance of first cracks in reinforced concrete corresponds to about the same stretch as the appearance of cracks in plain concrete. This stretch may be taken approximately as 0.00012 of its length (corresponding to 3 600 lb. per sq. in. in the steel) for I : 2 : 4 stone concrete, and 0.00018 (corresponding to 5 400 lb. per 4o8 A TREATISE ON CONCRETE sq. in. in the steel) for cinder concrete.* The cracks, however, at this stretch, as discussed below, are very minute and not visible to the naked eye. The conclusion of Mr. Considere in France, as the result of his tests, that the stretch of concrete when reinforced was 0.002 of its length, or twenty times the stretch of concrete without reinforcement, has been disproved by further experiments. Professor Turneaure,t in testing moist beams, observed, at about the same stretch at which first cracks developed in plain concrete beams, dark marks which he called water marks. Part of these water marks developed later into actual cracks. Professor Bachf investigated the subject further and came to the con- clusion that water marks are places where adhesion between particles of concrete became loosened just previous to formation of cracks. In plain concrete, each water mark develops into a crack. In reinforced concrete, on the other hand, only a part of the water marks actually open because the steel strengthens these weakened spots and retards somewhat the appearance of actual cracks or prevents their formation altogether. Professor Bach's Tests. Professor Bach's testst in Stuttgart, sum- marized below, present the relation between actual and computed tensile stresses in concrete under different conditions. All of the values are high as Bach evidently worked with a stronger concrete than the same proportions give ordinarily. It must be noted further, as has been empha- sized elsewhere, that the actual stresses, low at this stage as compared with the computed stresses, do not affect the accuracy of the ordinary formulas for practical design as this does not increase the factor of safety nor the load at elastic limit. (See p. 412.) Influence at First Crack of Richness of Mix. The increase in strength with richness of mix is shown in the table on page 409. Here, as in the tables on the pages that follow, is shown, not merely the increase in strength with the richer proportions but also the eSect of the concrete in reducing the stress in the steel because of its own strength in tension at early periods of the loading. At the period indicated, which is that of the first crack in the concrete, it is seen that the computed stress in steel is almost 3I times the actual stress. As is shown later, this ratio decreases until at the actual break- ing load in tension they nearly agree. * Technologic Paper No. 2, U. S. Bureau of Standards, igi2, p. 39. t Proceedings American Society for Testing Materials, 1904, p. 498. X Bach-Spannungen unmittelbar vor der Rissbildung. "Deutscher Ausschuss, Heft, 24, 1913. TESTS OF REINFORCED CONCRETE 409 Actual and Computed Stresses at First Crack for Different Proportions o'f Concrete. {See p. 408.) Age of beams at test, 45 days; aggregates, Rhine sand and gravel; ratio of steel, p = 0.0056. Wet storage. Compiled from tests by C. Bach. Strength of Plain Concrete. Tensile Stresses at First Crack. Lb. per sq. in. Lb. persq. in Proportions. Compressive. Tensile. m Concrete. In Steel. Actual Stresses Computed by Formula ^c -''. f ^ I =3 -4 2 100 198 2 go 3 900 13 400 1:2:3 3 750 270 380 5 150 17 200 I : i.S : 2 4 400 330 48s 6 600 23 000 Tensile stresses, f'c, and actual stresses,/;, are figured by formulas on page 362, where the tensile stresses in concrete are taken into account. The stresses computed M by formula, fs - - — , on the other hand, are figured neglecting the tensile value of Asjd concrete. Influence of Storage. The tensile stress in concrete, f^, was smaller for beams stored dry than for beams kept wet, the difference amounting on an average to about twenty per cent. Concrete stored dry tends to shrink, causing initial tensile stresses in concrete because free movement of concrete is prevented by the adhesion of concrete to steel. Concrete kept wet, on the other hand, tends to expand, which, prevented by the steel, causes initial compressive stresses in concrete. When loaded, the initial tensile stresses increase tension on the section while initial com- pressive stresses decrease it. To concrete in building construction the values for dry storage are applicable because, even if the concrete is kept wet during construction, in course of time it will dry out and the ulti- mate amount of shrinkage will be substantially the same as if it were held in dry storage. (See p. 261.) Influence of Percentage of Steel. Professor Bach's tests* show that in concrete beams of the same proportions the actual unit stresses in concrete and steel at first crack are constant irrespective of the per- centage of steel in the beam. The theoretical stresses in steel at the first crack, however, figured by the ordinary formulas neglecting the * Bach-Spannungen unmittelbar vor der Rissbildung. Deutscher Ausschuss, Heft 24, 1013. 410 A TREATISE ON CONCRETE tensile resistance of concrete, vary with the percentage of steel Similar results, as shown in the table below, were obtained in the tests by the Bureau of Standards carried on by Mr. Richard L. Humphrey and Mr. Louis H. Losse.* Actual and Computed Stresses with Diferent Percentages of Steel. (See p. 410.) Proportions of Concrete. Age. Days. Tensile Stresses in Steel at First Crack. Lb. per sq. in. ' Experimenters. Actual Stress Lb. per sq- in. Computed by Ordinary Formula. p = .005 p = .01 p = .02 Bach I : i.S :2 1:2:4 45 28 6 600 4 200 25 000 25 000 13 000 13 000 8 000 Bureau of Standards 8 000 Influence of Consistency. A wet consistency reduces the strength. At an age of 45 days for i : 2 : 3 concrete, p = 0.0056, and for per- centages of water by weight, varying between 6.8% and 10.0%, the tensile stress, fc, at first crack ranged from 395 lb. to 310 lb. per sq. in., while the compressive strength of the same concrete ranged from 3800 lb. to 2360 lb. per sq. in., and the tensile strength in direct pull, from 485 lb. to 245 lb. per sq. in. Influence of Age. Increase in strength with age, as determined by Bach, is shown in the table below. Actual and Computed Stresses at Different Ages. (See p. 410.) Proportions of concrete, 1:2:3. Ratio of steel, p = 0.0056. Compiled from tests by C. BACH.f Stresses at First Crack. Lb. per sq. in. Age. Age. Age. Age., 28 Days. 45 Days. 6 Months. 1 Year. fc Actual stresses in concrete /j Actual stresses in steel /j Computed stresses in steel 360 4 goo 16 400 380 5 100 17 500 466 6 300 21 700 49S 6 700 23 000 The theoretical stresses,/i, are the stresses in steel figured by Formula (9), p. 355. Position of Neutral Axis. The position of the neutral axis in rein lorced concrete beams varies with the percentage of steel and the strength • Technologic Paper No. 2, U. S. Bureau of Standards, p. 39. t Bach-SpannuQgen unmittelbar vor der Rissbildung. Deutscher Ausschuss, Heft 24, 1913. TESTS OF REINFORCED CONCRETE 411 of concrete and also with the intensity of the loading. For beams with large percentages of steel, the initial position of the neutral axis is lower than for beams with smaller percentages of steel. With the same steel and stronger concrete, the neutral axis is higher than with a weaker concrete. In any beam the neutral axis at the beginning of the loading nearly coincides with the center of gravity of a section in which the steel is considered as replaced by an area of concrete equal to the area of steel times the ratio of the moduli of elasticity. With the progress of the loading, it moves upward. In Figure 118, page 41 1, is given the typical movement of the neutral axis during loading for beams with different percentages of steel. As is evident from the figure, the position of the neutral axis for different loadings was determined by plotting at proper Fig. 1 18. — Change in Position of Neutral Axis During Loading for Different Percent- ages of Steel.* (Seep. 411.) levels the deformation of the upper concrete fiber and the deformation of steel. The intersection of the line, obtained by connecting the two points, and the vertical section of the beam gives the position of the neutral axis. For usual percentages of steel the distance from the com- pressive side of the beam under working loads is three-tenths to four- tenths of the depth. The formula for location of neutral axis is given on page 354. Stresses in Steel for Varying Intensity of Load. Figure 119, page 413, gives the typical deformation of steel and of the upper fiber of concrete in inches per inch of length in beams with different percentages of steel, based on the tests of Messrs. Humphrey and Losse.f The deformation • Bach "Biegevereuche mit Eisenbetonbalken," Berlin, 1907, pages 7 and 8. t Technologic Paper No. 2, U. S. Bureau of Standards, IQ12, p. 39. 412 A TREATISE ON CONCRETE curve for steel is not a straight line but a composite curve, the shape of which varies with the percentage of reinforcement. The deformation and, therefore, the stresses in steel at the first stage of the loading, that is, before the first crack, are comparatively small and proportional to the load, so that the deformation curve for this stage is almost a straight line. At deformation equal to the ultimate deformation in plain con- crete beams, cracks in concrete open, and the tensile stresses borne by it are transferred to the steel, causing an abrupt change in the steel defor- mation curve. As is evident from the change in deformation, as shown in the diagram, the change in the direction of the curve is much larger for smaller percentages of steel because the amount of tensile stress, constant for beams of same cross-sections, which is transferred from the concrete to the steel, is distributed over a smaller amount of steel so that the increment in the unit stress in steel is larger. On the deformation diagram the load at first crack is marked by the change in deformation from a straight line to a curve. After the first crack, a large proportion of the total tensile stresses is carried by the steel. The concrete, however, still carries a small pro- portion dependent in amount upon the percentage of reinforcement in the beam. Because of these stresses carried by the concrete, the defor- mation in steel at different intensities of loading does not vary pro- portionally to the load. It is absolutely necessary that this be taken into account when analyzing results from tests not carried to the break- ing point, for instance, in tests of completed buildings. The actual stresses obtained in steel computed from deformation are smaller, for reasons indicated above, than the computed stresses for the same load. With small percentages of steel, concrete carries a consid- erable portion of the stresses up to the breaking point of the beam. (This is shown by the deformation curve for 0.49% of reinforcement.) For the larger percentages of steel, the dash line on the diagrams, which indicates the theoretical deformation of the steel obtained from Formula (9), page 355, strikes the actual deformation curve at the deformation corresponding to a stress of 39000 pounds to 43000 pounds per square inch. This indicates that near the elastic limit the actual stresses agree very well with the theoretical stresses. The diagrams on page 413 give a comparison of actual stresses with theoretical stresses computed by the ordinary formulas. From this it is seen that if a beam or slab is designed by formulas on page 482 for an allowable unit stress in steel of 16 000 lb. per sq. in., the actual stress for the design load is smaller than 16 000 lb. and varies with the per- TESTS OF REINFORCED CONCRETE 413 Deforma+ion Per Unit of Length Beam With Q49 FferCent Relnjoicetnent Deformation PerUni+of Lenath Beam With 058 FferCent Reinforcement Deformation Per Unit of Length BeoihWith 130 FferCent Reiriforcement Deformation Per Unit of Length BeamWith USFterCentReinforcemerrt Fig. 119.— Deformations in Steel and Concrete Due to Loading.' (.See p. 411, * Technologic Paper No. 2, V. S. Bureau of Standards, 1912, p. 39. 414 A TREATISE ON CONCRETE centage of tensile reinforcement. This does not, however, increase the factor of safety of the beam because, irrespective of the magnitude of the actual stress at the design load, double the load will bring the actual stress to about 32 000 pounds. It does, however, influence the formation of cracks so that the cracks do not appear at nearly so early a stage as would be expected from the ordinary formulas. In actual construction, tensile resistance of concrete cannot be counted upon as it is often destroyed either by shrinkage due to hardening or by temperature changes. Formulas on page 482, therefore, although they do not represent the actual conditions of stresses at the design load, give the required factor of safety and are recommended for use in design. The behaviour of a beam reinforced with steel in two layers is the same as of a beam with one layer. The steel in two layers is less effective than the same amountof steel placed at the lower level because the upper layer nearer the neutral axis is effective only in proportion to the ratio of its distance from the neutral axis to the distance of the lower layer. If, therefore, the upper layer is eight inches from the neutral axis and the lower, ten, the effective area is the area of the lower layer plus four-fifths of the upper layer. Compressive Stresses in Concrete. As is evident from the deforma- tion curves (Fig. 119, p. 413) the compressive stresses in concrete in the first stage are proportional to the loads. After the formation of the first crack, the deformation curve undergoes an abrupt change after which it is again almost a straight line. The theoretical stresses computed from ordinary formulas for per- centages of steel above one per cent agree fairly well with stresses com- puted from the deformation curves in beams and compared with defor- mation curves for cylinders of the same concrete. For small percentages of steel the computed stresses are smaller than the actual. This, how- ever, does not affect the design because in such a case the beam would fail by tension so that the actual concrete stresses are unimportant. Tests with Compressive Failure. Tests*t show that ultimate fiber stress determined from deformations is larger than the crushing strength of a cube of the same concrete so that it is safe to use larger stress for extreme fiber than for direct compression. The same phenomenon is observed in tests of T-beams. (See table on p. 416.) The number of tests, however, is not sufficient to draw a definite conclusion as to the ratio of crushing strength to ultimate fiber stress. • University of Wisconsin, Bulletin No. 17s, November, 1907. t Dr. E. Morsch, "Der Eisenbetonbau,'* 4th Edition, p.167. TESTS OF REINFORCED CONCRETE 415 TESTS OF T-BEAMS. The discussion of the phenomena of loading and the movement of the neutral axis given for rectangular beams and the results given in connection with the appearance of first cracks on page 405 apply also to T-beams. The initial position of the neutral axis, however, will be diflEerent in a T-beam than in the rectangular beams and depends upon the relative dimensions of the flange and the stem and the percentage of reinforcement. It must be remembered in applying to T-beams the discussion of influence of percentage of steel upon the appearance of first crack given for rectangular beams, that the percentage of steel must be figured for the widtli of beam equal to the width of the stem. T-beams may fail by either tension in steel, compression in concrete, diagonal tension, or bond. The tests discussed below are grouped ac- cording to the cause of failure. TensUe Failures of T-Beams. Professor Talbot's test of T-beams* consisted of nine beams. Dimensions: total length, 11 ft.; test span, loft.; depth to steel, d = 10 in.; height, h = 12 in.; thickness of slab, < = 3I in.; breadth of stem, b' = 8 in.; width of flange, b = 16, 24, and 32 in. (three, beams of each width). Concrete, i : 2 :4by volxune. Steel: the amount of reinforcement varied from 0.92% to 1.1% of the area of enclosing rectangle, bd. Longitudinal reinforcement: f-inch plain round bars with yield point of 38 300 lb. per sq. in., and f-inch corrugated square bars with yield point of 53 Soolb. per sq. in.,with I in. U-shaped stirrups (corrugated square) spaced 6 in. apart in the out- side thirds of beam. All beams failed by tension. Stresses in steel at maximum load, M figured by Professor Talbot by formula, /j = , agree well with 0.86 Asd stresses at yield point of the steel. Calculated stresses ranged, for plain bars, from 37 600 to 41 500 lb. per sq. in., with an average of 39 800 lb., and for corrugated bars, from 55 700 lb. to 64 300 lb., with an average of 55 700 lb. per sq. in. No beam failed by diagonal tension, although the maximum shearing V unit stress from formula, v — , reached the value of 605 lb. per b'jd sq. in. The web reinforcement, therefore, proved to be adequate. The total diagonal tension, considered as resisted by the stirrups only, would • University of Illinois Bulletin No. u, February i, 1907. 4x6 A TREATISE ON CONCRETE produce a theoretical stress in stirrups of 55 500 lb. per sq. in., or higher than the elastic limit of stirrup steel. Judging from the size of the diagonal cracks, the actual stress in stirrups was much below the elastic limit, which indicates that a part of the diagonal tension is carried by concrete, justifying the recommendation on page 371 allowing one-third of the total diagonal tension to be considered as resisted by concrete with the remainder carried by the steel. Tests of T-Beams to. Determine the Effective Width of Flange. The following test was made at the testing laboratory in Stuttgart,* with a number of beams of the same span, cross-section, and amount of steel, but varying widths of flange. Three beams of each type were tested. Loads were applied at one-third points. Beams 2, 3, and 4 failed by crushing of concrete in the flange. The failure in concrete occurred in about the same way as in cubes, by split- ting of wedge-shaped pieces of concrete. The shortening of the flanges of beam No. 3 was uniform throughout the width of the flange during the whole progress of the test. For Beam No. 4, there was a difference in shortening of only 8% for loads near the crushing strength of concrete. T-Beam Tests to Determine Ejfect of Width oj Flange. {See p. 416.) Compiled from tests by C. Bach.* Proportions of concrete, 1:3:4 by volume, with 95% of water by weight. Elas- tic limit 6f steel, 48 000 lb. per sq. in. Age of test, 45 days. Common dimensions: Total length, 10.89 ft-! testing span, 9.84 ft.; breadth of stem 6' = 7.o8 in.; total depth, ^( = 9.84 in.; depth of steel, 9 2-1 l-la 2-^t I It Round Dora ^ Round t t 1 1 I, k k \ \^isryy^ "ft' '"■^ Round Bars"^'Round ♦ > t i i 1 i___L__L 2-'f 1-4" 1^^" l-f l-t" r-l" Round Bars \ Round T t t t 1 4 4 4 L OfiQQQ^I I y\4^(^^^^ rw^rrrpF^ rT6 l-'il Round Bars"^^ Round 4 IF 1 "W Mil 1 1 1 1 i^ag^fflffl ffil T Fig. 121. — Effect of Diagonal Tension. Design and Loading of Test Beam. Group II. {See p. 418.) TESTS OF REINFORCED CONCRETE 423 Bent Bars. (9) Bars bent at one point only are more effective when bent at about 45° than if bent flatter at about 18° with the horizontal. Beam 29, on page 421, resisted 20% larger load than Beam 25, al- though the area of bars bent at 45° was 1.8 sq. in., against 1.98 sq. in. bent at 18° in Beam 25. No marked difference was found in strength for beams with bars bent at 30°, 40°, and 45° respectively. (10) Bent bars as well as stirrups are effective reinforcement for diagonal tension. Compare Beams 30 and 38, page 420, both of which failed by tension in steel. (11) The strength of beams with bars having sharp bends was smaller than for beams with a circular bend with a radius equal to about 12 dia- meters. (12) It is evident from comparison of the stresses at ultimate loads with the elastic limit of steel that almost all the beams with bent bars failed by tension in longitudinal steel. Tests of Beams to Determine the Efficiency of Web Reinforcement. (See p. 422.) Compiled from Tests by C. Bach.* E 3 2 Area of Cross Section of Bars.f Hori- zontal (Total) Ultimate Load. lb. Stresses at Ultimate Load. lb. per sq. in. Js Increase ia Ultimate Load by Hooking of Horizontal Bars. Per cent. Deflection. Ulti- mate Load. Half Ulti- mate Load. Cause of Failure. (See note.) Beams Loaded at Eight Points SI 3 .91 46 900 I 31° 22 420 252 S2 3 89 67 300 I 870 32 020 360 Si 3 91 SI 300 I 420 24 390 273 54 3 97 93 900 2 SS2 43 250 492 SS 3 81 1. 91 73 300 2 ISO 36 890 404 .?6 3 80 1. 91 100 300 2 920 50 300 S49 S8 3 86 2.32 9S 300 2 7S0 46 6go S16 60 3 91 2-37 9S 300 2 760 46 220 518 62 3 94 2.74 99 400 2 860 48 GIG S39 64 3 89 1.70 106 200 2 950 SO 4SO S66 66 3 91 2.73 loi 900 2 900 49 180 SS2 6 II 17 18 G.22 O.IO 0.37 o.iS 0.24 G.09 0.73 0.22 0.50 0.20 I. 01 0.27 G.74 0.2s 0.64 0.24 G.88 0.26 G.88 G.26 0.7s 0.26 DB DB D D T T T T T T Note: D = diagonal tension failure B = bond failure T = tension failure DB = diagonal tension and bond failure • Deutscher Ausschuss fur Eisenbeton, Heft X, XII, XX, igo8 and 1912. t Areas of bars are converted directly from the metric dimension. Diameters in Fig. 121 are approx- imate to nearest sixteenth inch. 424 A TREATISE ON CONCRETE f=H o 1 < 55 § H & -^ ri >. d ^ en rt Q E^ oi U 'S. >^ H o £' TESTS OF REINFORCED CONCRETE 425 BEHAVIOR OF REINFORCED CONCRETE BEAM FAILING BY DIAGONAL TENSION UNDER LOAD The difference between the intensity of loading at first diagonal crack and the ultimate loading for beams without web reinforcement depends upon the strength of the concrete. Lean, or green concrete beams fail with little or no warning, so that the load at first diagonal crack coin- cides with the breaking load, while in richer and stronger concrete beams, diagonal cracks are visible for some time before final failure occurs. Figure 122, page 424, shows a reinforced concrete beam of i : 2 : 3 concrete, 45 days old, with no stirrups, after failure by diagonal tension and shpping of the bar. At a load of 14 700 lb., the first crack devel- oped in the middle portion of the beam which was loaded at one-third points. At 17 640 lb., a diagonal tension crack developed in the out- ^ 3.125 o (5 0) Q. «| c 2 3, 100 75 50 25. v^ai^wiji -^^ v^i^J^ '-^ " Reinfor :emenv 0.98 Pe ■-Cent ^-^ Span 6 Ft. 20 30 40 Age in Oolis 50 60 70 Fig. 124. — Effect of Age Upon Web Resistance. Tests by Prof. Talbot. {See p. 426.) side third just beyond the load. This crack increased with increased intensity of load with an inclination toward the load. At 22 000 lb., the crack extended up almost to the bottom of the flange. The diagonal tension cracks were much larger than the tensile crack in the middle portion. At 22 000 lb., small horizontal cracks developed at the level of the horizontal bar. At further loading, more additional horizontal cracks appeared than all the previous horizontal cracks combined and formed at the failure which took place at the loading of -28 6qo lb., a continuous crack extending from the support to the load, as is shown in the figure. Fig. 1 23, page 424, shows a typical tension failure of a beam of similar dimensions as shown in Fig. 122, page 424, provided with stirrups where the cracks are confined to the center of the beam. These tests are both selected from "the series by Bach. 426 A TREATISE ON CONCRETE BEAMS WITHOUT SHEAR REINFORCEMENT The maximum unit shearing stress at which beams without web reinforcement fail by diagonal tension depends primarily upon the rich- ness of the concrete and the age, and in smaller degree upon the per- centage of steel and the ratio of depth to length of span. The last two items can be neglected in ordinary design. Since diagonal tension faU- 200 175 t-5 c — « g) g*0 125 100 8S. •C q "?"g 75 c o 3 0. SO y U3 ^ 1_,^ T to -Ky C\J y^ Rei Tforcem«ssn+ 0.98 P ar-Cent / Agt 60 Days Sp<3n 6 Ft. 10 15 20 Per-Cent of Cement 25 50 Fig. 125.— Effect of Proportion of Concrete Upon Web Resistance. (See p. 426.) Tests by Prop. Talbot. ure in beams without web reinforcement is sudden, a large factor of safety is advisable. (See page 374.) In all cases quoted below unit shearing stresses were computed by formula (ssa), page 367. Effect of Age upon Web Resistance. The effect of age is of great im- portance in determining the time for removal of forms and the age at which concrete can be loaded. It is illustrated in Fig, 124, page 425, taken from tests made by Professor Talbot at the University of Illinois.* %1225 ■5^ C 125 = D Q75 1.00 Mix 1:2:4 Age 60 DAl|3 Span 6 ft. aoo 2£5 1^5 1.50 1.75 Per-CenT Rein|^orcemenT Fig. 126.— Effect of Percentage of Horizontal Steel upon Web Resistance. (See p. 427). Tests by Prof. Talbot. Effect of Richness of Mixture of Concrete upon Web Resistance. Figure 125, page 426, taken from Professor Talbot's tests shows the increase of • Bulletin No. 29, January 4, 1900. " " " ' " TESTS OF REINFORCED CONCRETE 427 web resistance with the amount of cement in concrete. The increase is quite marked although somewhat less than the increase in compressive strength for the same cause. Effect of Percentage of Horizontal Steel upon Web Resistance. As is evident from Fig. 126, page 426, the percentage of steel has a marked effect on web resistance which can be attributed to two causes. First, for smaller percentages of steel, the deformation is larger with conse- quently increased tendency of concrete to crack. Second, with larger percentages of steel, the tensile stresses developed near the support are smaller, consequently the appearance of the tension cracks which later develop into diagonal tension cracks is retarded. Ratio of Maximum Shearing Unit Stress Involving Diagonal Tension to the Modulus of Rupture of a Plain Beam and to the Compressive Strength. In beams without web reinforcement, from tests by Pro- fessor Talbot* the ratio of maximum vertical shearing unit stress in beams failing by diagonal tension to modulus of rupture averages 0.5, and to the compressive strength, of 8 by 16-inch cyUnderst averages 0.09. BEAMS REINFORCED FOR TENSION AND COMPRESSION Tests prove conclusively the effectiveness of steel as compression reinforcement. Professor M. O. Withey's Tests.} The series of 1906 consisted of eight beams, 12 feet long; breadth = 8 inches; height = 11 inches; depth to steel = 9f inches, with 2.9% tensile reinforcement and varying amounts of compressive reinforcement. The web reinforcement con- sisted of three bars bent up in two different places at a very flat angle. The results of the tests, although interesting, do not bring out fully the value of steel as compressive reinforcement because aU beams failed by diagonal tension, with the exception of the beaan without compressive reinforcement, which failed in compression. Notwithstanding this, however, the maximum load of the beam without compression steel was 22 000 lb., while the maximum load for the beam with compressive reinforcement was 29 000 lb. Series of 1907 consisted of four beams similar in design to the beams previously described except that they were provided at each end with lo-i-in. round stirrups. All the beams failed in tension at an average * University of Illinois, Bulletin No. 29, January 4, igop. t In determining this ratio the authors have converted the results found on cuhtes to a cylinder basis (see p. 344). { Bulletins of the University of Wisconsin, No. 17s and 197, Series of 1906 and 1907. 428 A TREATISE ON CONCRETE load of 34 ooo lb., showing an increase of 55% over the beam without 3ft. 3f — 164> I 3zr ar sznr 12: x Fig. 127. — Dimensions of Beams, Stuttgart Tests. (See p. 428.) By Prof. C. Bach. compression reinforcement. Still, because of the tension failure, the fuU value of compression reinforcement was not demonstrated. Bach's Stuttgart Tests.* Bach's tests of beams with compressive steel consisted of six types of beams, the dimensions and arrangement of reinforcement of which is shown in Fig. 127. The results of the tests are given on page 428. The reinforcement of beams VII, VIII, and IX is alike except that beam VII in the middle portion has no stirrups while beams VIII and IX have stirrups of the shapes shown in the draw- Test of Beams with Compression Reinforcement. (See p. 428.) Concrete: i : 3 : 4 by volume. Aggregates: Rhine sand up to 0.27 in. diameter, and Rhine gravel up to 0.79 in. diameter; 9.5% of water by weight. Age gf test, 45 days. Compiled from Tests by C. Bach. Maximum Load. lb. Computed Unit Stresses in Steel and Concrete at Maximum Load Based on « = 15 Compressive Strength of Cubes. lb. persq. in. Ratio Computed Unit Fibre Specimens. Unit tensile stress in steel h lb. per sq. in. Unit compressive stress in steel fs lb. per sq. in. Unit stress in concrete U lb. per sq. in. Stress to Strength ol Cubes. I VI vn vm rx X 16 860 20 650 27 500 29 000 28 600 36 000 11 220 14 390 17 750 18 720 18 480 23 200 28 680 29 200 29 800 31 620 36 800 2 220 2 390 2 5°° 2 670 2 590 3 240 I 59° I 490 I 480 I 610 I 520 I S90 1 .40 1.60 1.69 1.66 1.70 2.04 * Mitteilungen uber Forschangsarbeiten aus dera Gebiete des Ingenieurwesen, Heft go and 91. TESTS OF REINFORCED CONCRETE 429 ing. The amount of the compj-essive reinforcement in beam X is the same as in beams VII and VIII, but the steel is of higher elastic limit. Beams VI, VII, VIII, and IX' failed by compression. Beam X, in which the bond strength of the compressive steel was exceeded, failed by spUtting the concrete. This latter beam shows a considerable increase in strength over beams with the same amount of reinforcement because of the u^e of cornpressipn steel with high elastic limit. The table on page 428 gives the ultimate loads, the stresses in steel and concrete at the ultimate load under the assumption of n = 15, the strength of cubes and ratio of strength of cubes to figured stress in concrete in the beam. In Beams VII to IX, the compression steel reached its elastic limit first, and for the farther loading kept the same stress till the elastic limit of concrete was reached. In Beam X, on the other hand, the elastic hmit in the concrete was reached first, and after this, stresses due to the additional loading were carried by the steel only until both mate- rials reached the elastic limit. This points to the adjustment between compressive stresses in steel and concrete after one of the materials passes its elastic limit. The same phenomenon was observed in the test of reinforced concrete columns. From inspection of the table, it is evident that for beams with com- pression steel, the theoretical unit stresses in the concrete itself com- puted at the ultimate test load by formulas on page 360, and on the basis of w = 15, are much larger than the similar unit stresses at which the beams without compression reinforcement failed. Since the same con- crete was used in aU cases it is rational to assume that this extra stress must be attributed to compressive steel. This shows that the compressive steel carries stresses larger than would be expected from the formulas, and that its actual effect is greater than the theoretical effect. It is especially noticeable in Beam X, for which the theoretical maximum fiber stress was 3 240 lb. per sq. in., while the crushing strength of the concrete was i 590 lb. per sq. in. The above tests prove conclusively that compressive steel may be relied upon to strengthen the compressive zone of a beam, and that its effect is even larger than would be expected from the formulas. TESTS OF BOND BETWEEN CONCRETE AND STEEL Bond between concrete and steel, or the resistance to withdrawal of steel imbedded in concrete may be divided into two elements: (i) grip caused by shrinkage of concrete; (2) frictional resistance caused by the unevenness of the surface of the bar. Both elements act together until 430 A TREATISE ON CONCRETE the bar begins to slip. Then the grip is destroyed and frictional resist- ance alone resists the pull. In deformed bars, the two elements are aided by the pressure or bearing of the projections on the concrete, but this does not come into play until after the first slip. The pull-out tests are treated separately from the bond tests in beams because the action of bond stresses in the two cases is different. PULL-OUT TESTS Pull-out test specimens consist of bars imbedded in blocks. The load is apphed at the free end of the bar and is resisted by the resist- ance to the withdrawal of the steel imbedded in the block. In practice similar conditions occur in end anchors for fixed or canti- lever beams where the concrete at the support corresponds to the block in the pull-out tests. The maximum stress in steel at the edge of the support, which is transferred to the support by bond, corresponds to the applied force in pull-out tests. In computation the bond stresses are considered as uniformly dis- tributed over the whole surface of contact between steel and concrete. (See Formula 36, p. 534.) Actually, however, the bond stresses vary from a maximum at the edge of the support to a minimum within the support. In many cases, in fact, the bar begins to slip at the place of appUcation of the force before the bond resistance of the whole bar comes into play. Therefore, ordinarily the portion of the bar near the point of support offers frictional resistance only, while the farther end of the bar offers grip and frictional resistance. The variation in magni- tude of bond stresses along the length of imbedded bar depends upon the length of imbedment. Hence in basing allowable unit stresses on the tests, the effect of the ratio of the imbedded length to the diameter of bar must be taken into account. When a bar imbedded in concrete slips, the movement of the free end is somewhat greater than of the imbedded end, the difference being equal to the deformation of the imbedded portion of the bar under stress. Effect on Bond Strength of the Ratio of Length of Imbedment to Diam- eter of Bar. The average bond resistance considered as distributed uniformly over the total surface area of imbedment is smaller for long imbedments than for short imbedments. At the University of Illinois,* • University of Illinois Bulletin No. 71, December 8, 1913, p. 39- TESTS OF REINFORCED CONCRETE 431 in tests by Mr. Duff A, Abrams for i J-inch plain round bars imbedded in 1:2:4 concrete, 74 days old, the average bond resistance for 6-inch imbedment (4.8 diameter of the bars) was 420 lb. per sq. in., while for 24-inch imbedment (19.2 diameters), it was 328 lb. per sq. in. Similar results were obtained by Prof. C. Bach.* /oo .^^ jare Inch ^^ ,^ "^lo; ^ '■^t^^ or 03 op^ ^500 10 / SS In PourK A /■ / i ( )"^-^.,^_^ -^/c "^ /t-o , Bond Stre I / JA^ Ors __, 1:2 4 Age Conor abou1 ete 2 Mo iths 200 \ 1 .01 .03 Bar in I nones .0/1 .OS 02 Slip of •jAinoh Deformed Round Bars, Embedment Variable +liinch PlaIrS Round BarSjEmbedment Variable opiain Round BarSj Diameter and Embedment VanaDle Fig. 1 28. — Relation of Bond Stress to Slip of Bar During Progress of Loading.f (See p. 432.) Method of Determining: Bond Resistance. In computing the bond resistance of a bar the ratio of the length of imbedment to diameter of bar, and not the length of imbedment, is the determining item. The * C. Bach, Zeitschrift des Vereines Deutscher Ingenieure, 1911, S. 859. t University of Illinois Bulletin No. 71, December 8, 1913, p. sj. 432 ^ TR&ATISE ON CONCRETE required length of imbedment increases in direct proportion with the increase of the diameter of bar. Thus a 2S-inch imbedment is suffi- cient for a |-inch bar because the ratio of the length to diameter is 50. It would not be large enough for a one-inch bar because the ratio then is only 25. (See p. 539.) Bond Resistance for Different Slips. Fig. 128, p. 431, shows the rela- tion between the bond stresses and slips for plain and deformed bars during the progress of loading. As is evident from this diagram, for plain bars initial slip occurred at 260 lb. per sq. in., or at about 60% of the maximum bond resistance. After the maximum bond resist- ance, which corresponds to a slip of o.oi inches, was reached, the resist- ance to withdrawal decreased. After a slip equal to five times the slip at maximum resistance has taken place, only 70% of the maximum load is required to produce further slipping. The curves for the de- formed bars are discussed on page 434. Effect of Surface Condition and Shape of Bars. The following con- clusions may be drawn from Abrams' tests. The bond resistance of square bars is only 75% of the bond resist- ance of plain round bars. Rusted bars (with no scale) give bond resistance 15% higher than similar bars with ordinary milled surface. The bond resistance of T-bars per unit of area decreases with the increase in size. For 1:2:4 concrete, imbedment 8 inches, and age 70 days,* the maximum bond resistance of i-inch round plain bar was 370 lb. per sq. in.; of i-inch T-bar, 310 lb. per sq. in.; and 2-inch T-bar, 220 lb. per sq. in. Influence of Age and Mix. The following table gives the efiect of age and mix on bond of |-inch plain round bars and of f-inch corru- gated square bars. Influence of Freezing. In Abrams' tests, specimens made out-doors in freezing weather, where they probably froze and thawed several times during the period of setting and hardening, were almost devoid of bond strength. Ratio of Compressive Strength to Bond Resistance. The ratio of bond strength at first slip to compressive strength of 8 by 16-inch cylinder. is abouto.13-, and of the maximum bond, strength, 0,19.^ . These ratios 'were determined by Mr. Abrams from tests on speci- mens varying in age from 2. days to 2 1. years, and proportions from ■;: • UiiiversiSy of nfinoiiBBlletiffNo. 71, bs'cgWbSr 8, igii, p. 49. " TESTS OF REINFORCED CONCRETE 433 i: i: 2-to i: 5: lo. These values agree very well with the results ob- tained by other experimenters. Maximum Bond Stress and Bond StrefS at o.ooi Inches Slip for Varying Proportions and Ages* (See p. 434.) By D. a. Abeams Age. Stress in Pounds per Square Inch of Surface of Bar. Proportions. Size of Bar. 1:1: 2.t i:j5:3- 4- 1:3:6. 1:4:8. a d S .•& B ,•& g ,■& g ,£■ fl il 3 B §2 8^ 1 H55 1 0^ "s OS sS oM dg C4 °S rt °^ s <" •s <" s <" 1^ < S ^" 2 days 141 107 IS9 123 123 89 S3 32 27 17 4 days 197 iS6 231 19s IS3 no 77 43 49 32 7 days 246 202 300 250 226 158 165 112 54 32 28 days to 393 300 S46 457 404 ?88 241 130 149 120 f-inch plain 32 days. round 60 days to S30 399 SS4 492 45 2 363 3" 227 190 135 6s days. 120 days to 666 479 667 538 603 469 536 398 210 172 132 days J 16 months 779 656 896I 87s 841 1 800 372 333 373 2S3 2 days 231 96 20s 92 . 219 97 157 44 64 13 4 days 368 176 258 "S 305 129 239 74 no 23 7 days 419 171 330 140 459 187 286 104 133 35 28 days] to [ 828 344 ■56° 281 641 306 462 179 273 97 f-inch cor- 32 days J rugated 60 days! square to \ 6s days J 120 days I 132 498 I oS3t 536 854 434 623 280 391 139 to I IS3 S99 I 070 564 I 079 576 746 326 470 159 132 days J 16 months I S3S 892 728 322 * University of Illinois Bulletin No. 711 t The reason' lot relatively low strength be an erratic result. { Bars stressed to or Beyofid yield point. December 8, 1913, pp. 82-83. of 1:1:2 concrete and 5-inch bare is unexplained and may 434 A TREATISE ON CONCRETE Deformed Bars. Results of pull-out tests with deformed bars are given* on pages 431, 433 and 435. The first slip for the deformed bars occurs at about the same stress as for plain bars. After the first slip, the projections help to resist farther slipping. Considering all the bond stresses except those resisted by frictional resistance taken by the projections, the bearing stresses on concrete for some types of deformed bars at large slips are very large, reaching in some cases 14 000 lb. per sq. in. of the area in contact. This high compressive stress on concrete explains the splitting of the blocks in pull-out tests. Since the allowable working stresses are only a fraction of the ultimate bond stress the bearing stresses on projections always are within safe working limits. The maximum bond stresses, being accompanied by large slips, can- not be utilized in construction, where only a very small slip is per- missible, consequently the working bond stresses must be based on stresses at a slip not exceeding o.oi inches rather than on ultimate bond strength. The factor of safety for deformed bars based on this slip, however, may be made smaller than for plain bars since the high ultimate bond strength and the existence of mechanical bond reduce the danger of actual bond failure. This is of special importance during construction when comparatively green concrete may be called upon to support a considerable construction load. Allowable Working Stresses, Allowable working unit stresses based on the tests are given on page 573. BOND STRESSES IN BEAMS The method of computing bond stresses in reinforced concrete beams is given on page 533. Although the formulas do. not represent the actual conditions in a beam, as explained below they form a proper basis for design with values for working stresses based on tests and figured for the same assumptions. The computed maximum bond stresses in a beam occur at points of maximum shear. With uniform loading, this is at the supports and decreases uniformly to zero at the center of the beam. In beams loaded at one-third points, maximum bond stresses act in the outside thirds and are zero in the central portion of the beam. Phenomena of Bond Tests. The bond stresses in beams are caused by the change from point to point, i.e., the increase, in the stresses in * University of Illinois Bulletin No. 71, Diicember S, 1913. TESTS OF REINFORCED CONCRETE 435 the longitudinal steel. This increase in stress in steel as computed is proportional to the amount of increase in the bending moment, and therefore, proportional to the vertical shear. Actually, however, the change in stress in steel is affected by the presence of tensile stresses Distribution of Bond Stress in Reinforced Concrete Beams. {See p. 436.) Beams 8 by 12 in. in section and 10 in. deep to center of reinforcing bar. Loaded at the one-third points of a lo-ft. span. All beams failed by excessive tensile stress in the reinforcing bars. Corripiled from Tests by Duff A. Abrams* Applied Load on Beam. Observed Bond Stress. Beam No. Size and Kind o( Bar. Age at Test Average Computed Bond stress Over Region Just Outside of toad Points, t Near Ends of Beam.t lb. lb. per sq. in. ib. per sq. in. Ib. per sq. in. 2 000 38 TOO 16 4 000 76 I2S 34 loss -6 One i-in. Plain Round 2 yr. ' 6 000 8 000 10 000 114 IS2 190 191 226 201 36 64 117 , II 700 222 i6s 238 2 000 38 48 IS 4 000 76 7S S4 loss -3 One i-in. Plain Round 2 yr. ' 6 000 8 000 10 000 114 190 iSS 141 200 9S 100 130 10 700 203 140 156 2 000 34 80 20 4 000 68 137 4S 6 000 102 226 9S 8 000 13s 28s 135 10 000 170 250 ISO 1049.3 One ij in. Cor- rugated Round 13 mo. < 12 000 14 000 16 000 204 236 270 31S 3SO 38s ISO 225 260 18 000 306 400 290 20 000 338 4SO 31S 21 000 3SS 200 360 21 goo 370 390 ♦ University of Illinois Bulletin No. 71, December 8, 1913, p. igj. t These stresses are, in general, the average bond stresses developed over a length of about 1 2 in. in the portion of the beam about a to 16 in. outside the load points. J The average observed stress over a length of 9 to 15 in. at the ends of the beam. 436 A TREATISE ON CONCRETE in concrete, the amount and the proportion of which to the total ten- sile stresses is dififerent in different parts of the beam. The effect is smaller near the point of maximum tensile stresses . (where the con- crete is cracked), and larger near the support where concrete may carry stresses even at maximum load. The increment of stresses in steel is not proportional to the shear; the bond stresses which are caused by that increment are, therefore, not proportional to the shear. The table on page 435 gives observed bond stresses and computed bond stresses for varying intensities of loading for a beam loaded at one-third points. Since the shear between the support and the point of apphcation of the load is constant, the computed bond stresses are con- jC o § I. — (D' T5 Q- O •» 400 350 500 250 200 ISO . 1 I —— ■ ^_i: lJ 1 '. ,, I 50 60 ISO ISO 90 120 Age in Days Fig. 129. — Effect of Age on Bond in Beams. (See p. 437.) Tests by Prof. Withey. stant. The observed bond stresses, however, near the support are smaller than just outside of the points of application of the load until the steel reaches the elastic limit, after which a readjustment takes place and the bond stresses become equalized. From the table, it is evident that in beams 1049.3, for example, the observed bond stress just outside of load points for a load of 16 000 lb. is larger than the average computed bond stress for the ultimate load, i.e. 21 900 lb. This explains why for beams failing by bond the average computed bond stress at the ultimate load based on Formula (36), page 534, is smaller than the maximum bond strength in pull-out tests. The bond stresses given in subsequent discussion are those obtained by Formula 36, page 534. Effect of the Distance of the Load from the Support on the Bond Stresses. As may be inferred from the discussion of the phenomena TESTS OF REINFORCED CONCRETE 437 of the bond stresses, the average maxunum bond stresses are larger as the load is placed nearer the support. Prof. C. Bach* in tests of beams of 1:2:3 concrete at age of 45 days, finds values of ultimate bond strength for distances 9.8 inches, 19.7 inches, and 29.5 inches from the support to average 507, 325, and 308 lb. respectively. • Effect of Age on Bond. Fig. 1 29 on page 436, from Professor Withey 's tests at the University of Wisconsinf shows the increase of strength with age. Professor Bach found for i : 2 : 3 concrete the following bond strength: Ages 28 dajfs. 45 days. 6 months. One year. Beams kept moist, lb. per sq. in. . . 278 308 393 435 " dry, " " .. 271 319 356 363 He suggests the following formula for increase in bond strength with age: " = ^^sG-^Ii^r) Where u = unit bond strength in lb. per sq. in. A = age in months. Effect of Mix of Concrete. From tests it is evident that the richness of mortar in concrete affects the bond strength considerably. The quaUty of stone is of little effect provided pockets around the reinforce- ment are prevented. The table below gives values for bond strength for concrete of different proportions. Bond Strength in Beams for Different Proportions oj Concrete. {See p. 437.) Beams, s in. by 3 in. by s ft. 6 in. long. Reinforcement, 3-f-iu. round bars. Lower bars imbedded in concrete for length of 10 inches at both supports. Beams tested on 5-foot span. Compressive tests on separate specimens. Compiled from Tests by Morton O. WiTHEvt Mbt. Age. days. Coarse Aggregate. Average Bond, lb. per sq. in. Compressive Strength, lb. per sq. in. 1:2:4 1:2:4 1:3:6 T:2i 60 60 60 60 Limestone Gravel Limestone 276 27s 216 267 1 790 2 200 830 I 600 * Wideretand Einbetonierten Eisens Gegen Gleiten. Einfluss der Haken, von C. Bach and O. Giaf. page 18. t University of Wisconsin, Bulletin No. 321. October, 1909, p. ij. % Ibid. 28. 438 A TREATISE ON CONCRETE Hooks as End Anchorage. The requirements of a properly con- structed hook are: (i) it should permit the stressing of the steel to its elastic limit without appreciable movement; (2) the bearing stresses on the concrete must be within a safe limit. Since the allowable bear- ing stresses on concrete depend upon the properties of the concrete, the factor of safety against crushing must be the same as that used in determining the allowable iiber stresses in concrete. Tests show that the crushing strength of concrete when confined is much larger than the crushing strength of cubes or cylinders. Hence, the safe bearing stress of the hook on the concrete should be based on the crush- ing strength of confined concrete. In comparing, therefore, the rela- tive efficiency of hooks, their bearing area is of first importance. When used for end anchorage, hooks which allow stressing the steel to elastic limit, but which at the same time split or crush the concrete, have not the required factor of safety as far as concrete is concerned because at working stresses the concrete would have only a factor of safety of two instead of four as required by rational design. Tests* made for the Eastern Concrete Construction Company at the Massachusetts Institute of Technology determined the capacity of the hook, but did not determine the load at which the first movement of the hook took place. In all the tests, f -inch round bars were imbedded in blocks 1 2 inches square and 15 inches long to a depth of 12 inches with additional bends of different lengths. Right-angular bends and semi-circular bends on a 3-inch diameter were tested. Several specimens of each type were tested, the results of which were extremely uniform. The following conclusions may be drawn from the tests. (i) A 4-inch right-angular bend in a f-inch round bar (5 diameters) combined with 12-inch imbedment (16 diameters) is sufficient to stress the steel to its elastic limit. This hook, however, crushed the concrete and split the block, therefore it does not give the required factor of safety against crushing of concrete. A longer bend does not increase the security because the bearing stress is not appreciably reduced. (2) A semi-circular bend with a diameter four times the diameter of the bar is more effective than the square bend and is preferable because the bearing stresses on concrete can be kept within working limits. Action of Hooks in Beams. Beams in which longitudinal steel is provided with hooks show a much larger load carrying capacity than similar beams with ends of bars straight. Tests at age of 45 days by • Concrete Plain and Reinforced, Second Edition, p. 466. TESTS OF REINFORCED CONCRETE 4.39 Professor Bach on beams of i : 2 : 3 concrete, 12 inches square and 6-foot span reinforced with one 0.98-inch diameter round bar provided with three different kinds of hooks, gave the carrying capacity of the beam without hooks as 14 330 lb.; with right angle hook, 24 250 lb.; with 45° hook, 25 800 lb.; and with circular hook, 28 060 lb. The beam with rectangular hooks failed by straightening the hook. 20000 isooa 18000 (Q T! 17000 C Q. •D D ■D 9 a. < ^ teooo 15000 14000 13000 12000 1 1000 10000 9000 eooo 7000 6000 5000 4000 3000 2000 1000 ^ ^. ^,t>X- :":""M^te -t .A M Lt ^^^ ,|^ T ^^ ,- .-;^ -'A _^_,__^^^^^-^-^^,=|^ J yy .Si''''j_t yy^'^-^^^" \ T ^'x''''^^''-'' -''^ '^y^y 'TT 1 :^^^:?;^:^r:<::::::;:::r::::::;::____:::: " ^'^'' ,-" .-"' ...,.^^^ --_,,. ::::::tt ""'A^-'^' ~"~ ""(t^ /] 005 0.10 0.15 O20 025 050 035 040 045 050 055 Deflection of Beam in Inches I Fig. 130. — Deflection of Beams with varying Percentage of Steel. {See p. 441.) Tests by Richard L. Humphrey and L. H. Losse. SPLICES OF TENSILE REINFORCEMENT IN BEAMS AT POINTS OF MAXIMUM STRESS Tests have been made by H. Scheit and 0. Wawrziniok* to determine the effectiveness of different methods of spUcing steel at the point of maximum stress. The beams were 12 inches square of spans 6 1 feet and 10 feet, reinforced with one-inch bar. They were tested with two symmetrical loads spaced 3 feet 3 inches apart for the shorter beams, and 5 feet apart for the longer beams. .^ ., • Deutscher Ausschuss fur Eisepbeton, Heft 14, 1912. 440 A TREATISE ON CONCRETE Straight splices were made with a lap of lo, 20, and 30 diameters respectively for the short beams, and 40, 50, 60, 70, and 80 diameters for the long beams; in hooked sphces, the hooks consisted of a semi- circle with an inside diameter of 5 diameters of the bar and an extra length of 6 diameters of the bar parallel to the bar, and the bars were lapped 10 inches, 20 inches, and 30 inches respectively. Results. For straight sphces, the best results were obtained with a splice of 50 diameters with which the elastic limit of steel was reached. Hooked sphces proved very effective. Even a lo-diameter lap (the smallest lap used) in combination with a hook, as described above, was suflScient to provide the same carrying capacity as tlie beam without the splice. DEFLECTION The deflection in reinforced concrete depends primarily upon the ratio of the depth of the beam, or slab, to the span. It also depends upon the percentage of tension and compression reinforcement, and in T-beams, upon the width of the flange. Influence of Percentage of Steel upon Deflection. Foi equal depths and widths, the deflection of beams increases with the percentage of Deflection of T-Beam with Varying Widths of Flanges. (See p. 441.) Span of beams, 9.84 feet; reinforcement, four iiVinch round bars; load applied at one-third pomts. By C. Bach.* Deflection in inches. Total Load. Rectangular T-Beam, depth 9.84 in.; width of stem, 7.1 in. Beam 7.1 X 9.84 in. Width of Flange in Inches. 18.9 29-S 39.4 lb. in. in. in. in. 8 800 0.106 0.071 0.047 0.042 17 600 0.376 0.177 O.IIO 0.097 26 SCO 0.368 0.188 0.161 35 300 0.290 °-235 44 100 • 0.467 0.35I 52 900 0-544 * Mitteilungen uber Forschungsarbeiten aus dem Gebeite des Ingemeurwesen. Heft go and 91. TESTS OF REINFORCED CONCRETE 441 tensile steel. Fig. 130, page 439, shows the deflections of beams 13 feet long, 8 by II inches in cross section, tested on a 12-foot span, by two equal loads applied at one -third points. The test was made by Messrs. Richard L, Humphrey and L. H. Losse.* The deformations in steel and concrete for the same beams are shown on page 413. Influence of Width of Flange upon Deflection. In Bach's testsf to determine the effect of width of the flange, the results given in the table on page 440 were obtained. It will be seen that although the percent- age of steel based on the area of the stem was the same in aU cases, the deflection for equal loads is smaller for beams with larger widths of flange. Deflection of Beams with Compression Sieel. {See p. 441.) All beams, 7.1 X 9.8 inches; span, 9.84 feet; tensile reinforcement, four i-^-inch round bars; load applied at one- third points. By C. Bach.J Deflection in Inclies. Total Load. Compression Steel in Percent. 0.4 1.58 i.S8§ lb. in. in. in. in. 4 400 8 800 13 200 17 600 22 000 0.046 O.I19 0.256 0.042 0.102 o.r84 0.298 0.038 0.086 O.I43 0.210 0.287 0.037 0.084 0.139 0.203 0.276 Influence of Compressive Steel upon Deflection. The table above gives deflection of beams without compressive reinforcement and with different percentages of compressive reinforcement. From the figures, it is evident that for equal percentage of tensile reinforcement the deflection decreases with the increase of compression reinforcement. TESTS OF CONTINUOUS BEAMS Since in concrete construction beams are usually continuous over several supports, it is of the greatest importance to determine by tests whether this continuity can be relied upon. * Technologic Paper No. b, U. S. Bureau of Standards. June 27, ign- f Mitteilungen uber Forschungsarbeitcn aus dem Gebiete des Ingenieurwessens, Heft go and 91. X Mitteilungen uber Forschungsarbeitcn aus dem Gebiete des Ingenieurwesen, Heft 90 and 9». § High elastic limit steel' used. 442 A TREATISE ON CONCRETE Tests of Continuous Beams by Prof. H. Scheit and Dr. Ing. E. Probst.* These tests included the concrete beams shown in Figs. 131 to 133, pages 442 to 444. Two beams of each type were tested to destruction. The spans and the reinforcement for the loaded spans were the same for all beams. The complete series included beams as follows : ^5 Ui%- -3R.7"- 7a i4j±/iiJ.|4i: -9ft 10' k2R.5i'-- 2Ft5J'M -3rt7- Position oj Loadin s-rtiQ- ^■vf-ls'l^ ' f',5-ffRojn Round -2R.7J Round [- — 9R.I0" mmmm eSt 3R.I0" 'r- SR.IO' ■ M .[HRJli \ 5-is'Roondl-2rt7£ -art 10" Arrangement of Ste© Section e-f Si !_ ^''/i Cracks in Beam During Loadinq Fig. 131.— Continuous Beam of Two Spans; Type j. (See p. 443.) Type I, simply supported beams. Type 2, continuous beams over two spans. Type 3, continuous beams over three spans, end spans loaded. Type 3a, beams similar to Type 3, but supported by columns; loading same as Type 3. Type 4, beams of five spans, alternate spans loaded. Figs. 131 to 133 show the cracks, and Fig. 132, Types, the deflec- tion at different loads. Results of tests are discussed below: Comparison of Theoretical Deflection with Actual Deflection. To determine the efficiency of continuous beams, the ratios of deflections of continuous beams to those of simple beams obtained from tests were compared with theoretical ratios for homogeneous beams. For continuous beams of two spans, the observed ratio of deflections • "Untersuchungen an durchlaufenden Eisenbetonkonstruktionen," Berlin, 1912. TESTS OF REINFORCED CONCRETE 443 was between 0.42 and 0.45, while the theoretical ratio was 0.40. For beams continuous over three spans with end spans only loaded, the observed ratio was 0.69 against the theoretical ratio of 0.74. For beams of Type 3 of the same design as the one above but in which the ends were connected with columns, the ratio varied from 0.34 to 0.37. From the theoretical figures, it appears that as far as deflection is concerned, this type is almost midway between a beam fixed y.i ^-J^-!4 mIh' n ,. -9FF.I0" -^ r~.—r- % 9R.I0 Sff.lO Posilion of Loadina 6-S Round lO-ftRound • llff.llg'lTl in ^"Is Round ]b 3" T6 Round Section a-b/ UftJ;'-' na-yifiiiJiriTrn mwmiTfTi-M|; a-ft'Round &S'Round Sft.lO l-tt'Round , I— 3ff.lO"-2-feRounQ 2.-ftRound -9 ft. 10" )T sfiiRound 4 Sff.lO" ^J ZfiRounS Arranqement of Steel ^^s^mM . .k M d ..u mm^ Cracks in Beam Durinq Loading Deflection of Beam Fig. 132. — Continuous Beam of Three Spans; Type 3. (See p. 444.) at one end, for which the ratio is 0.40, and a beam fixed at both ends, for which the ratio is 0.20. Type 2. The beams continuous over two spans failed at the support at an average load of 14,240 lb. per lin. ft. The theoretical negative bending moment at the support is — — . The stress in steel at the 444 A TREATISE ON CONCRETE support for the maximum load figured on the basis of the above bending moment is about 64 000 lb. per sq. in. It is evident that this stress is much higher than the elastic limit of the steel used in the test, which shows that the assumed theoretical bending moment coefficient is too large. Based on the moment of resistance for the yield point of steel, we get a bending moment coefficient of 10 instead of the theoretical 8. The point of inflection was found to coincide with the theoretical point of inflection. (See Fig. 131, p. 442.) [-5-i Round ■I I- 1 Round fiRound 3-li Round- .-jE'Rouni ■9rf.(0" .6-TCRound .1 c" . ^ ^-fRound .IP-sRound C prfMiiiiji iiiWiiiMijiipi ;f^^^p^ ' *-f Round . 1 'snouna l i / „ (-31*33 tFS7i k- ., 7^3[t.Sl-|!R:lli>.. ■ -IZft.lli _ 3-feRoundJi- Lr6l6viiRili|ind ^ I 4|^^iRounc) iMiiysMii - 9ft. 10'- jRound -jiMMllSimmy ^fi. iV'-l"* 5-Ti'Round\ 4-li"F5ijnd J__/l3-Ti"B|iund 7-Bhoiir)d jS-lsRaund 7-f'Round 8-i"F^ound\ "* \ ,,. ^ /^nyf^roil -^Zhmnji 5-i"Round '^"'5 Round Section on c-d Arrangennent of Steel m. az it £G 20 li 29 ©®O®©®@0^ :; Cracks Dunne Loadinc Fig. 133. — Continuous Beams of Three Spans; Type 3a. (See p. 445.) Type J. In the beams continuous over three spans, the first cracks appeared at the bottom of the beam in the central portion of the loaded span at a load of 2 565 lb. per lin. ft. In the unloaded span, the first crack appeared at the top of the beam at a load of 5 600 lb. per lin. ft. The sequence of other cracks and the loads at which they appeared is evident from the illustration. The failure at a load of 12 600 lb. per lin. ft. was caused by passing of the elastic limit of steel in the loaded spans. The deflection diagram, Fig. 132, page 443, gives a positive proof of TESTS OF REINFORCED CONCRETE 445 continuous action of the beam. As is evident from the diagram, the deflection in the end span is positive, while in the center span, it is negative. The computed stresses and bending moments at the dif- ferent loads agree quite closely with the measured stresses. The measured compressive stress for the maximum load in the middle span (which was not loaded) was found to be i 500 lb. per sq. in., which is almost identical with the theoretical stress. The cracks in the un- loaded span, which are uniformly distributed over its whole length, furnish a conclusive proof of continuous action. If no provision had • been made for the negative bending moment in the unloaded span, failure would have been certain. Type ja. In the beam continuous over three spans and monolithic with columns, as shown by Fig. 133, page 444, the connection between beams and columns was not rigid, as would be used in rigid frames, but was built as in ordinary building construction. The beams were of exactly the same design as in Type 3. The comparison, therefore, gives the effect of the connection of the beam with the column. The first cracks in the loaded span appeared at a load of 4 590 lb. per hn. ft., and in the unloaded span, at a load of 10 935 lb. per Un. ft. The corresponding figures in Type 3 were 3 565 lb. per hn. ft. and 5 670 lb. per lin. ft. At a load of 13 905 lb. per lin. ft., the first cracks appeared at the top of the end colimm, and at 16 740 lb. per hn. ft., a crack appeared at the top of the middle column. The beam failed at 17 620 lb. per Un. ft. by steel passing the elastic limit. At the time of failure, cracks were observed in the compressive part of the interior column. After the tests, cracks were found at the bottom of the columns located in reverse position to the cracks at the top. During test, not onh' the beams but also the columns deflected, which shows that the whole construction acted as a unit. The deflection in the beams was smaller than in Type 3, as explained before. As was expected, the moment of resistance at the ultimate load does not agree with the bending moments for continuous beams based on the assumption of free ends. The construction must be considered as a frame. Mr. Probst finds that the positive bending moment coeflScient in the loaded span was 12.02, which agrees very closely with the bending moment coefficient computed by him by the rigid frame method. Type 4. The cracks in the T-beams continuous over five spans in- dicate clearly that the beams acted as continuous. From the compar- ison of the moment of resistance of the beam at the maximum load, with the theoretical bending moment obtained from ordinary continu- 446 A TREATISE ON CONCRETE ous beam formulas, we find a very close agreement, which proves that even for five spans a continuous beam acts as continuous. TESTS OF SLABS WITH CONCENTRATED LOADS Tests to determine what width of slab, supported at the two ends, may be considered as carrying a concentrated load, were made by Prof. C. T. Morris* for the Ohio State Highway Department, from which he draws the following conclusions: xttooo o _c oj oaooo m a> JC o _c caooo g ■foooi E o D saooi -irt.4- -1R.4- I aia- HWO 75Cl0lb. 225001b. HR.4."- -IR.4"- 6- 375001b. . ^ ' 1 ~ ^ ^ t^;;; .^ ^ 1 525001b. ! 1 L_ ■ — -..^ ^^ ' ^ ^ i\ y \. y \ y \ V ^ —- ' 0002 De'formation ol' Steel for Different Center Loads Fig. 134. — Deformation of Steel in Slab Along Section Parallel to Supports. {.See p. 447.) (i) The effective width is affected very little by the percentage of transverse reinforcement (parallel to support). (2) The effective width decreases in a small degree as the load increases. (3) The effective width in percentage of the span decreases as the span increases. (4) The following formula, in which e is the effective width in feet and 5 is the span in feet, gives a safe value of effective width where the total width of the slab is greater than 1.35 >S X 4 ft. c = 0.6 6'+ 1.7 ft. •State of Ohio, Highway Department, Bulletin No. 28, September, 1915. TESTS OF REINFORCED CONCRETE 447 The effective width of a slab, e, in this formula, is that over which a single concentrated load may be considered as uniformly distributed on a line parallel to the supports. (s) Thickness of slab shows small effect on the distribution of load. Test slabs were 4 inches and 7 inches thick, with widths for 3|-foot spans of I foot, 3^ feet, and 7 feet; for s-foot spans of i foot, 5 feet, and 10 feet; and for 7-foot spans of i foot and 7 feet. Main reinforce- ment for slabs consisted of 1.04% of steel, while transverse reinforce- FiG. 135. — Appearance of Slab After Failure. {See p. 447.) ment varied from 0.20% to 0.78% of steel. The tested slabs were supported on steel I-beams. Fig. 134, page 446, shows the deformation of steel across a section taken in the center of the slab parallel to the supports and Fig. 135, page 447, shows a 34-foot slab, 7 feet wide, after failure. TESTS OF SLABS TO DETERMINE DISTRIBUTION OF LOAD TO JOISTS The tests show that if a continuous concrete slab is supported by several parallel joists of any material, and a concentrated load is placed 448 A TREATISE ON CONCRETE directly above one joist, the load is distributed by the rigidity of the slab to several joists (see Fig. 136.) The distribution depends upon the ratio of the thickness of the slab to the span. The laboratory test, in question, consisted of slabs, 6, 7, and 8 inches thick, supported on three lines of lo-inch 25-pound I-beams as joists spaced 3 feet 6 inches on centers. (See Fig. 137, p. 449-) The span of the joists was 12 feet, and they were supported on other I- beams, which in turn rested on concrete pedestals, similarly as in bridge construction. The load was placed right over the middle joist in its center. £ 100 0) CD 90 "D T3 80 0) 70 D O O C 0) o 60 50 40 30 45 1 1 / / / / / / ^' ^ 5.0 5.5 6.0 6.5 7.0 7.5 8.0 aS 9.0 9.5 la Ratio o| Slab Span to Thickness Fig. \},f). — Distribution of Slab Load to Three Parallel Supporting Joists.. (See />. 448.) The following conclusions may be drawn from the above tests. (i) The percentage of reinforcement in the slab has Uttle or no effect upon the load distribution to the joists, so long as safe loads on the slab are not exceeded. (2) If the span is ten times the thickness of the slab, or more, total load must be considered as carried by the joist under the load. The amount of load distributed by the slab to other joists than the one immediately under the load, increases with the thickness of the slab. (3) The outside joists should be designed^for the same total live load as the intermediate joists. TESTS OF REINFORCED CONCRETE 449 (4) The axle load of a truck may be considered as distributed uni- formly over a 12-foot width of roadway. Fig. 138, page 450, shows the elongation in extreme fiber of the steel beam and deflection for the middle beam and for outside beams. Similar results would be obtained with concrete joists. The per- FiG. 137. — Relation of Slabs and Joists in Tests. (See p. 448.) centages of the load carried by the different joists are given in table, page 450. The conclusions apply only to cases in which ratio of span to thick- ness of slab does not exceed 10. The largest ratio used was 7, but the results may be exterpolated. 450 A TREATISE ON CONCRETE Equivalent Uniform Loads on Joists for a. Total Concentrated Load of 20 000 Lbs. Computed from Elongations of Lower Fiber By Proe. C. T. Morris. Number of Slab Al A2 Bi Ci Di D2 Ei Fi. Fi, Thick- ness. 6 in. 6 in. 7 in. 8 in. 6 in. 6 in. 7 in. 8 in. 8 in. "a* f% 1% J% 1% 1% 1% 1% 1% Equivalent Uniform Loads. Percentage of Load Carried by Side Beam. 4 480 4360 4430 4 480 4 480 3960 4790 4S30 5 000 Middle Beam. 9990 10350 6 220 4970 9030 10350 7050 7 290 6520 Side Beam. 4800 4 49° 4 54° 4440 4890 4020 4 54° 4510 4 020 Sum. 19 270 19 200 15 190 13890 18 400 18330 16380 16 400 15 540 Side Middle Side Beam. Beam. Beam. 22.4 21.8 22.2 22.4 22.4 19.8 24. u 22 .7 25.0 24.0 22.5 22.7 22.2 24-5 20.1 22.7 22.6 0.1 zo aioo aoso aoeo u ao40 "St O 0fl20 ~0 2OOD 4000 6000 800Q 10000 12000 14000 16000 18000 20000 Load in Pounds Fig. 138. — Elongation in Extreme Fiber of the Steel Beam and Deflection of the Middle Beam and of Outside Beams. {See p. 449.) Value of One Division on the Strain Gauge is 0.00019 inch. TESTS OF PLAIN CONCRETE COLUMNS Professor Talbot* made a very comprehensive series of tests, the results of which are given in the table on page 451. Conclusions, con- firmed also by experimenters abroad, are as follows: (i) Manner of Failure. Plain columns fail either by shearing at a • University of Illinois Bulletin No. 20, igo8. TESTS OF REINFORCED CONCRETE 451 Tests of Plain Concrete Columns {See p. 430.) Materials: Portland cement, Wabash River sand, crushed limestone. Columns, 12 in. diameter, round, 10 ft. long By Arthtje N. Talbot. Number of Specimens Tested. Proportions of Concrete. Average Age. Average Ultimate Unit Strength. Maximum Ultimate Unit Strength. Variation in Per Cent from Average. Minimum Ultimate Unit Strength. Variation in Per Cent from Average days. lb. per sq. in. lb. per sq. in. % lb. per sq. in. % 2 I :ii :3 64 2 300 2 480 8 2 120 - 8 7 1:2:4 6s I 740 2 210 27 I 16.C -33 2 1:3:6 6ii I 033 I no 7 955 - 7 2 1:4:8 63 192 S75 2 02s 575 2 680 575 I 770 6 1:2:4 32 -13 2 1:2:3! 14 mo. 2 710 2 770 2 2 650 — 2 diagonal plane of fracture, or by crushing, when the material is shattered and cracked longitudinally. The diagonal shearing failure almost al- ways occurs suddenly and with little, or no warning, whUe the com- pressive failure is more gradual. (2) Effect of Richness of Concrete. The strength of columns in- creases in nearly the same proportion, i.e., almost as a straight line, with the increase of the proportion of cement to total dry material used. (See pp. 312 and 316.) (3) Modulus of Elasticity and Poisson's Ratio. The modulus of elasticity of the columns is almost constant for the first one-third of the strength of the concrete. Beyond this point the modulus decreases till it reaches at the ultimate load about one-half of its initial value. The Poisson's ratio, or the ratio of the lateral to the longitudinal defor- mation (see p. 339) was found for i: 2: 4 concrete to be between o.io and 0.17 up to a load of about one-half the ultimate. It increases with the load, reaching probably 0.25 at the ultimate load. (4) Effect of Repetition. Repetition has no effect on deformation for loads up to one-half of the breaking strength of the column. For higher loads, the deformation increases after repeated applications of the load. After ten repetitions of a load three-fourths the- normal breaking strength, for example, the deformation was increased by 25%. It must be noted, moreover, that the suddenness of failure of plain concrete is increased by the length of the column. This absolutely excludes plain concrete columns from structures where they are apt to 452 A TREATISE ON CONCRETE be exposed to shock or to secondary stresses due to bending, as in build- ing construction. Concrete vs. Brick Columns. Tests carried out by the U. S. Bureau of Standards on columns of common, hard, . and vitrified brick laid with lime and cement mortar, indicate that the strength varies with quahty of brick and mortar, while large and small columns show about the same unit stresses. ^ series showing the strength of piers of common, hard and vitrified brick, laid with different mortars, is given in the following table. The lime mortar specimens showed a nearly entire lack of carbonation on the interior. Three piers of each kind of brick and mortar were made with headers every other course, every fourth course and every seventh course, but this variable appeared to have no effect. Bricks were laid flat. Two large size columns 48 inches square and 12 feet high, of common, Compressive Strength of Brick Piers* Tests by the TJ. S. Bureau of Standards. {See p. 452.) Dimensions 30 inches square by 10 feet high Kind of Brick. Mortar. Age. Months. Compressive Strength, lb. per sq. in. Common ■ Hard . Vitrified ■ 1 : 3 lime 1 : 3 cement 1 : 6 linje 1:3 /'iS% lime \ \8s% cement/ 1 : 3 cement 1 : 6 lime 1:3 ('15% lime \ \8s% cement/ 1 : 3 cement 4 I 4 I I 4 I I 170 57S 910 146s 1650 1360 2900 2780 • Engineering News, August 5, 1915, p. 242. hard burned brick, one laid in i : i cement mortar and one in i : 3 lime mortar, were tested by the Bureau and crushed at 2 920 and 760 pounds per square inch respectively.! Tests made at the Watertown Arsenal and quoted by the Committee of the American Society of Civil Engineers on the Compressive Strength of Cement J give the ultimate strength of common brick piers about t James E. Howard, Engineering Record, March 22, 1913, p. 332. t Transactions American Society of Civil Engineers, Vol. XV, p. 717, and Vol. XVIII, p. 264. TESTS OF REINFORCED CONCRETE 453 eighteen months old as ranging from 800 to 2 400 pounds per square inch, the results for brick laid with lime mortar averaging nearer the lower figure, and those for i : 2 Portland cement mortar nearer the higher figure. The unit stresses allowed by the New York Borough of Manhattan Building Code, 1916, for brickwork are. Brickwork in: lbs. per sq. in. Portland cement mortar 250 Natural cement mortar 210 Lime cement mortar i6o Lime mortar no The first value is but Uttle more than one-half that recommended for good i:.2: 4 Portland cement concrete on page 573. TESTS OF COLUMNS REINFORCED WITH VERTICAL STEEL Tests prove positively that in reinforced concrete columns, steel and concrete are effective in resisting the load carried by the columns. As explained in the Theory Chapter, page 376, the stress in steel equals the stress of concrete multiplied by the ratio of moduli of elasticity. This fact also is borne out by the tests. Mr. Spitzer* in Austria and Professor Witheyf at the University of Wisconsin observed that near ultimate load, adjustment between steel and concrete takes place so that finally the failure occurs by both of the materials passing the elastic limit simultaneously. This adjustment may be explained by the following consideration. After either of the two materials reaches its elastic hmit, any increase in stress in that material tends to cause very large deformations, which the other material, being stiU within elastic limit, cannot undergo. Therefore, this other material takes all the stresses due to any increase of the load till it finally reaches its elastic limit, and the column fails. The table on page 455 gives results of tests of full sized columns made at the Watertown Arsenal. Manner of Failure. Contrary to expectations, in most cases failure in columns occurs near the top or bottom instead of at the center. This has been explained as probably due to greater porosity of concrete. In most columns, hair cracks appeared at 85% to 90% of the maxi- • Mitteilungen Uber-Versuche ausgefUhrt vom Eisenbeton-Ausschuss des Ssterreichischen Ingenieui- und Architekten-Vereins, " Versuche rait Eisenbetonsaulen," Heft 3. t University of Wisconsin Bulletin No. 466, December igxx. 454 A TREATISE ON CONCRETE mum load. In some cases, however, the failures were sudden. In a number of cases, concrete split at the column reinforcement after its elastic limit was reached. The spUtting effect is caused by the lateral deformation of steel which exerts pressure on the concrete, which, if sufficient, breaks the concrete. The steel, therefore, should be placed at a sufficient dista.nce, say at least one inch, from the face of the concrete. With proper protection there is no danger of buckling till after the elastic limit of the steel is reached. From Spitzer's tests, it would appear that columns with steel placed well within the cross-section of column are somewhat stronger than with steel placed according to the usual custom. In practice, however, columns are apt to be subjected to eccentric loading; therefore, the placing of steel in abnormal positions must be discouraged. Factor of Safety. A column with vertical steel only is Uable to fail without notice when its ultimate strength is reached. The ultimate strength of columns even if built under the same conditions is more variable than steel columns. Therefore the commonly accepted factor of safety is larger 'than used in steel columns. When designed accord- ing to formulas given on page 562 with allowable unit stresses on page 573, columns with vertical steel only are very reliable. Modulus of Elasticity for Reinforced 'Columns. The modulus of elas- ticity varies for different intensities of loading and for different mixes of concrete. In selecting the ratio of moduli of elasticity to be used in design, it is proper to be guided more by the required factor of safety than by the actual modulus of elasticity at any particular stage of the loading. From the tests thus far made, the moduli of elasticity given by the Joint Committee with the suggested working stresses (see p. 573) seem to give the required factor of safety. Rich Versus Lean Mix. As evident from the table on page 455, cement is very good reinforcement for the column as the increase in strength is much larger than the additional cost of cement. Influence of Bands. In tests of Mr. Spitzer* of columns having different spacing of bands, those in which the spacing was equal to, or smaller than the diameter of the column gave somewhat greater strength than columns in which the spacing exceeded the diameter of column. Influence of the Percentage of the Steel. The tests show clearly that the effect of reinforcement in columns is the same whether the per- centage is large or small. In all cases the steel takes a stress equal to the stress in concrete times the ratio of moduh of elasticity. • See footnote on page 4.53. TESTS OF REINFORCED CONCRETE 455 Watertown Arsenal Tests. The table on page 455, from tests by Mr. James E. Howard at the Watertown Arsenal, gives the relation of actual tests to theoretical computations based on a ratio of elasticity of 15. It is noticeable that the actual strength is ahnost always more than the theoretical, and this is especially the case with the leaner mixtures because the modulus of elasticity of the leaner concrete is lower, and therefore the ratio of 15 is very conservative. An excellent analytical treatment of columns reinforced with vertical steel is given by Professor Talbot in one of his University Bulletins.* The problem is discussed briefly by one of the authors in a paper before the Boston Society of Civil Engineers, f Many of the tests at the Watertown Arsenal, for example, were made with vertical bars imbedded in columns 12 ins. square and 8 ft. long, with absolutely no bands or horizontal steel of any kind placed around these vertical bars to hold them in place; that is, the bars 8 ft. in length were placed in the four corners of the column — in some tests only 2 ins. from the surface — and simply held in place by the 2 ins. of concrete itself. { There was no sign whatever of buckling until Strength of Plain vs. Vertically Reinforced Concrete and Mortar Columns. Columns 12" X 12". Height 8 feet. Age of Mortar and Concrete 6 months. Watertown Arsenal. {See p. 453.) Plain Concrete or Mortar Columns Actual Strength lb. per sq. m. REINFORCED COLUMNS Reinforcement. Actual Strength lb. per sq. in. Computed Strength based on col. (4) and a ratio of n = 15 Ib.p.sq.in. s m Description. Ratio Area Steel to Area Column. TO "tests of metals" V. B. A. (I) 3 3 4 5 5 I 2 2 2 2 3 (3) 2§ 3§ 4 t (4) 3070 2380 1520 1080 1080 1720 1769 1413 1710 2400 145° 8-|" round bars 8-1" round bars 8- " round bars 8- " round bars 13- " round bars 4- "twisted bars 4-i" twisted bars 4-0" 0.74" X 0.74" trussed bars .4-1" twisted bars 8- " twisted bars 8-f " corr. bars (6) 0.029 0. 029 0. 029 0.029 u.046 0.014 0.014 U.014 0.014 0.029 0.019 (7) 4200 3840 3380 2810 3900 2890 2010 1900 1990 37°° 2290 (8) 4290 332° 2120 1510 1780 2060 2100 1689 2050 336° 1840 (9) 190S P- 377 i9°5 P- 377 i9°5 P- 377 1905 P- 377 1905 P- 377 1904 p. 386 1904 p. 386 1906 p. 538 1904 p. 386 1907 p. 242 1904 p. 379 1906 p. 535 • University of Illinois, Bulletin No. 12, Feb. I, 1907. t Sanford E. Thompson in Journal Association Engineering Societies, June 1907, p. 31S. X Test of Metals, U. S. A., 1905, p. 344. §i"to I K pebbles. II Age 17 months 22 days. 4S6 A TREATISE ON CONCRETE the compression was so great that the elastic limit of the steel was passed, when of course nothing further could be expected of it. TESTS OF SPIRAL COLUMNS In analyzing results from tests of spiral columns, it is necessary to examine not only the strength, but also the deformation, or change in length. In building construction, because of the dependence of the different members upon each other, it is advisable to permit a- shorten- — c^jK)5 — c\i m ^ OOOO OOC3c5 C3 O ^ ^ ^ ^ C3 ^ ^ ^ ^ ^ ^ Deformation per Unit Length Fig. 139. — Deformation Curves for Spiral Colunms with Varying Amount of Vertical Steel.* (See p. 457.) Concrete i : 2 : 3^; 1% Spiral High Carbon Steel; 0% Vertical Mild Steel. Concrete i : 2 : 3I; 1% Spiral High Carbon Steel; 3.8% Vertical Mild Steel. Concrete i : 2 : 3J; 1% Spiral High Carbon Steel; 6.1% Vertical Mild Steel. ing, or deformation, of not over 0.007 P^^ ^^^^ o^ length. The factor of safety, therefore, must be based on the load causing a certain defor- mation rather than on ultimate strength. Although the strength of column beyond the yield point is not available in ordinary construc- tion, the greater ultimate strength, ductility, and uniformity in strength * University of Wisconsin Bulletin No. 466, December, 1911, pp. 92, 93, 94. TESTS OF REINFORCED CONCRETE 457 of spiral columns reduces the danger of sudden failure, and larger unit stresses may be allowed. In practice it is more rational to increase working unit stress in concrete than to compute the stress by a for- mula which takes into account the steel in the spiral. (See p. 560.) Early European tests of spiral columns were made on short columns and without deformation diagrams, and as a result, very high working stresses based on the ultimate strength were recommended. More recent tests, notably by Talbot and Wi they in the United States, showed the excessive deformation of spiral columns at high stresses. Column Tests by Prof. M. 0. Withey. The tests at University of Wisconsin, Series of 1910, consisted of four series, two of which will be considered below; namely, series r, columns with varying percentage of longitudinal and lateral reinforcement, and series 2, columns with vary- ing proportions of concrete. The table on page 458 gives the gen- eral results of the tests. The following general conclusions may be drawn from the tests: , I. The cheapest way of increasing the strength of a column is by using a rich mix; but toughness is sacrificed to strength obtained in this way. 2. Spiral reinforcement greatly increases toughness and ultimate strength of a column, but does not raise the yield point. (See columns M and O, page 458.) The strength beyond the yield point can not be utilized in building construction; hence, the amount of steel for spirals should be made only large enough to produce required ductility and raise the factor of safety against failure. In practice, 1% of spiral reinforcement seems to be sufficient. 3. Longitudinal steel increases the stiffness of the column and raises the yield point. 4. Stress in steel at the yield point of columns is practically the same for all mixes of concrete and only a little below the yield point of the vertical steel. (See table, page 458.) This phenomenon may be ex- plained by the fact that for leaner concrete the ultimate strength is smaller, but the deformation at the yield point larger than for rich mixes. For rich concrete, the stress in concrete at the yield point is larger, but the ratio of the moduli of steel to concrete decreases. Since the stress depends upon the product of stress m concrete times the ratio of the moduli of elasticity, the two values simply adjust them- selves so that the product is the same in all cases. 5. Columns loaded eccentrically give results which agree closely with the formula given on page 382, as is evident from Fig. 140, page 459, in which the straight lines represent figvured stresses in steel and con- 4S8 1-9 m t-H H O H CO SB go GO §^ is hrtS SO o o o _ S o o H H CO \ IB 01}^^ B.UOSSIOJ •jnioj ppij^^ }B «= — qiSnsus siEimjjfl ^ }e « S,a aiajano3 m q^Saang o; sj9puiiX3 JO qiSuaiig ojiB^ O|o; •s«pniiX3 JO u q;3uaiig OAissajdrao^ ~^ .S 1 1 In Con- crete. fc 1 to 1 at p S..S 4 ^H la •qjSnans siEraum 0} }uio J ppjA IE SS3J1S )o ojlEH (Clo. ■mioj ppjA •qiSuans ajEiniJUi a,!^ ■pEOT mniiiixEj\[ 8.2 a S S n •jEjids ■lEOJJJSA 1"^ 01 uinnio^ JO q^Sus^ oij-e^ ^ 'jaqran^ uuiiqo^ hmwmOhmhm H MOO CO « 1 O O O t o o o o o o O o o o lotoo »o ^ H W N s-ss N M H H t- VO lommO IO^O o> t^OO OO ro ^ to H H M -+rOH 00 OVOO.O 660606 o'oobooo 8as,8S,8 8 8S'8aa8 lOcOcO^cOHOOOO -^ CO^ W »0 CON rotO^N N (OCO^O^IO^^ 6661- 1 O in lou^O OioO 0 O V) » f* OiOO « to ^ rO CO N N IWHHMWNCiejNM lOOO O 0>TO»00 QiJ^O coco 10 -^vo ^ t^»o 00*0 inHOO fOtO« 00 Oi O^oo tooo oiior^tococs io« OOOOOQOQQOO Sminoi^O too 6>ov) 5'*M00OO»'*H 'J-Nt- >»iO"0 ^ t^vo O 00 00 00 *o O O O O Q O C 10 O 10 ui O O C TO O O O iO»oOO O O locom I too CO t^^O ■ 1 to CO 'o ^ >o *o c CO to ^ (O P 00000000000000 tJ-h t^too O^o o>r^■■^•o »ooooo MWMtOHNNWrjTO^'^HN 1 <00000'0i0t0ir)0i00 00 CO VO N ^0 O>00 W 00 Oi (O lO N COWH\0 CTi-^O OllOOiO t^ « to ■* >o cs CO -+ •+« vo r^ -t ■* ) o o o ) O O to rj 10 O I^ T Ol^- « * »o « O < « CO ■* OOOOOOOQOO lo 10 10 lo O >o O O »o »- -tt^N w o*t^>o»Ot^P r».vO Oico co'O ^-vO * n 00«^0■THT^low^ H tOcOfCi/llOlOlOtO" 0000 loioioio 88 8 8 8'§,-S'§, 8 8 0000 W CI 000 H . *^ "^ 8^S8SgS 10 M COVO N co'ooo''Ood d V'„'.'. k H "^I^lllll^---" :„ •>leH3i Hlni-4i£t-n t-Ko r4.c«..c ^«C. » N N N e 1 w « ?"„ ^ N N * ■» N N W ■T M h" M l-T w" h" !■ ';lt ^ til 6 " ►i. Ji M la g pi, i pi au n 10 u) »o »o»o d d d d d d d odd to H d * f ■» loOOioOOOmOto CM> to -il-OO ■<*• 0> 0> ■* m 10 10 t^OO 00 00 lOlO*© ^ Q 00 O Q Q O O < 88888? op o >^ yi 5 O 6 O O O »o O O O - . _ _ 10 N io»o »« OiOr^H H "ifMO Oiw'* OHO Oi H 00 t^ lOH 0* H to ;??, »O00 " H H H H H M M H 000 III »0 l-. t^lT) tooo 00 *- l/ll>.co H ■+ 't ^ -"l- -^ ■+« 'O M 8| »oO ^f^ >oO »H ^- « ■* Tt -t ro to CO 10 »o 't 88ag,a Tl- CO CO to !>. |8 cooo« f. t>-0 •■O t-. t-."© 8 1 00 -a a .A »0\0 VO V3 vg'.S-S- ^* 000 ioOOOO»oOOOC rfOO 000 roOoO Oi^P \0 CO ^^ M >ooO O oO M ■«; W cOM-cO^fN ^^lOU 10 O O O Q O O 10 Oi Tj- 10 O OiOO 00 C4 CO H CO CO ^ O Q O O Q O 0000000 10 O O »o 10 »o 10 O CO O O »^ f~ r* <0 M n Th JH M pH «t m Tf >o "O \0 \0 8 88 88 8 8S;8g:'ig. M W M M M W H 10 10 °' WOO lO'O'O ■O H CO »0 to "" ■ k 6 1^ t^ t^ t^ t^ 6600006066 r-Ho l-|« r.|B t-WH|MM|tfr4BF^ 00 Coo Ooo OoOoooooooO \o\ovo 10 in 10 >o>o NO ^o ^ fOtOtO»0»olO»OtotOtOW oocooooooocoododcooood CO VO H t^vO \0 VO 1^ 0> CO Oi •* lO"© lOlOlOlOioiOlTH VO CO ton N oatotototo "rt;c;;" *• *^ ". *?-?'?'? cohhhhhmhhwm «<< TESTS OF REINFORCED CONCRETE 4S9 Crete by Formulas (75) and (76), page 382, while the dots and circles show the actual stresses obtained from deformation. Action of Columns under Test. Up to the point of breaking strength of plain concrete, the action of the columns with spirals was the same as for columns with vertical steel only. The observed stress in spirals was from 6 000 to 8 000 lb. per sq. in. For spiral columns with verti- cal steel, the deformation curve continues as a practically straight line to the yield point of the column. The yielding is indicated by scaling i 5000,-^ 10 2 4000--IJ S 3 (5(0^3000 C ID 2000 5 3 1000 1c °0 fs ■tft ;^-' h± 71 ^ ^tfc^ricHt fs aOOO 4000 6000 8000 10000 2000 4000 6000 8000 10000 20000 30000 40000 50000 10000 SOOOO 30000 40000 Unit Stress in Cortcrele or Steel in Pounds per Sa\n, 5.96 Per-Cent of Vertical Steel 0.97 Rgr-Cent of Spiral Steel fc- l-fi Fig. 140.- -Comparison of Theoretical and Actual Stresses for Eccentric Loading.* {See p. 457.) off of the protective shell and by an increase of ratio of lateral and longitudinal deformation to the applied load. The yield point is more marked for columns with large percentage of reinforcement (see Fig. 139, p. 456). For spiral columns without vertical steel, the deformation dia- gram is a curve without a marked yield point, so that the yield point is only distinguishable by scaling of the shell. After the yield point has been passed, the disintegration of the shell progresses very rapidly. The ratio of shortening due to the applied • University of Wisconsin Bulletin No. 466, Decembei , 1911, p. 71. 46o A TREATISE ON CONCRETE load becomes larger and final failure takes place by buckling of the column, or, in columns with a small amount of lateral steel, by break- ing of the spirals. Stresses in Steel and Concrete. The table on page 458 gives the stresses in steel and concrete at yield point and at maximum load. The stresses in vertical steel were obtained from the deformation by using a modulus of elasticity of 30 000 000. The remainder of the load assumed as carried by the concrete, and divided by the area of the core, gave the unit stress in the concrete. In figuring the stress in concrete, the area of the core was used in preference to the total area of the col- umn, because at yield point and at maximum load, either a part or the whole of the outside shell is destroyed and is then ineffective for carrying the load. The stress in spirals obtained from lateral deformation is very small at the yield point of the column, which corroborates the statement that up to yield point* the spirals do not affect the column appreciably. The table is of interest in giving a comparison of the stresses in steel with the stresses in concrete for different mixes and also in giving the values of the ratio of moduli, n. Although the value of this ratio was variable, the stress in steel at the yield point of the column was about the same for all columns, which seems to show that in a column under load an adjustment of stresses takes place. From the table, also, it is evident that the stress in concrete at the yield point was the same irrespective of the amount of vertical reinforcement. An interesting experiment was tried in connection with tests by Wayss and Freytag.f The columns after reaching the maximum stress were again loaded after nine months and after one year, and showed a large increase of strength over the original maximum strength, in some cases reaching 50% increase. After these two loadings, the column spirals were removed and the core tested again. In no case was the core after removing the spirals disintegrated; in fact, each core showed a considerable strength, which tends to disprove a conten- tion previously held by several authorities that the concrete in hooped columns becomes disintegrated after a certain point in loading is reached and is simply prevented from flowing by the hoops. TESTS OF SQUARE COLUMN WITH RECTANGULAR BANDS Tests by Wayss and Freytagf consist of eleven types of 12-inch columns, square and rectangular in cross-section. These tests prove • See also Professor Talbot's Bulletin No. 20, University of Illinois. t Marech, 4th edition, p. 117. TESTS OF REINFORCED CONCRETE 461 that the bands in square columns are not very effective. The out- side shell started breaking off as soon as concrete reached its maximum crushing strength. TESTS OF COLUMNS WITH STRUCTURAL STEEL REINFORCEMENT The size of column can be reduced by the use of structural shapes, rigid enough to serve as a structural steel column, imbedded in con- crete. Below are given results from tests of columns with two types of structural steel which proved very reliable. The results must not be considered as applying to all conditions and must be used with caution where the structural members differ materially from those in the tests. T). c Q. 400000 c sooooo D •D ~ Q- < 200000 100000 41- inRn ,6 ^^^ Length 15rT.4." /^ ^^ / /^ / / .0002 .0016 .0004 .0006, .0008 .0010 .0012 .0014 Deformation per Unit of Length Fig. 141. — ^Average Deformations of Plain Steel Columns.* (5ee p. 463.) .QOI{ Talbot-Lord Tests of Columns.f The Talbot-Lord tests consisted of thirty-two columns divided into four groups: 1. Plain steel columns. 2. Core type columns, i.e.; columns in which the portion within the structural steel members was filled with concrete. 3. Fireproofed columns, i.e.; core type columns having a 2-mch pro- tective covering. • University of Illinois Bulletin No. 56, 1912, p. ip- t University of Illinois Bulletin No. 56. 462 A TREATISE ON CONCRETE Tests of Steel Columns, Reinforced with Concrete By Talbot and Lord* (See Fig. 143, page 464.) Age of concrete, 59 to 61 days. P. S. = Plain steel column of 8-3" X 2^" X ^" angles with no concrete core. C. T. = Core type column of S — 3" angles' with concrete core. F. = Fireproofed column same as core type with 2" of extra concrete outside of structural steel. No spiral. 5 = Spiraled column same as core type with spiral steel and concrete core filled out to conform with diameter of spiral. 8 902 8 905-6 8 907-8 8 910-11-14 8 912-13 8 915-16 8 917-18 8 920-21 8 922-23 8 925-26 8 927-28 8 930-31 8 933 8 934 8 935 936 937 P. S. P. S. C. T. P. S. C. T. P. S. C. T. P. S. C.T. C. T. C.T. F. St St St St St Sq. in. 13 13 120 13 120 13 120 13 120 120 120 213 IS3 IS3 153 IS3 IS3 2:4 1:2:4 1:2:4 hi ft in. 2-0 4-8 4-' 1 0-0 1 0-0 15-4 15-4 19-4 19-4 1 0-0 1 0-0 1 0-0 •I 0-0 1 0-0 1 0-0 lo-o 1 0-0 bo s .2 s IS ►J 6.1 4 Total Load in lb. Column Load. 487 300 444 600 589 500 420 000 547 35° 372 000 500 35° 359 600 493 450 645 500 523 250 633 200 600 000 856 000 600 000 830 000 625 000 830 000 714 000 Load Considered Carried by Steel. 359 600 418 000 418 000 418 000 Load Considered Carried by Concrete. 444 600 144 900 418 000 129 350 372 000 128 350 133 850 227 500 los 250 215 200 Stresses in lb. per sq. in. In Steel. 37 500 34 200 34 200 32 400 32 ISO 28 600 28 600 27 650 27 650 32 150 32 ISO 32 150 In Con- crete, I 3SS 1 250 2 I2S 98s I 07s Applied s times; not broken. Not broken near ultimate. Applied 3 times; not broken. Second test; near ultimate. Not broken. Test with spiral and outside concrete removed. tO.75 % of spiral reinforcement, j 1.00 % of spiral reinforcement. * University of Illinois Bulletin No. 56, 1912, pp. 14 and 15. TESTS OF REINFORCED CONCRETE 463 Fig. 142. — Dimensions of Test Columns.* (See p. 463.) 4. Spiraled columns, i.e. ; core t3rpe col- umns enclosed in close fitting spiral and filled with concrete to outer surface of spiral. The cross-section of the structural steel, which is shown in Fig. 142, page 463, was the same for all columns. Ratio of length to minimum radius of gjnration varied from 6.1 to 59.5. The results of the tests are given on page 462. Plain Steel Col- umns. No bending was visible to the eye at the maximum load. After the maximum load was passed, bending developed very grad- ually. The average deformations per unit of length are shown in Fig. 141, page 461. The effect of the length of the column was more marked at high than at low loads. According to Professor Talbot, / the ultimate stress in column for different ratios of — may be repre- ^^ Out line of \/ spiraled type ;%>>>i — Outline, at core type (•■ — Outline cf fireproofed type — Note — Anc^les:3'y2i\i" Tie:5i"xi"xO'-8i" Rive+s r^'diamefer sented by a straight line formula, — = 36 500 155- l Core Type Columns. The columns of core type were very tough and failure slow. For short columns, the failure was caused in most cases by crushing of the concrete; for longer columns, by bending and crushing of concrete. No bending visible to the eye was observed until maximum load was reached. The effect of mixture of concrete on the •University of Illinois Bulletin No. 56, Fig. 1, p. 4. 464 A TREATISE ON CONCRETE 600000 500000 400000 SOOOOO V. "^ 200000 a. r- lOOQOO ■0 D 500000 T3 0) / z' / / / N /J' ■f / / Le ngth 4 rt8" / Numbe rs 8907-8 .0005 .0010 0015 .0005 .0010 Deformation per Unit o| Lenqth 0015 Fig. 143. — ^Load Deformation Diagrams for Plain Steel Columns and Correspond- ing Core Type Columns.* {See p. 465.) Note: — Curves labelled Column refer to core type; those labelled Steel refe.* to plain steel type. Se also Fig. 141. * University of Illinois Bulletin No. 56, March, 1912, p. 24. TESTS OF REINFORCED CONCRETE 465 strength was small, because the strength of the column was governed by the steel rather than by the concrete. In Fig. 143, page 464, are shown deformations per unit of length of core type column. Deformations of plain steel columns are also shown for comparison. (See also Fig. 141.) The relative loads carried by the concrete and by the steel, respec- tively, are given in the table on page 462. The amounts were deter- mined by assuming that for equal deformations the structural shapes in the core type column carried the same load as a similar plain steel column and the balance was carried by the concrete. As a result of this test, the ultimate strength of the core tj^^e column may be considered as consisting of the strength of the plain steel column plus the strength of the concrete core figured with a unit stress equal to the strength of concrete in cylinders. Fireproofed Columns. The behavior of fireproofed columns of the core t5^e was about the same as that of the column without fireproof- ing. The concrete shell outside of the structural shapes, however, remained intact until the ultimate deformation of the column was nearly reached, but its effective unit strength was lower than the unit stress of the concrete core, probably because the shell failed before the maxi- mum stress in steel and concrete core was reached. Even if the protective covering is not relied upon as adding to the strength of the column, it is advisable to tie it by means of hoops or spirals of large pitch so as to prevent spalling in case of fire. Spiraled Columns with. Structural Steel. The core type column with surface spirally reinforced exhibited larger strength and toughness than similar columns without spiral. The thin protective cover remained intact. The strength of the columns exceeded the capacity of the Illinois and Lehigh University testing machines, which is 830 000 lb. Because of the large deformation, the mcrease of strength afforded by the spiral is not available in ordinary building construction; hence a large percentage of spiral is not justifiable. One per cent of spiral rein- forcement, however, makes the column tougher and safer and also prevents the outer shell from spalling. Since the danger of sudden failure is removed, such columns may be designed with somewhat higher working loads than allowed for the fireproofed type. Tests by Professor Withey.* The structural steel reinforcement con- sisted of four angles 2 in. x 2 in. x j^ in. placed in four corners of square column. The out to out dimensions of the steel core were 8 in. square. The result of this test agrees with the tests previously described. • University of Wisconsin Bulletin No. 300, "Tests of Plain ind Reinforced Concrete Columns." 466 A TREATISE ON CONCRETE Recommendations for the Design of Fireproofed Columns. Tests by Professor Talbot and Professor Withey show that in columns with structural steel the protective cover does not fail until the column reaches its maximum load. In practice, the protective cover is not con- sidered as adding to the strength of the column. Therefore, in design- ing this type of column, the recommendations given in connection with core-type columns may be used. Similar results were obtained by Emperger and Spitzer.* TESTS OF LONG COLUMNS Tests by Spitzer on columns, 9.8 by 9.8 in. cross-section, 9.9 ft., 14.8 ft., and 23 ft. long respectively, with ratio of length to the least diameter of 12, 18, and 28, show no appreciable difference in strength and no buckling in any of the columns. To determine the effect of slenderness. Professor Bachf compared the strength of 4 ft. long column (ratio of slenderness 4.3) with that of a 29.5 ft. column (ratio of slenderness 32), and found the strength of the longer column to be 0.75 of the strength of the short column. As a result of this test. Professor Bach suggests the following formula for the strength of a long column in terms of the strength of a short column, which in turn may be assumed equivalent to the strength of 8 by 16-inch cylinders. •^' ^^'~ AP I + 0.0072 — - Where fc = allowable working unit stress, lb. per sq. in., for short columns. A = cross section, sq. in., of column. I = length of column in feet. / = moment of inertia inch units of the cross-section of the column. RESISTANCE OF CONCRETE AND REINFORCED CONCRETE TO TWISTING Testst made by C. Bach and O. Graf in Stuttgart, Germany, to deter- mine the resistance of concrete and reinforced concrete to twisting, * Mitteilungen Uber-Versuche aiisgefllhrt vom Eisenbeton-Ausschuss des Bstcrreichiachcn Ingenieur- und Architekten-Vereins, "Versuche mit Eisenbetonsaulen," Heft 3. t Kxiickungsversuche mit Eisenbetonsaulen Zeitschrift des Vereins Deutscher Ingenieure, Prof. C. Bach. igz3, p. ig6g. J "Versuche uber die Widerstandsfaehigkeit von Beton und Eisenbeton gegen Verdrehung" by C. Bach and 0. Graf, Berlin 1912, Heft 16. TESTS OF REINFORCED CONCRETE 467 consisted of two groups of specimens: (1) plain concrete with square, rectangular, circular, and circular ring cross-sections; and (2) square and rectangular reinforced concrete with varied amounts and dispo- sitions of reinforcement. The length of the specimens was. 6.4 ft., and the cross section was 11.8 inches square, 8.3 by 16.6 inches rectangular, and 15.8 inches diameter for circular reinforcement. Method of Testing. The specimens were tested by applying twisting moments at the ends. An initial twisting moment of 21 670 inch pounds was applied first and the instrument read. The load was then increased, until failure, in increments of 21 670 inch pounds; but after each reading, and before raising the total load by this increment, the load was reduced to the original 21 670 inch pounds so that the incre- ments as made actually consisted of multiples of 21 670 inch pounds. Resistance to Twisting of Plain Concrete. In all plain concrete speci- mens, the failure occurred in the center of the specimen by cracking at 45°. Failure always followed closely the appearance of the first crack. In specimens with rectangular cross-sections, the first crack started on the wide face. The ultimate torsional unit stresses are given in the table below and were figured by the following general formulas for homogeneous beams. Ultimate Torsional Unit Stresses. (See p. 467.) Concrete, 1:2:3 by volume. Aggregates, Rhine sand from o to i-inch diameter and Rhine gravel from J inch to J inch. Average compressive strength of 12-inch cubes at 45 days, 3 540 lb. per sq. in. Age of specimens at test, 45 days. Compiled from Tests by C. Bags and O. Grat. Cross Section- Square Rectangular. . Circular Circular Rings Values of Toisional Unit Stress. Lb. per sq. in. 432-33 462 . 20 364 OS 243 ■ 18 In Terms of Tensile Strengtti. 1.62 1-75 X.38 0.92 InTenns of Compressive Strength. 0.12 0.13 O.IO U.07 Let /, = ultimate torsional unit stress in concrete in lb. per sq. in. M, = the torsional moment in inch pounds. b = the short side of the section in inches. h = the long side of the section in inches. 468 A TREATISE ON CONCRETE For rectangular and square sections, For circular sections / = Tf) « Resistance to Twisting of Reinforced Concrete Specimens. Longi- tudinal reinforcement has very small influence on torsional resistance. For specimens reinforced with 1.13% and 2.26% of straight bars, the increase of torsional resistance was only 9% and 14%. More marked was the influence of inclined bars. In specimens with 1.13% of rein- forcement where the bars were inclined at 12°, the ultimate resistance was increased by 27%. The best reinforcement for specimens subject to twisting consists of stirrups, or spirals, inclined at 45°, because the cracks due to twisting open at 45° and therefore the spiral resists the twisting stresses directly. In specimens with 2.26% of longitudinal reinforcement and with stirrups, 0.276 in. diameter, spaced 3.93 inches on centers, the bending moment at first crack was 31% larger than at ultimate failure for plain Speci- mens. The ultimate bending moment for this specimen was 66% larger than the ultimate bending moment for plain specimens. Specimens reinforced with 2.26% of longitudinal steel and spirals, 0.276 in. diameter, arranged parallel to each side and inclined at 45", with a pitch of 3.7 inches, showed an increase of 55% at first crack, and 134% at the ultimate bending moment over plain specimens. TESTS OF REINFORCED CONCRETE BUILDINGS UNDER LOAD One of the most important developments in testing within the last few years is the testing of complete structures under load. Deflection tests of engineering structures have been customary to determine whether the structure can safely carry the load for which it has been built. Such tests, however, are of little scientific use as they do not give the stresses in the structure. Sometimes they are even misleading because with small deflection there may exist stresses in certain parts of the structure much higher than allowable. Weakness of details also and the effect of continuity cannot be determined from such tests. The recent tests on completed structures are much superior to the TESTS OF REINFORCED CONCRETE 469 old deflection tests as they measure not only deflection of the structure, but also the stresses in various parts of the members. These tests were inaugurated by Prof. Arthur N. Talbot of the University of Illinois, with the assistance of Messrs. A. R. Lord and W. A. Slater. The first building tested in this way was the Deere and Webber building in Minneapolis in October and November, 1910. Following, these several other tests were made under the auspices of the Reinforced Concrete Committee of the American Concrete Institute. The instruments used in such tests are (i) Extensometer for measur- ing the stretch or compression of the materials, (2) Deflectometer, for measuring deflection. The extensometer consists of a framework (which in the best exten- someters is made of invar steel to prevent appreciable changes in length due to the changes of temperature), two movable legs attached to it provided with sharp points, and of means for measuring accurately any changes in distance between the points. In order to find the stretch in steel, the bar to be tested is uncovered in two places a few inches apart, then small holes, called gauge holes (0.055 i^- i" diameter) are drilled. An observation on the gauge line is taken before the structure is loaded and then at each increment of the load. The difference between the original reading and the reading at any load gives the stretch of the steel due to that load. The stress is then found from the known relation between the deformation and the stress. The compression in concrete is measured by making small holes in the concrete, inserting metal plugs, and then marking the gauge holes in these plugs in a similar manner as was done for the steel. Read- ings and stresses are obtained in the same way as for steel. Since concrete flows gradually under heavy loads the readings must be made immediately after each loading. (See p. 339.) For measuring deflections, a rigid scaffold is built right under the members to be tested. In the place in which a deflection reading is desired, a steel plate is fastened by plaster of Paris to the under side of the beam, or slab. On a vertical line below, this steel plate a steel rod is fastened to the scaffold. Before beginning the test and at different stages of loading, the deflectometer is placed between the plate and the rod below, readings are taken and the difference between the original reading and the readings under the load give the deflection. For loading the panels, there may be used: (a) brick, (b) cement in sacks, (c) loose sand in boxes or in sacks, and (d) pig iron. In making 47° A TREATISE ON CONCRETE tests, care always must be taken that the material does not arch itself. The whole floor cannot be covered with the load because there must be left places uncovered in which measurements are taken, also there must be aisles left to make the points accessible. It is important that the test load should cover a sufladent floor space to insure that certain parts of the floor resist nearly the full load which, in the calculations, they are considered to take. Wenalden Building Test* The floor panels in this building are 15 feet by 20 feet. The slab is 3I inches thick ; the girders, placed between columns in the short direction, 75 inches by 205 inches, reinforced with four |-inch square bars in the middle. The longitudinal beams, 5 feet apart on centers, are 6| inches by i8| inches, reinforced with four f-inch square bars in the middle. Half as much steel was used over the sup- ports as in the center. The floor was designed for a live load of 200 pounds per square foot, and the total test load was made 400 pounds per sq. ft. and placed in layers of 80 pounds per sq. ft. A set of observations was taken after every additional loading. The measurements were taken in steel at the support and at the cen- ter of the span, also measurements of stresses in concrete at the support and at the center of the span. This test proved conclusively that the beams and the girders act as continuous ones. While the stresses in steel in the center and at the support were not excessive, the highest stress being 17 000 lb. for the total test load, the stresses in concrete at the supports of the beams were high and in some places even reached a stress of 2 200 lb. per sq. in. Even under the working load, stress in concrete was i 150 lb. per sq. in. The compressive stresses in the center of the beam were low, and it appeared from the test that the total slab acted as a compressive flange of the T-beams. It must be noted that in this case the overhang of the flange was 7 times the thickness of the slab, while in practical designs, we consider only an overhang of 6 times the thickness of the slab as effective in taking compression. The total compression in a beam, figured with the assumption of a straight line distribution of stress and no tension in concrete, was much larger than the total tension, showing that either arch action existed in the beam or considerable tension was carried by concrete. The difference was especially large at the supports where the tension must have distributed itself over the entire slab. 'University of Illinois. Bulletia No. 64, January 13, 19x3. TESTS OF REINFORCED CONCRETE , 471 Test Cracks. Tensile cracks were observed in the middle portion of the bottom of the beams. They formed at the same stress in steel as is usually found in the laboratory. Diagonal cracks developed in the girder which carried a very large shear (7=40 000 lb. and ^=360 lb.), just outside the junction with intermediate beams. The cracks were inclined at about 45". They did not close entirely after removal of the load. It is supposed that the restraint at the ends prevented fuller development of the cracks. (See also p. 442 on formation of cracks in continuous T-beams.) Deflections. The deflections offered further proof of the continuity of the beams, in the middle panel being much larger for one panel loaded than for three panels loaded, as would be expected from a continuous beam. With three spans loaded, deflection of intermediate beam was 0.09 inch, and for one span loaded was 0.15 inch. Turner-Carter Building Test. The panels in this building are 17 feet 4 inches by 19 feet 6 inches. The girders are placed in the short direction and their dimensions are 10 by 24 inches, with two i-inch square and three |-inch square bars at the niiddle, and two i-inch square bars over the support. Beams, 7 by 18 inches, reinforced with one i-inch square bar and two |-inch square bars at the middle, and one i-inch square bar (plus ten f-inch round bars in the slab) over the support, are placed between the columns and at one-third points of the girder. The thickness of slab is 4 inches. The structure was designed for a live load of 1 50 lb. per sq. ft. and the beams and girders were figured as simply supported, but reinforcement was supplied for continuity. The test load was 300 lb. per sq. ft. or double the designed load. Results of Test. The beams and girders acted as continuous. The stresses in steel in the beams were comparatively low, the maximum observed for the test load being 11 000 lb. The stresses in concrete, however, at the end of the beam reached i 100 lb. per sq. in. At the middle the compression in concrete reached only 350 lb. per sq. in., which shows that the compression there must have distributed itself over a large portion of the slab. In the girders the tensile stresses at the middle reached only 8 000 lb. per sq. in. At the supports no measure- ments were taken because the steel was not accessible. The compressive stress at the end of the beam in the bottom was 900 lb. per sq. in. and was very low at the center in the top surface. In both beams and girders the total compression was much larger than the total tension, a condition that was found in the previous test. 472 4 TREATISE ON CONCRETE As far as observation shows, the entire slab acted as compression flange of the T-beam. General Conclusions. In drawing conclusions from tests on completed structures it must be remembered that although the stresses in steel are low it does not indicate a large factor of safety. The conditions are the same as were explained in connection with laboratory beam tests (see p. 412) in which the stresses at half the maximum load were small, while the maximum load stressed the steel to the elastic limit. The results of such tests must be used with caution. TESTS OF OCTAGONAL CANTILEVER FLAT SLABS An interesting test of cantilever flat slabs supported on a central column, as shown in Fig. 144, page 473, was made by Mr. Edward Smulski under the supervision of Sanford E. Thompson. Eight specimen slabs were made : octagonal in shape, 6 feet 6 inches in small diameter, and with an octagonal column head in the center built monolithic with the slab and having an inside diameter of 2 feet. The slab was 4 inches thick. The reinforcement of Specimens i to 4 arranged as shown in Fig. 144, differed in the diameter of bars used for the five outside rings, as shown in the table on page 475. Specimens S and 6 were similar to 3 except that 10 and 5 radials respectively were used instead of 20. Specimen 7 was reinforced by four layers of bars running in four directions, each layer consisting of nine ^^-inch round bars. Specimen 8 was reinforced with steel in top and bottom; the tensile reinforcement consisted of two layers placed at right angles, with twelve |-inch round bars per layer, and the compressive reinforce- ment consisted of two layers with eight |-inch round bars per layer. Purpose of Test. The purpose of the test was to compare the effec- tiveness of circumferential with band reinforcement and to determine the most effective distribution of steel between rings and radials.' Materials of Construction. Concrete in proportions 1:2:4 was used. The compressive strength of 6-inch cubes, tested at 52 days, was 2 100 pounds per square inch. Reduced to 8 x 16-inch cylinders and to 28 days, the strength of the concrete was about 1 400 pounds per square inch, or lower than first-class 1:2:4 concrete (see p. 310). Plain round bars with an average elastic limit of 35 000 pounds per square inch were used. Method of Testing. In testing, the slabs were placed on a wooden column resting upon a base which distributed the load to the soil. The TESTS OF REINFORCED CONCRETE CO 14: m%4iyJ^-^ XMd. Position o| Swing" 1° ° j ^Holes for Wires Swlhga l|or Pig I I : i-i Fig. 144.— CantUever Slab and Loading Platform. (5ee ^. 472.) 474 A TREATISE ON CONCRETE > ■ ^ ^ ^ / ^ y y ( \ R{ngl\ Rm2 ^^ ' 10 20 30 40 10 20 so -W so ^ -^ ^ ^ t 7 / ^ / ^ / / Z' / Rings Rir S'f s s \4 ' / 7 20 SO /O 20 so 10 > -^ y y /^ > ^ ^ ^ V / r \ Radial AiBietc. Radial AjBzetc. Radial AsB^etc. X) 20 so 40 .0 iO 20 O lO 20 Unit 5tre^ iii Thousand Pounds Specimen 2 1^ f, ^ > 1 _^ y ^ -^ ^ ■^ /' / / Ring/ \ Rin ?' \ R hgs \l Q. /O 20 10 20 SO /O 20 SO 40 SO ^ V r r y ■^ y y / f / I Ring4^ J m VS iRir ff<^ 7 ?J 10 20 SO 40 (■ iO 20 SO C /O O /o is .Q ^ -• . ^^ ^ •^ "^ ^ ^ / k f / / t Radial- AS,etq. 1 Radial AzPie fe. 'AsBsetc e> /O 20 so 40 O IO 20 so 40 Unit Stress in Thousand Pounds Specimen l Fig. 145. — Deformation Diagrams for Slab Specimens. No. i and 2. {See p. 474.) load, consisting of pig iron averaging 56 pounds per pig was placed on swings arranged along the circumference of the cantilevers as shown in Fig. 144, page 473. By this method the point of application of the load, and therefore the moment arm, was positively fixed. Further- more, actual conditions occur- ring in a continuous flat slab floor were substantially repro- duced, the stresses in the canti- lever corresponding to those produced by the negative bend- ing moment at the column in a floor. Deformation Readings. De- formations in steel, due to the loading, were measured by a Berry extensometer on 8 inch gage lines. For this purpose gage holes about ^-inch diameter were drilled in the steel. Each ring and each bar was provided with at least four gage lines to ehminate the possibility of erratic re- sults. Average stresses were plotted in a defor- mation diagram. Fig. 145, page 474, shows the deformations at different loadings for Specimens No. I and 2 and Fig. 146, o ~~a^o page 475, for Specimen 7. The curves for Specimen 8 are substantially like Specimen 7. TESTS OF REINFORCED CONCRETE 47 S M^ Jkj^' ^ Sj y /i? 20 JO 40 b /o 20 30 40 ■SO b /o zo Jp 4o o Jo 20 so ^ ^b. B b io2oso'iosobh2oso b. b 20 Jo ^o so b h 20 Jo 40 Unit 5tress in Thousand Ftounds 5PEC1MEN 7 Fig. 146. — Deformation Diagrams for Slab Specimen No. 7. {See p. 474). Results of the Tests. The results of the tests are shown in the table on page 475, which gives the dimension of specimens, total loads, and load per pound of tensile steel. The measured stress and the load at first visible crack also are given in the table, from which it is evident that the first visible cracks occurred at about two-thirds of the load at the elastic limit. Judging from the stress diagrams, hair cracks invisi- ble to the eye must have appeared at a smaller load corresponding to the break in the deformation curve. Summary of Results of Tests of Octagonal Cantilever Flat Slabs. Octagonal slab 6 ft. 6 in. inside diameter; column head 2 ft. diameter; 1:2:4 concrete; mild Specimens Nos. i to 4, Radial; Specimen 7, 4-way; Specimen 8, 2-way. All slabs 4 inches thick. steel. 1 ■•0 1 .2 s s "o s NUMBER AND DiAMETEE OF ROUND BARS IN INCHES l.gg .i 1 1-^ t3 1 1 1 .■3£ §2 Is jl 1 1 14 i 1 Radial bars Outside rings Straight bars Pi I 2 3 4 7 8 47 44 42 3S SI so 42.6 so. 2 71-7 101.2 60.0 s6.o 20-f 20-1 20-1 20-i s-A 5-f s-J s-l 36 -A 24-Jl i6-ii ■ji.2 2.2 .i.2 -^ . £ S-i 0.368): 0.484! O.QOlt ..38 2.s6 2.62 2.60 2.50 2.25 2.2s 18800 22 soo •32000 t42Soo 12 600 12 600 442 448 447 421 210 225 12400 IS 000 2r 200 26600 89SO 8goo 14000 iSooo 160C0 ISOOO 15 000 IS 000 fTens ■ ■ \Comi on >ression * Estimated from stress diagram. Broken by accident at 29 500 lb., before elastic limit was reached t Estimated from stress diagram. Elastic limit not reached at maximum applied load. X Only part of the area of Ring s was considered as effective becai^e it was placed too near the col umn head and therefore carried smaller stress than the other rings. 476 A TREATISE ON CONCRETE The first crack, at first hardly noticeable, extended all the way around the circumference of the column head several inches from its edge. For additional loading, the crack opened slowly and additional circum- ferential and radial cracks appeared. The test was discontinued after the steel had reached the elastic limit with the exception of Specimen 4, in which the elastic limit of the slab was not reached on account of the difl&culty of appljdng further loading. No cracks developed within the column head although the radials were stressed to elastic limit and the hooked portions did not bear against the center ring. Of interest is the fact that the cracks in Specimens 7 and 8, reinforced with bands of bars, were also radial and circumferential. ■ Splicing of Rings. From the stress diagrams, it is noticeable that in Specimens i to 3, the outside Rings i to 4, and in Specimen 4, Rings I to 3, were equally effective in resisting the bending moment, the stresses at different loads being almost equal. The stress in Ring 5 was smaller than in the other rings, which can be accounted for by the fact that the ring was placed too near the column head. The stresses in Rings 6 and 7 within the column head are very small, showing that very little stress is transferred by the radials to the center rings. Evidently most of it is transferred to concrete by bearing. AU rings were spliced with a 50-diameter lap. During testing, special attention was paid to the behavior of the steel at the splices and it was found that the elastic limit was reached without any movement being observed at the sphces. Conclusions, (i) First crack occurred at substantially the same measured stresses in the steel, irrespective of the arrangement and amount of reinforcement. The load at first crack increased with the increase of reinforcement. (2) The actual load sustained in all specimens is larger than would be expected from ordinary methods of computation, proving the effect of Poisson's ratio. The reduction of bending moment coefficients sug- gested for flat slabs on page 547 is justified. (3) The relative effectiveness of the various arrangements of steel can be obtained by comparing the load per pound of tensile steel which for specimen i to 4 varied between 420 poimds and 450 pounds and for specimens 7 to 8 between 210 and 225 pounds. (4) In specimens reinforced by rings the stresses were uniformly dis- tributed over all rings. (See stress diagrams, p. 474). (s) The lap of 50 diameters of a plain bar was sufficient to develop the elastic limit of the rings. REINFORCED CONCRETE DESIGN 477 CHAPTER XXII REINFORCED CONCRETE DESIGN In this chapter are given the definite principles and rules used in the design of reinforced concrete structures. The matter is based on the two preceding chapters of which the first goes much more fully than the present chapter into the fundamental theory of reinforced concrete, giving formulas and their derivations for rectangular beams, T-beams, beams with steel in top and bottom, columns, and members under direct compression and flexure, while the second describes the tests which verify both theory and rules for design. In the present chapter are taken up the working formulas which are necessary in actual de- sign. Before using these final formulas, the designer should become acquainted with the derivations already given so as to have a thorough understanding of the subject. The formulas and recommendations are grouped under headings and sub-headings for convenient reference. At the end of this chapter are tables and diagrams for use in design. Many of these are copied from office standards of the authors. RATIO OF MODULI OF ELASTICITY As seen from the tests, pages 400 to 404, the value of the modulus of elasticity of concrete depends upon the quality of the aggregates used, the consistency, and the age. It varies also for different stages of the loading, but may be considered constant within working limits. The modulus of elasticity of steel being practically constant (see p. 400), the ratio of moduli of steel to concrete, n, changes in direct pro- portion with the change of the modulus of concrete. In computations, it is advisable to vary the ratio according to the ultimate strength of the concrete. The ratios, 11, recommended* for use are: (a) For concrete having a crushing strength of 2 200 lb. per sq. in. or less, a value of 15. (6) For concrete having a crushing strength between 2 200 and 2 900 lb. per sq. in., a value of 12. (c) For concrete having a crushing strength exceeding 2 900 lb. per sq. in., a value of 10. • These values agree with the recommendations of the Joint Committee. 1916. 478 A TREATISE ON CONCRETE The value of 15 has been adopted in the British, German, and Austrian rules up to 1916. The French rules for 1907 authorize a range from 8 to 1 5 according to conditions. For determining deflection of beams when using formulas which do not take into account the tensile strength devel- oped in the concrete, a ratio of 8 may be used. The effect of the ratio of moduli on the stresses in beams may be seen A from the formulas and also the tables. For a given beam with a definite ' amount of steel, the use of higher ratio of moduli lowers the position of the theoretical neutral axis, and for a given bending moment decreases the stresses in concrete and increases the stresses in steel, the latter, however, in much smaller proportion. For the same unit stresses and^ bending moments, but different ratios of moduli, the beam designed for the larger ratio will have a smaller depth, but at the same time a larger amount of steel. Therefore, in beam design, if a concrete richer than ordinary is used, the question of economy must be carefully considered. Modulus of Elasticity in Tension. But few tests of modulus of elas- ticity of concrete in tension have been made, but these indicate* that the value is probably the same as the modulus in compression. aUALITY OF EEINFORCING STEEL The 1914 Specifications of the American Society for Testing Materials require the following properties for reinforcement: Tensile Properties of Concrete Reinforcement Bars Properties Considered. ' Tensile strength, lb. per sq. in Yield point, min.. lb. per sq. in Elongation in 8 in., min., per cent. . . Plain Bats Deformed Bars. Structural- steel Grade. Inter- mediate Grade. Hard Grade. Structural- Steel Grade. Inter- mediate Grade. Hard Grade. 5S ooo to 70 000 33 000 1 400 coot 70 000 to 8s 000 40 coo I 300 ooot 80 000 min. so 000 I 200 ooot SS 000 to 70 000 33 000 I 250 ooot 70000 to 80000 40 000 I 125 ooot 80 000 min. SO 000 I 000 ooot Tens. str. Tens. str. Tens. str. Tens. str. Tens. str. Tens. str. Cold- twisted Bars. Recorded only. t Deduct r per cent for each increase of i-inch above |-incb diameter, or for each decrease of A-inch below ^-inch diameter. It is generally recognized in reinforced beam design that the yield point of the steel should be considered as the point of failure of this • Prof. W. K. Hatt, Journal Association Engineering Societies, June 1904, p. 32. REINFORCED CONCRETE DESIGN 479 material. Tests show that when the metal reaches its yield point, the beam sags, and this deflection, due to the stretch of the steel and in some cases to the slipping of the steel because of its reduced cross- section is likely to produce crushing in the concrete. Many engineers do not approve of the use of high steel because of its brittleness when of poor quality, and the danger of sudden accident, and because of the fact that it is prohibited in ordinary structural steel work. Brittleness in steel, however, is less dangerous in reinforced concrete than in many classes of structural steel work because the concrete pro- tects it from shock, and also because smaller sections of steel are used in concrete beams than in steel beams, and the large and irregular shapes of the latter render them much more sensitive to irregular cool- ing during the process of their manufactinre. Mild steel, that is, ordinary market steel, is manufactured and sold under such standard conditions that for unimportant structures it often may be used without other test than the bending test given on page 480. High steel, on the other hand, must be thoroughly tested. When tested, however, it is entirely safe and to be preferred to mild steel. The objection to it for reinforced concrete is based largely upon the use of a poor quaUty of material and the extra cost. Another objec- tion which has been raised is that before the elastic limit is reached, the stretch in the high steel may produce excessive cracking in the concrete in the lower portion of the beam, and thus expose the steel to corrosion. The mere fact that cracks are visible does not prove that they are dangerous, because the steel is always designed to take the whole of the tension. Mr. Considere's and Professors Talbot's and Tumeaure's tests indicate that there is no dangerous cracking even with high steel until the yield point of the steel is reached. Tests made in Europe in 1907 (see p. 292) prove quite conclusively that the cement protects the steel from ordinary and even extraordinary corrosive action until the elastic limit of the steel is nearly reached. In cases where very minute cracking of the concrete may cause anxiety (even although not dangerous), the steel, whatever its quality, should not be stressed beyond the ordinary limits of, say, 16 000 pounds per square inch. A yield point in steel of 30 000 pounds per square inch corresponds to a stretch of o.ooio of its length and a yield point of 50 000 to a stretch of 0.00167. If steel could be made with a high modulus of elasticity it would be par- ticularly serviceable for reinforced concrete, because the higher the mod- ulus of elasticity of a material the less is the deformation under any given 48o A TREATISE ON CONCRETE loading. Unfortunately, however, all steel, whether high or low in carbon, has substantially the same modulus of elasticity (30000000 lb. persq. in.). It may be stated, then, that high carbon steel, say, 0.56% to 0.60% carbon, of the quality used in the United States for making locomotive tires, is better than mild steel for reinforced concrete provided the steel is well melted and rolled, and is comparatively free from impurities, such as phosphorus.* However, a high carbon steel, unless limited by chemical analysis, and made under careful inspection, is in danger of being more brittle than low carbon steel. Its use, therefore, should be limited strictly to work important enough to warrant the ordering of a special steel and the taking of sufl&cient trouble on the part of the purchaser to insure strict adherence to the specifications. Since manufacturers cannot always be depended upon to exactly follow specifications of this nature, it is necessary that an inspector be sent to the works either by the dealer or the purchaser. Bending Test for Steel. The most important test in the specifications is the bending test and no steel which fails to pass this bending test should be used under any circumstances. The bending test of the 1914 Specifications of the American Society for Testing Material is as follows: Test specimens for bending shall be bent cold to the following angles without fracture on the outside of the bent portion: Bend-Test Requirements. Thickness Plain Bars. Deformed Bars. or Diameter of Bar. Struc- tural- Steel Grade. Inter- mediate Grade. Hard Grade. Struc- tural-Steel Grade. Inter- mediate Grade. Hard Grade. twisted Bars. Under ''in 180 deg. d = t 180 deg. d = t 180 deg. d= 2t go deg. d=2t 180 deg. d = 3t 90 deg. d = .?t 180 deg. d= t 90 deg. d= 2t 180 deg. d = 3t go deg. d = 3t 180 deg. d = 4t go deg. d = 4t 180 deg. d=2t 180 deg. d = 3t Explanatory Note; d = the diameter of pin about which the specimen is bent; t = the thickness or diameter of the specimen. Steel with high elastic limit, whether due to high carbon or to manipula- tion in manufacture, should be purchased with these reservations even if the working stress is to be no higher than is used with mild steel, say, i6 ooo pounds per square inch, because it is liable to be brittle. In case a lot of steel has been delivered without previous test by the purchaser, one bar * In Bessemer steel, phosphorus should be not over o.io per cent and in open hearth steel not over 0,05 per cent. In hard steel, manganese should be between 0,40 and 0.80 per cent, and sul phur should be not over 0,06 per cent. REINFORCED CONCRETE DESIGN 481 selected at random in every 100 should be subjected to this test and if it fails to pass, the portion from which it is taken should be rejected. FORMULAS FOR DESIGN OF RECTANGULAR BEAMS From the discussion on page 350 it is evident that a beam must have breadth and depth sufficient to prevent excessive compression in the concrete in the top of the beam and enough steel to take all the pull without exceeding the working stress of the steel. Rules for this are given in the simple formulas which follow. The steel must also have sufficient bond (see p. 533) and in most cases inclined or vertical re- mforcement is required as treated in connection with diagonal tension, pages 516 to 533. Continuous beams also require reinforcement over the supports, as described in pages 496 to 499. STEEL Fig. 147. — Resisting Forces in a Reinforced Concrete Beam. {See p. 482.) Considering the design of a simple beam, let d = distance from outside compressive fiber to center of gravity of steel, b = breadth of rectangular beam or breadth of flange of T-beam. p = ratio of cross-section of steel in tension to cross-section of beam, bd. A^ = cross-section of steel in tension. M = moment of resistance or bending moment in general. C = constant in table, page 483. Having computed the maximum bending moment due to the loads (see p. 510) the breadth of the beam, b, is assimied and then the d«pth of the beam, d, and the amount of steel are found from the following for- mulas: d = C ? « and As = pbd (2) 482 A TREATISE ON CONCRETE The constants C and ^ may be taken from Table on page 483, selecting values corresponding to the working stresses in steel and concrete and to their ratio of elasticity. Substituting in (i) and (2), for C and p, the values corresponding to 650 lb. per sq. in. in concrete and 16 000 lb. per sq. in. in steel: d = 0.096 ■J-T- (3) and As = 0.0077 bd (4) Equations (i) and (3) give the minimum allowable depth for assumed working stresses. Sometimes for construction reasons, it is necessary to use a larger depth than obtained by these formulas. For such cases a smaller amourit of steel is permissible and may be obtained from equa- tion ^^ = -^77 (4a) For ordinary cases the value of _/ may be taken as \. Example i: What depth of beam and what area of steel are required, tor a freely supported beam having a span of 18 feet using 1:2:4 concrete, with a load of 600 pounds per running foot ? t. , • -o J- ^ ,^ ' W^ . 600 X 18 X 18 X 12 ^ ■„ u Soluhon: Bendmg moment, M, for — - is — = 291 600 inch / 8 o pounds. Assuming a breadth of 8. inches and using formula (3) ! = 0.096 "Y' ?2l5?? = 18.3 inches With 2 inches of concrete below the steel, the total depth of beam is thus 20.3 inches. The area of steel from formula (4) is A = 0.0077 X 8 X 18.3 = i.ij square inches, thus (from table page 574) requiring four |-inch round bars, or their equivalent. The steel and concrete stresses, /j and/; and ratio, p, are interdependent and for any values of / and /^ there is always a corresponding value of p. See formula (s), page 354.) With /j and /^ given, the corresponding ratio, p, must never be exceeded, else, if the stress in the steel is main- tained, the stress in the concrete would be increased beyond the permis- sible values given on page 573. If it is necessary to use a larger ratio of steel than the value p cor- responding to the required stresses and at the same time maintain the stress /j the excess steel must be balanced by compression steel as dis- cussed on page 493. REINFORCED CONCRETE DESIGN 483 Example 2: To the stresses/, = 16 000 and /^ = 650 corresponds a ratio of steel p = 0.0077. If a ratio of say p = o.oi is used and the steel is stressed to 16 000 pounds per square inch the corresponding stress in concrete would be 770 instead of 650 pounds per square inch. To maintain with a. ratio p = o.oi the stress in con- crete fc = 650 pounds per square inch without adding compression steel it would be necessary to limit the stress in steel to only 13 000 pounds per square inch. This shows that with too large a ratio of steel the full working value of steel can- not be utilized and therefore the beam is not economical. The following table gives the values of constants for selected stresses. Constants in Beam and Slab Design For use in beam formula d = C -W t- and in slab formula 1:1:2 i:ii:3 1:2 :4 i:2|:S 1:3 :6 3 000 2 500 2 000 I 600 1 300 3 000 2 500 2 000 I 600 I 300 10 12 IS IS IS 10 12 IS IS IS 16 000 18 000 97S 810 650 S20 420 97S 810 650 520 420 0.378 0.378 0.378 0.327 0.282 0.3SI 0.351 0.351 0.302 0.259 0.874 0.874 U.874 0.892 0.906 0.883 0.883 0.883 0.900 0.914 0.0115 0.0096 0.0077 0.0053 0.0037 0.0095 0.0079 . 0063 0.0044 0.0030 0.079 0.086 0.096 0.II5 0.137 0.081 0.089 0.099 0.II9 0.142 0.023 0.025 0.028 0.033 0.040 0.024 0.026 0.029 0.03s 0.041 Depths and Loads for Different Bending Moments. The depth may be obtained in terms of the unit load, if desired, by substituting for M in formula {x) its value in terms of the load and the span. This may be readily transposed also to give the load, w, which a given beam will carry. Formulas To Review A Beam Already Designed. To review a beam already designed, the following formulas may be used, the derivation of which is given on page 354. Let fc = compressive unit stress in concrete in pounds per square inch, /j = tensile unit stress in steel in pounds per square inch. b = breadth of beam in inches. 484 A TREATISE ON CONCRETE d = depth of beam from compressive surface to center of steel in inches. k = ratio of depth of neutral axis to depth of beam d. j = ratio of distance between the centers of compression and tension to depth of beam, d. jd = dli——j = distance between the centers of compression and tension. As = area of cross-section of steel in square inches. p = ratio of cross-section of steel to cross-section of beam above center of gravity of steel. M = bending moment in inch-pounds. n = ratio of modulus of elasticity of steel to concrete. Then P = -TT (s) k= ^2 pn-\- {pnY - pn (6) j = 1 (6a) f = — ( ) /■ = ^^ (8) A;jd hd^jk The value of p is figured first, then k and j computed or taken from Table on page 482, and substituted in equations (7) and (8). ' For rectangular beams designed with stresses ordinarily used, the moment arm, jd, is about ^ d and the above formulas may be expressed as 0.87^ 5^ hd^ Neither the allowable tension iu steel nor the allowable compression in concrete should be exceeded. Tables for determming the dimen- sions and loading of rectangular beams are given on pages 576 to 578, and the methods of practical computation and details of design are illustrated in Example 8, page 553. T-beams are treated on page 487. The selection of bending moments to use in design of continuous beams is treated on page 510. DESIGN OF SLABS A slab, so far as computation is concerned, is a rectangular beam. The dimensions and stresses, therefore, can be obtained by the formulas given for rectangular beams. The bending moment is figured for a definite width of slab so that the formula for depth of slab can be simplified by combining the selected REINFORCED CONCRETE DESIGN 485 value of 6 = 12 inches with the constants given for rectangular beams, changing forniulas as given below. In the formula for required area of steel, A^, it is most convenient to assume a width of slab, b= 1 inch. The formula then gives the area of steel per inch of width of the slab, and the spacing of the bars can be readily determined by dividing the cross sectional area of a bar by the determined area per inch of width of slab. Using notation on page 484, and making M = bending moment in inch-pounds per foot of width of slab, As = area of steel in square inches per inch of width, Ci = constant based on these units, the formulas (i) and (2), change to d = 0.29 cVm = CiVm (inches) (9) As = pd (per inch of width) (10) The table on page 483 gives the values of constants, Ci , for concrete of selected proportions. For 1:2:4 concrete, adopting stresses in this table, the formulas become d = 0.028V Jlf (inches) (11) As = 0.0077 d (per inch of width) (12) in which d is found from equation (9) . If larger depth of slab is used than required by this formula, the area of steel may be found from M M As = — —7 = — (per mch of width) (13) 12] dfs 10.5 fsd The use of these formulas is illustrated in Example 8, page 553. Table 7 on page 582 gives dimensions and reinforcement for slabs for different live loads based on stress in concrete, fc = 650, stress in steel, /j = 16 000, and ratio of elasticity, w = 15. Slabs which are continuous over the supports, such as those in a floor or in a buttressed retaining waU, must be designed with provision for the negative moment at the supports. For uniformly loaded spans continu- ous over two or more intermediate supports, a moment M = y^wP may be used both in the centers of the spans and also at the supports, while for end spans a moment M = xV "'^ is necessary. Moments at Support. To provide for the moments over supports some designers bend up all the bars near the | point, but a better way, 486^ A TREATISE ON CONCRETE to be sure that no point in tension is unprovided with steel, is to bend up one-haU, two-thirds or three-quarters of the bars and run them over the supports allowing the remainder to continue at the bottom of the slab. To provide the rest of the steel at the support, the bars in the adjoining span can be carried back over the support. Where the bars are so long as to extend over several spans, they can be arranged to break joints at different places,- and so keep as much steel over top of supports as at center of span. The bend in the bars should be near the j points in the span, and usually at an angle of about 30 degrees with the horizontal. Too sharp an angle may tend to crack the slab, while, on the other hand, they must be brought to the top of the slab far enough from the support to properly provide for the negative moment. Tables for determining dimensions and loading of slabs can be found on pages 579 to 582, and examples and details of design are given on pages 552 to 557. Cross Reinforcement of Slabs. Cross reinforcement, that is, bars at the bottom of slab at right angles to the principal bearing rods, is cus- tomarily used to prevent shrinkage and temperature cracks. The amount of steel to use for this usually is selected somewhat arbitrarily, a cross-sectional area of bars equivalent to 0.2 per cent, to 0.3 per cent. (p = 0.002 to 0.003) of the cross-section of the floors being the usual practice. Reinforcement over Girders. The top of the slab over a girder or beam which is parallel to the principal reinforcement bars should be reinforced transversely not only for stiffening the T-beam (see p. 418) but also to provide for the negative bending moment produced with the bending of the slab next to the beam or girder. This reinforcement is also necessary even when the beam is simply a small stiffener. (See p. 491.) Computing Ratio of Steel. The ratio of steel in a slab is most readily found by dividing the cross section of one bar by the area betvy^een two bars, this area being the spacing of the bars times the, depth of steel below top of slab. For example, a slab with steel 4 inches below the top and I inch round bars spaced 6 inches apart has a ratio, 0.196 „ p = = 0.0082, or 0.82 per cent steel. 4X6 Square and Oblong Slabs Supported by Four Beams. When a slab is supported by four beams and its length does not exceed i| times its REINFORCED CONCRETE DESIGN 487 width, the loads will be carried by the slab to all four beams, and there- fore the slab must be reinforced in two directions, as shown below. The following table gives the ratio of the unit load, Wg , carried by the short span for different ratios of - .* B Ratio of Load Carried by the Shorter Span. (See p ■ 487.), Ratio of Length to Breadth of Slab. Ratio of Load Carried by the Shorter Sp.an. Ratib of Length to Breadth of Slab. Ratio of Load Carried by the Shorter Span. 1. 00 u.SO 1-30 0.80 I. OS O-SS 1-35 0.8s I.IO 0.60 ' 1 .40 0.90 I IS 0.6s I -45 "•9S 1.20 0.70 1-5° 1 .00 i-2S 0.7s It must be noticed that the shorter span carries the larger propor- tion of the load. After the proportion of the load is determined, the bending moments are found as for slabs reinforced in one direction and the dimensions or stresses are found by the ordinary formulas. The thickness of the slab, of course, is governed by the larger bending moment of the two. DESIGN or T-BEAM The formulas given below are sufficient to design or review a T-beam for a given bending moment. To Design a T-Beam. Design the slab. Determine width of flange (see p. 488) . Determine bending moment and end shear. If headroom is not limited, determine most economical depth (see p. 490). (In de- signing a number of similar beams the economical depth needs to be figured only for one beam, and estimated for the remainder.) Before * The load carried in either direction can be determined from the following formulas. Let "^B = unit load carried by the short span. '"'L = unit load carried by the long span. L - length of slab. B = width of slab. Then and KiB= _ . ■"'L ■o.s (14) (IS). 488 A TREATISE ON CONCRETE selecting final depth of beam and breadth of stem, b', see that the com- pression in concrete and the shear do not exceed the allowable working stress (pages 588 and 489) . Figure amount of tension steel (formula (20) p. 491) . For large beams, a saving in steel may be effected by using the more exact formulas. In such case, preliminary A^ for k and z may be found from formula (20) and final As from formulas (21) to (26) page 357. To Review a T-Beam. Dimensions are given and the stresses are to be determined. Determine width of flange. Find compressive stresses in concrete by use of table on page 588. The stresses in steel may be found from formula (20) page 491. If desired, k and z may be determined from formulas (15) and (16) page 356, and then/^ and/, from (18) and (19) page 357. Fig. 148.— Section of T-Beam. (See p. 488.) Width of Flange. The width of the slab, b, to use for the flange of the T-beam in compression is selected somewhat arbitrarily. In no case, of course, can it be taken greater than the distance between beams. The Joint Committee has recommended the following rules, which are approved by the authors, for the width of slab to be considered effective: (a) It shall not exceed one-fourth of the span length of the beam; (b) Its overhanging width, on either side of the web, shall not exceed six times the thickness of the slab. (c) It must not exceed the distance between beams. This practice is conservative. (See tests, pages 415 to 418.) Beams in which the T-form is used only for the purpose of providing additional compression area of concrete should preferably have a width of flange not more than three times the width of the stem and a thickness of flange not less than one-third of the depth of the beam. Cross-section of Web as Determined by the Diagonal Tension. The width of the web of a T-beam is governed by the layout of the tension bars (see p. 537) and by the shearing stresses (see p. 515). REINFORCED CONCRETE DESIGN 489 The area of the web required for shear involving diagonal tension, using notation on page (491) and letting V = total vertical shear, and V = shearing unit stress may be found from the formula (see also form- ula (32a) p. 517)- / ,\ 17 That is, the area of web at any point in the beam (considering this up to the middle of the slab) must not be less than the total shear divided by the maximum allowable unit shear for the reinforced beam. The vertical unit shearing stress (used as measure of the diagonal tension) in a beam effectively reinforced with bent bars or stirrups, or both, is limited by the Joint Committee to 120 pounds per square inch for ordinary concrete having a compressive strength (in cylinders) of 2 000 pounds per square inch at 28 days. See Example 8, page 553. Miniiiium Depth of T-Beam. The minimum depth is the depth at which concrete and steel are stressed simultaneously to their working limits. It is governed by the compression in the flange which must not exceed the working compressive stress in the concrete. Greater depth than the minimum is generally used for economy. A smaller depth gives excessive compressive stresses. For an example, see page 587. - To find the minimum depth the rectangular beam formula, (i) page 481 , may be used where the depth of the beam is not greater than four times the thickness of slab, using in this formula the breadth of the flange, b for the breadth of the beam. For ratios of depth of T-beam to thickness of slab larger than four, the rectangular beam formula gives unsafe results and the following formula must be used. (See page 554, and Tables 11 and 12, pages 586 and 587.) ,,. . J MCi , . Minimum a = (17) Minimum Depth at the Support for Continuous Beams. At the sup- port a continuous T-beam becomes practically a rectangular beam with steel in top and bottom. The minimum depth for known stresses /j and /c , bending moment M, and the selected ratio* of compressive to tensile steel, may be found from formula (18), illustrated in example 3, page 490. For the definition of px see page 492. Minimum d = \ (18) •The use of a ratio greater than i.o should be avoided because of the cost, and the difficulty of placing and keeping the steel in position during construction. 490. A TREATISE ON CONCRETE Txample 3: Given: M = 1 200 000 inch pounds, /^ = 7S°>/s = '^ °°°' » = 'S- Find the minimum depth if it is desired to limit compressive steel to one-half the ten- p' sile steel, so that f— = 0.5. pi Solution : Assume a = 0.06. From Table 14, page 589, in the section for /^ = 16 boo and/ = 750, find, in the column for a = 0.06, the value of p' = 0.007 corre- P' spending to pi = 0.014. This satisfies the requirement that — = 0.5. Assummg J = 0.89 (it is not necessary to be very exact in the choice of j) , we find the mini- mum depth to be , I M I I 200 000 ;i — , • , ' mmimum - 5TS ^ i o 6 Q LI >< U. 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Ti 's I, — ■s; ■^ \ — ^, / ^ \ Q. -I" \, o r- \ /- \, n •> \ O o '•/ \ i± \ O \ \ a \ \ o / \ f -S- V ^ t — 1 — — ■— r— ^ j — -^ / ^^ \ / t: -_ ,.1 ^_- ■^ ^ . . _^ -=r x ._ _\ >. ^^ ^ , . , L_ ■m- •t — — — — — ■^ "ui '=\-~ — ^^ f- — =^ — — — — ^^ ._. o > — — — — — ■a ^.^ t~ ■ in -IS -|,^ ■V N 0) ^ ■■ •\ m co' / \ O D / s a UJ S^ / N UI \ / -^ \ z z N / -^ n — N f o- ^ f- _, \ o a ^ \ !r ^ 7 z :J 1 ■ -1° \ n n a / '^ y O o lO 1 " s \ a o "i / U _ i.!ii:li 9. __ "i 1 5^ s; ;i: " iz ~ — ZJ ZI iX / Jj: V ^21 ^J _ _ s- =*- ^ — — — — •%- f ~- — — — — [ ^ — 'S -S — — — — ^i- — — in •^ w -l« -1- "4 -1^ — — _^ v C\ ' D / \ D n UJ / s Ul >i ^v .^ S, cc ^ ;:; ^ nJ s > a S' _ __[ _ -1^ _ _ _ _ — 2. a -i -P- \ -Z m- — — 0. 3 o. — — = =z — fU __ — 1- JO CO XT i~ — "o -to t ■^ ■+1 — -A "^1 B^*- — zz NO _-LH s p- rz — ^Z D i! ^7 — — ■ — — - i ^/= ^ ^ ^ !ri H r^ i? o r Z ■Vs - Irf Y- « 1? ,^^ 1 ^ -' 1 ^ I [ I 1 1 1 Fig. 151. — Bending Moments and Shears for Continuous Beams, Distributed Loads. (See p. 504.) So6 — ~ m o = • s :i a Ul H ^^ / i ■w 3 •^ 'n ri O Q. x. in in m 1 n / 'r \ o o NO -L 3A n 4 NO LOAC o / ^. > ^- ! — L_ -- -~ ■^ — — 1 1_ — — — -- ■ ■II 1 s -1 ^ ■^ M ''^ i^ ^J <-' ■*■ ^ ■ 1 -« ^ -s ■^ 1 "s. .n, -1= ^ j-^ ' ■|r ^3 1-"^ „ im /' s /^ S / \ / \ m / Q y \ 3 V \ o t- 1 \ h , Ti V / c< 1 , ^ -^ ^ L a / N ^ a / ' a D / ■N -I-- \ o O O / -u D 1 ' NOX OAD i / ■+ • 1 ■ • ■ > -~j -- "^ V ■ ■J ■s 3 \ iri ■• V, ■0 \ -1° s''. ■* •A en (0 Q ^ s D D a t- / s 7 ^ — ^ rr / ^' s -V SI , 7 O ,,1 tj A 7 >. — ^^ / s o a 1 ■s, 1-0 1 < r , 7 e4- o D 1 S -|^ 1 - ^ O O ■ / M \ O o i° LC AC \ ^ H \ O _ — 1 _. -^ X s I -^ ■■ V S ' _ „,— ■ V ' ':i -1 -. \ -- s / — ^^ , ,— m \ (D y- ■ A \ ■^ 1 / - 1 \, 1 \ 1 - — — \ 1 ^ ' N, to ~ - m /" ■ s n 1 J Q / s 1 - -D- ^ / ^ / «. ^. 1- -V, / '-^ \ n ^v -, ^ 3 Z. o "O in- •-V :;, O" 'a "V n a / -, - — ~1< ^ ^..J^ — -t ^s - — i; \ n. a / N -' HSX \ a \ ^ V i:- '■■ 1 -^ 4- \ N. V o- /- '-. s ' -"l. 1 -o- \ =1 ■-. \ t. s. =i •-, \ ^, / \ _o_ o V \ _['='/ ~ V; H-y— - - — - -\^- i \ 1 \ \ A 1- - — (/) — - — - CO LJ > ^ / \ CI =. ^ / r. s . ::. ■-- ^ ^ s. / s :^ . 7 "x s -P' CO a- -\i ^ NC 1^ O / N, '" \ O =-- D ^ ^ JAU "i / X — ' — — ■ ' ' ^- -^ -s _. _ _■ ■ / \ ' J 's S 1 ■^ ^5- -fe r-^ Cj N CO / -^ \ ^ v^ / z. ■^ \ l-j ^ n m / -1? ~ r S O o f -o K "i ^ ■ ^ + o \ '■ j ' ,\ ' \ \ ^ f s^ li -^ w I X -2L \ Hrf -la f ' -!f -If "^^ \ 1 1 '■y (■■ 1 N , / / / _ Fig. 152. — Bending Moments and Shears for Continuous Beams, Distributed Loads. (See f. 504.) Wmm --5 ^ C 5 "^ 3 -J L-SS %. < in ^ -SlS: ^ Nq_LpA L = ;^ g|S o Dt^ "^ Ct:"-Z ^ u~ 4 A " XS-IX •-VS. sZ i.Y"S ^- %% WL. a S =is: •«; I '^' 1 ji.-ij 5^ 4- Cl Cz c T- \t- T Z I r 4r "f J^t z ^ — ^ S >^ ^ "^ z ^ -□-■;""^Z- is: S F '^ "S „ ht ^ ( '^i 1" " 1 ^ ffl Ms Is 2 s 33Z Ko O Mn riAn ^-ii2 S ■e" £ zi i"^ E* .^— 4.-^ ;7 -t ^ ' -. C ■B ^^ s ^~4 S5 3SX ^'2 ^ -q it 1^ _i T r 0) t s ^ .-fi 9N ^ ■C -^ ^. -^ ^ ':? ^ U ti:i^ ^::3^^ ^ -stS- 2i^ 3t-S: ,9 ■ill-iL-^i 3-" ■-, r^ '^ ^ d^^ 1 ^ -j/ "" ■- CS ?^z "n r~^ ? t '-in ■s / =^ V ff 3^'^ 3° Bs'~ ste _L illi J- C z fc t- X r z ^ I^ t ^ — J > s t- 3 » .a ~. -w i_ 2. Q S-sZ „_ V .0 Hi .£L . Distance of Neutral Axis Moment of Inertia, from most Strained Fiber.' bh_' 13 12 12 ib\/r BH — bh ^j(BH=-bh») — RECTANGULAR CELL 44 T SECTION r Area of flange + area of web = Ai + As Aihi' + AJ12' ^^^h. Aih2 — Aah: T 2(Al + A2) , AiMhi+M! !L Aihz— Azb. 4(Ai+A2) ^"^ 2 + 2(Ai+A2) jr(r'— ri«) ir(r*— r.*) HOLLOW CIRCLE HOLLOW ELLIPSE ir(ab— aibi) — a 4 4 ♦Applicable only to homogeneous (not to reinforced^ beam& Sio A TREATISE ON CONCRETE at the quarter points, middle points, and third points respectively. This diagram is of special use in studying girders supporting cross beams. The stresses are computed for a beam of four spans and as the curves are symmetrical at each end, the diagram is broken in two, one-half being shown with fixed end and the other half with end sup- ported. The results with a larger number of spans will not be ap- preciably different. The vertical scale for concentrated loading is 0.05 per division for bend- ing moments and 0.2 per division for shears. The concentrated loads are given in terms of W, the load which is con- centrated at each point. The continuous beam is statically indeterminate, so that the moments and reactions have to be found by the theory of flexure, using the form- ula of three moments first evolved by Clayperon.* In applying this to the various cases, the assumption is made that the moment of inertia of the beam is constant throughout its length. While this is not strictly true, extensive studies of various cases in reinforced con- crete show that a large change in the moment of inertia makes a very small change in the bending moment, so that the relations are substantially correct until a member enters a much larger member, (See p. 499.) BENDING MOMENTS TO USE IN DESIGN OF REINFORCED BEAMS Tests in the laboratory and on actual structures show that a reinforced concrete beam built continuous over several supports and properly reinforced for the positive as well as the negative bending moment acts as continuous and may be designed as continuous. The bending moment for any span of a continuous beam depends not only upon its length and loading but also upon the number of spans in the beam, their relative lengths, and the condition of loading in the re- maining spans. In buildmg construction the loadings are indefinite so that instead of refined and laborious computations the following rules are recommended as safe for ordinary beams designed for uniformly distributed loading. 'Let M = bending moment in inch-pounds. w = load uniformly distributed in pounds per inch of length. I = length of beam in'inches. Then (a) For l->eams continuous over two or more intermediate supports, • See Lanza's "Applied Mechanics." REINFORCED CONCREIE DESIGN 511 the bending moment at the center and at the support for interior spans, shall be taken at — , and for end spans at ~ for the center and the 12 10 adjoining support, for both dead and live loads. (b) For beams continuous for two spans only the bending moment at the central support shall be taken as -— and near the middle of the o span, as — . 10 When the end of the above beam is monolithic with the column and provided with negative bending moment reinforcement, the bending moment at the central support may be taken as — and near the middle 10 wp . of the span as — instead of the bending moments specified above. 12 (c) At the ends of continuous beams running into a column provision shall be made for the negative bending moment, the amount of which will depend upon the condition of fixedness. In any case provision should be made for at least a bending moment — . In ordinary cases — should be used. Where beams run into very 20 16 heavy columns or piers, use — . (See also p. 513.) 12 ( page 539, taking six-tenths of the length of one leg as effective m bond. Diameters to use are discussed on page 525. Free end of stirrup requiring anchorage to prevent Its nulling out due to force acting below. Shear due to loads and * reaction on remoued portion of beam tending to open the crack. I Direction of force acting on stirrup, BEAM WITH VERTICAL STIRRUPS Resisting force in stirrup. Attached end of stirrup receiving the stress. BEAM WITHOUT WEB REINFORCEMENT, Free end of stirrup requiring anchorage to prevent its pulling out due to force acting below. Attached end of stirrup receiving the stress. Shear due to loads and reaction on removed portion of beam tending to open the cracli. Diagonal cracli. Resisting force in stirrup. Direction of force acting on stirrup. Horizontal component tending to mcue the stirrup horizontally. BEAM WITH INCLINED STIRRUPS. Fig. 157. — ^Action of Vertical and Inclined Stirrups in Simply Supported Beams. {See p. 522.) (4) Bars should be bent at an angle with the horizontal not greater than 45° nor less than 30° to be considered effective web reinforcement. (5) The spacing of stirrups, obtained from formulas (33a) and (34a), pages 518 and 519, to be effective, must not exceed three-quarters the depth of beam. To Design "Web Reinforcement. Determine the maximum total shear, V (see p. 516) and from this the shearing unit stress,' v. See that v does not exceed the maximum allowable stress.* (See p. 573.) •The Joint Committee, 1916, recommends for bent bars, or for stirrups simply looped about the longitudinal reinforcement, stresses } less than normal. 524 A TREATISE ON CONCRETE Vertical or Inclined Stirrups. If vertical or inclined stirrups only are used, determine the maximum diameter of stirrup. (See p. 525.) Select the, diameter and shape of the stirrup so that the minimum spacing is not too small (preferably not less than six inches), and the total niunber of stirrups in a beam not too large. Remember that the maximum spacing of stirrups in the part of beam where stirrups are re- quired must not exceed three-quarters of the depth of beam. Use the same size of stirrups and the same design for the whole length of the beam and if possible for all similar beams in the entire structure, as a variety of designs may lead to errors and confusion. Common sizes of stirrup bars are j^-inch, f-inch, j^-inch, and |-inch diameter in the shape of a U with the free ends hooked. For uniformly loaded beams, vary the spacing as given on p. 526. The number and the spacing of stirrups for different conditions may be taken from the table on page 585. Tension\Steel ■al / xls DireetioriyOf force acting on atinupa ^ Attached end «/ stirrups receiving the stress ^ Shear due to loads and reaction on removed portion of beam tending to open the crack Compression Steel Reaction >f Free end of stirrupimust be nJ anchored to prevent Its pulling out by force acting above) Fig. 158. — Action of Stirrups in Continuous Beams. {See p. 522.) For concentrated loads, a graphical method of determining the spacing of stirrups is the most satisfactory. (See p. 5?8.) Vertical Stirrups and Bent-Up Bars. Determine the maximum total shear, V, and shearing unit stress, v, as in previous case. (See p. 517.) Determine the number of bars to be bent and the places where the bends can be made. (See p. 534.) Select proper diameter of stirrup as suggested in previous case. For xmiformly distributed loading, either make the spacing of the stirrups constant and vary the spacing of the bent-up bars, or make the spacing of bent-up bars constant and vary the spacing of stirrups. Remember that if bent-up bars can not be bent in places where they can resist diagonal tension or are bent in one or two places only, their full value as web reinforcement must not be counted upon, Bent-up bars may be considered as effective web reinforcement for a distance from the point of bending-up equal to three-fourths of the depth of the beam. REINFORCED CONCRETE DESIGN 525 Maximum Diameter of Round or Square Stirrups with Straight Ends. {See p. 525.) At least 50% Larger Diameters may be used with Hooked Ends. VERTICAL STIRRUPS. INCLINED STIRRUPS. DEPTH or BEMI.d. Allowable bond unit stress. Allowable bond unit stress. INCHES. lb. persq. in. lb. persq. in. »-=8a u = 100 u = 80 j u = 100 10 i i ft ; i . IS A i i i 20 1 1 ft 1 ft 2S ft 1 i ^ 30 f ft ft 1 35 ft i H f 40 \ ft 1 il Diameter of Stirrups. The diameter to select for stirrups is governed by the limiting spacing of the stirrups as given in the preceding paragraphs, by the bond of the stirrup prongs, and by convenience in selecting and placing the reinforcement. The effective length of the stirrup prong should be taken less than the total length because of the slight change in the intensity of shear below the neutral axis and because also a lower bond strength may be expected there. Tests by Prof. Talbot indicate that it is safe to use up to at least six- tenths of the total length of the stirrup in figuring the bond. The maximum diameter of stirrups with straight free ends which can be used by these assumptions without danger of slipping, as determined by the bond, is given in the table above. The unit stress in stirrups is assumed at 16 000 pounds per square inch. For plain bars, the bond unit stress of 80 pounds per square inch may be accepted (see p. 567.) For deformed bars, this may be increased to 100 to 150 potmds per square inch according to the character of the bar. It is evident from the above table that the diameters that can be used with straight free ends are smaller than practicable in most cases. Consequently, stirrups should be made with hooked ends. Tests (p. 438) indicate that a right-angle bend of 5 diameters or a semi- circular bend of similar length is sufficient to stress the steel to its elastic limit provided the hook is well imbedded in the concrete so that it can- not kick out. As a more conservative recommendation for practice, stirrups ranging from -rg inch for beams 10 inches deep up to |-inch for 40-inch beams are advised with intermediate sizes for intermediate depths. 526 A TREATISE ON CONCRETE GRAPHICAL METHOD OF SPACING STIRRUPS By the graphical method, lay out the length of the beam to scale and plot the shearing unit stresses (which are accepted as measures of diagonal tension) as ordinates in the respective points of the beam. The diagram of shearing unit stresses is similar to the shear diagram so that one can be used for the other by changing the scale. Uniformly Distributed Loading. The shear is the maximum at the support and zero at the center so that the figure representing the shear (and also shearing stresses) will be a triangle as shown in Fig. 159. Fig. 159. — Spacing of Vertical Stirrups for Uniform Load. {See p. 526.) Vertical Stirrups. Draw shear diagram Fig. 159. Determine sec- tion where total diagonal tension is resisted by concrete. To the right of C2 all diagonal tension is carried by concrete. To the left, two-thirds is resisted by web reinforcement, and one-third, by concrete. Mark ofi the diagonal tension resisted by concrete aia^dCi. Find the total amount of diagonal tension equal to the area, aoiCiC times the width of beam, b. Required number of stirrups equals the total diagonal tension divided by safe strength of one stirrup in pull, AJ^. Divide area aaiCiC into the required number of equal divisions in the following manner: REINFORCED CONCRETE DESIGN 527 Draw a half circle, taking ab as the diameter. With & as a center, and be as radius, draw an arc till it intersects with the half circle at d. Erect a vertical dd'. Divide the distance, ad', into the required number of equal parts. From the points of division, drop verticals till they intersect with the circle, thus obtaining points e, /, g, h. With 6 as a center, draw arcs till they intersect with the line ab at ei,fi, gi, and hi. Verticals erected in the last mentioned points divide the trapezoid into the required number of parts. The stirrups are placed in the center of gravity of the divisions. Analytically the same results may be obtained by using Table 10, P- 585- Inclined Stirrups or Bent Bars. The diagonal tension to be resisted and the spacing may be determined by drawing a line from the center Fig. 160. — Spacing of Stirrups and Bent Bars for Uniform Loading. {See p. 528.) of the span at the angle of inclination of the stirrups and projecting half of the span on this line. With this new line, axh, as a basis, one may proceed in exactly the same manner as in the previous case. It will be found, however, that for the same conditions the points of spacing of inclined stirrups on the neutral axis will coincide with the points obtained by the method suggested for vertical stirrups. The same method; therefore, may be used for inclined stirrups as for vertical stirrups. The points of division plotted on the neutral axis will give the point of intersection of inclined stirrups with the neutral axis. It must be remembered that the actual diagonal tension to be resisted by the inclined stirrups is seven-tenths of that to be resisted by verti- cal stirrups. For inclined stirrups, therefore, the area aa\Cic (Fig. 1 59) times the width of beam, b, must be multiplied by 0.7. 528 A TREATISE ON CONCRETE Combination of Stirrups and Bent Bars. In Fig i6o we obtain the trapezoid to be resisted by the web reinforcement in the same way as explained in connection with Fig. 159. Eaiowing the number and the strength of the bent bars in pull, we may mark ofif at the top a triangle of diagonal tension that can be resisted by the bent bars. The bottom part of the trapezoid then represents the diagonal tension to be taken by stirrups. The stirrups may be spaced uniformly, and the spacing of the bent bars may be easily determined by dividing the top triangle into the required number of parts, as explained in the previous example. If the bent bars cannot be bent in the required places, or if they are bent ZftOQ lb. rZft.O^ 26000 lb. \aOOQlh 20000 2'&, -m^o- -SfLO- 3000 2i>. -7/t70^ -•iOft. Of- (a) <-3/f.O^ ■nrnnil 23000/6. Fig. 161. — Spacing of Stirrups for Concentrated Loads. {See p. 529.) in one place only, their full value in resisting diagonal tension cannot be counted on and stirrups must be used instead. Concentrated Loads. For concentrated loads, the shear diagram (being a measure of diagonal tension) obtained by plotting the shear on the length of the beam will not always be a regular figure, as it depends upon the number of concentrated loads and their position. One Load Concentrated in the Center. In this case the shear will be uniform for the whole length of the beam (except the small difference in shear caused by the dead load of the beam). After determining the shearing unit stress and selecting the kind of web reinforcement, deter- mine the spacing by dividing the tensile value of stirrup by the shearing REINFORCED CONCRETE DESIGN 529 unit stress times the width of the beam. The spacing then will be uni- form throughout the beam. Loads at Third Points. In this case, as in the last, the spacing of stir- rups is uniform. The stirrups, however, will extend only from the support to the load. No stirrups are theoretically necessary in the middle thurd of the beam. Concentrated Loads, Irregularly Spaced, with Uniform Load. Draw the shear diagram, Fig. 161, page 528, (as the measure of diagonal ten- sion) and mark off the amount of shearing stress that can be taken by the concrete. Then from the figure, starting at the support, determine and mark off the area that can be resisted by one stirrup, and place the first stirrup in the center of gravity of that area. Next mark off the area for the second stirrup and place the stirrup and proceed till the total area is provided for. This method although the simplest that can be devised, is quite laborious. With some practice, however, it is possible to divide the shear diagram into equal areas without much figuring, as illustrated on page528. After the diagram is drawn,it is easyto find the total amountof shearing stress and thenmnberof stirrupsrequired. Then with the diagram as a guide, the stirrups may be placed by inspection. To illustrate the method more clearly the detailed computations are given for the number and the spacing of stirrups for a beam 20 feet long, the dimensions of which are 6= 10 in., d= 25 in., jd= 22 in., and the load- ing as shown in Fig. i6r. Find first the reaction and then the total shear at points a, b, c, and d. Dividing the total shear by hjd, which in this case is 10x22 = 220, we get the shearing unit stresses at the respective points as follows : Total shear. Shearing Unit Stress. Point Left Right Left Right a 25 000 114 6 24. 200 22 000 IIO 100 c 20 200 5 200 92 23 d 4000 —16000 18 —73 e —18 800 —21 800 — 86 —99 f ~ 23 000 — 104 Lay out the shear diagram as in Fig. 161. Find section where concrete can resist the total diagonal tension by drawing a horizontal line for v' = 40 lb. At the left end of the beam, this line strikes the outline at g. To the right of section g and to the left of d, all diagonal tension is resisted by concrete, and to the left of point g and to the right of d, one-third is resisted by concrete and two-thirds by web reinforcement. S30 A TREATISE ON CONCRETE Mark off the one-third area resisted by concrete. Total amount of diagonal tension, the measure of which are the shear- ing stresses, for left end of beam equals the areas aaihb and bbiCiC times wid]th, 6= lo inches. Areas aaM + bhcc = i(^-i^) X 24 + ^('^^") >< '° = I 792 + 3 440 = s 232 lb. Multiplying by 6=10, we obtain 52 320 lb. Using J-inch stirrups with two legs, area ^dj = 2 X o. 196 = 0.392 and ; .4j/j=o.392Xi6 000=6 272 lb. C2 ^20 Number of stirrups N^ = ^—^ — = 8.3 Use 9 stirrups. 6 272 By trial, starting at the support, find shear areas on diagram equal to the resisting value of stirrup divided by b= 10, or 627.2 lb. This may be done by scaling the ordinates above the line, af, and dividing 627.2 lb. by them. The space for the first stirrup would be about 9 inches, so by scaUng the ordinate distant about 4 in. from a, we get the average 627.2 ordinate equal to 73 lb. The first division, — -^~ = 8.6 inches may be 73 laid t>ff and the stirrup placed in the middle. Next scale an ordinate 4 inches from the end of first division and find the next spacing. In our case, as the effect of the uniform load is small, we may simplify the matter by considering the ordinates in the portion aaib^b and also in bbiCic as constant and finding the spacings for these two constant values. Thus we find the spacing in portion ab to be 8.5 inches, and in portion be, 10.5 inches. So we may make arbitrarily 3 spaces 8 inches and 6 spaces at 10 inches, giving the required number of stirrups. The same method may be used in determining the spacing in the right end of the beam. The shear here is somewhat smaller, but it facilitates the erection to adopt the same spacing at both ends. Of course the stirrups must extend to the point d. Bent Bars or Inclined Stirrups. When spacing bent bars or inclined stirrups by graphical method, we may proceed as in previous case except that the total amount of diagonal tension must be multiplied by seven-tenths. The spacing obtained gives the points of intersec- tion of stirrups with the neutral axis. If a combination of bent bars and stirrups is used, mark off on the dia- REINFORCED CONCRETE DESIGN 531 gram the areas allotted to the bent bars and the stirrups and divide each of them separately into the required number of spaces. STIRRUPS FOR MOVING LOADS For beams carrying moving loads, as bridges and crane runways, it is necessary to determine for every section the maximum total shear,'then draw the shear diagram and, bearing in mind that shear is the measure of diagonal tension, space the stirrups as suggested above. For heavy moving loads, it is advisable to add a certain percentage for impact, depending upon the character of the structure, the loading, and the — * ililllllllllllilllllllllllllllllllllllllllllllllllllllli . 1 — '■ - > (a) Fig. 162. — Shear Diagram for Unifonnly Distributed Moving Load. {See p. 532.) relation of the weight of the structure to the moving load. For rail- road bridges and bridges carrying electric cars, the ordinary formulas may be used; for crane runways and highway bridges, from 25 to 50 per cent should be added. (See Chapter XXV.) Shear Diagram for Uniformly Distributed Moving Load. Assume moving load w per lin. ft.; then the maximum positive shear at any section occurs when the load extends from the right support to the section under consideration and the portion between the left support and the section is unloaded. (See Fig. 162.) 532 A TREATISE ON CONCRETE The general equation of the maximum shear then is, F — This is an equation of a parabola. w (I — x)^ 2l l,V = o. For » = o, F = — ; for « = - , F = -5- ; for a; 2 20 To the shear due to moving loads, the shear due to stationary (dead) loads must be added. In Fig. 162 the diagrams for dead and live loads are drawn. Line (i) gives the diagram for dead load only; line (2) for moving load plus impact only; and line (3) for the sum of the two. Stirrups must be provided for the sum of shears. As the moving load can approach from either end, the spacings must be made the same for both ends. Si Ql («) Fig. 163. — Shear Diagram for Two Moving Loads a Constant Distance Apart. P- S33-) (See Shear Diagram for Two Equal Moving Loads a Constant Distance Apart. This case occurs in a beam carrying cranes and in highway bridges, (see p. 693.) The maximum shear is obtained by placing one load at the section considered. A general equation is: REINFORCED CONCRETE DESIGN 533 Let P = concentrated moving load. e = constant distance between the loads P. l-ix-Y-) ,, . 7=2P-A_^ or P '^^-f-U oro.l- e. V The variation in shear is a straight line for both equations. We need thus to determine two points. (See Fig. 163, page 532.) 2I — e T Maximum shear where a; = o is F^ax = -P ; — and shear for x = l~ e is V= F-r. V With these two values we may draw the shear diagram. To this must be added the shear due to the dead load. Having drawn the shear dia- gram, the spacing is determined as in previous cases. For bridge design, the shear may be found as given in Chapter XXV on Bridge Design, the diagram plotted and the web reinforcement spaced as suggested above. BOND OF STEEL TO CONCRETE IN A BEAM The bonding of the steel to the concrete is discussed on page 429, the values being based on the resistance to slipping of a steel bar imbedded in concrete. In a reinforced concrete heam the bond of the steel per unit of length must not exceed its safe working value. The concrete sur- rounding the steel acts as a web between its tensile and compressive parts, and the pull in the rods as it becomes less and less, because of the reducing bending moment, passes into the beam, thus producing a bond stress between the steel and the concrete. If the bond is insufficient the rod will slip. Care must be taken that the size of horizontal bars in a beam is not too large to give sufficient bond surface between the steel and the concrete. Using the formula suggested by Prof. Talbot,* let V — total shear. V = shearing unit stress in lb. per sq. in. u = bond unit stress in lb. per sq. in. of surface area of tension steel. = perimeter of bar in inches. * Bulletin No. 4, University of Illinois, 1906, p. 19. S34 A TREATISE ON CONCRETE So = sum of perimeters of all horizontal tension bars at section consid- ered. jd = distance between centers of tension and compression. d = depth from surface to center of tension steel. Then* (36) and 2o = - — (36a) jd So jdu These formulas apply to tension steel only. The unit bond stress recommended by the Joint Committee for con- crete whose strength is 2 000 pounds at 28 days is 80 pounds per square inch, and assuming also as a close approximation thdXjd=i d, the total perimeter of bars which is required at any point of a beam is So = -L (37) 70 rf The bond stresses being dependent upon the shear are, in a uniformly loaded beam, the maximum at the supports and decrease towards the middle. With concentrated loads, the maximum bond is at the sup- port and is constant between the support and the nearest load. In continuous beams at the support, this formula applies to the top steel which is in tension. Special attention must be paid to bond in footings. POINTS TO BEND HORIZONTAL] REINFORCEMENT The bending moment in a reinforced concrete beam decreases toward the ends, reducing in the same ratio the pull in the tension bars. Since these must be designed to take the maximum moment at the center of the beam, the steel at the ends, when the bars are carried horizontally through the whole length of the beam, is stressed away below its working strength. By bending up a part of the bars not required for tension, the inclined portion assists in providing for the diagonal tension, and by carrying the ends horizontally over the top of the supports the tension due to negative bending moment may be resisted there. * The formula may be derived from the relation of the bond to the shear. The tendency to slip, or the bond stress, is equal to the shearing stresses at the plane of bars be- cause both are caused by the increment of the moment (see p. 36S). Hence '«So= vb, from which, since V ^ V V = — then u = 7— r;- bjd 3d Zo REINFORCED CONCRETE DESIGN S3S The points where the bars may be bent may be obtained analytically.* It is easier, however, to obtain them graphically by means of the bending moment diagram. For uniformly distributed loads, one bending mo- ment diagram may be used for a number of cases. For concentrated loads diagrams have to be made for each particular case, but they are quickly drawn. Fig. 164 gives the bending moment diagram for simply supported beams, and also for the center span of continuous beams, and Fig. 165 for end spans of continuous beams. It may be noted that in the last two cases the curves for the negative bending moment are not a continua- tion of the positive bending moment curves. The reason for this is that the maximum positive bending moment is obtained for difEerejit posi- tions of the loading than the maximum negative bending moment (see P- 504-) I A A / c ' > ^ J 0} « d 1 d * 2 * /\i \ a 10 d a> d 00 d g ^ d 1/ \ d 6 6 V d \ y^ •^x V-^ b\^ l^^"' Fig. 164.— Bending Moment Diagram for Simply Supported Beams and for Center Span of Continuous Beams. {See p. 535.) To use diagram proceed as follows : Suppose that a beam is reinforced in the center with six bars of the same diameter. The bending moment resisted by each bar is one-sixth of the total bending moment. Divide the ordinate of the maximum bending moment from the diagram into six equal parts and draw horizontal lines through the points of division (see Fig. 164) ; then, the distance between two successive horizontal lines will give the amoimt of the bending moment resisted by each bar . From the diagram we see that if the required number of bars at the. centex is • Analytical treatment is given in editions of this book previous to igi6.. 536 A TREATISE ON CONCRETE six, only five are needed at point a, four at point b, three at point c, and so on. Points a, b, c, d, are theoretical points where one, two, and three bars respectively may be bent without overstressing the steel. To be well on the side of safety, it is advisable, however, to carry the bars beyond the theoretical points. A large proportion of the bars must not be bent at one place, neither must the angle of the bend be too steep. If the bars are bent at a steep angle and in one place, they suddenly stop being available as tensile reinforcement, and the stress in the remaining part will be increased suddenly with a consequent cracking of the beam at the point where the bars are bent up. An angle of 40° with the hori- zontal is satisfactory. A / / T / ^_>, s / -* / \ n « ^ SL ^ !Xa «^ « / \ a ffl 0) CO CO a 2 . / \ ^ to DO 0> 0) CO °. / \ q 'V \ 6 d d d d / 7 Fig. 165. — Bending Moment Diagram, End Span of Continuous Beams. {See p. S3S-) Having determined the points where bars may be bent see by the use of formula (39), page 539, that they are secure against slipping. When bars are cut short at the places of reduced bending moment, (see p. 499) care must be taken that the number of bars to be cut short at one point be small (preferably one at a time) and the place where each bar is cut be a sufficient length distant from the theoretical point. The short bars also must be positively anchored to the remaining reinforce- ment, or else to the concrete above the bars by a curved hook, or by some other practical method. To illustrate the danger of cutting off the bars without anchorage, suppose that at a certain point we have four bars and the figured stress in each of them at this point is 8 000 pounds. So far as the allowable stresses in steel are concerned, two bars may be omitted at this point. If two bars are cut short here, we would have, REINFORCED CONCRETE DESIGN S37 theoretically, in the long bars at the right of the point, a stress of 8 ooo pounds, and at the left, i6 ooo pounds. At the extreme ends of the short bars, there would exist an unbalanced stress of 8 ooo pounds. As there is no provision for the large increase in stress of the longer bars and no means of transferring the stress from the short steel to the concrete, the short bars would tend to slip and form a crack. On account of the destroyed bond between the short bars and the concrete, they would then not be available as reinforcement for quite a distance and the stress would be thrown on the long bars. The diagrams, Fig. 164 to 165, may be drawn to a large scale on trac- ing cloth, taking as a basis a span of say 10 feet. This diagram can then be used for spans of any length by multiplying the distances from the center to the point of bending bars by the ratio between the span and 10 feet. For dividing the bending moment into equal parts, the tracing may be placed over a cross-section paper on which the division lines may be marked. LATERAL SFACIIfG OF TENSION BARS IN A BEAM The parallel bars in a beam must be a sufficient distance apart to properly transmit the stress to the concrete in the beam and prevent cleaving the concrete between the bars. In practice it is advisable to make a rule that the rods shall not be spaced nearer together in the clear than i| times their diameter with I inch as a minimum. The minimum distance of the rods from the sides of the beam should be i| inches in the clear. There is less danger of vertical than of horizontal splitting and where two layers of rods are used, the rods in a vertical plane may be placed directly over each other with sufficient space to permit the mortar to run between them. A limiting clear space of one-half inch is usually sufficient. Prof. McKibben has suggested a mathematical method for deter- mining the width of concrete required between the bars in order to make the resistance in shear equivalent to the adhesion of the concrete to the steel. A beam may fail in bond either by breaking the adhesion of the bars and the concrete around their whole circumference, or by shearing through the concrete between the bars on a plane with their centers and breaking the adhesion between the upper half of the bar and the con- crete. To make the factor of safety equal for both cases, the shearing strength of the concrete between the bars must be equal to half the ad- hesion of the bars to the concrete. For a working bond unit stress, 538 A TREATISE ON CONCRETE M= 80 lb. per sq. in., and a working direct shearing unit stress d= 120 lb. per sq. in., and letting 5j = distance in the clear between two bars in inches. i = diameter of bar in inches. Then* 5j=i.os i (38) Since the concrete is not easily placed between the bars, it may have a lower shearing strength there so that the lateral spacing of bars sug- gested above, is recommended. DEPTH OF CONCRETE BELOW BARS The selection of the thickness of the concrete below the bars is governed more by the proper fire and rust protection of the metal than by the stresses in the beam. Prof. Charles L. Norton considers a thickness of 2 inches essential for efficient fire protection. (Seep. 289.) Since an excessive thick- ness adds to the danger of cracking, because the tension in the concrete increases with the depth below the steel, this thickness, measured from the lower surface of the steel, and not from its center of gravity, may be taken as a maximum. For secondary members and floor slabs, J inch to 2 inches is enough. The following thicknesses of concrete below the steel may be em- ployed under ordinary conditions: Thickness of Concrete below Steel. Depth of slab or beam, Thickness below lower surface of inches rods, inches li to 2 1 2* to 4 f 4i to 8^ I 9 to 12 ij 13 to 18 ij 19 to 20 if Greater than 20 2 The Joint Committee, 1916, recommends 2 inches for columns; ij inches for beams; and i inch for slabs. 'For a short length of bar (, equate the strength in shear of the concrete between the bars to the adhesion between the concrete and the upper half circumference of the bar. Hence, if m = unit bond between steel and concrete, S/^lv = .9, = T.57 — i For M ^ 80 and v = 129 m; si = 1.05 i. REINFORCED CONCRETE DESIGN 539 LENGTH OF BAR TO PREVENT SLIPPING In cantilevers and restrained beams, also in the ends of cotumns, the full stress in the steel exists at the point of support. Therefore to trans- fer the stress from the bar to the support, the bars must be anchored to the support. The simplest means of anchoring is by imbedding the bar in the concrete of the support for a sufficient length beyond the point of maximum stress so that the bond (that is, the resistance to slipping) of the bar in the concrete is great enough to resist the direct tension or direct compression in the body of the bar. The support must be strong enough to withstand the stress transferred by the anchored member. Whenever it is necessary to splice tension steel, the length of the lap is determined by the safe bond stress for the stress in bar at the splice. Unless a bar is bent up or anchored by some mechanical means (see P- 438) the length of imbedment (also of lap) necessary to develop a re- quired holding power through bond may be determined thus: Let fs = actual tensile or compressive stress per square inch in the bar. i = diameter of bar in inches. u = bond in pounds per square inch of surface. h = necessary length of imbedment of bar in inches. Then,* for both square and round bars, h=^l^i (39) For 1:2:4 concrete of 2 000 lb. per sq. in. crushing strength, the necessary length of imbedment is Plain Bars, Deformed Bars, u = 80 lb. per sq. in. u = 100 to 120 lb. per sq. in. /s = 16 000 h = 50 i fs = 16 000 h = 40 i to 33 i fs = 18 000 h = $6 i fs = 18 000 h= ^s i to 37 i For steel in compression, the stresses, fs, usually vary between 7 000 and 10 000 lb. per sq. in. The required length of imbedment, therefore, is smaller than given above for steel in tension and may be taken from table given on page 540. • It the bar is round the total force to be developed in the body of the bar is • /, while the 4 holding power of the bar, or its resistance to slipping is wiul. Equating these and solving for (, we fs obtain h — i — *• S40 A TREATISE ON CONCRETE Length of Imbedment Required for Round or Square Bars. STRESS IN STEEL f^_ lENOTH or BARS TO IMBED IN TEEMS OP THE DIAMETER. Allowable bond stress, pounds per square inch. Lb. per sq. in. 40 60 80 100 120 6 OOO 38 25 19 IS 13 8 OOO SO 33 25 20 17 10 OOO 63 42 31 25 21 12 OOO 75 50 37 30 25 14 000 83 S8 44 35 29 16 000 100 67 50 40 33 18 000 "3 75 56 40 38 20 000 125 83 62 50 41 Note: The length of imbedment may be obtamed by multiplying the value selected from this table by the diameter of the bar. Recommendations as to the Size and Shape of Hook. Another expe- dient used is the bending of the end of the bar into a hook. The effec- tiveness of the hook, as shown by tests (see pages 438 to 439), depends to a great extent upon the strength of the concrete. In transferring the stress from the bar to the concrete, the hook exerts bearing stresses on concrete, which for a properly designed hook must not exceed the safe bearing stress on the confined concrete. The best anchorage is obtained by a combination of straight imbedment and a semi-circular hook, the diameter of which is at least four times the diameter of the bar. To insure against splitting of the concrete, it is advisable to place a cross-bar of proper length against the hook to distribute the bearing stresses on a large area of concrete. With a hook designed as suggested above, the elastic hmit of the steel can )e reached without causing excessive secondary stresses in concrete. FLAT SLABS The term "flat slab" is generally applied to the type of floor con- struction which consists of a flat plate, with no beams or girders, con- tinuous over the whole floor and supported by columns only. To reduce the thickness of the slab the column head is enlarged, thus shortening the span and increasing the shearing resistance at the sup- port. The thickness of the slab at the center may be still further re- duced and the rigidity of the structure increased by the use of a drop panel, or plinth resting on the column head. The sizes of column head and drop panel are discussed on page 551. REINFORCED CONCRETE DESIGN FLAT SLAB SYSTEMS 541 Several systems of reinforcement for flat slabs have been developed. These may be classified, accorduig to reinforcement, as the four-way, the two-way, and the circumferential system. Four-way System. The four-way system, introduced by Mr. O. W. Norcross and Mr. C. A. P. Turner, consists of four bands of parallel ft — TT Mil ,. I I I I I I V\ /I I I I I I I I iKr rS-^ J- Section on A A Section on B B Fig. i66.— Four-Way Flat Slab System. (See p. 541.) bars of small diameter placed lengthwise, crosswise, and in both diagonal directions, across the panels from column to column and across the columns, as shown in Fig. 166, page 541. All the bars are sometimes bent up over the column head, but the authors recommend that only two bands — usually the diagonal — be bent up at about the one-fifth point of the. span to serve as tensile reinforcement, and that the other two bands continue across the column at the bottom of the slab to serve as compressive reinforcement. The compressive stresses in the slab at 542 A TREATISE ON CONCRETE the column head are sometimes high, but with only a single span loaded, the bottom of the slab is in tension. In either case the bottom of the slab should be reinforced. Two-way System. The two-way system, developed by the Condron Company and the Corrugated Bar Company, consists of bars placed in two directions only, as shown in Fig. 167, page 542. The spacing of the bars right between the columns, where only one layer is used, is as f H 1 1 1 1 H 1 1 fttt "hH'h EEE = E-:::(:HM:::: i\.\i\.L J i i 1. i J. L_l 1 ^ 1 I 1. T " t 1 1 n _i_i ' . i 1 -S ! ! a ^ _ __ 7--r ;■- . I. ill . I \All.\ --» ■ "■- '.Zl\zttl'-\'-'-'-'. III.'. ... l wr i_--. J IhlilillllllLTl 11 1 11 ^7 u.>..M^^^^>..,^>riM>..J.■■.■,»,^vv■,^.l il,jllU,,l:^ Fig. 167.— Two-Way Flat Slab System. {See p. 542.) a rule closer than in the central portion of the slab where two layers of bars at right-angles are used. Part of the bars are carried through to serve as compressive reinforcement, and some of the bars are bent up at about one-fourth of the span and carried over the support to serve as negative bending moment reinforcement. Circumferential System. The circumferential system, (developed by Mr. Edward Smulski, (see Fig. 168, page 543,) consists of three types of units; one at the column head; a second between adjacent columns; REINFORCED CONCRETE DESIGN 543 and a third in the center of the slab. Unit A at the column head con- sists of a combination of rings and hairpin-shaped bars placed radially as shown in Fig. 168, page 543. The upper prong, longer than the lower, runs from within the column head out beyond the point of mflec- tion and serves as tensile reinforcement; the lower prong carries the compressive stresses; and the hook transfers the stress to the con- crete through bond and bearing. The inner ring keeps the inner ends of the radials in place and reduces the bearing stresses. The rings on Section on XY Fig. 168. — Circumferential Flat Slab System. {See p. 543.) top of the radials resist circumferential and, with the radial bars, radial bending moment. The steel in Units A and C follows pretty closely the contour lines shown in Fig. 169, page 544. ■ Units B and C consist of two and four trussed bars, respectively, supporting rings, and extending from center ring to center ring and hooked around them. These trussed bars increkse the steel at the column head. S44 A TREATISE ON CONCRETE The trussed bars are used to connect with the column head the parts of the slab under positive bending moment. The inclined part of the trussed bar, shown in section in Fig. i68, carries diagonal tension and the horizontal part in the top of the slab resists negative bending moment. The rings of the second and third units .(those between columns) overlap and bind together all parts of the slab. ._L Plan u_ JIX IT ^p^ "TT Diagonal Section Fig. 169. — Contour Lines. {See p. 544.) ACTION OP FLAT SLABS To get an understanding of the action of a flat slab consider its de- flection under load. Fig. 169 shows, by means of contour lines, the de- flection of one panel taken from a continuous floor where it and the surrounding panels were uniformly loaded. The contour lines are curves connecting the points of equal deflection, i.e., the points which, after loading, deflect an equal distance below the original level of the slab. The points were obtained by drawing cross-sections along the edge of the panel and along a diagonal section and plotting their deflec- tion curves. This curve of deflection, just as for continuous beams, is determined by the requirements that the tangents at the support and at the center of the span shall be horizontal and that the points of in- REINFORCED CONCRETE DESIGN 545 flexion shall be at about one-fifth of the span. Having drawn the deflection curves, the contour lines are plotted from the deflection curves. From the contour lines it is evident that a flat slab after de- flection assumes the shape of an umbrella at the column head, of a trough between the columns, and of a saucer in the central portion. Points of Inflexion. Since the bending moments change from nega- tive at the column head to positive at the center of the slab, there must be a line of zero moment, or a line of points of inflection surrounding each column. This line of points of inflection divides the slab into cir- cumferential cantilevers concentric with the columns and firmly clamped to them, and slabs extending between adjacent columns and supported on both ends, and square or rectangular panels supported on four edges. Stresses at Column Head. It is evident from the contour lines and lines of deflection that the portion of the slab at the column head, which acts as a circumferential cantilever, is subjected to a negative bending moment causing tensile stresses at the top and compressive at the bottom. Assuming the umbrella shape, the slab undergoes deforma- tion in two directions, namely, in the direction of the radius of any circle drawn on the slab around the column, and also along the circum- ference of the circle, because both the radius and the "circumference are increased by the deflection. The particles, therefore, are subjected to two stresses, radial and circumferential, acting at right angles to each other. The reinforcement at the column head, therefore, must be placed in two directions, preferably radial and circumferential. As explained in text books on mechanics, when a particle is subjected to forces acting at right angles to each other its actual deformation is smaller than if the stresses acted separately, because the deformation due to one force is decreased by the deformation of the force acting at right angles. The ratio of the decrease is equal to Poisson's ratio and is taken into account in fixing the constants on pages 547 and 548. Stresses in Central Portion. The central portion of the slab between the points of inflection is subjected to positive bending moment, caus- ing tension below and compression above. The portion of slab between adjacent columns develops stresses in one direction only since the con- tour lines are practically perpendicular to the center line through the columns. The portion in the middle of the panel, on the other hand, is stressed in two directions since the conditions there are somewhat similar to those at the column head, except reversed. In the first case the steel must be placed in one direction only, while in the other case it must be circular or placed in two directions. The bending moments recommended for design are given on page 547. S46 A TREATISE ON CONCRETE DESIGN OF FLAT SLABS In designing flat slabs the following points must be considered: (i) Stresses in concrete and steel at the column head due to negative bending moment. (2) Stresses m concrete and steel in the central parts of the slab due to positive bendirig moment. (3) Punching shear at the edge of the column capital. (4) Diagonal tension at the capital, and edge of the dropped head. Mid-Section 1 /Column Head^i Q Section / / / Outer Sect ion it Inner Section I Outer Section zl- J^ / h- Fig. 170. — Division of Flat Slabs. (See p. 547.) Bendini: Moments in Flat Slabs. The theoretical determination of bending moment is very compUcated, but simple formulas based partly on theory and partly on tests have been evolved which give safe results. For the purpose of determining stresses and bending moments the slab will be divided as shown in Fig. 170. Negative Bending Moment. The negative bending moment, which acts in radial and circumferential directions, may be resolved into com- ponents acting along sections at right angles to each other. One sec- tion shown in the figure as ABCDEF, follows the circumference of the column head, and the panel edge from column head to column head. REINFORCED CONCRETE DESIGN 547 The largest part of this negative moment is resisted by the portions ABC and DEF, called the column head sections, and whose projected width equals half the panel width. Section CD, half a panel wide, is called the mid-section. Similar bending acts at right angles to this section, and has the same relation to the column head and the panel. Positive Bending Moment. The maximum positive bending moment acts along lines at right angles to each other drawn through the center of the panel, one of which is shown as GUI J in Fig. 1 70. The sections GU and //, the combined width of which equals one-half of the panel width, is called the outer section, and EI the inner section. FORMULAS FOR BENDING MOMENTS FOR FLAT SLABS It is not necessary to use the full static moment, which would be obtained by following the method of analysis indicated above, because (i) The tensile resistance of the concrete appreciably reduces the stress in steel near support; (2) the stress in one direction is reduced by the resistance of the concrete in directions at right angles (see p. 476); (3) scarcely ever in practice are all panels of a floor fully loaded so as to produce maximum stresses at the column head; (4) experience with structures under load shows less stress and deflection than would be expected from the theoretical analysis. In view of these considerations the authors recommend the use of coefficients lower than the purely statical analysis would require.* They correspond substantially to the requirements of the Chicago Building Code introduced in 1914. Let w = total unit live and dead load. / = length of panel. c = diameter of column head. Square Panels. Negative Bending Moment. For a square interior panel, the total negative bending moment along the line ABCDEF may be taken as tV wlQ—lcy Of this bending moment, 85 per cent should be provided for in the column head section AB and EF, and the remain- ing 15 per cent in the mid-section CD. Square Panels. Positive Bending Moment. For a square interior panel the total positive bending moment along the line GHIJ may be taken as -jV wl {I — I c).^ Of this moment, not more than 60 per cent should be placed in the outer sections GH and //. Oblong Panels. The above formulas may be used for oblong panels in which the length of the panel does not exceed the width by more than •The final report of the Joint Committee, 1916, uses a coefficient for negative moment, 12%, and for positive moment about 16% higher than those adopted by the authors. 548 A TREATISE ON CONCRETE S per cent. In such a case the mean of the two sides should be taken as the length of span. For panels with larger variation in ratio of length to width, special formulas are required. In addition to the notation on page 547, Let h = width of panel. h = length of panel. Oblong Panels. Negative Bending Moment. For oblong panels on a section at the edge of the panel parallel to the width, h, as explained in connection with square panels, the negative bending moment may be taken as yV w^2 (^i - f c)^ and along the length, h, the value is tV '^h (.h - |c)2. This bending moment should be distributed as recommended in connection with square panels. Oblong Panels. Positive Bending Moment. For oblong panels the positive bending moment on a section through center of the panel paral- lel to the length, h, may be taken as -gV wh {k - I cY and on a section parallel to the width, h, as ^/o- w^i ih — I cY- The moments should be distributed among the inner and outer sections as recommended in connection with square panels. Units. In all the above formulas, if w is in Rounds per square foot and I, h, or k in feet, the bending moment is in foot pounds. To get inch pounds, multiply the result by 12. FLAT SLAB END PANELS End panels must be subdivided into two classes, (i) where the wall columns are provided with brackets and concrete spandrel beams; and (2) where the wall panels rest on brick walls or on steel spandrel beams. In the first case, the slab is partially restrained at the wall column , and in the second case, it is simply supported. End Panels with Spandrel Beams and Column Brackets. Since the slab is only partially restrained by the wall column , the bending moment at the first interior column head and in the center of slab is increased. First Interior Column Head and Center of Span. The bending moment at the first interior column head and in the center of the span along sections parallel to the wall should be increased by 20 per cent. No increase is necessary at sections perpendicular to the wall. Wall Column Head. The negative bending moment at the wall column should be 25 per cent smaller than given on page 547 for interior columns. Reinforcement should also be provided on the top of the slab at the juncture of spandrel and slab, the amount per foot com- wr- puted for a bending moment, — . REINFORCED CONCRETE DESIGN 549 Spandrel Beams. The spandrel beams must be designed to carry, besides the brick wall, the live and dead load from the slab for one- fifth of the distance between the wall column and the adjacent interior column. End Panels Resting on Brick Piers or Steel Spandrel Beams. Since the slab is completely unrestrained the bending moments must be in- creased above those where the slab is partly restrained. Negative Bending Moment. For panels resting on brick piers, increase the negative bending moment at the nearest column along sections par- allel to the wall by 30 per cent over that at interior columns. Positive Bending Moment. The positive bending moment at sec- tions parallel to the wall for interior panels should be increased 40 per cent over that given for interior panels on page 547. Provision for Negative Bending Moment along the Wall. If the slab is freely supported on the wall and no masonry is placed above it, there can be no possibility of any negative bending moment, there- fore, all the steel may be placed at the bottom. If the slab is restrained in any way there is a possibility of negative bending moment, and there- fore of cracks and some reinforcement should be provided and hooked at the wall end. It may extend to about one-sixth of the span and need not exceed 0.25 per cent of the concrete section. REINFORCEMENT FOR FLAT SLABS After determining the bending moment the required area of steel is found in the ordinary way. CSee formula (4a), p. 482). Only rein- forcement crossing the section under consideration should be taken as effective in resisting the bending moment at that section. The effec- tive area of bars crossing the section at an angle (as the diagonal bars in the four-way system or radial bars in the circumferential system) is found by multiplying their area by the sine of the angle between the bars and the perpendicular to the section. Since each' ring in the cir- cumferential system, is cut twice by any section, it may be considered as equivalent at that section to two straight bars, the sectional area of each being equal to the sectional area of the steel ring. PUNCHING SHEAR AND DIAGONAL TENSION Punching Shear. The punching shear at the edge of the column capital should not exceed the working value recommended on page 567. Diagonal Tension. The critical sections so far as diagonal tension is concerned are (a) at the column head, and (b) at the edge of the drop 550 A TREATISE ON CONCRETE panel. At the column head the measure of diagonal tension is the unit shear, v, determined from formula (32), page 517, at a distance out from the column capital equal to the thickness of the slab plus the depth of the drop panel. At the edge of the drop panel the measure of diag- onal tension is the unit shear, v, from forniula (32) page 517, determined at a distance out from the drop panel equal to the thickness of the slab. The unit shear so determined must not exceed 60 pounds per square inch for 1:2:4 concrete. Larger values for v than in simple beams may be used, because failure by diagonal tension is retarded by the resistance of the slab adjoining the plane at which diagonal tension was figured. In both of the above cases the total shear V in the formula is the vertical shear at the sections at which the unit shear is being figured. DETAILS OF DESIGN OF FLAT SLABS. Steel at the Column Head. If bands of steel are used, the reinforce- ment must be bent up and securely held at the proper distance above the form. The bands should be arranged in such a way that the nega- tive bending of the steel is available where required. If the bars are extended beyond the column head and are assumed to take the bend- ing moment on the opposite side of the column, they must be extended at least 6 inches beyond the point of inflection. The bars at the column head must be securely wired together so as to avoid the danger of mis- placing during the pouring of the concrete. If practicable, the bars running over the columns shall be placed between those coming from the opposite direction so as to allow proper imbedment for all the bars. If the bars are not carried far enough across the column to serve as nega- tive bending moment reinforcement, they must be extended a sufficient distance to develop their full strength. It is suggested that in such cases the bars should extend beyond the line through the center of columns 60 diameters with a minimum of 3 feet to allow for any discrepancy in the length of the long bars, and also to provide for any possibility of the bars extending farther over on one side than on the other, contingencies which are very apt to occur in the construction. Bars should be actually bent and never allowed simply to sag to place, because the steel area will fall off more quickly than the bending moment so that the slab will be actually weaker away from the column than at the column head. This weakness does not show during the early stages of the loading because the concrete area is sufficient to take the stresses, but if the loading is con tinned,, the slab eventually fails by REINFORCED CONCRETE DESIGN 551 tension in the concrete instead of by tension in the steel. A good illus- tration of this case are the tests to destruction by Prof. Wm. H. Kav- anaugh.* The failure of the slab occurred outside of the column by the breaking of the concrete. In the circumferential system the rings at the column head should be properly lapped to develop the strength of the bars by bond as recommended on page 539. A still better plan is to hook the bars down when the hooked ends may be used as a chair to support the unit. Column Heads. The column head may be considered as starting where the thickness below the slab is at least 2 inches and the shape of its cone must be such that the angle with the vertical must in no place be larger than 45°. The size of the column head is dependent upon the shear and compression in concrete. It is advisable to make the column head of a diameter equal to at least 0.225 of the span. The punching shear, as explained on page 520, must not exceed 120 pounds per square inch for 2 000 pound concrete, and the shear at a distance from the column head equal to the thickness of the slab (which may be consid- ered as the measure of diagonal tension) must not exceed 60 pounds. The cross section of the column head may be either octagonal or round. The forms are made of wood or of metal. In the latter case there is opportunity for ornamental treatment. Drop Panel. The thickness of the slab at the column head may be increased by the introduction of a drop panel (sometimes called a plinth) either to decrease the shear or reduce compressive stresses. The width of the drop panel should be 0.4 of the span and its thickness should be limited to 0.6 of the depth of the slab. The use of the drop panel reduces the amount of steel at the column head, but it complicates the form work. In many cases it is unneces- sary. Thickness of Slab. The thickness of slab is governed by the bend- ing and shearing forces and sometimes, in the slabs, by deflection. Let t = total thickness of slab in inches. L = panel length in feet. / w = sum of live and dead load, pounds per square foot. Then, / = 0.023 L y/w. In no case should the slab thickness be less than 6 inches or less than -sx L. Roof slabs should be Umited to ^ L. • Flat Plate Theory of Reinforced Concrete Floor Slabs, by Henry T. Eddy, 1913, p. 71. SS2 A TREATISE. ON CONCRETE EXAMPLE OF BEAM AND SLAB DESIGN The use of the formulas given in the preceding pages can be best illustrated by the design of a floor bay consisting of slabs, beams and girders. The design of reinforced concrete structures permits of so many variations by locat- ing steel in different ways that more than one type of design for the same member is almost always possible. The dimensions and reinforcement shown illustrate common methods, and the ariangement of details in the different members is also given as typical. The principles of design follow the recom- mendations of the Joint Committee on Concrete and Reinforced Concrete, 1916. . ■ -. ^J. ^ u SECTION A-A -6 ft- T -18 FT, -6 FT.- PLAN Fig. 171. — Design of Floor System. (See page SS3.) REINFORCED CONCRETE DESIGN 553 The computations are given with but few comments, but references are entered to the pages upon which each part of the calculation is based. Example 8: Design a typical slab, beam and girder for a reinforced- floor to sup- port a live load of 250 pounds per square foot with columns spaced 18 by 19 feet on centers. Solution: The girder will be made 18 feet long and the distance between centers of beams 6 feet. The beams are 19 feet long on centers. Ti 1 t_i Refer to page Take allowable fiber stress in concrete, 650 lb. per sq. in. 573 Take allowable tension in steel, 16 000 lb. per sq. in. 573 Take ratio of elasticity of steel to concrete, 15 477 Take direct shear in concrete, 120 lbs. per sq. in. 573 Take shear in concrete involving diagonal tension, 40 lb. per sq. in. 5 73 Take bond between concrete and plain bars, 80 lb. per sq. in. 573 Notation used in Example is Joint Committee standard 353 Slab. Span of slab is 6 ft. Live load, 250 lb. per sq. ft. Assumed dead load, 50 lb. per sq. ft. Total loading, 300 lb. per sq. ft. ^7- ^00 X 6^ X 12 Use for moment, if = — , then M*= - — — — — = 10 800 in. lb. i;i2 ■ 12 ' 12 ^ Same value may be found directly from curves 606 Since /c = 650, /s = 16 000 and » = 15, then Ci = 0.028 and p = 0.0077, from table on page 483 Hence, depth to steel is, d = 0.028 y 10 800 = 2.9 in. 485 Taking J in. concrete below steel, thickness of slab is 3! in. 538 Area steel. As, = 2.9 X 0.0077 = 0.0223 sq. in. per inch of width 485 Round rods f inch in diameter spaced s inches on centers will give required area. Table i. 574 The same results may be obtained by using the Slab Table 5: 580 Since this table is based on M = and we use here M = the total unit load of 10 12 300 pounds per square foot may be reduced by 5 or to 250 pounds and this value treated in the table, which gives a 3! inch slab. Rods must be bent up to give same steel at top of slab over supports. Beams. Span 19 feet. Distance between beams, 6 feet. Dead and Uve loads of the slab per foot of length of beam, 6 X 300 = i 800 pounds. Assumed dead load of stem of the beam, 200 pounds per foot of length. Total unit loading, 2 000 pounds. TT r ^ ir *"'* »u >f 2000X19^X12 . , • Use for moment J/ = , then M = = 722 000 men pounds. 12 12 Reaction at support, which is the maximum shear, is ,,. 2000 X 19 J y = = 19 000 pounds. 2 Breadth of Flange. Taking 12 times the thickness of slab plus the breadth of stem of beam (assumed as 10 inches) ft = (r2 X 3i) + 10 = SS inches. • Only one 12 is inserted in the numerator to change the 6 ft. to inches because the 300 is pound per foot 55* 'i TREATISE ON CONCRETE Minimum Depth. The minimum depth, or depth at which steel and concrete stresses are the maximum permissible, must be found by trial. Assume a depth, d. and find from Table ii, page 386, the value of Cd and from Table 12, page 587, the corresponding value of /. Then from formula (17) page 489, compute the mini- mum depth. If it does not check the assumed depth closely another computation must be made. In this case assume d = 11 inches. Then 3 = 0.34 and, from a Tables 11 and 12, Cd = 45 and 7 = 0.876. (See also example, p. 587.) , 722 000 X 45 • V mmunumrf = —r-^ -r:— ^'^tt = 11.2 mches. 0.876 X 16 000 X SS X 3.7s A larger value of d will be used in order to reduce the steel. Cross-section of Web as Determined by the Shear. V = ig 000 pounds (see above) hence Refer to page y (d-L\> I9_ooo ^^ ^ formula (16), 489 \ 2/ 120 / / r M Economical Depth. From formula (19), rf = \/7~n7T' '^ ^^^ ratio of unit 2 \ J s /\ cost of steel to cost of concrete, »• = 70 490 for V = &,d — ' V = 9,d - b' = 10, d — 2 For convenience in placing steel take b' = 10 inches, d = 2o| inches, /» = 22§ inches; hence b' Id- -j — 186. 537 With this value of d,j = 0.918. Table page 491, also Table 13, page 588 Sectional Area of Steel. From formula (20) 491 . 722 000 . , As = ■ — — — — = 2.4 square mches 0.918 X 20.5 X 16 000 4 round bars | inches diameter will be sufficient. Two of these may be bent up and lap over the top of the support 496 Steel at Top and Bottom. Negative bending moment at support equals positive M at middle or — M = 722 000 inch pounds. 512 At support the flange of T-beam being in tension is negligible and since four j-in. round bars are in tensile and two in compressive part of beam, the T-beam changes into a rectangular beam with steel in top and bottom. The ratios of steel in tension and compression are respectively 2.4 , , 1> p = — = 0.0117 and *' = -!- = 0.0058 10 X 20.5 ■^ 2 ^ With these values of p and p' and a = o.r we obtain, from Diagram 2 (p. 594), -^ = 1.5. Assuming,/ = 0.875, the maximum tension in steel is njc , M 722 000 ., „ js = -rj-r — ~S — '^ T, = 16 750 lb. per sq. in. 406 jdAs 0.875X20.5X2.4 " ' ^ ^y 2 = 19.85 inches or d = 21.7 inch. 2 = 18.7 " or (/ = 20.6 " / = 17.8 " or d - 19.7 it and fs 16 750 ,, REINFORCED CONCRETE DESIGN 555 All ui • ■ Refer to page Auowawe compression in concrete at the support may be 15% larger than that at middle, hence, no haunch necessary. ^qy Girder. Span 18 feet, breadth to use for T-beam, 59 in. (assuming breadth of stem as 14 in.) 48g Concentrated loads at ^ points. Assumed dead load of the stem of the girder, 360 pounds per linear foot. Load transmitted by the beams is considered as concentrated. Reaction of concentrated loads, F = 38 000 pounds. 503 Maximum moment of concentrated loads with ends of beam simply supported would be, Af = 38 000 X 6 X X2 = 2 740 000 inch pounds. 51 1 This corresponds to formula M = -— ; to correspond to Jlf = — it may be 8 12 g reduced by the ratio — or ■;i2 12 •' Q M = 2 740 000 X — = 1 827000 inch pounds. 12 Moment of dead load, M = 116 600 inch pounds, based on — . 512 Total moment, M = 1 943 600 inch pounds.* Minimum Depth. Assuming 4 = ^-4 nfc f M I 043 600 ,, . ^„, fs = TT-r- = —- — ^^ — — = 17 no lb. per sq. m. 496 jdAs 0.875X26.5X4.9 and fc = — "° = 815 lb. per sq. in. 496 1.4 X 15 H H which are excessive. Depth and Length of a Haunch. For depth try a = o.i, (Z = 28 inches 497 For this depth of beam the ratios of steel in tension and compression change , 26.5 _ , , J,/ _ 0.0125 fs From Diagram 2 (as before), -^ = 1.48 njc , I 943 600 i 11. ■ i. ^' = 0.875 X 28X4-9 ^ ' '°° '^- P" "'■ '"■ ^' and , 16 200 ,, . , ^' " 1 48 X 15 " "° ^^"^ ^"^^ '"■ '^^ This stress is allowable and the depth of haunch from top of beam of 28 inches will be accepted. Length of haunch may be approximated. Moment of resistance of beam without haunch. 496 Mr = 0.875 X 0.0132 X 16 000 X (26.5)2 X 14 = I 820 000 inch pounds. For- mula (18) Mh = I 943 600 inch pounds. 496 Hence from formula (28) length of haunch X = ; X 12 = 2.6 inches I 943 600 5 Since maximum negative moment occurs in middle of column and necessary length of haunch is only 2.6 inches, no haunch will be introduced outside of the column. Diagonal Tension Reinforcement of Beam. Vertical stirrups in beam on page 553 V = ig 000 pounds to = 2 000 pounds. 6' = 10 inches jd = 18.625 inches and the unit shear 11 = — - , — = 102 pounds per sq. in. (formula 32a), 517 Since this shearing unit stress is greater than 40 lb. per sq. in., stirrups are necessary. Diameter of Stirrups. From Table on page 525, the maximum diameter for stirrups with straight ends for a beam 20.5 inches deep is J-inch. However, since U-shaped stirrups with hooked ends will be used |-inch round bars will be selected. Location of Stirrups. Stirrups are unnecessary [with »=io2 lb. and !;' = 4o lb.] at a distance from the support : Xi= — l^~ — ) = 5.8 feet. REINFORCED CONCRETE DESIGN 557 Number and Spacing of Stirrups. Tensile value of one stirrup is Asfs = 2Xo.ii X16 000 = 3 520 pounds. Assume that stirrups take two-thirds of total diagonal ten- sion. Total diagonal tension to be taken by stirrups may be represented by a trapezoid similar to Fig. 159. Area of the trapezoid times width of stem, b', is i '"-^^ Xx, Xi2X6' = 32 9641b. Divide this total diagonal tension by value of stirrup in pull gives 9.3 or 10 as the number of stirrups. The same results may be obtained more easily from Table 9, p. 585. Spacings of stirrups from this table, for — , =« — = 2.55 V 40 are 4-9. 5-2, S-3, 5-7, 6.1, 6.4, 7.0, 8.0, 8.9, 10.6 in. The same result may be obtained graphically. (See p. 526.) MISCELLANEOUS EXAMPLES OF BEAM AND SLAB DESIGN. Example 9; A^That is- the value of C and the ratio of steel if pressure in concrete is limited to 500 pounds per square inch and pull in steel to 14 000 pounds per square inch, the ratio of moduli of elasticity being 15? Solution: Approximate values, which are sufficiently exact, may be obtained from the Table 15, page 596, from which C equals 0.114, and ratio of steel, p = 0.0062. Example 10: What is the value of C for a beam in which the pressure in the con- crete is 650 pounds per square inch, the pull in the steel 16 000 pounds, and the area of steel 1.0%, the ratio of moduli of elasticity being 15? Solution: The requirements in the example are impossible. With the pressure in the concrete limited to 650 pounds per square inch, the pull in the steel, if 1.0% is used, cannot be as high as 16 000 pounds. From Tabje 15, page 596, whfen p = o.oio and fc = 650, C = 0.093 ^nd the pull in the steel is 14 000 pounds. Further- more, comparing this item witli the line for 0.008 steel in the same table, it is evident than an increase of 25% in the area of the steel, i.e., from ratio 0.008 to ratio o.oio, decreases the value C, and therefore the depth of beam, only about 3%. Example 1 1 : What safe load per square foot can be supported by a slab 5 inches thick ^.nd lo-foot span reinforced with J-inch round bars placed 8 inches apart? Solution. From Slab Table, page 581, since the given reinforcement from page 574 is equivalent to 0.196 X ij = 0.294 square inches for one foot of width, we find by inspection that for a 5-inch slab the nearest area of steel in column (18) is 0.288. Hence, the total safe load for a lo-foot span is slightly more than 136 pounds, say, 140 pounds per square foot; and deducting the weight per square foot of the slab, colunm (15), gives 140 — 64 = 76 pounds per square foot safe live load. If slab is square, contintfous and reinforced in two directions,, the safe load of 140 pounds may be multiplied by 2. Deducting the dead load of 64 pounds, the live load will be 280 — 64 = 216 pounds per square foot. Example 12; What safe load per square foot can be placed upon an 8-inch slab 16 foot span, having steel reinforcement of 0.007? Solution: Since by Rule 3, on page 580 total loads are inversely proportional to the squares of the span, the load for. a 16-foot slab is J the load for afi 8-foot slab. For the total safe load of an 8-foot slab, we must interpolate between steel ratios of 0.006 and 0.008, thus obtaining 649 -f 831 2 = 740 pounds per square foot. For the 16-foot slab the total safe load is therefore — = 185 pounds, and deducting the weight of the slab from column (15) gives a 4 net live load of 185 — 103 = 82 pounds per square foot. SS& A TREATISE ON CONCRETE Example 13: Using Table 4 of rectangular beams, page 578, what should be the dimensions and reinforcements of a beam 12 feet span, continuous and loaded uni- formly with I 000 pounds per foot of length? Solution: The assumed stresses are the same as those adopted in the Beam Table. Assuming a width of beam 12 inches, a total load per inch of width of —— = 84 pounds per running foot. Referring directly to the Beam Table, we find that the total depth corresponding to a 12-foot beam with this load is about 12 inches. The reinforcement from column (25) is 0.083 X 12 = i.oo square inch. Example 14: What total load per foot of length can be carried by a 12-foot simply supported beam 12 inches wide and 25 inches deep? Solution: There is no value in the Table 4, page 578, for a beam whose total depth is 25 inches, but since, from rule 4, loads are proportional to the square ofthe depth of the steel, we may calculate the load in this case from the load for a 26-inch beam 12 inches wide. Assuming in both cases that the depth to steel, d, is 2 inches less than the total depth, we have 364 X —^ X 12 = 4 000 pounds per running foot of beam. Since the table is based on M = — for simply supported beams, deduct 10 20% from the above amount. Hence the safe load is 4 000 — 800 = 3 200 pounds. CONCRETE COLUMNS Columns or piers of short length, not more than four times the least lateral dimension, may be built of plain concrete with no reinforcement provided the loading is central with no possibility of side thrust. The carrying capacity of such columns may be determined by multiplying the safe unit stress as given on page 573 by the effective cross-sectional area of the column. The unit stress is determined by dividing the load to be sustained by the effective area. Let P = total load. A = effective area of crtiss-section of column. fc = allowable compressive unit stress in concrete. Then P P P=Af, -(40) A==— (40a) /, = - (40b) Ic A Efiective Area in Columns. The compression area used in computa- tion should ordinarily be less than the total area to allow for surface damage in case of fire. An extra thickness where fireproofing is needed, varying from one to two inches in accordance with the inflammability of the contents of the building, should be allowed. The Joint Com- mittee recommends that the protective covering shall be taken to a REINFORCED CONCRETE DESIGN 559 depth of i| inches where fireproofing is required since in a severe fire the concrete to this depth may be affected by the heat. The effective area of a hooped column must be taken as that within the hooping both for fireproofing and for strength. Fireproofing. The steel in all cases should be imbedded at least i| to 2 inches. Where the fire risk is great, round columns should be used, as experience teSches that these suffer much less from extreme heat than square columns. Rounding or beveling the corners of square col- umns is always advisable. DESIGN OF REINFORCED CONCRETE COLUMNS Columns must be provided with reinforcement consisting either of vertical steel bars or of hooping, or a combination of the two. Concrete is especially adapted for sustaining compression on account of its comparatively large compressive strength and its cheapness. Therefore, when conditions permit, the minimum allowable percentage of vertical steel should be used. For ordinary conditions, bars having a total cross-sectional area of 1% of the effective area of the column may be considered a minimum requirement. In building construction, it usually is difficult to keep the size of the columns, especially in the lower stories, within the limits required by the uses for which the building is constructed. To reduce the size of the columns, the following meth- ods may be used separately, or in combination. (i) Rich proportions of concrete. (2) Increased amount of vertical reinforcement. (3) Hooping with or without vertical steel. (4) Structural steel shapes in combination with the concrete. Rich Proportions of Concrete. The cheapest way of increasing the strength of a column is by using rich proportions of concrete, since the compressive strength of concrete is approximately proportional to the amount of cement which it contains. (See p. 454.) A rich concrete also works smoother in placing so that it is easier to produce a homo- geneous column. The strength of concrete for different mixtures is indicated on page 315, and recommended working stresses are given on page 573. Vertical Steel Bar Reinforcement. The column may be strengthened by the introduction of vertical steel up to about 6% of the effective area of the concrete. Ordinarily it is not advisable, however, to use more S6o A TREATISE ON CONCRETE than 4% on account of the dfficulty in accommodating any larger amount of steel, especially when the reinforcement is spliced by lapping. Tests given on page 455 prove positively that the steel imbedded in concrete takes its proportion of compressive stresses as indicated in formulas (41) to (45), page 562. Hooped Columns. As shown by the tests, hooping, if properly applied-, increases the ultimate breaking strength of the column. The deforma- tion, however, corresponding to the ultimate strength is excessive, so that the working stress in a hooped column must be based on the elastic limit of the column and not on ultimate strength (see tests, page 458). Hooped columns without • vertical steel are flexible and their use is not recommended. Hooped columns with steel reinforcement are tough and more reliable than reinforced concrete columns with vertical steel only. If continu- ous spiral hooping is used, the danger of sudden failure, especially during construction, is lessened. An amount of spirals beyond 1% of the total volume of the column within the hooping does not seem to in- crease the elastic limit of the column so that it is economical to limit the amount of hooping to 1%. Not more than 6% of vertical steel should be used. Recommendation for Column Design.* As a result of tests and practice, the authors recommend as follows: {a) Piers, the length of which does not exceed four times the least lateral dimension and in which there is no danger of bending, may be built of plain concrete with allowable unit stresses given on page 573. {b) Columns reinforced with not less than 1% of vertical steel and not more than 6%,t in which the unsupported length does not exceed fifteen times the least lateral dimension, may be de- signed by formulas on page 562 with unit stresses given on page 573. For longer columns, the working stresses should be reduced as stated on page 466. (c) Columns reinforced with structural shapes, the area of which exceeds 6% of the cross-sectional area of concrete, may be de- signed as specified on page 563. * These recommendations agree with those of the Joint Committee on Concrete and Reinforced Con- crete except as indicated. t Joint Committee limits the amount of vertical steel to 4%. REINFORCED CONCRETE DESIGN 561 {d) Hoops and bands should not be figured as adding directly to the strength of the column. (e) Columns should not be designed with hoops alone. (/) Columns reinforced with not less than 1% and not more than 6%* of longitudinal bars and with not less than 1% in bands or hoops may be given a working stress in concrete 55% higher than columns with vertical steel only. The ratio of unsup- ported length to the diameter of the core in such columns must not exceed 10. If for 2 000-lb. concrete, the unit work- ing stress in concrete for columns with vertical steel only is taken as 450 lb. per sq. in., the hooped and vertical reinforced columns may be thus given 700 lb. per sq. in. To the strength of the concrete in the column also must be added the strength of the steel according to the formula given below. Design of Columns with Vertical Steel only and of Hooped Columns with Vertical Steel. The formulas given below apply to columns with vertical steel bar reinforcement and also to hooped columns. The dif- ference between the two types is taken care of in the unit stress. The unit stresses, /c, recommended, are given on page 573. The derivation of the formulas is given on page 376. Let / = allowable average unit pressure upon the reinforced column, equal to the total load divided by the effective area. fc = allowable unit pressure upon the concrete of the column. /j = allowable unit pressure upon the vertical steel in the column. -p « = -r = ratio of modulus of elasticity of steel to modulus of elasticity Ec of concrete. P = load to be sustained by the column. A = area of total effective cross-section of column (see p. 558.) Ac = area of concrete in cross-section. As = area of steel in cross-section. A — = p= ratio of cross-section of steel to cross-section of column. A Formulas to be Used in Reviewing Columns Already Designed. Find safe load, P. Given: unit stress, /„• effective cross-sectional area of column, A; area of steel, A^. * Joint Committee limits the amount of vertical steel to 4%- S62 A TREATISE ON CONCRETE P=fAA + {n- i) A,] or (41) P=f,A[z + in-i)p] (41b) Find unit stress in concrete, fc, and in steel, /j. Given: load, P; effective area of column, A; and area of steel, A^ = pA. f^ = or (42) A + {n--L)A, fc = ; (42a) ^' A[i + {n- i) p] f's =nfc (43) Formulas to be Used in Designing Columns. Find required area of sled, A^, or required ratio of steel, p. Given: load, P; unit stress, fc', and effective area of column, A . -1. = ^^^ (44) P=r-^ (45) n~ I (n — I) A Relation between the average unit stress, /, (which equals the load, P, divided by the effective area. A,) and the allowable unit stress in con- crete, fc; f = ^-fcU + {n-i)p] (46) A Values of / for different percentages of steel are given on page 599. Data for Designing Spirals. The following formulas can be used to advantage in determining the pitch of the spirals, length of spirals, and weight of spirals. Let d = diameter of column in inches. As = cross-sectional area of wire used for spiral. s = pitch of spiral in inches. L = length of spiral in feet per height of column. h — height of column in feet. REINFORCED CONCRETE DESIGN 563 Then Pitch of spiral* for given percentage of spiral reinforcement and cross- sectional area of wire is If As is in square inches and d in inches, the pitch is in inches. Where one per cent of spirals is used as recommended on page 561, the pitch of spiral equals 5 = 400-^ (48) a Total length of spiral in feet in a column of a given height, h, in feet, and a given pitch, s, in inches, equals L = T — (49) The weight of spiral can be obtained from the above formulas by multi- plying the length of spiral by the weight per foot of bar used for spirals. The above formulas are approximate because they consider the length of spiral as equal to the circumference of the column. The error is largest for small diameters of columns and large pitch, as then the difference between the actual length of spiral and the approximate length of spiral is largest. For columns ordinarily used in practice and small pitch, the error is only a fraction of i per cent. The maximum of error in spacing of spirals in any case does not exceed 2 per cent. COLUMNS WITH STRUCTURAL STEEL ^ Structural Steel Reinforcement. Sometimes, when, in order to reduce the size of the column, larger percentage of steel is required than 4%, structural shapes are used for column reinforcement. If small struc- * Above formulas were derived as follows: X.ength of spiral per pitch equals vd inches (because of the pitch, the circumference of the spiral can be taken as equal to the circumference of the column). The total volume of spiral reinforcement per foot of height of column for a given ratio of steel to concrete, p, equals ~Xt2XP = 3Trd'p 4 Since the length of spiral per pitch equals ird inches and its volume equals irdAs, the number of spirals per foot is obtained by dividing the volume of the required spiral reinforcement found above by the volume of one spiral, which is — . Finally the pitch of spu-al is obtained by dividing 12 inches by the number of spirals required per foot. 4^s Therefore, s =- - — • dp S64 A TREATISE ON CONCRETE tural members, such as angles, are used and the ratio of area of con- crete to the area of steel does not exceed 6%, the formulas given for columns with vertical bars may be used. It is advisable, however, to tie the angles by occasional tie plates, or lacing, to keep them in place during erection. In building construction, it is sometimes necessary, to reduce the size of colunm, to use structural steel columns of an area up to 15 or 20% of the concrete area. In this case, the column must be considered as a structural steel column strengthened by the concrete. The best struc- tural steel shapes to be used are shown in Fig. 142, page 463. When properly laced, the strength of such columns may be considered as equal to the strength of the structural column, computed in the same fashion as for structural columns not imbedded in concrete, plus the strength of the concrete core, — that is, of the concrete enclosed by the steel, which may be figured on the basis of the unit stresses recommended for the columns with vertical steel only. COLUMNS UNDER FLEXURE Columns subject to an eccentric load require special formulas: these are given in Chapter XX on pages 377 to 389. COLUMN TABLES Table 18, page 599, gives values for/, for different values of p and fc. Tables 19 to 21 give safe loads for columns of different diameters, with vertical steel and with spirals, for different mixes of concrete. For col- umn details see Chapter XXIII. COLUMN EXAMPLES Example i5: What size of square column reinforced with 2 per cent, of longitudi- nal bars without spirals will be required for a load of 94 000 pounds? Solution: By column (4), page 573, the allowable compression on 2 000 pounds concrete is limited to 450 pounds per square inch. For this allowable stress, using 2% of longitudinal reinforcement and a ratio of moduli of elasticity of 15, the area of column from formula (46), page 562, is A = 94000 450 (i -I- 14 X 0.02) = 163 square inches, corresponding to 12.8 inches square. Allowing 2 inches for protective covering gives 14.8 inches, or, say, 15 inches square. REINFORCED CONCRETE DESIGN 565 Example 16: What sectional area of vertical steel will be required for a round spiraled column liniited to 36 inches diameter, which has to bear i 000 000 pounds with pressure in plain concrete limited to 450 pounds per square inch? Solution: By column (4), page 573, in a column reinforced with vertical bars and 1% of spirals, the allowable pressure on the concrete may be increased 55% over that on plain concrete, hence /c = 450 + 55% = 700 pounds per square inch. Con- sidering the area within hooping equal to — ^^ = 858 square inches as efifective, the unit pressure from page 558, will be , _ I 000 000 = 1160 pounds per square inch. Assume n = 15, then by transposing formula (46), page 562, _ 1160 — 700 14 X 700 = 0.047, 3-nd area of steel A, = 858 X 0.047 = 4°-4 square inches. From table on page 574, 22 square rods if inches thick are chosen. Example 1 7 : What should be the area of a column 10 feet high supporting i 000 000 pounds, reinforced with 3.5% of longitudinal reinforcement and 1% of hooping for n = 1$ and an allowable compression in plain concrete limited to 450 pounds? Solution: Since the column is reinforced with longitudinal and hooping reinforce- ment, the unit compression on concrete may be taken as fc = 450 + $5% = 7°° pounds per square inch (column (4), page S730 Then from formula (46), page 562, the column area is , I 000 000 , . , A = -. — ; — r = goo square mcnes, 700 (i + 14 X 0.03s) requiring a 35-inch diameter inside the spiral. REINTOKCEMENT FOR TEMPERATURE AND SHRINXAGE STRESSES All masonry is subject to temperature cracks, but when they are dis- tributed in the many joints between bricks or stones they do not show so plainly as on the smooth surface of concrete. Expansion from a rise in temperature rarely causes trouble except at angles where the lengthening of the surface may produce a buckhng or a sliding of one portion of the wall past the end of the other. In a building, the walls and floors are generally so well bonded together and free to move S66 A TREATISE ON CONCRETE as a unit, that no provision need be made for expansion. In a structure like a square reservoir, the effect of expansion must be taken into account in the design to prevent failure at the corners. Contraction is often more serious, although cracks are by no means neces- sarily dangerous. To prevent cracking due to the shrinkage of the concrete in hardening (see p. 261) or to the lowering of the temperature, reinforce- ment should be inserted or joints formed to localize the cracks. (See p. 2S9-) Reinforcement properly placed distributes the contraction stresses so as to make the cracks very small, practically invisible, but it does not prevent them entirely. The steel must be sufficient in quantity, and should be of small diameter and placed as close as practicable to the surfaces to distribute the cracks and thus make them very fine. Deformed bars, that is, bars with irregular surfaces which provide a mechanical bond with the concrete, are more effective than smooth bars, and steel of high elastic limit also is advan- tageous. In practice, from tt of 1% to ttt of 1% (a ratio of 0.002 to 0.004) of steel, based on the cross-section of the concrete, is commonly used as tem- perature or shrinkage reinforcemenl:. The tensile strength of concrete is so low that a small change in tempera- ture will crack it. For example, the coefficient of expansion of concrete is 0.0000055 (see p. 261) and the modulus of elasticity is generally assumed as 2 000 000; therefore, the stress (see p. 400) per degree Fahrenheit is 0.0000055 X 2 000000 = iipoundspersquareinch, and a fall in tempera- ture of ^rr = 27° is sufficient to crack a concrete the tensile strength of which is 300 pounds per square inch. It is evident, and it has been proved by experience, that there is less cracking in concrete laid in cold than in warm weather. Longitudinal reinforcement is especially necessary in conduits which must be water-tight. Shrinkage cracks due to the hardening of the concrete may be prevented by keeping the concrete wet. (See p. 261.) It has been suggested by Mr. Charles M. Mills that the relation between the tensile strength of the concrete and the bond with the bars is an impor- tant factor in governing the size of the cracks, and the following analysis, based on his suggestions, gives a means of estimating the size and dis- tance apart of the cracks so as to form a basis for judgment as to the sizes and percentages of steel to use. The tensile stress in the steel at a crack tends to pull out the bars from REINFORCED CONCRETE DESIGN 567 the concrete, and referring to Fig. 172, the bond stress of the bar in the length ah must equal the tensile stress in the whole cross-section of the con- crete at b caused by the contraction of the concrete. Let X = distance apart of cracks. D = diameter of round bar or side of square bar. p = ratio of cross-section of steel to cross section of concrete. Then,* if, as is sufficiently accurate for practical purposes, the strength of concrete in tension is assumed to be equal to the bond between plain steel bars and concrete, the distance apart of cracks is D X = — ^ for square or round bars. 2/> The distance apart is inversely proportional to the unit bond*, so that a deformed bar having twice the bond strength would space the cracks one-half as far apart and allow them to be only one-half as wide. U- Fig. 172. — Reinforcement for Temperature Stresses. {See p. 567-) It is evident that the distance apart of the cracks is proportional to the diameter of the reinforcing bars, and inversely proportional to the percent- age of steel. From this formula is tabulated the estimated percentage of reinforcement for different spacing of cracks and different sizes of bars, assuming the bonding strength of the steel to the concrete to equal the tensile strength of the concrete. u = unit bond between plain steel and concrete. fs =" unit tensile stress in steel. D = diameter of bar. * In addition to above notation, let Ac = area of section of concrete. Ag = area of section of steel. = perimeter of steel bar. fc = tensile stress in concrete. Then Af. f/ = ^ uoxj or .* 2Ag Ao D , ^ D X = Also, — = — for both round and square bars, hence x = i — f a n t ^^ic If/'c ■ , and since ft == — S68 A TREATISE ON CONCRETE Estimated Percentage of Reinforcement for Different Spacing of Cracks DI8IANCE APART OF CBACKS WITH 12" 8" 18' 12" 24" 16" 36" 24" 48" 32" 60" DEFORMED BARS * 40" % % % % % % i" 1.04 0.70 0.52 0-3S 0. 26 0.21 *" 1.56 I .04 0.78 0.52 °-39 0.31 Diameter of round or side of i" 2.08 1-39 I .04 0.69 0.52 0.41 square bar. ...... { ¥' 2 .60 1-74 1.30 0.87 0.65 0.52 i" 3.12 ii.o8 -S6 1 .04 0.78 u. 62 i" 3.65 ^•44 1.82 1 .22 0.91 0-73 t'' 4-17 2.78 2.08 1-39 1 .04 0.83 Note : To express the steel as the ratio of area of cross-section of steel to cross-section of concrete, divide the percentages by 100; thus 1.04 becomes p = 0.0104. * Assuming the bond of deformed bars to be 50% greater than plain. The size of the crack is governed by the amount of shrinkage and for cracks due to temperature changes may be estimated as the product of the coefficient of contraction (0.0000055) by the number of degrees fall in temperature by the distance between cracks. Estimated Width of Cracks for Different Distances Apart WIDTH FOB DIFFERENT TEMPER- ATURE CHANGES 30° Fahr* 50° " 70° " DISTANCE APART 12" o. 0020 0.0033 0.0046 18" o. 0030 0.0050 0.0069 24" o. 0040 0.0066 0.0092 36" 0.0059 tj. 0099 U.0139 48" 0.0079 0.0132 o. 0185 60" o. 0099 0.0165 0.0232 From this, if it can be determined how large a crack will be allowable the corresponding spacing can be obtained. To avoid large cracks it may be necessary to use enough steel to prevent its passing its elastic limit. If the bars are continuous for such a length that the ends are practically immovable, as in a long retaining wall, a drop * 30° corresponds to a shrinkage of 0,017%; 50° to 0.028%; 70° to 0.038%. REINFORCED CONCRETE DESIGN 569 in temperature, tending to shorten them, produces a tensile stress which is independent of the distance between the restrained ends. Assuming the coefficient of expansion of steel the same as concrete and the modulus of elasticity of steel as 30 000 000, this stress is 30 000 000 X 0.0000055 = 165 pounds per square inch per degree of temperature, or for5o°Fahr. is 8250 pounds per square inch. This is well within the elastic limit of the steel and would not, of itself, cause the steel to take a permanent set. How- ever, since the concrete surrounding the steel will be continuous except at certain cracks, the stretch in the steel may be unevenly distributed and largely confined to the immediate vicinity of the cracks. If cracks occur while steel is unstressed, through the concrete shrinking, the steel tends to resist the shrinkage by tension at the crack and compression at the center of the block of concrete, and the tensile stress will be equal to the compressive and each equal to one-half the tensile strength of the concrete. This may be expressed by the following formula, using the foregoing notation:* Since the tensile stress in the concrete is liable to be low at the time shrinkage cracks are formed, it may be assumed, for illustration, as 200 pounds per square inch making 100 ^' = y This represents the stress due to local cracks which is additional to the temperature stresses above described. The total stress is, therefore, for 50° change of temperature 8250 -|- /^ or 8250 -f- — . If the elastic limit P of the steel is 40 000 pounds per square inch, and we must keep below this 100 40 000 = 8250 -f- — and p = 0.0031 P For steel, the elastic limit of which is 50 000 pounds per square inch, 100 50 000 = 8250 + — and p = 0.0024 These values of p represent the lowest theoretical ratio of area of cr^e- (section of steel to area of cross-section of concrete which can be used with- out the steel passing its elastic limit at certain of the cracks when the ends are restrained or the length is so great that intermediate parts are practi- cally restrained. * ^ = ^/>r/; = ^/: hence /; = ^/; S70 A TREATISE ON CONCRETE In view of the very slight stretch required to relieve the stress in the bars when the elastic limit is exceeded, and the probability of its distribution by the restraint to movement by the mass, it is not always essential to consider the elastic limit. SYSTEMS OF REINFORCEMENT One of the earliest recorded examples of the application of reinforced concrete is a boat of concrete and iron, built by Mr. L. J. Lambot in France, and shown at the Paris International Exhibition in 1855.* In 1861 Mr. Coignet began his investigations, and in 1866 Mr. Monier, to whom the invention of reinforced concrete is often attributed, applied the combination of concrete and iron to various structures, and laid the foundation for its future widespread applications. As long ago as 1872, Mr.' W. E. Ward,t at Port Chester, N. Y., built a house entirely of concrete, reinforced with iron I-beams and round rods. The rapid development of reinforced concrete has resulted in the intro- duction of numerous systems, many of them covered by patents, for arrang- ing the metal in the concrete, or for special forms of metal. These systems are fully described in the various French works on reinforced concrete.! A few of the systems, representing both the arrangement and the form of the metal, are described below, and forms of metal extensively used in the United States are illustrated in Fig. 173. Systems of Reinforcement Bonna. Metal of cruciform cross-section. Berlini. Girder Frame. Horizontal tension members with vertical stir- rups shrunk on to them. Chaudy and Degon. Cross rods passing under bearing rods, but looped up between them. Coignet. Round bars in top and bottom of beam connected by diagonal wire lacing. Columbian. Vertical steel plates with horizontal ribs. Corrugated. (See Fig. 173, page 571.) Coftacin. Round rods interlaced in the same manner as in wire netting. Cummings. Bars of diflerent lengths having their ends bent up to an incline and formed into a loop to resist internal stresses. * Christophe'S Beton Armi, 1902, p. 1. •j- Transactions American Society Mechanical Engineers, Vol. IV, p. 3S8. J See among others Christophe's Beton Arm^, 1902, pp. 10-71, and Morel's Ciment Arm^, 1902. pp. 88 to 152. REINFORCED CONCRETE DESIGN Cold Twisted Square Bax Corrugated Bars Kalin Wing Bars Havemeyer Bars / '4^/ /U / L / H Ti New Rib Bar Elcannes Bar Herringbone Bar '^ . Monotype Bar Fig. 173. — Types of Reinforcing Steel, {See pp. 570 and 572.) 572 A TREATISE ON CONCRETE Diamond Bar. Bars rolled round with parallel ribs passing along and around the bar forming diamond-shaped shoulders on its surface. Donath. Inverted T-beams or I beams connected by horizontal di- agonals of Ught, fiat metal on edge. Elcannes. (See Fig. 173, page 571.) Expanded Metal. Sheet steel, slit and expanded to form a diamond mesh. Ferroinclave. Sheet steel with inversely tapered corrugations to be covered on both sides with concrete. Gabriel. Deformed tension members with trussing of hard drawn wire. Habrich and Busing. Flat metal twisted hot. Havemeyer. (See Fig. 173, page 571.) Hennebique. A combination of alternate straight bars and bars with ends bent up at an angle, with vertical U-bars, or stirrups, of flat iron passing around the straight bars and reaching nearly to the top of the beam. Herringbone. (See Fig. 173, page S7i-) Holzer. Metal in form of I-beams. Hyatt. Flat plates or bars set on edge and pierced with holes through which pass small round rods to form the cross reinforcements. Johnson. Corrugated bars. KahnWing. (See Fig 173, page 571.) The horizontal flanges are sheared up at intervals to serve as diagonal reinforcement. Lock-Woven Steel Fabric. Steel wire mesh, locked at intersections. Lug Bars. (See Fig. 173, page 571.) Melan. Steel ribs, either I-beam or 4 angles latticed, imbedded in the concrete of the arch. Monier. Two series of round parallel bars at right angles to each other. Monotype. (See Fig. 173, page 571.) Mushroom. Flat floor slabs supported by columns with enlarged heads. New Rib. (See Fig. 173, page 571.) Parmley. Bars with bent ends, to place in the sides of a conduit or the haunches of an arch to resist tension. Rabitz. Various combinations employing galvanized wire. Ransome. Square steel rods twisted cold. (See Fig. 173, p. 571.) Roebling. Flat steel bars set on edge, clamped to supporting beams, and held in aUgnment by flat bar separators. SchuUer. Like Monier System except rods are placed diagonally. Triangle Mesh. Wire mesh reinforcement with transverse metal placed diagonally. Trussit. Expanded metal or herringbone lath bent to V-shaped section. Visintini. Beams of concrete, cored out so as to form lattice girders. Welded Wire Fabric. Wire mesh reinforcement with wires at right angles to each other and welded at intersections. REINFORCED CONCRETE DESIGN Working Unit Stresses 573 Kind of Stress^ (I) Bearing Axial compression. Columns (as de- scribed on page s6i) Compression, in extreme fiber Vertical steel i to6%t Vertical steel i to 4% and spirals 1% Ordinary. In continuous beams adjacent to the support. . Shear (punching shear) Beams without Shear (as meas- ure of diag- onal tension web reinforce- ment Notation and No. of formula . (2) Beams with web reinforcement . Bond . j Plain bars 1 Deformed bars... Steel in tension' Structural grade. . First class high carbon steel .... }c (41) to (46) fc (41) to (46) /c (4a) to (20) }c (4a) to (20) "(32) ■» (32) " (36) « (36) fs (4a) to (25) /i (4a) to (25) AJlowable Working Stresses. Percentage of crushing strength at 28 days (3) 32-5 22.5 22.5 32. S 32-S 37-S 6 For 2000 lb. Concrete. Lb. per sq. inch. (4) 650 45° 450 700 650 750 120 40 Remarks. 4 5 to 6 16 000 sq. 18 000 sq. 80 100 to 120 lbs. per in. lb. per in. (s) Length of pier not to exceed 4 diameters Length not to exceed 15 di- ameters Length not to exceed 10 di- ameters of core Use in beam formulas Two-thirds of this stress must be pro- vided for with web rein- forcement * Strengths at 28 days and other ages, and for different aggregates and different consistencies are given on pp. 310 to 329. t Joint Committee limits the amount of vertical steel to 4%. 574 A TREATISE ON CONCRETE TABLE 1. AREAS, WEIGHTS AND CIRCUMFERENCES OF BARS. Areas and Weights' of Square and Round Rods and Circumferences of Round Rods, One cubic foot weighs 490 lb. 1 11 a d i •si =1 h 13 1, 11 2. q'- 1' ■og' < l| f St r M •si •sl 313 5S •so 5S f 2 4.0000 3.1416 ' 6.2832 13.60 10.68 ^ 0.0039 0.0031 0.1963 0.013 O.OIO tV 4.2539 3.3410 6.4795 14.46 11.36 i 0.0156 0.0123 0.3927 0.053 0.042 4 4.5156 3.5466 6.6759 15.35 12.06 A 0.0352 0.0276 0.5890 0.119 0.094 A 4.7852 3.7583 6.8722 16.27 12.78 J 0.0625 0.0491 0.7854 0.212 0.167 i 5.0625 3.9761 7.0686 17.22 13.52 A 0.0977 0.0767 0.9817 0.333 0.261 A 5-3477 4.2000 7.2649 18.19 14.28 i 0.1406 0.1 104 1.1781 0.478 0.375 1 5.6406 4.4301 7.4613 19.18 '^■S^ A o.igi4 0.1503 1.3744 0.651 0.5 1 1 A 5-9414 4.6664 7.6576 20.20 15.86 i 0.2500 0.1963 1.5708 0.850 0.667 2 6.2500 4.9087 7.854^ 21.25 16.69 <^ 0.3164 0.2485 1.7671 1.076 0.845 A 6.5664 5.1572 8.0503 22.33 17.53 i 0.3906 0.3068 1.9635 1.328 1.043 1 6.8go6 5.41 19 8.2467 23.43 18.40 a 0.4727 0.3712 2.1598 > r.6o8 1.262 \l 7.2227 5.6727 8.4430 24.56 19.29 i 0.5625 0.4418 2.3562 1.913 1.502 f 7.5625 5.9396 8.6394 25.00 20.20 i 0.6602 0.5185 2.5525 2.245 1.763 \l 7.9102 6.2126 8.8357 26.90 21.12 0.7656 0.6013 2.7489 2.603 2.044 I 8.2656 6.4918 9.0321 28.10 22.07 a 0.8789 0.6903 2.9452 2.989 2.347 it 8.6289 6.7771 9.2284 29.34 23.04 1 1. 0000 0.7854 3.1416 3.400 2.670 3 9.0000 7.0686 9.424? 30.60 24.03 ^ 1. 1 289 0.8866 3.3379 3.838 3.014 A 9.3789 7.3662 9.6211 31.89 25.04 i 1.2656 0.9940 3.5343 4.303 3-379 \ 9.7656 7.6699 9.8175 33.20 26.08 -h 1.4102 1.1075 3.7306 4.795 3.766 A 10.160 7.9798 10.014 34.55 27.13 i 1.562s 1.2272 3.9270 5.312 4.173 i 10.563 8.2958 10.210 35.92 28.20 A 1.7227 1.353° 4.1233 5.857 4.600 A 10.973 8.6179 10.407 37.31 29.30 i 1.8906 1.4849 4.3197 6.428 5.049 1 11.391 8.9462 10.603 38.73 30.42 A 2 .0664 1.6230 4.5160 7.026 5.518 A 11.816 9.2806 10.799 40.18 31.56 i 2.2500 1.7671 4.7124 7.650 6.008 i 12.250 9.6211 10.996 41.65 32.71 ^? 2.4414 1.9175 4.9087 8.301 6.520 A 12.691 9.9678 11.192 43.14 33.90 f 2.6406 2.0739 5.1051 8.978 7.051 1 13.141 10.321 11.388 44.68 35.09 H 2.8477 2.2365 5.3014 9.682 7.604 \\ 13.598 10.680 ".585 46.24 36.31 I 3.0625 2.4053 5.4978 10.41 8.17.8 k 14.063 11.045 1 1. 781 47.82 37.56 i* 3.2852 2.5802 5.6941 11.17 8.773 ¥ 14.535 11.416 11.977 49.42 38.81 J 3.5156 2.7612 ^■H°A 11.95 9.388 i 15.016 11.793 12.174 51.05 40.10 H 3.7539 2.9483 6.0868 12.76 10.02 If 15.504 12.177 12.370 52.71 41.40 REINFORCED CONCRETE DESIGN 575 BEAM AND SLAB TABLES Beam Tables. Tables 2, 3, and 4, pages 576, 577 and 578, give the loading and reinforcement for beams, based on i inch of width under different conditions. For a beam 10 inches wide, for example, both the safe load per Unear foot and the steel area will be ten times the values given in the tables. The tables are for rectangular beams but may be used for T-beams which have a depth 3 or 4 times the thickness of slab by taking the width of flange as the breadth, b. Table 2 is for a simply supported beam and is based on a working compressive stress in concrete of 500 pounds per square inch and in steel of 14,000 pounds per square inch — lower values than are custom- arily used in construction, but required in many building laws. If the compression in concrete is Umited to 500 pounds, while 16,000 pounds is permitted in the steel, use the same loading but reduce the steel in the ratio of 16 to 14. Tables 3 and 4 are for ordinary design, approved by the authors and corresponding to recommendations of the Joint Committee. Slab Tables. Table 5 is for slab design with different working stresses in the steel and concrete. Ordinarily, the series at the top of the second page of the table is used. Table 6 is more convenient for review of beams already designed. It is computed by using formulas (8) and (10) on page 355, and select- ing the lower value of M. The most economical ratio of steel for the limiting stresses is p = 0.0077. For ratios lower than this the safe loads are governed by the tensile strength of the steel, while for larger ratios they are limited by the compressive strength of the concrete. Table 7 is for designing fully continuous slabs. Table 8 covers cinder concrete slabs. Stirrup Tables. Tables 9 and 10 give, respectively, the number and spacing of stirrups in uniformly loaded beams. T-Beam Tables. Tables 11 to 13 are for designing and reviewing T-beams. Beams with Steel at Top and Bottom. Table 14 and Diagrams i, 2, and 3 are for use in designing and reviewing beams with tensile and compressive steel. Tables of Constants. Tables 15, 16, and 17 are useful in giving constants in convenient shape for use in beam and slab design. Column Tables. Tables 18 to 21 are for designing and reviewing columns. Bending Moment Diagrams. Diagrams 4, 5, and 6 give bending moments for different spans and loads. 576 A TREATISE ON CONCRETE 10 g a o ^ P4 n 1 ^ ^ i-i ^ <>> > VO Pi •• o\ M o tH 1 o t^ ^ in :§ ^ X ^ .S H s P« -"!> 1 2 CO o n U) i2 n § i o s M W5 11 S ^ o s p< tin iv-i & I 11 CO 8 e !h K. S! ^ il=« ^ CO Pi O CO H hJ ^ a j; esse -S s^s) '-s:2 ■(asraopi 3JBS 3.S Otn to N *^ « H H N O r- « en r-vOoO MOO (0 0\H t^oo o COM O o 0«0i0 00 rr O-O CNOO « ■* r^ « to to O o lO NO to ffl ^f. O O O O O 'C O CT* 00 Nlrt B ui tj3JV I^aiS §■ ,^ « tOfO tn O O v-^cJ d d d d d Oi-O vnvo r^ o o o 6 6 6 ■O NCO 1^00 00 GOO d d d rt w -a- OvO O O H H d o o d d d 6 6 6 c* « « odd Jioiaq qjdaa -.5 ^O 0*^^ «u-nn IrtiOlO iflio O O O GOO loiom w" " " M H H M M M M M H Www « « « « W M ^ o o mm t^r- O O O o o o o o o GOO GOO GOO N T(-m«o t^r-oo 0> O M N to t un>o r- 00 O t^ COM H N to ■d-^ i> OsG H u^ Ov -^ mu^^O t^ 00 O* O M IN to u-j-O .'- 00 O H (Ou-> r-G « M to to CO "-. ■ to^irt to -0 N o Tt-O 00 tOQO W to to 't ■•r o>oo OOO w to to-* woo O 0\ WO M H t- ■o H o\ Ooo G tt t-* Om to « (H w ■^\n r* \0 MO i-,o t»- •*oco mow 0\ Tt O I (M to "-> too ) t^OO Ov/1 O H W M W « to inooo O W Ch «1 ■*"* tOcO « O M 00 Oi M ro O W 00 M W W C4 to to MU-) CO Oi CO »rt 00 O to 1-" G « « to to "JiO too „ OvO Oi irt looo COO ^ fOu-> roo 00 «o TfOO o "^ H M w w to to CO ■* ^ H Tf H « t^ (*i 1*1 "5 ^ ^lO ui •tnBag JO mdaQ i/>oc« 00O^O Meic*) t^«) o\ O « '* ja o 3 ^ S u .3 .4H 4J ^ S o ^ - II S"*; to M .s a " S o o 3 o " ^ -3 -a !» ■= S o o o -a ^ c< r*i -"I- Ln H REINFORCED CONCRETE DESIGN STl ■a ^ 30 ^^uauioj^ SjBg ^ : 000 000 000 000 ^NH «NH Wltm IDCON '*'iHM(0 mooo On^ *oo4N 000 000 000 000 010 ro M TflO lo to 00 fOO C7> M w « to CO •*"> \0 *^M «o « MOOO m ° ° ° in to 0\ &2n r-. w M or^ ooOm ^fvooo (Ocmo ,^ MM Ht-lw MMW IHC^M NNN tO<0^ ^.^ ^ ^in -COt^ oooOOi OOm mwto ^«0 t^ Oi O >-" in Qi ^ Nl0^or^ odovO HNtO loOr^ ooOiO M^m t-ON cot'-' ^ M MHW HUM HH« WWW NCOrO*0 t^^ 5 c u ^ ■S cl ?: li s IH n a ^ B U 3 ^ w Tn c ll s ti Ph ^ vy aj C '^ 'ii, 1- ^.^ .3 ( 00 o\ «»« r-00 Cl vO " to om MOO Tj- m r-oo 2"S so « M Oi t-o w M to CO O-CO ■>t H t-00 00 to moo M ri v3 to TflO •^% ■^mvo eq tO" 00 wvO M M 't -^OO r- to tH w « C1\0 TT r* N to tTO S.'Si? CO M M w 00 o*o tt ■* CO to<0 TfOO -J- wsO M « N 00-0 1- t* w tomO CN tO"*m M too O^O M M H N M w Minoo r-\0 MIO o» « N M « to f> 0-0 r-00 t^Ov NSO -* -H « 00 CO cot- M I-. N w « to com to r-ooO TtOOO « « to 00 -t t^OO xO (H t-i 10 -* m 0\ CO M w M 000 w to to ^%0"-i 00 '*'0 « tO'-t tom to 00 •-' CO -< M COUTO (^ Ch 00 wo M W « OOO N 1^ fO CO CO -a- tX to NOW -H MOO 0» to to-*- MOOVO « CO iO»n>0 m 1^00 OOO M Om w N C* to r- ^ to ^10 m t^OO w to r, to N OtOO W M « r^ooo to -^m JISSS CKOO w coxo N-OOO 00 M ■* 00 « CO CO CO - Oi rf Tt (ON M « to "2? ■* IH M M «Oin W « « M 00 00 CO w to-* 00 i^ >. - 10 -o e^ «0 0, »- 00 -*00 M M M I^CO *oo t m'Ooo w ■* 1? 0\ xO 3- - W N CO ro«O00 CO -rtm CO r* -J- c) coin •O t^oO « 00 »- M « M tO'^ ■gss oo^ooo wm r- Om to •H -fl-OO « « « toco CO CO fOm »a-m>0 m 0>i r- o» « U-1 M 00 ro-i 00 M so w 0\ \0 Him « CO CO 0> TT N moo « utOoo ocm to 0* - to CO -sO CO ■- M to in 00 Cs to tot* H M M 00*0 00 Tt CO to ■«*■-* m^O CO to ■* tnOO M 000 t^oo 00 000 o» ■**> 00 w 00m CO ri r~ r-m CO oo>o>o w ft r- r-oooo M «0 00 •->o CT.N ■* .5 o g & .2 -S *^ H K E « oj t! E-2 o • S 3„ B B !i ■i 1.2 T3 U O ^ '^ ;S -5 " ^ -a I'g I g s ^ 3 G " -y ... ^ 6 « ^ ^ t* t3 d o -^"S > \B R Ml — 0) rt fe « « B « O O o u_4 CO a> U ^■- Mia g o . « ^, Vh .. ^ p^ « a> 4> .ii t « Af fa ? O p b h -s „ §•« m m.S _ rt* rt '^ ^ S a "» "'■a-s > 5 O O O O .4 n H c*^ ^ i« tii O o.m TjN^ m-^t^ w«or- OCO m t^Om M«oco HOr» ooOiiH ^cO O MM w « CO -^mio *0 r~ 0\ O h « • ! -nreaa ^ a i jO ti»t^OO ^2 n N CO -* vo-o r- 00 « ■*\O00 to o»o to to ■* TUBsg JO jqaiaAl .-^ ^ TUn vO-O r- 0000 M M N CO Tfvo r* 0> M *0 O* t Nio\o r- 00 ov H N (O irt »0 r* M MM 00 o« H M W H fOlO « « N t-0 w N to to 00 ■^M to ■*»o Total Safe Load (w) per Linear Foot for BeaTn One Inch Wide including Weight of Beam. For aafe live load deduct weight of beam in column (22) (See important foot-notes.) 01 « s ^ fa C '5 :? Q, Oi 00 OoO 10 »o too "* 00 MW %9 00 CO 0, vo*o r^ tooo & HIO H M « 10 M fO'f* *^00 ■o r^oo OSM « (OiO t^oo M 10 TfCO tOvOCO N»0 Ol too M to to ^ 0000 ■*iOO 00 to MO M 00 Ov M ■*o Ol H 10 P) f0'*O 0*H ■* H H r-w Tj- Ov to OS «.OSO t to ■*10 10 M woo 't 0\ «o t^OO 00 ■■i-^ o« TT 0» to w « to Ov« to tO'fl'irt 1^00 OOO to 00 t t-too CO *o tr 00 ot w •niBag }on}da( I S.g M M M M S-S'S r»eO o« H H M SSJ ^^Sl %i% TABLE S. USE FOR DESIGNING SLABS, IF FULLY CONTINUOUS, ADD 20% TO LOADS Safe Loadings per S^vare Foot and Reinforcement for Slabs for Various Working Stresses in Steel (/«) and Concrete (/c). {See pp. 575 and 484.) Based on Jlf =. ^— For supported ends, ( Jf = ^ ) ■ deduct 20% from loads. For fully continuous, \"^ ■= ■j2"j.add20%. For square slabs multiply by 2. Use same ateel area always. 4 Total sate load (lo) per square foot, including weight of slab. i; So . 0) P •3 For safe live load deduct weight of slab in column (14) XI S •§•« CO J) i (See important foot-notes on opposite page.) ^8 2 'i II a I'd'? *§! 01° Seep. 355 Span in feet (2). IS (d) (e) m M (A) 4 5 6 7 8 9 XO IX 12 X3 X4 x5 lb. in. in. sq. in. n.-lb. (X4) Ci5) (x6) (17) Cx8) f 2i 147 243 360 94 l56 231 66 108 161 79 118 90 32 38 45 i5 2i 0. 130 0. 167 0. 2o5 2830 4670 6930 II II 5 S07 589 768 326 378 494 226 262 343 166 192 25l 127 147 192 100 116 l52 8x 94 X23 .X02 5i 53 64 3i 3i 4 I 0.242 0.260 0.298 975o X1320 X4780 „ 6 7 8 1201 1729 23S3 772 liii l5l2 536 771 io5o 393 565 770 300 432 588 238 342 471 X92 276 376 1S9 229 3x2 134 193 262 X13 163 222 X43 X95 X23 X67 77 90 X03 5 6 7 0.372 0.446 0.52I 23x00 33260 45270 II II 9 3081 3898 I97I 2495 1369 1733 1006 1273 770 975 608 770 493 624 407 5x5 342 433 292 369 25x 3x8 2x9 277 X16 X28 8 9 0.595 0.670 59x40 74S40 Is 2* 195 322 48a 125 207 308 87 143 214 64 lo5 i57 80 120 95 / 32 38 45 i! 1 0. 176 0. 227 0.277 3760 6x90 9230 II II 5 675 784 1023 434 5o3 657 301 349 457 221 256 334 523 753 1024 1 6s 196 256 134 i55 203 108 X25 X63 X04 X36 XX4 96 . 5x 58 64 4 i 0.328 0.353 0.403 X2990 x5o7o X9680 1 in M 6 7 8 l599 2303 3134 1027 1479 2013 713 1027 1398 400 S75 783 317 456 621 255 367 5 00 212 30S 4x7 X78 257 349 x5o 217 295 X32 X90 259 114 163 223 77 90 103 5 6 7 o.5o4 o.6o5 0.706 307S0 44280 60270 II II 9 10 4101 5191 2625 3321 1823 2307 1339 1694 1025 1298 810 1025 656 830 542 686 456 577 388 49X 335 424 292 369 X16 X28 8 9 0.806 0.907 78720 99630 § 246 407 604 l58 261 388 no 181 369 80 133 197 102 i5i 81 120 96 32 38 45 xf 2 2* 0. 225 0.289 0.353 4730 783c XX620 II II 1^ 8S0 986 1293 546 633 827 379 440 574 27a 322 421 212 246 322 168 195 255 X36 1S7 205 X13 X31 xyx 95 IXC 143 93 X2I X06 5x 58 64 ^1 4 i 0.417 0.449 o.5i4 X63S0 X8960 24770 M m ° " 6 7 8 2012 2S98 3945 1292 1861 2S34 898 1293 1760 658 947 1289 S03 724 986 399 5 74 781 321 462 629 267 384 523 224 323 '440 X89 273 372 x66 239 326 143 206 28x 77 90 103 5 6 7 642 0.770 0.899 38700 55730 75860 e P. 9 10 5i6i 6534 3303 4181 2294 2904 i685 2133 1290 1633 1019 1290 826 1045 682 864 573 726 489 6x8 42 X 533 367 464 xx6 128 8 9 , 1.027 i.i56 99080 X 25400 It 3i 137 2S6 335 87 145 2l5 loi 149 74 109 ■ 84 66 32 38 45 1} 2i 2} 0. loS 0.135 O.I65 3620 434° 6440 ^^ 1' 471 546 713 303 35i 458 210 244 318 .54 III 118 178 93 108 141 75 87 1x4 72 95 61 80 5x 58 64 3i 3i 4 i 0. rgS 0. 210 0. 240 9060 loSio X3730 M 6 7 8 iii5 i6o5 2186 716 1031 1404 498 716 975 7i5 279 401 546 221 318 433 X78 2S6 349 148 213 290 124 179 244 xo5 x5i 206 92 133 x8x 1x4 x55 77 90 X03 5 6 7 0.300 0.360 _ 0.420 " 2x450 30880 43040 ] ^ 9 10 2860 3619 1831 2317 1271 1609 934 1182 7l5 9o5 565 7x5 457 579 378 479 318 402 27X 343 233 295 203 257 xx6 X28 8 9 0.480 0. 540 549x0 69S00 2i 183 303 45o 117 195 289 82 135 201 99 147 112 89 72 32 38 45 2I ■ 0. 141 0.181 o.2ai 3530 5830 865o II II 5 632 734 958 406 471 6i5 282 327 427 207 240 313 i58 183 239 125 145 X90 XOI 117 x53 84 97 127 70 82 107 90 79 Sx 58 64 4 i 0.261 0.2S1 0.323 X2X60 I4XXO 18430 w 6 1 1497 2i56 293S 962 1385 i885 668 962 1309 489 7o5 959 374 539 734 297 427 58x 239 344 468 386 389 167 240 327 X4X 203 377 'xr8 243 106 l53 209 77 90 X03 5 6 7 0.402 0.482 0.563 38800 41470 564S« II n 9 10 3840 4860 2458 311 1 1707 3x60 1254 l587 960 I2j5 7S9 960 6x4 778 S08 645 ni 364 46a 313 397 273 346 1x6 138 8 0.643 0.734 73740 93330 ■uif s8o TABLE S— Continued. Based on 10 ' 3 Total safe load (w) per square foot including weight of slab. 5 11 .si,- 11 £oS 1^ For safe live load deduct weight of slab, column {14) (See important footnotes.) 1 3 -1 (A) '2 II <0 CD 1 Q (e) io-g ill See r.. 35S (A/) E Span n feel . CO in. 4 5 6 7 8 9 10 11 12 13 14 l5 lb. in. in. sq. in. in. lb. , 2l 206 340 509 218 326 92 226 67 III 166 52 85 127 61 101 54 67 % 45 2i 2f 3 0.162 0.208 0.2S4 9770 n II s 824 1077 690 316 356 479 232 209 352 178 206 269 140 163 213 114 132 172 94 lug 142 79 92 120 102 U 77 11 64 3i 3i 4 f 0.300 0.323 0.370 13650 15830 20680 o in 9 H O 6 •7 8 1683 2423 3297 1077 I5SI 2111 748 550 791 1077 421 606 824 332 17^ 269 386 528 223 320 436 187 IS9 229 312 269 120 172 234 •7', 90 103 I 7 0.462 0.5S4 0.647 32310 46520 63320 c a 9 L lO 4jo8 S454 2758 3491 I9I5 2424 1407 1781 1077 I3J 556 646 844 357 4i5 542 248 28S 376 182 211 276 139 161 211 110 128 167 89 103 135 86 112 94 79 ii 58 64 ^1 4 i 0.183 0. 197 0. 226 ■ 10700 12420 16220 6 7 8 1318 J 898 2S84 846 1219 l659 588 847 Il52 431 620 844 329 474 646 261 376 572 210 303 412 175 252 343 147 212 288 124 173 243 109 i57 214 04 135 184 77 90 103 5 6 7 0. 282 0.338 0.395 28350 36 5 00 49680 D D 9 lO 3381 4279 2164 2738 l502 1 90 1 1104 1397 845 1070 668 845 541 684 4^7 566 376 475 320 4o5 276 349 240 304 116 128 8 9 o.45i o.5o8 64900 82140 o o 2i 202 334 497 130 21S 319 90 149 221 66 109 162 8^ .24 98 35 38 45 2I 2} : 0. 126 0. 162 0. 198 3890 6430 9S5o II II as « J. 698 810 io58 679 311 361 472 22£ 265 346 175 202 264 138 lOc 2IC 111 129 169 93 107 140 90 iiS 100 87 5i 5S 64 3i 3^ 4 i 0.234 0. 252 0.288 13430 l558o 20350 O -1 o 6 7 8 l653 2381 3240 1062 1530 2082 737 1062 1445 540 778 io59 413 810 327 47; 64: 264 3S0 5i7 219 316 430 184 266 361 i56 - -4 3^5 137 197 268 117 169 231 77 90 103 5 6 7 0.360 0.432 o.5o4 31800 45790 62330 r. ta. 9 lo 4241 5368 27i5 3435 i885 2386 1385 1753 1060 1342 83: 1060 67?; 56 1 859; 710 471 402 596| 5o8 346 438 302 382 116 128 8 9 0.576 0.648 81420 103030 HuLii:s. 1. For load for any width of slab multiply by width in feet. 2. For area of cross-section of steel for any width of slab multiply column ( 18) by width in 3. Total loads for other spans (0 and same depth of steel are inversely proportional to the squares of the spans. •' ^ ' 4. Total loads for other depths of fteol (d) and same span are proportional to the sauares of the depths of steel. * TABLE 6. USE FOR REVIEWING DESIGNS. IF FULLY CONTINUOUS ADD 20% TO LOADS. Safe Loads per Square Foot and Reinforcement for Slabs. Proportions i: 2:a; (Seep. S7s). u>P I wP \ Based on Jlf =. — For supported ends, I -W = — I , deduct 20% from loads ^0 = or < 650 n = 15 / wP\ /, = or < 16000 ^°'' '""y continuous. 1 ^ = J^ ) . add 20% to loads / VlP\ I -W = ^ I , multiply loads by 2. S8i Fpr square slabs, ^p)* Total safe load iv)) per square foot including weight of slab. For safe live load deduct weight of slab in column (15). (See important footnotes.) Span in feet (/.) 4 5 6 7 8 9 10111213x415 lb. U) II m sq. in, E-i See p. 353 (M) in. lb. .006 .ooS 95 198 300 469 675 919 1201 zSl9 i85 385 584 913 I3M 1788 2336 2957 6o| 125 190 133 297 428 582 760 962 117 244 370 578 832 1133 1479 1873 207 i5i 116 92 298 218 167 132 406 296 227 180 272 17 567 359 858 544 1342 85o 1932 1223 2630 i665 3435 4348 3 34S 4 726 5 HOC L 10 1719 2475 3369 4401 5570 374 781 1182 1847 2660 3618 2175 ^753 220 460 697 i567 2134 2787 3527 237 494 749 1170 1684 2292 4727 2993 5986 3790 531 671 82 170 258 403 58l 790 1032 1307 120 25o 379 593 854 i5i8 1921 i53 321 486 760 1094 1489 1945 2461 i65 345 522 816 I175 l599 2089 2645 387 60 124 294 423 5 76 752 9S2 87 183 276 296 375 46 95 144 225 324 441 576 730 67 140 432 331 622 477 847 649 1106 1400 112 234 354 553 797 io85 1417 1793 120 25l 38 235 298 36 76 114 179 2S7 35o 458 579 52 III 168 263 378 5i5 48 74 107 146 190 241 29 61 1S7 199 5o 7 144 120 208 172 283 234 370 468 43 90 136 212 306 416 673 544 1073 852 688 68 55 142 iiS 2x5 174 86 179 271 424 611 831 1086 1374 92 193 292 595 456 856 656 ii65 893 l522 1927 1166 1477 337 485 660 862 1091 73 l53 232 362 521 709 926 1172 306 387 36 74 112 176 253 345 45o 570 167 64 100 144 196 257 325 62 94 147 212 289 377 478 145 189 239 167 219 277 246 321 278 407 3S1 164 208 46 95 80 144 121 272 225 I 392 324 272 533 441 370 697 882 59 124 187 292 421 573 748 948 577 730 49 X02 i55 242 348 474 619 784 86 130 203 292 397 5l9 657 231 3i5 173 249 339 (l5) 5i 64 77 90 103 116 128 5i 64 77 90 103 116 128 38 5i 64 (16) 2i 3l 4 5 6 7 (17) J i 77 5 90 6 103 7 200 27 356 45o 149 2l5 292 242 116 306 12S 442 382 56o . 720 o. S40 0.960 i.oSo 83600 io58oo 7100 1-4820 224O0 35090 5o520 687S0 89S00* I13700 o.ooS 0.0 10 65o 65o * Percentaeea of Pteel are values in this column WiultiplK'd by too. - ^ . Comoression in concrete under tabular loads with the different percentages of steel: Ratio of steel 0-002 °-oo4 0.006 Compression in concrete, lb. ppr sq. m : ; V : ' v ^ 3^° ^°° ^'° RuLM. I. For load for any width of slab multiply by width in feet. , ^v . • ixu • r * 2 For area of cross-section of steel for any width of slab multiply column (18) by widtbin feet. 3! Total loads for other spans (x) and same depth of steel are .mveraely proportional to the squares of the spans. . ,,* , *• 1 ± ii_ r *i. 4. Total loads for other depths of steel (d) and same span are proportional to the squares of the di>ptha of steel. S82 to m O O o B m Q o CO & I 3 I ^ to i ■= S =o H --S (4 to sISS? ^ -2 i E !• •a n 1 ■s o h-l > 3 • -^ W-S tnoo w M M odd H ^ M d d d 00 e<»0 (O ■* rt 6 6 6 io>o*o d d d O r,t>. d d d d d -*! .5 m W3 »*j in>o»o He* Hn O r- t^ 00 00 Ch o o M M ■^'' o'.S g-Jg to r* w M W CO '^^^ CO to h- « t^ CO OO t- 00 ■* P-00 O GOO GOO COO GOO O .5! .2 p:i (OfO ■s;^-? »0 vjO vo t-r- 00 00 Oi ao « ■^'^ ti ^:?? H ^0 to t- H to to -^ loO 'J- Tj-lOlO hO 0> ooo o o o o o o O GOG O O O -« .C CO ro to CO '*'<1- \r, \r,\Q Hn Hlw O i>.r^ •So » to •^ •^ ^i O K w O POOO >O00 « fO to ■* ■^a^s 00 cooo lOOO cooo GOO COG coo o o ■^ .a *0 rO to fO ■0 oo a tOfO to 9^ a ^%^ O ^- GOO GOO O GOO O O O o o •* .s to fO fO tOtO "* ■*■*<« Hn Hn loOO ^t:» Hn 00 o> *5 ^ W-S •s?? OO H (O 00 TO r* M CO to ^3^ W ION lo too SR GOO O O O O O O GOO O -J5 .a fOfO to tO(0'Oio loOO 1 •M TfvivO t-00 o. O H « (O Tt lO o t^oo S8 1 9 \3 * 8 ^"^ ^.S 6 6 6 MOO to to to ■* odd d d d O r^r- d d d d d d 32 H H -« •S if}tfi^ -** *0 t^oo WOO* H H M W to CO g'.S •25^ OVO H to to -t r* to O .^vg--^ tooo ■* 0000 Oi mO o o O o o o O O O O O O H H -SS .a vim^ ;^^t: 00 oi a h's'H W to E ^"^ ti \0 MvO H N W tow)0 tow* ^Si% >Sfis MQO Pt 00 00 o. §■§ O O o o o O w -« ro to •* Tl-lOO S'.-t: 00 00 C?i o'o'h r s? O o o o o o o o o H ■Ja .g w) wj'* IJ-IOVO O t- r- OOOO Ol O O M H M H nir *o -^ §•■2 ;???? O "AM toco ■* Tj-lOlO OO to OO t^ OitoO *^00 Ol -ss O o o o o O O COO H -Si .S fO tOTt ■*iOio o o r^ 00 00 Ch ■S-S'h M M H rt * S-a ■*w t^ to CO to ^a'Si 00 -^o lOO t^ t^OOOO tO« a.H O O O O o O H -« .s to ro to >4n rj-ioio ■O-O t^ ■00 00 Oi CO H M H F«1 S j-s fO H lO OicOOO N COCO S'^R O>o0 »oo *-. to OO (^00 00 ss o o o o_o O O o o o o •« .s W) to to *.o-s; ««•^, I>.00 00 a o H H " ^ ?.« too ■* ■ss^ HO M t- COOO moo as O O o o o -Si d to to gK5 £8, o O O o O -« .s CO to to lOOO r-OOOO OiOiO M H *S -fl'^ S-a 6 o 6 •*0 w N (O to d d d 6 6 6 fOOO to io»oo odd O x^^oo odd «4' d d -« ^ PO (O fO lOOO t^t^OO 00 Ol o> H lO ia oo o O to « to to t^ HO to^n- OiioO ■^lOO SRS wis O O O O o o o O ►« .2 to to to to «* vj r4N HM* v-,0 00 Ok Ol 22 1 d ■(J-IOVO r-00 Oi H N to "d-^ M H M O b~00 ss S8,5 1% •4 d "6 0-9 a .9 28 SB una 11 5«>4 TABLE 8. CINDER CONCRETE SLABS A ratio of elasticity of n = 35 is used in the table below, although it is permissible to design with a ratio of 15 in very conservative practice. The loads for slabs with a ratio of steel of 0.002 are limited by the work- ing strength of the steel, and the values with the higher ratios by the work- ing strength of the cinder concrete. It is noticeable that less steel can be used economically for a given thick- ness of slab than with broken stone or gravel concrete, because the strength of the slab is more apt to be Hmited by the strength of the cinder concrete than by the strength of the steel. Safe Loading and Reinforcement for CINDER CONCRETE SLABS One Foot in Width. Proportions 1 : 2i : 5. Mild Steel. (See p. 584). Based on M = or< 225 fa = or < 14 000, n = 35 Total safe load («;') per square foot including _, "rt tu r.S weight of slab. fe _; 1 gg §! B For safe live load deduct weight of slab in a 1 "S s| ■jS ^A column (12). 11 la ^ 4 (See V. 355.; ll ■a a (S^e important foot-notes.) s _o 1^ « " ■ss ^ 1 •::a Span in Feet (I) i 5 6 7 8 9 10 & p (d) 0. (e) in. lb. in. in. sq. in. in. lb. (10) {") C12) (13) (14) 2i 48 31 24 li 0. 042 920 3 70 5i 35 26 29 ) 2i 0.054 IS2O 3i 119 76 53 39 34 2J 0.066 2280 4 166 106 74 54 '^l 39 3i i 0.078 3180 0.002 44 192 123 85 63 48 43 3i I 0.084 3690 5 25l 161 112 82 63 5o 48 4 I 0.096 4S2O 6 302 25l 174 128 98 78 63 58 5 I 0. 120 7530 7 565 361 2S1 184 141 It2 90 68 6 I 0. 144 IOS4O 8 768 492 341 35i 192 1S2 123 77 7 I 0. 168 14750 2> 76 48 34 25 24 1} i 0.084 1460 3 12S 80 56 41 31 29 2i 0. 108 2400 3I 187 120 83 61 47 37 34 2} i 0. 132 3590 4 261 167 116 85 65 52 42 39 3I n o.i56 5020 0.004 4i 303 IQ4 135 99 76 60 48 43 3i I 0. 168 5820 5 396 253 176 129 99 78 63 48 4 I 0. 192 7600 6 '619 396 275 202 l55 122 99 58 5 I 0.240 1 1880 7 891 570 396 291 223 176 143 68 6 I 0.288 I7II0 . 8 1213 776 539 396 303 240 194 77 7 I 0.336 23290 2h 86 55 38 28 24 i| 2 t 0. 126 1640 3 141 90 63 46 35 29 5 0, 162 2710 3i 211 135 94 69 53 42 34 34 2J 1 0. 198 4o5o 4 295 189 131 96 74 58 47 39 3l } 0.234 566o o-oo6 4i . 342 219 l52 112 85 68 55 43 3i I 0.252 6570 5 447 286 199 146 112 88 72 48 4 I 0.288 858o 6 698 447 310 228 175 ■38 TI2 58 5 I 0.360 13400 7 ioo5 643 447 328 25l 199 161 68 6 I 0.432 19300 . 8 1368 876 608 447 342 270 219 77 7 I o.5o4 26270 ♦Percentages of steel are values in this column multiplied by icx). Rules, i. For load for any width of slab multiply by width in feet. ■J. For area of cross-section of steel for any width of slab multiply column (13) by width in feet. 3. Total loads for other spans (e) and same depth of steel are inversely proportional to the squares of the spans. 4. Total loads for other depths of steel (d) and same span are propor- tional to the squares of the depths of steel. S85 Table 9. NUMBER OF U-STIRRUPS IN UNIFORMLY LOADED BEAM Number of stirrups per beam is 2Ns=^Cnhl. aiVj = number of stirrups per entiie beam. ^ , I — span of beam in feet. h = breadth of beam in inches (in T-beam, breadth of stem). v^ = maximum shearing unit stress in beam in lb. per sq. in. ^ v' = altowable shearing unit stress (or diagonal tension) in concrete .alone in lb. per sq. in. Cf^ = constant.- 4 (l,2 _ jj'Z) Note: Table is based on general formula sN^ ^AsJs bl in which stress /. = i6 ooo lb. per sq. in. has been accepted as a unit stress steel and A^ the corresponding area of two legs of the U stirrup. Values of Constant C„for Finding Number of Stirrups in Beam. ^-in. round g-in. round T^-in. round J-in. round S-in, round U-stirrup, U-stirrup, U-stirrup, U-stirrup, U-stirrup, -As=.i$ .4^=. 22 ^s = •30 ^s = -39 ,^s = .6i I> i,' = 4o 60 u' = 40 fio v' = 40 60 v' = 40 60 v' = 40 60 70 0.079 0.031 0.054 '■ 0.021 0.039 o.ois 0,030 0.012 0,019 0,008 P 0.090 0.045 0.061 0.031 0.044 0,022 0,034 0.017 0,022 o,oii 8o 0.1 00 0.058 ' 0.068 0.040 0.049 0.029 0,038 0.022 0.024 0.014 8S O.IIO 0.071 0.075 0.049 O.OS4 0.03s 0.042 0.027 0.027 0,017 go 0.120 0.083 0.082 0.057 O.OS9 0.041 0,046 0.032 0.029 0,020 QS 0.130 0.095 0.085 0.065 0.064 0.047 050 0.036 0.032 0.023 zoo 0.140 0.107 0.006 0.073 o.o6g 0.052 0,054 0.041 0.034 0.026 I OS J. ISO 0.118 0.102 0.080 0.073 0.058 0,057 0,04s 0.037 0.029 no O.IS9 o.i2g 0.108 0.088 0.078 0.063 0.061 0,049 0,039 0.032 IIS 0.169 0.140 0.115 0.09s 0.083 0.068 0,06s 0,053 0,041 0.034 I20 0.178 0.150 0.121 O.I02 0.087 0.074 0,068 O.OS7 0,044 0.037 125 0.187 0.160 0.128 o.iog 0,092 0.079 0.072 0,061 0.046 0,039 130 o.iq6 0.170 0.134 0.116 0,096 0.084 0.07s 0,065 0.048 0,042 140 0.214 0.190 0.146 0.130 0,105 0.093 0.082 0.073 0.052 0.047 ISO 0.232 0.210 0.158 0.143 0.114 0.103 0.089 0,080 0.057 0.051 160 0.250 0.229 ,0.171 0.156 0.123 0.112 0.096 0,088 0.061 0.056 Table 10. SPACING OF STIRRUPS IN BEAMS WITH UNIFORMLY DISTRIBUTED LOADING Spacing in inches, s—Cil i = span of beam in feet. Ng = number of stirrups in each end of beam. V = maximum shearing unit stress in beam in lb. per sq. in. v' = allowable shearing unit stress (or diagonal tension) in concrete alone in lb. per sq. n. Values of Constant Ci for Finding Spacing of Stirrups. V V V ^s ISt 2nd 3rd 4th Sth 6th 7th 1 Sth 9th loth ISt 2nd 3rd 4th j 5th 1 6th 7th Sth 9th loth i 1.26 1,74 [ 1. 432. 17 1 t 3 0,800,95 1,24 0.91 1. II I ,,58 4 0,39,0-67 0.780,97 0.670.760.92 1-25 5 0.47 0,51 o.S7|0.6s'o,8o 0.53,0.58,0.66 0,791,0/ 6 O..10 0,42 0,450,500,57 0.67 o,440.47|o,52 0,590,690,89 7 0,3,1 o-^$ 0,380,410.45 0.50 O.S5 0,370,400,43 0,470,5310,62 0,77 8 0,29 0,30 o,32|o, 340,3710,41 o.45'o.S2 0,320,340,37 0,400,440.49 0,56 o,6(: 9 0.26 0,27 0,2s 0.300.320.34 0,370,41 0.46 0,290,300,32 0.340.370.40 0,45 O.SI 0,62 10 0,23 0,24 0,25 0.260.280.29 0,310,34 0.37 0.42 0,260,270,28 0.300,320,34 0,37 0,42 0,47 0.56 V ? = 3.5 ^. ISt 2nd 3rd 4th sth 6th 7th Sth 9th :oth ISt 2nd 3rd 4th Sth 6th' 7th sth 9th loth 2 I. S3 2-47 1,592-70 3 0,97 1,20 1,83 1,001,262,02 4 0,710,82 1,01 1.46 o,73,o.86|i,o7 1,64 0,560,620.72 0.87 1.2,1 0.580,650,750,93 I., 18 5 0.460.500.560.64 0.77 1.05 0.48 0.520,580,68 0,83 i,ig 7 0.390,42 0,460,51 0.580.70 0.93 0,41 0,4410,480,54 0,62 o,7.S 1.05 S 3,340,37 3.390,-43 0.470.54 0.64 0.83 o„36 0,380,4110,45 0,.5o 0,57 0,69 0.9S 9 3,300,32 3,34 0..17 0.400.44 0.500.59 3.7S 0.31 0,330,360,38 0,42 0,46 0.53 0,64 0,86 10 3,27|0,29 3.30 0.32 0.340-37 0.4l|O.46 3.540.69 3,28 0,300,310,33 0,3b 0.39 3.430,50 o,S9 0,78 If larger number of stirrups are used divide the number by 2, find the spacing for this number from the table, and place intermediate stirrups between. ;86 A TREATISE ON CONCRETE 13 I to i 13 a i i I .8 I 0= s 1 a CI 4 o C. fl 2 g> d 1 .2 1 1 moo ^ tow « CO in -* Ow t-Tt (OfO^ N Oi to to to ss % ■* 00 M^O to CO tO« W CO to »Ob- w ■* to«o " ??• >0 O »rt N to to W N ■^ to CO tO»0 M -*tOco 7 \0 Oi»0 H to W « W 55 ■■J-eoc^ CM O M ■* lO-rl-to to 00 t ^ ir, *J- to tOOO Tt-H to W W W as O tooo »o ■ ■<»■ to COM ^ iO(OP0 w r- too ■^3 00 W t^ Ti- to to P« « 00 M »oio V)00 NCO Tt to co« 1 i 1 s, O>00 ■* a-gas .g-^S t^ MO to to too N lOOO »o-t tOvO M t^ -^ CO to « CO as-s? ft?S W OO to to COM N \o lO -t (s »o OO ^COtON \o *0 TftOtO ©.■■l-M Ol «0 1-MOO (O ej N W lO Ol "* O to O.ooin ■O -^fOCO N r^ CO M to t^ tN CH a%'^% f- W t^ Tf to coo N Oif^ O MOO t^io ro to .»0 -(^ to to OO CO to to W N s i oO Tj- 000 OoO r^io to tOM W W H H a^o -t toeo O >o N O to M W N Ol O « M ^- O t-.io -ft CO ■-tJ-tO« M WH CTt;;j- ■* t^ to "*-< OO lO 'T toco t>xo es oi OvO ■* to to ^^'SiJS ■* XCO »O00*O -O TT to N W •+ WOO'O Oct H too fr->0 T^ COM CO -t H Ol N cor^oo to Oi^O •* to to to w w « « \0 -^ tO« N to OOOO CO M 0> WON r~io to tof^ r^ to OOO 00 to Tt CO to MO to H tON W W o ON (O P-IO IO-+IOM « (O o i>.\o ^^%'^n VO to OOO CO to lots 00 »0 ^ CO to OO too- CO« « and Cj- below. Ratios of Thickness of Flange to Depth of Beam, -j 0.4 0-45 OS o.SS 0.6 0.6s 0.7 0-75 0.8 Values of h 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 O.S7 0.38 0.40 0.42 0.44 0.4S 0.52 • 0.95S 0-9SS 0.95s 0.954 0.9S4 0.9S4 O.0S4 0.954 0.9S3 O.0S3 0.9S3 0.953 0.953 o.9'S3 0.953 0.9S3 0.953 0.9S3 0.952 0.9S2 0.952 0.952 0.951 CIO 0.12 0.14 0.16 o.iS 0.20 0.22 0.24 0.26 0.28 0.30 0.136 0.208 0.269 0.145 0.217 0.277 0.154 0.225 0.285 0.164 0.233 0.292 . 0.242 0.300 0.250 0.308 0.258 0.315 0.267 0.323 0.27s 0.331 0,283 0.338 0.346 0.321 0.34S 0.367 0.329 0.352 0.373 0.336 0.359 0.380 0.343 0.36s 0.387 0.350 0.372 0.393 0.3S7 0.379 0.400 o!386 0.407 0.371 0.393 0.413 0.379 0.400 0.420 0.386 0.407 0,427 0,393 0,414 0,433 0.387 0.406 0.424 0.393 0.412 0.430 0.400 0.419 0.436 0.406 0.425 0.442 0.413 0.431 0.448 0.419 0.437 0.4S5 0.426 0.444 0.461 0.432 0.450 0.467 0.439 0.456 0.473 0.445 0.462 0.479 0.452 0.469 0.485 0.441 0.457 0.472 0.447 0.463 0.478 0.4S3 0.469 0.483 0.4S9 0.474 0.489 0.465 0.480 0.494 0.471 0.486 0.500 0.476 0.491 0.506 0.482 0.497 o.sii 0.488 0.503 0.S17 0.494 0.509 0.522 0.500 0.514 0.528 Values of /. Use to find /„ in Formula/^ = :; — r-.. Ratios of Thickness of Flange to Depth of Beam, —r 0.948 0,948 0,947 0,947 0,946 0,946 0,946 0.946 0.945 0.945 0.945 0.945 0.945 0.944 0.944 0,944 0,944 0,944 0,944 0.943 0,943 0.943 0.943 0.14 0.940 0.940 0.939 0.938 0.938 0.937 0.937 0.936 0.936 0.936 0.935 0.935 0.935 0.935 0.934 0.934 0.934 0.9.34 0.933 0.933 0.932 0.932 0.931 o.t6 0.937 0.935 0.934 0.933 0.933 0.932 0.931 0.931 0.930 0.930 0.929 0.929 0.929 0.928 0.928 0.928 0.927 ■0.927 0.927 0,926. 0,926 0,925 0,92s 0,18 0.20 0.22 0.24 0.26 0,933 0,931 0.929 0.928 0,930 0.927 0.925 0.923 0.924 0.921 ' 0.927 0,926 0.925 0.924 0.922 0.920 0.919 0.918 0.919 0.917 0.916 0.914 0.917 0.914 0.912 0.910 o,gi3 o,gog 0,906 0.924 0.923 0.922 0.922 0.917 0.916 0.915 0.91S 0.913 0.912 0.911 o.gio 0.90S 0.907 0.905 0,904 0,904 0,902 0,900 0,898 0.921 0.921 0.920 0.920 0.914 0.913 0.913 0.912 o.gog 0.908 0.907 0.907 .0,903 o,go2 o.goi 0,900 0.897 o.8g6 0.894 0.893 0.920 0.919 0.919 0.918 0.912 0.911 0.911 0.910 0.906 o.gos 0.964 0.903 0,899 0,899 0,897 0,897 0.892 0.891 o.8go 0.889 0.918 0.917 o.gi6 o.gio 0.909 0.909 0.903 o.go2 o.goi o,8g6 0,896 0,895 0.888 0,887 0,886 0,904 o,goi 0.899 0.89s 0.893 0.887 0.88s 0.883 0.879 0.877 0.900 0.897 0.894 0.892 0.890 0.888 0.886 0.884 0.-883 0.880 0.88a 0.879 0.878 0.870 Values of Cj in Formula / = Cj.f ,* Values of k 0,22 0,24 0,26 0.28 0,30 o,oj9 0,024 0,028 0,021 0.026 0.032 0,023 0,029 0,03s 0,026 0.032 0.039 0.029 0.036 0.043 0.031 0.039 0.047 0.034 0.043 0.052 0.36 0.38 0.038 0.047 0.036 0.041 0.051 0.061 0.044 0.055 0.067 0.400 0.421 0.440 0.458 0.47s 0.491 0.S06 o 520 0.533 o.8g3 0.890 0.887 0.88s 0.883 0.880 0.879 0.87s 0,872 0,870 0,868 0,866 0,42 0.048 0.060 o 073 •/ = C'pf is another form of Formula (19) page 357. TABLE 14. USE FOR DESIGN OF BEAMS WITH COMPRESSION STEEL. 589 Values of Ratio of Compression Steel p' for Different Values of a, fs, fc, and pi. Based on Formula {21) p. ^<)2. fc Pi Ratios of Compression Steel, ^' Is Ratios of Depth of Compression to Tension Steel , a 0.03 0.04 0.06 O.0S O.IO 0.12 0.14 0.16 0.18 0.20 0.22 0.24 16 000 500 0.006 0.003 0.002 0.003 0.Q03 0.003 0.003 0.004 0.004 0.005 0.006 0.007 0,009 C«=i5) 0.008 0.007 0.007 0.008 0.009 0.009 O.OIO O.OII 0.013 O.OIS 0.017 0.021 0.026 O.OIO 0,011 0.012 0.013 0.014 0.016 0.017 0.019 0.021 0.025 0.029 0.034 0.043 0.012 0.016 0.017 0.018 0.020 0.022 0.024 0.027 0.030 0.034 0.040 0.048 0.060 0.014 0.021 0.022 0.024 0.026 0.028 0.031 0.034 0.039 0.044 0.052 0.062 0.078 0.016 0.025 0.027 0.029 0.031 0.034 0.038 0.042 0.047 0.054 0.063 0.076 0.09s 0.018 0.030 0.032 0.034 0.037 0.040 0.04s 0.050 0.056 0.064 0.074 0.089 0.112 0.020 0.034 0,037 0.039 0.043 0.047 0.051 O.OS7 0.064 0.074 0.086 0.103 0.129 0.022 0.639 0.042 0.045 0.048 O.OS3 0.058 0.06s 0.073 0.083 0.097 0.117 0.147 0.02^ 0.043 0.046 0.050 O.OS4 O.OS9 0.06s 0.072 0.081 0.093 0.109 0.131 0.164 0.026 0.048 0.051 0.05s 0.060 0.06s 0.072 0.080 0.090 0.103 0.120 O.I.15 0.181 0.028 0.052 0.056 0.061 0.066 0.072 0.07Q 0.088 o.ogg 0.113 0.132 0.158 0.198 0.030 0.057 0.061 0.066 0.071 0.078 0.086 0.095 0.107 0.123 0.143 0.172 0.216 16 000' 600 0.008 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004 O.OOS 0.005 0.006 0.007 t«=i5) 0.010 0.006 0.007 0.007 o.ooE 0.008 0.009 O.OIO 0.011 0.012 0.013 0.015 0.018 0.012 O.OIO O.OII O.OII 0.012 0.013 0.014 0.016 0.017 o.oig 0.022 0.025 0.029 O.OI^ 0,014 O.OIS 0.016 0.017 0.018 0.020 0.022 0.024 0.026 0.030 0.034 0.040 0.016 0.018 O.OIO 0.02a 0.022 0.023 0.025 0.027 0.030 0.034 0.038 0.043 0.051 ! 0.018 0.022 0.023 0.024 0.026 0.028 0.031 0.033 0.037 0.041 0.046 0.052 0.062 0.020 0.025 0.027 0.02( 0.031 0.033 0.036 0.039 0.043 0.048 O.OS4 0.062 0.072 0.022 0,029 0.031 0.033 0.035 0.038 0.041 0.045 0.050 o.oss 0.062 0.071 0.083 . 024 0.033 0.035 0.037 0.040 0.043 0.047 0.051 0.056 0.062 0.070 0.081 0.094 0.0.16 0.037 0.039 0.042 0.045 0.048 0.052 O.OS7 0.063 0.070 0.078 0.090 0.105 0.018 0.040 0.043 0.046 0.049 0.053 0.057 0.063 0.069 0.077 0.087 0.099 0.116 0.030 0.044 0.047 o.osc O.OS4 0.058 0.063 0.069 0.076 0.084 0.09s 0.108 0.127 16 000 650 0.008 O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI 0.001 O.OOI O.OOI O.OOI O.OOI Cn=i5) O.OIO 0.004 0.004 0.005 0.005 0.005 0.006 0.006 0.007 0.007 0.008 0.009 0.010 0.012 0.008 0.008 O.oog O.oog O.OIO O.OIO O.OII 0.012 0.014 O.OIS 0.017 0.015 O.OI^ O.OII 0.012 0.012 0.013 0.014 O.OIS 0.017 0.018 0.020 0.022 0.025 0.02S 0.016 O.OI^ 0.015 0.016 0.017 0.019 0.020 0.022 0,024 0.026 0.029 0.033 0.037 o.oiS O.OlJ 0.019 0.02c 0.022 0.023 0.025 0.027 0.029 0.032 0.036 0.041 0,046 0.020 0.02I 0.023 0.02. 0.026 0.028 0.030 0.032 0.03S 0.039 0.043 0.048 o.oss 0.022 0.025 0.026 0.02i 0.03G 0.032 0.035 0.037 0.041 0.045 0.050 0.056 0.065 0.024 0.028 Q.030 0.032 0.034 0.037 0.039 0.043 0.047 0.051 0.057 0.064 0.074 0.026 0.032 0.034 0.036 0.03S 0.041 0.044 0.048 0.052 0.058 0.064 0.072 0.083 0.028 0.035 0.037 0.04c 0.042 0.045 0.049 0.053 0.058 0.064 0.071 0.080 0.092 0.030 0.039 0.041 0.044 0.047 0.050 0.054 0.058 0.064 0.070 0.078 0.088 O.IOI 16 000 750 0,010 0.000 O.OOI O.OOI 0.001 O.OOI O.OOI O.OOI O.OOI O.OOI 0,001 O.OOI O.OOI Cff=i5J 0.012 0.003 0.004 0.004 0.00^ 0.004 0.005 0.005 0.005 0.006 0.006 0.007 0.008 0.014 0.006 0.007 0.007 o.ooS 0.008 0.009 0.009 O.OIO 0.011 0.012 0.013 0.015 0.016 o.oog O.OIO O.OIC O.OII 0.012 0.013 0.014 O.OIS 0.016 0.017 p. 019 0.021 0.018 0.012 0.013 0.014 o.oi; 0.016 0.017 0.018 0.019 0.021 0.023 0.025 0.028 0.020 0.015 0.016 0.017 o.oii 0.019 0.021 0.022 0.024 0.026 0.028 0.031 0.035 0.022 o.oiS 0.019 0.02c 0.022 0.023 0.025 0.026 0.02S 0.031 0.034 0.037 0.04: 0.024 0.021 0.022 0.024 0.025 0.027 0.029 0.031 0.033 0.036 0.039 0.043 0.04S 0.026 0.024 o.o2r 0.027 0.029 0.030 0.033 0.03s 0.038 0.041 0.045 0.049 o.oss 0.028 0.027 0.029 0.03c 0.03; 0.034 0.037 0.039 0.042 0.046 0.050 o.oss 0.062 0.030 0.030 0.032 0.034 0.036 0.038 0.041 0.043 0.047 0.051 0.056 0.061 0.068 , 800 O.OIO 0.000 O.OOI O.OOI O.OOI 0.001 0.002 0.002 0.002 0.002 0,002 0.002 0.003 (n=i2) 0.012 0.005 0.005 0.005 0.006 0.006 0.006 0.007 0.008 0.008 0.009 O.OII 0.01: 1 0.014 0.008 0.009 o.oo? O.OIC O.OIO O.OII 0.012 0.013 0.015 0.016 0.019 0.02 0.016 0.012 0.012 0.013 0.014 0.015 0.016 o.ozS 0.019 0.02I 0.024 0.027 0.03] 0.018 0.015 0.016 0.017 0.018 0.020 0.021 0.02; 0.02 s O.O2E 0.031 0.03s 0.04c 0.020 0.019 0.020 0.021 0.023 0.024 0.026 0.021 0.031 0.034 0.038 O.O.W c.o4( 0,022 0.022 0.024 0.025 0.027 0.029 0.031 0.034 0.037 0,040 0.04s 0.051 0.05 0.024 0.02^ 0.027 0.02s 0.031 0.033 0.036 0.039 0.042 0.047 0.052 0.059 0.06 0.026 0.029 0.031 0.033 0.035 0.038 0.041 0.044 0.04! O.OS3 o.os? 0.067 0.07 0.028 0.033 0.03s 0.037 0.039 0.042 0.Q46 0.050 O.OS4 0,060 0.066 0.07S 0.08 00.03 0.036 0.03S 0.041 0.044 0.047 0.051 o.oss . 06a 0.066 0.074 0.083 0.09 59° TABLE 14. BEAMS WITH ^c *i TJ a fins of rnmnression Steel, ^' A Ratios of Deoth of Comoression to Tension Steel, a 5 0.02 0.04 0.06 0.08 O.IO 0.12 0.14 0.16 0.18 0.20 0.22 0.24 i6 ooo ' 850 012 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.005 o.oos 0.006 0.006 0.007 (»=I2) O.OIz 0.006 0.007 0.007 0.007 0.008 0.008 0.009 O.OIO O.OII 0.012 O.OI3 O.OIS 0.016 o.oog O.OIO O.OII O.OII 0.012 0.013 0.014 0.015 0.017 0.018 0.021 02S 0.023 0.018 o.oi; 0.014 0.014 0.015 0.016 0.018 0.019 0.021 0.023 0.025 0.032 0.020 0.016 0.015 0.018 0.019 0.021 0.022 0.024 0.026 0.02S 0.031 0.03s 0.040 0.022 o.oig 0.021 0.022 0.023 0.025 0.027 0.029 0.031 0.034 0.038 0.042 0.048 0.024 0.023 0.02:<1 0.025 0.027 0.029 0.031 0.034 0,037 0.040 0.044 0.050 0.056 0.02C 0.026 0.02J 0.029 0.031 0.033 0.036 0.039 0.042 0.046 0.051 O.OS7 0.064 0.064 0.028 0.029 0.031 0.033 0.03s 0.037 0.040 . 04: 0.047 0.052 0.057 °"Sf 0.030 0.033 0.035 0.037 0.039 0.042 0.045 0.045 0.053 ■ 0.058 0.064 0.071 0,001 i6 ooo goo 0.012 O.OOI O.OOI O.OOI O.OOI O.OOI 0.002 0.002 0.002 0.002 0.002 0.002 0.003 (k=I2) 0.014 0.004 0.004 0.005 0.005 0.005 0.006 0.006 0.007 0.007 0.008 0.009 O.OIO 0.016 0.007 0.008 0.008 0.009 0.009 O.OIO O.OII 0.012 0.013 0.014 O.OIS 0.017 0.018 O.OIO O.CII 0.012 0,012 0.013 0.014 0.015 0.017 0,018 0.020 0.022 0.025 0.020 0.014 0.014 0.015 0.016 0.017 0.018 0.020 0.021 0.023 0.026 0.028 0.032 0.022 0.017 0.018 0.019 0.020 0.021 0.023 0.024 0.026 0.029 0.032 0.03s 0.039 0.024 0.020 0.021 0.022 0.024 0.025 0.027 0.029 0.031 0.034 0.037 0.041 0.048 0.047 0.026 0.023 0.024 0.026 0.027 0.029 6.031 0.033 0.036 0.039 0.043 0.054 0.061 0.069 0.028 0.026 0.028 0.029 0.031 0.033 0.03s 0.038 0.041 0.04s 0.049 o.oss 0.030 0.029 0.031 0.033 0.035 0.037 0.040 0.042 0.046 0.050 0.055 0.061 j6 ooo 1000 0.014 O.OOI O.OOI 0,001 O.OOI O.OOI O.OOI O.OOI 0.002 0.002 0.002 0.002 0.002 (n=i2) 0.016 0.004 0.004 0.004 0.004 O.OOS 0.005 O.OOS 0.006 0.006 0.007 0.007 0.008 0.018 0.007 0.007 0.007 o.ooS 0.008 0.009 0.009 O.OIO O.OII 0.012 0.013 0.014 0.020 0.009 O.OIO O.OIO O.OII 0.012 O.OI2 0.013 0.014 0.016 0.017 0.018 0.020 0.022 0.012 0.013 0.014 0.014 0.015 o.ot6 0.017 0.019 0.021 0.022 0.024 0.026 0.024 0.015 0.016 0.017 0.018 0.019 0.020 0.021 0.073 0.026 0.027 0.029 0.032 0.026 0.018 0.019 0.020 0.021 0.022 0.024 0.025 0,027 0.030 0.032 0.03s 0.038 0.028 0.021 0.022 0.023 0.024 0.026 0.027 o.o2g 0.031 0.03s 0.037 0.040 0.044 0.030 0.023 0.025 0.026 0.027 0.029 0.031 0.033 0.036 0.040 0.042 0.046 0.051 i8 ooo 500 0.00s 0.002 0.003 0.003 0.003 0.003 0.004 0.004 0.005 0.006 0.007 0.009 0.012 ("=13) 0.006 0.005 0.005 0.006 0.006 0.007 0,008 0,009 O.OIO 0.012 0.014 0.018 0.025 0.008 o.oro O.OII 0.012 0.013 0.014 0.016 O.OI& 0.021 . 024 0.029 0.037 0.051 O.OIO 0.015 o.oiC 0.018 0.020 0.022 0.024 0.027 0.031 0.037 0.044 0.056 0.077 0.012 0.020 0.022 0.024 0.026 0.029 0.032 0.036 0.042 0.049 O.OS9 0.075 0.103 0.014 0,026 0.028 0.030 0.033 0.036 0.040 0.045 0.052 0.061 0.074 o.oos 0.129 0.156 0.016 0.031 0.033 0.036 0.039 0.043 0.048 O.OS5 0.063 0,074 o,o8g 0.114 0.018 0.036 0.030 0.042 0.046 0.051 0.056 0.064 0.073 0.086 0.104 0.133 0.182 0.020 0.041 0.044 0.048 0.053 0.058 0.06s 0.073 0.084 0.099 0,119 0.152 0.20S 0.022 0.046 0.050 O.OS4 0.05Q 0.065 0.073 0.082 0.094 O.III P-I34 0.171 0.234 0.024 0.051 0.055 0.060 066 0.072 0.081 0.091 O.IOS 0.123 0.150 0. 190 0.260- 0.026 0.056 0.061 0.066 0.072 0.080 o.o8g O.IOO o.iis 0.136 0.165 0. 209 0.286 0.028 0.062 0.066 0.072 0.079 0.087 0.097 O.IIO 0.126 0.148 0.180 0.228 0.312 0.030 0,067 0.072 0.078 O.0S6 0.094 o.ios 0.II9 0.137 0.160 0.19s 0.247 0.339 i8 ooo 600 0.006 O.OOI O.OOI 0,001 0,001 O.OOI 0.002 0.002 0.002 0.002 0.003 0.003 0.004 (»=IS) 0.008 0.005 0.006 0.006 0.007 0.007 o.ooS 0.009 O.OIO O.OII 0.013 O.OIS 0.018 O.OIO 0,010 O.OIO O.OII 0.012 0.013 0,014 0.016 O.OT7 0.020 0.023 0.027 0.032 0.012 0.014 0.015 o.oi6 0.017 0.019 0.020 0.023 0,025 0.028 0.033 0.038 0.047 0.014 0.018 0.019 0.021 0.022 0.024 0.027 0.029 0.033 0.037 0.043 0.050 0.061 0.016 0.022 0.024 0.026 0.028 0.030 0.033 0.036 0.041 0.046 O.OS3 0.062 0.07s 0.018 0.027 0.029 0.031 0.03.1 0.036 0.039 0.043 0.048 0.05s 0.063 0.074 O.OQO 0.020 0.031 0.033 0.03s 0.038 0.042 0.045 0.050 0.056 0.063 0.073 0.086 O.TO4 0.022 0.03s 0.0.58 0.040 0.044 0.047 0,052 O.OS7 0.064 0.072 0.083 0.007 O.II8 0.024 0.039 0.042 0.04s 0.049 0.053 0.058 0.064 0.071 0.081 0.093 0.109 0.133 0.026 0.044 0.047 0,050 0.054 0.059 0.064 0.071 0.079 0.089 0.103 0.121 0.147 0.028 0.048 0.051 O.OS5 0.059 0,064 0.071 0.078 0.087 0.098 0.113 0.133 O.161 0.030 0.052 0.056 0.060 0.065 0.070 0.077 0.085 0.09s 0.107 0.123 0.145 0.176 i8 ooo 650 0.008 0.003 0.004 0.004 0.004 0,004 0,005 0.005 0.006 0.006 0.007 0.008 O.OIO (n-is) 0,010 0.007 0.008 0.008 0.009 O.OIO O.OIO O.OII 0.013 0,014 0.016 0.018 0.022 0.012 0,011 . 01 2 0,013 0.014 0.015 0.016 0.018 0,019 0.021 0.025 0.028 0.033 0.014 o.ois 0.016 0.017 0.018 0.020 0.022 0.024 0.026 0.029 0.033 0.038 0.045 0.016 o.oig 0.020 0,022 0.023 0.025 0.027 0.030 0.033 0.037 0.042 0.048 O.OS7 0.018 0.023 0.024 0.026 0.028 0.030 0.033 0.036 0.040 0.044 0.050 0.058 0.068 0,020 0.027 0.020 0.031 0.033 0.035 0.039 0,042 0.047 0.052 0.059 0.068 0.080 O.OZ2 0,031 0.033 0.035 0.038 0.041 0.044 0.048 0.053 0.059 0.068 0.078 0.092 0.024 0.035 0.037 0.040 0.042 0.046 0.050 0.054 0.060 0.067 0.076 0.088 0.104 0.026 0.039 0.041 0.044 0.047 0.051 0.05s 0.061 0.067 0.074 0.085 0.008 o.iis 0.028 0.043 0.04S 0.048 0,052 0.056 0.061 0.067 0.074 0.082 0.093 0.108 0.127 0.030 0.047 0.050 O.OS3 0.OS7 0.061 0.067 0.073 o.oSi 0.089 0.102 0.117 0.139 REINFORCED CONCRETE DESIGN ^gi TABLE 14. BEAMS WITH COMPRESSION STEEL— Continued. h h Ratios of Compression Steel. i>' h Katiosot Depth of Compression to Tension Steel, a 0.02 0.04 0.06 0.08 O.IO 0.12 0.14 0.16 0.18 0.20 0.22 0.24 i8 ooo 7SO O.OIO 0.003 0.004 0.004 0.004 0.004 0.005 o.ops 0.006 0.006 0.007 0.008 0,000 («=IS) O.OI2 0.007 0.007 o.ooS 0.008 o.oog o.oog O.OIO O.OII 0.012 0.013 0.015 0.017 0.014 O.OIO O.OII O.OII 0.012 0.013 o.oi^ O.OIS 0.016 o.oiS 0.020 0.022 C.025 o.oi6 0.014 0.014 0.015 0.016 0.017 o.oig 0.020 0.022 0.024 0.027 0.030 0.034 0.018 0.017 o.otS 0.019 0.020 0.022 0.023 0.025 0.027 0.030 . 033 0.037 0.042 0.020 0.020 0.021 0.623 0.024 0.026 0.02S 0.030 0.033 0.036 0.040 0.045 0.051 0.022 0.024 0.02s 0.027 0.028 0^030 0.033 0.03s 0.038 0.042 0.047 0.052 0.055 0.024 0.02; 0.029 0.030 0.032 0.03s 0.037 0.040 0.044 0.048 0.053 0.060 0.068 0.026 0.030 0.032 0.034 0.036 0.039 0.042 0.045 0.049 0.054 0.060 0.067 0.076 0.028 0-034 0.036 0.03S 0.040 0.043 0.046 0.050 0.055 0.060 0.067 0.07s 0.085 0.030 0.037 0.039 0.042 0.044 0,048 0.051 0.055 0.060 0.066 0.073 0.0S2 0.093 l8 CX30 8oo 0.008 O.OOT O.OOI O.OOI O.OOI O.OOI O.OOI O.OOI 0.001 O.OOI O.OOI O.OOI 0.002 (» = I2) O.OIO 0.005 0.005 O.OOS 0.006 0.006 0.007 0.008 0.008 0.009 O.OII 0.012 O.OIS 0.012 0.009 0.009 O.OIO O.OII 0.012 0.013 0.014 0.015 0.017 o.oig 0.022 0.027 0.014 0.013 0.014 O.OIS o.oi6 0.017 0.018 0.020 0.022 0.025 0.028 0.033 0.039 0.016 0.017 0.018 0.019 0.020 0.022 0.024 0.026 0.029 0.033 0.037 0.043 0.051 0.018 0.021 0.022 0.024 0.025 0.027 0.030 0.033 0.036 0.040 0.046 0.053 0.063 0.020 0.025 0.026 0.02a 0.030 0.033 0.036 0.039 0.043 0.048 0-055 0.063 0.075 0.022 0.029 . 03 1 0.033 0.035 0.038 0.041 0.045 0.050 0.056 0.063 0.073 0.087 0.024 0.033 0.035 0.037 0.040 0.043 0.047 0.051 0.057 0.064 0.072 0.084 0.099 0.026 0.037 0.039 0.042 0.045 0.048 0.053 0.058 0.064 0.071 o.oSi 0.094 O.III 0.028 0.041 0.043 0.046 0.050 0.054 0.058 0.064 0.071 0.079 0.090 0.104 0.123 0.030 0.04s 0.047 0.051 0.055 0.059 0.064 0.070 0.078 0.087 0.099 0.II4 0.13s 1 8 ooo 8so O.OIO 0.003 ^ 0.003 0.003 0.003 0.004 0.004 0.004 0.005 0.005 0.006 0.007 0.008 («=I2) 0.012 0.007 ' 0.007 0.007 0.008 0.009 0.009 O.OIO 0.011 0.012 0.014 0.016 0.018 0.014 O.OIO O.OII 0.012 0.012 . 013 O.DIS o.oi6 0.017 o.oig 0.022 0.02s 0.029 0.016 0.014 0.015 0.016 0.017 o.oiS 0.020 0.022 0.024 0.026 0.030 0.034 0.039 o.oiS 0.018 0.019 0.020 0.022 0.023 0.02s 0.027 0.030 0.033 0.037 0.043 0.050 0.020 0.021 0.023 0.024 0.026 0.028 0.030 0.033 0.036 0.040 0.045 0.052 0.060 0.022 0.025 0.027 0.029 0.031 0.033 0.036 0.039 0.043 0.047 0.053 0.061 0.071 0.024 0.029 0.031 0.033 0.03s 0.038 0.041 0.045 0.049 0.054 0.061 0.070 0.081 0.026 0.033 0.03S 0.037 0.040 0.043 0.046 0.050 0.055 0.061 0.069 0.079 0.092 0.028 0.036 0.039 0.041 0.044 0.048 0.051 0.056 0.062 0.068 0.077 0.088 0.102 0.030 0.040 0.043 0.04s 0.049 0.052 0.057 ,0.062 0.068 0.07s 0.085 0.097 O.II2 i8 ooo goo 0.010 O.OOI O.OOI O.OOI O.OOI O.OOI 0.002 0.002 0.002 0.002 0.002 0.002 0.003 (»=I2) 0.012 0.005 0.005 0.005 0.006 0.006 0.006 0.007 0.008 0.008 0.009 O.OII 0.012 0.014 0.008 0.009 0.009 O.OIO O.OIO O.OII 0.012 0.013 0.015 0.016 0.019 0.021 0.016 0.012 0.012 0.013 0.014 0.015 0.016 0.018 0.019 0.021 0.024 0.027 0.031 0.018 0.015 0.016 0.017 0.018 0.020 0.021 0.023 0.025 0.028 0.031 0.03s 0.040 0.020 0.019 0.020 0.021 0.023 0.024 0.026 0.028 0.031 0.034 0.038 0.043 0.049 0.022 0.022 0.024 0.02s 0.027 0.029 0.031 0.034 0.037 0.040 0.045 0.051 0.058 0.024 0.026 0.027 0.02Q 0.031 0.033 0.036 0.039 0.042 0.047 0.052 0.059 0.068 0.026 0.029 0.031 O.C3J 0.035 0.038 0.041 0.044 0.048 O.OS3 0.059 0.067 0.077 0.028 0.033 0.035 0.037 0.039 0.042 0.046 0.050 0.0s A 0.060 0.066 0.075 0.086 0.030 0.036 0.038 0.041 0.044 0.047 0.051 0.055 0.060 0.066 0.074 0.083 0.095 z8 ooo 1 ooo 0.012 O.OOI O.OOI O.OOI 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 (M=I2) 0.014 0.004 0.005 0.005 0.005 0.006 0.006 0.007 0.007 0.008 0.008 o.oog O.OII 0.016 0.008 0.008 0.009 0.009 O.OIO O.OIO O.OII 0.012 0.013 0.014 0.016 0.018 0.018 O.OII O.OII 0.012 0.013 0.014 O.OIS 0.016 0.017 0.019 0.020 0.023 0.026 0.020 0.014 O.OIS 0.016 0.017 0.018 0.019 0.020 0.022 0.024 0.026 0.029 0.033 0.022 0.017 0.018 0.019 0.020 0.022 0.023 0.025 0.027 0.029 0.032 0.036 0.041 0.024 0.020 0.021 0.023 0.024 0.026 0.027 0.030 0.032 0.03s 0.038 0.043 0.048 0.026 0.023 0.02s 0.026 0.028 0.030 0.032 0.034 0.037 0.040 0.044 0.049 0.056 0.02S 0.027 0.028 0.030 0.032 0.034 0.036 0.039 0.042 0.046 0.050 0.056 0.063 1 0.030 0.030 0.031 0.033 0.03s 0.038 0.040 0.043 0.047 0.051 0.056 063 0.071 592 A TREATISE ON CONCRETE DESIGN OF BEAMS WITH COMPRESSION STEEL. Table 14. For the design of beams with steel in top and bottom Table 14, pages 589 to 591, may be used. Diagrams 2 and 3, pages S94 and 59s, may be used also but are less convenient except for stresses not covered in Table 14. The use of Table 14 is illustrated as follows : Example: Given, bending moment, M = 2 000 000; available depth and breadth of beam, 32 inches and 14 inches; allowable stresses /j = 18000 and/^ = 750; and n = 15. The depth of the compression steel is oi = 2 inches. Determine the amount of tensile and compressive steel. 2 Solution: Since A = 32 inches, d = 2g inches and a = — ■ =0.069. From the 29 M formula .4s = — , where we may assume ;' = 0.89, (see page 496) we have. 2000000 As 4-3° . , As = = 4.30 square mches. Compute p = — = = o.oioo. 0.89 X 29 X 180C0 bd 14X29 Refer to Table 14 in the section for/j = 18000 and fc = 750, and find the va'ue of p corresponding to o = 0.06 and pi = 0.0106. p = 0.0052. Check the value of j by referring to Diagram i, Page 593, and recompute if necessary. REVIEW OF BEAMS WITH COMPRESSION STEEL. Diagrams 2 and 3. For the review of beams with steel in top and bottom, where it is required to determine the stresses when the dimensions of the beam and steel area are given, Diagrams ^ and 3, pages 594 and 595, are to be used, as illustrated below. Example: Given As =3.3 square inches; M = 1 230 000 inch pounds; A^ = 2.0 pi square inches; and ratio — ■ = 1.75. The depth of compressive steel is aa = 1.5 P' inches. Find /j and fc. 1.5 Solution: Since h = 24.5 inches, i = 23 inches and a = = 0.065. Com- 23 S- 5 / 2 .0 pute />! = = 0.0152. and p = = 0.0087. From Diagram 2, (page 23 X 10 23 X 10 594) for a = 0.06 and />, = 0.0152 and p = 0.0087 we have, by interpolation, a value of — = 1.3. From the formula /j = where y = 0.89, (see p. 496) we have fs = =17 200 pounds per square inch. Since = 1.3 and 0.89 X 23 X 3-5 «fc .17 200 /j = 17 200 we have, for « = 15, J c = = 880 pounds per square mch. Check the value of ; by referring to Diagram i, ))age 593, and recompute if necessary. REINFORCED CONCRETE DESIGN 593 DIAGRAM 1.— VALUES OF j FOR BEAMS WITH STEEL IN TOP AND BOTTOM. {See p. 496.) 0.35 0.90 o.as o.so \ ^ =,f^ Jj 0.00 — D,60 ^zz:zz ^ %^ 1.50 a- yoe ,0.1c ).O.I 2 0.95 0.90 oas QSO ^ ?; = 0^ ^ - — ^ =^ ;;;;^ ^^ ^ ^^ a- 3 20 QZZ ,0.1 4 0.a 1.0 1.2 1.4 16 IS £0 £.2 £4 2.6 2S aO 3.2 Values of -^ u. = ratio of depth of steel in compression to depth of steel in tension. 594 A TREATISE ON CONCRETE ao5o O040 0030 0020 0010 0002 .Q( 0050 0050 0040 0050 0010 m '% u. tW. tiii: It, w •tlt ',ny.y- V-U U'7. h tA n^ i--/ Ma -I'Li^ z: ~.i. '.i- Ff — .007 QfllO 0015 0020 0025 0030 0035 0040 007 OOIO 0015 0020 0025 0-002 0=004. lU 7-- III -/. m r>- !?=:: ?!i7 -V. TiiJ4l t 007 ODIO 0015 0020 0025 O030 0035 0040 Q07 QOIQ Q0IS 0020 O025 0030 0035 004 (D a«006 ____ a-O08 O O050 I 0040 ao3o 0020 0002 O070D 0050 0040 Q030 Q020 001)0 W- p h- m m it ip^ i f-.* -ft j.%- -/- i> :s^: -/■ '7 5 0020 0025 Q03O 0035 004 <:^ 0020 0025 0030 0035 0040 O07 OOIO O0I5 Percentage of Tensile S+eel a»OI0 • a-Q.12 patio of Depth o'f Steel in Compression to Deptl^ o| Steel in Tension Diagram 2. — Relation between Tensile and Compressive Steel in Beams with Steel in Top and Bottom. (See p. 492.) REINFORCED CONCRETE DESIGN 595 Q050 aosor 0) 0050 ,007QOIO aOI5 Q02Q Q025 Q03O Q055 QDAfwaOlO MIS 0020 Q025 Q050 0035 Q040 O'OSi QOSOr 5i^^ lO I 0040 0) 10 £ o o Q030 1- QD20 ^QOIO :/5 n s /:^ ?; -^s^ ;;:^- t 4^ 7. 0040 O030 002C 0010 0002 n iU, £ 7^ til 7^ s n m c oooas Q .007 0010 Q0I5 Q020 0025 O03Q Q035 QQ40J)07QOIO 0015 Q020 O025 0030 Q035 0040 P nn.;n~^, o^lM „„.„ 0^020, aosD Q030 0020 'QOlO O002. ^1 ~^-- % io -/- W- % -/- %■ 7i OOSOr O030- 0.020 0010 i 7^' *;: 007 0010 0015 Q020 0025 ' Q030 Q035 a040j007 00IO 0015 0020 0025 0030 Q035 O040 Percentage of Tensile Steel a=a22 __, a-0.24 Ratio of Depth of Ste.el in Compression 1d Depth of Steel inlension Diagram 3. — Relation between Tensile and Compressive Steel in Beams with Steel in Top and Bottom. {See p. 492. J 596 A TREATISE ON CONCRETE TABLE IS. TABLE FOR CONSTANT C FOR BEAMS Data for Determining Depth of Beam, Moment of Resistance and Reinforcement To be used in formula for Depth of rectangular beams or slabs, d = C ^iy and in formula for Moment of Resistance M ■■ Ml CSee. pp. 483 and 355.) Based on dimensions in inches and moments in inch-pounds. Ratio of Moduli of Steel to Concrete Ratio of Moduli of Steel to Concrete M = 12 « = = 15 ■3 C cr. u it of Moment tc Depth of Is CO u 11 (3 r pKij atio of Moment Arm to Depth of Steel (i-|) ■0.2 1 ^-3 P « *J %< CO ■II •11=^ .2S r ^ ^ ei (3 f« Pi PI C/3 fs /. k i p c k ;■ .* C lb. iier lb. per sq. in. sq. in. 12 000 850 0.460 0.847 0.0163 0.077 o.SiS 0.828 0.0183 0.074 14 000 Soo 0.300 0.900 0,0054 0.122 0.348 0.884 0.0062 0.114 SSO 0.320 0.893 0.0063 0.II3 0.372 0.876 0.0073 o.ro6 600 0.340 0.887 0.0073 0.105 0.392 0.869 0084 0.099 650 0.3S8 0.881 0.0083 o.ogg 0,409 0.861 0.0095 0.093 700 0.37s 0.87s o.oo;4 0.093 0.428 0.857 0.0107 o.osa 7 SO 0.391 0.870 0.0105 0.088 0.446 o.8si 0.0120 0.083 Soo 0.407 0.864 0.0116 0.084 0.462 0.846 0.0132 0.080 850 0.422 0.860 0.G128 0.081 0.477 0.841 0.0145 0.077^ 16 000 SOO 0.273 0.909 0.0043 0.127 0.319 , 0.894 0.0050 0.II8 55° 0. 292 0.903 0.0050 0.117 0.339 0.887 0.0058 O.IIO Goo 0.310 0.897 0.0058 0.109 o.3s8 0.881 ' 0.0067 0.103 650 0.328 0.891 0.0067 0.102 0.378 0.874 0.0077 0.096 700 0.344 0.88s 0.0075 0.097 0.397 0.868 0.00S7 0.091 7SO 0.360 0.880 0.0085 0.092 0.414 0.S62 0.0097 0.086 800 0.37s 0.87s 0.0094 0.087 0.429 0.8S7 0.0107 0.083 850 0.389 0.870 0.0103 0.083 0.444 0.852 0.0118 0.079 900 0.403 0.866 0.0113 0.080 0.458 0.847 0.0129 0.075 18 000 SOO •0.250 0.917 0.0035 0.132 0.294 0.902 0.0041 0.123 SSO 0.268 o.gil 0.0040 0.123 0.314 0.89s 0.0048 0.113 600 0.286 0.90s 0.0048 0.113. 0.333 0.889 0,0056 0.106 650 0.302 0.899 0.0055 0.106 0.3SI 0.883 0.0063 0.099 700 0.318 0.894 0.0062 O.IOO 0.360 0.877 0.0072 0.094 750 0.333 0.889 0.0070 0.094 0.385 0.872 0.0080 o.o8q 800 0.348 0.884 0.0077 o.ogo 0.400 0.867 0.0089 0.08s 850 0.362 0.879 0.0085 0.086 0.41S 0.862 . 0098 0.081 900 0.37S 0.87s 0.0094 0.082 0.429 0.857 0.0107 0.077 30 000 500 0.231 0.923 0,0029 0.137 0.272 0.909 0.0034 0.127 SSO 0.248 0.917 0.0034 0.126 0.292 0.903 0.0040 0,118 600 0.26s 0.912 0.0040 0. 117 0.311 0.896 0.0047 0.109 630 0.281 0.907 0046 0, no 0.328 0.891 O.OOS3 0.103 700 0.296 o.goi . 00^ 2 0.103 0.344 0.88s 0.0060 0.097 750 0.310 0.897 0.005S 0.098 0.3S9 0.880 0.0067 0.092 800 0.324 0-892 0065 0.093 0.374 0875 0.0075 087 850 0.338 0.887 0.0072 0.088 0.389 0.870 0.0081 0.083 900 0.351 0.883 0.0079 0.085 0.403 0.866 0.0091 c oSo 24 000 8so 0.298 o.goi O.O0S3 0.093 0.347 0.884 0.0061 0.088 REINFORCED CONCRETE DESIGN 597 TABLE 16. DATA FOR DETERMIWING DEPTH OF RECTANGULAR BEAM OR SLAB OR MOMENT OF RESISTANCE FOR DIFFERENT PERCENT- AGES OF STEEL. Ratio of elasticity, « = 15. Rule I. To find depth of beam or slab for a given percentage of steel: On line with the given percentage, select the higher value of C. This, substituted in formula (see p. 481), gives the smallest permissible depth. Thus for 0.004 steel ratio the value of C from column (9) must be used instead of from column (6) because the latter would stress the steel to 23 700 pounds, which would not be allowable. It is evident also that the ratio of steel is too low for econ- omy, because concrete is stressed only to 440 pounds. Rule 2. To find amount of steel for a given beam or slab and given load- ing with stress in concrete limited to 650 pounds per square inch and stress in steel to 16 000 pounds per square inch: iCompute value of C from formula M = -^ (see p. 3SS). Locate this value either in column (6) or (g), whichever satisfies the allowed stresses, and find the corresponding value -of p in xhr first column. Thus, if C = O.OQ7, it must be located in column 1,9) instead of column (6), because the latter would give a higher stress in steel than is allowable. The desired ratio of steel is therefore 0.0077. If C = 0.088, it must be located in column (6) because column (9) would give too high a stress in concrete. At 1^^ c IS a 0) c — III Maximum fibre stress in steel corresnond- iug to fg = C50 Constant in formula d=cv'^ seepage 483 Maximum fiber stress in concrete corre- sponding to fa = 1 000 ' Constant in formula seepage 483 p k ;• u /. C fa fc C (1) (2) t3) (4) (5) (6) (7) CS) (9) U.002 0.217 0.928 650 32900 0. 124 16000 290 0.183 0.00^ 0.004 0.258 0.914 650 28000 0. 114 16000 370 U.151 0. 292 °-9°i 650 23700 0. 108 16000 440 0.132 0.005 0.320 0.893 650 20800 0. 104 16000 500 0.118 0.006 0.344 0.885 650 18600 0. 100 16000 560 0. 108 0.007 °-36s 0.878 650 16900 0.098 16000 616 0. lOI o.ooS 0.384 0.872 650 15600 O.P96 16000 670 0.095 0.009 0.402 0.866 650 14500 0.094 16000 720 U.089 O.OIO 0.418 0.861 650 13600 0.092 16000 760 0.08s O.OT2 0.446 0.851 650 I2TOO 0. 000 16000 860 0.078 0.014 0.471 0.843 650 I 1000 0.088 16000 95° 0.072 U.O16 "■493 U.836 650 lOOOO 0.086 16000 1040 o.c68 0.018 ■ 5 13 0.829 650 9300 0.085 16000 1120 0.065 0.020 "■531 0.823 650 8600 0.084 16000 1210 0.061 598 A TREATISE ON CONCRETE I TABLE 17. PROPORTIONAL DEPTHS OF NEUTRAL AXIS Proportional Depth of Neutral Axis Below Top of Beam, k, and Ratio of Stress in Steel to Stress in Concrete, j-, for Dijerent Percentages of Steel and Various Ratios of Jc Moduli of Elasticity. {See p. 400.) The table below gives the proportional depths of the neutral axis, k, calculated from formula 6, page 484, for various percentages of steel and moduli of elasticity and the corresponding ratio of stress in steel to stress in concrete, j. Its principal use is for determining the moment of resistance, and consequently the safe loading for beams already built. Its use is not advised for ordinary calculations of moments of resistance and dimensions of beams or slabs, because it presents no means of de- termining, without further calculation, the stress in the steel or the concrete, and therefore is liable to lead to uneconomical design. p Ratio of n = 10 n = 12 n = z' n = 20 re = » = 3S Area of Steel to Cross-Sec- tion of A /, /.. /. /. /. Beam Above Steel k Tc * fc k fc k Jc k /. * /. O.OOI o.*i32 66 0.143 72 0.158 79 0.181 91 217 109 232 116 0.002 0.181 45 0.196 49 0.217 54 0.246 62 292 73 3" 78 0.003 0.217 36 0.235 39 0.258 43 0.292 49 344 57 365 61 0.004 u. 246 31 U.266 33 0.292 37 0.328 41 384 48 420 53 o.oos 0.270 27 U.292 29 0.320 32 0.358 36 418 42 442 44 0.006 0.292 24 0.314 26 0.344 29 0.384 32 446 37 471 39 0.007 0.3II 22 0.334 24 0.365 26 0.407 29 471 34 497 36 0.008 0.328 21 0-353 22 0.384 24 0.428 27 493 31 519 32 0.009 0.344 19 U.369 21 0.402 22 0.446 25 513 29 539 30 O.OIO 0.358 18 0.384 19 0.418 21 0.463 23 531 27 557 28 0.012 0.384 16 0.402 17 0.446 19 0-493 21 562 23 588 25 0.014 0.407 15 0.436 16 0.471 17 0.519 19 588 21 614 22 0.016 U.428 13 0.457 14 0-493 IS 0.542 17 611 19 637 20 0.018 U.446 13 U.476 13 0.513 14 0.562 16 631 18 u 657 18 0.020 0.463 12 0.493 12 0.531 13 0.580 15 649 16 675 17 0.030 0-S3I 9 0.562 9 0599 10 0.649 II 0.040 U.580 7 U.611 8 0.649 8 0.697 9 0.050 0.618 6 u.649 6 0.686 7 0.732 7 599 USE FOR REVIEWING DESIGNS OF COLUMNS WITH VERTICAL REINFORCEMENT TABLE 18. AVERAGE WORKING UNIT STRESS, /, ON CONCRETE COLUMNS Reinforced with Longitudinal Bars, for Different Unit Stresses in Concrete and Different Per- centages of Steel. {See p. 564.) Based on/ = /c [i + (n — i) p]. (See p. 562.) ^■S s^ Ratio of ^=-? Steel P Allowable Average Unit Stress, J , oa Columns in Lb. per Sq. In. M fc = fc = /. = /. = /. = 4 = fc = fc = /. = 400 450 500 550 600 650 700 750 800 H Ci) (2) (3) (4) (5) ■ (6) (7) (8) t9) (10) (11) IS 0.007s 442 497 553 608 663 718 774 829 884 O.OIOO 4S6 513 570 627 684 741 798 85s 912 0.OI2S 470 529 588 646 705 764 823 881 940 0.0150 484 545 60s 666 726 787 847 908 968 O.OI7S 498 S6o 623 68s 747 809 872 934 996 0.0200 S12 576 640 704 768 832 896 960 1024 0.0225 526 S92 658 723 789 85s 921 .986 IOS2 0.0250 S40 608 675 743 810 878 945 1013 1080 0.02 7-5 554 623 693 762 831 900 970 1039 II08 0.0300 S68 639 710 781 852 923 994 1065 II36 0.032s S82 6SS 728 800 873 946 1019 1 091 1 164 0.0350 S96 671 745 820 894 969 1043 1118 1192 0.0375 610 686 763 839 915 991 1068 1144 1220 0.0400 624 ■702 780 858 936 1014 1092 1170 1248 0.0425 638 718 798 877 957 1037 IH7 I196 1276 0.0450 652 734 81S 896 978 1059 1141 1223 1304 0.047s 666 749 833 916 999 1082 1165 1249 1332 0.0500 680 76s 850 93S 1020 lios 1190 1275 1360 0.0550 708 797 885 973 1062 1150 1239 1328 1416 0.0600 736 82S 920 1012 1 104 1196 1288 1380 1472 /. = /. = /. = /. = /. = /. = /. = /. = fc = /. = 0.0075 SSO 600 650 700 750 800 850 900 950 rooo 12 S9S 650 704 758 812 866 920 974 1028 1083 0.0100 611 666 722 777 833 888 943 999 105s mo O.OI2S 626 683 739 796 853 910 967 1024 I081 1138 0.0150 641 699 757 816 874 932 990 1048 1 107 1165 0.0175 656 716 775 835 894 954 1014 1073 1 133 1193 0.0200 671 732 793 854 91S 976 1037 1098 IIS9 1220 0.022s 686 749 811 873 936 998 1060 1123 1185 1248 0.0250 701 765 829 893 957 1020 1084 1 147 1211 1275 0.027s ,716 782 847 912 977 1042 1107 1172 1237 1303 0.0300 732 798 86s 931 998 1064 1130 I197 1263 1330 0.032s 747 815 882 950 lOlS 1086 1154 1222 1290 1358 0.0350 762 ^^l 900 970 1039 1108 1177 1247 1316 1385 0.037s 777 S48 918 989 1059 1130 1201 1271 1342 1413 0.0400 792 864 936 1008 1080 1152 1224 1296 1368 1440 0.0425 807 88i 954 1027 IIOI I174 1247 1321 1394 1468 0.0450 822 897 972 1047 1121 I196 1270 1345 1420 1495 0.0475 837 914 990 1066 1 142 1218 1294 1370 1446 1523 0.0500 853 930 1007 1085 1163 1240 1317 1395 1472 1550 0.0S50 883 963 1043 I124 1204 1284 1364 1444. 1525 1605 o.o&oo 913 996 1079 1162 1245 1328 141 1 1494 1577 l66o /. = /. = /. = /. = fc = fc = fc = /.= /. = /.= 0.007s 600 650 700 750 Soo 850 900 950 1000 IIOO 10 641 694 747 801 8S4 907 961 IOI4 1068 II74 O.OIOO 654 709 763 818 872 926 981 1035 1090 1199 0.0125 668 723 779 834 890 946 lOOI IOS7 1113 1224 o.oiso 681 738 795 851 908 96s 1022 1078 1135 1249 O.OI7S 695 752 810 868 926 984 1042 1100 1158 1273 0.0200 708 767 826 88s 944 I003' 1062 II2I 1 180 1298 0.022s 722 782 842 902 962 1022 1082 II42 1203 1323 0.0250 735 796 858 919 980 1 041 1 103 1164 1225 1348 0.027s 749 811 873 936 998 1060 II23 I185 1248 1372 0.0300 762 826 889 953 1016 1079 II43 1206 1270, 1397 032s 776 840 90s 969 1034 1099 1163 1228 1293 1422 0.0350 789 855 921 986 1052 II18 II83 1249 1315 1447 O.057S S03 869 936 1003 1070 II37 1204 I271 1338 I47I 0.0400 816 884 952 1020 1088 iiso 1224 1292 1360 1496 0.042s 830 899 968 1037 IioS "75 1244 I3I3 1383 1522 0.04.50 843 9M 984 1054 1124 1 194 1264 1335 I4OS IS46 0.047s 8S7 928 999 107 1 1142 1213 128s 1356 1428 1570 o.osoo 870 942 1015 1087 Z160 1232 I30S 1377 1450 159s o.osso 897 972 1047 I121 1196 1271 nil 1420 149."; 164s o.ofiqo 924 1000 1078 I155 1232 1309 1463 1540 1694 6oo TABLE 19. USE FOR DESIGNING' SQUARE COLUMNS WITH VERTICAL REINFORCEMENT. Safe Loadings for Column of Various Sizes and Steel Required for Given Load. (See p. 564.) Based on P = Afc [i + (n - i) p] {See p. 562.) Of the total width of column, i i inches on all faces is considered as protective covering and is not included in the area (A) carrying load. If total area of column is to be used, select sizes 3 inches smaller than those given. is Ratio of Area of Gtccl to HITcctivc Area of Concrete. d S P = O.OIO P = 0.0:5 1 P = 0.020 P = 0.0:; 5 p = 0.0:0 * = 0-033 ^ = 0.040 1 "o -6 399 000 18.8 419 000 21. 9 439 000 25.0 30 27 174 000 7.3 107 000 10 9 420 000 14.6 443 000 18.2 465 ooo 21.9 489 000 25.5 512 000 29.2 32 20 431 000 8.4 ■tss 000 12.6 484 ooo 16.8 5ir 000 21.0 537 000 25.2 564 000 29-4 SOO 000 .13.6 3» 31 403 000 0.6 523 000 l-(-4 554 000 19.2 584 000 24.0 614 ooo 28.8 644 OOD ^l-" 67s 000 ,38,4 3l> 33 SSO 000 10.9 SOI 000 16.3 627 ODO 21. S 662 000 27.2 695 ooo 32.7 730 000 38.1 765 000 43-6 .'iS 3.5 62S 000 12.3 667 000 18.4 7o'i 0^0 24. s 74-1 000 30.6 781 00 T 3'i.S 821 000 42.0 860 000 49.0 i: 5:.1 Concrete fc = 570 n — 13 1 10 7 31 000 o.S 32 SOO 0-7 34 100 1 .0 35 600 1.2 37 100 1 -5 33 700 1-7 40 200 2.0 II 8 40 500 0.6 42 SOO 1.0 44 SOO 1.3 45 500 1.6 48 500 i.g SO SOO 2.2 52 SOO 2.6 12 SI 300 0.8 53 800 1.2 56 300 1.6 58 800 2.0 61 400 2.4 04 000 2.8 66 500 3.2 13 10 63 300 1.0 66 400 1.5 00 500 2.0 72 700 2.5 75 800 3.0 79 000 3-5 82 100 4.0 14 II 76 600 1.2 80 400 1.8 84 100 2.4 87 900 30 91 700 3.6 96 000 4.2 99 300 4.8 IS 12 01 100 1.4 05 600 2.2 100 000 2.0 los 000 3.6 109 000 4.3 114 000 5.0 118 coo 5.8 16 13 107 000 1-7 112 000 2.5 118 000 3-4 123 000 4.2 128 000 S.I 133 000 5.9 1,19 000 6.8 17 14 124 000 2.0 130 000 2.0 136 000 3.9 142 000 4.9 ,149 000 5.0 iSS 000 6.0 161 coo 7.8 18 15 142 000 2.3 140 000 3.4 I,S6 000 4.5 164 000 5.6 171 000 6.8 178 000 70 185 00c 9.0 19 16 162 000 2.6 170 000 3.8 178 000 S.I 186 000 6.4 194 000 7.7 202 000 9.0 210 coo 10.2 20 17 183 000 2.9 192 000 4-3 201 000 s.c 210 000 7.2 219 000 8.7 223 000 10. 1 237 ceo TT 6 22 10 22S 000 3.6 240 000 5-4 251 000 7.2 262 000 9.0 274 000 10.8 285 000 12.6 296 ooo 14.4 24 21 270 000 4.4 203 000 6.6 307 000 8.8 321 000 II. 334 000 13-2 3-18 000 15.4 362 000 T7 6 26 23 335 000 5-3 3SI 000 7,-9 368 000 10. C 3S3 000 13.2 401 000 15.0 418 000 18.5 434 ooo 21.2 28 25 395 000 6.3 41 S 000 9.4 435 000 12. E 434 000 15. t 474 000 18.8 493 000 21.9 513 000 25.0 30 27 4S1 000 7-3 484 000 10. 507 000 14. C 530 000 l3.2 553 000 21.9 576 000 2S.S 5nR 32 20 532 000 8.4 559 000 12.6 58s 000 16.8 611 000 21,0 638 000 25.2 664 000 29.4 690 coo 11 r. 34 11 608 000 9.6 638 000 14.4 668 000 19.2 69S 000 24.0 729 000 28.8 759 000 11.6 780 ooo 38.4 16 33 680 000 10. 723 000 10.3 757 000 21. 8 791 000 27.2 826 000 32-7 860 000 18.1 894 ^1 6 38 35 775 000 12.3 8l4 000 18.4 X52 ono 7A.. r Pno 000 .'o.r. 029 000 36.8 067 poo 42.0 I 005 coo 49.0 i: i; 2 Co-icrcts fc = 63o n = TO 10 7 36 300 0.5 37 800 0.7 39 300 1 .0 40 800 1.2 42 300 1.5 43 800 1-7 II 8 47 400 0.6 49 400 1.0 SI 400 1-3 53 300 1.6 55 300 1.9 57 200 2.2 12 60 000 0.8 62 SOO 1.2 65 000 1.6 67 SOO 2.0 70 000 2.4 72 400 2.8 13 10 74 100 l.o 77 200 1.5 80 200 2.0 83 300 2.5 80 400 30 89 400 3.S 14 II 89 600 1.2 93 400 97 100 2.4 lOI 000 3.0 104 000 3.6 108 000 4.2 15 12 107 000 1.4 III 000 2.2 116 000 2.9 120 000 3.(5 124 coo 4.3 129 ooo 16 13 125 000 1.7 130 000 2.5 136 000 3.4 141 000 4.2 146 000 S.l 151 coc 17 14 145 000 2.0 ISI 000 2.9 157 000 3.9 163 coo 4.9 169 000 SO 17s 000 6.9 18 15 167 000 2.3 174 000 3.4 181 000 4.5 187 000 S.6 194 000 6.8 201 000 7 -9 19 16 190 000 2.6 198 000 3-8 205 coo S.I 213 000 6.4 221 000 7.7 229 COO 9.C 20 17 214 ooo 2.9 223 coo 4.3 232 coo S.8 241 000 7.2 2SO 000 8.7 258 000 10. 1 22 10 268 000 3.0 279 000 5-4 290 000 7.2 301 000 9.0 312 000 10.8 323 coo 12.6 24 21 327 000 4.4 340 000 6.6 354 000 8.8 367 000 II. 3S1 000 13-2 394 ooo 15.4 26 23 392 000 5.3 408 000 7.9 425 000 441 coo 13-2 457 000 IS. 9 4 73 000 18. 5 23 25 463 000 6.3 482 000 9.4 S02 coo 12.5 521 000 15.6 54c 000 18.8 559 000 21.9 30 27 540 000 7.3 S63 000 IC.9 585 ooo 14.6 607 000 l3.2 630 00c 21. 9 652 ceo 25. 5 32 20 623 000 8.4 649 000 12.6 67s ooo 16.8 701 000 21.0 , 726 000 ''5 2 752 000 31 712 000 0.6 742 000 14.4 771 000 19.2 801 000 24.0 830 000 28.8 859 coo ., 6 36 33. SC17-.QOO 10.9 841 000 161.3 aj4-Qoo .J.I.& —90;. ooo -27-2 - 041 000. 32.-7 ■ 974- 00c 38.1 ,18 35 008 000 12.3 94 o_ 000 18.4 083 000 24-5 I 020 000 30.6 I cjS 000 36.8 I C95 000 42.9 45 300 59 200 74 900 92 SCO 112 000 133 I.S6 181 208 237 267 334 408 489 578 674 779 I C07 133 6oi TABLE 20. USE FOR DESIGNING ROUND COLUMNS WITH VERTICAL , REINFORCEMENT. Safe Loadings for Columns of Various Sizes and Steel Required for Given Load. {See p. 564.) Based on P = Afc [i + (« — i) p]. {See p. 562.) Of the total diameter of the column, ij inches on all sides is considered as protective coating and is not included in the area (.1) carrying load. If total area of column is to be used, select sizes 3 inches smaller than those given d s s 1 5d a Ratio of Area of Ctocl to Effective Area of Concrete. 2 2 p = O.OIO p = O.OI3 p = 0.020 t = 0.02 s ^ = 0.030 i> = 0.03 s p = 0.040 ll 1I < i^ 0-3 ■i ■S.3, Is "o -^ 13 in 1" (n It 1- ■^1 in 1- p ^s p A, p As P A, P /, P -Ij P A, in. in. lb. sq. in. lb. sq. in. lb. sq. in. lb. IS: lb. sq. in. lb. sq. m. lb sq. in. i: . : 4 Concrete fc =43 K = 15 10 7 19 700 0.4 20 goo 0.6 22 2O0 0.8 23 400 1,0 24 600 1.2 2S 800 1.3 27 000 1.5 II 8 2,'; 800 0.5 27 400 o.S 29 000 1 .0 30 SOO 1,3 32 100 l.S 33 700 1.8 35 300 2.0 12 32 600 0.6 34 Ooo 1.0 36 600 1.3 38 700 1,6 40 700 1-9 42 700 2.2 44 700 2,5 13 10 40 300 0.8 42 800 1.2 43 200 1.6 47 700 2.0 SO 200 2-4 52 700 2.7 55 100 3.1 14 II 48 800 I.O SI 700 1-4 S4 700 1-9 S7 700 2.4 60 700 2.9 63 700 3.3 66 700 3.8 IS 12 ■;8 000 I.I 61 6oo 1.7 6S 100 2.3 63 700 2.8 72 300 3.4 75 800 4.0 70 400 4-5 16 13 68 100 1-3 72 300 2.0 76 Soo 2.7 80 600 3-3 84 800 4.0 89 000 4,6 «-1 200 5-3 17 14 70 000 I -.5 83 800 2.3 88 700 3.1 91 500 3.8 98 400 4.6 103 OOD 5-4 108 000 6.2 18 IS go 700 1.8 96 200 2.7 102 000 3.5 107 000 4,4 "■^ 000 5-3 118 000 6.2 124 000 7-1 19 16 103 000 2.0 I09 000 3.0 116 000 4.0 122 000 S.o 128 000 6.0 135 000 7,0 141 000 8.0 20 17 n6 000 2,3 124 000 3-4 131 ooo 4-5 138 000 5-7 I4S 000 6.8 152 000 7-9 ISO 000 91 22 10 14,'; 000 2.8 134 000 4-3 163 000 S-7 172 000 7.1 181 000 8.S igo 000 g,g 199 000 11,3 24 21 178 000 3-5 180 000 S.2 200 000 6.9 210 000 8.7 221 000 10.4 232 000 12. 1 241 000 13,8 26 23 213 000 4.2 226 000 6.2 2 30 000 8.3 2';2 000 10.4 26s 000 12, S 279 000 14-5 292 000 16,6 28 25 252 000 4-9 267 000 7.4 283 000 9.8 298 000 12.3 314 000 14-7 329 000 17.2 345 000 19,6 30 27 204 000 f,-1 312 000 8.6 330 OOD II. .S 348 000 14,3 3S6 000 17.2 384 000 20,0 402 000 22,9 ,12 20 ,330 000 b.b 360 000 9-9 381 000 13.2 401 000 'S-' 422 000 19.8 443 OOO 23-1 464 000 26.4 34 31 387 000 7-S 411 000 II. 3 433 OOO IS. I 459 000 18.9 4S2 000 22.6 50a 000 26,4 5.10 000 30,2 .16 33 430 000 8.6 466 000 12.8 401 000 17. 1 S20 000 21.4 547 000 25. 7 574 000 29, g 600 000 34,2 38 35 494 000 0.6 •i'i'l 000 14.4 ,';.S4 000 in. 2 585 000 24.1 615 000 28.0 645 000 31,7 675 000 38.5 1:1 1 : 3 Concrete /c=5 -0 » = 12 10 7 24 300 0,4 25 500 0.6 26 800 0,8 28 000 I.O 29 200 1,2 30 400 1.3 31 600 l-S II 8 31 800 0,5 33 400 0,8 35 000 1,0 36 500 1,3 38 100 1,5 39 700 1.8 41 300 2,0 12 9 40 300 0,6 42 300 1.0 44 200 1.3 46 200 1,6 48 200 1,9 SO 200 2.2 52 200 2,5 13 10 49 700 0,8 52 200 ,T ■ 2 54 boo 1,0 57 100 2,0 59 500 2.4 02 000 2.7 64 500 3.1 14 u 60 100 1.0 63 100 1.4 66 100 1.9 69 100 2.4 72 100 2,9 75 ODO .3-3 78 000 3.8 IS 12 71 600 1,1 75 100 1.7 78 700 2.3 82 2O0 2.8 83 8do 3,4 89 300 4.0 92 800 4.5 16 13 84 000 1.3 88 100 2.0 02 300 2.7 96 SOD 3,3 lOI ODD 4.0 lOS OOD 4.6 log 000 5-3 17 14 07 000 1.5 102 000 2,3 107 000 3.1 112 OOD 3.8 117 ODD 4,0 122 OOD 5-4 126 000 T« 15 119 000 1.8 117 000 2.7 123 000 3.5 128 000 4,4 1,14 000 5-3 140 000 6.2 14s 000 ?■' 19 16 127 000 2.0 134 000 3-0 140 OOO 4,0 146 000 s,° 152 000 0,0 IS9 000 7.0 165 000 8,0 20 17 144 000 2.3 ISI 000 3-4 158 000 4.5 165 000 5,7 172 000 6,8 179 000 7-9 186 000 9.1 22 19 179 000 2.8 188 000 4-3 197 000 S,7 206 000 71 215 000 8,5 224 000 9.9 233 000 11,3 24 21 210 000 3-5 230 000 5-2 241 000 6,9 252 OOD 8,7 263 ODD 10,4 273 OOD 12,1 284 000 13,8 26 23 26, 000 4-2 276 000 6,2 28g 000 8,3 302 000 10,4 31 S OOD 12,5 •''25 000 14-5 341 000 16,6 2S 25 311 000 4-9 326 000 7-4 341 000 9,8 357 000 12,3 372 000 14.7 388 OOD 17,2 403 000 19,6 '27 162 000 5-7 380 000 8,6 30S 000 ri,S 416 000 14.3 434 OOD 17.2 452 OOD 20.0 470 000 22, g 32 29 1t8 000 5,6 419 000 9-9 45g 000 13.2 480 000 16, S ■SOI OOD 19.8 521 OOD ■23.1 S42 000 26.4 31 47R 000 7,8 SOI OOO 11-3 525 OOD IS- 1 549 ODO 18, g 572 ODD 22,6 ,59s ODD 26.4 620 000 30,2 16 S4I 000 8.6 S68 000 12,8 .sgs 000 17,1 622 000 21,4 649 ODO 25,7 675 000 29.9 702 000 34,2 38 35 eig 000 9,6 6^n 000 14,4 660 ODO 10,2 699 000 24.1 720 OOD 28. 7 bo 000 31.7 790 000 38,5 i: T : 2 Concrete fc = 6S0 « = 10 10 7 23 ';oo 0,4 29 700 0,6 30 900 0.8 32 000 I.O 33 200 1.2 34 40= 1,3 35 600 i.S 8 37 300 0,5 38 800 o.a 40,300 1,0 41 900 1.3 43 400 IS 44 goo 1,8 46 SOO 2.0 0,6 49 100 1,0 51 000 1.3 53 000 1.6 54 900 1.9 56 900 2,2 38 800 2,3 58 200 0.8 60 600 1,2 63 000 1,6 65 400 2.0 67 800 2.4 70 200 2.7 72 600 3,1 14 " 70 400 I.O 73 400 1,4 76 300 1.9 79 200 2.4 82 100 2,9 83 000 3-3 87 900 3-8 IS 12 Ri Roo 1. 1 87 300 1,7 90 900 2,3 94 200 2.8 97 700 3-4 loi 000 4,0 105 000 4,5 t6 13 08 400 1.3 102 000 2,0 107 000 2,7 III 000 3.3 115 000 4.0 no 000 4,6 123 000 5,3 nnn I-S iig 000 2,3 124 000 3-1 128 ODD 3.8 133 000 4.6 138 000 5-4 142 000 T« 1,8 136 000 2,7 142 000 3-5 147 000 4,4 153 000 5.3 158 000 6.2 163 000 Z-' 19 16 149 000 2,0 ISS 000 3.0 161 000 4.0 167 000 5-0 174 000 6.0 180 000 7.0 186 000 8,0 17 t68 2,3 175 000 3-4 182 000 4,5 189 000 ,5., 7 .196 000 - 6.8 203 000 7.9 210 000 9,1 noo 2,8 2ig 000 4,3 228 000 5.7 236 000 7.1 245 000 8.5 254 000 9,9 262 000 11,3 '.t 21 257 000 3,5 267 000 5-2 278 000 6,9 289 000 8.7 2gg 000 10.4 310 000 12,1 320 000 13.8 23 ,nS 000 4.2 321 000 6,2 333 000 8.3 346 000 10.4 339 000 12,5 372 000 14.5 384 000 16,6 28 2,S 364 000 4-9 379 000 7-4 394 000 9.8 409 000 .12.3 424 000 14-7 439 000 17.2 454 000 19,6 7.7 onn 5-7 442 000 8,6 4S9 000 II. 5 477 000 14.3 494 000 17,2 512 000 20.0 330 000 22,9 32 29 ft. 6 SIO OOD 9.9 S30 000 13-2 SSO 000 16. s 571 000 lg,8 591 000 23.2 611 000 26,4 560 000 7.5 583 000 11,3 606 000 15 I 629 000 18.9 634 000 22,6 673 000 26.4 698 000 30, J 36 fill 000 8,6 660 000 12,8 686 000 17.1 713 000 21.4 739 000 2.5,7 763 000 29,9 791 000 34-2 38 3S 713 000 9.6 743 000 14,4 772 000 19.2 802 000 24.1 831 000 28,9 860 000 33-7 890 000 3S.S 6o2 A TREATISE ON CONCRETE tj g 1 -? t.3 II ptoi IV, • ■ft, =PS ~ JO tajy 'J t3 d II 0, :£ ^ IMJS jo^siV '^ S'.H ■a, pEO-i ajus a^ ^ 0. F»1S 1 » jo^aiV 1 ^ tB u o' s p^o«o«ow Nwto^>o oodo*o« tot^o-^oi ifoiwjMi^ lo O ( v> O t 1^0 o c CO >o (^ C M IN to to ■«*• ^o\o ^^oo o H-if^-o^ coto*^ 2.^ 8 O O Q o o o 5 OOOO r* ■* O »0 Olio to CO Tff«.NOiOi Oil^W^cO ro lOOO O f*i \0 CO M CTCO HHMMN NCO**-*!-!^ t^ to C\ lo to M oo o WCO'O t^ H 00 r^ O »o to M « « CO ■'I- lO^O^OC0 O. O « irtco N s^S's.g 00 woo ■>*■ O r* w Tf eooo :) •* lo *0 t^oo Oi C lO CO N H O w COM "CO Oi ^ C* ^ wi"© r^oo 0> M coO Oi N >0 C 8 O Q o o 5 I OOOOOO t^ OiOO CO^O •a- O r^ »o CO N to <0 -^lo »o O ^ ^ O O r^oo 0» O tOoO W t^ CO o to'O a o\0 -fj- o c CO Oi*0 to H OiOO oo OS C M w CO tf »n >TO t^oo c xj- GO CO O to ■* '^ io»0 CO >o ■^i \O00 O * I o o > O Q 1 o -* 88888 ■^ N o o o ■O H -^ f* 1^ Oi^£> O O vO ;noo^moO >oioio»oto N IN to ** ^ tO"0 r~00 0> O (OO O '+ CO rOCO ■*0 t^M^^^tO (OlOOl-^l- MHMW« WCO'0^'« lO t^OO O M ^O OO H ■^ to ^*o I-OO M CO fOOO Oi ■O00 O w ■* t^ O to t^ tj- to W « -^ O CT.CO00 ■* M H M H tM N M CO CO -t lOO t^ 00 O W W -^t H M H »OlO Oi ^ lO M H to M lO Tf OlOO ^f "d- OlfOOilOH OOlOtOOH M tN W CO ^ ^ »0>0 t^OO ■O00 O cooo »0 W t> t^vO 10*0*0 o O O O H M H M M « W « CO ■* ■* v>»0 t^M Ov t». MOOO Ol ( lOlO H H VO t^ O M <0 )Mt>.cOOi »0«0000 1 « 0 « t^ lOVO r-00 Oi REINFORCED CONCRETE DESIGN 603 fo Ooo t^ ^ N TO (O '* »i 00 o ( o" 00 o* 6 < « 000 OiMi ^'OtofOf 00 to O O O 000 OODQO OUUUU « « « TO ■* •n'O r^ 00 Oi M N Tj- H N CO to •* t^vO t^oO M »o\d t*oo O ^O O t^OO M 00000 to woo «tvO to to ^ >o^o ) M H OOO ft M tJ-00 W > 0« O H (O t^ CO Oiwj CO H Oi INO0« t^ M 00 t^ »«co M oio to to ** »o^o WOO ■* t-^O \0 f* Q COOO t^OO O H CS 100 t OHOO Irt TON M H COOO^OO Ol-* N N »0 H M ( "t COCO ■■tio-o t^oa OH to-O Oi M M M H «\o -^oo W W CO CO CO ■^WO O O »o O 00 r^oo H ^ ^ ^ t^ Oi f^ O coO Oi CO 0"*0oooo OOr^Nwi ■*« OiHI'^f OOiONhO MHMNN «CO^ lOVO ■* 00 CO O TO -t ■* mo 00 >o 'i-m ^- 000 O w -^ OivD O o "O r~oo Oi O 00 O cn O M M H H TO t- H tn o « W CO to ^ 10 r-. Oi COOO ■^in\Ooo Oi m « H I- w TO vo^ TO C0»0 MOO vit^\0 O H t O t^ >o to « to CO ■*r»o O 10 O t^ o TH H N-O HOO ro 100 00 0> Tf to Oi Ooo TO Oi »o ro O M N TO -^lO TO TO N loco CiOOOOOO o> ■^UTOOO O 6 6 6 6 » 88888 0\0 ^~ f-oo CO P|N t^ « to ^vO «^ 0> ^»■00 Oi O •H I CO >ooo O I H H H « TOOO to N Oi W N fO t ^ TOO r^oo o» 10 O O O O M O M cow ToOnMOt^ 'tO\nv)0 Wt^-sJ-WDO O 10 **• »* 10 w « CO "+ ^ lo^O i>-00 Oi ■^ Tj- ui\0 I^ Oi ^ O M « CO ^ W^O t^OO a to Ooo t>.t^ 00 0)\O M .NO 0,00 Oi^ Tf-O to fO t^ Ci TO CO-* 10 "OOO O- tH (Oi^ ■* 01 H M tS N M Tf Oi>o H r- TO to ■* io»o vOOO M >o O CO t^ to CT ^- OlO N to >0 H M M H Oiow o>oo r^^O t-00 H CON COOO Vi ^0 r-00 H H « CO to ^ »OVO 1^00 H Tt l> ■* 00 COt-NCO N CO to ■+'^ OiO NOO ■< tT CO CO fO i" to ^ "OVO f O H O m o 00 N'O woo 00 O H to ■^ t^ tOOlVOTO H 0.0 NOOvO t^ H 00 t^ 10 CO M « « tO"* lOO-OoO Oi f4 V)00 M ioo> -too to IN N TOtO ■* OlOO Ol CO Ov NO 01 NVO OS M H C^ P) C4 00 NVOOO O »0 O »0 MOO H TOOO NO »0 Oi H fONO CT' (O C* N 10 O >0 Oi W »o O* H H M N N -OiOOCO »OOiOi»oCv I O O O O N toco toco i r(- >J^^O r». 00 O O tN CO COOO N ^ to ONO ^M OOM WW M ^ OS r* H W P» N CO ■-t Tj-lOO 1-^ r~ Oi N -t r* tONO OitO C^ N N P4 TO oO vj ^NO O toco M ^00 H H CH W N NOlOtOOlTf OOOHHO H OiCO t-^CO 01 N »0 Ol ■* CO to -t "Oso ^^ Oi O H to « 00 ■>* Oi ■* OnO CO 00 »o -^tor^ NCONO t^ a ^ H H N N CO -t'l-lOO NO 00 N Tj- »^ OlN 1000 I O o ) O O > o o 10 NNO Ol O OoOnO »Ono CO CO -t >ONO H O >0 O 1 r~oo O w ( too ■* 00 COOO ti-O l>.M t^-d-CO tOlO Ol-tH M M M « « N to to -tm lot^oo w M-NOOO M Tt '. N Q O H tooo O O r^ 1 1^ O too OiO >o ^ to < M N N n M to ^ »oo ^00 O O o> ^1000 M ^ r^oo o> M ct 00 too tOl>.M 100 10 r* CTCOCO W M i-i HI n H W M H N r^ CO to -t -two 00 o* H to»Of* Ol O O < OOO-. HOOO ( 4 H H N O N to ^ 100 O o t O O c _ _ 00000 00 'too M H N Tj-lO O *^QO O* O N 000 N ^ i> to t^ -t TO W « -^ OifOOO -t H M H H W N N to to -two ^. 00 OH W ^ to w t^ Q O f* -t H O Oi N to ^ W W Oi WOO coo 00 On O e^ W O t-« 0> O H -two 00 M to woo tOOO WW 0( r^O wioo H H H H M N « N CO-*-* wNa.i>oo o» I COOO ■*« «oo00^^ N-*NOifi ■jiot^Oco WNOooo 00 r^co M IHHNM NtO^^W no t^OO Oi H I CO ^ WO t>.CO Oi 6o4 A TREATISE ON CONCRETE DIAGRAM 4. BENDING MOMENTS FOR DIFFERENT SPANS AND LOADS. 8 11 1 1 T \l \'.\ -\ 1 \\ \ V \ I \ \ i.NV''^ 5000 I ' \ \ Yo ,o 1 \ ^ \ \ \ \ W^ v^- \ \ in \° \°c\ \^ \ \ \; \ \_\ *\gsj^ ?x 1 \ \ yi \°o \i \ \ \ \ \ \ \ 3\^^M ' 1 ?. ° %\' \ \ i ' ' 1 , V \ w^m\ ' u \° \o \ \ 1 \ \ \ A »>B°o\o\ \ Vf \° I \ \ \ \j SVaS^Yli \ \ \% o V \ ^ \ \ \ \ ^ -W?\^ \\ 1 \ \ \f\9 \% \ 1 \ \ ^ \ \ \ V m°^ ^\ \ \' V\ = ° \ \ \ ^ \ _\ AoY?.\%\" \ \'^^ \ \ ill e\Si l\ \ \ \ 1 \ \ \ W, ft\°nK^ \^ \ w \ \ « (ore \ \ \ ^ \ \ \^ '%W' \ \ \ \' 1 oW \o\ \ \ \ 1 \ V\°\ M °\ \ \ \ \ \ \ \ ! Vn |o\ 1 j^ \ ^ \ \ \ \ \ % ft \'' ^ \ w \' S^ s oWfe \ \ \ \ \ \ \ ?, \ s \ 1 \ \ ^ s \ \ \ \ w \ \ \, Wo v^ \ \ \^ \ \ \ \ \ \ 5? s \ k \ \\ ^ .» \ \ \ \ \ \ s \ \ ^°o^ \ \ , \ \ »\ \, \ \ \ \ \ \ ^^ n\°0 \ \ ' \ \ \ ->^^\n \ \ \ \, \ \ \ \ . ^oJ«i-^ S \ ' \ f^S^ \^ ^ \ \ \ \ \ \ N \ \ \ t ^°\ \ \ \ \ \ \ S s \ \ sy =0^4, r; \ N s N s s \ \ \ \° \ i, s, \ \ \^ s \ \ \] ^ \ Xt ^o-o ^°s^ S S N \ ■v. ^ -V, \ \ \-i V"c \ \ s \ \ \ \ ^ \ \ ^s f^°n^ ^ >\ s % \ ~^ ---. ^ ■^ \' \i \^J\ \ \ \ s \ \ \ s \ ^„^'o„^ ^ X ^ ^ ^ ■\ ^ ^ ^-». ^ \ \ \°o \ \ \ s s \ V s :::i^ ^ssd':^ ■x ■^ ^ -V. >s ■^ \ y? N > \ s^ \ ■N N X 3^«^ >-j ■~- ^ ~^ -~; \'T°n \°o \ \ X ^. •^ V ~^ .'1 Sgwi. 5b" ^ --~ ^ ^. ;^ --- i 400- =o\ s X ^ V ^ ~~- ^ •~-. ^r "^^ 5 5 — ^ ~~- c: i — 300 V^V C\ \ ^ ^ ^^ -i fS. p? 5~- ~_ ^^ :^ ::; — = 200^ ■^^g^ v,;;^ ^ -~- ' - ' — — -; oooj- 6 7 9 1 1 2 3 4 5 li ■/ i U i D a 1 i li 1 3 i 1 s 5! li S V 1 i'i » '. u s 1 : 2 : 3i 4 ! 5' a 6 : 7 i 8: Zt SPAN OF BEAM IN FEET REINFORCED CONCRETE DESIGN 601; DIAGRAM 5. BENDING MOMENTS FOR DIFFERENT SPANS AST) LOADS. 10 -.-]i\L \\ 'ML Lll\ L \ L ll^^A 13^" ] V \''n\ 1 ._-.ffl Ji^ittrtr^ 1 hV A-UCtV I VU. \ V Vo _.- 1 iTLltrTII S£_|_t4 CV44 \ vtuA' ^Vo\%l --_._._t1I, 11411 ltl.l^. rv \ ri XT!" ■#W4 tr irii^^±To_fi \ 4 \ V l\4n-\= iirltr^ A--i\ V- V4 ttX 4 (J, \o -i \b C \ \ \ ^ LriitriniJili 1 ri. Xa \ V \q \o \o \ \ \ y ITT \\\\\WfV \ \ _V^\a° -K?,K?X \ \ \ \] liytMrlsYi r ri ^ L^^l M . \° \ \ \, \. \ ii, L^m|rrti t l. 3 t4&:^£ ? ^ \ \ \ \ \ \ IT triAsllrni 4 v. ^ VK°\ ttX \ \ \ ^ -_ .iptilP|imtX4^^^4- _Y_^^, \ \ ^ \ \ \ itiiuiimt r , \ \V ^ ^-^^^ \ , \ " 11 tin v\i\f\ \ n^ ^ t-i^V \ \, \ \ ^ \ ' W% \A tl^A \ \ \ " \ li^rl" r \ 1 ' \ \ \ \ V ' V° " S^ 4 \ \ N, V \ \ 1^ ° 1_ ^ L\ao\°\°l\ \. \ mLA l_\-\- -j^ "1 ^\ \ \ \ s \ \ 11 '°l°lo°l\ \ \ \ \ y ' \ \ \ V h^ 4 V s \ \ \ \ KI U'pioii 1 \ \ \ \ \ \ \ 4 ' \ \ - ill \ t I ^ \ \ \ \ S' \ ^ !:::::i§]ln4Qi JiiiL^ u&" \- \- \ ^ y s \ \ \ s -..-stittir LrL_J4V^\ra^" ~t X V" \ \ ^ \ \ ^ _.i:m-iu4tviitv4 «^^^- -4 \ ^" \ \ \ \ s 14" if 1 \ tnV \ \ \ \ \\ v-T. °° \4 A A \ \ ^, \ \ ^ ' ,°J: 4-4U44 ^im si^::^ : V ^ ^ \ ^ s Nv s g hU4XQ k-Ltt?l^°o-4"^^ v\ ^ \ \, ^.v \i ?p\ trniTi ViaWw^^^ \- A ^^ s h \°o. _ L-tiipioi^OTfN ^1^^ ^.^ V - \ \ ^ fn X°oN ...Liiiirri^^Volm^V^^^- -v-\ ^^- A ^ i ^ _rt4i_44lv^V»4 114 ^^, -^ V S- - ^^ \ -.414 ^Cu44t-|I%xvv^V V- ^ ^^ X . -%.- \ja^ s, ■ 444 i_tivrn^fei^5N4X^- A v\ - -% ^ s .\ 444 t4444W%A^^v^^S^^ ^ .^v^\ %°n ^ \ V V 44^ VJ»l-^^5 N^r^Cv 5^^ S-1 y -% \ \ ^4 ^t¥w^V^^^^ Vv _^^^^ 1^?= ^> \ ^ti^X^'of^AV vS^I^v\S^ ^ ^ ^ tt \ H til ti3M:v Vv^ v^^iv^ \ \yo "^Pf f? \ V ^14^ 4 ISa^^Nx ^^v\V^ vVj„rNp_^ ^ \ ^- N^ tij r ^Av^v X^^\s\^X^. ^3«^^ ^s \. \ ■^ V^lT _SvtX^!^vv\\ \^4\- i^^S^- V X V ■s ~N 4 t4-l'I^A\X\ v^\ \^v^ ^e%^^^ \ ^ ^s \ "^ 4^-S^^ v^^\^^4vv^^.^^ ^^^^^ N. ^^^ N \. ■-V £^^.?o^L \^. ^X^^S^^ 0^^^^^ ■^ ^4 >.^^ ^v V \4s.^^s^^^ ^^^^- ■~^^s^ 4^ ■^ "^■~^ tA^^o^ \ ^v^v^^^^\^^ ^^^^< ^^^-^ ^ ^^ ' — ^ ^^ \ ^=o^^S\ ^^X^^^^M "^cr^- ^~^ \^:^^^\^-^^ ^^^^^^» ^"^-^^"^■^-, -"^■""-^^ ~^ ^^ ^0, \ ^. ^.^^. ^--^^^^p^: """~-^ — ^■~- — _ -;;;^ — ^— ~:::~ =^E= -Lj rr~ p^'^^~^ ^^~. ""-—::: i2Ws^t~ t~ '""■" ~ b 1 ' '. 10 II 12 13 14 IS 16 17 i 9 20 1 1 22 23 24 25 t 26 27 28 29 30 31 32 33 ; 4 35 JO a 7l i 39 ' SPAN OF BEAMS IN FEET 6o6 A TREATISE ON CONCRETE DIAGRAM 6. BENDHTG MOMENTS FOR DIFFERENT SPANS AND LOADS. wl' M=- 12 m 1 T T T T \^ ~\ V" ~\ r V "\ -^ 1 — V V v» r- \ \t \l \ ^^ \° I \ \ \ \ \ \ p3 oY i 1 1 i ,, % \ \ \ \ \ i1 "" 1 S \o \ \ \ \ \ Vp 1 Vo \i \c \ \ \ \ \ V \^ \\°o) "in - 1 l^ Vn V p\ ^ \ \ \ \ \ \-n% °p \ \ ,30 \ \°\ M \ \ \ 1 \ \ \ Vo ^n \°o \\ \ ,]0 1 \" \o\ \ \ \ r.\°r \i\ \ \ 1 1° V \\ \ \ \ \ \ \ yU^ \ \ \l uV '\n' \ \ \ \ \ \ A?, %%^ \ \ \ 1 \\ °n\ sV \ \ \ \ \ , \^z Vo \ \ \ \ ~|T A i\ \n \ \ \ \ k T" \° \ \ \ \ \ ' \ \ % \ \ \ \ - A - V % K^ \° \ \ \ \ \ % isV \ \ \ t° i \ \ \ \ \ \ \?\ \ \ \ \ "¥ Kk \ \ \ \ \ \ Tr ;\° \3io \ \ \ _\ \ \ V J \ \ \ \ \ \ \ TT r c mim \ ^ \ \^ \% \ \ \, \ \, \ I \ iwr'pl' 3l 1 \ \ \ \ \. \^ \ \ \ \ \ \ \ I IgteisC^ \ \ \ \ \ *n "o \ ^ \ \ \, \ \, \ \ \ \ \ Vn\°. \ \ \ \ y s \ ^ > In i \\ \ \ \ * - ^°nVo -^ - _\ \] s \ \ ^J fe^ ' \ \ \ \ \ \ \ ?.\ \ \, \, % ' ■J ° nr \ \ ^\ \°o\ \ \ \ V '*?• f. < o ^^ \ s \\\ \ \ \\\ \ \ M \h\- \ ' \? \ \ \~\ yv \ ^^ \%\ii K 1 ^ \ \ \ V„ Vn S \ \ ~\ \ \ \ \ ' n \% \i &^ t^ \l ^. \ \ \ \"o \" s| ^ |\ ■0 3 \-\ \ \ %\ 2 \ O A \ ^ r ^ \ fo ^-^ \ \ ~\ \ ^ \ \ \\ V \% y"\ \ \\ \ s \ T \ \ r \ \ \ V \ h f\°< 1 \ \ V \ \ \ \\ , V ^o^o \ \ \ \ \ N N x% ^4,1 K s \ \ \ \ > \ \ \.\ 'Mi\ \ \ \ \ \ Vo t\° k \ s \ \ V \ \ w \ -fnj \°oV\^ \ \ \ s<- ^°n \ \ N \ s \ \ \ \ ? \i\^ \ \ \ \ \ \ \l\ \ h \" \ s \\ \ v^ \->o\ o .\ s^ S \ \ \ \ %o ^°o s N \ s K "°\ V \ \ \- \o N° \ \, \ \ \ \ \| \ \ ^ ?oi^°n \ \ \ \ N 110 \ \ I w \ K 6\ \ > s \ \ \ \ \ xrJ n°o^ \ N \ \ \ \ \ \ V \ \ \ \ \ \ \ S \ "% %-< \ '\ \ •s \ X \ ^ ^ s, \ \ \ \ \ ^ \ w""* i'>.\ \ \ N. \ s \ s ^'% v \ \ s s \ \ \ \ fc \°o, \\ s N ': V \ s \ X \ s. ^ !^ \ lll^ A s \ \ \ \ \ ,>^ x°o S ^ \ \ N \ \ 11 ^ \AVo V ' ^ \ \ \ \ s ■"^^ i^ ?" ^ \ N . \ ^ \ ^ ^ \ * \ \°\"°, •, \ N \ \ S4 ^ ■^ -~. ^ ^ ~~- -^ "~ ■!^'^ 5,\»)\ s .\ V s s s n r*^ ■^ ^ ~.> ■ — ^ "-- -~- .^ ■~- ;^ J" s \ ■--/On r h -^ ■"■ — ,^ ;;^ — - ^ — , .)Oc-H» '^\]S^ \ ^^ ^ -i«~ ^ ~~ - — - 1 ~ ' — Z; — — s ^ s : - fe^-^; --- ~~.." — ~ ■^— - - L l_ L_ L 1_ |_ 7 8 9 10 1 1 12 13 14 15 IB 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 SPAN OP BEAM IN F££T CONCRETE BUILDING CONSTRUCTION 607 CHAPTER XXIII BUILDING CONSTRUCTION Reinforced concrete has taken its place as an established material for building construction. Durable, fireproof, and economical in first cost; adaptable to various types of design; capable of carrying heavy loads; and at the same time susceptible of pleasing architectural treat- ment, its position as a building material is unique. Fig. 174. — Placing Brick Veneer on Concrete Building. {See p. 612.) Gray and Davis Building, Cambridge, Mass. Used as the structural frame of factory and ofl&ce buildings, for foun- dations and floors of steel frame structures; or as artificial stone for fac- ing or trimming, its adaptability is recognized. For small buildings such as dwellings, its use is not so general because of larger ui;iit costs on small jobs, but in certain cases where, on the one hand, expense is not the criterion, and, on the other hand, where duplication of design reduces the costs, it is being adopted to advantage. For first-class construction there are three requisites: (i) thoroughly tested materials; (2) design by an engineer familiar with reinforced 6o8 A TREATISE ON CONCRETE concrete design; and (3) construction by an experienced builder working under careful supervision. RELATIVE COSTS OF BUILDINGS OF DIFFERENT MATERIALS For industrial and office buildings reinforced concrete naturally competes with the steel frame, plain or fireproofed, and with mill con- struction. Cost is usually the important factor, but sometimes speed after breaking ground is the main consideration, as is the case, for ex- ample, in high buildings in the business sections of large cities, and structural steel may be selected on this account. If the time of rolling of the structural steel must be included, however, the concrete building can be put up in a shorter time. In selecting the type of building, the first cost should not be con- sidered alone, but only in connection with the average annual expense and depreciation over a term of years. In other words, it is economical to increase the first cost for the sake of an annual saving in expense that ultimately, in the course of the useful life of the building, makes up for the higher initial expenditure. Fireproofed steel frame construction almost invariably is more ex- pensive in first cost than reinforced concrete. This is due chiefly to the fact that in the reinforced concrete structure the concrete itself is not simply for fireproofing, but at the same time, by its strength in compression, forms a load-carrying part of the members. Moreover, placing the fireproofing on the steel frame is a separate and expensive operation that is practically incidental in a reinforced concrete building. The first cost of the reinforced concrete structure, in turn, may be greater than that of a steel frame, not fireproofed, or of mill construction. This depends, however, to a considerable extent on the type of building. Thus, with very heavy loads, especially on long spans, concrete is cheaper than steel or mill construction. The dividing line varies with relative costs of material. Frequently it occurs at loads of 200 pounds per square foot on spans in the neighborhood of 20 feet.* To get any real comparison between buildings of different materials a detailed estimate should be made of the first cost and the annual expenditures. The following tablef issued by the Universal Portland Cement Company^ illustrates the method. • See paper by L. C. Wason in Proceedings National Association of Cement Users, Vol. VII, igii, p. 44S. t Similar computations are given by J. P. H. Perry in Proceedings National Association of Cement Users, Vol. VII, igti, p. 443. ,1 See also Concrete Cement Age, July igi6, p. 25. CONCRETE BUILDING CONSTRUCTION 609 Comparative First and Maintenance Costs oj Reinforced Concrete and Mill Constructed (From standpoint of Owner) Building 100 ft. x 175 ft. 7 stories and basement. Total Floor Area 140 000 sq. ft. Reinforced Mill Concrete Construction (Fireproof) (Not Fireproof) First cost of building, $189 000.00 $168 000.00 First cost of sprinkler system 14 000.00 14 000.00 Total first investment • $203 000.00 $182 000.00 First cost fireproof more than mill construction $21 000.00 Maintenance Interest on first investment 6% $12 180.00 $10920.00 6% Tax on first investment 1% 2030.00 1820.00 1% Depreciation on building 0.5% 94Soo 3360.00 2% Obsolescence 1.0% [890.00 3360.00 2% Depreciation on sprinkler 10% i 400.00 i 400.00 10% Repairs to building 0.25% 472.50 i 680.00 1% Damage to building by vermin . . . None 200 . 00 Est. low Auxiliary fire equipment Estimated 200.00 300.00 Estimated Fire insurance on building, None required 235-20 i4cts. on $100 $19 117.50 $23 275.20 Yearly expense fireproof less than non-fireproof $4 157. 70 The yearly saving of $4 157.70 capitalized at 6% represents $69 295. There- fore, actual cost of concrete building is $119 705, in comparison with one of mill construction costing $168 000. Furthermore there is a lower rate for fire insurance on the contents of the concrete building which still further reduces the cost. Reinforced concrete has been used economically for dwelling houses, but only where cheap cottages can be built in groups of similar pattern. With this exception wood is cheaper and, in fact, the cost of forms alone exceeds in many cases that of the material and concrete labor. Pre- cast blocks, requiring no forms, can best be used for this class of work, but unless the surfaces are tooled the appearance is apt to be monoto- nous. In estimating the labor where forms are used allowance must be made for time lost waiting for the concrete to harden so that the forms can be raised. For this reason a small gang of men should be used, — only enough to lay concrete to the height of one section of the forms per day. 6io Average Costs of Concrete Buildings per Square Foot of Floor Area (See p. 6ii.) Costs include all items except interior finish Cost in Dollars per Square Foot of Floor Area Width in Feet Length of Building in Feet Length of Building in Feet 50 $ 100 $ 200 $ , 300 $ 400 $ 600 S $ 100 $ 200 $ 300 $ 400 $ 600 $ l-Story 2-Story 25 2-34 X.83 1 .60 1.46 1.40 1.38 2.29 1.77 I -55 1-43 1-37 1.30 Sc 1.67 1-43 1.26 1. 14 1.08 I. OS 1.64 1.30 i-iS I 05 i .01 0.98 7S 152 1.32 I 15 i.03 0.98 0-9S 1.44 1. 19 '•03 0.96 0.91 C.87 100 1.44 X.24 1.08 0.98 0.91 0.89 1-35 1 . 10 0.97 0.89 0.84 0.81 ISO '■39 1.18 1.03 0-93 0.86 0.84 1.27 1 .04 0.91 0.83 U.79 0.76 4-Story 6 to 10-Story 25 2". 22 1.68 1.46 '•37 '■31 1. 25 2.22 1.66 '•45 1^35 1.32 I^2S so 1-54 1 . 20 1.07 1. 00 0.97 0-93 1-53 1. 18 1 .06 1. 00 U.97 o^93 7S •■■35 1.08 0.96 0.90 0.87 0.84 1-33 1.08 0.96 0.89 0.8s 0^83 100 I -25 1 .01 0.89 0.83 0.80 0.78 i.24 0.99 U.88 0.82 0.79 0.77 ISO 1. 18 0-9S 0.84 0.78 "•75 0.72 1. 16 0-93 0.82 0.77 "•75 0.72 Average Costs of Concrete Buildings per Cubic Foot of Volume {See p. 611.) Costs include all items except interior finish Cost in Dollars per Cubic Foot of Volume Width in Feet Length of Building in Feet Length of Building in Feet 50 JOG $ 200 $ 300 $ 400 600 $ % 100 $ 200 $ 300 T 600 1-S tory 2-Story 25 195 OIS3 0-133 O.I22 O.II7 o.iis o.igi 0.147 0.129 0.119 0. 114 0.108 so 0.139 0.119 0. 105 0.09s 0.090 0.087 o^i37 0.108 0.096 0.088 0.084 0.082 7S 0.126 0. no 0.og6 0.086 0.082 0.079 0.120 0.099 0.087 0.080 0.076 0.072 TOO 0. 120 0.104 0.090 0.082 0.076 0.074 0.113 0.092 0.081 0.074 0.070 0.067 150 0. 116 0.098 0.086 0.077 0.072 0.070 0.106 0.087 0.076 0.069 0.066 0.063 4-S tory 6 to 10 -Story 25 0.18s 0.140 0. 122 0. 114 0.109 0. 104 0.18s 0.138 0. 121 0. 112 O.IIO 0.104 SO 0.128 O.IOO 0.089 0.083 0.081 0.077 0.128 0.098 0.088 0.083 0.081 0.077 7S 0.112 0.090 0.080 0.07s 0.072 0.070 O.III o.ogo 0.080 0.074 0.071 0.069 100 0. 104 0.084 0.074 0.069 0.067 0.06s 0.103 0.082 0.073 0.068 0.066 0.064 ISO 0.098 0.079 0.070 0.06s 0.063 0.060 0.097 0.077 0.068 0.064 0.062 0.060 Values are based on conditions outlined on page 6ii. The tables are taken from "Concrete Costs" by the same authors, and the values are made up from tables of unit times and costs given in the same book carefully checked by contractors' estimates. For more complete details and far the unit values which are adapted to all conditions, see other tables and examples in "Concrete Costs." Values are for symmetrical buildings. V^alues must be corrected for the high prices obtaining during the war. CONCRETE BUILDING CONSTRUCTION 6ii For cellar and foundation walls of all classes of buildings, including brick and frame (see p. 643), concrete is superseding rubble masonry except where rubble stone is taken' from the excavation so as to be very cheap. Cement mortar plastered on to metal or wood lathing is used not only for outside walls but in some cases for fire resisting partitions in large buildings. (See p. 645). ACTUAL COST OF REINFORCED CONCRETE BUILDINGS The tables presented on page 610 present the approximate average cost per square foot of floor area and per cubic foot of volume of plain rectangular reinforced concrete buildings of various sizes and heights. The costs include all details of construction, not only the concrete forms and reinforcement, but also windows, stairs, roof covering, and plumbing. . Interior finish, which varies widely with the type of con- struction, is not included. The basis of the tables is as follows: (i) Floor loads, 150 pounds per square foot. (2) Story heights: first floor on a 3-foot fill; other floors 1 2 feet from slab surface to slab Surface. (3) Column spacing, 18 feet on centers. (4) Floor design: girders between columns in one direction; beams between columns in other direction with two intermediate beams. , (5) Excavation and foundations.* story Height Outside Walls per Linear Foot Inside Walls per Linear Foot ' I $2.00 $1-75 2 2.90 2.2s 3 3.80 2.80 4 4.70 3-4° S S.60 3-9° 6 6.50 4- SO (6) Filling under first floor: 3-foot fill at 50^ per cubic yard in place. ■ (7) Stairs: material and labor, $100 per flight per story. (8) Stairways and elevator towers: 2 stairways and i elevator tower for buildings up to 150 feet long. 2 stairways and 2 elevator towers for buildings up to 300 feet long. 3 stairways and 3 elevator towers for buildings over 300 feet long. * Taken from paper presented before the New England Cotton Manufacturers' Association, April 1904, by Mr. Charles T. Main. Pricfes revised by Mr. Main to conform to prices prevailing about Janu- ary, 1910. Values must be corrected for the high prices obtaining during the war. 6i2 A TREATISE ON CONCRETE (9) Floor finish: all floors of concrete with granolithic finish. (10) WaUs: (a) Curtain walls between pilasters, 3 feet high and 8 inches thick; (J) Concrete walls for penthouses, 6 inches thick. Dimensions of penthouse are 10 feet by 10 feet; (c) Concrete walls around the elevator and stairway openings are taken 6 inches thick, the elevator opening being 10 by 20 feet and the stairways 10 by 10 feet, these two being adjacent so that the one intermediate lo-foot wall serves for both openings; (d) For toilets, concrete walls 6 inches thick and 20 feet long, one wall for each 5 000 square feet of floor space. Walls 8 inches thick, including reinforcement and forms, $0.35 per square foot. Walls 6 uiches thick, including reinforcement and forms, $0.30 per square foot. (11) Windows and doors; all openings for windows and doors, $0.40 per square foot. (12) Roof and flashing: five-ply tar and gravel roofing, $0.60 per square foot. (13) Plumbing; two fixtures on each floor up to 5 000 square feet of floor surface, and one additional fixture for each additional 5 000 square feet, $75.00 per fixture. (14) Labor rates: carpenter labor, $0.50 per hour; steel labor, $0.30 per hour; and common labor, $0.25 per hour. (is) Concrete in place (including labor and materials); $7.00 per cubic yard, or $0.26 per cubic foot. (16) Form lumber: $30.00 per i 000 feet B. M., delivered. (17) Steel for reinforcement: $37.00 per ton, delivered. For lighter loads than specified, the costs are slightly decreased, this decrease running up to 12^ cents per square foot for a 75-pound load in a lo-story building. For a 300-pound load, the prices are increased from 6 cents for a 2 -story building up to 12 j cents per square foot for 10 stories. It must be remembered that the tablss are based on rec- tangular, symmetrical buildings. Allowance must be made for irregular layouts, which increase materially the cost of form construction. The variation in cost due to variation in spacing of columns is small. If columns are spaced fifteen feet apart the cost is 6 per cent greater than where columns are spaced twenty-five feet apart. BUILDING DESIGN AND CONSTRUCTION The factory* of Gray & Davis, Inc., Cambridge, Mass., built by the Aberthaw Construction Company, is shown in Fig. 174, page 607. The photograph shows the brick veneer being laid from a scaffold, but the same builders now omit the scaffold on their work and use a pat- ented platform swung from the roof. In the frontispiece is -shown the new buildings of the Massachusetts * Monks & Johnson, Engineers. CONCRETE BUILDING CONSTRUCTION 6x4 -I" O 1 en vD 1 .,fZ-5b"°'^^^ ?f. H CO o s CONCRETE BUILDING CONSTRUCTION 6iS Institute of Technology, Cambridge, Mass., designed and built by the Stone & Webster Engineering Corporation; Wilham W. Bosworth, Architect. The concrete design and construction was under' the super- 5~J 5 ® 5 ® © ® ® ® ® ® ® ® ® ® ® Fig. 177. — ^Typical Framing Plan and Steel Schedules. {See p. 617.) Buildings i, 3, and 5, Massachusetts Institute of Technology, Cambridge, Mass. 6i6 A TREATISE ON LUl\LKliili. vision of Mr. Sanford E. Thompson, Consulting Engineer. This work is one of the most comprehensive schemes for an educational institu- tion that has been developed in this country. The buildings cover an area of 3I acres and if placed end for end would extend some 2 500 feet in length. Except for the structural steel stairways and exterior finish (see Fig. 180, page 619) reinforced concrete was used throughout. About 40 000 cubic yards of concrete and 3 600 tons of steel reinforce- ment were used. Typical Layouts. A number of figures are given to show practical solutions of problems encountered in ordinary building design. Fig. 17s, page 613, shows the first floor plan of the Youth's Companion Qr'tCk ParapeK Cast Stone Coping •■Brick Parapet Brick Cbncre^i Copper Flashing Carried Over Curb -Cast Stone Sill ■ Brick Stool ^'' T c Furring All windowshavc Cast Stone Sills ' Brick Stool. nfth Floor ■-AirSpooe Fig. 178. — Elevation Showing Brick Veneer and Concrete Columns and Spandrel Beams; also Wall Section. {See p. 617.) Youth's Companion Building, Boston, Mass. Building,* Boston, Mass., Densmore and LeClear, Architects and Engi- neers.* The size of the panels was determined by the arrangement of the printing presses. The type of reinforcement is illustrated in Fig. 168, page 543. The construction is simplified by the location, outside of the building proper, of the stairs and elevator wells. The first floor plan of the Paine Furniture Building, Boston, Dens- more and LeClear, Architects and Engineers, f is shown in Fig. 176, page 614. In this case the layout is governed by the allowable loads on the soil and by the requirements of retail salesrooms and shops. The floor is a 4-way flat slab system. (See Fig. 166, p. 541.) The framing plan of one floor of Buildings i, 3, and 5 of the New • W. F. Keams Co., Builders; Sanford E. Thompson, Consulting Engineer. t James Stewart & Co., Builders: Sanford E. Thompson, Consulting Engineer. CONCRETE BmLDING CONSTRUCTION 617 Technology, Cambridge, Mass., is shown in Fig. 177, page 615. This is the key plan which ties in the numerous detail sheets covering the individual slabs, beams, and columns. The 'figure shows also the typical slab reinforcement and beam and column steel schedule. Fig. 181, page 624, shows a steel schedule for a beam. A portion of the elevation and wall section of the Youth's Companion Building is shown in Fig. 178, page 616. The building is situated on a boulevard in Boston, and is a combination of a factory and a commercial building. For such cases the arrangement of brick veneer and con- crete columns and spandrel beams shown in the drawing is specially suitable. (See also Fig. 174, p. 607.) For the fine architectural treat- ment of the new Technology buildings limestone and granite were used except on unimportant parts which were faced with brick. (See Fig. 180, p. 6ig.) A cross-section of one of the new Technology buildings is shown in Fig. 179, page 618. In this instance a long corridor, with class rooms opening out on either side, ran the entire length of the building. By using long span beams in the class room and short spans in the corri- dors, all columns were located in the walls and partitions except in large drawing rooms and shops. (See Fig. 183, p. 626). In some large class or lecture rooms columns were avoided by using heavy long span beams as shown in Fig. 182, p. 625. (See also page 627,) FLOOR LOADS In designing any structure the local building laws must be consulted. To illustrate good practice the following provisions for floor loads are taken from the 1916 New York City Building Code, Bureau of Manhattan. Floor loads. Every floor, roof, yard, court or sidewalk shall be of sufficient strength in all parts to bear safely any imposed loads, whether permanent or temporary, in addition to the dead loads depending thereon, provided, however, that no floor in any building or extension to an existing building hereafter erected, shall be designed to carry less than the following live loads per square foot of area, uniformly distributed, according as the floor may be intended or used for the purposes indicated. 40 pounds for residence purposes, 100 pounds for places of assembly or public purpose, excfept that for classrooms of schools or other places of instruction the floor need not be designed for more than 75 pounds, and 120 pounds for any other purpose,* except that the floors of offices need not be designed for more than 60 pounds. Theliveloadfor which any and every floor may be designed shall be clearly shown in the application and on the plans before any permit to erect is issued. .. ., ...,:.... • Loads on warehouse floors run trom 200 to 500 pounds with an average of 250 to 300. — ^Authors. 6i8 A TREATISE ON CONCRETE Concentrated loads. Every steel floor beam in any building hereafter erected used for any business purpose shall be capable of sustaining a live load concentrated at its centre of at least 4 000 pounds. Moving loads. Running machinery or other moving loads shall be considered as increasing the live loads in proportion to the degree of vibratory impulse transmitted to the floor. f. Gr 74.60 , — 6 — 2:3 res- J_ ■o 12: 10- 23ff.6" — 16 i3ft.6 16- — 6 23R/4i" T — Sft*— 16— —6 — 8Ft4^- ^w: 6- — 8Ff.4- — -Hl6 -aR4- Roof. 23 R 8" — 4 Thirrinoor Gr. 61.60 23 fF.6" — 6 Second Hoor Gr46.IO 23ft.e' — 6 First Floor Gr 28.60 23R4i" Baa'rrit Floor. Sr.l7IO Flo. 179. — Typical Cross-Section Showing Classrooms Opening on Corridor. {Seep. 617.) Massachusetts Institute of Technology, Cambridge, Mass. Roof loads. Every roof hereafter erected, shall be proportioned to bear safely a live load of 40 pounds per square foot of surface when the pitch of such roof is twenty degrees or less with the horizontal, and thirty pounds per square foot measured on a horizontal plane, when the pitch is more than twenty degrees. Loads on vertical supports. Every column, post or other vertical support shall be of sufficient strength to bear safely the combined live and dead loads of such portions of each and every floor as depend upon it for support, except that in buildings more than five stories in height the live load on the floor next below the top floor may be assumed at ninety-five per cent, of the allowable live load, on the next lower floor at ninety per cent., and on each succeeding lower floor at correspondingly decreasing percentages, provided that in no case shall less than fifty per cent, of the allowable live load be assumed. CONCRETE BUILDING CONSTRUCTION T 619 race of Qeinforred Column IG. 180. — Ornamental Facades on Major and Minor Courts. Massachusetts Institute of Technology, Cambridge. {See p. 617.) Sidewalk loads. For sider walks between the curb and building lines, the live load shall be taken at 300 pounds per square foot. Yard and court loads. For yards and courts inside . the building line, the live loads shall be taken at not less than 120 pounds per square foot. Weight of Concrete. The weight of concrete varies with the weight of the aggregate and with the proportions. For ordinary stone and gravel concrete, a weight of 150 pounds per cubic foot can be used in computation. Ah approximate value of 144 pounds per cubic foot is sometimes used because of convenience in cancellation when figuring bending mo- ments. For certain conditions, more exact values are necessary, in which case the weights on page 9 should be employed, and the ex- cess weight of the steel reinforcement, which sometimes amounts to several pounds per cubic foot of the struct- ure, may be allowed for. Tables of volume of concrete in slabs, beams, and columns of 620 A TREATISE ON CONCRETE different dimensions, are given in the authors' book on "Concrete Costs," pp. 526-533. These are convenient to use for computations for both quantities and weights. MATERIALS FOR BUILDING CONSTRUCTION A first-class Portland cement must be used which fulfills the standard specifications given on page 62. The rules for the selection of the ag- gregates are the same as for other classes of concrete. Since the con- crete may be loaded way up to its working stresses, it is particularly necessary to see that the sand is satisfactory. (See page 115.) The size of the coarse aggregate is often limited to i inch. If well graded, however, so that the larger pieces will not collect and prevent the flow of the mortar around the steel, the limit of size where the floor thickness is not less than 4 inches may be as high as i^ inches. The usual proportions are i : 2:4, that is, one barrel, or four bags, of Portland cement, 8 cubic feet of sand, and 16 cubic feet of broken stone or gravel, the relative proportions of the sand and stone being varied shghtly to suit the particular aggregates. In certain cases, especially where the cost of cement is relatively low, it is economical to use richer proportions, such as i: i|:3, and in columns, particularly, where size is an important factor, the proportions may be even richer. Although higher unit stresses may be used, it mvot be remembered that the modulus, and therefore the ratio of elasticity (see page 483), as well as the strength, changes with the proportions so that there is less reduction in the size of the member on account of a richer mix than might be expected. It is necessary to make allowance for this difference in modulus both in figuring columns (see p. 376) and also in the formulas for beams and slabs (see pp. 353 to 362). The quantities of cement and aggregates required per cubic yard of concrete in different proportions are tabulated on page 214. Conveni- ent tables for figuring material costs are presented in "Concrete Costs," pp. 165 to 173. Steel requirements are discussed on page 478. Cinder Concrete. For short-span floors of steel frame buildings, cinder concrete sometimes may be used economically for light loads because of its light weight. The span for cinder concrete slabs is gener- ally limited to 6 or 8 feet. Cinders are not suitable for the structural members of reinforced concrete structures. For fireproofing (see p. 289) cinder concrete may be employed providing a first-class cinder is available. CONCRETE BVILDrNG CONSTKUCTION 621 Cinders for concrete should contain but little unburned coal and be tree from soot. A clean cinder will not discolor the palm when held in it and rubbed with the fingers. Usually a better mixture can be obtamed by screening the fine stuff from the cinders, and then, if gritty, mixing it with sand, than by using unscreened material, although if the fine stuff is found by tests to be uniformly distributed through the mass, it may be used without screening and a smaller proportion of sand added. Concrete Blocks. Concrete blocks are specially adapted to dwellings, farm buildings and similar structures. None should be used, however, unless they are known by test and experience to be satisfactory and durable. The National Board of Fire Underwriters specifies that the compressive strength calculated on the gross area, including cellular spaces, shall be not less than 800 pounds per square inch with the cells vertical; and not less than 300 pounds per square inch, with no block testing at less than 200 pounds per square inch, with the cells hori- zontal. The average absorption of three blocks shall not exceed 10 per cent, in 48 hours nor 15 per cent, in any case. Special care is needed in selecting and proportioning aggregates. One of the chief difficulties has been the selection of too lean proportions. Ornamental Stone. For balustrades, cornices, interior work, and the like, artificial stone made with special aggregates is cast in carefully shaped molds. Such products have been found satisfactory archi- tecturally and from the point of view of durability. To prevent hair cracking or checking, density is the most essential requirement. The aggregates must be accurately graded with as large a maximum size as possible, half -inch or even three-quarters inch, pref- erably. The consistency must not be too wet, a sluggish consistency about like very thick pea soup or even stiffer is best. A very wet mix is almost sure to check, while too dry a mix is apt to be porous. Molding in sand produces blocks of a rough, rather pleasing surface, and is also suitable for blocks which are to be tooled. A wooden core is made and fine damp white sand is packed around it, then the core is removed and the mortar is poured in. When this concrete is hard the sand is removed and the blocks stored where they may be kept moist for at least two weeks. If flasks are used, they may be stored in the flasks. The requirements mentioned as to grading and consistency must be followed. Tooling the surface of concrete blocks is an effective treatment, exposing the aggregate and producmg a pleasing surface resembling 622 A TREATISE Oi\ L,ui\L.KJbiJ^ cut stone. If sand molded blocks are tooled so as to produce sharp arrises or corners it is possible to use a stiff consistency and coarse aggregate. CONCRETE FLOOR SYSTEMS In reinforced concrete construction, the panel in a floor system, that is, the space between four columns, may be of three general types: (i) Reinforced concrete slabs, beams, and girders. (2) Reinforced concrete slabs supported on steel beams. (3) Reinforced concrete flat or girderless slabs supported directly on columns. Design of Members. In designing the members of a reinforced concrete floor system, the formulas and allowable unit stresses given in Chapter XXII, on Reinforced Concrete Design should be used. The economy of a design depends in a large measure upon the proper selection of the type of panel to use and the proper spacing of the columns. In warehouses and factory buildings, the spacing of columns, and therefore the size of the panels, often is governed by economical con- siderations, while in other structures, the architectural requirements control to a large extent. With free choice, economical spans range between 18 feet and 25 feet. In determining the economical spacing of columns for a building of given size, it frequently is well worth while to make comparative sketches for panels of different sizes and shapes and then figure the amount of concrete, steel, and form work required for each size. In comparative estimates, it is useless to figure the quanti- ties of concrete and steel unless the cost of form work is taken accurately. Such computations may be made accurately and very quickly by ref- erence to "Concrete Costs." In that book are given tables of volumes and costs of concrete and costs of forms for concrete members of differ- ent sizes. To illustrate the accuracy with which the cost of different designs may be compared, the table on page 623 is quoted from a paper by Mr. Thompson presente3~before the American Concrete Institute. In many cases the comparison must be made between flat slab and beam and girder construction, the same method, however, being used for this as in the case given and the data required being taken from the various tables in "Concrete Costs." Frequently when the spans of the panels in two alternate designs are nearly aHke, the difference in cost of the columns and footings them- selves is small and need not be considered. In other cases where the building is high with heavy floor loads, that may be, the controlling Relative Cost of Different Slab Designs. (See p. 622.) 623 . cu. yd. .cu. yd. . cu. yd. . piece Concrete per panel: Slab Beam Girder Total Steel per panel: Slab lb. Beam jlj_ Girder lb. Total Tile per panel: Slab Total cost of concrete Form Lumber: Slab ijin. stock ft. B.M. Beam ijin. stock ft. B.M Girder ijin. stock ft. B.M. Total for 4 floors Total per floor per panel. . . M Form Labor, Slab: .'. Make Place and remove first floor Place and remove second floor. . , Place and remove third floor Placejand remove fourth floor. . . Total cost 4 floors Cost per panel per floor Form Labor, Beams: Make Place and remove first floor Place and remove second floor. . . Place and remove third floor Place and remove fourth floor. . . Total cost per beam 4 floors Cost per panel per floor. ...';.. Form Labor, Girders: Make Place and remove first floor , . Place and remove second floor. . . Place and remove third floor Place and remove fourth floor. . . Total cost 4 floors Cost per panel per floor Total cost forms Total cost Unit Cost Amount Cost $5.82 $30.00 ■■a ff M 00 Concrete Slab Span IS ft. 6 in. 1 080 944 772 496 268 S67 $4-39 12.88 9.88 11.02 11.02 $49.19 $3.00 S.79 S.20 6.92 6.92 $2 7.83 Amount $78 S13i $17 $12 $6 $36 $170 Concrete Slab Span 7 ft. 9 in. I intermediate Beam. Hollow Tile IS ft. 6 in. 6.1 2.6 0.6s 9-35 43 S I 620 690 2 74S 43S 680 267 2 382 S9S $3.78 11.48 8.S7 9-31 9-31 $42.45 $2 10 4 40 3 90 5 10 S 10 $20.60 $2.30 4.80 4.10 6.26 6. 20 $23.60 Cost Amount $SS. 00 $130. «0 $17.86 $10.61 $10.30 $9. sot $48.27 $178.27 6.6 2.2 607 944 I SSI 286 772 429 2 201 SSO $439 12.88 9.88 11.02 II .02 $49 . 19 $2.70 S.io 4.60 6.80 6.80 $26.00 Cost $51 88 57.20 $150.30 $16 $13 $6 $35 $185 tj a ai bo O O Ph3 617 619 619 644 639 641 Cost of forpas, not cost of materials used in beams and'slab, determines relative cost of alternate designs. Forms assumed to be used four times and remade once (qt a change in size of columns. Costs are from "Concrete Costs" by Taylor and Thompson according to pag^ numbers given. Size of beam below slab, 12 in. by 19 in. Size of girder below slab, 14 ia. by 19 in. * From Design and Construction of the Massachusetts Institute of Technology Buildings by Sanford E. Thompson, Journal American Concrete Institute, July 1915, page 377- t Multiply cost per panel per floor by 1.6 instead of 2.0 to allow for spandrel beiam. 624 A TREATISE ON CONCRETE iliilii it O) o s J5 w- le- z - ■^ ^ a> 2 10 in « ri o u d >, "i « o o 3 -s "d f^ O Tl o a "ti Hi (U c W t— 1 !1 •«-> CONCRETE BUILDING CONSTRUCTION 625 factor. For large panels it may be necessary to use structural steel rein- forcement instead of bars. As this is more expensive and complicates, to some extent, the erection, smaller panels may be desirable although by themselves they may show no advantage. The thickness of the structural slab should not be smaller than 3 inches or better still 4 inches because of the difficulty of placing the concrete properly, and preferably not greater than 8 inches, except in occasional cases of flat slab construction, because of the weight of the structure. Fig. 182. — Arrangement of Long Span Beams in Large Lecture Room. (See p. 627.) Massachusetts Institute of Technology, Cambridge, Mass. Where possible, the layouts should provide for a typical design all through the building and do away as far as possible with odd panels, which not only complicate the design but also make the construction more difficult and costly. In rectangular buildings, the dimensions of the panels should be preferably multiples of the width and the length of the building. 626 A TREATISE ON CONCRETE Panels of Reinforced Concrete Beam and Slab Design. The design of a complete floor system with reinforced concrete beams, girders, and slabs, is illustrated on page 552, and on pages 553 to 557 are given the complete computations for determining sizes of members and reinforce- ment. Other arrangements of beams are shown in Figure 181, page 624. Fig. 183. — ^Tjrpical Arrangement of Beams and Columns for Drawing Rooms and Classrooms Opening on a Corridor. (Seep.Qij.) Massachusetts Institute of Technology, Cambridge, Mass. The method of comparing the cost with different spacings of beams is illustrated on page 623. The slab span between beams gives the minimum quantity of steel and concrete, but on account of the excess cost of forms, and in some cases the possibility of omitting girders, longer spans may be more economical, as in the example just referred to. As different floors in the building are designed for different loadings, it is sometimes economical to keep the stems of the T-beams alike to permit the repeated use of the same beam forms and change only the reinforcement and the design of the floor slabs in accordance with the loads. The common t3TJe of beam and girder floor is made up of girders CONCRETE BUILDING CONSTRUCTION 627 running from column to column with beams running into the same columns and one or two intermediate beams between columns. The principal slab reinforcement runs at right angles to the beams. By using longer spanned slabs, the girders and intermediate beams fre- quently may be omitted entirely, as shown in Figure 187, page 630. In girders carrying concentrated loads from beams fewer stirrups are required to carry the shear than is the case in beams carrying a distrib- uted load. Except for the dead load and possibly some hve load the shear is constant between the support and the first beams. This per- mits a uniform and a wider spacing than in beams. Square Panels. To obtain smooth ceilings, the panels are sometimes made square, or nearly so, with beams on all four sides. The reinforce- ment then consists of bars running in two directions, or arranged as shown in Figure 168, page 543. The latter arrangement, in which certain features are patented, requires less steel because the bars run more nearly in the direction of the actual stresses (see p. 544). For a ^ Fig. 184. — Steel Beams, Fireproofed, Supporting Concrete Slab.* (See p. 628.) large square room, like, a lecture room, where it is advisable to have no obstacles, the girders may be placed in the walls with two intermediate beams running in each direction and intersecting at the third points in the span. (See Fig. 182, page 625;) By assuming a distribution of the load to aU of these beams, spans as long as 40 feet may be readily attained without excessive depth of beam. Panels with Slab Supported on Steel' Beams. A structural steel frame for beams, girders, and columns may be preferable co reinforced con- crete for certain structures, such as city office buildings, simply for the reason that if the steel is fabricated in advance the buildings can be erected more rapidly although at higher cost. For structural steel buildings concrete is commonly used for the slabs. Concrete slabs supported by beams framed into girders are reinforced in one direction only. Steel may be run over the top of the beams so as to make the slab continuous, or the surface of the slab may be flush with the top of the I-beam. The former plan is usually preferable, requiring thinner slabs, because of the continuous action with less danger of cracks over • Redrawn from a cut piepared by the author for Marks' Mechanical Kngineers' Handbook. 628 A TREATISE ON CONCRETE the beams. If the panel is square, or nearly so, the slab between the steel beams is reinforced by bars running in two directions, or by radials and circles as shown in Figure i68, page 543. For fireproof construction, the steel beams, girders, and columns must be encased in concrete, tile, or other fireproof material. This fireproofing increases the cost so as to make the steel frame building always more costly than reinforced concrete construction. (See page 608. The fireproofimg of steel girders is shown in Figure 184, page 627. When floors are built of a combination of steel girders and reinforced concrete beams and slabs, care must be taken to see that proper seats in the steel frame are provided for the concrete beams. The slab between steel beams sometimes is constructed in the form of a concrete arch. If unreinforced, the beams should be connected with tie rods spaced to resist any possible unbalanced thrust. For arches with curved upper surfaces, a fill of cinders or a very lean con- crete is used for leveling. an □□ □□ □□ □□ o," nn □□ nn □n Fig. 185.— Details of One-Way Hollow Tile Floor Slab.* {See p. 628.) Hollow Tile and Reinforced Concrete Floors. For floors of compara- tively long span and light load a combination of concrete and hollow tile is suitable in certain cases. The substitution of light weight hollow tile for a part of the concrete below the neutral axis reduces the dead load of the buUding, and the amount of steel is also reduced becatfse the depth of the tile may be greater than is customary with concrete. The one-way system shown in Figure 185, page 628, consists of a series of reinforced concrete ribs from one to two feet on centers with hollow tile between, and a slab of concrete 2 inches or more in thick- ness covering it and extending from rib to rib. In designing, each rib may be treated as a T-beam and the formulas for bending moments and shears used as recommended in Chapter XXII, page 487. Diagonal ten- sion and bond stresses must receive special attention (see pages 516 and 539). Along the beams the tile are omitted and the slab is made solid to provide a flange for the beam and to reduce the compressive and shearing stresses in the joists at the support. • Redrawn from a cut prepared by the author for Marks' Mechanical Engineers' Handbook. CONCRETE BUILDING CONSTRUCTION 629 In the two-way system shown in Figure 186, page 629, the ribs run in two directions, as shown, and the load may be considered as distributed equally in the two directions. In constructing this combination of tile and concrete slab, flat form work is built and the tiles are placed on this centering in proper position. The steel is placed between and the concrete of the ribs and slabs is poured as in any other monolithic construction. The advantages of this construction are that the joists may be made of the same thickness as the supporting beams so as to give a smooth ceiling and the weight of the construction is somewhat reduced. The Fig. 186. — DetaUs of Two-Way Hollow Tile Floor Slab and Structural Steel Columii Fireproofing. (See p. 629.) disadvantages are the high cost of tiles and of the labor of placiag and keeping them in position during construction. The ceilings also have to be plastered or else the appearance is not neat. The fiat ceihng sur- face in most cases can be obtained more readily by the use of flat slab construction, except in the case of narrow buildings. Flat Slab Floors. In recent years, girderless floors, or flat slabs, supported directly on columns, provided usually with a flaring head, have come into very common use. This type of construction has the following advantages: 630 A TREATISE ON CONCRETE (i) Reduced story height because of elimination of beams and girders. (2) Better distribution of light. (3) Economy in construction. (4) Reduced cost of form work because of omission of beams. Figures 166, 167 and r68, pages 541, 542 and 543, illustrate the meth- ods of reinforcing girderless floors, and Fig. 187, page 630, shows the interior of a flat slab building. Fig. 187. — Typical Flat Slab Interior Showing F'lat Ceiling, Columns, Column Brackets. {See p. 630.) Youth's Companion Building, Boston, Mass. and Wall Shafting Hangers and Inserts. — Shafting, sprinkler systems, and the like may be suspended from concrete beams and slabs by various means. Many types of sockets are on the market intended to be placed on the forms and imbedded in the concrete when it is laid. Expansion bolts set into the concrete are widely used, especially for heavy loads. Fre- quently several types are used in the same building. At the New Technology buildings, for example, two styles of patented sockets were concreted into the slab (see Fig. 188, p. 631) but were not considered CONCRETE BUILDING CONSTRUCTION 631 strong enough for the heavy shafting. The shafting hangers were iastened, by lag screws,* to hard pine stringers which were in turn fastened to the slab by expansion bolts. Concrete Columns. In designing concrete columns it is necessary, first, to determine the size of the column, the proportion of the concrete, and, from formula (44), page 562, the required amount of reinforcement. The methods of designing are given on pages 558 to 565 and the allow- able working stresses on page 573. Steel in compression is more ex- pensive than concrete, therefore the most economical column is obtained where the minimum amount of steel is used, which, as explained on page 559, is one per cent of the net area. Ordinarily, however, in building construction the size of the columns is limited; therefore the strength of the concrete column must be increased by either of four methods: (r) a richer mix; (2) a larger amount of vertical steel; (3) spiral steel; (4) structural steel with or without spiral steel. Fig. 188. — Inserts Used in Slabs at Massachusetts Institute of Technology, Cam- bridge, Mass. {Se-e p. 630.) The cheapest column usually is that in which the required strength is obtained by a rich mix using only a minimum amount of vertical steel, say about 1%. Proportions i:i|:3 or 1:1:2 are customary. When the size of the column is hmited so that a large percentage of vertical steel is required, it is likely to be cheaper to use spirals with vertical bars, and thus obtain the advantage of the larger unit stresses allowable. With a structural steel core the size of the column may be still further reduced although a t additional cost. Each case should be studied to determine the relative advantages from the cost and ' Through bolts are sometimes (;onsidered preferable to lag screws. -632 A TREATISE ON CONCRETE structural standpoints. The following table illustrates a practical com- parison of the cost per lineal foot of a 22-inch column carrying 230 000 pounds with very heavy vertical steel (5.8%) and a similar column reinforced with spirals and vertical bars. With li inches fireproofing, the effective diameter is 19 inches and the effective area is 282 square inches. The average stress, therefore, is , 250 000 - ,, / = — =815 lb. per sq. m. 282 and the required amount of reinforcement for the proper working stresses, /c, can be taken from Table 18, page S99- Relative Economy of Reinforced Concrete Columns in a Partictdar Case. {See p. 632.) Cost of steel per pound in vertical bars, 3.SC.; in spirals, 3.9c; Cost of concrete per cubic foot; proportions 1:2:4, 20c; proportions i: i^: 3, 2Sc. Volume of concrete per foot of length: 22 inch round columns, 2.64 cubic feet; 21 inch round columns, 2.4 cubic feet. 1:2:4 Concrete Vertical bars only Spirals and vertical bars 1: rj: 3 Concrete Vertical bars only- Spirals and vertical bars Diameter of column Effective area Vertical Percentage, area, arid weight of steel per foot of column Cost of steel per foot of column Vertical bars . . Spirals . . Cost of concrete per foot of column bars . Spirals.. 22 m. 282 sq. in. S.8%, 16.4 sq, in. SS.8 lb. «i.9S 0-53 22 m. 282 sq. in-; 1 .48%, 4-1 sq. in. 14 lb. i%,2.8sq.in. 9.6 1b $0.49 0.38 0-53 22 m. 82 sq. in. 4.0%, ii.2sq. in. 38.2 lb. 21 m. 252 sq. in. 1%, 2.S2sq. in., 8.6 lb. fi.34 0.66 $0.30 0-34 0.60 Total cost per foot of column $2.48 $1.40 $1.24 It is evident from the table that a i: 15:3 mix with spirals is the most economical column in this particular case. With a large diameter of column permissible the relative results would be different. How- ever, if the job is small and the inspection not efficient, it may be ad- visable to use spiralled columns and 1:2:4 concrete, even if the expense is larger, because of the possibility of failure on the part of the work- men to use the richer mix in the columns. CONCRETE BUILDING CONSTRUCTION 633 Details of Design. In buildings of several stories it is advisable to design the columns so as to make the num- ber of changes in size from story to story as small as possible. The re- duction of the size of columns in the upper story requires not only the re- making of colunin forms used in the floor below, but also remaking of beam forms, because of the increase in length of the net span. Ordinarily it is possible, as the building goes up, to reduce the strength of the column by gradually reducing the amount of steel and possibly omitting the spiral reinforcement. In that way the same size of columns can be kept through several stories. Sometim.es it may be advisable to waste some concrete in the columns to avoid the remaking of column and beam forms. Methods of design are treated on pages 558 to 565. In flat slab construction metal forms are generally used for columns and column caps. As the metal forms are very easily adjustable, little attention needs to be paid to the changes in sizes of the columns. Round columns and columns with rounded corners are less affected by fire 'than columns with sharp corners. (See p. 289.) Concrete Columns Reinforced with Vertical ' Bars Only. The reinforce- ment consists as a rule of bars up to i| inches in diameter, placed around the circumference of the column about 2 inches from the outside face. The bars should be evenly distri- buted except in columns subject to £ Roof Slab. •4--J"? 12"9" 5*-il"f5"6" about 9 •J. 5" apart .^14." 14--|"*6"6" about 12" apart -8-i"$17"5" Dowels Fig. 189. — ^Typical Details of Column Reinforcing. {See p. 634). 634 A TREATISE ON CONCRETE eccentric loads, or bending moments, in which case the largest num- ber of bars should be placed near the surface under the largest stress. If tension occurs in the column, it must be provided for. The bars as a rule are carried through only one story and are spliced on the floor level, as shown in Fig. 189, page 633. For bars up to one inch diameter the splicing is effected by extending the bars a sufficient length above the top of the floor to develop their strength by bond (see p. 533). Bars over one inch diameter should be faced true and butted. To keep the bars in position, their ends should be enclosed in a tight fitting sleeve. If there is a possibility of tension in such columns, shorter bars extending below and above the floor should be used. The bars should be held in place at regular intervals by ties of small bars J-inch diameter in columns up to 20 inches diameter, and |-inch diameter for larger columns. The spacing of these ties should not exceed 18 inches, nor the smallest diameter of the column. When erecting columns, it is ordinarily advisable to assemble the bars and the ties in the yard and place them as a complete unit. If the amount of stqel in the column is too large, making the assembled unit too heavy to handle, it may be advisable to make a unit using a portion of the bars only and place the remaining bars after the skeleton is in place. If the sizes of the columns in two successive stories are different, it is necessary to bend the bars of the lower column so as to enable them to fit into the smaller column form without interfering with the steel of the column above. If the size of the bars and the difference in sizes of the columns is large, it is advisable to bend the bars beforehand. Small differences can be adjusted after the bars are in place. In column footings the stress in the steel must be distributed on the concrete by bearing plates or by dowels long enough to transfer the stress by bond. Spiral Columns. Spiral columns consist of vertical bars and circular spirals placed outside of the vertical bars. The pitch of the spiral preferably should not be greater than y^ of the diameter of column. In no case, however, should it exceed 2^ inches or J of the diameter of column. Formulas for pitch and weight of spirals are given on page 563- The requirements for spirals are: (i) The pitch should be uniform; (2) The spiral should be continuous, or else properly welded or spliced; (3) The spiral should be even, as any irregularities are harmful. After erection the core should be straight and well centered. CONCRETE BUILDING CONSTRUCTION 635 In best practice, spirals are built in the shop and transported in col- lapsed form to the job. Guide angles, notched to insure accurate spac- ing, are used. The spiral must extend from the bottom of the column practically to the top of the slab. Structural Steel Columns Imbedded in Concrete. If the area of the structural steel column does not exceed 6 per cent of the section of concrete and the shapes consist of small angles, the column should be treated as reinforced concrete. In such cases it is suflScient to imbed the angles in concrete and provide f-inch round ties, spaced 12 inches on centers. At the floor level the angles should be faced and butted and provided with bolted splice-angles. If the structural shapes are designed to resist the larger part of the load they must be built rigidly in conformity with standard practice for structural steel columns. The shapes should be latticed or provided with tie bars. The structural steel columns may consist of four angles placed in corners of a rectangle with legs turned in. Another type sometimes used is the Gray column, consisting of eight angles arranged in four groups of two angles each placed face to face. (See Fig. 142, p. 463.) Bethlehem H sections and built-up columns are sometimes used. The spUces of structural shapes must be made according to standard practice. Seats must be provided for beams and girder. In flat slab design the load is transferred to the column by means of clip angles, placed near the bottom of the column head. To prevent concrete from separating from the structural column, it is advisable to use ties spaced not more than 18 inches on centers. FLOOR SURFACES* The type of floor surface to select for reinforced concrete or fireproofed steel frame buildings must be governed by the use to which the building is to be put and the relative costs of different materials. Granohthic made with the right materials, properly proportioned and laid makes a most durable and satisfactory floor. Special conditions may lead to the adoption of terrazzo, mosaic, magnesium composition, hard wood, or a covering of battleship linoleum upon the concrete. Granolithic Floors. A cement or granolithic surface is in keeping vvith the type of structure of a reinforced concrete building, and not- *For more complete discussion, including a treatment of methods and costs of different types of floors and specifications for laying granolithic see paper on "Floor Surfaces in Fireproof Buildings" by Sanford E. Thompson, Transactions American Society of Mechanical Engineers, Vol. 36, r9i4, p. 387. 636 A TREATISE ON CONCRETE withstanding the numerous instances of floors which dust and ravel under service, it is possible to lay satisfactory and durable floors which will resist severe wear, and even trucking, with inappreciable dusting. The objection occasionally heard of coldness is not borne out by the facts except where the floor is laid directly upon the ground or is over an unheated room. If the building is warm the floors will be warm. The color of cement, a dead gray, is not particularly pleasing but can be improved upon by adding coloring matter, or by coating the surface with linseed oil or similar material. The darkening of the surface also produces a "warmer" color, in fact it changes the appearance so that it gives the sensation of greater warmth to the occupants of the room. The hardness of the surface from a practical standpoint is more apparent than real as it is found that operatives in the plant readily become accustomed to the slight difference and do not notice it. Machinery can be readily held in place and shafting can be hung by bolts imbedded as described on pages 269 and 630. The essentials for a surface which will resist wear and prevent appreci- able dusting are: the selection of aggregates which contain no dust and consist chiefly of particles ranging from x? to ^ inch in size; proportions about one part cement to two parts mixed aggregate; a consistency that will not flow but that will hold its shape in a pile without settling; a perfect bond with the concrete base; the avoidance of temperatures below fifty degrees Fahr.; trowelling so that there is no excess water brought to or remaining at any time on the surface; and maintaining a wet surface at all times for at least ten days or two weeks after laying. The soft dusty surface so often found on granolithic floors is usually due to one or a combination of 3 causes: (i) excess water in mixing, giving a weak, white concrete; (2) the use of too fine sand and screen- ings; (3) water remaining on the surface, especially serious in cold weather, which prevents the proper crystallization of the cement. Improper curing, that is, too rapid drying out through lack of moist covering or because of excessive heat in the building may produce checking of the surface. Compounds of various kinds have been brought out and many of them patented for use on granolithic floors. With the proper con- struction, however, no treatment is necessary. In case of a poor sur- face with a good body of granolithic, that is, where the soft material is only a small fraction of an inch in thickness, a hardening compound may be of value to aid in resisting abrasion. If the poor surface, how- ever, goes to any depth there is no material which will penetrate satis- CONCRETE BUILDING CONSTRUCTION 637 factorily so as to give permanent results. In such cases probably the best treatment, although a very radical one, is to grind down the surface to hard substance, somewhat as described below for a new floor. Brief Specifications for Laying Granolithic Finish on a Set Concrete Base. The following specifications are quoted in substance from the paper by Mr. Thompson referred to on page 635. 1. Roughen surface of base concrete at the age of about 24 hours, so as to remove most of surface scum. 2. If surfaces have not been thus roughened, pick with a bushhammer to remove a part but not all of the surface skin. 3. Spread dilute muriatic acid about one part acid to four parts water over the surface, allow it to stand for a few minutes, then soak thoroughly with water, and wash off the surface. 4. Sweep off the excess water on the surface of the concrete and spread on a coating about | in. thick of stiff neat cement paste, and broom it well into the concrete. (Do not use dry cement for this.) 5. Mix the granohthic in proportions i part cement to f parts coarse sand, Hke Plum Island, to li part crushed granite or trap screened through a f-in. screen and caught on j^-in. dust jacket. An alternate plan* is to use a single aggregate consisting of fine stone retained on a No. 30 sieve, with no sand. 6. Make the consistency of granohthic rather stiff so that the mortar wiU just flush to the surface. 7. Have the screeds laid parallel and level so that the granolithic can be spread even with straight-edge. Run over the screeds. See that plenty of material is being pushed ahead of the straight-edge at all times so as to avoid pockets in the surface. 8. Ram granohthic with hght square-faced tamper. 9. Trowel granolithic surface as soon as it begins to stiffen. 10. Trowel granolithic surface hard as soon as the proper stage has been reached. (If surface is to be ground do not give surface this final troweUing.) 11. Cover the surfaces of the granohthic about 24 hours after lay- ing with wet burlap or similar material which will hold water. Wet material each day, and oftener if necessary, for a period of 14 days. Bond of Granolithic to Base Concrete. One of the most important essentials in laying granolithic is to see that it is properly bonded to the concrete base. The best and in fact the cheapest plan is to lay the granolithic immediately after placing the base concrete, say within a * L. C. Wason in Transactions American Society of Meclianical Engineers, 1914, p. 400. 638 A TREATISE ON CONCRETE half hour of placing, so that they will bond together and form a mono- lithic mass. This avoids special treatment of the concrete base. In many cases this is inconvenient, because of danger of injury by workmen and the possibiUty of sudden showers which will roughen the surface. If the granolithic is to be laid after the concrete is hard, the base concrete after it has stiffened, but before it is thoroughly set, can be roughened with a wire brush so as to remove any- scum and leave an irregular surface. In this case, however, the surface must be gone over in places before or when ready to place granohthic to remove any soft spots. A still further and positive precaution against separation of the granolithic is to go over the entire surface of the base concrete with a hammer and chisel or a pneumatic tool and cut down deep enough to get into the body of the concrete. In any case it is essential when laying the granolithic to thoroughly wet the base and spread on neat cement, as described in the brief specifications. Preparing Base for Other Surface Materials. If hardwood finish, composition or other surfacing is to be used, the base can be brought suflSciently level by careful screeding and troweling of rough places and filling of holes. An allowance of one cent per square foot may be made in cost estimates for this treatment. For hnoleum only a thin mortar surface is required. Concrete Surface Without Granolithic. It is possible where an especially smooth surface is not required and where the wear will not be very severe to trowel the concrete of the base without laying grano- lithic. It is especially necessary in such cases that the sand used in the concrete be coarse, and that an excess of water be avoided in mixing. Grinding Granolithic Surface. A method which has been followed satisfactorily in practical construction and which prevents any tendency to dust and produces a pleasing appearance, is the grinding of the sur- face of the granohthic, when it is a few days old — the time being usually from four to seven days — with a machine similar to that which is used in grinding terrazzo floors (see Fig. 190, p. 639). This plan was followed in the floors of the New Technology Buildings, laid in 1916. In this case the aggregates were specially selected, using for the coarser material a crushed granite which contained numerous black particles, in some cases mixed with crushed marble. The grinding removes the scum and the top film of the surface and cuts into the sand and stone grains so as to expose them and leave the surface smooth, but not shiny. "If any small pinholes remain in the surface they may be filled by rubbing in neat cement paste. Care must be taken in spreading the granolithic CONCRETE BUILDING CONSTRUCTION 639 to see that the surface is level without excessive trowelling,— in fact the final troweling may be omitted. CONCRETE STAIRS The design of concrete stairs is a simple problem in reinforced concrete construction. A stairway may consist (i) of an inclined slab of rein- forced concrete with the steps molded upon its upper surface, or (2) of two or, for a wide stairway, three inchned girders to form the stringers, with the stairs between them. The first method is suitable for short flights not over 8 or 10 feet in length measured on the slope, and the Fig. 190. — Machine Used for Grinding Granob'thic Floors. (See p, 638.) thickness and reinforcement are calculated as for a slab supported at the ends. (See pp. 484 to 487.) The principal reinforcement is of course in the direction of the length with occasional cross metal for stiffening. To prevent cracking provision must be made at top and bottom of the flight for negative bending moment. This necessitates steel in the upper part of the slab at these points. A slab 5 inches thick measured at the foot of the risers is suitable for a stairway half a story high. When built with side girders, the dimensions of each of the latter may be calculated as a concrete beam with reinforcement near the lower surface. A small bar also runs across from girder to girder at the foot of 640 A TREATISE ON CONCRETE each riser so that the risers are practically reinforced beams. It is usually cheaper to construct the under side of the stairs as a slab than to build forms for each stair. The forms for the stringers may consist of planks notched for treads and risers, with boards nailed across as molds for the faces. If a fine finish is desired, the method of surfacing described for curbing may be followed. (See p. 806.) ^1" ■03 m -j'Tzne' ■Jr. ■ Lp-j-vaits' Plan of2"'5teri( J ' stairs i 2 Fig. 191. — Details of Concrete Stairs Designed as Inclined Slabs. {See p. 639.) Massachusetts Institute of Technology, Cambridge, Mass. Representative details of concre.te stairs built by the first method (as an incUned slab) are shown in Fig. 191, page 640. On stairs of factories, office buildings, and similar structures a live load of 70 pounds per square foot is customary. The span of a flight of stairs is the horizontal distance between supports. CONCRETE BUILDING CONSTRUCTION 641 M'Oig 01(03 Djjai 642 A TREATISE ON CONCRETE CONCRETE ROOFS Eoof design and construction is similar to that of floor slabs. As the live load is usually relatively small, cinder concrete is more , suitable than for floors. The thinness is frequently governed by construction limit instead of strength. There may be in cold weather .some annoyance from condensation of vapor on the under side of concrete roofs. This can be obviated by a suspended ceiling, a double roof, or some form of insulation. Ordi- nary cinder covering (see Fig. 192, p. 641) also acts as a non-conductor. The plan and sections of the roof of the Paine Furniture building are shown in Fig. 192, page 641. This is a typical layout for penthouses for elevators, sprinkler tanks, and any mechanical apparatus that may be necessary. The cinder fill is used partly to give the proper drain- age pitch and partly to provide a double roof to prevent condensation on the ceiling below. A four inch conductor box was used for every 20 000 square feet of surface. Saw Tooth Roof. In manufacturing plants, to obtain more light, a saw-tooth roof is often built. The cross-section of this type of roof is a series of triangles, similar to the teeth of a saw. The longer side is a concrete slab supported, at the top, by inclined posts between which are placed the windows. The slab and posts may be supported on longitudinal beams across the tops of the columns or the longitu- dinal beams may run across transverse beams supported, in turn, by the columns. By the second method no horizontal thrust is transmitted to the columns. At the junction of the post and the slab, at the peak of the roof, reinforcement must be used to take the bending moment. Rigid Frames. Sometimes the roof girders are built monolithic with the columns and may be designed according to the formulas for the rigid frame method so as to permit longer spans and lighter framing.* The rigid frame construction is very popular in Europe, but as yet has not come into use to any great extent in America. It is well adapted to manufacturing plants and in a good many cases besides being fire- proof may easily compete with structural steel trusses. Roofs of Special Design. Reinforced concrete is admirably adapted to the construction of roofs of special design, such as domes and roof arches. In domes concrete can take all the compressive stresses and the steel the tensile stresses developed in the lower curves of the dome and in the arch ring. Roof trusses have been built but are not generally recommended. •"Rigid Frames in Concrete Construction", by Sanford E. Tliorapson and Edward Smulski, EHgi- neering and Conlracting, January is. I0i3. P- 75. CONCRETE BUILDING CONSTRUCTION 643 Roof Loads. A roof load is made up of the weights of the roof itself, the roof covering, the snow load, and the wind load. The weight of the concrete may be obtained from the tables mentioned. Prof. Mansfield Merriman* gives the following estimates for the. weight of roof covering: Tin, I lb. per square foot of roof surface. Iron, I to 3 lb. per square foot of roof surface. Slate, 10 lb. per square foot of roof surface. Tiles, 12 to 25 lb. per square foot of roof surface. Average may be taken at 12 lb. per square foot. The snow load varies with the slope of the roof and the locality. Prof. Merriman allows for an approximate average 15 lb. per square foot of horizontal area. The wind load, which acts horizontally, varies with the velocity of the wind, a usual pressure being assumed as 40 lb. per square foot of vertical surface. This pressure multiplied by the sine of the angle of slope of the roof gives the pressure normal to the surface. In practice it is common to specify a minimum value for the roof load to include the weight of the roof covering, snow, wind and any moving loads which may come upon it. A usual value for this total is 30 pounds per square foot. CONCRETE WALLS Concrete building walls above ground are built of single or doubk thickness. For cellar walls or foundations they are built solid. Interior partitions may be built of concrete also but various forms of tile or fireproof compounds are lighter and, requiring no form work, are cheaper to erect. A 6-inch wall of concrete will cost no more than a 12-inch wall of brick and will be stronger and more durable. Cellar Walls. Cellar or basement walls adapted to withstand earth pressure may be thinner when of concrete than when built of stone, because laid as a continuous vertical slab supported at top and bottom. For a wall of i : 2^ : 5 Portland cement concrete with a spreading base imbedded in the earth, a thickness of 10 inches will withstand, without reinforcing metal, a pressure of 6 feet of earth. If the top of the wall is strengthened by a wooden sill imbedded in or dogged to the con- crete, and the sill is stiffened by floor joists, the wall becomes a slab * Merriman's "Roofs and Bridges," p. 4. 644 A TREATISE ON CONCRETE supported at its bottom by the earth and at its top by the sill. A 6-inch wall 8 feet high will thus withstand the pressure against it of 6 feet of earth. However, f-inch bars, spaced about 2 feet apart in both di- rections, will greatly stiffen so thin a wall, and prevent cracks before the concrete is thoroughly hard. If desired, a coping of concrete wider than, the wall itself may be formed at the top and a |-inch rod placed Fig. 193.— Design of Overhanging Cornice Cast in Place. {See p. 645.) horizontally in its inner face. The earth must not be filled in against the back of the wall until three or four weeks after placing, unless pbr- tions of the interior forms are left in place and carefully braced. A cellar wall failed* completely by overturning, in Chicago, because allowed to stand unsupported during construction. • Henry Blood in Engineering News, October 29, 1914, p. 894. CONCRETE BUILDING CONSTRUCTION 645 Building WaUs. The double building wall is advantageous because it is more completely moisture proof. Moisture is likely to collect on the inside of a wall , especially on a north wall. A smgle concrete wall 4 inches thick with its base spread to provide a footing is at least equivalent to an 8-inch brick wall, and 6 inches of concrete is at least equivalent to 12 inches of brick. Itis advisable to place small reinforcing bars about f-inch in diameter, 12 inches to 2 feet apart in walls 6 inches thick or under, not only to increase their per- manent strength, but to guard against accidents during or immediately after construction. Occasional projections or pilasters improve the appearance and add to the strength of a single wall. Each face of a hollow wall is usually 3 to 4 inches thick, 3 or 3 J inches being the minimum thickness at which concrete can be conveniently placed. Cornice. — In reinforced concrete buildings the cornice may be buUt either entirely of reinforced concrete or the frame may be built of con- crete and the facing of stone or terra cotta. To support the facing, anchors, angles, or other structural shapes, are sometimes imbedded in concrete. Fig. 180, page 619, illustrates two of the cornices used on the New Technology and Fig. 193, page 644, a reinforced concrete cornice molded in place on a 12-story warehouse by the Aberthaw Construction Com- pany. In the latter figure the forms also are shown. WALLS OF MOKTAR PLASTERED UPON METAL LATH Partitions of plaster from metal lathing are used extensively for fire- proof office buildings and hotels, and are also adapted, when made with Portland cement mortar, to certain classes of outside walls. For a one-story building, timber or steel posts may be set upon con- crete foundations, and the walls constructed by using |-inch or i-inch channel irons for studding, to which the metal lathing is attached, and then covered (on both sides) with Portland cement mortar about 2 inches in total thickness, the studding being generally set from 12 to 16 inches on centers, depending on the height of wall. Such walls are also adapted for high buUdings where steel frames are used, as the stud- ding can be securely bolted to the steel work, and the metal lathing and cement appUed in the same manner as for one-story buildings. For curtain walls the first coat of mortar is usually mixed with one barrel of first-class Portland cement to three barrels of coarse sand, and 646 A TREATISE ON CONCRETE one cask of lime putty, or paste, into which is mixed a small quantity of long cattle hair. The second coat, which is applied before the first coat is thoroughly dry, consists of one barrel of Portland. cement to three barrels of sand with about a bucketful of lime putty, without hair. The finish coat is generally mixed in the proportions of one part Port- land cement to two parts sand. This finish coat may be trowelled or floated to a smooth or rough surface, as may be desired, or it may be given what is known as a "slap-dash" finish by throwing |the. mortar on with a brush or twig broom. UNIT BUILDING CONSTRUCTION Buildings and bridges of precast separately molded units have been used to advantage on structures where a large number of members of the same dimensions are required. This scheme permits of consider- able saving in form lumber and labor and by using a central plant or factory much of the work can be done under more advantageous con- ditions than on the job itself, and better concrete results. For buildings the members are usually made on the job; for bridges, especially on railroad work, a central plant is used. More material, especially steel, is required for this type of construc- tion because beams and slabs are not continuous. In spite of this, however, it is an economical method under certain conditions. FORMS FOR BUILDING CONSTRUCTION Forms for building construction are important because they con- stitute so large a proportion of the tptal cost. Standardized designs and methods of construction are therefore essential. A few designs for columns, beams, walls, and slabs,are shown on pages 649 to 657. These and alternate designs are given, and more fully discussed than is possible here in "Concrete Costs," chapter XVI. A designer familiar with structural layout and also practical building construction can save money by making detail sketches of all forms so as to use the minimum amount of lumber and of labor in making and placing. Tables giving the spacings of column clamps, and joists, studs, and stringers for various conditions, are given in Chapter XX of "Concrete Costs." It is important to know the order of removal of forms, this being usually column sides, joists, girder sides, beam sides, slab bottoms, girder and beam bottoms. Walls usually are built independently and the forms can be removed without disturbing the CONCRETE BUILDING CONSTRUCTION 647 rest. Wall and slab forms should be built in sections to prevent bind- ing when removing. For the same reason beam forms, if removed as a unit, should be built with slightly tapering sides. For making forms most easily the carpenter's bench* should be de- signed so ithat cleat holders may be set in place for each type of sec- tion and piece after piece of forms made up with no further measuring. Lumber for Forms. The best lumber for forms or molds for concrete is white pike because it is easily worked and retains its shape after exposure to the weather. Except, however, where a very fine face is required, motives of economy usually prompt the use of cheaper material, such as spruce or fir, or, for very rough work, even hemlock. Green lumber is preferable to dry because it is less affected by the water in the concrete. If the planks or boards are thoroughly oiled and are not exposed too long a time to the hot sun and dry air, which tend to warp them, they may be used over and over again. Long exposure, however, wiU throw the surface out of true, and open up the joints. In some instances the same lumber can be employed in different places. For example, in the construction of a one-story factory buUding, Mr. Thompson specified 2-inch tongued-and-grooved roof plank of green spruce for the forms, and after using at least four times, no difficulty was found in laying it on the roof. The planks were merely sKghtly gritty and discolored by the oil employed to prevent adhesion of cement. Lumber which is planed on one side is essential to a smooth face, and where the forms must be removed within 24 or 48 hours it is sometimes advantageously employed for rough work because the concrete adheres less to planed lumber and that which does stick is easily scraped off, thus effecting a saving of labor which more than balances the cost of planing. Many concrete experts advise the use of beveled edge stuff in preference to tongue-and-grooved. The edges crush as the board or plank swells, and this prevents buckling. Square comers and thin .projections should be avoided when possible; beveled strips in the corners of forms will eliminate the former. Steel vs. Lumber. The use of steel forms on building work is limited; the first cost is high, and it is difficult to adapt them to changes in dimensions of the structure. They are useful where they can be used repeatedly without changes, as is sometimes the case for slab and wall panels. For circular columns steel forms are especially satisfactory. • See drawing of carpenter's bench in "Concrete Costs," page 487. 648 A TREATISE ON CONCRETE Removal of Forms. The time that forms have to remain in place depends upon the character of the members, weather conditions, the span, if a beam or slab, and the relation of the dead to the live load. Vertical members, such as walls thicker than 4 inches, or columns, will bear their own weight when quite green, while horizontal members; such as floors, must harden until the concrete can sustain the dead weight and the load during construction. The weather conditions greatly affect the setting and hardening of concrete. Heat causes it to harden quickly while cold retards the hardening and therefore prevents early removal of forms. If, through accident, the concrete should be frozen, it will not begin to harden imtil it has thawed and then it may require several months to attain the strength usually reached in two or three weeks. A long span beam or slab must be supported, in general, a longer time than a short one, chiefly because of the larger dead load. If the dead load, i.e., the weight of the concrete, is heavy in comparison with the live load, i.e., the load which the floor must bear later on, forms must be left a longer time because the compression in the concrete is large even before the hve load comes upon it. Experienced builders have definite rules for the minimum time which the forms must be left in ordinary weather and then these times are lengthened for poor weather conditions and special members ac- cording to judgment. As a guide to practice the following rules are suggested:* Walls in mass work: One to 3 days or until the concrete Avill bear pressure of the thumb without indentation. Thin walls: In summer, 2 days; in cold weather, 5 days. Columns: In summer, 2 days; in cold weather, 4 days, provided the girders are shored to prevent an appreciable weight reaching the columns. Slabs up to '/-foot spans: In summer, 6 days; in cold weather, 2 weeks. Beam, and girder sides: In summer, 6 days; in cold weather, 2 weeks. Beam and girder bottoms and long span slabs: In summer, 10 days or 2 weeks; in cold weather, 3 weeks to i month. Time to vary with the conditions. Conduits: 2 or 3 days provided there is not a heavy fill upon them. Arches: If of small size, i week; large arches with heavy dead load, I month. * See also paper on "Form Constniction" by Sanford E. Thompson, in Bulletin No 13, Association of American Portland Cement Manufacturers, and Proceedings National Association of Cement Users Vol. 3, p. 64, 1907. CONCRETE BUILDING CONSTRUCTION 649 lx2'C Fig. 194. — Column Form Showing Various Designs. (Seep. 651.) 650 A TREATISE ON CONCRETE All these times are of course simply approximate, the exact time varying with the temperature and moisture of the air and the char- acter of the construction. Even in summer, during a damp, cloudy period, wall forms sometimes cannot be removed inside of 5 days, and other members are delayed proportionally. Occasionally, too, batches of concrete will set abnormally slow, either because of slow I'x.^" Bottom Cleat /~x4-'\Joist Bearer Iron C/amp-s Fig. 195. — Beam Form Showing Three Methods of Construction. (See p. 651.) setting cement or impurities in the sand, and the foreman and inspec- tor must watch very carefully to see that the forms are not removed too soon. Trial with a pick may help to determine the right time. One large builder* requires that a 20-penny spike driven into the concrete must double up before it has penetrated one inch. A plan which is being introduced on some of the best construction work is to take a sample of concrete from the mixer once or twice a ' Mr. r. A. P Turner. CONCRETE BUILDING CONSTRUCTION 651 day and allow it to set out-of-doors, under the same conditions as the construction work, until the date when the forms should be removed, then, before beginning to remove, find the actual strength of the con- crete by crushing the blocks in a testing machine to see whether it is strong enough to carry the dead and the construction load. Column Forms. Column forms for square or rectangular columns differ principally in the type of clamp. (See Fig. 194, p. 649.) For round columns metal forms are commonly used. The most economical method of erecting wood colunrn forms is to nail three sides together before erecting, and the fourth side afterward. If the column sizes are to be reduced in the upper stories it is convenient to use in the largest sizes, in making, narrow strips of sheathing that can be re- moved without splitting the boards when the column is made smaller. Every column form should be made with a clean-out opening at the lower end. . Beam and Girder Forms. The principal methods of beam construc- tion are shown in Fig. 195, page 650. Girder forms are similar to beam forms except for the beam openings, which are framed by inch or inch and a half stock, as is the case with beam openings in column forms. If the beams are of the same or nearly the same depth as the girder, the girder sides should be made in sections between beam openings; if the beams are shallower than the girders the forms may be made in one piece. Beam and girder forms should be erected as a unit after assembling the sides and bottom on the floor below. Beam sides may be made of i-inch (|-inch) or 2-inch (i|-inch) stock — the former is more economical. Beam bottoms, unless very narrow, should not be thinner than 2-inch stock. Cleats should be spaced symmetrically about the center line. A simple form of clamp for beam or small column forms, used originally in Europe, is shown in Fig. 196. The hook, A,\s z, plain piece of flat iron J inch by I J inches, with one end bent and curved as shown. The dog, B, is a square piece of iron, with the end shghtly turned and a hole slightly larger than the flat iron, A, punched through it. This is tightened by hammering on its HOLE „ Fig. 196. — Clamp for Beam or Small Column Form. [See p. 651.; 6s2 A TREATISE ON CONCRETE lower end. The outward pressure of the form boards upon its upper end causes it to bind, and prevents it from slipping back. If it fails to hold, in any case, a wooden wedge is readily driven in to assist in tightening. bo o 2 Beam Forms for Fireproofing Steel Beams. If the building is of steel frame construction with concrete slabs, the beams and columns CONCRETE BUILDING CONSTRUCTION 653 may be covered with concrete for fire protection. In such a case, the concrete should be carried around under the bottom of the flange to protect it from fire. One type of beam form in this class of construction is shown in Fig. 197, page 652. The section shows in detail one method of construction. Wire is passed through the bottom form around the cleat and then bent over Fig. 198. — Forms for Flat Slab Construction Using Joists and Stringers. {See p. 655.) the top of the I-beam to hold the form in place. To be really fire-proot, the concrete must surround not only the sides but also the bottom of the I-beam. To reinforce the strip of concrete under the lower flange of the I-beam, clips may be attached to the flange as shown in the figure. There are several patented designs of clips in the market. Slab Forms. Slab forms for a panel should usually be made in two, three, or four sections, to facilitate removal. The sheathing may be made up into panels with thin cleats or battens, and the panels supported 6S4 A TREATISE ON CONCRETE ?3. K OJ o H pq XI o In CONCKl^TlL aOILDING CONSTRUCTION 655 by joists or joists and stringers. The latter method is most economical and is illustrated in Fig. 198, page 653. Another type of form, designed by Wilham O. Lichtner, where the panels, including the joists and the sides of the beam forms, are made up in advance, is shown in Fig. 199, p. 654. Fig. 200. — -Forms for Curtain Walls Between Columns. (5ee p. 656.) Flat slab forms must be entirely supported by posts, but in beam and girder construction the slab joists may be supported on a horizontal ledger or joist bearer nailed to the beam cleats, or these beam cleats may be notched to receive the joists. 6s6 A TREATISE ON CONCRETE In remaking slab forms when the beams are made narrower the joists are lengthened on alternate ends by nailing on short lengths. To avoid increasmg the length or width of the sheathing, a strip of zinc may be placed over the crack. Whenever columns are reduced in size, the panels must be cut back to beyond the first cleat and patched out to fit the new size. Fig. 201. — Sectional Wall Form. {See p. &$■;.) Wall Forms. A form for a cellar wall is illustrated in Fig. 6, page 19. Occasionally the face of the excavation can be trimmed so that only one side of the form is necessary. A form for a curtain wall is shown in Fig. 200, page 655. This type of wall is usually built after the structural part of the building is complete. CONCRETE BUILDING CONSTRUCTION 6S7 For building solid walls a sectional form is convenient. A very economical and much used type of wall form is shown in Fig. 201, page 656. This wall form is made in sections 3 feet high by 12 feet long and is bolted as shown. A form of this size is very easily handled by two carpenters. The bolt holes left in the wall can be utilized for attaching an outside scaffolding, as shown in Fig. 201, after which they can be very easily plugged up in the usual manner. Fig. 202. — Forms for Hollow Walls. {See p. 657.) A design for a form for a hollow wall is shovm in Fig. 202. The ribs and bolts are so arranged that the latter do not pass through the con- crete, the form being raised when the concrete reaches their level. In the same figure is shown a style of tongued and grooved molding with edges sUghtly beveled, which may be used to form the horizontal joint instead of nailing a triangular strip upon the planks. If the surface is finished as a monolith of course no moldings are required. The forms must be nearly watertight, to prevent the mortar running away from the stones. 6s8 A TREATISE ON CONCRETE STRENGTH OF FORMS Forms that are sufSciently strong and rigid and at the same time economical in the use of lumber must have the dimensions and spacing of all joists, stringers, studs, and posts determined by computation. The loads to consider are: (i) on beam, girder, and slab forms, the vertical pressure of concrete (assumed — for convenience in figuring at 144 pounds per cubic foot), and the construction load of — in average cases — 75 pounds per square foot; and (2) on column and wall forms the hydraulic pressure of a liquid weighing 144 pounds per cubic foot. The head to be used in figuring the hydraulic pressure should be the depth poured in the time that the concrete takes to begin to set; in summer this is about half-an-hour.* The allowable stress in 3 by 4-inch posts is 350 and in 4 by 4-inch, 450 pounds per square inch; in joists and stringers subject to a vertical load, I 200 pounds per square inch; and in studs and column clamps, where the load is somewhat relieved as the concrete sets, 2 400 to 3 000 pounds per square inch. The bending moment formula is If = risWl, 3 WP and the deflection formula is d = — — . 384 EI The stress in column clamps is governed to a certain extent by the type of clamp; the closer to the sheathing the bolts or ties are placed the shorter the span and the smaller the bending moment. In wide columns an extra bolt can be run through the middle of the column. If weak or poorly braced forms are forced out of place by the con- crete they can be realigned only at the risk of cracking and seriously injuring the green concrete. Forms should be designed so that the pressure of the concrete forces the boards against their cleats; nails are then required only to hold the parts in place before concreting, and very few are needed. CONSTRUCTION METHODS Construction methods are covered fully in the preceding chapters. The most important references are to be found in Chapter XIII, Mix- ing; Chapter XIV, Depositing; and Chapter XVI, Laying Concrete in Freezing Weather, It is important to keep the bottom steel above the forms in order to imbed the bars enough to develop their strength and to get the proper thickness of fireproofing. Near, columns, especially in flat slabs, the location of the top steel is essential. Either concrete blocks or wire * For other conduions see Concrete Costs, Table 127, page 610. CONCRETE BUILDING CONSTRUCTION 659 chairs are satisfactory for keeping steel many cases, it is bad practice to place and pry it up as the concrete is placed. in position. Although done in the steel directly on the forms / \ Y\ CD/ -/ m JC c/ \ \\ <0 he 1. (U (1) \ ■^- C +- c 3 m E ■-A^ 42 ^ X J) 0) C > H- 0) 1 tr u mo Q. J2 •4- D -E li Q. d) 5i c k. .X 10 II CM ^ .X X ."K "J ig hi 10 l5 r. TJ s 5 c k ■D • Q) ,_J <0 i= 1^ Q. VO -0 < 5 ^ 53. (0 ? 1 E pq 0) 10 ■d 10 c ■2 3 "0 '53 12 \ « M D ID _C \ °^ C -3 ^\ "5 c *-* W -2 0^ U ^m'/ ! CO L \ \/\. X cs M WAV \ fe BENDING STEEL Numerous patented machines for bending steel are in the market. A table with two devices for bending bars is shown in Fig. 203, page 659 66o A TREATISE ON CONCRETE REINFORCED CONCRETE CHIMNEYS High factory chimneys of reinforced concrete are being built in this country and abroad. The cost, especially of those over loo feet high, is usually much less than brick. If designed and built upon the same prin- ciples and by the same methods which have proved essential in other types of reinforced concrete construction, they can be depended upon to give permanent satisfaction. Reports* from a large number of chimneys have shown that concrete is unaffected by the heat from an ordinary steam boiler plant. The temper- ature in such chimneys seldom exceeds 700° Fahr. while 400° to 500° Fahr. is more usual. Experimental tests also indicate that concrete is not appre- ciably injured at temperatures of 600° to 700° Fahr.f To provide for extremes, it is advisable, however, to build an independ- ent inner shell of concrete or firebrick for at least a portion of the height. Concrete should not be used for a chimney in connection with special high temperature furnaces. Since concrete and steel have substantially the same coefficient of expan- sion! there is no danger of heat causing a separation of the reinforcement from the concrete. The expansive effect of heat is a more serious question. Stresses are set up in the shell of any masonry chimney because of the hot interior and cold exterior surfaces. A concrete chimney, however, has thinner walls so that the stress is less than in one of brick or tile and it is also better reinforced. Provision for temperature stresses are discussed in paragraphs on design which follow. Construction. A reinforced concrete chimney is more difficult to con- struct than many other kinds of concrete construction because of its height and shape, and it therefore should be handled by experienced builders. It is essential in chimney construction that the materials be very carefully selected. The sand as well as the cement should be tested by determining the actual tensile strength of mortar made from it. The stone preferably should be of the nature of a hard trap rock ^ inch_ maximum size. Propor- tions 1:2:3 have been found to give good results. A dry mix should not be used, since insufficient water will produce a porous concrete which does not adhere to the steel. The consistency must be wet enough to quake and form jelly-like mass when lightly rammed, so as to properly imbed and * A special investigation of reinforced concrete chimneys was made by Sanford E. Thompson in 1907 for the Association of American Portland Cement Manufacturers. Many of the points here discussed are summarized from the report, which is printed as Bulletin No. i8 of the Association f Tests of Metals, U. S. A. X See page 261 . 66 1 AIR OUTLETS 1 — ie-FT.a^ — ]• .— I5-FT.2^ \ / o / \ SECTION C-D SECTION A-B Pf;-tiwiM»;: e f y I^^TOa?H'T^ ' o H t : i ! a^i&^^dCT 1 i : ] co 1 g'i^^kgh ; ip^^ffi;|;i : l^i'^l;! ;: Fig 204— Design of Chimney of the Edison Electric Illuminating Co., Br6oklyn, N. Y. {Seep. 662.) 662 A TREATISE ON CONCRETE bond the reinforcement. No exterior plastering should be permitted because it is liable to check and scale. The steel should be good quality round or deformed bars. Bars with flat surfaces like T-bars are inferior because the flat surfaces give a poor bond and the angles make the placing of the concrete difiicult. Deformed bars of small size quite closely spaced are specially good for the horizontal steel to distribute the temperature stresses and high carbon steel of first-class quality also has advantages' for the hor- izontal reinforcement. Design. The design of a chimney built in Brooklyn, N. Y., in 1907 is illustrated in Fig. 204. Design of Reinforced Concrete Chimneys. A reinforced concrete chim- ney consists primarily of a concrete shell vnth vertical steel bars imbedded in it all around the chimney. The shell must be of proper thickness and the steel bars sufficient in size and number to withstand the stresses due to the weight of the chimney and to the action of the wind. A chimney of this type differs essentially from one of brick in that the diameter at the base is so small as compared to the height that it would overturn under a heavy wind were it not for the vertical bars of steel which serve as anchors and hold it on the vrindward side. Wind, in blowing against a chimney, causes compression on the side oppo- site to the wind and tension on the side against which the wind is acting. This compression is resisted by the concrete and steel on the leeward side, while the tension or pull is taken by the steel on the windward side. In addition to the vertical reinforcement, a reinforced concrete chimney should be provided with horizontal hoops of steel, the object of which is to stiffen the vertical steel, to distribute cracks in the concrete due to a dif- ference in temperature between the interior and exterior and to resist the diagonal tension. In designing a reinforced concrete chimney the problem then is primar- ily to determine at various horizontal sections the necessary thickness of the concrete shell and the required amount of vertical reinforcement, so that the allowable working stresses in the concrete and in the steel shall not be exceeded. under the action of the forces to which the structure may be sub- jected. The problem is one in mechanics, involving the equilibrium of a system of forces, and, with certain reasonable assumptions, the laws of me- chanics may therefore be applied to these forces, producing thereby certain rational formulas from which the necessary proportions of the chimney may be determined. The complete analysis and development of the most useful formulas are given in Chapter XX, page 390, of this treatise, the for- mulas themselves being reproduced below. CONCRETE BUILDING CONSTRUCTION 663 The problem of the determination of stresses due to the difference in temperature between the interior and the exterior of the shell involves many uncertainties. The heat tends to expand the inner surfaces, producing tension ^n the outside surface of the shell and compression in the interior surface. Although the distribution of the stress is not clearly known, the variation of the heat through the shell not being uniform, tentative compu- tations indicate high stresses so that it is a question whether vertical tem- perature cracks can be entirely prevented any more than they can be pre- vented in brick or tile chimneys. The function of the horizontal steel may therefore be to distribute these cracks and to resist the vertical shear or diagonal tension. This horizontal steel should be distributed therefore by using srnall diameter bars closely spaced rather than large bars spaced fur- ther apart. Because of the possibility of vertical temperature cracks, the concrete should never be relied upon to carry tension or vertical shear, and the amount of horizontal reinforcement to resist this may be obtained in a similar fashion to the determination of vertical stirrups in a beam. In Chapter XX, page 397, the analysis for the shearing stresses is indicated, and the final formula is presented below together with suggestions for adapt- ing the horizontal reinforcement to temperature stresses. The amount of vertical reinforcement, the thickness of the shell, and the percentage of horizontal reinforcement may be obtained from the following formulas, the derivation of which is given in Chapter XX, page 390. Let W = weight in pounds of the chimney above the section under considera- tion. M = moment in inch-pounds of the wind about that section. /j = maximum tension in the steel in pounds per square inch. /^ = maximum compression in the concrete in pounds per square inch (measured at the mean circumference) . n = — ' = ratio of modulus of elasticity of steel to that of concrete. D = mean diameter of shell in inches (i. e., diameter of center of ring). r =' mean radius of shell in inches. t = total thickness of shell in inches. A^ = total cross-sectional area, in square inches, of reinforcing bars in the section under consideration. k = ratio of distance of neutral axis, from mean circumference on compres- sion side, to the mean diameter I). a, Cp, Cf = constants for any given value of k, Tables i and 2, pages 6$^, 666. 664 A TREATISE ON CONCRETE pQ = ratio of area of steel hoop to area of concrete. h^ = height in feet of chimney above section under consideration. F = effective wind pressure against chimney in pounds per square foot. Then & (M - W z D) . ) 2 W + (CV/, - Cpf^n) ^ t = ^ ? + ^ (^) CpfcD nD *„ = i + 0.002S (3) iS.& f,t Formulas (i), (2), and (3) correspond to formulas (96), (97), and (98) in Chapter XX. In the formula for po, the first term gives the ratio of steel to resist verti- cal shear or diagonal tension, and the second term is an arbitrary ratio designed to distribute the temperature strains. To best distribute the tem- perature strains, a maximum spacing of the horizontal bars is recommended as 6 inches to 10 inches. In the formulas the terms z, Cp and Cj, are constants, the values of which are fixed for any given position of the neutral axis. By means of tables I and 2 (pp. 665-6) these constants may be easily and quickly determined so that the solution of formulas (i) and (2) is rendered quite simple after the selecting of the diameter and height of the chimney and computing the bending moments due to the wind at the various sections considered. The thickness of shell must be assumed in formula (i) in order to determine the average diameter D and to compute the weight W. A new computation may be made to correct this if necessary. For economical distribution of concrete and steel, computation must be made for several sections in the height. It is advisable to make the thickness of exterior shell never less than 5 inches but the number of steel rods may be gradually reduced toward the top.' Summary of Essentials in Design and Construction. In the investiga- tion* referred to, the essential requirements are summarized as follows: (i) Design the foundations according to the best engineering practice. (2) Compute the dimensions and reinforcement in the chimney with conservative units of stress, providing a factor of safety in the concrete of not less than 4 or 5. + See footnote, p. 660. CONCRETE BUILDING CONSTRUCTION 66s (3) Provide enough vertical steel to take all of the pull without exceed- ing 14,000 or at most 16,000 pounds per square inch. (4) Provide enough horizontal or circular steel to take all the vertical shear and to resist the tendency to expansion due to the interior heat. (s) Distribute the horizontal steel by numerous small rods in prefer- ence to larger rods spaced farther apart. (6) Specially reinforce sections where the thickness in the wall of the chimney is changed or which are liable to marked changes of temperature. (7) Select first-class materials and thoroughly test them before and dur- ing the progress of the work. (8) Mix the concrete thoroughly and provide enough water to produce a quaking concrete. (9) Bond the layers of concrete together. (10) Accurately place the steel. (11) Place the concrete around the steel carefully, ramming it so thor- oughly that it will slush against the steel and adhere at every point. (12) Keep the forms rigid. The fulfillment of these requirements will increase the cost of the struc- ture, but if the recommendations are followed, there should be no difficulty in erecting concrete chimneys which will give thorough satisfaction and will endure. Table i. Values of Constants Cp, Cji, z and j for Different Positions of the Neutral Axis, (i. e., for various values of k) For use with equations (i), (2) and (3), page 664, and (96), (97) and (98), pages 396 to 399. k is ratio of distance of neutral axis from mean circumference on compression side to the mean diameter D. Value of k to suit the condition of the problem is obtained from Table 2, page 666. k ; -' Ct z / 0.050 0.600 3.008 0.490 0. 760 0. 100 0.852 2.887 0.480 0. 766 u.ISO i 1-049 2.772 0.469 0.771 0. 200 1.218 2 .661 0.459 0.776 0.250 i 1-370 ^■551 u.448 0.779 0.300 ; 1 . 510 2.442 0.438 0.781 o-35° 1.640 2-333 0.427 0.783 U.400 1-765 2.224 U.416 0.784 0.450 1.884 2. 113 0.404 0.785 0.500 2 . 000 2.000 0-393 0.786 °-S5° 2-113 1.884 0.381 0.785 0.600 2.224 1-763 U.369 0.784 666 A TREATISE ON CONCRETE Table 2, Location of Neutral Axis for various combinations of compressive stress, f^, tensile stress, fg and ratio of moduli, n, (see p. 663.) 11^ fa ^ RATIO OF DEPTH OF k NEUTRAL AXIS TO DEPTH OF STEEL BELOW MOST COMPRESSED B % M sag SURFACE OF BEAM n = 10 n = 12 n= 15 Maximum compressive stress Maximum compressive Stress Maximum compressive stress s in concrete, f^. in concrete, fj. in concrete, ff. 300 400 5 00 600 700 300 400 5oo 600 700 300 400 5 00 600 700 8000 .272 . 334 .384 .428 .466 ■ 310 ■ 375 .428 .474 .5l2 .360 .428 .484 ■ 530 .56, 9000 .2i0 .308 .3i7 . 400 .4.IS .285 .348 .400 ■444 .483 .334 .400 .454 . 5oo .53' lOOOO .231 .286 ■334 .37i .412 .264 ■ 324 .37i ■ 418 .456 .310 .375 .428 ■ 474 ■ bi liooo .214 .266 ■312 .3i3 .389 . 246 .304 .353 ■ 39i .433 ■ 29a .3b 3 .405 ■ 45o .48, 12000 .200 .2!!0 .294 .334 .368 .231 .285 ■ 334 ■ 37i .412 .272 ■ 334 .384 ■ 428 .46, 13000 .188 .236 .278 .316 .3io .217 .270 .316 .3S6 • 392 .2b7 ■ 316 ■ 366 ■ 409 ■ 44 14000 .176 .222 .203 .300 ■334 .204 .2bi .300 • 340 .375 ■ 243 .300 • 349 .391 .42 iSooo .166 . 210 .2S0 .28i .31K . 198 .242 .286 ■324 . 360 ■ 231 .286 ■ 334 .37 b .41 16000 .1S8 . 200 .238 .272 ■304 . 184 ■ 231 .272 ■ 310 ■ 344 . 220 .272 ■ 319 .360 ■39' 17000 .lio . 190 .228 .261 . 291 .I7i . 220 . 261 .298 ■ 330 . 210 .261 ■ 306 -346 ..38 18000 • 143 . 182 .218 .25o .280 .166 .210 .2bO .28i .318 .200 .250 ■ 294 .334 .36: 19000 • 136 .174 .208 .240 .270 . 160 .201 .240 .27i .306 .192 .240 .283 ■ 322 .3b^ 20000 • 130 .166 . 200 •231 . 260 .l52 ■ 194 •231 .264 .296 .184 • 231 ■ 272 ■ 310 .34, In connection with reinforced concrete chimneys, the problems which arise are of two general kinds : (i) A problem in design, involving the determination of the necessary thickness of shell and required amount of reinforcement at the various sections of a chimney of given height and diameter. (2) A problem in the review or investigation of a chimney of given height and diameter having a certain thickness of shell and a given amount of reinforcement to determine the stresses in the concrete and the steel under the action of certain forces. The application of the foregoing formulas to such problems and the use of the accompanying tables may best be illustrated by the following numeri- cal examples, although the designer is advised also to refer to Chap- ter XX, pp. 390-399 for a thorough understanding of the subject. Design of a Chimney. Example i. Given a chimney with height above section considered, no ft.; mean diameter at section considered, lo ft.; allow- able pressure in concrete (/„), 500 lb. per sq. in.; allowable tension in steel (fj), 14 ooolb. per sq. in.; ratio of moduli M, 15; wind pressure (on normal plane) 50 lb., per sq. ft., weight of concrete taken as 150 lb. per cu. ft. What is the necessary thickness of shell and amount of reinforcement at the given section ? Solution. As in all chimney designs, it is necessary here to make a trial assumption of the thickness of shell in order to estimate the weight. Supposn CONCRETE BUILDING CONSTRUCTION 667 we assume a 6-inch shell for the entire height above the section. Assuming that a wind pressure of 50 lbs. per square foot on a normal plane corresponds t° lis of so pounds or 30 pounds per square foot on the projected diameter of a cylindrical surface we have the bending moment due to the wind, M = [10.5 X no X 3°] X i|^ X 12 = 22 869 000 in. lb. and the total weight of the chimney above the section, W = 3.1416 X 10 X u.S X no X 150 = 259 180 lb. For /c = 500, /j = 14 000, and n = 15, table i gives k = .349 For k = .349 table -^ gives Cp — 1.637, Crp — 2.335, ^ = .427 Substituting in equation (i), 8 (22 869 000 — 259 180 X .427 X 120) .4j = = 19.6 2-335 X 14 000 X 120 Therefore 19.6 square inches of steel are required. If i inch round rods are selected, 45 of them would be required. Substituting in equation (2), we have 19.6 ^ ^ 2 X 259180 + [(2.335 X 14000) - (1.637 X 500 X 15)] 3.1416 1-637 X 500 X 120 19.6 ■j =6.6 inches 3.1416 X 120 Therefore a 6.6 inch shell would be used. In general the values of Ag and t as thus obtained should be readjusted by computing W on the basis of the computed thickness of shell. In the case at hand, however, the original assumption of a 6-inch thickness corresponds, for all practical purposes, with the computed thickness of 6.6 inches, so that recomputation is, in this case, unnecessary. If the walls of the chimney taper in thickness the value of W must be altered accordingly.* Having determined the required thickness of shell and amount of vertical reinforcement there remains the question of the necessary horizontal or cir- cular reinforcement. Substituting in formula (3) for /, say 14000 lb., we have no X 30 *„ = . X 0.0025 = 0.0044 ^'' 18.8 X 14000 X 6.6 ' Area of steel, ^g = 6.6 X 12 X 0.0044 = 0.35 sq. in. Thus J inch round rods should be spaced 6f inches on centers. In a similar manner any other section of the chimney may be proportioned. Review of a Chimney. Example 2. Given a chimney with height above section considered, 90 ft; mean diameter at section considered, 8 ft.; thickness of shell at section considered, 6 in.; vertical steel at section condsidered, 60 — f in. round rods; wind pressure (on normal plane, 50 lb. per sq. ft.); weight of concrete taken as 150 lb. per sq. ft.; ratio of moduli, n, 15. What are the maximum stresses in the concrete and in the vertical steel at the section under consideration? * In relatively high chimneys steel cannot be stressed to 14,000 lbs. per sq. in. (see p. 399). 668 A TREATISE ON CONCRETE Solution. A problem of this kind must necessarily be solved by a method of successive trials, since the position of the neutral axis is not known. The location of the neutral axis is determined by the values of fe, fa ^-^d n, two of which, in this case, are unknown. The method of procedure, therefore, is to assume outright a trial position of the neutral axis, select the constants accord- ingly, substitute in equations (i) and (2) and solve them for fg and fc- Then see if the position of the neutral axis, as fixed by' these values of fg and ff. and the given n, is the same as the position assumed at the start. If the two positions agree, then /j and fc as found are the actual stresses; if not, a new position of the neutral axis must be assumed, new constants selected, and new values of /j and /^ computed from equations (i) and (2). Thus a series of trials must be made until the location of the neutral axis as assumed is consistent with the computed values of fc and fg together with the given n. In this problem, assuming 30 pounds pressure on the projected area, we have the bending moment due to the wind, M = [8.5 X 90 X 30] X — X 12 = 12 393 000 in. lb. 2 and the total weight of the chimney above the section, W = 3.1416 X 8 X 0.5 X 90 X 150 = 169 646 lb. Ag = 60 X .3068 = 18.41 sq, in. Now suppose we assume the neutral axis at, say, k = .400 For k = .400, table i gives Cp = 1.765, Cy = 2.224, ^ = -416 Substituting in equation (i) we have 8 (12 393 000 — 169 646 X .416 X 96) . 18.41 = 2.224 X /s X 96 whence /, = 11 400 Substituting in equation (2) we have 18.41 2 X 169646 + (2.224 X 11400 — 1.765 ./„ 15) 3.1416 18.41 ° = ; — ., r ., — ; + — 1-765 X /c X 96 3. 1416X96 whence /c =416 Now fs = II 400, fc = 416, and r = 15 gives k = .354 which does not cor- respond with our original assumption of z = .400. Evidently the true yfe must lie somewhere between the assumed and determined values, hence if we now assume, say, k = .375 and recompute, we obtain fg = 11 000 and f^ = 435, the values of which together with « = 15 gives k = .371 which checks fairly well with the assumption of k = .375. For all practical purposes we may therefore say that the maximum stress in the steel is 11 000 pounds per square inch, while the maximum stress in the concrete is 435 pounds per square inch. The results indicate that both the thickness of shell and the amount of steel are greater than are necessary for safe stresses. FOUNDATIONS AND PIERS 669 CHAPTER XXIV FOUNDATIONS AND PIERS Concrete excels as a iriaterial for foundations, and here finds a wide and important field of usefulness. It is pre-eminently adapted to such construction, because the stresses are chiefly compressive, the forms are easily built, and the surface appearance need not be considered. Since the design of a foundation or sub-structure is governed almost as much by the character of the underlying rock or soil as by the super- structure, brief reference is made to the standard practice in estimating loads, although the treatment of engineering principles, as such, is not within the province of this treatise. Reinforced concrete footings are treated in detail (see p. 673). BEARING POWER OP SOILS AND ROCK Sound hard ledge will support the weight of any foundation and superstructure, but if the rock is seamy or rotten it may require thor- ough examination and special treatment. If its surface is weathered, it must be removed. A sloping surface must be stepped or the founda- tion designed with sufficient toe to prevent sliding. The sustaining power of earths depends upon their composition, the amount of water which they contain or are likely to receive, and the degree to which they are confined. Mr. Joseph R. Worcester* suggests the following unit loads on soil in and around Boston based on an examination of over i 000 borings and experience with the behavior of. heavy structures actually built. Dry, hard, yellow clay, "boulder clay," dry sand or gravel, 6 tons per sq. ft. Compact, damp sand, hard sandy clay, hard blue clay, 5 tons per sq. ft. Medium blue clay, whether or not mixed with fine sand, 35 tons per sq. ft. Soft clay, running sand (confined), 2^ tons per sq. ft. These pressures may be considered as guides for general use, al- though the variation in materials and in local conditions is so great that each problem should be individually investigated. * Journal Boston Society of Civil Engineers, Vol. I. January 1914, p. 19. 670 A TREATISE'ON CONCRETE For estimating the safe load on piles driven to firm strata, such as rock or hard pan, the loading which a pile wiU stand is determined by the crushing strength of the timber. If supported whoUy or in part by friction, it is customary to calculate the safe loading by a formula based upon factors obtained by experiment, or by one based upon the penetration of the pile from the blow of the pile driver. The Engineer- ing News formula is commonly used: Let P = safe load in tons upon a pile. W = weight of hammer in tons. k = height of fall in feet. p = penetration in inches under last blow. Then 2Wh ~ p + i Mr. Worcester* suggests the following modification of the Engineer- ing News formula for local practice around Boston. P = — {Eng. News formula + So per cent.) p + i Mr. Worcester statesf with reference to spacing piles: The minimum distance between centers of piles depends upon two factors: the hardness of the soil and the size of the butts. Ordinary spruce piles may be well driven 24 inches on centers, while large and long piles can not be driven to advantage closer than 30 inches. Another governing condition must be taken into account, however, and that is the supporting power of the soil as a whole. Where the piles reach a real hard pan, the soil \yill generally resist all the pressure that the piles can bring on it, unless it consists of a thin crust overlying a soft mate- rial; but when the soil is so soft that the piles hold by friction only, and there is enough friction to carry all- the soil between the piles down with them, in case they go together, the spacing becomes a question of how much the underlying soU will support per square foot. For example, if the soil can only support 2 tons per square fopt, and the piles could each carry 18 tons, it is useless to place them closer than 3 feet on centers. CONCRETE CAPPING FOR PILES While formerly stone capping for piles was advocated, it is now gen- erally accepted practice in plain and reinforced concrete foundations to * Journal Boston Society of Civil Engineers, Vol, i, January r9T4, p. ig. t Journal Association Engineeiing Societies, June 1903, p- 289. FOUNDATIONS AND PIERS 671 lay the concrete directly upon the head of the piles which have been cut to the required grade. The heads of the piles are usually imbedded in the concrete to a depth of 6 inches. Sometimes the ground may be excavated to a depth of i or 2 feet around the piles and a layer of broken stone, or chips, spread and ramrned hard upon it before laying the concrete so that the supporting power of the soil between the piles may be utilized. Generally, however, it is not safe to rely at all on the soil. The thickness of the concrete above the piles must be sufficient to prevent the head of the pile shearing through the concrete. In a well- designed footing, however, the thickness required for strength is suffi- cient to resist the punching shear of the piles. GENERAL RULES OF DESIGN In designing foundations, two requirements must be borne in mind: (i) that the settlement of the structure be as small as possible; and (2) that settlement, if any, be uniform throughout the structure. This last requirement is specially important in a reinforced concrete struc- ture, because on account of the rigidity of the construction, uneven settlement causes secondary stresses in the columns, beams, and slabs, which may exceed the stresses produced by the loading, and in extreme cases may even cause failure. The first requirement will be satisfied by selection of a proper unit pressure on the soU. To satisfy the requirement for uniform settlement, it is necessary to design the footings so that the pressure in all parts of the structure is uniform. The size of the footing, therefore, must be varied with the superimposed load. For footings carrying more than one column, the center of gravity of the loads from the columns should coincide with the center of gravity of the upward reactions, which for footings resting directly on the soil, coincides with the center of gravity of the footing. For pile foundations, the center of gravity of the upward reaction coincides with the center of gravity of the piles. In proportioning footings, the effect of the dead load upon settle- ment is much larger than of the live load because in most structures the full live load may not be imposed upon all floors at the same time, while the dead load is always there. A suggestion for reduction in the live load is given on page 618. Mr. Schneider, in his specification* for structural design of buildings, specifies: I • Transactions of the American Society of Civil Engineers, Vol. LIV, June, igos, p. 492. 672 A TREATISE ON CONCRETE The live loads on foundations shall be assumed to be the same as for the footings of columns. The areas of the bases of the foundations shall be proportioned for the dead load only. The foundation which receives thelargest ratio of live to deadload shall be selected and proportioned for the combined dead and live loads. The dead load on this foundation shall be divided by the area thus formed and this reduced pressure per square foot shall be the permissible working pressure to be used for the dead load on all foundations. Frequently the building line nearly coincides with the property line and the foundation must be placed entirely inside the building. In such cases, to prevent eccentric pressure on the foundation, either canti- lever construction may be used for transmitting the exterior column loads centrally to the footings, or a combined footing design, as ex- plained on page 678. In structures such as chimneys or narrow buildings which are sub- ject to wind pressure, the foundation should be designed with due con- sideration of the eccentricity caused by the wind. Safe Bearing on Concrete. Bases and bearing plates for steel columns must be made of sufficient area to transmit the pressure to the con- crete foundation without exceeding the unit working stress in bearing, as specified on page 573. Anchoring. Columns subject to uplift due to lateral forces, as in trestles, must be securely anchored to the foundation. The anchors must be made strong enough to resist the uplift, and imbedded deep enough in the concrete so that the weight carried by them will be enough to counteract the uplift. PLAIN CONCRETE FOOTINGS The area of the base of the footings is determined by dividing the superimposed load by the allowable unit pressure on the soil. The area of the top is governed by the allowable bearing stress on the concrete. If the difference between the area of the base and of the top is large, the footing may be stepped or battered. The depth will depend upon the allowable ratio of the length of the projection to the height of the block. The projection should be figured as a cantilever loaded by the reaction of the soil assuming the critical section at the face of the super- imposed step. The ratio of length of the projection to its height is therefore governed by the allowable tensile strength of the concrete and the magnitude of the upward pressure. The tensile stress in the concrete must not exceed the allowable value. (See p. 332.) FOUNDATIONS AND PIERS 673 REINFORCED CONCRETE FOOTINGS To distribute the column load over a large area of the ground without carrying the foundation in successive steps to a considerable depth and using a large mass of concrete, the foundation may be built of reinforced concrete. This in aknost all cases permits a great reduction in the cost of the foundation. Reinforced concrete footings utilize the compressive strength of the concrete and therefore are more economical than the I-beam type of design formerly used.* Reinforced concrete footings may be divided into three groups: (i) Wall footings; (2) Independent column footings of rectangular or square shape; (3) Combined footings carrying more than one column. Wall Footings. A wall footing, as a rule, consists of a slab projecting the required distance on both sides of the wall as cantilevers. In figur- ing bending moments, each portion should be considered as a cantilever with the critical section at the face of the wall. The reinforcement, determined from the bending moment in the usual fashion (see p. 510), consists of bars placed at the bottom of the footing at right angles to the wall. Special attention must be paid to bond stresses. The depth of the footing and the diameter of the bars must be arranged in such a way that the unit bond stress, based on the total external shear and deter- mined by formulas given on page 534, does not exceed the allowable unit stress. It is of great advantage to use bars with small diameters. The use of deformed bars may also prove economical. Diagonal tension also must be considered (see p. 516). As a basis for figuring the diagonal tension, the shear is taken, figured at a dis- tance from the wall face equal to the effective depth of the footing. It is preferable to design the footings of such dimensions as to avoid ythe use of diagonal tension reinforcement. In stepped footings, the steps must be made of such depth that at no point of the footing shaU either the bond or the diagonal tension exceed the allowable working unit stress. Independent Column Footings. A column footing generally consists of a square or rectangular slab reinforced with bars placed at the bottom of the footing and running in two or sometimes in four directions. In such slabs the moments and stresses act in radial and circumferential directions similarly as in flat slabs at the column head. Bending Moments. Referring to Fig. 205, page 676, the bending * See Second Edition of Concrete Plain and Reinforced, page 643. 674 A TREATISE ON CONCRETE moments at the critical section taken at the face of the column 1-2 may be determined by considering the footing as detached along the diagonal lines i-j and 2-6 formed by connecting the corners of the column with the corners of the footing. The load on each trapezoid thus obtained produces a bending moment about the face of the column which can be determined by multiplying the load on the rectangle 1234 durectly in front of the column face by the length of half the projection of the footing from the column, and the load on the remaining triangles 134 and 2j6 by a moment arm equal to two-thirds of that projection. Dead load of footing does not need to be considered in figuring bending moment and shear. The bending moment may be expressed by the following formula. Let, for square footings, o = length of side. c = diameter of column. -P = total column load. Cp= constant. Then, for square footing, 24 \ 0/ \ a/ or M = CpaP (2) in which Cp equals -Lfi— £.) (2+1)- 24 \ 0/ \ a/ For rectangular footing, let a and b = length of sides (see Fig. 205). Cf , = constant. Then moment in a direction (at 1-2 Fig. 205). M = CpflP (3) The moment is in the same units as a, b, and P- FOUNDATIONS AND PIERS The value of Cp and Cp, may be taken from the table below. Constants Cp for Square Footings To be used in formula for bending moment, M = CpaP {See #,674). 675 c a Ratio of Diameter of Column to Side of Footing, —. O.IO o.is 0.20 0.2s 0.30 0.3S 0.40 0.4s 0.50 Cp 0.071 0.06s O.OS9 O.OS3 0.047 0.041 0.036 0.031 0.026 Constants Cp^ for Rectangular Footings To be used in formula for bending moment, M = CpiaP. {See p. 674.) Ratio of Diameter of Column to One Side of Footing Ratio of Diameter of Column to the Other Side of Footing, ~ c a CIO 0.15 0.20 0.2s 0.30 0.3s 0.40 0.4s 0.50 O.IO 0.20 0.071 0.063 0.056 0.073 0.065 0.057 0.074 0.066 0.059 0.076 0.068 0.060 u.078 0.069 0.061 U.079 0.071 0.063 0.081 0.072 0.064 0.083 0.074 0.065 0.08s 0.07S 0.067 0.2s '0.049 0.050 0.052 0053 0.054 0.05s 0.056 0.057 0.059 0.30 U.043 0.044 0.045 0.046 0.047 0.048 0.049 UO50 0.051 0.35 0.037 0.038 0.039 0.040 0.041 0.041 0.042 0.043 0.044 0.40 0.032 0.032 0-033 0.034 0.035 0.035 0.036 0.037 0.038 0.4S 0.027 0.027 0.028 0.028 0.029 0.030 U.030 0.031 0.032 0.50 0.022 0.022 0.023 0.023 0.024 0.024 0.025 0.026 0.026 Effective Reinforcement and Effective Width. In determining the re- sisting moment, which must be equal to the bending moment, the steel considered as effective is that placed within a width consisting of the width of the column plus twice the thickness of the footing plus half of the remaining distance to the edge of the footing on each side. (See Fig. 205.) Additional steel should be placed outside the effective width at a spacing twice the spacing of the effective reinforcement. Minimum Depth of Footing. The minimum depth of footing as deter- mined by the unit punching shear is obtained by dividing the total shear at the edge of the column by the circumference of the column times the allowable unit punching shear. If the area of column is small in comparison with the area of the footing, the shear may be taken as equal to the column load. Bond Stresses. In designing footings, the most important and often the determining feature is the bond stress. The depth and the diameter 676 A TREATISE ON CONCRETE of the bars must be selected so that the bond stress does not exceed the allowable working unit stress (see p. 573)- I^^ figuring bond, the same loads and the same steel bars should be taken as were used in determining the bending moment, and the moment of resistance of the footing. Formula (36), page 534,' should be used in figuring the unit bond stress. Besides this, the length of the bar beyond any pomt must be large enough to develop the tensile stress in bar by bond.^ Thus at a point where the stress in a bar is 16 000 lb., not only the unit bond, u, must not exceed the working stress, but also the length of the bar beyond the point under consideration must be equal to the required number of diameters unless the bar is anchored at the end. Formula (39), page 539, should be used in figuring the length of bar to pre- vent slipping. Rectangular Footing Fig. 205. — Square and Rectangular Column Footings. (See p. 673.) If the footing is stepped, or beveled, the bond must be figured at the points of change in thickness to determine whether in all places the design fulfills both of the requirements as to the unit bond stress, u, and the length of imbedment to prevent slipping. Diagonal Tension. Tests indicate that in reinforced concrete foot- ings, diagonal tension develops at a distance from the face of the column equal to the effective depth of the footing. In figuring the maximum V diagonal tension, therefore, by the formula, v = — — (see p. 517), V bj d should be taken as the upward load between the edge of the footing and a line concentric with and distant from the column face a distance FOUNDATIONS AND PIERS 677 equal to the efiective depth of the footing; b is the length of this circum- ferential line; and d is the effective depth of the footing at the point considered. The following example illustrates the method of designing reinforced concrete column footings. Example i. Find the dimensions of a footing for a column 28 inches square carry- ing 350 000 lb., when the allowable pressure on the soil is two tons per square foot. Solution. Necessary area, of footing is found by dividing the total superimposed load plus assumed weight of footing (40 000 lb.), by allowable unit pressure on soil, which gives — = 98 sq. ft. as the required area of base. A base 10 feet square, 4 000 therefore, wiU be selected. The final dimensions and reinforcement selected, from the computations below, are shown in Fig. 206, page 677. -- :::::::;: it: .. C - - X '.z y \ / lOffO" 0-7 So .__! QG e" »^»U ...n. . T 00 •dj^ze Spaces at 4.^ inches— HdH" Fig. 206. — Details of Square Footing. {See p. 677) Find Minimum Thickness of Footing as De'ermined by Pmiching Shear, Since the gross area of base of footing is 100 sq. ft., and area of column, 5.43 sq. ft., the net area of footing is 100 — 5.43 = 94.57 sq. ft. The load on the net area produces punching shear at the edge of the column, which f or i ; 2 : 4 concrete must not exceed 120 lb. per sq. in. The load producing punching shear may be determined by multi- plying the total load on the footing (exclusive of the weight of the footing which pro- duces no shear) by the ratio of net area to gross area of the footing. It is, therefore, ?i^X 350 000= 332 000 lb. By dividing this load by the circumference of the 100 column, or 112 inches, and the allowable unit shear, we get Minimum depth = -^^^-r-, = 24.7 inches. 112 X 120 678 A TREATISE ON CONCRETE Accept 25 inches as the depth of the footing. Find Diagonal Tension. To determine whether the minimuna depth is sufficient, diagonal tension will be determined at a distance from column equal to effective depth of footing, as explained on page 676. The side of the square is 28 + 2 X 25_ = 78 inches, or 6.5 ft., and the circumference, 78 X 4 = 312 inches. The area outside 57*7 this circumference equals 100 — 6.5^ = 57.7 sq. ft., and the load X 35° °°° — 202 000 pounds. The unit shear involving diagonal tension, therefore, is - = 30 lb. per square inch. JX25X312 Hence, no shear reinforcement is necessary. Find Bending Moment. As explained on page 674, the bending moment can be found by the use of table on page 675. The ratio of diameter of column to side of footing is — = — ^ = 0.2^?, and the corresponding constant from the table, by a 10 X 12 interpolation, Cj, = 0.0567. The bending moment, therefore, is M = 0.0567 X 10 X 12 X 3SO 000 = 2 380 000 inch-pounds. Find Area of Steel. The reinforcement will be placed in two directions parallel to the sides of the footing. The area of steel in each band is found by dividing the bending moment determined above by the moment arm times the allowable unit stress in steel. . 2 380 000 , „ . . . ^ . , J u A^ = — = 6.8 sq. m. requirmg 23, |-mch round bars. ^ X 25 X 16 000 All these bars must be placed within the effective distance, which is 28 in. + , ft (2 X 25 in.) + - — - = 8 ft. (See p. 675.) Add two bars at each side, making a total of 27, f-inch round bars. Find Bond Stress. Bond stresses are determined by. Formula (36), page 534. Since the shear at one edge of column is V =— = 83000 lb., and the number of 4 effective bars per band is 23, j-inch round bars, the periphery of which is 23 X 1.96 = 45.2 inches; therefore the unit bond stress is 83 000 „ ,, . , " = "TTT Z7~ — = 84 lb. per square mch. 1X25X45-2 This bond stress may be used for deformed bars, but is somewhat excessive for plain bars in 1 : 2 :4 concrete (see p. 573). If plain bars are used, the depth would have to be increased or smaller bars used. Hence use deformed bars. The weight of the footing does not need to be considered in figuring bending moment, shear, diagonal tension, and bond stresses, because it is balanced by the up- ward reaction. It increases, however, the unit pressure on the soil; therefore it was considered in determining the size of the base of the footing. An example of this type of footing, founded on piles, is shown in Fig. 20'jj page 679. This is one of the interior footings used for the new buildings of the Massachusetts Institute of Technology, Cam- bridge, Mass. COMBINED FOOTINGS. Sometimes it is necessary to connect the footings of two or more columns, as when the face of the columns coincides with or is near the edge of the building lot. To insure equal distribution of the pressure on FOUNDATIONS AND PIERS 679 the foundation, it is of utmost importance that the center of gravity of the loads coincide with the center of gravity of the upward reaction. The shape of the footing and the relative position of the columns on the footing are governed chiefly by this requirement. Combined footings for two columns carrying loads of different sizes may be made in the shape of a trapezoid, the center of gravity of which coincides with the center of gravity of the loads, or it may be rectangu- lar in shape, but with a longitudinal projection beyond the heavier column of a sufficient length to bring the center of gravity of the rec- tangle in the required position. Basmt. Fl. 3^ '-2V Gr. 17.10 T ut: Gr. 1 4.50 Ml -'.»._. + '4R3' y-T "^ Gr . 13.00 -AftZ" eft6" 5> s Fig. 207-7-Section of Interior Footing. {See p. 678.) A combined footing may be either a slab of uniform thickness, or its cross section may be in the shape of an inverted T. In designing, the footing should be treated as a beam or slab, applying the principles and formulas given in the chapter on Reinforced Concrete Design. The pressure acts upwards, consequently the tensile stresses due to the posi- tive bending moment will be in the top of the footing, and the nega- tive bending moment at the bottom. Special attention must be given to bond stress and diagonal tension. The main reinforcement is placed longitudinally, that is, extending from column to column and beyond. If the width of the footing is 68o A TREATISE ON CONCRETE much larger than the width of the column, it is advisable to providj? transverse reinforcement of sufficient amount to resist the transverse bending moment. This reinforcement is either distributed over the whole footing, or concentrated near the columns, in which case a few bars are added to the figured amount and placed between columns. The following example illustrates the design of a combined footing. COMBINED FOOTING Example: Find the dimensions of a combined footing in which Pi = 400 000 lb., and i>2 = 580 000 lb., are the respective loads of columns i and 2, with cross-sections 24 and 30 in. square. The distance between their centers is 15 ft. and the allowable unit pressure on the soil is 8 000 lb. per sq. ft. (See Fig. 20S, p. 681.) Solution: Area of Footing. The area of footing will be determined by dividing the total superimposed load by the allowable unit pressure on the soil. Since the weight of the footing, which is assumed at 50 000 lb., increases the pressure on the soil, it must be included in the total superimposed load used in determining the area of footing. It should not be taken into account, however, in determining bending moments and shears. The total superimposed load is 400 000 + 580 000 + 5° 000 = I 030 000 lb. The required area of footing therefore is — =129 sq. ft. o 000 Shape of Footing. A footing of a rectangular shape, one side of which is flush with the outside face of column i will.be accepted. The footing extends beyond column 2 (which carries the larger load) the required length to make the center of gravity of the superimposed loads coincide with the center of gravity of the upward reaction of the soil. Center of Gravity. The center of gravity of the column loads, from simple mechanics, is distant from column i, 15 X r-; — r = 8.9 ft. Since center 400 000 X 580 000 of gravity of upward reaction coincides with the center of gravity determined above and the footing is flush with the outside face of columiL' i, the distance from the edge of the footing to its center of gravity is 8.9 ft. + i ft. = 9.9 ft. In a rectangle the center of gravity is in the middle, and therefore the total length must equal 9.9 X 2 = 19.8. Width of the Footing. The width is determined by the required area and is 19.5 Shears. The %hear diagram is shown in Fig. 208. The columns are represented by theoretical points of application of loads. Since the columns are large the shear at the edge of the columns will be smaller than the theoretical maximum shear and can be determined by plotting the dimensions of the columns. (See Fig. 208, page 681.) The upward reaction per foot of width of footing determined by dividing the total downward load by the length of the footing is 5-? = 49 500 lb. perlin. ft. 19 ■ 8 The shear at the left of column 2 equals the total upward reaction on the cantilever, or 49 500 X 3 . 8 = 188 000 lb. To the right of column 2 the shear equals the differ- ence between the column load and the upward reaction, or 580 000 — 188 000 = 392 000 lb. The shears are obtained similarly at the other column. Bending Moment. Weight of footing is not considered in determining the bending moment becaus^e it is balanced by the upward reaction. The bending moment diagram shown in Fig. 208 is determined by simple statics. For the purposes of com- putation, the footing may be considered as a slab supported at the columns and loaded by the uniformly distributed pressure of soil. Since the uniform load acts upward the bending moment will be of opposite sign to that in ordinary beams. The maxi- mum bending moment of the cantilever was determined by multiplying the total FOUNDATIONS AND PTERS 1= = 400000 Pounds Fi= 580000 Pounds — 30"- f Round Stirrups l2.Leq& Cach 1 5 Bent Bars Lines of^^tirrups k,F ound C ross Bars to T M -J 1 1 h 2 _ 1 1 1 ■ 1 1 CD CO 1 ro ti: OJ Fig. 2o8. — Design of Combined Footing, (See p. 68o.) 682 A TREATISE ON CONCRETE upward load on the cantilever by half the length of the cantilever. Their magnitude is indicated on the diagram. The maximum bending moment in the central por- tion of the footing is determined from the principle that thepoint of maximum bending moment coincides with the point of zero shear, the distance of which from either column can be determined by dividing the vertical shear at that column by the up- ward unit reaction. For column i, therefore, the point of zero shear is distant 350 500 lb. ^ 49 soolb. = 7.08 ft. from center. The maximum bending moment = 24700ft. lb. — 3505001b. X 7.08ft. + 49 500 lb. X 7.08 ft. X — — = I 215 700 ft. lb. where 24 700 ft. lb. is the bending moment at the column due to the projec- tion; 350 500 lb. is the shear at the reaction; and 49 500 lb. is the uniformly dis- tributed upward pressure per foot of width of footing The bending moment in the central portion of the footing depends upon the magni- tude of the bending moment at the column which in turn depends upon the length of projection; i.e. the length of the cantilever. Depth of Footing, Depth of footing is determined by the punching shear, by diagonal tension, ajid by bending moment. The largest depth, of course, must be used. Depth Determined by Punching Shear. At column 1, the load equals 400 000 lb. Since the footing is flush on the outside, the column has only three shearing sides of a length equal to 24 X 3 = 72 in. Allowing for the load transmitted directly by the column, depth required is ^ X -^-rz = 42-3 in. At colurtm 2, although the load 40 72 X 120 is larger the shearing area is so much larger than at column i, that the required depth is only 37 in. Depth Determined by Diagonal Tension. From the shear diagram, the maximum shear at edge of column 2 is 7 = 330 000. Since the width ot footing is 78 in. and the allowable shear 120 lb., required depth is ^^—^ — — r =40.3 in. ^ 120 X .875 X 78. Depth Determined by Bending Moment. Since the bending moment is i 215 700 ft. lb., or 14 600000 in. lb., the depth, from Formula (3), p. 482, is d = 0.096 1 14 600 000 k/ -7, ~ 41 ■ 5- In this case the depth required 'by punching shear is a maxmium. To reduce amount of steel and bond stresses an effective depth of 48 in. is accepted. Longitudinal Reinforcement. The amount of longitudinal reinforcement may be determined from Formula (4a), p. 482. As = — z zz — ttt, — ;: = 21.7 sq. in. " 0.87s X 48 X 16 000 ' ^ which requires 28, i-in. round bars. The reinfoKement of the cantilever determined o ^ ^ 000 ^^ T 2 in the ; same fashion is ^5 = — r — — tt-t-, — ; = 6.3 sq. in. This reinforce 0.87s X 48 X 16 000 ^ ^ ment can be supplied partly by bending down of the steel and partly by short bars. Since the bond stresses are very large it will be necessary to provide a much larger amount of steel than that determined by the bending moment. It is advis- able to use reinforcement as shown in Fig. 208. Stirrups. The stirrups are determined from the shear diagram in the irianner ex- plained on page 528. It must be remembered that the stirrups are designed for the shear at the face of the column which is smaller than the maximum shear as found from tests. To be effective, the first stirrup should be placed from the edge of the column a distance equal to \ of the depth of the footing. Cross Bending. Since the footing is wider than the support, it is subjected to cross bending. To prevent the projections from breaking, enough cross steel at the bottom of the footing must be provided. As the sizes of the columns are different, the projections at the base are different. In practice, it is accurate enough in determining the bending moment to divide the footing by lines 01 and 2j as shown in the figures and compute the bending moments in respect to lines 01 and 23. The load at each dantilever is 12_55£ X 2 . 25 X 8 . 08 = 138 200 and 42-i22 x 2 X 11.72 6.5 6.S = 178 200 lb. respectively. ' The bending moment, obtained by multiplying the loads by half of the length of FOUNDATIONS AND PIERS 683 the projection is Af 1 = i 870 000 in. lb. and Af 2 = 2 140 000 in. lb. The required amount of steel, from formula (4a), p. 482, is 2.8 sq. in. at column i, and 3.2 sq. in. at column 2, requiring 9, f-in. and 11, f-in. bars respectively, spaced as shown in the figure. Influence of Projections on the Bending Moment. The bending moment in tlie center of a combined footing depends upon the ratio of the length of cantilevers to the distance between columns. Fig. 209 illustrates three cases which may occur in the design of footings. In Fig. 209 — Bending Moment in Center of Footing for Varying Lengths of Cantilevers. (5ee p. 683.) ■Baam't. n. Gr. 1710 ,8l5sp . c(t ^ * * * SL -3R.2^ £ 10-1"? *-20"-* ■■ .-■— ,1 6; LlLiJ. liJ]..iLiLJLlL Ji JL..IL ii i ^5-|T ■7-4:"¥ SPfS" -8-l"¥ Ssp^i^ ► ^ ^ * ♦ * *^ -3FF.a" 16R.0" Fig. 210 — Section of Combined Footing. Massachusetts Institute of Technology. {See p. 684.) (a) the projection is smaller than one-half of the length, /. In this case the bending moment in the cantilevers and at the columns is positive and in the central portion negative. In {b) is illustrated a case in which the length of the cantilever equals ^l; hence the bending moment in the center equals zero. In case (c) the cantilevers are larger than 1 1 therefore the whole footing is subjected to positive bending 684. A TREATISE ON CONCRETE moment which is a maximum at the column and a minimum in the center. An example of the combined type of footing is shown in Fig. 210, page 683. This is one of the exterior footings from the new buildings of the Massachusetts Institute of Technology. SPREAD FOOTINGS When the allowable pressure on the soil is very small or when the building is supported by piles sustained by friction, it may be necessary to spread the foundation over the whole area of the building, either using a thick mass of plain concrete or a thinner slab of reinforced con- crete design as a flat plate, or a beam and slab system. Flat Slab Foundations. A flat slab may be designed by the method of flat plates explained on pages 540 to 551. The slab is considered as an inverted flat plate loaded by the reaction of the ground and sup- ported by the columns. Special provision should be made in the design where there is unequal loading. Since the distributed pressure acts upward, the bottom of the plate under the columns and the top of the plate between the columns is in tension; hence the steel must be in the bottom of the slab under the columns, and should be bent up to the top of the slab between columns. The column base must be large enough to prevent excess loading or too great moments and shears in the concrete. Beam and Slab Foundation. For a combination of beams and slabs the principles of floor design are followed except that the distributed load acts upward. The beams or ribs may be built either above or be- low the slab, the former method permitting a T-beam design, but, on the other hand, requiring an extra fill and separate floor surface in the basement. The formulas and discussion relating to slab design in Chapter XXII apply. FOUNDATION BOLTS It is often difficult to locate bolts in concrete with sufficient exactness for settmg a machine. To obviate this difficulty, the head of the bolt should be provided with a large washer* to give a good bearing surface, * The washers, which are used for transmitting the pressure of large bolts to the concrete or other foundations, should be carefully designed with heavy ribs so as to transmit a uniform pressure per square inch of area. Neither wrought nor cast iron plates should be used for washers under large bolts. FOUNDATIONS AND PIERS 685 the bolt placed in its approximate position, with washer down, and an iron pipe or a Ught wooden box placed around the bolt resting upon the washer. When the machine is set, to prevent the bolt from rusting, the iron tube or box should be filled with mortar. In any case the tube or box should be filled with sand before the machine is poured up with sulphur or cement grout, in order to keep these materials from running down the bolt holes. CONCRETE PILES Concrete piles may be employed in place of wood where the loading is excessive, and where the durability of timber piles is questioned either because of probable worm action or the rotting of the timber. If the bearing is frictional and the piles are driven through ground which is continually wet, there is usually no advantage in concrete over timber piles unless in certain instances where the low level of the ground water or the tide water is so far beneath the structure that the concrete pUes permit the commencement of the foundation at a considerably higher level and thus save excavation and material. Concrete piles are formed in place, or are molded above ground. Various methods have been suggested for forming the hole in to which the concrete is to be placed. One of the patented processes consists in driving a double shell of metal into the ground, removing the inner one, and leaving the outer to form a mold for the concrete. The two shells and pile driver are shown in Fig. 211, page 686. The inner shell or pile core, which is of heavy sheet steel and constructed so that it can be made to collapse for removal from the ground, is placed within the other thinner shell, and driven like an ordinary pile. The core is then collapsed and withdrawn, leaving the outer shell, which is closed at the bottom, to be filled with concrete. By providing considerable taper, additional support is obtained from the soil. Another system, illustrated in Fig. 212, consists in driving a single shell with either a concrete or a steel point, then slowly withdrawing it, and filling the space which it occupied with concrete whose surface is kept far enough above the lower end of the tube to maintain the head necessary to resist the pressure of the ground. In a modification of tliis system a pedestal is formed at the foot of the pile. Both these piles are patented. Still another type, especially adapted, to underpinning, is the caisson pile in which a steel cylinder is sunk to a strata of earth, strong enough to carry the load, and filled with concrete. With a^minimum diameter of 3 feet, the interior can be excavated by hand as the shell is sunk. 686 A TREATISE ON CONCRETE Fig. 211. — Method of Forming Concrete Piles in Place. (See p. 68s.J FOUNDATIONS AND PIERS 687 PuJIing Gables Pulling Clamp jSteel Driving F^orm By undercutting the edge when the cylinder is just above grade a spread base can be secured capable of carrying a large load. A pile of this type has been driven to carry a goo ton load on a 6 foot shaft and a base 15 feet 4 inches in diameter. Piles made in situ may be re- inforced if desired. Cast Piles. Reinforced piles which are formed above ground are designed like columns with vertical reinforcement connect- ed at intervals with horizontal wire rods. The pile* used in a foundation for the Boston Woven Hose & ?^ Rubber Company, Cambridge, Mass., is illustrated in Fig. 213. These piles averaged about 30 feet long. The hammer weigh- ed 4 700 pounds and the blows were cushioned by a head con- sisting of a plate iron collar 16 inches square on the inside and 3 feet in height, which incased an oak block 16 by 16 by 18 inches, to the bottom of which six thicknesses of rope and four layers of rubber belting were nailed. The piles were driven at the age of thirty to forty days. The usual drop was 3 feet but in some cases this was increased to 19 feet without injuring the pile. ■ The designs drawn up in 1903 for the Pennsylvania Railroad Tunnelf under the Hudson River call for a shell of cast Concrete DeposH-ed Pile form Partlu Completed Pulled Fig. 2J2. — Method of Forming Concrete Piles in Place. {See p. 6S5.) • For full description of piles and driving see " Cast Reinforced Concrete Piles," by Sanford E. Thomp- son and Benjamin Fox, Journal Association of Engineering Societies, Vol. XLII, igog. t Engineering News, Oct. is, 1904, p. 331. 688 A TREATISE ON CONCRETE ^ s: Fig. 213.— Piles used at Cam- bridge, Mass. (See p. 687.J iron surrounded by concrete and supported at intervals by steel screw piles filled with con- crete. Sheet Piling. Poling boards of concrete were employed by Mr. Howard A, Carson, Chief Engineer in the construction of the ap- proaches to tlie East Boston Tunnel. These are described* as follows: The excavation was through gravel and day, and through sand containing some water. Trenches 16 feet long and 16 feet apart were dug to about the level of the bottom of the building foundation. Below the foundation one-half of each trench, or 8 feet in length, was carried down to grade. The bank below the foundation was held in place by means of concrete slabs used as sheet piling, as illus- trated in Fig. 214. These slabs were from 6 to 8 feet long, 6 inches wide, and 2 inches thick, and each was reinforced with six square steel rods running the entire length of the slab and shown in Fig. 215. If wooden sheeting had been used, it would have been necessary either to have concreted directly against it and left it in place, or to have pulled the planks as the concrete was filled in. If the first method had been used, the planks would in time have become rotten, leaving a vacant space. If the planks had been pulled, there would have been danger that some of the earth under the building would run and a settle- ment of the building follow. In order to guard against any slight voids which might have been left in driving, grout was poured in behind the sheeting. This sheeting served not only to hold the bank in place, but was used, in place of a back wall, to waterproof against. The sheeting was not disturbed, and the wall of the tunnel was built directly against it. * Ninth Annual Report, Boston Transit Commission, p. 41. FOUNDATIONS AND PIERS 689 BRIDGE PIERS Concrete is employed for bridge piers either as filling for ashlar or cut masonry or for the entire pier. In the latter case, in which the face is also of concrete, the chief question is as to its ability to with- stand the wear of the water, the ice, and floating debris. In the Kansas City flood of 1903, the piers of soUd concrete, although located where they were struck by all the heavy debris which totally destroyed many of the stone masonry structures of the same size, re- mained practically uninjured. Fig. 214. — Concrete Sheet Piling in Approaches to East Boston Tunnel. (See p. 688.) Plastering of concrete piers and abutments should be prohibited. If a mortar surface is required, an excellent facing, to be placed next to the form as the concrete is laid, is a mixture of one part cement to 25 parts hard broken stone screenings |-inch in size and imder. Ordi- narily, however, no surface finish is required unless superficial treatment is given for the sake of appearance. (See p. 262.) Pier Design. Most railroads have substituted concrete for ashlar masonry in bridge piers. 690 A TREATISE ON CONCRETE The standard pier of the N. Y. Central R. R., adapted to any height up to 40 feet, is shown in Fig. 216, page 691.* The width, which de- pends upon the length of span, is as follows: Spans up to 40 feet width. A, = 4 ft. in. Spans 40 to 60 feet width. A, = 4 ft. 6 in. Spans 60 to 80 feet width, A, = 5 ft. o in. Spans 80 to 100 feet width. A, = 5 ft. 6 in. Spans 100 to 125 feet width. A, = 6 ft. o in. Spans 125 to 150 feet width. A, = 6 ft. 6 in. Spans 150 to 200 feet width. A, = 7 ft. o in. Spans 200 to 250 feet width. A, = 7 ft. 6 in. For skew crossings, increase width. A, if necessary. I^'-S-J ^:;r^ Foundation is varied to suit local conditions. Concrete 1:3:6 is employed for it unless stone masonry is cheaper. The starkweather is carried 2 feet above high water, and its cap is of 1:1:2 concrete. The coping of the pier is reinforced with galvanized wire netting or wire cloth, a somewhat unusual requirement. The Illinois Central R. R., in their 1904 design, reinforce the surface of piers with vertical and horizontal steel rods, and imbed a single I-beam in the pointed nose at each end of the pier.f All of the roads named above have piers in streams which subject them to considerable wear from ice and drift, and the concrete has proved satisfactory. FOUNDATIONS UNDER WATER The best and most durable concrete foundations, espe- cially in work in sea-water, are laid within cofferdams from which the water has been pumped, or in pneumatic cais- sons. However, because of the difficulty and expense of these methods, they can not usually be followed. If the bottom is prepared by dredging, and, if necessary, driving pUes, good practice permits the use of a single line of sheet- ing, suitably supported with rangers, to prevent the wash of the water * Arranged from origiaal drawing. t From drawing kindly furnished by H. W. Parkhurst, Engineer. ELEVATION Fig. 215.- Sheet Pil- ing. {Sec p. 688.) FOUNDATIONS AND PIERS 691 and keep the concrete from spreading.* Permanent metal cylinders are sometimes sunk in place of the sheeting. Methods of laying concrete under water are described in Chapter XIV, page 267s and the effect of sea-water upon concrete is discussed by Mr. R. Feret in Chapter XV, page 271. BAgE O^^^IL TO SUIT SUPERSTRUCTURE 1:1:2 CONCRETE 2 O* l:3:e CONCRETE 5 10 TO 12 C. TO C. WHERE SOFT M^TERr 'VTERTAL^OCCURSN tr ij Li LJ Li LJ Li U U 01 DTu^ gF^"' U ill Li Li DOTTED LINE TC BE USEO IF STARKWATER IS UNNECESSARY SIDE AND UP-STREAM ELEVATIONS ONE^BOLT EVERY 7 18 STAGGERED . , , •. PLATES 4^4X 'A % PLAN DETAIL OF PROTECTION FOR STARKWEATHER Fig. 216.— Standard Concrete Bridge Pier, N. Y. C. R. R., G. W. Kittredge, Chief Engineer. {See p. 690.) For under-water work, a larger factor of safety should be einployed than for work above ground, the concrete should be shghtly richer in carefuUy selected cement, and the aggregate so proportioned as to give a dense and impervious mixture. (See p. 304.) • See Foundations for New Cambridge Bridge, by Sanford E. Thompson, Engineering News, Oct. 17, 1901, p. 283. 692 A TREATISE ON CONCRETE Concrete for the foundations of walls and piers for high office buildings is usually laid in oblong or circular caissons of steel or wood,* after ex- cavating under air pressure. Steel pipes are sometimes sunk with the aid of the water jet, and afterwards filled with concrete. f * Engineering News, Sept. 26, 1901, p. 222. t Jules Breuchaud, Transactions American Society of Civil Engineers, Vol. XXXVII. p. 31. BEAM BRIDGES 693 CHAPTER XXV BEAM BRIDGES Unlike steel bridges, which frequently have plank flooring for high- ways or open tie construction for railways, the concrete bridge, except in rare instances, is built with a solid deck of concrete which serves not only as the base for the flooring but also as an essential part of the bridge structure. Aside from its structural value this solid concrete deck affords a simple and efiicient means of obtaining solid floor con- struction which is highly desirable along important lines of traffic. Thus the concrete bridge, rigid and durable, has little or no vibration, reduces maintenance to a minimum and becomes a permanent part of the roadway, permitting, as it does, an unbroken extension of the highway pavement or railway ballast. In general, concrete is adapted to two principal classes of bridge superstructures; the arch bridge and the beam bridge. Strictly speak- ing, the arch is a beam, but being a curved beam its structural analysis is essentially different from that applied to the common straight beam. The term "Beam Bridges," as here used and as distinguished from "Arches" discussed in Chapter XXVI, is intended to include that class of bridges wherein the loads are supported by simple slabs, or girders, or by a combination of the two. In such structures the supporting members are essentially beams and are proportioned in accordance with the fundamental principles of design as established for straight beams. No attempt is here made to enter into an exhaustive discussion of the design of concrete bridges, as it would be impossible to illustrate or even to mention the. unlimited number of special cases and peculiar problems which might arise. To illustrate the fundamental principles involved in the design of beam bridges of both the slab and girder type, typical examples have been drawn up showing methods of computation and the resulting designs. Slab Bridges. The simplest type of beam bridge is merely a flat slab spanning from abutment to abutment and is practical only for comparatively short spans, the Hmit, as fixed by considerations of econ- omy, being dependent -upon the nature of the live loads called for 694 A TREATISE ON CONCRETE in any particular locality. If designed for trolley cars or heavy auto trucks, the limit of economical span for the slab bridge is probably not more than lo or 12 feet, whereas for less severe loading it may prove economical up to spans of 18 or 20 feet. In general it may be said that when the combination of span and loading is such as to call for a slab thickness of more than 16 to 18 inches the simple slab will not prove as economical as the T-beam or girder type. Girder Bridges. As the requirements of strength increase, a pomt is reached at which the simple slab ceases to be economical or even practical, owing to the fact that beyond certain limits an increased thickness of slab does not give added strength in any reasonable pro- portion to the amount of material used. For longer spans or heavier loadings than those for which the simple slab is economical, it there- fore becomes necessary to modify the type of construction so as to obtain increased strength without using a solid slab of extreme thick- ness. This is accompUshed by placing deeper ribs or girders beneath the slab to strengthen and support it, resulting in a type of construc- tion known as the "girder" bridge. Thus the girder bridge is in reality a modification of the slab bridge whereby a comparatively thin slab spans between a series of relatively deep beams which in turn span from abutment to abutment. As commonly built, the supporting ribs or girders are constructed monolithic with the floor slab obtaining thereby the structural advantages of the T-beam. The girder type of construction, supplementing as it does the slab type, becomes practical at the point where the simple slab ceases to be economical, while its maximum economical span is determined not only by the kind of loading provided for but also by the spacing and arrangement of the girders. In railroad bridges and highway bridges carrying trolley cars a girder is usually located at or near each rail, whereas girders receiving roadway loads are usually spaced so that the floor slab will have a thickness of from 5 to 7 inches. Owing to the greater complexity of the girder bridge it is impossible to establish the limits of economical spans as definitely as in the case of the more simple slab bridge. Girder bridges of well proportioned design have been used for spans up to 80 feet, but whether or not they are practical for this or even shorter spans is dependent upon the severity of the loading and other practical as well as theoretical elements which must necessarily involve' the judgment of the designer and which must be carefully considered in each particular case. BEAM BRIDGES 695 LOADS In the examples, the design has been based upon the following as- sumptions as to live loads and unit stresses and these may be considered typical. Live Loads: On sidewalks, a uniform load of 100 lb. per sq. ft.; on roadways a 20-ton auto truck having 6 tons on one axle and 14 tons on the other axle, the axles being 1 2 feet apart, and the distance between wheels 6 feet. Distribution of Concentrated Loads: The results of recent tests conducted by the highway department of the State of Ohio* indicate that a concentrated load applied to the concrete slab of a highway bridge floor may be safely taken as distributed over a width of floor represented by the formula / e = 0.6 S + I.J where e — effective width in feet of a slab of greater width than length, and S = clear span in feet. In considering the concentrated loads represented by a wagon, auto truck, or other highway vehicle the effective width of distribution for each wheel can not of course be taken as more than the half the "gage" or distance between wheels at each side of the concentrated load with- out overlapping the distribution from the other wheel. Where concentrated loads are apphed directly to the slab this method of distribution gives a loading, which, while distributed across a certain width of slab, is taken as concentrated with respect to the length of span in determining moments and shears. In case the slab is covered with paving material the stiffness of the paving tends to give some distribution along the span and, when applied over a fill, it is permissible to consider a further distribution through the fill along the customary 45° lihes. Assuming the pavement to give a wheel a longitudinal distribution of at least 12 inches and assuming say a fill of 6 inches, it would be permissible to consider a concentrated load as distributed across the span in accordance with the above formula and also to consider the load per foot of width as apphed along a length of at least 2 feet longitudinally with the span. Impact. An impact allowance of 25% has been made in the case of all live loads except the loo-lb. uniform load used on sidewalks for which no impact has been added. •See page 446. . _... . 696 A TREATISE ON CONCRETE Unit Stresses. The unit stresses used in designing have been taken as those recommended by the authors on page 573. DESIGN FOR A SLAB BRmGE.* Example i : Design a iiighway bridge of the simple slab type having a single span of 10 feet in the clear. Solution: The following assumptions and computations are required to produce the design shown in Fig. 217, page 696. Loads. Assume weight of road material 75 lb. per sq. ft. Assume weight of slab 125 lb. per sq. ft. Total dead load 200 lb. (jer sq. ft. Live load is auto truck, the heaviest wheel load being 14 000 lb. A single con- centrated load may be distributed over a width of slab e = (0.6 X 10) + 1.7 = 7.7 ft. Since, however, the two rear wheels of our auto truck are spaced only 6 feet apart the weight of one wheel can not be distributed over a width of more than 6 feet without overlapping the distribution from the other wheel. Hence live load per foot of width = 14 000 = 2 333 lb. -16 2H •{. lert.o Road ^Material 'W^f= ^ =^ I" Round Rods5i"C.C. . g F?ound Rods I2"C.C. Cross Section m miMMi^msiimmiM M m 'mt lOFt.O I: Tt I'Round Rod^ 8" C.C. i-" Round Rods 12" C.C. f Round RodsSi'C.C. Longitudinal Section Fig. 217. — Design for a Slab Bridge. {See p. 696). Bending Moment. Maximum live moment occurs with heaviest wheel at center of span. Take effective span as clear span plus 1 2 inches and concentrated load as distributed over a width of 6 feet and length of 2 feet. JW(Uve) =£130(gg_gj = 70 000 in. lb. Impact = 25% of 70 000 = 17 500 in. lb. ,. ,, ,, 200 X 11^ X 12 ^ . „ M (dead) = = 36 300 m. lb. Total M per ft. of width =123 800 in. lb. Shear. With load assumed as distributed over a width of 6 feet and length; pf 2 feet maximum shear occurs with heaviest wheel one foot inside support. Take effective span as clear span. - 1: M. v * The authors are indebted to Mr. Royall D. Bradbury for assistance in worlcing up the details of the following examples. . • BEAM BRIDGES 697 V Give) = 2 330 X — = 2 100 lb. 10 Impact = 25% of 2 j.oo = 525 lb. V (dead) = = i 000 lb. Total V per foot of width = 3 625 lb. _ Thickness of Slab. For fc = 650,/s = 16 000 and 42 = 15, the table on page 483, gives Ci = 0.028, p = 0. 0077 an dy = 0.874. Hence required depth to steel (fomxula (9) P; 48s) t-s oo-*, 0.874 X 3 X 2 X 1. 18 This is O. K. for bond. Hence use f -inch round bars 6 in. on centers. Facia Girders. Take span of girders as clear span plus about 16 inches or, say, effective span of 26.3 feet. Assume weight of railing = 350 lb. per lineal ft. Assume weight of girder = 450 lb. per lineal ft. Weight of slab = 63 X 2.5 = 158 lb. per lineal ft. Live load = 100X2.5 = 250 lb. per lineal ft. Load on girder = i 208 lb. per lineal ft. •»r HI ^ T^ir '^ 208 X 26. 3^ X 12 ... Max. Moment, Jh = = i 250 000 m. lb. o TVI CU T' 1208X25 ,, Max. Shear, V = =15 100 lb. 2 Selection of proper depth of a facia girder, which is usually panaled or otherwise embellished, is governed as a rule more by appearance than by requirements of actual strength. In order to give good proportions to the elevation of our bridge, we will make the facia girders 36 inches deep. BEAM BRIDGES 699 sjog punoy ^§1-9 700 A TREATISE ON CONCRETE In checking this depth for strength consider girder as a rectangular beam with its top at surface of sidewalk. Assuming a width of 12 inches we obtain, from Formula (3), page 482, i = 0.096 /i^5°°°°=3Hn. \ 12 By placing the steel 3 inches above bottom, the 36-inch beam will have a depth d = 3i inches, which is O. K. since only 3 1 inches depth is actually needed. Required area steel at center of span, from Formula (4a), p. 482, . I 250 000 As = ; = 2.71 sq. m. 0.874X33X16000 ' Use three ij inch round bars (As = 2.gS). Bending up one bar as shown in Fig. 218, page 699, we obtain from Formula (36), p. S34, for maximum unit bond stress on the two remaining if-inch round bars IS 100 ,, II = = 74 lb. per sq. in. 0.874X33X706 ''^ f '^ Therefore size of longitudinal bars is O. K. with one bent up as shown. Testing section of beam for shear we obtain, from Formula (32), page 517, IS 100 ,, ~ 44 lb. per sq. m. 0.874 X 33 X 12 While this exceeds the a Uowable unit of 40 lb. per sq. in. for diagonal tension this slight excess would be more than taken care of by the bent up bar without using any stirrups. However, as it is not considered the best practice to build a girder of these dimensions without some web reinforcement, stirrups are arbitrarily provided of size and spacing as suggested in sketch. Roadway Slab. With curb girders spaced 25 feet on centers use five intermediate roadway girders spaced 4 ft. 2 in. on centers. Assuming that these girders will be 12 in. wide, the roadway slab will have a clear span of 3 ft. 2 in. or 38 in. Take effective span of slab for moment as clear span plus 6 in. or 3 ft. 8 in. Assume weight of paving brick = 50 lb. per sq. ft. Assume weight of fill = 60 lb. per sq. ft. Assume weight of slab = 62 lb. per sq. ft. Total dead load =172 lb. per sq. ft. Take 14 000 lb. wheel load of auto truck carried by a slab width of e = (0.6X3.17) + i.7 = 3-6ft. Hence live load per ft. width = p — = 3 900 lb. Considering this load as distributed over a length of 2 ft. longitudinally with the span of slab and allowing for continuity by taking f of the moment for a simply sup- ported slab we have M (Uve) = l^S2^ X f = 23 400 in. lb. M (impact) = 25% of 23 400 = s 850 in. lb. ir fj j\ '72 X 3.67' X 12 . Jlf (dead) = — = 2 320 m. lb. Total JW = 31 570 in. lb. From Formula (11), page 485, d = 0.0281/31 570 = 4.92 inches. Making d = 5 in. and allowing i inch below steel, a total thickness of 6 in. is required. In considering shear, it will be permissible, in view of the very short span and the distributing action of fill and pavement, to take both live and dead loads as uniformly BEAM BRIDGES 701 distributed over fiill span. Live load of 3 900 lb. together with an allowance of 25% for impact would be equivalent to i 540 lb. per sq. ft. when distributed over a length of 3.17 ft. With a dead load of 172 lb. per sq. ft. the total load is i 712 lb. per sq. • • 1*712 "y^ "i TT ft., giving a maximum shear V ^ — ^— ' = 2 700 lb. per ft. width of slab. Testing our slab for shear we have, from Formula (32), page 517, 2 700 0.874 X S X 12 = 51.5 lb. per sq. in. While this exceeds the allowable unit of 40 lb. per sq. inch for diagonal tension, still, in view of the small loaded width assumed in our computations and tlie fact that the reinforcement wiU be bent diagonally through the slab near each end, we will permit this increasd value of diagonal tension and call the 6-inch slab O.K. Required area of steel per inch width of slab from Formula (13), page 483, As = 31 57° 12 X0.874X S X 16 000 = 0.037s sq. in. Thisis provided by J-in. round bars s inches on centers. Testing these bars for bond we find, from Formula (36), page 534, I 706 — — — — — = 164 lb. per sq. m. 0.874X5X2.4X1.57 Since this is so greatly in excess of the allowable of 80 lb. per sq. inch it becomes necessary either to increase thickness of the slab or use deformed bars with which an allowable bond of 1 20 lb. per sq. inch may be used. Keeping 6-inch slab and using deformed bars we obtain, for the total circumference of bars in one foot width, from Formula (36a), p. 534, So ■■ 2 700 0.874 X 5 X 120 = S-iSin. Using a f-inch round bar, the circumference of which is 1.96 in., there will be re- quired— ^-7 = 2.62 bars per foot of width or a spacing of — — = 4.6 in. 1.96 ° 2.62 Therefore use |-inch round deformed bars 4J inches on centers. Roadway Girders. The design of the girder is given below. Sending moment. From mechanics a system of concentrated loads produces abso- lute maximum bending moment when placed so that the center of the span is mid- way between the resultant of all the loads on the span and the nearest load, this moment occurring under the nearest load. Placing our auto truck in this position on a span of 26.3 feet, the loads will be located as shown in Fig. 219, since the resultant of the 6 000 lb. and 14 000 lb. loads spaced 12 feet apart is 3.6 feet from the 14 000 lb. load. R =20000 Pounds 6000 Pounds -lEft.O"- 13.15 ft. 14000 Pounds iaff.-'l.8Ft.- 26.3 ft. Fbai+ion of Load Maximum Bending Momen-f Fig. 219. — Position of Load for Maximum Bending Moment. (Seep. 701.) 702 A TREATISE ON CONCRETE The maximum moment occurs under the 14 000 lb. load and is equal to 20000(13.15 — 1.8)' . ,, ^^^^ '- X 12 = I 176 000 m. lb. 26.3 Distributing this over a width of 6 ft. we have the live bending moment per foot width of bridge as ^ = 196 000 in. lb. With the girders spaced 4 ft. 2 in. on centers each girder must therefore resist a moment, produced by live load, M = 196 000 X 4.17 = 818 000 in. lb. For dead loads we have no lb. fqr fill and paving, and 75 lb. for slab, giving 185 lb. per sq. ft., or 185 X 4.17 = 772 lb. per foot per girder. Assuming stem of girder to weigh 300 lb. per ft., we have a total dead load of i 072 lb. per ft. per girder. Therefore the total maximum bending moment per girder is M (live) = 818 000 in. lb. M (impact) = 25% 818 000 = 205 000 in. lb. ir /J J^ I 072 X 26.3 X 12 • lu M (dead) = '- — ^^-j — ^—^ — =1 115 000 m. lb. 8 Total M = -> 138 000 in. lb. Maximum Shears. Maximum live shear will occur with the 14 000 lb. wheel load just inside the support and with the 6 000 lb. wheel as shown in Fig. 220. Maximum shear due to these loads is equal to (14 000 X 25) + (6 000 X 13) ,, = 17 120 lb. Distributing this over a width of 6 feet, the live shear per foot width of bridge is 6000 14000 Pounds Pounds — ISn-.O" + IZft.O"- 25R.0" Posllion of Load Maximum Shear Fig. 220. — Position of Load for Maximum Shear at Support. {See p. 702.) 17 120 — T — = 2 853 lb. Therefore the maximum live shear per girder is F = 2 853 X 4.17 = II 900 lb. Hence the total maximum shear per girder is F(live) = II 900 lb. F (impact) = 25% of 11 900 = 3 000 lb. 7 (dead) = ' °'^^^ '^ = 13 400 lb. Total V = 28 300 lb. Dimensions of Girder. Tbe girder may be considered as a T-beam with a 6 in. fiange. The effective width of the flange, which ordinarily could be taken as twelve times the thickness of slab plus width of stem (see p. 488), in this case is limited by the spacing of girders, which is 50 inches. Selecting depth of girder equal iV of span and the depth below center of steel 4.5 inches, we have d = 25.5 in. and ^ = 30 in. The dimensions are evident from Fig. 218, p. 699. Area of Tension Steel. The area of steel may be found from Formula (4a), p. 482. 2 138 000 ^' = 0.88X25.5X16000 = 5.9.?sq.m. BEAM BRIDGES 703 Use six ij-inch round bars arranged in two layers of 3 bars each. Spacing the bars three diameters on centers and allowing a concrete covering of 2 in. on each side, the stem of the girder must be at least 12 in. wide. The compression stresses in the flange found by the use of Table 13, page 588, is 481 lbs. per sq. in. Checking the maximum stresses by the exact formulas (see p. 357) we find Sc = 483 and/j = IS S°o- Therefore section O. K. for bending moment. Bars at Support. Consistent with our consideration of the girder as a simply supported beam, no top steel is theoretically required. It is nevertheless advisable to bend up some of the bottom bars at each end of the span obtaining thereby a mate- rial strengthening of the stem against shear and the corresponding web stresses. Unit shearing stress as measure of diagonal tension. Using the maximum shear determined above the unit shearing stress in girder, from Formula (32), p. 517, is 28 300 ,, " = 0,88X25.5X12 = '°^ *^- P^' "^^ ™- Therefore stem O. K. for shear. Stirrups. Since the girder is subjected to moving load the variation of shear along the girder will be different than for uniformly distributed load (see p. 531). For determining stirrups, unit shearing stresses should be computed at the end of the beam and in the center of the span and a variation according to a straight line assumed. The maximum unit shearing stress at support, as determined above, is 105 lbs. per sq. in., or 105 X 12 = i 260 lbs. per width of beam. At the center of span the 6000 14000 Pounds Pounds 'Of- I2ft.0" \zn.B" E5fT-.0" Fig. 221. — Position of Load for Maximum Shear at Center of Span. (See p. 703.) shear due to dead load equals zero. Maximum live load shear at the center occurs when the load is in the position shown in Fig. 221 with the heavy load at the center of span. The shear then is equal to — — X 1 4 000 -\ — '— X 6 000 = 7 1 20 lbs. This can be . ^S . .25. distributed over 6 ft. and since the spacing of girders is 4 ft. 2 in. the proportion of shear carried by one girder is 7 120 X -7^ — = 4 95° lb. Allowing 25 per cent for impact the vertical shear at center of span is 4 950 X i . 25 = 6 200 lbs. and the shearing .„ , / N 6 200 ,. umt stress, Formula (32), page 517, v = — rj— — = 23 lbs. per sq. m. or 0.00 Ps 25.5 ^ r2 23 X 12 = 276 lbs. per the total width of stem. The spacing of stirrups shown in Fig. 218 was determined as explained on page 529. It was found that it is necessary to extend stirrups only 10 ft. from support at each end since in the remaining portion the unit shearing stress never exceeds 40 lb. per sq. in. However, it is advisable to continue stirrups through the entire length by using 29 stirrups per girder instead of 26 actually required. THROUGH GIRDER BRIDGES Very often it is not possible to construct girders of the required depth below the roadway of the bridge without interfering with the required waterway, or the neces- sary clearance in overhead crossings. In such cases the girders are placed above the roadway, thereby reducing materially the depth of the construction below the roadway. 704 A TREATISE ON CONCRETE Fig. 222, p. 704, illustrates a typical design by the authors for a bridge of 30 ft. clear span for a loading given on p. 695. The bridge consists of 6 ft. deep girders spanning from abutment to abutment. The roadway supported by a slab is carried by joists which in turn are supported by girders. The sidewalk slab is carried by cantilevers which are a continuation of the roadway joists. The method of design of through bridges, although essentially the same as of the girder bridges, is somewhat complicated by the fact that the loads are not carried directly by girders but are transferred to them by joists in panel points. Ordinarily, however, it is accurate enough to consider the loads as carried directly by the girders, in which case the determination of the bending moments and shears is the same as in previous examples. The joists are suspended from the girders and as no reUance can be placed on the resistance of concrete in tension, enough steel must be used in the hangers to trans- fer the maximum joist reaction to the girders. -6Ft3 ISFf.O" \6rtZ" 5 "Round Stirrups l"Round Bara / JJe Round Bars / J- ^ Round Bars 6' Round Bars / '4-1 1 Round Bors / 5- li" Round Bars Cross Section 1 iSV/a-i Round Bars i'Round Stirrups Round Stirrups , - , 14 .14 i^: fSl^lTljrfoyJiiWeleklGlGy -4— AFf_B - 3ft.9- :24 E-levation Section Fig. 222. — Design for a Girder Bridge {See p. 704.) CONTINUOUS GIRDER BRIDGES In crossings consisting of several spans, the girders may be designed and built as continuous. Fig. 223 illustrates a continuous girder bridge of three spans, designed by the authors to carry two tracks of electric railroad over a street. The exterior spans were made smaller than the interior so as to make the maximum bending moments in the end panels about equal to those in the interior panels. The principle of design is similar to that explained in connection with the design of a simple girder bridge, the main difference being in the method of determining the bending moment. In important bridges where it is warranted by the size of the job, it may be advisable to make a thorough study of the bending moments by the theorem of three moments. In smaller jobs the bending moments for the dead load should be taken as recommended on page 510. The bending moments for the live load must be determined by taking f of the bending moment computed for a simply supported girder. This bending moment then may be considered as acting in the center of the span as positive bending moment, and at the support as negative bending moment. Details of design are clearly shown in Fig. 223. BEAM BRIDGES ARCHES 707 CHAPTER XXVI ARCHES* BY FRANK P. MoKIBBEN The treatment of arch design by what is termed the elastic theory, although generally considered a complicated problem, as a matter of fact is easily handled by one who is familiar with elementary mechanics and with the priilciples of reinforced concrete beam design. The process is necessarily somewhat lengthy, involving extended operations in simple arithmetic, but by following the analysis presented in the following pages it can be readily understood. It is doubtful whether in the whole category of the design of structures there is a prettier application of mechanics and mathematics than the design of a reinforced concrete arch bridge. While in a volume of this size it is impossible to present all phases of the subject, the underlying principles are treated in sufficient detail and with a discussion thorough enough to permit an engineer to safely design an arch. Following a brief historical introduction discussing the use of concrete versus steel construction, the different forms of arches are reviewed with suggestions for design; the loading for different conditions is scheduled (p. 715) ; the outer forces are analyzed, including the effect of tempera- ture (p. 723); the method of procedure to be followed in arch design is taken up in a practical example item by item (p. 733); allowable unit stresses are suggested (p. 741) ; the design of abutments is outlined (p. 741); and a few illustrations of existing bridges are presented. Beam bridges are treated briefly in Chapter XXV. The design of such bridges follows closely the principles of reinforced concrete beam and slab construction as treated in Chapter XXII on Reinforced Con- crete Design. The treatment of conduit or sewer arches which are so deeply imbedded as to require computations for earth pressure is referred to on page 777. Perhaps the most interesting feature of the present chapter is the com- plete analysis of a typical arch which is presented on page 733. The steps to be followed are outlined consecutively and the mathepiatical processes indicated in full. The formulas for distribution of stress given on page 377 apply not only to column and beam design where there is eccentric loading or • The authors are indebted to Prof. McKibben for this chapter, which has been especially prepared by him for this treatise. 7o« A TREATISE ON CONCRETE thrust in place of or in addition to the ordinary loads but also to arch design. To facilitate the understanding of the formulas, a departure is made from the usual notation schedule, which must necessarily be several pages away from the work, by placing in addition, at the bottom of each page, a brief definition of all the symbols used on that page. CONCRETE VERSUS STEEL BRIDGES Reinforced concrete, either as arch or girder spans, is being used not only in preference to steel trusses or steel girders, where the stone arch is too expensive to be considered, but the concrete bridge is frequently replacing the old steel structure. The reasons generally conceded for this wide- spread growth may be briefly stated as: (i) greater durability; (2) less cost of maintenance; (3) less vibration and less noise; (4) more assthetic effects. The relative first cost for concrete and steel depends upon the local con- ditions. In many places a concrete bridge can be built for less than a first- class steel span, although it cannot so readily compete with the flimsy trussed spans frequently seen. The concrete may be laid with less skilled labor than the steel bridge, but since the concrete structure is built on the spot, while the steel is prepared in an established shop, even more careful super- vision and inspection are necessary with the concrete. The foundations for a concrete arch are frequently more expensive than concrete abutments for a steel truss because of the greater area required to take the thrust, while on the other hand, in rock or other hard material, a less quantity of concrete may be required for the arch abutments. This part of the design may often be the determining feature from the economical standpoint. The most serious objection to steel, especially for highway bridges, lies in the fact that unprotected it cannot resist for a great length of time the oxidation due to air, water and locomotive gases, and unless properly cared for and frequently painted, it rusts badly. The examination by the author of this chapter of approximately 600 highway bridges carrying electric railways proves that frequently these bridges are not properly maintained, many of them receiving little or no attention for years at a time, so that the structures are often badly corroded, and in fact, cases are on record where subordinate members of steel bridges have rusted away completely in less than fifteen years. In a concrete bridge the steel is effectively prevented from rusting by the concrete in which it is imbedded (see p. 292), so that, when properly designed and built, no repairs whatever should be required, and no limit can be placed upon the life of the bridge. ARCHES -jog Concrete is strongest in compression, and is therefore eminently suit- able for use in arch spans where the stresses are largely compressive. The mass of the concrete and the quantity of earth filling or ballast over the arch so deaden the impact due to traffic that in many cases no impact allowance need be made, while at the same time the noise and vibration which occur in steel spans are avoided. USE OF STEEL REINFORCEMENT The use of steel reinforcement in a concrete arch is desirable but not absolutely necessary, as it is possible to construct a concrete arch like the Walnut Lane Bridge in Philadelphia (see pp. 706 and 750) with the concrete laid in blocks, each block forming a voussoir like the stones in a masonry arch. At the same time under ordinary conditions, while the intro- duction of steel does not, with the present knowledge of concrete arch design, permit great diminution in section, it does give considerable added strength at comparatively low cost and may prevent the formation of cracks in the concrete and take tension caused by any unforeseen action of the arch, such as settlement of foundations, improper allowalice for temperature or shrinkage of the concrete while hardening. The area of the cross section of the longitudinal steel bars in solid arch rings is to a certain extent arbitrary. Good practice sanctions J% to i J % of the ring at the. crown and the exact quantity to use must first be selected by judgment, and then tested by the computation and revised if necessary. As in column design (see p. 375), it is impossible to stress the steel in ' compression to an amount ordinarily proper in structural steel work, because in so doing the deformation would be so great as to overstress the concrete. The actual compressive stress in the steel, therefore, can never be greater than the working stress in the concrete multiplied by the ratio of the modulus of elasticity of steel to that of concrete. Under ordi- nary conditions this limit on the steel may be taken as 7500 pounds per square inch. Since the beginning of this century there has been a remarkable development in methods of construction and in our knowledge of the principles of rein- forced concrete arch bridges, but even yet engineers incline to employ a somewhat excessive quantity of concrete in the solid rings of ordinary high- way concrete arches. This is frequently out of proportion to the quantity of material used in a reinforced concrete ribbed arch or a steel arch. Improve- ments in arch design evidently lie, as is indicated in subsequent, pages, in the substitution of comparatively narrow ribs for solid arches and in the 7IO A TREATISE ON CONCRETE use of hollow abutments with earth filling in place of solid concrete abut- ments. This will considerably reduce the cost of reinforced concrete arches. HISTORY OF CONCRETE ARCH BRIDGES In the development of concrete bridges it is natural that the arch rather than the beam should have been the first type of bridge to be constructed. It was a comparatively short step from the stone voussoir arch to the con- crete voussoir or to the monolithic arch. One finds therefore many concrete arch bridges, and, until recently, few beam bridges, although for short spans beam bridges are now being constructed in considerable numbers, both in this country and abroad. The first plain concrete arch of any importance was built in Europe in 1869 and is known as the Grand Maitre bridge at Fontainebleu Forest. It has a maximum span of 115.8 feet and carries the aqueduct of the Paris waterworks from Vanne. The first plain concrete arch in the United States was constructed in 1871 by John C. Goodridge in Prospect Park, Brook- lyn, and has a span of 31 feet. The earliest reinforced concrete arch in Europe of which there .is a well defined record was built in Copenhagen, Denmark, in 1879, with a span of 71.7 feet. It is probable, however, that Jean Monier of Paris was the inventor of the reinforced concrete arch and that he built some bridges before the dates mentioned. In the United States the first reinforced concrete arch on record was erected in 1889, with a span of 35 feet, byErnestL.Ransome at Golden Gate Park in San Francisco. When these structures are compared with the 233 feet span of the Walnut Lane Bridge in Philadelphia, which in 1908 was, with perhaps one excep- tion, the longest plain concrete arch in existence, with the 230 feet, 3-hinge Griinwald Arch at Munich, Bavaria, or still more sharply with the Hudson Memorial design for an arch across the Spuyten Duyvil Creek with a span of 703 feet, a wonderful development is observed. Although in a very few cases concrete bridges built during this develop- ment have failed, every such failure can be traced to a direct disregard of well known principles of design or construction. Moreover, as a matter of fact, accidents to concrete arches have been much fewer than the failures of wrought iron or steel bridges during tM corresponding period of metal bridge development. CLASSIFICATION OF ARCHES Arches in general may be classified with reference to the material of which they are made, the arrangement of the spandrels and arch rings, r.r the ARCHES 711 number of hinges. Reinforced concrete arches may be divided as to the arrangement of the reinforcement into three groups: the Monier, Melan and Wiinsch types. The Monier arch in its developed form is the type most commonly used in the United States. This system of reinforcement was invented by Jean Monier about theyear 1876. As first devised, a wire net- ting was imbedded in the concrete near the soffit, but later two nettings were used, one near the soffit, and the other imbedded in the concrete near the extradosal surface. Wire netting of small mesh witli wires of equal size in both directions obviously is not well suited for use in an arch and considerable improvement was soon effected in this type by making the longitudinal bars of the reinforcement heavier than the transverse. In the usual design a layer of longitudinal bars is imbedded near the intrados and an equal number near the extrados, the bars of the two layers being connected with small bars or stirrups. Transverse bars, at right angles to the longitudinal, form with them a netting both in the top and bottom of the arch. They serve to prevent cracks in the concrete and dis- tribute the loads laterally. These cross bars also act with the stirrups in holding the longitudinal bars in place during construction. The principal longitudinal bars are designed to carry tension due to the bending moment and to assist the concrete in compression caused by the thrust and the bending moment. Melan Type. This system was invented by Joseph Melan of Briinn, Austria, in 1892. The reinforcement consists of curved steel ribs imbedded in the concrete and extending from abutment to abutment. For short spans the ribs are simply curved I-beams and for long spans each rib is made of two angles near the extrados latticed to two angles near the intrados. The built-up ribs thus formed are usually deeper at the springings than at the crown of the arch. The principal function of the lattice bars is to hold the angles in position when the latter are stressed, and to make a unit which is easy to handle during erection. By far the most important function of steel reinforcement is to carry bending moment, and the steel in the Melan type can be easily placed and kept in position during erection so as to fix positively its location in the finished structure. The material in the lattice bars of the ribs or in the webs of the I-beams is not economically placed. The first Melan arch in the United States, of 30 feet span, was erected at Rock Rapids, Iowa, in 1894, and many other bridges have since been built of this system. W'unsch Type. Comparatively few bridges have been constructed on this system. The arch, which was invented by Robert Wiinsch of Budapest, Hungary, in 1884, has a horizontal extrados and a curved intrados and the 712 A TREATISE ON CONCRETE reinforcement of the arch ring consists of steel ribs spaced from ij to 2 feet apart, with a horizontal upper member placed near the extrados and a curved lower member near the intrados. The two members are con- nected at each abutment to a vertical member imbedded in the concrete. The bridge at Sarajevo in Bosnia, of 83 feet span, is one of the largest built of the Wiinsch system. ARRANGEMENT OF SPANDRELS AND RINGS The spandrel, which is the space between the roadway surface and the top or extrados of the arch ring, may be treated in one of two ways. Pirst, it may be entirely filled with earth or with concrete which carries the road- way; or, second, it may be left more or less open, and the roadway sup- ported upon a deck carried on a series of transverse walls, longitudinal walls, or columns resting upon the arch ring. Filled Spandrels- In this form of construction the earth or concrete filling rests directly upon the arch ring, and is held in place laterally by retaining walls which also rest upon the arch ring. As the depth of these walls, unless they are of reinforced design, increases from the crown to the springing, their thickness, designed to resist the earth pressure, also increases until at the abutments the spandrels may be largely filled with the concrete composing the side walls. If the side walls simply rest upon the arch ring, a crack is liable to form at the junction of ring and wall due to the deflection of the arch ring from the weight of the earth upon it. On the other hand, if the ring and wall are connected by sufficient steel to prevent the formation of this crack, indeterminate stresses are set up which are undesirable and which may result in transferring the crack to another place. This danger may be obviated by building the spandrel walls as gravity walls, leaving a vertical expansion joint at each junction of spandrel and wing walls and at some intermediate point between this joint and the crown. Another plan is to build thinner reinforced side walls as vertical slabs tied together, with the lateral pressure resisted by reinforced cross walls. The principal objections to the use of solid fillings are as follows: (1) They increase the weight of the superstructure, and consequently thicker arch rings and larger foundations are required. (2) Unless the earth filling is carefully compacted by rolling, tamping or wetting, it will sink and allow the roadway to settle with it. (3) It is difficult to make theside walls and the arch ring act in unison, and unsightly cracks may be formed. Filled spandrels may be therefore limited properly to bridges with solid arch ARCHES 713 rings of short span, say not over 80 feet, or to those having a rise of less than Y*ij- the span, where the cost of form construction prohibits an open design. Open Spandrels. The objections just mentioned to the use of filled spandrels are of such importance that during the last few years the use of open spandrels in the larger structures has made rapid progress. In addi- tion to being lighter, the open spandrel construction facilitates inspection and lends itself to more pleasing architectural treatment. It permits indeed a treatment peculiar to concrete, which does not follow the type of design used for so many centuries in stone arch bridges. With open spandrels the roadway may be laid upon small arches or upon I-beams carried by trans- verse or longitudinal walls which in turn rest upon the arch ring; or it may be laid with reinforced concrete beam and slab construction, making a floor similar to those used in reinforced concrete buildings. The beams in this case are placed longitudinally with the roadway, and rest upon transverse walls. Upon the adoption of the open spandrel it was soon seen that considerable material was wasted in the transverse walls and in the solid arch rings. The next step, therefore, was to reduce the walls to columns and the ring to a series of longitudinal ribs spaced similarly to the ribs of a steel arch. In some cases these ribs are very wide, in fact, are really two independent arch rings as in the Walnut Lane bridge, Philadelphia,* and in other cases the ribs are narrow as in the Rock Creek bridge on Ross Drive in the District of Columbia.f HINGES The use of hinges in concrete arches is by no means of recent origin. As early as 1873, an arch was constructed near Erlach, Germany, with three asphalt "joints" and many others with hinges have been built since then. The chief object of the hinge in the arch rings or ribs is to render the structure more nearly determinate. Although two or even one hinge can be used, three hinges offer the advan- tage of definitely fixing the pressure line throughout the ring so that it can be easily and accurately located. Except for the friction of the hinges, the stresses are practically independent of changes of temperature or of any reasonable settlement of the foundations. On the other hand, the hinges are often an expensive detail. It is sometimes claimed also that three- hinged arches are not so rigid as fixed arches, but because of their great weight this criticism does not appear to be well founded. • See p. 750, t See p. 748. 714 A TREATISE ON CONCRETE In the design of a hinged structure the moment is usually assumed to be zero at the hinge. This assumption is not strictly correct because as the structure deforms under its load it tends to rotate about its hinges and this produces friction at the hinge due to the thrust acting thereon. The design of the hinge is a most important feature. One of the most instructive failures in arch construction was that of the Maximilian Bridge at Munich, a three-hinged voussoir masonry arch of two spans, each 144.3 feet, when during construction, both spans of the bridge slipped [off the hinges at the springings and dropped about 12 inches. This failure was due to an error in the design of the hinges. The bearing surfaces of the hinges were not given sufficient curvature, and the friction which was relied upon to prevent slipping of the two parts composing each hinge was reduced to a minimum by the use of a lubricant, which gave a low coefficient of friction. Three-hinged construction is best suited to arches of small rise where the center line of the rib can be made to fit closely the line of pressure resulting in small bending moments. Arches with one or two hinges are more indeterminate than three-hinged arches and have practically all of the disadvantages of both the fixed and the three-hinged types. SHAPE OF THE ARCH RING For hingeless arches the intrados should be either three-centered, five- centered or elliptical, while, if desired, theextrados may be the arc of a circle so placed as to give greater depth to the arch ring at the springings than at the crown. A segmental arch, that is an arch formed by the segment of a single circle cannot often be used to advantage, for it seldom can be made to fit the line of pressure. While many arches are elliptical in form, the three-centered intrados is perhaps the most common and it is pleasing to the eye, easily constructed and gives an economical design. Ribs with three hinges should be deepest at sections nearly midway between the crown and spring hinges, decreasing in depth toward the hinges, since sections near the hinges take only thrust and shear with practically no moment, while the intermediate sections resist a moment in addition to the thrust and shear. THICKNESS OF RING AT CROWN The next step in the design of an arch after deciding on the shape of the intrados is to choose a trial thickness of the ring at the crown and at the springing. The choice may be made by judgment based on experience or ARCHES 71S with the aid of one of the various empirical formulas in use. Since the crown thickness depends not only on the amount of thrust but also upon the bending moment, which varies greatly in a given arch due to the varying positions of the live load, it is diflScult and in fact impossible to devise a rational formula for its determination. The thickness of the arch ring should vary with the shape of the arch, with the span, rise, amount of filling over the ring, the amount of live load and the material of which the arch is made, and while there is no formula that will apply even approximately in all cases, the formula by Mr. F. F. Weld* gives fairly correct results in ordinary cases. It is as follows: Let /f= crown thickness in inches. L = clear span in feet. w = live load in pounds per square foot, uniformly distributed. w'= weight of fill at crown in pounds per square foot. Then , /— L w w' h^- Vl+~ + + (1) 10 200 400 Obviously the thickness for a hingeless arch should increase from the crown to the springing. The radial thickness of the ring at any section is frequently niade equal to the thickness at the crown multiplied by the secant of the angle which the radial section makes with the vertical. For a 3- centered intrados and an extrados formed by the arc of a circle, these trial curves may be at the quarter points a distance apart of i| to i^ times the crown thickness and at the springings 2 to 3 times the crown thickness. These empirical rules should be used only in preliminary study and never for the final design. The true shape of the ring and the thickness at different sections must be fixed by computation based on the Une of pres- sure as described in the pages which follow. LIVE LOADS FOR HIGHWAY BRIDGES For highway bridges the kind and magnitude of the live load depend upon the location of the structure. Each location should be studied and the live load chosen to fit the requirements. The following classification is sufficient for stone or concrete arches or for beam bridges.f • Engineering Record, Nov. 4, 190s, p. 529. t Loads for beam bridges are discussed on page 695. 7i6 A TREATISE ON CONCRETE City Bridges. For floors of city or other bridges carrying heavy traffic, three types of loads are recommended as follows: 1. A uniform live load of loo pounds per square foot on sidewalks and roadways. 2. On each street railway track, one 8-wheel electric car having a wheel spacing of 5, 15, 5 feet between centers of wheels along one rail; each wheel carrying 12,500 pounds. The car is assumed to cover an area 9 feet wide by 40 feet long. 3. One wagon weighing 20,000 pounds on each of two axles 1 2 feet apart. In applying these loads to find the maximum stress in the floor, either of the loads mentioned, or that combination of any of the above loads which produces the maximum stress, should be used. If the uniform load is used simultaneously with either of the concentrated loads, the former should cover only that part of the roadway not covered by the latter. For arch rings or ribs having a span of 100 feet or less, a uniform load of 1800 pounds per linear foot of each railway track together with a uniform load of 100 pounds per square foot of remaining area of roadway and side- walks. For spans of 200 feet or more, a uniform load of 1200 pounds per linear foot of each railway track together with a uniform load of 80 pounds per square foot of remaining area of roadway and sidewalks. The load on each track should be assumed to cover a width of 9 feet, thus giving 200 pounds per square foot under the track for spans of 100 feet or less and 133 pounds per square foot for spans over 200 feet in length. For spans between 100 and 200 feet, the loads are to be taken proportion- ally. Suburban, Town or Heavy Country Bridges. For floors of suburban, town, or heavy country bridges, the same uniform load and electric car load as for floors of city bridges but with wagon weighing 10,000 pounds on each of two axles 10 feet apart. For arch rings or ribs having a span of 100 feet or less, a uniform load of 1800 pounds per linear foot of each track, together vrith a uniform load of 80 pounds per square foot of remaining area of roadway and sidewalks. For spans of 200 feet or more the values corresponding to the above are 1200 pounds per linear foot of each track and 60 pounds per square foot of remaining area. The load on each track should be assumed to cover a width of 9 feet. For spans between 100 and 200 feet, the loads are to be taken propor- tionally between the limits stated. Light Country Bridges. For floors of light country bridges, sub- ARCHES 717 jected to light highway or electric railway traffic, on each track one 8-wheel electric car carrying 9000 pounds on each wheel, or one wagon weighing 6000 pounds on each of two axles 10 feel apart. These two loads should be assumed to act together where necessary to produce the maximum stress in the floor. For arch rings or ribs having a span of 100 feet or less, a uniform load of 1200 pounds per linear foot of each track, together with a uniform load of 80 pounds per square foot of remaining area of roadway. For spans of 200 feet or more, the values corresponding are 1000 pounds per linear foot of each track, and 50 pounds per square foot of remaining area. For spans between 100 and 200 feet the loads are proportional between the limits stated. It is customary to see that the design is sufficient to carry a steam road roller. The heaviest roller usually specified weighs 30,000 pounds, 12,000 pounds on the front roller, which has a width of 4 feet, and 9000 pounds on each of the two rear rollers, each of the latter having a width of 20 inches. The axles are taken as 1 1 feet apart and the two rear wheels as 5 feet center to center. LIVE LOADS FOR RAILROAD BRIDGES For railroad bridges the loading depends upon the location of the line, and hence the future traffic which may be expected. Two consolidated locomotives, with 25 000 pounds on each driving wheel, followed by 5000 pounds per foot of each track, is a common loading. An alternate plan quite generally followed for the rings of stone or concrete arches where the filling is of sufficient thickness to distribute the concentrated loads over a considerable area of arch ring is to use 5000 pounds per foot of track with no concentrated load. This load of 5000 pounds per foot of track is equivalent to about 625 pounds per square foot of horizontal area. These values are satisfactory for spans, say, over 80 feet in length. , Generally speaking, the shorter the span the greater should be the assumed uniform load, and hence for spans of, say, 80 feet or less, a uniform load of 1000 pounds per square foot is frequently adopted, this being approximately equivalent to the heaviest locomotive loadings. A concentrated load on top of a fill is generally assumed to be distrib- uted downward at angles of 45°. The top of the distributing slope may be taken from the ends of the ties. Wheel loads may be taken as dis- tributed over 3 feet of length of surface of fiU and at 45° angles through the filling. 7i8 A TREATISE ON CONCRETE DEAD LOADS AND EARTH PRESSURE With open spandrels having columns or transverse walls, the dead loads act vertically upon the arch ring and can be more accurately found than with filled spandrels. With spandrels filled with earth the dead load carried by the arch ring is that due to the weigh, of the roadway, of the filling, and of the arch ring itself. The earth filUng is usually assumed to act vertically, in which case the forces acting on the arch are easily computed. For arches in which the ratio of rise to span is small, such an assumption is sufficiently correct. A common assumption for weight of earth fall where the actual value is unknown is loo pounds per cubic foot. Since the pressure produced by the earth filling against the extradosal surface of the ring is really inclined, being nearly vertical near the crown and considerably inclined near the springings, it is sometimes advisable in an arch of large rise to take account of the horizontal component of the pressure near the springings. The earth pressure acting against an inclined plane may be found either algebraically or graphically. The algebraic solution is given under the subject of retaining walls, page 759, and in the example of arch design the inclined pressure is taken into account for illustration, although it is really unnecessary in the case selected. (See p. 734.) OUTLINE OF DISCUSSION ON ARCH DESIGN The method of designing an arch by the elastic theory is illustrated by the example on pages 733 to 740. The steps to be taken are there stated in full. In the following pages the reactions at the supports, which in an arch are not simple vertical forces, and the relations'between the outer loads and the internal stresses, are first treated briefly so as to understand the theory in a general way. Next (p. 727), the working formulas are given for find- ing the thrust, shear and bending moment at the crown, and at intermediate points in the arch ring. From these, the force polygon and the line of pressure, which is an equilibrium polygon drawn for a pole distance equal to the horizontal thrust, may be drawn (p. 729). The method of determin- ing the stresses due to temperature and rib shortening is given (p. 730). Since the lines of pressure do not ordinarily pass through the center line of the arch ring, the pressures on the various sections are eccentric. The distribution of stress in an arch under eccentric loading is the same as in any other member, such as a column. The analysis is discussed at length on pages 377 to 389, Chapter XX. Diagrams are presented ARCHES 719 to aid in the determinations. Following the example, the design of arch abutments is given (p. 741), and beyond this are general directions w-ith reference to construction details. Several typical arches are illustrated (P- 747)- RELATION BETWEEN OUTER LOADS AND REACTIONS AT SUPPORTS An arch differs from a beam in that under vertical loads the reactions at the supports of the arch are inclined, while for a beam the reactions are vertical. The loads acting on the arch, together vsdth the reactions caused by the loads, constitute the entire system of forces acting, and for a com- plete analysis of the arch the relation between these forces should be deter- mined. This relation is more simply deduced if for each reaction there are substituted its horizontal and vertical components. For arches symmetrical about the center line of span the following analy- sis is applicable. For unsymmctrical arches, methods similar to those pre- sented in the following pages are to be employed although the necessary formulas are too long to be given here. NOTATION Hi and F,= horizontal and verticaj components of the left reaction. H^ and Fj = horizontal and vertical components of the right reaction. M, and Af 2 = moments at left and right supports respectively. M = moment at any point on arch axis having coordinates x and y. M„ H^, F„ = moment, thrust and shear at the crown. Mj^ = moment at any point on left half of arch axis of all loads between the point and the crown. M^ = moment at any point on right half of arch axis of all outer loads between the point and crown. m = number of divisions into which the half length of arch axis is divided. 5 = short length of arch axis. 7 = moment of inertia of cross section about the gravity axis. L = horizontal span of arch axis. r = rise of arch. E^ -= modulus of elasticity of concrete. n = ratio of moduli of elasticity of steel to concrete. - R = resultant force acting on any section of the arch ring. N = thrust =normal component of resultant R. V = shear = radial component of resultant R. 720 A TREATISE ON CONCRETE H = horizontal Gomponent of resultant R. P = any concentrated load. J^ = change in span length due to any cause, + for an increase, — for a decrease. t = rise or fall in temperature of the arch ring from the mean in degrees Fahrenheit, c = coefficient of linear expansion or contraction. / = average unit compression in concrete of arch ring due to thrust. (f> = central angle subtended by the a.xis of the arch. x,y = coordinates of any point on the axis of the arch ring. Three-Hinged Arch. The use of the three-hinged arch is discussed on page 713. Since its analysis is simplest and at the same time illustrates important principles of arch design, it is considered first. Referring to Fig. 225, it is seen that there are two unknown components ^^ P \ ^^ ^:::^^^^ ' \ \ y^^ a. 1 \ A, \ JlrC/^ s\ m n K ■ Fig. 225. — ^Arch with Three Hinges. {Seep. 720). of each reaction, making four unknown quantities, H„ F„ H^, Fj, which require four equations to solve them. From statics we have the three equations of equilibrium: Algebraic sum of vertical components = zero. Algebraic sum of horizontal components = zero. Algebraic sum of moments of all forces about any point = zero. We have here an additional equation from the fact that the bending moment at the crown hinge = o. Therefore the four components of the reactions can easily be found. Suppose there is only one load, P, on the span. Then V,= Pz (2) and Fj = P {L-z) (3) Since, for equilibrium, the moment at the crown hinge must be o, the resultant reaction on the left must pass through the left hinge, or "4.7 /// = o. Hence H^ (4) ■= rise. components of left reaction. V^j H^ = components of right reaction, Z, = Bp;in, ARCHES 721 When all loads are vertical, or in any case when the loads are symmetrical about the center, H^ = ilj- When the loads are not symmetrical and also not vertical, H^ can be easily found, after H, has been determined as above, from the relation that the algebraic sum of all the outer horizontal forces =0. In a three-hinged arch, then, the reactions having been found by means of simple statics as above described, the thrust, shear and bending moment on any section of the arch can be computed and sections designed.* Two-Hinged Arch. Under the action of the loads on this arch there are produced two components of the reaction at each support, making in all four unknowns, ff,, F,, H2, V^. From statics we have the three funda- mental equations of equilibrium, as given above. We must find an addi- tional equation from the theory of elasticity. This additional equation is obtained from the fact that the span does not change its length under the Fig. 226. — Two-Hinged Arch. (See'p. 721). action of the loads. From mechanicsf we know that if the arch were fixed at B and free at A, the horizontal motion of A (the origin of coordi- s nates) is given by ^ My ynr, where i* denotes the summation of the products of My —for each section of the arch. Now, since the arch is really pre- EI vented by the support from moving horizontally at point A, the above deformation can be placed equal to o, and we have then the fourth equation s I My — -= o, which, in addition to the three from statics, enables us to EI find the reactions iT„ V„ H„ Y^. As soon as the reactions are known, the thrust, shear and bending moment at any section of the arch can be found- *Three Hinged Masonry Arches; Long Spans Especially Considered, by David A. Molitor, Transactions American Society of Civil Engineers, Vol. XL, p. 31. ■[■"Mechanics of Engineering," by Irving P. Church, 1908, p. 449. 722 A TREATISE ON CONCRETE In a similar manner the conditions of equilibrium can be obtained for an arch with only one hinge (at the crown). "Fixed" or "Continuous" Arches. A method frequently followed with the hingeless arch is to consider the reactions at the ends in the same way as in hinged arches, but the simpler method is to take the forces at a section through the crown. However, in order to better understand the theory and the relation of the external to the internal forces, the arch reac- tions at the supports will be discussed first and afterward the analysis will consider the forces at the crown. Let Fig. 227 represent a hingeless arch. The loads having been deter- mined, there are at each support three unknown quantities, namely, the vertical and the horizontal components and the point of application of the reaction. Or, instead of saying that the point of application of the reaction Fig. 227. — Continuous Arch, (Seep. 722). is unknown, we can say that there is a bending moment at each support, and that this moment, together with the horizontal and vertical components of the reaction, makes three unknown quantities at each support to be found. There are then six unknown quantities to be determined, namely, H^, Fi, M„ H„ V,, lU. Statics provides the three fundamental equations of equilibrium (see page 720), hence three additional equations must be determined from the theory of elasticity. These three additional equations are given from the three following conditions; The change in span of the arch = Ax = O The vertical deflection at A (the origin of coordinates) ^ Ay = O The change in direction of the tangent at the arch axis zX K -= Aj> = These three conditions must be true since the arch is fixed at A and at B. the abutments being assumed immovable ARCHES 73,3 From mechanics,* Ax =^2\My~=Q (5) Ay^llMx^j=0 (6) i^ = i'>^=0 (7) These three equations are general formulas. They are not used directly in arch computations but are necessary in the theoretical derivation of the working formulas given in paragraphs which follow. These three equations express the conditions that the horizontal, vertical and rotary movements of the left end of the arch ring each equal zero, so far as these motions are caused by the bending moments only, acting on the different sections from B to A. The movements due to the thrust and shear within the ring are not here considered. By means of equations (5), (6), (7) and the three from statics (see p. 720) we can solve for the six unknown quantities at the supports, namely, the horizontal and vertical components of each reaction and the moment at each support, and having thus found the reactions, the stresses within the ring can be computed. RELATION BETWEEN OUTER FORCES AND THE THRUST, SHEAR AND BENDING MOMENT FOR THE FIXED ARCHf In Fig. 228 let the arch A B be fixed at the two supports. If the loads are 4ni-wn, the horizontal and vertical components of the reactions and also the noment at each support of the arch may be found, as has been shown above. Having these three quantities for each support, the faint of appli- cation of each reaction may then be determined. Thus in Fig. 228 the point of application at the left support is at a, dis- ^1 . . M^ , tant yi vertically from A, where y, = — . Similarly at B , yj = ~ . Having computed y^ and y,, thus locating the points of application of the reactions, the force polygon and its equilibrium polygon, abed, can be drawn, as described more fully on page 735, and the latter will be the true line of pres- sure for the loading shown. The stresses on any section such as D may M = moment, s = short length of arch axis. E = modulus of elasticity. / = moment .nertia. Jx = change of span length, xy = coordinates of a point. *See "Mechanics of Engineering,"by Irving P. Church, 1908, p. 449, or any general treatise on mechanics. t This method of analysis corresponds to that adopted by Messrs. Turneaure and Maurer in their boolc on *'Principles of Reinforced Concrete Construction." 724 A TREATISE ON CONCRETE be then studied. The resultant of all outer forces on the left of D is a force actin<; along the line a 6 of the equilibrium polygon and having a magnitude eauai to the force 0„ of the force polygon. This resultant outer force O^ Fig. 228. — Line of Pressure in an Arch. (See p. 723). Pig. 229. — Forces Acting upon an Arch Section. (See p. 724.) acting along ab is resisted by inner forces, i, e., stresses, on the section D which is redrawn in Fig. 229. Thj force R is the force opposing the resultant Oo- This force is equiva- ARCHES 725 lent to a force R acting at the arch axis and a bending moment = Ru' = Hu, where H is the horizontal component of R and u is the vertical distance from point D on the arch axis to the equilibrium polygon; u' is the perpen- dicular distance from point D to the force R = Oo- For vertical loads // is constant throughout the length of the arch ring. The resultant force R acting at D can be resolved into two components one of which, N, is tangential to the axis at D and therefore normal to the section of the arch ring; the other component, V ,[s perpendicular to the axis and parallel to the section. -/Vis the thrust, that is, the tangential component of the resultant force on the section. V is the shear, that is, the radial component of the resultant force on the section. Hu or Ru' is the bending moment about the gravity axis of the section. Evidently there are sections of the arch where the equilibrium polygon intersects the arch axis. At these sections the bending moment is zero. Furthermore, if the equilibrium polygon is normal to any section there will be no shear on that section. It is possible then to find sections where there is no moment, or no shear, or possibly where there is neither moment nor shear. There is always a thntst on every section. THRUST, SHEAR AND MOMENT AT THE CROWN Instead of actually finding the components of the reactions and the moments at the supports by the plan indicated on page 723, it is simpler to find the thrust, shear and moment at the crown. Having these, the equilib- rium polygon may be drawn and the tiirust, shear and moment at any point may be found. The thrust, shear and moment at the crown can be found by use of equations (5), (6), (7), page 723, in which M is the moment of any point D of Fig. 228, page 724, expressed in terms of the values at the crown. Instead, however, of determining these quantities by means of these equations, shorter expressions for the thrust, shear and moment at the crown may be obtained by taking the origin of coordinates at the crown and studying the motion at that point. In Fig. 230, CD represents the vertical section at crown, upon which acts the resultant pressure along the line AB. In the lower part of the figure, for this resultant force is substituted the horizontal thrust, H^, the shear, V^, acting at the center of the section CD, and the moment M^. Referring to Fig. 231, page 726, and accepting C as origin of coordinates. 726 A TREATISE ON CONCRETE Let x,y, = coordinates of any point D, M i =■ moment at any point D on left half of arch axis of all loads between the point and the crown. Mjj = moment at any point D on right half of arch of all loads between the point and the crown. m = number of divisions of half of the arch axis. Fig. 230. — Moment and Thrust at the Crown. (,See p. 725.) c Fig. 231. — Coordinates of Any Point in Arch Axis. {See p. 725.) The fornnilas given below require that the arch be divided so that the ratio of length of any division to its average moment of inertia is constant. Because of this requirement the end divisions with large moments of inertia may be long, even with comparatively short divisions at the crown. This may cause an inaccuracy which can be largely elimi- nated by subdividing the load on the end divisions. The greater the number of divisions the more accurate the results. For an arch divided in such a way that the ratio of the length of any division to its average moment of inertia is constant (see page 728) ARCHES 727 the three unknown quantities, V^, 2T^, and M^ may be found from form- ulas* ^ mIMj,y + mIM^y-lM^Iy-IM^Iy " 2 [mif - (lyY] IMjjx — IMj^ ^c = 7-^2 (17) 2 Ix IM„+ IMj- 2 He ly M, = ^ ^ '—^ (18) 2m *The horizontal motion of C, Fig. 231, as in preceding analysis, due to bending moments on sec- B * tions between B and C,isl! „ My ^' The horizontal motion of C due to the bending moments on sections between .<{ and C, is 2 *^ ^y — ' These two motions are equal but opposite in direc- C EI tioD, hence, Similarly the vertical motions at C are equal, Also the changes in direction of the tangent to the axis at C are equal, but opposite in direction, hence, s If each half of the arch axis be divided into m divisions in such a way as to make ~T constant for all the divisions (See p. 728) the factor —r and also E may be cancelled. In the equations (8), (9) (10), M, I, i<, y, denote respectively the bending moment, moment of inertia of the cross-section, and coordinates at the center point of each division of the arch axis. At center of any division between A and C the bending moment is M = Mc-Vcx + Hey -Mr ' (n ) At center of any division between B and C the bending moment is M = Mc+ Vcx + Ilcy- Ml (") Placing these values of M in equations (S), (9) and (lo) and collecting terms, we have 2McI y + zHcI y' -.2 Mny-I Miy=o (13) iFelx^-SMLx+lMRx^o (14) 2mMc + 2HcIy-.2MK-.SML = ° ('S) Combining (13) and (15), ml Mr y + ml M^y - -T Mr ly - 2 Ml^ y ^^ " 2lmly^-(lyy] ^'^' 2MLX-2 Mrx , , From (14) Vc = ^"J^^^ ('7) ^ / > .. J:MR+j:ML-2Hc2y From (15) Mc = — — (") M — moment. He = crown thrust, Vc — crown shear, m = number divisions of half axis. X, y — coordinates of a point. 72$ A TREATISE ON CONCRETE These are fundamental equations in arch analysis. The method of application is illustrated in the example, page 733. All I signs denote summations for one-half of the arch axis. All numerical values of Mj, M^, x, y, are positive. A positive value of F„ indicates that the line of pressure at the crown slopes upward toward the left; a negative value, upward towards the right. A positive value of M^ indicates a positive moment at the crown; a nega- tive value, a negative moment. The moment at any point between B and C is if = M„ - V,x +Hj- M„ (19) while at any point between A and C M =il/„ + V,x+ H^ y - M^ (20) Fig. 232. — Diagram for finding Constant -. (Seep. 728) J7 Fig. 233.— Diagram for finding Length of Arc of a Circle. (See p. 728.) GRAPHICAL METHOD FOR FINDING CONSTANT — Fig. 232 and Fig. 233 give a graphical method of determining the length M = moment. He •=• crown thrust. Vc = crown shear. *•,)!= coordinates of a point. J = length of division of axis. / = D)9H>S!it of inertia ARCHES 729 of divisions for a constant y . If the arch axis is made up of arcs of circles, the length of any arc ACB is equal to three halves of the straight line AC* The point C is found in Fig. 233 by dividing the chord AB into thirds and drawing a radius through the one-third point. If the arc is an ellipse, a simple method of drawing which is given on page 192 , the length may be measured from the drawing. Having found the length of the half axis and ... i drawn it as a horizontal line, the constant yls found as shown in Fig. 232 by computing four or more values of 7, the moment of inertia, at different points and plotting these to locate the curves as shown. Beginning at the lower left corner of the diagram, trial diagonals (parallel to each other) and vertical lines are drawn, so that the number of spaces between the verticals will represent the number of divisions into which the half arch must be divided. If at the first trial the final diagonal does not come out exactly at the upper right corner which represents the crown of the arch, a new slope is tried for the parallel diagonals. LINE OF PRESSURE Having determined the thrust and moment at the crown, the line of pres- sure may be drawn as shown in folding Fig. 235, opposite page 738, from which the compression and tension at different sections may be found after determining the thrust and eccentricity from the formulas which follow. It is well to draw the line of pressure before considering the temperature and the effect of the rib shortening, and then afterwards study these, adding or deducting the stresses for the most unfavorable conditions. EFFECT OF TEMPERATURE AND THRUST The thrust acting throughout the ring tends to shorten the span. A change of temperature of the ring tends to shorten the span when the tem- perature falls or to lengthen the span when the temperature rises. The tendency for the span to change its length by a distance i^ due to any cause is resisted by a horizontal component // and a moment J/, acting at each support, and by a thrust and moment in the arch ring. J^ is positive for an increase and negative for a decrease in span length. ♦Method given in Nouvelles Annales de Mathematiques, Jan. 1907. The error for 40 degrees is less than xj^uifj for 70 degrees is less than tjjV (T) ^°' 9° degrees is less than yjstsu- The thrust and moment at the crown may be found from formulas* / mEJ ^" S2[mlf-(lyr] ^'^^ and Mo = - -^-^ (24) m Rise in Temperature. Under a rise of temperature of the arch ring of t degrees Fahr. the span L would tend to increase in length an amount of ctL, c being the coefficient of linear expansion. Substituting for ^^ in (23) the value of ctL, the thrust at crown is I ctLmE ^'^^7 2 [mi'/- {lyY] ^'^^ The value of the temperature coefficient, c, in equation (25) may be taken for concrete as 0.0000055. Dimensions must all be in same units; if in feet, E must be in pounds per square foot. Using a value of £^ of 2,000,000, E is therefore 2,000,000 X 144= 288,000,000 pounds per square foot. Moment at crown is M,= - -~^~^ (26) *The change In total span length, the two halves of the arch being equal, is %I^My'^j= JL (21) The change in inclination of tangent to axis at crown is 2l^M~ = („) Replacingthe A/of equations (21) and (22) hy Mc + Hey, which is the moment at any point D, s Fig. 234, in terms of moment and thrust at the crown, and making j constant, there results ^~McJ:y + z~HcIy'=JL mMc + HcJy=o From which / mEii, ^'^'s 2 [m I y'- (J: y)'] (»3) and Holy ^^ = - -^ M M = moment. He = crown thrust, m = number divisions of half axis, j = length of division of axis. J = moment inertia. L -= span. £ = modulus of elasticity. Jl=- change of span length, t = rise or fall of temperature, c = coefficient of expansion. «, y —coordinates of a point. ARCHES 731 The moment at any point D may be found as soon as the values of f/, and M^ have been determined by means of the relation M ^M^ + H^ (27) or we can say that the moment at any point equals the thrust H* multi- plied by the distance from the point in question to the line OO, Fig. 234. Fig. 234. — Moments and Thrusts due to Changes of Temperature. {See p. 730.) Above the line OO, Fig. 234, the moments are all negative, being a maxi- mum at the crown, and below OO they are all positive, being maximum at A and B. The line OO is below the crown a distance d = ly. At the two points where OO intersect the arch axis the moments are zero, as is evident from equations (24) and (26). Fall in Temperature. Here the thrust at croWn is I c tLniE ^^"^ ~J V\i^~f - {Iyf\ ^^^^ where c is 0.0000055, ^"<^ moment at crown is ''' = - ^ - (^9) and, as above, M = M, + Hj (30) In placing a numerical value for 11^ in the last two equations, it should be observed that it is a negative quantity. If in the equations the values of L and y are in feet, E is in pounds per square foot. Above 00 the moments are all positive, below they are all negative. The thrust at the crown is really a tension in this case. M = moment. He = crown thrust, m = number divisions of half axis, s = length of division of axis. / — moment inertia. Z. = span. £ = modulus of elasticity, i = rise or fall of temperature from mean, c = coefficient of expansion, x, y = coordinates of a point. *The horizontal thrust is constant throughout the arch, hence He at the crown equals H at the support. 732 A TREATISE ON CONCRETE An increase and a decrease of 20 degrees Fahr. is probably a sufficient allowance for concrete arches mth filled spandrels. For arches with open spandrels the range in temperature of the concrete is somewhat less than that of the surrounding air. For example, in the latter case with a range of temperature of the air from -20 degrees to +100 degrees Fahr., the range for arch computation should be taken at least 40 degrees on each side of the mean temperature. The methods of combining the temperature moments and thrusts with those due to loads is illustrated in the example, page 737. EFFECT OF RIB SHORTENING DUE TO THRUST The thrust acting throughout the arch ring tends to cause a shortening of the span, which, if / is average compression (obtained by aver£^ging values in computation of ring) for umt area, = -^ = ^^ Hence I f Lm and He ^ y M, = - ^— - (32) and, as in temperature stresses, if = M, + H,y {33) All the summations above are for one-half the span only. w = num- ber of divisions in one-half of the arch axis. The effect of rib shortening is slight in many cases but in a flat arch it may be considerable. It is similar to a fall in temperature. DISTRIBUTION OF STRESS OVER CROSS SECTION Knowing the thrust, shear and bending moment at the selected sections of the ring, the distribution of stresses on the sections must be computed to insure against excessive working stresses and an uneconomical design. On pages 377 to 389 are given formulas for de- termining the stresses caused by eccentric forces or by an axial force and a bending moment. Shear in all cases is negligible. M = moment. Ho = crown thrust, m = number divisions of half axis, j = short length of arch axis. / = moment inertia. L =■ span, y ■= coordinate of a point. / = compression in concrete. ARCEES 733 METHOD OF PROCEDURE FOR THE DESIGN OF AN ARCH The design of an arch is a trial process; the design being selected and then investigated to see if the sections are of sufficient strength. If the arch first chosen is too large or too small it must be revised. Since the location of the line of pressure and also the stresses are affected by the loading, it is customary either to compute the arch for the dead load plus concentrated loads located at the most unfavora- ble positions, or else to compute it for the dead load plus a uniform live load covering one-half the arch and also covering the entire arch. The following pages indicate the steps in the design of a highway bridge shown in Fig. 235, page 739, with the live load over one-half the span. The procedure is similar when the entire span is loaded. I. Draw a preliminary curve for the intrados. (See p. 714.) 2 . Assume a crown thickness in accordance with the formula on page 715. 3. Lay out the curve of the extrados and the surface of the roadway. The extrados may be a 3-centered curve, but it is better to use an arc of a circle if possible. It should be so placed as to give a ring thickness at the quarter points of the span of ij to ij times the crown thickness, and a ring thickness at the springings of 2 or 3 times the crown thickness in this first trial. 4 Draw the arch axis midway between the extrados and the intrados. 5. Divide the arch axis into distances such that the ratio of each distance to the moment of inertia of the cross-section of the ring at the center of the s distance is a constant; that is, y is a constant. This can be done by trial by beginning at the crown and working towards the springings or by the method described on page 728. The momeni of inertia is of the combined section of concrete and steel about the gravity axis, hence the size and posi- tion of the steel rods must be first assumed, when / may be computed by the formula on page 381. Theratioof area of steel to total area of section at crown may be arbitrarily taken in the first place from 0.007 '^ 0.0125, that is from 0.7% to i\%. The divisions are separated by vertical sections. In the problem here solved the distance, s, next to the crown is 1.14 ft., s and that next to the springing is 7.82 ft. The constant ratio, y for this arch is 1 1 .4* On folding Fig. 235 the centers of the divisions are shown by circles and are numbered i, 2, 3, etc. All distances are in feet and all quantities ♦Greater accuracy may be obtained by using a larger number of divisions than here chosen, and also by subdividing loads Pj and P.^. • 734 A TREATISE ON CONCRETE involving distance are in foot units. A section of the arch i foot wide transversely is considered. 6. Compute the dead and live loads and enter these loads as indicated by Pi Pj, etc., at the center of gravity of each division. In the accompany- ing design, a live load of loo pounds per square foot covers the right half span, while on the left is the dead load alone of the masonry taken at 150 pounds per cubic foot plus the earth fill taken at 100 pounds per cubic foot. Table i. Ordinates and Moments In Compulation of Example Points X y x' f Mi Mr Mjx ^R" Mjj MRy 10 and II 0.56 0.01 0.3 0.04 2.9 o.oc 00 00 00 00 00 00 q and 12 1. 71 0.00 391 521 668 891 16 21 8 and 13 ^.88 u.ii; 8.3 O.OI I 205 I 603 3470 4616 132 176 7 and 14 4. II 0.23' 16.9 0.05 i 520 3346 10357 •3752 580 770 6 and 15 5-43 0.39, 29.5 U.I5 4 4V I 5923 24277 32 162 •743 2 310 5 and 16 6.89 0.63; 47.5 a. 40 lV-1 9672 50483 66 640 4616 6093 4 and 17 S.,7 0.97I 73.5 0.94 11584 15 216 99275 130 401 II 237 '4 759 3 and iS ■o-W 1.50, 112. 2 2.25 18242 23791 193 >83 251 947 27363 35686 z and 19 13.17 2.39 173. s 5-7' 29480 38045 388 252 501 053 70457 90 928 I and 20 17-94 5.14 321.8 26.41 58553 74192 1 052 235 I 331 004 301 476 38' 347 I 71.85 II.4IJ 786.4 35-9^ 133 873 172 309 I 822 200 2 332 466 417 620 532 090 All distances in fuot-units; all moments in foot-pounds H„ Values of H^, V ,. and M^ at crown for Live and Dead Loads. 10 U'7 620 + 532090) — 11.41 (133 S73 + 172 309) 2 [10 X 35.92 — (11.41)^] 1822200 — 2332466 1573 + 13 107 lb. Vr.= T^ii, lb. 172 309 + 133 873 - 2 X 13.107 X 11.41 , , „ Mc = ~ = + 354 ft- lb Values of H^ and M^ at crown for Rise in Temperature. I .0000055 X 20 X 41.88 X 10 X 2000000 X 144 11.4 2(10 X 35.92 - (11.41)2] - 2545 X 11.41 = — 2900 ft. lb. 10 ^ Values of H^ and M^ at crown for Rib Shortening. I 66 X 41.88 X 10 X 144 ff.= M, 2545 lb. H. Mr 11.4 2[io X 35.92 - (ii.4i>-] — 760 X 1 1. 41 = +870 ft. lb 7601b. The horizontal components of the earth pressure are so small that they are neglected, except that, for purposes of illustration, they are shown in the case of the load adjoining each springing, where the horizontal compo- nents are computed by formulas for earth pressure on page 760. The point of application of the horizontal and vertical components, as shown for P„ is taken at the arch axis. Tn practice, earth pressure is negligible ARCHES 735 m the design of flat arch rings of the type here selected, and all loads may be taken as vertical. Only where the ratio of rise to span is large need the horizontal components of the earth pressure be considered. 7. Make a table similar to TaJ^le i, page 734. The values of x and y are scaled from the drawing, and are the coordinates of the center points of the divisions of the arch axis. The crown point of arch axis is here taken as the origin of coordinates. The values of Mj^ and Mji are computed. M^ represents the moment at each of the center points i to 10 inclusive of all loads l)dng between the point in question and the crown. Thus Mj^ for point 10 is o; for point 9, Mj^^ 340 X 1.15 =391 ft. lb.; for point 8, Mj,= 391 + 696 X 1.17 = 1205 ft. lb., and so on. The moment at each "center" point being obtained from that at each preceding "center" point. Mj^ of course represents the moment at each of the center points 1 1 to 20 inclusive of all loads lying between the point in question and the crown. For a symmetrical loading Mj^ would equal M^^ for each pair of center points, such as I and 20. 8. Compute H^ V^ M^, that is, the thrust, shear and moment at the crown, as on page 734, by using equations (16), (17), and(i8),page 727. If the sign of V ^ is plus the line of pressure (equilibrium polygon) at the crown slopes upward towards the left; if minus, as in the present case, upwards toward the right. A pus sign for M^ indicates a positive moment: a minus sign, a negative moment at the crown. For the arch in folding Fig. 23s, the crown thrust H^ = 13107 pounds, V^= - 324 pounds and Mc= + 354 ft. pounds. 9. Draw a force polygon as shown in folding Fig. 235 by laying off to scale the loads P„ P^, etc., as o - i, i - 2, etc. Find the pole by laying off V^ downward (because negative) from the crown point, 10, and then laying off H^ horizontal. The hypothenuse of the triangle having H^ and Fg for sides thus slopes upward to left or upward to right, according as Fg is + or — . 10. Draw the equilibrium polygon as shown on the arch of folding Fig. 235. The resultant pressure acts above the axis at the crown a distance, M ■ — - = c if Mc is plus, and below by the same amount if M^ is minus. Since here, as is shown later, e = +0.028 feet, this distance is laid off verti- cally above the axis at the crown and through this point the resultant pres- sure is drawn parallel to the ray Ojo of the force polygon and so on. It is not really necessary to draw the equilibrium polygon if the moments and eccentricities are computed for the various sections as outlined under item II, but the polygon, which is the line of pressure, affords a good check on the algebraic work. 736 A TREATISE ON CONCRETE 11. Determine the moment, thrust, and eccentricity, and if desired the shear at the center points, i, 2, 3, etc., of the divisions, and enter in a table asshown below. The moment is computed from formulas (19) and (20) on page 728, the values of -whose terms have already been found by items 7 and 8. The thrust and shear may be scaled from the force polygon. For example, at section i on folding Fig. 235 the thrust line is drawn parallel to the tangent to the axis at i, and the shear line at right angles to the thrust line. The eccentricities, e, of the sections i, 2, 3, etc., are computed by dividing the moment on the section (see page 379) by the thrust for that section just scaled. For positive moments and therefore positive values of e, the line of thrust lies above the arch axis. 12. Compute the thrust and moment at the crown due to variation in temperature by formulas (25) and (26), page 730, the moments on the Table 2. Final Moments and Thrusts LIVE AND DEAD TEMPERATURE RIB SHORTENING Point Hey f^c" Mom. Thrust Ecc. Mom. Thrust Mom. Thrust , 67370 -5812 +3259 + 14360 + 0.23 ±10180 ±1970 -3030 -610 2 31325 -4267 -2068 + 14000 -0.15 ± 3'8o ±2310 - 95° -700 3 19660 -3431 -1659 + 13920 — 0.12 ± 910 ±2430 - 270 -73° 4 12713 -2777 -1293 + 13600 -c. ro ± 440 ±2500 + 130 -74° 7 3014 -'33' - 483 + 13240 -0.04 =F 2320 ±2530 + 690 — 760 9 524 - 554 - 67 + 13160 —0.005 =F 2800 ±^545 + S40 -760 12 524 - 554 + 911 + 13120 +0.07 =F 2S00 ±2545 + 840 -760 H 3014 -1331 + '353 + 13200 +0.10 =F 2320 ±2530 + 6go -760 •7 12713 -2777 + 627 + 13640 +0.05 ± 440 ±2500 + 130 -740 18 19660 -343' - 346 + 14040 • — 0.03 ± 910 ±=43° - 270 -73° '9 313^5 -4267 -20-9 + 14200 -0.15 ± 3180 ±2310 - 950 -700 20 67370 -5812 - 656 + 14S40 —0.04 ±ioiSo ±1970 -3030 -610 Thrusts in lb. Moments in ft. lb. Shear in arch design is small and need not be computed. various sections by formula (27), page 731,, and the thrusts and shears by resolving the crown thrust into tangential and radial components, as shown in the small force polygon in the diagram. A rise in temperature of 20 degrees Fahr., and a fall of the same amount, is sufficient even in the northern part of the United States for arches with filled spandrels. For the arch shown on folding Fig. 235 the crown thrust H^, due to temperature, is a tension of 2545 lbs., and a compression of equal amount. The crown moment M^\s + 2900 ft. lb. and — 2900ft. lb. 13. The effect of rib shortening due to the thrust is comparatively slight. Where necessary to compute it, use formula (31) and (32), page 732. (See P- 734-) For the problem here shown the thrusi: at crown due to this cause is — 760 lb., and the moment is +870 ft. lb. 14. Having prepared a table similar to Table 2, page 736, showing ARCHES 737 thrusts and moments on the various sections i, 2, 3, etc., due to dead and live loads, temperature, and rib shortening, compute the maximum unit compression in the concrete and maximum unit tension, if any, in the steel by use of formulas on pages 382 to 389. Table 2 shows thrusts and moments for only a few of the sections of this arch, since it is unnecessary to compute all of them. A selection of the more critical sections may be made by inspection of the equihbrium poly- gon. The following shows the computation of the maximum unit stresses at the crown for the arch infolding Fig. 235, as outlined in items 11 to 13. Live and Dead Loads and Rib Shortening Plus Temper- ature. Moment Thrust + 1224 + 12347 + 2900 — 2545 Temp. Live and Dead Loads and Rib Shortening. Moment Thrust + 354 + 13 107 Live and dead + 870 — 760 Rib shortening + i224ft.lb. +12347 lb. M 1224 = 0.1 ft. N 12347 /> = ratio of steel at crown = 0.0092 From formula (77), page 384, it is seen that the value of — for h 0.92% is greater than — =0.1. n Hence there is compression over the entire section. From formula (75), page 382, max. compression in concrete, I + 4124 ft. lb. + 9802 lb. M 4124 «= '^ = ~^ — = -42 ft. N 9802 ^ From formula (77), page 384, it is seen that the value of -^ for _ 12347 ?t + ■ I X I Li + 14 (-0092) 6 (i) 0.1 1 (1)2 + 12 (14) .0092 {iy_ = 17 280 lb. persq. ft. = i2olb. per sq. in. Stresses in steel need not be com- puted. The above may be more quickly solved by the use of the curves in Fig. 108, page 383. 0.92% of steel is much smaller than — = -^ — = 0.42. Hence there is h I tension over a part of the section. From formula (88), page 386, the value of k is found to be 0.6. From formula (86), page 386, the value of the maximum compression = 35 700 pounds per square foot = 248 pounds per square inch. From formula (81), page 385, max- imum tension in steel = 1 440 pounds per square inch. The approximate value of the above compression in concrete may be more quickly found by the use of curves, Figs, iii and 112, and pages 387 and 388 as shown below. fc — compression in concrete, c = eccentricity. M « moment. JV » depth neutral axis, e = distance cenLer of gravity to steel. thrust. = height. * ■= ratio 738 A TREATISE ON CONCRETE The method of computation for other points in the arch is similar, and stresses should be determined at sections where they appear to be the max- imum. From table 2 it is evident that although at point 20 the moment due to dead and live load is very small, its combination with moments due to tem- perature and rib shortening makes it one of the critical points. The moment and thrust due to live and dead load and rib shortening is M = - 656 -3030 = - 3636 ft. lb. and N = 14840 — 610 = 142301b. ^686 e„ Hence, e„ = = 0.26 ft, for h = 1.97, -^ = 0.13, p = 0.0037. 14230 h From formula (77), page 384, it is seen that the whole section is in compression. From Fig. 108, page 383, for - = 0.13 and p = 0.0037, n the value of the parenthesis in formula (75) = 1.65. Using formula / \ r, r 14 230 X 1.6'; _ ,, (75), page 384, /, = -^L^- -^ = 83 lb. per sq. m. 1.97 X 12 X 12 Combine now the moment and thrust due to live and dead load with those due to temperature and obtain M — — (10 180 + 3 686) = — 13 866 ft. lb., i\^ = — I 970 -1- 14 230 = 12 260 lb., e = 1.13 ft. — h = 0.57- In Fig. Ill, page 387, k = 0.37 corresponds to — = 0.57. By locating n this value of h in Fig. 112, the constant C<, = 0.094 is obtained, which sub- stituted in formula (86), page 386, gives /^ = 0.094 X 12 X (1.97 X 12)- = 264 lb. per sq. in. The stress in steel from formula (81) is /, = i. 8o-(o.37Xx.97) ^ g„, ^^ .^_ 0.37X1.97 ^ • ^ Similar computations should be made for all critical points and when the stresses are either too small or too large, the dimensions or even the shape of the arch must be changed. Small changes may be made without refigur- ing the whole arch. For larger changes, all computations should be re- peated and a new line of pressure determined. LOADINGS TO USE IN COMPUTATIONS The usual practice is to make two sets of computations; in the first place, proportion the arch ring for a live load covering the entire span and then for one covering only one-half the span. These two loadings are approxi- mations, more or less exact, to the true loadings which produce the maxi- FIG. 235. EXAMPLE OF ARCH DESIGN (See pp. 733 to 738) ARCHES 741 mum effects. By computing a table for the thrusts and moments due to a load of unity at different points, or by the use of influence lines, the exact loading to cause maximum stresses may be found. ALLOWABLE UNIT STRESSES For highway bridges the maximum compression in the concrete of the ring should not exceed 500 pounds per square inch due to live and dead loads, nor more than 600 pounds per square inch due to live and dead loads, temperature and rib shortening combined. For railroad bridges three-fourths of the above values may be used. DESIGN OF ABUTMENT The design of the foundation of an arch bridge is as important as that of the arch itself. The arch is designed on the assumption that the founda- tion is unyielding, and this condition must be approached as nearly as pos sible in order to insure the stability of the whole structure. The depth of the foundation as well as the shape is dependent upon the local conditions, and in the more difficult cases these have to be chosen after exhaustive studies. A certain shape of abutment is first assumed, and this is then reviewed to see that the load upon the ground does not exceed the allowable load and that it is well distributed. Allowable loads are discussed on page 715. The forces acting on the foundation are: (i) the thrust of the arch; (2) the weight of the foundation; (3) the weight of the earth above it; and (4) the lateral earth pressure. The thrust of the arch is the largest when the live loading extends over the whole span of the arch, and for this the line of pressure should be drawn first. A line of pressure for the thrust on account of the total dead load and of the live load extending only over one-half the span opposite to the abutment also should be drawn to see whether, because of intersecting the abutment higher up, it does not produce larger pressure on the foundation. A good scheme is to design the abutment in such a way that the line of pressure on account of one thrust intersects the base a little way to the left of the center while the other intersects to the right of the center. In some cases a third line for the total dead load, plus live load on the half span nearest the abutment should also be drawn. The line of pressure of the foices should be as near to the center of the base as possible, since the maximum unit pressure is the smallest when the load is distributed uniformly over the entire section. This also prevents uneven settling of the foundation, and thus adds considerably to the stability of the whole structurt 742 A TREATISE ON CONCRETE 300 LB. Fig. 236.— Design of a Foundation for an Arch. (See p. 743). (To rimplify the drawing only one position of thrust and one line of pressure is drawn.) ARCHES 743 Fig. 236, page 742, clearly illustrates the design of an abutment. The outline is assumed, then the location and magnitude of the forces acting upon the abutment are found and the line of pressure determined. If the assumed outline is not satisfactory it should be revised. For the benefit of those who are not familiar with the common principles of such design, the steps will be considered in detail. The magnitude, 20,500 pounds, and position of the arch thrust is given in the arch example. Since the weight of the masonry acts through its center of gravity, this point must next be found and this is most readily done by dividing the outline of the abutment into triangles and rectangles. The weights of each of these prisms one foot thick are readily computed, and the center of gravity found through which the weight force acts. A force polygon for any pole distance, as shown in the upper left corner of the diagram, is drawn and the equilibrium polygon, by the intersection of the closing lines, locates the resultant of the weight which, by computation, is found to be 5850 pounds. The pressure on AB consists of the horizontal pressure on BE, and the weight of the prism of earth whose cross-section is ABFG* and thickness one foot. Taking the weight of one cubic foot of filling at 100 pounds, the weight of the prism would be ■ X 6.3 X 100 = 7880 pounds. 2 The horizontal pressure on BE is equal to the difference between the pres- sures on BF and EF. Let w = weight of one cubic foot of earth, then, if the weight of earth is assumed at 100 pounds, from formula (2), page 758, pressure on the plane jBF = C^M'£r*=o.i4X 100X15X15 = 3150 pounds, and on the plane EF = CpwH^— 0.14X100X10X10=1750 pounds. Hence horizontal pressure on plane BE = 1750 pounds. The point of application is found from the formula (7), page 760. ^In the case under consideration H = 15 feet, h = 10 feet, where H is the depth of point B and h the depth of ^ or £ below the line of surcharge. " The horizontal pressure on BC is by formula (6), page 760, 300 pounds, and the point of application may be assumed in the middle of BC without appreciable error. * The live load being lOo pounds per foot is equivalent to a surcharge one foot in heighl. 744 A TREATISE ON CONCRETE Having thus located all forces and found their magnitude, the line of pressure is drawn. This procedure consists simply in finding the resultant of two forces intersecting in one point. The line representing the thrust is prolonged until it intersects the line representing the weight of masonry, 5850 pounds. Beginning at this, the magnitude of the thrust, 20,500 pounds, is laid oE to any desired scale and the resultant of this with the weight of the masonry, 5850 pounds, is found to be 25,200 pounds. Combining this new force in turn with the earth pressures of 8070 pounds and 300 pounds com- pletes the line of pressure with a final resultant thrust of 31,500 pounds. Having found the line of pressure, the thrust is divided by the projection of the base on a line at right angles to the thrust and the maximum pressure on the ground is found by formula (70), page 379, to be 5000 pounds per square foot. The same result is obtainable by the following simple graphical method: Find the average unit pressure by dividing the thrust by the area of the projection of the base, drawn perpendicular to the thrust. In this case we have ^-^ — = 4500 pounds per square foot. Plot this, to any convenient 7 _ scale, perpendicular to the projection to the base at its center; connect the ^points of the base with the top of this perpendicular, as shown by the dash lines in Fig. 236, and produce one of these lines till it intersects the line rep- resenting the direction of the thrust. The perpendicular distance of this point from the projection of the base is the maximum thrust and the dis- tance of the other intersection of a slanting line with the thrust line is the minimum thrust. To draw the trapezoid of pressure, draw, through these two intersections, lines parallel to the projection of the base, as shown, and the extremities of these parallel lines will fix the two corners of the trap- ezoid. The maximum pressure is always at the end of the base nearest the thrust. ERECTION As in other reinforced structures, the erection is as important as the design. Perhaps the first essential is the centering which should be planned out in advance almost as carefully as the arch itself. Methods of Arch Construction. There are two general methods of lapng the concrete in an arch, each of which has strong advocates. By the first, the arch is laid in separate blocks across the bridge, and by the second, in narrow ribs from abutment to abutment. If the block method is followed, the lowest stones at the springing line are laid first, then stones ARCHES 745 intermediate between the spring and the key, next the two stones each side of the key, and finally, after filling in the intermediate blocks, the key is placed. This distributes the weight of the concrete uniformly over the arch center, and prevents unequal settlement, which tends to crack the arch near the springing lines. On the other hand, the entire weight falls upon the center, and the latter must be very strongly built. The arch thrust acts at right angles to the joints, and as the blocks extend clear across the bridge, there is no danger of longitudinal splitting, but the radial joints offer planes of weakness in bending. By the other method the work can be readily arranged so that a day's labor consists of the laying of a single rib, thus forming a complete arch of itself, which as soon as it sets bears its own weight. This arch section has no joints, so that when subsequently loaded the bending moment is best resisted. A small arch, where the center can be solidly built, may be laid at one operation, commencing at both abutments and working toward the key so that it is in fact a monolith. The spandrel or face walls may be carried up at the same time the arch ring is laid, or may be connected with it later by leaving short lengths of steel projecting radially from the concrete of the arch. If steel is introduced, the consistency of the concrete must be wet enough to thoroughly coat it. This may be accomplished by a quaking or jelly- like mixture, which requires but slight ramming. From an architectural point of view, the treatment of the face is of much importance. For a discussion of the different methods reference should he made to page 262. Railings and ornamental work may be cast in molds if preferred and put in place after hardening. Centering. The falsework for concrete arches is practically the same as for stone arches except that close lagging is necessary. It must be rigid during the construction of the arch and stiff enough to prevent its distor- tion from the unsupported weight of the concrete before the keying of the arch. The design of the centering is frequently governed by the character of the ground underneath. In general the framed wood centering made into a truss rests upon pile or trestle bents. The spacing of these bents is deter- mined by the foundation and the difiSculty of placing them, and by the height and span of the arch. In certain cases it is possible to support the centering in whole or in part by the reinforcement, although this is not usually economical because more carefully framed steel is required than is 746 A TREATISE ON CONCRETE necessary for reinforcing the arch. In at least one case* reinforced con- crete forms were used. In connection with the description of arch centers which he has built, Mr. James W. Rollins, Jr.,t gives the following notes: For small arches the simplest center is a circular rib made of three pieces of 2-inch plank, laid with broken joints, all being spiked solidly together, with a tie of plank at the springing. On this, i-inch lagging is laid close. For a larger arch, the circular rib, as above described, with generally three braces, one at center and one on the quarter at each side, is used, the center of the whole rib having a post under it. We have used such a center up to 30-foot span for both brick and granite arches, carrying a 30-inch arch sheeting. The design of a center for larger arches depends upon local conditions, also upon the relation of rise to span. In flat arches, with low side walls, it is well to use posts with intermediate bracing, on numerous supports. In a high arch we may use long braces extending directly from a center support to the rib, at intervals of 6 feet to 8 feet. Mr. Rollins advocated for wedges, seasoned oak, 8 inches wide, 4 inches thick at the thick end, 2 inches at the thin end, and 18 inches long^ planed on sUding faces, and thoroughly greased. When setting the center, these wedges, placed between the caps on the bents and the corbels under the lower chord of rib, are tacked together to prevent slipping. Boxes fiUed with sand are frequently used between the caps of the bents and the lower chords of the trusses in place of wood wedges. The sand in these must be thoroughly packed to prevent settlement of the concrete before setting. The sand is readily removed by letting it out through a hole in the box. Jack-screws also may answer the same purpose as wedges or sand boxes. By any of these means the centering is easily lowered. The ribs of the centering are usually made of several pieces of plank spiked or bolted together. Upon the ribs rests the lagging, which usually consists of one or two layers of planking having the top surface smoothed to give a good surface to the soffit of the arch, and laid with tight joints. With thin lagging care must be taken to prevent deflection. Instead of the ribs forming a part of the truss, they are frequently supported directly upon the wedges resting upon the caps of the bents, the posts of which run up to the soffit of the arch for that purpose. The centering should be cambered, that is, should be made higher than called for in the arch plans at the center, so that when it is removed, the arch will be in the position assumed for it in the design. Some engineers make * Engineering News, Aug. 30, 1906, p. 215. t Journal Association of Engineering Societies, July 1901, p. 10. For examples of centers built in various places, see References, Chapter XXXIII. 748 A TREATISE ON CONCRETE the camber equal to the deflection of the arch which would be caused by the live and dead loads. In striking the centers sudden settlement must be avoided and the cen- ters must not be removed until the concrete has attained good strength. The time of removal must be determined by the design of the bridge and the weather. For light highway bridges four weeks is usually suffi- cient, while for a heavy arch of long span eight weeks may be required. EXAMPLES OF ARCH BRIDGES Mystic River Bridge, Medford, Mass. This arch, illustrated in Fig. 237, page 747, is of the Monier type and carries a parkway over the river. It was built in 1906 by the Metropolitan Park Commission, Mr. John R. Rablin, Chief Engineer. The arch has a span of 60 feet, a rise of 8 feet, and a crown thickness of 18 inches. Both the intrados and the extrados are segmental. The side walls are of concrete with a vertical expansion joint at each abutment. The retaining wall for the earth fill over the abutments is of reinforced design and curved as shown in the details in the drawing. Granite Branch Railroad Bridge. A railroad bridge of similar de- sign to the Mystic River Bridge was built by the Metropolitan Park Commission of only 4 feet longer span than the highway bridge described. The heavier loading necessitated a thickness of crown of 24 inches instead of 18 inches with a thickness at springing still greater in proportion. 3-Hinged Ribbed Arch on Ross Drive, District of Columbia. A different type of structure and one which illustrates the combination of arch ribs with a reinforced concrete floor system is illustrated in Fig. 238, page 749. This was built in 1907 by the Engineering Commissioner, Washington, D. C, Mr. W. J. Douglas, Engineer of Bridges. The central arch is 100 feet clear span and 15 feet rise, and the roadway, which is 16 feet wide and macadamized, is laid upon a 6-inch reinforced concrete floor slab supported by longitudinal concrete girders which in turn rest upon columns supported directly by the concrete ribs. The three arch ribs, which are reinforced as shown, are 2 feet wide throughout their length with a thickness of 2 feet 6 inches at the crown. Each hinge consists of two steel castings, shown in detail, with a pin 4 inches in diameter, and these hinges are imbedded in the concrete. An expansion joint is provided in the roadway deck over each springing. The floor of the arch was computed for a 6-ton wagon, and the ribs for a live load of 100 pounds per square foot of roadway. The maximum compression on the concrete of the ribs under live and dead loads is 500 pounds per 739 740 SURFACE OF ROADWAY l-IVElfOAD6N-HAlfF.SPAN#I00 POUNDS PER SQUARE FOOT 'm Fig. 235. — Example of Arch Design. 75° A TREATISE ON CONCRETE square inch, and there is no tension. The cost of the structure was $8000, which is equivalent to about $3.00 per square foot of the roadway. Walnut Lane Bridge, Philadelphia. A notable structure in concrete is the Wahiut Lane Bridge built as it is with a clear span of 233 feet. The arch was completed in 1908 under the direction of the Bureau of Sur- veys, Mr. George S. Webster, Chief Engineer and Mi. Henry H. Quimby, Assistant Engineer. The principal arch consists of two ribs, upon which rest cross walls connected by small longitudinal arches of 20 feet span carrying the spandrel wall supporting the I-beams of the floor. A fine photograph of the arch is shown in Fig. 224, page 706, and cross sections illustrating the design in Fig. 239, page 750. The balustrade is entirely of concrete, the posts being molded on the ground and the sur- face washed ofif with water to reveal the aggregate. Other Notable Bridges. For references to other bridges built in recent years, see Chapter XXXIII. Pio. 239 Walnut Lane Bridge, Philadelphia. {See p. 750.) DAMS AND RETAINING WALLS 751 CHAPTER XXVII DAMS AND RETAINING WALLS For walls to resist the pressure of earth or water, concrete frequently possesses marked advantages over other classes of masonry. With proper management, in most localities its cost may be brought below that of rubble masonry. Its adaptability for thin walls and for certain classes of face work often make it a suitable substitute in complicated designs for first- class masonry, with a consequent large saving in cost. In combination with steel its possibilities for special designs are almost unUmited, and the future will see continued advancfes in its use for ordinary engineering and hydraulic construction. Water-tightness, often an essential element for this class of structures, has received general treatment in Chapter XVIII, page 296. Portland cement concrete may be made water-tight more readily than stone ma- sonry laid in mortar of similar proportions to the cement and sand in the concrete, since large voids or stone pockets in the concrete are more easily prevented than the "rat-holes" so frequently found in the bedding of stones in mortar. Moreover, skill in laying combined with special treat- ment of the surface or the addition of certain ingredients permits con- struction in concrete — strengthened with steel reinforcement — of thinner walls for resisting the flow of water than is possible in stone masonry. Reinforced concrete retaining walls cannot be designed by "rule of thumb," and therefore a careful consideration of the forces acting and of the stresses in the concrete is presented in this chapter. Since the earth pressure is the controlling factor, it has been necessary to introduce a practical discussion of this before taking up the details of the design and examples of the two principal types. RETAINING WALLS Retaining walls to support the pressure of earth may be designed: (i) of gravity section with plain concrete or stone masonry; (2) of thin reinforced concrete section of the inverted T type with spreading base or footing; (3) of thin section, reinforced and supported by buttresses or counter- forts. Another plan sometimes adapted to cellar wall construction (see p. 643) consists in embedding the base and supporting the top of the wall with tim- 752 A TREATISE ON CONCRETE ber, steel or reinforced concrete beams, so that the concrete forms a vertical slab supported at top and bottom. Reinforced concrete retaining walls are almost always more economical than a gravity section of either plain concrete or masonry. In walls of gravity section the materials cannot be fully utilized because the section must be made heavy enough to prevent overturning by its own weight, counterforts or buttresses being of comparatively little advantage because, in stone masonry, the wall is liable to break away from them. In reinforced concrete retaining walls, on the other hand, a part of the sustained material is used to prevent overturning, and the section need be made only strong enough to withstand the moments and shears due to the earth pressure. Since the wall is lighter, exerts smaller pressure on the soil, and may be made if necessary with a very broad base, the special foundations or piling which are often necessary for a gravity wall frequently may be avoided. Reinforced concrete properly designed can he depended upon as absolutely reliable. The economy of a reinforced concrete wall over one of gravity section for either stone masonry or plain concrete is obvious because of the saving in material. The cost of forms is practically the same for gravity section and reinforced designs. Mr. J. I. Oberlander reports* that 23 bids submitted on alternate designs of gravity and cantilever sections showed the average cost per linear foot for the gravity section to be about one-third greater than that for the reinforced section. The unit price for the concrete in the latter, however, was about 20% greater than that for the former. Whether the T-section of reinforced wall or the wall with counterforts is the more economical depends upon certain conditions. The principal condition is the height of the wall, but the intensity of the earth pres- sure and the relative cost of concrete and steel and forms also enter into the consideration. The construction of the T-section is simpler and the placing of steel easier, so that it is preferable where skilled labor is scarce. The form construction in the counterforted wall is consid- erably more expensive. Comparative studies of the two types indicate that the counterfort type is scarcely ever economical when the height is less than 18 feet. Rules for designing walls of gravity section are first given and then, after the discussion of earth pressure, the designs of both a T-type and a counterforted section are treated. Special designs have been worked out with considerable ingenuity where local conditions require departure from the standard sections. For example, two different railroads were each obliged to build retaining "Engineering and Contracting, May 19, igis, p. 457. DAMS AND RETAINING WALLS 753 walls where every inch of available room up to the edge of the right-of- way was valuable and where no trespassing on adjoining property was permissible. The solutions for the same problems were radically differ- ent. In one* an L-section was used but the horizontal leg projected from the middle of the back instead of the bottom so that the result resembled the letter T on its side. In the other casef a horizontal reinforced slab supported on transverse walls was used. The walls rested on another continuous horizontal slab and the rectangular cells thus formed were closed at the back by a vertical slab that retained the earth. An interesting wall is that designed by Gustave Lindenthal for the New York Connecting Railroad. Here two walls 65 feet high enclosed a railroad fill nearly 60 feet wide carrying a surcharge loading of 4 tracks (E 60 loading) and 100% impact. Rather than use the very heavy sections that would have been required under ordinary assump- tions, it was decided to use steel tie rods 10 feet on centers, and to tamp the earth fill in 12-inch layers with pneumatic tampers so that a slope of 3 to I could be counted on for passive resistance.! FOUNDATIONS A firm foundation is essential whatever the type of the design. Piles may be necessary, or to avoid sliding, a stepped base may be required. Unequal settling is more dangerous for a retaining waU than for many other structures, because if it is thrown out of plumb, the earth will move and produce forces much in excess of the calculated ones. Allow- able pressures on different soils are referred to on page 669. In France several walls§ were constructed approximately rectangular in section, except that the bottom width was somewhat greater than that at the top, lying back, or reclining, on the slope of the cut, or fill. A wall somewhat similar to this, but built of separate blocks on a soft foundation, was built in Wisconsin. || Drainage of Retaining Walls. The drainage of retaining walls is a highly important matter and lack of it may cause either complete or partial failure. A common plan is to lay a drain of tile or of broken stone along the back of the base, opening at the ends of the wall or dis- charging through weep-holes. * Engineering News, February 15, 1912, p. 292. t J. H. Prior in Engineering and Contracting, May 10, 19x1, p. 530. t The computations are discussed in Engineering News, May f , 1915, P- 886. I Engineering Record, November 12, 1910, p. 544. II W. S. Lacher in Proceedings Western Society of Engineers; See also Engineering News, May 27, i9rs, p. 1048. 7S4 A TREATISE ON CONCRETE The Delaware, Lackawanna, & Western R. R.* builds 4-mch tiles through the wall at frequent intervals along the footing with a right angle elbow, turned up, on the inner side. A chimney of loose rubble, about 2§ feet by 3 feet, runs from each weeper up to the top of the wall. The Rock Island Railroadj in some track elevation work laid a line of tile drain along the back of the wall and carried the water through the abutment by a weeper running to a storm sewer. Mr. Lindenthal's high walls (see p. 753) were drained through weep holes, placed every ten feet, through each wall. From each weeper one 4 by 4-foot dry rubble chimney was built up back of the wall to the surface. The French wall described on page 753 is drained by a layer of loose stone over the entire back with weep holes placed at intervals. Frost. The depth of foundation must be sufficient to prevent heaving of the material in front of the wall, and to protect it from frost. A depth of 3 feet may be given as a minimum, while 4 or 5 feet is necessary in temperate or very cold climates. Even with the base safely below frost level, special precautions are sometimes necessary to prevent heaving by frost-grip on the side of the wall or abutment. Such a case cited by Edward H. RigbyJ was encountered in China where frost gripped the side of bridge abutments to a depth of 5 feet and Hfted them, railroad, girder bridges, and abut- ments, clear off the pile foundations. Piers and abutments with slop- ing faces were lifted as much as those with vertical faces. Computations showed the average lifting power of the frost to be i 000 pounds per square foot of exposed surface and that the remedy was to design the piers and bridges to overcome this force by dead weight. DESIGN OF RETAINING WALLS OF GRAVITY SECTION The thickness of gravity retaining walls is frequently determined by rule-of-thumb, but this is an unsafe procedure unless there is absolutely no doubt about the foundation. On work of any importance, much more economical results are obtained by special designs, governed by the character of the foundation soil and the earth backing. Partial failures, — tipping forward, cracking and sinking, — are prevalent among retaining walls. In one case a heavy gravity wall failed under the weight and impact of the backfilling dropped through a distance of 30 * Engineering Record, Jan. 3, 1914, p. 2g. ^Engineering News, April 8, 1915, p. 670. t Engineering News, March s, 1008, p. 260. DAMS AND RETAINING WALLS 7SS feet or 40 feet from a large drag line scraper bucket; and where the foundation is so poor that such action is possible, the line ofpressure should pass through the base well within the middle third. Uneven settlement is then less hkely to take place, and in any event the line of pressure has more chance to move without causing tension on the base or overturning than if the line passed through the forward edge of the middle third.* The methods of design are similar to those discussed in connection with reinforced walls. (See p. 757 to p. 768). If empirical rules are to be used, one easily remembered is to make the base three-eighths of the height. Another is to make the base at least the thickness necessary if the wall were to be subjected to water pressure under a head two-thirds the height of the wall.f A table of empirical values adopted by Mr. Trautwine for thickness of base of masonry walls to resist earth pressure is given below. Thickness of Retaining Walls of Gravity Section with Earth Surcharge. By John C. Trautwine. (See p. ^i^?) Ratio of Height of Earth to Height of Wall. Thickness of Base as ratio to Height of Wall. Ratio of Heigit of Earth to Height of Wall. Thickness of Base as ratio to Height of Wall. I . 0-35 •A . 0.58 I . I 0.42 2 5 0.60 , i. . -A 0.46 3 0. 62 1-3 1-4 0.49 0-5I 4 6 0.63 0. 64 1.6 0.52 0.54 9 14 0.65 0.66 1-7 1.8 °-S5 0. 56 25- or more 0.68 Designs according to these empirical methods are unsafe under unusual pressures, such as quicksands, and detailed analyses must be made. The height of the wall is assumed to be measured above the surface of the ground in front of it. The batter of the face of a retaining wall is customarily limited to 1 1 inches to the foot, and the back is usually vertical. This fixes the width on top. The values in the table may be employed for long walls of concrete with no reinforcement. In many cases, because of the monoUthic char- • Certain failures of this type are discussed by Charles K. Mohlcr in Eniinemns News, Oct. 13, igio, p. 384. t Suggested by Engimering News, Sept. 26, 1912, p. 593. 7s6 A TREATISE ON CONCRETE acter of concrete, a ratio of thickness to height from io% to 20% less may be adopted with safety, if the character of the filling back of the wall precludes excessive pressure, and if the base is slightly spread. For more accurate determinations of gravity sections, the principles which follow relating to reinforced designs are applicable. When two walls enclose a narrow fill they may be tied together by rods as dis- cussed on page 753 and thinner sections used. Similarly, the ordinary single wall may be anchored to the ground behind it. WEIGHT OF EARTH In the calculation of retaining walls, and many other structures, the weight of earth in place is a prime factor. The weights of dry material, based upon experiments by the authors, are represented in the following table. Most of the figures for weights of earth give the weights per cubic foot after excavation in a loose or a compacted condition. In the authors' experi- ments the excavation was measured, so that the weights represent the material in place. As fills will eventually assume much the same charac- teristics as earth in original excavation, the figures may be employed for either natural earth or filled material. The weight of earth containing water varies with the character of the material and with the conditions. Gravel containing ordinary moisture weighs about 2% more than dry gravel and sand may weigh from 3% to 10% more, depending upon its fineness, since fine sands absorb the most water. Wet muck weighs about 75 lb. per cubic foot. These percentages assume that the bank is provided with natural drainage; if the earth is fiterally filled with water which cannot run off, its weight will be increased by a quantity of water nearly equal in volume to the voids in the material, which vary with the character of the material from 20% to 50% of the bulk of the earth in the bank. Many of the values appear high, but they are the result of careful tests. Average Weight of Orditmry Earth before Excavation. Pounds per cu. ft. Sand 105 Gravel 135 Gravelly clay 130 Loam 90 Hard pan 130 Dry muck 40 BACKING Since the weight of soil saturated with water is much larger than when it is dry, the pressure increasing with the amount of water so that it may even DAMS AND RETAINING WALLS 757 exceed the hydrostatic pressure, the backing should be provided with adequate drainage. For this, a filling of gravel or crushed stone may be placed directly against the wall with weep holes at suitable distances apart. The question of drainage is discussed on page 753. EARTH PRESSURE The principal force governing the dimensions of any retaining wall is the earth pressure. Its magnitude varies largely with the character and wet- ness of the soil, the incKnation of the back of the wall, and the slope of earth above it. Of the numerous theories, all of which are based on some assumptions not always met with in practice, Rankine's theory seems to be the most reliable yet developed, and although it does not always represent the true conditions, it gives safe results. It is based upon the assumptions that the earth is com- posed of granular homogeneous particles without cohesion, held only by friction developed between them, and that the mass of earth extends indefinitely. On a vertical plane the resultant pressure always acts parallel to the slope of the earth and at a point one-third of the height from the base, when the surface of the earth is level with the top of the wall or slopes back from it. The following table of pressures determined by Rankine's formula gives horizontal earth pressures for different heights of wall, based on an angle of repose of earth of 7,5° — a fair assumption under average conditions — and also average unit pressures for the same assumptions. For other heights of wall, the horizontal unit pressures with the same angle of repose are directly proportional to the heights, and the total pressures are propor- tional to the squares of the height. Total Earth Pressure and Average Unit Pressure upon Vertical Walls of Dif- ferent Heights (See p. 757.) Height of' Wall in Feet. 5 10 IS 20 25 3° 35 40 Total pressure P, in lb 35° 1400 315° 5600 8750 12600 17150 22400 Average unit pressure in lb. per sq. ft 70 140 210 280 350 420 490 560 7S8 A TREATISE ON CONCRETE The table assumes (a) horizontal surface of earth, (6) vertical back of wall, (c) weight of earth per cubic foot, loo pounds, (d) angle of repose, 35". For other weights of earth the values in the table are proportional tc the weight per cubic foot. Passive pressure, that is, the resistance of a mass of earth against mov- ing, is many times as great as the active pressure but because of the shrink- age of filling as ordinarily placed it cannot be counted on for its full value unless the earth is in its natural state. The general formulas evolved by Mr. Rankine from the assumptions given above and which apply both to gravity walls and to reinforced walls, are presented below. Wall with Vertical Back. Let P = resultant earth pressure in pounds on a vertical surface for a length of wall equal to one foot. H = total height of wall in feet, i?! = depth below top of wall of any point in feet. h = height of surcharge in feet. w = weight of earth per cubic foot. S = angle of inclination of earth behind the wall. = angle of internal friction of the earth. Cp = constant depending upon d and SURCHARQE A ri s / ^ — \ ; _ f / * \ 'p \ ? \ \ \ \ / \ ■ P = wH' Cp - wh' Cp = h') Cp (6) and this may be represented by the trape- zoid aced (see Fig. 241). The distance of the point of appUcation of this force from below the middle point in the height of the wall, (H - hy X = 6 {H + h) (7) Fig. 241. — Earth Pressure on Vertical Back of Wall with Surcharge. (See p. 760,) Wall with Inclined Back with Sur- charge. For an inclined back, the pres- sure, as in the case of a wall with inclined back without surcharge, is the resultant of P, the pressure on the vertical projection of the wall found by formula (2) and W, the weight of the prism of earth one foot of length, tlie cross- section of which is a trapezoid. Equation (7) gives the vertical distance of the point of application of the resultant below the middle point in the height of the wall. DESIGN OF REINFORCED RETAINING WALLS A properly designed retaining wall, whether of reinforced concrete or of plain masonry, must fulfil the following conditions: It must be stable (i) against overturning, (2) against sliding, (3) against settling, (4) against crushing or overstressing of the material. DAMS AND RETAINING WALLS 761 To prevent failure by overturning, the moment of downward forces about the outer edge of the base, Mi = 1^1/1+ W^ h, must be greater than that of the overturning moment, M2 = PI3 (see Fig. 242). The ratio of those two moments, — -, is called the factor of safety. For reinforced concrete v/alls, M, the factor of 1.5 to 2 may be considered as ample, because the stability of wall is increased by the resistance of earth to shear along the line a6, Fig. 242, and the passive pressure of the filling in front of the wall, which two items are not considered in figuring the factor of safety. The horizontal component of the resultant pressure on the foundation causes the tendency of the wall to slide. This force is opposed by the resistance to compression of the earth on the plane dc (see Fig. 242) and by the friction F. The friction is equal to the vertical pressure multiplied by the tangent of friction between concrete and earth, or, if F = total friction, Wi + W2 = weight of concrete and earth,

    = 0.0045. Then the corresponding values from Table 17, page 598, * = -305, j = ■898- V V From page 534 u = — — hence d = . Substituting values, jdZo iijZo II 000 d = = 25.5 in., and total depth 27 in. 80 X 0.9 X 2.18 X 2.75 f / The depth of beam must be increased to 27 in. in order to decrease the bond stress to 80 lb. per sq. in. Smaller depth can be used with deformed bars of approved design. DAMS AND RETAINING WALLS 765 Right Cantilever. It is evident from Fig. 243, page 763, that three forces act on the right cantilever: the upward pressure of the soil, the down- ward weight of the earth filling, and the vertical component of the earth pressure. The resultant of these forces acts downward, hence the moment is negative. The computations for amount of steel and the shear and bond stresses Are similar to that for the left cantilever. The length of imbedment necessary to prevent slipping is not treated in the previous case, so it may be given here in detail. Area of concrete, A = 12 X 27 = 324 sq. in.; area of steel, A^ = 1.07 1 . 07 sq. m. and ratio of steel, p = = 0.0033. From table 15, p. 596 find 3 ^4 the corresponding k and /, k = .268, / = .911. From formula (7), p. 484, Since IVL = 329000 inch pounds, f. = = 12 500 pounds. 27 X .91 X 1.07 For this stress in steel, the length of imbedment from table on page 540 is 39 X i = 29 in. Both cantilevers may be tapered toward the end to a minimum practicable depth, since the moments decrease from the support to zero at the end. Horizontal Reinforcement for Temperature. Temperature reinforcement is treated on page 563. EXAMPLE OF RETAINING WALL WITH COUNTERFORTS Example 2. Design a reinforced concrete wall with counterforts to support a sand filUng 20 ft. high above ground, using same assumptions as in Exam- ple i, page 762. Solution. ' In this type of wall the vertical slab acts as a slab supported by the counterforts, the principal steel being horizontal. The projecting toe of the footing is a cantilever and the footing below the earth is a slab supported by the counterforts. The counterforts tie the imbedded footing to the ver- tical slab and act as cantilevers fixed to the footing. Design is shown in Fig. 244. P- 767- The slabs may be considered as partly continuous, using the moment M= — . If carefully designed for negative moment ilf =• — - might be 10 12 permissible. (See p. 496.) Instead of forming a projecting toe as a cantilever, it is sometimes more economical when the projection is large to introduce small buttresses and construct this part of the footing also as a partly continuous slab. The first step in operation of design is to determine by trial the length of base and the relation between the projecting toe and the base, the allowable pressure on the soil and minimum angle of inclination of the resultant earth pressure being the determining factors. The method is the same as for a T-type wall, as outlined on page 764. 766 A TREATISE ON CONCRETE Spacing of Counterforts. The spacing of counterforts or ribs may be found on the basis of minimum material*, from which 8 feet may be adopted. Vertical Wall. The vertical wall must be considered in narrow horizon- tal strips as slabs supported by the counterforts, partly continuous, and loaded uniformly. The earth pressure changes with the height, so that the pressure upon the different strips decreases from the bottom up. The pressure against the bottom strip as given on page 766 is 1480 lb. per sq. ft., or :23 , , toP ,, 123X64X12 lb. per ft. of width for i-inchof height. Using M = — , M = - = 9500 inch pounds per inch of width. Hence (p. 4S1) d = .118 ^9500 = n-S in.; thickness of wall is thus 13 in., and area of steel, A^ = 0.005 X n-S X 12 = 0.69 sq. in. per ft. of height. ' Round bars f in. diameter spaced si inches on centers may be used. For convenience in construction the thickness of the wall may be 'made uniform, and the spacing of rods increased with the decreasing earth pressure, as shown on the drawing. The negative bending moment may be provided for by introducing short rods in front of buttresses, or by bend- ing the rods. (p. 496.) ♦ For full discussion, see "The Design of Retaining Walls," by H. A; Petterson, Engineering Record, Vol. LVII, 1908, p. 777; for practical purposes the following demonstration illustrates the necessary steps. Use notation page 353, also let x = spacing of buttresses in feet; ^ = the maximum horizontal unit pressure on vertical wall, which occurs at the bottom of the wall. ^, from formula(3),page 758,15 1480 lb. per sq. ft. Taking a strip of the vertical slab one ft. in height, whose 148 X x'' X 12 span is the spacing of the counterforts, the bending moment is then M = = 1780^?^; the depth to steel, (p. 485), (i= .29 X.118 '\/i78o jf = 1.43^, and the volume per foot of '43* length of wall is X i X 22 = z.6x cu. ft. Maximum unit weight acting on horizontal footing 5 325 X 12 X a:' slab is 5 325 pounds per sq. ft. Hence M = , li = .29 X .118 \/5i^S ^ ^-^"^ z.-jix = 2.72^, and volume per foot of length of wall is X i X 8.25 = 1.9;^ The thickness below steel is a constant for any spacing and therefore need not be considered in fixing the volume. Assume the thickness of counterfort as 16 in., and volume will be — r, ~ '^' 2X12 121 cu. ft., and for one foot of length of wall, . Because of the greater cost, per unit of volume, of the counterforts over that of the slab work in a wall of this type, the quantity representufg the counterfort volume may be increased by, say, 100%. The expression for this quantity then becomes — Y, z. Hence total volume, 5. = 2.6x + i.i)x + — X 2 X 242 dS 2i2 „ . . .... , , Of O = ^,tx H and ~1~= 4*5 — — 2 — ™ ° U°'' minimum, first derivative equals zero_). X = Ji^: \ 4-5 = 7.3 ft. For practical purposes, say 8 ft. DAMS AND RETAINING WALLS 767 Horizontal Footing Slab. This slab may be con- sidered as composed of narrow strips uniformly loaded and supported by the counterforts. The loading is the difference between the weight cf the earth above it plus the vertical component of the earth pressure, and the upward pressure of the soil. As indicated in the drawing, this dif- ference is a maximum at a and decreases to- ward b. In this case the maximum unit 'load- ing is 5566 - 241=5325 lb. per sq.ft. The max- imum bending moment in this slab, considering it as partly continuous is ,. 5325 X 64 X 12 10 = 40 800 in. lb. Depth of steel, d = 0.29 X Fig. 244.- -Design of Retaining Wall with Coun- terforts. {See p. 765.) o.ii8-\/4o8oo = 2i.75in., hence thickness may be taken as 23.25 in. The area of concrete is then 261 sq. in., hence area of steel required is .4^ = 1. 31 sq. in., which is satisfied by J-in. bars spaced 5 J in. on centers. The thickness of this founda- tion slab may be made uniform, and the spacing of the rods increased as the loading decreases. The negative bending moment must be provided for by introducing at the top of the slab, under the counterforts, short rods of equal size and spac- ing to the bottom ones or else these bottom rods must be bent down at each counterfort. (See p. 496.) Counterforts. A counterfort is really an upright cantilever beam sup- ported by the horizontal foundation slab and carrying as its load the vertical slab of the wall, which, in turn, takes the earth pressure. The thickness of the counterfort, which must be sufficient to insure rigidity and resist unequal pressures during construction, may be selected by judgment. 768 A TREATISE ON CONCRETE To determine the quantity of steel required in the counterfort, we find the horizontal component of the earth pressure per foot of wall to be (from for- mula (2), p. 758) .41 X 22 X 22 X 100 X .819 = 16 200 lb.; hence, the total force transmitted to the counterfort, since they are spaced 8 ft., is 8 X 16 200 = 129 600 lb. Since the force acts at one-third the height, the bending moment is 22 M = 129 600 X — X 12 = II 400 000 in. lb. The thickness of the counter- 3 fort is taken at 16 in., the depth to steel, d = no in. From Formula (i), p. 481, C = — = */ — — ^ "° = 0,130. By interpolation in Table 16, on page 597, M * n 400 000 between items 3 and 4, the required ratio of steel, p = 0.00416 and area of steel ^s = no X 16 X .00416 = 7.36 sq. in. Six ij-in. round bars will satisfy this. The portion of the counterfort receiving the greatest tension is the inclined edge, so these bars are placed near to this surface. Besides these bars, horizontal and vertical bars are necessary to tie the vertical and horizontal slabs to the counterfort, to transfer the forces and provide for diagonal ten- sion. These bars should be bent into the slabs to obtain as good a bond as possible. The principal tension bars in the counterforts also must be well imbedded in the horizontal foundation slab, and bent so as to attain their full strength in tension. The value of hooking is discussed on page 438. COPINGS On many structures a coping is necessary and frequently it must be built separately from the main wall. Instead of stopping at the underside of the coping, the Delaware, Lackawanna, & Western R. R. has found it more economical and better workmanship to carry the main wall i| inches above the bottom of the coping, and after the concrete has set, to place the coping form tightly against the face of the wall* and pour the concrete. DAMS In dams the important requirements are strength and water-tightness, low cost, and speed in construction. Current practice, as indicated by the written opinions of engineers and by structures actually built, indi- cates that concrete on the whole fulfills these requirements better than any other material. While this is true of the standard gravity section, it is particularly true of thin arch dams, reinforced or plain, and of hollow reinforced dams, both of which have proved satisfactory. Under the present methods of concrete construction, stone masonry is nearly always more expensive than concrete or rubble concrete. In some cases where the cost of transporting cement from the nearest miU " Enginecrits Record, Aug. 19, ion, l>, 221. DAMS AND RETAINING WALLS 769 to the dam site has been prohibitive, instead of using masonry, it has been more economical to set up a mill and manufacture cement on the job. Sand-cement, for example, was used on the Lohantan, Nevada, dam* and hydraulic lime on the "Tiger Hill" damf in Mexico. The choice between plain and rubble concrete and, — if the latter is selected — the amount, of rubble to use, is governed by local conditions, and comparative estimates must be made in each case. Large stones save cement, crushing, and mixing, but placing them in the dam has become slow work compared to placing concrete by up-to-date methods, and frequently an independent plant must be used to place the rubble. In the Medina Valley dam| only 10% of rubble was used, as it was found that a larger percentage would have so delayed the progress of the work that interest and overhead charges would have outrun all saving in cement, crushing, and mixing. On the Las Vegas, New Mexico § dam bids were received for both concrete and rubble, and the concrete design proved cheaper. On the same type of dam built in Austraha,|| 30% of rubble was used. In the Shoshone dam1[ 25% of rubble was used. The dam at Boonton, N. J., a section of which is shown in Fig. 246, p. 772, contains 240 000 cubic yards of concrete rubble, and was built at a contract price, not including the cement, of $1.98 per cubic yard. Only 0.6 barrel Portland cement was used per cubic yard, although the proportions of the concrete matrix were i : 2j : 63:. This small quantity of cement was due to the large proportion of stones which averaged from one yard to 2I yards each and occupied 55% of the total volume. The contract price mentioned includes the preparation of the large stones and the crushed stone, and their transportation from a quarry three miles away. It is believed by the authors that the price and also the quantity of cement per cubic yard represent minimum figures in first-class construction, but the force account show^ed that the contractor was making a fair profit, and inspection of the work and its water-tightness prove that there was no skimping in the use of cement. On this particular job the quotation of the highest bidder was nearly double the accepted price. The concrete should be of soft mushy consistency and the large stones dropped onto it and joggled with bars in order to obtain proper * L. E. Sale in Engineering and Contracting, December 3, 1913, p. 623. t Guy S. Newkjrken, Engineering News, July 3, 1913, p. 19. t Terrell Bartlett in Engineering News, Sept. 11, 1913, p. soi. § Charles W. Sherman in Engineering News, October 27, 1910, p. 446. II L. A. B. Wade in Engineering News, May 19, 1910, p. 588. U H. N. Savage in Engineering News, December 9, 1909, p. 627 and June g, igio, p. 679. 770 A TREATISE ON CONCRETE imbedment. In the Boonton dam the consistency was about that of pea soup and the rubble stone was dropped with considerable force. Types of Dams. The standard dam section continues to be the gravity type, but the hollow, arch, and multiple arch* are gaining favor in situations particularly adapted to them. In some cases where a narrow rock gorge makes the arch design possible, a gravity section has been used and the dam arched to provide an additional factor of safety or to prevent cracking. In other cases, dams have been built arched with a partial gravity section where failure would result incase the arch action did not take place. There are, also, many dams in existence designed as arches, pure and simple, with very thin sections, and some not even reinforced. An arched damf at Crowley Creek, Boise, Idaho, 55 feet high, 5.2 feet wide at the base, and 3 feet wide at the top, was raised to a height of 90 feet with a base 9.2 feet and a crest 3.2 feet wide. No reinforcement was used. On the other hand, when the Sweetwater dam near San Diego, California, was enlarged,! it was changed from arch to gravity section because, as the addition was built with the reservoir filled, it was doubtful if the old and new parts could be made to act together as an arch. The Las Vegas dam required two-thirds the yardage that a gravity section would have taken. The hollow reinforced concrete dam§ reduces the quantity and cost of materials but permits a very broad base, and a sloping watertight deck upstream by means of which the water pressure is made to increase instead of oppose stability. An example of this type of dam — patented — is shown in Fig. 245, page 771. DESIGN OF DAMS Gravity Dams. Gravity dams must be constructed to withstand overturning and sliding caused by water pressure or by ice pressure on the upstream face; also, water pressure on the base and on the interior horizontal planes must be allowed for. To avoid tension in the foundation it is necessary that the resultant * A partial list of arch dams is given in Engineering Newst October 27, 1910, p, 517, and November 10, 1910, p. 520. other arch dams are described in Engineering and Contracting, May 20, 1914, p. 587 and 594, and Transactions American Society of Civil Engineers, Vol. LXXV, p. 112 and Vol. LXXVIII, pp. 564 and 685. Multiple arch dams are described in Engineering News, April 30, 1914, p. 962; April SS, 191S, p. 818; May 27, 1915, p. 1909; and October 28, 1915. t Engineering Record, June 20, 1914, p. C93. X The design and methods of construction are discussed by James D. Schuyler in Engineering Record, September 2, rgri, p. 264. § Four studies by Edward Wegman for such a hollow darti for Stony River are shown in Engineering News, September s, 1912, p. 446- DAMS AND Retaining walls 771 of all the forces of pressure and weight shall pass through the middle third of the base. Dangerous sliding need not usually be feared if the dam is designed to resist overturning. In considering the resistance of friction, Mr. Joseph P. Frizell* states that smooth stone slides on smooth stone under a horizontal force of two-thirds its weight, and to slide on gravel or clay, stone requires a force nearly equal to its weight. Max. H.W,EI.398 tv^rq ^^ Bar B4nt Up SK iSq.BarWlO'CC. Bent Over 2-4Bar5 ^^ ^'Sq.Bars Z4C.Z. Section A. A. 4ft.O ;; f:.i>:A Cut-off Grouted •ViiffiSee Trans. A.S.C.L.I9 15 Paqe 447 Fig. 245.— Section through Reinforced Concrete Dam at Estacada, Oregon. {See p. 770.) The pressure of the water upon any submerged surface is equal to the area of the surface in square feet, times the weight of a cubic foot of water, times the depth of the center of gravity of the surface below the water level. This pressure tends to overturn the dam, and is re- sisted by the weight of the dam, and in some cases, where the up- stream face slopes, by the weight of the water upon the dam. The treatment in Frizell's Water Power of the location of the center of pressure, and the moment produced by it, is especially clear and practical. Fig. 246 represents a section through the overflow of the rubble con- crete dam at Boonton, N. J., akeady referred to on page 769. The extreme height of the dam at the highest point above the foundations •Frizzell's, "Water Power," p. 19. 772 A TREATISE ON 'CONCRETE is no feet. An interesting practical test of the water-tightness of con- crete occurred when the reservoir was filled. A vertical well was left in the dam in order to provide access to two drainage gates, and although the water in the reservoir was loo feet deep, and was separated from the well by only 5 feet 6 inches of concrete mixed in the proportions I : 2} :6j, the well remained entirely dry. ELEVATION 3I0.25> = 47.90 FT. r3io 180 270 260 240 230 -220 -210 I-JOO Fig. 246. — Section through Overflow of Boonton, N. J., Dam. (See p. 772.) Upward Water Pressure. With a firm and impervious foundation, there is little likelihood of material upward pressure on the base, and with first-class construction horizontal joints may be made practically impervious. With permeable material or thin strata between which the water can penetrate upward, pressure is bound to occur and must be provided for in one of three ways: (i) making the dam heavy enough DAMS AND RETAINING WALLS 773 to overcome the upward pressure; (2) draining the foundation, and if necessary, the interior; and (3) making the pervious foundation im- pervious. The allowance for upward pressure varies not only with the struc- tural conditions but also with the possibility of property damage and loss of life in case of failure. In the Kensico dam for New York City a pressure of two-thirds the total head at the heel, and zero at the toe was assumed, and in spite of an interior drainage system, similar pres- sures were assumed on all interior construction joints. The few tests made indicate beyond all question that upward pressure does take place on the base of a dam if the foundation is poor. German tests* showed a pressure equivalent to the full head near the heel and one-half the full head near the toe. A valuable and complete account of laboratory and of field tests, both on a small scale and on fuU size structures, is given by Captain W. A. Mitchell in Professional Memoirs, U. S. Army, for January-February, 1915. Tests on adhesion, upward water pressure, and percolation, including original army tests and those described in literature, are summarized, conclusions drawn, and the application of the evidence to the design of dams is discussed. Under-drainage is economical and is accomplished by sinking a ciit- off wall near the heel of the dam, and draining off through drain tilej aU water that passes it. The hoUow dam may be built with no floor, thus providing the freest possible drainage once the seepage gets by the cut-off wall. During the construction of the Lost River Dam, in Oregon and Cali- fornia, one-half the weep holes under the floor became stopped. The floor bulged up under the upward pressure, falling as soon as the drain- age channels were put back in commission, t Interior drainage is provided in much the same way as under-drainage. In the Olive Bridge and the I&ensico§ dams, in New York, vertical pipes were used, while in the Loch Raven|| dam near Baltimore the drains were laid horizontal. Grouting is extensively employed in improving poor foundations. Seamy, porous rock, limestone full of cavities, and sand and gravel beds may be made reasonably tight by sinking drill holes and pumping in * C. R. Weidner in Engineering News, July 31, 1913, p. 202. t Engineering Record, September 14, 1912, p. 2S4; Engineering and Contracting, February 17, igis, p. ISO. ISO- t W. W. Patch in Engineering News, April 30, 1514, p. g68. I Alfred D. Flinn in Engineering News, Apr. 15, 1912, p. 772 II Engineering and Contracting, Feb. 17, 191S, p. I75. 774 A TREATISE ON CONCRETE grout under pressures of about loo pounds. The Lahontan dam site* in Eastern California for example, was treated in this way. Ice Pressure. Ice pressure depends not, only on climate, but also on the shape of the storage basin. In a narrow gorge where the ice cannot expand up the banks, it sometimes exerts large pressure on the dam. In a dam near Minneapolis this caused complete failure, and in a second case failure was narrowly averted by cutting the ice away from the dam face. In the Kensico Dam, an ice pressure > allowance of 23.5 tons per linear foot was made. In wing walls, particularly, provision must be made in northern climates, not only for ice pressure, but in connection with small dams, for the possibihty of tipping as the pond rises under the ice. Flash Boards. Flash boards for an arch dam may be designed to eliminate arch action in the boards themselves by making the boards long enough and placing them so that the ends, instead of butting, overlap. Movable dam crestsf are sometimes necessary. Durability. Concrete in dams has proved as durable as any other material. The destructive agencies are abrasive material in the water flowing over the dam, certain chemicals in the water adjacent to or seep- ing through the dam, and frost action. Large quantities of hard sand and gravel flowing over the dam wear away the concrete face, and measurements have shown that half an inch has been lost in this way in a comparatively few years. The amount, however, is a very small proportion of any dam and does not affect the stability. An allowance should be made, however, in design- ing dams with thin sections and in protecting reinforcing bars with a, sufficient thickness of concrete. CORE WALLS Concrete is largely superseding rubble masonry for core walls in earth dams and dikes. The forms can be roughly made without reference to the appearance of the faces, while a thin wall of concrete may be built water-tight more easily than one of rubble masonry. Unless reinforced, core walls are generally of the same thickness as those of rubble masonry. The Natural cement concrete core wall of the Sudbury Dam, buih by the Boston Water Commissioner and his successor upon the work, the Metro- politan Water Board of Massachusetts, is 2 feet thick at the top, with a batter *D. W. Cole in Engineering Record, March 29, 1913, p. 340. t Ernest W. Schroder in Engineering News, October 27, 1910, p. 517. t W. L. Marshall in Engineering News, June 4, 1914, p. 1264. DAMS AND RETAINING WALLS 775 of one in fifteen on both faces, until it reaches a maximum width of 10 feet. At Spot Pond Reservoir, several dikes with core walls of Portland cement concrete, of 15 to 18 feet average height, are aj feet in thickness throughout. The dike for the Jersey City Water Supply Company at Boonton, N. J., is designed for a total height of 54 feet. The lower 30 feet is 4 feet 8 inches thick, and at this height it begins to batter, so as to reach a width of 3 feet at the top. Although core walls may often be economically built of rubble concrete, the stones must be of smaller size, and cannot occupy so large a volume of the mass as in gravity dams, since the sections are thinner. In the construc- tion of the Boonton Dike, mentioned above, one contractor was placing rub- ble to the extent of 20% of the total mass, while another was placing 33%. In the former case the stones were loaded on to derrick skips and unloaded by hand; in the latter case, they were hooked by the derrick. This 33% probably represents a maximum for a wall 5 feet thick or less. Since a thin wall of reinforced concrete may be made equally strong, and more elastic than a thick wall of plain concrete, reinforcement may event- ually be employed to reduce the section, and therefore the quantity of material. TEMPERATURE CHANGES IN CONCRETE DAMS The temperature variations in concrete dams, due to chemical action of the cement in setting and to atmospheric temperature changes, are important as effecting the expansion and contraction. Investigations have been made in the Boonton, N. J., dam, the Panama Canal locks,* the Arrowrock damf in Idaho, and the Kensico damj in New York. The results thus far obtained indicate that the temperature rise caused by the heat of setting is governed by the richness of the concrete and by the opportunities for radiation while the heat is being generated. Radiation is greatest in small dams and in large dams built in relatively thin layers where each layer partially sets before another is added. The seasonal temperature changes, after setting heat is dissipated, are governed by the atmospheric temperature changes and by the dimen- sions of the dam. The method of making the observations has an important effect on the results; thus at Arrowrock the concrete in which the thermometer was buried was placed slowly, in layers, allowing considerable radiation, while at Kensico the reverse was the case. * igio Report, Isthmian Canal Commission, p. 122, t Trans. American Society of Civil Engineers, Vol. LXXIX, 1915, p. 1225. t American Society of Civil Engineers, Vol. LXXIX, 1915, p. 1247. 776 A TREATISE ON CONCRETE Setting Heat. The rapid rise in temperature due to chemical changes reaches a maximum in a few days or a few weeks after the concrete is placed and lasts for one or more years. Observations indicate in a general way that the total rise above the temperature of the air during concreting is from 25" to 40° Fahr. and that this maximum is apt to be attained in the first week, or at the most, the first month. The obser- vations on the Boonton dam, which is 94 ft. high by 55 ft. wide at the base, and made with a lean 1:3:7 mix, showed the maximum tempera- ture at 24 hours with a gradually decreasing temperature up to about a year. The Arrowrock dam, 315 ft. high by 215 ft. wide at the base, built with a richer r: 2J: 5 mix, showed that the concrete 20 ft. or more from the face is affected by the setting heat for several years, that near the center for as much as five years. The investigations at the Kenisco dam, which is nearly as rich as the Arrowrock, were more exhaustive than the others, but substantially confirmed the results indicated. In these investigations the variation in rise was shown to depend in a measure upon the richness of the concrete. The maximum tempera- ture was reached at a period varying from five to ninety-five days. Eifect of Atmospheric -Changes. Observations on the effect of sea- sonal atmospheric changes are complicated by setting heat for one or more years after the dam is built. The temperature of the concrete varies much less than that of the atmosphere. For example, in the Arrowrock dam, with a daily atmospheric variation of 50° Fahr., the variation in the temperature of the concrete one foot from the face was only 2° Fahr. ; the seasonal changes, on the other hand, produce appreci- able effects. In the Arrowrock dam, with a seasonal change of 75° Fahr., the temperature of the concrete 3I ft., 10 ft., and 20 ft. from the nearest face was 32°, 12°, and 0° Fahr. respectively. The Boonton dam observations indicated that the seasonal range in temperature of the concrete varied with the seasonal range in the temperature of the air, and with the distance from the dam face, in accordance with the formula r R = 3 Fig. 248.- -Typical Section of Jersey City Water Supply Conduit in Loose Earth. {See p. 783.) Strength tests. Strength tests of pre-cast pipe are of value in insur- ing the uniform quaUty of the product. A simple but efficient machine for this purpose is described by Prof. Arthur N. Talbot and D . A. Abrams in the Proceedings of the National Association of Cement Users, 191 2, Vol. VII, page 713. Results are also given of tests on concrete and clay drain tile. Tests were made in Philadelphia* by A. T. Goldbeck to determine the best method of curing and bedding concrete pipe. Egg-shaped, 36 by 24 inches, and 36-inch circular pipe bore larger loads with less * A. T. Goldbeck in Journal American Concrete Institute, May igis, p. 240. CONDUITS AND TUNNELS 785 deflection and cracking when bedded in concrete than when bedded in loose sand. Keeping the pipe thoroughly wet for two weeks increases its strength. An excellent discussion of the loads on pipes laid in trenches and the necessity for bedding is given in Bulletin 31, Iowa State College of Agriculture, "The Theory of Loads on Pipes in Ditches and Tests of Cement and Clay Drain Tiles and Sewer Pipe" by A. Marston and A. O. Anderson, 1913. Methods of Conduit Construction. There are four general methods of construction of concrete conduits: (i) The lower portion of the invert is laid by template and the remainder of the circle by centering. (2) The invert is formed by an inverted center, and the arch by an upright center. (3) A center the size of the entire sewer, but with a removable bottom, is placed, the sides and arch are built, and then the bottom of the center is removed, and the invert is laid. (4) The entire sewer is formed as a monoHth. The size of the sewer and the character of the work influences the choice of method. If the invert is to have a brick Uning or a granolithic finish, after excavating the material to the required grade and shape, profiles or templates are placed in advance of the finished concrete, and the surface is formed with the aid of a straight-edge placed longitudinally from the finished concrete to the nearest template. If the sides run up sharply, as in a Small sewer, the concrete may be held in place by strips of lagging, 2-inch by 2-inch for a very small sewer, or wider for a larger size. This lagging rests at one end on the finished concrete, and at the other end on the template, and is placed as the work progresses. In horseshoe sewers the invert may be shaped with templates and straight-edge, and the side walls laid back of plank forms. In a large conduit the smoothest and best wearing surface is obtained by laying a comparatively narrow strip of invert by means of profiles or templets and straight-edge, and troweling it< If desired, a granolithic (or mortar) finish may be given, but with thorough troweling, excellent results are secured with concrete. The arch center, which in such cases must be nearly a complete cyhnder, is placed after the strip of invert concrete has set, mortar is spread on the edges of the invert strip already laid, and the circle is completed with fresh concrete. A longitudinal groove also assists in forming a tight joint. To avoid this joint, a plan similar to that just described has been followed, except that the form, which is a complete cylindeir, open at the bottom, is placed, before laying any concrete, upon concrete blocks 786 A TREATISE ON CONCRETE previously prepared in molds and then laid in the bottom of the trench, The lowest strip of invert is not laid until after the sides and arch are in place, the concrete for it being let down through holes left in the crown for the purpose, and troweled as thoroughly as the obstructions of the forms will permit. It would at first appear that the sewer could more readily be made monolithic by placing a complete cylinder and pouring concrete around it for the invert arch. The objection to this, however, is the great difficulty in placing the concrete in the extreme bottom, and also the tendency of the center to "float" from the upward pressure of the concrete This difficulty is also encountered to a less extent in the method described in the preceding paragraph. In a sewer whose invert and arch are constructed separately, the arch centers are made and placed as for brick, except that a smoother and tighter surface is necessary, and the forms are oiled to prevent adhesion. A covering of sheet metal has often been successfully used. In order to lay the concrete of the arch sufficiently wet to obtain a smooth surface, an outside set of forms, open at the crown, is usually essential. Methods of Construction and Forms. The field is specially fruitful in conduit work for getting low unit costs by planning the work to avoid lost time. Progress along this line has been largest in the erec- tion of buildings* but the opportunities are equally good or better in building conduits because of the comparative simplicity of the work and consequent ease in systematizing. Standardization of forms and construction should be carried out as far as possible. In the building of the Los Angeles Aqueductf stand- ards were worked out from experience as the work progressed. The work also was planned for a maximum efficiency of men and plant. Some parts of the work were done by task and bonus. { Many difficulties were encountered and solved in building the Cats- kill Aqueduct and the 17-foot circular conduit at Kensico§, built in monohthic sections for a 29-foot head of water is specially interesting. Forms and reinforcement were placed before pouring. Proper placing and ramming of the concrete at first appeared impossible but improve- ments, in the forms eventually remedied the trouble. The circular reinforcement was very heavy and it was necessary to bend it to a •See paper on "Construction Management" by William O. Lichtner, in Journal Western Society of Engineers, also " Concrete Costs," by Taylor- & Thompson. t Engineering Record, January 6, 1912, p. 6. t- Engineering Record, January 12, 1912, p. 72. J Heno' \y; Nelson in Engineering Record, May 3, 1913, p. 502 and G. T. Seabury in Engineering Record, September 5, 1914, p. 277. CONDUITS AND TUNNELS f&7 template altogether different from the final shape taken by the rods when suspended with no bottom support inside the forms. On another section of the Catskill Aqueduct the steel forms, horse- shoe in shape, bulged near the invert* under the heavy pressure of con- crete and were skillfully trussed without interfering with the working space. i'ig. 249. Center for Invert of 30-inch Sewer at Medford, Mass. (See p. 787.) A good design for a collapsible formf of wood covered with gal- vanized sheet steel was used by the New York Board of Water Supply on circular conduits running from 2 feet 6 inches to 7 feet 8 inches in diameter. A collapsible steel formj for medium sized sewers 6 feet by 8 feet was employed. The forms for the Catskill Aqueduct are well described- in a paper§ by Alfred D. Flinn. Invert centers for a small sewer, designed by Mr, William G. Taylor •Arnold Becker in Engineering Record, November 25, 1911, p. 617. ^Engineering Record, October 3, 1914, p. 370. X Engineering News, March 11, 191s, P' 494- § "Concrete Forms -for. the XTatskiH-Aqueduet," Jourftal American- GoficretC' Institute, June, 1915. 788 A TREATISE ON CONCRETE and employed in the Medford, Massachusetts, sewers, are illustrated in Fig. 249 page 787. A similar form* with a top segment, completing the circle was used at Hartford, Conn. Pre-cast concrete pipe built in factories or on the job are economically used for both pressure and gravity conduits. TUNNELS Tunnels differ from sewer and water conduits chiefly in size and in being designed for heavier internal and external loads. The construc- tion methods differ in so much as they are adapted to underground work and to the larger scale on which the work is done. Structures, how- ever, such as are involved in the water or sewer conduits built by Los Angeles, New York, and Baltimore, and other cities, differ very Uttle from heavy railway tunnels either in design or construction. In some cases water-tightness is essential, but in the majority of railway tunnels the drift is through dry materials and the ballast may be laid directly upon the bottom. The most important developments in connection with the use of con- crete in tunnels have been due to a better knowledge of the prope^rties of materials resulting in greater attention id details and to a greater efficiency in construction plant and methods. Tunnel Design. The principles of tunnel design are the same as have been discussed for conduits. For double track railroad tunnels the quantities of concrete and steel can be cut down by using a center wall or center column. Where tunnels must be waterproofed various methods (see p. 296) are used, but grouting back of the walls through pipes placed with the concrete is exceedingly effective. With careful construction dense con- crete with very few temperature and shrinkage cracks can be secured and those that do occur, together with any local defects, can be grouted. About 90% of the leakage in the New York Aqueduct City Tunnel was stopped in this way.f Interior dramage is usually provided for by channels in the invert leading to the tunnel exit or to pump wells. Construction Methods. The chief improvements in tunneling con- struction has been due to a better knowledge of materials and to better forms and more highly, developed plants. Materials for important work, should be graded to insure the maxi- * Engineering and Contracting, July 7, igog, p. 7. t Walter E. Spear in Engineering News, February 4, 1915, p. 194. CONDUITS AND TUNNELS 789 mum density, and the work planned so as to construct as large mono- lithic sections as possible. Special precautions were taken on the New York Aqueduct to protect the green concrete from flow of water. Large leaks were grouted but small leakage was taken care of by placing large or small drip pans as needed outside the concrete to catch the water. These pans were eventually grouted. The length of tunnel lining to be placed at once is limited on one hand by the speed with which concrete can be delivered to the forms and on the other by the necessity of keeping construction joints as few as possible. A discussion of the problem as it was solved on the New York Aqueduct City Tunnel is given in fuU by Walter E. Spear in Engineering News, February 4, 191S, p. 194. Steel forms designed for local conditions have proved economical and satisfactory. Tunnel forms must be rigid, easily braced, without trespassing on the working space in the center of the tunnel, and at the same time easy to take down, move, and set up. These requirements necessitate new designs for every job.* The mixer and storage bins in large and deep tunnels are often placed near the bottom of a shaft, although usually just outside the portal. Concrete is generally carried to place in cars and poured into the forms from two levels. The invert, if there is one, is built from the lower level. From the upper level, concrete is shoveled or poured directly into the side wall forms and shoveled into the arch form overhead, t The pneumatic method (see p. 253) of mixing and transporting, or of transporting only, has been used to advantage in tunnel work.t Concrete has been carried by compressed air to heights of 80 feet and to horizontal distances of 450 feet. A labor saving device § for placing the key was developed on the New York City Aqueduct. A steel box is filled with concrete and clamped to the forms; the bottom of the box is then pushed up like a piston flush Vvdth the arch forms by means of a screw. SUBWAYS Subways are technically distinguished from tunnels as constructions in open-cut instead of drift, although portions of a subway often are • The fonns used in the Catskill Aqueduct tunnels are described in the Journal American Concrete Institute, June 191S, p. 291. This article is of special interest because it describes the development of the forms from the early failures to the types finally successful. t An excellent discussion of this type of construction is given by Walter E. Spear in Engineering News, February 4, 1915, p. 194, in an article describing the New York City Aqueduct Tunnel. X Engineering News, October 29, 1914. P- 880; August 10, 1911, p. 172; July 31, 1913, p. 208; and February 18, 1915, p. 314 and Engineering Record, October 11, 1913, p. 404. i Engineering News, February 4, igis, p. 194. 790 A TREATISE ON CONCRETE really of tunnel construction. The term subway is applied to access- ible conduits for water mains, electric cables, etc., as well as to under- ground passages for traffic, but it will be considered here in the latter sense only. Design. Subway design is governed almost entirely by local condi- tions. Reinforced concrete is usually better adapted than any other material to such work so far as cost and convenience are concerned. However, in the New York subways steel framing with concrete jack arches has been found more practical because of the heavy street traffic that can be readily transferred from the timbering to the steel girders and columns. Instead of an arched structure wide enough to carry all tracks in a single barrel, the relative cost of concrete and excavation usually makes it economical to flatten the arch, saving headroom, and to widen the structure enough to put in a center wall or center columns. The separation of tracks by center walls is also an aid in securing venti- lation. Construction'. Subway construction does not differ materially from ordinary conduit or tunnel construction so far as the concrete work is concerned. For references to articles describing subways, see Chapter XXXIII. RESERVOIRS AND TANKS 791 CHAPTER XXIX RESERVOIRS AND TANKS Concrete has become a standard material for reservoirs and tanks both for water and chemicals. The results from the point of view of water-tightness, durabihty, economy, and freedom from vegetable growth, are exceedingly satisfactory. OPEN RESERVOIRS The walls of large open reservoirs usually are built as retaining walls (see Chapter XXVII, p. 751, for methods of design), but under many conditions concrete slabs supported by banks of earth or but- tresses of concrete* are economical. The bottoms are built of large rectangular slabs reinforced or not, according to the foundation. From 4 to 8 inches of i : 2 : 4 or i : sf : 5 concrete is satisfactory, and if prop- erly laid and troweled is sufficiently impervious provided the joints are taken care of. Various expedients are employed in making reservoirs water-tight. Expansion and contraction joints are best filled with asphalt mixed with limestone dust or sand.f Such joints must be supported or backed up by concrete or mortar to prevent the water pressure forcing out^the asphalt.J In securing adhesion between concrete and asphalt, it has been found necessary to paint the concrete with hot coal tar. The membrane method and the appHcation of an interior layer of mortar has also proved successful. The chief reliance in making the concrete water- tight should be in the quahty of the concrete itself, — by selection and grading of the aggregates, and care in placing, it should be sufficiently tight for all practical purposes. (See. p. 296.) For certain exceptional cases the membrane method is necessary. Construction joints are discussed on pages 259 to 260 and 795. In small reservoirs where earth and rock meet in the foundation,, presenting a danger of unequal settlement and consequent serious leak- age, steel reinforcement may be placed over the line of division, even if used nowhere else. To be effective, the cross-section of the steel must ♦Alexander Potter in Engineering Record, Nov. 29, 1913, p. 616. t C. R. Sessions in Engineering and Contracting, Mar. 11, 1914, p. 304. t Such a failure and the repairs necessary are described in Engineering Record, Apr. 4. 1914, p. -398. 792 A TREATISE ON CONCRETE be large enough to actually add strength; chicken wire or other mesh of small wire is useless. COVERED RESERVOIRS The usual type of covered reservoir consists of a concrete floor, reinforced or gravity walls, and a concrete roof supported by piers and covered with earth to a depth of 2 or 3 feet. Reservoir Floors. The floor should be smooth, fairly impervious, and strong enough to resist the upward water pressure from the under- lying soil when the reservoir is empty. A thickness of 4 to 6 inches, p \ \ ■ -"i - '■* ST g ^4r \ -jj lull 1 1 HWWKfci Mf^ I'm -^ Itetote^j-^*^ 1 ■Blj^i^V-v^ j^^ !^»^. ' -^ f^BRSS?^ vl Hfe'.^... . ^ s^^ HhHI ^Efi ^K^SBIm^^iBm.M^:^ ■ -■^ iH pBH^^^I Fig. 250. — Reservoir Floor. (See p. 793.) depending upon the character of the underlying material and the head of water, is sufficient. Inverted groined arches are frequently used, the greater thickness at the piers providing footings to distribute the pressure, while the lower areas between footings form channels for the flow of water. The groined arches are laid in alternate diamonds before the piers are built, so that each pier rests upon the comers of four diamonds.* A granolithic surface may be placed before the concrete is set, as in sidewalk con- struction or preferably the concrete itself may be troweled. The * See paper by Allen Hazen, Transactions American Society Civil Engineers, Vol. XLIII, p. 262. RESERVOIRS AND TANKS 793 joints between blocks must be made water-tight. In the Albany plant the 6-inch floor was underlaid with 16 inches of clay and gravel puddle, and joints between the blocks, 3 inches deep and | inch wide, were filled with asphalt. (See Fig. 250, page 792.) A floor of reinforced concrete, designed to take the loads from the piers, and the upward pressure, requires fewer joints, is more hkely to be water-tight, and requires less expensive treatment of the foundation. A comparison of the cost of the two types should be made for any reservoir. Reservoir Walls. The walls may be designed as supported at the bottom by the floor and at the top by the roof, thus saving material over the ordinary retaining wall type. Buttresses, or rather, vertical beams supporting the reinforced wall slab, will transfer the pressure to the floor and roof. Joints in the walls must be thoroughly reinforced or designed as contraction joints with suitable waterproofed connections. (See p. 259.) In long walls a certain amount of cracking from tem- perature is almost unavoidable, but this is minimized after the reser- voir is completed and the range in temperature reduced. Reservoir Piers. Pieis should be designed as columns (see p. 559) with suitable reinforcement, not less in amount than a f-inch bar in each comer. The bars also assist in taking unbalanced thrust from the roof. A compressive stress of 375 pounds per square inch may be allowed safely when the concrete is in proportions i: 2^ : 5. Provision for distributing the load from the roof to the soil must be made by the groined arch floor, independent footings, or special design of the slab floor. Reservoir Roofs. Groined elliptic arches* have been used to a large extent for roofs to distribute the weight of the concrete and the earth to the piers. Mr. Leonard Metcalf has compiled a tablef of data relating to reser- voirs in the United States covered with groined arches, which shows a range in span of arch from 10 feet 6 inches to 16 feet, a rise varying from one foot 6 inches to 4 feet, and a thickness at crown, in all cases but one, of 6 inches. The proportions of the concrete range from i: 2|:4 to 1:3:5. More recently the economy of groined arches has been surpassed by * See paper on Groined Arch Construction by Thomas H. Wiggin, Proceedings National Associa- tion of Cement Users, Vol. VI, igio, p. 216, and Frank H. Carter in Engineering Record, Sept. s, 1014, p. 26s. t See Report of Annual Convention of the New England Water Works Association, igo3, Bnjinwf- ing News, Sei/tember, 1903, p. 238. 794 A TREATISE ON CONCRETE flat slab construction, one of the first of this type being the roof of the reservoir at Webster, Mass., designed by Mr. Thompson for Mr. Frank L. Fuller in 1914. ♦ For small circular reservoirs a dome roof may be used. To resist the thrust, rings of steel must be inserted in the circumference, of amount and size determined by computations. STANDPIPES Water-tightness is a requisite in the design and construction of stor- age reservoir tanks buUt as standpipes entirely above ground if the structure is not to become unsightly. Up to the present time this re- quirement has not been met with entire success in tanks under high heads although reasonable satisfaction has been obtained. The con- -aLs 3"x3"x4:" vl^SO d. d CU. yd. i u bbl. cu. yd. i cu. yd. d V E U bbl. cu. yd. d & bbl. d w cu. yd. d i u bbl. 0] cu. yd. 2| 3 3i 4 4 .5 i.ofi 1.27 1.46 1.68 I. go 2.13 0.40 0.47 0-54 0.62 0. 70 o.yg 0.79 0.94 1.08 1.24 1. 41 1.58 0.90 1.08 1.24 1-43 1 .62 1.82 0.41 0.48 o-SS 0.64 0. 72 0.80 0.81 0.96 1. 10 1.28 1.44 I .60 0.80 1-23 1.66 2.09 2-53 3-32 0. 12 0. 19 0. 2<1 0.31 0-37 0:50 0.64 0.98 1.32 1.66 2.00 2.64 0. 14 0. 22 0.30 °-37 0.44 0.58 0-53 0.81 1 .09 1.38 1.66 2.19 0.24 0.32 0.41 0.50 0.6s Note. — Select and add together the quantities of each material corresponding to the required thicknes and proportions of base and wearing surface. 8i2 A TRFATISE ON CONCRETE sand are measured loose by shoveling into boxes or barrels, on the basis of the volume of a cement barrel of 4.0 cubic feet. For example, proportions 1:3:6 are equivalent to i barrel Portland cement, 12 cu. ft. of sand and 24 cu. ft. of broken stone or gravel, while proportions 1:2 are equivalent to i barrel of Portland cement to 8.0 cu. ft., or one bag of Portland cement to 2.0 cu. ft. of sand or crushed stone. The variation in volume of mortar produced with sand and crushed stone of different fineness may affect the quantities for wearing surface by at least 10%, but to provide for such variation, and to allow for waste, 10% has been added, in computing the values, to the quanti- ties in the table on page 214. Since the volumes are given separately for the base and wearing surface, the quantities required for walks of other thicknesses rriay be readily esti- mated, as illustrated in the following example: Example: — What materials will be required for a walk 8 ft. in width and 150 ft. long, the base to be 3 in. thick, of concrete in proportions 1:3:6, and the wearing surface one inch thick, in proportions i part cement to I part sand? Solution: — Referring to the table we find directly that for 100 sq. ft. of base 3 in. thick, 1.08 bbl. Portland cement, 0.48 cu. yd. sand, and 0.96 cu. yd. broken stone or gravel are required. Similarly, for 100 sq. ft. of the wearing surface one inch thick we should require 1.66 bbl. cement and 0.24 cu. yd. sand. For each 100 sq. ft. of completed walk there would therefore be needed 2.74 bbl. cement, 0.72 cu. yd. sand, and 0.96 cu. yd. broken stone or gravel; and since there are i 200 sq. ft. in an area of 150 by 8 ft., for both base and wearing surface we should require 33 bbl. Portland cement, 9 cu. yd. sand, and 12 cu. yd. broken stone or gravel. CEMENJ- MANUFACTURE 813 ( CHAPTER XXXI CEMENT MANUFACTURE This chapter contains a short historical sketch followed by a brief out- line of the processes of modern cement manufacture, illustrated with views of typical machinery. HISTORICAL Lime must have been used by the Egyptians thousands of years before Christ, as the stones in the pyramids apparently were laid in mortar of common lime and sand. It is even thought by some that these ancients understood the principle of mixing lime and clay together to make a real cement. Concrete was made by the Romans as early as several centuries before Christ. For most of their work, they used lime mixed with sand and stone, but understanding the value of puzzolana or volcanic ashes to render lime hydraulic, they employed these two materials in combination with the sand and stone for marine construction. For less important work, they often mixed lime and coarsely powdered brick with the aggregate. Vitru- vius, writing in the first century, describes methods of making concrete with lime alone, and also gives as the formula for making it of slaked lime and Italian puzzolana: 12 parts of puzzolana, well pulverized. 6 parts of quartz sand, well washed. 9 parts of rich lime, recently slaked; to which is added 6 parts or fragments of broken stone, porous and angular, when intended for a "pise" or a filling in. It is interesting to note that the Romans caUed their concrete made from these materials "opus caementum," literally, "chip- work," and that the word "cement," derived from the aggregate, has in our day been transferred to the hydraulic binding material. In the Middle Ages concrete was employed, after the Roman fashion, for both walls and foundations. In the former it was generally laid as a core faced with stone masonry. Large stones were often imbedded in the mass. The fact that clay contained in certain limes rendered them hydraulic was discovered by John Smeaton, when studying the designs for the third 8i4 A TREATISE ON CONCRETE Eddystone Lighthouse, about 1750. Early in the following century, Vicat, by his extended scientific researches in France, earned for himself the name of the founder of hydraulic chemistry. In England, in 1796, James Parker made from nodules of argillaceous limestone, calcined and ground, what he called Roman cement. This process he patented, and from it the Natural cement industry was developed. It was Joseph Aspdin, of Leeds, England; who really invented Portland cement by discovering in 1824 that an artificial mixture of slaked lime and clay, highly calcined, formed a hydraulic product. On account of its resemblance in color and hardness to the Portland stone which was much used in England at that time, he called his invention Portland cement. Two patents had been granted in England a few years before his time, but as in these the materials were not heated to vitrification, hydraulic hme instead of cement was produced. The Portland cement industry was not developed to any great extent until about twenty years after Aspdin's discovery, when J. B. White & Sons in Kent, England, commenced its manufacture. Later, Mr. John Grant gave a great impetus to Portland cement manufacture by experi- mental studies upon the practical action of cements, mortars and concretes under varied conditions. The results of his tests he presented to the In- stitution of Civil Engineers in 1866, 1871, and 1880. The first manufactory for producing Portland cement in France was established toward the middle of the last century at Boulogne-sur-Mer. In Germany the first factory was erected soon after this, for the production of the Stettin Portland cement, and with such successful results that in 1900 Germany produced more Portland cement than any other country. The discovery in the United States of a rock suitable for Natural cement was made in 1818 by Canvass White, an engineer connected with the construction of the Erie Canal, and Natural cement was made in Madison and Onondaga Co., N. Y., in that year. The first Natural cement in the Rosendale district was made at Rosendale, Ulster Co., N. Y., about 1823. Mr. D. O. Saylor was the founder of the Portland cement industr}- in the United States. His discoveries were made in the Lehigh Valley. He experimented from 1871 to 1875 and marketed cement in 1875. PRODUCTION OF CEMENT The total production-* of hydrauUc cement in the United States for 1914 was 89 049 766 barrels, of which 88 230 170 barrels were Port- land cement, 751 285 barrels were Natural 9ement, and 68 311 * Mineral Resources of the United States, 1914. CEMENT MANUFACTURE 8iS barrels were Puzzolan or Slag cement. The average values per barrel were: for Portland cement $0.927, for Natural $0.468, and for Puzzolan $0,926. The superior quality of Portland over Natural cement and the increasing economy of its manufacture is evinced by a comparison of these figures with those of 1890, when only 335 500 barrels of Portland cement were produced against 7 082 204 barrels of Natural cement. The imports of cement in 1890 were i 940 186 barrels, and in 1908, 842 121 barrels. The production of Portland cement in the United States by individual States is represented in the following table. Production of Portland Cement in the United States in igio and 1914 by States. State. igoo 1914 Producing Plants. Quantity, barrels. Value. Producing Plants. Quantity, barrels. Value. Peimsylvania 14 I I 3 2 6 I 8 6 2 I I I I I I 4 984 417 30 000 80 000 240 442 I i6g 212 664 750 44 565 465 832 534 215 26 000 38 000 35 70S 70 000 S8 479 40 000 400 4 984 417 37 500 100 000 300 552 I 169 212 830 940 89 130 582 290 667 769 52 000 76 000 71 416 175 000 73 099 70 000 I 200 20 S 9 S 3 II 5 7 5 8 5 3 3 17 26 S70 151 9 595 923 3 431 142 5 401 005 3 674 800 4 28s 34S 4 723 906 5 075 114 2 017 344 S 886 124 1 962 047 4 233 707 9S1 100 8 291 521 $24 630 529 Kansas 3 180 669 5 007 288 3 972 515 Washington I 870 078 New York..- 5 456 437 I 818 817 3 924 646 Texas South Dakota Utah Massachusetts Georgia* North Dakota Other States! 7 686 240 50 8 48 2 020 9 280 525 no 88 230 170 81 789 368 * Product in igoo combined with Virginia, t Product in 1900 combined witii Missouri. ^ X Alabama, Arizona, Colorado, Georgia, Kentucky, Maryland, Montana, Nebraska, Oklahoma, Tennessee, Virginia, and West Virginia. About 36% of the total production in 1914 was in the Lehigh Valley of Pennsylvania and New Jersey. In 1900 73% came from that district. PORTLAND CEMENT MANUFACTURE Portland cement is made from a mixture of calcium carbonate with silica and alumina. 8i6 A TREATISE ON CONCRETE The processes of manufacture differ with the natural state in which these materials are found, but the operation consists essentially of (i) pulverizing and mixing the two ingredients, (2) heating to a temperature which is near the melting point, i.e., calcining, and (3) grinding to a fine powder. The great bulk of the raw materials used in the manufacture of Port- land cement are found in a dry state, and the grinding is done in iron mills or tube mills of various kinds, the material being ground dry. Where either of the raw materials occurs in a moist state and also in many cases of dry materials, they are mixed and ground wet and in this condition are introduced into the kiln. Dry raw materials for calcining or burning in the old style stationary kilns must be formed into plastic bricks with the aid of water, but the rotary kiln invented in 1885 by Mr. Frederick Ransome has revolutionized the manufacture of Portland cement by making it possible to introduce the mixed sub- stances into the furnace, in either a dry or wet state, without hand labor. After calcination, the methods of grinding the clinker are independent of the character of the raw materials or the type of kiln. The Association of German Cerrient Manufacturers, to protect the good name of German Portland cement, requires that its members shall sign an agreement to introduce no adulteration into its product. Raw Materials for Portland Cement Manufacture. The raw ma- terials, as stated above, consist essentially of calcium carbonate and silicate of alumina. Their exact proportions are determined by their chemical composition. A usual ratio is such as wiU produce about 75% calcium carbonate in the raw mixture. The two substances occur in nature in so many forms that we have a large range of choice in raw materials. The following combinations are actually used in different cement manufacturing plants in the United States; Cement rock and limestone Limestone and clay. Limestone and shale. Marl and clay. Chalk and clay. Limestone and slag. Alkali waste and clay. Cement rock is an argillaceous limestone, rather soft in texture, which in the Lehigh Valley usually requires from s to 20% of limestone to CEMENT MANUFACTURE 817 give it the correct Portland cement composition. Occasional deposits are found which are suitable to use with no admixtures, or from which the desired proportions may be obtained by mixing two different strata in the same quarry. Several other States, among them the Virginias, Alabama, Colorado, and Utah, have a geological formation from which Portland cement, similar to that in the Lehigh Valley, has been made. In the Hudson River Valley, New York, are situated large manu- factories employing a hard limestone which is nearly pure carbonate of lime, requiring 20% to 25% clay or shale and producing a fine quaUty of cement. A somewhat similar mixture is used in California and in scattered locaUties in the Central States. The marl used for cement usually is a wet, calcareous earth, in some locaUties of organic origin from shell deposits, and in other places of chemical formation. There are large cement plants using marl and clay in Ohio, Indiana, and Michigan. Chalk and clay deposits resembling those in England are worked in Texas. Certain blast furnace slags similar to those used in the manufacture of Puzzolan cement, when combined with a suitable admixture of lime- stone, produce, after calcination, a true Portland cement with normal characteristics. The waste from the manufacture of soda, when employing the ammonia soda process with suitable raw materials, is substantially a precipitated chalk, and may be burned with clay and made to produce a Portland cement. In Germany the Alsen and Stettin brands are made from chalk and clay, the Dyckerhoff and Mannheimer brands from limestone and clay, whUe the Germania and Hanover works use marl and clay. In England raw materials consist principally of chalk and clay. Belgium manufac- turers use chalk and clay, and a so-caUed Portland cement from natural rock is also manufactured in that country. In France, marl and clay and chalk and clay are the chief raw materials for commercial Portland cements. The character and proportioning of the raw materials and the pro- cesses of chemical combination are discussed by Mr. Spencer B. New- berry in Chapter V. The following table illustrates the composition of various classes of materials which are used for Portland cement, and also the resulting analysis of the cement in each case: 8i8 A TREATISE ON CONCRETE Comparative Analyses of Raw Materials and Portland Cements. Cement Rock and Limestone. Limestone and Clay.* Marl and Clay. Chalk and Clay.* g u a 2 E 3 £ i u i 3 • D a u U 2 <9 I i Silica Si O2 19.06 i.gS 19.92 3-30 55-27 21.50 I-7S 62. TO 22.52 0.35 60.30 22. 10 Alumina Iron Oxide Ala O3 FeaOs 4.44 0.70 9-831 2-63J 1.30 28.15 10.50 1-57 20.09 7.81 6.69 354 0-7S 11.07 8.13 11.32 Calcium Oxicle CaO 38.78 53-31 60.32 52-15 5-84 63-50 49.24 0.65 63.82 54-95 440 60.7O Magnesian Oxide Mg O 2.01 0.97 3.12 1.58 22.5 1.80 0.44 0.06 069 1.27 I. TCI Sulphuric Acid SO3 1-13 0.30 0.12 1.50 o.is 0.49 0.98 2.50 1.40 Carbonic Oxide Water CO2 H2O 32.66 42.94 40.98 8.37 30-16J 8.00 43-17 7-47 1-94 Organic Matter 7.50 4.06 Other Constituents 0.40 1.08 0.8s 0.45 .-38 Note. — Carbonates in raw materials, given in some of the amlyses, have been transformed into oxide. ' Cement Rock. Lehigh Valley District, Penn. 21st Annual Report, U. S. Geological Survey. Pt. 6, p. 404. 2 Pure Limestone, Lehigh Valley District. W. E. Snyder, Analyst. 2 Lehigh Valley Cement. Booth, Garrett & Blair, Analysts. * Hudson River Valley. Mineral Industry, Vol. 6, p. 97- 6 W. H. Simmons, Analyst, 22d Annual Report, U. S. Geological Survey, Pt. 3, p. 650. 8 Shale. Mineral Industry, Vol. 6, p. 99. , ' Michigan. W H. Simmons, Analyst, 22d Annual Report, U. S. Geological Survey, Pt. 3, p. 680. 8 Water, 23%. Analysis from David B. Butler, England. ' Estuary Mud. Roughly dried, lost 33^%. Analysis from David B. Butler, England. '" English Portland Cement. Analysis from David B. Butler, England. Dry Process with Rotary Kilns. The rotary kiln is used almost uni- versally, superseding the old stationary kiln. The rotary was made a success La this country after failing totally abroad. The successful use of powdered fuel also was accomplished in the United States, and after- ward adopted, with the rotary kilns, in Europe. Where rock, or rock and clay, form the raw materials, they as a rule, are mixed and ground and introduced into the rotary in the form of a dry powder. If marl or chalk furnish the carbonate of lime, the wet process of mixing and grinding is usually employed, as described on page 822, although in a few plants each of these materials is dried when entering the mill, and the operations are similar to those described below for rock mixtures, except that driers and disintegrators are substituted for stone crushers. The process of manufacturing Portland cement from rock, or rock and * The authors are indebted for these analyses of chalk and clay to David B. Butler, of England, who prepared them for this Treatise. CEMENT MANUFACTURE 819 clay mixtures, in plants equipped with rotary kilns, consists essentially of crushing the materials, — either separately or after mixing them,— dry- ing, grinding, calcining in the rotaries, cooling, grinding to powder, and packing. If two stones of fairly similar texture and each of uniform composition form the raw materials, they may be carefully weighed and thrown to- gether into the breaker, which may be either a large jaw or gyratory crusher (see pp. 222 to223). Otherwise, they are crushed separately, and mixed just before the grinding which preceeds the calcination. A further reduction in size to about ^-inch is accomplished by rolls, crackers of the coffee mill type:, hammer mills, or similar machinery. Clay, if used, is dried in broken lumps, and then may be pulverized by passing it through a disintegrator consisting of two horizontal rolls, one corrugated or toothed and the other smooth. An economical form of dryer for clay or stone consists of a long re- volving steel tube about 5 or 6 feet in diameter by say, 60 feet long, pro- vided with shelves on its interior surface, formed by horizontal Z-bars. The hot gases from the kiln may be made to pass through the tube and meet the raw material. By treating the two materials separately up to this poiat, an extremely accurate mixture is obtained by weighing the ingredients in a pair of auto- matic weighing machines so arranged that one of the pair will not dump until both are charged. Samples of the two materials are taken, just before mixing, at definite periods throughout the day, and analyzed to determine the correct pro- portions. A partial analysis showing the quantities of the principal constituents may be all that is necessary except at occasional intervals. The maintaining of correct proportions is one of the most essential ele- ments in the manufacture. Another grinding of the mixed materials in mills of various types, to such a fineness that 82 to 92% will pass through a screen having 200 meshes per linear inch, completes thB preparation for the rotary kilns. A modem kiln located at the plant of the Atlas Portland Cement Co. at Hudson, N. Y. is shown in Fig. 258, page 820. This is 232 feet 3 J inches long by 12 feet in diameter and is elevated so that the clinket flows to subsequent machinery by gravity. Fine grinding before burn- ing is one of the secrets of successful manufacture. The best type of rotary kiln used for calcining dry materials, con- sists of an inclined steel tube from 100 to 250 feet long. The diameter is generally 8 to 12 feet, though occasionally smaller than this at the 820 A TREATISE ON CONCRETE CEMENT MANUFACTURE 8«i upper end and tapering to the larger size at a point about one-third of its length from the upper end. The lower end of the rotary is closed by a movable brick wall, and through the center of this passes a pipe that feeds the powdered coal which in a separate building is crushed to pea size and pulverized in tube mills, or other pulveriziag machines, so that about 95% is finer than a loo-mesh screen; the finer the coal the greater its efficiency. The ground stone may be fed into the upper end of the rotary by a spiral conveyor enclosed in a pipe which is water-jacketed to prevent the feed pipe from burning out. The degree of calcination is governed by the supply of raw material, the speed of rotation of the rotary, which rests on rollers geared to a speed-changing device, and the quantity of fuel. If coal is used for fuel, it is fed by a blast from a fan, and the quantity is regulated by a spiral conveyor running at changeable speed. The heat in the kiln is so intense that the coal bums as a gas without apparent smoke or cinder. The proper temperature, which is said to be 2700° to 3000° Fahr., is determined by the appearance of the burn- ing cUnker. At a certain point in its descent the material becomes semi-vitrified and forms into irregular balls or clinkers, which roll around and finally faU out red-hot at the lower end in pieces ranging in size from |-inch to one inch in diameter. The clinker, when properly burned, is of a greenish black color with a faint glisten, and contains but few large pieces. It slightly resembles in appearance the clinker often found among the ashes of hard coal. The output of a rotary varies with the length and diameter from 150 to 200 barrels per 24 hours for a 60 foot kib. to i 000 to 2 000 barrels for a 150 to 200 foot kiln with a smaller coal consumption per bbl. The clinker, after being cooled in some form of cooler, is crushed by passing between horizontal rolls or through some other form of crusher, and is then ready for the fine grinding, or, if desired, it may be stored either out of doors or under cover until needed. Strangely enough, wetting the clinker does not injure it provided it is dry when it enters the fine grinders. The fine grinding is accomphshed by passing the clinker through one or more special mills*, such as ball mills, tube mills, Griffin, Kent or Lehigh Fuller Mills. A tube mill, which is used to a large extent in grinding cement, con- sists of a long horizontal cylinder filled nearly to its axle with flint pebbles imported from Europe, which average about 2 to 3 inches in diameter. The cement is ground by rolling around with the flints. It is then • See illustrations in advertising pages at back of book. 822 A TREATISE ON CONCRETE thrown against the screen, which prevents the passing of pieces oi flint. A tube mill which passes, say, 2,50 barrels of cement per day, will re- quire the renewal of the flint pebbles at the rate of about 600 lb. per week. Such small mills as these, however, are being superseded by larger ones, i.e., by combined ball and tube mills having a capacity up to 75 to 100 barrels of cement per hour. It is customary to store the cement in bulk and weigh it out by auto- matic weighing and bag packing machines into bags or barrels as required for shipment. In outhning the cement machinery, no reference has been made to the methods for conveying the material from one machine to another. Bucket conveyors, chain drags, belts and spiral conveyors are all more or less used. A spiral conveyor is a helical blade on a revolving shaft, set in a square or circular trough or tube of larger size than the spiral, so that the material packs around the circumference, and the blade comes in contact only with the powdered material. Plaster of Paris (calcium sulphate CaS04) or gypsum (CaS04 + 2H2O), the same substance in crystalline form, is an important addition to cement as a regulator of its setting, and from 2 to 3% is used in nearly all Portland cement manufactories. The gypsum must be added after the calcination and before the final grinding, in order to insure the proper result. The laboratory of a cement plant is an important feature. Not only must the raw materials and the finished cement be analyzed at frequent periods to insure uniformity of product, but the cement must be mechani- cally tested also for fineness, time of setting, tensile strength at seven and twenty-eight days, and, perhaps most important of all, for sound- ness. Most manufacturers use some form of the accelerated or hot test. This is not only due to the fact that many engineers require the cement to pass an acclerated test for reception, but because the chemists in the cement factories consider this test of great value in checking up the quahty of cement. Wet Process with Rotary Kilns. The rotary or Ransome kiln was first used in England on wet materials. Rotaries have been widely, in fact almost universally, adopted in the United States for calcining dry materials. More recently this field has been extended to use with slurry formed from the mixture of pulverized materials such as marl and clay and containing some 40% or more of water, which is pumped into the end of the rotary and dried by the same flame used for calcination. CEMENT MANUFACTURE 823 In the United States the raw materials most commonly employed in the wet process are marl and clay. The marl as it comes to the mill is broken up in some form of a disintegrator. The clay is dried and pulverized and is then mixed with the marl, which is about of the con- sistency of thick cream, in a pug mUl, or an edge-runner. In some cases the clay is ground and water is added to it before mix- ing with the marl. The mixed materials must now be ground wet before burning. This is sometimes accomplished in null stones, consisting of a pair of horizontal stones the upper one of which revolves upon an upright shaft, but more often in wet tube mills similar to those described on page 819. Stationary Kilns. Before the introduction of rotary or revolving kilns aU cement was burned ia stationary kiLns. Stationary kUns are of two general types: (i) intermittent kilns, which are completely charged and then burned, and (2) continuous kilns, where the fire is maintained continuously and the exhaust heat is used to dry and heat the raw materials before burning them. The bricks of cement slurry and the coke are placed ia these kilns in layers by hand and then burned. While the old style of stationary kilns are practically obsolete, small, vertical kUns taking material in small cakes and operating under air pressure, were beiag introduced in Germany before the war. These were said to be lower in first cost and more economical in operation than the. rotary Idln. The most common form of intermittent kiln is the Dome or Bottle Kiln. This consists of a single shaft into which alternate layers of moist bricks of cement slurry and coke are placed by hand and burned. After cooling, the cUnker is drawn out by hand through a door at the bottom, picked over to remove under-burned clinker, — which is of a yellowish shade instead of black, — and clinker which has fused to fragments of the firebrick lining. The Johnson Kiln is a more economical form of intermittent kiln. The slurry is placed in chambers, and dried by the exhaust gases from the burning of the previous charge before being placed in the kilns. Of the continuous kilns, the Hoffman Ring Kiln consists of several chambers or furnaces around a central chimney. As the material in one furnace is burned, the heat passes around through the other furnaces so as to raise the temperature of the bricks in them and utilize the exhaust heat. In the Schoefer Kiln, which is also of the continuous type, the bricks and fuel are loaded from time to time into the upper end of the 824 A TREATISE ON CONCRETE shaft, and pass down, iacreasing in temperature, through the flame, where the area is contracted, to be cooled below and drawn out at the bottom. The Dietzsch Kiln is of a somewhat similar type of construction, except that hand -labor is required in passing the dried material into the heating chamber. NATURAL CEMENT MANUFACTURE The process of manufacture of Natural cement consists, in brief, of burning a natural argillaceous limestone at low heat and grinding it to powder. The stone used in England is very soft, in fact nearly as disin- tegrated as marl. Raw Material. Many of the limestones used for Natural cement con- tain a high proportion of magnesia and an excess of clay, while others are nearly free from magnesia. It must be calcined at a temperature much below that required for Portland cement or it will fuse to a slag which after grinding has no hydraulic properties. Suitable formations occur in many parts of the United States, one of the most noted being that found in the region of eastern New York where Rosendale cements are made. Sometimes the stone is taken entirely from one ledge, while in other cases mixtures of two strata are employed. Little attention is paid to the analysis of the rock, as there is a wide range in the required chemical composition of the product (see p. 40), and the price at which Natural cement is sold does not warrant great refinement. Process of Manufacture of Natural Cement. There is less variety in the methods employed for producing Natural cement than for Portland. In a typical plant, the stones, of about the size that would be required for a large crusher, are brought from the quarry in carts or cars and dumped directly into the top of the kilns, which are of boiler iron lined with firebrick. They have no chimneys, but are open at the top and of the same size throughout. Thick layers of stone are alternated with thin layers of pea coal. The clinker is drawn out at the bottom as it is burned. In the older plants the burned clinker is crushed and then ground be- tween mill stones, while the newer mills use grinding machinery similar to that in Portland cement plants. When burnt. Natural cement rock is more readily powdered than Portland cement clinker. PUZZOLAN CEMENT MANUFACTURE Puzzolan cement has been made in the United States fi:om blast furnace slag mixed with slaked lime. In Europe, natural puzzolanic CEMENT MANUFACTURE 825 materials have been employed. This cement must not be confused with true Portland cement which may be made by employing slag and lime as raw materials and calcining in the usual way. The process of manufacture* consists essentially of cooling the slag, mixing it with slaked lime, and grinding to a very fine powder. Slag for Puzzolan Cement. For making pig iron a blast furnace is charged with a mixture of iron ores, fluxes (consisting of limestone, either calcite or dolomite) and fuel, in the proper chemical proportions to pro- duce, after reduction by heat, products of definite chemical composition. These resulting products are pig iron and slag. Any one unacquainted with metallurgy naturally thinks of blast furnace slag as a compound composed to a large extent of iron. This is incorrect; nearly all the iron is drawn off in the pigs and only enough to form a very small impuHty goes off with the slag. All slags are not suitable for Puzzolan cement, as they ordinarily con- tain too high a percentage of magnesia and are often too high in alumina. The specifications for slag used in the manufacture of Steel Portland ce- ment are as follows :t Slag must analyze within the following limits : Per cent. Silica plus alumina, not over 49 Alumina .* 13 to 16 Magnesia, under 4 Slag must be made in a hot furnace and must be of light gray color. Slag must be thoroughly disintegrated by the action of a large stream of cold water directed against it with considerable force. This contact should be made as near the furnace as is possible. Mr. E. Candlot saysj "The slag must be basic; according to Mr. Tet- CaO majer, when the ratio — — falls below unity the slag is useless; the S1O2 ratio of alumina to silica must be between 0.45 and 0.50. According to Mr. Prost, the composition of slags habitually used in the manufacture of Puzzolan cements must be nearly represented by the formula 2 Si02, AI2O3, 3 CaO." Mr. E. C. Eckel§ gives the following three analyses of slag and slag cement: *An investigation of the manufacture and properties of Puzzolan cement is given in Report ot Board ot Engineers, U. S. A., 1900, on Steel Portland Cement. tReport of Board of Engineers, U. S. A., 1900, on Steel Portland Cement. tCiments et Chaux Hydrauliques, 1898, p. 157. §Hineral Resources of the United States, 1901. 826 A TREATISE ON CONCRETE Analyses of Slags in Actual Use and Composition of Slag Cements \ Choindez, Switzerland. Saulnes, ) France. / 0" u "1 CEMENT CONSTITUENT. S a u SiOs 26.24 24.74 0.49 46.83 0.88 0-59 0.32 1.78 0-93 ■ 5' -50 16.62 0.62 46.10 1.46 0.52 32.20 15-5° 48.14 2.27 1.49 0.48 19-5 I7-S S4-0 22.45 13-95 3-30 51.10 I -35 °-35 7-50 28.95 11.40 0.54 50.29 2.96 Al, O3 FeO CaO MgO CaS CaS04 S 1-37 SO3 Loss on ignition CaOl 3-39 sio^l Al.O, 1 Si02 Process of Manufacture of Puzzolan Cement. No kilns are required except for burning the lime. Molten slag as it flows from the blast furnace is granulated by coming in contact with a stream of cold water. This renders the product more strongly hydraulic, and most of tlie sulphur is removed as it strikes the water. As sent to the cement plant, it usually contains from 30% to 40% of water, and the first operation is to pass it through a dryer. The dried slag may or may not have a preliminary grinding before adding the slaked lime. The lime is produced by burning a pure limestone, and then slaking it with water to which has been added a small percentage of caustic soda or other similar material, to make the resulting cement quicker setting. After drying, the slaked lime is mixed with the slag and ground in ball mills and tube mills, or in other forms of fine grinding machinery, and is ready for packing in bags or barrels for shipment. MISCELLANEOUS STRUCTURES 827 CHAPTER XXXII MISCELLANEOUS STRUCTURES. The more important structures are treated with considerable detail in preceding chapters. The uses of concrete and reinforced concrete are now so numerous and are increasing so rapidly that only brief reference can be made to a few of the smaller and of the less common structures. In railroad work, not only for the more important structures like piers, abutments and arches, but for the numberless smaller details like telegraph poles, ties, bumping posts, and signal posts, is reinforced concrete being employed. Roundhouses, stations and terminal warehouses are being designed either exclusively or in part of this material. In power development, not only the dams are of concrete, but the canals, penstocks, flumes, and the power stations themselves. In water-works construction the use of concrete has extended to reservoirs, filter basins, tanks and conduits, and, in some of the recent works, concrete with its imbedded steel for reinforcement is almost the only ' structural material. Even the farmer and the householder are utilizing concrete in various ways for barns, garages, chicken houses, floors, fences, silos, tanks, troughs, drains and many other of the small details which make for economy, dura- bility and convenience. By mixing and placing the concrete according to the directions laid down in Chapter II and using sufiicient reinforcement (in some cases ordinary fence wire is suitable), many an inexperienced man has built permanent structures of pleasing appearance. For reinforced con- crete work such as floors, roofs and stairs, an engineer should be called upon to design the dimensions and reinforcement. Telegraph Poles. Wooden polesare being replaced in many localities by poles of reinforced concrete because of their greater durability. The Pennsyl- vania lines west of Pittsburg* have installed poles from 20 to 28 feet high, 8 inches square at the bottom, tapering to 6 inches square at the top, with comers chamfered 2 inches. Holes are left in the pole for the brace and cross-arm bolts and also for the climber steps. The reinforcement may be greatest at the bottom and reduced above to allow for the lessening stress. * Concrete Engineering, July 1908, p. 189. 828 A TREATISE ON CONCRETE In 1907 Mr. Robert A. Cummings* made comparative tests of reinforced concrete and white cedar poles. The former were 13 inches square at the butt and 7 inches at the top, reinforced to withstand the weight of 50 wires all coated with ice to a diameter of one inch. These were stronger than the wooden poles of substantially the same size. After breaking, the ends of the concrete poles were held in a slightly inclined position by the reinforce- ment, while the wooden poles broke square off and fell to the ground. Ties. Concrete ties of varied designsf have proved satisfactory for slow speed traffic, especially in yards and on turnouts. They also have been used to a certain extent on high speed track. One of the most important fea- tures is the connection with the rail which is generally made through a cushion block of wood. If the tie supports both rails, it must be reinforced in the center at the top to resist the negative bending moment. The ends of the ties should also be well reinforced to prevent breakage in case of derail- ment. Road Beds. For tunnels, concrete roadbeds have been found economical because of the very great saving in maintenance expense. Roundhouses. Reinforced concrete affords a durable and inflammable material for the structural portions and the roofs of roundhouses, while the walls may be built either of concrete or of brick. Cinder and Ash Pits. Concrete will stand as high temperature as will be given to it by hot ashes and cinders. Grain Elevators. By building of reinforced concrete the danger from fire is avoided as well as the necessity for constant repairs. Coal Pockets. For coal storage the strength and fireproof ness of rein- forced concrete is bringing about its general adoption. Boiler Settings. Reinforced concrete boiler settings have been in success- ful use in several plants for a number of years. The initial cost is prob- ably not less than brick but greater durability and freedom from repairs is claimed by the users of concrete settings. Double walls are required with an air space between. The inner wall may be about 5 inches thick and the outer about 6 inches, both thoroughly reinforced to prevent as far as possible the development of cracks. Bars f-inch diameter, spaced 6 inches apart both ways, afford effective reinforce- ment. The walls may be tied together at intervals with bars. The rein- forcement permits building the setting to any shape over the boiler, although wherever it comes in contact with the boiler, a 3-inch layer of mineral wool should be introduced to allow for variation in expansion. * Cement Age, Aug, 1907, p. 84. f Concrete Review, 1908, published by the Association of American Portland Cement Manu- facturers. MISCELLANEOUS STRUCTURES 829 A fire-brick lining must be used. A thickness of 8 or 9 inches is more economical than a 4i-inch lining because it can be replaced without dis- turbing the concrete. Spaces must be left at the ends of the fire-brick lining to allow for expansion. The concrete should be as rich as i : 2 4 and the best aggregates are quartz sand and trap rock about f inch maximum size. For high temperatures gravel and limestone aggregates should be avoided. Cinders of first-class quality should make durable walls when mixed with sand and cement in rich proportions. Fences. Fences have been built of solid concrete, of mortar plastered on wire lath, of concrete rails set in concrete posts, and of concrete posts vrith galvanized fence wire between them. The last plan is the most common. For farm or division fences the length of posts may be 7 feet, allowing 3 feet of this to set into the ground, and the size may be 5 or 6 inches square at the bottom and 4 or 5 inches square at the top v/ith ^-inch rods in each corner. Forms are easily made singly or so as to mold several posts at once. Silos. Silos of solid monolithic concrete built in circular forms may have walls 6 inches thick reinforced with ^-inch bars bent to circles and placed 12 inches apart. Occasional vertical bars are also necessary. The con- crete must be mixed wet and placed very carefully so as to give a perfectly smooth interior surface, so solid and dense that the ensilage will not be dried out next to the wall. Greenhouses. Greenhouses themselves, as well as the floors, tables, water troughs, hotbeds, and minor appurtenances, are being built of con- crete. The directions throughout the various chapters in this treatise for structures of different classes will be found to apply to these details. House Chimneys. Chimneys for residences may be of concrete if heavily reinforced, but the expense of forms usually will make them more costly than brick. Chimney caps of concrete should be well reinforced to prevent cracking. Residences. Residences are built of solid reinforced concrete; concrete blocks (see p. 623) ; concrete tile, plastered (see p. 628); and mortar plas- tel^d on metal lath (see p. 645). Solid or monolithic concrete is especially adapted to fine residences and permits unique architectural treatment. Eventually vrith the development and consequent reduction in cost of form construction, reinforced concrete may be more generally employed for dwellings of small and moderate size. 830 A TREATISE ON CONCRETE CHAPTER XXXIII REFERENCES TO CONCRETE LITERATURE While this chapter is not a complete bibliography of concrete literature, it presents a comprehensive list of valuable books and articles relating to the subject. v Under General References the names of authors are arranged alpha- betically. The various subject headings under Subject References are also arranged alphabetically, and the references are printed in order of dates, the latest first. Articles are usually described by their subject-mat- ter instead of giving their titles verbatim. In the case of similar articles printed in two or more periodicals, preference is generally given to the one bearing the earlier date. For references to this treatise see the Index. ABBREVIATIONS The following abbreviations (most of which correspond to those adopted by the Engineering Index) are employed: Ann. de Fonts et Chauss. — Annales des Fonts et Chaussdes. m. Paris. Arch. Rec. — Architectural Record. New York. Belon u. Risen. — Beton und Eisen. Vienna. Can. Eng. — Canadian Engineer. Montreal, Canada. Cement and Eng. News. — Cement and Engineering News. Chicago. Comptes Rendus — Comptes Rendus de I'Acad^mie des Sciences. Paris, Con. Eng. — Concrete Engineering. Cleveland, Ohio. Deutsche Bau. — Deutsche Bauzeitung. Berlin. Eng. Contr. — Engineering Contracting. Chicago. Eng. Mag. — ^Engineering Magazine. New York & London. Eng. News. — Engineering News. New York. Eng. Rec. — Engineering Record. New York. Gen. Civ. — Genie Civil. Paris. Ins. Eng. — Insurance Engineering. New York. Int. Eng. Cong. — International Engineering Congress, St. Louis, 1904. Jour. Am. Chem. Soc. — Journal American Chemical Society. Wash- ington, D. C. Jour. Assn. Eng. Socs. — Journal of the Association of Engineering So- cieties, Philadelphia. Jour. Fr. Inst. — Journal Franklin Institute. Philadelphia. Jour. W. Soc. Engs. — Journal of the Western Society of Engineers, Chicago. Mimic. Engng. — Municipal Engineering. Indianapolis. Oest. Monaischr. /. d. Oeff. Baudienst. — Oesterreichische Monatsschrift fur den Oeffentlichen Baudienst. Vienna. REFERENCES TO CONCRETE LITERATURE 831 Pro. Am. Soc. Civ. Engs. — Proceedings of the American Society of Ci\'il Engineers. New York. Pro. Am. Soc. Test. Mat. — Proceedings of American Society for Testing Materials. Philadelphia. Pro. Assn. Ry. Supts. — • Proceedings of the American Association of Railway Superintendents of Bridges and Buildings. New York. Pro. Engs. Club of Pkila^ — Proceedings Engineers' Club. Philadelphia. Pro. Engs. Soc. of W. Penn. — Proceedings of Engineers' Society of Western Pennsylvania. Pittsburgh. Pro. Inst. Civ. Engs. — Proceedings of the Institution of Civil Engineers. London. Ry. b" Eng. Rev. — Railway & Engineering Review. Chicago. R. R. Gaz. — Railroad Gazette. New York. Rept. Chief of Engs., U. S. A. — Report of Chief of Engineers, U. S. A. Rept. Eng. Dept. — Report of Engineering Department, Washington, D. C. Rept. Met. W. &= S. Board. — Report of Metropolitan Water & Sewerage Board, Massachusetts. Revue Gen. des Chemins de Per. — Revue Generale des Chemins de Fer. Paris. Rev. Tech. — Revue Technique. — Paris. Schw. Bauz. — Schweizerische Bauzeitung. Zurich. Tech. — Technograph. University of Illinois. Champaign, III. Tech. Qr. — Technology Quarterly. Boston. Trans. Am. Soc. Civ. Engs. — Transactions American Society of Civil Engineers. New York. Trans. Am. Soc. Mech. Engs. — Transactions American Society of Me- chanical Engineers. New York. GENERAL REFERENCES *An asterisk precedes the references which are especially noteworthy. Andrews, H. B. Practical Reinforced Con- Heidenreich, E. Lee. Engineers' Pocketbook Crete Standards for tne Design of Rein- of Reinforced Concrete. M. C. Clark forced Concrete Buildings. Simpson Publishing Co., Ctiicago, Illinois. Bros. Corporation, Boston, Mass. Kersten, C. Briicken in Eisenbeton. 5 vo^ Balet, Joseph W. Analysis of Elastic Arches. umes, Wilhelm Ernst & Sohn, Berlin, Three-hinged, Two-hinged and Hingeless, 1909. of Steel Masonry and Reinforced Con- *Marsh, C. F., and Dunn, Wm. Reinforced Crete. Engineering News Publishing Co., Concrete; Tnird Edition. D. Van Nos- New York, 1908. trand. New York, 1907. *Eckel, Edwin C. Cements, Limes and Plas- *lVlorsch, Emil. Der Eisenbetonban-Seine ters. Their Materials, Manufacture and Theorie und Anwendung. Konrad Wit^- Properties. John Wiley & Sons, Inc., JNew wer, Stuttgart, Germany, lgi2. York, 1Q05. Reid, Homer A. Concrete and Reinforced *Feretr'R.' Etude Experimentale du Cement Concrete Construction. M. C. Clark Arm^. Gauthier-Villars, Paris, 1906. Publishing Co., New York, 1907. *Feret, R. Chimie Appliqufe. Baudry et Reuterdahl, Arvid. Theory of Practice of Ci'e, Paris. Reinforced ' Concrete Arches. M. C. Gillette,'H. P. Concrete Construction, Meth- Clark Publishing Co., Chicago, Illinois, ods and Costs. M. C. Clark Publishing 1908. Co., Chicago, Illinois. Taylor, W. Purves. Practical Cement Test- Gilbretli, F. B. Concrete System. Engineer- ing. Myron C. Clark Publishing Co., ing News Publishing Co., New York, New York, igoS. igoS. Taylor, Frederick W. and Thompson, Sanford Hawkesworth, J. Graphical Handbook for E. A Treatise on Concrete, Plain and Reinforced Concrete Design. D. Van Reinforced. 3d edition, John Wiley & Sons, Nostrand, New York, 1907. Jnc, New York, 1916. 832 A TREATISE ON CONCRETE ♦Turneaure, Prof. F. E., and Maurer, Prof. E. R. Principles of Reinforced Cpncrete Con- struction. John Wiley & Sons, Inc., New York, ad edition, 1915. ' Twelvetrees, W. N. Concrete Steel. Mac- millan Co., New York. Vacchelli, Giuseppe. Le Construzioni in Cal- cestruzzo ed in Cement Armato. Ulrico Hoepli, Milan, 1906. Von Emperger, F. Handbuch fuer Eisen- betonban. Wilhelm Ernst and Sohn, Berlin, 1907- Alexandre, Paul. £tude sur la resistance des mortiers de ciment. Annales des Fonts et Chauss^es, 1888, I, P.37S. * Recherches exp^riraentales sur les mor- tiers hydrauliques. Annales des Fonts et Chauss^es, 1800, II, p. 277. Baker, Ira O. A Treatise on Masonry Construc- tion. John Wiley & Sons, Inc., New York, 1C»09. *Berger, C* et V. QuIUerme. La construction en ciment armfi. Applications g^n&ales theories et sept&mes divers. Dunod, Paris, igoa. Boltel, C. Les constructions en fer et ciment, Berger-Levrault, Paris, i8g6. Bonnami, H. Fabrication et contr6Ie des chaux hydrauliques et des dments; theorie et pratique. Gauthier-Villars et Fils, Paris, 1888. Brown, Charles C. Directory of American Cement Industries and Hand-Book for Cement Users. Municipal Engineering Co., Indianapolis, Ind. Buel. A. W. and C. S. HHI. Reinforced Concrete. Engineering News Publishing Co., New York, ZQ06. •Burr, William H, The Elasticity and Resist- ance of the Materials of Engineering. John Wiley & Sons, Tjc., New York, 1915. •Butler, David ^.. Portland Cement, Its Manu- fa cure. Testing, and Use. Spon, London, Cain, William. Theory of Steel- Concrete Arches and of Vaulted Structures. Van Nostrand'a Science Series, New York, igo6. •Candlot, E. Ciments et chaux hydrauliques: fabrication — propridtfo — emploi. Baudry et Cie, Paris, 1898. Castanheira das Neves. Estudos sobre resistencia de materiaes. Lisbon, 1802. *Cement Industry, The. The Engineering Record, New York, 1900. *Christophe, P. B^ton arm^ et ses applications, Ch. B^ranger, Paris, 1002. Coignet, E. et de Tedesco. Du calcul des ouvrages en ciment avec ossature m^tallique. Socilt6 des Ingenieurs Civils, igo?. •Commission des methodes d'essai des materlaux de construction. Vol, I et IV. Paris, 1893 and 1895. ^ •Congres International des methodes d'essai des mat^riaux de construction, Vo.. II, sd Part. Dunod, Paris, igoi. •Considere, A. Resistance a la compression du b^ton arm^ et du b^ton frett^. Dunod, Paris, G6me Civil, igo3. Experimental Researches on Reinforced Concrete, translated and arranged by Leon S. Moisseiff. McGraw Publishing Co., New York, igo3. Cummlngs, Uriah. American Cements. Rogers & Manson, Boston, i8g8, Daubresse, P. De I'emploi des ciments Portland dans les constructions civiles et industrielles. Bruxelles, 1897. •Durand-Claye, Derome et R. Peret, Chimie ap- pliqu^e k I'art de I'lng^nieur. Baudry et Cie, Paris, i8q7. Falja. H. Portland Cement for Users. London, 1884 Falk, Myron S. CementR, Mortars and Concretes, their physical properues. M. C. Clark, New York, 1904. Feret, R. Sur la compacitfi des mortiers hydrau^ liques. Annales des Fonts et Chauss^es, Paris, i8g2, II, p. i. (See Durand-Claye.) French Commission. (See Commission des me- thodes d'essai des matdriaux de construction.) German Association of Portland Cement Manufac- turers. Der Portland Cement und Seine An- wendungen im Bauwesen, Berlin, 1012. aiUmore, Q. A. Practical Treatise on Limes, Hydraulic Cements, and Mortars. D. Van Nostrand Co., New York. • Notes on the Compressive Resistance of Freestone, Brick Piers, Hydraulic Cements, Mortars and Concretes. John Wiley & Sons, Inc., New York, 1888, Report on Bi^ton Agglom^rd or Coignet- B^ton and the Materials of Which it is Made. Professional Papers, U. S. A., No. 19, Wash- ington, D. C, 1871. •Oollnelli, L. How to Use Portland Cement (Das Kleine Cement-Buch). Translated by Spen- cer B. Newberry. Cement and Engineering News, Chicago, 1899. Grant, John. Portland Cement: Its Nature, Tests, and Uses. Institution of Civil Engineers, Vols. XXV, p. 66, XXXII, p. 266, and LXII, p. gS. London. Guillerme, V. (See Berger.) Hill, C.S. (See Buel.) Jameson, Charles D. Portland Cement: Its Man- ufacture and Use. D. Van Nostrand Co., New York, 1808, •Johnson, J. B. The Materials of Construction. John Wiley & Sons, Inc., New York, igi ";. Lavergue, Gerard. Etude des divers syslfcmes de constructions en ciment arm6. Le GiSnie Civil. Baudry et Cie., 1907. •Le Chatelier, H. Proc^d^s d'essai des mat(!riaux hydrauliques. Annales des Mines, 1893. Du- nod, Paris, i8g3. Leduc, E. Chaux et Ciments. J. B. Baillifere & Fils, Paris, 1902. Lefort, L. Calcul des poutres droites et planchers en bdton de ciment arm^. Baudry et Cie., Paris, 1899. Mahiels, Armand. Le B^ton et son emploi. Ma- tdriaux — chautisrs — coEfrages — prix de re- vient — applications. B^nard, Lifege, 1893. Marsh, Charles F. Reinforced Concrete. D. Van Nostrand Co., New York, 1904. •Morel, Marle-Augustc. Le ciment armd et les applications. Gauthier-Villars & Masson et Cie, Paris, 1903. Newberry, Spencer B. (See GolinelJi.) Newman, John. Notes on Concrete and Works in _ Concrete. Spon, JLondon, 1887. Noe, H. de la. Ciment armd. Annales des Fonts et Chauss^es, I, 1899, p. i. •Potter, Thomas. Concrete: Its Use in Build- ing. D. Van Nostrand Co., New York, 1008. Redgrave, Gilbert R. Calcareous Cements: Their Nature and Use. With Some Observations upon Cement Testing. J. B. Lippincott Co., Philadelphia, 1905. Sabin, Louis Carlton. Cement and Concrete. Mc- Graw Publishing Co., 1907. *Schoch, C. Die Modeme Aufbereitung und Wertung der Mortel Materialen. BerUn, igw. ♦Spalding, Frederick P. Hydraulic Cement; Its Properties, Testing, and Use. John Wiley & Sons, Inc., New York. ioo6. *An asterisk precedes the references which are especially notewortliy. REFERENCES TO CONCRETE LITERATURE 833 Sutcliffe, Geors^e L. Concrete: Its Nature and Uses. Crosby, Lockwood and Son, London, 1893, *Taylor, Fredrick W. and Thompson, Sanford E. A Treatise on Concrete. Plain and Reinforced. John Wiley & Sons, Inc., New York, 1916. Tedesco. N. de. Traits thdorique et pratique de la resistance des raatdriaux appliqude au b^ton et au ciment arm^. Ch. B^ranger, Paris, 1904. Thompson, Sanford E, (See Taylor.) Vicat, L. J. A Practical and Scientiiic Trea- tise on Calcareous Mortar and Cements, Artificial and'Natural. Translated from the French by Capt. J. T. Smith. John Weale, London, 1837. SUBJECT REFERENCES Bond of Steel to Concrete Berry, H. C. Tests of Bond of Steel Bars Embedded in Concrete. Eng, Rec, July, 1909, p. 93. , ^ , , ^ Van Ornum, J. L. Tests of Bond between Concrete and Steel. Eng. News, Feb. J908, p. 142. Withey, Morton O. Tests of Bond in Rein- forced Concrete Beams, Proc. Am. Soc. Test. Mat., Vol. VIII, 1908, p. 469. Shuman, Jesse J. Tests of Cold Twisted Steel Rods. Eng. Rec, July, 1907, p. 77- Noble, C. W. Choice of Steel for Reinforcing Concrete. Eng. News, May, 1907, p. 5 16. Boost, Von H. New Tests of Bond of Steel to Concrete, Berlin. Beton u. Eisen, Heft II, 1907, p. 47. Withey, M. O. Variation of Bond with Com- gressive Strength. Univ. of AVisconsin ulletin No. 175, 1907. Talbot, A. N. Tests of Bond. Univ. of Illinois Bulletin, No. 8, 1906. *Schaub, J. W. Some phenomena of adhesion. •Eng. News, June, 1904, p. 56i. *Spofford, Chas. M. Tests of adhesion of concrete and steel at Mass. Inst. Tecnol- ogy. Beton & Eisen, III Heft, 1903, p. 200. *Christophe, Paul. Adhesion of metal Bdton Arm^, 1902, p. 476. Mensch, Leopold. Adherence of concrete and steel. Jour. Assn. Eng. Socs., Sept. 1902, p. lOI. Hatt, W. K. Tests of rods imbedded in con- crete. Pro. Am. Soc. Test Mat., 1902, Carson, H. A. Adhesive resistance of steel bars in concrete. Tests of Metals, U. S. A., 1901, p. 620. Kurtz, C, M. Tests of bolts imbedded in con- crete. Jour. Assn. Eng. Socs., Feb. 1901, p. io'9. Bridges Max. span Location ft. Switzerland 239 42d St., Phila. 25o C. B. & Q. R. R. . Trestles Delaware River i5o D. L. & W. R. R. PaulinsKill 120 D. L. & W. R. R. Grand River 160 L. S. & M. S. Ry. Cumberland Valley 100 Ry. Wyoming Ave. , Phila. 90 Harrisburg, Pa. Viaduct Maumee, Waterville, 90 Ohio Sandy Hill, N. Y. 60 Walnut Lane 233 Phila. Paterson, N. J., 54 Plainwell, Mich., 54 Waterloo, Iowa, 72 Yellowstone River, 1 20 Max. rise ft. 87' 53 60 7ii 32 2S 84 Crown thickness ft. 6 7 5 2i i4 Reinforcement Longitudinal & trans- verse bars Double steel arch ribs Longitudinal & trans- verse bars None Horizontal longitudinal rods in spandrel walla. No other reinforcement Authority Eng. News, Aug., 1909, p. 133. Eng. News, May, 1909, p. S40. Eng. News, May, igog, p. S46, Eng. Rec, Apr., 1909, p. 542. Eng. Rec, Apr., 1909, p. 541. Eng. Rec, Apr. & May, 1909. Eng. News, Apr., 1909. p. 377- Eng. Rec, Feb., 1909, p. 233. 54 1.8 1.25 7.2 i5 Longitudinal & trans- verse rods Ribs, angle bars, latticed None II ribs about 4 ft. apart 4-inch 6-lb. chan- nels 1. 9 ft. apart Steel Ribs Lattice girders Eng. Rec, Aug., 1908, p. 228. Cement, Aug. , 1908, p. 116. Trans. Am. Soc Civ. Engrs.,Yo\. L2X, p. 195. Eng. News, Jan., 1907, p. 117- Eng. Rec, Sept., 1904, P- 303 Eng. News, May, 1904, p. 456 Eng. Rec, Feb., 1904, p. 1 85 Eng. News, Jan., 1904, p. 3 5 *An asterisk precedes the references which are especially noteworthy. 834 A TREATISE ON CONCRETE Max. Max. Crown span rise thickness Location. ft. ft. ft. Reinforcement. Authority Piano, 111., 7S 38i 3 J" and I" cor- rugated bars Eng. Rec, Jan., 1904, p.i8 3rd St., Dayton, Ohio, no 14.2s 2.1 Melan, 4 angles, I iced Melan, 4 angles, ,lat- ■ Edwin Thacher, 1904 Newark, N. J., 132 16.2 3 lat- Edwin Thacher, 1904 ticed Kankakee, 111., 73 8.4 1-33 Thacher. rods near top and bottom Edwin Thacher, 1904 Mishawaka, Ind., no 14 2 Melan, 4 angles, ticed lat- Edwin Thacher, 1903 Prospect Ave., N. Y, 8s 8i 2.2s Corrugated bars Eng. News, Dec, 19031 p. 588 Eng. News, Oct., 1903? Riverside, Cal., 87 36.9 3-5 None , P-353 Leominster, Mass., 45 6.2s i.r Round rods anchored J. R. Worcester, 1903 Des Moines River, 100 28 1.67 Melan Cement, July, 1902. Zanesville, Ohio, 122 "•5 2-5 5"x5" bars p. 200 Eng. News, March, 1902. p. 261 Concord, Mass., 65 7 I.I None J. R. Worcester, 1901 Edwin Thacher, 1901 Lansing, Mich., 120 23 2 Melan, 4 angles, lat- liccd « South Bend, Ind., 100 II 2-5 Melan, 4 angles, ticed lat- Edwin Thacher Chatellerault, France, 164 15-7 1.7 Hennebique Revue Gen. des Chemins de Fer, Dec, 1901 Kirchheim, Germany, 124.6 18 2.6 None Eng. News, Oct., 1899, p. 246 Germany, 132 14-7 0.82 Monier Eng. News, Sept., 1S99, p. 179 Switzerland, 128 II 0.56 Monier Eng. News, Sept., 1899 Southern Ry., Austria, 32.8 3-3 0-5 Monier p. 179 Eng. News, Sept., 1899, Topeka, Kan., I2S 12 1.8 Melan beams Eng. Rec, April 16, 1898 Iijzigkofen, Germany, 140 I4-S 2-3 33 000 lb. cast iron Eng. News, Sept., 1896, p. 17S Inst Civ. Engs., V. ii9t Munderkingen, Germany, 164 16.4 3-3 None Cincinnati, Ohio, 70 10 1.25 Melan beams p. 224 Eng. News, Oct., 1895, Maryborough, Queensl'd 50 4 I.2S Steel rails p. 214 En^ng., London, May 10, 1895, p 395 Neuhausel, Hungary, SS-V8 3-7 0.82 Skeleton girders Inst. Civ. Engs.,V., 114, Philadelphia, Penn , 2S-39 6-S 3 lit" mesh, i" wire p. 402 Enq. News, Sept., 1893, netting p. 189 Buildings Reinforced Concrete Dome of Porto Rico Capitol. Eng Rec, May 1909, p. 5 Baxter Building, Portland, Me. Eng. Bradford, A. M. Mill Building of Cement Brick, Plymouth Cordage Company. Average Cost 12 per cent Less than Clay Brick. Eng. News. Mar., 1909, p. 288. Perry, J. P. H. Cold Storage Warehouses. Eng. News, Feb., 1909, p. 209. Mill of Androscoggin Pulp Company. Eng. Rec, Feb., 1909, P- 190- , Christopher Warehouse, Jacksonville, I'la. Eng. Rec, Jan., 1909, p. 72- . , JHason, W. H. Methods and Costs with Separately Molded Members. Nat. Assn. Cem. Users, Vol. IV, igoS^p. 48. Repairs at Pumning Station, EvansviUe, Ind. Eng. Rec, Dec, 1908, p. 719. . Great Western Railway Freisht Terminal, Cost of Walls at Camp Perry, Ohio. Cone, Eng., Sept., 1908, p. 249. Torrey Building, Boston, Mass. Eng. Rec, Eng. Rec, England. Eng. News, Dec 629- 1908, p, *An asterisk precedes the references which are especially noteworthy. Sept., 1908, p. 319. Sugar Warehouse, Detroit, Mich. Sept., 1908, p. 269. Construction with Reinforced Concrete Joints. Con. Eng., Aug., 1908, p. 214. Reinforced Concrete Mausoleum. Cone Eng July, 1908, p. 183. New Orleans Court House. Eng. News, July 1908, p. I. ' Chimney of Colusa-Parrott M. & S. Co., Butte Mont. Eng. Rec, June, 1908, p. 735. Chimney at Cumberland Mills, Me. Eng. Rec, May, igoS, p. 593. Hostetter Building, Pittsburg, Pa. Eng News, May, 1908, p. 521. First National Bank Building, Oakland, Cal. Eng. Rec, May, 1908, p. 648. Bostwick-Braun Buildmg, Toledo, O. Eng. Rec, May, 190S, p. 575. REFERENCES TO CONCRETE LITERATURE 83s Cantilever Girders in the Boyertown Build- ing, Philadelphia. Eng. News, Apr., 1908, p. 447. Pnelpa Fublisning Co. Building, Springfield, Mass. Eng. Rec, April, 1908, p. 459. Burr, W. H. Thirty-ninth Street Building. New Yorlc. Trans. Am. Soc. Civ. Engr., Vol. LX, p. 443 ■ Harwooi, S. Q> Wisconsin Central Railway Depot, Minneapolis, Minn. Eng. Rec, March, 1908, p. 394. Foundry Building at Sloline, 111. Eng. Rec, -March, 1908, p. 297. Cement Stock House near Montreal, Canada. Eng. Rec, Feb. 1908, p. 1S9. Westport Power House, Baltimore, Md. Eng. Rec, Feb., 1908, p. 116. Terrell, C. B. Garage, White Plains, N. J. Eng. News, Dec, 1907, P- 633. St. Mark Hotel, Oakland, Cal. Eng. Rec, Dec, 1907, p. 686. Newark Warehouse Co., Newark, N. J. Eng. liec, Aug., 1907- P- i52. Chateau des Beaux Arts on Huntington Bay, Long Island. Eng. Rec, Aug., 1907, p. 186. Separately Moulded Members Edison Portland Cement Co. Building, New Village, N. J. Eng. News, July, 1907. P> 5. R. H. H. Steel Laundry Building, Newark, N. J. Eno;. Rec, June, 1907, P- 677- Burleig:h. W. F. Murphy Varnish Co. Build- ing, Newark, N. J. Eng. Rec, May, 1907, p. 555. Holy Angels School, Buffalo, N. Y. Eng. Rec, April, 1907. P- 49i- Ketterlinus LithoEcrapbic Manufacturing Co. Building, Phila. Eng. Rec, Feb., 1907, p. 128. ♦Stadium. Athletic field of Harvard University. L. J. Johnson, Jour. Assn. Eng. Socs., June, igo4, p. 293. *Store building, Chicago, 111. Eng. Rec, June, 1904, p. 713- Chimney reinforced with T-bars, Zeigler, 111. Eng. Rec, May, 1904, p. 661. *Kelly & Jones Company's factory building. Eng. Rec, Feb., 1904, pp. 153 arid 195. Lighthouse at Nicolaieff, Russia. Eng. Rec, Jan., 1904, p. TOO. ♦Factory building. Long Island City, N. Y. Eng. Rec, Jan., 1904, p. 67. College of Music, Cincinnati, Ohio. Eng. Rec. Nov., 1903, p. 666. *The Filtration works of the East Jersey Water Supply Company, Little Falls, N. J. G- W. Fuller, Trans. Am. Soc. Civ. Eng., Vol. L, p, 394- *IngaUs Building, Cincinnati, O. Eng. Rec, May, 1903. P- 540- Robert A. Van Wick Laboratory, New York. Cement, Sept., 1901, p. 203. Elevator, Buffalo, N. Y. C. R. Neher, Jour. Assn. Eng. Socs., April, 1901, p. 275. Nassau County Jail, Long Island. Cement, March, 1901, p. 37- Medieval Castle of Badajos, Spain. G. L. Sut- cliffe, Concrete, 1893, p. S* St. James's Church, Brooklyn, N. Y. Cement, Nov., 1900, p. 196. Singer Manufacturing Go's. Bmldings and Chim- neys. Cement, Sept., 1900, p. 162, and May, 1901, p. 88. . Office Building, Washingon, D. C. A. L. Harris, Cement, Sept., 1900, p. 155. ^ Library Building at University of Virgima. Ross F. Tucker,' Cement, March, 1900, p. 26. Eagle Warehouse and Storage Co. Building- Brooklyn, N. Y. Eng. Rec, Jan., 1907. p. 19. Marlborough Apartment House, Baltimore, Md. Eng. Rec. Jan., 1907, p. 99. ■Derfel Ing. Rob. A Print Mill Building, Briinn, Germany. Beton u. Eisen, Heft I, 1907, p. TO. Hotel Traymore, Atlantic City. N. J. Eng. Rec, Nov., 1906, p. 523. Cadillac and Packard Automobile Shops. Detroit, Mich. Eng. Rec, Nov., 1906. p. 544. Traders Paper Bond Co. Building, Bogota, N. J. Eng. Rec, Oct., 1906, p. 457. A. T. & S. F. Railway Station. Eng. News, Sept., 1906, p. 246. Marlborough Hotel Annex, Atlantic City, N. J. Eng. News, March, 1906, p. 25 1. Taylor & Wilson Manufacturing Co. Building, McKees Rocks, Pa. Eng. Rec, Dec, 1905. p. 695. B. T. Babbit Works, Jersey City, N. J. Eng. Rec, Dec, 1905, p. 747. North West Kpitting Co. Building, Minne- apolis, Minn. Eng. News, June, 1905, P- 593- Concrete Medical Laboratory, Brooklyn, Navy Yard. Eng. News, March, 1905 p. 310. Masonic Temple Building, Toledo, Ohio. Eng. News, March, 1905, p. 2S7. United Shoe Machinery Shops, Beverly, Mass., Eng. Rec, March, 1905, p. 257. Bilgram Machine Shop, Philadelphia. Eng. Rec, Feb., 1905, p. 136. Chapel of the United States Naval Academy, Annapolis. Eng. Rec, Jan., i9o5, p. 36. ♦Chimney of Pacific Electric Ry., Los Angeles, Calif. J. D. Schuyler, Cement, March, , 1903, p. 30. Chimney of the Laclede Fire Brick Manufacturing Co., St. Louis, Mo. Cement, March, 1903, P- 37- Dome on Yale University Building, New Haven, Conn. Cement, March, 1903, p. 15. Strasburg Music Hall, Strasburg. Beton & Eisen, III Heft, 1903, p. 149. Salvation Army Building, Cleveland, Ohio. Ce- ment and Eng. News, Jan., 1903, p. 10. Cold Storage Plant, Oklahoma City, Okla- homa. Cement and Eng. News, Jan., 1903, p. I. Amand Apartment House, Paris. Jean Shopfer, Arch. Rec, Aug., 1902. Hecla Portland Cement & Coal Co., Michigan. Eng. News, June, 1902, p. 449. College Fraternity Building, New Haven, Conn. Cement, Jan., 1902, p. 334. Factory Building, Cambridge, Mass. Cement March, 1900, p. 18. Pacific Coast Borax Co's Plant, Bayonne, N. T- Eng. Rec. July, 1898, p. 188. Museum Building of Leiand Stanford, jr., Uni- versity, Calif. Charles D. Jameson, Port- land Cement, 1898, plates V and VI. Record Building of Discount Bank, Paris. Re?. Tech., May 10, iSgS.f Beocsin Cement Works, Germany.t Oest. Mo- natschr. f. d. Oeff. Baudienst, July, 1897. Concrete Structures in Denmark and Russia. Eng. News, April, 1896, p. 253. A Concrete House Built in 1872. W. E. Ward, Trans. Am. Soc. Mech. Engs., Vol. IV, p. 388 *An asterisk precedes the refercDces which are especially noteworthy, f Engineering Indeie. Ss6 A TREATISE ON CONCRETE Dams Ohio River Bear-Trap Dam. Eng. News, Mar., 1909, D. 235. Scranton, Pa. Buttressed Dam. Eng. Rec, Mar., 1909, p. 347. Connecticut River Power Company Hydro- Electric Plant. Eng. Rec, Mar., 1909, p. 340. Kern River Hydro-Electric Plant. Eng. News, Dec, 190S, p. 701. Chicago Drainage Canal Movable Dams and Lock. Eng. News, Nov., 1908, p. 5i2. Bellows Falls, Vt. Erection Plant. Eng. News, Dec, 1908, p. 74S. Croton Falls Reservoir Dam. Eng. Rec, Dec, 1908, p. 675. Berrien Springs, Mich. Hydro-Electric Devel- opment. Eng. Rec, Dec, 1908, p. 728. Uncas Power Company Hydro-Electric Plant. Encr. Rec, Nov.,> 1908, p. S72. Roosevelt Dam, Salt River Project. Eng. News, Sept., 1908, p. 265. Horse Shoe, N. Y. Combination Dam and Bridge. Eng. News Apr., 1908, p. 385. Westchester County, N. V., near Croton Falls. Eng. Rec, Mar., 1908, p. 377- McCall Ferry, Pa. Eng. News, Sept., 1907, Katonah, N. Y. Cross River Dam. Eng. Rec, Sept., 1907, P- 281. West Point, N. Y. Buttress Dam. Eng. Rec, Aug., 1907, p. 214. ,, ^ ^ ^ Bates, L. Croclter's Reef, N. Y. Eng. Cont., July, 1907. P- 17- , , _ Utica, N. Y. Eng. Rec, July, 1907. P- 75. Markiissa. Dumas, A. Gen. Civ., June i5, 1907. Ellsworth, Me. Eng. News, May, 1907, P. Holland' de Muralt, Dr. L. R. Baton u. Eisen. Heft I, 1907, P- 8. Warriors Ridge Gap, Pa„ above Huntmgton. Eng. Rec, Dec, 1906, p. 678. Plattsburg, N. Y. Eng. Rec, Mar., 1906, p. 335. Columbus, O. Scioto River Gravity Storage Dam. Encr. Ren., Seot., J9o5, p. 302- Schuylerville, N. Y. Eng. Rec, Mar., 1905, p. 267. Fenelon Falls, Ont. Eng. News, Feb., igoS, p. 135. •Lynchburg, Va. Eng. Rec. July, 1904, p. 108. *Ithaca, N. Y. Eng. Rec, April, 1904, p. 446. Danville, III. Eng. Rec, April, 1934, d. 396. South Australia. A. B. MonerieEf, Eng. News, April, 1934, p. 321. ♦New Milford, Conn. Walter Scott Morton, Eng. Rec, Feb., 1904, p. 187. Birmingham, Eng. Eng. Rec, Jan., 1904, p. 120. Theresa, N. Y. Ambursen & Sayles, Eng. News, Nov., 1903, p. 403. San Diego, Calif. Eng. Rec, Nov., 1903, p. 590. *.Spier Falls, Hudson River. Geo. E. Howe, Eng. Rec, June, 1903, p. 688. ^Chaudiere Falls, Province of Quebec. Eng. News, May, 1903. P- 3P8' *Noiwich, Conn. H. M. Knight, Eng. News, June, 1902, p. 470. Lake Winnibigoshish. W. C. Weeks, Cement, March, 1901, p. 20. 0«age River, Missouri. Rept. Chief of Engs., U. S. A., 1900, p. 80. Milllnocket, Maine. Eng. Rec, Dec, igoo, p. 560. Johannesburg, So. Africa. Eng. Rec, Jan., 1899, p. 112, ♦Mechanicsville, N. Y. Eng. News, Sept., 1898, p. 130. Muchkunki, India. Eng. Rec, May, 1898, p. 570. Pioneer Power Plant, Ogden, Utah. Henry Gold- mark, Trans. Am. Soc. Civ. Eng., Vol. XXXVni, p. 246. Rock Island Arsenal, 111. O. C. Homey, Jour. W Soc. Eni?s., Vol. II, p. 339. Rio Grande River. Eng. News, July, 1897, p. 36. Arch Dam, Ogden, Utah. Eng. Rec, March, 1897, p. 291. Cold Spring, N. Y. Eng, Rec, July, 1896, p. 105 Manchester. England. Eng. Rec, Nov., 1891, ^ P- 387. *Croton River, New York. J. R. Croes, Trans. Am Soc Civ. Eng., Vol. Ill, p. 337. Elasticity of Concrete and Mortar Heintel. Elasticity of Concrete in Shear. Cement, Apr., 1908, p. 461. Howard. J. E. Elasticity of Materials Com- pared. Eng. Rec, May, 1906., p. 658. Discusaion Ti-ans Vol. LIV, part X Thompson, Sanford E . A n. Soc Civ. Engs. p. 594. Woo'son, Iran. [Recent Tests. Eng. News Juno, 1905, p. 56r. Watertown Arsenal. Elasticity of Mortar Prisms. Tests of Metals, 1902, p. 467. Watertown Arsenal. Elasticity of Concrete Cubes. Tests of Metals, 1898 to 1933. Sewell, John S. Study of Stress-strain Curves. Int. Eng. Con;., St. Louis, 1904. Thompson, Sanford E DiscUssion on Stress- strain Curves. Int. Eng. Cong., St. Louis, 1904. Hatt, W. K. Experiments on Elasticity of Con- crete Jour. Assn. Eng. Socs., June, 1904, p. 321- Van Ornum, J. L. The Fatigue of Cement Prod- ucts. Trans. Am. Soc. Civ. Eng., Vol. LI, P- 443- Johnson. J. B. Miscellaneous Tests of Elasticity. Various authorities, Johnson's Materials of Construction, 1903, p. 575. Falk, Myron S Elasticity during Flexure. Trans. Am. Soc. Civ. Eng., Vol. L, p. 473. Chrlstophe Paul. Data from various authorities. B^ton Arm(S, 1902, p. 468. Thacher, Edwin. Effect of Age and Composition on Elasticity. Cement, May, July, and Nov., 1902. Kurtz, Charles M. Austrian Society Values for Steel, Concrete, and Mortar. Jour. Assn. Eng. Socs., Feb., 1901, p. 109. *Henby, W. H. Relative Elasticity of Cinder and Broken Stone. Jour. Assn. Eng. Socs., Sept.» 1900, p. 145. Moliter, David. Curves from Tests of Prof. Bach Jour, Assn. Engs. Socs., May, 1898, p. 349. Brown, W. L. Tables and Curves. Pro. Inst. Civ. Engs., Vol. CXXXVII, p. 402. Bach, C. Experiments on the Elasticity of Con- Crete. Jour. W. Soc. Engs., Jan., 1896, p. 84 Hartig, E. Formula for Variation with Age of the Modulus of Elasticity. Pro. Inst. Civ. Eng., Vol. CXX, p. 375. Baker, Benjamin. Effect of Sand on the Elastimy Pro, Inst. Civ. Eng., Vol. CXV, p. io8. ♦ An asterisk orecedes the teferences which are especially noteworthy REFERENCES TO CONCRETE LITERATURE 837 Ezpansioti and Contraction Qowen, C, S. Effect of Temperature Changes on Masonry. , Trans. Am. Soc. Civ. Engs. Vol. IiXT, p. 3t)9- 'Heat Expansion Stresses m Chimneys. Eng. News, March, 1908, p. 259. Expansion Joints in Pressure Sewer. Eng. News, March, 1908, p. 335. Expansion Joints in Viaduct. Eng. News, Dec, 1907, p. 628. White, Linn. Expansion Joints in Concrete. Eng. News, Jime, 1907, p. 6S3. Fuller, Qen*. W. ExpaJision Wells in Wate^ Puri- fication Works, Little Falls, N. J. Trans. Am. Soc. Civ. Engs., Vol. L, p. 406. ''Johnson, A. L. Continuous Concrete Walls with- out Expansion Joints. R. R. Gaz, March 13, 1903. *Rallway Superintendents. sion and Contraction. 1900, p. 166. Adams, A. L. Contraction Cracks in Reservoir Lining. Trans. Am. Soc, Civ. Engs., Vol. XXXVI, p. 30. LewerenZi A. C. Expansion and Contraction of Concrete Structures. Eng. News, May, 1907, p. 5i2. Expansion Joints in Sandy Hill Bridge. Eng. News, May, 1907, p. 503. Becker and Lees. Expansion Joint in Con- crete Roof in Carp and Bldg., May, 1907, p. 167. Webb, W. L. Long walla built without ■joints with J% of steel, Munic. Eng., Aug., 1906, p. 112 Joints in Butte, Mont., Reservoir* sn. Eng. Socs., Oct., 1902, p* Provisions for Expan- Pro. Assn. Ry. Supts., Paine, C. W. Jour. A; ♦Pence, W. D. The Coefficient of Expansion of Concrete. Eng. News, Nov., 1901, p. 380. Gary, Max. Tests showing Shrinkage in Air and Expansion under Water. Trans. Am. Soc. Civ. Engs., Vol. XXX, p. 17. A. S. C. E. Comniittee. Expansion and Contrac- tion Experiments. Trans. Am. Soc. Civ Engs., Vol. XV, p. 722, and Vol. XVlI. p. 214. Fire Resistance of Concrete and Mortar Waite, Guy B, Cinder and Stone Concrete Under Fire. Trans. Am. Soc. Civ. Engs., Vol. LX, p. 470. Woolsen, Ira n. Fireproof Qualities of Con- crete Partitions. Cement Age, June, 1908, p. 578. / Thompson, Sanford E. Concrete in the Chel- sea Fire. Cement Age, June, 1908, p. 569. Report on Parker Building Fire, N. Y. City. Eng. News, May,' 1908, p. 567. Gilbert, J. B. Fire at Dayton Motor Car Works. Eng Rec, March, 1908, p. 384. Report on Fire and Earthquake Damage to Buildings at San Francisco. Trans. Am. Soc. Civ. Engs., Vol. LIX, p. 208. Woolson, Ira H. Investigation of the Ther- mal Conductivity of Different Mixtures and Efifect of Heat upon Them. Pro. Am. Soc. Test Mat.. Vol. VI and VIL Effect of Heat on the Strength and Elastic- ity of Concrete. Pro. Am. Soc. Test Nat., VoL V, p. 335. *Watertown Arsenal. Tests of Cement set at Differ- ent Temperatures. Tests of Metals, U. S. A., 1902, p. 383. ♦Norton, Chas. L. Tests of Fire Resistance of Concrete. Tech. Qr., June, 1900; Dec, 1902; June, 1904. Ins. Eng., Dec, 1901. P- 483; Feb., 1902, p. 72; March, 1902, pp. 118 and 211. ♦Norton, Chas. L., and Gray, Jas. P. Report on the Baltimore Fire. Eng. News, June, 1904, p. 528. Sewell, John S. Report on the Baltimore Fire. Eng. News, March, 1904, p. 276. Jtofahson, J. B. Miscellaneous Tests. Materials of Construction, 1903. P- 625. Newberry, S. B. Theory of^ Protection. Cement, May, 1902, p. 95. Thompson, Sanford E. Fire Resistance of Reinforced Concrete Construction. Con. Eng. June, 1907, p. 261. MacFarland, H. B. Fire and Load Test of Beams. Eng. Rec, March, 1907, p. 380. Teats of the Effect of Heat on Reinforced Concrete Columns. Eng. News, Sept., 1906, p. 316. Comparative Resistance to Fire of Stone and Cinder Concrete. Eng. News, May, 1906, p. 603. San Francisco Earthquake and Fire. U. S. Geological Survey Bulletin, No. 324, April, 1906. Fire and Water Tests of Stone Concrete and Cinder Concrete Floors. Eng. News, Feb., 1906, p. 1 1 5. Probst, E. A Model Reinforced Concrete Theater for Studying Theater Fires. Cement & Eng. News, Feb., 1906, p. 34, Fire Resistance of Different Concretes. Eng. Rec, July, 1905, p. 97. Cement, Pacific Coast Borax Co., Bayonne, N. J. May, 1902, p. 85. Norton, Charles L. Tests to find Temperature of Steel during a Fire. Ins. Eng., Feb., 1902. Test Building at Mineola, L. I. Cement, Jan., 1902, p. 358. Moore, Francis C. Extracts from Publications of the British Fire Prevention Committee. Can. Eng., Aug., 1898. Tests of Fireproof Floors. Eng. News, Sept., 1896, p. 182; Nov., 1896, pp. 296 and 314; Jan., 1897, pp. 6 and 15; Dec, 1897, p. 367; Nov., 1901. p. 378; May. 1902 p. 441. nimmelwright. A. L. A. Fireproof Construction and Recent Tests. New York. Eng. Mag., Dec, 1896, p. 460. Forms Adjustable Forms for Heavy Battered Walls. Eng. Rec, April, 1909, P- S40. Scott. C, P. Patented Steel Form for Arch, Culvert and Bridge, ^ng. Contr., Feb., 1909, p. iSo. Adjustable Steel Centers for Sewer. Eng. Contr., Jan., 1909, p. 65. Caldwell, W, L. Metal Forms in Reinforced Concrete Construction. Nat. Asssn, Cem. Users, Vol. IV, p. 2S6. A Collapsible Form for Small Culvert. Eng. Cont. Dec, 1908, p. 408. *An asterisk precedes the references which are especially noteworthy. 838 A TREATISE ON CONCRETE Steel Forms Used in the Blue Island Avenue Sewer, Chicago. Kng. News, Oct., 1908, p. 441. Patented Forms Used in Bronx Valley Sewer. Cement Age, Oct., 1908, p. 309. Wooden Forms for Concrete Manhole. Eng. Coat. Oct., 1908, p. 270, . Steel Centering, Harlem Creek Sewer at St. Louis, Mo. Eng, News, July, 1908, p. 131- Adjustable and Portable Forms for Concrete Building Construction. Eng. News, March, 1908, p. 264. Desim and Construction of Forma. Con. Eng., March, 1908, p. Sg. Forms for Big Cottonwood Conduit, Salt Lake City. Eng. Rec, March, 1908, p. 353. Teichman, F. Traveling Mold for Makmg Concrete Pipe. Eng. News, Feb., 1908, p. 184. Proposed Traveling Form for Construction of Water Pipes and Sewers. Eng. Contr., Jan., 1908, p. 30. Thompson, Sanford E. Forms for Concrete Construction. Trans. Nat. Assn. Cem. Users, Vol. Ill, p. 64. Centering and Forms in Selby Hill St. Tunnel, St. Paul, Minn. Eng. Rec, Sept., 1907, p. 308- Reinforced Concrete Syphon on an Irrigation Canal in Spain. Eng. News, Aug.; 1907, p. 116. Forms for Jacksonville Viaduct Piers and Spandrels. Eng. Rec, May, 1907, P- 606. Hotchkiss, L. J. Retaining Wall Forms. Eng. Rec, Marcli, 1907, P- 339- Steel Centers. Eng. News, Oct., 1904, p. 350. *Courtrlght, P. A. Center for 54-ft. Span Arch. Eng. News, May, 1904, p. 456. Clark, H. G. Catch-basin Forms. Eng. News, May, 1904, p. 473- *Centers for 5-ft. Egg Sev/er, Washington, D. C. Eng. News, Feb., 1904, p. 163. A Tie for Concrete Forms. C. M. & St. P. Ry. Eng. News, Jan.. 1904, p. o6- *TunneT Forms, Central Mass. R. R. Eng. Rec, Jan., 1904, p. 5. *Forms for Core Walls. Cedar Grove Reservoir. Eng. Rec, Dec. 1903, p. 680. Taylor, C. 0. Methods of Building a Cellar Wall. Car. & BIdg., Aug. 1903, p. 213. *Arch Center in New York Subway. Eng. News, June, 1903, p. 514. *Kleinhans, Frank B, Centering Arch Bridge, Collapsible Centering for Street RailwayCon- d:uis. Eng. News, March, 1907, p. 3i5, Centering for Piney Creek Bridge, Washing- ton, D. C. Eng. Rec, Jan., 1907, p. 88. Forms for Molding Concrete Pipe Culverts. Eng. News, Dec, 1906, p. 65 1. Portable Arch Centering — Hodges Pass Tun- nel. — Eng. New., Dec, 1906, p. 586. Centering for the Concrete Arches for P. & R. R. R. Bridge. Eng. Rec, Oct., 1906, p. 399. Heavy Panels for Retaining Walls Handled by Locomotive Crane. Eng. Rec, Sept., 1906, p. 273. Reinforced Concrete Forms for Arch Rib Bridge. Eng. Rec, Sept., 1906, p. 237. Arch Rib Bridge, Grand Rapids, Mich. Eng. News, Aug., 1906, p. 2i5; March, 1906, p. 322. Centering for 5o ft. Span Segmental Arch. Eng. News, Aug., 1906, p. 207. Forms for a S ft. 9 in. Sewer, New Orleans. Eng. Rec, June, 1906, p. 678. Forms for Sewer, South Bend, Ind. Eng. Rec, June, 1906, p. 736. Forms for Connecticut Ave. Bridge, Wash- ington. Eng. Rec, June, 1906, p. 675. Special Falsework for a Concrete Bridge. Eng. Rec, April, 1906, p. 484. Retaining Wall Forms, N. Y. Central R. R. Eng. Rec, Jan., 1906, p. 24, Evans, R. R. Traveling Form for Construct- ing Invert of Sewer. Eng. News, March, J905, p. 254. Carver, G. P. Forms for 36-in. Sewer, Bev- erly, Mass. Eng. News, June, 1904 p. 55o. ' C. M. & St. P. Ry. Eng. News, March, 1903, p. 267. Skew Back Forms. Long Island R. R. Eng. News, Dec, 1902, p. 519. *Arch Centering. Zanesville, O., Bridge, Eng. News, March. 1902, p. 264. Template for Sewer Invert, New York Rapid Transit Railway. Eng. News, March, 1902, p. 200. Wall Forms in Nassau County JaiJ . Photograph. Cement, March, ipoi, p. 37. Abbot, F. V. Details of Forms in Improvement of Mississippi River. Cement, Jan., 1901, p. 229. =^Hazen, Allen. Groined Arch at Albany Filtration Plant. Trans. Am. Soc. Civ. Engs., Vol. XLIII, p. 270. A Collapsible Center for Sewer Arches. Eng. News, Jan., 1899, p. 22. Foundations Colber^, Otto. Tests of Strauss System cf - Piles, Vienna. Beton u Eisen, Heft III 1909, p. 54. Howell, C. S. Straight or Tapered Concrete Piles. Eng. News, Feb., 1909, p. 223. Method of Pipe Protection on Piles. Eng. Rec, Jan., 1909, p. 67. Thompson and Fox. Cast Reinforced Concrete Piles. Jour. Assn. Eng. Socs., Jan., 1909. Cannon, M. M. Concrete Piles, Brunswick, Ga., and Charleston, S. C. Jour. Assn. Eng. Socs., Jan., 1909, p. 24- Mensch, L. J. Shop-made Reinforced Con- crete Piles. Eng. News, Dec, 1908, p. 620. Usina, D. A. Recent Developments in Pneu- matic Foundations. Trans. Am. Soc. Civ. Engs., Vol. LXI, 1908, p. 211. Foundation Wall Supported by a Reinforced Concrete Girder. Eng. Rec, Feb., 1908, p. 175. Compressol System of Concrete . Founda- tions. Eng. Cont., Oct., 1907, p. 220. Chamber of Commerce, V ienna. Beton u . Eisen, Apr., 1907, p. 85. Foundation of Buildings in Mountaneous Regions. Beton u Eisen, Mai, 1907, p. ti3. Foundations of Singer Building Extension, New York Eng. Rec, Feb., 1907, p. it6. Concrete Foundation Mat for a Power Station. Con. Eng., Feb., 1907, p. 77. Caisson Foundations for The Trust Company of America Building. Eng. Rec, Oct., 1906, p. 470, Footings for Transmission Poles. Eng. News, June, 1906, p. 648. *An asterisk precedes the references which are especially noteworthy. REFERENCES TO CONCRETE LITERATURE 839 Hollow Concrete Foundation Piers, U. S. Post Office at Cleveland, Ohio. Eng. Rec, May, 1906, p, 607. Machinery Foundation in Quicksand, Knick- erbocker Building, New York. Eng. Rec, March, 1906, p. '247. Unusual Founaation at the Hoboken Termi- ual, Eng. Rec, Nov., igoS, p. 546. Foundations for the Yonkers Power House of the N. Y. 0. & H. R. R. R. Eng. Rec. , Dec, 1904, p. 676. Concrete Piling at Washington Barraclcs, D. C, Eng. Rec, Oct., 1904, p. 463- Concrete Pile Foundation of the U. S. Ex- press Co. Bldg., New York City. Eng. News, Oct., 1904, p. 348, Anderson, W. P. Concrete Piles. Eng. Rec, Oct., IQ04, p. 404. Holmes, J. Albert. Reinforced Concrete Piles with enlarged Footings. Eng. News, June, 1904, p. 567- Concrete Piles. Eng. Rec, May, 1904, p. 596. Concrete Piles. Cement, Nov., 1903, p. 331. Kimball, Qeo. A. Foundations for the Elevated Structure of the Boston Elevated Railway. Jour. Assn. Eng. Socs., June, 1903, p. 351. ♦Francis, Geo B. Foundations. Jour. Assn. Eng. Socs., June, 1903, p. 336. . •Worcester, Joseph R. Boston Foundations (with discussion). Jour. Assn. Eng. Socs., June, 1903, p. 285. Making Concrete Piles in Place. Eng. News, March, 1903, p. 27s. Concrete-steel Piles. Cement, March, 1903, p. 16. A Concrete-steel Pile Foundation in Germany. Eng. News, Feb., 1903, p. 173. Concrete Pile Foundations at Aurora, 111. Eng. News, Dec, 1902, d. 495. Menscli, L. Reinforced Piles and Sheet Piling. Jour. Assn. Eng. Socs., Sept., 1902, p. 108. Concrete-steel Column Footing with Corrugated Bars. Eng. News, April, 1902, p. 273. Franklin Building Foundations, New York. Eng. Rec, May, 1898, p. 566. •Breuchaud, J. The UnderpiiminE of Heavy Build- ings. Trans. Am. Soc. Civ. Engs., Vol. XXXVn, p. 31. Hunt, Randall. The Design of Foundations for Tall Buildings. Jour. Assn. Eng. Socs., July, 1896. p. I. •Murphy, Martin. Bridge Substructure and Foun- dations in Nova Scotia. Trans. Am. Soc. Civ. Engs., Vol. XXIX, p. 620. Marine Construction Sub-structure and Concrete Pier, White Shoal HarbOT Work, Huron Light, Lake Michigan. Eng. Rec, June, 1909, P- 735. Sea War " 'Eng. Rec, Apr. Vall, Fort Morgan, Ala. 1909, p. 545. Welcker, Rudolph. De Muralt System of Shore Protection. Eng. News, Dec, 1908, p. 674. Judson, W. V. Reinforced Concrete Caissons for Breakwater at Algoma, Wis. Eng. News, Oct., 1908, p. 421. Improvement of Milwaukee Harbor, ting. Rec, Oct., 1908, p. 452. . Cameron, H. F. Sea Wall, Cebu, PhiUppme Isls. Eng. Rec, Apr., 1908, p. 544. Quay Walls for Dry Dock, Charleston, S. C, Navjr Yard. Eng. Rec. Feb., 1908, p. 120. ^„. ., , , Ohio. Eng. Rec, Oct., 1907, p. 45o, Low, Emile. Breakwater at Harbor Beach, Mich. Eng. News, March, 1907, p. 339. The Racine Reef Lighthouse and Fog Signal in Lake Michigan. Eng. Rec, Mar., 1907, p. 384. Docks, Port Chalmette, La. Eng. Rec, July, igo6, p. 88. Pier, Atlantic City, N. J. Cement, July, 1906, p. 119. Connor, E. H. Wharf, Tampico, Mexico. Eng. News, June, J9o5, p. 603. Pier, and Bulkhead Construction, New York Harbor. Eng. News, May, igoS, p. 503. Failure and Reconstruction of a Sea Wall. Clar- ence T. Fernald, Jour. Assn. Eng. Socs. June, 1903, p 343. , Hennebique System applied to Hydraulic Works. A. von Horn, Oest. Wochenschr. f . d. OeS. Baudienst, June 27, I903- , „ , •South Pier, Duluth, Minn Clarence Coleman. • Cement, Sept , 1900, p. 141- , Bruo-es Ship Canal, Belgium. 3,000 ton blocks. Eng. News, Nov., 1890, P- 300- Dock Wall, Clinton Ave., Brooklyn, N. Y. Eng. Rec, Jan., 1897, P-,".4- „ ., __„ Monolithic Dock Foundations, Newcastle, Eng. Eng. News, April, 189s, p. 222. •Breakwater Construction, Buffalo, N. Y. Emile Low, Trans. Am. Soc. Civ. Engs., \'ol. LII, •Concrete Breakwaters at various places. Re- port Chief of Engs., U. S. A., 1900 an Whan at Portslade, Sussex, Eng. Joseph Cash, Pro. Inst. Civ. Engs., Vol. CXVIII, {>. 392., Breakwater, near Middlesborough, Eng. Eng. News, Aug., 1893, p. 153-, „ , „ . . •Colombo Harbour Works. John Kyle, Pro. Inst. Civ. Eng., Vol. LXXXVII, p. 76- •Wicklow Harbour Improvements. WO. Strype, Pro. Inst. Civ. Engs., Vol. LXXXVII, p. H4- Permeability and Porosity Davis, J. L. Tests on Water-retaining Ability of Stone and Concrete. Eng. News, July, Fuller a°nd Thompson. Tests of Penneability. Trans. Am. Hoc. Civ. Engrs., Vol. LIX, Feret''°K. ^ Tests of Permeability. Trans. Am. Soc. Civ. Engra. V ol. LIX, 1907, P- 1S7. Thompson, Sanford E. Tests of Permeability. Pro. Am. Soc Test Mat. Vol. VI, p. 377- Method of Determining Porosity of Cement. Cement, May, 1905, p. 67. Thompson, Sanford E. Permeability Tests of Concrete with the Addition of Hydra ted Lime. Am. Soc Testing Mat., Vol. V III, 1908. p. 5oo. *An asterisk precedes the references which are especiaUy noteworthy. 840 A TREATISE ON CONCRETE •Marston, A, Porosity of Sand-lime and Sand- cement Brick and Concrete Building Blocks. Eng. News, April, 1904. p. 387. Ttionipson, Sanford E. Results of French Experi- ments. Trans. Am. Soc. Civ. Engs., Vol. LI, p. 131. *Ani. Soc. Civ. Engs. Discussion on Impervious Concrete. Trans. Am. Soc. Civ. Engs., Vol. LI, p. 114. ♦Thompson, Sanford E. Recommendations for Testing. Pro. Am. Soc. Civ. Engs., Aug., Percolation Testing Machine for Cement. Cement, May, 1903, p. 88. Mclntyre & True, Permeability under High Pres- sures. Eng. News, June, 1902, p. 517. Lang. Permeability to Air. Ann. des Trav. Pub. de Belgique, April, 1900. Hazen, Allen. Voids in Ordmary Concrete. Trans. Am. Soc. Civ. Eng., Vol. XLII, p. 128, Tetmajer. Tests. Tetmajer's Communications, Vol. VI. „ , „ . Ross, H. H., Broenniman, A. E. Tests of Pqroslty of Neat Cement and Mortar. Jour. W. Soc. Erigs., Vol. II, p. 449. French Commission. Standard Methods of Tests and Results of Tests. Commission des Mi- thodes d'Essai des Mat^riaux de Construc- tion, 1893, Vol. I. . , r, *Feret, R. Tests and Conclusions. Ann. des Fonts et Chauss., 1892, II, p. 77. Protection of Metal Schaub, J. W. Silicate of Iron Formation, which is soluble in. Water. Trans. Am. Soc. Civ. Engs., Vol. LI, p. 124. ♦American Society Civil Engineers. DiscU'rsion: The Preservation of Materials of Construction. Trans. Am. Soc. Civ. Engs., Vol., L, p. 293. Toch, Maximilian. The Permanent Protection of Iron and Steel. Jour. Am. Chem. Soc, 1903. Pabst Hotel Steel Frame, New York. Eng. News, Jan., 1903, p. 113. Reservoirs and Tanks Reservoir, Rolla, Mb. Eng. Reo., Mar., 1909, Tufts,' R.'b. Water Tower, Atlanta, Ga. ♦Norton, C. L. Tests to determine the Protection afforded to Steel by Portland Cement. Ins. Eng. Experiment Station, Reports No. IV and IX. Tech. Qr., Dec, 1902. ♦Newberry, S. B. The Chemistry of Concrete-Steei Construction. Eng. News, April, 1902, p. 335. Action of Cinder Concrete on Steel. Eng. News, 1897, p. 186. Eng. Rec, Jan., 1900, p. 9. Water Tower, Grand Rapids, Mich. Eng. Rec, Dec, 1908, p. 662. Torrance, Wm. M. Reinforced Concrete Freezing Tanks. Eng. News, Dec, 1908, p. 64r. Torresdale Preliminary Filters, Philadelphia. Eng. Rec, Nov., 1908, p. 577. Carver, George P. Coal Pocket, Charlestown, Mass. Eng. News, Aug., 1908, p. 229. Locomotive Coaling Station, Concord, Va. Eng. News, June, 1908, p. 690. Hudson, Wilbur Q. Locomotive Coaling and Ash-Handling Plant, Elizabethport, N. J. Eng. News, Apr., 1908, p. 414. Elevated Water Tanks in Cuba. Eng. News, Apr., 1908, p. 471. Brewer, B. Storage Well, Waltbam, Mass. Eng. Rec, Mar., 1908, p. 272. Septic Tank, Ithaca, New York. Eng. Rec, Feb., 1908, p. 136. Stewart, C. B. Tanks and Tubes for Experi- mental Purposes at University of Wis- consin. Eng. News, Jan., 1908, p. 3°. Power Plant Reservoir, Cos Cob, Conn. Eng. Rec, Sept., 19071 P- 312- Circular Tanks, Lancaster Filtration Plant. Eng. Rec, Sept., 1907, p. 298. Water Tower, Anaheim, Cal. Eng." Rec, Aug., 1907, p. 203. Ellis, A. W. Sand Bins and Drycjr. Con.' Eng., Aug., 1907, p. 47. Coal Pockets, Greenaburg, Pa. Eng. Rec, May, 1907, p. 5S4. Collapse 9f Reservoir in Madrid, Spain. Beton u. Eisen^ Apr., 1907,0. 106. Stand Pipe, Attleboro, Mass. Eng. News, Feb., 1907, p. 212. Reservoir, Waltham, Mass. Eng. Rec, Jan., 1907, p. 32. Gas Holder Tank, New York City. Eng. Rec, Mar., 1906, p. 262. Water Tower, Bordentown, N. J. Eng. Rec, Jan., 1906, p. 39. Godfrey, Edward. A 75, 000 Gallon Cistern, Allegheny, Pa. Eng. News, Sept., igoS, p. 330. Filtration Plant, Marietta, Ohio. Eng. Rec, Apr., 1905, p. 452. Doten, Leonard S. Water Tower and Stand- pipe, Fort Revere, Hull, Mass. Cement Age, Feb., i9o5, p. 353. Meol^nical Filters, Haokensaok, N. J. Eng. Rec, Nov., 1904, p. 590. Hot Well, New York Subway Power House. Eng. Rec, Nov., 1904, p. 611. Bins for Grain Elevator. Eng. News, June, 1904, p. 597. ♦Canadian Pacific Grain Elevator, ^Eng. Rec, April, 1904, p. 44S. Tanks for Cornell University Filter Plant, Ithaca, N. Y. Eng. Rec, April, 1904, p. 444. Tanks for Acid Liquor under Pressure. A. C. Arend, Eng. News, April, 1904, p. 384. Reservoir, East Orange, N. J. Eng. Rec, March, 1904, p. 386. ♦80-ft. Standpipe, at Milford, Ohio. Eng. News, Feb., 1904, p. 184. ♦The Groined Arch Roof. Leonard Metcalf, Eng. News, Dec, 1903, p. 564. Cement Storage Tanks, Illinois Steel Company. Eng. News, Aug., 1902, p. 148. Swimming Tank for New York Apartment House. Eng. News, July, 1902, p. 17. Frankley Reservoir, Birmingham, Eng. Cement, March, 1902, p. 5. Reservoir Lining and Dome, Nyack, N. Y. J. H. Fuertes, Trans. Am. Soc. Civ. Eng., Vol. XLV, p. 492. Tanks of Singer Manufacturing Co., Cairo, 111. Cement, May, 190T, p. 88. Reservoir with Expanded Metal at Waalheim, Belgium. Rev. Tech., Oct. 10, 1900. *An asterisk precedes the references which are especially noteworthy. REFERENCES TO CONCRETE LITERATURE 841 ♦Reservoirs in the United States. Leonard Metcalf, *T-, ^^' News, Sept., 1003, p. 238. ^Filtration Works of the East Jersey Water Co. at Little Falls, N. J. Geo. W. Fuller, Trans. Am. Soc. Civ. Eng., Vol. L, p. 394. Works and Water Supply of the Butte Water Co. Chas. W. Paine, Jour. Assn. Eng. Socs., Oct.. Ii>02, p. 143. Reservoir at Auvers, France. Rev. Tech., VoL XXI. p. 385. Aussig, Bohemia Reservoir. Zeitschr. d. Oest. Inp. u. Arch. Ver.. April 23, iSpr-t Beton Tank in Water Tower. Monier. Calbe, Germany.f Zeitschr. d. Ver.Deutscher Ing., March. 13, 1897. Sewage Tank. Paris. J. F, Flagg, Eng. Rec^ Dec, 1S96, p. 5. Sand and Stone, — Their Physical Characteristics (See also Strength of Concrete and Mortar^ Spackman and Lesley. Sands — Their Relation to Mortar and Concrete. Pro. Am. Soc. Test Mat., Vol. VIII, p. 429. Lamed, E. S. The Importance of Sand in Concrete. Proc. Nat. Assn. Cera. Users, Vol. IV, p. 20S. ^Thompson Sanford E. Sand for Mortar and Concrete. Am. Port. Gem. Manf. Assn. Bulletin, No. 3, 1006. Concrete Aggregates. Nat. Assn. Cem. Users, 1906, 13. 27. Eckel, Edwin C. Specific Gravity of Stone and Cemeita. Eng. News, Sept.. i9o5,p. 23S. Km. Ry. Eng. & M. of W. Asan. Weight of and per cent, of Voids in Broken Stone. Erig. News, March, jgo3, p. 284. Method of Washing Sand on Work of L. I. R. R. Eng. News, Dec, 1902, p. 5ig. *Candlot, E. Nature of Sand and Yield of Mortars. Ciments et Chaux HydrauHques, 1898, p 241. *Wheeler, E. S. Change in Volume of Sand by Addition of Water. Rep. Chief of Engs., U, S. A., 1895, p. 2935. Sandem&n. Voids in Different Stones. Pro. Inst. Civ. Engs., Vol. CXXI, p. 218. ♦Feret, R. Experiments with Different Sands for French Commission. Commission des M^- thodes d'Essai des Mat^riaux de Construc- tion, Vol. IV, 1895, pp. 73 and 309. Hazen, Allen. Relation of Voids to Specific Grav- ity. Trans. Am. Soc. Civ. Eng., Vol. XLII. p. 126. Roper, W. H. Sand Washing Machine. Eng. News, Feb., 1899, p. iii. *Ha2en, Allen. Physical Properties of Sands and Gravels. Mechanical Analysis. Rep., State Board of Health of Mass., 1892. *Feret, R. Density of Hydraulic Mortars. Granu- lometric Composition of Sand. Ann. des Fonts ct Chauss., 1892, II. Bulletin de la Social d'Encouragement pour ITndustrie Nationale, 1897, Vol. II, p. 1591. ^Alexandre, P. Experimental Researches on Hy- draulic Mortars. Ann. des Fonts et Chauss.. 1890, II, p. 277. Sea Water, — Its Effects Upon Concrete and Mortar Vetillart and Feret. Note on the Addition of Puzzolana to Mortars Setting in Sea Water. Ann. d. Ponts et Chaus, Vol. I, p. 121. Feret, R. A Quick Method for Comparing the Decomposition of Cements in Sea Water. Ann. d. Fonts et Chauss, Vol. I, p. 107. Thacher, Edw. Effect of Sea Water upon Concrete. Trans. Am. Soc. Civ. Engrs. Vol. LXJ(, p. 42. Examples of Tidal Injury to Concrete. Eng. News, Oct., 1908, p. 453. Effect of Sea Water at Charlestown Navy- Yard. Eng. News, Aug., 1908, p. 238. *Le Chatelier, Rebuffat, Feret, etc. Papers in Congres International des M^thodes d'Essai des Materiaux de Construction. Tome 2, 1901, pp. sii 79. 91 and 95- Schuljatschenko. The Destruction of Hydraulic Cement by the Action of Sea Water. Cement, Nov., 1901, p. 291. de Rochemont. Note sur la Decomposition des Ciments de Portland dans I'Eau de Mer. Ann. des Fonts et Chauss., 1900, IV, p. 2S1. Lidy, itt. Alteration of Reinforced Concrete by Sea Water. Ann. des Ponts et Chauss., 1899, IV, p. 229. *Feret, R. Addition of Puzzolanic Matter to Ce- ment. Chimie Appliqude, 1897, p. 490. Ann. des Ponts et Chauss., 1901, IV, p. 191. Candlot, E. The Influence of Sea Water on Mor- tars. Eng. Rec, Nov., 1897, p. 557. Michaelis, Wm. The Behaviour of Hydraulic Cements in Sea Water. Digest of Physical Tests, Feb., 1897. P- 198. "= The Action of Sea Water upon Hydraulig Cements. Pro. Inst. Civ. Engs., Vol. CXXIX, V- 325- *KyIe, John. Experience in laying Concrete in the Sea. Pro. Inst. Civ. Engs., Vol. CXXX, p. 183. Feret. R. Effect of size of Sand on Decomposition. BaumateriaUenkunde, I, Jahrgang, 1896, p. 139- Le Chatelier* H. Composition of Artificial Sea Water. Commission des M^thodes d'Essai des Materiaux de Construction, 1895, Vol. IV, p. 279, Methods of Testing Hydraulic Materials. Ann. des Mines, Sept. and Oct., 1893. Alexandre, P. Miscellaneous Mortar Experi- ments. Ann. des Ponts et Chauss., i8go, U, p. 277. 'English Authorities. Marine Construction in Eng- land. Pro. Inst. Civ. Engs., Vols. LXII LXVII, LXXXVII, CVII. CXI. Clarjce, E. C. Tests. Trans. Am. Soc. Civ. Engs., Vol. XIV, p. iss. Becljwith, L. F. Action of the Sea on B^ton-Coig- net. Trans. Am. Soc. Civ. Engs., 'VoU I. p. no. *An asterisk precedes the references which are especially noteworthy. 842 A TREATISE ON CONCRETE Sewers and Conduits Culbertson, M. S. Water Power Develop- ment at Loch LeveD, Scotland. Eng. Rec, May, 1909, p. 56o. Consaul, F. 1. Concrete Block Sewer, Toledo. O. Eng. News, Feb., 1909, p. 123. . Thompson, W. A. Outlet Sewer, E. St. Louis, 'in., Eng. News, Jan., 1909, P- ii5. Bronx Valiey Sewer. Eng. Rec, Jan., 1909, p. 32. Smith, C. W, Reinforced Pipe for Carrying Water at High Pressure. Trans. Am. Soc. Civ. Engs., Vol. LX, 190S, p. 124. Methods and Cost of Lining Ditches and Canals. Eng. Cont., Dec, 1908, p. aSi. Reinforced Pipe with Reinforced Joint. Eng. News, Dec, 1908. p. 643. Details of Baltimore Sewerage System. Eng. Rec, Dec, 1908, p. 698. Triple Barrel Sewer, The Bronx, New York City. Eng. Rec, Apr. 1908, p. 409. Sewer as Flood Protection in Grand Rapids, Mich. Eng. Rec, Oct., 1908, p. 495. Big Cottonwood Waterworks Conduit, Salt Lake City, Utah. Eng. Cont., Aug., 190S, p. 78. Pumping Station Conduits and Outfall Sewer, Washington, D. C. Eng. Rec, Aug., 1908, p. 237- Conduits for Electric Cables, Long Island K. R. Eng. News, July, 1908, p. 90. Lamed, E. S. Underground Conduits. Ce- ment A^e, May, 1908, p. 496. Flat Top Concrete Spans for Waterways. Eng. Rec, Apr., 1908, p. 396- Details of Mold for 38-in. Concrete Pipe. Eng. Rec, Apr., 1908, p. 400. Taylor, Wm. Gavin. Intercepting and Out- fall Sewer. Waterbury, Conn. Eng. News, Mar,, 190S, p. 333. ♦Standard Concrete Culvert, So. Mo. Ry. Chas. A. Sheppard, Eng. Rec, April, 1904, p. 478. ♦Philadelphia Filtration System. Eng. Rec, Feb., 1904, p. igi. ♦Jersey City Water Supply Company Conduits. Eng. Rec, Jan., 1904, p. 72. Concrete-jacketed Steel Pipe under Hackensack River. Eng. News, April, 1903, p. 327. ♦Concrete-Steel Culvert, Kalamazoo, Mich. Geo. S. Pierson, Eng. News, Feb., 1903, p. 163. Penstock at Grenoble, France. Eng. News, Jan., 1903, p. 74. Harrisburg Interceptmg Sewer. Cement, Nov., 1902, p. 374, Eng. Rec, Oct., 1904, p. 444. Sewer Pipe Trestle across Los Angeles River Eng. Rec, Mar., 1908, p. 299. Concrete Pipe Drain and Outfall Sewers, Baltimore, Md. Eng. Rec, Feb., 190S, p. 163. Intercepting Sewer, Salt Lake City. Eng. Rec, Feb., 1908, p. 216. Main Conduit, Los Angeles Water System. Eng. Rec, Feb,, 1908, p. 231. Conduit of Special Design, Ogden, Utah Eng. Rec, Jan., 1908, p. 65. Harlem Creek Sewer, St. Louis, Mo. Eng. Rec, Dec, 1907, p. 664. Circular Trunk Sewer in Borough of Queens, N. Y. Eng. Rec, Nov., 1907, pp. 5i& and 599. Reinforced Sewers in Staten Island. Eng. Rec, Nov., 1907, p. 486. Siphon on an Irrigation Canal in Spain. Eng, News, Aug., 1907- p. 116. Sewer Construction under Brooklyn Subway. Eng. Rec, Aug., 1907, p. 228. Catskill Aqueduct. Eng. Cent., Dec, 1906, p. 193. Buchartz, H. Method of Testing Clay and Concrete Pipes. Eng. Rec, Aug., 1906, p. 190. Hardesty, W. P. Conduit Built of Block Sec- tions, Los Angeles, Cal. Eng. News, May, 1906, p. 596. Reinforced Pipe Sewers in St. Joseph, Mo. Eng. Rec, Apr., 1906, p. 543; May, 1906, p. 555. Holmes, A. E. Reinforced Sewers at Des Moines, la. Eng. Rec, Apr., 1906, p. 537. Ferguson, J. N. Charles River Standard Manholes and Crossings of Existing Over- flows. Eng. Rec, Mar., 1906, p. 301. Bursting Strength of Reinforced Concrete Pipes. Eng. Rec, Dec, 1905, p. 656. Chicago Transfer and Clearing Co. Sewers. E. J. McCaustland, Cement, Sept., 1002, p. 265. New York Rapid Transit Sewers. Eng. News, March, 1902, p. 199. Paris Sewerage Disposal Works. Eng. News, March, 1898, p. 170. Paris Sewer under Pressure. A. Dumas, Gen. Civ., Vol. XXVIII, p. 277. Paris Sewers, their Dimensions and Cost. L. F, Beckwith, Trans. Am. Soc. Civ. Engs., Vol.1, p. 107. Specifications for Cement and Concrete Report of Joint Committee on Concrete and Reinforced Concrete. Proc Am. Soc Civ. Engs., Aug., i909-. , Report of Committee on Remforced Concrete. Proc. Nat. Assn. Cem. Users, Vol. V, 1909. „ Lesley and Lazell. New German Cement Specifications. Eng. News, Dec, 1908, Austrian Government Regulations for Con- crete and Reinforced Concrete Construc- tion. Cement, Feb., 1908, p. 377. and Mar., 1908, p. 43p- , „ * ri French Rules on Remforced Concrete. Ue- ment Age, Nov 1906, p. 410. and Sept., 1907, p. 1159. Steport of Britis'i Jomt Committee on Kem- forced Concre-c Eng. Rec, July, 1907, C. B. & Q. R. R. Specifications for Culverts. Eng. Cont., Oct. 3, 1906, p. 86. Specifications for Reinforced Concrete, Na- tional Fire Protective Association. Eng. Rec, Jime, 1906, p. 716. Miller, R. P. Proper Legal Requirements for Use of Cement Construction. Eny:. Rec, Apr., 1906, p.' 538. Moisseiff, Leon S. German Specifications for Concrete Structures. Eng. News, Nov., 1905, p. 478. Lesley, R. W. British Standard Specifica- tions for Cement. Proc. Am. Soc Test. Mat. Vol. V, p. 363. Prussian Regulations for Reinforced Concrete in Building Construction. Eng. Rev , July, 1904, p. 25. OAn asterisk precedes the feferences which are especially notfwcr^h\. REFERENCES TO CONCRETE LITERATURE 843 ♦Thompson, Sanford E. Recommendations for Testing Compression, Bending, Adhesion, Porosity, and Permeability. Pro. Am. Soc. Civ. Engs... Aug., 1903, p. 645. Can. Soc. C. E. Canadian Standard Specifica- tions for Portland Cement. Cement, May, 19^3. P- 98. ♦Am. Sdc. C. E. Committee, Standard Specifica- tions. Pro. Am. Soc. Civ. Engs., Jan., 1903. Swiss Societies. The new Swiss Standards com- pared with the old. Schw. Bau., April 19, 1902, p. 173. *Am. Ry. Eng. & M. W. Assn. Specifications for Portland Cement Concrete and for Portland and Natural Cements. Eng. News, March, 1902, p. 246, and March, 1903, p. 284. Newberry, S. B. Report of Assn. of German Port- land Cement Manufacturers. Cement, Jan., 1902, p. 3SO. Jatncso :, C. D. German Specifications for stand- ari Portland Cement Tests. Portland Ce- ment, 1898, p. 80. •Ferct, R. Studies on the Intimate Composition of Hydraulic Mortars. Bulletin de la Soci^tfi d' Encouragement pour I'lndustrie Nationale, 13^7, Series 5, Vol. II, p. 1591. Le C::-tcIi-j-, H. Methods of testing Hydraulic Materials. Ann. des Mines, Sept. and Oct., 1893- *U.S A. Engineers. Testing Hydraulic Cements. Prof. Papers No. 28, U. S. A., 1901. ♦Humphrey, R= L. The Inspection and Testing of Cements. Jour. Fr. Inst., Dec, 1901, Jan. and Feb., 1902. Assn. Ry. Supts. of B. & B. Specifications of Various Railroads. Pro. Assn. Ry. Supts., 1900. Butler, D. B. German and French Specifications for Standard Portland Cement Tests. Port- land Cement, pp. ^30 and 340. *Thacher, Edwin. Specifications for Concrete and Concrete-steel. Eng. News, Sept., 1899; p. 179- Candlot, E. Cement Specifications for French and German Public Works. Ciments et Chaux Hydrauliques. 1898, p. 375. Tests of Hydraulic Products. Ciments et Chaux Hydrauliques, 1898, p. 184. *French Coniniission. Recommendations for Tests of Cement. Commission des M^thodes d'Essai des Matdriaux de Construction, Vol. I, 1S93. Faija, H. The Manufacture and Testing of Port- land Cement. Trans. Am. Soc. Civ. En2., Vol. XXX, p. 43. *A. S. C. E. Committco. Uniform tests of Cement. TranS. Am. Soc. Civ. Eng., Vol, XIII, p. 53. Trans. Am. Soc. Civ. Eng., Vol. XIV, p. 475. Pro. Am. Soc. Civ, Eng., Jan., 1903, p. 3. Strength in Compression of Plain Concrete and Mortar Woolscn, Ira H. Testa of Concrete at Col- umbia University, Eng. News, June, 1905, p. 56i. Thompson, Sanford E. Stren::th of Concrete. Jour. Assn. Elng. Socs., Apr., igoS, p. 171. Howard, J. E. Compressive Strength of (Concrete Prisms and Columns. Tests of Metals, 1904, igoS, 1906, 1907, 1908. Fuller, W, B., and Thompson, Sanford E. Law of Proporfioning Concrete. Trans. Am. Soc. Civ, Engrs., Vol. LIX, p. 67. Johnson, J. B. Quotations from various authori- ties. Materials of Construction, 1903, p. 603. McCaiistland, E. J. Strength and Elasticity of 6-inch cubes and lo-inch Columns. Trans. Am. Soc. Civ Eng., Vol. L, p. 482. Clark, T. S. Effect of Mica in the Stone. Eng. News, July, 1902, p. 68. Costijun, J. S. Tests of Concrete Cubes. Eng. Rec, 1902, p. 393. Carson, H. A. Prisms of Pebbles vs. Gravel vs. Trap Concrete. Tests of Metals, U. S. A., 190T, p. 617. Clarke & Son, William Wirt. Cubes of Stone and Gravel Concrete, with Natural Cement. Tests of Metals, U. S. A., 1901, p. 609. *Wat2rtown Arsenal. Miscellaneous Tests, includ- ing the effect of Retarded Set and the effect of Plaster Adulteration. Tests of Metals, U. S. A., 1901, p. 471- ^ _ ICingGlsy, M. W. Slag vs. Limestone. Tests of Metals, U. S- A., 1900, p. 1099. *Henby, W. H. Tables of Tests and Curves for Stone and Cinder Concrete. Jour. Assn. Eng. Socs., Sept., 19^0. P- 152. Hawlcy & Krahl. 6-inch Cubes with different per- centages of Voids. Eng. News, June, 1900, Boston Transit Com. 1:2:4 Prisms at different ages. Tests of Metals, U. S. A., 1899, p. 839. U. S. Engineer Corps, Fla. Concrete of Brick, Sand, and Gravel. Tests of Metals, U. S. A., 1S99, p. 835. *Watertown Arsenal, t 2-inch Cubes of Mortar and Concrete with different sizes of Stone and Gravel and Brick. Tests of Metals, U. S. A., 189S, p. 57S; 1899, p. 783;i9oi. P- 600; 1902, p. 513- Black, W. M. Gravel and Stone Concrete, Natural and Portland Cem6nt. Rep. Eng. Dep., D. G, 1898. Aberthaw Construction Co. Columns of varying heights and proportions, Hand and Machine Mixed. Tests of Metals, U. S. A., 1897, .^ P- 351. ♦Talbot, A. N. Stone Screenings vs. Sand in Con- crete. Jour. W. Soc. Engs., Aug., 1S97, p. 391. Gary, Max. Roman Cement, and Portland Ce- ment Mortar Cubes, and mixed Roman and Portland. Also Lime i : 2. Baumaterialen- kunde. Vol. V, Heft 14, p. 217. Magens. Safe strength with different proportions. Kleinen Cement Buchs. Deutsche Bau., Vol. XXXI, p. 636. Dyckerhoff, R. Cubes of different proportions. Portland Zement, Berlin, pp. 90, 94 and 112. *Bruce, A. Fairlie. Experiments on the Strength of Portland Cement Concrete. Pro. Inst. Civ. Eng.. Vol. CXIII. p. 220. Worcester Polytechnic Institute. Prisms of differ- ent proportions. Eng. News, Nov., 1896, p. 302- Patton. 6-inch and 12-inch Cubes, compressed and not compressexi. Civ. Eng., 1895, p. 306. Simeon, P. Studies of Form for Compression Specimens. Commission des Mdthodes d'Es- sai des Mat^riaux de Construction, 1895, Vol. IV, p. 187. *Feret, R. Tests of Mortars under various condi- tions. Complete Tables and Curves. Ann. des Fonts et Chauss., 1892. II, p 117. Sociift6 d' Encouragement pour I'lndustrie Nationale, 1897, Series 5, Vol. II, p. 1591. Cfaimie Ap- pliqu^e. 1897. *An asterisk precedes the references which are especially noteworthy. 844 A TREATISE ON CONCRETE *KiniDaii, George A. 12-inch Cubes of different proportions. Tests of Metals, U. S- A., iSgp, p. 717. Rogers, W. A. Gravel vs. Hard Stone vs. Soft Stone Concrete. Eng. News, Dec, 1899, p. 386. Mass. Institute of Technology, z-inch Cubes of Cement and Mortar, and tests of same Mate- rials in Tension. Tech. Qr., 1899, Vol. XII, pp. 239-244. Rogers, W. A. 12-inch Cubes of different propor- tions, Portland and Natural Cement. Ry. & Eng. Rev., Feb., 1809, p. 88. *Candlot. E. Tests of Morfar and Concrete of various proportions, aggregates and condi- tions. Ciments et Chaux Hydrauliques, 1898. *Watertown Arsenal. 12-inch Cubes of Cinder Concrete. Tests of Metals, U- S. A., 1898, p. 561. •Rafter, George W. Tests with different percent- ages of Mortar, varying consistency and differ- ent Stones, Tests of Metals, U. S. A., 1898, p. 415- •Alexandre, P. Experimental Researches on Hy- draulic Mortars. Ann. des Fonts et Chauss., 1890, II, p 277. Grant, John. Concrete with various aggregates. Pro. Inst. Civ. Engs,, Vol. XXXII, p. zoo- Am. Soc. C. E. CommUtee. Tests of Cubes and Prisms of different heit^hts. Trans. Am. Soc. Civ. Engs.. Vol. XVIII, p. 266. Von Mauk. 8-inch Cubes of different proportions. Portland Zement, Berlin, p. 02. Kyle, John. Concrete and Mortar Cubes. Pro. Inst Civ. Eng., Vol. LXXXVII, p. 88. Unwin, W. C. Formula for rate of hardening of Cement. Pro. Inst. Civ. Engs., Vol. LXXXIV, p. 400. Hamilton, Schuyler. Tests comparing Concrete of Cement and of Hydraulic Lime. Trans Am. Soc. Civ. Engs., Vol. IV, p. 98. Cubes of different proportions. Otto Lueger's Lexikon der Gesamter Technik, Vol. II, p. 295. Strength in Tension of Plain Concrete and Mortar Johnson, J. B. Tests from various' authorities illustrating different Mixtures and Conditions Materiq-ls of Construction, looj, p. 568. Taylor and Thompson. Variation m Strength of Mortars. Cement, July, 1903. p. 165. Duryec, Edw. Tests of Sand Cement. Eng. New.t;, May, 1903, p. 487. *Griesenaucr, G. J. Compirative Tests of Lime- stone and Gravel Screenings and Torpedo Sand. Eng. News, April, 1903, p. 3^2. Clark, T. S. Slo:ie Dust versus Sand in Mortar. Eng. Newg, July, 1902, p. 68. Taylor, Harry. Tests of various Sands. Rep. Chief of Eng., U. S. A., 1902, p. 2455. Carson, H. Ac Tests oi^ Concrete Briquettes. Eighth Rep. Boston Transit Com., 1902, p. 62. Humphrey, R. L. Th'- Inspection and Testing of Cements. Jour. Fr. Inst., Dec, 1901, Jan. and Feb., 1902. Haft, W. K, Tests of 4 brands of Slag Cements and Diagram. Pro. lud. Eng. Soc, 1901, p. 45. *Henby, W. H. Tables and Curves for various Concrete Mixtm-es. Jour. Assn. Eng. Socs., Sept., 1900, p. 145. a™. Soc. C- E. Committee. Answers to questions propounded to various authorities. Pro. Am. Soc. Civ. Eng., April, 1900, p. 99. U. S. A. Engineers. Tests of Puzzolan Cement. Rep. on Steel Portland Cement, 1900. ^Humphrey, R. L. Tests of Natural and Portland Cement. Pro. Engs., Club of Phila., May, 1899, p. 178. *Candlot, E. Tests of Strength of Hydrauhc Limes, Cements, and Mortars. Ciments et Chaux Hydrauliques, 1898, pp. 399 and 410. *Dow, A. W. Tests from one day to 4 years Neat and with Sand. Rep. Eng. Dept., D. C, 1808, p. 120. Joly, M. de. Experiments on Strength and Elas- ticity. Ann. des Ponts et Chauss., 1898, III, p. 198. Gary, M. Comparative Tests of Standard Sands from different countries. Baumaterialen- kunde, i8g8. Lundteigen, Andreas. Notes on Portland Cement. Trans. /m. Soc Civ. Eng., Vol. XXXVII, p. SOI. Thompson, Sanford E. Tests of Mortar from Neat to 1 : 9 at Holyoke Dam. Eng. News, May, 1897, p. 294. *Ferct, R. Mortars of Fine Sand. Baumateriahen- kunde, I Jahrgang, 1896, p. 139. Baker, I. O. Mortars affected by different qualities of Sand. Jour. W. Soc. Engs., Jan., 1896, P- 73- Wheeler, E. S- Experiments with different Sands at different Ages. Rep. Chief of Engs., U. S. A., 1895, pp. 2953 and 3013; 1896, pp. 2829 and 2862. Cooper, A. S. Experiments with different Sands. Jour. Fr. Inst., Vol. CXL, p. 326. *Feret, R. Miscellaneous Tests of Strength. Ann. des Ponts et Chauss., 1892, II, p. 117. Russell, S. B. Neat Tests vs. Sand Tests for Port- land Cement. Trans. Am. Soc. Civ. Eng., Vol. XXV, p. 29=;. '''Alexandre, P. Experimental Researches on Hy- drauhc Mortars. Ann. des Fonts et Chauss., 1890, II, p. 277. Faija, H. Portland Cement Testing. Trans. Am. Soc. Civ. Eng., Vol. XVII, p. 218. Whlttemore, D. J. Tensile Tests of Cement. Trans. Am. Soc. Civ. Eng., Vol. IX, p. 329. Maclay, W. W. Notes and Experiments on the Use and Testing of Portland Cement. Trans, Am. Soc. Civ. Eng., Vol. VI, p. 311. Beckwith, L. F. Strength of Bdton-Coignet, Trans. Am. Soc. Civ. Eng., Vol. I, p. 100. ♦Grant, John. Time Tests of Lime, Cement, and Mortars. Pro. Inst. Civ. Eng., Vol. XXV, p. 88, XXXII, p. 2S0, LXII, p. 165. Strength of Beams and Arches of Plain Concrete and Mortar CaiBon, Howard A. Tests of Reinforced Beams. Report Boston Transit Comipission, 1904. Falk, Myron S. Stress in Concrete and Mortar Beams. Tables and Curves. Trans. Am. Soc. Civ. Eng., Vol. L, p. 473- Clark, T. S. Tests of Neat Portland Cement Beams, and relation between Tensile and Transverse Strength. Eng News, July, 1902, p. 68, Carson, H. A. Screenings vs. Sand in Concrete Beams. Eighth Rep., Boston Transit Com. 1902, pp. 61 and 63. Clean vs. Dirty Gravel in Beams. Seventh Rent. Boston Transit Com., 1901, p. 39. Moored Robert. Tests 1:3:6 Limestone Concrete. Eng. Rec, Feb., 1000, p. 187. Contractors Plant Co. Table of Transverse Tests. Tests of Metals, U. S. A., 1900, p. iiio. ♦An asterisk precedes the references which are especially noteworthv- REFERENCES TO CONCRETE LITERATURE 845 von Schon, H. Tests with various Mixtures. _ Trans. Am. Soc. Civ. Eng., Vol. XLII, p. 139. Moller, M. Testing a Concrete Girder. Pro. Inst.- Civ. Eng., Vol. CXXXIX, p. 435. *Talbot, A. N. Concrete with Screenings vs. Sand. Jour. W. Soc. Engs., Aug., 1897, p. 394. ♦Wheeler, E. S. Tests of Beams at St. Mary's Falls. Rept. Chief of Engs., U. S. A., 1895, p. 2924. Durand-Claye. Relation of Tension to Flexion. Commission des M^thodes d'Essai des Ma- t^riaux de Construction, 1895, Vol. IV, p. 211. *Abbott & Morrison. Comparison of Flexure and Tension. Eng. News, Dec, 1893, p. 466. ♦Bruce, A. F. Experiments at Glasgow, with for- mula for growth in Strength. Pro. Inst. Civ. Eng., Vol. CXIII, p. 217, and Vol. CXVIII, p. 380. Kyle, John. Stone and Gravel Concrete of differ- ent proportions. Pro. Inst. Civ. Eng., Vol. LXXXVII, p. 88. Hutton, D. Shingle Concrete of different propor- tions. Pro. Inst. Civ. Eng., Vol. LXII, p. 196. Lowcock» Richard. Tests and Formulas. Pro. Inst. Civ. Eng., Vol. Ill, p. 356. Strength of Reinforced Concrete Wathey, .M. O. Testa of Plain and Reinforced Concrete Coiumns. Eng. Rec, July, 1909, p. 41* Talbot, A. N. Teats of Reinforced Concrete Beams: Resistance to Web Stresses. Univ. of Illinois Bulletin No. 29, 1909. Talbot, A. N. Tests of 3 Large Reinforced Concrete Beams. Univ. of Illinois Bul- letin No. 28, 1908. Thompson, Sanford E. Discussion on Con- crete Columns. Trans. Am. Soc. Civ. Engs., 1908, Vol. LXI, p. 46. Lindau, A. E. Analysis of Semicircular Arch. Trans. Am. Soc. Civ. Engs., 1908, Vol. LXI, p. 387. Cantibver Girders, Philadelphia, Pa. Eng. News, Apr.,'1908, p. 447. Van Ornum, J. L. The Fatigue of Concrete Beams. Trans Am. Soc. Civ. Engs. , Vol. LVIII. p. 294- Tiirell, C. E. Concrete Girders, 75-foot Span. Eng. News, Dec, 1907, P- 633. Moisseiff, L. S. Compression Tests of French Government, Cement, Sept., 1907, P. 175. Diagrams for Design of' Beams. Eng. News, July, 1907. P- 28. Talbot, A. N. Tests of Reinforced Concrete T-Beams. Univ. of Illinois Bulletin No. 12, 1907. Hatt, W. K. Effect of Time Element . m Loading. Proc. Am. -Soc. Test. Mat,, 1907, p. 421. McKibben, F. P. Loads, Bending Momenta and -Shears for Bridges. Eng. News, Apr., 1907, p. 372. Talbot, A. N. Tests of Concrete Columns. Univ. of Illinois Bulletin No. 10, 1906, and No. 20, 1907. *Talbot, A. N. Tests of Reinforced Beams. Pro, Am. Soc. Test. Mat., 1904. *Turneaure, F. E. Tests of Reinforced Beams. Pro. Am. Soc. Test. Mat., 1904 *Marburg, Edgar. Tests of Reinforced Beams. Pro. Am. Soc. Test. Mat., 1904- *Howe, M. A. Tests of Reinforced Beams. Jour. W. Soc. Engs., 1904. *Prussian Kegulaiions for Reinforced Concrete in Building Construction. Eng. Rec, July, 1904, p. 25. ' Johnson, L- J. Tests of Reinforced Beams. Jour. Assn. Eng. Socs., June, 1904, p. 308. Am. Ry. Eng. & M. of W. Assn. Rept. Com. on Steel-concrete, 1904. French, Gov. Com. Preliminary Conclusion on Reinforced Concrete. Cement, Jan., 1904, p. 414* ♦Considere, A. Test of a 6s-ft. Truss Bridge. Ann. des Ponts et Chauss., 1903, III, p. 5. *Con5idere, A. Concrete-Steel and Hooped Con- crete. Reinforced Concrete. J003, p. 119. Thullie, Dr. M. R. V. Column Tests. Beton u, Eisen, Heft II, 1907, p. 43. Sewell, J. S. Economical Design of Rein- forced Concrete Floor Systems. Trans. Am. Soc. Civ. Engs., Vol. LVI, 1906, p. 2S2. Withey, M. O. Testa of Plain and Rein- forced Concrete. Univ. of Wisconsin Bulletin No. 197, 1907, and No. 17S, 1906. Jonson, E. F. Theory of Continuous Col- umns. Trans. Am. Soc. Civ. Engs., Vol. LVI, p. 92. French, A. W. Reinforced Concrete Beams and Floor Systems. Trans. Am. Soc. Civ. Engs., Vol. LVI, 1006, p. 360. Dana, R. T. A Rapid Method of Calculation of Reinforced Concrete Sections. Eng. Rec, Sept., 1906, p. 249. Thompson, Sanford E. Discussion on Plain and Reinforced Columns. Proc. Boston Soc. Civ. Engs., Sept., 1906. ♦Howard, J. E. Tests of Columns. Eng. News, JuIy,'i9o6, p. 20. Tests of Metals, 1905, 1906, 1907, 1908. Goldmark, H. Discussion of Formulas for Beams. Eng. Rec, Mar., 1906, p. 420. Talbot, A. N. Tests of Reinforced Concrete Beams, Univ. of Illinois Bulletin No. I, 1904; No. 4, Z906. Harding, J. J, Tents of Reinforced Concrete Beams. Eng. News, Feb., 1906, p. 168. Condron, T. L. Strength of Reinforced Con- crete Munie. Eng., Sept., 1905, p. 167. Tests of Efficiency of Vertical Stirrups, Bush Terminal. Eng. News, July, igoS, p. 5. Elwitz, E. Economic Beam Designs. Beton u. Eisen, Heft II, 1905, p. 38. ♦Burr, Wm. H. Theories of Steel Reinforcement. Elasticity and Resistance of the Materials of Engineering, 1903, p. 619. New York Bureau of Buildings. Regulations in regard to the Use of Concrete-Steel. Eng. Rec, Oct., 1903, p. 429. Bortsch, Robert. A Graphostatical Investigation of Compound Bodies of Concrete and Iron. best. Wochenschr. f. d. Geff. Baudienst, July 4, 1903. *Schaub, J. W. Diagram and Formula for deter- mining Percentage of -Steel in Beams. Eng. News, April, 1903, pp. 348 and 392. Johnson, A. L. Steel-Concrete Construction. R. R. Gazette, March 13, 1903, p. 183. *Thacher, Edwin. Tests, Formulas, and Tables for Beams and Slabs. Cement, July, 1902, p. 179- Sewell. J. S. Tests of Concrete Steel Slabs. Eng. News, Jan., 1903, p. 112, *An asterisk precedes the references which are especially noteworthy. 846 A TREATISE ON CONCRETE Ramlsch, Q. Influence Lines. Beton & Eisen, II Heft, 1903, p. 122. Thullie, Max R. v. Shearing Stresses in Rein- forced Concrete Beams. Beton & Eisen, II, Heft, 1903, p. 117. ^Sanders, L. A. Comparative Tests upon Rein- forced Concrete, Beton & Eisen, I Heft, 1003, p. 27, and II Heft, 1903, p. 94. *von Empcrser, Fritz. Tests of Beams and Slabs of Steel-Concrete. Beton & Eisen, 1903, Heft I, p 23; Heft II, p. 94; Heft III, pp. 181 and 105, Rabut. 1S\. Rupture Tests upon Hennebique Floors. Beton .& Eisen. I Heft, 1903, p, 17. Ribera, M. J. Eugenic. Details of Computation of a Reinforced Arch of 35 metres Span. Beton & Eisen. I Heft, 1903, P- i. Tests of Hennebique Arch Bridge, Chattelerault, France. Cement, July, 1902, p. 169. *Hatt, W. K. Theory of Reinforced Beams. Eng. News, Feb., 1902, p. 170. Spitzcr. J. A. Development of Reinforced Con- crete Construction. Zeitchr. d. Ing. u. Arch. Ver. Oest., Jan., 1902, p. 73, Carson, H. A. Tests of Reinforced Concrete Beams. Eighth Rept., Boston Transit Com., 1902, appendix V. Tests of Concrete Floors of various systems. Jour. Assn. Eng. Socs., Feb., 19:11, pp. 73 to 148. Molitor, David. Theories of Masonry and Con- crete-steel Arches. Jour. Assn. Eng. Socs., Jan., igoo, p. 46. Rosshander, Josef. Theory and Applications of Concrete-Iron Construction. Schw. Bauz., Sept. 8, 1900. t Barberis, C. Hennebique Slabs Tested. Rivista di Artiglieria e Genio, 1900, Vol. Ill, p. 122. Hoch, A. 'i'esting a Concrete Bridge Arch. Pro. Inst. Civ. Engs.. Vol. CXXXIX, p. «6. *Noe, Harel de la. Theory and Recent Applications of Reinforced Concrete. Ann. des Fonts et Chauss., 1899.+ Consldere, M. Variations in Volume. liifluence of Reinforcement. C>mptes Rendus, Sept. 18, 1899,1 , „ *Tedesco, N. de. Construction in Remforced Ce- ment. Ing. Civ. de France, Jan., iSgg.t Hill, George. Steel-Concrete Construction; Tests of Slabs, Tables and Formulas. Discussion. Trans. Am. See. Civ. Eng., Vol. XXXIX, p. 617. Lavergne, Qerard. Reinforced Cement Construc- tions. G^nie Civ., Nov. 12, 1898, p. 22. Thullie. M. R- v. The Computation of Stresses in Monier Arches. Zeitschr. Oest. Ing. u. Arch. Ver., Sept., 1898,! P- 549- Osaenfeld, A. Calculations for the Monier System of Construction. Zeitschr. d. Oest. Ing. u. Arch. Ver., Jan., 1898.! Hermanek, J. The Influence of Temperature Changes on Concrete-Steel Construction. Zeitschr. d. Oest. Ing. u. Arch. Ver., Dec, i897,t P- 694. ^ ^ r ^ , Aberthaw Construction Co. Tests of Columns Plain and Reinforced. Tests of Metals, U. S. A., 1897, p. 355. Johnson, J. B. Calculation of Ultimate Strength of Concrete-Steel Beams. Eng. News, Oct., 1897, p. 261. von Emperger, F. The Theory of Reinforced B^ton Beams. Zeitschr. d. Oest. Ing. u. Arch. Ver., May, p. 351, and June, i897,t p. 364. Spltzer, Josef Anton. The Theory of Concrete- Steel Construction. The Monier Arch. Zeit- schr. d. Oest. Ing. u. Arch. Ver., Jan., 1897, f p. 26. Marstrand, O. J. Strength of Monier Plates. Eng. News. July, 1896, p. 32. Melan, J. Concerning the Computations for Con- crete-Iron Construction. Oest. Monatschr. f. d. Oeff. Ban., Dec, i8o6.t von Emperger, F. Tests on Brick, Concrete, and Steel -Concrete Arches. Eng. News, Aug., 1893. P- 157' Strength of Cement Affected by Admixtures ALCOHOL Tetmajer, L. Curves showing Effect of Addi- tion. Tetmajer, Vol, VII, p. 24. CLAY AND LOA-M Effect of Clay in Cement Mortar. Eng. Rec. June, 1907, p. 703. Thompson, Sanford E. Impurities in Sand for Concrete, Trans. Am. Soc Civ. Engs., 1909. Hain, J. C. Testa of Impure Sand for Con- crete. Eng. News, Feb., 1905, p. 127. The Effect of Loam on Concrete. Eng. Rec, July, 1904. P* 89. *Qriesena'ier, G. J. T^sls of Loam and Clay in Sand. Eng. News, April, 1904, p. 413- ♦Sherman, C. E. Experiments and Dia- grams. Eng. News, Nov., igoSi P* 443- Richey, and Prater. Table of Tests. Tech- nograph, 1902-3, p. 36. Wheeler, E. S. Tests. Rept. Chief of Ensrs. U. S. A., 1895, p. 3002; 1896, pp. 2826 and 2830. ■Grant, W. H. Test of Mortar with Sand Con- taining Clay. Trans. Am. Soc. Civ. Engs. Vol. XXV, p. 269. Clarke. E. C. Tests of Roaendale Mortar Con- taining Loam. Trans. Am. Soc. Civ. Engs., Vol. XIV, pp. 163 and 164- GLYCERINE Tetmajer, L. Curves showing Effect of Addition of Glycerine. Tetmajer, Vol. VII, p. 24. LIME Lazell, E. W. Hydrated Lime and Cement Mortars. Proc. Am. Soc. Test. Mat.. Vol. VIII, 1908, p. 418. Alexandre, P. Tests of Strength. Ann. des Fonts et Chauss., 1890, II, p. 306. Candlot, E. Table of Tests of various Mixtures of Cement, Lime, and Sand. Ciments et Chaux Hydrauliques, 1808, d. 203 *Feret, R. Tests. Chimie Appliqu^c, p. 4S0. PEAT Grant, John. Experiments with Lime and Cement Mortar. Pro. Inst. Civ. Engs., Vol. LXII, p. 160. Li^vcn, O. Experiments. Pro, Inst. Civ. Engs., Vol. LXXXVIII, p. 463. *An asterisk preceQcs the references which are especially noteworthy. REFERENCES TO CONCRETE LITERATURE 847 PLASTER *Watertown Arsenal. Curves and Tables. Tests of Metals, U. S. A., ipoi, p. 507. *Candlot, E. Influence of Chloride of Calcium and of Sulphate of Lime on the Setting and Hard- ening of Mortars. Ciments et Chaux Hy- drauliques, 1898, p. 318. .Wheeler, E. S. Tests. Kept. Chief of Engs., U. S. A., :8t>6, p. 2854. Tefmajer. Tests. Tetmajer, Vol. VII, p. 39- *Feret, R. PUZZOLAN CEMENT Chimie Appliqu^e, 1897, p. 490. SALT Johnson, J. B. Tests quoted from various author- ities. Materials of Construction, 1903, p. 615. ♦Wheeler, E. S. Tests. Rept. Chief of Engs., U. S. A., 1895, pp. 2955, 2968; 1896, p. 2829. Hill, W. F. Tests at Cornell University. Eng. News, May, 1895, p. 282. Carey, A. E. Tests. Pro. Inst. Civ. Engs., Vol. CVII, p. 40. SAWDUST Wheeler, E. S. The Use of Sawdust in Portland Cement Mortar. Rept. Chief of Engs., U. S. A., 1S96, p. 2866. SODA Hatt, W. K. Strength Affected by Soda, AJura, Soap, etc. Trans. Am. Soc. Civ. Engs., V6I. LI, p. 128. Carey, A. E. Tests. Pro. Inst. Civ. Engs., Vol. CVIL SUGAR Carey, A. E. Tests. Pro. Inst. Civ. Engs., Vol. CVII, p. 71. TALLOW Clarke, E. C. Experiments with Briquettes of Ce- ment and Tallow. Trans. Am. Soc. Civ. / Engs., Vol. XIV, p. 165. Strength of Concrete and Mortar Affected by Frost and Heat AberthaM' Construction Co. Tests of Effect of Low Temperature on Setting, Eng. Nevi^s, March., 1909, p. 257. Goodrich, E. P. Use of Concrete in Freezing Weather. Cement and Eng. News, Dec, 1907, p. 279. Gow, C. R. Tests of Concrete Piles Frozen and Thawod. Jour. Assn. Eng. Socs., Oct., 19071 P* 263. *Qowen, C. S. Tests of Portland Cement Mortar exposed to cold. Pro. Am. Soc. for Test. Mat., 1903. Jolt/iiSOT), J. B. Notes from various authorities. Materials of Construction, 1903, p. 613. Costisan, J. S. Frost Tests at Chaudiere Falls, P. Q. Eng. News, Oct., 1902, p. 262. ♦Watertown Arsenal. Specimens exposed to differ- ent temperatures. Tests of Metals, U. S. A., 1901, p. 530. Railway Superintendents. Notes from Practical Experience. Eng. News, Oct., igoo, p. 271. Pro. Assn. Rv- Supts., 1900, pp. 168, 170, 177. Hobart, A. C. Tests of Frozen Mortar. Techno- graph, 1897-98, p. 72. Barker & Symonds. Thesis Experiments on Freez- yig. Eng. News, Vol. XXXIII, p. 262. Concrete Work at 2 5° to 30^ below Zero. Eng. News, July, 1907, p. 49. Howard, J. E. Tests of Effect of Low Tem- perature. Eng. Rec, May, igoS, p. 52i Safeguards for Concrete Work in Frosty Weather. Eng. Rec, March, 190S, p. 249. Rogers, W. A. Experiments on Freezing. Jour. W. Soc. Enss., Vol. HI) p. 264. *Wheeler, E.S. Experiments on Mortar at various temperatures and under various conditions. Rept. Chief of Engs., U. S. A., 1894, pp. 2335, 2353. 2349, 2360; 189s, p. 295s; 1S96, pp. 2829, 2863. ♦Noble, A. The Effect of Free7ing on Cement Mortars. Trans. Am. Soc. Civ. Engs., Vol. XVL p. 79- Godfrey, C. H. The Effects of Frost on the Strength of Portland Cement. Pro. Inst. Civ. Engs., Vol. CXXXIV. p. 378. Maclay, W. W. Effect of Temperature in Testing Cement. Trans. Am. Soc. Civ. Engs., VoU VI, p. 329. Strength of Concrete and Mortar Affected by Retarded Set Johnson, J. B* Tests from various authorities. Materials of Construction. 1903, p 593. Richardson, T. F. Mortar Experiments. Rept. Met. W. & S. Board, 1902, p. 93; 1903, P- 120- Skeels, G. V. Regagmg from 20 minutes to 9 hours. Eng. News, Nov., 1902, p. 382. >'=CIark, T- S. Retempering Portland and Rosendale Mortars. Eng. News, July, 1902, p. 68. ♦Watertown Arsenal. Experiments on Retarded Set of Cement Mortar. Tests of Metals, U. S. A., 1899. P- 799; 1901. P- 497. . =t'Candlot, E. Discussion and Tables on Cohesion and Adhesion. Ciments et Chaux Hydrau- liques, 1898, pp. 3S5 and 365. Wheeler, E. S. Regaging Cement Mortar. Co- hesion and Adhesion. Rept. Chief of Engs., U. S. A., 1895, p. 2979; 1896, pp. 2814 and 2868. Faija, H. Experiments on Regaged Mortar. Soc. of Encs., London, 1888. Kinipole, W. R. Plasdc Concrete. Pro. Inst. Civ. Engs., Vol. LXXXVII, p. 66. Clarke, E. C. Briquettes Rctemuered after Pulver- izing. Trans. Am. Soc. Civ. Engs., Vol. XIV, p. 169. **An asterisk precedes the references whieh are especially noteworthy. 848 A TREATISE ON CONCRETE Tunnels Shaft and Gate Chamber, Blue Island Avenue Tunnel, Cnicago. Eng. News, Oct., 1908, p. 440. Buffalo Water Worka Tunnel. Eng. Rec, Oct., 1908, p. 396. Rotherhithe Tunnel under the Thames, Lon- don. Gen. Civ., Sept., 1968. Plant and Methods, Detroit River Tunnel. Eng. Rec, Sept., 1008, p. 312. Machinery and Methods for Placing Tunnel Linings. Eng. Cont., July, igo8, p, 3. Shelby Hill Tunnel, St, Paul. Eng. Rec, Sept., 1907,, p. 306. Construction of Penn. R. R. Tunnels at New- York. Eng. News, Dec, 1906, p. 603. Reinforced Concrete Tunnel Caisson, Sub- way System, New York. Eng. Rec, Sept., 1906, p. 340, Oct., 1906, p. 377. Tunnel Roof of Concrete Blocks. Eng. News, July, 1906, p. loi. The Simplon Tunnel. Gen. Civ., June 23, 30, 1906. Penn. R. R, Tunnel, Washington, D. C. Eng. News, Sept., 1905, p. 267. Volumes of Materials for Concrete and Mortar *Thacher, Edwin. Table of Materials for Mortar and Concrete. Cement, July, 1902, p. 194. Metropolitan Water & Sewerage Board, Mass. Cement per cubic yard of Concrete. Kept, for 1933, p. 112. Qillette, H. P. Formulas for computing Cement Required. Eng. News, Dec, 1901, p. 422, and June, 1902, p. 482. Parkhurst, H. W. Materials in Wet versus Dry Concrete Specimens. Jfour. W. Soc. Engs., April, 1902. *SavilIe, C. M. Materials used at Forbes Hill Reser- voir, Quincy, Mass. Eng. News, March, 1902, p. 220. Sherman, L. K. Experiments for Chicago Drain- age Canil. En^. Mews, Jan., 1922, p. 31. Railway Superintend snts. Materials for one cubic y.ird of Concrete. Pro. Assn. Ry. Supts., iQDo, pp. 170-1. Colenian, Clarence. Materials used at Duluth Harbor, Minn. En?. News, July, 1900, p. 56. Baker, Ira O. Tables of Materials for one cubic yard of Mortar and Concrete. .Masonry Con- struction, p. 88. ♦Rafter, QeorgB W. Volume of Mortar from differ- ent proportions. Trans. Am. Soc. Civ. Engs., Vol. XUI, p. 1^4. and XLVIII, p. 96. *Hazen, Allen. Method of Computing Quantities by Weight. Trans. Am. Soc. Civ. Engs., Vol. XUI, p. 129. Fowler, C. E. Table of Materials for one cubic yard of Concrete. Trans. Am. Soc. Civ. Engs., Vol. XLH, p. 117. *5abin, L. C. Table of Materials for one cubic yard of Mortar. Munic Engng., Feb., iSpp, p. 69. Jameson, Chas. D Concrete made with different proportions of Materials. Portland Cement, 1898, p. 139. Watertown Arsenal. Weights and Volumes 01 Materials in Specimens of Mortar and Con- crete. Tests of Metals, U. S. A., 1898, p. 655; i8qo, p. 736. *Wheeler, E. S. Materials for Beams at St. Mary's Falls Canal, Mich. Rept. Chief of Engs.. U. S. A., 1895, p. 2924. Feret, R. Production and Density of Mort'^rs. Commission des M^thodcs d'Essai des Mi- tiSriaux de Construction, 1895, Vol. IV, p. 243. Cement per Cubic Meter with different propor- tions. Zcit. f. Bau., 1894, p. 542. Mortar from different proportions. Portland Ze- ment, Berlin, p. 127. Grim, F. Tests of Mortar and Stone for one cubic yard of Concrete. Technograph, Vol. XIII, P- 53- Grant, John. Tests of Cement and Sand per cubic yard of Mortar. Pro. Inst. Civ. Engs., Vol. XXII, p. 102. Water in Concrete and Mortar Taylor and Thompson. Quantity of Water to Use in Gaging Mortars. Cement & Eng. News, Nov., 1903, p. 112. •Lamed. E. S. Effect of Water on the Setting and Strength of Cement. Pro. Am. Soc. Test Mat., 1903, p. 40. Doyle & Justice. The Strength of Concrete as affected by different percentages of Water. Eng. News, July,, 7903, p. 97- -Henby, W H. Cinder Concrete Wet and Dry. Jour. Ajsn. Eng. Socs., Sept., igoo, p. 157. Hazen, Allen. Quantity in Actual Worlt. Trans. Am Soc. Civ. Engs., \'ol. XLII, p. 128. Rafter, O. W. Tests of Concrete of different con- sistency. (Discussion.) Tests of Metals. U. .S. A., 1898. p. 553. Sussex, James W, The Relative Strength of Wet and Dry Concrete. Eng. News, July, 1903, P 67. •Parkhurst, H.W. Wet, Dry, or Medium Concrete. Jour. W. Soc. Engs., 1902. *Hitz, irvlng. Experiment with Wet and Dry Concrete. Jour. W. Soc. iings., Dec, 1900, p. 488. Candlot, E. Influence of the Degree of Humid- ity of the Sand on the Sotting and Hard- coin'? of Mortars. Ciments et Chaux Hydrauliques, 1S9S, p. 349. *Feret, R. Quantity of Water for Gaging Mor- tars. Ann.desPontsptChauss., II, 1892, P 3^ *An asterisk precedes the references which are especially noteworthy. * APPENDIX I 849-855 APPENDIX I METHOD OP COMBINING MECHANICAL ANALYSIS CURVES In Chapter X the method of forming mechanical analysis curves is dis- cussed, and approximate rules are given for combining individual curves to form the curve of the mixture. More exact methods, which also illus- trate the principles, are given in the foUovying pages, taking up first simple cases and then the more complicated ones. Case I. Curves which meet, but do not overlap. In Fig. 259 are shovra. three curves, No. i. No. 2, and No. 3, representing ideal grades of sand and stone, which may be combined in such proportions that the curve of the mix- ture will be of the ideal form required. The problem requires the deter- mination of the percentages of each of the three materials which when com- bined will form a mixture whose curve is nearly the ideal. In order to prove that the percentages found wiil produce the resultant curve, and also to illustrate the theory of the mixture, the resultant curve will be first plotted and described in. a very elementary manner, and afterwards by the method of ratios which would be employed in practice. Curve No. 3 represents a material all of whose particles will pass through a sieve having holes 2.00 inches diameter and all of whose particles will be retained on a sieve having holes 0.75 inch diameter. Stone represented by curve No. 2 lies between diameters 0.75 and 0.25 inch, while the material of curve No. i is all finer than 0.25 inch, that is, is all under \ inch. Curves No. 31 and No. 32 are referred to later. The curve OebA is first plotted* as a parabola. Although the latest tests indicate that the best curve is a combination of an ellipse and a straight line,f the parabola will illustrate the principle of combination as well as any other, and so for this problem we may assume now that the required theoretical mix of materials lies in this parabolic curve. This is equivalent to saying that the desired theoretical mixture of materials is such, that at aijy ordinate ♦ Construction of the Parabola. D — largest diameter of stone , d = any given diameter P = per cent, of mixture smaller than any given diameter The equation of the parabola is a = ■ icooo The parabola can be constructed in any of the numerous ways given in text-books, the writer finding it easiest to use a slide rule. Set D on the B scale of the rule opposite loo on D scale, read any value of d on the B scale opposite any corresponding value of P on the D scale. •f'Laws of Proportioning Concrete," by William B. Fuller and Sanford E. Thompson, Trans- actions American Society of Civil Engineers. 8^6 M 1 I I II I I I I*" B o s- s h PERCENTAGES, RETAINED ON SIEVES S g S g =. ^ |-K ___ 1 1 — ~ u c4 V "•' -~~\\^ '\ s S, ■-- ^ 4 A 5 =^ i::^ / ~ = S^l y^ \ \ '^ \ \ \, 1 1 -N ' \ \ \ — \ 1 \ )^ i \ )^ 1 1 \f ° ~\ \\ \ k 1 I \ \ \ \ T \ \ |\ i-^j \ w 1 V y =? \ \ \ 1 1 A \ \ \ \ \ \ 1 \ \ \ \ \ \ 1 ^ ■^ \ \ \ \ -» v^' fj t \, ^ ^ ^'^ \ \ A"- \ \\ \ (6 r^ \ \ ^\ \r 1 c is \ ]_ *;. \- ^"^ ^ 1 ^ u ^ \3 \ 4- ■^ \ \ "1 1 \ ■^ \ t \ ^A i _ r \, ^ « " \ ^V ^ s^ J* \ \A J^ '^, ■^ I N ij CO c; iA_\ 1 •-5; — o ^ K •\ ■^ ■~ \ v^_ i\ \ ■V- \ « = \- \ o ■\ V '' °;t \ ^ > ^ \ \ = ^ ^^ ■^ \ n \ ^^ ■^ \ ^ V ?^ \ \ \ — C3 5 ^ --* J \^ \ ^ "A/ ■fj* ■x; \ i. — — ' . - ^ ^=56 c PERCENTAGES PASSI^ g g § , G SIEVES § S 2 ■= 1 1 1 1 1 1 1 1 1 1 D ^ 8 8 t- S s i S s g = ■IS, ■^ .<<1 p. > o J3 3 o o O o -a a 1 APPENDIX I 8S7 or vertical line cutting the parabola, the proportion or percentage of the ordinate below the intersection represents the percentage by weight of the mixed materials which passes a sieve the diameter of whose openings cor- responds to the given ordinate, and the percentage above the curve represents that percentage which is too large to pass through this sieve. The parabola shows, for example, that 87% of the mixture of materials should pass a i-So-inch sieve, 71% should pass a i-inch sieve, 49% a ^-inch sieve, and so on. We may now take up the stone curves in succession to determine what percentage by weight of each should be used, so that when they are com- bined, the mixture will be as nearly as possible like that called for in the parabola. The chief difficulty in the method of determining the percentages of each material lies in combining the individual curves so as to form a single curve which represents the mixture. This involves drawing on the same piece of paper two different lines, each of which exactly represents the composi- tion of the same lot of stone, that is, the exact per cent, of each size of stone in the lot. For example, as is explained below, on Fig. 259, Unes BKA and bkA , each accurately represents the percentage composition of the same batch of stone, namely. No. 3, and the full meaning and value of these diagrams cannot be understood until it is clear how the same values can be accurately represented on the same diagram by two such totally different curves. In the first place it is seen that the ordinates, that is, the vertical lines in the diagram, are divided into 100 parts representing percentages. It is clear, therefore, as the divisions are relative, that the diagram would accom- plish the same results and curves could be drawn accurately representing the percentages passed and retained by the different sieves, whether the distance from o to 100 on the ordinates were, say, three times as large as it is, or whether it were only -^ or \ of the present length. All that is needed is to divide these vertical Hnes, whether they are long or short, into 100 parts and let each division represent 1%. Referring now to Fig. 259, the percentage composition of the No. 3 lot of stone is represented by line BKA. This lot of stone contains no stone smaller in diameter than 0.75 inch and none larger than 2.00 inches. Running vertically upward from B on the 0.75-inch line to h where it crosses the parabola, we see that the parabola from b \.o A also represents a lot of stone none of which is smaller than 0.75 inch and none larger than 2.00 inches, and we can look upon this lot of stone for the moment as entirely separated from the rest of the mixture which the whole parabola represents. If we wish to find the" exact percentages of the various sizes 858 A TREATISE ON CONCRETE of stone which are in the portion or lot represented by' the portion of the parabola from 6 to ^ , all that is necessary is to draw the horizontal line rq through the point b, then divide the vertical distance from A to rq into 100 parts, so as to obtain a new set of horizontal lines or abscissas representing percentages. Now if we start at the base hne rq and follow up any one of the vertical lines or ordinates until it meets the parabola, and then follow horizontally to the right along the Hne which intersects the parabola at the same vertical Une or ordinate point, the reading on the new smaller percen- tage scale will give us the per cent, of stone in the lot bA which is larger than the diameter represented by this ordinate, etc. For example, taking intersection of i.oo ordinate with the parabola and running across we find that 75% of the lot is coarser than i inch diameter. It is desirable to see how nearly the stone in lot No. 3 agrees with the theoretical lot of stone called for by section bA of the parabola. In prac- tice, the comparison may be made most readily by ratios with the aid of the shde rule, as is described more fully below, but the reasoning will be more clearly understood if the plan described in the last paragraph is followed. Taking first cur\4e No. 3 we may redraw it on the same smaller scale as the portion of the parabola bA is drawn, that is, it may be constructed on rbq as a base line instead of on the zero coordinate BF. Since the vertical per cent, line between q and A has been divided into 100 parts, this section of the diagram may be used instead of the original per cent, divisions ex- tending from A to F. A piece of paper the length of ^4^ may be divided into 100 parts and placed with its upper or o end in hne with the upper line CA of the diagram. The vertical distance from the Une CA to the various points G, H, J, K, etc., may be read by the eye and replotted, — with the assistance of the small scale, — as g, h, j, k, etc. It is evident then that the broken line bghjk A represents (referring to the small percentage scale Aq) lof No. 3 of stone as accurately as line BGHJKA represents the same lot of stone referring to the larger percentage scale AF. Stone curve No. 3, however, would never, in actual practice, be an absolutely straight line from A to B. It would be in all practical cases an irregularly curved line, similar, for instance, to some of the actual stone curves shown in Fig. 56, p. 189, or it might be either convex like the curve No. 32, Fig. 259, or concave like No. 3]. These curves may be redrawn in exactly the same way as curve No. 3, and if the lower end of each is assumed to start at point b where the new base Hne or bq crosses the parabola, we should have for No. 3^ the new curve bg^h^j^, etc., and for No. 3i the curve whose beginning is shown by bh^j^, etc. Thus again APPENDIX I 859 it is seen that the stone curves No. 2,2 and No. 2>i on the original full-size diagram are accurately represented also by the curves hgji^j^, etc., bh^j^, etc., drawn to the smaller scale on the same piece of paper. Thus far only the principles involved in understanding the curves and replotting them have been considered. The result at which we are aiming is the determination of the percentage of each material which will be required in the final mixture of the aggregates. Let us first take for this curve No. 3. The curve of stone No. 3 ends at B, which indicates that all of this stone is larger in diameter than 0.75 inches (although about 4% of it, for instance, is smaller than 0.80 inches in diameter). Now following up from B on the vertical line which represents 0.75 inches in diameter until we come to the parabola at point h, we see that the parabola demands that — or or 61% of all the stone and sand in the entire mixture of CB 100 stone and sand shall be smaller than 0.75 inches in diameter, and conversely that — or — or 39% of the mixture shall be larger than 0.75 in diameter. CB 100 No. 3 stone is the only one of the three lots of stone which is larger in diameter than 0.75 inches, and therefore 39% of this grade of stone should be used in making up the mixture. These ratios give us a clue to the method of plotting the curves to the smaller scale with the aid of the slide rule, instead of employing the longer method of actually dividing the spaces into 100 equal parts. The principle in each case is exactly the same. By the method of ratios the curve hkA Cb Tg Sh would be plotted from the knowledge that ;:rr = =-:; = -i^ = , etc. The CB 1 tr O-tl distances Tg, Sh, etc., may be read directly from the slide rule or from the TG X Cb equation which follows from the preceding, viz., that Tg = — -^ — = ?^^ = 37%, and so on. 100 This actual plotting of the curves may be unnecessary, in fact, it is usually unnecessary for an experienced calculator, as the percentages can be obtained and the general direction of the curve estimated by inspection.* *It is evident that neither of the two batches or lots of materials shown by curves No. 32 and No. 3, are so well adapted to form a parabola as curve No. 3 Curve No. 32 would more nearly fit the parabola than it now does if its new curve were plotted slightly lower so that it would cross the parabola at a different point and a larger percentage of it would be required for the mixture. If it crossed the parabola at V, the percentage of it to use could be found by plot- ting it in this new location and taking for the percentage the vertical distance from C to tht end of the curve, or what is the same thing, taking the percentage as — — — - = |i = Si%. ori2 65 86o A TREATISE ON CONCRETE The next curve in order is No. 2. We note that this lot of stone is the only one of the three whose particles lie between 0.25 inches diameter and 0.7s inches, and that therefore all of the stone called for by the para- bola between these two sizes must be supplied from No. 2 lot. Following down from the upper end, C, of No. 2 to the parabola at b and up from the lower end E to the parabola at e and drawing horizontal line ex, we see that the proportion of No. 2 stone which is called for by the parabola is represented by the distance between the lines rq and ex or by line re, re 26 and we have the ratio 7777= — = 26%, as the percentage of the weight of DE 100 the No. 2 material to the total weight of the mixture. Plotting curve No. 2 in its new location as a part of the mixture we have the dotted line eb as representing the No. 2 material after it becomes a part, that is, 26%, of the mixture. The upper end must join the Hne bA because we are now plotting a curve which represents a mixture of the two materials, No. 3 and No. 2, and the mixture must be represented by one single, continuous curve. We may consider rb and ex as two base lines, divide the vertical distance between them into 100 parts, and then plot the percentages downward from rb, equivalent on the small scale to the percentages downward from DC to the original No. 2 curve CE, as described on page 188, or we may take ratios, as described on page 190, and using the slide rule set DE (100) on De (65) and on any vertical dis- tance from DC to the line CE, we may read the distance from rb to the resultant curve eb. In practice, the line rb need not be plotted, but each ratio as it is obtained may be added to the per cent, already found for the No. 3 material to obtain the distance down on the ordinate for the final curve of the mixture, as shown on page 867. The rer^uired percentage of material No. i may be obtained by deducting the sum of the percentages of No. 2 plus No. 3 from 100, or by inspection of the parabola and the curve of the portion of the final mixture already plotted, ebkA. From the location of the point e it is evident that 35% of the total mixture of the material must pass a 0.25-inch sieve. Since No. i is the only material whose particles are finer than this, it is evident that this percentage of the total mixture must be entirely formed by No. i. In other words, the percentage of No. i to the total mixture of 100 parts is 3S%- To plot the curve OD as a part of the mixture, we may divide the distance eE into 100 parts, and plot the percentages, or we may take the slide rule and set Ee on DE, that is, 35 on 100, and read the correspond- PERCENTAGES RETAINED ON SIEVES 86i = s M ^ ? o i^ o o 3 ~c» M < l\ \, \ ^ s \ \ ■\ \, \ -V \\ * ■°^ \ o \ ^>. \ c \ ^ 1 \ -V. 1 1 r \ \ ° sc ^ [ ca w S. \ ^ 1 1 \ \ \ 1 \ s p "■^ 1 *; > \ \ ^ \ ^\ \ -^ \ ^ '\'' 1 \ N s \, \ k 1 \ \ o \ \ \ \ \ \ — \ \ \1' \ \ °> \ \ \ \ \ \ |\ \ \ o \ 1 1 I \ ^\ \ \ = \ II \ \\ \ V 1 1 s \ \ \ i \ i \ = 11 s \ => i ^; 3 \ I -1 ^\ \ 1 \^ e ■^ 3 1 w, "x ° 1 ^^ \ \ 1 \. X N 1 4 ) 'n ^ \ ^ n \ ■^ a. \ u. '--^ --^ \\ ^ Tr< no ' ^ _J — ■s ^ ^1^ O ■s I CO £ 3 u o Xi § Q I PERCENTAGES PASSING SIEVES 862 A TREATISE ON CONCRETE ing ratios for the other ordinates. Thus, at ordinate o.io, DE: eE = ZWii zW^, or loo: 35= 'ji-.zW^, hence zW^ = 25. The final curve of the mixture of materials No. 3, No. 2, and No. i in proportions represented by the percentages obtained is represented by the dotted line AkhezO.' To illustrate how simply such a diagram as Fig. 259 is solved in practice without really going through the processes described, we may determine the percentage by weight of each material to the weight of the final mixture as follows: Cb 39 For material No. 3, ;^ = — - = 39% Cx) 100 re De — 39 26 For material No. 2 , 7-7; or - — vtt; — = — = 26% DE DE 100 Ee 35 For material No. i, ^— = — ■ =35% tjU 100 We have thus the percentages of each aggregate material which must be contained in the total mixture of aggregate. The actual proportions of the concrete expressed in parts are obtained in the same manner as is described for example 2 on page 868. Case II. Curves which overlap. Fig. 260 shows a more complicated combination of materials than Case I. Curves of four materials are drawn. From the foregoing it is clear that the percentage for material No. 4 is represented by Ch or 14%. Since curves No. 2 and No. 3 overlap each other, their values are less easily determined, and we may leave them and first take No. i. Curve No. i is determined and may be plotted in the same way as curve No. i in diagram, Fig. 259, p. 856, giving the gF 33 curve Osg, and the percentage — — == — • = 33% the percentage by weight GF 100 of No. I in the final mixture. Having found the per cent, of No. i sand to use and also of No. 4 stone, namely, 33% for No. i and 14% for No. 4, we have left 53% of the total mixture which must be made up from No. 2 and No. 3 lots. On curve FE the portion from £ to / is overlapped by that part of the DC curve extending from D to K. We note first that about 20% of the material in the parabola (that portion extending from g to L) must be supphed with stone from the No. 2 lot, while about 10% of the material of the parabola (the portion extending from h to M) must come from the No. 3, or DC curve. There is left then 53% — (20% + 10%) = about APPENDIX 1 863 23% of the parabola which must be supphed from the overlapping portions of the two curves. Judging from the general appearance of the two curves it would appear that No. 2 curve contained stone more nearly corresponding to the needs of the parabola than DC. For a trial, therefore, we will give a larger proportion to No. 2 than to No. 3 stone, say, 14% of the remaining 23% to No. 2 and 9% to No. 3. No. 2 stone must then furnish 20 + 14 = 34% of the final mixture and No. 3 must furnish 10 + 9 = 19% of the final mixture. Through g draw a base line gN on which to construct the new curve for FE. 34% higher up draw Hne PQ which forms the upper limit for new curve to represent FE and the lower hmit for new curve to represent DC. Then 19% higher up draw line bT, which forms the upper base line for new curve to repre- sent DC. Now, by dividing the vertical distance between the lines ^iV and PQ into 100 equal parts, — or else by ratios, taking the sHde rule and setting Pg on OF and reading from the ordinates of FE, the distances from the base line gN to the points which locate the curve ge, — we can readily transfer curve FE into the new curve indicated by the dotted line ge which is assumed to supply 34% of the stone stiU needed by the parabola, and in the same way by dividing the vertical distance between the lines PQ and Tb into 100 equal parts, — or else by taking ratios, — the new db curve can be laid down. The curve from g to / and from h to k remains as it is. With a pair of dividers transfer the distance at each ordinate from base line PQ up to curve db down to curve ge, and add it to the curve. These new points will give the dotted curve jk as the exact location of the two batches of stone No. 2 and No. 3 combined, 34% of the one being used and 19% of the other. The resultant curve, jk, may be found in another manner after selecting the percentages of the different materials by adding on any ordinate the percentages of each material in the final mixture. For example, on i.oo diameter, 26% of No. 3 stone passes a i-inch sieve, but since No. 3 actually occupies only 19% of the mixture, the percentage of No. 3 stone passing the 1-inch sieve in terms of the weight of the total mixture (which is 100%) would be 19% of 26% = 5%. Similarly, the percentage of the portion of the No. 2 stone in the final mixture which passes a i-inch sieve is 34% of 88% or 30%. All of the No. i material (33%) passes the i-inch sieve, so this too must be added to the others, and we have 5% -f 30% -f 33% = 68% as the percentage of the final mixture which wiU pass a i-inch sieve. An inspection of this dotted line jk resulting from combining these 864 A TREATISE ON CONCRETE curves leads us to the conclusion that we should have done rather better to have taken more of No. 2 stone, say, 38% instead of 34%, and 15% of No. 3 instead of 19%, in which case the combined curve would have more nearly corresponded with the parabola. We would have, therefore, as a result of our study the required percentages of material as 14% of No. 4, 15% of No. 3, 38% of No. 2, and 33% of No. j. Practical Examples of Proportioning. Having taken up in a very elementary fashion the principles by which curves are drawn and com- bined, we may take two examples of other combinations of materials liable to be met with in practise. Example I. — Curves of two materials. Suppose we have for concrete lOOp / r- E r: ■p^ M r- p r- r r r V- p r p F •r- - r- r- — _l ^ ^ ', <" / • VI- -? / ' -' X / 1 ^ --' , <, / •■ OK 1 -- ■ / y "*' ^ ^ ^ y 1 ^ ■' ■^ } / 1 ti y ^ ^ y L ^ -M 9 -'■ / •' ^ ' i .' ^ i / 1 , ^ ^ 1 / 1 / / v , '' / n ^ / / R 1 /' ^ 1< '1 ^ ^ ^ n- ^ ^ t. \m 0.75 1.00 1.25 DIAMETERS OF PARTICLES IN INCHES Fig. 261 . ^ Method of Proportioning Two Aggregates. (5ee p. 864.) the fine sand of Fig. 57, p. 190, to use with the crushed stone of Fig. SS, p. 188, what proportions of each should be employed and how could the mixture be improved? Solution. — The curves of the two materials are plotted to the same scale in Fig. 261 as OF and DBLA, and then the theoretical curve OCA drawn for convenience as a parabola by the method previously described. The curve indicates that for a theoretical mix of sizes of aggregate up to if inches, 93% of the mixture should pass a i^-inch sieve, 76% should pass a i-inch sieve, 53% a ^-inch sieve and so on. Where, as in this case, the materials to be mixed are represented by r nly two curves, no combination of which will make a curve as close to the theo- retical as is desirable, there is another limiting condition which was brought APPENDIX I 86s out by the experiments, viz., that for the best results the combined curve shall intersect the theoretical on the 40% line, at C, and that the finer mate- rial shall be assumed to include the cement. In this case, therefore, vfhere the stone and sand curves do not overlap each other, to determine the best proportions of stone and sand, we have merely to take such proportions of each that the resultant curve will pass through the ideal curve at the point C where it crosses the 40% abscissa. EC 60 This percentage is obtained by taking the ratio -=- = — — = 61%. The EB 98 percentage by weight of sand plus cement to total aggregate will be 100% — 61% = 39%. The curve of the mixture may now be drawn by re- plotting the curve DBLA in its new location JCGA and the curve OF in its new location OJ, thus making the combined curve OJCGA. Now decide upon the amount of cement to use in the mix to give the required strength of concrete, say, one cement to eight aggregate (the pro- portion of aggregate being based on measurement before mixing together the sand and stone), which will make the cement one-ninth or 11% of the total materials. Deducting this from the sand plus cement, we have 39% — 11% = 28% sand, and our best proportions for a i: 8 mixture wUl be II parts cement: 28 parts sand: 61 parts stone, which is equivalent to 1 : 2.5: 5.5. If the proportions are required by volume and the relative weights of the sand and stone differ from the relative volumes, the pro- portions should be corrected accordingly. Plotting the analysis curves of the two materials, as described above, shows immediately how to improve the mix. If, for instance, the crushed stone had been better proportioned so as to contain more particles of 0.5 and i.o inch diameter, — see curve DHA, — a curve much nearer the parabola could have been constructed. In this case the ratio would have EC 60 ^ ^ been — - = — = 66% of stone, and the proportions of cement, sand, ER gj and stone for a i : 8 mixture, 11:23: 66 or 1:2:6, a stronger and a more impermeable mix. A still better mixture would have resulted with the use of coarser sand having a curve similar to the broken line OMN, which with the first material, DBLA, would have brought the continuous line . MC of the mixture very much nearer the ideal curve, by usmg the ratio — — = — = e.A% of curve DBLA and 46% of curve OMN. This method thus shows not only the best proportions for given materials, but also the de- fects in the materials and how to remedy them. 866 A TREATISE ON CONCRETE The most valuable use of the method of proportioning by mechanical analysis is in cases where the character of the work warrants employing several grades, that is, several sizes, of stone and sand. Such mixtures are being increasingly employed as engineers and contractors more fully appreciate the necessity of so economically proportioning the materials as to produce a mixed aggregate of the greatest possible density, — that is, with the fewest possible voids, — thereby reducing the quantity of cement and at the same time improving the quality of the concrete, in other words, making both a better and a cheaper concrete. The process of determining the percentages of each material is more complicated than where only two aggregates, sand and stone, are used, but it is not very difficult in practice, especially if one is familiar with the slide rule, and, as illustrated in Example 2, the method is more exact than ^ -• •■ / ■' •■ ■^ s= w " I ^ / n ^ — ' / , — • ■^ ^ / / ^ ^ f / ^ - ' *? / / , ^ •* / 7 'c -f -- '' / 1 ^ J f ' j f 1 ■T / 1 1 V / ^ 1 / 1 1 <; » ■ , 1 / L / ■,c '/ ' ', y *^ > /^ / / ■ M / v ^ 1 / , / 1 [* ^ / , -^ ^ F D 25 so 0.7 5 1 00 1 25 1 50 1 75 2, [|0 4 .25 ? «!' 76'a IE a 100 DIAMETERS OF PARTICLES IN INCHES Fig. 262. — Method of Proportioning a Graded Mixture. {See p. 866.) with two materials, for the reason that the resulting curve can be made to more nearly approach the parabola. Example 2. — Graded Materials. Given the medium sand, represented by curve in Fig. 57, page 190 and the three sizes of crushed stone repre- .sented by the curves in Fig. 56, page 189, find what percentage of each will best combine to make the strongest and densest concrete. Solution. — Since mechanical analysis of each material has already been made, we will immediately replot the four curves on the same scale in Fig. 262 and draw parabola passmg through point O and the point at which curve No. 4 reaches 100%. We see at once that percentage of No. 4 Kk 36 stone required is ^ = — = 36%. (To be sure, about 8% of No. 4 is overlapped by No. 3, but this is so slight it need not here be considered.) APPENDIX I . 867, Let us determine sand curve No. i at o.io diameter ordinate, since it can be seen by inspection that the portion oh of curve No. i very nearly fits the parabola and grains smaller than o.io diameter _ must be supph'ed wholly from this curve, while the larger grains represented by portion hG are found also in No. 2 curve. Accordingly, we have the percentage £}_ 20 Fh^'&E^ ^^'^^' A part of No. 3 curve, that portion extending from D to /, is overlapped by nearly the whole of No. 2 curve. We can see, however, that No. 3 curve alone must supply 14% of the material in the parabola (that portion extending from e to k). This leaves 100 — (36 + 23 + 14) = 27% of the mixture to be furnished by the overlapping portions of No. 3 and No. 2 in such ratio as best fits the parabola. From a study of the two curves, we find by inspection and trial plottings that most of the material required would be better supplied by No. 2 curve, since it contains stone corresponding very well to the needs of that part of the parabola extending from / to e. Let us consider 23% as the proper amount of the final mixture to be furnished by No. 2 curve, which would leave 14 + 4 = 18% as the total portion which must be supplied by No. 3 curve. Now, on any of the ordinates, we can locate points through which a curve may be drawn which represents a mixture of the given sand and stone in the proportions just found, for example: Ordinate. % Retained. 1.75 40x36%' = 14 1.50 57x36% = 20 i.io 92x36% = 26 1.60 (100x36%) + (8x18%) = 36+ I =37 0.80 36 + (31 x 18%) = 36+6 ■ = 42 0.60 36 + (66jc 18%) = 36+12 = 48 0.40 36+(88xi8%)+ (2ix23%) = 36+ 16+5 =57 0.30 36+ (93x18%) + (40x23%) = 36+ 174-9 =62 o.is 36 + 18 + (92x23%)+ (6x23%) =36+ 18 + 21+ I = 76 0.0s 36+18 + 23+ (30x23%) = 36+ 18+ 23 + 7 = 84 These percentages are plotted on the diagram as small circles. The same points would have been obtained if we had begun at the left of the diagram and calculated the percentages passing the sieve. We find that a curve drawn through these points satisfies the parabola sufficiently well to assume that 23% of sand, 23% of finest stone. No. 2, 18% of medium stone. No. 3, and 36% of the largest stone. No. 4, would make the best concrete mixture out of the given materials. 868 A TREATISE ON CONCRETE If 1 : 7 concrete is wanted there would be — = 14.3 parts cement, and 7 the proportions would be 14 : 23 : 23 : 18 : 36 on : i .6 : 1 .6 : i .3 : 2 .5 by weight. This would give very nearly an ideal mix, and the resultant concrete would be impermeable and very strong. INDEX Absolute volumes of sand, 158 in mortar, 148, 159 Abutments, design of, 741 Accelerated tests of cements, 106 See also Soundness Acids, effect upon concrete, 293 Adhesion tests of cement and mortar, 102 Adhesion of concrete to steel, 429 References, 833 Adhesion of old and new concrete, 258 Aggregate, definition, g Aggregates. See also Broken stone See also Gravel See also Sand coarse, 29 essentials, i fine, 28 laws of volumes and voids, 120 properties of, i, 2 selection, 12 specifications, 28, 29 tests, IIS voids and density, 129 Alcohol, effect of. References, 846 Alkalies, effect of, 294 Alum and lye, waterproof wash, 299 Alum and soap, waterproof mixture, 300 Alumina, limiting percentage for cement in sea water, 269 Am. Soc. C. E., standard cement tests, 62 Analysis, air, 88 chemical. See Chemical analysis mechanical. See Mechanical analy- sis Apparatus for cement tpsting, 83 Aqueducts. See Conduits Arches, 707 References, 833 abutments, design of, 741 bridges. See Bridges centering, 74S classification, 710 Arches, concrete vs. steel, 708 construction, method of, 744 dead loads, 718 earth pressure, 718 erection, 744 example of design, 733 Arches, fixed or continuous, 722 formulas, general, 723 formulas, moment, thrust and shear at crown, 727 groined, 792, 793 history of concrete arches, 710 loading to use in design, 738 Melan system, 711 moment at the crown, 725 Monier system, 711 notation, 719 relation outer loads and reactions at supports, 719 rib shortening, 732 shape of ring, 714 shear at the crown, 725 steel reinforcements, 709 strength. References. 844 stress, allowable unit, 741 temperature, effect of, 729 thickness of ring at crown, 714 three-hinged, 720 thrust at the crown, 725 two-hinged, 721 Wiinsch system, 711 Ash pits, 828 Asphalt for waterproofing, 302 Autoclave test, 112 Automatic concrete elevator, 246 Automatic measures for materials, 239 Bag of Natural cement, weight, 82 Portland cement, weight, 63 Bags for depositing concrete, 268 Banded columns, 377, 456. 561 Barrel of natural cement, vreight, 82 of Portland cement, weight, 63 Barrel, volume of, 9, 206 weight of, 9 Barrow. See Wheelbarrow Bars, concrete splitting at, 537 deformed, use, 6, 434, S66, 673, 76s depth of concrete below, 538 length to imbed in concrete, S39 table of areas and weights, 574 types of, 571 Basement walls, 643 Batch mixers, 23s 869 870 INDEX Beams, plain. References, 844 Fuller's tests, 333, 334 strength, 334 tests of cement, 102 Beams, reinforced, 481. See also T- beams References, 845 analyses, 352 bending moments to use, 510 circular, 399 concrete bearing tension, analysis, 360 continuous at the support, 496, 555, 589, S92, SQ4 cracks and corrosion, 292 deflection curves, 439 deformation curves, 413 diagonal tension, 364, 418, 516 end beams and wall columns, 513 end reinforcement, 496 examples of design, 482, 483, 490, 493, 49S, SS3, SS7 experiments, 405 bond in beams, 434 continuous beams, 441 deflection, 440 diagonal tension, 418 double-reinforced beams, 427 phenomena of loading, 405 rectangular beams, 405 steel splices, 439 T-beams, 415 formulas for concrete bearing ten- sion, 360 formulas for rectangular, 353, 481 formulas for review, 484 formulas for steel in top and bottom, 358, 492 formulas for T-beams, 355, 487 foundation, 684 general principles, 350 haunch, 497 horizontal shear, 362, 515 modulus of elasticity, 400 neutral axis, location of, 410 plane section before and after bending, 403 rectangular, 481 reinforced, slab load, distribution of to supporting beams, 447, 501 shearing forces, 362, 515 spacing of tension bars, 537 steel in top and bottom, 358, 492, 589, 592, S94 steel in top and bottom, example, SS4, SSS straight line theory, 352 tables of constants, 596, 597 table of depth of neutraJ axis, 598 tables of safe loads, 576-578 Beams, Talbot's tests, 415 T-beam design. See T-beams tensile resistance, 405-414 vertical shear, 362, 515 working stress, 573 Belt conveyor for concrete machinery, 244 Bending moment. See Moment Bending moment diagrams, 505, 506, 507, 508, 604, 605, 606 Bending moments and shears, 502 Bending tests for steel, 480 Bent bars, points to bend, 534 Bertini system, 570 Beton-coignet, definition, 9 Beton, definition, 9 Bin gates for sand and stone, 225 Bins, for stone crushing plant, 224 Blocks, concrete building, 623 in sidewalks, 803 molded, 268 ornamental stone, 623 • Boiler settings, 828 ' Boiling tests, 106. See also Soundness Bolts, foundation, 684 Bonna system, 570 Bond of concrete and steel, 429, 533 hooked bars, value of, 438, 540 working stress, 573 to resist direct pull, 430 Bonding old and new concrete, 258 Boonton, N. J., dam, 772 Bottle kiln, 823 Boulogne method of testing consistency of cement, 71 Brick, as a substitute for sand, 172 Brick vs. concrete columns, 452 Brick vs. concrete conduits, 778 Bridge piers. See Piers Bridges. References, 833 arch, 707. See Arches. beam, 693 girder, 694, 698, 704 Granite Bi"anch Bridge, 748 Mystic River Bridge, 748 Ross Drive Bridge, 748 slab, 693, 696 Walnut Lane Bridge, 706, 750 Briquettes, for tensile tests, 77 German standard, 96 Broken stone, classification of, 121 characteristics. References, 841 compacting of, 140 concrete vs. gravel Concrete, 324 cost of, 25 cost of crushing, 227 crushing, 221 hauling, 226 plant for, 224 quality affecting concrete, 323 INDEX 871 Broken stone, screened vs. unscreened, 180 screenings vs. sand, 166 selection of, 12 size affecting strength, 322 size and shape, effect upon per- meability, 308 specifications, 29 tables of quantities for concrete, 214 ts^pical mechanical analyses, 188 uniform vs. graded sizes, 15 voids vs. gravel voids, 13s weight, 226 Buckets for depositing concrete, 268 Building construction, 607 References, 834 advantages of concrete, 607 average costs per square foot of floor area, 610 average costs per cubic foot of volume, 610 cost, 608, 611 curtain walls, 645 mixing concrete, 243 unit construction, 646 walls, 643 Buildings, typical plans, elevations, sections, and details Gray and Davis Building, construc- tion photograph, 607 Massachusetts Institute of Technology, frontispiece beam and column reinforcement, 626 beams, long span, 625 beams and columns, 626 column reinforcement, 633 chuting concrete, 256 crdss-section, 618 footings, 679, 683 framing plan, 615 inserts, 631 ornamental facades, 619 stairs, 639 Paine Furniture Building floor plan, 614 roof plan, 641 Youth's Companion Building elevation, 616 flat slab ceiling and columns, 630 floor plan, 613 wall section, 616 Burning Portland cement, 821 over-burning and xmder-burning, 60 Calcining Portland cement materials, 821 Calcium chloride, 288 Cambridge bridge, concrete machinery, 248 , Car for conveying concrete, 254 Carborundum for rubbing, 266 Castings, concrete, 623 Cast piles, concrete, 687 Cellar walls, 643 forms, 19 Cement. See also Cement testing affected by sea water, 271 affected by sulphate water, 272 air analysis, 88 approximate quantity formula, 16 barrel, volume, 9, 206 barrel, weight, 9 chemical analyses, 40 classification, 40, 48 cost, 24 effect of freezing, 281 effect of percentage upon strength of mortar, 316 essentials, i fatigue, 338 fineness, 8j flash set, 92 Iron Portland, 41 manufacture, 813 materials for manufacture, 52, 816 mixture with Puzzolan and slag, 279 Natural Portland, 41 per cu. yd. of concrete, tables, 214 production, 814 proportion in rubble concrete, 216 proportion in selecting concrete, 178 Puzzolan, 44. See Puzzolan cement quantity for concrete sidewalks, 811 sand, 41 selection of, 12 specifications, 62 specific gravity, 68 storage, 219 to resist sea water, 274 Tufa, 42 water for chemical combination, 88 weight of, 113, 206 white Portland, 41 Cement rock, 52 Cement testing, accelerated tests, 106 adhesion, 102 American vs. European sieves, 91 apparatus for laboratory, 83 autoclave test, 112 cautions, i chimney test, 112 color, 112 compression machines, 340 , compression tests, 100, 146 compressive strength, 78 consistency, normal, 70 effect of shape of specimen, 145 fineness, 68 fineness below No. 200 sieve, 88 microscopical examination, 114 mixing, 69 872 INDEX Cement, moist closet, 79 purity test, 66 rate of applying strain, 78, 96 rate of setting, 91 relation of different tests, 145 setting, 75 European methods, 90 shearing, 146 soundness, 72, 103 specifications, 62 specific gravity, 68 standard methods, 63 standard sand, 76 steaming apparatus, 73 tanks for briquettes, 79 tensile briquette, 77 tensile machines, 97 tensile strength, 63 tensile tests of cement and mortar, 98 transverse tests, 102, 146 water for normal consistency, 88 weight, 113 Centigrade to convert to . Fahrenheit, Third cover Centimeter, English equivalents. Third cover Centers, arch, 745 Chalk, chemical analysis, 818 Charlestown bridge piers, 248 Chaudy and Degon system, 570 Chemical analysis, cement testing, 64 clay, 818 lime, 40 Natural cements, 46 Portland cements, 40 Puzzolan cement, 40, 826 Chemical analysis, raw materials for cement, 818 sand, 118 slag, 826 Chemistry of hydraulic cements, 48 Chimney expansion test, 112 Chinmeys, reinforced concrete, 660 analysis of stresses, 390 construction, 660 design, 390, 662 Edison Electric Illuminating Co.,66i example of design, 666 formulas, 390, 664 house, 829 shear and diagonal tension, 397 tables, 665, 666 Chutes for depositing concrete, 253 under water, 267 Cinder concrete, rust protection, 292 slabs, 620 slabs, table, 584 strength and elasticity, 327 vs. stone concrete in fires, 292 weight, 9 Cinder pits, 828 Cinders, selection, 620 specific gravity, 123 Circular beams, 399 Classification of broken stone, 121 of cements, 40, 48 Clay, bearing power, 669 chemical analyses, 818 effect upon mortar, 160 effect upon mortar. References, 846 for Portland cement manufacture, S3 water-tightness, effect upon, 301 Clinker, microscopical tests, ri4 Coal pockets, 828 Coatings for sea water work, 280 Coatings for waterproofing, 299 Coefficient of expansion, 261 Coignet system, S7° Coke breeze, 329 Cold. See Freezing Coloring concrete, 810 Color of cement, 112 Columbian system, 570 Columns, 375, 4So,_ 558, 631 concrete w. brick, 452 deformation of plain and hooped, 456 eccentric loading, 377, 459 economy, vertical bars vs. spirals and vertical bars, 632 flexure, formulas, 377 footings. See Footings, reinforced Columns, formulas for, 375 experiments, 450 long columns, 466 plain columns, 450 spirals and vertical steel, 456 square columns, rectangular bands, 460 structural steel, 461 vertical steel, 453 illustration of reinforcement, 633 modulus of elasticity, 403 plain concrete, strength of, 450 reinforced, 375, 450, 633 rich proportions of concrete, 559 spiral columns, 377, 634 strength, 450, 560, 573 structural steel reinforcement, 464, 563, 63s table of working loads, 573 vertical bar reinforcement, 453, 561 wall columns and end beams, 513 working stress, 573 Combined footing, 678 Compacting of broken stone and gravel, 140 Composition, of cement mortars, 143 chemical. See Chemical analysis Portland cement, 53 various mortars, 146 INDEX 873 Compressive strength, References, 843 Compressive strength of concrete, 310 average, tables, 312, 315, 316 brief tabJe for safe strength, 27 cinder concrete, safe strength, 628 columns, 450 concentrated loading, 330 formula, 313 growth, 320 safe strength, 27, 311, S73 short prisms, 344 tests, 316 vs. transverse strength, 337 working, in extreme fiber, 573 Compressive strength of mortar, 146 Feret's formula, 153 Feret's tests, 146, iSQ form of specimens, 81, loi prisms, 403 various, 146 vs. tensile strength, loi Compressive strengfli of stone, 324 Compressive tests of cement, 100 Concentrated loading, effect of, 330, 446 diagram for moments and shears in continuous beams, 508 Concentrated iis. distributed loading, 331 Concrete blocks, 623 Concrete tile, 628 Concrete, specifications, 28 Concrete, definition, g gravel vs. broken stone, 324 mixer, 235 mixing. See Mixing concrete plants, 241 proportioning. See Proportioning rubble, 218 rubble, definition, 10 strength. See Strength stretch, 401 tables of quantities of materials, 214 tables of volumes, 215 theory of mixture, 178, 207 uses, II vs. brick columns, 452 vs. brick conduits, 778 weight, 9 working stresses, 573 Concreting, elementary outline of pro- cess, II. Conductivity of concrete, 291 Conduits, 777 References, 842 arch top, 782 brick vs. concrete, 778 construction, 785 design, 780 earth pressure on, 781 forms, 786 formulas for rectangular, 782 Conduits Jersey City Water Supply Co.> 783 rectangular, 782 thickness of, 780 water-tightness, 778 Weston aqueduct, 783 Conglomerate concrete, weight, 9 Conglomerate, specific gravity, 123 Consistency, Boulogne method, 71 , Consistency of concrete, 250 depositing through chute, 253 effect on modulus of elasticity, 403 effect on strength, 317 effect on water-tightness, 298 specifications, 31 Consistency of mortar, effect upon strength, 165 Consistency of paste and mortar, normal, 70,88 Constancy of volume. See Soundness Continuous beams, bending moments use, 510 Continuous beams, design, 496, 555 diagrams shear and bending moment, S04 moment of inertia, effect upon bending moment, 499 shear and bending moment dia- grams, 504 span, 500 stirrups, method of placing, 519 Continuous mixers, 23s Contraction joints, 259 Contraction. References, 837 Conveyor belt. See Belt conveyor Copings, 768 Core walls, 774 rubble concrete, 774 thickness, 774 Cornice, 645 Corrosion of steel in beams, tests, 292 Corrugated bar, 570 Cost, building construction, 608, 611 cautions, 7 columns; vertical steel vs. vertical steel and spirals, 632 concrete, 24 essentials in estimating, 7 hand mixing, 9 labor laying concrete, 25 materials for concrete, 24 quarrying and crushing, 226 ramming concrete, 257 rubble concrete, 769 screening sand and gravel, 219 sidewalk construction, 808 stone crushing, 221, 226 various slab designs, 621 Cottacin system, 570 Counterfort retaining walls, 765 874 INDEX Cracks in reinforced beams, 407 corrosion of steel, 292 Cross reinforcement of slabs, 418, 486 Crushed stone. See Broken stone Crusher, gyratory, 223 Crusher, jaw, 222 Cubes vs. cylinders vs. columns, 344 Cummings systeiii, 570 Ciu-bing, concrete sidewalk, 807 Dams, 751, 768 References, 836 arched, 770 Boonton, N. J.,- 772 building of rubble concrete, 769 Estacada, Oregon, 771 gra\'ity design, 770 reinforced design, 770 Dead loads, arches, 718 Definitions, 9 See material in question Deformation and deflection curves of a reinforced beam, 413, 443 Deformation of hooped columns, 456 Deformed bars, use, 6, 434, 566, 673, 765 Density, definition, 9 method of determining, 148 Density of concrete, 310 curves of maximum, igo relation to strength, 194 studies of, igo table of tests, 334 Density of mixed aggregates, 129 Density of mortar, application of laws, 163 relation to strength, 145 tests of mortar, 149 tests of mortars of coarse vs. fine sand, 162 Depositing concrete, 249 cautions, 4 specifications, 31 Depositing concrete under water, 267 Depth, concrete below rods, 538 Depth of T-beam, economical, 490 example, 554, 555 minimum, 489 tables, 586, 587, 588 I Derrick for laying concrete, 252 Design. See articlein question; cautions,6 Destructive agencies, 289 Diagonal tension. See Tension, diagonal Diagrams, for bending moments, 505-508, 604-606 double-reinforced beam design, 493- 495 , . mechanical analysis, 197 members under flexure, 383, 387, 388 Diamond bar system, 572 Dietzsch kiln, 824 Dikes. See also Core waljs Metropolitan Water Works, 774 Parsippany, laying, 244 Distribution of beam and slab loads to girders, 501 Distribution of slab load to supporting beams, 500 Distribution of stress, diagrams, 383, 387, 388 plain concrete, 377 reinforced concrete, 380 Domes, 642 Dome kiln, 823 Donath system of reinforcement, 572 Driveways, 810 Dry concrete, 251 rammers for, 258 Dry concrete under water, 267 Durability, concrete inverts, 779 concrete piers, 689 Dwelling houses, 829 Earth, bearing power, 669 weight of, 756 Earth pressure, 757 arches, 718 Conduits, 781 formulas, 758, 760 inclined back of wall, 759, 760 tables for, 757, 759 vertical back of wall, 758 wall with surcharge, 760 Eccentric loading, 459 Eccentric loads, diagrams, 383, 387 distribution of stresses, plain con- crete, 377 distribution of stresses, reinforced concrete, 380 Economical depth of T-beam, 490 example of, 554, 555 Edison Electric Illuminating Co., chim- ney, 661 Elastic limit. See Yield point Elasticity. See Modulus Elcannes bar, 572 Electrolytic action, 295 Elementary volumes, 148 Elevator, automatic, concrete, 246 Elevators, grain, 828 Elongation in concrete, 407 Elongation required in first-class steel, 478 Elongation required in mild steel, 478 Estimating, essentials, 7 Erection of arches, 744 Expanded metal, 572 Expansion joints. See Contraction joints Expansion of cement. See also Sound- ness INDEX 87; Expansion of cement, measurement, iii Expansion of concrete, while hardening, 261 coefficient for temperature, 261 moisture changes, effect of, 261 Experiments upon reinforced beams, 405 bond in beams, 434 continuous beams, 441 deflection, 440 diagonal tension, 418 double-reinforced beams, 427 phenomena of loading, 405 rectangular beams, 405 steel splices, 439 T-beams, 415 - Facing concrete walls, 262 color effects, 267 mortar facing, 267 panels, 267 photographs of surfaces, 263, 263 plastering forms, 267 Factory construction, cost, 608 Fahreiiheit to convert to centigrade. Third cover Fatigue of cement, 338 Felt, waterproofing, 302 Fences, 829 Feret, R. Effect of Sea Water, 271 Feret's formula for normal consistency, 89 Feret's formulas for strength of mortar, Feret's tests of strength of mortars, 146 Feret's triangles, 157 Ferroinclave system, 572 Fiber stress vs. tensile, stress, 145 Fineness of cement, advantages of, 87 below No. 200 sieve, 88 effect on weight, 113 specifications Natural cement, 82 specifications Portland cement, 62 standard test, 68 strength affected by, 87 Fire protection, cinder vs. stone con- crete, 289 concrete, 289 theory, 290 thickness concrete required, 289 Fire resistance. References, 837 Woolson's tests, 291 Fire-resisting qualities of concrete, 289 Flash set, 92 Flat slabs, 540, 629 foundation, 684 tests, 472 Flexure and direct stress, diagram, 383, 387, 388 plain concrete, formulas, 377 reinforced concrete, formulas, 380 Float, plasterer's, 805 Floors, cinder concrete, 620 construction, 624, 635 design, 552, 624 forms, 653 hollow tUe, 628 loads, 617 materials for, 620 proportions of concrete, 620 reservoirs, 792 slabs. See Slabs. surfaces, 635 Footings, design, 672 combined, design of, 678 independent, design of, 673 reinforced concrete, 673 spread, 684 square, design of, 677 wall, design of, 673 Forms. References, 837 beam, 651 brief directions for constructing, 19 cautions, 4 cellar wall, 19 damp for beam, 651 column, 649 conduit, 786 cornice, 644 design, 658 floors, 653 girder, 651 greasing, 647 hollow walls, 657 lumber, 647 plaster, 267 removing, 648 slab, 6S3 . specifications, 32 steel, 647 strength, 658 time building, 8 wall, 656 Formulas. See article in question. Foundation bolts, 684 Foundations, 669 References, 838 See also Footings beams and slabs, 684 bearing power of soils and rock, 669 column, 673 flat slabs, ^84 safe loads (bearing), 573 spread, reinforced, 684 under water, 690 under water, laying, 267 Freezing. References, 847 effect of, 5, 281, 319 effect of calcium chloride, 288 effect of salt, 287 effect upon sidewalks, 806 experiments, 282 protection from, 286 876 INDEX Freezing weather, construction in, 284 specifications for laying in, 32 French commission, method of pro- portioning, 184 French commission, setting tests for cement, 91 standard sand, 94 Frost. See Freezing Fuller's beam tests, 334 Fuller's rule for quantities, 16 Fuller, WilUam B. Proportioning Con- crete, 17s Gabriel system, 572 Gaging. See eJso Consistency water for sand, 140 with sea water, 166 Gang for mixing concrete, 233 Gates for sand and stone bins, 225 German standard briquette, 96 Gillmore vs. Vicat needles, 91 Girder bridges, 694, 698, 704 Girders. _See also Beams, reinforced, typical illustration of, 552 Glycerine, effect of. References, 846 Grain elevators, 828 Gram, English equivalents. Third cover Granite Branch Bridge, 748 Granite, specific gravity, 123 Granolithic, floors, 635 grinding, 638 specifications, 637 Granolithic finish for water-tight work, 300 . Granulometric composition of sand, 155 conversion to mechanical analysis, 164 Grappiers cement, 44 chemical analysis, 40 Gravel, bearing power, 669 characteristics. References, 841 compacting of, 140 cost of, 25 cost of screening, 220 screened vs. unscreened, 180 selection of, 12 size affecting strength of concrete, specifications, 29 specific gravity, 123 ^ tables of quantities for concrete, 214 voids vs. broken stone voids, 135 weight of, 756 Gravel concrete, vs. broken stone con- crete, 324 weight, 9 Gravity mixers, 237 Gray and Davis Building, see Buildings Greasing forms, 647 Greenhouses, 829 Griffin mill, 821 Grinding cement, 816, 818 See also Fineness Groined arches, 792, 793 Groover for sidewalks, 805 Grout for water-tight surfaces, 300 Grouting, foundations, 688, 773 Growth in strength of cement mortar, 99 Growth in strength of concrete, 321 Gutter, concrete., 807 Gypsum, effect in sea water, 272 effect on time of setting, 92 Gyratory crushers, 223 Habrich and Diising system, 572 Handling concrete, 252 data, 7 Hand mixing of concrete, 231 vs. machine, 231, 320 Haunch, design, 497 length, 498, 556 Havemeyer system, 572 Heat. See also Temperature effect upon concrete, 289 References, 847 Heating concrete materials, 286 Hennebique system, 572 Herringbone, 572 High carbon steel, specifications for, 478 vs. mild, 479 Highway bridges, liveloads, 695, 715 Hinges for arches, 713 Historical notes, 813 Holzer system, 572 Hooked bars, value in bond, 438, 540 Hooped columns, 456, 561 Hot tests, 106 See also Soundness Houses, 829 Hyatt system, 572 Hydrated lime, 47 added for water tightness, 301 Hydraulic lime, 45 chemical analysis, 40 Hydraulic modulus, 54 Impermeable concrete. See Water-tight concrete Impermeability. See Water-tightness Impurities of sand, character, 168 effect upon strength of mortar, 167 vegetable or organic, 168 washing tests for organic, 118 Inertia, moment of. See Moment of inertia Inserts, 631 Inverts, durability of concrete, 779 Jackson specific gravity apparatus, 85, 119 INDEX 877 Jaw crusher, 222 Jersey City Water Supply Co. conduit,' 783 Johnson ring kiln, 823 Joints. See also Contraction joints construction of, 258 in reinforced concrete, 259 old and new concrete, 258 specifications, 32 Kahn bars, 572 Kent mill, 821 1 Kilns, rotary. See Rotary kilns Kilns, stationary, 823 Kilograms per sq. cm., ratio to lb. per sq. in., Third cover Kilograms, ratio to pounds, Third cover Labor. See Time Laboratory, cement testing apparatus, 83 Laitance, chemical analysis, 251 effect on strength, 318 Lath, metal, plastered walls, 645 Laying, concrete, elementary outline, 11 methods, 252 specifications, 31 time, 7 Laying rubble concrete, 769 Laying waterproofing felt, 303 Length to imbed bars, 539 Lime, added for water-tightness, 301 chemical analysis, 40 effect of. References, 846 effect upon strength of mortar, 170 hydrated. See Hydrated lime hydraulic. See Hydraulic lime in cement, limited in sea water, 273 in Portland cement, S9 manufacture, 45 of Teil, 4S unslaked, 172 weight and volume of, 172 Limestone, chemical analyses, 818 for cement manufacture, 816 specific gravity, 123 Limestone concrete, weight, g Line of pressure in arches, 729 Liter, English equivalents. Third cover Literature, references to, 830 Live loads for highway bridges, 695, 715 railroad bridges, 716 Loads, bridges, 695, 715 column, 600, 601, 602 distribution from slab to beams, 500 floor, 617 foundation, safe, 669 impact, 69s roof, 643 Loam, effect upon mortar, 168 weight of, 756 Lock-woven steel fabric, 572 Louisville cement, chemical analysis, 40 Lubricating forms, 647 Lug bars, 572 Machine mixing vs. hand, 231, 320 Magnesia in cement for sea water, 272 Magnesia in Portland cement, tests, 53, limiting percentage, 62 Magnesian lime, 46 chemical analysis, 40 Manufacture cement, 813 Manufacture lime, 46 Manufacture Natural cement, 824 Manufacture Portland cement, 815 processes, 816 raw materials, 52, 816 Manufacture Puzzolan cement, 825 Manure, effect upon concrete, 294 Marine construction. See also Sea water References, 839 Marl for cement manufacture, 816 chemical analysis, 818 Massachusetts Institute of Technology drawings and photographs, see Buildings specifications, 28 McKibben, Arches, 707 Measures for materials, automatic, 239 Measuring box, illustration, 18 Measuring materials for concrete, 232 Measuring water for concrete, 240 Mechanical analysis, 185 broken stone, 188 conversion to granulometric com- position, 164 curves, plotting of, 187, 855 proportioning, 194 sieves, 186 typical sands, 190 Melan system, 572 Melan system of arches, 711 Metal lath, walls plastered, 645 Meter, English, equivalents, Third cover Metric system, ratios for converting. Third cover Metric units of strength converting to English units. Third cover Mica, effect on strength of mortar, 169 Microscopical examinatibn of cement, 114 Mild steel vs. high carbon, 479 Mill construction, cost, 609 MiU, tube, 821 Millimeter, ratio to inch. Third cover Minimum depth of T-beams, 489, 586, S87 example, 554, 587 878 INDEX Mixers for concrete, 235 batch, 23s continuous, 235 duplex paddle, 237 gravity, 237 pneumatic, 258 rotary, 237 rotary cube, 237 Mixing concrete, 231 belt conveyors, 244 building construction, 243 Cambridge bridge piers, 248 cautions, 4 central plant, 248 cost of hand mixing, 8 detail directions, 20 elevated hopper, 243 gang, 233 gravity plants, 243 hand, 231; cost, g hand vs. niachine, 231, 320 machine, 234 movable plants, 244 Parsippany dike, 247 platform over mixer, 243 pneumatic plants, 246 river and harbor work, 248 specifications, 31 stationary plant, 242 time, 7, 238 Mixing machinery, portable, 244 Modulus of elasticity of concrete, 400 beams us. columns, 403 determining of, 400 effect of consistency, 403 in compression, 400 ratio of moduli, 400, 477 tests with different proportions, 402 Modulus of elasticity of steel, 400 Moist closet, illustration, 79 Molded blocks, 268 Mold, for briquettes for tension, 78 for mortar cubes, loi for mortar cylinders, 81 Moment, bending, concentrated load, 508 crown, arches, 725 diagrams, 604, 606 diagram, continuous beam, 505-507 for beam design, 510 formulas for, 504 Moments of inertia, table 509 effect of varying, 499 Moments of resistance of beams, 355 Money, foreign, U. S. equivalents. Third cover Monier system, 572 arches, 711 Monotype bar, 572 Mortar, affected by freezing, tests, 282 affected by sea water, 271 Mortar, composition of various, 146 compressive tests of prisms, 403 definition, 10 density, 149 elasticity tests of prisms, 403 effect of regaging, 1 73 Feret's tests of strength, 146, 159 gaging with sea water, 166 Election of sand, 163 strength and composition of, 143 table of quantities and volumes, 213 tests. See Cement testing tests with coarse vs. fine sand, 162 tests of sand for, 115 weight, 9 Mushroom system, 572 Mushy concrete, 251 Mushy concrete, rammer, 258 Mystic River bridge, 748 Natural cement. See also Cement Natural cement, chemical analyses, 40 classification, 43 definition, 10, 82 manufacture, 824 specifications, 82 weight, 9 where used, 43 Natural Portland cement, 41 Neutral axis, location of, 410 table, 598 Newbury, Spencer B., Chemistry of Ce- ments, 48 New Rib bar, 572 New York Aqueduct, 788 subway, 302, 790 Notation, standard, 353 Oil, effect upon concrete, 294 Oil for greasing forms, 647 Organic impurities in sand, 118 Ornamental construction, 619, 623, 645 Paddle mixers, 237 Parabola, construction of, 855 TO. straight line theory, 404 Parmley system, 572 Parsippany dike, mixing plant, 247 Paste. See also Mortar definition, 10 weight and volume, 9 Pavement, street, 798 Peat, effect of. References, 846 Percolation. See Permeability Permeability. See also Water-tightness Permeability. References, 839 cement, percentage of, 307, 308 concrete, 296 coarseness of sand, effect of, 309 laws of, 304 INDEX 879 Permeability, method 01 testing, 306 mortar, 296 pressure, increase with, 308 results of tests, 307 shape of stone, effect of, 308 size of stone, effect of, 308 specimen for testing, 305, 306 tables, 307, 308, 309 Picked surface of concrete, 263 Piers, bridge, 689 Cambridge bridge, 248 design, 690 reservoir, 793 standard, N. Y. C. R. R., 691 Piles, concrete, 650 Boston Woven Hose and Rubber Co., 687 cast, 651, 687 cores for, 686 reinforced, 687 sheet, 688 with enlarged footing, 685 Piles, timber, 670 concrete capping for, 670 formula, 670 safe loads, 670 spacing, 641, 670 Pipes, circular, 782 Placing concrete. See Depositing Plane section before and after bending, 403 Plants for making concrete, 243 Plastering, 262 Plastering, for water-tight work, 300 Plaster of Paris. See also Gypsum, effect of. References, 847 effect on time of setting, 92 Plasters and coatings in seawater, 280 Pneumatic mixers, 238 Pneumatic placing of concrete, 255 Poisson's ratio, 339, 451, S4S Poles, telegraph, 827 Poling boards of concrete, 688 Porosity. References, 839 Portable mixing machinery, 244 Portland cement, 41. See also Cement affected by freezing, 281 chemical analyses, 40 color, 112 composition, 53 definition, 10, 41 fuU specifications, 62 growth in strength, 99 Iron, 41 manufacture, 815 materials for manufacture, 52, 816 Natural Portland, 41 Sand, 41 weight, packed and loose, 9, White, 41 Pounds per sq. in., ratio to kg. per sq. cm.. Third cover ratio to tons per square foot. Third cover Probst's tests on corrosion of steel, 293 Pressure, earth. See Earth pressure Pressure, line of, in arches, 729 Prisms, strength of, 344 Production of cement, 814 Proportioning concrete, 175 arbitrary selection, 179 cautions, 4 determination of cement, 178 determining proportions of old concrete, 339 elementary directions, 13 French method, 184 Fuller's method, 192 importance of proper, 175 inaccurate methods, 182 in practice, 202 laws of, 194 materials by weight, 240 mechanical analysis, 185 mechanical analysis diagrams, 196 methods of, 176 practical, duringprogressof work, 201 principles, 177 Rafter's method, 184 sea- water construction, 278 trial mixtures, 200 typical structures, 202 units for, 205 void determination, 181 volumetric synthesis, 200' volumes, 205 water-tight work, 298 Proportions, expressing, 205 for concrete floors, 637 for concrete sidewalks, 802 for concrete pavements, 799 for various structures, 14 raw material for Portland cement, S3, 816 sand and stone affectmg strength, 13s specifications for concrete, 30 Protection of metal, 289 References, 840 Puddling concrete, 257 Pug mill, 823 Pulverized rock, effect upon water- tightness, 302 Purity test for cement, 66 Puzzolan cement, 44 chemical analysis, 40 effect of addition. References, 847 manufacture, 826 mixed with Portland, in sea water, 27S> 279 where used, 44 88o INDEX Quaking concrete, 251 Quantities of materials. References, 848 for concrete, 14, 214 for concrete sidewalks, 811 for mortar, 213 for rubble concrete, 216 formulas, 16, 208 Quartering, method, 344 Quicklime. See Lime. Rabitz system, 572 Rafter's method of proportioning, 184 Railroad bridges, live loads, 716 Rammers, for dry concrete, 258 for mushy concrete, 258 Flamming concrete, 257 labor, 9, 258 Ransome system, 572 Reaction at supports, formulas, 502 Rectangular beams. See Beams, rein- forced References to concrete literature, 830 Regaging mortar and concrete, 173 effect upon setting, 174 retarded set. References, 847 Reinforced beams. See Beams, rein- forced Reinforced columns, 559 See also Columns Reinforced concrete, 349, 400, 477 brief laws, 7 principles of design, ^z, 349, 477 strength. References, 84s working stresses, 573 Reinforced concrete footings. See Foot- ings Reinforced floors, 624 Reinforced slabs. See Slabs Reinforcement. See also Steel arch, 709 caution, 5 diagonal tension, example, 554, 555, 'SS6 placing, 658 stirrups, types, 522 typical floor, beams, and columns, 623, 625, 626 vertical and inclined, 524 Removing forms, 648 Reservoirs, 791 References, 840 Albany Filtration Plant, 793 circular, design, 795 covered, 792 floors, 792 open, 791 piers, 793 roofs, 793 walls, 793 • waterproofing, 791 Residences, 829 Retarded set. See Regaging Retaining walls, 751 backing, 756 copings, 768 earth pressure, 757 foundations, 753 gravity section, 754 Retaining walls, reinforced concrete, 760 table for gravity sections, 755 T-type, design of, 762 with counterforts, design of, 765 Revolving screens, 230 Rib shortening, effect in arches, 732 Roadbeds, 828 Rock, bearing power, 669 Rods. See Bars Roebling system, 572 RoUer, dot, for sidewalks, 806 Rollers for conveyor belt, 244 Roman cement, chemical analysis, 40 Roofs, construction, 642 loads, 643 reservoirs, 793 Rosendale cement, chemical analysis, 40 Ross Drive bridge, 748 Rotary kilns, for dry materials, 818 for wet materials, 822 vs. stationary, 818 Rotary mixers, 237 cube mixer, 237, 258 Roundhouse, 828 Rubble concrete, 216, 769 Boonton dam, 772 core walls, 774 definition, 10 laying, 769 proportion of rubble, 769 table of materials, 216 table of volumes, 217 Rusting of steel in concrete beams, tests, 293 Rust prevention, 292 Rusty steel, protection, 293 Salt in mortar, 287 References, 847 percentage to use, 288 Sampling cement, standard method, 63 Sampling iron, illustration, 63 Sand, absolute volumes, 158 American vs. European standards, 94 bearing power, 669 cautions, i characteristics. References, 84I chemical composition of, 118 coarseness, effect on permeability, 309 INDEX 88i Sand, compacting, 142 comparative tests, 164 cost, 25 cost of screening, 220 efifect of shape of grain, 13s effect of size, 160 essentials, a. Feret's 3-screen analysis, 155 for sea-water construction, 278 granulometric composition, 155 impurities, 167 limestone sand, 166 moisture in, 137 mortar tests with various, 146 photographs, 136 properties, i sampling and shipping, 115 selection, 12, 163 shaken vs. loose, 158 sharpness, 167 specific gravity, 119, 123 specifications, 28, 116 standard, 76 strength of particles, 119 table of quantities for mortar, 213 tables of quantities for concrete, 214 tests for mortar and concrete, 115 typical mechanical analyses, 190 vs. screenings, 166 washing, 228 water for gaging, 140 weight of, 756 Sand cement, manufacture, 41 use of, 41 Sandstone concrete, weight, 9 Sandstone, specific gravity, 123 Sawdust, effect of. References, 847 Saw for shaping concrete test speci- mens, 341 Scales for weighing cement, illustration, 69 Schoefer kiln, 823 Schulter system, 572 Screened 11s. unscreened gravel or stone, 180 Screening sand and gravel, 220 , Screenings, effect of moisture, 137 specifications, 28 vs. sand, 166 Screens, inclined, 220 rotating, 220, 224 Sea water. References, 841 ' action of sulphate waters, 272 alumina in cement, 269 concrete in, 268 effect of, 271 experiments with cement in, 274 gaging with, 166 laying concrete under water, 267 Sea water, marine construction. Refer- ences, 839 sign of injury from, 271 Set, flash of cement, 4, 92 Setting of cement, arbitrary periods, 90 chemical process, 53 European tests, 90 flash set in concrete, 4, 92 rate, 91 regaged mortar, 173 rise in temperature, 93, 774 specifications. Natural cement, 82 specifications, Portland cement, 62 standard tests, 75 typical cements, 92 Sewers. See also Conduits References, 842 Sharpness of sand, 167 Shear, chimney, 397 computation in beams, 446 . crown, arches, 725 diagonal tension, 364, 516 horizontal, in a reinforced beam, 362, SIS strength of concrete, 337 vertical, in a reinforced beam, 362, vertical, in flange of a T-beam, 363 working stress, 573 Shears and bending moments, 502 diagrams, 505 Shearing forces in beams and slabs, 362, SIS Shearing tests of concrete, 337 Sheet piling, concrete, 668 Shrinkage. See Contraction reinforce- ment, 565 Sidewalks, 802 affected by frost, 806 color, 810 cost and time of construction,' 808 foundation, 802 materials, 811 method of laying, 802 proportions of concrete for, 802 thickness, 802 tools, 810 vault light construction, 808 wearing surface, 804 Sieves, for mechanical analysis, 186 for sand tests, 117 for standard cement tests, 68 Silica cement. See Sand cement Silos, 829 Slab bridges, 693, 696 Slabs, reinforced, 484 cost of various designs, 621 cross reinforcement, 486 design, 484 example of design, 553 882 INDEX Slabs, flat, 540 ratio of steel, computing of, 486 shearing forces, 362, 515 span of continuous, 500 square and oblong, 486 tables for cinder concrete slabs, 584 tables of safe loads, 576-582 Slab load, distribution to the supporting beams, 501 Slag cement, 44. See Puzzolan mixture with cements, 279 Slag, chemical analyses, 826 for concrete aggregate, 326 for Portland cement manufacture, 813 for Puzzolan cement, 825 Slate, specific gravity, 123 Soap and alum waterproof mixture, 300 Soda, effect of. References, 847 Soil, bearing power, 669 Soundness of cement, 103 apparatus for steaming, 73 appearance of pats, 74, 105, 108 specifications, Natural cement, 83 specifications, Portland cement, 62 standard test, 72 Spacing of stirrups. See Stirrups Spacing of tension bars in a beam, 537 Spandrels for arches, 712 filled, 712 open, 713 Specific gravity, cements, 84 cinders, 123 device for dropping material, 86 gravel, 123 Jackson apparatus, 85 Le Chatelier's apparatus, 67 sand, 123 specifications, Natural cement, 82 specifications, Portland cement, 62 standard cement test, 68 stone, 122, 123 test for sand and stone, 124 Specifications. References, 842 first-class or high-carbon steel, 478 Massachusetts Institute of Tech- nology, 28 mild steel, 478 Natural cement, 82 Portland cement, 62 Portland cement concrete, 28 proportioning concrete, 205 reinforced concrete, 28 Specimens for testing concrete, 343 Specimens for testing permeability, 305, 306 Standard notation, 353 Stairs, design, 639 Stand-pipes, 794 Stationary kilns, ,823 vs. rotary, 818 Steaming. See Soundness Steaming apparatus, illustration, 73 Steel, adhesion to concrete, 429, 533 adhesion. References, 833 areas and weights of rods, 574 area in T-beams, 491 area in T-beams, example, 554, SSS bars. See Bars bending tests, 480 bond to concrete, 429, 533 high carbon vs. mild, 479 modulus of elasticity, 400 protection by concrete, 289, 292 protection. References, 840 quality for reinforcement, 478 reinforcement of arches, 709 rods. See Bars spacing of bars in beams, 537 specifications for first-class, 478 specifications for mild, 478 types of bars, 571 working stress, 573 jdeld point, 478 Stirrups, 370, 418, 517, 585 diameter, 525, 556 illustration of action of, 522 in continuous beam, 374, 524 points, where not needed, 519 spacing, 371, 517, 556, 585 spacing, graphical method of, 526 tables, size and spacing, 525, 585 Stone, broken. See Broken stone Stone, compressive strength, 324 specific gravity, 122, 123 washing of, 228 Stone crushers, 222-224 Stone crushing, 221 cost, 225-227 • Storage of cement, 219 Straight line theory, 352, 404 Street pavements, 798 Strength, compressive. See Compressive strength transverse. See Transverse strength shearing. See Shearing strength Strength of cement, 98 affected by fineness, 87 Strength of cinder concrete, 327 Strength of columns, brick, 452 long, 466 plain, 450 spiral steel, 456 structural steel, 461 vertical steel, 453 Strength of concrete, 310 References, 843 consistency, effect of, 317 cubes Ds. cylinders vs. columns, 344, 466 curing, effects of, 320 density, relation to, 194 INDEX 883 Strength of concrete, eccentric loading, effect of, 457 effect of fine material in filling voids, 169 growth, 321 heat, effect of, 291 Joint Committee recommendations, 3 IS laitance, effect of, 318 machine vs. hand mixed, 319 methods of testing, 342 percentage of cement, effect of, 316 quality of stone, effect of, 323 relative proportions of sand and stone, effect of, 134 safe, 29, 311 size of stone or gravel, effect of, 322 tables, 315, 316 variations in aggregate, 329 Strength of mortar, 98, 143 affected by freezing, 282 affected by impure sand, 167 affected by lime, 170 affected by mica, 169 affected by quantity of water, 165 affected by size of sand, 160 Feret's formulas, 153 Feret's tests, 146, 159 gaging with sea water, effect of, 166 laws, 3, 144 relation to density, 145 Strength of reinforced beams, tables, 576-578, 585-598 Strength of reinforced slabs, tables, 579- 584 Stresses, working unit, in arches, 741 in reinforced concrete, 573 Stretch in concrete. See Elongation Structural steel, protected by concrete, 292 reinforcement of columns, 461, 563 Structures, miscellaneous, 827 Subways, 789 Sugar, effect of. References, 847 Sulphate waters, effect on concrete, 272 Sulphuric acid, effect on concrete, 272 limit in Portland cement, 52, 62 determination, 65 Sulphuric anhydride. See Sulphuric acid Surfacing walls, 262 Systems of reinforcement, 571 Tables. See also matter in question areas, weights, and circumferences of bars, 574 beams with steel in top and bottom, 589 chimney design, 665, 666 constant C, for design of reinforced beams, 596, 597 Tables, depth of neutral axis, 598 earth pressure, 759 retaining_ walls, 755, 757 safe loadings for rectangular beams, 576, 577, 578 safe loadings for slabs (for design- ing), 579-584 safe loadings for slabs (cinder concrete), 584 safe loadings for slabs (for review) 581 Talbot's tests of buildings under load, 468 column tests, 450, 462 reinforced beam tests, 515, 525 Tallow, effect of. References, 847 Tanks, 796 References, 840 construction, 795, 796 for immersing briquettes, 79 Tar for waterproofing, 303 T-beams reinforced, breadth of flange, 416, 488 design, 487 details of design, 491 economical depth, 490 economical depth, example, SS4 example of design, 553, 555 formulas, 355 minimum depth, 489 minimum depth, example, 554 shear, vertical, in flange, 363 steel, area of, 491 steel area, example, 554, 555 tables for design, 586-588 tests, 41 s tension diagonal, 418, 425 tensile failure, 4x5 width of flange, 416 web determined by shear, 488 web determined by shear, example, .554,555 Teil, lime of, 45 Telegraph poles, 827 Temperature, dams, 774 effect on strength, 283 rise in concrete while setting, 94, 774 rise in mortar while setting, 93 Temperature stresses, 565 arches, 729 reinforcement, 565 table of percentage of reinforcement, 566 Tensile resistance in concrete, 332 Tensile strength. References, 844 cement and mortar, 98 machines for testing, 97 specifications, Natural cement, 82 specifications, Portland cement, 62 standard cement test, 76 ■ various mortars, 146 884 INDEX Tensile Strength, vs. compressive, loi vs. fiber stress, 102, 145 Tension, diagonal, 364, 41S, 516 chimney, 397 formulas, 366, 516 illustration, 367, 370 reinforcement for, example, 556 tests, 418 working stress, 573 Terracotta, substitute for sand, 172 Testing cement. See Cement testing Testing concrete, form for records, 347 methods, 343 Testing machines, compressive, 340 , circular saw, 342 tensile, 97 Testing permeability, 306, 307 Testing sand for concrete, 115 sieves for, 117, 187 washing tests for organic impurities, 118 Testing steel, specifications, 478 Tests. See material in question See also Cement testing Theory, of a concrete mixture, 178, 207 reinforced concrete, 349 Thermal conductivity of concrete, 291 Three-hinged arch, 720 Thrust in arches, effect of, 729 Thrust at crown, arches, 725 Ties, railroad, 828 Tile, concrete, 828 Time, building forms, 8 facing concrete, 262 filling barrows, 7 mixing and laying concrete, 4, 8 ramming concrete, 257 screening sand, 219 sidewalk construction, 808 Tonne, English equivalent. Third cover Tons, per sq. ft., ratio to lb. per sq. in., Third cover Tools for concrete work, 17 for sidewalk construction, 810 Transporting concrete, 252 chuting, 2 S3 pneumatic placing, 255 Transverse strength, concrete, 332 concrete, table, 334 various mortars, 146 vs. compressive, 145, 337 Transverse stress, formula, 333 Transverse tests of cement, 102 Trap, concrete, weight, 9 Trap, specific gravity, 122, 123 Triangle mesh, 572 Triangle, Feret's, 157 Trowel, edging, 806 Trowel, plasterer's, 805 Troweling surface for water-tightness, 300 Trussit system, 572 T-shaped beams. See T-beams Tube mill, 821 Tubes for depositing under water 267 Tunnels, 788 References, 848 Two-hinged arch, 721 Unit building construction, 646 Unsoundness. See Soundness Vassy cement, 44 chemical analysis, 40 Vault light construction, 807 Vegetable impurities, 168 Vicat needle, illustration of, 72 vs. Gillmore needle, 91 Vissintini system, 572 Voids, in aggregates, laws, 120 in concrete, 344 in gravel vs. broken stone, 132 in mixed aggregates, 129 in pile of spheres, 129 in sand and stone, determining, 126 in sand and stone, tables, 127 in sand, effect of moisture, 137 proportioning concrete by, 181 Volume of concrete, formulas, 208 tables, 214 Volume of loose concrete, 249 Volume of mortar, tables, 213 Volumetric composition of mortar, 148 Volumetric sjmthesis, 200 Volumetric tests, concrete, 153 mortar, 151 Walls, cellar, 643 facing, 262 forms, 656 hollow, 645 mortar, plastered upon metal lath, 64s photographs of surfaces, 263-265 reservoir, 793 retaining. See Retaining walls Walnut Lane bridge, 706, 750 Washed surface of concrete, 263 Washing sand and stone, 228 Washing test for organic impurities, 118 Water, approximate percentages for testing cement, 89 depositing concrete under, 267 effect of excess in concrete, 251 effect upon strength of mortar, 165 for chemical combination, 88 for mortar of normal consistency, 89 for paste and mortar, 88 in concrete. See Consistency in concrete. References, 848 measuring for concrete, 239 required for gaging sand, 140 DEX 88s Waterproofing, alum and lye, 2Q9 asphalt, 302 materials and methods, 299 felt, 302 treatment of surface, 299 granolithic finish, 300 grout, 300 plastering, 300 troweling surface, 300 Water-tight concrete, construction with- out waterproofing, 296 laying, 299 proportions for, 298 thickness for, 297 Water-tight joints, 258, 297 Water-tightness, 296 alum and soap, effect of, 300, 302 brief laws, 5 conduits, 778 effect of consistency, 298 experiments, 307 piJverized rock, effect of, 301 Wear, ability to withstand, 773 Wearing surface, concrete sidewalks, 804 Weighing machine, automatic, 819 Weight, bag of Natural cement, 82 bag of Portland cement, 63 barrel of Natural cement, 82 barrel of Portland cement, 63 broken stone, 226 cement, affected by fineness, 113 Weight cement, loose and packed, 206 cement, test, 113 concrete, 9 concrete, loose, 249 concrete, table of tests, 334 earth, 756 gravel, 756 hardpan, 756 lime, 172 loam, 756 mortar, 9 muck, 756 proportioning concrete by, 240 sand, 756 Welded wire fabric, 572 Weston aqueduct, 783 Wet concrete, 251 depositing through chute, 253 for protection of steel, 292 Wheelbarrow, illustration, 18, 241 loads, 7 , time filling, 7 Woolson tests, fire resistance, 291 conductivity of concrete, 291 Wunsch system of arches, 711 Yield point, effect on reinforced beams, 479 required in first-class steel, 478 Youth's Companion Building, see Build- ings ADVERTISEMENTS PAGE Sanford E. Thompson xxiii Concrete Costs .......". xxiv Cement • Atlas Portland Cement Co xxxiii Dragon Portland Cement (Lawrence Cement Co.) xxxii French's Portland Cement (Samuel H. French & Co.) xxxiv Helderberg Cement Co '. xxxii Lehigh Portland Cement Co xxxii Penn-AUen Cement Co xxxiv Saylor's Portland Cement (Coplay Cement Manufacturing Co.) xxxv Sandusky Cement Co xxxi Cement Machinery Lehigh Car, Wheel & Axle Works xxiz Concrete Machinery Automatic Concrete Mixer Co., Inc xxxv Cement Gun Co., Inc xxxvi Insley Mfg. Co xxxvii Koehring Machine Co. . . . ; xxxviii Municipal Engineering & Contracting Co xxxix Traylor Engineering & Mfg. Co xxxv Flat Slabs S-M-I Engineering Co xiv Hydrated Lime Charles Warner Co xxxiv Reinforcing Metal American Steel & Wire Co xxviii Concrete Steel Co xxvii Consohdated Expanded Metal Cos xxvii Corrugated Bar Co xxvi Gabriel Reinforcement Co xxviii Laclede Steel Co xxviii Waterproofing Sandusky Cement Co xxx Toch Brothers xxx xxi SANFOED E. THOMPSON M. Am. Soc. C. E. M. Am. Soc. M. E. CONSULTING ENGINEER Federal St. Building BOSTON, - - MASS. Consultation: Expert investigations and advice in matters pertaining to structural steel, to reinforced concrete, and to management. Design and Construction: Complete design and supervision during erection of structures of steel and reinforced concrete, independently or in co- operation with architects and contractors. Eeview of Designs: Special attention given to review of plans, involving ordinary design or complicated problems in steel and reinforced concrete with a view to economy and safety. Tests: Tests and special investigations of cement, sand, and concrete. Fully equipped laboratory. , Management: Scientific methods of manage- ment applied to construction and industrial operations. By the Authors of this Volume CONCRETE COSTS BY Fredebick W. Taylor AND Sanford E. Thompson This book has been designed to meet the needs of the Contractor, the Engineer, and the Architect in the Con- struction and Design of reinforced concrete structures. It contains the results of 17 years of painstaking, scien- tific study of the building trades. The information presented comprises — Approximate costs of miscellaneous concrete work useful as a guide in making very rough estimates. Approximate costs of reinforced concrete buildings in terms of cost per square foot of floor surface, covering a wide range of areas and types of buildings. Labor costs in general, and practical ways of organizing construction work along scientific management lines. The economical selection and proportioning of materials for concrete; the quantities required per cubic yard; and the cost based on definite prices of cement, sand and stone. Labor costs of preparing and mixing materials. The design and building of form, work in the best and cheapest manner; and the times and cost of placing steel. Tables for use in the preparation of form designs and of estimates. John Wiley & Sons, Inc., Publishers, New York S-M-l Flat Slab System Patented Developed by Edwaed Smulski See pp. 542-543 for description and illustration IfAn economical and scientific system of reinforced concrete construction. ^Thoroughly tested and found satisfactory in actual practice. II Requires least amount of steel. If Used in great number of buildings. 1[ Approved by authorities on concrete construction. Booklets, Estimates and Suggestions furnished upon request S-M-l Engineering Company Designing and Consulting Engineers Park Row BIdg. New York Federal St. BIdg. Boston ^ v^^?^ I 'an w i 1 1 HI m i ii A* !' ' ^ CORK -PRODUCTS CORRUGATED BARS Made in rounds and squares; give the most perfect mechanical bond; have an international reputation, and are standard for concrete reinforcement. CORR-BAR UNITS Have all the bars for a girder assembled in one piece. The frame is made collapsible for shipment. CORR-MESH A ribbed expanded metal for light, quick, fire-proof construction at small cost. For walls and partitions Corr-Mesh is stud and lath combined. For floors and roofs it saves the expense of centering. CORR-RIB FLOORS A System of ribbed floor construction — minimum dead load — suitable for light loads and long spans, jj CORR-PLATE FLOORS Give a beamless ceiling and are the most scientifi- cally designed of all types of flat slab construction. Unlike other types, the theoretical strength can be realized in practice. Write for free copy of "Useful Data on Corr-Products" CORRUGATED BAR COMPANY MUTUAL LIFE BLDG. BUFFALO, N.Y. NEW YORK CHICAGO ST. LOUIS BOSTON PHILADELPHIA SYRACUSE DETROIT IPIPP "''"'«> X \\\\ ^^^^^^^ STEELCRETE" meshes are the standard expanded metal reinforcing meshes. The sheets may be obtained up to 16 feet in length and the sectional area up to 1.00 square inch per foot of width. This provides the most economical form of reinforcing. The steel has a high elastic limit, great ductility, and uniformity of quality. Send for handbook of tables. THE CONSOLIDATED EXPANDED METAL COMPANIES BRADDOCK, PA. Offices and Warehouses in Principal Cities HAVEMEYER BARS "Every Pound Pulls" Can be used economically on any type of Concrete Structure. Rolled to same weight and area as plain bars — ^Round, Square, and Flat sections. No excess metal — New Billet Steel. Concrete Steel Company 42 Broadway, New York Chicago Philadelphia Boston Youngstown Syracuse Birmingham Gabriel Reinforcement Co. STEEL FOR CONCRETE REINFORCEMENT DESIGNS AND ESTIMATES FURNISHED PENOBSCOT BUILDING DETROIT, MICHIGAN LACLEDE STEEL COMPANY Manufacturers OPEN HEARTH STEEL BILLETS, MERCHANT BARS, STRIP STEEL, DEFORMED AND SQUARE TWISTED CONCRETE REINFORCING BARS WORKS: ALTON, ILL. MADISON, ILL. GENERAL OFFICES: 1209 FEDERAL RESERVE BANK BUILDING ST. LOUIS. MO. Tr-i%n4le- WE ISSUE a book on Reinforced Concrete Pave- ments and Roadways, covering the new and modern way of rolling roada on concrete and the employment of steel wire reinforcement to strengthen and bind. Illustrated, showing all uses and valuable to all interested in construction and maintenance of roads. Also for Buildings, Levees, Canal Locks, Chimneys, Sewer (Pip e, Viaducts , Retaining Walls, Wall Slabs. Also, our Engineers" Handbook'ot Concrete Reinforce- ment." Sent FREE on Request SALES OFFICES: 208 S. La Salle St. . 30 Church St. . . 94 Grove St. 120 Franklin St. a . Widener Bldg. . . . Frick Bldg. 337 Washington St. . Foot of First St. . Union Tr. Bldg. Cleveland . West. Reserve Bldg. Baltimore . . . 32 S. Charles St. Wilkes-Barre . Miners Bank Bldg. St. Louis . 3rd Nat. Bank Bldg. St. Paul-Minneapolis Pioneer Bldg., St. Paul Oklahoma City St. Nat. Bk. Bldg. Birmingham . Brown-Marx Bldg. Denver ... 1st Nat. Bk. Bldg. Salt Lake City . Walker Bk. Bldg. Export Representative : U. S. Steel Products Company, New York Pacific Coast Representative: U. S. Steel Products Company Los Angeles Portland Seattle San Francisco American Steel & Wire Company The Fuller-Lehigh Pulverizer Produces Commercially CEMENT HAVING A HIGHER PERCENTAGE OF IMPALPABLE POW- DER THAN CAN BE OBTAINED BY ANY OTHER MILL. FINELY GROUND CEMENT INSURES: MAXIMUM PERCENTAGE OF ACTIVE HYDRAULIC PROPERTIES HIGHER SAND CARRYING CAPACITY HIGHER COMPRESSIVE STRENGTH SUPERIOR COVERING QUALITIES DENSER CONCRETE UNIFORM FINENESS May we send you illustrated catalogue. LEHIGH CAR, WHEEL & AXLE WORKS MAIN OFFrCE: CATASAUQUA, PA. New York: 50 Church St. Chicago: McCormiek BIdg. Pittsburgh: Farmers Bank BIdg. MEDUSA Waterproofed White Portland Cement pONSISTS of Medusa Waterproofing ground in the ^ process of manufacture with Medusa White Portland Cement. It is a pure white, permanent, non- staining and waterproof product for stucco, stainless mortar, concrete blocks, bridges, floors, building trim, garden ornaments, interior decoration, etc. „ WUr-BWiWSlSBl^^K^- „— ' I$^«^f ^' '"'''^, It husetts c^Aiexiur laiso columns and balustrades) of Medusa Waterproofed White Portland Cement on Hollow Tile Brovm &* Von Beren, Archs. Faucker Bros. &" Co., Plastering Contrs. Medusa Waterproofed White Cement gives your work character, beauty, dignity, individuality — quality predominates Write for Illustrated Booklets of "Medusa Waterproofed White Cement" and "Medusa Waterproofing" The Sandusky Cement Co. ENGINEERS BLDG., CLEVELAND, OHIO nxmi? WEMEMBER ITS WATEHPROOFI MEANS PROTECTION PRESERVATION PERMANENCE ftEO "'e^S, PAT. Of.". VflEMEMBER /TS WATfPPROOf] MV.I.Wf. ,0ea, V.S. PAZ orr. TOXEMENT \t Integral waterproofing compound A POWDER which, owing to its collodial -^ nature lubricates the concrete mass, maliing the particles flow together into a denser body. MIXING. In large operations, U. I. W. Toxement can be mixed with the clinker at the cement mill, if desired. When mixed on the job it should be added • in quantities of two per cent by weight of the amount of Portland Cement used on ordinary construction. Where no water pressure is present, a smaller amount may sometimes be used. Preferably, it should be mixed dry. Especially adapted for waterproofing con- crete construction of dwellings, factories lofts, office buildings, floors, elevator and . boiler pits, cement mortar troweled on the " outside of rubble foundations, also stucco surfaces of buildings. Ideal for use in moulded cement work such as urns, balustrades, benches, statues and posts. , For foundations, bridges, dams, piers, etc Used by tile-setters in cement grout. Toxement booklet upon request from Depl. 70 TocH Brothers, Technical and Scienlific Paint Makers Since 1848 320 Fifth Avenue, New Y< fu. i^-J HELDEHBEEG PORTLAND CEMENT ^^^r|p^b\ Uniformity in Compo- Manufactured for 18 |R^__H_^^ sition gives uniform years by one company /j^Btt JH^Wj strength, fineness and with one organization li»^I^M' IBH^jO color, insuring the best using one process. \ ^V fifl m\J results in all concrete N^j^/ work. THE HELDERBERG CEMENT COMPANY Works: Howes Cave, N. Y. Sales Offices: Albany, N. Y. IN USB SINCE 1889 r^40rt portland <^^cement The Lawrence Cement Company 1 Broadway, New York CONCRETE FOR PERMANENCE THE NATIONAL CEMENT LEHIGH !"'.BA.-0«^'= YEARS of constant improvement in manufacturing and selling facilities have developed a service that is distinc- tively Lehigh service and a cement that is demanded throughout the nation. Mills from coast to coast. Lehigh Portland Cement Connpany Allentown, Pa. Chicago, III. Spokane, Wn. 12 Mills— Annual Capacity over 12,000,000 Barrels mmmxiMmnmimmmmir m^' Concrete— an Investment In 1914, the Hoboken Land & Improvement Com- pany started a group of six loft buildings for renting to manufacturers. To get good tenants quickly and keep them, required that the buildings be fireproof, low in cost and upkeep — therefore reasonable in rents Reinforced concrete gave them fireproof buildings at 10 per cent less cost than steel, with upkeep and insurance lower than for any other kind of construction. They rent as fast as built The high uniform quality that makes Atlas the standard in all other engineering work makes it the cement for industrial buildings also The Atlas Portland Cement Company Members of the Portland Cement Association New York Chicago Philadelphia " ^^ . ..■ Minneapolis Boston St. Louis Dayton Des Moines \ XiUklMJkritiihii'M Miiur iLiii^ iit;i MsUausJi OUALIIT . ^^^^ GUARANTEED ^^^^^^^^^portland;^ fA p vsm r ^^^^^■PrCEMENT:< w SERVICE ^ ^^^ '■^ ECONOMY PENN-ALLEN PORTLAND CEMENT Manufactured by PENN-ALLEN CEMENT COMPANY General Office, Allentown, Pa. Works, Penn-Allen, Nazareth, Pa. 4€ WARNER'S (Pure "Cedar Hollow" Hydrated Lime) Is manufactured under methods of strict mill con- trol involving continual chemical supervision by- graduate chemist. It is guaranteed to pass speci- fications of Am. Soc. for T. M. i Proper Percentages of "LIMOID" in Concrete WILL make Concrete flow more freely in chutes WILL minimize separation of the aggregates WILL make concrete more dense and impermeable FREE LITERATURE ON REQUEST Cfjarless OTarner Company Wilmington, Del. 18 E. 41st St., N. Y. Philadelphia, Pa. SAYLOR'S PORTLAND CEMENT USED BY THE U. S. GOVERNMENT SINCE 1876 FIFTY YEARS ON THE MARKET COPLAY CEMENT MANUFACTURING COMPANY Est'd. 1866 WiDENER BlDG., PhILA. 200 FiFTH AvE., Nbw Yoek 453 Washington St., Boston Heabd Bldg., Jacksonville, Fla. CoPLAY, Pa. HAINS GRAVITY BATCH CONCRETE MIXERS AND CONTROLLABLE DISCHARGE BOTTOM DUMP BUCKETS Knowing the whole story about them now may save you doUais latei. AUTOMATIC CONCRETE MIXER CO., Inc. 432 Kinsley Ave., PROVIDENCE, R. I. S01.E MAKERS AND DISTRIBUTORS The "WORLD'S RECORD" In placing Concrete was made by H. S. KERBAUGH, Inc. at Valhalla, N. Y. When they placed 89,200 Cu.Yards in 26J working days in the "Kensico Dam" TRAYLOR built and equipped their stone crushing plant for supplying the aggregate TRAYLOR CRUSHING EQUIPMENT thereby proved its RELIABILITY. Send For Our Bulletins TRAYLOR ENGINEERING & MFG. CO. Main Office and Works: ALLENTOWN, PA., U. S. A. New York Office, 30 Church Si. Western Office, Sail Lake City. Utah A Coating of "GUNITE" That dense Cement Mortar pneumatically placed or shot by the CEMENT GUN Will render that plain or reinforced concrete structure of yours water proof and seepage proof. Will repair cracked or badly disintegrated concrete walls. Adhering to the old concrete as though a part thereof. For inexpensive and quickly erected reinforced buildings "GUNITE" is unsurpassed. Write for full information CEMENT GUN COMPANY Incorporated S. 10th and Mill Streets, AUentown, Pa. New York Office, 30 Church St. THE INSLEY GRAVITY PLANT for Concrete Distribution The Quality of the Concrete is improved for the reason that the Plant automatically detects inferior mixtures; it is only when in a plastic, homogeneous, viscous mass with all aggregates in sus- pension that the mixture will satisfactorily pass through the chutes. The Cost of Placing the Concrete is reduced by at least 2)2)% per cent as compared with other existing methods of distribution. Write for detailed information iNSLEY Mfg. Co., Indianapolis, Ind. ENGINEERS AND MANUFACTURERS KOEHRING BETTER MIXED CONCRETE KoehrinK mixed concrete is better mixed — more uniform — and everj'- last aggregate is thorougly coated — because of the five action mixing principle, which gives a breaking-up, scattering action, and prevents the separation of aggregates according to size. Automatic water-measuring tank, and batch meter standardizes quality of concrete. Koehring means heavy duty construction, fast loading, discharging and distributing. KOEHRING SIZES IN CUBIC FEET CAPACITIES Mixers for construction work: lo, 12, 15, 20, 24., .30, 44.. Equipped with low charging hopper, batch hopper and side loader. Hot MLxers for bituminous pavements: 12, 20, 22. Side discharge type and end discharge type . Paving Mixers: 6, 11, 16, 22. Equipped with distributing boom and bucket or spout. Gtisoline power, steam power or electric power. Write for Catalog- [KOEHRING MACHINE COMPANY, MILWAUKEE, WIS. Austin Cube Mixer A BATTERY of four2-cu.-yd. Austin Cubes mixing concrete for the Gatun Locks, Panama Canal. These mixers made one of the most mar- velous records ever made of great output, life, speed of mix- ing and freedom from repairs. Performance At Panama is one of the most marvelous incidents in the history of concrete construction. Consider the typical per- formance records of 1912 — taken from Govern- ment Reports — All Austin mixers worked 3118 eight hour days and mixed 1,209,506 cu. yds. of concrete or one cubic yard every IJ minutes — All Austin mixers mixed 1,209,506 cu. yds. of con- crete with a total time lost for repairs of 302 hours, or one hour per 4000 cubic yards of concrete mixed. These are averages of all mixers; individual mix- ers showed much higher records. For example four mixers worked 5794 continuous hours without a delay for repairs. Two other mixers mixed 40,272 cu. yds. at a rate of 68| cu. yds. per hour per mixer. We manufacture a line of mixers for every purpose — large apd sma,ll — both tilting and non-tilting. The "Cube Principle" is the principle of kneading in mass by impact in a unit batch without lifting and the consequent lesser possibilities of aeration. It gives better, stronger concrete; stronger concrete means a higher factor of safety and longer life to the concrete structure. Engineers will he interested in our booklet — "The Science of Mixing Concrete." Municipal Engineering & Contracting Co. Eastern Office: 30 Church Street, New York Main Office: Railway Exchahge Building, Chicago CONVERSION OF FOREIGN TO AMERICAN VALUES LENGTH — m. = meter, .cm. = centimeter, mm. = millimeter 1 m. = 100 cm. = 1,000 nun. = 39.37 in. = 3.28 ft. SURFACE — m^ = square meter, cm^ = square centimeter, mm^ = square millimeter 1 m2 = 10,000 cm^ = 1,000,000 mm^ = 1.196 sq. yd. = 10.764 sq. ft. = 1,550 sq. in. VOLUME— m' = cubic meter, 1 = liter 1 m= = 1,000 1. = 1.308 cu. yds. = 35.315 cu. ft. = 61023.4 cu. in. = 264.2 liq. gal. WEIGHT— kg. = kilogram, g. = gram, t. = metric ton, ton = short ton (2000 lb.) 1 kg. = 1,000 g. = 2.205 lb. =35.274 oz. 1 t. = 1,000 kg. = 1.102 ton = 2204.62 lb. 1 kg. per m^ = 1.686 lb. per cu. yd. = 0.0624 lb. per cu. ft. 1 t. per m^ = 1,685.57 lb. per cu. yd. PRESSURE 1 kg. per cm^ = 0.01 kg. per mm^ = 14.223 lb. per sq, in. 1 kg. per m^ = 0.0001 kg. per cm^ = 0.205 lb. per sq. ft. = 0.0014 lb. per sq. in. MONEY— £ = pound, s = shilling, d = penny, t = franc, c a= centime, m = mark, pf = pfennig, 1 = lire England : 1 £ = $4.8665, 1 s = $0.2433, 1 d = $0.0203 France, Belgium, Switzerland : 1 f = 100 c =$0,193 Italy: 11 = 100 c = $0,193 Germany: Im = 100 pf = $0,238 Unit prices: 1 f. per t. = $0,175 per ton 1 f. per kg. = $0.0875 per lb. 1 m. per t. = $0,216 per ton 1 m. per kg. = $0,108 per lb. TEMPERATURE Water freezes at 32° Fahrenheit, 0° Centigrade, and 0° Reaumur. Water boils at 212° Fahrenheit, 100° Centigrade, 80° Reaumur. 180 To convert a Centigrade reading into Fahrenheit, multiply by — (= 1.8) and add 32. convert a R( and add 32. 180 To convert a Reaumur reading into Fahrenheit, multiply by -^ (= 2.25) CONVERSION OF FOREIGN TO AMERICAN VALUES LENGTH— m. = meter, cm. = centimeter, mm. = millimeter 1 m. = 100 cm. = 1,000 mm. = 39.37 in. = 3.28 ft. SURFACE — m' = square meter, cm^ = square centimeter, mm^ = square millimeter 1 m^ = 10,000 cm^ = 1,000,000 mm^ = 1.196 sq. yd. = 10.764 sq. ft. = 1,550 sq. in. VOLUME— m! = cubic meter, 1 = liter 1 m^ = 1,000 1. = 1.308 cu. yds. = 35.315 cu. ft. = 61023.4 cu. in. = 264.2 liq. gal. WEIGHT— kg. = kilogram, g. = gram, t. = metric ton, ton = short ton (2000 lb.) 1 kg. = 1,000 g. = 2.205 lb. =35.274 oz. 1 t. = 1,000 kg. = 1.102 ton = 2204.62 lb. 1 kg. per m' = 1.686 lb. per cu. yd. = 0.0624 lb. per cu. ft. 1 t. per m' = 1,685.57 lb. per cu. yd. PRESSURE 1 kg. per cm^ = 0.01 kg. per mm' = 14.223 lb. per sq. in. 1 kg. per m^ = 0.0001 kg. per cm'' = 0.205 lb. per sq. ft. = 0.0014 lb. per sq. In. MONEY— £ = pound, s = shilling, d = penny, i = franc, c a= centime, m = mark, pf = pfennig, 1 = lire England: 1£ = $4.8665, 1 s = $0.2433, 1 d = $0.0203 France, Belgitun, Switzerland: If = 100 c = $0,193 Italy: 11 = 100 c = $0,193 Germany : 1 m = 100 pf = $0,238 Unit prices: 1 f. per t. = $0,175 per ton 1 f. per kg. = $0.0875 per lb. 1 m. per t. = $0,216 per ton 1 m. per kg. = $0,108 per lb. TEMPERATURE Water freezes at 32° Fahrenheit, 0° Centigrade, and 0° Reaumur. Water boils at 212° Fahrenheit, 100° Centigrade, 80° Reaumur. 180 To convert a Centigrade reading into Fahrenheit, multiply by t^ (= 1.8) and add 32. 'o convert a R and add 32. 180 To convert a Reaumur reading into Fahrenheit, multiply by -— - (= 2.25) 80