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 Reinforced concrete; a manual of practice 
 3 1924 004 652 321 
 
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fro 
 
 <SyxA.uU7(^^. 
 
REINFORCED 
 CONCRETE 
 
 A MANUAL OF PRACTICE 
 
 BY 
 
 ERNEST McCULLOUGH 
 
 M. W. S. E., Author of "En0neering Work in Towns and Citlest" 
 
 "The Business of Contracting." "Engineering Contractors' 
 
 Pocket Book." Etc., Etc. 
 
 CHIC&OO AND NEW YORE 
 
 THE MYRON C. CLARK PUBLISHING CO. 
 190S 
 
 3 
 

 Copyright 1008 
 
 By 
 
 The Myron C. Clark Publishing Co. 
 
 9W 
 
 'H 
 
 % 
 
 47 
 
To 
 
 W. A. STEVENSON, ESQ., 
 
 of the 
 
 NORWOOD ENGINEERING CO., 
 
 This Book is respectfully 
 
 DEDICATED. 
 
PREFACE. 
 
 This book is intended to be what its title indicates, A 
 Manual of Practice. The intention in the sections on design 
 has been to keep within the usual requirements of the ordinary 
 conservative building ordinances of American cities. This 
 explains the use of the straight line formulas for stress and the 
 limitations imposed by the employment of working stresses. 
 The ambitious designer wishing to learn more of the theory 
 of the subject and the design of higher structures can go to the 
 larger standard treatises and have nothing to unlearn. 
 
 So far as construction is concerned, the principles stated 
 herein as the result of personal experience, apply to all manner 
 of work in reinforced concrete, and to this extent the book 
 should be of some value to a large number of men. Good work- 
 manship implies no knowledge of, or dependence upon,, theory 
 of design. It simply calls for the exercise of common sense, 
 unremitting vigilance and care on the part of the man in charge, 
 a willingness to learn from every intelligent workman on the 
 job, and the kind of pride that takes honestly to heart the les- 
 sons of experience. The motto, if the manager is the sort of 
 man who believes in mottoes, is Do not forget! 
 
 If the manager, however, does not know something about the 
 theory of design, then the owner is taking great chances. The man 
 in charge should be an engineer. 
 
 The writer feels the preface would be incomplete unless 
 he acknowledged here the assistance given him by his son 
 George Seymour McCullough in checking and recalculating the 
 tables, many of them original. The work was at times irksome, 
 and we trust no errors will be discovered. 
 
 Some assistance received from readers who followed the 
 articles as they appeared in The Cement Era has been acknowl- 
 edged in the proper places in preparing the articles for pub- 
 lication in book form. 
 
 Errors and omissions discovered and reported by readers 
 
 will be gratefully acknowledged, and whatever the readers may 
 
 do to assist in making future editions mor*- valuable will be 
 
 appreciated. 
 
 E. McC. 
 Chicago, 111., U. S. A., May, 190§, 
 
CONTENTS. 
 
 Chapter I. — Strength of Beams 9 
 
 Simple, Practical Formulas — Neutral Axis — Modulus of Elasticity — 
 Tables of Factors — Elastic Limit — Per Cent of Steel — Design of a 
 Beam — Strength of Concrete of Stone and Cinders — Fibre Stresses — 
 Empirical Formulas — Beam Failures — Web Stresses — Stirrups — Weights 
 and Areas of Steel — Double Reinforced Beams — T Beams — ^Allowable 
 Stresses in Building Ordinances — Adhesion of Concrete — Floor Slabs — 
 Continuous Beams. 
 
 Chapter II. — Loads on Beams 35 
 
 Reactions — Bending Moments — Deflection — Shear — Concentrated Loads 
 — Distributed Loads — Combinations of Loads — Parallel Forces on Beams 
 — Freely Supported Beams — Tied Beams — Cantilever Beams — Dead Load 
 — Live Loads — Methods for Assuming Beam and Slab Calculations — 
 Load Permitted by Building Ordinances — Highway Bridges — Sidewalks. 
 
 Chapter III. — Columns 44 
 
 Comparison of Sizes in Different Materials — Methods of Reinforcing 
 Columns — Ratio of Length to Thickness — ^Area — Tables of Column 
 Divisors — Different Formulas for Strength and Stiffness — Increase of 
 Strength with Added Steel — Comparison of Steel and of Steel and 
 Concrete — Safe Fibre Stresses — Methods of Working — Pouring Columns 
 — Foundations — Footings — Placing Vertical Steel. 
 
 Chapter IV. — Walls, Tanks and Footings 52 
 
 Plain vs. Reinforced Walls — Calculation of Pressure — Unit Pressures 
 Surcharged Walls — Detailed Calculations for Wall — Restrained Walls — 
 
 Circular Tanks — Design of Chimney — Footings. 
 
 Chapter V. — Design and Cost 64 
 
 Examination of Reasons for Reinforced Concrete Construction — ^Ad- 
 hesion — Shrinkage of Concrete — Connections — Use of Wire — Holes in 
 Slabs — Comparison with Wood — Remarks on Cost and on Conduct of 
 Work — Different Methods of Design — Forms — ^An Approximate Method 
 of Estimating Costs. 
 
 Chapter VI. — Forms 75 
 
 General Remarks from Practical Experience — Studded Frame Forms — 
 Ransome Panels — Framed Panels — Board by Board Methods — Wiring — 
 Bracing — Bolts and Ties — Spacers — Corner Forms — Beam and Slab 
 Forms — Column Forms — Hints on Form Design and Estimating. 
 
 Chapter VII. — The Conduct of Work 93 
 
 Unit of Measurement — Table of Mixtures — Hand Mixing — Machine 
 Mixing — Measuring Aggregates — Wheelbarrows — Quantity of Water — 
 Filling Forms — Finishing Surfaces — Dense Concrete — Tools for Good 
 Work— Importance of Placing Steel — Pouring Concrete — ^Tables of 
 Pressure of Concrete — Spacing of Wire and Bolts — Safe Loads on 
 
Posts and Braces — Weights of Nails, Spikes and Bolts — Strength of 
 Beams — Oiling Forms — Soap — Wetting Forma — Compressed Air — Steam 
 for Cleaning — ^Joining New Work to Old — ^Perfect Joints — ^To Prevent 
 Freezing — ^Protecting Work. 
 
 Chapter VIII.— Tools HI 
 
 Ordering Steel — Shears and Punches — Keeping Track of Steel — Forges 
 — Benders for Steel — Cold Chisels — Cold Cutters — Snips — Pliers — Bars 
 — ^Hammers — ^House Raising Jacks — Blocks and Tackles^Saws — ^Nail 
 Pullers — Concrete Boxes and Doors — Hoists — Electricity — Gasoline 
 Engines — ^Air Compressors — Steam — Pipe Coverings — Wheelbarrows — 
 Concrete Carts — Dumping Buckets — Conveyor Systems — Sub-letting 
 Work. 
 
CHAPTER I. 
 
 Strength of Beams. 
 
 Formulas for reinforced concrete design are in reality very 
 simple and can be used by any practical man. The majority of 
 writers on the subject, however, write for men who retain a knowl- 
 edge of the mathematics of college days and give the derivation of 
 the formulas. Men who have forgotten their higher mathematics 
 and men who have not gone to college look for something short 
 and easy and use empirical formulas and easy rules rather than 
 wade through pages of mathematical reasoning to finally reach 
 
 M = K bd' 
 
 which is the formula wanted and which is not recognized when 
 reached. 
 
 It means that the resisting moment of the beam is equal to 
 K (a moment factor), multiplied by the breadth of the beam 
 times the square of the depth. 
 
 Nothing can be more simple, and when tables containing values 
 of "K" are available the application is easy. 
 
 To obtain the size of a beam change the formula to read: 
 
 d=\/^ 
 V Kb 
 
 in which M=bending moment=resisting moment in inch pounds. 
 
 d^depth in inches from top of beam to center of steel rein- 
 forcement. 
 
 b=breadth in inches. 
 
 The moment, M, is found when we know the clear span and 
 load. The breadth, b, we can generally assume at 1/20 to 1/34 
 the span, and K is taken from tables. 
 
 Remember that in the following pages the depth of the beam is 
 always the distance from the top to the center of the steel rein- 
 forcement. The concrete below the steel is simply there for pro- 
 tection and is not relied upon to add strength to the beam. 
 
 Assume the breadth, b, at from 1/20 to 1/24 the span, for 
 the reason that the upper part of the beam is a column and to 
 prevent side bending, or undue stresses at its junction with the 
 
10 Reinforced Concrete. 
 
 slab on top, the length should not exceed 24 times the least 
 thickness. Therefore assume a breadth as above and solve for 
 d. The best shaped beam is one in which b lies between J4d 
 and 54d. To obtain such a beam may require two or more 
 trials, until designing experience has been gained. 
 
 There must be enough concrete surrounding the steel to 
 permit of a good grip. Practice has shown that this should be 
 not less than 1 inch; and when the bars are more than ^ of 
 an inch in diameter or thickness, this covering should be not 
 less than one and one-half such thickness or diameter. 
 
 When several bars are used the space between them should 
 be at least twice their thickness or diameter. If the beam is too 
 narrow to permit of this they should then be in two planes, stag- 
 gered. Rods or bars should be of such a size that their length 
 will exceed 50 times their thickness. On this point we will speak 
 later. 
 
 Grip is not alone to be considered. Where danger from fire is 
 to be feared then the least covering should be 3 inches. Experi- 
 ments have proven that the adhesion between steel and concrete 
 is impaired by continuous submersion, so walls designed to hold 
 water should have a covering of not less than 2 inches over the 
 steel, and should be made of very dense concrete. 
 
 At this point the writer believes it will be well to give a few 
 reasons. Few men are satisfied with a rule until they know why 
 it exists in the particular form given. In this respect all writers 
 agree, but in the present instance the formula is given first and the 
 reasons follow. The practical man wants to know the meaning of 
 the terms "Neutral ^vxis," "Elastic Limit" and "Modulus of Elas- 
 ticity" and why the theorist makes use of them. 
 
 Neutral Axis. 
 
 The position of the neutral axis in a rectangular beam de- 
 pends upon the material of which the beam is made. Wood, 
 wrought iron and steel being practically as strong in compres- 
 sion as in tension are made into beams of such shape that the 
 neutral axis is in the middle. Cast iron being about four 
 times as strong in compression as in tension is made into beams 
 shaped like a letter T upside down. The neutral axis is at a 
 point which divides the area of the beam so that the area in 
 compression is equal to one-fourth of the area in tension. 
 
 Concrete is about ten times as strong in compression as 
 in tension, but is so much weaker than cast iron that it cannot 
 
Neutral Axis. 11 
 
 be fashioned the same. So it is cast into rectangular beams and 
 steel bars are placed in the bottom to take care of the tension. 
 
 The exact location of the neutral axis is very important in 
 the design of reinforced concrete beams and slabs; but the undue 
 prominence given this point has been the cause of much bad 
 work, for when touching upon this point exact writers soar into 
 realms of mathematics where most men cahnot follow. Believing in 
 a dim way that all the x's, y's and z's are a part of the rules, men 
 with practical rather than theoretical training use rules given in 
 manufacturers' catalogues or picked up loosely from any source, 
 caring nothing for the derivation, provided they look easy. 
 
 When a beam bends, the fibres in the lower part, below the 
 neutral axis, stretch. Above the neutral axis the fibres are com- 
 pressed. The neutral axis therefore lies in a plane in which the 
 longitudinal fibres undergo no change. 
 
 I 
 i^ Gompression—. — > 
 
 1-/- - . - -.-i^- i^S.ljtrS!/ /7xiS. 
 
 t / 
 
 ^ / \ 
 
 * ;' ■ ' . ''•' ^-4- 
 
 ]< Tens /on 
 
 Fig. 1 — Diagram of Tension and Compression. 
 
 Figure 1. The stretching force exerted at the bottom 
 may be plotted as a horizontal line. Erect a perpendicular 
 from the middle of the line, the height being equal to the depth 
 of the beam. Connect the ends of all the lines and we have a 
 triangle, the apex being at the top of the beam and the base 
 being at the bottom. Through the apex draw another horizontal 
 line, the length being equal by scale to the compressive force. 
 Connect the ends to the middle of the base of the first triangle 
 and we have a second triangle superimposed on the first. A 
 perpendicular connecting the middle points in the base of each 
 triangle, the side lines of each cross at a point proportional to 
 the length of the bases. The neutral axis passes through the 
 points where the side-lines cross. 
 
 The stress is proportional to the distance from the netural 
 axis but we can see by the above description that the neutral 
 
12 
 
 Reinforced Concrete. 
 
 axis is not like a fulcrum, but is located where opposing forces 
 balance. All this preliminary explanation is necessary in order 
 to show how "K" is obtained, that we may use the moment fac- 
 tor intelligently. 
 
 To some men educated in the mechanics of materials. 
 Fig. 1 looks strange, so Fig. 3 will be more acceptable to them. 
 
 When a beam bends the assumption is made that a section 
 plane before bending remains plane after bending; that is, a 
 section of the beam such as would be made by a vertical saw 
 cut. In Fig. 3 the section before bending is represented by the 
 vertical line and the differences betwen its position and that of 
 the inclined line represent the tensile and compressive stresses 
 in the beam. 
 
 Representing the extreme fibre stress in the concrete by c, 
 and the steel fibre stress by f, we have 
 
 fp = ^ck 
 which will be explained in the next section. 
 
 It is assumed that all tension is carried by the steel and 
 that the unit deformation in any horizontal fibre varies directly 
 as its distance from the neutral axis. 
 
 To illustrate this graphically look again at the two .force 
 triangles. Erase all the lines except the top one representing 
 compression and the lower one representing tension. Join the 
 opposite ends so there will be two small triangles with the 
 apices at the neutral axis. Forces act through the center of 
 gravity of bodies and the center of gravity of a triangle is one- 
 third the distance from the base. 
 
Modulus of Elasticity. 13 
 
 k . , . 
 
 This explains -q-, which indicates the position of the point 
 
 where the compressive strength of the concrete is concentrated. 
 
 Modulus of Elasticity. 
 
 This is a force which, if such a thing were possible, would 
 stretch a material to twice its original length or compress it 
 one-half. It is generally designated by the capital letter, E. In 
 reinforced concrete work Es is the designation for this force 
 
 Es 
 in steel, and Ec for concrete. The ratio -g- is n. To deter- 
 mine the modulus of elasticity of a material, stretch or com- 
 press a piece of unit size, some definite amount by means of 
 some definite force. Multiply the original length by this force. 
 Divide the product by the area of cross-section multiplied by 
 the amount of compression or stretch. The result is E. 
 
 E for steel is taken at from 29,000,000 pounds to 31,000,000. 
 A value of 30,000,000 is commonly used. As the values are aver- 
 ages the difference between the E of high carbon and medium 
 steel is not worth considering. 
 
 E for concrete varies with the mixture, the age and the care 
 with which the concrete is mixed. It is not uniform throughout 
 a piece of concrete. 
 
 It is usual in building ordinances to specify "n," and the 
 ratios most in use are 8, 10, 12, 15 and 20. 
 
 Take beams of some unit width and some unit depth. Rein- 
 force each with some percentage of steel and apply a certain 
 load to each beam. Assuming some ratio of extensibility be- 
 tween the two materials we find that the position of the neutral 
 axis varies with the percentage of steel and the ratio assumed 
 between the moduli of elasticity. 
 
 Table I has been calculated by such a method. The values 
 of "n" are shown at the tops of the columns. The letter "p" 
 stands for percentage of steel, being the area of the steel di- 
 vided by the product of the depth and breadth of the beam, the 
 depth being distance from center of steel to top of beam. 
 
 The decimals give the values of "k" and show the distance 
 from the top of the beam to the neutral axis, expressed in per- 
 centage of total depth, "d." The formula is: 
 
 k = Y^2p.n-|-p? n=i^ — p. n 
 
14 
 
 Reinforced Concrete. 
 
 The values of "k" thus obtained, are used to calculate 
 "K" in Table III. It is usual to assume some definite value in 
 
 TABLE I. Values of k. 
 
 Area 
 
 
 Es 
 
 
 
 of 
 steel 
 
 
 Ec -" 
 
 
 
 
 
 
 
 
 =P 
 
 8 
 
 10 
 
 12 
 
 15 
 
 20 
 
 .005 
 
 .25 
 
 .27 
 
 .29 
 
 .32 
 
 .35 
 
 .006 
 
 .27 
 
 .29 
 
 .31 
 
 .34 
 
 .38 
 
 .007 
 
 .28 
 
 .31 
 
 .33 
 
 .36 
 
 .41 
 
 .008 
 
 .30 
 
 .33 
 
 .35 
 
 .38 
 
 .43 
 
 .009 
 
 .31 
 
 .34 
 
 .37 
 
 .40 
 
 .45 
 
 .01 
 
 .33 
 
 .36 
 
 .38 
 
 .42 
 
 .46 
 
 .0125 
 
 .36 
 
 .39 
 
 .42 
 
 .45, 
 
 .50 
 
 .015 
 
 .38 
 
 .42 
 
 .45 
 
 .48 > 
 
 .83 
 
 compression for concrete and some definite tensile stress for 
 steel, and by so doing we can obtain values of "k" by this 
 formula. 
 
 ^ " c 
 
 Where k := percentage of depth of neutral axis below top of 
 beam. 
 
 p=percentage of steel. 
 
 f=fibre stress in steel per square inch. 
 
 c=extreme compressive stress in concrete. 
 
 Table II has been computed by means of the above formula, 
 using values of "i" and "c" in common use. 
 
 The Chicago building ordinance will not permit a value of 
 "c" exceeding 500 pounds per square inch. The value of "t" 
 may be one-third the elastic limit. The value of "n" is fixed at 
 12. What steel can we use? 
 
 In Table I look under 12 for values of "k." In Table II 
 we next look under 500 to get the same values, and find we 
 can use from .7 to 1.0 per cent of steel stressed 10,000 pounds 
 per square inch, from 0.6 to 0.9 of steel stressed 12,500 pounds, 
 from 0.5 to 0.7 of steel stressed 15,000 pounds, or 16,000 pounds, 
 0.5 to 0.6 of steel stressed 18,000 pounds, or 0.5 of steel stressed 
 20,000 pounds. Of course for , the stronger steel much smaller 
 percentages might be used but less than 0.5 of steel makes an 
 expensive beam, which remark will be better understood after 
 learning how to use Table III. When a small percentage of steel 
 is used the size of the beam is increased. 
 
t)esiffn of Beams. 
 
 15 
 
 Looking in column 500 in Table III we obtain a moment 
 factor "K" opposite the values of "k" taken from Table I and 
 by the formula 
 
 V Kb 
 
 the size of the beam may be computed. Narrow, deep beams 
 are cheaper and stiflfer than wide and shallow beams. 
 
 Beams should be limited if possible in width as already 
 explained and the depth should not exceed 1/10 the span. When 
 impossible to keep within the limits set, the internal stresses 
 require careful investigation and provision must be made to 
 take care of them. 
 
 
 
 
 TABLE II. Values of k. 
 
 
 
 
 
 Area 
 
 {=10000 
 
 f=12500 
 
 £=15000 
 
 
 
 
 of 
 
 Values of c. 
 
 Values of c. 
 
 Values of c. 
 
 steel 
 
 
 
 
 
 
 
 
 
 
 
 
 
 =P 
 
 500 
 
 600 
 
 700 
 
 800 
 
 500 
 
 600 
 
 700 
 
 800 
 
 500 
 
 600 
 
 700 
 
 800 
 
 .005 
 
 .20 
 
 .17 
 
 .14 
 
 .13 
 
 .25 
 
 .21 
 
 .18 
 
 .16 
 
 .30 
 
 .25 
 
 .21 
 
 .19 
 
 .006 
 
 .84 
 
 20 
 
 .17 
 
 .15 
 
 .30 
 
 .25 
 
 .21 
 
 .19 
 
 .36 
 
 .30 
 
 .26 
 
 .83 
 
 .007 
 
 .28 
 
 .23 
 
 .20 
 
 .18 
 
 .35 
 
 .29 
 
 .25 
 
 .22 
 
 .42 
 
 .35 
 
 .30 
 
 .86 
 
 .008 
 
 .32 
 
 .27 
 
 .23 
 
 .20 
 
 .40 
 
 .33 
 
 .29 
 
 .25 
 
 .48 
 
 .40 
 
 .34 
 
 .30 
 
 .009 
 
 .36 
 
 .30 
 
 .26 
 
 .23 
 
 .46 
 
 .38 
 
 .33 
 
 .29 
 
 .54 
 
 .45 
 
 .39 
 
 .34 
 
 .01 
 
 .40 
 
 .33 
 
 .29 
 
 .25 
 
 .50 
 
 .42 
 
 .36 
 
 .31 
 
 .60 
 
 .50 
 
 .43 
 
 .38 
 
 .01^5 
 
 .50 
 
 .42 
 
 .36 
 
 .31 
 
 .63 
 
 .52 
 
 .45 
 
 .39 
 
 .75 
 
 .63 
 
 .54 
 
 .47 
 
 .015 
 
 .60 
 
 .50 
 
 .43 
 
 .38 
 
 .75 
 
 .63 
 
 .54 
 
 .47 
 
 .90 
 
 .75 
 
 .64 
 
 .56 
 
 
 f =16000 
 
 f=18000 
 
 f=20000 
 
 Area 
 
 
 
 
 
 
 
 of 
 
 Values of c 
 
 Values of c. 
 
 Values of c 
 
 steel 
 
 
 
 
 
 
 
 
 
 
 
 
 
 =P 
 
 500 
 
 600 
 
 700 
 
 800 
 
 500 
 
 600 
 
 700 
 
 800 
 
 500 
 
 600 
 
 700 
 
 800 
 
 .005 
 
 .32 
 
 .27 
 
 .23' 
 
 .20 
 
 .36 
 
 .30 
 
 .20 
 
 .23 
 
 .40 
 
 .33 
 
 .29 
 
 .25 
 
 .006 
 
 .38 
 
 .32 
 
 .27 
 
 .24 
 
 .43 
 
 .36 
 
 .31 
 
 .27 
 
 .48 
 
 .40 
 
 .34 
 
 .30 
 
 .007 
 
 .45 
 
 .37 
 
 .32 
 
 .28 
 
 .51 
 
 .42 
 
 .36 
 
 .32 
 
 .56 
 
 .47 
 
 .40 
 
 .35 
 
 .008 
 
 .51 
 
 .43 
 
 .37 
 
 .32 
 
 .58 
 
 .48 
 
 .41 
 
 .36 
 
 .64 
 
 .53 
 
 .46 
 
 .40 
 
 .009 
 
 .58 
 
 .48 
 
 .41 
 
 .36 
 
 .65 
 
 .54 
 
 .46 
 
 .41 
 
 .72 
 
 .60 
 
 .52 
 
 .45 
 
 .01 
 
 .64 
 
 .53 
 
 .46 
 
 .40 
 
 .72 
 
 .60 
 
 .52 
 
 .45 
 
 .80 
 
 .67 
 
 .57 
 
 .50 
 
 .0125 
 
 .80 
 
 .67 
 
 .57 
 
 .50 
 
 .90 
 
 .75 
 
 .64 
 
 .56 
 
 X 
 
 .84 
 
 .78 
 
 .63 
 
 .015 
 
 .96 
 
 .80 
 
 .69 
 
 .60 
 
 X 
 
 .90 
 
 .77 
 
 .68 
 
 X 
 
 X 
 
 .86 
 
 .75 
 
 In Table III, "k" is the distance from top of beam to the 
 k 
 neutral axis, -g- is the distance down to the center of gravity 
 
 of the compression triangle, d' is the moment arm or distance 
 
16 
 
 Reinforced Concrete. 
 
 from the steel to the point -g- The moment factors K, in the 
 
 columns headed 500, 600, 700 and 800 are obtained by the 
 formula 
 
 K=H c d' k, 
 where c=fibre stress in most remote fibre of concrete. 
 
 d'=moment arm. 
 
 k=depth of neutral axis. 
 
 
 TABLE III. Values of Moment Factor K. 
 
 
 k 
 
 J4k 
 
 d' 
 
 
 Values of c 
 
 
 
 
 
 500 
 
 600 
 
 700 
 
 800 
 
 .85 
 
 .083 
 
 .917 
 
 57.3 
 
 68.8 
 
 80.2 
 
 91.7 
 
 .87 
 
 .09 
 
 .91 
 
 61.5 
 
 73.7 
 
 86.0 
 
 98.3 
 
 .28 
 
 .093 
 
 .907 
 
 63.6 
 
 76.1 
 
 88.8 
 
 101.5 
 
 .89 
 
 .097 
 
 .903 
 
 66.5 
 
 78.5 
 
 91.6 
 
 104.8 
 
 .30 
 
 .10 
 
 .90 
 
 67.5 
 
 81.0 
 
 94.5 
 
 108.0 
 
 .31 
 
 .103 
 
 .897 
 
 69.6 
 
 83.4 
 
 87.3 
 
 110.1 
 
 .38 
 
 .107 
 
 .893 
 
 71.5 
 
 85.7 
 
 100.0 
 
 114.1 
 
 .33 
 
 .11 
 
 .89 
 
 73.4 
 
 88.1 
 
 108.8 
 
 117.5 
 
 .34 
 
 .113 
 
 .887 
 
 75.3 
 
 90.5 
 
 105.3 
 
 120.5 
 
 .36 
 
 .117 
 
 .883 
 
 77.3 
 
 98.7 
 
 108.0 
 
 183.5 
 
 .36 
 
 .12 
 
 .88 
 
 79.2 
 
 95.0 
 
 110.9 
 
 186.8 
 
 .37 
 
 .i23 
 
 .877 
 
 81.0 
 
 97.8 
 
 113.4 
 
 129.7 
 
 .38 
 
 .127 
 
 .873 
 
 83.0 
 
 99.5 
 
 116.0 
 
 132.7 
 
 .39 
 
 .13 
 
 .87 
 
 84.8 
 
 101.8 
 
 118.8 
 
 135.8 
 
 .40 
 
 .133 
 
 .867 
 
 86.7 
 
 104.0 
 
 181.4 
 
 138.8 
 
 .41 
 
 .137 
 
 .863 
 
 88.5 
 
 106.0 
 
 183.9 
 
 141.5 
 
 .48 
 
 .14 
 
 .86 
 
 90.3 
 
 108.3 
 
 126.3 
 
 144.4 
 
 .43 
 
 .143 
 
 .857 
 
 92.0 
 
 110.5 
 
 129.0 
 
 147.4 
 
 .45 
 
 .15 
 
 .85 
 
 95.6 
 
 114.8 
 
 134.0 
 
 153.0 
 
 .46 
 
 .153 
 
 .847 
 
 97.4 
 
 116.8 
 
 136.2 
 
 155.8 
 
 .48 
 
 .16 
 
 .84 
 
 100.8 
 
 120.9 
 
 141.0 
 
 161.0 
 
 .50 
 
 .167 
 
 .833 
 
 104.0 
 
 125.0 
 
 145:8 
 
 166.6 
 
 .63 
 
 .177 
 
 .823 
 
 109.0 
 
 130.9 
 
 152.8 
 
 174.5 
 
 Sometimes a wall or partition of concrete can be reinforced 
 with steel and thus be strengthened to carry certain loads and re- 
 lieve the footings. As the breadth and depth are fixed, assuming 
 a certain percentage of steel, p, a stress, c, in the concrete and a 
 depth, k, of the neutral axis, the fibre stress, f, of the steel is ob- 
 tained by the formula 
 
 f - 
 
 K c k 
 
 With the explanations given there should be no trouble in 
 selecting a moment factor, K, when given p, c, f and n or when 
 given two of them with the others assumed. 
 
Elastic Limit. 17 
 
 The theory on which the above treatment is based is deduced 
 from experiments made at the University of Illinois, Engineering 
 Experiment Station, under the direction of Prof. Arthur N. Talbot, 
 but regards only what is called the straight line distribution 
 of stresses for working loads. For ultimate loads the para- 
 bolic distribution of stresses is used. 
 
 Elastic Limit. 
 
 Nearly all materials have a certain amount of elasticity and 
 will resume their original shape and size after being stressed. 
 There is a point, however, beyond which they cannot be stressed 
 without permanent distortion and this point is called the elastic 
 limit. In steel it is from five to six-tenths the ultimate strength. 
 
 After steel has been stressed past its elastic limit it stretches 
 faster under load and the cross-section, of course, is reduced. 
 If imbedded in concrete, the adhesion is destroyed and as the 
 steel stretches, more load is thrown on the concrete. Conse- 
 quently the strength of the beam depends upon the elastic limit 
 of the steel and the ultimate strength of the concrete, for con- 
 crete can hardly be said to have an elastic limit. 
 
 Up to within a year or two the claim was made that when 
 steel having a high elastic limit was used, a considerable saving 
 could be effected. If it took one per cent of steel having an 
 elastic limit of 36,000 pounds per square inch then it would take 
 only about six-tenths per cent of steel having an elastic limit of 
 64,000 pounds per square inch. 
 
 This is true, however, only when the question of deflection 
 is not considered, but not true if it is. We have seen that the 
 relative extensibility of steel and concrete must govern and 
 that the E of high carbon and medium steel differ slightly, 
 although one may have double the strength and nearly double 
 the elastic limit of the other. 
 
 The steel stretches per unit of length as indicated by the 
 division of the fibre stress in pounds per square inch by the 
 modulus of elasticity. , 
 
 The Ransome, Thacher, Kahn and Johnson bars made of 
 medium steel have the elastic limit raised and the ultimate 
 strength increased, by the processes to which they are subjected 
 in preparing them for market. The drawing of wire has the 
 same effect, in a greater degree, on the metal of which it is 
 •nade. 
 
 Medium steel has been found more reliable in general struc- 
 
18 Reinforced Concrete. 
 
 tural work than high carbon steel, and it is to be supposed, is 
 therefore best for reinforced concrete work. As the ultimate 
 strength of a reinforced concrete beam depends upon the elastic 
 limit and not upon the ultimate strength of the steel, for eco- 
 nomical design, where not restricted by conservative building 
 ordinances, a high elastic limit is desirable. This is furnished 
 by the numerous deformed bars of medium steel and also by 
 plain and twisted bars of high carbon steel made from old rails. 
 For situations where shocks may be experienced, as in 
 water pipes, floors, floor beams, arches, etc., medium steel should 
 be used and if high stresses are permitted in the concrete, the 
 bars should be deformed. In retaining walls, tank walls, sewers, 
 etc., high carbon steel may be used. As a rule the twisted, high 
 carbon steel now advertised by many firms, will cost as much 
 per pound as plain bars of medium steel and be much cheaper 
 than deformed bars of medium steel. It can be usually shipped 
 more promptly. 
 
 Per Cent of Steel. 
 
 Reinforced concrete design has not yet reached the point 
 where formulas can be used without judgment. Seven-tenths 
 per cent of steel, as compared with one per cent, does not al- 
 ways mean just what it seems. 
 
 Take for example, a beam to resist a bending moment of 
 100,000-inch pounds. We know that n=12, so in Table I. we find 
 under 12 that k=.33 when 0.7 per cent of steel is used, and k=.38 
 when 1.0 per cent of steel is used. 
 
 It is assumed that the concrete cannot be stressed more 
 than 500 pounds per square inch, so in Table II. we find in the 
 column headed 500, that opposite 0.007 the fibre stress in the 
 steel is about 12,000 pounds, corresponding to an elastic limit of 
 36,000 pounds, if we are held to one-third the elastic limit. One 
 per cent of steel means a little less than 10,000 pounds or prac- 
 tically an elastic limit of 30,000 pounds. 
 
 We look next in Table III under column headed 500, and 
 opposite k=;.33, we find K=73.4 and the moment arm is 89% of 
 d. Opposite k=.38, we find K=83.0 and the moment arm is 
 87.3% of d. 
 
 Assume a width of 8 inches and our first beam is as follows: 
 
 \A 
 
 100 000 ^ i3 05„ 
 
 73.4 X 8 
 Allowing for concrete to cover the steel, call the total depth 15 
 
Factor of Safety. 19 
 
 inches. 13.05x8=104.4"x.007=.73 square inches of steel. The 
 nearest to this will be three J4" square bars, weighing .85X3=2.55 
 pounds, per foot of beam. Our beam 8"xl5" contains .833 cubic 
 feet of concrete. At $6.00 per cubic yard this means 22 cents 
 per cubic foot or 18.3 cents per lineal foot. At 2 cents per pound 
 the steel will cost 5 cents, making a total cost for the beam of 
 23.3 cents per lineal foot. 
 The second beam is 
 
 V: 
 
 100 OUO _ J2.2" 
 
 83X8 
 
 Allowing for the same depth of concrete to cover the steel, 
 we get a beam 8x14". It should really be 14.15", but we will keep 
 to the nearest half inch. By calculations similar to those just 
 completed, we find the cost of this beam to be 23.9 cents per 
 lineal foot. The difference is a trifle less than three per cent, 
 due to the fact that the smaller percentage of steel goes with a 
 larger beam. 
 
 Factor of Safety. 
 
 The statement that steel having a high elastic limit gives a 
 better factor of safety than steel having a low elastic limit, per- 
 haps need some explanation, since we have explained the difference 
 between modulus of elasticity and elastic limit. 
 
 Turn to Table I. with n^l2 take k=.38, corresponding to 
 one per cent of steel. From Table III under concrete stressed 
 500 pounds K=83.0. 
 
 Under 600 pounds, K=83.4 and k=.31. 
 
 Under 700 pounds, K=83.1 and k=.26. 
 
 As we have taken n=12, turn again to Table I and opposite 
 k=.31, p=0.6%. Opposite k=26, p=0.4% (about). 
 
 This value of n limits us in using Tables II and III. 
 
 Under f=:10,000, c=500, k=.38, p=0.95%. 
 
 Under f=15,000, c=600, k=.3l, p=0.62%. 
 
 Under f=16,0C0, c=600, k=.31, p=0.58%. 
 
 Under f=18,000, c=700, k=.26, p=0.5%. 
 
 Under f=18,000, c=700, k=.36, p=0.5%. 
 
 Under f=20,000, c=700, k=.26, p=0.4%. 
 
 This shows how the different percentages of steel in a beam 
 of a specified size alter the unit stresses in both concrete and 
 steel when a definite value is given to n, the ratio of extensi- 
 bility. 
 
 If a beam is designed for a certain percentage of steel hav- 
 ing a low elastic limit and the state of the steel market and the 
 
20 Reinforced Concrete. 
 
 time limit on the job compel the use of high carbon steel, the use 
 of an equal amount of high carbon steel insures a stronger 
 beam. 
 
 If high carbon steel is used and the designer decides to keep 
 to the same factor of safety, thus using less of the high carbon 
 steel, the beam will not be so stiff as with the larger amount of 
 steel. When a concrete beam bends innumerable cracks open in 
 the bottom. They may be microscopic, but if in depth they extend 
 to the steel, moisture may enter and corrode it. 
 
 Where values of c, f and n are not fixed by ordinance, the 
 designer can exercise his judgment to secure economy, care 
 being taken not to lean too far toward the danger line. 
 
 Therefore it is best to pay no attention to the ultimate 
 strength of the steel but keep within a factor of safety of three, 
 or one-third the elastic limit. 
 
 The following table gives the ultimate strength we should 
 consider for different concrete mixtures, and the safe fibre stress 
 should be one-fourth the ultimate strength, to correspond to 
 one-third the elastic limit of the steel. The values given are 
 averages for concrete 30 days old and good workmanship will 
 put the strength above the average. Concrete grows stronger 
 with age and the greatest strains come on beams and floors gen- 
 erally about one month after the concrete is poured. 
 
 ROCK CONCRETE. 
 
 1:2:4 3,450 pounds per square inch in compression. 
 
 1:2:5. 2,400 
 
 1:3:5 2,000 " 
 
 1:3:6 1,900 
 
 1:3:8 1,800 
 
 1:4:8 1,500 
 
 CINDER CONCRETE. 
 
 1:2:4 900 pounds per square inch in compression. 
 
 1 :2 :5 700 „ „ „ „ „ 
 
 1 :3 :6 500 „ „ „ „ „ „ 
 
 The modulus of elasticity, with usual loads, at end of 30 
 days is about as follows: 
 
 ROCK CONCRETE. 
 
 1:2:4 2,600,000 pounds. 
 
 1:2:5 2,450,000 
 
 1:3:5 2,400,000 
 
 1:3:6 2,300,000 
 
 1:3:8 2,100,000 
 
 1:4:8 2,000,000 
 
Simple Formulas. 21 
 
 Cinder concrete has a modulus of elasticity of about 1,040,- 
 000 pounds. 
 
 For the above values of rock concrete n will be from 13 
 to 15 and for cinder concrete it will be from 23 to 30. Some 
 men use 35 to 40 for cinder concrete. 
 
 Rock concrete weighs from 140 to 145 pounds per cubic 
 foot, and for estimating purposes with the steel in it, the weight 
 is generally assumed at from 145 to 150 pounds. Cinder con- 
 crete is generally assumed as weighing from 110 to 115 pounds 
 per cubic foot reinforced. 
 
 The designer should endeavor to get just the right amount 
 of steel in the beam. Too much steel means increased expense 
 and also danger that the beam will be destroyed by the con- 
 crete crushing out at the top. This does not give warning 
 enough. If the amount of steel is small the beam will deflect 
 considerably before the concrete is over-stressed. 
 
 The foregoing formulas place the neutral axis in the posi- 
 tion it occupies just before the beam fails, when the steel is 
 stressed to the yield point, the elastic limit. As the formulas 
 given are termed "Straight line" formulas, the actual position 
 of the neutral axis is a trifle below this point, so there is an 
 additional factor of safety up to a load which implies that the 
 fibre stresses calculated have been reached. For ultimate loads 
 we must use formulas based on the parabolic distribution of 
 stress, and such formulas are not discussed in this book, as we 
 deal only with working loads. 
 
 The only drawback to the straight line formula in the opin- 
 ion of some designers, is that the amount of steel is too small 
 for the ultimate load that can be borne by the concrete. For 
 the most economic designing a knowledge of the parabolic the- 
 ory is desirable, but for all practical work, and for designing 
 under the limitations imposed by building ordinances, the 
 straight line theory is perfectly satisfactory. 
 
 To obtain the fibre stresses in a beam already designed the 
 preceding pages may be consulted. For the benefit, however, 
 of men not used to transposing equations the following formulas 
 are given. Representing the moment arm by d ' = d — x (ex- 
 pressed as a decimal, representing a percentage of d, precisely 
 as k is represented as a percentage of d), then 
 
23 Reinforced Concrete. 
 
 T ^ total tension in the steel in pounds. 
 C = total compression in the concrete in pounds. 
 M = bending moment to be resisted, in inch pounds, 
 then 
 
 The material deficient in amount determines the actual 
 strength of the beam, so to find M as fixed by the steel, 
 
 M =: fpd'dbd' 
 
 in which d'd represents the moment arm in inches, and p ="j~3" 
 
 the percentage of steel, bd being the area of the concrete above 
 the center of the steel. 
 
 The strength of the beam as fixed by the concrete is 
 
 M = i^c k d'd bd". 
 
 T 
 The fibre stress in the steel is f = "T~, where. A is the area 
 
 of the steel in square inches. Another formula is given under 
 Table III. 
 
 The fibre stress in the concrete is 
 
 2fp 
 
 Other Formulas. 
 
 From the results of experiments in which the above for- 
 mulas have been demonstrated to be correct, another set of 
 formulas have been derived. 
 
 There are three stages in the testing to destruction of a re- 
 inforced concrete beam. Until the steel has been stressed to 
 about one-third the 'yield point the neutral axis is stationary. 
 It then rises until the steel is stressed to about one-half the 
 yield point, after which it remains nearly stationary in position 
 until the beam fails, when it drops. 
 
 Some men believe it is perfectly safe to design for safe 
 loads and assume the neutral axis to be in the middle of the 
 beam and ignore the relative extensibilities of the two materials. 
 
 Let c=stress in extreme horizontal layer of concrete per 
 square inch. 
 
 f=fibre stress in steel. 
 
 b=:breadth of beam. 
 
 d=depth from top of beam to center of steel. 
 
 x=concrete modulus. 
 
Simple Formulas. 33 
 
 d'^moment arm. 
 p=percentage of steel 
 
 c-j- = X bd 
 
 M=xbdXcl'd==Kbd'. 
 
 Take the concrete at 500 pounds, then 
 
 bd 
 500 — = 125 bd. 
 
 125 
 Take f=10,000 lbs., then -JJoOU =0-0125=p. 
 
 Assuming the neutral axis at the middle of the beam and 
 the center of compressive forces in the concrete at one-sixth of 
 the depth of the beam we have f d=0.833d=d', the moment arm, 
 and 125 b dX0.833d=104b d'=M. 
 
 Recognizing that the modulus of elasticity and the elastic 
 limit are dififerent factors having different influences on the 
 strength of the beam, and that the position of the neutral axis 
 in the middle of the beam is true only when percentage of steel 
 is from 1.0 to 1.25 per cent, the following modification has been 
 proposed to the above formula: 
 
 This value of K=104, is maintained as a basis, but p varies 
 
 with the fibre stress in the steel=: -^ 
 
 The value of K obtained as above, is maintained for p=1.0% 
 
 — — ^~^ ) =d', 
 which varies as may be seen, with p. Then 
 
 xbdXd"dXp=Kbd'. 
 Example: Use p = 0.8% then 
 
 / 0.833 — 0.50 \ . ,„, 
 
 0.50 +[^ ^ j=.916d=d"c 
 
 125 bdX0.916dXo.8=91.6bd'. 
 
 The depth of the neutral axis from the top of the beam 
 will then be k = 0.27 + 0.18 p. 
 
 By the above method tables of K may be calculated and 
 used. The only excuse for such a formula is that it is more 
 readily remembered than the more exact ones, but this excuse 
 
24 Reinforced Concrete. 
 
 vanishes when it requires modification to permit of more ra- 
 tional designing with varying percentages of steel. 
 
 Such a formula is useful at times when some piece of work 
 is to be done and table books and abstruse formulas are not at 
 hand. The rationale is simple, hence easily remembered and 
 applied. 
 
 For all practical purposes it is first-class practice to con- 
 sider the neutral axis as occupying a position in the middle of 
 the beam and use 1.35% of steel; making the depth of the beam 
 from 1-10 to 1-12 the span and having the breadth between J4 
 and ^ the depth. It may not be the most economic beam but 
 it will certainly be safe if shown to be able to resist the bending 
 moment caused by the loading. 
 
 Beam Failures. 
 
 When a beam breaks by showing large cracks near the mid- 
 dle at the bottom and an appearance of crushing at the top, 
 the cause generally is failure by tension in the steel. In such 
 a case not enough steel is used for the quality of concrete ob- 
 tained. 
 
 When the failure is by breaking of the concrete on top, 
 then too much steel has been used. The beam fails by compres- 
 sion in the concrete. 
 
 Beams failing by showing diagonal cracks at the bottom 
 near the supports fail by diagonal tension in the concrete. 
 
 When the width of a beam is 1/20 to 1/24 the span and is 
 at least one-half the depth, the beam will likely fail by tension 
 in the steel or compression in the concrete. When the beam 
 is short and deep, it may fail by diagonal tension or the bond 
 may be destroyed between the steel and concrete. 
 
 Let V=:vertical shear on the beam. 
 
 o^circumference or periphery of bar in inches. 
 m=:number of bars. 
 u=bond per square inch. 
 d'=moment arm. 
 
 *^« "=S5d^ 
 
 As the adhesion is expressed in pounds per 8q. in. mo= 
 total surface of bars per sq. in. of length. 
 
 The periphery of a half inch bar is 4 X J4 = 2 inches and 
 the periphery of a one-inch bar is 4 inches. Four half-inch bars 
 have the tensile strength of one bar one inch square but have 
 
Beam Failitres. 35 
 
 4X8=8 inches of bond surface, or double that of the one- 
 inch bar. 
 
 Building ordinances generally specify the bond or adhesion 
 so the amount should be tested by the above formula. If the 
 amount of steel has been found sufficient for bending moment 
 but not sufficient for bond, it is plain that smaller bars may be 
 used in order to get the increase of surface necessary. 
 
 The stresses tending to destroy the bond between the con- 
 crete and the steel are transmitted to the surrounding concrete. 
 This gives a horizontal unit shearing stress we will call v. In 
 value it is equal to 
 
 v = 
 
 bd' 
 
 where b = breadth of beam. This v is also equal to the vertical 
 unit shearing stress at a point just above the level of the rein- 
 forcing bars. 
 
 V 
 The formula vb= -jr gives the rate of vertical stress per 
 
 unit of length of Beam that will go into stirrups if they are 
 found necessary. 
 
 To illustrate: Having found the bending moment, calculate 
 the size of the beam and amount of steel necessary to resist it. 
 Next determine the number of rods required, remembering the 
 space between the rods should be at least equal to the thick- 
 ness. Next test for bond. When this is settled test for the 
 horizontal and vertical unit shearing stress and if it exceeds 
 the tensile strength of the concrete, stirrups must be provided. 
 Stirrups as a rule are necessary only in deep short beams. 
 
 By the above formula stirrups will be placed the entire 
 length of the beam. Some designers use stirrups in every beam 
 while others simply use them when the analysis indicates the 
 necessity for them. Even when an analysis may show them to 
 be really not necessary it adds considerably to the strength of 
 the beam to provide them and the cost is not great. A sheet 
 of expanded metal or wire fabric in the web of the beam is 
 excellent and performs the work of stirrups. 
 
 Stirrups should be either fastened to the bottom steel or 
 should be bent in U shape with the bottom rods going through 
 this loop. They may be inclined at an angle of 45 degrees to- 
 ward the ends of the beam, or they may be vertical. Inclined stir- 
 rups are most efficient, but they are troublesome to place. 
 
26 Reinforced Concrete. 
 
 An empirical rule given by E. L. Ransome for stirrups is 
 to place four at each end of the beam, the first to be J4 the 
 depth from the end, the second to be J^ the depth from the 
 first, the third to be J4 the depth from the second, and the 
 fourth to be a distance equal to the depth from the third. These 
 stirrups are generally % to J^-inch rods. In small beams they 
 may be of extremely heavy wire, one stirrup hooking around 
 each bottom reinforcing rod. 
 
 All stirrups should go to within one inch of the top of the 
 slab on the beam and then run about six inches into the slab. 
 In any case they should go to within about an inch of the top 
 of the concrete and be bent to run parallel with it for about six 
 inches. They should be used even when the reinforcement is 
 bent upward toward the ends of the beam. 
 
 Beams having some of the reinforcing bars bent up near 
 the ends are stronger than beams having all the bars straight. 
 This is because of better bond, or is due to a change in di- 
 rection of the stresses. Each designer seems to be at present 
 a law unto himself as to manner of bending the bars. The 
 writer turns up one-fourth of the rods at the quarter span point, 
 one-third of the remainder at the sixth point and one-fourth of 
 the remainder at the eighth point. The remainder go straight 
 to the support and when a little past it are turned straight up 
 at least six inches. 
 
 The bent rods go at an angle of 45 degrees to within one 
 inch of the top. If at the end of a simple beam they bend at 
 the top and go clear over to the support and are anchored by 
 bending. If the beam is continuous, or fastened at the end (as 
 common with reinforced concrete beams), the bent rods stop 
 at the top of the beam. In the top of the beam across the 
 supports are placed one-half as many bars as are used in the 
 bottom. These top bars go across to the quarter span points 
 and are there turned down at an angle of 45 degrees and termi- 
 nate one inch from the bottom. 
 
 It is common now to have brackets connecting beams to 
 walls and heavy pillow blocks under beams at posts. Diagonal 
 tie bars go through these projections which thus act as braces 
 and stiffen the structure in case of unequal settlement of founda- 
 tion or in case of earthquake. 
 
 When bars lap past each other they should lap at least 
 twenty-five times the thickness. No bar should be of a size 
 
Amount of Reinforcement. 
 
 37 
 
 that its length in a beam will be less than fifty times the thick- 
 ness or diameter. 
 
 When the reinforcing steel is stressed more than 10,000 lbs. per 
 sq. in. deformed bars should be used. Twisted bars are good enough 
 for all practical purposes, but all the bars in the market are good, 
 although extravagant claims are made for some. 
 
 The important fact must be remembered that it makes no dif- 
 ference in what form the reinforcement comes. The amount to use 
 for strength can be determined by the formulas already given and 
 no matter what the claims of the advertiser no smaller amounts 
 can be used without lowering the value of the factor of safety. 
 This remark applies to the strength of the steel to resist breaking. 
 
 Deformed bars and rods increase the hold of the concrete and 
 thus enable the designer to utilize more of the strength of the steel 
 than if adhesion alone is depended on. As a general rule at present 
 prices the most economical beam contains steel stressed about 16,000 
 lbs. per sq. in., with the concrete stressed about 570 lbs. per sq. in. 
 The writer would not think it safe to stress plain steel to exceed 
 10,000 lbs. per sq. in., so in using a higher stress he employs de- 
 formed bars or rods. 
 
 TABLE IV. 
 
 Weights per lineal foot and areas of square bars and round 
 
 rods. 
 
 One cubic foot of steel weighing 490 lbs. 
 One cubic inch of steel weighing 0.383 lb. 
 
 Thickness 
 
 Weight 
 
 Area, 
 
 Weight, 
 
 Area, 
 
 or 
 
 lb. 
 
 in. 
 
 lb. 
 
 in. 
 
 Diameter. 
 
 (Square.) 
 
 (Square.) 
 
 (Round.) 
 
 (Round.) 
 
 }4 inch 
 
 .212 
 
 .0625 
 
 .167 
 
 .0491 
 
 Vs " 
 
 .478 
 
 .1406 
 
 .376 
 
 .1104 
 
 Vi. " 
 
 .85 
 
 .25 
 
 .668 
 
 .1963 
 
 Vi •' 
 
 1.328 
 
 .3906 
 
 1.043 
 
 .3068 
 
 M " 
 
 1.913 
 
 5625 
 
 1.502 
 
 .4418 
 
 y% " 
 
 2.603 
 
 .7656 
 
 2.044 
 
 .6013 
 
 1 
 
 3.4 
 
 1.00 
 
 2.67 
 
 .7854 
 
 Table IV will be of assistance in using ordinary plain and twist- 
 ed steel. The manufacturers of special reinforcing material gladly 
 give to all inquirers pamphlets and circulars containing tables of 
 sizes and weights of their materials. 
 
 Fabrics, whether woven, welded or expanded from sheets, so 
 
28 Reinforced Concrete. 
 
 bind the concrete that the stress is distributed over a wider area 
 than when bars are used, but not enough to safely reduce the amount 
 of steel. The advantage claimed for fabrics is that they should cost 
 less to put in place than it costs to put in rods or bars properly. 
 When beams and slabs are designed the steel is assumed to occupy 
 a definite position. To insure this all pieces should be wired at in- 
 tersections. This costs a great deal and the makers of fabrics 
 claim that by the use of their material the cost of placing steel is 
 lessened and the certainty of getting it in the correct position as- 
 sured. 
 
 Double Reinforced Beams. 
 
 There is seldom any occasion to design a beam reinforced 
 both in the top and bottom, but occasionally it is unavoidable. 
 Steel used, however, in the compression side of a beam is ex- 
 pensive, for it cannot be stressed as high as steel in the tension 
 side. 
 
 When the bottom of the beam is stressed we know that 
 innumerable small cracks open that can seldom be detected 
 even with a microscope, for they are distributed because of the 
 adhesion to the steel. For this reason we neglect the tensile 
 strength of the concrete, as the cracks open before the steel 
 is stressed more than three or four thousand pounds per square 
 inch. 
 
 In the upper part of the beam we cannot exceed a certain 
 fixed fibre stress in the concrete, so can only stress the steel 
 in proportion to the ratio of the moduli of elasticity of the two 
 materials. Consequently while the fibre stress in the tension 
 steel may be as high as 16,000 pounds per square inch, the com- 
 pression steel cannot be stressed to exceed 6,000 to 9,000 pounds 
 per square inch, depending upon its depth below the top of the 
 beam. 
 
 M. Bonna placed steel in both sides ol' all beams he designed 
 and his formulas are as follows: 
 
 Let A=area in square inches of tension steel. 
 
 A'=area in square inches of compression steel. 
 
 M^bending moment in inch pounds. 
 
 d^jnoment arm between centers of steel reinforcement 
 
 in bottom and top of beam. 
 
 M 
 Then A=-jj-, and A' = % A. 
 
 The compressive strength of the concrete is depended upon 
 
Dovble Reinforced Beams. 29 
 
 for a certain amount of resistance and it is not necessary to 
 make any calculations for the position of the neutral axis. To 
 the moment arm, d, it is simply necessary to add enough to 
 thoroughly cover and protect the steel in each side of the 
 beam. This total depth, therefore, will depend upon the head 
 room wanted and the consequent depth of beam that can be 
 permitted. 
 
 The bending moment being obtained from the span and 
 loading and f being assumed, according to the grade of steel 
 used, 
 
 -j- = Ad. 
 
 Usually, however, the problem comes to us in the form of 
 a beam that has already been designed and which cannot be 
 enlarged because the plans have proceeded to such a point that 
 alterations cannot be made, yet some new ideas have arisen 
 which call for a much heavier loading on the beam. The only 
 way to take care of this load is to proportion the steel in the bot- 
 tom to carry it, thus increasing the iibre stress on the concrete. 
 
 If the building ordinance will not allow the higher stress 
 in the concrete, then enough steel must be placed in the com- 
 pression side of the beam to balance the additional amount of 
 steel in the tension side, without changing the position of the 
 neutral axis as originally designed, and thereby keeping the 
 concrete fibre stress down to where it was originally calculated. 
 
 In order that the steel and the concrete will deform equally, 
 f = nc, 
 and this cannot be exceeded. 
 
 If this ratio is used, however, it would imply that the com- 
 pression steel will be placed in the top of the beam, for c is the 
 extreme fibre stress, decreasing to at the neutral axis. As 
 the compression steel will be placed below the top of the beam, 
 where the stress will be less than c, and in amount = c' we then 
 have, calling the compression steel stress = f, 
 f := nc'. 
 
 The moment arm of the beam as originally designed ex- 
 tended from the plane of the tension steel to the centroid of 
 compression of the concrete. When the compression steel is 
 added there is another moment arm added which is equal in 
 length to the distance between the planes of the tension and 
 
30 Reinforced Concrete. 
 
 compression steel. The length of this moment arm is chosen 
 arbitrarily. 
 
 The area of the original tension steel is A and the addi- 
 tional steel added to that side of the beam we will call a, while 
 the area of the compression steel will be A'. Then to find the 
 area, 
 
 A'=^ 
 nc 
 
 That is, we multiply the fibre stress in the tension steel by 
 the additional area of the tension steel and divide by the fibre 
 stress of the concrete in the plane of the compression steel, 
 multiplied by the ratio between the moduli of elasticity, in 
 order to obtain the area of the compression steel. 
 
 The area of the compression steel being governed by its 
 depth below the top of the beam, if a floor slab rests on the 
 beam and is to be poured at the same time, a calculation can 
 be made to increase the depth of the beam by considering the 
 thickness of the floor slab as a part of it. Placing the com- 
 pression steel then in the floor slab will result in some saving 
 of steel, by materially lengthening the moment arm between the 
 steel reinforcements. 
 
 To prevent any tendency to buckle on the part of the com- 
 pression steel, small stirrups should be hung over it at inter- 
 vals not exceeding twelve times the thickness of the bars or 
 rods used, and these anchoring stirrups should go clear to the 
 bottom steel. 
 
 The internal stresses in the beam should be carefully com- 
 puted when double reinforcement is used and it may be found 
 advisable to make the reinforcement in the top and bottom of 
 angle iron connected by a sheet of expanded metal, or of rods 
 fastened together by expanded metal or wire fabric, thus mak- 
 ing the beam practically a plate girder. 
 
 T Beams. 
 
 Some designers have a great fondness for designing what 
 are known as T beams, in which the floor slab above the beam 
 is intended to carry all compression and the beam consequently 
 is simply a concrete stem wide enough to carry the steel. 
 
 Many theories have been proposed for such beams, but the 
 latest and most satisfactory are those of Prof. Talbot, in which 
 the amount of steel is a percentage of a beam having a width 
 equal to the width of the slab in the T section, and a depth 
 
Formulas for T Beams. 31 
 
 found by the usual methods. That is, the formulas already 
 given will do for T beams as well as for ordinary beams, but 
 in determining the amount of steel it must be a percentage of 
 such a large area that the writer has found no resulting econ- 
 omy in using such beams, especially when taken in connection 
 with the objections mentioned in a later chapter concerning 
 the construction work. 
 
 For any reader who may wish to investigate such beams 
 it may be stated that the width of the slab varies from three 
 to five times the thickness of the stem. Some men consider 
 the width of the slab as being the clear span, thus calling on 
 the floor for compressive strength half way on each side to 
 the next support. T beams with wide flanges lack in stiffness. 
 
 The position of the neutral axis when determined should 
 be such that the thickness of the flange will not be less than 
 Yi k, so that the neutral axis may well be in the flange if de- 
 sired. When the amount of steel is determined it should be 
 in as large bars as possible in order to have the rib narrow, 
 but the bond should be carefully investigated and the steel have 
 enough peripheral area to furnish bond. Web stresses also 
 are high and should be carefully determined, and stirrups or 
 other web reinforcement provided. Careful attention should 
 be paid that cross bearing steel is placed in the slab across the 
 stem, in girders, or cross bearing beams. In the calculations 
 the rib is not considered and its thickness depends upon the 
 size of the steel. At its junction with the floor slab a fillet 
 should be placed to prevent cracks because of the sharp angle. 
 
 Common values assigned to concrete and steel by ordinances 
 are as follows: 
 
 Steel. — Fibre stress not to exceed one-third the elastic limit in 
 tension. 
 
 Concrete. — Tension no value. Compression, 500 lbs. per sq. in. 
 for beams, 350 lbs. per sq. in. for columns. 
 
 Shear.— 50 lbs. per sq. in. (as internal stress). 
 
 Adhesion to steel. — 75 lbs. per sq. in. of surface of steel. 
 
 General rules for lengths of reinforcing bars and rods have 
 been given. The following table gives the matter in a little more 
 complete form. When a certain fibre stress is assumed for the 
 steel and a certain value given per square inch for adhesion, we 
 obtain the length of steel necessary for bond by ascertaining the 
 area of the cross section of the steel, multiplying this by the fibre 
 
32 
 
 Reinforced Concrete. 
 
 stress and dividing the result by the adhesion per square inch, 
 multiplied by the circumference or perimeter of the rod or bar. 
 
 TABLE V. 
 
 Minimum lengths (minimum clear span of beam) require'd to secure rods and 
 bars against slipping under stated fibre stresses in the steel. Adhesion 75 lbs. 
 per sq. inch of surface. 
 
 Diameter 
 
 Adhesion per 
 lineal inch 
 
 
 Values of f . 
 
 
 or 
 
 10,000 
 
 16,000 1 18,000 
 
 1 20,000 
 
 Thickness 
 
 
 
 
 
 Bars 
 
 Rods 
 
 Lengths 
 
 Ji in. 
 
 75.0 
 
 59.3 
 
 1 ft. 5 in. 
 
 2 ft. 3 in. 
 
 2 ft. 7 in. 
 
 2 ft. 10 in. 
 
 % in. 
 
 112.5 
 
 88.5 
 
 2 ft. 3 in. 
 
 3 ft. 4 in. 
 
 3 ft. 9 in. 
 
 4 ft. 2 in. 
 
 Kin. 
 
 150.0 
 
 117.5 
 
 2 ft. 7 in. 
 
 4 ft. 7 in. 
 
 5 ft. 2 in. 
 
 5 ft. 8 in. 
 
 % in. 
 
 187.5 
 
 147.0 
 
 3 ft. 7 in. 
 
 5 ft. 8 in. 
 
 6 ft. 4 in. 
 
 7 ft. 1 in. 
 
 %in. 
 
 225.0 
 
 177.0 
 
 4 ft. 2 in. 
 
 6 ft. 8 in. 
 
 7 ft. 6 in. 
 
 8 ft. 4 in. 
 
 Vs in. 
 
 262.5 
 
 208.0 
 
 4 ft. 11 in. 
 
 7 ft. 10 in. 
 
 8 ft. 10 in. 
 
 9 ft. 10 in. 
 
 1 in. 
 
 300.0 
 
 236.0' 
 
 5 ft. 7 in. 
 
 8 ft. 11 in. 
 
 10 ft. 1 in. 
 
 lift. 2 in. 
 
 This gives half the length of the steel in the beam (for there 
 are two, opposite and equal, pulls) and multiplied by two gives 
 the minimum clear span to be used in connection with the rods 
 or bars. The table shows this, and when a beam has been figured, 
 the size of the steel can be taken readily from this table in order 
 to be safe as respects bond. One-half the lengths given in the 
 table will be sufficient to run the steel into walls or other sup- 
 ports or to lap pieces past each other. Of course, as great a length 
 can be used as the designer wishes, but the lengths given are 
 minimum. When lapping steel reinforcement, the pieces should 
 not be spliced together with wire so they touch throughout the 
 whole length, but should preferably be so spliced that a space be 
 left between equal to their thickness or diameter. This is best 
 accomplished by bending each piece so the pull will be in a direct 
 line and putting small spacers at intervals of a few inches. The 
 connection of these lapping pieces, however, should be strong 
 and certain in order that the concrete be not unduly stressed to 
 give the required adhesion. The spacers should be first-class metal 
 clamps, similar to those used for cables. The ideal lap is one 
 where each end is so bent that when fastened in place the shape 
 will be a loop similar to a turnbuckle, with strong clamps at the 
 end connections and several spacers across the loop. Another 
 good connection is a screwed connection. It is really the best if 
 properly made. It should always be used in columns. 
 
 The writer is a firm believer in reinforcing all beams on top 
 across supports. Unless means are especially provided to localize 
 the stresses, the top of all beams will exhibit more or less canti- 
 
Floor Slabs. 33 
 
 lever action, for the connection causes it. In fact, it would do no 
 
 harm to design all beams in two ways : First, a? a plain beam, 
 not allowing for contraflexure ; second, as two cantilever beams, 
 joined in the middle of the span. Place reinforcement in the beam 
 accordingly, turning it down or up for web reinforcement when 
 it passes the point where it is required for bending moment in 
 the top or bottom. Such a beam will be safe, no matter how 
 loaded, and if a fire consumes the contents of the room below and 
 should happen to destroy the concrete protecting the under steel, 
 the steel in the top of the beam will carry the load. The writer 
 believes too many chances have been taken with reinforced con- 
 crete designing in the past, and too many chances are taken today. 
 
 Floor Slabs. 
 
 Owing to the monoUthic character of reinforced concrete 
 
 work there is a continuous action at supports, but it is bad practice 
 
 to lessen the amount of bending moment developed at the center 
 
 of beams or girders because of it. Negative stresses set up at 
 
 supports is all we can provide for and this has been touched upon. 
 
 Therefore, we should take care of the bending moment of a simply 
 
 wl' 
 supported beam at the center by the formula, M= -r- and the 
 
 S 
 
 negative bending moments at the supports by pladng enough steel 
 
 in the top to take care of the bending moment as given by the 
 
 wl'' 
 formula, M = Tr-. 
 
 With floor slabs, however, it is usual to compute the bending 
 wP 
 moment by the formula, M = ~, although some designers use 13 
 
 instead of 10, in which formula w is the load per square foot and 1 
 
 the span in inches, the moment, M, being in inch pounds. The span 
 
 is always the shortest span when the floor panel is not square. If the 
 
 wl" 
 panel is square the formula is M = — and the reinforcement runs 
 
 both ways. That is, when this formula is used it is figured that half 
 the load goes to two sides and the other half to the other two sides. 
 Then two layers of steel will be used for reinforcement, at right 
 angles to each other. To the thickness obtained by the formula, 
 
 '^~ vKb ™"^'' ^^ ^dded sufficient concrete to protect the steel 
 underneath and also the extra thickness caused by the second layer 
 of steel. This additional concrete to allow for the two layers of 
 
34 
 
 Reinforced Concrete. 
 
 steel is often overlooked by designers, with the result that the 
 moment arm is shortened and the slab deflects unduly. 
 
 Mr. Robert B. Hansell, C. E., Baltimore, Md., has asked the 
 writer to insert the following table in order to make it clear that 
 in the case of a uniformly loaded beam supported at several equi- 
 distant points the portion of the load bearing on each support is as 
 follows : 
 
 TABLE VI. 
 
 Number 
 
 of 
 supports. 
 
 1st. 
 
 Num 
 2d. 
 
 jer of each 
 3d. 
 
 I support. 
 4th. 
 
 5th. 
 
 6th. 
 
 2 
 
 3 
 4 
 5 
 9 
 
 H 
 
 4/10 
 11/28 
 15/38 
 
 'A. 
 
 10/8 
 11/10 
 32/28 
 43/38 
 
 11/10 
 26/28 
 37/38 
 
 4/10 
 32/28 
 37/38 
 
 11/28 
 43/38 
 
 15/38 
 
 It is seldom that more than three supports will occur in prac- 
 tice, but the above table will be useful in helping distribute the load 
 to all the beams under floor and roof slabs. The load per square 
 foot on the slab will be the assumed floor loading, and the load per 
 lineal foot on the beams and girders under the slab will be deter- 
 mined by the reactions shown in the above table. 
 
 To space the rods equally both ways in a square slab is not 
 correct, for if we consider a 13" strip as the unit and the floor 
 consists of a number of 13" strips side by side we know that the 
 diagram for bending moment will be a parabola. The steel should 
 therefore be closer together in the middle running both ways. To 
 determine this draw the beam and the parabola with the vertex as 
 M. Then dividing the beam into a number of 13" sections determine 
 the bending moment on each. Reinforce each for its bending 
 moment. While this is a little labor and there may be some diffi- 
 culty in securing the right spacing of the steel it is more correct 
 than the usual method. When a floor slab freely supported at all 
 
 wl' 
 four sides, designed for a bending moment expressed by -r- 
 
 o 
 
 develops so much strength that the use of 10 as a divisor seems to 
 fit better than 8, part of the reason is in the excess of steel in the 
 outer edges of the slab. 
 
 In this connection see end of Chapter II. 
 
Reinforced Concrete. 34a 
 
 CHAPTER I.— (Continued.) 
 Parabolic Theory of Stress. 
 
 It has been mentioned in tlie preceding pages that for economy 
 in design the formulas there given do not give the best results. In 
 fact for the ideal beam the cost of the steel should exactly balance 
 the cost of the concrete above the center of the steel. Certain obvi- 
 ous considerations prevent the attainment of this ideal but by using 
 what is known as the Parabolic Theory of Stress, it can be more 
 closely approximated than by the straight line theory given under 
 Fig. 2 on page 12. 
 
 When we study the stress strain curve of a reinforced con- 
 crete beam it is easily seen that the material does not act so that 
 the unit deformation in any horizontal fiber varies directly as its 
 distance from the neutral axis. In fact the tensile strength of the 
 concrete is gone by the time the steel is stressed up to about one- 
 fourth the usual working stress, and this is shown by innumerable 
 small cracks in the bottom under the steel. By the time the steel is 
 stressed to the elastic limit it is believed the cracks extend, almost, 
 if not quite, to the neutral axis. 
 
 Neglecting therefore the tensile strength of the concrete and 
 concentrating the entire tensile stress in the line of steel near the 
 bottom the straight line theory for the steel is correct, so that no 
 matter what formula may be used to determine the resisting moment 
 as determined by the concrete, the resisting moment as determined 
 by the steel is always 
 
 M = f pd'b d==f Ad'd 
 which is the formula given on page 22, which unfortunately contains 
 a typographical error. 
 
 By testing reinforced concrete beams to destruction and plot- 
 
 FIG. 3A. 
 
 ting the results we obtain a stress strain curve for the concrete in 
 compression closely approximating a parabola. The agreement ts 
 
54b Parabolic Theory of Stress. 
 
 so remarkable that the parabola has been chosen as representing 
 more nearly the actual stress strain curve than the triangle. This 
 is shown in Fig. 3A. 
 
 To illustrate the difference this makes, the following formulas 
 are used to give the exact stresses in the beam. 
 
 The average abscissa of a triangle equals one-half the greatest 
 but the average abscissa of a parabola equals two-thirds the great- 
 est so that the equation on page 12 becomes, for the parabolic for- 
 mula 
 
 fp= 2/3 ck 
 
 The formula for determining the position of the neutral axis 
 in the straight line formula is given on page 13, and this becomes, 
 for the parabolic formula, 
 
 k = VSpn + (ipn)« — Jpn 
 
 In a triangle the center of gravity is one-third the height from 
 the base, which gives k/3, as shown on page 13. In a parabola, how- 
 ever, the distance is 3/8, so that, for the parabolic formula, 
 d'= 1—3/8 k 
 
 It is easy to remember the parabolic formulas for ultimate 
 loads by simply substituting 3/8k for l/3k and by substituting 2/3 
 for 1/2 when dealing with the stresses in concrete. The moment of 
 resistance for the beam as determined by the concrete is 
 M = 2/3kd'dbd' 
 
 Another very important difference must be pointed out. The 
 material deficient in area determines the strength of the beam. If 
 the steel is deficient in area the parabolic formulas for ultimate 
 loads cannot be used for they are based upon the possibility of uti- 
 lizing the kill strength of the concrete, It is only when the steel 
 "balances" the concrete that the resisting m.oment for the steel gives 
 the exact resisting moment for the beam.-- With parabolic formulas 
 we should not use less than one per cent of steel and some beams 
 require nearly two per cent. With straight line formulas we can 
 use as small a per cent of steel as desired. This statement, of 
 course, must be modified by the character of concrete used, for a 
 very small per cent of steel will develop the full strength of some 
 concretes. 
 
 Using straight line formulas we secure rigidity and a certain 
 excess of concrete. The advantage is that when a beam is under- 
 reinforced (has too small an area of steel to balance the concrete) 
 it gives warning long before it breaks. A "balanced" beam goes sud- 
 denly. This partly accounts for the general use of straight line 
 formulas in building laws. Another reason they are greatly used is 
 
Reinforced Concrete. 34c 
 
 that the formulas in general use up to within a year or two were 
 empirical and in this form, so that the majority of designers used 
 them. Another reason is that until within the same time few engi- 
 neers or architects could procure simply written books on rein- 
 forced concrete design. The greater part of the information was 
 given free by companies selling steel. To prevent the charge of 
 trying to sell too much steel they all used straight line formulas 
 and advocated small percentages of reinforcement. Now, however, 
 that it is generally known "the more steel the less concrete" and 
 that the concrete costs about three times as m.uch as the steel in a 
 beam, the steel companies are generally using parabolic formulas. 
 
 With straight line formulas we are limited to the use of work- 
 ing stresses in both steel and concrete with vague ideas as to the 
 actual factor of safety. With parabolic formulas the beam is sup- 
 posed to contain enough steel to develop the full strength of the 
 concrete by the time the steel stress equals the elastic limit. 
 
 The straight line theory is therefore known as the Fiber Stress 
 Method and the parabolic theory is known as the Factor of Safety 
 ■ Method. As we have here two materials differing in many re- 
 spects, joined together in a structure the factor of safety method 
 seems most logical to use for economic design. Therefore, instead 
 of designing to obtain a resisting moment equal to the bending mo- 
 ment, with safe fiber stresses in the two materials, the bending mo- 
 ment produced by the load should be multiplied by the desired fac- 
 tor of safety to get the ultimate bending moment. Then instead of 
 a safe fiber stress in the concrete the actual or assumed, ultimate, 
 strength is used. Instead of a safe fiber stress in the steel the 
 elastic limit is used. The resisting moment obtained is equal to 
 the ultimate bending moment. 
 
 To secure the maximum economy in design when a test load is 
 prescribed some ambitious designers assume a load equal to the test 
 load plus the estimated dead load of the beam or slab. To obtain 
 the resisting moment they assume a strength for the concrete of 
 about two-thirds the actual or assumed strength. For the steel they 
 assume a stress about five per cent less than the elastic limit. This 
 insures the beam against failure under the test load. It would 
 hardly do to require the test load to stress the concrete to the ulti- 
 mate and the steel to the elastic limit or beyond, yet it is too often 
 done in competitive designing. 
 
 Straight line formulas give a certain stress in the concrete un- 
 der load. The stress is actually about fifteen per cent less when we 
 calculate it by parabolic formulas. Thus there is really a larger 
 factor of safety under working loads than is apparent. 
 
Ud 
 
 Parabolic Theory of Stress. 
 
 . A table like Table I can be calculated for parabolic formulas by 
 using the formula for k already given; that is, 
 
 k «= V3 pn + (I pn)" — | pn 
 To calculate a table like Table 11 to ascertain the value of "k'' 
 in connection with unit stresses, use the formula 
 
 k = ^ 
 ^ 2c 
 
 in which 
 
 k = depth to neutral axis; 
 
 f = elastic limit of steel; 
 
 c = ultimate strength of concrete ; 
 
 p:= ratio of steel to concrete. 
 
 A table of moment factors "K," like Table III can be calculated 
 by the formula 
 
 K = 2/3c d' k 
 which is similar to the formula given on page 16, using 2/3 in- 
 stead of 1/2. 
 
 Analysis of Beams and Slabs. 
 
 When a beam or slab shows signs of failure and it is possible 
 to ascertain the area of the reinforcement, parabolic formulas are 
 used to analyse the failure if the steel is shown to be in excess of 
 or balances the concrete. If the steel is confessedly inadequate then 
 use straight line formulas. We do not care about the actual stress 
 in the material in excess. 
 
 Instead of straight line formulas, however, the flexure formu- 
 las of Professor Talbot may be used. They are parabolic also and 
 we can use them practically as straight line formulas but instead of 
 taking a definite fiber stress, a fraction 
 
 FIG. SB. 
 In Fig. 3B the diagram on the left shows c' which is the ulti- 
 
Reinforced Concrete. 
 
 34e 
 
 mate strength of the concrete in compression and "c" the strength 
 the concrete reaches at the time the strength of the steel (the elastic 
 limit) is reached. Instead of assuming the strength of the steel at 
 the elastic limit any assumed strength can be given to it, thus ap- 
 proximating the safe fiber stress if desired. The diagram on the 
 right is the deformation diagram in which "e' " is the total defor- 
 mation in the concrete at the time of failure, and "e" the deforma- 
 tion reached when the steel has reached the strength assumed. At 
 the bottom of the diagram "f" is the steel stress and "fe" the defor- 
 
 e 
 mation in the steel. The fraction 'V stands for tt. For example, 
 
 when "q!' = \/\ the concrete is strained to one- fourth its limit of 
 compression, etc. 
 
 
 » •! S ,3 .4 .s . 
 
 6-f->-ess " 
 
 6 .7 .6 . 
 
 9 . 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 B 
 
 10? 
 
 
 
 
 
 
 
 y 
 
 9^ 
 
 
 
 
 
 
 
 
 
 
 
 ] 
 
 
 Ws 
 
 
 
 
 
 y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 Ml 
 
 
 
 y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 (■^I 
 
 y 
 
 y 
 
 
 
 
 
 
 
 oor 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 ^ 
 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /. 
 
 ' 
 
 / 
 
 / 
 
 
 l^s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ^ 
 
 / 
 
 
 
 ^ 
 
 2-p: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y< 
 
 V 
 
 y 
 
 
 
 
 
 
 S.9 
 
 i 
 
 
 
 
 
 
 
 
 
 
 — V 
 
 V 
 
 V 
 
 
 
 
 
 
 
 •i: 
 
 S.% 
 
 s 
 
 
 
 
 
 
 
 
 
 3 
 
 y 
 
 
 
 
 Tm 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Sf-i-ess /h lbs pth s^jn 
 
 FIG. 3C. 
 
 IX) 
 Ti- 
 ll 
 
 ■9u|b 
 II 
 
 I 
 
 Fig. 3C is a diagram taken from the bulletins from the Illinois 
 Experiment Station containing the reports of tests made under the 
 direction of Professor Talbot, with some additional notes. 
 
 These flexure formulas are rather unwieldly and are therefore 
 a method of analysis rather than for designing. By using them to 
 construct diagrams they can be of great service but for every day 
 work the straight line formulas are all right for partial loads, below 
 the ultimate. 
 
34f 
 
 Parabolic Theory of Stress. 
 
 The idea in view in developing these flexure formulas for loads 
 below the ultimate is to keep the stress in the steel below the yield 
 point (elastic limit) and yet ascertain the real stress in the concrete. 
 By assuming different values for "q" the actual stress in the con- 
 crete for any assumed stress in the steel can be found, irrespective 
 of the percentage, or area, of reinforcement. Thus it may be seen 
 that the factor of safety method and the fiber stress method are 
 practically combined. 
 
 To show how the foregoing simple formulas are complicated 
 by the introduction into them of "q" the expression on page 12, be- 
 comes 
 
 kc (3 - q) 
 *P- 3(2-q) 
 and that at the bottom of page 13 becomes 
 
 i 
 
 3pn 
 3-q 
 
 im' 
 
 3pn 
 3-q 
 
 Stress Strain (Stress Deformation) Curve. 
 
 In analytical mathematical work every line described by its 
 relation to an origin, that is by ordinates and abscissas, is termed a 
 curve, even when it is a straight line. 
 
 Stress is a force applied. Strain is a deformation resulting 
 from that stress. Deformation is amount of change of form or 
 shape. 
 
 On a sheet of squared paper let the vertical graduations upward 
 from zero, represent the deformation and the horizontal gradua- 
 tions from left to right, represent the stress. When points are 
 plotted showing the deformation for any stress and all the points 
 are joined we have a stress strain curve. As already mentioned the 
 stress strain curve for the concrete in compression in a reinforced 
 concrete beam approximates a parabola in form. 
 
 FIG. 3D. 
 Fig. 3D shows a parabola, which is a curve such that any point 
 
Reinforced Concrete. 34g 
 
 on the curve is equi-distant from a given point and a given straight 
 line. The given point, S, is called the focus and the given straight 
 line, A — B, the directrix. 
 
 CD = DS; MP=PS;EF = FS. 
 The point O is called the vertex and when the directrix touches 
 the vertex, O, the equation for the parabola is 
 y^ = 4x 
 y = +2 Vx" 
 The general equation for the parabola with any other position 
 of the directrix, is 
 
 y2 == 4 ax 
 y = + 2 Vax 
 In Fig. 3C, the position in which the parabola is drawn is that 
 in which it is generally drawn when plotted as a stress strain curve 
 of the concrete in compression. The stress is represented by "x" 
 and the deformation by ''y". In this diagram for convenience the 
 ultimate strength of the concrete is assumed at 2000 lbs. per sq. ia 
 and the deformation per unit = 0.002 = e. 
 
 Ratio of Deformation. 
 
 Over the modulus of elasticity much discussion has been waged 
 and as concrete has no true modulus of elasticity the ratio known as 
 "the ratio between the moduli of elasticity of the concrete and steel" 
 should really be termed "the ratio of deformation." No one objects 
 to the statement that some ratio of deformation exists but decided 
 objection is made to that ratio being termed the ratio between 
 moduli of elasticity when one of the materials has no such modulus. 
 
 This ratio of deformation is expressed in terms of a tangent to 
 the parabola representing the stress strain curve of the concrete in 
 compression. The stress is the tangent of an angle between the 
 deformation and the tangent to the parabola ; essentially the co- 
 tangent. 
 
 When the concrete commences to deform the stress strain curve 
 is almost straight but gradually changes in shape, becoming more 
 'nearly vertical until when the limit of deformation is reached it 
 has assumed a parabolic form as shown in Fig. 3C. 
 
 The line representing the initial modulus of elasticity is repre- 
 sented by the line A — C and is tangent to the parabola at its 
 origin. This origin is not that usually assumed as the origin of the 
 parabola but is the origin of the stress strain curve of compression 
 in the concrete. 
 
 In Fig. 3E let x and y represent respectively the abscissa and 
 
34h 
 
 Parabolic Theory of Stress. 
 
 ordinate of the parabola. PT represents the tangent at the point 
 where intersected by y, and a is the angle of the tangent, dx is an in- 
 finitesimal increment of x and dy is an infinitesimal increment of y. 
 
 N 
 
 FIG. 3E. 
 Plotting them as shown we obtain the triangle P, Q, R in which 
 to find the angle P = da. Then dy/dx gives the tangent of the 
 angle P. 
 
 Conceive the quantities dx and dy as being so small that the 
 line P Q extended to T, will assume the position P T, swinging as 
 indicated by the arrows. 
 
 At this point 7= 
 
 which represents the slope of the curve, 
 
 being coincident with dy/dx, which represents the slope of the line, 
 
 gives the following equation for the tangent of the parabola 
 
 Tan a = y/2x 
 
 The angle b is one used to express the value of Ec. In Fig. 3D 
 
 it is marked A and the angle for which we have just found the 
 
 equation for the tangent, is marked C. 
 
 2 X Tan b = Ec 
 
 Let — = Tan b 2 c 
 
 Then -— = E,, 
 X = c e 
 
 y = e c = J Ece 
 
 When diflferent values of n are used they of course represent 
 the Ec obtained from different points of tangency but instead of the 
 line being tangent to the parabola at the point fixed by the selected 
 concrete fiber stress, it is parallel to said tangent and starts from 
 the point of origin of the stress strain curve. 
 
 As a matter of fact the line forming the side of an angle, the 
 tangent of which represents the modulus of elasticity of the con- 
 crete cannot be tangent to the parabola at a point where the con- 
 crete stress = 0. It must be a tangent at some definite value of the 
 stress in the concrete. 
 
CHAPTER II. 
 Loads on Beams. 
 
 This chapter is intended as a review for the reader and an aid 
 for quick reference when some useful and necessary formula is for- 
 gotten. 
 
 A moment is the product of a force multiplied by the distance 
 at which it acts. For example, a load suspended from the extreme 
 end of a cantilever beam causes it to bend more than if placed near 
 the fast end. That is, the bending moments vary with the distance 
 from the load to the support. The bending moment is opposed by 
 a resisting moment in the beam. 
 
 When the resisting moment is less than the maximum bending 
 
 moment the beam fails. When one is equal to the other the beam 
 
 has no factor of safety. The factor of safety is represented by the 
 
 Rm 
 fraction j^ , where 
 
 M = maximum bending moment. 
 
 Rm = resisting moment of beam. 
 
 When a beam is designed to carry a load four things are to be 
 considered : 
 
 1st. Reactions. This is the name given to the proportion of 
 the load carried by each support. The name is given because action 
 causes reaction and it is convenient to assume that there is an up- 
 ward push at the supports to balance the downward push of the 
 beam with its load. 
 
 2d. Bending moment. 
 
 3d. Deflection. While a beam may be strong enough to carry 
 a certain load it may deflect, or bend, enough to crack plastering. 
 Consequently there are cases where deflection is of more importance 
 than absolute strength. Formulas for deflection will not be here 
 considered in connection with reinforced concrete beams. If the 
 design calls for a stress in the concrete not exceeding 600 lbs. per 
 sq. in. and not exceeding 16,000 lbs. per sq. in. in the steel the de- 
 flection will not exceed 1/360 of the distance between supports. 
 This is a limit beyond which it is hardly wise to go if the under side 
 of the beam is to be plastered. 
 
 35 
 
36 Reinforced Concrete. 
 
 4th. Shear. This is a term applied to the action tending to 
 cut the beam vertically and is caused by the downward push of 
 
 the load resisted by the upward push of the supports. 1-2-4 concrete 
 can safely stand 300 lbs. per sq. in. of such action. 
 
 What is termed shear in a beam of reinforced concrete is 
 really diagonal tension. When a beam bends the bottom fibres 
 stretch and the upper fibres are compressed. At the neutral axis 
 there is a tendency to shear, and this grows less toward the top 
 and bottom of the beam, where one set of stresses, of course, over- 
 comes the effect of the other set. Shear in this case should not 
 exceed 60 lbs. per sq. in. 
 
 Having, then, two sets of forces acting at continually chang- 
 ing angles with each other, we have resultants to these forces act- 
 ing at right angle to the tangent of the curve formed. The re- 
 sultant acts as a tensile stress in the concrete and stirrups are 
 placed at right angles to it. 
 
 This explains why stirrups should be fastened in some way to 
 the bottom rods, or hooked under them, and why they should go 
 farther than the top of the beam; for as put in many beams, the 
 stirrups are too short for bond. See Chap. I. 
 
 Let W ^ total load in pounds, uniformly distributed, including the 
 
 weight of the beam =; wl -j- w'l. 
 w=:load per lineal foot on beam. 
 w'= weight per lineal foot of beam. 
 P = concentrated load on beam. 
 B := total weight of beam = w'l. 
 1 = length in inches of beam. This is usually assumed as 
 
 equal to the clear width between supports plus a bearing at 
 
 each end, as it gives a better margin of safety than when 
 
 the clear span alone is used. 
 M = maximum bending moment in inch pounds. 
 
 Case A. Beam supported at both ends (freely resting on sup- 
 ports) and loaded uniformly. 
 
 Wl 
 M=: -g", at middle of beam. 
 
 W 
 
 Maximum shear at points of support = "2". 
 
 When the shear acts upward on the left side of a section, or 
 downward on the right side, it is termed positive. The reverse case 
 gives negative shear. As all beams are subjected to positive and 
 negative shear there is a point where the sign changes, and this is 
 where the maximum bending moment occurs. 
 
Loads on Beams. 
 
 Moments- 
 
 X M \, 
 
 37 
 
 Beam Lo/jo/ngs. 
 
 C/!S£ I. Siogmm tS/- weight 
 
 of ieam-iSame as 0?se H, 
 
 CffSE D. 
 
 Fig. 4 — Beam Loadings. 
 
38 Reinforced Concrete. 
 
 On the left half, the shear is positive and on the right half nega- 
 time, and at middle of beam. 
 
 W 
 Reaction at each support = -k'. 
 
 Case B. Beam supported at both ends with load concentrated 
 at the middle. 
 
 PI Bl 
 
 M = -J- + -g-, at middle of beam. 
 
 P + B 
 Max. shear at points of support = — s — ^""^ *' middle of 
 
 beam = 0. 
 
 In this case (B) the shear at all points on the beam ^ — J— 
 
 P + B 
 
 Reaction at each support = — ^ — . 
 
 Case C. Cantilever beam uniformly loaded. 
 
 Wl 
 M = "o" ^t point of support. 
 
 Maximum shear at point of support ^W. 
 Reaction at point of support = W. 
 
 Case D. Cantilever beam with load concentrated at any point. 
 In this case 1 = distance from point of support to a vertical 
 line through center of gravity of load. 
 
 Bl 
 
 M = PI + -H" at point of support. 
 
 Max. shear at point of support = P + B. 
 
 Reaction at point of support =:: P + B. 
 
 Case E. Beam supported at both ends with load concentrated 
 at any point. 
 
 Call distance from left support to load, a, and from right sup- 
 port to load, b. 
 
 a(8Pb + Bl — Ba) ^ , , 
 
 M = 5j , under load. 
 
 Pb B 
 
 Max. shear at support a = j + 2 • 
 
 D— 1 + 2 • 
 
 Reaction at each support equal to shear. 
 
 At this point the general rules for shear and reactions may be 
 introduced. 
 
 The weight of the beam being a distributed load, one-half goes 
 to each support in addition to the proportionate part of the loads 
 
Loads on Beams. 
 
 39 
 
 on the beam. In shear one-half is plus (the left) and one-half is 
 minus (the right). 
 
 Rule for reactions for combinations of loads. — Multiply each 
 load by its distance from one support. Add the products and di- 
 vide the sum by the span. This gives the reaction on the opposite 
 support. The other reaction is obtained by subtracting the reaction 
 thus found from thewum of the weights of the loads. The sum of 
 the reactions is always equal to the sum of the loads. 
 
 Rule for shear for combination of loads. — The maximum shear 
 will equal the greater reaction. The shear under each load is found 
 by setting down either reaction with its plus or minus sign and 
 adding, algebraically, to it successively the weights of the loads, 
 commencing with the one nearest the reaction chosen. 
 
 Case P. Beam supported at both ends with two loads equally 
 distant from the ends. 
 
 Call the distance from each end, a. 
 
 Bl 
 M =: Pa -|- -g- at middle of beam. 
 
 Max. shear at points of support = 5 . 
 
 B 
 
 Reaction at each support = P -(- -g-. 
 
 Case G. Beam supported at both ends with several concen- 
 trated loads. 
 
 Fig. 6— Case G. 
 
 The most simple method for this case is to make a scale draw- 
 ing, showing by a single horizontal line the length "of the beam. 
 Calculate each M as shown for case E. Draw vertical lines down- 
 ward under each load, the lengths of the lines under each load rep- 
 resenting the bending moment caused by the load at that point 
 Connect the lower ends of these lines to the ends of the beam. This 
 
40 Reinforced Concrete. 
 
 gives a number of triangles equal to the number of loads, and each 
 vertical line will be divided into the same number of sections. 
 
 Add the lengths of these sections together to obtain the bend- 
 ing moment at each point. In other words, the total bending mo- 
 ment at any point produced by the weights of all the loads is equal 
 to the sum of the moments at that point produced by each of the 
 weights separately. * 
 
 Under each load extend the vertical line until it is equal in 
 length to the bending moment at that point caused by all the loads. 
 Connect the ends of these lines and the ends of the beam. Above 
 
 Bl 
 the beam draw a parabola with an extreme height =:~g~. The posi- 
 tion and amount of the maximum bending moment will be found 
 by scaling the longest possible vertical line intercepted by the para- 
 bola above and the irregular figure below the beam. 
 
 Case H. Beam fixed at both ends and loaded uniformly. 
 
 A beam supported at the ends bends downward when loaded 
 and is concave on top. When fixed at the ends it is convex on top 
 at each end and concave in the middle. When uniformly loaded the 
 points of contrafiexure are 0.2113 the length from each support. 
 
 ,, Wl 
 
 M = -j2 at pomts of support. 
 
 Wl 
 M=-2T at middle of beam. 
 
 W 
 Max. shear = -g- at points of support. 
 
 Case I. Beam fixed at both ends with concentrated load in 
 
 middle. 
 
 Points of contraflexure=0.25 the length from each support 
 
 „ PI Bl . , 
 
 M = -g--f -jg- at pomts of support. 
 
 PI Bl 
 M =~8" + "gz" at middle of beam. 
 
 P-fB 
 Max. shear = — s — at points of support. 
 
 Parallel Forces on Simple Beams. 
 
 All the forces acting on a beam may be determined graphi- 
 cally and thus the foregoing formulas proven. Combinations 
 can be worked out without the labor of going through the cal- 
 culations and the work will prove itself. 
 
 Let A B represent a beam resting on supports as shown 
 
Loads on Beams. 
 
 41 
 
 by the arrows pointing upward at C and D, these arrows rep- 
 resenting the reactions. At the left the line A' B' is the sum 
 of all the weights drawn to some scale, each weight being rep- 
 resented by the amount between the figures, e. g., from A' to 1 
 is force 1; from 1 to 2 is force 2, etc. The line T O is per- 
 pendicular to the line A' B' and is of any length, generally 
 taken at some even number of hundreds or thousands of pounds, 
 depending upon the scale to which A' B' is drawn. From O 
 draw lines to 1, 2, 3, etc., and to the ends. With triangles or 
 parallel ruler transfer these lines to form the polygon a, 1, 2, 
 3, 4, b, under the beam. Connect the points a and b and trans- 
 fer the line so it will be represented in direction by the line O S. 
 
 Fig. 6 — Parallel Forces on Beam. 
 
 Then the reaction under A is shown by C = A' S, and the 
 reaction under B is shown by D, = B' S, to scale. 
 The bending moment at any point is equal to the length 
 
 of OT multiplied by the ordinate of the polygon at that point. 
 For example, the bending moment at 2 is equal to OT multi- 
 plied by f2. If our scale is in hundreds of pounds and the 
 
42 Reinforced Concrete. 
 
 length OT is equal to one unit of the scale, then the ordinate 
 is equal to the bending moment. 
 
 Shear is obtained by the third diagram with the shaded 
 rectangles. The construction of this figure needs little explana- 
 tion. Simply produce the horizontal and vertical lines as 
 shown and hatch the rectangles thus formed. The shear at 
 any point on the beam is equal to the length of the longest 
 vertical line at that point. The diagram shows that the point 
 of maximum bending point is the point where the shear equates 
 to zero. 
 
 To consider the weight of the beam, which is uniformly 
 distributed, it will be well to make a separate diagram and after- 
 ward take the sums of the moments, shears and reactions, 
 caused by this distributed load and the concentrated loads 
 shown by the arrows. This is shown in other figures. 
 
 In calculating a beam, the load per lineal foot is used as ex- 
 plained in the formulas. In calculating a floor slab, consider it as 
 a number of beams 13 inches wide lying side by side. It is thus 
 necessary to figure only one 12-inch beam in order to ascertain 
 thickness of slab and amount of steel. Retaining walls may be 
 calculated as a series of horizontal beams, one on top of another, 
 or as a series of vertical beams standing edge to edge on end. To 
 secure proper intervals in slabs, it is customary to have reinforce- 
 ment at right angle to the principal reinforcement, to which the 
 latter will be connected by wiring at intersections. This crossing 
 steel is generally assumed as being equal to one-third of 1 per 
 cent of the area and spaced accordingly. Where the extremes 
 of temperature are not great, even less than this amount may be 
 used. Bars of the same size are used, which would mean that 
 when the reinforcement in the line of the beam is 1 per cent, the 
 bars are spaced six inches apart; then the crossing bars will be 
 18 inches apart. Nothing is settled about this point yet, and 
 two considerations enter into the question. One is temperature 
 and the necessity for some provision to avoid temperature cracks. 
 The other is shear in the concrete between adjacent beams of 
 which the floor is assumed to be composed. 
 
 The following loads are those allowed in different cities of the 
 United States, in addition to the dead load. The load of the 
 structure is termed the dead load. The load imposed on the floor 
 by the materials stored there is termed the floor loading and is 
 often spoken of as the live load. Strictly speaking, however, a 
 live load is a moving load and has double the effect of the same 
 
Floor Loads. 43 
 
 weight in pounds of a stationary load. For example, a live load 
 of 200 lbs. per sq. ft. might be calculated as if it were a steady load 
 of 400 lbs. for a bridge but as 200 lbs. in a building. 
 
 Floor loads. Dwellings, apartment houses, hotels, tenement 
 houses, or lodging houses, 70 lbs. per sq. ft.; office buildings, first 
 floor, 150 lbs. per sq. ft.; above the first floor, 100 lbs.; schools 
 and places of instruction, 80 lbs.; stables or carriage houses, 80 
 lbs.; building for public assembly, 150 lbs.; ordinarj' stores, light 
 manufacturing and light storage, 120 lbs.; stores for heavy ma- 
 terials, warehouses and factories, 150 to 250 lbs. ; roofs, pitch less 
 than 20 deg., 50 lbs. ; pitch more than 20 deg., 30 lbs. 
 
 Live load on slabs to be used for highway purposes should be 
 about 100 lbs. per sq. ft. (equal to dead load of 200 lbs.) and the 
 fibre stress in the concrete should not exceed 400 lbs. per sq. in. 
 with n^l5. For spans not exceeding 50 feet a highway bridge 
 can be calculated in the same manner as given for floor slabs. 
 Sometimes considerable economy can be effected by calculating 
 two beams about 18 inches thick, to carry the load, and using them 
 as parapets. The floor slab across will be connected to these beams 
 a little below the neutral axis, but this, of course, depends upon the 
 head room required. Such parapets should have double reinforce: 
 ment and be designed that way. The steel in the floor slab should 
 be turned up into the beam far enough to provide for hanging (re- 
 action). Abutm.ents must be rigid and go to a good foundation. 
 See bulletin No. 15, "Concrete Bridges," American Association of 
 Portland Cement Manufacturers, Land Title building, Philadel- 
 phia, Pa. 
 
 Sidewalks in Chicago are calculated for 300 lbs. per sq. ft., 
 including weight of slab; in St. Louis and some other cities, for 
 300 lbs. per sq. ft. in addition to weight of slab. 
 
CHAPTER III. 
 Columns. 
 
 Columns of reinforced concrete are used because they cost 
 less in place than columns of steel or iron. They are also used 
 because the majority of men who design in reinforced concrete like 
 to use as much of the material as possible. To them it seems a 
 profanation to use a column of steel or iron and have the walls and 
 floors of concrete. 
 
 Concrete columns occupy more space than columns of other 
 materials commonly used for such purposes. Taking for example 
 a load of fifty tons to be supported by a column 18 feet high, 
 the sizes are as follows: 
 
 Reinforced concrete 18 x 18 inches 
 
 White pine or spruce 13 x 13 inches 
 
 Oak 13 x 12 inches 
 
 Yellow pine 11 x 11 inches 
 
 Cast iron (hollow and round) 8 in. diameter 
 
 Steel (3 6-inch latticed channels) 6x 8 inches 
 
 In a floor having twenty columns the space occupied by round 
 cast iron columns will be less than six square feet. The space 
 occupied by the same number of steel columns will be less than 
 eight feet, while the space occupied by the same number of rein- 
 forced concrete columns will be over forty square feet. When 
 space is rented by the square foot, or, rather, the value of space 
 is based on its rental value, the economy of reinforced concrete 
 columns is sometimes questionable. In situations where the space 
 occupied is of little consequence and where durability is the chief 
 thing sought, the reinforced concrete column has a place. Even 
 in such a place, it may not be as good as columns of other materials 
 when the cutting off of the light is also considered. 
 
 Two methods are used for reinforcing columns. In one all 
 the reinforcement is vertical. It is tied at intervals or is wrapped 
 with wire, but such tying or wrapping is empirical and is more 
 to keep the reinforcement in place than for any other purpose. 
 The other method is to have simply enough vertical rods to tie the 
 
 44 
 
Different Types of Columns 45 
 
 wrappings to and to reinforce by spiral wrappings of wire or steel 
 rods. 
 
 There are two modifications that are hardly entitled to be 
 called reinforced concrete, but should rather be styled "concrete 
 protected" columns. In one the column must be of steel suffi- 
 cient in size to carry the load and with concrete to protect it and 
 add the necessary stiffness and factor of safety. In the other the 
 reinforcement is built as a column large enough to carry all the 
 dead loads and the construction loads. The concrete, when added, 
 makes it strong enough to take care of all live loads. This last 
 form is coming rapidly into use, together with built-up reinforce- 
 ment for beams. It admits of certainty in placing the reinforce- 
 ment, while at the same time lessening the time occupied in con- 
 struction. In the opinion of the writer, the building ordinances 
 in all cities will gradually insist upon such construction. 
 
 When columns are reinforced with vertical rods, the few 
 experiments made do not show results that are entirely satis- 
 factory. They do show, however, that this method is good if 
 the concrete is well proportioned, well mixed and thoroughly 
 compacted when placed. The steel should be as straight as 
 possible and rest upon bed plates at the bottom. The total load 
 should not exceed 350 or SOO pounds per square inch. 
 
 Generally building ordinances require that reinforced concrete 
 
 columns have a ratio not exceeding—?- = 13. In other words, 
 
 the least thickness or diameter will be in inches equal to the 
 clear height in feet. It is plain that, as the steel rods carry 
 part of the load, they might bend enough to destroy the con- 
 crete. In a long column, flexure might be caused by a heavy 
 load, although in the tests made up to date no bending seemed 
 to have been developed in columns having a ratio of less than 
 25. Some designers use a ratio of 20 with c = 350 and a ratio 
 of 12 with c = 500. 
 
 Columns reinforced by spiral wrappings can be loaded up to 
 about liOOO pounds per square inch, because the concrete is en- 
 cased in the wrappings as in a steel cylinder. As the load comes 
 upon it the tendency is to bulge outward. This, being resisted 
 by the spirals, enables greater strength to be developed than by 
 the use of longitudinal bars or rods alone. 
 
 A spirally wound column is not very stiff, and if such rein- 
 forcement is used in long columns it must be assisted by longi- 
 tudinal rods. The place for these rods, of course, is inside the 
 
46 Reinforced Concrete. 
 
 spiral. One objection to the use of spirally reinforced columns 
 is that there must be some settlement before the bulging is suflS- 
 cient to call into play the strength in the spirals. Within a fibre 
 stress of 1,000 pounds per square inch, if the column is well 
 made, this need not cause anxiety. The writer, however, prefers 
 to use lower stresses and longitudinal reinforcement. 
 
 Recent experiments seem to indicate that when vertical rods 
 are used in spirally wound columns they are an element of 
 danger. As already stated, the ultimate strength of the column 
 is increased, but there is nothing gained when loads are light, 
 as they are generally. That is, if the steel is used in the form 
 of spiral wrappings it will generally be found to be expensive 
 reinforcement unless high stresses are used. When some of it 
 is in the form of longitudinal rods and the stress is so high 
 that the column settles enough to call the spiral wrapping into 
 service, then the steel is apt to be stripped from the longi- 
 tudinal rods, thereby dividing the body of the column. When 
 this is done and each rod is free to act alone, it buckles and the 
 column is rapidly destroyed. Therefore when a column is 
 wound there should be as little vertical steel as possible. 
 
 A volume of steel in the form of a large wire or small round 
 rods wrapped spirally has 2.4 times the effect that the same 
 volume of steel would have if disposed in vertical reinforcement. 
 That is, provided it is wrapped with a pitch of from one-sixth 
 to one-seventh the diameter. 
 
 A knowledge of this fact permits one of two alternatives. The 
 column size may be retained and a smaller amount of steel used 
 than if vertical reinforcement is adopted, or the size of the column 
 may be reduced by using a stress in the concrete 2.4 times greater 
 than the stress ordinarily considered safe. This means that we 
 can use in a spirally wound column a stress of 840 pounds per 
 square inch instead of the 350 pounds used in a vertically rein- 
 forced column, or we may use 1,200 pounds per square inch instead 
 of 500 pounds. The placing of vertical reinforcement is cheaper 
 and it is easier to get the reinforcement right than to wind the 
 steel. Compilers of conservative building ordinances so far do 
 not look kindly upon spirally wound columns except when they are 
 fabricated in shops and brought to the building. Neither do they 
 like high stresses. 
 
 The tables of column divisors are used as follows: Assume 
 
 a value of -^ and thus get the area of the cross section of the 
 
Percentage of Steel. 
 
 47 
 
 column. Perhaps the building ordinance fixes this ratio, in which 
 case use it and obtain the area. Divide the weight in pounds to 
 be carried by the column by the area. Under the value of "n" 
 fixed by the ordinance, find the column divisor. On the same 
 horizontal line will be found the percentage of steel. 
 
 If a certain percentage of steel is assumed and a value of "n" 
 selected, the column divisor in the "n" column on the same line 
 as the steel percentage will be used as a divisor of the weight in 
 pounds. The result will be the area of the column in square inches. 
 
 The tables, as may be seen, have been calculated with c = 350 
 and = 500 pounds per square inch, with values of "n" ranging 
 from 8 to 20 and with from 1 to 10 per cent of steel. 
 
 TABLES OF COLUMN DIVISORS 
 for longitudinally reinforced-concrete columns. 
 
 
 
 Table VII. 
 
 c = 350 lbs. per sq. in. 
 
 
 Per cent 
 of steel 
 
 n= 8 1 
 
 10 
 
 12 1 15 
 
 20 
 
 f = 2800 1 
 
 3500 1 
 
 4200 1 5250 1 
 
 7000 
 
 
 - 
 
 -DIVISORS— 
 
 ' 
 
 1 
 2 
 3 
 4 
 5 
 6 
 10 
 
 374.5 . 
 
 399 
 
 423.5 
 
 448 
 
 472.6 
 
 497 
 
 595 
 
 381.5 
 
 413 
 
 444.6 
 
 476 
 
 507.5 
 
 539 
 
 665 
 
 388.5 
 
 427 
 
 466.6 
 
 504 
 642.5 
 581 
 735 
 
 399 
 448 
 497 
 546 
 595 
 644 
 840 
 
 416.3 
 483 
 549.5 
 616 
 682.5 
 749 
 1015 
 
 
 
 lable VIII. 
 
 c = 500 lbs. per sq. in. 
 
 
 Per cent 
 of steel 
 
 n= 8 
 
 1 10 
 
 12 1 15 
 
 20 
 
 £ = 4000 
 
 1 5000 
 
 6000 1 7500 
 
 10000 
 
 —DIVISORS— 
 
 1 
 2 
 3 
 4 
 S 
 6 
 10 
 
 535 
 570 
 605 
 640 
 675 
 710 
 850 
 
 545 
 590 
 635 
 680 
 725 
 770 
 950 
 
 565 
 610 
 665 
 720 
 775 
 830 
 1050 
 
 570 
 640 
 710 
 780 
 860 
 920 
 1200 
 
 595 
 690 
 785 
 880 
 976 
 1070 
 1450 
 
 While the percentages of steel are given as though no limit 
 is considered, there is a practical limit depending on the cost 
 of the steel and the ease of getting it in the form of rods and 
 bars as compared with getting structural shapes and using con- 
 crete protected columns instead of reinforced concrete columns. 
 The heavy lines are drawn where the same amount of steel in 
 a steel column would carry the entire load without the concrete. 
 
48 Reinforced Concrete. 
 
 The tables were calculated by the following formula: 
 
 P = c (Ac+nAs), in which 
 
 P = total load in pounds or compressive strength of section. 
 
 c = compressive load per square inch permitted on concrete. 
 
 A,=: area of steel ) . „„ „,„..:„„ 
 
 A:=area of concrete \ '" "°^= ^^'=*'°"- 
 
 n == ratio of moduli of elasticity. 
 
 To understand and use this formula, assume a unit value for 
 steel and concrete, when it becomes 
 
 P = c(l + iil), 
 and by multipljring the quantities in the parenthesis by an assumed 
 value of c (for example, 350) and of n (for example, 13), we 
 have 
 
 P = 350 (1 + 12 (1) ) = 350 + 12 X 350. 
 
 The following example illustrates the method of calculation, 
 taking the values already assigned and starting with a 1 per cent 
 reinforcement of steel: 
 
 350 X 12 X 0.01 (the per cent of steel) = 42.0 
 
 350 X 0.99 (the per cent of concrete) = 346.5 
 
 Column divisor 388.S 
 
 The total load in pounds diivded by 388.5 will give the area 
 in square inches of the column section for a reinforcement of 1 
 per cent of steel, when "c" is 350 and "n" is 12. 
 
 The factor "n" is very important in column formulas. Pro- 
 fessor Talbot says it is apt to be misleading to use it, and to term 
 it the ratio between the moduli of elasticity is indefinite and un- 
 desirable. He therefore uses a formula having a different ratio, 
 as follows: 
 
 P = Ac (1+ (n — 1) p), in which 
 
 P = total load in pounds or compressive strength of section. 
 
 A = total area of section (including concrete and steel) in 
 square inches. 
 
 c = compressive load per square inch allowed on the concrete. 
 
 n = ratio of stress in steel to stress in concrete. 
 
 p = percentage of steel or ratio which area of steel bears to 
 the area of the concrete. 
 
 The tables of column divisors obtained by the first formula 
 were checked by the second. 
 
 The ratio of the moduli of elasticity has been considered of 
 great importance in column design, assuming the adhesion or 
 bond between steel and concrete to be sufficient. When a load 
 
Loads on Columns. 49 
 
 comes upon the column, part is supposed to be taken by the con- 
 crete and part by the steel. Each must, therefore, be compressed 
 precisely in the ratio of the relative extensibility. If they do not, 
 then the adhesion will be destroyed, after which each material will 
 act independently, making certain the destruction of the column. 
 When the adhesion is destroyed, each rod becomes a long and 
 extremely slender column. 
 
 To call "n" the ratio between the moduli of elasticity is not 
 correct. The term "ratio of stress in steel to stress in concrete" 
 gives a clearer idea. The ratio is sometimes as high as 20, but 
 the safest value to use when a factor of safety of from 4 to 5 is 
 wanted in the concrete, lies between 12 and 15. 
 
 Calling A the total area of the column section (including the 
 steel) and "p" the percentage of reinforcement, the area of the 
 steel will be 
 
 pA 
 the unit stress in the steel will be 
 
 nc 
 and the area of the concrete will be 
 A (1-p) 
 The total compressive stress in the steel will be 
 pAnc 
 and in the concrete will be 
 Ao(l-p) 
 How much strength does the longitudinal steel add to the 
 concrete? The formula: 
 
 P==Ac(l + (n — l)p) 
 indicates that each addition of 1 per cent of steel adds (n — 1) % 
 of strength to the concrete. 
 
 The same formula enables us to find when the steel in the. 
 
 usual structural shapes will carry the load without the concrete. 
 
 Let s =r the ordinary stress used in steel columns. Usually 
 
 16,000 pounds per square inch. 
 A' = area of steel in steel column (cross section).. 
 pA = area of steel reinforcement in reinforced concrete 
 column 
 
 Then A^ (1+ (n — 1) p) =sA' 
 pA = sA' 
 
 c 
 
 P— f — c(n — 1) 
 
 That is, the safe fibre stress allowed in the concrete is 
 
50 Reinforced Concrete. 
 
 divided by the usual fibre stress in steel structural work minus 
 the safe concrete stress multiplied by (n — 1), to get the per- 
 centage of steel that will carry the load without the concrete, 
 provided it is in the usual structural form. 
 
 It is then simply a question of the balancing of costs. If 
 the concrete column containing reinforcement can be built at 
 less cost, or if the steel can be obtained in the form of rods and 
 bars within less time than it can be obtained in shapes that can 
 be worked into the usual form of steel column, then the rein- 
 forced column may be best. 
 
 The steel should be so disposed in the column that it will be 
 protected by at least one inch of concrete, and so the concrete 
 can flow readily between the bars. Large bars should be used 
 in preference to small. They may be so placed that the column 
 may be square, round or octagonal in section. The writer believes 
 it is well to allow a part of the area for fire protection of the 
 steel. In the examples given at the beginning of this chapter 
 the area of a reinforced concrete column is given at 18" x 18" = 
 324 square inches. Using the tables above, the exact dimension 
 will be found nearer 16 inches square, and the additional size is 
 given for the thorough protection of the column. 
 
 In this connection it may be stated that the logical position 
 for the steel is in the center of the column, but it should be 
 nearer the outside, because the concrete should be in as large a 
 body as possible and be not too much cut up. The writer believes 
 that the body of concrete inside the steel should make a column 
 
 of clear concrete having a ratio of -r- equal to three-fourths the 
 
 ratio of the whole column. That is, if calculations show the 
 column should be 16 inches square, the steel can be arranged to fit 
 inside a 13-inch square. This rule is wholly empirical, and by 
 some designers may not be considered good. It should not be 
 adhered to if it results in an interior section of less than 8x8 
 inches, and does not need to be followed closely if a larger inside 
 square can be obtained for the steel and still leave a thickness 
 of at least one inch of concrete protection. In columns liable to 
 exposure to fire it will be a safe precaution to increase the dimen- 
 sions of the column by at least 3 inches. 
 
 When the reinforcement calls for four large bars, a good 
 plan is to use four angles of equivalent area and make of them a 
 latticed column. Otherwise use square bars wrapped with No. 8 
 or No. 10 plain wire, tying it with No. 16 or No. 18 wire at each 
 
Distribution of Steel. 51 
 
 intersection, merely to preserve the pitch, which should be equal 
 to half the thickness or diameter. The wrapping should be com- 
 menced at one comer and go around in as long strands as possible. 
 When spliced, it should be by hooking the ends and making long 
 twisted joints. Four rods generally suffice, except when their size 
 would render them difficult to handle, when a larger number of 
 smaller rods can be used. 
 
 Owing to the shrinkage stresses developed in concrete, which 
 may stress the steel unduly before the load comes on the column, 
 it is good practice to use plain bars or rods in columns and pour 
 about five diameters in height at a time, leaving an interval of 
 about two or three hours between pourings. The columns should 
 be completed before the pouring is commenced for the floors, and 
 beams they support. Concrete in columns usually settles consider- 
 ably in setting, and for this reason it is well to allow about three 
 or four hours' time to elapse before pouring the beams connecting 
 to the top of the columns. 
 
 This rule for pouring columns does not always work well, 
 for some engineers have told the writer that they noticed small 
 cracks that appeared in the concrete below when it was set rather 
 hard but not quite hard enough to bear the weight of the fresher 
 concrete poured above. It is quite likely they waited too long 
 between pourings. The idea of having a little time elapse is to 
 permit of thorough settlement in small masses and to allow a 
 somewhat uniform setting thereby. 
 
 When vertical rods used in columns are shorter than the col- 
 umn, pieces put on to lengthen them should rest on top instead of 
 being wired side by side, and the joint should be made in a sleeve 
 of pipe just fitting the steel. Alongside each joint and about 
 four times as long as the sleeves, which should be twenty-four 
 diameters long, should be set a half-inch bar as a joint stiffener. 
 It should not be wired to the column reinforcement, but should be 
 a separate piece, entirely surrounded by concrete. 
 
 Mr. W. A. Hoyt, C. E., structural engineer with the Corn 
 Products Company, informs the writer that he does not set his 
 vertical rods until ready to go on with the columns. It often 
 happens in construction work that the column footings are com- 
 pleted long before the columns are poured. The long steel rods 
 are a problem to handle. Some men place in the footings short 
 sections of pipe and set the steel in the pipe when ready to go 
 up with the work. In spite of all care, more or less dirt will 
 collect in the pipes. Mr. Hoyt uses instead short sections of 
 steel which project a foot or two above the footing. When 
 ready to go ahead a sleeve is placed around them and the ver- 
 tical rods are set in this sleeve. 
 
CHAPTER IV. 
 Walls, Tanks and Footings. 
 
 Retaining walls fail by sliding forward, by overturning, or 
 by breaking across at a point approximately one-third of the 
 height up from the bottom. 
 
 Until the advent of reinforced concrete all walls were de- 
 signed to have enough bulk to prevent failing by any of the 
 above ways. It was realized that if masonry could be made 
 with enough cohesion to stand bending, walls could be sunk 
 far enough in the earth so they would not slide forward; that 
 they could be anchored in some way to prevent overturning, but 
 that all this involved the production of strains that would cause 
 the wall to break. Therefore, the strong masonry was needed. 
 This is apart from the fight between the men who designed walls 
 by theoretical formulas and those who stood faithfully by empir- 
 ical formulas, or, as some called them, "'rule-of-thumb methods." 
 
 There was never any reason for the latter fight, for walls 
 that were designed according to theory, coupled with judgment, 
 always stood. It was when a man's passion for pure, theoretical 
 reasoning overcame his better judgment that walls fell, except 
 in the very few exceptional cases where the circumstances were 
 such that even walls designed by empirical rules, supposed to 
 embody the best judgment in exceptional cases, would have 
 failed. Empirical rules simply set a thickness for a wall accord- 
 ing to the height and practically independent of the character of 
 the backing, except when a man liked to add a guess of his own. 
 When walls commenced to be built of reinforced concrete all 
 the carefully treasured empirical rules as to weight and thickness 
 of walls had to go; for whereas in the case of bulk the pressure 
 was of little or no moment, so long as certain procedures were 
 adhered to, when it came to the designing of a wall in which the 
 minimum of material was the goal, pressures had to be taken 
 into account. Reinforced concrete walls are in shape like a cap- 
 ital letter L or like an inverted capital T. The weight of the 
 wall is small and the weight of the backing upon the rear leg 
 has to be taken into consideration. Therefore, bending moments 
 
 53 
 
Retaining Walls. 
 
 53 
 
 develop which cannot be withstood in old style masonry hav- 
 ing joints, so are taken care of by the reinforcement. 
 
 Considering a vertical strip 12" wide on a wall the total 
 pressure is found by the formula: 
 
 P = yXd^ 
 
 in which d is the depth in feet from the top of the wall to the 
 point at which the pressure is wanted, and the material is no 
 higher than the wall. 
 
 The following table gives values of y for different materials: 
 
 The 
 
 TABI.E IX. 
 
 Water y = 31.25 
 
 Fine dry sand y =:15.7 
 
 Dry loose gravel y = 12.1 
 
 Dry loose earth y = 8.8 
 
 Moist earth y = 5.6 
 
 Dense, natural earth y^ 6.3 
 
 Ojnsidering a horizontal strip 12" wide; at any depth the 
 
 pressure, w (or load), per square foot, is as follows. 
 
 w = 3y X d 
 
 A surcharged wall is one that supports a sloping fill. 
 pressure on any foot will be 
 
 w = 3y X (2d — 1) 
 and the total pressure will be 
 
 P = 1.5y X d' 
 
 The depth is the depth from the top 
 of the wall as already explained, and 
 while the formula is not exact, it is 
 close enough for all practical pur- 
 poses. 
 
 Reinforced concrete retaining w.alls 
 may be designed as cantilevers, in 
 which case the formula for P is used, 
 or they may be designed with coun- 
 terforts, in which case the formula 
 for w is also used. Fig. 7 represents a wall which is a compromise 
 between the L and the inverted T. In order that the system of let- 
 tering used may apply to both designs, DC or EI represent the 
 height, which will hereafter be designated by h. The pressure P 
 
 n E 
 
 Fig. 
 
 ^13., 
 
54 
 
 Reinforced Concrete. 
 
 is applied at h/3, to obtain the bending moment at CI, which will 
 determine the thickness at that point. The pressure is applied at a 
 point one-third the height for the reason that the area of pres- 
 sure is a triangle and forces act always through the center of 
 gravity of bodies; the center of gravity of a triangle being one- 
 third up from the base. 
 
 Fig. 8 — Two Types of Retaining Walls. 
 
 Two calculations will always be made to obtain the economic 
 design. The first calculation will not take the weight of the 
 wall into account, and the base AH will be taken at a length 
 equal to h/2. The area DFHK in square feet, multiplied by 100 
 lbs., the weight of one cubic foot of earth, will be taken as the 
 weight of the wall to resist the pressure, P. Find the center of 
 gravity and through it vertically pass a line to represent to scale 
 the weight just found. Through it horizontally pass a line to 
 scale representing the pressure. Complete the parallelogram and 
 draw the resultant. The position of this resultant is of import- 
 ance, for in order that the maximum pressure on the base be 
 not greater than twice the average, and that there be no ten- 
 sion on the back side of the foundation, the distance from the 
 
Retaining Walls. 55 
 
 resultant to the middle point of the base must not exceed 1/6 
 the base. 
 
 To find pressure on base: 
 
 Let F = pressure on base in pounds per sq. ft. at A. 
 
 Let W = weight in pounds of the wall and backing (area 
 
 DFHK). 
 Let b = length of base, AH. 
 
 d =: distance in feet from point of intersection of result- 
 ant with bottom of base, to the nearest extremity of the 
 base. 
 
 2W 
 Then F = - . , when d is equal to or less than b/3. 
 
 4W 
 And F = .2 (b — 1.5d), when d is equal to or greater 
 
 than b/3. 
 Or the following general formula can be used: 
 
 P =( ^rrzT^ |W 
 
 This pressure, F, on the base is the maximum pressure which 
 it is estimated can be borne by the earth on which the wall is 
 built. If the foundation will not stand such a pressure the base 
 may be lengthened or piles can be driven under the toe, AB. 
 
 The bending moment at CK will be practically equal to 
 
 M=: — X BC X .55BC; when BC^— r — , or for shorter toe 
 
 W X IG 
 The bending moment at IJ is, M = r 
 
 As the pressure against the wall is at right angle to the sur- 
 face pressed, it brings the resultant a little nearer the center if the 
 pressed surface is sloping instead of vertical. This increases the 
 stability and decreases the bending moment in the case of water, 
 but makes practically no difference for earth. 
 
 The dotted lines indicate how the steel will be placed to take 
 
 care of the bending moments developed. As the shearing stress 
 
 on CK will be great the thickness should be made double 
 
 IC 
 what the bending moment would demand, when BC < -r- 
 
 o 
 
 thus using the calculation for bending moment simply to obtain 
 the steel area. The thickness at IJ should be sufficient to develop 
 the bond strength of the steel rods in the wall. Before deterroin- 
 
56 Reinforced Concrete. 
 
 ing this, however, the thickness, IC, should be obtained, and the 
 thickness of the wall at regular intervals, in order to obtain the 
 correct shape, which will approximate a curve. Three points 
 should be enough, and they may be connected by straight lines, 
 the front of the wall being vertical, or if desired may have a 
 slight batter. The last slope of the back towards the bottom 
 may be such that the steel parallel with it may extend into the 
 base far enough to develop bond, or at its connection with the 
 base the angle may be divided and the steel given a different 
 slope in order to secure length of embedment without unduly 
 thickening the base. 
 
 The thickness, IJ, will be used to determine the amount of 
 steel, but the actual thickness, as seen, depends upon the bond 
 embedment of the steel in the wall. All the steel must be run 
 far enough past the points of maximum moment to develop suf- 
 ficient bond. (See Table V, Chapter I.). 
 
 The steel in the base will run from the front to the back 
 (perpendicular to the length of the wall), and the steel in the 
 wall will be vertical. All of it need not run to the top of the 
 wall, but it may be reduced as shown by the calculations for 
 bending moment. Longitudinal rods should be placed in the 
 wall and in the base at regular intervals to take care of tem- 
 perature stresses and to assist in preserving the intervals be- 
 tween the main reinforcing rods. The steel should be well wired 
 together at all intersections. 
 
 Before figuring the steel, however, a second calculation 
 should be made after the dimensions of the wall have been fixed 
 as shown. The wall should be drawn to scale and a new center 
 of gravity found, representing the compound section made up 
 of the wall weighing 150 lbs. per cu. ft. and the earth filling on 
 the slab weighing 100 lbs. per cu. ft. To allow of some reduc- 
 tion in size it may be best to use 120 lbs. for the concrete por- 
 tion. With this calculation, which may result in some changes 
 being made in sizes, the work can stop and the steel be calcu- 
 lated for the wall. The longitudinal steel should be equal to 
 about one-third of one per cent in area of cross section. The 
 edges, BA, GH and DE may be of any thickness sufficient to 
 give adequate protection to the steel, the slope being gradual 
 and thus effecting some saving in material. 
 
 As walls designed in this manner are more apt to be heaved 
 by frost than the usual type of gravity wall, the bottom slab 
 must be placed deep enough to avoid any danger of frost ac- 
 
Retaining Walls. 67 
 
 tion, but as this is a case where moments enter in the following 
 formula may be used, in which f = depth below surface in feet. 
 
 f = .0007 F, which gives a minimum value for the depth. 
 
 Reinforced concrete walls are often designed with counter- 
 forts back of them, tieing the face slab to the bottom slab in the 
 rear. This is a simple wall to figure and easy to build, but on 
 account of more form work, by reason of the counterforts, may 
 be more expensive at times than the cantilever wall, although 
 generally requiring less material. 
 
 First determine the spacing between the counterforts. Then 
 design the vertical wall as a slab between the counterforts, with 
 horizontal reinforcement. Calling the distance between counter- 
 forts, in inches, L; the bending moment on each horizontal strip 
 la" wide will be: 
 
 in which w ^ 3y X d (load per sq. ft. at depth, d.) 
 
 The total load on any horizontal strip will be wL, and one- 
 half of this at each end is reaction, thus indicating how far the 
 steel must run back into the counterfort for bond. In addition 
 to this horizontal reinforcing steel there should be yertical steel 
 of approximately one-third of one per cent area used to space 
 the horizontal rods and going to the top of the wall. At the 
 bottom it should turn gradually into the slab at the back, going 
 into it to help tie the face and base together. 
 
 The rear slab may be lifted by the tendency of the wall to 
 overturn because of the pressure. In this case w is equal to the 
 weight of a column of earth 12" square, with a height=h, at the 
 back edge of the slab, but is zero at the wall. Using then this 
 value for w, which is different for each 13" strip parallel with the 
 wall, 
 
 for each strip, thus the reinforcement will be spaced at greater 
 intervals nearer the wall and the slab should really be thinner. 
 The thickness, however, is maintained for the benefit of the weight 
 given and to furnish bond for the vertical rods and the rods from 
 the toe. The total load on each parallel strip is wL, and one-half 
 of this at each end is reaction, showing how far the steel must 
 project up into the counterfort for bond. 
 
 The counterfort will have a width at the bottom equal to 
 the base and at the top will run to the wall or inay end in a 
 beam along the top of the wall. Its thickness will depend almost 
 
58 Reinforced Concrete. 
 
 wholly on the thickness required to protect the rods embedded 
 
 in it. It is calculated as a cantilever having a load = PL and 
 
 PLh 
 the bending moment at the bottom is, M = — 7. . With this 
 
 value of M, calculate the steel required and make the counterfort 
 wide enough to take it. This steel will run along the back edge 
 of the counterfort and into the top of the wall, where it must 
 
 PL 
 
 be embedded for bond to take up g ■ At the bottom the 
 
 steel must be bent back into the base for anchorage and be era- 
 
 2 PL 
 bedded so it will stand a pull^ — 5—. 
 
 Usually it will be found that the comparative post of plain 
 and reinforced concrete retaining walls depends so largely upon 
 local costs of materials and labor that, for heights less than six- 
 teen feet the plain wall may be far cheaper. This is owing to 
 the generally wider base of the reinforced wall which calls for 
 more excavation, the cost of form work and of the steel and 
 labor in placing steel, and extra labor involved in pouring thin 
 walls. 
 
 For comparison use for the plain wall the common rule that 
 the breadth of base will be one-third the height. With the grav- 
 ity wall, the strength being in the weight and solidity, a very 
 much cheaper concrete can be used than for a reinforced wall. 
 Comparative estimates should be always made before deciding 
 upon the type of wall, remembering also that with a gravity wall 
 not reinforced, the liability of error in the computations is rela- 
 tively small. 
 
 Restrained Walls. 
 
 Some walls are designed as restrained at the ends, of which 
 an example was given above in designing the slabs between 
 counterforts. Occasionally, however, a wall is designed that is 
 restrained at the top and bottom, as, for example, foundation 
 walls around basements, pressing against the basement floor and 
 'first floor, and tanks having floors and roofs into which to tie 
 the walls. 
 
 In such cases P is found as before. The reaction at the top 
 P 2P 
 
 is —5- and at the bottom is ~3~i thus showing how far the steel 
 
 must run into the slabs, or beams, to which the wall is con- 
 nected, for bond, or the pressure which a basement wall will ex- 
 ert against the floors at its top and bottom. 
 
 If the wall is connected to slabs at top and bottom, the rein- 
 forcement in those slabs must run into the wall far enough for 
 
Retaining Walls. 59 
 
 bond, in addition to the wall reinforcement running into them. 
 The steel, however, that ties the slabs to the wall must be in 
 addition to the steel required in the slabs, as it is sufficiently 
 stressed, by reason of it being reinforcement. Some designers 
 do use the reinforcement ste€l for tying the walls, but when this 
 is done it is dangerous. 
 
 Sometimes instead of a slab at the top, the tank is open 
 and a beam is run along the upper edge, being designed for a 
 
 P 
 uniformly distributed load= -g-. This gives a finish as a cop- 
 ing, the span of the beam being from one end of the tank to the 
 other, or sometimes being designed as a continuous beam with 
 intermediate supports determined by steel rods running to the 
 opposite side, or by counterforts. 
 
 Sometimes the thickness of the tank wall is determined in 
 advance and the reinforcement is horizontal. At intervals, de- 
 termined by the strength of this wall, are run vertical beams, 
 projecting each side of the wall, as pilasters. The strength of 
 the vertical beams being ascertained, the resisting moment of the 
 beam is equated to P for different lengths and at the points thus 
 fixed steel rods will be used to tie the opposite sides of the 
 tank together through these beams. 
 
 In a wall restrained at top and bottom, the maximum stress 
 
 Ph 
 is 0.853h from the top, and, M = - g 
 
 Fox a 13" vertical strip on a wall designed to resist water 
 pressure, 
 
 M = 4h' in inch lbs., when h is in inches. 
 
 The wall will be of uniform thickness from top to bottom, 
 the reinforcement being vertical with the usual horizontal bear- 
 ing steel. 
 
 Circular Tanks. 
 
 For circular tanks the steel resists all the tension and the 
 concrete serves only to protect the steel. The mixture should 
 be fairly rich and well mixed so it will be dense and water tight. 
 All the rods should be bent to circles and ends firmly fastened to- 
 gether. They should be either in the center of the concrete, or 
 not to exceed twice the thickness of the steel from the outer face. 
 
 The pressure, w, on the side is the same as for the pressure 
 against a vertical wall. The tension in the sides, to be taken by 
 
 wD 
 the steel is, T = — ^, in which w represents the unit load, or 
 
60 
 
 Reinforced Concrete. 
 
 nE-INrOKCEMENT 
 
 £k»o- H int 
 
 SO- ■* e ne 
 TO- 9-c 'K 
 
 f fti 
 
 no •* 1 
 
 SB -so ■»■ 
 70 ■ 90 ■^' 
 
 9o 110 - ■«" . 
 B^ttrasn (7-2) »mv utA t-immai 
 
 
 Fig. 9 — Reinforced Concrete Chimney. 
 
Circular Tanks. 61 
 
 pressure per sq. ft., at any definite depth, and D = internal diam- 
 eter in inches. T= total tension on 13" width. 
 
 The area of steel to take care of this tension is found by di- 
 viding the tension by the safe unit stress in the steel. By calcu- 
 lating the tension for each foot in width the closest economy 
 may be obtained in design. 
 
 The least thickness of concrete should be four inches to a 
 depth of about six feet, but for deeper tanks the bottom thickness 
 in inches should be equal to h/3 in feet, and the thickness at 
 a point six feet from the top can be four inches, remaining at that 
 to the top, while the remainder of the wall gradually increases to 
 the maximum thickness at the bottom. 
 
 There should be some vertical steel to help preserve the in- 
 tervals between the horizontal rings, and if the tank is a very 
 high one this vertical steel should be proportioned to resist 
 stresses caused by wind against the tank as a circular hollow 
 cantilever beam. This will now be discussed, as it is also of 
 value in designing chimneys. 
 
 For chimneys the depth of the foundation is from 1/10 to 
 1/6 the height. If the ratio of base to height is small the foun- 
 dation must be spread, and it is often made in the form of a 
 truncated cone or pyramid. When reinforced concrete is not 
 used a common rule is to make the width of the foundation equal 
 to the width of the chimney, or tank, plus one-tenth. The bot- 
 tom of the foundation is one and one-half times that width. 
 When a reinforced concrete base is used the upward reaction on 
 the base is the action of a load on a cantilever beam having a 
 length equal to the distance from the edge of the tank or chim- 
 ney to the edge of the foundation, and pressure per sq. ft. at edge is. 
 
 Vb Xd^ 
 
 W 
 
 The pressure of the wind will be 50 lbs. per sq. ft. on a plane 
 equal in height to the chimney, or tank, and having a width equal 
 to the outside diameter. Through the center of gravity of the 
 structure drop a vertical line and make it equal in length to the 
 weight. Through this point draw the total amount of the wind 
 pressure and obtain the resultant. If it falls outside the middle 
 third of the base then it requires reinforcement. Having the wind 
 pressure the bending moment at the bottom is found and it is re- 
 quired to find the steel to resist it. 
 
63 Reinforced Concrete. 
 
 To find the resisting moment of the steel we have to find the 
 section modulus of a hollow steel cylinder and to find the resist- 
 ing moment of the concrete we have to find the section modulus 
 of a hollow concrete cylinder. The thickness of the concrete in 
 this case, for a high structure, will be found by taking a minimum 
 thickness at the top and maintaining it until a depth is reached 
 where the load is about 200 lbs. per sq. in. The thickness will then 
 be increased from time to time so the pressure, due to the weight 
 of the concrete, will at no time exceed 200 lbs. per sq. in. This will 
 then give the thickness of the shell at the bottom, which is the 
 thickness we will use in the calculations. 
 
 / d*— di*\ 
 The section modulus for a hollow beam is S = 0.09821 — -j — I 
 
 in which d ^= external diameter in inches, and di= internal diameter 
 in inches. 
 
 When M^ bending moment in inch lbs 
 S := section modulus in inches. 
 f^= fibre stress in lbs. per sq. in. 
 
 M M 
 
 M = Sf; S =-p-; ^ = "s"* 
 
 To find the section modulus for the steel reinforcement con- 
 sider it as a thin sheet arranged in a cylindrical form, and, put- 
 ting the two diameters, d and di in inches, find S. Divide the 
 overturning moment in inch lbs. by the fibre stress and get a 
 second value of S. Take the area in sq. ins. of the steel in one 
 circumferential foot of the structure as assumed by the thin 
 sheet, and multiply by the second value of S, obtained by divid- 
 ing the moment by the fibre stress in the steel. Divide the quo- 
 tient by the first value of S, found by the foregoing formula, 
 and the result will be the number of inches of steel (area of 
 vertical rods) required in each foot. 
 
 To find the maximum intensity of compression in the con- 
 crete is the next step. Having already obtained diameters for 
 the concrete, find S by the formula. To get the second value of 
 S we take one-third of the first value of S for the steel and mul- 
 tiply it by n (the ratio of the moduli of elasticity) and add to it 
 this first value of S of concrete. Dividing the bending moment 
 by this second value of S for the concrete we get the pressure 
 per sq. in. on the windward side of the structure. To this must 
 be added the unit weight of the structure, of course, and we thus 
 get the total compression in the concrete at the base on the 
 windward side. If it exceeds 350 lbs. per sq. in. the thickness at 
 the base must be increased. 
 
Footings. 63 
 
 The steel rods are vertical and must extend into the base far 
 enough to have sufficient bond. 
 
 Footings. 
 
 The area of the footing under a wall must, be sufRcient to 
 keep the load within the permissible amount. In the case of a 
 wall the footing must project a certain number of feet on each 
 side so that it will really be like two cantilever beams, each 
 carrying half the load. The width of each beam will be 13 inches 
 and the length will be the quotient found by dividing half the 
 load by the permissible load per square foot on the foundation. 
 
 The shear at the edge of the wall will be equal to the load 
 on the beam at that side and we may assume not more than 300 
 lbs. per sq. in. for direct shear. This will fix a minimum 
 thickness for the slab. The calculation for bending moment 
 will give a thickness and the greater thickness is to be selected. 
 The thickness given by the bending moment, however, will be 
 used to proportion the steel. The steel rods must run clear 
 across from one edge to the other, under the wall, near the bot- 
 tom of the footing slab. They must be of a size that will furnish 
 sufficient area for bond and then the amount of steel for stirrups 
 should be calculated to take care of internal stresses. These 
 stirrups will be close together just under the edges of the wall. 
 (See pages 35, 31 and 36.) 
 
 Footings under columns will have enough square feet in 
 them to spread the load sufficiently and the steel will be propor- 
 tioned on the theory of the column standing on two beams 
 crossing under the column, each equal in length to the width of 
 the slab. There will then be four cantilever beams, each having 
 a width equal to the thickness of the column and a length equal 
 to their projection beyond the column. To help bind the base 
 together, diagonal rods, equal in number to the rods in each of 
 the beams mentioned, will run to the corners. Sometimes rods 
 are placed around the outside as well to connect the ends of 
 the cross rods. Usually steel is placed both ways like a net- 
 work, or expanded metal or wire fabric are used in addition. 
 Investigations must be made for shear and bond, and stirrup 
 reinforcement provided where found necessary. 
 
 In putting down footings it is well to place three or four 
 inches of concrete and lay the steel on this; in the footing put 
 steel plates on which to rest the vertical steel. 
 
CHAPTER V. 
 Design and Cost. 
 
 Do not approach the design of a reinforced concrete structure 
 with the idea that the material is miraculously endowed with won- 
 derful properties and has utterly changed its character because of 
 the reinforcement 
 
 A noted Frenchman, M. Considere, made some experiments 
 on beams by loading them until they broke. He sawed slices from 
 the bottom underneath the reinforcement, and claimed to have 
 discovered that concrete beams, when reinforced, stretched ten 
 times Hi much in the bottom as plain beams, without injury to the 
 concrete. 
 
 So far as an ordinary mortal could see, the concrete had the 
 appearance of ordinary concrete. There was nothing to distinguish 
 it except the fact that the professor said it was different. Strange 
 to say, when separated from the steel, it was exactly as strong in 
 tension and compression as before. 
 
 Professor Tumeaure, of the University of Wisconsin, was 
 one of the unbelievers in this miracle, so made tests of his own. 
 He placed beams in a testing machine with the reinforced side on 
 top. Instead of resting them upon supports and having the load 
 applied as weight, he applied pressure at the bottom, and the sup- 
 ports were on top at the ends. As the pressure was applied, the 
 beams bent upward, and when water was poured on the surface 
 fine dark lines appeared. When the beam was removed from the 
 testing machine and pieces sawed from it for testing, it was dis- 
 covered that when cut between two dark lines there was no ap- 
 parent change in the general properties of the concrete. When a 
 piece, however, included one of the fine dark lines it fell apart, thus 
 proving the line to be a crack. 
 
 This set of experiments showed that the concrete, when rein- 
 forced, was the same old concrete. Instead of having miraculous 
 properties developed by the reinforcement, it was the reinforce- 
 ment that stretched. The concrete simply developed innumerable 
 fine cracks. If the adhesion is good, these cracks are uniformly 
 distributed and are not visible to the eye. In fact, some may 
 require a remarkably good microscope to discover them. 
 
 64 
 
Design and Cost. 65 
 
 A very few men dispute the experiments of Professor Tur- 
 neaure as being not conclusive, but by the majority of engineers 
 they are accepted as establishing the true action of concrete in the 
 tensile side of a reinforced beam. If this is the fact, then it is 
 proven that failure begins in a reinforced concrete beam from the 
 moment the load begins to act. Cracks form just as soon as the 
 load exceeds the tensile strength of the concrete, and these cracks 
 continually enlarge until the beam fails, either by the steel parting 
 or by the concrete crushing at the top, alone or in combination 
 with breaks caused by internal stresses in the concrete. 
 
 Assuming that cracks open in the bottom under the steel, the 
 importance of having the steel protected by plenty of mortar un- 
 derneath is seen. A very small crack will admit moisture and 
 corrosion commences. This is a warning not to attempt to use 
 too small a percentage of reinforcement, nor too small a factor 
 of safety. Deflection must be considered, for when a beam deflects 
 it bends, and when it bends the concrete underneath the steel 
 cracks. 
 
 Strictly speaking, there is no modulus of elasticity for con- 
 crete, for the reason that concrete is not a uniform material. It 
 is no more unif.rm than stone, so far as mere strength is concerned, 
 and every one knows that stone varies in strength in the same 
 specimen. The variations in concrete come from differences in 
 proportioning the mixture and also in mixing the aggregates. This 
 being the case, the terra "factor of safety" is a misnomer. There 
 is no factor of safety with concrete as there is with steel. 
 
 What we know about concrete, that renders it suitable for use 
 in building when combined with steel is : 
 
 That owing to the presence and even distribution of the 
 cement, it is more durable than the best of stone when exposed 
 to the atmosphere; 
 
 That when carefully made, with the aggregates proportioned 
 and manipulated as experience has shown to be best, we know 
 that a stress of 500 pounds per square inch in compression may be 
 used with a reasonable certainty that the ultimate strength of that 
 particular concrete may be five or six times the stress allowed. 
 As steel is a carefully made, homogenous material, such a ratio 
 can be assumed as exact through every portion, and can be termed 
 a factor of safety. With concrete, however, the factor of safety 
 is entirely an assumption which applies to the concrete as a whole. 
 It may be large for some portions and be small for other portions 
 of the mass. 
 
66 Reinforced Concrete. 
 
 That the strength of concrete depends upon the character of 
 the aggregates. Thus cinder concrete is stated to be one-half as 
 strong as stone concrete. Sandstone concrete is not so strong as 
 concrete made of basalt or granite. Limestone concrete is very 
 strong and satisfactory under certain conditions, and not so reliable 
 when conditions are not right. 
 
 That the strength of concrete increases and its resistance to 
 atmospheric influences is greater the older it is, for the cement 
 protects the other aggregates. 
 
 That in setting concrete shrinks, and consequently it grips 
 fast all steel, or anything else of an impervious nature that is 
 enclosed within its mass. This gripping action is entirely physical 
 and not chemical. It is termed adhesion, and this adhesion is 
 said to be impaired by continuous vibratory shocks, and is known 
 to be impaired by continuous submersion in water. This impair- 
 ment may never proceed to the point of destruction of the adhesion, 
 but if high stresses are used in the steel it is well to have the 
 additional safeguard of mechanical bond, obtained by the use of 
 deformed rods and bars. 
 
 On the point of adhesion it is well to remember that there is no 
 special affinity between steel and concrete, any more than there is 
 between oil and water. To test this, place concrete on a smooth 
 steel surface and let it set. When dry, kick it oflf, which can be done 
 easily. Set a steel I beam on edge and plaster the space on one 
 side with concrete, or, better, set a board alongside as a form and 
 pour concrete into the space. When perfectly set, hit the other 
 side of the I beam with a hammer and see the concrete drop away. 
 
 Put a flat steel bar on edge across a shallow box, the one 
 edge resting on the bottom, the other level with the top, thus 
 making a partition. Fill the box with concrete and allow the 
 concrete to set. When dry, remove the sides of the box, and, after 
 the material is thoroughly set, see how slight a blow will cause 
 the concrete to separate from the steel. 
 
 The shrinkage proceeds from the outside toward the interior. 
 The special fact that enables us to use concrete and steel in 
 combination is that each material expands and contracts in almost 
 identical degree under the influence of changes in temperature. 
 If it were not so, then changes in temperature would cause each to 
 move in a different degree, and the adhesion would soon be de- 
 stroyed. 
 
 When it is known that the adhesion is entirely a gripping 
 action, the value of small rods and bars for reinforcement is proven. 
 
Gripping Action of Concrete. 67 
 
 In fact, when discussing adhesion, the values given should be given 
 to half-inch bars. Bars of less diameter will have proportionately 
 greater and those of larger diameter proportionately smaller ad- 
 hesive value. This difference probably varies as the cube root of 
 the diameters, although there is no absolute basis yet for stating 
 the difference to exist in such degree. 
 
 In his own practice the writer has the space between reinforcing 
 bars, or rods, never less than twice the thickness or diameter. 
 Underneath the steel the minimum thickness is twice the thick- 
 ness or diameter of the steel, except when the steel is in the form 
 of wire, when the least covering is half an inch. In slabs liable 
 to be exposed to the action of fire, the minimum thickness is one 
 and one-half inches and for beams two inches. For columns two 
 inches, and for tank walls subjected to constant immersion, two 
 inches. 
 
 The gripping action of concrete should not be too greatly 
 checked, and for this reason round rods are favored by many 
 designers. It requires no argument to show that the wet material 
 is more apt to set well in contact with a round bar than with a 
 square bar. Assuming very low unit stresses in both steel and 
 concrete, the use of plain round bars is entirely defensible for 90 
 per cent of the structures erected in reinforced concrete. The other 
 10 per cent may be in situations such that the designer feels a 
 deformed bar to be necessary. To discuss the deformed bars in 
 the market in this connection would place the writer in an em- 
 barrassing position. He has used practically all, and, as before 
 stated, to get a certain strength requires a certain percentage of 
 reinforcement, regardless of shape. The deformation acts as 
 anchorage, except with the Kahn bar, where it performs a double 
 function, being anchorage as well as web reinforcement. 
 
 A round bar permits the material to flow around and grip it 
 better than will a square bar, yet it does not offer the same surface 
 for adhesion. A square bar twisted gives the adhesive surface, 
 while it makes practically a round bar with corrugations through 
 which the concrete may readily flow. For this reason a square bar 
 twisted is economical, as every square inch of cross section is 
 available for reinforcing purposes, while the twisting gives the 
 mechanical bond. Some men claim the edges cause cracks to start 
 when the concrete is shrinking. Others make this charge against 
 all bars not having rounded edges. The writer believes most of 
 this talk to be purely theoretical, and that any bar in the market 
 is good, provided enough area is used to give the desired strength. 
 
68 Reinforced Concrete. 
 
 When designing a structure, go over the design carefully sev- 
 eral times. If wind strains are to be feared, it is wise to use 
 round bars and have the ends threaded, so that all connections 
 will be made by screwed couplings. Connect columns, walls and 
 girders by bolsters or brackets, reinforced to take care of twist- 
 ing strains liable to be caused by wind or earthquake. See that 
 all connections at corners and at beams, girders and walls are 
 carefully computed and not merely guessed at. 
 
 It is such a common practice to make a continuation of rein- 
 forcement by simply lapping ends past a few inches that a warn- 
 ing must be sounded, although the matter was dealt with fully 
 in Chapter I. Lapped connections greatly increase the stresses 
 in the concrete at those points. Screwed connections are good. 
 In columns the ends of the steel should rest on plates, as already 
 mentioned, and the ends of the bars should be milled. A con- 
 tinuation should be made inside a sleeve, and if high winds are 
 feared, the ends should be connected by screwing. 
 
 Bars and rods should be wired together at all crossing points 
 topreserve the intervals. Black stove wire is generally used. This 
 is known as No. 18, and should be black, as galvanized wire is not 
 so good for adhesion as black wire. No. 16 wire is favored by 
 many engineers as being stronger than No. 18, and a number of men 
 require the use of No. 14, which is excessive and is more con- 
 suming of time to place and twist. For all-round use No. 16 is 
 best, but requires the use of pliers, whereas No. 18 can be twisted 
 by hand. The way pliers disappear on a job is an argument in 
 favor of the lighter wire. 
 
 Never use painted or coated wire for reinforcement. Galvan- 
 ized wire or steel rods should not be used except when provided 
 with mechanical bond. The galvanized fabrics in the market, of 
 course, have the mechanical bond created by the fastening of the 
 crossed wires. A slight rusting is not harmful. The writer made 
 some experiments several years ago by enclosing slightly rusted 
 steel in wet concrete. After a year the blocks were broken and 
 the steel was found without rust. The surrounding concrete was 
 found to be slightly discolored. When the rust is in the form of 
 scales, it should first be removed. 
 
 Many buildings are weakened by holes cut at random through 
 slabs and walls. Common sense should be a guide here. It is 
 well to remember that when a slab is made the strength is as- 
 sumed to be that of the slab with the reinforcement complete and 
 tied from support to support. If the steel is cut, it is equivalent 
 
Aitention to Details. 69 
 
 to destroying one support, and the action of the slab on each side 
 of the hole is a cantilever action, but as the reinforcement is in the 
 bottom, the steel is of no assistance. This is an argument in favor 
 of double reinforcement, in addition to the argument that may 
 be presented from the fire protection standpoint. 
 
 Holes, therefore, should be located while the structure is 
 being planned and the reinforcement arranged accordingly. The 
 reinforcement should generally be in the form of two double rein- 
 forced beams each way, one on each side of the hole, or the slab 
 can be designed as a cantilever beam on the four sides of the hole, 
 the remainder of the slab resting on and being carried by the can- 
 tilevers. 
 
 As the fibre stresses in wood and in reinforced concrete differ 
 slightly, the sizes of beams and thickness of floors in a slow- 
 burning wood construction building and a reinforced concrete 
 building are near a size. The reinforced concrete, however, will 
 be more massive than the wood. 
 
 For this reason some men become panic-stricken when they 
 see the building going up, and are apt to make some members 
 smaller or lean toward the danger point in designing because "the 
 thing looks too big." A reinforced concrete structure is unlovely 
 from a structural standpoint. In the preceding chapter an example 
 was given of how column sizes compared in different materials. 
 A comparison in beams would be even more striking. 
 
 The eye accustomed to wooden beams as the biggest beams 
 required to give certain strength does not like the appearance of 
 reinforced concrete beams, and, as many of them show the grain 
 of the wooden forms and the gray color is much like that of 
 seasoned, weather-stained wood, a reinforced concrete building 
 sometimes looks like a big, clumsy wooden structure. Perhaps a 
 style of architecture peculiar to reinforced concrete may arise 
 and have a beauty of its own so it will not offend. 
 
 Most of the data obtainable about cost of reinforced con- 
 crete work is misleading. It has generally been given out by 
 men who simply were on the work at intervals in the capacity 
 of supervising engineers and who did not know anything of the 
 thousand and one exasperating delays incident to the work and 
 who knew nothing of the dense stupidity of the laborers often 
 employed. Sometimes the data has been given on the authority 
 of some company controlling a splendid organization and all of 
 the employes were skilled men working to standards and on 
 only one class of work. 
 
70 Reinforced Concrete. 
 
 Look where one will it is almost impossible to secure actual 
 cost data of reinforced concrete work. Most of the work is done 
 by men who look aghast at the figures when a job is completed 
 and are ashamed to publish the costs. They seem so much 
 higher than current published data that they think it a reflec- 
 tion upon themselves and wish to try another job before giving 
 out figures. 
 
 Their vnpTk is comparatively small and no jobs last long 
 enough to enable them to perfect an organization. Neither do 
 jobs follow quickly enough to enable them to retain men who 
 have been broken in as foremen. This class of work, not done 
 by regularly organized companies engaged in training skilled 
 foremen, carpenters and laborers on one job for employment on 
 another, is the real criterion for gauging the cost of work. 
 
 Much is written about the low cost of reinforced concrete 
 work because of the fact that unskilled labor is largely employed. 
 A visit to a good job will show that the unskilled laborers are 
 in the minority. For every laborer who pushes a wheelbarrow 
 and shovels concrete materials there will be employed a carpen- 
 ter or skilled man. 
 
 While unskilled labor can be, and is largely, employed, 
 there is a vast difference between the unskilled man who is born 
 and reared in America, who can understand English, ■ and the 
 unskilled foreigner who has to be addressed in the sign lan- 
 guage. Unskilled laborers are divided into two classes, the 
 intelligent and the unintelligent. The intelligent ones are the 
 kind to employ in reinforced concrete work, for the various 
 operations are rapidly assuming the importance of trades. After 
 a few months' work the active intelligent laborer has a right to 
 be classed among skilled workers. Intelligent unskilled laborers 
 are divided into rapid and slow, drunkards and nondrinking 
 men, men who care and men who take no interest in anything 
 except the whistle and the pay check. The success of the con- 
 tractor can be gauged by his luck in picking up good men. 
 
 Carpenters have been mentioned. The men who apply for 
 jobs as carpenters on this class of work are divided into wood 
 butchers, bluffers, saw and hammer men, half trained appren- 
 tices, sidewalk and fence builders, cabinet makers, inside fin- 
 ishers, millwrights, bridge and trestle builders and good plain 
 ordinary old-fashioned carpenters. The best carpenters are men 
 who have really learned their trade and who have worked some 
 years in small towns. Such men generally take to the work as 
 
Kind of Men. 71 
 
 ducks to water. All the others above enumerated have to be 
 taught. Some never learn. Form and scaffold work for rein- 
 forced concrete jobs call for a distinct class of woodworkers 
 and if they can be obtained, time and money are saved. 
 
 The average job of reinforced concrete is done by men 
 who commence the work without a skilled worker to assist. 
 They must advertise for men and try to select from the appli- 
 cants such men as they think may develop. At first they take 
 all who come and begin to weed and select after a start has 
 been made. For weeks they conduct a kindergarten and just 
 as a good working force is developed may be discharged and a 
 hustler comes who takes the trained crew and makes excellent 
 progress. 
 
 It must be remembered that skilled men in concrete work 
 are hard to find, although the streets are full of men making 
 great claims of proficiency. The really skilled men are in the 
 permanent employ of the men who trained them or are in 
 well-organized unions and averse to leaving the larger cities. 
 ' It is well to be very careful in taking men who claim to have 
 had experience. So many contractors (and engineers and ar- 
 chitects as well) are criminally careless in placing reinforcement 
 and looking carefully after details that a large number of ex- 
 perienced men are abroad who can not be trusted to do any- 
 thing well on such a job except to "hustle 'er tru'." 
 
 An ordinary reinforced concrete job has carpenters and 
 their helpers, making, setting and removing forms; men plac- 
 ing, altering and removing scaffolds and changing running 
 plank; a steel yard where steel is assorted according to sizes 
 and lengths and men engaged in bending and cutting steel; 
 men placing steel in position before the forms are placed; 
 men cleaning concrete and steel ahead of the forms and men 
 putting in concrete. The unskilled, low browed unintelligent 
 laborer has really no place except between the handles of a 
 wheelbarrow and it takes many of a superior kind to keep the 
 work so fixed that a few of the stupid ones can be kept moving. 
 What is wanted on such work are handy men possessing con- 
 siderable intelligence who will do anything, even to pushing a 
 wheelbarrow if laborers run short. 
 
 There is nothing in low cost labor. Really cheap labor is 
 well paid intelligent labor. When a man is efficient he must be 
 paid correspondingly well for there is a constant demand for 
 such men. The man at the head can not be always running a 
 
12 Reinforced Concrete. 
 
 school. It is argued that there is nothing great in placing steel 
 or placing concrete. Neither is there anything great in making 
 a table, but the table made by the amateur does not look like 
 the table of the craftsman. Reinforced concrete work requires 
 intelligent men, but generally several hundred men go through 
 a job before fifteen good ones are secured and twice that number 
 before one decent foreman can be obtained. 
 
 All concrete work is not alike, hence the unreliability of 
 most of the published cost data as a basis for estimates. Some 
 structures are made completely of concrete with thin walls. 
 Some have thick walls. In some the reinforcement is vertical 
 and in some it is horizontal. In some all material is wheeled 
 in barrows to the mixer and in barrows from the mixer to the 
 forms. In some places automatic elevators, super-hoppers and 
 grab buckets and a multitude of labor-saving devices are em- 
 ployed. 
 
 Some buildings have merely columns and girders and beams 
 of reinforced concrete with reinforced concrete floors and roofs 
 and the exterior walls of brick with interior walls of tile. 
 There are good systems in use for flooring, involving a com- 
 bination of reinforced concrete beams and tile. Some systems 
 use frames of I beams instead of concrete beams. Some build- 
 ings have been erected having all the structural framework of 
 reinforced concrete cast in shops near the work and erected 
 like steel after the concrete has hardened thoroughly. 
 
 Remember that in erecting a reinforced concrete structure 
 with solid walls two complete wooden structures are erected 
 and taken down. Nearly all the lumber is afterward useless 
 unless the forms are made in interchangeable panels and a new 
 job is at hand so they can be used immediately. Scaffolds for 
 ordinary buildings do not require to be so strong as scaffolds 
 for concrete work, so the costs for scaffolding and running 
 plank are high. 
 
 The greatest improvement in the future must be in the line 
 of reduced cost for forms and simplicity of forming. Many build- 
 ers are ashamed to tell what their forms cost. Each time 
 they bid higher on work they blame the increased prices to 
 the increased labor and material prices. 
 
 The cost of concrete can readily be figured. The cost of 
 getting materials to the mixer and of mixing them can easily be 
 figured. The cost of getting concrete from the mixer to the 
 walls depends upon the length of run and convenience of 
 
Cost of the Worh. 73 
 
 arrangement of the running plank. In a well arranged, well 
 managed job, $1.00 per yard should take the stone, sand and 
 cement from the stock pile and shed through the mixer and into 
 the wall. 
 
 The forms can not be figured on a yardage basis, except in 
 the case of a company engaged in certain kinds of work of a 
 standard nature. After several jobs a per yard cost for scaf- 
 fold and forms can be obtained. It will, however, not be a safe 
 guide for other work. To estimate the form work, the style 
 of forms to be used must first be decided upon. Then figure it 
 on a per thousand foot basis. With cheap carpenters it will 
 cost from $8.00 to $20.00 per thousand to make forms. With 
 good, higher paid carpenters it will cost from $5.00 to $7.00 
 per thousand to make forms. It will cost about $6.00 per thou- 
 sand to place them and about the same to take them down and 
 clean them for use again. 
 
 There is a big waste of lumber in form work and to reduce 
 this waste only carpenters or the best of the workmen should 
 take down old forms. If the wheelbarrow man is put at the 
 work he will ruin them. The cost of cleaning up and the general 
 expense on a job will be nearly $2.00 per cubic yard of concrete. 
 To estimate work exactly, careful detailed drawings should be made 
 of the forms. They should be designed as carefully as the rest of 
 the building. 
 
 As some approximate rules are always wanted, the writer can 
 offer the following as fitting very closely actual conditions on a 
 job having experienced, well-trained foremen, and among the labor- 
 ers a good proportion of men who have worked on similar jobs. 
 . This rule applies to ordinary building construction, for the cost 
 per yard for sewers, culverts, retaining walls, etc., is much less 
 than for buildings. 
 
 Get exact costs of sand, stone and cement delivered on the job 
 and reduce the costs to cubic yards of concrete. To this add $5.00 
 per cu. yd. for steel. This will be one-half = 3/6, the cost of the 
 concrete per cubic yard in place. The labor on concrete and steel 
 will be 1/6 and the material and labor on forms will be 2/6. For 
 average buildings containing about 2,000 cu. yds. of concrete this 
 will be about true. Add 2 per cent to cost for each 100 cu. yds. 
 less than 2,000. Complicated work will increase the cost greatly. 
 To this must be added cost, or rent, of plant, and the profit of the 
 contractor. 
 
'J'4: Reinforced Concrete. 
 
 If the materials are obtained at exceptionally low prices, of 
 course the above rule does not hold. It holds for average pay in 
 the locality in which the work is done, for, left without a union 
 organizer to run up pay, laborers in different sections are generally 
 paid what they earn. It is always best to pay ruling rates of wages 
 everywhere and not raise the pay, except to good men. 
 
 Sometimes men are frightened when estimating on reinforced 
 concrete work because the costs run so high. While the cost of 
 the building seems to be all right, the cost per yard of concrete 
 seems fearfully high. A common sense rule is to consider that a 
 reinforced concrete building does not cost less than a brick build- 
 ing equally as well constructed. The cost of a brick building be- 
 ing, say, 15 cents per cubic foot measured from the basement floor 
 to the average height of the roof, with the length and breadth 
 taken as over all dimensions, make first an estimate of the rein- 
 forced concrete building in that way. Then go through the plans 
 carefully, taking out the exact yardage. Dividing the total esti- 
 mated cubic foot cost by the yards will give a cost per yard close 
 enough for a check on the careful detailed computations that will 
 later be made by the careful estimator. 
 
 The writer would like to see more men making money at this 
 class of work and knows of many who have lost money through 
 wrong estimates, or through rushing into work with ideas fixed. 
 Left to himself, the experienced man will generally get out a good 
 plan and a close estimate of cost. There is so much irresponsible 
 matter floating around in papers about reinforced concrete that 
 few designers are given a free hand in the design and none of them 
 are allowed to make a correct estimate. The employer will always 
 declare the estimate "Too high !" and give instances of work he cas- 
 ually read about, or some forgotten individual told him about. 
 As a result few buildings in this material are erected at the esti- 
 mated cost. When the owner has his work done on a percentage 
 basis it falls on him, but if some contractor new at the business 
 takes the contract on poor information he is ruined. 
 
 Good work costs money, and work of a certain grade differs 
 little in cost, no matter what the material. If reinforced concrete 
 is absolutely fireproof, earthquake-proof, everlasting and never 
 needs repairs, it is reasonable to suppose that for such perfection a 
 price must be paid. 
 
CHAPTER VI. 
 Forms. 
 
 The ideally conducted job is where the men in charge of the 
 steel hanging ^et out of the way of the form placers so the forms 
 may be filled. The steel should be placed, forms erected, concrete 
 poured, additional steel placed, forms re-erected and concrete 
 poured again, all without a hitch and without the mixer having to 
 stop. As a matter of fact it is almost an impossibility to get the 
 average sized job so well organized. On very large jobs and on 
 concrete work where there is no reinforcement and where the walls 
 are comparatively thick it must be done and is done right along. 
 
 The chief reason for delay is in the setting or erection of forms 
 and the intelligence and experience of the men charged with the 
 work of form erection and changing. On comparatively thick walls 
 the time it takes to do the form work is seldom sharply drawn to 
 one's attention for it takes so long to fill such walls that the form 
 workers keep ahead of the concrete gang without trouble. It 
 takes as long, however, to erect forms for a thin wall as for a 
 heavy wall and sometimes considerably longer, for thin walls are 
 generally cut up with pilasters or panels. The pouring of the 
 concrete, however, is almost as rapidly done in a thin wall as in a 
 thick one and as there is so much less concrete to pour the con- 
 crete gang soon overtakes the form gang. 
 
 Because of this the cost of forms per cubic yard of thin walls 
 is much higher than for thick walls. It requires more lumber and 
 while it takes little more labor the labor cost is higher in propor- 
 tion, the thinner the wall. When very thin walls are used the cost 
 is very high until the men become experienced and work like 
 machinery. A great many inexperienced men think the cost of 
 lumber the largest item but when lumber costs less than twenty-five 
 dollars per thousand and inexperienced men alone can be had it 
 will be found least expensive to sheet right along up and pay little 
 attention to trying to use the material several times. The proper 
 way to estimate forms is by square foot of surface and not per 
 cubic yard of concrete. 
 
 Dressed and matched lumber is good for use once or twice 
 
76 
 
 Reinforced Concrete. 
 
 3ECr/0N TM/1CUC/i BSAM 
 
 
 SlCT.Of TftPOOGff Gl»S£l>S 
 
 Fig. 10 — FoKM Plans (General Fireproofing Company). 
 
Men and Materials. 77 
 
 and is not such a good material for re-use as plain edged lum- 
 ber. Therefore it is better for thick walls than for thin ones, 
 as the cost per yard for forms, when figured that way, is not 
 high. While the pressure is as great in thin as in thick walls, 
 considering concrete as a semi-fluid, thinner lumber can be 
 used to advantage in thin walls, for it is easily handled and can 
 be tied through the wall readily when necessary. 
 
 When experienced men can be had and lumber goes over the 
 twenty-five dollar mark per thousand then it will pay to use some 
 form of panelling or try the "board by board" method. Whether 
 panels, or single boards, or the studding and sheathing method is 
 considered best, it pays to use the boards and pieces in as near 
 standard lengths as possible for they might be worth something 
 after using. If this item is not looked after, all the lumber will be 
 fit only for the scrap heap. 
 
 The writer believes the best carpenters to use are experienced 
 men who have thoroughly learned their trade and the boss carpenter 
 should be an elderly man accustomed to handling men. A few first- 
 class men can do much more work than cheaper laborers. It is 
 customary to hear men say that common laborers are good enough 
 for carpenters on a concrete job. The writer begs to diflfer with 
 them and say that if for nothing else than the habit a trained 
 man has of staying with a job, the experienced, well-trained car- 
 penter is best. The ordinary unskilled laborer is nomadic and as 
 soon as he thinks he has learned something new he leaves the job 
 to sell his services elsewhere. The writer prefers good carpenters as 
 gang bosses and under each good carpenter put three to five handy 
 unskilled laborers as apprentices and to do the roughing work. 
 This is especially true if any calculation is made on using the 
 material more than once. 
 
 The unskilled or incompetent man will use many more nails 
 than the trained man. This means expense for nails, more time 
 putting up the forms, more time taking them down and the likeli- 
 hood of ruining a great deal of the lumber in trying to take it 
 down and re-use it. 
 
 Fig. 11 represents the regulation form built up of boards nailed 
 to upright studding and braced. The planks may be of any thick- 
 ness according to the fancy of the carpenter or of the contractor. 
 The studs may be of any convenient size and the braces and posts 
 against which they rest will be arranged according to the ideas of 
 the men in charge. For this style of forming each man's fancy 
 is every man's guide. Common custom, however, seems to be 
 
78 
 
 Reinforced Concrete. 
 
 coming around to one inch boards against two by four studs set 
 two feet apart. The braces, however, may vary in size from two 
 by" four inches to six by six inches with little attention paid to the 
 manner of securing the ends. 
 
 Fig. 11 — Simple Braced Form. 
 
 In the illustration the braces are bevelled where they rest 
 against the studs and are supposed to be fastened by "toenailing." 
 This is very poor as the full strength of the brace cannot be secured. 
 In spite of everything the nails will move a little and sometimes 
 the end of the brace will slide up the stud and pull the nails entirely 
 out. 
 
 The upper end of the braces should be cut square and butt 
 against a block nailed to the stud. Instead of the push helping to 
 draw the nail it will be at right angles and the nail cannot give 
 without shearing. The length of the block and the number of nails 
 to use depends upon the push. These things are seldom figured 
 out. 
 
 The trust the ordinary wood butcher places in nails is pathetic, 
 especially after a bad spill caused by a form giving way. Plenty of 
 nails will not always do the work which should be done by plenty 
 of brain. In a most excellent booklet distributed by a well known 
 cement company is an illustration of forms braced by having the 
 braces nailed to the sides of the studs instead of butting against 
 them. Instead of the lower end of the braces resting against posts 
 or on sills they rest simoly upon the ground. The writer has 
 seen many braces thus placed and he has ceased to wonder at it 
 being done but does wonder at the mental processes wherefrom 
 
Bracing. 79 
 
 such ridiculous results proceed. Common sense seems to be at a 
 discount. 
 
 It is common to hear of braces giving way and yet in every 
 case investigated by the author he has found it to be due to 
 improper securing of the braces, except when a rain may have 
 softened the ground into which the supports were driven. If the 
 ground is exceedingly firm it is sometimes sufBcient to drive a 
 post as shown in Fig. 11. Whether or not the ground is firm the 
 best and safest way to secure the lower ends of braces is shown in 
 Fig. 12. Here a line of posts is driven and a two by six or heavier 
 plank laid against them. Back of this line is driven a second line 
 of posts with a brace from the top of the first line resting against 
 their feet. The braces from the forms rest against the plank and 
 it is wise to have two hard wood wedges at the end to take up 
 whatever slight movement may develop. 
 
 Fig. 12 — Method of Securing Forms. 
 
 While on this subject the writer wishes to say he does not 
 consider bracing to be good practice when forms are used on both 
 sides of walls and can be connected by wires or bolts readily. 
 Bracing is only excusable when all the securing can only be done 
 properly from the outside and from one side. Braced forms give 
 way more readily than bolted forms, take more time to put up, use 
 up more lumber and all round are least satisfactory of all methods 
 used. Bolts are best and wires next with braces in the third place 
 as regards merit. 
 
 When braced forms give way it is generally through ignorance 
 of proper methods of securing the braces. The times, however, 
 when the foundations give way are so numerous that one cannot 
 be absolutely certain a properly braced form will not burst. When 
 
80 
 
 Reinforced Concrete. 
 
 bolted or wired forms give way it is only when the bolts or wire 
 are ignorantly placed. 
 
 Wire is very expensive for it requires a great deal of material 
 and a tremendous amount of time. When the forms are taken 
 down the wire projects and the ends must be cut off. They leave 
 rust spots, disfiguring to the wall. A green man will run wire 
 through both forms and twist the ends to form a loop. On one 
 side he will put a soft wood wedge under the wire thinking that 
 when the form gives he can drive it down' and tighten the wires. 
 Vain hope. If he can drive the wedge at all, which is something 
 
 i^'^.Xo'''^ vO^- 
 
 >*- ^^<'^\y 
 
 ,v 
 
 :^^- 
 
 Chain of /oops for fhick wa//s. 
 
 Fig. 13 — Method of Wiring Forms. 
 
 to consider, he will either shear it off so it does not tighten the 
 wire, or he will only succeed in driving it so the twisting will come 
 undone and his wedge makes things worse. To use wire properly 
 
Tieing the Forms. 81 
 
 it should be passed through both forms and twisted inside the forms 
 by means of a bolt or stick used as shown in Fig. 13. To keep the 
 forms the right distance apart a piece of wood should be placed 
 beside the wire and left there until the concrete reaches that 
 height, when it is fished out. It happens many times that the fishing 
 is forgotten and the ends of the stick may be seen when the form 
 is removed. Or it may happen that in fishing for it the stick is 
 knocked down into the concrete, there to remain, a weak spot 
 although concealed from view. This happens so often that some 
 men use pieces of concrete instead of wood for spacers and make 
 no attempt to remove them. 
 
 Bolts passing through the wall have none of the objections 
 mherent with wire. A well greased bolt can be removed easily 
 from the wall after the concrete has set. Trouble always ensues 
 when the greasing is not properly performed. Sometimes, however, 
 the bolts pass through paper tubes or are wrapped in several 
 thicknesses of greased paper in addition to being greased. Some 
 men use hollow tubes of concrete through which pass the bolts, 
 the tubes serving also as spacers. Wooden spacers used with bolts 
 can be removed as soon as the bolts are screwed up. With wire 
 the tendency, because of the twisting, is to draw up and for this 
 reason it is best to leave the spacer in place until the pressure of 
 the concrete relieves it. Wire will, give a^ little and this give 
 cannot be taken up. A bolt, however, is secured by a nut on the 
 end bearing against a washer. AVhen the nut has been screwed 
 down far enough the spacer can be removed. If the form does get 
 a little slack it will move out under the pressure of the concrete 
 until a bearing is obtained against the washer. If the forms give 
 while the concrete is being poured the nuts can be tightened. 
 
 While wires leave rust spots, bolts leave holes. These holes 
 are generally filled with a neat cement paste pushed in with a small 
 stick. If the wall is to be watertight the paste has mixed with it 
 some waterproofing material. The grease with which the bolts 
 were treated, or the paper tube left in the wall will not allow a 
 perfect seal so it is almost impossible to secure a water tight wall 
 when bolts alone are used. 
 
 While holes on the surface may be filled and thus sightliness 
 be preserved, the hole through the body of the wall is an objection. 
 Several arrangements have been made to overcome this by using 
 short bolts connected to wire loops in the body of the wall. The 
 bolts being greased are withdrawn when the forms are removed, 
 leaving the wire loops and thus sealing the wall. While many such 
 
82 
 
 Reinforced Concrete. 
 
 devices are in use the writer for years has used ordinary thumb 
 nuts connected hy wire loops as shown in Fig. 13. A machine for 
 making the loops is illustrated in the chapter following. When 
 one loop is not long enough several may be connected in chain 
 form as shown. The small surface holes left by the bolts may be 
 plugged with neat waterproofed cement, although the greasing is 
 an objection, for it interferes with the bond. 
 
 Unless the faces of the forms are smooth and clean the surfaces 
 will be bad. How to overcome roughness of surface on concrete,' 
 due to forms, will be taken up in the next chapter. Tables to 
 determine proper sizes and spacing for braces, wires and bolts will 
 also be given there. 
 
 The form illustrated in Fig. 11 is usually made by erecting 
 studding and nailing the boards to the inside when the walls are 
 
 Fig. 14 — Forms of Matched Lumber. 
 
Dressed and Matched Lumber. 83 
 
 thick. If the walls are thin the boards are nailed to the studding 
 while lying down and then the whole side is raised, precisely like 
 sheathing the side of a wooden house when erected close to 
 another house. A departure is made by erecting the studding and 
 putting in one board at a time. The lower board is set against 
 the studding and filled with concrete when a board is placed on 
 top and the work continues in this manner until a height of eight 
 or ten feet is reached. No nailing is required except for an occa- 
 sional four or sixpenny nail to merely keep the boards from fall- 
 ing down. 
 
 By starting with one board at a time a foot of concrete per 
 day can be assured on a very large building and it should be pos- 
 sible to keep the mixer going all the time. When a height of about 
 eight feet is reached a plate is placed on the top of the studs and 
 another set started. At the bottom they are wired through the 
 wall and when the concrete has gone up a foot or two on the 
 second set the lower set of studding can be removed and the boards, 
 not being nailed, fall out. 
 
 Fig. 14 shows a method where the boards are one and one-quar- 
 ter to one and one-half inches thick, dressed and matched. Be- 
 cause of the tongue and groove no nails whatever are required 
 and joints may be broken an3rwhere. A two by six sill is laid to 
 start and this is set with an instrument and secured so the line 
 can be maintained. Studs are set two feet apart and carefully 
 plumbed so the wall will be truly vertical. Such forms are readily 
 kept to line and if they get out of line can be quickly pulled back. 
 It is important that lines be kept stretched while concrete is poured 
 so that bulging may be remedied before the concrete sets. 
 
 The boards are set in one at a time and when a height of 
 about eight feet is reached a new set is started. The longitudinal 
 stringers shown with bolt heads are two to four feet apart and 
 the upright studs are lightly fastened to them with small nails 
 merely to preserve the intervals. The bolts run through the walls 
 independently of the upright studs and through holes in the boards. 
 This method is rapid and satisfactory for walls not very thin. 
 
 With the systems of forming just described it is usual to have 
 braces against the lower set and have wire ties or bolts in the 
 higher sets. An objection to braces not already mentioned is that 
 they interfere with getting close to the walls to pour unless the 
 pouring is done from a considerable height. 
 
 Fig. 15 shows a panel method developed by Mr. Ransome and 
 very popular for thin wall work. The uprights are made of two 
 
84 
 
 Reinforced Concrete. 
 
 pieces of two by four, separated at each end by blocks, thus form- 
 ing slotted braces. To start a wall, spacers the thickness of the' 
 wall at the bottom are set on the ground level and an upright 
 board set at each end. On the outside of the boards are placed 
 sets of the upright slotted frames bolted through at top and bot- 
 tom and with a spacer at the top equal in length to the thickness 
 of the wall plus the thickness of the two boards. 
 
 Fig. 15 — Panel Method. 
 
 The lower bolt is slid down the slot until it rests on top of 
 the boards and remains there. The form is built up one board at 
 a time until the upper bolt is reached, when it is slid down to 
 the top of the nearest board below it. The building up is con- 
 tinued until the top of the slotted frames is reached, when the 
 lower bolt is withdrawn, the slotted frames moved up to a height 
 as great as may be obtained when the upper bolt reaches the bot- 
 tom of the slot. The lower bolt is now passed through the upper 
 part of the slot, with a new spacer there to preserve the interval, 
 and work is recommenced. When the slotted frame is moved up 
 the boards held by it are released and can be used again after 
 cleaning. 
 
other Methods. 85 
 
 Sometimes the slotted frames are moved up oftener than 
 here indicated. Sometimes, also, instead of putting in one board 
 at a time, panels are made of three to five narrow boards, fastened 
 together by cleats on the back. The slotted frames are seldom 
 more than five feet long. Panel forms of this kind have many 
 points of weakness about them on account of the joints, unless 
 care is taken to have the slotted frames lapping over the ends or 
 to have two frames close together and near the ends of their re- 
 spective panels. The amount of lumber required is small and 
 thin boards may be used. To prevent undue deflection a great 
 many frames must be used with thin boards and this means con- 
 siderable labor. Each panel being, to a certain extent, independent 
 of the others makes it extremely difficult to keep true lines with 
 ordinary care. Men become expert in using them after awhile 
 and as they require less material and skilled workmanship than 
 any other style of forms their use is increasing. With such forms, 
 however, it is found as with others that every endeavor to save 
 material results in an increase of labor. The contractor has, there- 
 fore, to strike a balance so that by saving lumber he can use such 
 a system of forms that the lowest paid labor can be employed to 
 advantage. 
 
 Fig. 16 shows another panel form greatly used. Som.etimes a 
 bolt is put through the bottom with a spacer to preserve the in- 
 terval and a cleat nailed across the top. The panels are made 
 about three feet wide and can be of any length. When filled to 
 the top the concrete is allowed to set. The form is then raised so 
 the bolt rests on top of the old concrete and another cleat is 
 nailed across the top. The bottom of the form is on each side of 
 the concrete already poured which thus acts as a spacer. 
 
 It often happens with concrete work that work cannot pro- 
 ceed with such regularity that the forms can be moved one at 
 a time, for some concrete sets slowly. Two sets of forms will 
 then be used, which permits of one set being left in place while 
 concrete is poured in the set above. It is most satisfactory to 
 have three sets. The bolts have large washers about two by five 
 inches on the ends. As men seem to be very slow and experience 
 much trouble in putting the bolts through the bottom of the forms 
 it is convenient to put them through the top with a spacing cleat 
 nailed across above them. This cleat is of course knocked off 
 when the panel is filled. When the panel above is placed the 
 washer is turned so the edge of the frame is caught and thus 
 one bolt serves two forms. The forms are generally made of one- 
 
86 
 
 Reinforced Concrete. 
 
 inch boards with frames of two by four stuff. The panels are 
 generally made with the upright two by fours two feet apart. 
 
 The last mentioned panel forms are more expensive than the 
 slotted frame forms, but walls made with them can be kept to 
 line as well as walls made with studding set up. All the skilled 
 labor is employed in making the panels and ordinary men can 
 set up and remove them. The writer, however, has had a job 
 lately where the setting of these forms seemed beyond the ability 
 of ordinary labor and the men who were on the pay roll as car- 
 penters killed so much time on the form work that it was heart- 
 breaking. So, after all, the costliness of any particular kind de- 
 pends very much upon the class of labor employed and the spirit 
 it is possible to infuse in the men. 
 
 Fig. 16 — Another Panel Form. 
 
 In illustrations on pages 87 and 89 are shown several 
 patented methods of placing forms by means of steel clips and 
 fastenings that permit of the use of one board at a time and no 
 nails or uprights are required. 
 
 The writer has a decided preference for the panelled forms 
 shown in Fig. 16 for use in ordinary thin walls of reinforced con- 
 
Special Forms. 87 
 
 Crete. For heavier walls and especially for walls not reinforced 
 the system shown in Fig. 14 is his favorite. This expression, how- 
 ever, is to be modified by the statement already made referring to 
 cost of lumber and class of labor. 
 
 For long walls, not much broken by projections or recesses 
 and where appearance is not placed high above most other con- 
 siderations the forms shown in Fig. 11 can be used to advantage 
 with very cheap labor and poor carpenters and the forms shown in 
 Fig. 15 can be used with cheaper labor and no carpenters. The 
 slotted frames can be made at a planing mill or carpenter shop. 
 
 Fig. 17 — Sullivan's Plank Holder. 
 
 For thick walls the cost of forms does not cut much figure 
 and can be kept low, per cubic yard of concrete, so that any of 
 the kinds mentioned can be used. The studding and boarded 
 forms made in place will generally be found cheapest and most 
 advantageous in every way. 
 
 When walls are cut up at close intervals by pilasters and 
 counterforts or buttresses, and especially when such walls are bat- 
 tered, the forms shown in Fig. 16 will be the cheapest and most 
 satisfactory to use, for they may be of standard lengths and the 
 projections can be formed by special pieces. Fig. 18 shows special 
 pieces for corners, permitting the use of standard length forms. 
 
 No office draughtsman is competent to design any reinforced 
 
88 
 
 Reinforced Concrete. 
 
 01 
 
 ^ 
 
 1 
 1 
 
 ; 
 
 f 
 
 
 «* t 
 
 J 
 
 "+ 
 
 --:*■ .T 
 
 i^ 
 
 K 
 
 1 
 
 /h 
 
 C\J 
 
 
 \i 
 
 
 — <%* 
 
 cvj- 
 
 / 
 
 
 S5 
 
 i 
 
 
 E LBV fin ON. 
 
 Elevht/on. 
 
 Plan. 
 Outs/de corner. 
 
 (m\ 
 
 
 1 
 1 
 
 1 , 
 
 -^ 
 
 
 m/ 
 
 y 
 
 1 
 
 ' / 1 
 
 CoPvftiGH-r igo7 By thk ClMeHT Kra 
 
 Inside corner. 
 
 Fig. 18 — Corner Forms for Battered Walls. 
 
Special Forms-. 
 
 89 
 
 concrete structure out of the ordinary unless he has had actual 
 construction experience. Forms should be as carefully designed as 
 the rest of the details of actual construction. They should be in- 
 tended to strike a happy medium between economy in material 
 and economy in labor. Forms designed with a view to only one 
 or the other will not do. It is well to design forms with a view 
 to re-use if possible several times. 
 
 Fig. 19 — Parrel's Plank Holder. 
 
 For retaining walls all the foregoing applies, for the actual 
 construction work is the same for all walls. For sewers and 
 tanks, panels of curved shape made on the principle of the panels 
 shown in Fig. 16 must be used. For arches, adaptations of the 
 forms in Fig. 11 and Fig. 16 are used, for all the material must 
 remain in place until centers are struck. 
 
 Fig. 20 — Dietriches Plank Holder. 
 
 Draughtsmen occasionally send out designs for pier and column 
 footings showing a pyramidal form. Avoid forms of such shape 
 for they will invariably float and it is next to impossible to fasten 
 
90 
 
 Reinforced' Concrete. 
 
 Fig. 21 — Three Standard Methods for Securing Column Forms. 
 
 them down. Owing to the difficulty of tamping next the face 
 they will be rough in spite of all work done to assure a nice face. 
 The writer uses for footings, frames six to eight inches high. 
 One frame is put down and filled. While the concrete is still 
 somewhat soft the next frame is put in place and filled, so pro- 
 ceeding until the height of the footing is attained. The frames 
 are then removed and if the sloping shape is insisted upon the 
 steps are filled with stiff mortar trowelled to a nice finish. Other- 
 wise the steps' remain. 
 
 For columns it is customary to make a form for each side 
 anJ place around them frames of two by fours at intervals de- 
 
Columns and Beams. 
 
 91 
 
 cided upon by the pressure to be resisted. Bolts are run through 
 the ends of the pieces, or they have blocks and wedges. Fig. 21 
 illustrates column forms in general use. 
 
 Beams and girders are best poured in forms that are braced 
 on the side like trusses. Then posts can support these forms and 
 framing under the floor panels will rest on the lower chords of 
 the beam and girder forms. It will not be necessary to carry sup- 
 ports to the floor underneath to carry the floor or roof forms 
 above. This means a tremendous saving in lumber for bracing. 
 It also means a saving in labor for removing the bracing. The 
 writer knows contractors of great experience, who look closely 
 into savings, who give the lumber and braces used under floors 
 to any one who will remove them, if the material has to be passed 
 out of narrow or small openings. When this material is cheaper 
 than the labor to remove it some thought taken in saving the 
 amount means a great deal. 
 
 Fig. 22 — Beam and Floor Forms, Illustrating Method of Trussing and 
 Bracing to Save Posts Under Floors. 
 
 Simplicity in design should always be aimed at to save cost 
 of forms. It is surprising how high the cost can be when the 
 work is at all complicated. When walls are so thick that spouts 
 can be arranged to deliver the concrete inside the reinforcement 
 without disturbing it then high forms can be used. Sometimes as 
 much as twenty feet can be poured and vertical joints instead of 
 horizontal be obtained. In such walls braces may be preferable 
 to wires or bolts. 
 
92 Reinforced Concrete. 
 
 When walls, however, are thin and the falling concrete cannot 
 miss the steel, it is risky, to say the least, to pour more than 
 three or four feet at the most, for the falling concrete may dis- 
 arrange the steel. If high forms are used the pouring should not 
 stop until the form is filled, even if a night crew is put on. If 
 this is not attended to a great deal of concrete will adhere to the 
 steel and to the sides of the forms and get dry. When pouring 
 is resumed this dry stuff will be knocked off and falling into the 
 fresh concrete will make a bad wall. Some of it will still cling 
 to the steel and prevent a good adhesion of the newer concrete to 
 the reinforcement. 
 
 In erecting forms, building lines must be carefully preserved 
 by means of strings stretched between points previously accurately 
 set by surveyor's instruments. Do not put any confidence in the 
 ability of the average carpenter to carry walls vertically with a 
 level. The plumbing of all the lines should be done by a few 
 careful men and the rank and iile in the form gang should be 
 required to keep the lines fixed. Before pouring concrete all 
 forms should be instrumentally tested for position and horizontal 
 and vertical alignment. Warped forms should be rejected. During 
 the pouring of the concrete there should be men at hand whose 
 duty it shall be to notice when forms give way and rectify the 
 trouble at once. 
 
 The finish of the forms depends upon the degree of finish 
 called for in the specifications. If matched boards are not used 
 it is a good plan to chamfer one edge of the boards so that the 
 joint will close tightly when the wood is wet. If cracks open more 
 than an eighth of an inch the forms should be rebuilt. 
 
 After all it is a question of price of lumber and of cost and 
 efficiency of labor. When lumber is high in price small panels and 
 shallow pourings will be the rule. When lumber is cheap deeper 
 pourings will be had and higher panels. The man who ties him- 
 self to one standard is weak. Interchangeability is good and an 
 endeavor should be made to standardize the work as much as pos- 
 sible. Each structure must be a special study. 
 
 The construction of a reinforced concrete structure is vastly 
 different from that of a plain concrete structure. Reinforced con- 
 crete calls for a richer concrete than plain concrete work, as 
 strength must be obtained. In many situations, however, especially 
 in tank walls, mass and weight often accomplish as much as 
 strength obtained by reinforcement. Where weight will do, a very 
 cheap concrete can be used in heavy walls at a less cost than with 
 thin reinforced walls. 
 
CHAPTER Vn. 
 
 The Conduct of Work. 
 
 The cement used for reinforced concrete work must be a Port- 
 land cement. It should be tested in order to insure uniformity. 
 It should be used directly from the original packages as received 
 from the factory. Batches should be of a size that do not call 
 for parts of bags or barrels as no exact measurement can then 
 be made. If the specifications do not state the bulk of cement 
 to be used the packed barrel or packed bag must be used as the 
 unit and the size of the unit must be determined by the engineer. 
 Common custom now makes four bags equal to one barrel 
 of cement, and in bag batches one bag is considered equal to 
 one cubic foot. This is about a mean between a packed foot 
 and a moderately loosened foot of cement, and in the absence 
 of a strict definition in the specifications is about all that can 
 be insisted on. In this connection the writer received from 
 Mr. Robert B. Hansell, C. E., of Baltimore, the following table. 
 The sizes of cement barrels showed such variations that many 
 tables appeared before the bags came into common use, based on 
 barrels containing 3.5, 3.8 and 4.0 cubic feet. This table shows 
 the number of cubic feet of each aggregate based on one cubic 
 foot per bag. 
 
 TABLE X. 
 
 Cu. ft per 
 barrel = 
 
 3.5 
 
 3.8 
 
 4.0 
 
 Proportions 
 
 Bag 
 
 Sand 
 cu. ft. 
 
 Stone 
 cu. ft. 
 
 Bag 
 
 Sand 
 cu. ft. 
 
 Stone 
 cu. ft. 
 
 Bag 
 
 Sand 
 ft. 
 
 Stone 
 cu. ft. 
 
 1:3 : 5 
 1 :2^:5 
 1:2 :4 
 
 1 
 1 
 1 
 
 10.5 
 8.7 
 7.0 
 
 17.5 
 
 17.5 
 14.0 
 
 1 
 1 
 
 1 
 
 11.4 
 9.5 
 7.6 
 
 19.0 
 19,0 
 15.2 
 
 1 
 
 1 
 1 
 
 12 
 
 10 
 
 8 
 
 20 
 20 
 16 
 
 Two mixtures at present seem to be in general use for rein- 
 forced concrete work. For work requiring concrete of consid- 
 erable density when the percentage of steel is high a 1 :3 :4 mix- 
 ture is favored. Taking stone and sand as usually received, esti- 
 mates for purchasing material can be made on the basis of six 
 
94 Reinforced Concrete. 
 
 bags of cement, 0.4 cubic yards of sand and 0.8 cubic yards of 
 stone for each cubic yard of concrete. For the greater amount of 
 work done a 1 :3 :5 mixture is used. This will call for 4.5 bags 
 of cement, half a yard of sand and 0.8 cubic yard of stone per 
 cubic yard of concrete. Rules for proportioning concrete materials 
 abound, but after all none are exact, for an exact determination of 
 quantities depends upon the percentage of voids in the stone and 
 sand. A rule credited to Mr. Fuller, used by many contractors, is 
 to add the proportions together and divide 11 by the sum. For 
 example the sum of 1 :2 :4 is 7. Eleven divided by 7 gives 1.58, 
 the number of barrels of cement per cubic yard. The barrel of 
 cement in this rule contains 3.8 cubic feet. Multiplying the two 
 numbers together gives 1.58x3.8^6 bags of cement. For sand, 
 6x3=:12 cubic feet, or 0.45 cubic yard, and for stone 6x4=:24 cubic 
 feet, or 0.9 cubic yard. This rule, it is understood, was obtained 
 by taking the number of barrels of cement known to have been 
 used on very large works, together with the number of cubic 
 yards of sand and stone, and ascertaining the number of cubic 
 yards of concrete made. It is necessarily very general, but allows 
 liberally for waste and is safe enough for ordinary jobs. For close 
 competition the voids should be ascertained and careful calcula- 
 tions made. 
 
 All concrete for reinforced work should be mixed by machine. 
 This rule is imperative. If hand mixing is required in an emer- 
 gency the inspector should pay the closest possible attention to it. 
 It should be done carefully and with due deliberatoin. All hurry 
 that smacks of haste should be avoided. The ordinary methods 
 good enough for mass work cannot be tolerated. The sand and 
 cement should first be mixed until the color is uniform and no 
 streaks show. A minimum number of turns should be six after 
 spreading the cement first carefully over the sand. Then the 
 water should be added gently through a rose nozzle. A minimum 
 number of turns during this operation is four and one set of turn- 
 ings should not be considered sufficient to mix the sand and cement 
 and at the same time apply the water. When the mixing is done 
 the paste should be somewhat thick. The stone must be previously 
 wetted and when the paste is ready thrown into it and the whole 
 mass quickly turned until all the stone is covered with cement 
 paste. Water will be added until the concrete is of the right 
 degree of plasticity. For this final mixing with stone a minimum 
 number of turns will be four. 
 
 No matter what the directions of the makers no batch of con- 
 
Mixing cmd Measuring. 95 
 
 Crete should be given less than twenty turns in the mixer. If a 
 mixer of the continuous delivery type is used the length of the 
 trough should permit a number of turns equivalent to twenty turns 
 per batch or should be so arranged that the mass can be held in 
 place until it receives such turning. In continuous feed machines 
 the cement is apt to clog so the cement feed should be closely 
 looked after. Several tests should be made each day to see that 
 the cement delivery is constant. 
 
 The writer wishes to state as a result of his own experience 
 that it pays to equip a mixer with charging apparatus to reduce 
 the number of men wheeling stone and sand. With a batch mixer 
 it is well to have a super hopper containing one batch in reserve. 
 In addition there should be an elevating hopper which can be 
 loaded on the ground level by men and do away with inclines. 
 While a batch is being mixed there is one in reserve in the super 
 hopper and another being placed in the charging hopper. It will 
 reduce the number of men required by two-thirds in charging alone. 
 Charging hoppers generally have a steel diaphragm, on one side of 
 which the sand is placed and on the other the stone. The measur- 
 ing is thus to a certain extent automatic. When the hopper is 
 discharged into the super hopper a fair mix is obtained. The 
 cement can be added while the charge is in the super hopper and 
 when the materials run into the mixing drum another fair mix is 
 obtained. This tends to lessen the time required for actual mixing. 
 
 When materials are delivered by wheelbarrows the incline 
 should be easy. When starting the work place the mixer as low 
 as possible and send the material down through a chute to the 
 bottom of the work. As the walls rise the chute can be shortened 
 until the work reaches the height of the mixer. Then the mixer 
 can be raised until the incline is as steep as men can work on. 
 After that a hoisting elevator of some sort should be used to 
 take the concrete to the elevation where wanted. A concrete hoist 
 is a good investment if the concrete has to be elevated more than 
 ten feet. 
 
 Measuring stone and sand by wheelbarrows is simply guessing 
 and should not be tolerated. The illustration shows a form of box 
 used by the writer. The length and widths given fit the average 
 concrete wheelbarrow. The height of course depends upon the 
 size of load wanted. The boxes are bottomless and are placed 
 in the wheelbarrow and filled flush to the top. It is easy to lift 
 them by the handles and the material drops out. By using such 
 boxes exactness and uniformity can be attained in proportioning 
 
96 
 
 Reinforced Concrete. 
 
 the ingredients. The ordinary wheelbarrow is said to hold three 
 cubic feet. This means three cubic feet, water measure, when the 
 wheelbarrow is held in such a position that the water exactly 
 touches all the edges. If left to themselves the men will not load 
 much more than two feet and seldom load with as much as two 
 feet. When driven hard they will carry much more and the lack 
 of uniformity is bad. 
 
 Fig. 23 — Measuring Box. 
 
 Concrete must be wet enough to flow readily around and 
 cover the steel, but must not be thin and watery. The ideal mix- 
 ture is one that will not slip too readily from the wheelbarrow or 
 cart and is best described by the word "pasty.'' It should be as- 
 sisted out by a shovel. 
 
 Thin concrete is discharged more rapidly from the mixer and 
 is consequently favored. The water, however, during the setting 
 and seasoning process leaves the concrete porous if too thin when 
 poured. Speed in operating a mixer depends largely upon the 
 amount of water pressure available and it pays to insure a good 
 pressure even if an elevated tank must be put up when the pres- 
 sure in the city mains is low. Measuring the water is best done by 
 an experienced man with good judgment. It simply requires 
 training and such a man is better than the best automatic device 
 ever invented, except of course for very large mixers. After a 
 rain the sand and stone contain so much water that the amount 
 used must vary with each batch. In dry summer weather more 
 water must be used than in wet, cool weather. 
 
Placing the Concrete. 97 
 
 The importance of using plenty of water in dry weather 
 should be impressed upon workmen. This water should not 
 all be added in the mixer. In hot weather the stone and sand 
 pile should be wet, precisely as brick masons wet brick, and for 
 the same reason. The stone may be of a kind that will absorb 
 water rapidly and interfere with the proper setting of the cement 
 next to it. 
 
 The concrete must be worked to the face of the forms to in- 
 sure a good surface and must be well worked into all interstices 
 to insure a good job. The methods used must be those calculated 
 to best secure the desired, results. Heavy tamping is not neces- 
 sary with pasty concrete and is apt to displace the forms. What 
 is wanted is something that will insure every piece of stone being 
 thoroughly imbedded in the mass and also see that all the steel 
 is surrounded and that none is displaced. All air must be released 
 so far as that is possible. Churning with rods and pipes is good. 
 A piece of one by three wood is as good as anything when the 
 lower end is sharpened and fixed like a butter paddle. 
 
 The concrete must be worked back from the forms and many 
 tools are used by different men — wooden paddles as above, 
 potato forks and manure forks with curve taken out. There 
 are several special concrete spades on the market also. The writer 
 uses wood and also slicers and spades made with handles seven 
 feet long of three-quarter-inch pipe, having on the end a piece of 
 sheet steel one-eighth of an inch thick, ten inches long and with a 
 width at the lower end of four, six and eight inches. That is, the 
 three widths are used on the job. The narrower ones are very 
 handy for cleaning forms. Churning with rods is so good that a 
 number of men should, be kept at it. 
 
 In pouring columns or filling forms exceeding three feet in 
 height the directions given in the chapter on columns should be 
 carefully followed. 
 
 To assist in obtaining a dense, impervious concrete for floors 
 and roofs a wooden float about ten or twelve inches wide and not 
 less than four feet long should be used as a tamper, two men con- 
 tinually tamping with same to consolidate the mass and help draw 
 the cement to the surface. There has lately been placed on the 
 market a tamper for floor surfaces consisting of flat bars ar- 
 ranged like a grating. These bars cut down into the concrete and 
 do the work the stirring rods do in wall forms. The usual top 
 coat and finish can be applied within the customary time. 
 
 Particular care must be exercised to see that steel is not dis- 
 
98 Reinforced Concrete. 
 
 placed when pouring concrete. Occasional tapping or pounding on 
 the forms as they are filled helps the flow of the concrete around 
 the steel and prevents to some extent the lodging of stones in 
 such positions that a rod or bar may be permanently displaced. 
 
 Unless prevented by accident, beams and girders should be 
 poured with the floors, regardless of design. If designed as T 
 sections this rule is imperative and no accident can be an excuse 
 for not doing it. Beams and girders of T section are designed 
 for economy. The economy is usually all on paper. The design of 
 T beams has been discussed in Chapter I. There are times 
 often when it is an absolute impossibility to pour the beams and 
 slab at one operation and complete the work. To stop properly 
 would require that a stop be placed in the center of the beam, 
 running its entire length and going clear to the bottom. This 
 makes in effect two narrow beams. Practically this is an impos- 
 sibility owing to the presence of the reinforcement, so the work 
 is stopped somewhere on the beam with a small ledge left on 
 which to rest the beginning of slab work the next day. With 
 the class of labor usually to be had one cannot always stop where 
 theoretically he should, so there is always more or less of a ques- 
 tion about the job. There are days when it makes no difference 
 but the days occur so frequently when there is a difference, that 
 one is safest in so designing that if considered advisable all the 
 beams and girders may first be poured and the floor later. 
 
 The steel must be correctly placed and all the steel must go 
 in. This is imperative. The work is designed with the steel cal- 
 culated to occupy a certain definite position. To the extent that a 
 bar or rod deviates from its proper position to that extent the 
 work is defective. Wherever rods or bars cross they should be 
 wired together securely. No. 18 wire is the best. The writer 
 uses it cut into lengths of about eight inches and generally has 
 the men use two of such pieces at each intersection. This has 
 already been mentioned. Several parties have written to the writer 
 saying it was not necessary to be so finicky and that the wiring 
 was too expensive! The only reply possible to such critics is 
 that the structure must be erected as designed and it is not possi- 
 ble to so erect it unless the steel is actually occupying the position 
 intended. The writer has seen contractors placing steel in a hurry 
 ahead of a concreting gang. He has seen it displaced and very 
 irregular and confesses he does not like it. He has seen floors 
 with steel all in, according to the superintendent, that called for 
 twenty per cent more bars after they were regularly spaced and 
 
Placing the Steel. 99 
 
 wired. Wiring is expensive, else experienced men would not use 
 ready fabricated materials at the high prices charged for them. 
 These fabrics sell readily because they do not cost much to place 
 and when placed it is a great comfort to know that every strand 
 is where the designer wanted it. 
 
 Lastly it must be taken into consideration that the height from 
 which concrete can be poured depends to a great extent upon the 
 security with which the steel is fastened together. So it must be 
 wired to get it to the place it belongs and to keep it there during 
 construction. 
 
 It is not diifitult to place steel in walls and keep it the right 
 distance from the face. With flat slabs however it is different. 
 Some provision must be made to insure a flow of concrete under 
 the bars. Some contractors have men ahead of the wheelbarrow 
 gang hastily prying up the mat to allow the mortar to flow under. 
 Others use small pieces of steel under the bars to hold them up, 
 which are consequently imbedded and show on the underside. 
 Others use small blocks of concrete broken from thin slabs made 
 for the purpose. Some use regular concrete supports made for the 
 rods used and others use a recently patented chair of thin steel 
 which acts also as a clip and saves the expense of wiring. The 
 writer has used them all and also uses a method which is about 
 as satisfactory as any. He places lines of two by fours about 
 four or five feet apart over the floor and suspends the reinforcing 
 mat from them by wires. The supports for the timbers serve also 
 as supports for running plank. Thin mortar is first poured to a 
 depth of about an inch when the wires are cut and the steel drops 
 into the mortar. The timbers and their supports are removed and 
 the concrete rushed in on running plank laid on the steel. 
 
 Opinions and practice diflfer on the subject of the thin 
 mortar coat placed on the floor, into which the steel is allowed 
 to drop. It costs less and is quicker work when concrete is 
 poured first along one side of the floor and the concrete after 
 that is poured on the concrete so that the thin mortar flows 
 away from it and under the steel. This makes it unnecessary 
 to first mix batches of mortar, with the attendant annoyance 
 and delay and going over the floor twice. The only objection 
 to the method of pouring on the advancing edge and letting 
 the mortar flow ahead under the steel is that the steel may not 
 always drop as far as it should, so that some may be held 
 nearer the neutral axis than is right. With an experienced crew 
 and careful boss who does not rattle the men by hurrying them, 
 
100 
 
 Reinforced Concrete. 
 
 any method is good, and this method of dispensing with the 
 first coat of thin mortar is excellent. The floor forms should be 
 soaked with water before pouring concrete. 
 
 Steel placed in beams and girders should be suspended in 
 some way until mortar can t)e placed under and around it. In 
 fact no harm is done if the beam is filled half way to the neutral 
 axis in order to set and retain the steel in place. Care must be 
 taken, however, to insure a good joint when the pouring is com- 
 pleted. If the beam is one that will show, such a proceeding is not 
 possible for the line between the two pourings will be well defined. 
 
 Care must be taken that forms are secure, either by wiring, 
 bolting or bracing. 
 
 The writer has computed some tables for his own use con- 
 sidering that concrete will exert a pressure equal to a fluid weighing 
 eighty pounds per cubic foot. 
 
 The first table shows the pressure per square foot at different 
 depths and the pressure on a strip one foot wide for the heights 
 indicated. The second table gives the spacing vertically for wires 
 and bolts and a comparison is afforded between wires of different 
 gauges and bolts of different diameters. This gives the user an 
 opportunity to take whatever the market can give. The. horizontal 
 distances are twenty-four inches, the vertical spacing alone varying. 
 For example if a form six feet high is poured it will require 
 twenty-five ties of No. 18 wire with intervals as shown, or ten 
 wires of No. 14, or only three of No. 9. The wires to be doubled, 
 as shown in drawing, and twisted. 
 
 TABLE XI. 
 
 
 PRESSURE OF FRESH " 
 
 SOUPY" CONCRETE 
 
 
 i5 
 
 
 H 
 
 
 ^11 
 
 :i 
 
 ■s 
 
 
 li 
 
 3 
 t 
 
 
 
 .5 
 t 
 
 
 
 .3 : 
 t 
 
 g.S| 
 11^ 
 
 £0. 
 
 Q 
 
 Ii.>r4 
 
 Phih 
 
 Q 
 
 0.>M 
 
 Pk*H 
 
 Q 
 
 (i<>rt 
 
 £rH 
 
 1 
 
 40 
 
 80 
 
 9: 
 
 3,240 
 
 720 
 
 17 
 
 11.560 
 
 1,360 
 
 2. 
 
 160 
 
 160 
 
 10 
 
 4,000 
 
 800 
 
 18 
 
 12,960 
 
 1,440 
 
 3 
 
 360 
 
 240 
 
 11 
 
 4,840 
 
 880 
 
 19 
 
 14,440 
 
 1,520 
 
 4 
 
 640 
 
 320 
 
 12 
 
 5,760 
 
 960 
 
 20 
 
 16,000 
 
 .1,600 
 
 5 
 
 1,0.00 
 
 400 
 
 13 
 
 6,760 
 
 1,040 
 
 21 
 
 17,640 
 
 1,680 
 
 6 
 
 1,440 
 
 480 
 
 14 
 
 7,840 
 
 1,120 
 
 22 , 
 
 19,360 
 
 1,760 
 
 7 
 
 1,960 
 
 560 
 
 15 
 
 9,000 
 
 1,200 
 
 23 , 
 
 , 21,160 
 
 1,840 
 
 8 
 
 2,560 
 
 640 
 
 16, . 
 
 14,240 
 
 1,280 
 
 24 , 
 
 ' 23,044 
 
 1,920 
 
Wire and Bolts. 
 
 101 
 
 TABLE XII. 
 
 WIRE AND BOLT TABLE FOR CONCRETE: 
 
 Showing vertical intervals, measuring from the top, to se* 
 cure forms. Horizontal spacing, two feet. Wires doubled. 
 
 
 SIZES or BOLTS. 
 
 CADGE OF WtlB. 
 
 
 
 H' 
 
 JS" 
 
 H' 
 
 54" 
 
 S 
 
 S 
 
 10 
 
 12 
 
 M 
 
 10 
 
 u 
 
 ftin. 
 
 ft.in. 
 
 ft.in. 
 
 ft.in. 
 
 ft.in. 
 
 itla. 
 
 ft.in. 
 
 ft.in. 
 
 ftin. 
 
 ftin. 
 
 ft.hi. 
 
 8 6 
 12 6 
 15 
 17 6 
 10 6 
 
 e 6 
 
 9 6 
 
 12 
 
 14 
 
 16 
 
 6 
 
 7 6 
 
 
 10 6 
 
 n a 
 
 3 6 
 
 5 
 
 6 
 
 7 
 
 8 
 
 3 6 
 
 5 6 
 
 6 6 
 
 7 6 
 '8 .6 
 
 a 6 
 
 5 
 
 6 P 
 
 7 P 
 
 8 
 
 3 p 
 1 P 
 6 
 
 6 
 
 7 P 
 
 2 P 
 .3 
 
 4 .0 
 
 5 P 
 5 6 
 
 2 
 2 8 
 8 4 
 4 
 4 4 
 
 1 
 S 
 
 2 8 
 
 3 
 
 3 i . 
 
 
 21 6 
 23 3 
 21 e 
 
 • • > • 
 
 17 6 
 
 18 8 
 1910 
 21 
 23 6 
 
 13 
 
 14 
 
 14 9 
 
 15 6 
 •16 3 
 
 8 6 
 
 9 
 9 6 
 
 10 
 .10 6 
 
 9 6 
 
 10 3 
 
 11 
 
 11 9 
 
 12 6 
 
 9 P 
 9 6 • 
 
 10 
 IP 6 
 
 11 P 
 
 8 
 J 6 
 
 9 
 9 6 
 
 10 P 
 
 6 P 
 
 6 6 
 
 7 
 
 7 6 
 
 8 
 
 4 8 
 
 6 
 6 4 
 6 8 
 6 
 
 3 S 
 
 4 
 '4 3 
 
 4 8 
 4 9 
 
 210 
 
 ^» • • • 
 
 y.'.'.'. 
 
 • t • • 
 
 23 
 
 24 
 
 25 
 
 17 
 
 17 9 
 
 18 6 
 
 19 8 
 
 20 
 
 11 
 
 11 6 
 
 12 
 
 12 6 
 
 13 Q 
 
 13 
 
 13 '6 
 
 14 
 
 14 6 
 
 15 
 
 11 6 
 
 .12 
 
 12 6 
 
 13 
 13 6 
 
 10 6 
 
 11 P 
 
 11 6 
 
 12 
 12 6 
 
 8 4 
 
 8 6 
 
 9 
 9 4. 
 9 8 
 
 6 4 
 
 a 8. 
 
 ^7 
 
 7 8 
 7 8 
 
 6 
 
 5 8 
 
 6 6 
 
 6 8 
 610 
 
 8 11 
 
 •■•• 
 
 .... 
 
 2.0 8 
 81 4 
 22 
 
 22 6 
 
 23 p 
 
 13 6 
 
 14 
 14 5 
 14 10 
 1? «• 
 
 15 6 
 
 16 
 
 16 6 
 
 17 
 17 4 
 
 14 
 
 14 6 
 
 15 
 Jl5 6 
 
 16 '0 
 
 13 
 13 4 
 
 13 8. 
 
 14 P 
 14 i 
 
 10 
 
 10 4 
 IP 8 
 
 11 
 11 4 
 
 ■7 9 
 8 
 8 3 
 8 6 
 8 8 
 
 6 
 
 6 a 
 
 6 4 
 
 e 6 
 
 6 8 
 
 4 10 
 4 11 
 
 1 ? 
 
 • • ■ t 
 
 
 23 6 
 
 24 
 24 6 
 23 
 
 15 8 
 
 16 
 16 4 
 
 16 8 
 
 17 p 
 
 17 8 
 
 18 P 
 18 4 
 
 18 8 
 
 19 
 
 15 4 
 
 16 8 
 
 17 
 17 i 
 17 S 
 
 14 8 
 
 15 P 
 15 4 
 15 8 
 .16 
 
 11 8 
 
 12 .0 
 12 3 
 12 6 
 12 9 
 
 8 IP 
 
 la" 
 
 9 6. 
 9 8 
 
 «10 
 7 
 7 4 
 7 7 
 1 
 
 610 
 611 
 
 .... 
 
 .... 
 
 .... 
 
 17 4 
 
 17-8 
 
 19, 4 
 19 8 
 
 18 
 
 .... 
 
 13 
 
 910 
 10 P 
 
 711 
 8 
 
 9 
 
 Wt.pe 
 
 r Foot of Rods, lbs. • 
 
 Fee 
 
 t per Found. 
 
 
 
 l.ff43 
 
 .668 |..376- .167 
 
 14.29 1 17.05(20.27 |' 
 
 33.69 58.58 | 
 
 95.98 |l 
 
 66.2P 
 
 The third table gives the total load in pounds for columns, 
 struts or braces having lengths varying by single feet. If the 
 brace is placed at an angle of forty-five degrees the length will 
 be 1.41 times the height from the ground to the top of the brace. 
 For convenience in mentally estimating the length it is called 1.5 
 times the height. From the first table the pressure at any point 
 can be ascertained and thus the load to be carried by the brace. 
 Looking in the third table for braces of the required length the 
 load can be found on the same line and at the top of the column 
 in which this load is found will be found the size of brace re- 
 quired. This table is also useful for putting supporting posts and 
 studdmg under floor forms. The loads are for ordinary white 
 
103 
 
 Reinforced Concrete. 
 
 TABLE XIII. 
 
 SAFE LOADS FOR POSTS AND BRACES (Commoa Pine). 
 
 
 
 
 
 Sizes in Inches. 
 
 
 Lengths 
 
 2x4 
 
 2x0 
 
 2x8 
 
 8x4 
 
 4x4 
 
 4x» 
 
 <xt 1 6x8 1 8x8 
 
 in Feet 
 
 Load in pounds. 
 
 1 
 
 
 
 
 
 
 
 
 
 
 2 
 S. 
 
 4 
 6 
 
 4,800 
 4,136 
 8,648 
 8,860 
 
 7.200 
 S,904 
 6,472 
 6,040 
 
 9,600 
 8,278 
 7,296 
 6,720 
 
 7,200 
 6,048 
 6,760 
 
 o',6o6 
 
 8,160 
 
 u.'rn 
 
 12,240 
 
 • • • • 
 
 • • • • 
 
 • •• • 
 
 • •• • 
 
 • •• • 
 
 6. 
 7. 
 8 
 9 
 10 
 
 8,072 
 2,784 
 2,490 
 
 2,208 
 1,920 
 
 4,608 
 4.170 
 8,744 
 3,312 
 
 2,880 
 
 6,144 
 6,668 
 4,992 
 4,416 
 8,840 
 
 6,472 
 6,184 
 4,896 
 4,608 
 4,320 
 
 7,872 
 7,684 
 7,296 
 7,008 
 6,720 
 
 11,808 
 11,376 
 10,944 
 10,618 
 10,080 
 
 81,000 
 18,676 
 18,144 
 17.712 
 17,280 
 
 28,800 
 84,768 
 84,198 
 88,616 
 83,040 
 
 • •• • 
 
 • •• • 
 
 88,400 
 88,280 
 
 11 
 18 
 IS 
 U 
 U, 
 
 1,639 
 
 1,344 
 
 1,066 
 
 768 
 
 480 
 
 2,448 
 2,016 
 1,684 
 1,162 
 720 
 
 8,264 
 2,688 
 2,U2 
 1,636 
 960 
 
 4,032 
 ?,744 
 8,466 
 8,168 
 2,880 
 
 6,438 
 6,144 
 6,866 
 6,668 
 6,880 
 
 9,648 
 9,81« 
 8,784 
 8,868 
 7,980 
 
 16,848 
 16,416 
 16,984 
 16,963 
 16,180 
 
 22,464 
 21,683 
 81,312 
 80,736 
 20,160 
 
 82,768 
 82,266 
 81,744 
 31,231 
 30,720 
 
 IS 
 
 ir 
 
 18 
 19 
 20 
 
 192 
 
 288 
 
 • t • 
 
 884 
 
 2,692 
 2,304 
 2,016 
 1,728 
 1,440 
 
 4,992 
 4,704 
 4,416 
 4,188 
 3,840 
 
 7,488 
 7,056 
 6,624 
 6,198 
 6,760 
 
 14,688 
 14,266 
 13,884 
 13,392 
 18,960 
 
 19,684 
 19,008 
 18,432 
 17,866 
 17,280 
 
 30,208 
 29,696 
 29,184 
 28,672 
 28,160 
 
 SI 
 23 
 23 
 24 
 26 
 
 • • • • 
 
 • ■ ■ • 
 
 :::: 
 
 1,168 
 864 
 676 
 288 
 
 3,638 
 3,264 
 2,976 
 2,6S8 
 2,400 
 
 6,328 
 4,896 
 4,464 
 4,032 
 3,600 
 
 12,628 
 12,096 
 11,664 
 11,232 
 10,800 
 
 16,704 
 16,128 
 16,662 
 14,976 
 14,400 
 
 27,648 
 27,180 
 26,624 
 26,118 
 26,600 
 
 20, 
 27 
 28. 
 
 :.••: 
 
 
 • • . • 
 
 :::: 
 
 2,112 
 1,824 
 1,636 
 
 3,168 
 2,736 
 2,304 
 
 10,368 
 9,936 
 9,604 
 
 13,824 
 13,248 
 12,672 
 
 86.088 
 84,676 
 (4,064 
 
 TABLE XIV. 
 
 THICKNESS OF HORIZONTAL BOARDS FOR FORMS. 
 VERTICAL STUDDING, 2x4 INCHES. 
 
 Thickness 
 
 of 
 
 Boards. 
 
 inches. 
 
 Studding Intervals. 
 18« 1 18* 1 24* 
 
 . It is assumed all boards tre 
 a in. less thickness than here 
 given. 
 
 Studding is assumed to be suf- 
 ficiently braced or tiedt 
 
 As heights of form increase 
 use thicker boards at bottom or 
 set studding closer. 
 
 Height of Forms — Feet 
 
 1 
 
 iS'* 
 
 81 
 28 
 89 
 
 S 
 6^ 
 
 toy. 
 
 6^ 
 18 
 
spikes cmd Nails. 
 
 103 
 
 pine or spruce. For yellow pine (southern) the loads may be 
 thirty per cent greater and for white oak twenty per cent. 
 
 The following table shows the spans that may be used for 
 boards of different thickness. This is assuming that studding is 
 used vertically and the boards are nailed or held in some way 
 against them horizontally, the uprights being secured by wires, 
 bolts or braces. 
 
 The following tables containing the strength of beams one 
 inch thick and giving sizes of nails and spikes and weights of 
 nut and bolt heads are from the Carnegie Pocket Book and will 
 be useful in ordering material for forms. 
 
 TABLE XV. 
 SPIKES AND NAILS. 
 
 Standard Steel Wire Nails 
 
 Steel 
 
 Wire Spikes 
 
 Connioii Iron 
 Nails 
 
 .1 
 
 tl 
 
 Common 
 
 Finishing 
 
 
 
 do 
 
 s 
 
 t" 
 
 !l 
 
 
 Diam. 
 
 No. 
 
 Diam 
 
 No. 
 
 10 
 
 M*^ 
 
 
 Ins. 
 
 terlb. 
 
 Ins. 
 
 per lb. 
 
 •^i-» 
 
 ao, 
 
 a<^ 
 
 Sd 
 
 1 
 
 .0524 
 
 1060 
 
 .0453 
 
 1658 
 
 3 
 
 .1620 
 
 41 
 
 2d 
 
 1 
 
 800 
 
 3d 
 
 iH 
 
 .0688 
 
 640 
 
 .0508 
 
 913 
 
 8VS 
 
 .1810 
 
 30 
 
 Sd 
 
 J^ 
 
 400 
 
 4d 
 
 ,0720 
 
 380 
 
 .0508 
 
 761 
 
 4 
 
 .2043 
 
 23 
 
 4d 
 
 800 
 
 8d 
 
 m 
 
 .0764 
 
 275 
 
 .0671 
 
 600 
 
 *'A 
 
 .2294 
 
 17 
 
 6d 
 
 11^ 
 
 200 
 
 «d 
 
 a 
 
 .0808 
 
 210 
 
 .0641 
 
 350 
 
 ■6 
 
 .2576 
 
 13 
 
 6d 
 
 2 
 
 160 
 
 7d 
 
 iVi 
 
 .0858 
 
 160 
 
 .0641 
 
 31S 
 
 t>yi 
 
 .2893 
 
 11 
 
 7d 
 
 ig 
 
 130 
 
 8d 
 
 sy> 
 
 .0935 
 
 115 
 
 .0720 
 
 214 
 
 « 
 
 .2893 
 
 10 
 
 8d 
 
 86 
 
 9d 
 
 254 
 
 .0963 
 
 »3 
 
 .0720 
 
 195 
 
 6V< 
 
 .2249 
 
 7« 
 
 »d 
 
 iVi 
 
 76 
 
 lOd 
 
 3 
 
 .1032 
 
 77 
 
 .0808 
 
 137 
 
 7 
 
 .2249 
 
 7 
 
 lOd 
 
 8 
 
 go 
 
 12d 
 
 3 'A 
 
 .1144 
 
 60 
 
 .0808 
 
 127 
 
 8 
 
 .3648 
 
 6 
 
 12d 
 
 iVi 
 
 60 
 
 l«d 
 
 ZVi 
 
 .1285 
 
 48 
 
 .0907 
 
 90 
 
 9 
 
 .3648 
 
 454 
 
 16d 
 
 8V4 
 
 iO 
 
 sod 
 
 4 
 
 .1630 
 
 31 
 
 .1019 
 
 «a 
 
 
 
 
 2nd 
 
 4 
 
 20 
 
 sod 
 
 «!4 
 
 .1819 
 
 22 
 
 
 
 
 
 
 30d 
 
 «f4 
 
 1« 
 
 40d 
 
 s 
 
 .2043 
 
 IT 
 
 • .>. • 
 
 .... 
 
 
 
 
 40d 
 
 5 
 
 14 
 
 60d 
 
 654 
 
 .2294 
 
 13 
 
 
 .... 
 
 
 
 
 50d 
 
 KW 
 
 11 
 
 dod 
 
 6 
 
 .2576 
 
 11 
 
 
 .... 
 
 
 
 
 60d 
 
 6 
 
 8 
 
 
 
 WROUGHT SPIKES. 
 
 Number to a Keg of 150 lbs. 
 
 
 
 
 Length 
 Inches 
 
 Vt 
 
 Vo- 
 
 \'o- 
 
 Length 
 Inches 
 
 \'o"- 
 
 No. 
 
 Vo"- 
 
 \'o'^ 
 
 Hln. 
 No. 
 
 3 
 354 
 
 4 
 
 6 
 
 2250 
 1890 
 1650 
 1464 
 1380 
 1292 
 
 1208 
 1135 
 1064 
 930 
 
 868 
 
 '742 
 670 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 1161 
 
 662 
 635 
 678 
 
 482 
 466 
 424 
 891 
 
 446 
 384 
 300 
 270 
 249 
 236 
 
 S0« 
 35« 
 240 
 229 
 803 
 180 
 
 —Carnegie Pocket Book. 
 
104 
 
 Reinforced Concrete. 
 
 TABLE XVI. 
 
 SAFE LOADS TTMIPORMtJT DISTRIBUTED FOR REC- 
 
 TANGULAR SPRUCE OR WHITE ^INB BEAMS 
 
 ONE INCtl THICK. 
 
 The following table has been calculated for .extreme liber 
 stresses of 750 lbs. per square inch corresponding to the follow- 
 ing values for Moduli of Rupture recommended by Prof. Lanza, 
 viz.: 
 
 Spruce .and white pine., S.OOOlbs. 
 
 Oak , 4,000 lbs. 
 
 Yellow pine 5,000 lbs. 
 
 For oak increase values in table by }4. For yellow pine 
 increase values in table by J^. 
 
 The safe load for any other values per square inch is found 
 by increasing or decreasing the loads given in the table in the 
 same proportion as the increased or decreased fiber stress. 
 
 Span 
 
 
 
 
 t)EPTH OE 
 
 BEAM- 
 
 —INCHES. 
 
 
 
 in 
 Feet. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 ,10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 IS 
 
 1» 
 
 s 
 
 ,600 
 iSOO 
 
 820 
 
 1,070 
 
 1,360 
 
 1,670 
 
 2,020 
 
 2,400 
 
 2,820 
 
 3,270 
 
 3,730 
 
 4.270 
 
 s 
 
 680 
 
 890 
 
 1,120 
 
 1,390 
 
 1,680 
 
 2,000 
 
 2,360 
 
 2.730 
 
 8,120 
 
 8,660 
 
 7 
 
 :480 
 
 680 
 
 760 
 
 960 
 
 1,1'90 
 
 1,440 
 
 1,710 
 
 2,010 
 
 2,330 
 
 2,680 
 
 8,060 
 
 8 
 
 .880 
 
 610 
 
 670 
 
 840 
 
 1,040 
 
 1,260 
 
 1,600 
 
 1,760 
 
 2,040 
 
 2,340 
 
 2,670 
 
 9- 
 
 ,380 
 
 460 
 
 690 
 
 750 
 
 930 
 
 1,120 
 
 1,330 
 
 1,660 
 
 1,810 
 
 2,080 
 
 2,870 
 
 10 
 
 .SOO 
 
 410 
 
 630 
 
 670 
 
 830 
 
 1,010 
 
 .1,1!00 
 
 1,410 
 
 1,630 
 
 1,880 
 
 2,130 
 
 11 
 
 ;270 
 
 370 
 
 490 
 
 610 
 
 760 
 
 920 
 
 1,090 
 
 1,280 
 
 1,490 
 
 1,710 
 
 1,940 
 
 12, 
 
 .260 
 
 840 
 
 440 
 
 660 
 
 690 
 
 840 
 
 1,000 
 
 1,180 
 
 1,860 
 
 1,660 
 
 1,780 
 
 .18. 
 
 .230 
 
 310 
 
 410 
 
 620 
 
 640 
 
 780 
 
 930 
 
 1,080 
 
 1,260 
 
 1,440 
 
 1,640 
 
 14 
 
 Jaw 
 
 290 
 
 880 
 
 480 
 
 690 
 
 720 
 
 860 
 
 1,010 
 
 1,170 
 
 1,340 
 
 1,630 
 
 16 
 
 -.200 
 
 270 
 
 860 
 
 460 
 
 660 
 
 670 
 
 800 
 
 040 
 
 1,090 
 
 1,260 
 
 1,420 
 
 18 
 
 .190 
 
 280 
 
 330 
 
 420 
 
 620 
 
 630 
 
 760 
 
 880 
 
 1,020 
 
 1,180 
 
 1,880 
 
 IT 
 
 .180 
 
 240 
 
 310 
 
 400 
 
 490 
 
 690 
 
 710 
 
 830 
 
 960 
 
 l.ltJO 
 
 1,260 
 
 18 
 
 .170 
 
 280 
 
 290 
 
 370 
 
 460 
 
 660 
 
 670 
 
 780 
 
 010 
 
 1,040 
 
 1,190 
 
 19 
 
 .160 
 
 210 
 
 280 
 
 860 
 
 440 
 
 630 
 
 630 
 
 740 
 
 860. 
 
 990 
 
 1,130 
 
 20 
 
 .160 
 
 200 
 
 270 
 
 340 
 
 420 
 
 610 
 
 600 
 
 710 
 
 820 
 
 940 
 
 1.070 
 1,020 
 
 21 
 
 .140 
 
 190 
 
 260 
 
 320 
 
 399 
 
 480 
 
 670 
 
 670 
 
 780 
 
 890 
 
 22 , 
 
 .140 
 
 190 
 
 240 
 
 810 
 
 380 
 
 '460 
 
 640 
 
 640 
 
 740 
 
 860 
 
 S70 
 
 23 , 
 
 .180 
 
 180 
 
 230 
 
 290 
 
 360 
 
 440 
 
 620 
 
 610 
 
 710 
 
 810 
 
 «2n 
 
 24 
 
 .180 
 
 170 
 
 220 
 
 280 
 
 860 
 
 420 
 
 600 
 
 690 
 
 680 
 
 780 
 
 800 
 
 26 
 
 .120 
 
 160 
 
 210 
 
 270 
 
 330 
 
 410 
 
 480 
 
 660 
 
 660 
 
 760 
 
 860 
 
 26 
 
 .110 
 
 160 
 
 210 
 
 260 
 
 320 
 
 390 
 
 460 
 
 640 
 
 630 
 
 720 
 
 820 
 
 27 
 
 .110 
 
 160- 
 
 200 
 
 260 
 
 310 
 
 370 
 
 440 
 
 620 
 
 610 
 
 690 
 
 790 
 
 28 
 
 .110 
 
 140 
 
 190 
 
 240 
 
 SOO 
 
 360 
 
 430 
 
 600 
 
 680 
 
 670 
 
 760 
 
 29 
 
 .110 
 
 140 
 
 180 
 
 230. 
 
 290 
 
 360 
 
 410 
 
 490 
 
 660 
 
 640 
 
 740 
 
 To obtain the safe load for any thickness.: Multiply value* 
 for 1 inch by thickness of beam. 
 
 To 9^tain the required thickness for any load: Divide by 
 
 safe loaa~'for 1 inch. 
 
 —Carnegie Pocket Book. 
 
Weight of Bolts. 
 
 105 
 
 TABLE XVII. 
 
 WEIGHT, IN POUNDS, OP 100 BOLTS WITH SQUARE 
 HEADS AND NUTS. 
 
 .Length 
 
 
 
 DiAUETsa or 
 
 jgtM — INCHES. 
 
 
 
 Under Head 
 
 
 
 
 
 
 
 
 
 
 to Pbint 
 
 % 
 
 A 
 
 H 
 
 A 
 
 a 
 
 a 
 
 y* 
 
 H 
 
 1 
 
 k 
 
 . 4.0 
 
 7.0 
 
 lO.B 
 
 16.2 
 
 22.6 
 
 89.6 
 
 63.0 
 
 ... • 
 
 ... 
 
 . 4.4 
 
 7.6 
 
 11.3 
 
 16.8 
 
 23.8 
 
 41.6 
 
 66.0 
 
 .... 
 
 . .. 
 
 . 4.8 
 
 n 
 
 12.0 
 
 17.4 
 
 26.2 
 
 43.8 
 
 69.0 
 
 109.0 
 
 163 
 
 . 6.2 
 
 12.8 
 
 18.6 
 
 26.6 
 
 45.8 
 
 72.0 
 
 113.8 
 
 169 
 
 . 5.S 
 
 9.0 
 
 18.6 
 
 19.6 
 
 27.8 
 
 48.0 
 
 76.0 
 
 117.6 
 
 174 
 
 J« 
 
 . 6.8 
 
 0.6 
 
 14.3 
 
 20.7 
 
 29.1 
 
 60.1 
 
 78.0 
 
 121.8 
 
 180 
 
 . 6.3 
 
 lO.O 
 
 16.0 
 
 21.8 
 
 S0.S 
 
 52.3 
 
 81.0 
 
 126.0 
 
 186 
 
 4 
 
 . 7.0 
 
 11.0 
 
 16.6 
 
 24.0 
 
 33.1 
 
 66.6 
 
 87.0 
 
 184.8 
 
 196 
 
 . 7.8 
 
 12.0 
 
 18.0 
 
 20.2 
 
 86.8 
 
 60.8 
 
 93.1 
 
 142.6 
 
 207 
 
 . 8.6 
 
 13.0 
 
 19.6 
 
 28.4 
 
 88.4 
 
 66.0 
 
 99.1 
 
 161.0 
 
 218 
 
 5 
 
 9.8 
 
 14.0 
 
 21.0 
 
 30.6 
 
 41.1 
 
 69.3 
 
 W5.S 
 
 169.6 
 
 229 
 
 V 
 
 .10.0 
 
 IS.O 
 
 22.5 
 
 32.8 
 
 48.7 
 
 78.5 
 
 111.8 
 117.8 
 
 168.0 
 
 240 
 
 10.8 
 
 IS.O 
 
 24.0 
 
 85.0 
 
 46.4 
 
 77.8 
 
 FS-J 
 
 261 
 
 7 
 
 
 
 25.6 
 
 87.2 
 
 49.0 
 
 82.0 
 
 123.4 
 
 186.0 
 
 862 
 
 . « .. 
 
 . .. 
 
 27.0 
 
 89.4 
 
 61.7 
 
 86.8 
 
 129.4 
 
 193.7 
 
 273 
 
 » 
 10 
 
 u 
 
 
 
 28.6 
 
 41.6 
 
 64.3 
 
 90.6 
 
 185.0 
 
 202.0 
 
 284 
 
 
 
 30.0 
 
 43.8 
 
 69.6 
 
 94.8 
 
 141.6 
 
 210.7 
 
 295 
 
 
 
 
 46.0 
 
 64.9 
 
 103.8 ' 
 
 163.6 
 
 227.8 
 
 817 
 
 
 
 
 48.8 
 
 70.2 
 
 111-.8 
 
 165.7 
 
 244.8 
 
 839 
 
 . ... 
 
 ... 
 
 ... 
 
 60.4 
 
 76.6 
 
 120.3 
 
 177.8 
 
 261.9 
 
 860 
 
 18 
 
 il 
 
 
 
 
 62.6 
 
 80.8 
 
 128.8 
 
 189.9 
 
 278.9 
 
 882 
 
 
 
 
 
 86.1 
 
 137.3 
 
 202.0 
 
 296.0 
 
 404 
 
 
 ^ 
 
 . . • 
 
 
 91.4 
 
 146.8 
 
 214.1 
 
 813.0 
 
 426 
 
 
 . . . 
 
 . .. 
 
 
 96.7 
 
 164.8 
 
 226.9 
 
 830.1 
 
 443 
 
 
 ... 
 
 ... 
 
 ... 
 
 102,0 
 
 162.8 
 
 238.8 
 
 847.1 
 
 470 
 
 17 
 
 18 
 
 
 
 
 
 107.3 
 
 171.0 
 
 250.4 
 
 864.3 
 
 492 
 
 
 
 
 ... 
 
 112.6 
 
 179.6 
 
 262.6 
 
 881J 
 
 614 
 
 IS 
 
 t ■ .. 
 
 
 ... 
 
 
 117.9 
 
 188.0 
 
 274.7 
 
 898.8 
 
 686 
 
 
 ... 
 
 ... 
 
 ... 
 
 123.2 
 
 206.6 
 
 286.8 
 
 416.8 
 
 668 
 
 Per Inch 
 
 1.4 
 
 2.1 
 
 3.1 
 
 4.2 
 
 6.6 
 
 8.6 
 
 12.3 
 
 16.7 
 
 21.8 
 
 Additional. 
 
 
 
 
 
 
 
 
 
 
 WEIGHT OF NUTS AND BOLT-HEADS IN POUNDS. 
 For Calculating the Weight of Longer Bolts. 
 
 Diam ol Bolt in Inches. 
 
 
 •A 
 
 H 
 
 •A 
 
 H 
 
 H 
 
 H 
 
 Weight of Hexagon Nut 
 and Head 
 
 Weight of Square Nut 
 and Head 
 
 ... 
 
 .017 
 .021 
 
 .067 
 .069 
 
 .128 
 .164 
 
 .267 
 .320 
 
 .43 
 
 .56 
 
 .73 
 .88 
 
 Diam of Bolt in Inches. 
 
 1 
 
 VA 
 
 m 
 
 m 
 
 a 
 
 iii 
 
 8 
 
 Weight of Hexagon Nut 
 and Head 
 
 Weight of Square Nut 
 and Head 
 
 1.10 
 1.31 
 
 2.14 
 Z.56 
 
 3.78 
 4.42 
 
 6.6 
 
 7.0 
 
 8.76 
 10.5 
 
 .17.0 
 21.0 
 
 28.8 
 86.4 
 
 —Corne^ifi PocVvt l^ofe 
 
106 Reinforced Concrete. 
 
 At one end, or at both ends of all walls, there should be a 
 hole in the form, the bottom of the hole being level with the top 
 of the concrete already poured. This hole is to enable the space 
 between forms to be thoroughly cleaned. It is impossible to raise 
 the waste matter so the best way is to provide a hole through 
 which to drive it. In the bottom of all column forms there should 
 be a hole. In the bottom of all beam and girder forms there 
 should be a generous sized hole. These holes are absolutely neces- 
 sary to secure a good job and no great ingenuity is required to 
 devise efficient methods for closing them. It does require watch- 
 fulness however to insure their being closed before pouring begins. 
 For this reason a definite location for all such holes should be 
 determined beforehand and adhered to. For example, in columns 
 the holes may be on the north side and for walls in the middle 
 of the space between cross walls and for beams at the north end 
 and at the west end. 
 
 Forms must be so attended to that concrete cannot adhere 
 to them and thus make a rough looking job. Wooden forms oiled 
 should be thoroughly soaked in crude oil and each time they are 
 used they should be again coated. The objections to oil are the 
 expense, the weight of oil-soaked forms in handling, the liability 
 of making the wall dirty, and the fact that if the walls require 
 plastering or any subsequent treatment the oil skin must first be 
 removed at great expense. 
 
 Soap is excellent. It should be dissolved in water to the 
 consistency of very thin paste and is applied with brushes. The 
 objections are that it is expensive and is seldom applied properly. 
 The use of soap helps make a dense surface and does not inter- 
 fere materially with subsequent treatment, provided the surface of 
 the concrete is washed well with clean water before applying the 
 treatment or plaster. 
 
 The cheapest and most satisfactory all round method for 
 securing a good surface is to thoroughly soak the forms with 
 water so they will not absorb water from the concrete. A sprinkling 
 of the inside with a hose is not sufficient. See that the hose is 
 applied to both sides thoroughly until the boards can take up no 
 more water. When dry spots appear, wet them. 
 
 The surface obtained with oiled, soaped or wetted forms is 
 practically identical. The great objection to water is that it is not 
 always possible to thoroughly wet the forms and many times it 
 is absolutely impossible to keep them wet without adding too 
 much water to the concrete already poured. Hot summer days, 
 
Treatment of Surface. 107 
 
 for example, are poor days in which to use wetted boards unless 
 there is a plentiful supply of water and it can be applied from 
 the outside. 
 
 The following rules deserve to be printed in large type and 
 pasted in the hats of all foremen or in places where all the men 
 can read them : 
 
 See that all the steel goes in. Check closely. 
 
 See that all the steel is wired in position. 
 
 See that forms are well scraped and cleaned and properly 
 "doped" before concrete is poured. 
 
 See that forms are in line and are plumb. 
 
 See that the proper space between forms is obtained. 
 
 See that all bracing or wiring is done. 
 
 See that all holes are closed and all cracks stopped up with 
 soft clay well tamped into the spaces. 
 
 All joints should stop with a key. Never allow sloping 
 joints. Vertical joints should be vertical and consist of a board 
 placed across the form having on the side towards the con- 
 crete a key equal in width to one-half the thickness of the wall 
 and projecting into the concrete a depth equal to at least one 
 and one-half times the thickness of the key. It should be so 
 shaped that it will admit of comparatively easy removal. This 
 will make a groove in the end of the wall which will assist ma- 
 terially in bonding the new work to the old. A similar g^roove 
 should be made in the top of all concrete when pouring is stopped 
 and in this groove should be poured a water-tight compound of 
 some sort if the walls are to be water tight, for it is at the joints 
 most leaks occur. 
 
 In joining new work to old (meaning to concrete poured 
 so long that it has alreday set), see that the old surface is 
 scrubbed vigorously with a wire brush. The excess of water 
 rising to the surface as concrete sets contains a great deal of 
 partially set cement. It forms a muddy deposit on top and 
 slowly sets and forms a scale hard to detach yet which pre- 
 vents a perfect bond. It must be gotten rid of at any cost. 
 Brushing with wire brushes is one method. A solution of ten 
 per cent chemically pure hydrochloric acid in ninety parts of 
 water has been used for years for plain concrete work. Its use 
 in reinforced work is questionable on account of the acid having 
 a tendency to go down the very small space between the steel 
 and concrete, ultimately destroying the adhesion. When acid 
 is used it must be washed off with clear water. 
 
108 Reinforced Concrete. 
 
 Compressed air has been used to clean shavings and sawdust 
 out of forms with great success. The writer used on a piece of 
 work he had charge of the past winter (1907-8) live steam at a 
 pressure of considerably over one hundred pounds. He was so 
 well pleased with results that hereafter the use of steam will be 
 required in his specifications. 
 
 Nothing is so absolutely bad for joints as sawdust and 
 nothing is so hard to get rid of. Shavings and blocks of wood 
 are picked up with rag pickers' sticks, which are pieces of wood 
 about one inch square having a sharpened nail driven into one 
 end. Loose gravel, etc., can often be brushed out. Sawdust 
 however remains. Even a strong stream of water fails to get 
 rid of it. Live steam at a high pressure will however clean off 
 the surface of the concrete to the bone. It removes all the half 
 set and dead cement and all the sawdust. The writer also used 
 this steam to clean his forms. It was directed against the forms 
 until the concrete adhering to them softened," when it was 
 scraped off readily. 
 
 Knock all loose scale from the steel before cleaning the space 
 for another pouring. Clear the steel entirely of all concrete 
 that may have become attached during the previous pouring. 
 This is imperative. When this cleaning is done remove all the 
 dirt and dust before erecting the next set of forms. After the 
 next set is erected clean out the space with the rag pickers' rods 
 and then with steam. 
 
 Before pouring see that the surface of the old concrete is 
 thoroughly wet. Then give it a coat of neat cement applied 
 preferably with a brush. After the neat cement wash has been 
 applied, deposit an inch of cement mortar pretty wet, composed 
 of one part of cement and two parts of sand. This should not be 
 poured but should be thrown in with shovels, half a shovelful 
 at a time. Then begin to deposit the concrete. If the joint is 
 vertical and the mortar cannot be readily applied, use rods or 
 spades or pieces of wood to work the mortar in the concrete up to 
 the face of the joint and into the key. It is imperative that old 
 concrete be well soaked with water before new concrete is joined 
 to it. 
 
 Experiments lately made in France showed that practically 
 perfect joints were made by first thoroughly wetting the old 
 surface and then painting it with neat cement paste and thor- 
 oughly tamping a layer of concrete on top before proceeding 
 to fill the forms. This tamping was good hard pounding, and 
 
Making of Joints. 109 
 
 this is a good thing to know-, for joints are hard to make. Up 
 to the present time perfectly satisfactory joints between old 
 and new work were deemed to be a practical impossibility. The 
 reinforcement may be in the way of getting the hard pounding 
 in thin walls, but still some of the pounding may be secured. 
 
 When possible to precure the men, work should be carried on 
 in two eight hour shifts for the concreting gang and three eight 
 hour shifts for the form gang so that not more than eight hours 
 will intervene between pourings. Sometimes the carpenters 
 are worked on the two eight hour shifts having daylight and the 
 laborers are worked on three shifts. The contractor should not 
 be permitted to evade this method until an actual trial demon- 
 strates the impossibility of doing it and getting a satisfactory job. 
 
 Work left over night must have the surface roughened before 
 the concrete is entirely set. When forms are removed the walls 
 must be at once attended to. If appearance is an object all pro- 
 jections must be removed by chiselling or bush hammering. All 
 pitting must be brushed out with steel brushes until the surface 
 is rough. It must then be soaked with clean water, painted with 
 a neat cement wash and plastered with a one to two or one to 
 three mortar floated with a wooden float to the level of the 
 surrounding concrete. The finish should be a sand floated surface 
 for this patching. Do not point up with a mortar richer than 
 the mortar used in the matrix of the concrete, for cracks will 
 appear around the edges of the patch, besides which the color 
 will be different. 
 
 If the appearance of the work requires a coat of plaster, clean 
 the surface with steam, afterward using wire brushes and then the 
 steam again. Wet it with water, paint it with neat cement and 
 immediately follow with two coats of one to three mortar, the 
 lower coat scratched and the top coat wood floated to a sand 
 surface. 
 
 For work done in cold weather the writer uses steam and hot 
 water. He has steam pipes perforated with small holes running 
 all through the sand pile and the steam continually escaping. It 
 is well to have this done under the stone pile as well, using only 
 the stone that has no ice on it and the sand that is not lumpy, 
 for the lumps may be frozen sand. He has a steam coil in a 
 water barrel to get the water almost to boiling heat and the 
 steam pipe ends in the mixer drum, keeping it so hot that it is 
 warm to the hand. A little salt added to the water also is used 
 occasionally. 
 
110 Reinforced Concrete. 
 
 Sometimes long cylinders of sheet steel are laid on their 
 side and over them are placed coarse screens. A fire of scrap 
 form lumber is kept going in the cylinders and a stove pipe in 
 the farther end insures a draught. The sand and stone are 
 shovelled over the screens and lumps thus broken up, the 
 materials falling down to the hot cylinder and keeping warm 
 until used. 
 
 Hot concrete sets up quickly. If it obtains its initial set 
 inside of thirty minutes add a little cold water while mixing, to 
 reduce the temperature. Heat the steel and inside of the forms 
 before pouring concrete. This is done best with steam, followed 
 by hot water. It is a mistaken notion that hot water freezes more 
 quickly than cold water. 
 
 Some European experiments seemed to show that hot con- 
 crete is much weaker than concrete mixed with cold water. 
 Little has been said about it in America, but the general cus- 
 tom is to use hot water, and some men even heat the stone, 
 believing that it will hold the heat a long time. The writer does 
 not approve of this heating of stone and sand, but merely warms 
 them enough to take the frost and ice out of the voids. The 
 water he does not allow to reach the boiling point, and if the 
 stones are not hot they will prevent the mixture from becoming 
 warm enough to injure the cement. 
 
 Calcium chloride is the best material known to prevent con- 
 crete from freezing before it sets. About one pound per bag 
 of cement seems to be sufficient and all tests made seem to show 
 that the strength of the concrete is increased. 
 
 If possible it is a good idea to have a salamander in the 
 room under the floor that is being poured to prevent the under 
 side of the forms from getting too cold. Yet there is danger 
 of the concrete baking in the forms, so it is well to have the 
 under side continuously sprinkled with cold water until they do not 
 feel warm to the hand. 
 
 Salamanders should be kept burning during the night in con- 
 creted rooms or tanks and in freezing weather all surfaces of 
 concrete poured during the day should be covered with sawdust 
 or straw. Old manure is heating but fresh manure is injurious 
 to fresh concrete. Boards placed one inch above the surface of 
 floors and covered with sacks or straw make a good covering. 
 
CHAPTER VIII. 
 
 Tools. 
 
 When ordering steel for a piece of work it is usual to have 
 the mills cut all the pieces to lengths, especially when there is no 
 extra charge for such cutting. 
 
 It is almost impossible to keep exactly to the schedule, as men 
 will make mistakes, especially when working with pieces varying 
 by only a few inches, so it is better to cut some of the steel on 
 the job. A good rule to follow is to have no pieces cut to lengths 
 when less than twenty-five of any certain length are required. 
 When less than that number may be wanted then order long pieces 
 in multiples of the required lengths, exactly as a carpenter orders 
 lumber. 
 
 Every job should have a shear for cutting steel into lengths 
 required. Such shears cost from fifteen to one hundred and fifty 
 dollars. If properly used a fifteen dollar shear is about all that is 
 required. The writer has used on his work the Badger and the 
 Edwards but knows that there are others as good, though those 
 mentioned gave perfect satisfection. With them he has cut high 
 carbon twisted steel three-quarters of an inch square. As a rule 
 high carbon steel is easier to cut than medium steel. In using 
 such shears the steel should be pushed well into the jaws and bear 
 well against both, before the power is applied. If the jaws have 
 to move a little before coming in contact with the bar there is 
 danger of the shear being broken when the men throw their 
 weights on to the handle. All the bolts on the shear should be 
 tightly screwed up also. When the jaws are tight the best work 
 is done. 
 
 An extremely useful tool on a reinforced concrete job is a 
 combination shear arranged for cutting round, square and flat bars 
 and also for punching holes in flats half an- inch thick. Such a 
 combination shear and punch costs between forty and fifty dollars. 
 
 Ill 
 
112 
 
 Reinforced Concrete. 
 
 The two following cuts illustrate the method the writer has 
 adopted for keeping track of his steel. 
 
 'VU. 
 
 % 
 
 c 
 
 i" 
 
 
 n' 
 
 
 V 
 
 Zio 
 
 Vg" 
 
 
 '/z" 
 
 Zoo 
 
 ^s" 
 
 
 'A- 
 
 ¥(H3 
 
 ^T££l Of?D£f? FoF 
 
 s' 
 
 ISV 
 
 Zs/]^/-A>s 
 
 //' 
 
 /9' 
 
 /Of 
 
 aa' 
 
 /<72 
 
 13' 
 
 
 SV 
 Slho 
 
 linm 
 
 IQ 
 
 Steel /T^coftd 
 
 t/e. 
 
 "f- 
 
 %•' 
 
 Bun 
 
 ', 
 
 L^fl^s ih fke.f 
 
 Doies 
 
 71 
 
 Uit4 
 
 13 
 
 fetJ- 
 
 Ust4 
 
 2/ 
 
 fccf 
 Used 
 
 3j> 
 
 KeM 
 
 fee.t 
 Used 
 
 %h./ 
 IQcc3 
 
 IfO 
 
 II 
 3 
 
 ^2 
 
 U> 
 
 WO 
 
 SO 
 
 li 
 
 
 !0 
 
 lo 
 
 
 \lo 
 
 
 ko 
 
 
 78 
 
 When he sends his order to the dealer he rules on a page in 
 a book, as many columns as there are lengths ordered, as shown. 
 On a vertical line he places the sizes. Then from his order sheet 
 he copies the number of pieces in each column in lead pencil, 
 As each car is received the number is checked off and when all 
 the steel has come he writes the number of pieces in each column 
 in red ink. About five per cent surplus should be ordered in 
 half inch bars. Extra pieces are often wanted. 
 
 He also has a small blank book ruled for keeping track of each 
 
Forms and Systems. 113 
 
 size and the lengths. This is the Steel Record. When the steel is 
 received the proper entries are made in the column headed "Re- 
 ceived" and as the steel is used the number of pieces is entered in 
 the "Used" column. It is thus an easy matter at all times to know 
 exactly how many pieces of a certain size and length there should 
 be on hand. 
 
 The following cut shows how orders for steel are given to 
 the steel boss: 
 
 (D<-^ O-e^-^ -T9-7 (J 
 
 "h [cL/t.«xi (2/ 8 -'di-^A'iv. 
 
 ^" 
 
 - — wr- - - ^ 
 
 V-8'4"--/ 
 
 One man has charge of the steel yard. To him all orders are 
 given for steel to be delivered in the building. He has charge of 
 the steel bending gang also." In the book where the steel record is 
 kept all orders for bending or delivery of steel are entered. The 
 book is turned upside down and entries made in what was the back. 
 The writer s:enerally uses a quadrille ruled book so front and back 
 are merely relative terms. The accompanying illustration is a copy 
 of one page in this book. The steel boss has a small leather bound 
 book that he can carry in his pocket. When an order is given it 
 is first entered fully in the ofBce book and entered in the "Used" 
 
114 Reinforced Concrete. 
 
 column of the Steel Record. Then the bending order is copied 
 into the steel boss's book in full, date also. He bends the steel and 
 piles it in a convenient place until wanted. 
 
 When there is plenty of room the most convenient way to take 
 care of the steel is to put it in piles on the ground with posts along- 
 side telling the size and length. If there is not much room then a 
 steel rack must be made. These racks are simple and do not 
 require description. Any intelligent carpenter should be able to 
 make one after inspecting the store room of a hardware dealer or 
 of a blacksmith shop. But whether the material is laid on the 
 ground or put on racks one man alone should have charge of it 
 and if this is not done there will be trouble. 
 
 Formerly on every job a blacksmith was employed and all 
 bending of steel was done by first heating it. A blacksmith is as 
 hard to get as a carpenter, although many hundreds of men may 
 apply for the job and call themselves blacksmiths. The result is 
 that much of the steel is burned and weakened. It is best to bend 
 all of it cold but there should be a forge on the job for occasionally 
 heating steel and also for sharpening and tempering picks, gads, 
 chisels, etc. 
 
 Nearly all the benders sold are intended for bending metal 
 hot. The writer uses a bender, which, so far as he knows, was 
 developed by Mr. R. S. Hunt, C. E., of Charleston, W. Va. It 
 consists essentially of a bar about one and one-quarter inches 
 diameter and three feet long. On one end is fastened a pintle at 
 right angles, of the same diameter and about one foot long. This 
 pintle goes down through a piece of ten by ten timber used as a 
 bench, the hole through which the pintle goes being lined by an 
 iron pipe. About two inches away from the pintle is another one 
 about two inches long. This rests upon a steel plate on top of the 
 bench. The steel to be bent is placed in the two-inch slot between 
 the two projections and men turn the bender round. The writer 
 has bent high carbon steel cold, one inch square, and medium steel 
 one and one-quarter inches square, cold, with such a bender. 
 Sometimes the smaller projection has an anti-friction roller on it. 
 
 Sometimes it is necessary to bend a small piece of steel with 
 a shoulder almost square and this is done by placing a steel pin in 
 a hole in the plate a short space away from the large pintle. 
 
 The hot bender is a small bender that can be attached to an 
 anvil (which should be on the job), for bending rods that have 
 been heated or for bending very small rods and bars cold. It is 
 remarkably efficient. It consists first of a round piece of iron about 
 
115 
 
116 Reinforced Concrete. 
 
 five inches long with a square extension of about the same length 
 to fit into the hole on the anvil. A piece of three-quarter inch 
 round steel about four feet long is split at one end and the pieces 
 formed into a yoke about eight inches long. The ends have holes 
 to fit over the upright round piece sticking up from the anvil. 
 Along the sides of the yoke are holes to hold pins which shorten 
 the space according to the size of the rod to be bent. When the 
 heated rod is passed through the yoke between the upright standard 
 and the pin run through the sides of the yoke the blacksmith turns 
 the bender so the bar is bent to any required degree. There should 
 be a cold bender and a hot bender on every job. 
 
 Hand benders are readily made by bending some pieces of the 
 reinforcing steel on the job. Three-quarter inch bars are best, 
 although sometimes something heavier is needed. The bar is first 
 bent at right angles. Then the short end is bent again parallel 
 with the main piece and about an inch and a half away from it. 
 Then at a distance of an inch it is bent again toward the main 
 piece thus forming a letter U at right angles to the bar. Small 
 pipes are used satisfactorily as hand benders in many cases but 
 there is nothing really as satisfactory as a twenty-one inch monkey 
 wrench. 
 
 Occasionally rods and bars have to be cut in situations where 
 it is impossible to use the shear, so for such work cold chisels 
 must be used and a plentiful supply should be on hand. They are 
 made of tool steel properly hardened by a competent metal worker. 
 The edge is held on the steel and a hand hammer used for striking. 
 Cold cutters have longer edges than cold chisels and are fastened 
 to a handle like a hammer. By means of this handle the cold 
 cutter is held in place by one man while another does the striking 
 with a sledge hammer. Cold chisels and cold cutters are useful 
 and occasionally necessary but they are very expensive tools to use. 
 While they should be on the job it is seldom any use will be had 
 for them if the shears are properly handled. As the edges go fast 
 a number must be handy when needed. 
 
 Bolt cutters are scissors-like tools having jaws of well tempered 
 steel and powerful levers in the jaws. They come in several size* 
 and as they are intended for cutting iron should not be used for 
 cutting steel bars although some are large enough to cut a half 
 inch bolt readily. The best size to use on a reinforced concrete 
 job is the No. 0, intended for cutting a quarter inch bolt. Many 
 uses will be found for bolt cutters as considerable wire is used. 
 There should be two or three on an ordinary job. 
 
Handy Tools. 117 
 
 A pair of tinners' snips are very handy and also a few pieces 
 of sheet iron for making a smooth job of patching a hole in 
 
 forms. 
 
 The handiest tool for cutting, tying and bending the small wire 
 (No. 16 or No. 18) used for fastening steel is a ten-inch black- 
 smith's cutting nipper. It is better than a flat plier for bending 
 the wire and the end jaw is good for cutting close to the surface 
 when wires project. These nippers can be used for cutting wires 
 as heavy as No. 10, but to do this requires a twist of the wrist few 
 ignorant unskilled laborers can acquire, and the edges of the cutting 
 nippers are broken, rendering the tool useless for anything but 
 bending. 
 
 Flat pliers do well for bending but there should be a cutting 
 edge. Some of the many fence tools on the market are good. 
 They combine pliers, wire cutters, staple pullers and hammers. 
 They are really very efficient.but for the fact that the cutting edges 
 are on the side, whereas an end cutter is most convenient. The 
 edges of all cutters break quickly when used by the average 
 laborer as they will twist the wrong way in spite of all instruction. 
 The furnishing of pliers and cutting nippers is expensive. It is 
 really a good plan to have a few men do all wiring and make them 
 furnish their own pliers, etc. 
 
 Every job should have at least two crowbars. The writer 
 generally has a number of pieces of the reinforcing steel sharpened 
 on the end with chisel-like edges. Such bars can be used as pinch 
 or crowbars and as slicing or cutting bars in breaking out keys 
 or chipping concrete. 
 
 Some small bars with claws on the end for removing forms 
 and drawing nails are useful. They can all be used for reinforce- 
 ment toward the end of the job. A number of chisels for cutting 
 concrete and a number of steel gads are also needed. 
 
 A couple of 4 or 6 pound sledge hammers on a job will pay 
 for themselves many times over. A couple of post mauls come in 
 handy and a post auger is a very convenient and sometimes neces- 
 sary tool. 
 
 Forms give way suddenly and occasionally there are heavy tools 
 or pieces of machinery to raise, so there should be about four 
 bottle or house-raising jacks on the job. It is well to have also 
 a good rope about two hundred feet long, one inch in diameter, 
 with a set of triple blocks. There should be several half or three- 
 eighths ropes and some hooks, which can be made from pieces of 
 reinforcing steel, for raising forms and cleaning up. A timber saw 
 (cross cut) and one or two twenty-six inch hand saws, a couple 
 
118 Reinforced Concrete. 
 
 of hammers, two hand axes and a couple of pole axes should be 
 included in the outfit. The carpenters furnish their own tools of 
 course, but these tools are for the use of men on odd jobs at which 
 a carpenter would not be put. Two or three plumb bobs, a square, 
 good level and several hundred feet of chalk line (not forgetting 
 balls of chalk) and some marking crayons and pencils must not be 
 forgotten. For marking steel for cutting and bending, soapstone 
 crayon used by machinists is best. 
 
 When power is obtainable, a circular saw for ■ cutting and 
 ripping lumber for forms is a good investment. A great deal of 
 sawing must be done on every job and a circular saw will soon pay 
 for itself. The writer knows some contractors who have planers 
 and buy all their lumber in the rough, thus saving one dollar and a 
 half per thousand in first cost and also being sure of getting the 
 stuff when in a hurry. Surfaced lumber sometimes demands a day 
 or so extra time to furnish. 
 
 Several nail pullers are a necessity. There should also be a 
 good grindstone on the job. A boring machine is needed if there 
 will be many holes to bore, as for wires and bolts through forms. 
 Boring such holes with brace and bit is slow, expensive work and 
 the holes are not always exact. 
 
 On a reinforced concrete job, big bills for work at machine 
 shops run up with alarming frequency. For this reason it is well 
 to have the forge and anvil mentioned and in addition there should 
 be a bench vice, pipe cutter, stocks and dies for threading pipes 
 and taps and dies for bolts and rods. These articles are cheap and 
 oftentimes one oiece of work will pay for the entire outfit. 
 
 Some concrete mixers admit of loading directly into wheel- 
 barrows and with such mixers no loading box is required. When 
 the work has reached a height where a concrete hoist is put in 
 operation there should be a box into which to dump the concrete 
 and from which to load the wheelbarrows or carts. Boxes and 
 chutes of steel for this purpose are made by a number of firms 
 and it pays to buv them when over five hundred yards must be 
 handled. However, they may be made on the job, the box of wood 
 and the gate of sheet steel. While the home made ones work all 
 right, when they work, they are likely to break and as every man of 
 experience knows, breaks generally occur when the work can be 
 prosecuted advantageously and the repairs are just completed when 
 the weather changes. The hope of saving a few dollars should not 
 influence the contractor in the making of tools unless he can make 
 them as well as those he can buy. 
 
119 
 
120 Reinforced Concrete. 
 
 The writer has several times used wooden boxes for hoisting 
 concrete with a horsepower hoist. It is very efficient and lessens 
 the cost of handling concrete amazingly. Yet one or two careless 
 droos may make such a box much more expensive than a steel box, 
 high priced though the latter may be. The horsepower hoist in 
 small towns, however, is excellent. The cost is about one-fourth 
 or one-sixth the cost of a gasoline or steam hoist of equal capacity 
 and it may be required only a few days. 
 
 The ideal power for all purposes is electricity. One motor 
 cannot be used on all jobs, however. When a contractor possesses 
 an alternating current motor and can get only direct current, or 
 vice versa, he expresses violent opinions regarding electricity as a 
 motive power. If alternating current is supplied then his motor 
 must be suitable as regards voltage, phase and cycle. The differ- 
 ences found in power plants may require a contractor to own a 
 number of motors for one mixer and hoist if his work covers 
 much territory. Assurning, however, that his motor can be used 
 he has only to keep the apparatus well protected from rain and 
 dust and not neglect proper lubrication. To throw the switch is 
 simple and any man can do it after one showing. The power is 
 always there when wanted. The absence of dirt and grease and the 
 saving in cost of skilled attendance count on the right side of the 
 ledger. 
 
 Gasoline engines come next in convenience to electricity. The 
 power is there when wanted and it is no trouble to start and stop. 
 Like electricity, no skilled attendant is necessary. Simply an intelli- 
 gent careful man is needed. The trouble, however, lies in the 
 engines sold. Contractors seldom obtain good gasoline engines for 
 they look alike and the lowest priced are seldom the best. 
 
 The best of gasoline engines give trouble occasionally. The 
 secret in operating gasoline engines lies in attending properly to 
 the lubrication and in keeping them absolutely clean. That is, 
 provided a good engine is purchased. A gasoline engine sold at a 
 low price and not guaranteed by a responsible firm is a delusion 
 and a snare. As cost is not the proper criterion, a man bujring a 
 gasoline engine should employ a competent mechanical engineer 
 to buy it for him or else pay a good price for a guaranteed 
 engine. 
 
 With electricity or with internal combustion motors the power 
 when on is paid for. When not used the expense ceases. Steam 
 engines, however, require that steam be kept up ready for use 
 
Concrete Hoists. 
 
 131 
 
 when wanted. This means expense for fuel and also the wages 
 
 of a high priced attendant. The 
 
 fi engineer must be licensed in most 
 
 •li» states and is generally a union 
 
 k ft| TT man. When an engineer is em- 
 
 jr i|ij >^ ployed he does not want to do any 
 
 Js^ iljj^/ljl other work, even on a small job 
 with a small mixer. If the mixer 
 is a fairly good sized one he wants 
 a helper to act as fireman. There- 
 fore steam engines are not very 
 satisfactory on jobs where the 
 concreting is not continuous. Con- 
 ditions do not always permit of 
 coal or other fuel being stored or 
 handled on the job. 
 
 The foregoing remarks on mo- 
 tive powers apply especially to 
 summer work. Cleaning between 
 forms, ' especially between rein- 
 forcing steel set in the forms, is 
 almost impossible 
 
 with brooms, and 
 washing with water 
 is not always feasi- 
 ble because the re- 
 quired pressure can 
 not be had. Com- 
 pressed air is most 
 excellent and when 
 electricity or gaso- 
 line or oil may be 
 used for power 
 there should be an 
 air compressor ca- 
 pable of furnishing 
 plenty of air at not 
 less than eighty 
 pounds pressure, to 
 blow out dust, sawdust, etc., and clean the forms. As there 
 is a thin film formed on top of all concrete which prevents a 
 
 Hv— -0 *( 
 
 Fig. 26 — Ransoms Concrete Hoist. 
 
122 Reinforced Concrete. 
 
 good bond, the compressed air apparatus should be provided 
 with a sand blast to roughen the surface. 
 
 The writer has found compressed air excellent. He has found 
 steam better. In winter steam is the ideal power for it is capable 
 of so many uses. The boiler should be large and situated at a 
 convenient point, which is seldom one close to the mixer. One 
 pipe can lead to the engine on the mixer and a smaller pipe can 
 be led in a coil through a barrel of mixing water and end in 
 the drum, which will be kept full of live steam. Another line can 
 be led to coils under the piles of sand and stone and a line can be 
 led to the building, to which a steam hose may be attached for 
 blowing out the forms and cutting the skin off the top of the 
 concrete. The pressure should be not less than one hundred pounds. 
 When the number of uses to which steam can be put are considered 
 it may be termed the ideal thing to use in cold weather while 
 electricity and gasoline or oil are better in warm weather. 
 
 The loss by condensation of steam is great in long pipes, no 
 matter how well covered. They should be covered and if the con- 
 densation is considerable some simple form of separator should be 
 used close to the engine, or cylinders will be damaged. There are 
 a number of excellent coverings in the market, but generally ex- 
 pensive. The writer reduced condensation once about fifty per cent 
 by enclosing a long pipe in a box six inches square with a cover 
 that would shed water. Around the pipe was wrapped two thick- 
 nesses of asbestos paper and the box was filled with plasterers hair, 
 so the pipe had no less than an inch of this hair surrounding it. 
 Another good covering is composed of flour paste and sawdust. 
 This is placed in a box surrounding the pipe, the heat from which 
 bakes the paste, forming the air spaces so necessary for insulation. 
 
 Wheelbarrows of course are the usual conveyances for the 
 delivery of concrete. They may continue to be so for delivery of 
 material to the mixer, but many forms of cars and buckets are often 
 superior for delivery of concrete. 
 
 The size of wheeHjarrows has already been mentioned. The 
 most convenient and least wasteful wheelbarrows made for con- 
 crete work have the bed raised two or three inches in front. This 
 increases the capacity and prevents slopping. Such wheelbarrows 
 are a regular article of manufacture and can be purchased almost 
 everywhere. The No. 2 size is probably best as it is light and lasts, 
 in proportion to price, as well as any made. If the local store 
 does not handle them the ordinary pressed bowl barrow mounted 
 on a wooden frame can be readily altered by cutting down the 
 
Fig. 27 — Smith's Concrete Hoist. 
 19.3 
 
1S4 
 
 Reinforced Concrete. 
 
 supports for the bowl near the handle and putting bevelled pieces 
 under the bowl near the wheel. Some men favor ball bearing 
 wheelbarrows and others claim the old fashioned stapeled squeaker 
 to be better than the ball bearings, for the latter require too much 
 oil. The writer used both on jobs lately completed and was not 
 able to decide which was the better. He uses the 
 ordinary light pressed steel bowl barrow for carrying sand and 
 stone to the mixer and the raised bowl concrete wheelbarrow for 
 concrete, there being a difference of about iive dollars per dozen 
 in the price. Of one thing, however, he is certain, and it is that gas 
 pipe handles on wheelbarrows are not favored by the laborers. It 
 is hard to get a wheelbarrow crew, with such handles on the 
 work. Some contractors have enlarged the handles by putting 
 rubber hose over them or by wrapping them with cloth and sewing 
 painted canvas over the wrappings. The pipe handles without 
 some covering are hard to hold on account of their size and shape. 
 
 When running plank and scaf- 
 folds can be arranged properly two- 
 wheeled carts, each holding six 
 cubic feet of wet concrete, are 
 cheaper and better to use than 
 wheelbarrows. Time is saved in 
 loading from the mixer and in 
 dumping the concrete into place. 
 Two-thirds of the wheeler's are 
 also saved One cart holds as 
 much as three wheelbarrows, but 
 costs as much as six. There the 
 difference stops and is all the other 
 way in actual use, provided the car- 
 rying is all done on a level. The 
 only objection to the carts is that 
 they cannot be handled well on 
 an incline. When using them it 
 is best to use a hoist and take the 
 material to each floor level so there 
 will be no incline up which to push. 
 Much use is today being made 
 of derricks with bottom dumping 
 buckets, thus eliminating wheelbar- 
 rows and carts. When the job is 
 Fig. 28— Wallace-Lindsmith Hoist, large enough to warrant the cost of 
 
Conveyors. 125 
 
 installation some such method should always be used. It can be 
 used to carry stone and sand and cement from stock piles to the 
 mixer and to carry the mixed concrete from the mixer to the forms. 
 The writer wishes, however, to go on record as being opposed to 
 the use of bottom dumping buckets for reinforced concrete walls 
 less than eighteen inches thick. 
 
 Another method is to have cable ways from the mixer, and 
 one system contemplates the use of cable ways arranged on the 
 cash carrier system over all the walls, so the concrete can be 
 delivered at any point. It also involves a similar arrangement for 
 stone, sand and cement to the mixer. 
 
 Another system provides belt conveyors running alongside the 
 walls, with adjustable scrapers to throw the concrete off to one 
 side and into the forms. There is also a system consisting of 
 semi-circular troughs having the bottom made in detachable sec- 
 tions a couple or three feet long. The trough contains screw con- 
 veyors supplied with universal joints. The bottom is one sectibn 
 shorter than the frame and can be shifted to leave a hole through 
 which concrete will drop when carried to the point by the 
 conveyor. 
 
 Before starting a piece of work the man in charge should 
 obtain all the literature he can on the subject of conveying 
 machinery for contractor's use. Some men have too much 
 machinery and some do not have enough. It pays to be well 
 equipped, but it does not do to go to too great an expense for 
 one job. If a man, however, does not wish to spend enough 
 money to prosecute the work properly, he should sublet it 
 rather than try to do it himself. 
 
INDEX 
 
 Adhesion 10, 66 
 
 formula 24 
 
 length of steel to secure ... 32 
 
 Air, compressed 108 
 
 Amount of water 96 
 
 Angle steel in columns 50 
 
 Areas and weights of steel S7 
 
 Arm, moment, defined 16 
 
 Axes lis 
 
 Axis, neutral, defined 10 
 
 formula 13 
 
 tables .14-15 
 
 Bag and barrel of cement 93 
 
 Bars, areas and weights 27 
 
 bending of 36 
 
 deformed 18, S7, 67 
 
 lap 86 
 
 length for adhesion 10 
 
 patented 17 
 
 spacing in beams 10. 
 
 Base of walls 65 
 
 Beams, continuous 34 
 
 design of 14, 42 
 
 double reinforced 28 
 
 failures of 21, 24 
 
 forms for 91 
 
 formulas 9 
 
 loads OD 36, 43 
 
 proportions of 9, 10, 15 
 
 spacing of bars in 10 
 
 of T section 80 
 
 table of wooden 104 
 
 Benders for steel 114 
 
 Bending bars 26 
 
 steel 113 
 
 Blacksmith 114 
 
 Board by board forms 77 
 
 Boards, thickness for forms 102 
 
 Bolt cutters 116 
 
 holes in walls 81 
 
 Bolts in forms 79 
 
 table of 101, 106 
 
 Bond formula 24 
 
 Bottle jacks 117 
 
 Boxes for concrete 118 
 
 for measuring 96 
 
 Braced forms 78 
 
 Braces and posts, loads on 102 
 
 Breadth, proportion 9 
 
 of beam 16 
 
 Bridges 43 
 
 Buckling of steel 30 
 
 Built-up columns 46 
 
 Cableways 124 
 
 Calcium chloride 110 
 
 Cantilever beams 33 
 
 Carbon, high, steel 13 
 
 Carpenters 70, 77 
 
 Carts 124 
 
 Cast-iron, strength of 10 
 
 Cement measuring 93 
 
 Chalk line 118 
 
 Cheap labor 71 
 
 Chicago ordinance 14, 48 
 
 Chimney design 01 
 
 Cinder concrete, strength of. ... 20 
 
 Circular tanks 69 
 
 Cleaning forms 106 
 
 Coated steel 68 
 
 Cold chisels 116 
 
 Cold cutters 116 
 
 Cold weather 109 
 
 Column, various materials 44 
 
 beam acting as 9 
 
 divisors 47 
 
 forms 91 
 
 formulas 48 
 
 footings El, 68 
 
 stresses 46, 46 
 
 Compressed air 108, 122 
 
 Compression, concentrated 13 
 
 failure 24 
 
 formula 22 
 
 illustrated 11 
 
 steel 30 
 
 Compressive strength of concrete 11 
 
 Concrete, below steel 9 
 
 columns 44 
 
 joints 107 
 
 protected columnsi. 46 
 
 protection 10 
 
 quantities 94 
 
 stress 22 
 
 walls 62 
 
 weight of 21 
 
 Concentrated loads 36, 43 
 
 Condensation of steam 122 
 
 Connections 32 
 
 screwed 68 
 
 Considere's tests 64 
 
 Continuous beams and slabs.... 34 
 
 Conveying machinery 124 
 
 Cast-iron columns 44 
 
 Cost data 69 
 
 estimates 78 
 
 of forms 76 
 
 of lumber 77 
 
 of placing steel 28 
 
 of steel IS 
 
 of walls 68 
 
 Counterforts 67 
 
 Cracks in beams 64 
 
 Crayon 118 
 
 Crowbars 117 
 
 Cutters, for steel Ill, 116 
 
 Cutting steel Ill 
 
 Data on costs 70 
 
 Dead load 43 
 
 on columns 46 
 
 Deflection, defined 85 
 
 of beams 21, 66 
 
 Deformation, unit 12 
 
 Deformed bars 18, 67 
 
 when to use 27 
 
 Dense concrete 97 
 
 Design of beams 14 
 
 Designing forms 89 
 
 Depth of beam, definition 9 
 
 proportions , • 9 
 
 Depu of beam 15 
 
 Diagonal tension failure 24 
 
 defined 86 
 
 126 
 
127 
 
 Index, 
 
 Distributed loads 86, 43 
 
 Distribution of steel 34 
 
 Divisors, for column design 47 
 
 Double reinforced beams S8 
 
 Drawing of wire 17 
 
 Earth pressure 53 
 
 weight of 66 
 
 Elastic limit 17 
 
 Elasticity, Modulus of 13, SO 
 
 Electricity 120 
 
 Elevators 95 
 
 Estimating costs 73 
 
 Expanded fabric 27 
 
 Fabrics for reinforcement 37 
 
 Failures of beams 21 
 
 of walls 62 
 
 Fence tools 117 
 
 Fibre stress 17 
 
 Finishing work 109 
 
 Finish of forms 92 
 
 f re protection 10 
 
 Floor design 42 
 
 loads 43 
 
 slabs S3 
 
 space, value of 44 
 
 1 ootings for columns 51 
 
 forms for 90 
 
 for walls, etc 63 
 
 Forces in beams 12 
 
 Forges 118 
 
 Forms, boards for 102 
 
 cost of 76 
 
 designs for 89 
 
 per cubic yard 75 
 
 Framed forms 77 
 
 Galvanized steel 68 
 
 Gasoline engines 120 
 
 Girder' forms 91 
 
 Gravel, pressure of 53 
 
 Greased bolts 81 
 
 Grip of concrete 10, 66 
 
 Hammers 117 
 
 Hand mixing 94 
 
 Heating material 109 
 
 Heaving of walls. 56 
 
 High carbon steel 13, 18 
 
 Highway bridges 43 
 
 Hoists 95, 120 
 
 Holders for planks 89 
 
 Holes, bolt, in walls 81 
 
 in forms 106 
 
 in slabs 68 
 
 Hot concrete 110 
 
 Impervious concrete 97 
 
 Internal stresses 15 
 
 Iron, cast, strength of 10 
 
 columns 44 
 
 Jacks, house raising 117 
 
 Joints in concrete 107 
 
 screwed 68 
 
 K, moment factor 9 
 
 Labor, ideas on 70 
 
 Lap of bars 26, 68, 82 
 
 Length and thickness of columns 46 
 
 Limit, elastic, defined 17 
 
 Line, chalk 118 
 
 Lining forms 92 
 
 Live Toads 43 
 
 on columns 46 
 
 Loads, allowed 43 
 
 on beams 36, 43 
 
 on columns 45 
 
 dead and alive 43 
 
 on posts and braces 102 
 
 on supports 84 
 
 Longitudinally reinforced col- 
 umns 44 
 
 Low cost labor 71 
 
 Machine mixing 94 
 
 Manure 110 
 
 Material for forms 77 
 
 Measu^ring, cement 93 
 
 aggregates 95 
 
 Medium steel 13, 17 
 
 Mixing concrete 94 
 
 Modulus of elasticity 13, 20, 65 
 
 Moment, defined 36 
 
 arm 16 
 
 factor 9 
 
 formula 16 
 
 table 16 
 
 of resistance 9 
 
 formula 22 
 
 Mortar around steel 99 
 
 Nailing forms 78 
 
 Nail pullers 117, 118 
 
 Nails and spikes 103 
 
 Neutral axis 10 
 
 formula 13 
 
 table 14, 16 
 
 Night work 109 
 
 Oiled forms 106 
 
 Ordering steel Ill 
 
 Ordinances, Chicago 14 
 
 St. Louis... 43 
 
 fixing stresses 81 
 
 governing toads 43 
 
 Painted steel 68 
 
 Panel forms 83 
 
 Parabolic formulas 21 
 
 Parallel forces 40 
 
 Patented bars 17 
 
 Percentage of steel 13, 14, 18 
 
 in columns 47 
 
 Pinch bars 117 
 
 Pipe cutters Us 
 
 Placing steel 28, 98 
 
 Placing rteel 95 
 
 Plank holders 87 
 
 Plastering 109 
 
 Pliers 117 
 
 Plumbing forms 93 
 
 Posts and braces, loads on 102 
 
 Pouring columns 51 
 
 concrete 92, 97, 98 
 
 Pressure, circular tanks 59 
 
 of concrete lOO 
 
 different materials 58 
 
 against walls 53 
 
128 
 
 Reinforced Concrete, 
 
 Proportions for concrete 94 
 
 of beams 9, 10 
 
 of walls 68 
 
 Protection against fire 10 
 
 of steel 9, 10 
 
 Protected concrete columns 45 
 
 Qu'antities of aggregates 94 
 
 Racks for steel 114 
 
 Ratio of modulus of elasticity.. 21 
 
 stress 29 
 
 Reaction defined 36 
 
 Record of steel Ill 
 
 Reinforcement, double 28 
 
 over supports 32 
 
 Resisting moment 9 
 
 Restrained walls 68 
 
 Retaining walls 62 
 
 Rock concrete, strength 20 
 
 Rods, areas and weights 27 
 
 deformed 67 
 
 Roof slabs 33 
 
 Round rods 67 
 
 Rules for foremen 107 
 
 Rust 108 
 
 St. Louis Ordinance 43 
 
 Safety, factor of 19, 65 
 
 Salamanders 110 
 
 Sand pressures 53 
 
 Saw dust 110 
 
 Saws 118 
 
 Scale on steel 108 
 
 Screwed connections 68, 32 
 
 Shear 24, 25, 36. 43 
 
 Shears for steel Ill 
 
 Shrinkage, in columns 61 
 
 of concrete 66 
 
 Slabs, continuous 34 
 
 designing 83, 42 
 
 Sidewalks 48 
 
 Snips, tinners 117 
 
 Soap 106 
 
 Spacers between bars 83, 10, 67 
 
 in walls 81 
 
 Span, proportionate 
 
 Spikes and nails 103 
 
 Spirally wound columns 45 
 
 Square bare 67 
 
 Steam 108, 122 
 
 Steel colu'mns 44 
 
 in compression 30 
 
 cost of 18 
 
 cost of placing 28 
 
 distribution in slabs 34 
 
 galvanized or coated 68 
 
 high carbon 18 
 
 medium 13 
 
 ordering Ill 
 
 percentage of 14, 18,47 
 
 place in columns 60 
 
 protection 0, 10 
 
 record Ill 
 
 formula for stress 16, 22 
 
 too much 21 
 
 in walls 66 
 
 area and weights 27 
 
 use of high carbon 18 
 
 Stirrups, use and rules 25 
 
 Straight line formulas 21 
 
 Straw 110 
 
 Strength added to columns by 
 
 steel 49 
 
 of concrete 11, 20 
 
 ultimate, of steel 18 
 
 Stress, fibre 17 
 
 Stresses fixed by ordinance 81 
 
 illustrated n 
 
 internal 16 
 
 ratio of 29 
 
 shearing 35 
 
 steel and concrete 22 
 
 Studded forms 87 
 
 Supports, reinforcement over. . . 83 
 
 loads on 34 
 
 Surcharged walls 53 
 
 T beams 30, 98 
 
 Tamping concrete 97 
 
 Tanks, circular 69 
 
 Temperature 4% 
 
 Tensile strength of concrete 11 
 
 Tension failure 24 
 
 formula 22 
 
 illustrated 11 
 
 Testing beams 64 
 
 ihawing materials 109 
 
 Thickness of boards for forms.. 102 
 Thickness and length of columns 45 
 
 Thickness of slabs 33 
 
 Tinners* snips 117 
 
 Top reinforcement 32 
 
 Twisted bars 18, 67 
 
 Turneaure*s tests 64 
 
 Ultimate strength, vs. elastic 
 
 limit 18 
 
 Unit deformation 12 
 
 Variation in concrete 65 
 
 Vertically reinforced columns... 44 
 Vertical shear 24 
 
 Wall footings 63 
 
 formulas 66 
 
 pressures 63 
 
 proportions 56 
 
 restrained 68 
 
 retaining 53 
 
 Water, amount of 96 
 
 pressure of 63 
 
 Weight of earth 66 
 
 concrete 21 
 
 and areas of steel S7 
 
 Welded fabrics 37 
 
 Wetted forms 106 
 
 Wheelbarrows 95, 132 
 
 Width of beam 16 
 
 Wire drawing 17 
 
 table 101 
 
 woeking 117 
 
 Wiring forms 79 
 
 around columns. 44 
 
 Wooden beam table 104 
 
 Working concrete , 97 
 
 Wound Columns 45 
 
 Woven fabrics 37