STRUCTURAL DRAFTING AND THE DESIGN OF DETAILS CARLTON THOMAS BISHOP CORNELL UNIVERSITY LIBRARY Given to the COLLEGE OF ENGINEERING by the Machine-design dept. T 355.862°™" ""'"''"'"■"'"'y Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/cletails/cu31924003930934 STRUCTURAL DRAFTING AND THE DESIGN OF DETAILS STRUCTURAL DRAFTING AND THE DESIGN OF DETAILS BY CARLTON THOMAS BISHOP, C.E. ASSISTANT PROFESSOR OF STRUCTURAL BNOINEERING, SHEFFIELD SCIENTIFIC SCHOOL OF YALE UNIVERSITY FORMERLY DRAFTSMAN FOR THE AMERICAN BRIDGE COMPANY AND CHIEF DRAFTSMAN FOR THE HAY FOUNDRY AND IRON WORKS First Edition Second Impression Corrected NEW YORK JOHN WILEY AND SONS, Inc. London: Chapman and Hall, Limitisd 1920 COPYRIGHT, 1920 BY CARLTON T. BISHOP THE • PLIMPTON • PRESS NOSWOOD ■ MASS 'U'S'A 6/20 PREFACE This book has been prepared especially to meet the requirements of engineering students, structural draftsmen, and apprentices in structural drafting. It corresponds in scope to the duties of the structural steel draftsmen, and it therefore covers, not only the preparation of the de- tailed working drawings for steel structures, but also the design of the details of construction. It is a text-book in Structural Drafting, and it may be used as a text-book in elementary Structural Design. As a refer- ence book for structural draftsmen, it gives practical points as well as theory. A knowledge of the use of drawing instruments is presupposed, but the fundamentals of structural drafting are fully presented. The application of these fundamentals is illustrated by the drawings of many different types of members of steel structures. Exceptionally exhaustive are the chapters on the design of beams and the component parts of plate girders. The tables at the end of the book are sufficiently complete for most student courses, so that no steel manufacturers' handbook need be used. Many of the tables are arranged more conveniently for both stu- dents and draftsmen than the tables in the usual handbooks, particularly the tables for I-beams, channels, and angles. A more complete outhne of the book is given in Chapter I. The illustrative drawings have all been prepared by the author, but many of them have been adapted from similar or nearly identical draw- ings kindly furnished by structural companies, to which due acknowledge- ment is here made. The drawings and the standards of the American Bridge Company have been of exceptional value, and the drawings of the King Bridge Company, the Hay Foundry and Iron Works, the Bos- ton Bridge Works, the Mount Vernon Bridge Company, the Pennsyl- vania Steel Company, and the Central Railroad of New Jersey have been used to advantage. Abstracts from the Specifications of the Ameri- can Railway Engineering Association have been used freely throughout the text and in the tables by permission of the Committee on Publica- tions of that Association. Grateful acknowledgement is made to Professor J. C. Tracy, Head of the Department of Civil Engineering at Yale University, and to Professor J. R. Schultz, Head of the Department of Enghsh at Allegheny College, for their helpful criticisms of the manuscript. Professor Tracy gave much thought to the perusal of nine of the most fundamental chapters of Part II, and as a result of his constructive criticisms, these chapters, as well as the others in the book, have been greatly improved. Professor Schultz has read the whole manuscript and has made many valuable suggestions. Carlton T. Bishop New Haven, Connecticut, September 1919 LIST OF CHAPTERS PART I — INTRODUCTORY CHAPTER • PAQB I. Outline op the Book — Notation — Definitions 1 II. The Organization op a Stktjcturai, Company — The Engineer- ing Department 19 III. The Manufacture of Structural Steel 23 IV. The Fabrication of Structural Steel 27 PART II — STRUCTURAL DRAFTING V. Structural Drawings — The Drawing 33 VI. Structural Drawings — The Conventional Methods of Representation 37 VII. Structural Drawings — The Conventional Methods op Billing 43 VIII. Structural Drawings — The Dimensions 46 IX. Structural Drawings — The Notes, the Title, and the Border 62 X. Inking and Tracing 55 XI. Erasing 62 XII. Drawing Directly in Ink on Tracing Cloth 65 XIII. Rivet Spacing 68 XIV. Clearance, and Erection Considerations 72 XV. Layouts 75 XVI. Marking Systems 79 XVII. Beams 83 XVIII. Plate Girders 95 XIX. Latticed Girders 108 XX. Roop Trusses 113 XXI. Bridge Trusses 120 CHAPTER PAOB XXII. Columns 131 XXIII. Bracing Systems 138 XXIV. Miscellaneous Framing 146 XXV. Erection Plans and Diagrams 151 XXVI. Material Order Bills 162 XXVII. Shop Bills and Shipping . Bills 167 XXVIII. Miscellaneous Drawings and Lists 174 XXIX. Checking and Correcting Drawings 179 PART III — THE DESIGN OF DETAILS XXX. Shear and Bending Moment 183 XXXI. The Design of Beams 197 XXXII. The Design op Tension and Compression Members 206 XXXIII. The Design op Plate Girders 218 XXXIV. The Theory and Practice op Riveting 228 XXXV. Rivets in Typical Connections 233 XXXVI. Rivets in Eccentric Connections 237 XXXVII. Rivets in the Flanges of Plate Girders 241 XXXVIII. Cover Plates 259 XXXIX. Web Stiffeners 266 XL. Splices 270 XLI. Pins 278 XLII. Reinforcing Plates 284 XLIII. Bearing Plates and Column Bases 288 XLIV. Grillage Beams 291 Tables and Diagrams 297 Description op Tables and Diagrams 334 Index 339 Vll TABLE OF CONTENTS PART I — INTRODUCTORY Chapter I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS page Scope — The general arrangement — Outline of a course of study — Num- bering — Cross references — Type — Formulas — Notation — Definitions of engineering terms 1 Chapter II THE ORGANIZATION OF A STRUCTURAL COMPANY — THE ENGINEERING DEPARTMENT The structural draftsman — The Estimating or Designing Department — The Drafting Department — The templet shop — The manufacture of steel — The structural shop — Erection — The Engineering Department — The Designing Department — Design sheets — The Drafting Department — Method of procedure — Progress sheets — Cooperation 19 Chapter III THE MANUFACTURE OF STRUCTURAL STEEL Iron — Structural steel — Rolling the steel — The effect of spreading the rolls — Mill variation — Plates — The actual shapes 23 Chapter IV THE FABRICATION OF STRUCTURAL STEEL Fabrication — Elementary points — Shop methods — The plant layout — The templet shop — The stock yard — Shearing — Straightening rolls — Laying out — Coping — Other preliminary operations — Punching — Drilling — Sub-punching — Assembling — Riveting — Milling — Boring — Inspection — Painting — Shipping — Other operations 27 PART II — STRUCTURAL DRAFTING Chapter V STRUCTURAL DRAWINGS — THE DRAWING A structural drawing — Elements — Projection — The proper views — Top view — Front view — End view — Bottom sectional view — Sectional view — The distances between views — The position on the sheet — Parts shown — Symmetrical members — The usual working units — A prehminary freehand sketch — Too accurate plotting — The scale — The size of the drawings — — Drawings made on paper or tracing cloth — Black waterproof India ink — Systematic method of procedure — A draftsman should always check his own work 33 Chapter VI STRUCTURAL DRAWINGS— THE CONVENTIONAL METHODS OF REPRESENTATION The lines of a drawing — Sectional views — Breaks — Curved surfaces — Con- ventional representation — The shapes most used — A plate — An angle — An I-beam — A channel — Round and square rods — A tee — A Z-bar — A rail — An eye bar — Lattice bars — Shop rivets and holes for field rivets — All holes are shown — Bolts — Fillers — Bent plates — Other materials .... 37 Chapter VII STRUCTURAL DRAWINGS — THE CONVENTIONAL METHODS OF BILLING Billing — Conventional signs — • Plates — Angles — I-beams — Channels — Rods — Tees — Z-bars — Rails — Eye bars — Lattice bars — Washers — Rivets — Bolts — Holes — Special abbreviations 43 Chapter VIII STRUCTURAL DRAWINGS —THE DIMENSIONS Dimension and size — The dimensions — Actual measurements — Placed upon the drawing as soon as determined — Position — Dimension lines — Placed outside of the view — Space between dimension lines — Arrow heads — Dimension figures — Placed above the dimension lines — Fractions — Mis- takes — When the space between arrow heads is limited — Figures and notes read from the bottom edge or from the right-hand edge — Feet and inches — Decimals — Method of writing dimension figures — Recurring dimensions — A dimension should not be repeated — Rivets and holes — Staggered rivets — The gages — Edge distances — A line of rivet spacing — Edges of the flanges — Spaces dimensioned in a group — Supplementary dimension line X TABLE OF CONTENTS Chapter VIII — Continued STRUCTURAL DRAWINGS — THE DIMENSIONS — Continued PAGE — The sum of the dimensions — Shopmen should not be compelled to add or subtract — One method of dimensioning — Field connections — Lattice bars — The slope of a line r. 46 Chapter IX STRUCTURAL DRAWINGS — THE NOTES, THE TITLE, AND THE BORDER The notes — General notes — Other notes — Rivets and holes — Identification mark — Number of pieces — Reference to other drawings — Loose pieces bolted — Permanent bolts — Different members combined — AU notes should be made positive — The title placed in the lower right-hand corner — The first part — The second part — The smaller drawings — Sheet num- bers — The border 52 Chapter X INKING AND TRACING Structural drawings — Three methods of making drawings — The care of tracing cloth — The dull or unglazed side — The selvage edges — Cloth tightly stretched — The surface of the cloth — A good ruling pen — Pen in good con- dition — The compasses — The lettering pen — Black ink — Red ink — Should never be shaken — Frozen ink — The straight-edge — Drawing too close to the straight-edge — An easy posture — A continuous stroke — One setting of the pen — Stopping the pen ^ Lines drawn away from intersec- tions — Heavy lines — Parallel lines — Curves — Need not wait for ink to dry — Rush work — A blotter should not be used — Systematic method of procedure — Fine lines — Heavier main lines — Rivets and holes — Arrow heads — Dimension figures — Billing material — List of members — Notes — Title — Border — Tracing should be inverted 55 Chapter XI ERASING To erase properly — The object of erasing — Erase willingly — Guard against mistakes — The secret of erasing — The eraser — Ink eradicator — A knife or metal scratcher should not be used — An erasing shield — A brush — The surface of the cloth — Replace lines and figures erased by mistake — Pencil lines 62 Chapter XII DRAWING DIRECTLY IN INK ON TRACING CLOTH Method recommended — Tracers — Arguments — Not all drawings are well adapted to this method — A drawing must be carefully planned — Paper placed underneath the cloth — Illustration 65 Chapter XIII RIVET SPACING PAGE Rivet spacing — Rivet pitch — General rules — Set of standards — The specifica- tions — Standard gages — The minimum spacing — The maximum spacing — Wide cover plates — Edge distance — Stitch rivets — Lattice bars — Practical points — Usual spaces — Continuous rivet spacing 68 Chapter XIV CLEARANCE, AND ERECTION CONSIDERATIONS Clearance — Provision for overrun — Tight fits — Projecting parts — Erection clearance — Seat angles — Holes for anchor bolts — Other connections — Driving clearance — Other erection considerations 72 Chapter XV LAYOUTS A layout — When used — A simple layout — Three common types — Method of procedure for a gusset plate — The calculation of the slope — Lateral plates — Bent-plate work 75 Chapter XVI MARKING SYSTEMS Two kinds of marks — Assembling marks — When used — Three parts — The first letter — The second letter — The sheet number — Rights and lefts — Summary — Shipping marks — Two parts — Marked conspicuously — Rights and lefts — Members combined — Opposites — Office-building con- struction — Bridge trusses — Roof trusses — Tie rods — Direction marks ... 79 Chapter XVII BEAMS A simple beam — A cantilever beam — A continuous beam — Made of a single main piece — I-beam and channel — Printed forms — Beams are supported — Standard connection angles — Three different methods — The modified method — Single angles — Different depths — Standard angles are designed — Beams shown full length — Web connections located horizontally in two ways — The length of a beam — Ordered length — Mill variation — Bearing plates — Coping — Office-building construction — Purlins — Tie rods — Sag rods — Multiple beam punch — Nailing strips or spiking pieces — Holes in the flanges — Beam girders — Box sections — WaU plates — Skewback angles — Crane runway beams — Skew connections 83 TABLE OF CONTENTS XI Chapter XVIII PLATE GIRDERS PAGE Adaptability — Types — Main dimensions — End stiffening angles — Flange angles — Web plates — Intermediate stiffening angles — Fillers — Crimped stiffeners — Cover plates — Flange rivets — Rivets in cover plates — Gages — Rivets in outstanding legs — Holes for anchor bolts — Reference dimen- sions — Reference line — Box girder — Camber — Curved ends 95 Chapter XIX LATTICED GIRDERS Definition — Common form — End connections — Proportions — Worldng lines — Panel depth — Panel length — Dimensions — Plates — Different num- bers of rivets in diagonals — End connection plates — Double latticed girders — Stitch rivets — Typical connections — Stiffening girder 108 Chapter XX ROOF TRUSSES Steel roof trusses -r- Common types — The pitch — Purlin spacing — Form of support — Arrangement on the sheet — System of working lines — Form of members — Gusset plates — Stitch rivets — Center hanger — Shipment — — Ridge strut — Purhn connections — Bracing rods — Bottom-chord brac- ing — Future extension — Gable end — Louvres 113 Chapter XXI BRIDGE TRUSSES When used — Common types — The joints — Arrangement on the sheet — Ar- rangement of views — Shipping marks — Camber — Size of pin holes — Types of members — Milling — Splices — Reinforcing plates — Counter- sunk or flattened rivets — Protection from the weather — Clearance — Method of holding a counter 120 Chapter XXII COLUMNS Steel coliimns — Position on the sheet — Different types of columns — Plate and channel columns — The important dimension — Beam coimections — Sec- tional views — Typical mill-building column — Connections — Column base — Milling — Vertical dimensions — Gages — Gable column — Latticed columns 131 Chapter XXIII BRACING SYSTEMS Bracing — Considered as trusses — Statically complete — The lines of stress - Arrangement — Initial tension — Connections — Gages — Illustrations - Mill-building bracing — Bottom-chord bracing — Unsymmetrical bracing - Knee braces — Bottom lateral bracing — Top lateral system — Brackets - Cross Frames — • Office-building bracing 138 Chapter XXIV MISCELLAIiTEOUS FRAMING Illustrative drawings — Girts — Struts — Plate work — Skew work — Miscel- laneous material 146 Chapter XXV ERECTION PLANS AND DUGRAMS The plans and diagrams — The draftsman — The erector — Other contractors — Typical plans and diagrams — Plate girder bridges — Truss bridge — Anchor-bolt plan — Erection diagram for a mill building — Crane clearance diagram — Corrugated steel — Floor plan of an office building — Method of procedure — Different floors — Column schedule — Record of Drawings — Progress record for beam drawings — Progress record for columns 151 Chapter XXVI MATERIAL ORDER BILLS Purpose -^ Lists of material — Methods — Miscellaneous material — Two parts — Drawings conform to the material ordered — The arrangement — Ship- ments — Numbering — Specifications — Shipping direct to site — Changes — Ordered lengths — Beams — Angles — Plates — Lattice bars — Tie rods — Sag rods — Gas pipe — Rails 162 Chapter XXVII SHOP BILLS AND SHIPPING BILLS A shop bill — Form — Numbering — Three parts — Arrangement — Itemizing — Item number — Number of pieces — Section — Length — Calculated weight — A shipping bill — Shop and shipping bills combined — Combin'&tion sheets 167 Chapter XXVIII MISCELLANEOUS DRAWINGS AND LISTS Miscellaneous material — Special printed forms — Cast-iron base — Rods — Field rivets and bolts — Erector's list — Summary of field rivets and bolts — Erection bolts 174 xu TABLE OF CONTENTS Chapter XXIX CHECKING AND CORRECTING DRAWINGS page A checker — Not all drawings are completely checked — A detailer should be familiar with the method of checking — A checker should work systematically — Suggestions — Indicating mistakes — Check marks — Back-checking — Students' drawings — Corrections — ■ Revisions 179 PAKT III — THE DESIGN OF DETAILS Chapter XXX SHEAR AND BENDING MOMENT The terms — Principles — Signs — Forces considered — Shear — Bending mo- ment — Formulas — Sketches — Arrangement — Reactions — Concentrated Loads — Uniformly distributed loads — Combined loads — Short-cut rule — Relation between shear and bending moment — • Live loads — Impact — Live-load shear, simple and cantilever beams — Live-load bending moment, simple and cantilever beams, concentrated, uniformly distributed, and com- bined loads — Restrained beams — Continuous beams — Conventional wheel- load systems — Maximum shear on beam — Maximum shear for any section — Maximum floor-beam reaction — Absolute maximum bending moment — Maximum bending moment at any point — Through girders — Trusses .... 183 Chapter XXXI THE DESIGN OF BEAMS General — Points considered — Effects of bending — Resisting Moment — Theory — Unit stress — Section modulus — Units — Rectangular beams — Cylindrical beams — Steel beams — Beams must be self-supporting — A beam is weakened by holes — Lateral supports — Lateral thrust — Shear — Bear- ing — Deflection 197 Chapter XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS Practical points — A tension member — A compression member — The area of cross section — The form of cross section — Effect of rivet holes — Weakest point of a tension member — Loop rod — Clevis — Round rod — Eye bars — Riveted tension members — Net area of cross section — The design — The least net section is not necessarily a right section — Working rule for effective net section — Smaller net section near the ends — Compression members — ^^trength — Compression formula — The radius of gyration — The moment of inertia — The forms of members — Members which resist bending and direct stress — Lattice bars and tie plates — The design — A tie plate — Lattice bars — Method of design 206 Chapter XXXIII THE DESIGN OF PLATE GIRDERS The common forms — Analysis of forces — The depth — The web plate — The flanges — Flange angles — Cover plates — Distribution of area — The com- pression flange — Three methods of design — The degree of accuracy — Case A — Assumptions — Theory — Case B — Assumptions — Two more steps — Theory — The effective depth — Lateral forces — Vertical flange plates — Centrifugal forces 218 Chapter XXXIV THE THEORY AND PRACTICE OF RIVETING Rivets — Shop and field rivets — Position in member — Assumptions — The design of a riveted joint — Nominal diameter — The strength of a rivet in shear — Single shear — Double shear — The strength of a rivet in bearing — Bolts — Number of rivets required — Flattened and countersunk rivets — Indirect riveting — Typical riveted connections 228 Chapter XXXV RIVETS IN TYPICAL CONNECTIONS Typical riveted connections — Gusset plates, continuous and spliced chords — Symmetrical gusset plates — Web connection for beams — Seat connection for beams — Stringer connection — Floor-beam connection — Other connections 233 Chapter XXXVI RIVETS IN ECCENTRIC CONNECTIONS Definition — Method of designing — ■ Theory — Working rule 237 Chapter XXXVII RIVETS IN THE FLANGES OF PLATE GIRDERS Flange rivets — Rivet pitch — Inclined girders — Complete treatise — General discussion — Controlling factors — Forces considered — Depth — Different cases — Case I, Concentrated static loads applied to the web — How appUed — Bending moment theory — Shear theory — • Case II, Uniformly distributed static loads applied to the web — How applied — Theory — Case III, Com- bined concentrated and uniformly distributed loads apphed to the web — Method — Variable fixed loads — Case IV, Moving loads applied to the web — How applied — Theory — Approximate method — Case V, Loads applied to the flange — How applied — Theory — Loads applied to the bottom flange — Case VI, Girders in which the web is considered to resist part of the stress due to bending moment — Method — Case VII, Box girders, cantilever girders, and girders with non-parallel flanges — A box girder — A cantilever girder — Girders with non-parallel flanges — Case VIII, Girders with vertical flange plates, and girders with four angles in each flange — When used — Vertical flange plates — Theory — Four angles in each flange — The de- termination of the minimum pitch based upon the strength of the web — Importance — ■ A table of minimum pitches — Unit stresses — Theory — Summary 241 TABLE OF CONTENTS Xlll Chapter XXXVIII COVER PLATES page Use — Some cover plates extend the full length — The theoretical length — The graphic method — The algebraic method — Symmetrical loads — Uniformly distributed loads — Concentrated loads — Variable concentrated loads — Moving concentrated loads — Algebraic method — Rivets in cover plates — Four points considered — Increase in flange stress — Each plate should be developed by rivets 259 Chapter XXXIX WEB STIFFENERS .Shearing stresses — Vortical stiffening angles or stiffeners — The thickness of the web plate — End stiffening angles — Designed for bearing — The strength in compression — Rivets — Intermediate stiffeners — Spacing — Rivets — Crimping 266 Chapter XL SPLICES Definition — Design — Three types — Web splices — When used — The design — Design for shear only — Design for bending moment as well as for shear — Separate splice plates — Flange splices — When used — Component parts not spliced at same point — Cover-plate splice — Flange-angle splice — Splice at the curved end of a girder — Field splice in girder flange — Column splices — Mill-building columns — OfRce-building columns — Channel columns 270 Chapter XLI PINS Description — Pins are designed as cylindrical beams — Application of forces — Design for bending — Investigation for shear — Not every pin in a truss need be designed — Paclcing — Horizontal and vertical componenets — The forces which act — Computation 278 Chapter XLU REINFORCING PLATES When used — Type of member — Method of design — Design for bearing — The number of rrvets — Design for tension — The rivets in a tension member 284 Chapter XLIII BEARING PLATES AND COLUMN BASES Type — Size of bearing plate — The thickness of bearing plate — Expansion — Pedestals and shoes — Column bases 288 Chapter XLIV GRILLAGE BEAMS page When used — Arrangement — Tie rods — The loads — The allowed bearing pres- sure — Concrete mat — Method of design — Design for bending — Investi- gation for buckling — Investigation for shear 291 TABLES AND DIAGRAMS Weights and dimensions of Carnegie I-beams, American Bridge Company con- nection angles — Weights and dimensions of standard I-beams, Lackawanna connection angles — Weights and dimensions of Carnegie Channels, American Bridge Company connection angles — Weights and dimensions of standard channels, Lackawanna connection angles — Weights and dimensions of Bethlehem I-beams and girder beams, Bethlehem connection angles — Weights and areas of standard and special angles — Gages of angles — Areas of holes — Weights and dimensions of rivets and bolts — Rivet code — Clearance for machine-driven rivets — Minimum rivet stagger — Minimum rivet spacing — Maximum rivet spacing — Edge distances — Minimum rivet stagger — Minimum pitches for flange rivets — Multiplication table for rivet spacing — Tables of rivet values — Charts for determining resultants graphi- cally in decimals, inches and fractions, and feet and inches — Purlin con- nections — Lattice bars — Areas and weights of rods — Bearing plates — Separators — Anchors — Rod connections — Dimensions and properties of rails — Rail fastenings — Unit stresses for structural steel — Shear and moment table for Cooper's engine loading — Properties of wooden rectangular beams — Unit stresses for structural timber — Moments of inertia of rec- tangles — Areas of plates — Weights of plates — Properties of I-beams — Properties of channels — Properties of Bethlehem I-beams and girder beams — List of shipping marks — Properties of standard and special angles — Net areas and tensile strengths of two-angle members — Unit stresses for compression — Radii of gyration of two-angle struts — Safe loads of single- angle and two-angle struts — Table of squares — Resisting moments of pins — Decimal equivalents 297 Description of Tables and Diagrams 334 Index 339 STRUCTURAL DRAFTING AND THE DESIGN OF DETAILS PART I — INTRODUCTORY CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS Synopsis: In this chapter are summarized the arrangement, the notation, and the special features of this book. Brief definitions are given to show the meanings of the engineering terms used in the text. 1. Scope. — This book is planned to meet the requirements of en- gineering students, of apprentices, and of structural draftsmen. In scope it is designed primarily to correspond to the duties of the struc- tural draftsman. It is divided into three parts, emphasis being laid upon Part II — Structural Drafting. This Part II includes the funda- mentals of structural drafting, such as the methods of representation, of billing, and of dimensioning. The apphcation of these fundamentals to the drawings of common types of members is fully illustrated. In Part III the elements of design are shown with special reference to the design of details and of simple members with which the draftsman must be familiar. The design of other members and of complete structures is omitted for two reasons, (1) because they are usually designed in a special Designing Department instead of in the Drafting Room, and (2) because nearly all phases of structural design are admirably de- scribed in so many books that it would be futile to duplicate them here. Part I is introductory and is inserted primarily to give the student a conception of the relation between the drafting room and the other branches of the steel industry. Tables are inserted at the end of the book. These tables may supplant the handbooks of structural steel companies in some student courses. The tables are arranged to mini- mize the turning of pages when used either in drawing or in designing. This is accomplished by placing on one page the data usually given on several pages. For instance, by separating standard angles from special angles the properties of each may be shown on a single page. Further- more, the weights and areas of all angles are grouped with the gages of the angles and the areas of holes, an arrangement which is equally convenient for the draftsman when drawing and when designing. The scope and the use of the tables may be seen best by reference to the tables themselves and to the brief descriptions which follow them. 2. The general arrangement of the book is planned for convenient reference. It is believed that the text will be used chiefly for reference by students, apprentices, and draftsmen. The shape of the book is such that it will stay open on the desk without the use of weights or clamps. The size of the pages was selected so that the drawings and the tables could be made reasonably large and clear without the use of intolerable folded inset sheets. PART I — INTRODUCTORY 1. The author first planned a chapter which would give an outline of a course of study. It was felt that such an outline would simplify the assignment of student work, and that it would be useful to appren- tices and others who might use the book without instruction. It might also be of service to the younger instructors when planning to use the text for the first time. However, it was concluded that the large major- ity of readers would have no use for such a chapter. Each instructor should become familiar with the book before he adopts it as a text, and he should have little difficulty in selecting the proper sequence of para- graphs in the fundamental chapters of Part II. The author does not feel that it is wise for the student to devote much time to a study of the text before he begins to draw. The first drawing, if sufficiently simple, may be started at the first exercise, accompanied by references to the most important paragraphs that bear upon the drawing. This may be followed by other drawings each of which illustrates as many new points as the average student can master. The work should be progressive, but no drawing should involve points beyond the student's ability and he should be expected to make each drawing fundamentally correct. It may be difficult to obtain excellent results at the outset owing to the multiplicity of conventions and practical points which are new to most students; but to allow violations of drafting methods and conventions to stand uncorrected is a source of trouble. Reasonable requirements should be made and enforced, and all mistakes should be corrected by the students as a safeguard against repetition. It is rec- ommended that many of the penciled drawings be left uninked in order to facilitate the making of changes and to enable the students to make more drawings within the allotted time. The author has found it satisfactory to use printed forms for beam work at the beginning of the course, for they not only conform to the usual drafting room practice but they enable the student to concentrate his mind on points other than the arrangement of views and of dimensions Unes which he can learn gradually. In order to introduce the fundamentals as early in the course as possible it is expedient to have the students make free- hand drawings at their desks or at the blackboard instead of taking time for careful plotting. As soon as possible the data and suggestions given with each new problem should be reduced to a minimum in order to develop the student's resourcefulness. Frequent tests may be given, and one question on each test may well be devoted to the indication of mistakes on a given drawing, i.e., practice in checking. 2. Numbering. — In this book all pages are numbered consecutively. Each figure bears the same number as the page upon which it may be found. This facilitates the finding of any figure to which reference is made. When more than one figure is placed upon the same page they are lettered, thus: Fig. 24 (a) and Fig. 24 (&) are both on page 24. The paragraphs are numbered on each page independently, beginning with 1. This is done to avoid large paragraph numbers. 3. Cross references should be made to both the page and the para- graph. Reference to a page alone is not sufficiently specific, particu- larly where the paragraphs are short as in the fundamental chapters of Part II; reference to a paragraph without the page often results in an extended search because the paragraphs are of unequal lengths and on some pages no paragraph number is found. In this book the page numbers are followed by the paragraph numbers, while the paragraph symbol (1|) and abbreviation (Par.) are replaced by the colon, thus: Page 29 : 4. Furthermore, a distinction is made between two classes of cross references. Where an additional statement is required to sup- plement the text, needless repetition may often be avoided by reference to another, paragraph. These references are important. Other less important references are given for the convenience of those who do not grasp the full significance without them. Unless a distinction were made it is probable that students would either waste time in looking up points which may be obvious to them, or else they would become careless and fail to look up the more important references. In order to derive the greatest benefit from the cross references, therefore, the following interpretation should be made, viz.: All references which appear as part of the text or as separate sentences should be consulted, as for example: See page 23 : 2. All references which appear in parentheses need be consulted only in case additional information is desired, as for example: (page 29 : 4). 4. Type. — Bold-faced type is used for convenient reference to show the topic of each paragraph. In some cases separate paragraph headings are used, but this plan is not rigidly adopted. Usually words or phrases CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS are found which give the desired information, and when these are accentuated it seems unnecessary to duphcate them in special headings. In this manner the more important parts of a paragraph are often emphasized. Fine type is used to insert remarks or explanations at points where they would be more serviceable than in footnotes, but in such a manner that the sequence of the main text remains unbroken. 1. Formulas are so often used blindly by persons who have little conception of their meaning that the author sometimes feels that no formulas should be used by students lest they become "handbook engineers." He believes that no one should use a formula who is not positive that he can derive it. In other words a formula should be considered an expression of a method arranged for convenience in apply- ing that method. It is a "short-cut " application of the method but it should not be used without a knowledge of the underlying principles. Comparatively few formulas are used in this book. These are not summarized for reference but appear only in conjunction with the cor- responding derivations which in turn are clearly indexed. It is hoped that this plan wiU tend to cultivate the proper use of formulas. 2. Notation. — Considerable annoyance has been experienced on account of the lack of uniformity in the notation commonly used in formulas. For example, students constantly confuse bending moments and resisting moments in pound-feet with those in pound-inches; simi- larly in the usual reduction formulas, they often substitute the lengths of compression members in feet instead of in inches. While these mistakes are due chiefly to carelessness, yet they would be minimized by greater uniformity. In this book, all dimensions in feet, all moments \ pound-feet, and all quantities which involve compound units based ^nrj the foot are expressed by capitals. Similarly, all dimensions in •inches, all moments in pound-inches, and all quantities which involve compound units based upon the inch are (with two exceptions) expressed by lower-case letters. The capital / is used for moments of inertia in inches to the fourth power, and the capital E is used for modulus of elasticity in pounds per square inch. These letters are so universally and almost exclusively used that it seems unwise to institute a change. Significant letters, or letters commonly used, have been chosen wher- ever feasible, even though a single letter may thus have more than one meaning. It is felt that these meanings are so distinct that there is little chance for ambiguity; further distinction is made possible by the use of primes or subscript letters. Letters used in the tables at the end of the book or in certain other places are not included in the following summary, since these letters have no special significance outside of the places where their meanings are apparent. The term "pound-feet" is adopted after due deliberation in preference to the more common term "foot-pounds." This is done primarily to distinguish the unit of moments from the unit of work. Both are compound units derived from the product of weights or forces in pounds by distances in feet; but work is measured by the product of a force by the distance through which the body acted upon moves, whereas a moment is the product of a force by the perpendicular distance from the force to a point about which there is a tendency to rotate. It is confusing, for example, for a student in going from a class in Mechanics to one in Structural Design to find the same term used for these two distinct meanings. Furthermore, it seems more natural to define a moment as "the product of a force by its lever arm " rather than as "the product of the lever arm of a force by the force itself." In practice it is customary first to select a force whose moment is desired, and then to find the distance from this force to the point of moments. Thus it is logical to put the unit of the force before the unit of the lever arm. # = lb. or lbs. = pound or pounds; also number. ' = ft. = foot or feet. °' = sq. ft. = square foot or square feet. # ft. = lb. ft. = pound-feet. #/ft. = pounds per foot. #/sq. ft. = pounds per square foot. NOTATION a„ r = mean depth between rivet lines, in feet. D« = depth between centers of splice plates, in feet. Dm, = depth of web plate, in feet. {stress in rivet at unit distance from center of rotation due to eccentricity, in pounds, modulus of elasticity, in pounds per square inch. F = flange stress, in pounds or in thousands of pounds. /* = moment of inertia, in inches ^. conventional sign for I-beam. left. length, in feet. conventional sign for angle. a = area, in square inches h = back. breadth of beam, in inches. unit stress in bearing, in pounds per square inch- c = center. width of strip, in inches. distance from neutral axis to the extreme fiber, in inches. d = depth, or diameter, in inches. dh = depth from back to back of angles, in inches. dg = effective depth between centers of gravity, in inches. dr = mean depth between rivet lines, in inches. (ia = depth between centers of splice plates, in inches. du, = depth of web plate, in inches. e = eccentricity, in inches. i rivet stagger, in inches, unit stress in the extreme fiber due to bending, in pounds per square inch. g = gage, in inches. h = effective depth of arch, in inches. k = distance in eccentric connections from the center of gravity to the center of rotation, in inches. I = length, in inches. ■ The capitals E and / are used instead of lower-case letters in order to conform to common usage (see preceding paragraph). CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS M — moment, in pound-feet. Mb = bending moment, in pound-feet. Mr = resisting moment, in pound-feet. P = concentrated load, in pounds or in thousands of pounds. right. R = I radius of curvature, in feet. reaction, in pounds or in thousands of pounds. Rl = left-hand reaction, in pounds or in thousands of pounds. Rg = right-hand reaction, in pounds or in thousands of pounds. (S = stress, in pounds or in thousands of pounds. r = tension. tensile stress, in pounds or in thousands of pounds. conventional sign for Tee. U = unit load uniformly distributed, in pounds per foot or in thousands of pounds per foot. U' = unit load imiformly distributed, in pounds per square foot. V velocity, in feet per second. vertical shear, in pounds or in thousands of pounds. W = total load uniformly distributed, in pounds or in thou- sands of pounds. length of cover plates, in feet, unknown distance, in feet. X = Y = unknown distance in feet. Z = conventional sign for Z-bar. m = inoment, in pound-inches, ms = bending moment, in pound-inches, mfl = resisting moment, in pound-inches. P rivet pitch, in inches. projection of bearing plate, in inches. q = statical moment, in inches '- radius of gyration, in inches, radius of curvature, in inches. limiting value of one rivet, in pounds or in thousands of pounds. section modulus, in inches'. unit stress in shear, in pounds or in thousands of pounds. t = thickness, in inches. V = intensity of shear, in pounds per square inch. unknown distance in inches. horizontal distance in eccentric connections from a rivet to the center of gravity of a group of rivets, in inches. y— vertical distance in eccentric connections from a rivet to the center of gravity of a group of rivets, in inches. s = direct distance in eccentric connections from a rivet to the center of rotation, in inches. PART I — INTRODUCTORY + = sign for upward forces, for forces toward the right, and for clockwise moments. C. L. or ^ = center hne. b. to b. = back to back. = sign for downward forces, for forces toward- the left, and for counterclockwise moments. o. to o. = out to out. D. L. = dead load. O.S. = outstanding. Sym. abt. $ = symmetrical about the center line, c. to c. = center to c\enter. PI. = conventional sign for plate. L.L. = live load. U.M. = universal mill (for plates with rolled edges.) l_j = conventional sign for channel. H equation = (HH = 0), or the sum of the horizontal components equals zero. V equation = (SF = 0), or the sum of the vertical components equals zero. M equation = (2Af = 0), or the sum of the moments equals zero. DEFINITIONS 1. On the following pages are summarized brief definitions of the engineering terms used in Parts II and III of this book.* The defini- tions of some of these terms are not found elsewhere, and the definitions of many others are not readily accessible. It is hoped that the student will be encouraged to consult these pages whenever the meaning of an engineering term is not fully comprehended. No attempt has been made to give every interpretation of the words defined, nor to define such com- mon words as bridge, building, etc. It is intended that every definition is sufficiently complete to explain the use of the word in the text. Abutment. The masonry support at the end of a bridge or arch. Anchor. A device for fastening steel work to masonry. Anchor Bolt. A bolt which fastens steel columns, girders, etc., to masonry. Anchor-bolt Plan. A drawing -n^ich shows the location of anchor bolts. Angle. A common structural steel shape the cross section of which is in the form of a right angle. Apex. Panel point. * For a more complete glossary of engineering terms, see Waddell's "Bridge Engi- neering," John Wiley and Sons, Inc., New York. Architects' Scale. A measuring scale graduated for convenience in plot- ting dimensions in feet, inches, and fractions of inches, as distinguished from an "Engineers' Scale." Assembling Marks. A system of marks used on the component parts of a member to facilitate assembUng in the shop. Axle Load. The load from a truck, car, or locomotive applied to a struc- ture through the wheels at both ends of the axle, hence twice the corresponding "wheel load." Back-check. To approve or check the corrections of a checker. Base Angle. An angle which connects the bottom of a column to the base plate or cast base. Base Plate. A distributing plate upon which a column rests. Batten Plate. A plate used to hold the component parts of a member at the proper distance apart. Generally used in conjunction with lattice bars. Beam. A member which resists flexure or cross bending. Commonly an I-beam or a channel. Beam Girder. A member composed of two or more I-beams or channels fastened together by bolts with separators or by cover plates. CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS Bearing. The support upon which a member rests. The resistance to crushing, as offered by a member which bears against another or upon a support, also as offered by a component part of a member to a rivet or a pin. Bearing Plate. A plate used to distribute the bearing over a greater area, as at the end of a wall-bearing beam. Bearing Value. The amount of pressure in bearing, either total or per unit of area. Bed Rock. The solid rock which underUes the looser sand, gravel, etc. Bending Moment. A term which expresses the measure of the tendency of a beam to bend. It is the sum of the moments of all external forces on one side of the point of moments. Bent. A vertical frame or truss used to support other members. Bevel. The slope of a line with reference to another line. Beveled Washer. A cast washer arranged to compensate for the inclina- tion between a bolt or rod and the member through which it passes. Bill. A list of material, such as a shop bill, shipping bill, etc. To prepare such a bill. Also to express the size of a component part of a mem- ber on the drawing. Block and Tackle. A set of pulley blocks with ropes used for hoisting. Block Out. To cut out by means of a rectangular pimch. Blueprint. The form of reproduction of a drawing which is issued from the drafting department. Blueprints are made from tracings by exposing sensitized paper to the Ught. Board Measure. Lumber is measured in imits of one foot board measure, equal to one-twelfth of a cubic foot, two dimensions being taken in feet and the third in inches. The abbreviation M. B. M. stands for "thousand feet board measure." Bore. To enlarge a punched hole by means of a cutter which accurately pares the inner surface. Box Girder. A compound girder with two or more web plates which, with the cover plates, form a closed box. Box Section. A member in which the component parts enclose a space which is accessible only at the ends. Brace. An inclined member placed between other members to make a structure more rigid. Bracing System. A series of diagonals and struts placed between main members to resist wind or other lateral forces. Bracket. A projecting type of connection usually made of a plate and angles. Buckle. To bend or bow transversely imder the effects of a force. Buckle Plate. A steel plate which is buckled or dished at regular inter- vals to increase its resistance to transverse bending. Used in bins and in the floors of highway bridges. Building Code. A compilation of the building laws and ordinances of a city which relate to building construction. Butt Joint. A joint in which the ends of the parts connected are cut to bear against each other. The ends are held in place by means of splice plates, or similarly. Calk. To make the seams of boats, tanks, etc., watertight, either by driving oakum or something similar into the seams, or by forcing the sharp beveled edge of one of two overlapping steel plates into the face of the other by means of an air hammer. Camber. A comparatively flat vertical curve placed in the bottom chord of a truss or girder to counteract the sag. Cantilever Beam or Cantilever Girder. A beam or girder which projects beyond one or both supports. A cantilever beam may have one end embedded in a wall and the other end unsupported. Cap Angle or Cap Plate. An angle or plate at the top of a column or portion of a column. Casting. Anj^thing formed by pouring molten iron, steel, or other ma- terial into a mold and allowing it to harden. Center of Gravity. That point through which the resultant of the par- allel forces of gravity acting upon a body in any position must pass. If the body could be supported at this single point it would remain in equilibrium in any position. Center Punch. A cylindrical piece of steel with a sharp point protruding from one end. It is inserted in the holes of templets and struck with a hammer to make dents in the steel to indicate where holes are to be punched. Change Order or Change Slip. An order issued to make changes in the material already ordered from the mills. 8 PART I — INTRODUCTORY Channel. A common structural steel shape the cross section of which is similar to that of an I-beam except that the flanges are on only one side of the web. Check. To approve the correct portions of a drawing and indicate the mistakes. To verify. Checker. A person in the drafting room who checks the drawings made by others. Checkered Plate. A steel plate with raised ribs to prevent slipping. Used for floors, stair treads, etc. Check Marks. Small v-shaped marks or dots placed over dimensions or other quantities to indicate that they have been checked. Chip. To cut off projecting parts, as with a pneumatic chisel. Chord. The main top or bottom member, or line of members, in a truss. Clearance. A space left between members, or parts of members, to allow for inaccuracies in cutting and to facilitate placing them in position. Clear Span. The length of span from face to face of abutments. Clearstory. The raised portion of the roof of a null building or similar structm-e, arranged with windows in the vertical sides. Clevis. A forging used to connect a clevis rod to a plate or angle. The clevis is arranged to screw on the end of the rod, and the plate is inserted between two flattened ends through which a pin is passed. Clip. A small connection angle. Collision Strut. An auxiliary member which gives intermediate support to the end post of a bridge. Column. A long member, usually vertical, which resists compression. It is the principal vertical member in a building. Column Base. The cast-iron base or pedestal upon which a column stands. Also the base plate and angles riveted to the bottom of a column. Column Formula. A formula by means of which the allowed unit stress in a column is determined. Its values depend upon the ratio of slendemess of the column.- Column Schedule. A drawing upon which is simimarized information regarding the composition and the lengths of different sections of the columns in an office building. Combination Sheet. A printed form upon which a drawing, a shop bill, and a shipping bill are combined. Combined Stresses. Stresses due to bending combined in the same member with direct stresses due to tension or compression. Compass. An instrument for drawing circles. Component. One of two or more parts into which a force or stress may be resolved. The force or stress is the resultant of its components. Compression Formula. Same as Column Formula. Compression Member. A member in which the principal stresses tend to compress or shorten the member. Concentrated Load. A load which is appUed over such a small area or to such a small portion of a member or a structm-e that in effect it may be considered as a single force. Concrete. An artificial stone made of cement, broken stone, sand and water which are first mixed together, and then placed in position and allowed to harden. Connection Angle. An angle used for connecting other parts. Connec- tion angles are often used in pairs. Connection Plate. A plate used for connecting other parts. Continuous Beam or Continuous Girder. A beam or girder which rests upon more than two supports. Contra-flexure. A change in the direction of bending in a colimin or a beam. Cooper's Conventional Loads. A system of concentrated wheel loads of two conventional locomotives followed by a train, commonly used in finding stresses in railway bridges. Cope. To cut away part of the flange of a beam to avoid iiiterference. Cored Holes. A hole in a casting made by means of a core in the mold which prevents the metal from flowing into the space. Cornice. The rain-tight jvmction of the overhanging roof and the side walls of a building. Corrugated Steel. Thin sheets of steel which are stiffened by having corrugations rolled in them. They are used for covering the roofs and sides of mill buildings. Cotter Pin. A cylindrical pin held in place by a split steel key or " cotter " placed through a hole in the pin. CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS 9 Coxmter. An adjustable diagonal placed across one of the panels near the center of a bridge in the opposite direction from the main diagonal tension member in the same panel. Its function is to relieve the main diagonal from stresses which might cause compression under certain positions of the live load. Countersink. To ream a hole to receive the conical head of a rivet, bolt, or screw so that the end thereof will not project beyond the face of the part connected. Couple. Two equal parallel forces acting in opposite directions and in different lines. The moment of a couple about any point of moments is the product of one force by the perpendicular' distance between the two. Cover Angle. A splice angle placed inside another angle with both legs in contact Cover Plate. A plate riveted to the flanges of a girder or compression member to increase the area of cross section. Crane. A hoisting machine arranged to move heavy loads both verti- cally and horizontally. An overhead traveling crane is commonly used in mill buildings, being supported by longitudinal girders on opposite sides of the building. Crane Girder or Crane Runway Girder. A girder which supports one of the rails upon which a traveUng crane runs. Also a girder of the crane itself. Crimp. To offset the end of an angle by forging so it can overlap another angle without the use of a filler. Cross Bracing. Bracing with two intersecting diagonals. Cross Frame. Vertical transverse cross bracing between girders. Cross Hatch. To draw sloping shade lines signifying a cross section. Cross Section. A transverse section. Also a view representing the ap- pearance of a structure or member where cut by an imaginary sec- tion plane. Curved Ruler. A guide along which irregular curved lines may be drawn. Dap. To notch a timber to fit over another timber. Data Sheet. A sheet upon which are given the necessary data for the manufacturers of cranes, elevators, etc., that they may make them conform to the building requirements. Dead Load. The comparatively constant static load on a structure due to its weight, etc., as distinguished from the live or moving load. Deck Bridge. One in which the principal loads are applied to the top chords. Deflection. A lateral movement at right angles to the principal axis. Also the linear measure of such movement. Degree. A measure of curvature iii railway work. The degree is the angle at the center of a circular curve subtended by a 100-foot chord. Depth. The principal vertical distance in a horizontal member or struc- ture, or the corresponding dimension in an inclined member. Derrick. A hoisting machine so pivoted that a load may be swung horizontally. i Design. To proportion one or more members or parts of a structure to properly fulfill the requirements. Also the act of designing or the results thereof. Designer. One who designs. The title given to one whose principal duty is to design structures. Design Sheet. A drawing prepared by the designer showing the prin- cipal dimensions of a structure and the sizes of the designed members. Detail. To make a detailed working drawing. Also a connection or other minor part of a member in contradistinction to the main member. Detailer. One who details. The title given to a draftsman who makes detailed working drawings. Develop. In drafting, to represent a bent or curved part as if it were flattened into a plane. In designing, to make a connection fully as strong as the part connected. Diagram. An outline drawing or sketch in which each member is usually represented by only a single line, as an erection diagram or stress diagram. Diaphragm. A stiffening plate or similar part placed between the webs of a member, or from one member to another. Die. A steel form used in forging or cutting any piece. Dimension. A linear measurement indicated on a drawing upon a dimen- sion line which shows its extent and significance. Dolly Bar. A tool for holding a rivet in place while the opposite end is being hammered to form the second head. 10 PART I — INTRODUCTORY Door Post. A vertical member in a door frame. Double Shear. The tendency to shear, or the resistance to shear, in two planes. Drafting. Making working drawings, usually including the designing of the details. Draftsman. One who drafts or makes working drawings. The title usually includes those who check the drawings. Drawing. A representation by means of lines drawn by pencil, pen, etc. Drill. To make a hole by means of a revolving cutting tool or drill. Driving Clearance. The distance from a rivet to the nearest projection which might interfere with the use of the machine which drives or upsets the rivet to form the head. Driving Nut. A nut which is temporarily screwed on the end of a bridge pin to protect it while it is being hammered into position. Eave Strut. A longitudinal strut between the tops of the columns of a building at the eaves. Eccentric Connection. A connection in which the line of action of the resultant stress does not pass through the center of the group of connecting rivets. Eccentricity. The distance from the center of gravity to some other point or center line. Edge Distance. The perpendicular distance from the center of a rivet or a hole to the edge of the piece which contains it. Effective Depth. The depth between centers of gravity of the chords, or the depth between the centers of pins. Effective Length or Effective Span. The length of span measured from center to center of end bearings. Elastic Limit. The maximum unit stress below which the unit deforma- tion is proportional to the unit stress. Elevation. The vertical distance from a reference surface or datum. Also a drawing or view which represents the projection of a member or structure upon a vertical plane. End Frame. The steelwork in the end of a building, especially when rafters are used instead of roof trusses. End Post. The vertical or inclined compression member at the end of a bridge truss. End Shear. The shear for a section taken near the end of a beam or girder. In a simple beam the section is taken just inside of the result- ant reaction, where it is maximum. Engineers' Scale or Decimal Scale. A measuring scale graduated in inches and decimals of an inch, as distinguished from an "Architects' Scale." Equilibrium. The forces which act upon any body are said to be in equi- hbrium when they so balance each other that the body has no tendency to move. For the "equations of equiUbrium" see page 183 : 2. Equivalent Load. A load or system of loads which causes the same effect as some other load or system of loads. Erasing Shield. A shield containing holes of different shapes through which parts of a drawing may be erased without disturbing the adjacent parts. Erection. The assembling and the connecting of the different members of a structure in their proper positions at the site. Erection Bolts. Bolts used in erection to hold members in position tem- porarily until the field rivets are driven. Erection Diagram. An assembly diagram made to show the interrela- tion between the members of a structure and to guide the erector in placing them in the proper position. Erection Mark. An identification mark which aids the erector in prop- erly locating a member. Same as Shipping Mark. Erection Plan. An erection diagram, more strictly appUed to horizontal projection rather than to elevations. Erection Seat. A seat angle riveted to a supporting member' to hold a girder or similar member in position until the supporting rivets are driven. Erector. The person in charge of erection, or collectively, the men who erect a structure. Erector's List. A list of the field rivets and bolts required to make the necessary field connections in a structure. Estimate. To compile the quantities, weights, and cost of a structure usually in advance of the construction. Expansion Bolt. A bolt used for attaching steel work to a masonry wall. The bolt is surrounded by a split sleeve which expands in the masonry as the bolt is tightened. CHAPTER I OUTLINE OF THE BOOK — NOTATION— DEFINITIONS 11 Expansion Rollers. A group of steel cylinders or segments of cylinders placed under the end of a bridge girder or truss to provide free longi- tudinal movement on account of temperature changes. Extension Figure. A dimension which extends beyond another dimension on the same line, as for example to the end of a beam (page 86: 5). External Force. A force such as a load or a reaction which acts upon a member, as distinguished from an internal force or stress. Extreme Fiber. The fiber which is farthest from the neutral axis. Eye Bar. A flat bar of rectangular cross section which is upset at each end to form an enlarged head. A hole is bored in this head for the insertion of a pin. Fabrication. The shop work required to convert the rolled shapes into complete structural members, or in short, the work done in a struc- tural shop. Face. To plane or smooth a surface. Also the exterior plane surface of any soUd. Factor of Safety. The ratio of the ultimate strength to the allowed work- ing stress. Falsework. A temporary trestle used to support a structure during erection or demolition. Fiber. One of the longitudinal elementary filaments which for conveni- ence are considered to exist in a beam or similar member. Field. A term used in conjunction with the work done on parts of a struc- ture at or near the site, in contradistinction to work done at the shop. Field Check. A partial checking of the drawings for a structure to insure the proper connection of the members in the field. Field Connection. A connection of different members in the field. Field Rivet. A rivet driven in the field, as distinguished from a shop rivet. Field Splice. A splice made m the field, in distinction to one made in the shop. Filler. A plate used to fill a space between two surfaces (page 96:4). Fillet. The additional metal which forms the curve at the junction of the flange and the web of a rolled shape (page 26: 1). Finish. To smooth a surface by planing. Fitter. A shop workman who assembles the component parts of a mem- ber and bolts them in position. Flange. The wider part of an I-beam or similar shape at the edges of the web. Also the corresponding portion of a girder or column; each flange is usually composed of angles or plates and angles. Flange Angle. An angle in a flange of a girder or similar member. Flange Plate. A plate in a flange of a girder or similar member. Flange Rivet. A rivet which attaches the flange angles to the web plate of a girder. Flange Splice. A sphce in the flange of a girder. Flange Stress. The stress in the flange of a girder due to bending. Flat. A plate not over 7 inches wide. Flexure. Bending. Commonly applied to the bending of a beam. Floor Beam. A beam in a floor. Also a transverse beam or girder placed at the panel points of a bridge to support the longitudinal stringers. Floor-beam Reaction. The load upon a floor beam at each line of stringers. Floor Plan. A plan showing the arrangement of the beams, etc., of a floor. Floor Plate. A plate of a steel floor, such as used in a furnace building. Footing. The masonry pier or foundation for a column. Force. That which tends to change the state of motion of a body. A force is known when its magnitude, direction, and point of applica- tion are known. Forging. An article formed by being hammered whfle hot. Foundation. The masonry which supports a steel structure. Foundation Plan. A plan which shows the layout of a foundation. Function. A quantity whose value varies to correspond to every varia- tion ia some other quantity. Gable. The triangular portion of the end of a building between the oppo- site slopes of the roof. Gage or Gauge. The distance from the back of the web to a rivet line in the flange of a channel or Z-bar; a similar distance in an angle; the distance between rivet lines in an angle or a flange of another rolled shape. Also the clear distance between the heads of the rails of a track, standard gage being 4.708 ft., or 4' 8§". Gas Pipe. Small wrought-iron pipe — often used in short lengths for separators. Gin Pole. A guyed pole, nearly vertical, equipped with blocks and tackle, used for lifting loads. 12 PART I — INTRODUCTORY Girder. A compoiind member usually made of plates and angles de- signed to resist bending due to transverse loads, as a beam. Girt. A horizontal member in the side or end of a building used to sup- port the side covering such as corrugated steel. Government Anchor. A short rod with a V-shaped bend in the center, used to anchor the end of a wall-bearing beam. Graph. A diagram or chart used in determining values by scaling instead of by algebraic computation. Grillage. Tiers of beams laid across each other and imbedded in con- crete to form the footing for a heavily loaded column. Grip. The combined thickness of metal connected by rivets, bolts, or pins. Gross Area. The full area of cross section, in contradistinction to net area. ' Grout. A liquid mortar which can be poured to fill small voids or to make a smooth finish. Guard Rail. Auxiliary steel rails between the service- rails, or wooden timbers outside the service rails, for keeping a train on the ties in case of derailment. Gusset Plate. A connection plate which stiffens a connection, such as a plate which connects several members of a truss or a bracing system. Hand Hole. A hole made for the insertion of a hand in placing bolts or rivets which would be inaccessible otherwise. Hanger. A vertical tension member used to support a load. Heel Plate. A gusset plate at the heel, or main support, of a roof truss. Hinged Joint or Hinged Shoe. A joint or shoe arranged with a pin or roller to permit rotation due to the deflection of a truss. Hip. The jxmction of the top chord of a truss with an inclined end post. Also the intersection of two roofs, provided the drainage is away from the intersection, as distinguished from a valley. Hook Bolt. A bolt with a hook at the head end. I-beam. A common structural shape the cross section of which is in the form of a letter I. Impact. The increased effect of live loads when suddenly applied. Im- pact is usually provided for by adding a certain percentage of the quiescent live load. Indirect Splice. A splice in which the splice plates or angles are not in direct contact with the part spliced. Information Sheet. A sheet which may accompany a drawing to impart additional information. Initial Tension. The tension placed in counters and in diagonals of bracing systems to insure tightness. Internal Force. A stress within a member. Itemize. To add the item numbers, etc., to a shop bill. Joist. A beam which supports wooden flooring. Knee Brace. A short diagonal brace usually placed between a horizontal member and a vertical member. Lag Screw. A large wood screw with a square head like a bolt head. Lap Joint. A joint in which the connected parts overlap each other. Lateral. Sidewise, or at right angles to the principal axis. Also a diago- nal member of a system of lateral bracing. Lateral Plate. A connection plate or gusset plate in a system of lateral bracing. Lattice Bar. One of a series of zigzagged or crossed bars riveted to separated component parts of a member to hold them in position. Latticed Girder. A light parallel-chord truss similar to a plate girder except that the web plate is replaced by web members iisually made of one or two angles each. Laying Out. The marking of the steel from templets or otherwise indicat- ing where holes are to be punched and where special cuts are to be made. Layout. A preliminary drawing or sketch by means of which distances may be determined by scaling. Lean-to. A building with a roof which leans against another building or a wall. The roof slopes in one direction only, the higher edge being against the other building. Left. A member is so marked when made exactly opposite a correspond- ing member marked "right," the latter being represented on the drawing. Leg. One of the two flanges or parts of the shape called an angle. Lever Arm. The perpendicular distance from a force to a point of mo- ments. CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS 1.- Linear. Pertaining to line or to length. A linear dimension is usually one measured parallel to the length of a member. Lintel. A horizontal beam which supports a wall over an opening. Live Load. A movable load on a structure. Load. The weight supported by a structure or part of a structure. Loop-rod. A rod with a loop at the end through which a pin may be passed. Louvres. Series of horizontal strips of bent sheet steel arranged along the sides of a monitor to provide ventilation and at the same time to exclude rain or snow. Lug. A small projecting connection, as a connection angle. Masonry. A general term for structures made of brick, stone, or con- crete. Masonry Plate. A bearing plate placed on masonry. Material Order Bill. A Kst prepared in the drafting room showing the material to be ordered from the rolUng mills, or elsewhere. Member. A part of a structure which is completely assembled in the shop and shipped to the site where it is combined with other members. Mill. The machine or the plant in which plates and shapes are rolled. Also to plane the end of a member by means of a rotary planer or milling machine. Mill Building. A steel-framed building with a roof of comparatively large pitch and span, but usually without partitions, intermediate floors, or intermediate bracing. Milled Joint or Milled Splice. A joint or spUce in which the connected parts are milled to bear against each other. Milling Machine. See page 31 : 1. Mitered Joint. A joint in which the angle between the connected parts is bisected by the plane of contact. Modulus of Elasticity. The constant ratio (within the elastic limit) be- tween the unit stress and the unit strain. For steel of all grades this is between 28 and 30 milUon pounds per square inch. Moment. The tendency of a force to cause rotation about a given point. It is measured in compound units as pound-inches or pound-feet and is equal to the product of the force by its lever arm. Moment of Inertia. A term applied to the sum of the products of the elementary areas of a given cross section by the squares of their dis- tances from a given axis about which the moment of inertia is said tc be taken. Moment Plate. A splice plate designed to transmit the stresses in th« web of a plate girder due to bending moment. Monitor. The raised portion of the roof of a mill building or simila: structm-e, arranged to give additional ventilation or light througt the vertical sides. Mtiltiple Punch. A machine that punches two or more holes at once Nailing Strip. A strip of wood bolted to a steel beam or other member to which strip wooden flooring or sheathing is nailed. Net Area or Net Section. The effective area of metal in a cross section The rectangular areas of "all rivet holes cut by the section are de- ducted from the gross area of the member or part of member undei consideration. Net Width. The effective width of metal in a plate, the diameters of al holes in a section being deducted from the width of the plate. Neutral Axis. The intersection of a cross section of a beam or girdei and the neutral surface. Neutral Surface. The part of a beam which is neither shortened noi lengthened when the beam is bent. Office Building. A steel-framed building with intermediate floors anc columns, and a comparatively flat roof. O. G. Washer. A flat round cast-iron washer commonly used under £ bolt head or nut in timber construction. One face is of smaller dr ameter than the other, a reverse curve or "ogee" curve connecting the two. Order Bill. A material order bill. Orthographic Projection. See page 33:3. Outlooker. A small angle or similar piece fastened to an end purlin o a building to support the roof which overhangs the gable end. Overrun. The increase in the actual size of a structural shape above the size indicated on the drawing or order bill. Ojcy-acetylene Flame or Torch. An outfit used for cutting steel by burn ing a narrow slot by means of an intense heat. Packing. The arrangement of the different members on a pin. 14 PART I — INTRODUCTORY Panel. That part of a truss between adjacent panel points. Panel Point. The intersection of the working lines of different members of a truss. Parabola. A curve in which the ordinates vary as the squares of the abscissas, or conversely. For the construct on, see page 260. Pattern. A wooden model for a casting, used in forming the mold. Pedestal. A cast-steel or cast-iron stool or support for a bridge girder. Piece Mark. An assembling mark. Pier. An intermediate masonry support for a bridge. Also a column footing. Pilot Nut. A nut which is temporarily screwed on the end of a bridge pin to guide it while it is being driven into position. Pin. A steel cylinder used for connecting the members of a truss, or similarly. Pin Plate. A reinforcing plate riveted to a truss member to give greater bearing on a pin. Pitch. The longitudinal distance between adjacent rivets in the main part of a member. Also the ratio of the center height of a roof truss to the span. Plan. A drawing which represents the horizontal projection of a struc- ture or part of a structure. Plane. To smooth to a plane surface. Plate. A flat piece of rolled steel of rectangular cross section. Plate Girder. A buUt beam with a solid web plate to which are riveted two flanges composed of angles or angles and plates. Pneumatic Chisel. A cutting tool, operated by compressed air, used for cutting off projecting parts. Pneumatic Reamer. A reaming tool, operated by compressed air used for enlarging holes. Point of Moments. A point where moments are taken, i.e., from which the lever arms of the forces are measured. Pony Truss. A bridge truss which is not deep enough to permit the use of overhead bracing between the trusses. Portal Bracing. The bracing in the plane of the end posts of a bridge. Post. A comparatively small compression member, usually vertical. Projection Line. A line drawn at right angles to a dimension line to indi- cate the extent of the dimension. Punch. To make a hole as explained on page 29 : 5. Also a punching machine. Purlin. A horizontal longitudinal mernber which rests upon the top chords of roof trusses to support the roof. Radius of Gyration. The distance from an axis of rotation to the center of gyration. For a given cross section, the radius of gyration about any axis is equal to the square root of the quotient of the moment of inertia about the same axis divided by the area. Rafter. An inclined member parallel to the roof slope which is used either to support the purUns in place of a truss, or, resting upon the purlins, to support the roofing. Rail Clamp. A small casting used for fastening a crane rail to the flange of a supporting girder. Ratio of Slendemess. The ratio of the length of a compression member to the least radius of gyration of its cross section. Reaction. The force on a beam, girder, or truss imparted by the support. It is equal and opposite to the pressure of the beam on the support. Ream. To enlarge a hole by means of a rotating fluted cutter. Reduction Formula. Same as column formula. Reinforced Concrete. Concrete in which steel bars are placed to strengthen it. Reinforcing Plate. A plate used to strengthen the weaker part of a member to develop the strength of the remaining parts. Resisting Moment. The moment of the internal forces which resist the bending moment on a beam or girder. Restrained Beam. A beam which is restrained or "fixed" at a support. Resultant or Resultant Force. The simplest single force or system of forces which can replace a system of forces and have an equivalent effect. Reversal of Stress. The changing of stress from tension to compression, or vice versa. Ridge Strut. A longitudinal strut along the ridge or peak of a roof. Right. A member is so marked when another member marked "left" is to be made exactly opposite from the same drawing. CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS 1^ Right Section, A section at right angles to the principal axis. Rivet. A short cylindrical rod of steel with upset heads used to rivet or fasten together component parts of a steel structure. One head is formed before the rivet is put in position, the other afterward. Rivet Code. The conventional representation of rivets under different conditions. Riveter. One who rivets or operates a riveting machine. A riveting ma- chine. Also an instrument for drawing small circles to represent rivets. Rivet Line. A line through the centers of a series of rivets. Rivet Pitch. The longitudinal distance between adjacent rivets in the main part of a member. Rivet Spacing. The dimensions which locate the centers of rivets. Rocker. A hinged shoe with a pin or other device to prevent unequal distribution of pressure upon the masonry when the supported girder or truss deflects. Rod. A rolled bar of steel with roimd or square cross section. Roller. A steel cylinder or segment of a cyhnder placed- under one end of a bridge girder or truss to facilitate longitudinal movement on account of temperature changes. Groups of rollers are held in place by a roller box, the whole forming a roller nest. Rolling Mill. The machine or the plant in which plates and shapes are rolled. Rotary Planer. See page 31 : 1. Rough Bolt. An ordinary bolt, as distinguished from a turned bolt or machine bolt. Round. A round rod. Ruling Pen. An instrument for drawing ink lines. Safe Load. A load which can be supported by a member without over- stressing the member. More commonly the maximum safe load. Sag Rod. A vertical or inclined tie rod used to prevent a girt or a purlin from sagging. Saw-tooth Roof. See page 113 : 2. Scale. A flat or triangular measuring stick used in plotting a drawing in proportion to the thing represented Also this proportion. Seat Angle. A small angle riveted to one member to support the end of a beam or girder. Secondary Stress. An indirect stress which results because the ideal conditions upon which the calculation of the principal or primary stresses is based are not realized. Section. A cut across a member or structure made by an imaginary plane. Also used in place of "sectional view." Sectional View. The projection of one segment of a member or structure upon a section plane. Section Line. To shade a sectional view by means of fine sloping lines representing the parts cut by a section plane. Section Modulus. The quotient of the moment of inertia of a cross sec- tion of a member by the distance from the neutral axis to the extreme fiber. Section Plane. An imaginary plane which cuts a section. Selvage Edge. The original woven edge of a piece of cloth where the threads are closer together than in the body of the cloth. Separator. A casting or piece of gas pipe placed between the webs of beams to keep them a fixed distance apart. Shank. The cylindrical part of a .rivet or bolt, as distinguished from the head. Shape. A general term for rolled steel of any cross section other than a plate. Shear. To cut by shearing (page 28: 1). Also an expression for the algebraic sum of certain forces which tend to shear a member. Sheared Plate. A plate which is rolled between two rolls and then sheared to the desired width at the mill, as distinguished from a Universal Mill plate which is rolled to the desired width by means of supplementary rolls. Shearing Stress. The internal forces which resist the tendency to shear. Shearing Value. The strength of a rivet, pin, or bolt in resisting shear. Shear Intensity. The shearing stress per imit area. Shears. A machine for shearing. Sheathing. A wooden covering of planks or boards. Shipping Bill. A list of members to be shipped from the shop to the site. Shipping Mark. An identification mark assigned to each separate mem- ber shipped. 16 PART I — INTRODUCTORY .Shoe. The part of a bridge that transmits the load from the end pin of a truss to the bearing plate or rollers. Shop. The place where the component parts of a structure are fabricated into members. Shop Bill. A summary of material required for fabricating members in the shop. Shop Drawing. A working drawing prepared for use in the shop. Shop Rivet. A rivet which is driven in the shop, as distinguished from a field rivet driven at the site. Sidewalk Bracket. A bracket which supports the sidewalk of a bridge. Simple. Beam. An imrestrained beam which is supported at both ends only. Single Punch. To punch one hole at a time. Single Shear. The tendency to shear, or the resistance to shear, in one plane. Site. The final location of a structure. Sketch Plate. An irregular plate which is cut to dimension at the mill according to a sketch. Sketch Sheet. A small sheet or printed form upon which a drawing is made. Skewback. An auxiliary angle or other support for a floor arch. Also a bent plate or casting used to attach a diagonal rod. Skew Bridge or Skew Span. A bridge or span which does not cross a stream or roadway at right angles; the end of one truss or girder is not opposite the end of the other truss or girder. Skew Portal. The portal or the portal bracing of a skew bridge. Skids. Parallel supports of timber or metal used to elevate members a convenient distance above the floor of the shop to make them more accessible. Slab. A flat solid of considerable area but of relatively small thickness, such as a portion of a concrete floor between the supporting beams. Sleeve Nut. A long tubular nut having a right-handed thread in one half and a left-handed thread in the other, used for joining two rods and pulling them together to tighten them. Slope. The bevel or inclination of one line with reference to another; it is measured by the tangent of the angle of inclination expressed in inches to a base of one foot. Slotted Hole. An elongated hole with semi-circular ends and parallel sides. Sole Plate. A plate riveted to the bottom of a plate girder to bear upon a masonry plate. Solid Floor. Any type of floor construction other than the so-called open floor of a railway bridge in which the ties rest directly upon the stringers or girders. Span. The distance between the supports of a beam, girder, truss, etc- Also a bridge or similar structure which spans an opening. Specifications. That part of a contract which prescribes the allowed unit stresses and gives directions and restrictions regarding proper construction. Spiking Piece. A wooden strip bolted to a steel beam or similar mem- ber to which strip planking or sheathing may be spiked. Splice. The connection of two similar members or segments of mem- bers in the same straight line. Splice Angle or Splice Plate. An angle or plate used in a splice. Staggered Rivets. Rivets which alternate on two parallel rivet lines. Statical Moment. The product of an area by the distance from an axis to the center of gravity of the area (see page 202 : 1). Statics. That branch of Mechanics which has to do with systems of balanced forces acting upon bodies at rest. Steel. A modified form of iron used in construction. See Chapter III. Stiffener or Stiffening Angle. An angle used to prevent a plate from budding or to prevent a seat angle from bending. Stitch Rivets. Rivets placed at comparatively long intervals, usually ■ in a member composed of two angles, to hold the component parts together and to equalize the stress between them. Straight-edge. A thin strip of wood, metal, or celluloid with a straight edge used as a guide in drawing straight lines. Strain. The deformation in a member caused by an external force. Strain is measured in linear units. Stress. An internal force which resists the tendency of an external force to change the shape of the body. CHAPTER I OUTLINE OF THE BOOK — NOTATION — DEFINITIONS 1? Stress Diagram. A diagram by means of which stresses are determined graphically. Also a stress sheet. Stress Sheet. A sheet upon which is recorded the stresses in the prin- cipal members of a structure. Stringers. The longitudinal members which support the track or the floor of a bridge. They are supported by transverse floor beams. Structural Company. A company engaged in the construction of steel structures. Structural Drafting. The preparation of the working drawings for the members of a steel structure, such as a bridge, a building, a tower; etc. Structural Shop. A shop where the rolled steel shapes are punched, cut, riveted, and otherwise prepared for use in a steel structure. Strut. A comparatively light compression member, usually with no intermediate connection. Sub-punch. To pimch to a smaller diameter. Substructure. The masonry abutments, piers, or foundation for a steel structure. Super-elevation. The vertical distance between the tops of the rails of a track on a curve. Superstructure. The main part of a structure above the masonry founda- tion or "substructure." Sway Bracing. Bracing in a vertical plane, as between the columns of a building or between the trusses of a bridge. Swedge Bolt. An anchor bolt with a nut at one end but with elliptical depressions near the other end to furnish greater bond when im- bedded in masonry. Tamp. To compact concrete, dirt, or other material by pounding. Tee or T-iron. A structural shape, the cross section of which is in the form of a letter T. Templet. A strip of wood upon which holes, cuts, etc., are laid out and from which the steel is marked accordingly. Templet Maker. One who makes templets. Templet Shop. The shop where templets are made. Tension Member. A member in which the principal stresses tend to lengthen the member. Through Bridge. One in which the principal loads are applied to a floor system near the bottom, and the trains, etc., pass "through" the structure between the trusses or girders. Tie. A light tension member, such as the diagonal in a bracing system. Also a transverse timber which supports the rails of a track. Tie Plate. A plate used to hold the component parts of a member at the proper distance apart. Generally used in tension members or else in conjunction with lattice bars. Tier. A row or layer placed above or below a similar row or layer. Tie Rod. A short rod used to tie the beams of a floor together in order to counteract the thrust from floor arches. Also a rod used similarly elsewhere. Trace. To copy a drawing or portion of a drawing upon a superimposed transparent sheet of tracing cloth or paper. Tracer. One who traces. A title given to a person in a drafting room whose chief duty is to trace drawings made by others. Tracing. A drawing on tracing cloth. Tracing Cloth. A linen cloth specially treated to make it transparent for use in copying drawings by tracing and blueprinting. Track. The rails, including their supports, along which a body or struc- ture with wheels or roUers may be rolled. The track on a railway bridge includes not only the service rails and the ties, but also the guard rails, and the bolts, spikes, and other fastenings. Traveler. A form of derrick used in erection; it is moimted on wheels so that it may be advanced as the work progresses. Triangle. A flat piece of celluloid or similar material used in draftmg. The three edges form a right tr' angle, and the complementary angles are usually 45°, or else 30° and 60°. Truss. A framed structure which acts as a beam The principal mem- bers form a series of triangles, and each member is primarily sub- jected to axial stress only. T-square. A T-shaped drawing instrument with a long thin blade at- tached to a shorter thicker head. The blade is used as a straight- edge for drawing parallel lines as the head is moved along the end of the drawing board. 18 PART I — INTRODUCTORY Tumbuckle. Similar to a sleeve nut except that a transverse opening is provided at the center for the insertion of a crow-bar by means of which the tumbuckle may be turned. See sleeve nut. Turned Bolt. A machine bolt which is cut in a lathe to accurately fit a hole. U-bolt. A rod bent in the shape of the letter U with nuts on each end. Underrun. The decrease in the actual size of a structural shape below the size indicated on the drawing or order bill. Uniform Load or Uniformly Distributed Load. A load which is uni- formly distributed over a given distance. Unit Stress. The stress per unit of area, or the intensity of stress. Universal Mill Plate or U. M. Plate. A plate rolled in a Universal Mill which is provided with vertical rolls as well as horizontal rolls. A plate with rolled edges, as distinguished from a sheared plate. Upset. To enlarge the end of a rivet, a rod, an eye bar, etc., by hammer- ing or pressing into a die while hot. Valley. The intersection of two roofs provided the drainage is toward the intersection, as distinguished from a hip. Vertical Flange Plate. A vertical plate in the flange of a plate girder, either between the web and a flange angle or outside the vertical leg of an angle. View. In orthographic projection, a view is the projection of an object upon a plane by means of parallel lines. Washer. Usually a flat disc with a central hole, used imder the head or the nut of a bolt, or similarly. Web. The web plate of a girder, column, or other built member, or the corresponding thin portion between the flanges of an I-beam, channel, etc. Web Member. An intermediate member of a truss or latticed girder between the chords. Web Plate. The main plate of a plate girder, column or similar member, connecting the two flanges. Web Splice. A sphce in a web plate. Wheel Load. The load from a truck, car, or locomotive applied to a structure through a wheel. Wind Bracing. A system of bracing which resists stresses induced by the wind. Wind Load. A load on a structure due to wind pressure. Working Line. A reference line to which the dimensions of a member are referred; usually used in conjunction with the working lines of other members to form a system of working lines of a truss, latticed girder, of bracing system. Working Point. The intersection of two or more working lines. Z-bar. A structural shape the cross section of which is in the form of the letter Z. CHAPTER II THE ORGANIZATION OF A STRUCTURAL COMPANY — THE ENGINEERING DEPARTMENT Synopsis : The student should have a conception of the relation which the structiu'al steel drafting department bears to other branches of the steel industry. An abstract is given in Chapters II, III, and IV. 1. The structural draftsman is not concerned directly with the manu- facture of steel or even with the rolling of the commercial steel "shapes." His drawings show how these shapes are cut, punched, and assembled to form members which in turn go to make steel structures. But every draftsman should understand the processes which are allied to the work of his company. The student has no time for a careful study of the different operations, but he should have a general idea of how steel is made and used. For his convenience an abstract is presented in this chapter and in the two subsequent chapters. Later he may acquire further knowledge from books or from inspection trips to rolling mills, to structural shops, and to erection sites. 2. In the Estimating or Designing Department of a structural com- pany are made the preliminary design and the estimate of cost of a proposed structure. These may be based upon the customer's layout, or upon an original design submitted to the customer for approval. Usually several different companies furnish estimates in competition. After a contract is awarded the design sheet is forwarded to the Detail- ing or Drafting Department. The design sheet usually shows the main form and dimensions of the structure, the principal stresses, and the sizes of all main members, together with special instructions regarding the details. The work of the Designing Department is explained more fully on page 20: 2. 3. In the Drafting Department the detailed working drawings are prepared for use in the shop. Various diagrams and lists are also made. such as the preliminary bills of material from which the steel shapes are ordered from the rolling mills. As far as possible, the material must be ordered before the drawings are made so that the mills may roll the steel while the drawings and the templets are being prepared. As soon as the drawings are made and checked, blueprints are sent to the templet shop, to the structural shop, and to others concerned. The work of the Drafting Department is described more fully on page 20: 4. 4. The drawings are first sent to the templet shop where templets are made for most of the members. These templets are virtually pat- terns for cutting and punching the component pieces. They are usually made of wood. Not only can the work be laid out on wood with greater facility than on steel but the templets can often be completed before the steel arrives from the rolhng mills and thus the completion of the struc- ture is hastened. Furthermore, the work may be laid out on wood once and then the templets may be used repeatedly in marking many steel pieces which are alike or similar. 5. The manufacture of steel and the rolling of the structural shapes are described in the next chapter. The finished shapes are shipped to the structural shop where all cuts and holes are first indicated on the steel by means of the templets. The steel is then taken to shears to be cut and to punches to have the rivet holes punched. The com- ponent parts of each member are then assembled, being held together temporarily by bolts until the shop rivets are driven. Other proc- 19 20 PART I — INTRODUCTORY esses may be required on some members before thay are painted and shipped, as described more fully in Chapter IV, page 27. 1. Erection.* — The different members of a structure are shipped to the site as far as practicable in the proper sequence for erection. The methods of erecting them differ with the size and the type of the struc- ture and with its location. Usually buildings are made self-supporting from the first, but truss bridges must be supported by "false work " or by other means until they are nearly complete. Locomotivp cranes are used extensively in the erection of mill buildings, girder bridges, and viaducts. Derricks are used for office buildings and "travelers" for truss bridges. Main members are usually placed in position first and secondary -members are filled in afterwards. Enough erection bolts are used to hold the members in position until the "riveting gangs" can drive permanent rivets. THE ENGINEERING DEPARTMENT f 2. The Engineering Department includes the Designing or Estimat- ing Department and the Drafting or Detailing Department. Both departments are in charge of a Chief Engineer and often one or more Assistant Chief Engineers, although these officers are usually more directly concerned with the work of the Designing Department. The organization of the Designing Department differs in different companies and the procedure depends upon the organization and also upon the nature and the magnitude of the proposed structures. Some com- panies have a special contracting Department which acts as interme- diary between the Designing Department and the customers. Some designs are made by the customer's engineers or by consulting engineers, and the structural companies simply estimate the cost and submit bids. Some structures are so simple or so similar to other structures that the designers, or the contracting engineers in charge of branch offices, can make quite accurate estimates quickly without complete designs. Often- * See Thayer's "Structural Design," Vol. I, D. Van Nostrand Co., New York, and Merriman and Jacoby's "Roofs and Bridges," Vol. Ill, John Wiley and Sons, Inc., New York. For erection tools and specifications see Ketchum's "Structural En- gineers' Handbook," McGraw-Hill Book Co. Inc., New York. t See also TyrreU's "Mill Buildings," The McGraw-Hill Book Co. Inc., New York. times the customer has little conception of the type of structure best suited to his needs and the structural companies prepare alternate designs from which the customer may make selection. 3. Design sheets or stress sheets are made by the designer or by a draftsman under his direction to illustrate the proposed structure. They show the general form of the structure, the principal dimensions and stresses, and the composition of each main member, as illustrated in Fig. 21. The design is made according to specifications approved by the customer. An estimator must have an intimate knowledge of drafting room methods and of shop methods and costs. He must know from experience how much to allow for the details of construction such as connection plates and angles. He must be familiar with the methods of erection and be able to determine the method best adapted to a given structure in a given location. The estimator may be assisted by draftsmen, tracers, and computers. As soon as a contract is awarded, the design sheet is adapted to the needs of the Drafting Department and any necessary alterations or additions are made. The design sheet should give all information necessary to enable the draftsmen to make the detailed drawings. It may be supplemented by an "information sheet " which gives the principal terms of the contract such as the time of delivery and whether the cost is quoted at a "lump sum " or at a price per pound. 4. The Drafting Department is in charge of a Chief Draftsman. His subordinate draftsmen are usually divided into squads, each in charge of a "squad foreman " or "squad boss." The drawings for each contract are usually all made in one squad, the drawings for other con- tracts often being carried on simultaneously. The size of each squad varies with the amount of work being done under the direction of a single squad foreman from 3 or 4 to 16 or 20, the normal number being from 6 to 8. In each squad are checkers, detailers, tracers, billers, and computers. The detailers make the working drawings, and design the details. The drawings show how the standard shapes are cut and com- bined to form the different members. The number and the spacing of the rivets are given so that the members may be properly constructed and so that they may be easily connected to other members in the structure. As far as practical the parts are combined in the shop in CHAPTER II THE ORGANIZATION OF A STRUCTURAL COMPANY 21 70-0 b. to b. La HALF END VIEW HALF SECTION SPECIFICATIONS - AMER. RY, EnS. ASS'N, - 1910 MATERIAL - STRUCTURAL 0. H. STEEL RIVETS- i" TIES - Sx 9x I0'-0"NOTCHED TO «|- ASSUMED DEAD LOAD OF TRACK - 400*/FT, ASSUMED LIVE LOAD - COOPER'S E BO GIRDERS SHEAR 0= 31,200 L= 1/7, 800 1=95,800 244,800* ^10,000-24.5°" EB SI x-f-,=.35,4 MOMENT D= 6,980,000 L=28, 810,000 1=23,420,000 59,210,000 HhSn. ■^81.5 =726,500 t- ^16000= 4S,4a" I" Web = 4,4 2 Lse x6x^l3,9 3 Pis, 14 xi=27,0 45,3 Length of Covers Top — Full, 47', 34' Bottom - 57, 47/ 34' STRINGERS SHEAR MOMENT INT. FLOORBEAM SHEAR MOMENT : 2,800 : 60,000 : 57,200 120,000 ^ ■^10,000 =12, Oa' WEB22xi- = l3.8 D= 103,000 L= 1,980,000 I^ 1,892,000 3,975,000-*-ln, ' ■^18,8=211,500* ■^16,000= 13.2°" {Web=- 1.7 2 LsS xS X ,^■=■11.7 13.4 D= 6,800 L = 78,300 1= 71,600 156,700 1 ^10,000=15.70" WEB32x{ =16.0 D= 347,000 L = 3,993,000 1 = 3,652,000 . 7,992,0001fhy ^28.7 = 878,500"'^ ■^18,000= 17.40" {Web= 2.0 2 Uex6 X i.= l5.4 IM. END FLOORBEAM SHEAR MOMENT D= 3,400 D= 173,000 L= 57,900 L= 2,953.000 1=55,300 1= 2,820,000 116,600 5,946,000*111. tI0,000 = II.7°" -i-27,0 =220,200* , WEB 32 Jti = 12,0 ^ 16,000 = ^Web=. 2 Lse X 6xj 13.8°" 1.5 ' =13.0 14.5 70 FT. THRU PLATE GIRDER SPAN OVER MILL RIVER WOODBRIDGE RAILROAD CO. NEW HAVEN, CONN. UNIVERSITY BRIDGE COMPANY Fig. 21. Typical Design Sheet. 22 PART I — INTRODUCTORY order to reduce the number of members to be shipped and to be erected at the site. The detailers often prefer to trace their own drawings or else to draw with ink directly upon the tracing cloth, thus making no use of the tracers. The detailers are often called upon either to make of to check shop bills and shipping bills and other lists of material. Most of the billing and the calculating of weights are done by younger men of limited experience often working in a separate squad under a chief biller. The checkers "check " or verify the drawings and indicate the mistakes. They are often called upon to make drawings also. They are men of greater experience than the detailers and they assist the squad foreman in laying out new work preparatory to ordering the material. The term " draftsman " has a double meaning. Some limit its use to detailers because they do the actual drafting, while others refer to everyone in the Drafting Department as draftsmen, particularly those who have reached or passed the rank of detailer. 1. Method of Procedure. — When a new contract is received in the Drafting Department the Chief Draftsman studies the general character of the structure, notes the time limit if any, and assigns the work to the squad foreman who can best handle it. The squad foreman makes a careful study of the whole contract and adopts the method of procedure by which the work under his direction can be carried out most effi- ciently. In general his first aim is to have all main material ordered as soon as possible because of the usual delay at the mills. In some types of structure either he or his more experienced men can list most of the material directly from the design sheets. In certain classes of work such as truss work it may become necessary to make small layouts of connections, or even to begin the working drawings in order to deter- mine the lengths of the material; later these prehminary drawings may be given to detailers for completion. In other types of structure such as office buildings it may prove feasible to make the plans and diagrams before listing the material. These diagrams may be made so complete that the material may be listed from them quickly and accurately, and the detailed drawings may become routine work which can be done by men of limited experience. The preliminary lists of material are usu- ally sent to an Order Department where the material is summarized and the short pieces are grouped in multiple lengths to be cut after they arrive from the mill. The squad foreman divides the drafting among the detailers to the best advantage so that the work may be carried on efficiently and in logical order. Part of the drawings may be sent to the shop before all are completed and as far as practical an attempt should be made to complete the drawings in approximately the same_ order that the corresponding members will be erected. For example, the drawings of the ground floor beams in an office building should be made before the drawings of the roof beams. Erection diagrams should be made as. soon as possible so that the marks of all members may be recorded as soon as determined. Drawings should be checked shortly after they are made and the shop bill for each drawing should be made as soon as the drawing is completely checked. A shop bill is a summary of all the material required to make all the members repre- sented by a drawing. Later shipping bills and fists of rivets and bolts to be used in erection are prepared. 2. The squad foreman should keep progress sheets so that he and the chief draftsman can tell what has been done, what is being done, and when and where the blueprints have been issued. He should keep separate files for the drawings and for the correspondence of each different contract. Usually all communications pass through the hands of the chief draftsman who writes all letters and serves as intermediary between the men in the drafting room and those outside. A detailed account of the duties of the draftsmen appears in Parts II and III. 3. There should be greater cooperation between the engineering de- partment and other departments than sometimes exists. Shop men and erectors often complain of points in the design or the details of a mem- ber which bother them, but seldom do their criticisms reach the source of the trouble. It would be to the advantage of all concerned if the erectors and the shop foremen would issue periodical bulletins which would reach each designer, each draftsman, and each shop foreman. Suggestions and constructive criticisms could thus be presented in such a manner that future trouble might be avoided. CHAPTER III THE MANUFACTURE OF STRUCTURAL STEEL* Synopsis: Thia topic has no direct bearing upon the work of the draftsman but he should have a general idea of how steel is made. It is important that he know the form it is in when it first reaches the structural company. 1. Iron. — Most of the iron bre is taken from open pit mines' in the Lake Superior region and shipped by boat and by rail to blast furnaces where it is smelted or reduced. The ores are oxides of iron and the re- ducing agent is carbon. A blast furnace is in continuous operation. It is charged at the top and the molten iron flows by gravity to the bottom where it accumulates until tapped at intervals of about 6 hours. Be- sides the ore the charge includes a flux, and the reducing agent in the form of coke which serves also as fuel. An intense heat is maintained by means of a continuous hot air blast. The blast is heated by being passed through a "stove " lined with fire brick. Four stoves are used in turn, the ones not in use being heated by the hot gases from the fur- nace. Limestone is the flux commonly used to unite with the impurities freed from the ore to form a fused mass called " slag." This floats on top of the iron and is tapped at a higher elevation. The iron tapped from a blast furnace is called " pig iron " because it is often cast into " pigs " of about 100 pounds for convenient handUng. Pig iron is used in iron foundries for making iron castings, but most of the pig iron is made into wrought iron or steel. When the steel furnaces are near the blast fur- nace the iron may be transferred in the molten state in large ladles. Pig iron contains small quantities of carbon (3 to 4 per cent), siUcon, sulphur, phosphorous, and manganese. It has so much carbon that it is not * The manufacture of iron and steel is treated more completely in many books, as for example: Stoughton's "The Metallurgy of Iron and Steel," McGraw-Hill Book Co. Inc., New York; Moore's "Materials of Engineering," McGraw-Hill Book Co. Inc., New York; or Burt's "Steel Construction," American Technical Society, Chicago. malleable at any temperature. The capacity of a blast furnace is about 500 tons of iron per 24 hours. 2. Structural steel is made by the "open hearth " process. A higher grade of steel for tools and instruments is made in crucibles or in electric furnaces. At first structural steel was made by the Bessemer process in a converter of from 10 to 20 tons capacity. A cold air blast was used for about 10 minutes after which the steel was ready to be poured. Besse- mer steel is inferior in quality and is less reliable than open hearth steel, and the Bessemer process has been largely superseded by the open hearth process. In the latter the charge is placed on a shallow hearth and sub- jected to a hot air blast. The charge includes besides the pig iron, iron ore, steel scrap, and usually limestone. Gas is used for fuel, and when the charge is melted the flux rises to the top. This flux contains the iron ore which forms a blanket to prevent the oxygen of the air from com- bining with the iron. The impurities in the iron become oxidized by the iron ore which in turn receives new oxygen from the air. The per- centage of carbon and phosphorus is thus reduced. The steel is tapped into large ladles where it is " recarbonized " by adding the proper amount of carbon and other ingredients to give the desired quality. Structural steel contains from 0.15 to 0.3 per cent of carbon. The capacity of an open hearth furnace is from 30 to 70 tons, and the operation requires from 6 to 10 hours. 3. Rolling the Steel. — From the ladles the steel is poured into ingot molds and allowed to cool until sufficient crust is formed to permit handling. The molds are then stripped off and the ingots are placed in 23 24 PART I — INTRODUCTORY ovens called "soaking pits " until the inside portion solidifies and the whole becomes of the proper uniform temperature for rolhng. Structural shapes are formed by passing the material between rolls of the proper shape, the cross section being reduced and the piece elongated at each pass. The ingot is first passed between the two cylindrical rolls of a Fig. 24 (a). Typical Roughing Rolls for an I-beam. {Courtesy of the Pittsburgh Rolls Corporation.) " blooming mill " and flattened. The rolls are then reversed and placed closer together and the material is passed between them in the opposite direction. In this manner slabs are made of suitable size to be placed in another mill to be rolled into plates. For other shapes, the ingot is rotated at right angles between successive passes to form a "bloom" of the size best adapted to the shape of the "roughing rolls." The blooms are cut into lengths which will result in the proper lengths of the final sections. The roughing rolls are grooved to work the blooms down gradu- ally to shapes which approximate the finished pieces, then "finishing rolls " are used. Both the roughing and finishing rolls are so shaped that at each pass the material is reduced in cross section to approach the finished shape. These rolls are " three high " so that they need not be reversed, the material passing alternately between the lower two in one ---^V^ ^\ y\ y\ - |iill|—i i 1. A channel is shown conventionally (Fig. 39 (d)) as follows: End View. — The depth and the flange width are plotted to scale. The thickness of the web is estimated and often exaggerated if necessary to indicate clearly whether a dimension extends to the back of the web or to the center line. The edge of each flange is made approximately of the same thickness as the web, and from the point thus located a sloping line is drawn until it intersects the inner web line; all curves are omitted. (Compare Fig. 25 (6).) This line is drawn to a slope of 2 in 12. (See note in fine print under I-beam.) Front View. — Each flange of the channel is represented conventionally by two lines spaced approximately to show the mean flange thickness. The distance between the outer lines of the two flanges is the depth of the channel to scale; each inner line is drawn so that, if extended, it would cut the sloping line of the end view about midway between the web and the edge of the flange. The distance between the two lines of each flange is roughly one and one-half times the web thickness. The inner lines of the flanges are full or dashed, depending upon whether the flanges are on the near side or on the far side of the web; this should correspond to the way the flanges are shown in the end view. Top View. — Two full lines are drawn to show the flange width to scale, one line showing also one face of the web; a single dashed line is added to show the other face of the web, the web thickness being esti- mated as before. It is important that the web be shown on the proper side of the flange to correspond to the other views. Bottom Section. — This is similar to the top view except that the web is shown by a heavy line equal in width to the web thickness (page 37 : 2) . The web should appear on the same side as in the top view. 2. Round and square rods are represented by true views, the ends being shown as circles or squares, and the other views as rectangles. No shade lines are necessary. Fig. 39(d). A channel. 40 PART II — STRUCTURAL DRAFTING ,Full because visible Fig. 40 (o). A Tee. E Dashed because invisible Full because -visible Dashed because invisible 1. A Tee oi- T-iron is shown much like an angle, except that the stem is in the middle of the flange, and hence an additional line is required (Fig. 40 (a)). Note that both the stem and the- flange taper slightly, but in most drawings they may be represented by parallel lines. 2. A Z-bar is shown convention- ally (Fig. 40 (&)) as follows: End View. — The depth and the flange width are scaled, but the thickness is estimated and often exaggerated; the thickness of the flanges is uniform and is equal to the web thickness. Front View. — • The depth is shown to scale between two fuU hnes. Additional lines are drawn just inside of these hnes to represent the inner edges of the flanges. One of these lines is full and the other dashed, because one flange is on the near side and the other is on the far side of the web; this should correspond to the way the flanges are shown in the end view. Top View. — The top flange is shown to scale between two full lines, one line showing also one face of the web; a dashed hne is added to show the other face of the web, the web thickness being estimated as before. A fourth line is drawn to show the outer edge of the bottom flange, the space between it and the dashed line representing the flange mdth to scale. The position of the full and |="=^— '^'^^■^-^'^-^-~-^'~~~~~'^"^'"'="~^'^^ ^ the dashed web lines should corre- spond to the other views. 3. A rail is shown conventionally (Fig. 40 (c)) as follows: End View. — The head, the web, and the flange are drawn from the dimensions given on page 317. On large scale drawings these are drawn to scale, and the curves are often shown. Ordinarily, however, straight hnes are sufflcient, the depth, the width and the thickness of the head, and the width of the flange being sealed. =^ Vu/y because .visible Fig. 40 (6). A Z-bar. Fig. 40 (c). A Rail. Frord View. — The head and the flange of the rail are each shown con- ventionally by two hnes spaced approximately to show the mean thick- ness. The distance between the upper hne of the head and the lower hne of the flange is the depth of the rail to scale; each inner hne is drawn so that, if extended, it would cut the sloping lines of the end view about midway between the web and the outer edges of the head or of the flange. To-p View. — The widths of the head and of the flange are each shown by two Unes to scale. These lines are placed symmetrically about two dashed hnes which represent the web, the web thickness being estimated. 4. An eye bar is shown in the main view to scale, from the dimensions given in the handbooks of the steel companies. The actual curves are drawn to scale. The edge and the end views appear as simple rectangles, although the curves are sometimes indicated by ILue shading, as shown in Fig. 40 (d). fc ^ I 5. Lattice bars are usually made from ^-^ standard dies according to the billed size, as c=n„=s=^=====i explained on page 45 :2. For this reason it is Fig. 40 (d). An Eye Bar. unnecessary to show the bars on a drawing in detail. One or two bars are often shown on each sheet, being drawn from the dimensions given on page 315; other bars are indicated simply by center hnes drawn from center to center of end rivets, as shown in Fig. 137. Often the intermediate bars and rivets of a group may be omitted (compare page 41 : 1), only one or two bars being shown or indicated at each end of the group. Dashed hnes instead of full lines are sometimes used to indicate an independent system of lattice bars, as for example, when the bars on opposite sides of a member are shown in one view (Fig. 129). 6. Shop rivets and holes for field rivets are usually indicated in the views where they appear as circles according to the Osborne Code, as shown on page 304. An open circle of the diameter of the rivet head indicates the shop rivet, and a circle of the diameter of the rivet hole, but inked sohdly, represents the field rivet. The diameter of the rivet hole is tV" greater than the diameter of the shank of the rivet (page 30 : 4), while the diameter of the head is as given on page 304. The drafts- CHAPTER VI THE CONVENTIONAL METHODS OF REPRESENTATION 41 man can usually estimate the sizes of the circles closely enough when drawing to an ordinary scale; but he should be particular to show a con- trast in size between the shop and the field rivets as an added safeguard in case he should neglect to fill in all the field rivets. It is well to re- member that for a rivet of a given size the diameter sf the circle for a shop rivet is approximately one and one-half times as large as the diam- eter of the circle for a field rivet. After making a sample circle preparatory to di-awing a large number of rivets, the beginner should measure the diameter to see if it is approximately to scale; in fact, this test is so quickly made that an experienced draftsman can often apply it to advantage, particularly when drawing to a small scale. Other views of rivets and holes are shown only when an extra view may be avoided or the drawing may be made more clear thereby. In general the side or the sectional view of a hole for a field rivet is a rectangle filled in solid. A similar open rectangle represents the shank of a shop rivet to which are added semi-circular heads. See G20, Fig. 92. When shop rivets are countersunk, cross lines are drawn perpendicularly to each other and preferably at 45° with the rivet lines. See page 304. If countersunk on the near side (outside) the Unes are only outside the circle, and if countersunk on the far side (inside), the lines are inside. Similarly the lines extend outside and inside if countersunk on both sides. To show this distinction in field rivets, auxiliary circles must be placed out- side the others. Flattened rivets are indicated by Hnes which slope in one direction only, preferably at 45° with the rivet lines. The number of sloping lines shows the height of the rivet head in eighths of an inch, i.e., three lines for f " and two lines for \". Eivets flattened to \" would be useless but they may be countersunk without being chipped after they are driven; they will then not project more than one-eighth inch. In order to insure the detection of countersunk or flattened rivets, notes are often added to supplement the code, especially when the rivets are in un- usual places, as for example: "Rivets countersunk far side but not chipped," "Rivets countersunk and chipped both sides," or "Rivets flattened to \" near side." (Figs. 129 and 133.) Such notes are omit- ted on shoe plates and column bases, or wherever rivets are usually countersunk, provided they are clearly indicated. Rivets should never be countersunk in metal thinner than that indicated in the table on page 304. 1. All holes for field rivets are usually shown, except in plate work or other work which requires a large number of field rivets, the position of which can be clearly indicated. All shop rivets should be shown in small connections and in all doubtful places, but some may be omitted when in large numbers if no ambiguity is Ukely to result. A short hne crossing the rivet line is often used to indicate the center of a rivet. When shop rivets are dimensioned in a group (page 49 : 7), the rivets at the ends of the group are shown, but most of the intermediate ones may be omitted ; it is well to indicate one space at each end of the group by means of a rivet or a cross line in order to emphasize the presence of intermediate rivets. On the pencil drawing enough rivets and holes should be shown to distinguish clearly between them when the tracing is made, without the necessity of further investigation. They may be made freehand in pencil, but they should be carefully made with a bow-pen or a "riveter " (page 60 : 3) on the finished drawing. 2. Bolts are occasionally drawn to scale from the actual dimensions (page 304), but ordinarily simply the holes for the bolts are indicated in the same way as holes for field rivets, whether the bolts are to be in- serted in the shop or in the field. Shop rivets should never be shown where bolts are to be used. Bolts which are put in place permanently in the shop should be billed and noted on the drawing (page 53 : 3) . If necessary to differentiate between shop and field bolts, small squares may be drawn around the solid circles for the shop bolts as illustrated in Fig. 140. 3. Fillers are used to fiU the spaces between other surfaces and it is not usually necessary to draw any additional lines to represent them, since the Hnes would be coincident with Unes already drawn. When clearance is allowed between the edges of the fillers and adjacent edges, additional lines (dashed if invisible) may be drawn, although these are sometimes omitted if the drawing is clearer without them. Round washers are used as fillers where there is only a single rivet, as at stitch rivets (page 69 : 4). 4. Beat Plates. — The true projections of bent plates and angles are usually simplified as shown in Figs. 143 and 149. The dimensions must 42 PART II — STRUCTURAL DRAFTING be shown accurately in the proper views, but most drawings would be complicated unnecessarily by an attempt to show all the edges. Often the drawing may be clearer and more easily interpreted if one view is drawn as if the plate or angle were not bent. The rivets and holes in inclined surfaces would appear as ellipses instead of circles (Fig. 78), but on account of the difficulty in making small ellipses this distinction is not always made on the drawing unless ambiguity would result from the use of circles. 1. Other Materials. — • It is sometimes convenient to represent ma- terials other than steel according to standard conventions. The more common conventions for this class of work are shown in Fig. 42. na MASONRY BRICK STONE CORRUGATED STEEL Fig. 42. Conventional Representations. P il"l iyi GLASS i CHAPTER VII STRUCTURAL DRAWINGS — THE CONVENTIONAL METHODS OF BILLING Synopsis: In Structural Drafting the term "billing" has two meanings, viz.: (1) the statement on a drawing of the number and the size of the component parts of a member; and (2) the preparation of a list or "bill" which is a summary of all the material used in the construction of one or more members, as an order bill (page 162 : 1), or a shop bill (page 167 : 1). In this chapter are explained the conventional methods of billing material on the drawings. 1. Billing. — The size or description of each component part of any member should be expressed or "billed " on the drawing near the prin- cipal view of that part. When two or more identical pieces occur together they may be billed together, but the number of pieces should indicate the number required at only one point of a single member. The object of billing is to show the commercial shape from which the part is to be cut, and the length of such shape required. The methods of billing must conform to the usual practice and indicate the com- mercial shapes in the same way that they are listed in the handbooks of the steel companies. The bill of material serves as the "name " of a piece, not only upon the drawing, the order bill, and the shop bill, but also upon the steel itself; it is painted upon the steel at the rolling mill as soon as the steel is cut to the ordered length, and it is used for iden- tification until the piece is placed in its final position in the structure, or until it is assembled with other pieces to form a member which is subsequently identified by means of a shipping mark (page 80 : 6). At the mill, the contract number as well as the bill of material is painted on the steel. If the material is recut in the shop to shorter lengths, the contract number and the revised bill are painted on each piece, along with the shipping mark and the assem- bling mark, if any (page 79 : 2). Similarly, the templets are marked to correspond. After a member is assembled and riveted it is painted before it is shipped; the con- tract number and the shipping mark are left uncovered or are repainted for use during shipment and erection. 2. Certain abbreviations and conventional signs are used in biUing, as shown in the following paragraphs. The multiplication sign (X) is used simply to distinguish the different dimensions. It is pronounced "by"; thus 8 X i X 12'-0" is read "eight by one-half by twelve feet, no inches." Similarly, the sign (#) is used for "pounds," (#/ft.) for "pounds per foot" and (#/yd.) for "pounds per yard." In billing, the "per foot" and often the "per yard" are' omitted. The size of the cross section is expressed in inches in billing, even if over one foot. The length is the extreme distance at right angles to the other figures; a length of I'-O" or over is expressed in feet and inches, while a length less than one foot may be written in inches alone, unless it seems clearer to prefix the 0' thus: O'-IO". See the illustrations below. The con- ventional methods of billing the common structural shapes are as follows: — length (feet and inches) 3. Plates: Number: PI. (or Pis.): width: thickness : (pieces) (inches) (inches) (fee Thus: 1 PI. 8 X i X 10" , or 14 Pis. 24 X f X 9'-10i". 43 44 PART II — STRUCTURAL DRAFTIXG Note that the width is across the grain, while the length is along the grain. See IX-(9), page 76 : 1. If possible, plates of even ^idth, i.e., whole inches without fractions, should be chosen in order that stock "sizes may be used without being recut. Fig. 44. Usually the w-idth is the smaller dimension, but this may be reversed in case the longer dimension can be made a stock width more conveniently; or in case material may be saved by cutting several plates as shown in Fig. 44. When plates are used as fillers the Fl. or Pis. is replaced by Fill, or Fills. For other special abbreviations used in plate work see page 45 : 7. For the areas and the weights of plates see page 321. 1. Angles: Number: L(orLs): 'longer leg: shorter leg: thickness: length (pieces) (inches) (inches) (inches) (feet and inches) Thus: 1 L 6 X 4 X i X 7^, or 12 Ls 3 X 2^ X 1% X 10'-6". In the offices of some companies, the angle sign (L) is placed after the thickness, thus: 8-5 X 31 X f Ls-18'-3". For special abbreviations used for angles see page 45 : 7. For the weights and the dimensions of angles see page 303. 2. I-beams : Number: depth: I (or Is): weight: (pieces) (inches) (pounds per foot) length (feet and inches) I 2 • Thus: one 12" I 31i# 18'-0", or 2-15" Is 42# 25'-7i In beam work the number of pieces often serves aJso as the number of members. If there is only one such member, the word "one" is used in preference to the figure "1". This obviates ambiguity between 1-S"I and 18"I, etc., when poorly executed or indistinctly printed. The figure 1 is iised in billing single beams elsewhere. For the weights and the dimen- sions of I-beams see pages 298 and 299. 3. Channels: Number: depth: l_l(orlsj): weight: length (pieces) (inches) (pounds per foot) (feet and inches) Thus: one 12" U 20|# 12'-10", or 7-8" Lsj lli# 15'-1U". For the method of billing single channels see preceeding paragraph. Note also that the channel sign (l_j) is made preferably with the web horizontal to diminish the UabiUty of confusion with the I-beam (I) if poorly made. A special interpretation is given to different ways of making this sign on floor plans. See page 157 : 1. For the weights and the dimensions of channels see pages 300 and 301. 4. Rods: Number: diameter or side: °or °: rod (or rods): length (pieces) unches) (feet and inches) Thus: l-f o rod 12'-0", or 10-1"° rods ll'-Of". Xote that a circle (°) is used for round rods and a square (°) for square rods. 5. Tees : Number : T (or Ts) : width of flange : length of stem: weight : length (pieces) (inches) (inches) (pounds per foot) (feet and inches) Thus: 1 T 3 X 3* X 8.6^ X 12'-11", or 3 Ts 4 X 3 X 9.3# X 13'-2". Xote the distinction between a 3 X 35 (3" flange) and a 3^ X3 (3" stem), etc. 6. Z-bars : Number: Z (or Zs) : depth: width of flanges: thickness: length (pieces) (inches) finches) vii^ches) (feet and inches) Thus: 1 Z 6 X 3i X t\ X S'-3i", or 4 Zs 3tV X 2| X A X 17'-0". 7. Rails: Number: Rail (or Rails) ; weight: standai'd: length (pieces) (pounds per yard) (feet and inches) Thus: 1 Rail 85 #/ yd. A.S.C.E. 20'-0", or 16 Rails 100 f yd. A.R.E.A. 33'-0". Note that the weights of rails are given in pounds per yard, instead of pounds per foot as in the case of other shapes; for this reason it is preferable to write the weight as above, although the (#/j'd.) is often written simply (#). The standards of the American Society of Civil Engineers, the American Railway Engineering Association, and the American Railway Association are in common use. The usual CHAPTER VII THE CONVENTIONAL METHODS OF BILLING 45 lengths are 30 ft. for rails up to 60 #/yd. and 33 ft. for the heavier rails. For the dimensions and the properties of rails see page 317. 1. Eye bars : Number : eye bar (or eye bars) : width of main bar : thickness : ^^^, , ^ " of holes (pieces) (inches) (inches) (feet and inches) Thus: 1 eye bar 14 X 1 X 15'-0" c. to c. of holes, or 2 eye bars 8 X f X 12'-0" c. to c. of holes. Note that the lengths of eye bars are given from center to center of pin holes instead of the extreme length. Eye bars are connected by means of pins. The distances from center to center of pins are calculated, and the eye bars should be made to correspond. The heads of the eye bars are upset while hot, and the holes are then sub-punched, i.e., punched to a smaller diameter than the required size. Two boring machines are carefully set so that the finished holes at both ends of a, bar can be bored simultaneously at the exact specified distance apart. The over-all length is therefore relatively unimportant. 2. Lattice bars: Number: Latt. bars: width: thickness: length c. to c. of holes (pieces) (inches) (inches) (feet and inches) Thus: 22 Latt. bars 2i X i X l'-2|" c. to c. Note that the lengths of lattice bars are given from center to center of rivet holes. Since this is not in accord with the method of billing other material, the lengths should always be followed by " c. to c." The distance center to center of holes is much more important than the extreme length in order to insure an accurate matching of the holes. Furthermore, this dis- tance is used in setting the adjustable stop in a special lattice bar punch. This machine cuts out the material between the curved ends of two bars and punches the holes in these ends simultaneously according to standard dies, as indicated on page 315. As the bar is advanced to the adjustable stop and punched again, a complete lattice bar is made at a single stroke. 3. Washers: Number: washer (or washers) : diameter: thickness (pieces) (inches) (inches) Thus: 4 washers 21 X j. 4. Rivets : Number: diameter: rivet (or rivets) : length (pieces) (inches) (inches) Thus: 450-f" rivets U" long. If rivets have countersunk heads the fact should be stated. The diameter of a rivet is the diameter of its shank (page 30 : 4). The length of a button head rivet is from the underside of the head to the end. The length of a countersunk rivet is the extreme length, includ- ing the thickness of the head (page 304). The number and the lengths of rivets are seldom specified except on the rivet hsts from which the field rivets are made and shipped. The size of shop rivets is given on structural drawings thus: f" rivets. 5. Bolts: Number: bolt (or bolts) : diameter: length (pieces) '(inches) (feet and inches) Thus: 2 bolts | X 2, or 4 bolts 1" X l'-3" Ig. If a bolt has a countersunk head the fact should be stated. The diameter of a bolt is the diameter of its shank (page 304). The length of an ordinary bolt is from the underside of the head to the end. The length of a countersunk bolt is the extreme length, including the thickness of the head. • ' ' Diameter: hole (or holes) (inches) Thus: \i" holes. Rivet holes are made ^^" larger than the diameter of the rivets to be inserted. (Why? See page 30:4.) Most bolt holes in structural work are made tV" larger than the corresponding bolts, except holes for anchor bolts (pages 73 : 3 and 106 : 5). 7. Special Abbreviations. — Adjectives may be used before the abbre- viations for plates and angles to aid in identification, as for example: — Bear. PI. for bearing plate, Bent PI. for bent plate, Gov. PI. for cover plate, Fl. PI. for floor plate, Reinf. PI. for reinforcing plate, Spl. PI. for splice plate, Web. PI. or Web for web plate, Flge. L. for flange angle. Spl. L. for splice angle. Stiff. L. or Stiff for stiffening angle. CHAPTER VIII STRUCTURAL DRAWINGS — THE DIMENSIONS Synopsis : Structural steel cannot be trimmed and fitted during erection as wood is cut in carpentry, but all parts of a structure must be made to fit the first time. Conse- quently, more elaborate precautions must be taken, first to insure the correctness of all dimensions, and second to make sure that the dimensions are so expressed on the drawing that they cannot be misunderstood. In few kinds of work is there a more exacting system of painstaking precautions and checks than in the work in a modem structural drafting room. The dra^^ings must be issued absolutely free from mis- takes, as far as possible, for each uncorrected mistake, unless detected in the shop, maj- cause the loss of a large sum of money. (For example, the use of 30'-0" instead of 30'-6" for the lengths of 1200 I-beams once caused a large loss.) In this chapter are given rules and suggestions for dimensioning a structural drawing, including the use of the dimension lines, the arrow heads, and the figures. 1. In this book a distinction is made between the terms " dimen- sion " and " size." The former impUes the use of a dimension Hne upon which the dimension is written, whereas the "size " applies to the figures which are used in biUing (Chapter VII, page 43), and may refer to the depth, the width, the thickness, the weight, the length, or to various combinations of them. 2. The dimensions form one of the principal parts of the working drawing. The shopmen and the draftsmen who use the finished draw- ings are never permitted to scale them, but must always use the figured dimensions. It is therefore important that all dimensions should be accurate, and the extent of each dimension should be apparent. A dimension is worthless unless it is of some use, unless it is perfectly legible, and unless there is no ambiguity regarding the two points be- tween which it is intended to extend. 3. Dimensions should indicate the actual measurements of the piece represented, regardless of the scale used in the drawing. 46 4. The dimensions should be placed upon the drawing as soon as determined, while fresh in mind. The dimensions should usually be determined in the order of importance, the main dimensions first, and those for the details last. The main dimensions for a drawing are generally determined from the erection diagrams or the design sheets, while the dimensions for the details are found in the tables of this book, in the handbooks or the standards of the different steel or structural companies, or else they are supphed by the draftsman. 5. Position. — Each dimension should be placed upon the drawing in such a manner that it wiU be of most use to those who read the drawing. The principal dimension should be made conspicuous by being placed upon a dimension line which intersects the fewest possible number of other lines. Thus the longest dimensions, such as over-all lengths and extreme depths, should be placed on dimensions lines which are farthest from the ^•iew to which these dimensions apply (usually the front %'iew), and the shorter dimensions, such as those for rivet spacing and CHAPTER VIII THE DIMENSIONS 47 other subdivisions, should be on dimension Hnes nearest the view. In this way the hnes for long dimensions are not crossed by the perpen- dicular projection hnes which mark the ends of shorter dimensions. When there are several dimension hnes close together, it is often de- sirable to make the figures of the principal dimension larger and bolder than the rest. 1. Dimension lines should be continuous black lines, as fine as prac- ticable without appearing ragged (page 37 : 1). They should be drawn parallel to the measurements to be dimensioned, and should extend between projection lines drawn at right angles to the dimension lines to indicate the distances intended. 2. Dimension lines should usually be placed outside of the view dimensioned, and preferably between the views if more than one. At times, however, a few dimensions may be placed in a clear part of the view itself if space or clearness is gained thereby. 3. Dimension hnes are usually placed about j" apart, although this may be reduced to j\" or increased to j\", depending upon the available space. The distance from the view to the nearest dimension hne is made twice the space between dimension lines, unless it must be in- creased to allow for projecting details, or for other shorter dimension lines. 4. Arrow heads should be placed on the dimension hnes to indicate the extent of the dimensions. They should be made definite, otherwise the dimensions are useless. The size and the style of arrow heads depend upon their location. For main overall dimen- sions they may be made large and bold, as in Fig. 47 (a). Flat curved arrow heads appear more graceful and may be used wherever there can be no ambiguity, Fig. 47 (6), but when a dimension extends to one of two Unes which are close together, the arrow heads should be made short and wide, Fig. 47. so that the vertex is distinct. See Fig. 47 (c). They should not be made large when close together. Arrow heads gener- ally point away from the dimension figures, but in narrow spaces they may be reversed. See Fig. 47 (d). A dimension extends from the vertex of one arrow head to the vertex of the first arrow head in the opposite direction. Usually only one dimension is placed between these arrow and this gives the correct result if referred to the nearest quarter of an inch, as for example: — 0.81 is 0.06 more than 0.75, hence t^ + f = it; and 0.19 is 0.06 less than 0.25, hence i - tV = A- If a web thickness given in decimal form should fall midway between sixteenths, the higher sixteenth is usually chosen in dimensioning to allow for "packing," since paint, scale, bends, etc., do not permit the surfaces of two pieces to be brought into perfect contact. The tables at the end of this book express the web thicknesses in both decimal and fractional forms. 5. The abbreviations (ft.) and (ins.) are not used in dimensioning. A single accent mark (') represents feet, and a double accent (") inches. Dimensions less than one foot are usually expressed in inches alone, but to avoid ambiguity dimensions of one foot or over (even if even feet) should always show both feet and inches with hyphens between. Note: The width of a plate is given in inches when billed (page 43 : 3), whether more or less than 12", but when given as a dimension with a dimension line it is expressed in feet and inches if I'-O" or over. Hence it is no exception to the general rule. The inch marks (") of dimensions less than one foot may often be omitted, provided there can be no doubt as to the meaning; but the inch marks should be used whenever the drawing can be made more clear thereby. The correct method of writing dimension figures can best be shown by examples, as follows: — Correct Incorrect 1 .2 not oi 2", or 61 not 0'-2", or 0'-6i" I'-O" not 1' or 12" 2'-0" not 2' 3'-4i" not 3'-04i" 4'-0f" not 4'-|", or 4'-00f" 6. Recurring Dimensions. — Ditto marks (") should never be used in place of dimensions. The use of arrows leading from one figure to two or more spaces should be avoided. Like dimensions should be repeated at every occurrence, unless grouped as explained on page 49 : 6. CHAI'TER VIII THE DIMENSIONS 49 1. A dimension which is clearly given in one view should not be repeated in another, for it usually complicates the drawing unneces- sarily, and causes trouble if one is changed. 2. Rivets and holes should be located by dimensions which extend to their centers. They should be dimensioned in the views which show them as circles, although exceptions to this rule are occasionally 1" 2W\ a CD ® -fit 4®2s m^ — Q-®-Q Q-0-®tt©' ^TW' Fig. 49. allowed in order to dispense with additional views (page 91 : 4). "Staggered rivets," i.e., rivets which alternate on two lines, should be dimensioned, not diagonally, but parallel to the rivet lines as if the rivets ^mn' ~ "^^re on a single line. See Fig. 49. 3. The gages of all structural shapes should be given in all cases (except latticed members, page 136:3). The standard gages given in the tables should be used, except in special cases which are noted elsewhere, as for example on pages 83 : 6, 106 : 3, 132 : 1, 132 : 3, 136 : 1, and 139 : 3. 4. The majority of edge distances are omitted unless they are im- portant. For example, a dimension should be given in order to limit an edge distance to provide ample clearance for a connecting part (page 72 : 4), or to tie a group of rivets to an important edge to which a main dimension extends (Fig. 148). But if a connection plate or angle, or a web member of a truss, is shown without edge distances, the shopmen will make the distances on opposite edges equal; with this understanding many dimensions may be omitted. 5. A line of rivet spacing should be confined to dimensions from center to center of rivets and holes, except at the ends where it is fre- quently necessary to give the distance from the first rivet to the end of the member or to some other definite point. Intermediate edge dis- tances and gages should never be given on the same line, because they are not used at the same time; they should be shown as separate dimen- sions, usually between the line of rivet spacing and the corresponding view of the member. See Fig. 49. 6. Dimensions should never be given to the edges of the flanges of structural shapes, but always to the backs of channels and angles, to the center lines of I-beams, and similarly for other shapes. The back of an angle or a channel is a well-defined Une, but the outside edges are not so well defined. More important than this, however, is the fact that the lengths of legs and the widths of flanges are frequently different from what they are supposed to be. As a rule, such variation is of no consequence in structural work, but it should be considered, particu- larly in the case of thick angles. See page 25 : 1. For illustration, suppose a girder is composed of a |" web plate and 6x4 angles. The total width of each flange is theoretically I'-Of", but if the angles should "overrun," as they are likely to do, the width would be more. Ordinarily this increase would not matter and for this reason the dimension should not be given; in case the extreme width is limited by the clear distance between column flanges or for other reasons, the dimensions should be given with the understanding that in case of overrun, the outside edges of the angles would have to be planed — a process too expensive to be used unnecessarily. It is unnecessary to give the widths of flanges or the dimensions of fillets and other curves which apply to the manufacture of the steel rather than to the fabrication. It should be borne in mind that the drawings are to be used for the purpose of putting standard shapes together, and therefore many dimensions may be superfluous unless they are directly related to shearing, bending, punching, riveting or similar processes. When an angle with unequal legs is represented in only one view it is often neces- sary to indicate which leg is shown. This may be noted as for example "3" leg," but more frequently the length of the leg is put on in the form of a dimension with the understanding that it is no more exact than the billed length and that the angle need not be out in case of overrun. 7. When three or more spaces are numerically equal and serve similar purposes, they may be dimensioned in a group, thus: — 5 (5) 6 = 2'-6", or 4 @ l'-2" = 4'-8", or as some companies prefer, 5 of 6 = 2'-6". If the rivets are staggered (page 49 : 2), the spaces are given just as if the rivets were on the same line, although the abbreviation "alt. spa." for "alternate spaces" is sometimes added, thus: — 5 alt. spa. @ 6 = 2'-6". Edge distances and gages should not be combined with distances from center to center of rivets and holes in this method, but should have the dimensions repeated, even though identical. In the same way it may be preferable to separate one or more of the spaces from the group if they serve purposes in addition to the spacing of 50 PART II — STRUCTURAL DRAFTING rivets along the same line as the rest of the group, as for example, the 2§ and 3 inch spaces in Fig. 49 which locate rivets in the stiffening angles and spUce plates. 1. When a long Hne of shop rivets and holes for field rivets are dimen- sioned in a single group, and the holes occur at such intervals that spaces must be counted to determine their location, a supplementary dimen- sion line may be added for the holes only, as in the top flange, Fig. 103. 2. If two or more lines of dimensions extend between the same points. the sum of the dimensions in each line should be the same as in the others. If a line of dimensions extends practically the whole length of a member it is well to complete it by adding one or more dimensions to afford a check with the over-all length. This is of special benefit to the templet maker, who would otherwise have to procure his own total for a check. Checking Subdivisions: Never complete a line of dimensions between two points without adding them to see if the sum equals the proper distance between those points. Neglect of- this precaution is a source of much trouble. 3. Dimensions should be placed upon the drawing in such a manner that the shopmen will not be compelled to add or subtract dimensions in order to obtain the figures they need. For example, one hole in the connection angle on the flange face of colunm C5 Fig. 137, is tied to one rivet in the other leg (or else each could be tied to the same end of the angle); otherwise, the templet maker could not make the templet for the angle without findiug the total distances from the rivet and from the hole to the bottom of the column and then subtracting these two sums. Similarly, the holes in the connection plate pb near the center of this same column are dimensioned independently of the rivets; a line is drawn, however, to show that the top holes and rivets are opposite. 4. No rivets or holes should be located by more than one method of dimensioning. They may be determined either by dimensions at right angles to each other (rectangular coordinates), or by "slopes and dis- tances " (polar coordinates), the slopes of the rivet hues being indicated in the usual manner (page 50 : 7) and the distances along these hnes being given. A combination of these two methods is not only unneces- sary, but is liable to cause difficulty in the shop, for the points that Fig. 50. (a) coincide on a small layout in the drafting room might fall noticeably apart on the full-sized templet. In order to avoid ambiguity on the drawing in case a line which locates one rivet or hole happens to pass through another rivet or hole which is located in another way, the line should be made to pass around the second rivet or hole by means of an arc of a circle, as shown iii Fig. 50 (a). Whether the drawing is made accurately to scale or whether the hne would actually pass through the center or not is immaterial, the object of the arc being to show clearly that the line is independent of the second rivet or hole. 5. For field connections — ■ connections of different members in the field — the dimensions on the drawing of one member should be given in exactly the same way as the corresponding dimensions on the draw- ing of the other member so that each person who uses the drawings may see at a glance that these dimensions do correspond. 6. The rivets in the ends of the lattice bars of a single system of latticing are dimensioned in groups much as staggered rivets are dimen- sioned (page 49 : 2) ; each space is measured parallel to the axis of the member latticed, from the center of the rivet at one end of a bar to the center of the rivet at the other end. See Fig. 137. The method of dimensioning a double system of latticing is the same as for a single system, the rivet at the intersection of each pair of bars being shown but not dimensioned. See Fig. 124. For lattice bars with two rivets at each end, see Fig. 127. f 7. The slope of a Ime, i.e., its "bevel," with reference to another Kne is given, as shown in (a) Fig. 50 (6), by in- dicating dimensions on two mutually perpendicular sides of a right triangle; the hypothenuse of this triangle is either coincident with or parallel to the line whose direc- . tion is to be given, and the other sides are respectively parallel and perpendicular to the reference line. The dimension on the longer perpendicular side is always 12", .vhile the corresponding dimension (in inches and frac- tions) on the shorter side must be calculated. This shorter dimension is usually obtained directly from dimensions between working points, as explained on page 76 : 2, without the necessity of 25'6i'" Fig. 50 (6) CHAPTER VIII THE DIMENSIONS 51 knowing the actual value of the angle. Angles are almost never given in degrees and minutes on structural drawings but the corresponding slopes are used. A workman in the shop usually has no such means as an accurate protractor for laying off angles, but he must work with a two-foot rule, a steel tape, or other device for laying off linear measurements. Parts of trusses or bracing systems are often laid out on the floor of the templet shop from the main dimensions instead of on the bench, pro- vided that the extreme dimensions do not exceed 30 or 40 feet. If the dimensions between working points are not clearly shown on the draw- ing they may be given on the triangle without being reduced to a base of 12", as shown in (b) Fig. 50 (b). The two schemes may be combined as in (c) Fig. 50 (b) in order to show the dimensions between working points for the convenience of the checker, and the corresponding reduced dimensions for use in the shop. This method may be used when a draftsman is in doubt as to whether the work will be laid out on the floor or on the bench. CHAPTER IX STRUCTURAL DRAWINGS — THE NOTES, THE TITLE, AND THE BORDER Synopsis: Structural drawings are made as self-explanatory as possible without supplementary notes, although notes can often be used to advantage. Some of the more common notes are discussed in this chapter, and suggestions are given for making titles and borders. THE NOTES 1. Drawings should be made complete and clear without the use of notes whenever practicable, but unless the drawing is perfectly clear, short and concise notes should be added wherever necessary. Care should be taken to make each note expHcit and easily understood. 2. AH general notes which apply to the whole drawing should be placed near the title, usually to the left, as in Fig. 98. Examples of the more common general notes are those which give the sizes of rivets, holes, and washers, the maximum pitch of rivets, and information regarding specifications, paint, inspection, and erection. 3. All other notes should be placed in clear spaces near those parts of the drawing to which they apply. If a note is too long for the avail- able space, it may be placed to one side with a reference to it at the proper point, as for example, "See note." If more than one such case occurs on one sheet, the notes may be numbered or lettered. 4. If the rivets and holes for any drawing are not all of the same size, the general note (see above) should be modified thus: "Rivets f" except as noted," or "Holes if" unless noted" (Fig. 104). All rivets or holes of sizes other than those specified in the general note should be clearly noted. Such exceptional rivets or holes may be dis- tinguished on the drawing in one of several ways, thus: (a) by placing the note at one end of that dimension line which locates all the rivets or holes in question but no others, as in F6, Fig. 90; (b) by drawing 52 supplementary lines with arrows to indicate the desired rivets or holes, as in ME, Fig. 117, or FIO, Fig. 147; (c) by drawing arrows from the note to those rivet lines which pass through all the rivets or holes noted but no others, as in the bottom view, Fig. 135; (d) by encircling the desired rivets or holes by a freehand loop or ring which in turn is connected to the note, as in the top view. Fig. 135; this ring should not include any dimensions or notes (page 181 : 1) ; (e) by noting all the rivets or holes in one view by a special note near the view as in B16, Fig. 92, or by a general note near the title as in Fig. 99. In order to attract attention to a change of size, the American Bridge Company has adopted the use of a heavy diamond as illustrated in most of the figures referred to above. Counter- sunk and flattened rivets are often noted as explained on page 40 : 6. 5. An identification mark is assigned to each member which is to be shipped separately. If more than one drawing appears on a sheet the identification mark should be placed conspicuously near the drawing of the corresponding member. For further description of such "Shipping Marks," see page 80 : 6. 6. The number of pieces to be made from each drawing should be clearly stated, either under the detail, as in beam work (Fig. 87), or at the right of the sheet above the title (Fig. 100). When more than one or two members are shown on one sheet a tabular " Required List " is made, as shown in Fig. 147. CHAPTER IX THE NOTES, THE TITLE, AND THE BORDER 53 1. Reference to other drawings may be made in order to save the repetition of details. Usually reference is not made to another sheet unless a system of assembUng marks is used, as discussed more fully on page 79 : 2. The size of all material should be given on each sheet, and also the spacing of all holes for field connections to facilitate com- parison with the drawings of connecting members. The outline of all material should be completely shown in at least one view to prevent the shopmen from overlooking a whole connection or other detail. The shop rivets and the dimensions which locate the shop rivets and cuts may be referred to another detail, provided the latter is complete in every respect without further reference to a third detail. 2. Loose Pieces Bolted. — Small pieces, such as splice plates, fillers, or connection angles, which cannot be riveted in the shop without com- phcating the field work, may either be shipped separately, or else bolted for shipment to one of the members to which they are eventually to be attached. The latter method is to be recommended wherever feasible, for the number of items shipped is reduced, and the pieces are available at once when needed for erection. Pieces which are bolted for ship- ment are fastened temporarily in or near their final positions by means of two or more bolts each. On the drawing, a note should be placed immediately following the billed size of any piece so bolted, thus: "Bolt for shipment," or "Bolt to ship." See Fig. 125. It is well to give each piece a separate mark for identification in case it becomes detached unless the nature of the piece is sUch that its proper position can be readily determined. The temporary bolts used are of odd lengths as picked up in the shop; sufficient washers are added to facihtate tightening and removing the bolts. To avoid handhng loose pieces in the field it is often feasible to make them enough longer so that they can be riveted in the shop independently of the field connections (Fig. 160) ; this should never be done, however, if the erection is rendered more diffi- cult thereby. 3. In case pieces 8.re to remain bolted in the completed structure without having the bolts replaced by rivets in the field, all the holes should be filled with permanent bolts of the proper size. The bolts should be billed on the drawing in the usual way (page 45 : 5), directly under the billed size of the piece bolted. See Fig. 133. A note, "Bolt complete " may be added to insure the use of a full number of bolts of the proper length, instead of a few temporary bolts (see above). The bolt heads are sometimes drawn but ordinarily, for the sake of simplicity, only the holes are indicated (page 41 : 2). 4. Different Members Combined. — When several members differ from each other slightly, i.e., in minor details, one drawing may be made to represent all of these members and the differences may be stated in notes. This should not be done, however, unless the differ- ences can be made clear and definite in notes which are' brief and com- paratively few in number; otherwise, drawings become so complicated that more time is lost by the shopmen than is saved by the draftsmen. This is often due to the fact that additional connections are discovered, or the design is changed, after the drawing is started. It is essential, therefore, to plan any combination very carefully before the drawing is commenced, using a sketch upon which are indicated the various connections. The notes regarding special connections follow the corre- sponding billed material, if any; otherwise, the holes may be noted as indicated on page 52 : 4. If there are more than a few simple differ- ences, it is better either to draw an additional view (Fig. 137), or to make another drawing. In the latter case it may be possible to show on one drawing simply the outUnes of all parts which are like those on the other, and to draw in detail only those parts which are different (Fig. 117). In order to shorten notes, when several different members are represented by the same drawing, one member may be referred to another after the shipping mark, as for example: — "C12, same as Cll except as noted," it being understood that every note which applies to Cll applies also to C12. The mark "C12 " will not appear in any of the notes, therefore, except where it differs from Cll. See also page 81: 3. 5. All notes should be made positive, except in rare instances. This precludes the use of the word "omit." • For example, if several mem- bers are represented by one sketch, and some of the details are on part of the members only, as the holes for rods in MN, Fig. 117, it is better to note that the holes are "in MN\, and MN2" rather than that they are "omitted in MN3" It is much more important to all concerned in making a member to know which details are to be placed on that member rather than to know which are not. 54 PART II— STRUCTURAL DRAFTING THE TITLE 1. A title is placed in the lower right-hand comer of each fuU-sized sheet, for convenient reference and for use in classification. This uni- form position enables a person to look through a pile of drawings for a particular sheet by merely turning back the comers. The title is com- posed of two parts, one of which refers to the specific drawing, the other to the company which makes the drawing. 2. The first part of the title contains the names of the members on the sheet, or the part of the structure shown; also the name of the structure, the name of the customer, and the place where the structure is to be situated. This part of the title is usually made of freehand letters about -j^" high, of simple Gothic style, and all capitals. Elaborate titles should be avoided, since they add to the expense, and are not in harmony with the rest of the drawing. Some com- panies maintain small presses for printing the titles of the larger contracts. 3. The second part of the title is more general, and is usually printed by means of a press or placed on the drawing by means of a rubber or metal stamp. If the drawing is made in the drafting room of a struc- tural company, the title contains the name of the company, and the name of the plant which fabricates the work; also blanks for the initials of the man in charge of the contract, of the detailer, of the tracer, and of the checker, together with the date of each signature. Additional blanks are often left for the signature of the man who makes a field check or the engineer who approves the drawing. Below these, and at the extreme bottom of the sheet next to the border, are placed the contract number and the sheet number. The contract number should be made bold and conspicuous and in a uniform position. A single letter "C " can be made more prominent than either "Cont. No." or "Contract Number " and although not as significant it has been found convenient for reference. If desired, the line for the number may be placed opposite the middle of the letter, leaving room for the sheet number below, as shown in many of the titles on the drawings of this book. Titles made in the offices of consulting engineers or in the structural departments of railroad or other companies are usually somewhat simpler than those made in the offices of structural companies; in general they are similar, but they have comparatively few signatures. 4. The smaller drawings and hsts are usually made on printed forms which contain the name of the company with blanks for the plant, the structure, the nature of the drawing, the initials of the detailer and the checker, with dates, and the contract and sheet numbers as shown in Fig. 85. 5. Sheet Numbers. — Drawings should be niunbered in different series in order to facihtate the reference to a sheet of a given number. For example, the maia drawings (24" x 36") of a contract may bear simply numbers, but other sheets should have a prefijced letter to distinguish them, thus : E for erection diagrams, B for beam details and other small drawings, C for combination sheets, S for shop bills, R for shipping bills, SR for combined shop and shipping bills, EF formisceUaneous lists, etc. THE BORDER 6. A simple border should be drawn on each fuU-sized sheet to form the boundary, to keep the sheets of uniform size, and to improve the appearance. Ornate borders should be avoided. Comers should be simply rectangular. Borders are not drawn on the smaller printed forms. 7. An effective border is composed of a heavy line with a light line I" outside. The nominal dimensions of the sheet, as for example 24" X 36", indicate the size of the finished tracing, and a rectangle of this size should be penciled to serve as a guide in trimming the cloth. The fine line is drawn J" inside of this to indicate where the blueprints are usually trimmed, and the heavy line is drawn J" inside the fine line to form the border on the prints. This makes the dimensions inside of the border each two inches less than the nominal size of the sheet, as for example, 22" X 34" for a 24" X 36" sheet. If smaller sheets are adopted, as for example 15" X 22" for student use, the fine Une of the border had better be omitted, the heavy line only being used, I" inside the edge of the sheet. In this case the tracing cloth and the blueprints should both be cut the same size as the sheet of paper. The heavy hne should not be over ^\" wide nor wider than can be drawn with a single stroke. See page 59: 3. CHAPTER X INKING AND TRACING Synopsis: Every draftsman should cultivate the abiUty to ink a drawing well. Some men are naturally more skillful than others, but any draftsman can develop skill with practice, if he follows with reasonable care the common rules for inking. Such rules and suggestions for inking are given in this chapter. 1. Structural drawings are made primarily for use in the shop, and therefore accuracy, speed, and utility are of much more importance than appearance. On the other hand, it is highly desirable that a drawing be neat, well arranged, and well executed, although it is not so important in this work as in map or architectural work. A good looking drawing not only adds to the prestige of the draftsman, but also gives to all who use it greater confidence in its accuracy. The appearance of a drawing is determined largely by the arrangement on the sheet, and also by the skill of the person who inks it. There are many practical rules for inking and tracing with which every draftsman should be familiar, whether he is a skilled tracer or not; by their adoption he will be enabled to make drawings much more definite and useful than he could otherwise, and he will gradually develop skill along the proper lines. 2. Three methods of making drawings are commonly used. A draw- ing may be made on paper and then inked ; it may be made on paper and then traced in ink upon tracing cloth ; or it may be made directly in ink on tracing cloth. The rules for inking are practically the same in all three methods. 3. The Care of Tracing Cloth. — Tracing cloth should never be folded or creased, for permanent cracks would result. It should not be handled with moist hands, and water -should not be allowed to come in contact with it, for not only would the surface be thus spoiled for inking, but it would also be rendered opaque so that white spots would show on each print taken from the tracing. 4. The dull or unglazed side of the tracing cloth is used for structural drawings for three reasons, viz.: (1) the dull side is the only side upon which pencil marks can be readily made or erased; not only is this cf advantage at times to the tracer and to the detailer but it permits the checker to note corrections in pencil directly on the drawing (page 181 : 1) ; moreover, if a part or the whole of a drawing is to be made in pencil directly on the tracing cloth (page 65 : 3) it must necessarily be made on the dull side; (2) extensive erasures may be made with less apparent unjury to the cloth than on the glazed side, especially if several erasures are made in one place; and (3) the tracings may be more easily handled and filed because they are less Hable to curl. 5. Before the cloth is stretched, the selvage edges should be torn off. These edges are woven with the threads closer together than in the body of the cloth, and are not so susceptible to atmospheric changes. Unless they are removed, the cloth is liable to pucker from one day to the next, particularly if there is a noticeable change in the amount of moisture in the air. It is often impossible to restretch the cloth flat until the selvage is removed, and at times it is difficult to do so at all; hence it is important to remove the selvage before the cloth is first stretched. Since the threads are parallel to the edges, the selvage may be torn off without difiSculty, provided reasonable care is exercised to prevent the cloth from tearing at right angles to the desired direction. The width of the strip to be removed is usually apparent, and varies from | to J of an inch with the different makes of cloth. Enough should be re- 55 56 PART II — STRUCTURAL DRAFTING moved to eliminate all the puckers, and to leave the cloth perfectly flat. 1. The cloth should be tightly stretched over the drawing to be traced, and held in position by thumbtacks. At least four tacks should be used, one in each corner, two diagonally opposite tacks being placed first. Additional tacks may be used, if necessary, to keep the cloth taut. The tracing cloth should be enough larger than the finished drawing to permit tacking the cloth to the board in such a manner that all thumbtack holes will be cut off when the completed tracing is trimmed to the proper size. The corners of the cloth may be folded under so that each tack passes through two thicknesses of cloth and is thus less liable to tear out. Be- fore the cloth is tacked completely, great care should be taken to see that the paper drawing is so placed that all horizontal lines are truly horizontal in order that the T-square may be used to the best advantage. If the drawing paper is too small to be held by the same tacks, it should be fastened before the cloth is put on. Two tacks are usually sufficient for this purpose and if put at the upper corners will seldom be in the way of the T-square. It may be desirable to use small upholsterers' tacks, driven with a hammer, to fasten the drawing paper to the board, for they wUl not interfere with the instruments during the making of the drawing or of the tracing. Some draftsmen prefer to use these tacks for holding the tracing cloth in place also, particularly when the T-square or the tri- angles must be used near the comers; but if the cloth needs to be re- stretched very frequently the use of such tacks is hardly practical. 2. Before beginning to trace, the draftsman should make sure that the surface of the cloth is in condition to receive the ink properly. This may be ascertained by trial on a small piece of the same cloth, upon the margin of the sheet which will be subsequently trimmed off, or even upon one of the lines of the drawing itself. Some of the better grades of tracing cloth will often "take " ink without treatment, and it is preferable to use it that way. More frequently the surface of the cloth is slightly oily and the lines appear ragged. The common method of overcoming this disadvantage is to sprinkle upon the cloth powdered chalk or pumice stone, specially prepared tracing cloth powder, or even talcum powder, and to rub it in with a clean cloth. After a thorough rubbing has spread the powder over the whole surface, another clean cloth, or a brush, should be used to remove completely all the excess powder to prevent the clog- ging of the pen. If too much powder remains, much of the ink falls upon it rather than upon the cloth, and the lines easily wear away. Further- more, when too much powder is used, the eraser soon becomes clogged and is made less effective. Accordingly, it is often preferable to "surface " the cloth by means of a sponge eraser, rubbing the grease off instead of cover- ing it or absorbing it with the powder. This is particularly true when the effects of the oil are not very apparent, for the cloth is thus rendered much more satisfactory to work upon. The surface of the cloth should be kept clean, and the path of the pen cleared of all lint, dust, and pieces of eraser. A brush should be constantly available for this purpose, but care should, be taken that all ink on the drawing is dry before the brush is used. 3. The draftsman's equipment should include a good ruling pen,* and he should not only be familiar with its use, but also be able to keep it in good working order. When not in use the pen should be left with the nibs separated in order to relieve the springs. The ruling pen should be held between the thumb and forefinger, resting against the middle finger to hold it firmly. The adjusting screw should be held away from the draftsman so that it may be readUy turned with the middle finger to change the setting. The nibs should be parallel to the straight-edge, and the handle should be slightly inclined, with the top in advance as drawn from left to right. The handle should re- main in a plane through the Hne to be drawn, the plane being nearly perpendicular to the plane of the drawing. See page 58: 6. The pen should never be piished back- ward, even for a short distance, but should always be hterally "drawn." It is important to keep the pen clean. The pen should not be filled until the draftsman is ready to use it, and it should be used practically continuously while it contains ink. Even when interrupted from work the draftsman should take time to wipe his pen before laying it down. This can be quickly done if a large cloth is kept hanging near the left- hand corner of the board or in some other convenient place. Old tracing cloth, thoroughly washed with soap and water, makes an ideal pen wiper. The wipers which are furnished with bottles of ink are too small to be serviceable. A pen wiper should be free from lint. * For more complete treatises on drawing instruments and their use see Blessing and Darling's " Elements of Drawing," John Wiley and Sons, Inc., New York; French 's "Engineering Drawing," McGraw-Hill Book Co., Inc., New York; or Kirby's "The Fundamentals .of Mechanical Drawing," John Wiley and Sons, Inc., New York. CHAPTER X INKING AND TRACING 57 If inlv is permitted to dry in the pen it should be removed before the pen is used again. If allowed to remain it will cause the pen to corrode; this will not only make it more difBcult to keep clean, but will eventually prevent precise work. Dried ink should never be removed from a pen with a knife or scratcher for the inner surfaces will become so roughened that the ink will not feed properly. Furthermore, a much simpler and more effective method is to dip the pen in red ink, which will dissolve the caked ink 80 that it may be wiped off. To avoid all of this, the draftsman should form the habit of always wiping his pen before laying it aside even momentarily, while the ink is still liquid; it takes only a moment for the ink to dry enough to clog the pen, and after this happens it is usually a waste of time to attempt to use the pen again without refilling it. The ink should flow as soon as the pen touches the cloth. In case the pen has been left unused only for a moment and the ink has dried shghtly in the extreme point, the flow may often be started without refilling the pen by maldng a few short strokes on a piece of paper, wood, or cloth. It is a good plan to wipe occasionally the side of the pen which bears against the straight-edge, for tliis not only keeps the ink flowing well, but prevents, in large measure, the ink from running under the straight-edge. If, when the pen is adjusted for fine lines the ink cannot be started by the expedients just mentioned, the nibs may be separated temporarily until a heavy line can be drawn, and then readjusted to give the desired width. The ruling pen is usually filled by means of the quiU in the cork of the ink bottle. When used immediately after a lettering pen or othei' pen in which considerable ink is left, the ink may be transferred from one pen to the other; this saves ink and often time, and'prolongs the life of the pen wiper. Similarly, ink may be restored to the bottle by touching the pen to the quiU. Care should be taken to avoid getting any inlc on any part of the pen other than between the nibs, particularly on the part that bears against the straight-edge. The pen while being filled should never be held over a drawing. It is important not to get too much ink in the pen, particiilarly for fine-line work. It is difficult to retain a constant width of hne if the amount of ink in the pen is greatly increased; it is better to increase the amount slightly before the pen is entirely empty. Experience will show the proper amount to use in pens of different shape under different conditions. For short fine lines the depth of inlc above the pomts should seldom exceed j^ or | of an inch. 1. If a pen is not working well, a draftsman should be able to fix the points so that a clear-cut even line of any width from the finest to the coarsest can be drawn. If the points are too dull it is impossible to draw fine lines satisfactorily, and if the points are of uneven length one edge or the other of a coarse hne will be ragged. If a pen is in good condition, it should be possible to draw lines at different speeds without having them vary in width, or to stop the pen completely and start it again with- out leaving a pool or other evidence of having stopped it. To sharpen a pen, rub the outside surface first of one nib and then of the other on a fine oil stone. In order to keep the outside siu-face of a nib curved, the pen should be moved in the form of a figure eight, with a slight rocking motion, so that the whole edge of the nib is sharpened uniformly. Care should be taken to avoid maldng flat spots, or sharpening one nib more than the other. After both are sharpened so that the edges show no shiny worn places, make the two nibs of the proper relative length by drawing the pen hghtly along the stone, holding it in the same plane as when draw- ing a hne, i.e., approximately normal to the stone, but swinging the handle in this plane to give a curved edge. Test the lengths of the nibs by drawing several heavy fines of different widths. If a hne appears ragged on one side, the nibs do not bear evenly, or else one nib is too dull. If the pen wiU draw heavy fines well, test it for fine fines. The nibs may have been dulled shghtly in the process of evening theii lengths; if so they should be re-sharpened. If reasonable precautions are taken to avoid excessive grinding the draftsman should be able to obtain edges at the fijst trial which are even and yet of the right sharpness. The pen should not be left too sharp, for it will either cut the cloth or else make such a deep impression that it is diffieult to erase a line when occasion arises. 2. The legs of the compasses should be bent at the knuckle joints until the pen and the arm which carries the pivot point are both perpen- dicular to the plane of the cloth. The compasses should be set to the proper radius by placing the pivot point at the center of the arc and moving the pen until it is immediately above the line to be inked, close to the drawing but not in contact with it. In drawing a curve the com- passes should be inclined so that the top of the pen is slightly in advance of the point. A curve should be drawn with a continuous motion, and a complete circle should be closed by carrying the pen a httle past the be- ginning. The weight of the pen is sufficient to insure a good line without additional pressure, and care should be taken to avoid pressure sufficient to alter the radius or to move the pivot so as to cause a crude junction. 3. The lettering pen should be well adapted to the individual who uses it, with a pen-holder of suitable size so that the hand will not become cramped. Some draftsmen obtain excellent results with fine points while others cannot use them without spreading the nibs so as to make lines of uneven width. A long fine stub pen will usually give excellent results for most letters and figures of a structural drawing (page 47 : 5), a fine pen being provided for drawing arrows and arrow heads or special work for which the stub is too coarse. A ball-pointed pen is often used for titles and other prominent lettering. Some draftsmen use a ruling 58 PART II — STRUCTURAL DRAFTING pen for a lettering, but when this is done a special pen should be kept for the purpose for it cannot be kept in condition for ruling. 1. Two bottles of best quality India waterproof black ink should be used, one for instrumental work and the other for lettering. The former should have a quill for filUng the ruling pen, but the latter may have the quill cut off, because it is quicker and more satisfactory to dip the letter- ing pen into the bottle than to use the quill. The bottle with the quill should be kept corked except during the actual fiUing of the pen, but the other may be left uncorked as long as the lettering pen is in constant use. This would not be feasible if only one bottle of ink were used; so much dust collects in the open bottle, and so much ink evaporates leaving a deposit, that the ink is soon unfit for use in drawing pens, though it may still be used in lettering pens. Each new bottle of ink should be reserved for instrumental work, the remainder of the ink in the former bottles being combined for lettering. Ink should never be diluted with water; if it becomes too thick for use it should be thrown out and replaced. 2. If red ink is used, a quality should be selected which can be erased. No red ink can be erased so easily as black ink, and some red inks cannot be removed at all. It should be waterproof; otherwise it is Hable to spread when stored in cool vaults. 3. An ink bottle should never be shaken, for no benefit is derived and the sediment is stirred up so that it is liable to get into the pen. Further- more, bubbles are formed in the neck of the bottle which draw the ink from the quill, so that it is difficult to obtain enough to fill the pen. 4. Frozen ink is useless and it is usually unsatisfactory when thawed. The bottles should be kept away from windows in extremely cold weather to prevent the ink from freezing. 5. The straight-edge should be placed between the draftsman and the line to be inked, so that the near side of the pen bears upon the far side of the straight-edge. Care should be taken to keep the pen against the straight-edge, but to exert no more pressure than necessary to insure this. The pressure should be constant, for otherwise the width of a Une will be reduced as the nibs of the pen are pressed together. The pressure of the pen upon the cloth or paper depends upon the sharpness of the pen and the quality of the surface, but it should never be greater than neces- sary to insure an even line. 6. The draftsman should not attempt to draw too close to the straight- edge, lest the ink run under and blot. This distance depends somewhat upon the shape of the pen and the thickness of the straight-edge, but after a little practice the draftsman will learn how close he can work to the best advantage. One-fiftieth of an inch may be taken as a guide to the beginner; this corresponds very closely to the smallest division (j") on the scale of 1" = 1'. After inking a hue one should never attempt to pick up the straight-edge until it has been moved a safe distance away from the fine, i.e., toward the draftsman. Otherwise it is difficult to pick it up without letting it slip into the wet ink and cause a serious blot. 7. An easy posture should always be assumed before a line is drawn, for it is difficult to do good work in a cramped position. The drawing board may sometimes be turned to advantage. Lines should be drawn with a full arm motion, with the third and fourth fingers resting lightly upon the straight-edge as a guide to give better control. The elbow should not be rested upon the drawing. Near the end of the line the guiding fingers should be stopped just before the fingers which hold the pen, to facilitate stopping the pen at the exact point. This may be done in such a manner that the motion of the pen will not be interrupted. Very short lines may be drawn with this finger motion alone. 8. Each full line should be drawn with a continuous stroke. It is important to have sufficient ink in the pen to complete the line. If it is discovered that the ink will give out before the end of the line is reached, it is best to stop abruptly, preferably at some intersection, and to begin at the same point after refilUng the pen.. If the ink runs out before the draftsman is aware of its being low, the ragged part of the line should be retraced after the pen is refilled. In this event it is important to try the pen on a separate sheet to make sure that the Une is of the proper width before applying it to the drawing, for a pen is hkely to make a wider line after being cleaned, and refilled than when nearly empty. 9. It is well to draw all Unes which are of the same width at one setting of the pen, if possible, in order to gain uniformity. Even the pens which are made so that they may be opened and cleaned without chang- ing the setting do not always make lines of the same width before and after cleaning. In order to produce a more constant flow, the pen should be refilled before it is entirely empty. CHAPTER X INKING AND TRACING 59 1. Care should be taken to stop the pen at the exact end of each line in order to give a finished appearance to the drawing. The pen should be lifted immediately, when the end is reached, to prevent the ink from running out and forming a pool, which it is liable to do, particularly when the pen and the cloth are not both in perfect condition. The pen should always be lifted vertically to avoid a false mark. 2. Lines should be drawn away from intersections, as far as possible, rather than toward them, particularly when several lines meet in a com- mon point. A line should never be drawn to meet another line until the latter is perfectly dry. 3. Heavy lines which represent web sections (page 37 : 2) and other lines which are wider than the main lines or the border lines of a drawing should each be made of two or more component parts, i.e., part of the width should be drawn and allowed to dry, then another part, and so on until the full width is completed. If the full width is drawn with one stroke or setting of the pen, the ink will flow so freely that it will take too long to dry, will pucker the cloth, and will make it impossible to get clean intersections because the ink will form a pool where two lines meet. If three lines are used for building up a heavy line, the first two are drawn to form the boundaries of the required line, and they should be so drawn that they are parallel and entirely within the desired width. After these two component parts are dry, the third line may be drawn to fill in the space between them. It should not be necessary to use more than three lines and usually two will suffice. Border lines are generally not so wide that they cannot be drawn with a single stroke, but often two strokes will give better results. 4. In the inking of several parallel lines, the triangles or T-square should be used in the same manner as in the penciling of the lines to in- sure their being parallel. If only a single triangle is used in the attempt to ink over the pencil lines, a slight variation usually results, which is quite apparent. For methods of drawing many parallel lines equidistant, as in cross section lining, see page 37 : 2. 5. All curves should be inked before the straight lines which are tan- gent to them. A straight line is tangent to a curved line when the center of the one is tangent to the center of the other, the width at the point of tangency being no greater than the width of either line at any other point. If the straight line is narrower than the curved line, as for example the projection line for a dimension to the extreme outside of a curved surface, the outer edges should be tangent instead of the centers. 6. At practically no time should it be necessary to wait for ink to dry. It does not require much ingenuity to find something to do on one part of the drawing while the ink is drying on another part. The man who idly fans the ink with a triangle not only wastes valuable time, but at- tracts the attention of others to the fact that he is not at work. 7. On rush work of revision, or other work which is confined to a small part of the drawing, it may be desirable to ink in the vicinity of wet lines. This may be done by placing a triangle on each side of the wet lines, and then laying across these two triangles a third triangle to be used as a straight-edge. This cannot blur the wet lines since the straight-edge is elevated above the surface of the cloth in such a way that it cannot touch the lines. For a small area it may be sufficient to lay one triangle across the central opening of a large triangle. Care should be taken not to draw a line which will intersect a wet line or figure. 8. A blotter should never be laid upon wet drawing ink to hasten dry- ing. In fact the blotter should never be used on a drawing except to absorb superfluous ink from a blot or from a line to be erased, and then only by touching its corner to the crest of the pool, without touching the cloth. If the blotter touches the cloth when wet, it makes the ink pene- trate so deeply that it is "difficult to erase it, in fact more difficult than if it were allowed to dry without the use of a blotter. 9. In order to obtain the best results in inking or tracing, a systematic method of procedure should be followed. The tracing should not be started until the penciled drawing is complete, especially if the tracing is made by a person other than the one who makes the drawing. In case the drawing and the tracing are done by the same draftsnian, he should either make the penciled drawing complete, or else work directly upon the tracing cloth, as explained in Chapter XII, page 65. The only modification of this rule is noted on page 66: 1. The order of procedure given in the following paragraphs is recommended. 10. All the lines of a drawing should be inked before any of the figures or notes. For widths of lines, see page 37:1. Ordinarily it is best to ink all the lines which are of one width before changing the setting of the 60 PART II — STRUCTURAL DRAFTING pen for another width (page 58:9); but if the work is to be interrupted for a considerable length of time so that atmospheric changes might cause the cloth to expand or contract it may seem better to confine the inking to one view, or to so much of the drawing as can be completed before the interruption, especially if the drawing is comphcated and the number of intersecting hues is large. 1. All fine line curves should be inked first, and then the rest of the fine lines, including the dimension lines, and the center lines, but not including cross section lines, or fine fines which are tangent to heavy line curves. The horizontal lines should be drawn first, beginning at the top and working down the sheet to save waiting for the ink to dry; next the vertical fines, beginning at the left and working toward the right; and then all other Unes of the same width, working in some systematic order to prevent the omission of any. 2. The heavier main lines of the drawing should be inked next, follow- ing the same order as given for the lighter lines in the preceding paragraph. 3. The rivets and holes may be put in next. These should never be drawn until the lines are drawn, for it is simpler and more satisfactory to center the rivets on a line than it is to draw a line through the centers of a row of rivets. The rivets should always be drawn approximately to scale with a bow-pen or a riveter. Few bow-pens can be adjusted to make circles small enough for the general require- ments of structural drafting, and riveters are much better adapted to the purpose. The riveters fitted for ink only, i.e., riveting pens, are recommended instead of those which are interchangeable for itiV and for pencil. A fixed needle point is held verti- cally while the revolving pen is twirled arotmd it. The pen can be set to make a circle which is so small that it is virtually a period, and can be lifted out of the way while the needle point is being centered. Such a riveter should form part of the equip- ment of every structural draftsman. The appearance of any drawing is marred by freehand rivets and holes. For the conventional method of indicating rivets and holes, and for the sizes of the circles, see page 40: 6. All shop rivets of the same diameter should be drawn with one setting of the riveting pen in order to make them of uniform size, and the same precaution should be observed in drawing the holes for the field rivets. The latter may be filled in solid at once, but considerable time is required for the little puddles to dry so that they will not smear, and for this reason it may save delay to wait until the rest of the drawing is completed before filling in the holes or else to fill them in a few at a time while dimensioning. Some draftsmen prefer to draw aU arrow heads before putting any of the dimension figures on the drawing; in this case the open holes may be filled in at the same time. See page 47 : 4 for the styles of arrow heads. When filling the circles for the field rivets it is an excellent plan to sUp a blotter under the cloth to absorb any ink that may run through the holes made by the needle point of the bow-pen or the riveter. By using a little forethought the draftsman can usually plan his work so that the ink will be dry on part of the drawing by the time that he completes the holes and arrow heads on the rest, so that he can proceed at once with the dimensions. 4. After the arrow heads have been inked, the dimension figures may be put on, but this should be done systematically in order that none will be omitted. On some drawings it may be well to ink them in the order of importance, and on others in the order in which the shopmen will use them, thus making sure that sufiicient dimensions are given. If the penciled drawing is weU made, however, the dimensions on one view may be inked first, one line of dimensions at a time, and then the dimensions on the next view, and so on. When a detail is dimensioned chiefly in one view, but has a gage or a few similar figures in another view, it is well to ink these figures in connection with the rest of the detail, rather than to wait until the remainder of the view is inked. 5. After the drawing has been dimensioned, all material should be billed as outlined in Chapter VII, page 43; then the list of members required and all notes should be inked, first the specific notes on various parts of the drawing, then the general notes, as outUned in Chapter IX, page 52. For aU of this work pencil guide Unes should be used, not merely by beginners, as students are wont to beheve, but by experienced draftsmen as well. Guide fines are essential to all good lettering; hke the carpenter's staging, they are used by the best men as well as by the novices, but, hke the carpenter's staging, they should be removed after the work has been completed. To obviate the necessity of ruling and erasing fines on each drawing, a small sheet ruled once for all with parallel fines at proper distances apart, may be slipped under the tracing cloth where the lettering is to be, and used instead of the pencil guide lines. It CHAPTER X INKING AND TRACING 61 is convenient to have a large number of parallel lines on this sheet not only to provide for notes which have many lines, but also to simphfy the placing of the sheet in the desired position. Diagonal red lines drawn at the standard slope for inclined letters are of great assistance in main- taining a uniform slant in lettering. A convenient size for this sheet is 5" X 8"; if smaller it is difficult to place it under the cloth in the right position. Sheets with different spacing may be made for various sizes of letters, or different spaces may be combined on one sheet, if the change from one to the other is made conspicuous. Uniform spaces of tV" make good units, for a single space may be used for small notes, two spaces for Required Lists, and three spaces for titles. Simple freehand letters should be used entirely, and the draftsman should practice lettering until proficient, for a good looking drawing may be easily marred by crude lettering.* Slanting letters are preferable to vertical letters because * The beginner should obtain some standard book on lettering, such as Reinhardt's deviations from a uniform slope are less apparent than deviations from the vertical. Most draftsmen can letter more rapidly with sloping letters than with vertical letters. 1. Finally the title should be traced and the border inked. For sug- gestions for making the title and the border see page 54 : 1-7. 2. As soon as the tracing is removed from the board it should be turned face downward so that the draftsman may ascertain if any ink has passed through defects in the cloth, or through holes made by the instruments. All such blots should be removed, for they would cause spots on the prints and thereby mar the appearance just as if on the face of the tracing; they might cause serious trouble if an important figure was thus altered or obliterated. "Lettering for Draftsmen, Engineers and Students," D. Van Nostrand Co., New York; Blessing and Darling's "Elements of Drawing," John Wiley and Sons, Inc., New York, or French's "Engineering Drawing," McGraw-Hill Book Co., Inc., New York. CHAPTER XI ERASmG Stnopsis: It frequently happens that parts of structural drawings must be removed on accoimt of mistakes or changes. Every draftsman should learn to erase in such a manner as to leave the least possible evidence of erasure, even when several erasures are made in the same place on a drawing. 1. To erase any part of a drawing properly is just as important as to ink or trace properly, and the draftsman should expect to devote a con- siderable part of his time to painstaking and careful erasing. In the first place, he must correct his own mistakes and errors of judgment, and in the second place, he must frequently make changes which may be due either to mistakes of others or to changes in design. Many good looking drawings are practically ruined by careless erasing. 2. The object of erasing is not merely to remove part of a drawing, but to remove it in such a manner that other lines and figures may be placed in the same spot without having the change apparent on the blue- print. This can be accompUshed only by a person who fully reaUzes the difficulty, and who exercises great care and patience. 3. Erase Willingly. — The first and often the only indication of friction between a beginner and his superiors usuaUj' arises because he objects to erasing. While he should never make changes until he approves them, yet he should stand in readiness to beheve that the more experienced checker has good reasons for most changes and he should try to see his point of view; moreover, the objections of the novice are more Ukely to be heeded, if, instead of attempting to convince the checker that minor changes should not be made because they involve too much erasing, he reserves his arguments for more important matters. The friction should be between the draftsman and the drawing not between the draftsman and the checker. To argue over erasing is usually futile, and more time is lost than would be used in making the corrections at once; furthermore, 62 the draftsman is Hable to lower himself in the estimation of the checker. He should be more tactful. 4. The draftsman should profit by the criticisms of the checker, and guard against mistakes similar to those which have been corrected on former drawings. Erasing mistakes wiU often help bim to remember them. A new man is judged not so much by the mistakes he makes, as by the mistakes he makes a second time; if he is careful not to repeat any mistake it wiU not be long before he wiU outrank the men who are not so careful. 5. Ink should be removed from tracing cloth by means of an eraser. The secret of erasing on cloth is to rub so Ughtly and slowly and with such frequent rests, that the cloth will not become noticeably heated ; if it be- comes a bit warm the preparation which makes the cloth transparent wiU become softened so that the eraser will remove it. If this prepara- tion is once removed the cloth is made opaque so that a white spot will show on the blue print, and the surface cannot be restored for further inking. A little experience will show how many strokes may be made without heating the cloth, the temperature of which may be tested with a dry finger. '^Tien there are several different parts to erase, the drafts- man can rub a few strokes in one place, then in another, and so on, until enough time has elapsed to allow the first part to becolne entirely cool, when the process may be repeated. The cloth should be supported by a smooth hard surface before the eraser is applied; unless the drawing board is unusually free from holes and dents, a triangle or something similar should be placed under the part to be erased. CHAPTER XI ERASING 63 1. The Eraser. — Either an "ink eraser " or a "pencil eraser " may be used for removing ink from tracing cloth. The former is more effective but it is liable to scratch or injure the cloth. One may obtain more satis- factory results with a pencil eraser if one has abundant patience and avoids excessive speed so that the cloth never becomes heated. When the ink is quite thick part of it may be removed with an ink eraser and the remainder with a pencil eraser. Whenever an ink eraser is used it should be followed by the use of a pencil eraser to clean the drawing properly. The center of contact should be kept on the ink to be re- moved lest the adjacent cloth become seriously damaged before the fact is realized. An eraser will often become soiled or clogged from use, particularly when used on heavy lines or on smooth paper. It should be cleaned by being rubbed on clean rough paper or on a clean portion of the drawing board reserved for the purpose. The Avhite or "ruby " erasers are firmer and better adapted to the removal of ink than the "emerald " ones; they are also more likely to be self -cleaning. 2. A special ink eradicator for tracing cloth is on the market but it should not be used too generally. It should not be used for small erasures, since it cannot be confined to small area to good advantage and it should never be used if any erasures or scratches haA-e been made pre- viously within the same area. For taldng out a whole detail or other large portion of a drawing the liquid eradicator usually proves satisfac- tory. 3. A knife or metal scratcher should not be used on a drawing in place of an eraser. The surface of the cloth is so damaged that it is impossible to re-ink properly the portion which has been scratched. The cloth often becomes so opaque where a knife has been applied that the scratched portion shows on the print almost as distinctly as if the ink had not been removed, and furthermore, the lines appear ragged. A very sharp scratcher in the hands of an expert can be used sparingly to advantage ; but as a rule, the use of a knife or scratcher is a confession of laziness, for there is nothing to recommend it except that it is sometimes easier to scratch out a small section of a line than it is to erase it and then have to replace the surrounding lines Avhich may be erased also. This advantage is offset by the fact that drawings fiequentl}- have to be re- traced when a later rcAision necessitates inking Avhere a knife has been used. Erasing with a knife nearly always involves the risk of injury to the cloth, and is in this sense a dangerous habit which is not justified by the results ; better results are almost invariably obtained when an eraser is used. 4. When erasing a figure, a rivet, or small detail, which is close to other lines or figures, one may use an erasing shield to protect the surrounding parts, and thus simplify the filling in afterwards. A shield may be made by cutting any desired size and shape of aperture through a thin, tough card. Erasing shields of nickle-plated brass or of steel may be bought, those of steel being recommended, if used enough to keep them from rusting, because they are much more durable. 5. A brush should be used to remove all pieces of eraser and other foreign matter from the drawing as soon as the desired parts have been erased. If pieces of eraser adhere to the cloth they may be brushed off more easily if a little tracing cloth powder (page 56 : 2) is sprinkled over them. 6. The stirface of the cloth where any erasure has been made must be treated before ink is appHed, or the ink will spread. Although chalk or pumice stone are frequently used, it is better to polish the cloth, for the new lines will be more durable if on the cloth itself, than if partly on the powder. A triangle or other hard surface should be sUpped under the cloth, and a smooth, clean piece of soapstone or celluloid rubbed over the erased area until the cloth shines. Other hard surfaces may be sub- stituted for the soapstone, but they are Hkely to soil the cloth. An end of a celluloid triangle serves very well if the corners are rounded and used for this purpose only, care being taken to avoid the worn part when the triangle is used as a straight-edge. 7. After erasures have been made and the cloth has been polished, all lines and figures which have been erased by mistake should be replaced whether there is anything to be added or not. This point is frequently overlooked, especially if only a small portion of a line is erased, but it requires only a few such omissions to mar the appearance of a drawing. In order to prevent blurring or blotting, especially if the erased surface is not very smooth, the heavier lines should each be built up by making several fine lines until the desired width is obtained, no line being drawn until the preceding one is dry. 64 PART II — STRUCTURAL DRAFTING 1. If pencil lines are used on the tracing cloth, they may be left until the tracing is finished, and then removed along with any accumulated dirt. The author prefers a soft sponge eraser for this purpose, particu- larly if it was used at the beginning instead of powder to surface the cloth (page 56 : 2). Care should be taken to rub between the lines as far as possible, rather than across them; rubbing the lighter lines tends to make them too dim to print well especially if the cloth has been surfaced with powder. The pencil lines may also be removed by rubbing the surface of the drawing with a cloth dampened with benzine; the benzine does not affect the waterproof ink. Care should be taken to use only clean cloths, lest the whole drawing be made dingy. Many draftsmen prefer, the use of benzine on account of its simplicity, but for various reasons many companies do not furnish it. The author feels that benzine renders the cloth more liable to crack in handling and thus the usefulness of a draw- ing is somewhat impaired. CHAPTER XII DRAWING DIRECTLY IN INK ON TRACING CLOTH Synopsis: The advantages of this method over the method of drawing on paper and then tracing are shown; suggestions are given regarding the use of this method. 1. Method Recommended. — Drawings may be made on paper and then inked or traced, or they may be made directly on tracing cloth. Some companies adopt one system, some another, while still other companies allow each draftsman to choose for himself. The majority of structural drawings are so similar to drawings already made that it is possible to draw many lines in ink without drawing them in pencil first. For this reason the method of maldng drawings directly on trac- ing cloth is recommended whenever practicable. 2. Some of the companies that adopt the system of penciled drawings employ tracers, who simply trace the drawings made by other men. The tracers are apprentices, recent college graduates, or others of hmited experience who are thus enabled to learn the points peculiar to the structural company for which they work as well as the usual conven- tions of the drafting room. Soon after a tracer becomes proficient he is usually allowed to make drawings himself, and his place is taken by a new tracer. By this process it is difficult to keep the tracing up to the proper standard and the tracings may be issued in very poor form ; the detailer may have to spend considerable time in preparing the tracings for the checker, or the checker may have so many errors to indicate that he cannot work efficiently. It is poor economy to allow good men to spend valuable time on drawings, only to have much of the meaning and good appearance lost through careless tracing; hence it is often better for draftsmen to make their own tracings. If the draftsman were to trace his own pencil drawing he would not need to make it quite so complete as if another person were to trace it; but even less penciling would be required were he to make his drawing directly on the cloth instead of on paper. In this way he might ink many lines and figures without first making them in pencil. 3. Arguments. — Although it is more serious to make false lines in ink than in pencil, this should not prevent any careful draftsman from adopting this method of inking much of the drawing without previously penciling it. He should cultivate accuracy by strict attention to his work, and he should check his work repeatedly to avoid carrying a mis- take so far that it will entail extensive alteration. When first attempting this method, the draftsman should ink only the lines and the figures which he is sure are right; on subsequent drawings he will find that a larger number may be inked, and it is believed he will gradually become an enthusiastic advocate of this method. Most men who are opposed to the method have not given it a fair trial; or they have attempted to ink too much, and naturally no time has been saved. The men who still persist in making complete pencil drawings after years of experience are being outranked, for the most part, by men of equal ability who work more efficiently by drawing directly in ink on the cloth. Even if an occasional drawing has to be retraced on account of mistakes made in inking directly on cloth, this fact should not be given too much weight, for the chances are that the same mistakes would have been made in pencil. If that part of the pencil drawing which is correct can be pre- served and traced, so also can the same part of the inked drawing be re- traced just as quickly. Doubtless a little more time is taken in making the original drawing in ink than would be taken to make it in pencil, but 65 66 PART II — STRUCTURAL DRAFTING since comparatively few drawings need be retraced, this loss is more than balanced by the time saved in making other drawings directly in ink on the cloth; this gain is approximately the difference between the time required for drawing once in pencil and then tracing, and the time required for simply drawing in ink once. 1. Not all drawings are well adapted to this method of drawing directly in ink. If a large number of pencil lines must be drawn, many of which may have to be erased, better results would probably be ob- tained by making a pencil drawing on paper. Sometimes the two methods may be combined to advantage. Thus, if a drawing is so complicated that the best positions for the different views must be determined by trial, the preliminary work may be done in pencil on paper; but as soon as the views are finally located and all necessary pencil Unes drawn, this much of the drawing may be traced, and the remainder completed on the cloth just as if all the lines were so drawn. 2. A drawing must be carefixlly planned in advance if the whole or any part of it is to be inked without previous penciling, in order to in- sure a good arrangement and to avoid crowding. This is not an argument in favor of a complete pencil drawing, because such preliminary plan- ning should be done also before a pencil drawing is started, so as to avoid the necessity of shifting the cloth while tracing to effect a change in the arrangement. The number of views and the number of dimen- sion lines should be determined, and also the extreme dimensions of each view, including the main member and all projecting parts. If any sectional views are to be placed in breaks in other views their positions should be anticipated to avoid erasing spaces for them later. 3. A sheet of clean paper should be placed underneath the tracing cloth before a drawing is started on the cloth; the paper makes the hues more distinctly visible and also covers the thumbtack and other holes in the board so that there is less danger of holes being punched in the cloth by the pencil. 4. Illustration. — As soon as the number of views and dimension lines and the main dimensions of a member are determined, points may be plotted to indicate the position of each line that extends practically the full length or depth of the member in each view; pencil lines may be drawn if necessary to show where these long lines stop. Then these full length lines, both dimension lines and Unes of the main drawing, may be drawn in ink without being drawn first in pencil, with a corresponding saving of time. In case some of the lines represent parts which are to be behind details to be added later, these lines may be drawn in pencil or omitted altogether until the details have been located; then the lines may be inked, with dashes to represent the invisible portions. For example, let us consider the drawing of a plate girder with cover plates (Fig. 102) . Suppose that front, top, bottom, and end views are required and that the girder is symmetrical about the center line. From a pre- liminary sketch we find how many dimension lines are needed. Points may now be plotted with due regard to margins and spaces between views to insure a good arrangement. Vertically, these points will show the position of (1) all full length dimension lines; (2) the three lines of each flange angle in the web view, with the corresponding rivet lines (usually at the standard gage); (3) the eight lines in the top view for the cover plate and flange angles, with the corresponding livet lines (usually two in number) ; (4) same as (3) for the bottom sectional view. Horizontally, these points will show the position of (5) the left end and the center line of the girder; (6) the cover plate and flange angle lines of the end view which are the same as those in the top view, and in addition the lines of the stiffening angles and their rivet lines; (7) the full depth dimension lines. Now the pen may be filled and set for fine lines, and lines may be drawn in the following order: (1) a continuous vertical line at the end of the girder drawn from the bottom view to the top view; (2) a dot and dashed line at the center drawn from the bottom view to the top view; (3) all horizontal dimension Unes and rivet Unes, including lines from the end view to the front view to indicate the depth from back to back of flange angles; the rivet lines should extend beyond the end of the girder to the proper dimension lines; (4) the rivet lines in the end view and the vertical dimension lines. Now the pen may be set for wider lines, and the following lines may be drawn : (5) the cover plate lines of the top view, provided the plate extends full length; (6) the lines which show the outstanding legs of the flange angles in the web view; (7) the heavy web line and the other lines of the bottom view, except the cover plate lines which cannot be drawn until the lengths are determined; (8) the vertical lines of the end view (except the dashed CHAPTER XII DRAWING DIRECTLY. IN INK ON TRACING CLOTH 67 lines) and the end line of each of the other three views; (9) the hori- zontal lines of the end view. The pen may now be set for shghtly nar- rower lines (page 37 : 1) and the dashed Unes may be drawn (10) for the flange angles in the top view, and (11) in the end view. The main dimensions may now be recorded in ink. Thus the drawing is well advanced without the use of a single pencil line. As soon as the stiffening angles are located, points may be plotted to show the three lines of each angle and the corresponding rivet lines. The rivet lines may be inked, then the stiffening angles in all three views, and the remaining lines of the flange angles in the web view which must be dashed behind the stiffening angles now located. As soon as the spacing of the rivets in the web view is determined and the totals checked in each panel as well as in the full half-length, the necessary rivets may be plotted and the cor- responding lines and dimensions inked. Similarly the other views can be completed, and when the cover plate lengths are definitely determined they may be shown in the top, front, and bottom views. The rivets and holes may be shown, the material may be billed and the notes and title may be made directly in ink without being penciled. CHAPTER XIII RIVET SPACING Synopsis: Rivets must be spaced to conform to general rules and specifications which are in common use; such rules are given in this chapter. The spacing is also dependent upon the number of rivets required under different conditions, as explained in the chapters of Part III. 1. " Rivet spacing," as a general term, refers to the dimensions which locate either shop or field rivets. These dimensions extend in- variably to the centers of the rivets. " Rivet pitch " is a more specific term usually limited to the spacing which locates the rivets that con- nect the component parts of a built member in the direction parallel to the longitudinal axis. This term is most frequently appHed to the flange rivets of plate girders, in which the pitch at different points must be determined from the given loads, as explained in Chapter XXXVII, page 241. 2. General rules for the spacing of rivets are given in this chapter to conform to those in common use. The spacing is also necessarily dependent upon the number of rivets required to satisfy the conditions of loading and other considerations which are discussed in different chapters of Part III. 3. Each structural company adopts a set of standards for the guid- ance of its draftsman in order to make the drawings more uniform. Each draftsman should follow, whenever it is feasible, the standards of the company for which he works. 4. The specifications which accompany each contract should be care- fully read, and the rivet spacing should never violate any clause therein. For the most part the different sets of specifications are quite similar; the rules of this chapter conform to the majority of them. 5. Standard Gages. — The flanges of I-beams and channels are so narrow that the usual rules for clearance and edge distance cannot be 6S applied transversely. Standard gages which will best meet all require- ments are therefore adopted. The gages given in the tables on pages 298 to 302 inclusive are in common use, although the standards of some companies differ slightly. Standard gages for angles are also adopted as shown on page 303. These standard gages should be used in all places unless there is good cause for deviation. However, it is usually better to change the gage slightly on one drawing than it is to make the distance between rivets on two or more drawings result in sixteenths or eighths, as in connection angles for beams and girders (pages 83 : 6 and 106:3), or in the flanges of girders and columns (pages 106:3 and 136: 1). The rivets in diagonal bracing are often placed in the centers of the angles instead of at standard gages (page 139: 3). The two rows of rivets in a 6-inch angle are often separated more than usual to accommodate the spacing on the members to which they connect, as in the base angles of columns (Fig. 133) or in struts (Fig. 147) . 6. The minimum spacing of rivets should be such that the strength of the metal between rivets fully develops the strength of one rivet. The minimum pitches for the rivets in the flanges of plate girders should be determined from the table on page 306 in accordance with the condi- tions of each problem, as explained on page 255:2. In most other cases it is more convenient and sufliciently accurate to use a certain minimum space for each different diameter of rivet regardless of other conditions. The values most commonly specified for absolute minimums are either " three diameters," i.e., three times the diameter of the rivets, or else CHAPTER XIII RIVET SPACING 69 the " usual minimum " tabulated on page 305; these specifications differ only for the smaller rivets. A preferred minimum is also shown to be used in work of the better class. These values are based upon average conditions. (Compare with the values for rivets in a single line given on page 306.) No two rivets should be placed closer together in any direction than the proper minimum space. The minimum spacing for staggered rivets in tension members should be taken from the diagram on page 305, as explained on page 209 : 1. 1. The maximum spacing of rivets differs not only with their diameter, but with the type of member and the position of the rivets in the mem- ber. When rivets are staggered on two lines, as in the flange angles of girders or columns, the maximum pitches given below refer to the dis- tance from a rivet on one line to the next rivet on the other line measured parallel to the rivet line as if the rivets were on a single line. (Compare the next to the last sentence of the preceding paragraph), (a) In gen- eral, the maximum pitch of rivets measured parallel to the principal axis of a member is 6" for 1", |" or f " rivets, 4J" for |" rivets, and 4" for I" rivets. Many specifications limit the pitch of f" rivets to 5". (6) The pitch should not exceed 16 times the thiclmess of the thinnest exposed plate or other shape, (c) For girders, which support moving loads applied to the flanges, as crane girders, or stringers of bridges and viaducts, a maximum pitch of 4 or 4J inches is usually specified for the flange rivets, (d) The pitch of the rivets which fasten the component parts of a compression member together should not be more than four diameters at the ends of the members and opposite the connections of heavy loads. This close spacing should extend the full depth of such connections, and at the ends for a distance which is variously specified as equal to one, one and a half, or two times the width of the member; the mean value of one and a half may be used unless otherwise specified, (e) Rivets in tanks should not exceed about four diameters to make the joints watertight.* (/) Rivets which do not transmit much axial stress may be spaced farther apart than the values given above; thus the rivets which fasten skew-back angles for floor supports to the webs of beams and girders may be I'-O" apart, rivets which connect stiffening * See table of spacing for watertight joints in Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Co., Inc., New York. angles to channel struts or stiffening channels to crane beams l'-6", countersunk rivets in column bases from 9" to I'-O", and stitch rivets as indicated on page 69 : 4. 2. Wide Cover Plates. — The rivets in the flange plates of a compres- sion member are usually placed in two rows unless the distance between the rivet lines, measured at right angles to the principal axis, exceeds forty times the thickness of the outside plate; in this case four rows would be used. If two or more plates project 3" or more beyond the edges of the angles, an extra row of rivets must be used to fasten them together, the pitch being twice that of the rivets which connect the plates to the angles. 3. " Edge distance " is a term applied to the perpendicular distance measured from the center of a rivet or hole to the edge of any structural shape. When possible the edge distance should be at least one and a half diameters, and preferably two diameters, as tabulated on page 305. This is especially important in the direction of the line of stress. Smaller edge distances are unavoidable in the flanges of the smaller beams (page 68 : 5), and it may seem best to use them in comparatively light work in places where the available space is limited, but it is usually best for the novice not to make such exceptions without due counsel. The edge distance should not be more than 5" nor more than eight times the thickness of the thinnest exposed plate or other shape. 4. Stitch Rivets. — A member composed of two angles should have them riveted together at frequent intervals in order that the stress may be distributed equally between the two angles. If the angles are sep- arated on account of connections to gusset plates, a washer is placed between them at each rivet in order to maintain a uniform distance between the angles. These equalizing rivets with or without washers are called " stitch rivets." They need not be dimensioned, but the proper number should be shown or else the approximate spacing should be noted. The distance between the last rivet of one connection and the first rivet of the next connection should be divided approximately equally. Stitch rivets are spaced from 2'-6" to 3'-0" apart in tension members, but from l'-6" to 2'-0" apart in compression members on account of the tend- ency of the latter to buckle. The specifications for railway bridges sometimes limit the spacing of stitch rivets in tension members to I'-O". 70 PART II — STRUCTURAL DRAFTING 1. Lattice bars are used in light compression members or diagonals instead of web plates or cover plates, and on the mider side of chord members where it would be impractical to use cover plates. Tie plates should be used at the ends of each group of bars. For the sizes of tie plates and lattice bars, see page 216 : 2-3. For the method of billing and the method of manufacturing lattice bars see page 45 : 2. For the method of representing and dimensioning lattice bars see pages 40:5 and 50:6. Either " single latticing" or "double latticing" may be used as shown on page 315, double latticing being used when the distance between rivet Knes is more than l'-3". A rivet is placed at each intersection of double lattice bars. The inclination of double lattice bars with the longitudinal axis of a member should not be less than 45°, i.e., the distance from center to center of rivets in any bar, measured parallel to this axis, should not exceed the corresponding distance meas- ured at right angles to the axis. The inclination of single lattice bars with the longitudinal axis varies from 60° in important members to 45° in comparatively light and unimportant ones; for most work an in- clination of from 50° to 55° proves satisfactory. When single lattice bars are used on opposite sides of the same member the bars should alternate, as shown in Fig. 129. The clearance between the end bar and the tie plate should preferably be from j" to IJ", or else the bar should overlap the plate with a common rivet. The spacing for different groups of lattice bars on the same or similar members should be made so that the bars are interchangeable as far as possible. 2. Practical Points. — (a) Every separate piece should contain at least two rivets even if one rivet is strong enough, because a single rivet is not sufficient to hold the piece in position properly, (b) Rivets should be spaced with due regard to the appearance of the finished member; for example, a single small pitch between two large pitches in a girder flange is conspicuous (page 70 : 4). (c) When multiple punches are to be used, the rivet spacing should be given so that the punches can be used to the best advantage. In multiple beam punches the spacing is usually fixed. In multiple plate punches the spacing may be made to correspond to the drawing, but the work may be facilitated if the holes for intermediate connections are made to line up with the other holes, (d) Templets are often made to serve for several different members; this fact should be borne in mind when the rivets are spaced. Long lines of rivet spacing on similar members should be kept alike as far as possible, the different spaces being kept near together, preferably at the ends so that different short templets may be used in conjunction with one long one. The differences may often be made in the same templet by boring different sets of holes; the centers of these holes should not fall less than J" apart or they will interfere with each other. 3. Usual Spaces. — The rivets which connect the main component parts of a member are spaced as far apart as is compatible with the con- ditions outlined in the preceding paragraphs, in order to minimize the number of rivets to be driven. But the rivets which connect one mem- ber to another, or part of one member to another part, are placed at the usual minimum or the preferred minimum distances as far as possible in order to reduce the size of the connecting material. 4. Continuous Rivet Spacii^. — The following suggestions may aid the beginner in spacing long hnes of rivets which extend virtually the whole length or depth of a member: — (a) First locate all rivets which are determined by given conditions, such as those in cormections to other members, those near the ends of compression members, or those which must line up with other rivets on account of fixed gages or working lines; then complete the spacing of the intermediate rivets as follows: (6) If the number of intermediate rivets is determined by the stress the rivets are spaced approximately equidistantly. The available dis- tance is divided into the proper number of spaces (one more than the number of intermediate rivets) ; imless the result is a multiple of J", the nearest J is usually chosen for part of the spaces, another value being used for the one or more remaining spaces. L'sually one odd space will serve to balance the line satisfactorily unless the spacing should be kept symmetrical as in the stiffening angles of a plate girder when two should be used, (c) If the intermediate rivets are spaced at a fixed pitch (usually the maximum allowed) as in columns or chord members, the number of such spaces is determined and any remainder is noted. This remainder may be inserted as a special space provided it is larger than the adjacent space; otherwise it is better to add it to one or more of the maximum spaces and subdivide the sum; this should preferably be arranged so that not more than one space results in sixteenths, and CHAPTEK XIII RIVET SPACING 71 so that all of the spaces are smaller than the fixed pitch but equal to or larger than the adjacent space for the sake of appearance. When more " balancing spaces " than one are used they may all be placed at one end of the group, or part may be placed at each end. (d) If the rivet pitch changes at intervals as in the flanges of plate girders, enough spaces of each pitch are used to extend the proper distance from the end (page 241 : 5) . Near the center, enough spaces of the last pitch must be used to complete the total length; in case a remainder is left, one or more odd spaces may be inserted at the last change in pitch, but the odd spaces should be larger than one pitch and smaller than the other for the sake of appearance. The odd spaces should not be placed at the center of the girder because a few small spaces in the middle of a group of large spaces would not look well. The spacing should be made symmetrical about the center line; the center line should therefore fall either at a rivet or midway between two rivets, whichever gives the better arrange- ment of balancing spaces. If the girder is divided into fixed panels by stiffeners, care should be taken that the spaces in each panel total the proper amount, and that ample driving clearance is allowed for all rivets (page 73 : 5) . (e) For the benefit of the shopmen sixteenths and eighths should be avoided whenever practicable. For instance, rather than make ten equal spaces in sixteenths, eight or nine spaces can be made alike leaving one or two odd spaces, not more than one of which involves sixteenths. (/) After a Ine of rivet spacing is completed it should always be totaled to make sure that the sum equals the proper amount; * similarly the sum of the spaces which subdivide any other dimension should equal that dimension, (g) The multiplication table for rivet spacing on page 307 may be used to advantage in this work. * There is a small adding machine (The Architects' Calcumeter) on the market, which is admirably adapted to this purpose, but at present its price is beyond the reach of the average draftsman. CHAPTER XIV CLEARANCE, AND ERECTION CONSIDERATIONS Synopsis: There are many points which the draftsman should consider in order to make the erection of a structure not only possible but comparatively easy. Clearance should be allowed so that members or parts of members may be assembled without interference, and so that rivets may be driven by machine. 1. Clearance should be provided wherever possible to facilitate the assembling of the component parts of members in the shop, and the erection of the whole members in the field. Clearance is of greater importance in field connections than in shop work because of the diffi- culty in handling the larger pieces which are involved and which must be put into comparatively inaccessible places. It is much simpler to trim a smaU piece in the shop than it is to cut a whole member in the field. The more common places where clearance should be provided are (a) between the component parts of a member, (6) between the pro- jecting parts of a member and the members to which it is to connect, (c) at the ends of a member which is to be inserted between the faces of the supporting members, and (d) between each rivet and any projecting part which might interfere with the use of a riveting machine. 2. Provision for Overrun. There is often a variation between the actual size of a structural shape and the size indicated on the corre- sponding drawing. This variation may be the result of the methods of rolling the material at the mills, especially angles, as explained on page 25 : 1; or it may be due to inaccurate cutting either at the mill or at the shop. In any event, due allowance should be made so that the assembling of the different parts will not be made unnecessarily difficult. For example, the rivets which connect the diagonal members of trusses, latticed girders, or bracing systems to the gusset plates should be so placed that these members may be cut short enough to avoid any inter- 72 ference with the chords or other members. This provides for any variation in the lengths of the diagonal members or in the depths or widths of the chord members. See pages 76 : 1 and 138 : 5. Similarly I-beams and channels are ordered short enough to allow for overrun as explained on page' 88 : 1, to avoid the necessity of recutting them. If the members are assembled in the shop the usual clearance is J", but if assembled in the field the clearance is increased to ^". In order to eliminate sixteenths and preferably eighths from the billed lengths of the members the above values may be increased by xV" or I", or in some cases reduced by ^V"- 3. In some places tight fits are necessary, but this work involves additional expense and should be avoided whenever possible. Stiffening angles of plate girders are usually fitted so that the outstanding legs are in contact with the flange angles. These angles must not only be cut carefully to length, but they must be cut to clear the curved fiUets of the flange angles (page 26 : 1). Similarly, stiffeners are used under seat angles and in similar places. 4. Projecting parts should be arranged so that they wiU not interfere with the erection of a member. Clearance should be left between members which connect independently to the same member. One or more angles of a member may have to be cut shorter than the remaining angles, as for example the chords of W 2, Fig. 111. Similarly a mem- ber may have to be notched or blocked out as in Figs. 87 and 104. The amount of clearance should be at least ^". CHAPTER XIV CLEARANCE, AND ERECTION CONSIDERATIONS 73 1. Erection Clearance. — When one member is to frame at riglit angles between the faces of two other members and is to be connected by- means of angles riveted to the webs, as for example B 10 (Fig. 87) and S 1 (Fig. 98), the extreme distance from back to back of connection angles should be made less than the clear distance between the faces of the supporting members in order to allow " erection clearance." It is not always possible to allow sufficient clearance to permit the member to be swung- into position without moving the supporting members; for if the ratio of the width of a member to its length is large, the neces- sary clearance would be so great that the surfaces could not be drawn together to make a satisfactory riveted joint. But even if the support- ing members must be spread while the other member is being inserted, a little clearance is desirable as a safeguard against an overrun which would prevent restoring the supporting members to their proper posi- tions. The amount allowed varies from ■^" to f^" at each end; some companies contend that •}^" is practically negligible on account of the paint, scale, and careless shopwork which may counterbalance it; but from a larger clearance may result loose joints, or else the columns and girders which support long lines of such beams may be drawn out of plumb. For most work ^" or ^" at each end should be allowed for erection clearance; thus: in order to make the length back to back of angles free from sixteenths, a total clearance of -fs" should be sub- tracted if the clear distance between supports results in sixteenths; otherwise |" should be subtracted. No erection clearance is required when one end »f the member is wall bearing or otherwise free to move, or when the member frames diagonally between two other members. 2. Seat Angles. — The end of a beam or a girder should be supported entirely by end connection angles, or else by a seat angle or some form of bracket, but never by a combination of the two because of the diffi- culty in making both act at the same time. Erection seats should be provided to support girders with end angles until the rivets are driven (Fl, Fig. 99) ; erection seats may also be provided for heavy beams or for beams which are to be connected to opposite sides of a web plate by the same rivets. Usually an erection seat is shown J" lower than the bottom of the girder so that if inaccurately set it will not prevent the placing of the rivets. When seat angles or brackets carry the whole load, top angles or side supports should b^ provided to prevent the beams or the girders from overturning. Top angles should be shipped bolted so that they may be removed during erection if desired. A clearance of \" should be left between the tops of the beams and these angles to pro- vide for any increase in the depth of the beam on account of the spreading of the flanges or the use of worn rolls during manufacture; a similar clearance of \" should be left between the angles and the tops of girders. 3. Holes for anchor bolts for columns and girders should be made Tff" or f" larger than the bolts. This either simplifies placing mem- bers on bolts which are already set, or else provides for drilling holes in the masonry after the steel work is in position. The holes should be located with these points in view. 4. Other Connections.* — The extreme width or depth of web mem- bers, top struts and laterals, and other members which must be inserted between two gusset plates, should be made |" less than the clear distance between the plates, thus allowing a clearance of iV" on each side. A like amount should be used if possible at column splices (page 276 : 4). When plates must be inserted between angles it is desirable to have the space between the angles |" more than the plate thickness; when this is not feasible, care should be taken that no shop rivets are placed in either leg of the angles which will prevent their being spread sufficiently to allow the plates to enter. If such rivets are required they should bew left to be driven in the field (Fig. 135). Often splice plates and con- nection angles may be held in position by one or more shop rivets (Fig. 133), but if erection is thus made more difficult it is better to omit all shop rivets and to ship the pieces bolted (Fig. 135). 5. Driving Clearance. — Both shop and field rivets are preferably driven by machine as explained on page 30 : 4, and if possible rivets should be so located that the machines can be used. A careless drafts- man sometimes locates rivets which can be driven only with the greatest difficulty, if at all. A common mistake among novices is to space the rivets in the cover plates of columns or girders independently of the stiffening angles on the web; as a result the outstanding legs of the stiffeners often interfere with the driving of the rivets in the cover plates. * See also Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Co., Inc., New York. 74 PART II — STRUCTURAL DRAFTING In order that machines may be moved into the proper position for driv- ing rivets, sufficient driving clearance must be provided between the rivet heads and any projecting parts to allow for the dies which form the heads. The amount of driving clearance required under different conditions is given in the tables at the bottom of page 304. 1. Other Erection Considerations. — (a) Too much care cannot be taken to insure the proper erection of each member at the site. Not only should the holes of one member match exactly the holes of a con- necting member, but the erectors should be able to put every member into position without interference and without undue labor. The difii- culty of attaining this end increases in proportion to the size of a con- tract and to the number of detailers and checkers who work upon it simultaneously. (6) Field rivets should be so located that they can be driven when the members are in position; bent plates and projecting parts of other members are liable to interfere, (c) Any mistake which leads to cutting or drilling in the field is very expensive, partly because of the lack of facilities but more especially because of the number of skilled workmen who are delayed during the investigation which neces- sarily precedes any alteration. If a member must be returned to the shop for changes, or if a new piece must be made to replace a member, the delay in erection is often very costly. • An actual blunder may be cited to show the importance of studying the structure as a whole. Two girders at right angles to each other were to be connected to the same column, one to the web and the other to the flange. Each connection would be correct if used independently or if one of the girders extended in the opposite direction, but the detailer and the checker both overlooked the fact that the two girders would intersect and hence could not be in position at the same time. It was necessary to cut one girder short and make it frame into the other; also to strengthen the other column con- nection to support the combined load. (d) Details should be arranged to facilitate erection whenever possible, but this is especially important in replacements, such as office and loft buildings, and railway bridges, so that the old structures may be left intact until the last possible moment. Special types of connections are often used for this class of work in order to reduce the number of field rivets (page 89 : 2). (e) The draftsman should be familiar with common methods of erection * in order to anticipate special requirements for which provision should be made on the drawings. Rivet heads which pro- trude far enough to prevent swinging a member into position should be flattened or countersunk (page 40 : 6), or else left to be driven in the field. " Hand holes " may have to be bored through solid web plates to give access to the inside of box sections for driving rivets. Similarly, shop rivets may be omitted from lattice bars or tie plates so that they may be removed temporarily (Fig. 129). Single field rivets at the intersec- tions of the diagonals of vertical bents may require special stagings for the riveters. Such rivets are very expensive and they should only be used when unavoidable. (/) When the position in which a member is to be erected cannot be readily determined from the member or from the erection diagrams, one end of the member should be marked N., S., E., or W., or otherwise, to show the proper position. Shopmen should always place a member right side up, before painting the shipping mark on the side. This system will prevent the erection of a member upside down. In some cases it may seem desirable to make the spacing of one or two rivets different at the two ends to prevent interchange. Similar pre- cautions should be taken to avoid mistakes in assembling connection angles or other parts of members which may cause trouble in erection. (g) When two or more members are to be supported by the same field rivets, they must all be erected before the rivets are driven. Such conditions are usually apparent from the erection diagrams, but the draftsman should make sure that any unusual connections are noted or indicated on the diagram in such a manner that the erector will not drive any rivets prematurely, (h) Bridge details should in general be arranged so that the trusses or girders may be completely erected before the floor system is inserted or, conversely, so that the floor system can be completely erected before the trusses are put in position, (t) Notes should appear on the erection diagram drawing attention to all drilling and cutting which must be done in the field, such as holes in existing structures for the connection of new members. This shows the erectors that such work is expected of them so that no claim for extra remunera- tion can be made. * See footnote, page 20. CHAPTER XV LAYOUTS Synopsis: There are three common types of layouts in which the graphic method of determining certain dimensions may be used to better advantage than numerical computation. 1. A "layout" is a preliminary drawing made for the purpose of sealing distances which cannot be obtained so easily in any other way. Layouts are used chiefly for determining the best shape and size of connection plates for members which meet at oblique angles, with due regard to rivet spacing, edge distance, and clearance. A layout is usu- ally made on a separate sheet, and having served its purpose it is gen- erally discarded just as a calculation would be; such a drawing need not be made so complete as a working drawing, but it should be drawn much more carefully to scale. In order that distances may be scaled with accuracy a layout should be drawn to a comparatively large scale; for most work a scale of 1|" = 1' is satisfactory, but 3" = 1' or 1" = 1' are often used. A separate layout is usually made for each gusset plate or bent plate connection, although similar layouts may often be combined. The term " layout " is also applied to a preliminary drawing which may afterward be completed for use as a working drawing. Thus, the drawing of a truss, for example, may be carried far enough for the draftsman to scale the lengths of all members with sufficient accuracy to enable him to order the material, and later this layout may be completed to serve as a working drawing. 2. When Used. — A layout is necessary only when the axes of the members intersect at angles other than 90°, for if members meet at right angles all dimensions may be determined easily by addition and sub- traction. Layouts are commonly used for practically all skew connec- tions, and for the gusset plates of trusses and various forms of bracing. When working drawings are made to a scale of 1" = 1' separate layouts are not usually required because the sizes of the gusset plates may be determined with sufficient accuracy from the drawings. 3. A simple layout, composed of a few limiting lines such as edges and ends of members, often suffices to give the experienced draftsman the desired information, but a novice can often save time by putting in extra lines to show the conditions more clearly. A draftsman should make a layout more complete if it is to be used also by someone else. If an elaborate layout is made for use in ordering material, particularly when conditions are rather unusual, this layout should be preserved for the use of the detailer and the checker. It need be carried only far enough at first to serve the purpose of the man who orders the material, when it may be handed to the detailer to be completed for his use. Most checkers prefer to make new layouts in order to obtain more positive checks, particularly if inaccuracies in plotting will seriously affect the results. 4. There are three common types of layout which will serve for illustration, viz.: gusset plates, lateral plates, and bent plates. The first two terms are often used interchangeably, but for convenience they will be treated as separate types with this distinction: gusset plates are used to connect main members of trusses or other members carrying considerable stress when it is important that their lines of action meet in a common point; lateral plates are used to connect the members of bracing systems or light latticed girders in which a single intersection is less important so that auxiliary working points may be used for con- venience. 75 76 PART II — STRUCTURAL DRAFTING 1. As an example of the first type there will be given the general method of procedure for making the layout of a gusset plate which con- nects two web members of a roof truss to the bottom chord, each mem- ber being composed of two angles. See Fig. 76. I. Determine the slopes of the diagonal members as explained in the next paragraph (see also page 115:2). II. Lay down the working lines (usually the rivet lines, see page 115 : 2), of all the intersecting members to the proper slopes, using a scale of I5" = 1' or 3" = 1'. III. Plot the limiting lines (out- side edges) of the angles, using the proper gages (page 68 : 5), and showing the backs of the angles on the proper sides. IV. Draw lines to show the desired clearance c (page 72 : 2). V. Cut each diagonal angle normal to its axis so that the nearest comer will fair in the clearance line just plotted. Make sure that ample clearance is left between the diagonals. VI. Place a rivet at the desired edge distance e (page 69 : 3) from the end of each diagonal angle; since the distances from these rivets to the work- ing point are to be dimensioned on the working drawing, it is usually preferable to Kg. 76. express them to the nearest i", either the amount of clearance or the edge distance being changed, if necessary, to accompUsh this result. VII. Lay off the proper number of rivets (page 231 : 1) in each diagonal member at the desired distance r apart; this dis'tance is generally made equal to the usual or the preferred minimum spacing given in the table on page 305, so that the resulting plate is not made unnecessarily large. VIII. Space the proper number of rivets in the chord member; if the chord is continuous, rivets need be provided only for the difference in the stress on opposite sides of the plate (see page 233 :2). These rivets can often be spread more than those in the diagonals without increasing the size of the plate; the outer rivets should preferably be placed at the distance e from the edges of the plate; this means that they can often be projected down from the last rivets in the diagonals, although in that case the shape of the plate must be anticipated and per- haps the size must be determined (see IX below) before the rivets can be located. If feasible one rivet should be placed at the working point where it is most effective, but care should be taken that no space exceeds the maximum allowed (page 69:1). IX. Draw in the edges of the gusset plate with due regard to the following points: (1) allow ample edge distance e from each rivet to the nearest edge of the plate; (2) leave no comers of the plate projecting beyond the angles, i.e., each vertex should be hidden by the angles; a comer which falls behind a single angle should preferably be made to come on one edge of the angle for the sake of appearance, but if between two angles this does not matter; (3) reduce the number of cuts to a minimum, for each cut increases the cost of the plate; (4) avoid cuts with reentrant angles, for they cannot be sheared; they must be cut by punching a series of connected holes and then chipping off the remaining projections between holes with a pneumatic chisel (page 14) ; this operation is reserved for very exceptional use (see SPl, Fig. 128); (5) make two edges of the plate parallel and a whole number of inches apart if possible, so that the plate may be cut from one of standard width (page 43 : 3) ; (6) cut across the full width of the plate if possible, so that a number of similar plates may be cut without waste from a long plate, by alternating the cuts as shown in Fig. 44; (7) the width of the plate is usually the shorter dimension but this may be changed if desired on account of (5), (6), or (8); (8) use as few different widths of plates as practicable on one drawing, and preferably on one contract; they may then be ordered or taken frOm stock to better advantage; (9) the nominal length of the plate as billed on the drawing is the extreme dimension at right angles to the width, i.e., the dimensions of the including rectangle are given; this length is preferably expressed to the nearest i" but eighths are used; in ordering material in multiple lengths advantage should be taken of any gain which may result from (6), for if the extreme lengths were added together more material than is required would be ordered. 2. The calculation of the slope or the bevel of one line with reference to another line is based upon similar right triangles. As explained on page 50 : 7, the slope is represented by the tangent of the angle reduced to a base of 12", although the actual value of the angle is seldom used. A system of working lines is usually laid down in such a way that the rectangular coordinates of any intersection measured from any other CHAPTER XV LAYOUTS 77 intersection may be easily determined. Often these coordinates are dimensioned on the drawing, or else they may be found from the propor- tion of similar triangles. These coordinates form the two legs of a right triangle, in which the slope and often the length of the hypotenuse are required. The tangent of the smaller angle of the triangle is found by dividing the length of the shorter leg by the length of the longer leg; if this division is effected by means of a table of logarithms arranged by feet, inches, and fractions of inches, the resulting tangent will be ex- pressed as desired in mches and fractions of inches (to the nearest six- teenth), corresponding to a base of a unit foot (12 inches). If the length of the hypotenuse is required also, it should be calculated at the same time as the slope, by means of parallel tables of logarithms and squares * as illustrated by the following problem. In Fig. 148 the holes along the diagonal edges of M 1 and M 2 are referred to the working line of the supporting angle. The given coordinates are 3'-7j" and 10'-25". The corresponding slope and length of the diagonal as shown on the drawing are obtained as follows: Length Logarithm Square 3'-7'," 10'-2.i" 0.556S0 1.00S95 (difference) 9 547So slope = 41" in 12" 12.9900 104.2101 (sum) 117. 2001 length = 10'-9i^-" Note that the tables are expressed to thirty-seconds to facilitate the selection to the nearest sixteenth of the desired slope or length from the corresponding logarithm or square. 1. Lateral plates are commonly used for lateral bracing in bridges, diagonal bracing in buildings, in place of gusset plates in light latticed girders, or wherever the stresses are so small that a slight deviation from a single point may be made in the intersection of the lines of action of the members. An auxiliary system of working lines is drawn through the end rivets of the diagonals. The two principal advantages of this * Copies of Smoley's "Parallel Tables of Logarithms and Squares," and Smoley'a " Tables of Slopes imd Rises," C. K. Snioley and Sons, Scranton, Pa., should be included iu the equipment of every structural draft.sman. type of plate connection are (1) that the clearance between members can be made more nearly equal with a corresponding reduction in the size of the plate, and (2) that a comparatively simple layout may be made; in fact the desired information may often be obtained easily without a layout. This type of connection is illustrated by a plate in a latticed girder, as shown in Fig. 77. I. The rectangular coordinates which locate the end rivets of the diagonals are usually made the same for the upper and the lower ends of the diagonals so that the plates may be made alike or similar. II. For most systems of diagonal bracing in which the leg of the diagonal is 3" or more, the rivets are placed on the center line of the leg in order to make all clearances nearly equal; for latticed girders and small diagonals the standard gage is used, and thus when pro- vision is made for the proper clearance for the corner at the back of an angle, a larger clearance will be left on the opposite side, since the gage is larger than the remaining distance. III. The slope of the diagonals cannot be calculated until the end rivets are located, and hence the position of the corners of the angles relative to the end rivets is unknown; it is customary to allow sufficient space in any direction for the maximum distance from the rivet to the farther comer of the angle. This distance is the hj^po- tenuse of a small right triangle one leg of which is the gage (page 68 : 5), and the other the edge distance e (page 69 : 3) ; this may be found from the diagram on page 313, or from .a full-sized layout.f IV. The vertical distance (usually to the nearest |") from the end rivets in the diagonals to the rivet line in the chord may now be found by adding three component parts, (1) the edge distance (leg minus gage) of the chord angle, (2) the desired clearance (page 72 : 2), and (3) the diagonal distance found in III. Similarly the horizontal distance between the end rivets of the two diagonals is twice the distance found in III, plus the clearance; in latticed girders this distance may be t A convenient table for use in spacing the end rivets in diagonals is given by E. Feldman in The Engineering News-Record, Jan. 16, 1919. Fig. 77. 78 PART II — STRUCTURAL DRAFTING changed slightlj' as explained on page 109 : 1. V. Either of two methods maj- be used for the remainder of the problem; (1) a layout may now be made of the working points already established and the remaining distances and the size of the plate may be determined graphically as outlined for gusset plates in steps Yll, VIII, and IX, page 76 : 1; or (2) the required data may be found without a complete layout, as follows: \T. From the proper number of spaces r in each diagonal find the corresponding horizontal and vertical coordi- nates; these may be found (1) from simple layouts drawn separately; (2) from the main working drawing upon which the working lines have been plotted to scale; the diagonal distances may be scaled along the proper working lines and the corresponding components measured with- out drawing any extra lines; or (3) bj' placing a straight-edge in the proper position on the diagram on page 313, and then reading the desired coordinates. VII. The dimensions of most lateral plates may be found arithmetically by the proper combination of the edge distances and the distances found in IV and ^^; when diagonal cuts are used the posi- tions of the comers of the plate may be determined from a few lightly penciled lines on the main drawing (see \1 (2) above). 1. In bent-plate work, a layout is often necessary in order to deter- mine the shape and the size of the connecting plate. Such a layout is made of the developed plate, i.e., the plate before it is bent. The bend line is plotted and parts of the members to be connected are drawn in proper relation to a definite point in this bend line, not in their actual relation to each other. The rivets and holes may be laid out to the best advantage in each member and then the plate may be formed around these rivets and holes according to the suggestions given under IX, page 76 : 1. Such layouts are used for special skew work beyond the range of this book; * they are not required for ordinary bent plate work in which the holes and the edges of the plate are laid off either parallel or perpendicular to the line of bend, and in which the dimen- sions for the plate are determined numerically. See Figs. 78, 93, and 149. When bent plates connect to web plates, it is usually better to refer dimensions to the center lines of webs as working lines instead of to the faces of the bent plates, as shown in the above figures. The drawing is thus simplified although a corresponding burden is imposed upon the templet maker; but the method is more direct and there are fewer sources of error. Dimensions should be so given that they truly represent the desired measurements; only distances which are parallel to the line of bend can be dimensioned in an oblique view of a plate, i.e., in the por- tion of a plate which is not parallel to the plane of the drawing. See page 141 : i. Care should be taken to place rivets far enough from the line of bend so that they can be driven after the plate is bent. If onlj' one bent plate is used it is better to place it on the obtuse-angle side rather than on the acute-angle side. Bent angles may sometimes be used instead of plates if they are not bent more than about 3" in 12"; the line of bend is likely to be at the edge of the fillet instead of at the vertex, so that larger bends are unsatisfactor^^ * For illustrations see the author's '"Hip and Valley Rafters," John Wiley and Sons, Inc., Xew York. Fig. 78. CHAPTER XVI ^ MARKING SYSTEMS Synopsis: An identification mark is assigned to each member, and this mark is used on the di'awing, on different lists and diagrams, on the templets, and on the steel. Similar marks may be used on the component parts of a member for use in the shop. 1. There are two kinds of marks in common use in structural work, the one "Assembling Marks " or "Piece Marks," and the other "Ship- ping Marks" or "Erection Marks." AssembUng Marks are used on the small component parts of a member to facilitate their fabrication in the shop. Shipping Marks are used on the completed members such as beams, girders, or sections of trusses, as they are shipped from the shop to the site, to serve for identification in the drafting room, in the order office, in the shop, in shipment, and in erection. ASSEMBLING MARKS 2. The assembling marks usually originate in the drafting room, where they are put on the drawings; in some companies they originate in the templet shop, where they are indicated on the blueprints with colored pencil, and then the prints are passed on to the structural shop. In either case, the marks are painted on the templets, and also, after the holes have been laid out from the templets, the marks are painted on the steel to aid the fitters in assembling the parts. The use of assembling marks enables the templet maker to make a single templet for a detail which occurs on many different sheets, although this may be done to a lesser degree when assembling marks are not used. No further mention will be made of any system of assembling marks which may be arranged between the templet makers and the fitters, for it has no bearing upon the drafting room. 3. "When Used. — The draftsman should ordinarily avoid the use of assembling marks unless some apparent benefit will be derived. The benefit to the draftsman will depend largely upon the system used, but the benefit to the shop will be in proportion to the number of times the same detail is repeated, especially if on different sheets. In some instances, the use of assembhng marks may increase the cost of the drawings, but this may be offset by the reduced cost of the shop work, particularly in large contracts. Assembling marks are not given to the main component parts of a member, but only to those details which occur more than once on the same or different sheets. When there are only a few details of the same nature on a sheet, there is less need of assembling marks than when many similar pieces occur on the same member to confuse the fitters. Moreover, the sheet number and the shipping mark (page 80 : 6) are painted on each piece, and frequently the assembluig marks are superfluous. Only large contracts with many details require the use of assembling marks. Occasionally, as in plate girder work, for example, it is convenient for the draftsman to use assembling marks on some parts, as the st'ffeners or fillers, in order to save repeating the dimensions and sizes, even though marks are not used on the remainder of the contract (see Fig. 102 or 103). 4. Many structural companies use systems of assembling marks which differ from each other in minor details, but the principles underlying most of them are essentially the same. The assembling mark immedi- ately follows the billed size of the piece, and consists of three parts, viz: (1) a characteristic letter which indicates the nature of the piece, (2) a specific letter (or number) which distinguishes the piece from others of the same nature, and (3) the number of the sheet where the detail is 79 80 PART II — STRUCTURAL DRAFTING first shown. The letters should be lower case to distinguish the assem- bling marks from the shipping marks. The use of assembling marks is illustrated by many of the drawings of this book, as for example Figs. 102 and 116. 1. The first letter indicates the style of the detail and should prefer- ably be suggestive, as for example: — b = bottom seat angles for beam connections, / = fillers, m = miscellaneous angles, p = miscellaneous plates, s = stiffening angles, t = top angles for beam connections, and w = light web members. Other letters are used for various pieces, as a = base or cap angles of columns, c = cap plates, base plates or splice plates, h = bent plates or angles, y — lattice bars, etc.; these are not so significant as the first group, and accordingly are not so generally used since each company adopts its own code. Some companies even differentiate between stiffeners which are fitted at both ends and those which are fitted at one end only, or between fillers with two rows of holes and those with only one. 2. The second letter (or number in some systems), is used to show the difference between similar details on a sheet. For instance, the end stiffeners of a plate girder might be marked sa, the next pair sb, and other different ones sc, etc., double letters being used when the alphabet is exhausted, as saa, sab, sac, etc. The letters i, 1, o, q, and u are usually omitted because they are not readily distinguishable. 3. The sheet number refers to the sheet where the piece is first de- tailed. On this sheet the number after the letters of the mark is often omitted; it may be understood that the men in the shop are to consider the number in the comer of the sheet to be a part of each mark, unless another number is given, and much time may thus be saved. For illustra- tion, if a fiUer was first detailed on sheet 6, where it might be marked simply fd, the shopmen would mark the templet and the steel fdQ; if a filler exactly like it occurred on sheet 8, it would be marked on the drawing fd 6 instead of fd, to show that it was detailed on sheet 6 and to prevent the shopmen from marking it fd 8, as they would if the sheet number were omitted. For the convenience of all concerned, the piece should be completely dimensioned and billed once on each sheet, but in all other positions on a sheet the dimensions and the billing may be omitted. The assembling mark is placed near the detail in each posi- tion. The dimensions for all field rivets are sometimes repeated to simplify comparison with those of connecting pieces. 4. All pieces which are identical should be given the same mark, and, conversely, pieces should have different marks if they are not inter- changeable. Not all companies indicate rights and lefts (page 81 : 2), in assembling marks, but expect the templet maker to distinguish them by means of the drawing. It seems preferable, however, for the drafts- man to complete the system if it is to be used at all, and to indicate rights and lefts on the drawing (see Fig. 104). 5. Sometimes a summary of assembling marks is placed in the comer of each sheet giving the number of pieces of each mark required for the members to be made from that sheet. A number is added to the sheet where each piece is first detailed, to show the total number re- quired for the entire contract. While this method is of convenience to the templet maker, it is not to be recommended unless it is possible to complete all drawings of similar members before any are sent to the shop. Otherwise, later drawings will refer to sheets already in the shop with a corresponding change in the totals; revised prints must then be issued — a practice .which should be reserved for unforeseen corrections or alterations. SHIPPING MARKS 6. The shipping marks should be clearly shown on the detailed draw- ings. From the time the draftsman determines the shipping mark of a member, until the member is in its final position in the structure, it is known by this mark. The mark appears on the drawing, on the order bills, the shop bills, the shipping bills, and the rivet lists, and it is painted on the templets and on the individual pieces of steel of which the mem- ber is composed. The mark is preserved when the completed member is painted before shipment, and it serves an important function during erection in enabling the erector to place the member in the proper posi- tion, as indicated by a similar mark placed on the erection diagrams which are prepared by the draftsman. 7. In general a shipping mark is composed of two parts, viz: a char- acteristic letter or letters and a specific number, as S 14, or LG 2. Capi- tal letters are used to distinguish clearly shipping marks from assem- CHAPTER XVI MARKING SYSTEMS 81 bling marks (page 79 : 4) . As far as possible the letters should be suggestive of the type of member, as for example, C = columns, G = girders, EP = end post, etc. For a list of letters commonly used for different members, see page 324. A special system of marks is used for ofl&ce-building construction in order to indicate the floor numbers, as explained on page 81 : 5. Truss members are usually marked accord- ing to a system of panel point letters, as explained on page 82 : 1. 1. Shipping marks should be marked conspicuously on the drawing either just below the drawing (Fig. 87) or at the right of the sheet above the title (Fig. 100). When several different members are shown on the same sheet the marks may be tabulated in a "Required List " above the title (Fig. 135) ; when these members are represented by differ- ent drawings on the sheet, each drawing should bear the corresponding shipping marks, as shown in Fig. 140. 2. Rights and Lefts. — All members which are identical should bear the same shipping mark (except in office buildings, page 81 : 5), and conversely no two members should be marked the same unless they are interchangeable. When pieces are exactly opposite they may be marked "Right" and "Left," one drawing serving for both. The drawing should be made for the member marked "Right"; the "Left" member is then made as if the drawing were reversed; the marks should be placed on the erection diagram accordingly. No indication of rights and lefts need be made on the main part of the drawing, the only difference being made in the list of members re- quired, where the rights and lefts are distinguished by adding the capital letters 7? or L to the shipping mark, as in B 4, Fig. 85, and C 5, Fig. 137. Before marking pieces right and left, the draftsman should satisfy himself that the pieces are really opposite, and that there are no Right Reversed about A A Left Reversed about BB c Left Reversed obout CC Fig. 81. Rights and Lefts. other differences. The novice frequently imagines that two members are opposite when in reality they are interchangeable if inverted or turned end for end. A conception of rights and lefts may be gained from Fig. 81. If all the details are reversed about any one of the three axes of symmetry a left is obtained, but if they are reversed about any two axes, one reversion counteracts the other and the piece remains un- changed. If a member were placed in front of a mirror the right would be represented by the real member and the left by the reflected image. 3. Members Combined. — One drawing may be made to serve for several different members if the differences are properly indicated or noted, as explained on page 53 : 4. Members which are marked rights and lefts may be combined with other members on a drawing, but the details should be shown just as if only the rights were combined. It is unnecessary to indicate "R " or "L " in the various notes on the drawing, but simply the remainder of the mark, since all notes must necessarily apply to both the "R " and the "L." For example, in Fig. 135, the required list calls for columns C 1^ and C 1^, but each individual note on the drawing refers to C 1 only, with the understanding that it applies to both, and that C 1^ is made like the drawing, and C 1^ is made opposite. No member should be marked "Left " unless there is a corresponding "Right." (See next paragraph.) 4. Opposites. — Two members which cannot be marked R and L because they are not exactly opposite may be so nearly opposite that they can be combined on the same drawing to advantage. They must be given different marks and in the required list the mark of one must be followed by the word "Opposite," as in R 22, Fig. 93. Such a mem- ber would be made as if the drawing were reversed, in much the same manner as a "left " is made, but in accordance with special notes or dimensions. All details which apply only to the member marked "Opposite " should be drawn in the proper relation to all other parts, subject to reversion with the rest when the member is made. 5. A special system of marks is usually adopted in office-building construction in order to distinguish between members which are erected at different stages. Usually the columns are erected in two-story lengths and the two corresponding tiers of beams and girders are erected at the same time; all the derricks are then raised two stories and the 82 PART II — STRUCTURAL DRAFTING process is repeated. Members should be shipped approximately in the order of erection; this is usually necessary because of the lack of storage facilities, and is desirable because it simpUfies erection. All identical beams and girders in any one floor bear the same mark; identical beams and girders in different floors may be combined on the same sketch and have the same specific number, but they must bear different floor marks (see C 17, D 17, E 17, Fig. 92). Ofiice-building columns are numbered consecutively according to some definite system for convenience in finding a particular number; thus no two columns bear the same mark even though they may be interchangeable. The columns are num- bered the same on all plans so that each column bears the same specific number as the column directly above or below it but the floor marks are different. Two methods of marking office-building members are in common use. First Method. Each beam should bear the character "/ " for "Number " (instead of a letter), followed by a specific number and by the fioor number, thus: #25 — 3rd FL., or #3 — ROOF. Each girder should bear the letter G followed by a specific niunber and by the floor number, thus: G2 — BASMT., or G5 — 4th FL. Each column should bear the abbreviation "COL.," and a specific number, followed in parentheses by the numbers of the floors between which it extends, thus: COL. 11 (0-2), or COL. 19 {10- ROOF). Second Method. A capital letter is assigned to each floor or tier of beams, as A = basement, B = first floor, C = second floor, and so on up to i? = roof; the letters I, 0, and Q are omitted to avoid confusion with similar letters or figures. Each beam should bear a floor letter followed by a specific number, thus: D 25, or R 3 (see also Fig. 87). Each girder should bear the letter G followed by a specific number and by the floor letter or number, thus: G 2 — A-TIER, or G 5 — Ath FL. Each column should bear the let- ters of the tiers of beams which it supports, followed by a specific num- ber, thus: AB 11, or MR 19 (see also Fig. 133). If another story were inserted between tiers M and R, the top section would become R 19 or preferably MNR 19, depending upon the length. 1. Truss members are marked according to the letters of the panel points or apices between which they extend. In bridge trusses the upper apices are marked U 1,IJ 2, etc., and the lower apices are marked LO, LI, L2, etc.; these marks are so arranged that L 1 is directly under U 1, etc., as shown in the sketch on page 324. Web members are marked with the panel marks at their ends, thus: L2-U 1, or L 2~U 2 (Figs. 126 and 129). Chord members need not have the letter L or U repeated, thus: L 2-3, or U 1-3 (Figs. 125 and 124). End posts are usually marked EP (instead of LO-U 1), (Figs. .122 and 127). For the sake of uniformity, drawings are made for the members in the left- hand half of the far truss and the members should be marked right and left accordingly. 2. A roof truss is usually erected as a whole in order to save falsework. A small truss may be shipped completely riveted, but a larger truss must be shipped in sections; these sections are assembled and riveted together on the ground and the entire truss is then Ufted into position. A whole truss is marked on the erection diagrams with the letter T followed by a specific number, but unless the truss is shipped com- pletely assembled, each member or truss section must bear a separate shipping mark. An assembUng diagram is shown on the sheet where the truss is detailed (Fig. 116), and sometimes this is duplicated on a smaller sheet more convenient for the erector. The apices are lettered as illustrated in the sketch on page 324, the letters being the same in both halves with the exception of A and X. When one half of a truss is shipped in one section it is marked either AH or XH followed by a specific number, the half trusses on one side of the building being marked AH to differentiate them from those on the other side which are marked XH, thus: 4H2« or XH 3 (Fig. 116). When smaller sections than one-half of a truss are shipped they are marked by the three letters at the extremities followed by a specific number, thus : A CG 3, or CEF 2. When single members are shipped separately they are marked with the letter at their ends, followed by a specific number, thus: HH 1 or FL 2 (Fig. 116). 3. Straight tie rods and sag rods may be identified by their lengths. On the drawings and erection diagrams these lengths are expressed in inches inscribed in a circle to avoid confusion with other marks. It is unnecessary to paint the number on each individual rod. Bent rods and main bracing rods are marked in the usual manner with an X fol- lowed by a specific number. 4. Special direction marks may be added to members in order to facilitate proper erection, as explained in (/), page 74 : 1. CHAPTER XVII BEAMS Synopsis: In the preceding chapters are given the more general fundamental prin- ciples of drawing. These are followed by chapters in which are given more specific information applicable to the drawing of the more common types of members. In this chapter are given the types of connections, the methods of dimensioning, and other conventions and practical points peculiar to I-beams and channels. 1. A beam is a member which resists flexure or cross bending. Usually it is placed in a horizontal position and is subjected to vertical loads. A simple beam rests upon two supports and all its loads are applied between the supports. A cantilever beam receives part or all of its loads upon the portion of the beam which extends beyond the supports. A cantilever beam may rest upon two supports and extend beyond one or both, or it may be fixed at one end by a masonry wall, or by other means, and be unsupported at the other end. A continuous beam rests upon more than two supports and its use should be avoided if practicable. A simple beam is encountered in practice more frequently than any other structural member. 2. Generally speaking, a beam is composed of a single piece, exclusive of details, and is usually of wood, of steel, or of concrete. In steel construc- tion, a member which is made of more than one main piece but which acts like a beam, is termed a girder, see Chapter XVIII, page 95. 3. The forms of steel beams which are most commonly used are the I-beam and the channel. Since I-beams are frequently called simply "beams," care should be taken to avoid ambiguity between the general term which applies either to I-beams or to channels, and the specific term which refers to I-beams only. In this book the term "beams " includes both I-beams and channels. 4. In order to reduce the cost of making structural drawings for beam work, the details of which are usually similar and comparatively simple, most companies furnish printed forms.* Upon these forms are outlined I-beams or channels, some with the top and bottom views, and some without. A few dimension lines are also printed, the others being added by the draftsmen as required. The use of these forms allows only one size of sketch regardless of the actual dimensions of the beams to be drawn, and consequently the drawings cannot be drawn to scale. It is best, if practicable, to plot the details according to the scale which most closely corresponds to the depth of the beam, but to estimate the distances between the details so that they are approxi- mately proportional to the total length. A complete sketch should be drawn to scale when the number of details or the complexity of special connections warrants it; a blank sheet of the same size, and with the same printed headings is provided for this purpose. 5. Beams are supported either by masonry walls, or else by connections to other beams, to girders, trusses, columns, etc. For any given type of connection the details used by the different companies are quite similar. 6. Standard Connection Angles. — The beams of mill buildings and similar structures are connected to each other so generally by means of * In order to enable the student to become familiar with blanks similar to those used in practice, the author has prepared several forms suitable for use in any uni- versity, copies of which may be obtained from the publishers, John Wiley and Sons, Inc., New York. The drawings of this chapter, before one-half reduction, were made on these forms. 83 84 PART II — STRUCTURAL DRAFTING angles riveted in the shop to the ends of the supported beams that most companies have adopted standard connection angles. In 1912 the American Bridge Company adopted the connection angles shown on pages 298 and 300. These differ from the older forms shown on ps^es 299 and 301 in the size of the angles and in the nmnber and the spacing of the rivets, but thej' were adopted only after siifficient tests had been made to justify their use. They have since been incor- porated in the handbook of the Carnegie Steel Company, and are used in the drawings of this book. The older forms are distinguished in the tables as "Lackawanna " angles although similar standards are shown in the handbooks of the Cambria, Phoenix, Pennsylvania, and Jones & Laughlin Steel Companies, and others, and formerly were used by the American Bridge Company. Connection angles for Bethlehem beams are shown on page 302. In the new form mentioned above the vertical spacing is 3" withoiit exception, while in the Lackawanna angles 1\" is used. On accoimt of the different web thicknesses either the gage in the angles or else the distance between the holes must vary. In the old form a standard gage is used, with a variable distance center to center of holes, while ia the new form the "constant dimension syst.em " is employed, i.e., the distance between holes is maintained 5J" regard- less of the resulting gages. The constant dimension system is some- times used with the old form angles as well, both tj-pes being shown in the tables on pages 299 and 301. The constant dimension sj^stem is recommended, for it simplifies the details, especially when beams of different web thicknesses frame on opposite sides of a supporting web with rivets in common. The system is also well adapted to inter- departmental short-cuts (see below), but it involves a larger number of standard templets. This number is reduced in the plants of some com- panies by the use only of the gages which are multiples of eighths. Where the tables give values for h in sixteenths these companies use the eighth above on one side of the web, and the eighth below on the other side, thus throwing the beam ^" off center. In the drawings of this book gages are used as they appear in the tables. 1. Fig. 85 shows an I-beam and a channel detailed according to three different methods. The upper modified method is the one adopted in this book, the lower one shows the old form of connection angles,* while the middle one shows the American Bridge Companj''s method which is greatly simplified by means of iaterdepartmental understandings.! The students should learn first the more general method, but later, as draftsmen, the}' must make their drawings con- form to the standards of the companies for which they work. 2. In the modified method the connection angles should be dimen- sioned and billed as shown in 5 1 and B 4, Fig. 85. The center of each connection should be located from one flange of the beam even though the angles are placed centrally on the beam as is usually the case. The holes in the webs to provide for the standard connection angles of other beams are dimensioned in groups, and then the centers of the groups are located vertically and hbrizontallj'. Note that the holes of each group are not definitely dimensioned from these centers but it is assumed that the holes are placed sjTnmetricaUy about the center lines. This is one of a few such assumptions made in structural drafting, most dinfiensions * The older forma of connection angles, as shown on pages 299 and 301 or with slight modifications, are used by many companies. The vertical spacing for all I-beams and channels is 2|" instead of 3". The gage in the out.standing legs is constant, and the distance between holes variable, as shown by the values of o, page 299. Two methods of dimensioning the connections of channels are used, the one giving the total distance center to center of holes as for I-beams but the other giving the distances from the holes to the backs of the chaimel webs, as shown in B 6, Fig. 85. The values of h, from the back of the web to tlie holes in the angle on the opposite face of the web are given on page 301. TVith these exceptions the method of detailing is similftr to the modified method outlined in this chapter. t The principle differences between the American Bridge Company's method and the method outlined in this chapter may be smnmarized as follows: — Channels are preferably drawn with the flanges on the far side to correspond to their position on the rollers in front of the multiple punch; the connection angles are neither billed nor dimensioned; the horizontal distances from center t-o cent-er of connections are omitted, only the extension figures being used except in compUcated work; the distances from the flange to the first holes of standard connections are given instead of the distances to the centers of the groups, because the holes are punched by a multiple punch and no templets are used; the holes for tie rods and for anchors are not dimensioned the former being marked "T" to distinguish them from the beam connections; single angle connections are marked "M" for distinction; beams under 15" which are coped to beams of the same size are shown coped but are not noted; the overall dimension, the ordered length, the number, the mark, and the size are combined on one of the dimension Unes, as shown in B 2 and B 5, Fig. 85. CHAPTER XVII BEAMS 85 DRAFTINQ FORM t UNIVERSITY BRIDGE COMPANY YALE BEAMS MODI FIFO METHOD ^d B2 6-8n ll-2-(s" ISisA". Ttr -M I I LJ One I I2x 3lix I9^lls (ord. IB^Ioi") 19 . HARK AMERICAN BRIDBE CO. Tl 1?. H^ 19-11 a e'-8u 2 LaS X 4>sx 7i \M- 4^6" ■ 4^31^" 1 5-Sh" ¥ I L fi^ Sx S x72r- ^X S-i > HAKE_0n^J2Zl3i^^W'_ IIARK__«L m^< I 2i- 4Uh V ■2i 3" RIVETS *^. VINS MADE BY L>l-3-. M.N.O. HOLES_U DRAWING CHECKED BY Jll'i.! OLD FORM STANDARDS _ JATE___''/?2/(l CONTRACT NO^iS0«__ .JATE— ?/5^/!l SHEET NO, R.! DRAFTrNQ FORM Z STSJUCTOIlE_ UNIVERSITY BRIDGE COMPANY -BRANCH ; OE Cope to 15 1 42* 2,iJ r bp*fe 2fl 4~ll IS Jd-^ S'-ll^" 2Lb4x 4x'7B X Il2 -5; MAKE i-!?Z±Jl*J:i!i-- jik»kIJz.b41_ MODIFIEC METHOD \l-B4'- MAKE HARK AMERICAN BRIDGE CO. 9-0" Cope to IS'I42* tra^ sr^us 5-0" M. 5-1 1 a 3-0 fs a lii 1 3- ? X 4xrx 10 '°, . cj^ ^2S ^K^JdS:!-^Jlti-IitL HARK_ ^ + 1, B6 OLD FORM STANDARDS ni , 5-//«" 2i ^ - - "1 1 if T -1 LJ BS 2^ ISx 53#J( 9'0" ord, 8'lli" ^.;Jx^:S^i,-^ RIVETS _« DRAWING MADE BY QiM;l: DATE 7L24JI4_ ^CONTRACT NO._i80P_ HOLES-X" DRAWING CHECKED DY__!^-^'ij; DATE ^l^lllt SHEET NO. B_f Fig. 85. Comparison of Different Methods of Detailing Beams. 86 PART II — STRUCTURAL DRAFTING being made more definite to permit of no misimderstanding. Holes other than those for standard connection angles may be dimensioned as in B 12, Fig. 87, or C 17, Fig. 92. The vertical dimensions should be referred to one flange only, because the actual depth of a beam does not always agree exactly with the nominal depth, on accovmt of the wearing of the rolls or of the spreading of the flanges while they are cooling. UsuaUy they are referred to the bottom flange, except when it is desirable to maintain a uniform elevation of the tops of the beams by referring them to the top flangb instead. 1. Where it is impossible to use two connection angles on account of interference with other connections, a single larger angle maj' be substituted. For the lighter beams, single angles are shown in the tables on pages 298 and 300, but for heavier beams similar connections should be used only when they are especially designed to satisfy the given conditions, as discussed on page 234 : 2. When a single angle is used care shoidd be taken to show by means of full or dashed lines upon which side of the web the angle is to be placed. See B 1, Fig. 85. 2. When beams of different depths frame on opposite sides of a web, standard connections should be used if possible, even though the angles have to be placed above or below the centers of the beams in order to accommodate the rivets which are in common. If the beams are not in the same vertical plane but too close to permit the use of independent standard connections, special connections must be provided; often two angles with special gages, or a single angle connection mentioned in the preceding paragraph, may be used. 3. Standard angles are designed for usual conditions, but they should not be used for short spans or for beams with concentrated loads near the ends unless the number of rivets is found sufficient according to page 234 : 2. If the number has to be increased, care should be taken that the angles are not made so long that they wiU interfere with the curved fillets of the beams (page 26 : 1). 4. Beams are usually shown full length even though they are sj-m- metrical about the center lines (compare page 34 : 5). If the connection angles are alike at both ends of a beam, the duplication of dimensions and also of the end view may be avoided by noting the right end "Same as other end," as in B 10, Fig. 87. See also page 53 :1. The angles should be shown in the web view in order that beams with connection angles at both ends may be clearly distinguished from beams with no angles or beams with angles at one end only. The angles should be billed at each end for the convenience of the billers. 5. The centers of the groups of holes for all intermediate web con- nections are located horizontally in two ways. For the convenience of the men in the drafting room the dimensions are given from center to center of groups and from the ends of the beam to the centers of the end groups (see next paragraph). For the convenience of the men in the shop in spacing the small templets on the steel from one setting of the tape, and also for the use of the inspector, " extension figures " are given to indicate the distance from the left end of the beam to the center of each group. AU of these extension figures may be placed on a single dimension line, provided single arrow heads are so arranged that each dimension extends from the nearest arrow head on the right to the first arrow head on the left that faces the opposite way, i.e., the one at the left end, see B 1, Fig. 85. It is not necessary to repeat the dimension at the left end; it is usually given on the line of extension figures. Simi- larlj-, it is unnecessary to insert the overall dimension on the line of extension figures, provided it is given elsewhere. Beams which have connection angles on one end only, should be drawn with the angles at the left end so that the extension figures extend to the more definite end (compare page 88: 1). The center of each group of holes is located on the drawings even though the connection is for a channel. Since the spacing of channels on the erection diagrams is given to the backs of the webs and not to the center lines, as for I-beams, it is important that this difference be taken into consideration when the dimensions which locate channel connections are determined. When the web thickness is given in six- teenths on page 300 or 301, the proper value to use for one-half the web thickness may be obtained by subtracting xV" from the value of c. 6. The length of a beam with connection angles at both ends is the distance from back to back of angles. This is made less than the clear distance between the surfaces of the supporting members in order to allow the proper erection clearance, as explained on page 73 : 1. In deteiToining this length the draftsman usually obtains the necessary data from an erection diagram upon which the dimensions extend to the CHAPTER XVII BEAMS 87 OnHFTINO FORM 1 UNIVERSITY BRIDGE COMPANY STBUCTURl LO£L£UJLD!NG, »1 S&i\ S®l-0"^8-0 1 4-811 10-11 t 1 10^5" 1?, S, lOi^" S Cut nejr fjge 1- r so ~^ >1 .$r!P'lJl?S*_!OUC jiARK_^^ RIVETS^- - HOLES U _DRAWlNa MADE BY ^B.f± DATE U.^A'1* CONTRACT NO ^^— .DRAWIKO CHECKED BT__y- or else the whole web thickness + tV" = c' depending upon whether the beam con- nects to the outer face (back) or to the inner face of the channel web; values for c' are given on pages 300 and 301. If the main dimension from back to back of angles results in sixteenths, it is preferable to decrease it to the nearest eighth (page 34 : 6), and to increase the distance from the working line to the back of the angles at one end of the beam to correspond. When connection angles are used at only one end of a beam no erection clearance is required, so the distance from the back of the angles to the working line should be reduced accordingly. 1. Beams are sawed at the roUing mills to the ordered lengths while still hot, and each beam must be cut into the desired lengths before the following one leaves the rolls; the lengths cannot, therefore, be measured with great precision and all lengths must be accepted if within the " mill variation " of |" specified by the steel companies. All beams should be ordered in multiples of |" in such lengths that they can be used even though they overrun or underrun f"; greater allowance is often made to avoid recutting the beams in the shop in case of greater overrun. The material is ordered usually before the detailed drawings are made, but with due consideration of the types of connections to be used. The de- tailer must make his drawings conform to the ordered lengths if possible. The ordered length is given underneath the detail along with the number of pieces and the size of the beam is billed as indicated on page 44 : 2-3, and as illustrated in the typical drawings of this chapter. When no con- nection angles are used the overall dimension must manifestly equal the ordered length; but when connection angles are used at one or both ends the overall dimension is assumed to extend to the backs of the angles and the ordered length may differ. Usually the beams are ordered to the nearest J" so that each pair of angles will project about |" beyond the end of the beam; thus, the ordered length of a beam with angles at one end is about I" (from f to f ) less than the overall length, while the ordered length of a beam with angles at both ends is about 1" (from f to 1|) less than the overall length. In order to use printed forms to the best ad- vantage the angles are shown on the drawing flush with the ends of the beams, as indeed they may be; the only indication that they are not flush is the discrepancy between the ordered length and the overall length. When conditions require that the end of the beam must not extend within a certain distance of the backs of the angles, the minimmn "set back " is indicated as in H 14, Fig. 87. Beams are detailed with the understand- ing that unless noted otherwise an end without connection angles is allowed to vary J" from the position indicated on the drawing; other variations may be noted at the end, as for example ±f in B 4, Fig. 85, or +i — 0mB7, Fig. 87; if no variation is allowed the end may be marked ±0 or else the dimension may be marked "exact." Wall bearing ends (see next paragraph) need not be noted as a rule, for it is evident that greater variation than J" is permissible. 2. Beams which are supported by masonry walls must rest on metal bearing plates in order that the loads may be distributed over the proper area (page 288 : 2). The size of the plate required for each beam is given in the tables, pages 298 to 302, and the width of the plate (the smaller dimension) indicates the length of the bearing, i.e., the distance which the beam must project on the wall. The bearing plates are not attached to the beams, but the latter are held in place by some form of anchor which is imbedded in the masonry. The anchor most commonly used is the Government anchor, which is a f" rod bent as shown on page 316. A hole must be provided for this in the beam 2" from the end, placed centrally in the web or else on line with CHAPTER XVII BEAMS 89 other holes (page 91 : 2). An angle anchor is sometimes used, as shown on page 316. The bearing platos and anchors are shipped separately, and are not shown on the drawing (see page 174 : 1). A wall bearing is indicated conventionally on the drawing by lines which represent masonry, as shown in B 4, Fig. 85, and M 15, Fig. 87. 1. Coping. — When a beam is to frame into the web of an I-beam or the flange face of a channel web, it may be necessary to cut away part of one or both of the flanges to prevent interference with the flange of the beam to which the beam connects; the end of the beam thus cut is said to be "coped." A beam may be coped by means of standard dies set in a punch, or by means of an oxy-acetylene flame. Standard coping is shown on the drawing without dimensions, but the size of the connect- ing beam should be noted, thus: "Cope to 18" I 55/"; the weights of beams less than 15" deep may be omitted because no difference is made in the amount of coping for the different weights, thus: "Cope to 12" l_l ." When beams are drawn on blank sheets the coped portions may be omitted, but when printed forms are used it is not feasible to erase the printed lines and so the coped portions are blackened as in B 4, Fig. 85. The blackened portion need not be scaled but for the sake of appearance the distance from the end of the beam to the vertical line drawn between the two lines of the flange should be estimated to be about one-half the width of the flange shown in the end view; the slop- ing line should be drawn parallel to the sloping line of the end view; i.e., to the standard bevel of 2 in 12, as shown in B 4, Fig. 85 and B 10, Fig. 87. Care should be taken to show the proper flange blackened, i.e., the top flange when the beams are flush top, the bottom when flush bottom, and both when beams of the same depth are flush both top and bottom. Every cope should be indicated, for a beam will be coped only where distinctly shown; when the connection angles at one end are referred to those at the other end, the note "Same as other end " does not necessarily apply to the coping, although in case it does not apply it is better to modify the note to read "Connection angles same as other end." One note at each end for the size of beam to which a beam is coped is sufficient whether one or two flanges are to be cut; in case one end is noted "Same as other end " the size need not be repeated if the same, but it should be given if it is different or if one end is not referred ~ I to the other. In general, the note "Same as other end " should be used only to save considerable duplication (page 86 : 4) ; it should not be used when dimensions or notes can be repeated with no more work. It is sometimes necessary to "block out " the flange of a beam according to special dimensions, as shown in B 7, and H 14, Fig. 87 or R 21, Fig. 93. It is difficult to block out one side of the flange flush with the web because the curved fillet pushes the beam away from the cutter sufficiently to leave a slight projection; the drawing should specify whether or not it is necessary to chip off this projection as in B 12, Fig. 87, or R 21, Fig. 93. 2. In office-building construction great stress is laid upon speed during erection (see (d) page 74 : 1), and the beam connections are designed accordingly. Seat angles are used wherever feasible, because the supporting rivets may be driven in the shop, and be- cause each beam may be erected indepen- dently of any other beam ; this is impossible when two beams are framed to the opposite sides of a web by means of standard con- nection angles with field rivets in common. The type of connection shown in Fig. 89 (a) is used for beams supported by other beams or girders which are deep enough to provide space for the seat angles; the whole loads are carried by the seat angles, designed according to page 235 : 1, and the webs are bolted to the side angles to hold the beams in place; ordinarily no holes are provided in the seat angles. Such connec- tions with and without stiffening angles, are shown in Fig. 104, and B 12, Fig. 87, is a typicail beam supported in this way. The type of con- nection shown in Fig. 89 (6) is used for beams which connect to columns; the seat is designed to carry the whole load (page 232 :2), and a top angle is used simply to hold the beam in position and to stiffen the con- nection; the beam is held by two bolts in the top angle and two in the seat angle unless more are required for wind bracing. Such con- nections, with and without stiffening angles, are shown in Fig. 133, and Fig. 89 (a). Fig. 89(b). 90 PART II — STRUCTURAL DRAFTING E 1, Fig. 87, is a tjrpical channel supported in this way. The beams for these types of connection should be ordered with provision for the usual overrun (page 88 : 1) and for easy erection, but they should not be ordered so short that the whole loads rest on the unsupported out-standing legs of the seat angles; unless stiffening angles are used the ends of the beams should extend at least over the fillets of the seat angles and preferably over part of the vertical legs. Beams should be ordered to the nearest half inch in length. 1. Purlins. — The beams in the flat roofs of office buildings are usually similar to the corresponding floor beams. The beams may have to slope to give the roof the desired pitch, but often the beams are made horizontal and a sHght pitch is provided by varying the thickness at the beams of the concrete or other material in the roof. Steep roof construction such as used in mill buildings is quite different. The roofing is supported by longitudinal lines of "purlins " which are connected to angles on the top chords of the roof trusses or rafters. The type and the spacing of the purlins depend upon the style of the roofing to be used (page 114 : 2). Typical connections for different types of purlins are shown with dimensions on page 315; web connections are provided in every case, but the flanges of only the heavier purlins are connected; extra holes in the webs are used when the purlins act also as struts (page 119 : 1). Channel purlins are used most commonly, usuaUy with the flanges facing up the slope. Purlins are usually made to extend over two bays with "broken joints " in order to stiffen the structure, i.e., the joints in oije line are arranged to come at different trusses from the joints in adjacent lines, as shown in the diagram on page 156. The purlins are usually ordered 1" shorter than the distance between the centers of the trusses, thus leaving 1" clearance between the ends. For typical purlin details see Fig. 90. 2. Holes should be provided in the webs of beams for tie rods when rods are necessary to resist the thrust of floor arches. The number and the size of the rods are usually determined by the designing de- partment; * the most common sizes are |" and J" in diameter. The holes are usually made the same size as others in the web for con- * For the method of design, see page 201 : 3. DRAFTING FORM 2 UNIVERSITY BRIDGE COMPANY YALE BRANCH CTnnerim c MILL BUILDING .DRAWING nr PUHLINS ii 9-lli" 39-11 19-1 Ij" ',29-llV' 39-9i" li In-P2 onh^-^ In P2 only- -ln-P2 only >ic — a ' c In P2 only l9-7i Vil^.JJ:i'03JJ±.i?-!I BARK.. ■ > 1* > I Si * | > f < - 7-//I-" 15-10 lodi-e -=15-0 /2\holes for wood HLYil^J-SAUA^JSdli'l 2i-.'. r -Its ^ n^ — 1^ ^r Cm- 3jlOi J. 10 m i-e = 15-0 LkP.iJ.ij'.Aj'J/sl. \sim3W"tio® 3S-9i «-*T le-®- l-6"=IS-0" If^j ffl, 'Jz1j^IjjJsJL'JJ-° -©- ■©-ei ^ l7-?i a, — » < >K ■■ JJii 6-10 i3 I5# 35-11 -HARK ?£_ RIVETS 4L DRAWING MADC BY P.W.B, ntr r Feb. 18, 1918 ^^.^^^f^^ iin . 1918 HOLEsfjg^g-"°terfnRAWINSCHECKED_K[- F.E.B. DATF Feb. 19. 1918 -iMFCTUMIIpr. B 9 Fig. 90. Typical Purlins. CHAPTER XVII BEAMS 91 venience in punching them; they are made in pairs (3" apart) to provide for the rods in adjacent panels as indicated in the floor plan in Fig. 158. The location of the holes vertically depends upon the floor con- struction because the rods should be placed where they will best serve their purjiose; this depends upon the type of arch, and upon whether the arch is supported by the top or bottom flange or by a skewback angle riveted to the web (Fig. 87). On account of the use of dif- ferent depths of beams in the same floor, the elevation of the rods is usually determined at the outset and noted on the plans, as shown in Fig. 158. 1. Holes should be provided in the webs of purlins for sag rods. The function of the sag rods is to give intermediate support to the purlins at right angles to their webs; this is necessary because the resultant forces for which the purlins are designed are not parallel to the webs. One line of rods is used if the span between trusses is from 15 to 20 feet and two lines if more than 20 feet. The upper purlins should be tied to each other, or to a strut at the ridge by means of bent rods (Fig. 175 (6). Rods from f" to |" in diameter are used but |" is the most common size. The holes are usually made the same size as others in the web provided they are small enough to leave sufficient bearing for the nuts. The holes are made in pairs (3" apart), either in the center of the web or on line with the holes for the truss connections (see next paragraph). 2. When a multiple beam punch is to be used all the rivets and holes in the web of an I-beam or a channel should, if possible, be so located that the beams will not have to be shifted laterally as they pass through the punch. Holes for tie rods, sag rods, and anchors may be moved slightly to meet this requirement. 3. Wooden floors and wooden sheathing are attached to steel beams or purlins by means of wooden nailing strips or spiking pieces which are bolted to the steel. The nailing strips are usually bolted to the webs of channel purlins and to the top flanges of beams, with J" bolts. ^^" holes must be provided, for these bolts at intervals of from I'-O" to r-6", preferably in multiples of 3" to permit the use of standard strip templets; in the flanges of I-beams the holes should be staggered. It is well to note that these holes are "for wood " so that shopmen need not waste time in useless refinements. See B 16, Fig. 92, and P 6, Fig. 90. Care should be taken to space the holes in the flanges of beams far enough from the ends to allow for any underrun or any coping, and far enough from the connections for any other beams which might prevent the insertion of the bolts. 4. Holes in the flanges of I-beams and channels may sometimes be dimensioned in the front and the end views in order to dispense with the top and bottom views, as in Figs. 90 and 92. When there is a large number of holes, or when the drawing might be misinterpreted, the flange views should be shown; for example, staggered holes should regularly be shown, as in B 16, Fig. 92. 5. Beam Girders. — In order to give greater strength or greater bearing, two I-beams or an I-beam and a channel may be used side by side. To distribute the loads and make them act as a single member they should be bolted together with separators of some form between them. Cast-iron separators are commonly used, but for heavy work, or for beams of unequal depth, special diaphragms .made of I-beams, or of plates and angles, are used. For lighter use, gas-pipe separators may serve, particularly if they are required simply for holding the beams at fixed distances apart. Gas-pipe separators are used between grillage beams with a single rod passing through all the beams of one tier. (See Fig. 291). Gas-pipe and cast-iron separators are shown on page 316. They are not drawn in detail, but are simply listed ■ on combination shop and shipping bills (page 174 : 1). The separators are spaced about four or five feet apart, and from six inches to one foot from the ends. If the beams have rigid connections at the ends, the end sepa- rators may be omitted. The I-beams and the separators are usually shipped separately and assembled in the fitld (C 17, Fig. 92), but this depends upon the number and the size of the beams, and upon the practice of the individual companies. If they are assembled in the shop the two beams should be detailed together and called a girder, as G 19, Fig. 92; a list of separators and bolts should then be given on the drawing and on the corresponding shop bill; on the latter, reference should be made to the shop and shipping bills from which the separators and bolts are made and these bills should bear the note: "Send to the shop for assembling." 92 PART II — STRUCTURAL DRAFTING DRAFTING FORM 3 UNIVERSITY BRIDGE COMPANY SrRUCTOBE OJIL't^JJ/L'-^L''^ DRAWING 0F___ _??:•«««_ Sj I.3' VT^i ^ 131 Salt spa.® l-e"= 12-0" . , /-g" .6 fe) holes for woo J 2 Lsx4x4J 7^" 3-10 n 2Lax4x4x^xi ^ \jij a LiU 2i-^ l-sr. 4 /-5r« s ^KE 32f2js_3l2yj5^'_ BIS JZ " • JZ BIVETS4 DDAWING MADE BY ''^l DATE — '^JyJ^JJ- CONTRACT NO '^$- BOLESrae«y!?f«^ DRAWING CHECKPD BT *t5'A Bk1^^M-Ji'J^ SHEET NUMBER B-5._ DRAFTING FORM 1 UNIVERSITY BRIDGE COMPANY BRANCH snvctuRZ____0mCE_B_UlL_DJN3 dj!AW1HG of.___e/ffOfffS. 15^" sl-e" 7S" ii'-e" \4U0" l2-ls'ls42*.l^-0" _JIARK_l£iC/Z_ i4-DI7 14-EIS 9^" 4^0" 8-3" X > -> '/>y//////A -A- -^ HAKE '^fii':^?£l_(_?r£"il(?lf-?rO'L ) M.BK S'^ ^^■fiJ^PI'J"t'Ji{ 3-Bolts fji 8 y 141-0" 2 4. 3 ^ ^ o 25&e= 12-S 3- --»-g 12 /S rt ^^ HAKE One Girder (2 -^2"ls 40* /.-^O'^J jrABK_ S?" I&_?/?-_'i:?T-i'^^"_( RIVETSJ^ DRAWING HADE BY KlP: DATE__^i?i?ft_'l_COHTR*CT NO. .'?", 8 &l 8=12-0 j^^^ — __1 r: 1-4" .3. .3 1-15142* I5'-II" ^ 12-Crane Beoms 15-e" 3) O^i RIVETS t_„DRAWING MADE_BY 'i'SA DATE_7-Z2r'iM__CO.NTRACT_JlO^. Wl. HOLES.JF^-JIRAWING CHECKED_B.Y__&E'e' \>K\^ Idt'l'J ^SMET NUMBER B-»_ Fig. 93. Typical Beams. 94 PART II — STRUCTURAL DRAFTING Special forms are often printed for double I-beam girders, but the form for single I-beams may be used by tracing an additional I-beam or channel in the end views from another sheet, as in G 19 and G 20, Mg. 92. 1. When I-beam girders with separators are insufficient, plates may be added to make a box section, the separators being omitted as in G 20, Fig. 92. The rivets are spaced 6" apart, with one or two smaller spaces near the ends. Obviously, rivets through the inner flanges would be inaccessible. 2. Wall plates or flange plates are sometimes riveted to the top flanges of beams which support masonry walls in order to furnish wider bearing. These plates are not necessarily concentric with the beams. 3. Skewback aijgles are sometimes riveted to the webs of beams to provide supports for floor arches at the proper elevations. Rivets should be spaced about I'-O" apart, as shown in 5 10 and H 14, Fig. 87. Similarly, stiffening angles are often riveted to purlins which act as struts, as shown in P 8, Fig. 90, and S 2, Fig. 147. These rivets may be spaced l'-6" apart. 4. Crane runway beams are sometimes stiffened laterally by chan- nels riveted as shown in G 24, Fig. 93. The rivets are placed at inter- vals of about l'-6", except at the ends where about two 3" spaces are used. For export work these channels and the I-beams should be shipped separately. ^^"^"^^ 5. For skew coonections see page 146 : 5. Note that it ' ' is usually better to cope out one flange of a beam to give Fig. 94. desired clearance, as in Fig. 93, than to require a diagonal cut which must be sawed. Even though the web must be cut diagonally, the flanges may often be blocked out to avoid sawing, as in Fig. 94. CHAPTER XVIII PLATE GIRDERS Synopsis : Specific suggestions tor drawing typical plate girders. 1. Plate girders are used extensively in every form of steel construc- tion, because of their adaptability. They resist transverse bending like beams [page 83 : 1), but they are used for heavier loads, for longer spans, or for conditions which the single rolled beams do not satisfy. With different depths, different forms of flanges, or different sizes of component parts, girders may be made to serve a great variety of purposes. L ^ nn FT^ jl 1 J e d Fig. 95. Typical Girder Cross Sections. 2. Types. — Girders may be composed of one or more web plates, with simple or composite flanges, as illustrated in Fig. 95. The most com- mon type of cross section, shown at (a) and (6), is composed of a single web plate and four angles, with or without one or more cover plates on each flange. This form may be adapted to suit most requirements, the heavier types of flanges being used only in special cases. Only the more common girders are illustrated in this chapter. 3. Main Dimensions. — The length of a plate girder which is dimen- sioned on the drawing is usually the extreme length out to out; when some other dimension is seemingly more important it may be given instead, as for example the distance from center to center of end holes when the end connection is of a type similar to the alternate form shown in the corner of Fig. 99. For convenience in the drafting room the distance from center to center of supports is usually given also, as in Figs. 98, 100, or 103. The distance from the end of the girder to the center of the support should provide for ample clearance, as explained on page 73 : 1. The nominal depth of a girder is usually the depth (width) of the web plate, for this is generally in even inches and often in even feet or half feet; the depth dimensioned upon the drawing is in- variably the distance from back to back of flange angles, which is |" (or J") more than the depth of the web plate. The flange angles thus project beyond the edges of the plate to allow for any irregularities in the latter which may result from rapid shearing in the mill (page 25 : 3) ; if part of the plate should project beyond the angles it would have to be chipped off before the cover plates or other parts could be put in proper position against the angles. Unless the upper edge of the plate is ex- posed to the weather, the depth of the girder from back to back of flange angles is usually made |" greater than the depth of the web plate, allow- ing j" variation on each edge. In bridge and viaduct work and in other structures in which the girders are exposed to the elements, the upper 95 96 PART II — STRUCTURAL DRAFTING edges of the web plates are made flush with the backs of the angles unless cover plates are used; otherwise, a rain pocket is formed which will lead to a more rapid deterioration of the girder. The distance back to back of angles is thus i" greater than the depth of the web plate for exposed girders without cover plates. It is well to add a note stating whether or not any projections which may occur should be chipped off. See Figs. 98 and 99. It is not feasible to draw extra lines to represent the edges of the web plate, the only indication of the difference in depth being the discrepancy between the billed width of the plate (usually in even inches, page 43 : 3) and the dimension back to back of angles (usually with a fraction). 1. Since the vertical shearing stresses of a plate girder are resisted by the web plate, they must be transmitted from the web to the supports. Sometimes the web plate is riveted directly to the face of a column or to the stiffening angles of another girder (Fig. 99); but more often end stiffeners are used either to serve as connection angles (Figs. 98, 100 or 104), or to transmit the stresses to the masonry or to the column seat upon which the girder rests (Figs. 101, 102, or 105). The size of the end stiffeners and the number of rivets in them are determined as ex- plained in Chapter XXXIX, page 266. Stiffening angles should be made to bear against the outstanding legs of the flange angles; since they are placed in contact with the vertical legs of the flange angles, they must be cut to fit the curved fillets, as shown in Fig. 267 (&). The billed length of the stiffeners is the exact distance in the clear between the outstand- ing legs of the flange angles; the ordered length is made J" greater (see next paragraph). For suggestions regarding the spacing of the rivets see page 70 : 4 (b). The spacing should ordinarily be made symmetrical about the center line, so that the stiffeners on opposite sides of the web are interchangeable; but if the holes for a connection to the outstanding legs are necessarily slightly unsymmetrical, it may be deemed advisable to space at least one rivet through the web unsymmetrically to prevent the possibility of the stiffeners being assembled upside down. 2. The flange angles usually extend the full length of a girder and should be billed accordingly. They are ordered about f " long and are then cut to the required length in the shop where they can be cut with greater precision than at the mill (page 28 : 1). The stringers and floor beams of bridges are often milled at the ends; otherwise the angles are sheared. The extra f " is indicated on the material order bills and on the shop biUs (pages 165 : 1 and 167 : 4). Web plates should extend to the extreme ends of a girder when they are to be milled or when no stiffeners are placed with their outstanding legs at the extreme ends of the girder; when stiffening angles are so placed the web plates may be billed long enough to come within J" or |" of each end. In the larger girders the web plates must be spliced because it is impossible to obtain plates long enough to extend the full length of the girder. For the location and the design of web splices see page 270 : 4. The lengths of the web sections should be billed to allow from j" to f " between them at the splices (compare page 165 : 2). 3. Unless the web plate of a girder is thick enough to resist the shear- ing stresses, it must be reinforced by intermediate stiffening angles, as explained on page 266 : 2. When the position of stiffening angles is definitely determined by members which are to connect to the outstand- ing legs, the stiffeners must be spaced before the flange rivets; otherwise it is better to fix the flange rivet spacing first, and then place the stiffeners at those rivets which are located most suitably to give the best spacing (page 269 : 3) . It is customary to place the stiffeners so that the backs of the angles are toward the nearer end of a girder. The rivets in the intermediate stiffeners should line up with those in the end stiffeners even when a smaller number is used; this saves extra dimensioning, and it simplifies the shop work, particularly when multiple punches are used (page 29 : 5). Instead of using the full number of rivets used in the end stiffeners, some may be omitted unless the resulting spaces exceed the allowed maximum (page 69 : 1), or unless the full number of rivets is needed for other reasons (as for example, when the stiffeners serve as connection angles for other members or when they are placed at web splices) . 4. Stiffening angles overlap the vertical legs of the fiange angles, and unless they are crimped (see next paragraph) spaces are left between the stiffeners and the web as shown in Fig. 97. Plates called " fillers " are inserted to "fill " these spaces so that the rivets can be effectively driven without bending the angles out of line, and so that no surfaces will be left inaccessible for painting. The width of a filler should be the same as CHAPTER XVIII PLATE GIRDERS 97 the width of the superimposed stilTening angle unless the filler is made to extend under two or more angles, or made wide enough to take an addi- tional row of rivets according to page 235 : 2. The thickness of the filler should be the same as the thickness of the flange angles, unless part of this space is occupied by a spHce plate or a reinforcing plate. In this case the filler should be thick enough to make up the difference; fillers less than -^j" are not used, and smaller differences should be made up by making the thickness of the splice plates or reinforcing plates equal to that of the flange angles. If the thicknesses of the top and bottom flange angles differ by tV" the filler may be made of either thickness. If they differ by g" the filler may usually be made the mean thickness. If they differ by more than J" two fillers should be used, one as thick as the thinner angle and the other equal to the difference in thickness; this second filler should extend to the fillet of the thinner angle. The length of the filler should preferably be made about |" less than the clear distance between the flange angles, allowing the usual shop clearance of j" at each end. On girders which are ex- posed to the weather it is well to reduce this clearance one- half to leave less chance for water to enter, but due allowance should be made for the overrun of heavy angles (page 25 : 1). Some specifications require the fillers under end stiffeners to fit tightly at the bottom. 1. Intermediate stiffening angles are sometimes "crimped " or bent so that they are brought into contact with the web, as shown in Section BB, Fig. 102. No fillers are required under crimped stiffeners. Stiffeners which transmit direct stress should not be crimped because straight angles are more effective; thus end stiffeners or stiffeners under con- centrated loads should not be crimped. Similarly stiffeners which have holes in the outstanding legs for the connection of other members should always rest upon fillers, because better results can be obtained in this way. Most specifications permit the crimping of all other intermediate stiffeners although not all companies are well equipped for this work. Many companies prefer to furnish fillers, particularly when the cost of the additional material is met by the customer, as in contracts based upon a price per pound. The billed length of a crimped stiffening angle Fig. 97. should include the amount of metal required for each crimp, which is equal to the depth of the crimp, i.e., the thickness of the flange angle. Thus the length of a crimped stiffener of a girder is equivalent to the depth of the girder from back to back of flange angles. An extra §" should be ordered for each crimp, so that the angles can be cut to fit properly after they are bent. 2. Cover plates may be used on plate girders to furnish additional metal in the flanges. Since the flange stress is a function of the bending moment, the greatest flange area is required where the moment is maxi- mum; as the moment decreases, the flange area may be reduced. This reduction is effected by cutting off the cover plates successively at points beyond which they are no longer needed, as explained in Chapter XXXVIII, page 259. If a girder is to be exposed to the weather, one plate on the top flange and sometimes one on the bottom flange are made to extend the full length of the girder in order to protect the surfaces of contact between the angles and the web from the action of the elements. Similarly, all the. cover plates on the top flanges of crane runway girders must be continuous in order to furnish uniform bearing for the rails which rest directly upon them. The cover plates on the top flange of a railway deck girder need not necessarily be made full length, since the ties may be "dapped " (i.e. notched), different amounts to make up for the differences in plate thickness; the ties must be notched, also, for the rivet heads. Special detailed drawings are often prepared in the drafting room for the ties of a bridge, especially when they have to be sawed to provide for the super-elevation of the outer rail on a curve. The cover plates may be billed with ^the flange angles (Fig. 105), or they may be billed on special dimension lines with the dis- tance from the end of each plate to the end of the girder, as shown in Fig. 101. To save space, all the plates of one flange may be billed as in Fig. 102, provided portions of the line are omitted so that the overlapping dimensions may be distinguished more easily. Universal Mill plates with rolled edges are usually ordered for cover plates, par- ticularly for girders which are exposed to the weather (page 25 : 3). Full length plates are ordered f" long the same as the flange angles (page 96 : 2) ; other plates are ordered the same as the billed lengths. 98 PART II — STRUCTURAL DRAFTING ^Hk l^0"c, toe, F.B. Z"^J &J03lt,sp3.^2i=l'fO^ Halt_spa, fj 3-=2-'9" ialtispa,^ 411-1- fJiiU', ff I3^9jf'nn. Length ^¥ <>-^ «- -©■ 2 LB6x.e^x 1-9^' 2 Fiirs, aji^sJi 94- « — ®- -®- ZLsexBx Web22xi 2 UBxBi -®- y.v!.vc>^?fce ' ' o& ^*Bi A A i«* o op^ 34i4i3 6S6 GIRDERS DECK PLATE GIRDER SPAH flivs. csk & ch ipped far side UNIVERSriY BRIDGE COMPANY •PUMT RIVETS i" iNCHAllGEOF__4l££ ' g^ HOLES ii"UHLESS NOnO ""^ "^ '^•^•^ Auif.IB.l4i 2617 as. IIJ4} Fig. 102. Deck Railroad Bridge Girder. CHAPTER XVIII PLATE GIRDERS 103 Sym. sbi, C. L. Sect A-A 8 GIRDERS G2 Rii/ets -i Holes Ji 13 CRANE GIRDEHS FVRNACE BUILDING NEW ENGLAND STE.EL CO HARTFORD- CONU. UNIVERSITY BRIDGE COMPANY IN CHARGE OE . A £.5- M4DEBY CLE.&.7/?S/I4 _. Q ^'^ CH'K'0BY_W._Atf._S/fl//4__ ° Fig. 103. Crane Runway Girder. 104 PART II — STRUCTURAL DRAFTING sisi For mb Floor Line Rivets 7 13 Holes IB unless noted TO CO ' aiai ONE GIRDER G7 FLOOR GIRDERS MERCANTILE BUILDING O.J. FROST S^ CO. CHICAGO ILL UNIVERSITY BRIDGE COMPANY — -J PLANT INCHAHGEOF C.O.N. MADE BY .PjL:^...7/?e]f4^^ n_299B_ CH'K'D BY i-ft* .//^SZW-I ' Fig. 104. Floor Girder. CHAPTER XVIII PLATE GIRDERS 105 Sole plate same as other end ONE GIRDER G 16 ^ffivets csk a chipped far side FOUNDATION GIRDERS POWER HOUSE LIGHT AND POWER CO. LOWELL, MASS UNIVERSITY BRIDGE COMPANY PLANT RIVSTS i HOLES li IN CHARGE "F... MADE B> - CH'K'D'BV -I"- M.\r.F. e/eT4 V' iai2 a Fig. 105. Box Girder. 106 PART II — STRUCTURAL DRAFTING 1. Flange Rivets. — The flange angles of a girder are fastened to the web plate by sufficient rivets to transmit the flange stress for which the angles are designed. The rivets are usually closer together toward the ends of a girder than they are near the center. The pitch for each section of a girder must be determined for the conditions of loading and the proportions which are peculiar to that girder. The maximum pitch for each panel is found as explained under the proper case in Chapter XXXVII, page 241. The minimum pitch depends upon the strength of the web, as explained on page 255 : 2. Between these limits the drafts- man should space the rivets according to the general rules for rivet spacing given in Chapter XIII, particularly pages 69 : 1, 70 : 2, and 70 : 4; the spacing of the rivets should be made the same in both flanges for the beneflt of the draftsman and the shopmen. 2. Rivets in Cover Plates. — The rivets which fasten the cover plates to the flange angles must satisfy the conditions given on page 263 : 3, but except in heavy or unusual work, the spacing is governed by the general rules for rivet spacing given in Chapter XIII, page 68. A single line of rivets is often used in each 5" or 6" angle even if a double line is used in the vertical leg. Extra rivet lines are placed in wide cover plates, as explained on page 69 : 2. Holes for lateral brac- ing should be spaced before the stiffening angles are located for usually the angles can be so placed that their outstanding legs will not interfere with the holes which best meet the requirements of the lateral plates. The flange rivets and the stiffening angles should usually be spaced before the remaining rivets in the cover plates. No rivets in the cover plates should be placed so near the outstanding legs of the stiffening angles that they cannot be driven by machine (page 73 : 5) ; it is well, there- fore, to tie the nearest rivet through the cover plate to the rivet line of each pair of stiffeners by a line or a dimension, as in Fig. 102, in order to show that this point has not been overlooked. The rivets in the plates should be so placed that the same templets can be used for the top plates and angles that are used for the bottom plates and angles; additional rivets or groups of rivets may be spaced differently to accom- modate connecting members, but the remaining rivets should be oppo- site (see (d), page 70 : 2). The rivets near the end of each cover plate should be spaced not over four diameters as explained in (d). page 69 : 1 ; this apphes to plates on the tension flanges as well as those on the compression flange so that the strength of the plates may be developed within a comparatively short distance. Since all cover plates which do not extend full length of the girder should be used as ordered, the end rivets should be placed If" from the ends of the plates to provide ample edge distance in case the plates underrun (page 165 : 2). 3. Standard gages are not necessarily used in the outstanding legs of the flange angles or of the stiffening angles. It is usually preferable to change the gage sufSciently to make the distance from center to center of rows a multiple of §", and the distance from the center of the web to either row a multiple of J"; in this way small fractions are used in the gages only, and are avoided in the cover plates and on the draw- ings of members which connect to the flanges or to the stiffeners. In order to ehminate thirty- seconds from the gages, web thicknesses in sixteenths should be considered tV" greater; this incidentally allows for paint, scale, or bends which might tend to separate the surfaces of contact. 4. When the outstanding legs of two stiffening angles are in contact they need not as a rule be riveted together. On girders which are exposed to the weather these outstanding legs should be riveted at intervals of 1' 0" if the girders are 3' 0" or more in depth. It is pref- erable where possible to place such stiffeners at least 2" apart so that they can be painted. 5. Holes for anchor bolts should be ^" or |" larger than the bolts (Fig. 102); this facilitates the placing of a girder if the anchor bolts have been set, and it provides for drilling holes in the masonry if the bolts are to be placed after the girder is in position. The holes at one end should be slotted to allow for expansion and also for inaccuracies in setting the bolts. Provision for expansion to the extent of |" for each 10' 0" should be made in all bridge girders. When cast-iron pedestals are used (see diagram, Fig. 153) the holes in the girder are made only the usual ^\" larger than the bolts, but at one end the holes should be slotted (Fig. 101). 6. Reference dimensions are often given on the drawings for use in the drafting room; for example, dimensions to the base of rail (Fig. 100), or to the floor line (Fig. 104). CHAPTER XVIII PLATE GIRDERS 107 1. When more than one sheet must be used to properly illustrate a long girder a reference line should be used on each sheet to indicate the points which are common to both drawings, as illustrated in Fig. 101 (compare page 121 : 2). 2. A box girder with more than one web is shown in Fig. 105. 3. A girder is sometimes " cambered," i.e., curved in a vertical plane, to prevent the center from sagging lower than the ends. The amount of camber should equal the maximum deflection so that the girder will assume a horizontal position under a full load. The camber is effected partly by the proper rivet spacing, but mostly by careful shop work; in fact, slight cambers may be made entirely by the fitters and riveters by placing the proper supports under the girders while assembling and riveting them. Since a web plate cannot be curved except by elaborate cutting, the usual camber is provided at the web sphces by spacing the rows of rivets in the splice plates farther apart at the top than at the bottom so as to separate the ends of the adjacent web sections more at the top. The corresponding spaces in the top flange angles are made greater than those in the bottom angles. It is important to note the amount of camber on the drawing even if special rivet spacing is pro- vided, for it is as easy to nulhfy the effects of such spacing by careless fitting up or riveting as it is difficult to avoid a curve in a girder which is intended to be straight. 4. Bridge girders are often made with curved ends for the sake of appearance, as illustrated in Fig. 101. It is not feasible to bend both ends of long flange angles, so short angles are used at each end. These angles extend far enough horizontally so that they may be spliced to the top flange angles satisfactorily. They serve as end stiffeners, and they may be crimped over the bottom flange angles or arranged as shown. 5. Typical drawings of plate girders are illustrated as follows: — Figs. 98 and 99 , a stringer and a floor beam for the same railroad girder bridge; Fig. 100, a floor beam for a truss bridge, showing the method of cutting the end to clear the pin; Figs. 101 and 102, railroad bridge girders; Fig. 103, a crane girder with holes in the top flange for rail- clamp bolts and for lattice bars which connect to the stiffening girder of Fig. 110; Fig. 104, a floor girder with beam connections; and Fig. 105, a box girder with two webs. CHAPTER XIX LATTICED GIRDERS Synopsis: Latticed girders are light trusses with parallel chords, but a different system of working lines is used from that of the next two chapters. 1. Definition. — The terms "latticed girder" and "latticed truss" are not distinctive because they are used interchangeably by some companies or individuals whereas they have different meanings when used by others. A girder becomes a latticed girder when the solid web is replaced by separate web members, but it also becomes a truss from the definition (page 17). Formerly, a latticed truss was of a form similar to that shown in Fig. 120 {h) which had from two to four inde- pendent web systems, the stresses of which were statically indeterminate. Since this type of truss is becoming obsolete except for very hght work (Fig. Ill), the name "latticed truss " is often used to apply to almost any form of riveted truss with parallel chords to distinguish it from a pin- connected truss. In this book the term " latticed girder " will be con- fined to comparatively light trusses with parallel chords, all members of which are composed of one or two angles. Heavier forms will be called trusses, and to avoid ambiguity the term "latticed truss " will not be used; it will be replaced by the more specific terms "Pratt truss," "Howe truss," etc., as illustrated in Chapter XXI, page 120. 2. The most common form of latticed girder is the "Warren " or "triangular," shown in Fig. 120. Some authorities Hmit the term "Warren " to girders formed of equilateral triangles, but this distinction is not generally maintained. In order to increase the number of panels, or to provide connections for other members, every triangle may be subdivided as in Fig. 120 (fc), alternate panels may be subdivided as in Fig. 120 (m) and (n), or single pariels may be subdivided as in Fig. 110. 3. End Connections. — The greatest number of latticed girders are used in building construction where they are supported by columns or other members. Typical column connections are shown in Figs. 110 and 111, the former to the face of a column perpendicular to the plane of the girder and the latter to the face parallel to this plane. Note that in the type of connection shown in Fig. Ill, one angle of each chord must be cut short to avoid interference with the column. Small foot bridges are often supported by latticed girders which rest upon the abutments, with shoe plates similar to those used on plate girders. 4. Proportions. — The depth of a latticed girder is determined in the designing department, and it is usually expressed in even half feet. In building work the depth is often dependent upon other framing because the position of both the top and the bottom may be fixed by other mem- bers. The panel lengths are made equal in the drafting room, but seldom are the resulting triangles equilateral (see above). 5. In general the different members of a truss are referred to a system of working lines. Theoretically these working lines should pass through the centers of gravity of the different members, but when a member is composed of one or two angles it is customary to use the rivet lines as working lines. These working lines should intersect in a common point at each apex as in roof trusses (Chapter XX, page 113) and bridge trusses (Chapter XXI, page 120); the stresses are determined upon this assumption. In the case of light latticed girders, however, the stresses are usually so small that a slight deviation makes practically no difference in the efiBciency of the girders, and better connections are thus 108 CHAPTER XIX LATTICED GIRDERS 109 obtained. The rivet lines of the diagonals are not extended to the rivet lines of the chords but they intersect parallel auxiliary working lines; the end rivets of the diagonals are placed at these intersections, as shown in Fig. 110. The position of these auxiliary working lines should be such that ample clearance is left between the angles of the diagonals and the chord angles, as explained in detail on page 77 : 1. 1. By means of the dimensions determined in step IV (page 77 : 1) may be found the panel depth and the panel length, each measured from center to center of the end rivets of a single diagonal. The panel length is found by deducting from the extreme length of the girder the sum of the distances from the ends to the first working points and the distances between the working points in each intermediate plate, and then dividing the remainder by the number of diagonals. This resulting panel length is expressed to the nearest sixteenth inch, or preferably the nearest eighth or quarter, the amount of clearance at two or more points being changed slightly if necessary to make the proper adjustment. Care should be taken, however, to keep all panel lengths equal, and all plates alike, as far as possible, in order to minimize the number of different templets. For illustration, let us determine the panel dimensions for the girder shown in Fig. 110. The diagonal distance from the end rivet to the farther corner of any diagonal is found by means of the diagram on page 313 to be 2^\" for a If" gage and l\" edge distance. The distance from the end rivet to the rivet line of the upper chord angles is 4.jj^" = 2i% + i + 3| - 2, allowing \" clearance (page 72 : 2); to eliminate sixteenths 4" is used. The corresponding distance at the bottom is made the same in order to keep the intermediate plates aUke. The panel depth from center to center of working lines is 7'-6" = 8'-6" — 2 (4 + 2). The distance in the intermediate plates between the end rivets of adjacent diagonals is 41" = 2^\. + \ -\- 2^%. Unless it is desired to make provision for assembling the diagonals with the out- standing legs on either the upper or lower edges, advantage may be taken of the fact that there is no plate similar to the end plate or the center plate; at each of these points the diagonals are so arranged ;that space need be provided only for the corners nearer the end rivets. The diag- onal distance from the end rivet to the nearer corner is found from the diagram to be IW for l\ (leg minus gage) and \\. The distance from the end of the girder to the first working point is b\i" = HI -|- i -f- 3^. From the center line to the nearest working point is 5|" = l-J-f + j + 31 + Tif ■ Considering one-half of the symmetrical girder,, the amount to be divided into four equal panels is 17'-9A" = 5 (39'-10f") - 5{i — 3 X 4| — 5|. This is not divisible by four within the usual working limits, but to the nearest J" we can use 4 panels of 4'-5Y' = 17'-9"; this leaves i'^" to be distributed among the other dimensions in order to make the total length check with the overall dimension. Each of the three 4|" dimensions could be increased by ^" ; but it would be preferable to avoid sixteenths, and consequently the 5{i" is increased to 5f " and the 5|" to 6", as shown. 2. The dimensions should be recorded on the drawing as soon as determined. When the panel depth and length are found they may be laid out and dimensioned, and the angles may be drawn and billed; the gages should be dimensioned on each angle though the standard gage is used. 3. The sizes of the connection plates may be determined either graphically or arithmetically as explained on page 77 : 1, V. The experienced draftsman usually prefers the second method, particularly for rectangular plates. The size of the plate will generally be deter- mined by the rivets in the diagonals, and afterwards the remaining rivets may be spaced. To illustrate, let us find the size of the plate pa, Fig. 110. On the main drawing along the working line of one of the diagonals already plotted to scale, a distance is laid off equal to the sum of the rivet spaces, 6" = 3 -|- 3, from the end rivet to the last rivet in the group. A scale of 3" = 1' should be used, or else the lines should be prolonged so that a full size scale may be used. The corresponding vertical and horizontal components may be scaled without drawing any additional lines. In the case at hand, the vertical component is 5|" and the horizontal component is S^". By combining these values with the edge distances and the proper distances from the second para- graph preceding, the dimensions of the plate are found. Thus, the width of the plate with IJ" edge distances would be 12|" = IJ + 4 + 5i + IJ; by reducing each edge distance to IfVi the commercial width of 12" may be used (see page 43 : 3). The length of the plate is l'-2" = I5 + 3tV + 4| + 3tV + 1|. The remaining rivets in the plate are ]110 PART II — STRUCTURAL DRAFTING 40U)"c, to c, Cols, 'd 1 -» ■ :^ 1 : W K I I r ^ 1^.--^ =^_ja n ^--^^ I PI. 18. i-x 1^71 I PI. 9x^1111 6 holes for wood ttark fi/lTTS -f HOLES-^ Onless noted WASHERS 2i*f I GIRDER LGI I BRACKET Mie LATTICED GIRDER FURNACE BUILDING NEW ENGLAND STEEL CO. HARTFORD CONN. UNIVERSITY BRIDGE COMPANY rale PI ANT IN CHIBRF nF S. C. p \ MAnFBV LT.O. 7-30-1* 56 ;S RHtKin BV C. A & 8-2-14 ll 9 Fig. 110. Typical Latticed Girder. CHAPTER XIX LATTICED GIRDERS 111 I PI. 12 xfi X 1-2 S^iyi' 8bt CLexc, eathewfi 2 LATTICED GIRDERS LG 2 LATTICED GIRDERS POWER HOUSE PORTSMOUTH STEEL CO. PORTSMOUTH, 0. UNIVERSITY BRIDGE COMPANY Rlretsi Holes 41- IN CHARGE OF L 2524 MADE By._S. !V..^2e^M. C To Fig. 111. Double Latticed Girder. 112 PART II — STRUCTURAL DRAFTING located with reference to the working points of the diagonals with due consideration to the edge distances and the maximum spaces allowed (page 69 : 1). For the sake of appearance the plate should be cut so that it is no shorter along the chord angles than elsewhere. In the plate referred to it is convenient to place two rivets directl}' below the end rivets of the diagonals in order to save additional dimensions. The remaining spaces are expressed to the nearest J" so that the edge dis- tances wiU be approximately 1| (in this case It^^). 1. When adjacent diagonals have different numbers of rivets, the connecting plate may be cut diagonally, or else the smaller number of rivets may be spread so that the resulting edge distances will not be excessive. Diagonal cuts should preferabljr extend the full width of the plate in order to save waste; in this case the width of the plate should be the perpendicular distance between the parallel sides even though this is the longer dimension. For other suggestions regarding the shape of plates see page 76 : 1, IX. 2. The size of the end connection plates maj- be governed either by the rivets in the diagonal, or b}' the number of field rivets required, whether connection angles are used or not. Compare Figs. 110 and 111. In general, the rivets along the chords and along the supporting mem- bers should be so spaced that the fuU width and length of the plate are used; that is, the plate should not be cut so that these edges are shorter than the opposite edges. 3. ^Vhen a double system of diagonals is used, as shown in Fig. Ill, the two single-angle members on opposite sides of any plate may be made to overlap in order to take one rivet in common. The adjacent rivets must be spaced far enough from the edges of the angles to allow sufficient driving clearance (page 73 : 5). The angles of such double latticed girders should be riveted at their intersections, with or without washers. 4. All members which are composed of two angles should be fastened together by means of stitch rivets, spaced as explained on page 69 : 4. The spacing in a tension web member may be made the same as that in a similar compression member if by so doing the members are made alike. 5. Typical connections for roof trusses are shown at the centers of both IG 1 and LG 2, Figs. 110 and 111. A girt connection is also shown at the center of LG 1. 6. A latticed girder is often used as a " stiffening girder." It is placed alongside a long-span crane girder with either the top or the bottom chord at the proper elevation so that it can be connected to the top. chord of the crane girder by means of tie plates and lattice bars; in this way the crane girder is stayed against buckling under the effects of transverse thrusts of the crane due to swinging loads, etc. Thus IG 1 is provided with holes in the bottom chord to correspond to those in the top flange of G 2, Fig. 103. In this case the stiffening girder is to be placed between two crane girders, and hence has holes in both sides. CHAPTER XX ROOF TRUSSES Synopsis: Directions are given for making drawings of typical trusses which support ordinary pitched roofs. "Flat roofs" are usually supported either by beams, or by trusses similar to latticed girders. 1. Steel roof trusses are used in mill building construction, or where- ever a comparatively large area is to be covered without the use of intermediate supports. The comparatively flat roofs in office-building construction are usually supported by beams (page 90 : 1). "Flat roofs " which are pitched just enough to provide proper drainage are simplest form it has only a single strut at the center of each top chord, but for longer spans additional panels are added, as shown at a and at b. In the Fink truss the top chord is divided into an even number of equal panels, and the struts are at right angles to the top chord; the number of panels may be doubled by the insertion of another strut in the center .^ .»Z « 1NCHAHGEOF M. G. O. ■^VOLEsi UNLESS mno^^^^^^B^, %/» WASHERS Zix^ KLB,Ms/iB__} Fig. 116. Typical Drawing for a Roof Truss. CHAPTER XX ROOF TRUSSES 117 REQUIRED 1 / HMF TRUSS AHI" / „ AHI'- / f, II XHI" / II II XHI'- 2 MAN6ERS FLI 4 POSTS ME/ ■* „ ME 2 ■* II ME3 6 ,1 NFI 2 RAFTERS MNI" 2 „ MNI'- A „ MN2 ■# „ MN3 Z DIAGONALS MFI 2 GIRTS ^ FIB 2 „ Fli- 2 /' F2 2 „ F3>> 2 „ rai- 2 „ FA" 2 „ F4'- 2 F5l 2 F Si- 2 „ re SHEETS 3 AND 4 SHOULD BE WORKED TOGETHER (SC£ OPPOSITC PA&LI ROOF TRUSSES FURNACE BI//LDIN6 METROPOLITAN STEEL CO. BOSTON, MASS. UNIVERSITY BRIDGE COMPANY WORCESTER puNT H0L£5JiEXC.mEDlZZ°^AM't^m::rjIie_ ay H.TB.^/m/Ja V> ■* RIVETS %" 'OlfSJ^EXCM WASHfliS2i'fe Fig. 117. Gable Girts and Monitor Framing. 118 PART II — STRUCTURAL DRAFTING The web members are composed of one or two angles with the longer legs vertical. The outstanding legs may be along either edge, but for the sake of appearance some systematic arrangement should be adopted. More frequently the backs of the angle are downward because the members appear to be stronger when viewed from below; as a matter of fact the compression members are not so strong, although the differ- ence is negligible. It is sometimes desirable to turn one member with the back on the opposite edge if by so doing two members or two con- nection plates may be made alike. i. The different members of a truss are connected by means of gusset plates. The number of rivets required in each member is determined from the stress in the member, as explained on page 233 : 2. The shape and the dimensions of the gusset plates are determined graphically by means of layouts, as explained on page 76 : 1. When a continuous web plate is used between the angles of the top chord a web member may be connected directly to this plate without the use of gusset plates, pro- vided there is room for the proper number of rivets; otherwise, part of the web plate must be replaced by a gusset plate, suitable splices being used to connect them. The size of a gusset plate may sometimes be reduced if the outstanding leg of an angle is connected to the plate by means of a "lug " or connection angle as shown in Fig. 118 (a). One leg only is connected as a rule unless the number of rivets exceeds 7 or 8. 2. Each truss member which is composed of two angles should have the angles fastened together by stitch rivets, as explained on page 69 : 4. Members composed of two channels are fastened similarly by pairs of rivets with a 2|" or 3" bar between, instead of a washer, as shown in Fig. 118 (a). A careless mistake quite common among draftsmen and tracers is to show stitch rivets in members composed of single angles. This is not a serious blunder, but unless it is detected in the templet shop it may cause the punching of extra holes. 3. Center Hanger. — A light auxiliary member or "hanger " is often used as an intermediate support for the longer bottom-chord members even though no corresponding stress results from the usual loads. Such members are shown by dotted lines in many of the trusses shown in Fig. 113. The purpose of these members is twofold. During erection a truss is assembled on the ground and then raised into its final position as a whole, without falsework, by a locomotive crane or a gin pole; during Fig. 118 (a). this stage the bottom chord is in compression and it may buckle unless the long center chord member is stayed. After the building is completed workmen are likely to attach block and tackle to the bottom chord for the purpose of lifting heavy loads, even though the truss is not designed for this purpose; this is less serious if the long center panel is subdivided. A single light angle is used as a center hanger, with the rivet line at the center of the truss unless it is offset to provide a connection for a ridge strut (see below). In either case the connection at the bottom should be made so that the bottom chord member is symmetrical about the center line to simplify erection. 4. Shipment. — A roof truss is usually riveted in the shop completely, or else in as large sections as can be shipped ; for export each member is usually shipped separately. The maximum height which can be shipped by rail is about 10' -6". If the center height exceeds this amount the truss is shipped in sections, as shown in the diagram in Fig. 116. Each half -truss is shipped on the top chord as a base; if the maximum normal distance exceeds 10'-6", smaller sections must be made. For the method of marking, see page 82 : 2. 5. A ridge strut must be provided as the compression member of the top-chord bracing system, unless purlins at the peak serve the same pur- Fig. 118 (6). Details at the Peak. pose. In a and b, Fig. 118 (6)., are shown two forms of purlins which also act as struts. When the central portion of the roof is raised to the top of a monitor (Fig. 113 (m)) there are no purlins at the peak of the main roof and a ridge strut must be provided. An I-beam may be used (c, Fig. CHAPTER XX ROOF TRUSSES 119 118 (6)), but more frequently a two-angle member similar to S 5 inverted (Fig. 147) is employed. A continuous line of ridge struts is used for the full length of a monitor; when two angles are used in the braced bays either one or two angles are used in the intermediate unbraced bays. The connection plate which projects from between the angles of the ridge strut is inserted between two connection angles on the peak plate of the truss. The center hanger may serve as a connection angle on one side of the truss, as shown in Fig. 116; when so used it is offset so that the strut is in the center of the truss. 1. Purlins are connected to the top chord of a truss by means of con- nection angles as shown on page 315; the larger purlins have a flange connection as well. Angles, channels, and Z-bars are stronger if the upper flanges or legs are turned up the slope. Channels are usually reversed when wooden spiking pieces are used. Purlins are usually bolted in place, and accordingly the connection angles are bolted to the truss, as noted in Fig. 116. Purlins which act as struts are connected by more bolts than the others; the strut connection is used not only in the braced bays but for the full length of the building. In Fig. 116 the purlin at panel point D is a strut purlin; as shown in the plan, cross bracing is used between this purlin and the ridge strut, and also between this purlin and the eave strut. For convenience, the distance between rivet lines in the top chord is made a multiple of I" even though special gages are used in the angles; a single rivet line is used in each angle. 2. Bracing rods may be attached to the top chords by angle clips, as shown in Fig. 116; these angles should be so placed that the rods will pass through one leg at right angles in order that the nuts will bear properly. Rods of minor importance may be bent to pass through holes in the gusset plates; holes are shown in plate pb (Fig. 117) and in pj (Fig. 116) for the rods in the sides of the monitor. Similarly, extra holes are punched in the top chord angles of the monitor for rods. Straight rods may pass through slotted holes in the gusset plates provided beveled washers (shown on page 316) are used to give proper bearing for the nuts. Clevises (page 316) are not used as extensively as formerly, be- cause other types of connection are more economical. 3. Holes must be provided for the bottom-chord bracing, as shown in Fig. 140. The plates are connected to the under side of the angles; when a connection angle is used at the heel, the plate is placed either between the connection angle and the bottom-chord angle or else on top of the latter. The bracing plate which connects to the truss at panel point H serves also as a splice plate for the bottom chord, and the number of rivets in the vertical legs may be reduced accordingly; a suitable plate must thus be provided for each truss even though there are no diagonals to be connected at this point. 4. So many buildings are extended after they have been completed, even though such extension was not anticipated at the time of construc- tion, that it is advisable to make certain provisions for future extension whether specified or not. During the author's experience one building in which no provision was made for extension, was extended three times before it was completed once. If the roof truss at the end of a building is made like an intermediate truss it does not have to be moved when the building is extended. If a special end frame is made with rafters supported by columns, not only the frame but at least one panel of roof and side covering must be removed. If future extension is expected, holes should be provided to facilitate such extension. It is often as cheap to punch a few extra holes in one member in order to make it like another, as to save the extra holes by means of special notes which complicate both the drafting and the shop work. 5. If the ends of a building are to be covered with corrugated steel, girts must be placed on the gable end to support it. When an end truss is used, the gable columns extend only up to the bottom chord and the gable girts must be attached to the truss. These girts are shown in position, and on simple drawings they may be added to the drawing of the truss, as in the monitor. Fig. 117. In case the drawing would be too complex if this method were adopted, a second drawing may be used in conjunction with the first. Thus in Fig. 117 the working lines of Fig.. 116 are reproduced and the girts are superimposed in the proper position. The truss members to which girt connections are to be added are shown in outline, and the new connections are detailed. The two drawings are worked together and a note to that effect should be added to each draw- ing. The required list on the second sheet should contain those members which are made wholly or in part from that drawing, while the hst on the first sheet should contain the members which are made entirely from that drawing. 6. Small holes for louvres are provided in the sides of the monitor. CHAPTER XXI BRIDGE TRUSSES Synopsis: Types of trusses are shown and practical suggestions are given for making drawings of bridge trusses. 1. When Used. — Trusses are used in bridges for which plate girders indicated: thus for example, the "counters "in (a) to {g) iu elusive are are not well adapted either on account of the length of the span or be- stressed only when a portion of the bridge is loaded, the "collision cause of economic reasons. The Umiting length of plate girders is struts " in (c) and the posts iu (k) are used to give intermediate support (a) THROUGH PRATT (e) BALTIMORE OR SUB-PRATT /VVV\ \AA/V (/) THROUOH WARREU 1 J 4 ♦ ♦ ♦ ♦ / 7 y V \ \ ZL / /\/\ \ \ k (rf) DECK HOWE ' (/') DECK WARREN Of) SUBDIVIDED WARREN (m) THROUGH SUBDiriDED WARREN Fig. 120. Types of Bridge Trusses. (n) DECK SUBDIVJDED WARREN approximately 130 feet, but truss bridges are often used for spans of 100 feet or less as well as for longer spans. 2. The most common types of trusses for ordinary bridges are shown in Fig. 120. Cantilever, suspension, swing, and hft bridges are outside the scope of this book. The compression members are represented in the figures by heavy lines and the tension members by fine lines. Dotted Unes represent members in which no direct stresses result from the loads 120 to long compression members, and other members are inserted simply to stiffen the structure or to hold other members in place. The term "Warren " is usually applied to trusses in which both the main tension and compression web members are inclined, forming isosceles triangles with the chords, as in ({) or (J). The most favorable slope of diagonal is 45°; when the panel lengths exceed 25 or 30 feet they may be subdivided, as shown in (fc), (m), or {n). The Warren truss is used for comparatively CHAPTER XXI BRIDGE TRUSSES 121 short deck bridges, and for through bridges of spans from 100 to 200 or 250 feet. A "deck " bridge is one in which the floor loads are applied at the upper chords and a "through" bridge is one in which the floor loads are applied at the lower-chord apices, and the trains pass "through" the bridge between trusses. The "Pratt" truss with parallel chords, (a) or (b), is used for spans from 100 to 175 feet, but for longer spans the "inclined chord Pratt " or "camel back " truss (/) is preferred in order to keep the stresses in the chords more nearly equal. For spans longer than 300 or 350 feet it is economical to subdivide the panels by verticals which extend to the middle points of the diagonals ; auxiliary half diagonals are added either below the center (e) or above the center (g). If the chords are parallel, either type of "Sub-Pratt " is termed a "Balti- more " truss, but if the top chord is inclined the truss is called a "Pettit." The "Howe " truss (c) or (d) is used for wooden trusses, but it is not so well adapted to steel bridges as the Pratt truss because the compression members (the diagonals) are longer than the tension members. The "Latticed " truss Qi) was formerly used for covered wooden bridges but it is not well adapted to steel construction; the stresses are statically indeterminate. 1. The joints of bridge trusses may be either riveted or pin-connected. Only one pin is used at each joint; a pin is virtually a large bolt designed as a cylindrical beam (page 278 : 2). Riveted joints are used for span^ up to about 200 feet in length, particularly on railways, for the sake of economy, rigidity, and durability. Pins are used at the joints of longer spans because the secondary stresses which result from riveted joints are less easily accounted for. Often the intermediate joints of the top chord are riveted, even though pins are used in the end posts and all other members. 2. Arrangement on Sheet. — The smaller and lighter riveted trusses may be drawn with the members in position in order to save the duplica- tion of details, even though the members are to be shipped separately, as illustrated in Fig. 122. More than one sheet may be required in order to show all of the necessary members; these sheets should be used to supplement each other and each should bear a note similar to that in Fig. 122. Reference points or lines may be used to indicate where the dimensions of one sheet end and those of the next sheet begin. For example, the connections at panel points L 2 and U 2 are fully detailed in Fig. 122; on the next sheet these panel points would be repeated and the working lines and the principal dimensions would be made to extend to these points. Enough of the gusset plates and other details should be shown in outline so that the extent of each dimension can be identi- fied, but beyond this no attempt should be made to duplicate details which are completely shown on the first sheet. If necessary a reference line may be drawn on each sheet similar to the line X-X, Fig. 101. Each member of the larger trusses is detailed separately to avoid crowd- ing. All vertical members are preferably drawn vertically if the size of the sheet will permit, and all horizontal members are drawn horizontally, i.e., lengthwise of the sheet; riveted diagonal members are usually drawn either vertically or horizontally in order to save space. Eye bars are drawn on small sheets or printed forms (page 174 : 2). For the sake of uniformity the members of the left half of the truss on the far side of a bridge are shown on the drawings. 3. When members are drawn in position great care must be taken to adopt the best arrangement of views and of dimension lines to avoid unnecessary crowding. The position of the main elevation view of each member is necessarily determined as soon as the working lines are laid down. The proper relation between views must be maintained, but views other than the front views may generally be placed so that they will not interfere with any other member; when this is not practicable a view should be so placed that only unimportant portions of a view need be omitted. For example, the side view of L 1-U 1 (Fig. 122) is so similar to that of L2-U 2 that it is combined with it by simply adding an extra line of dimensions and the necessary notes. If a separate view were necessary it might be drawn at the right of the corresponding front view, part of the member L2-U 1 being omitted where necessary. A drawing may be made clearer oftentimes if one or both ends of a view are offset from the true projection, provided that such offset is clearly indicated much as the center line through P 6 (Fig. 143) is offset for P 7. Space may be saved, when no ambiguity is likely to result, by combining a top view and a bottom sectional view, as illustrated in the end post and the top chord in Fig. 122; only one half of each view is shown, both views being symmetrical about the longitudinal center line. 122 PART II — STRUCTURAL DRAFTING TRUSSES DERBY AVE. BRIDGE OVER C.R.R.OFN.J. NEWARK, N.J. ^ UNIVERSITY BRIDGE COMPANY .VmMH PUNT IN CHARGE OP T :P-'^- ^m , _ -^^ M.OE ,v EP.B. 10-26- 14 r 1780 Fig. 122. Pony Truss for Highway Bridge. CHAPTER XXI BRIDGE TRUSSES 123 1. Shipping Marks. — Members of bridge trusses are identified by tiie marks of the panel points between wliich they extend, as explained on page 82 : 1. It is convenient to have a small key diagram on each sheet to show the location of each member detailed on that sheet, as illustrated in Fig. 125 and 128. 2. Camber. — Bridge trusses are sHghtly arched or "cambered" so that they will assume the desired form under full load. The amount of camber should equal the maximum deflection so that the track will approach a straight line as the load is applied. The position of the panel points should be based upon the amount of deflection, and the lengths of members should be determined accordingly. For long spans the deflection should be worked out accurately,* but for spans up to about 300 feet approximately the same results may be obtained by making the lengths of the top chord members slightly greater than the lengths of the bot- tom chord members. Instead of both shortening the lower chord and lengthening the upper chord, it is more convenient to make the bottom panel lengths equal to the quotient found hy dividing the effective span by the number of panels, and to increase the upper panel lengths enough to provide for the combined change of length in both chords. The amount of this increase for horizontal top chords or for the hori- zontal components of inclined top chords is ^V inch for every 5 feet. The mean panel lengths are used in finding the lengths of the diagonal members. See next paragraph. 3. In pin-connected bridges it is well to note the size of the pin holes, as in Fig. 127, in order to show the size of the pins as well as the amount of clearance allowed for driving the pins. This clearance is usually aV (or ^V) of ^n inch and it should be considered in determining the lengths of the chords and diagonals. Thus if the computed length of a compression member falls about midway between sixteenths the next larger sixteenth should be chosen. The lengths of eye-bar tension members may be dimensioned to thirty-seconds, the full clearance of gV being deducted from the calculated length. 4. Types of Members. — The usual forms of top-chord or end-post members are composed either of two channels and a cover plate as in Fig. 122, or of two webs, four angles, and a cover plate as in Fig. 124. * See Kirkham's "Structural Engineering," McGraw-Hill Book Co. Inc., New York. A cover plate is used on the top to furnish protection from the weather, but batten plates and lattice bars are used on the bottom to simplify the connection of the web members. A common form of bottom chord for light trusses is made of four angles latticed, as in Fig. 122; for heavier trusses four angles with side plates are used, as in Fig. 125. A solid horizontal web plate is impractical because proper drainage cannot be provided; tie plates may be used as in Fig. 125, or batten plates with lattice bars as in Fig. 122. Riveted diagonals and posts may be made of four angles, with a web or with lattice bars, as in Figs. 126 and 122. Vertical posts and hangers should have solid webs opposite the floor- beam and top-strut connections, even though lattice bars are used for the remaining portion. Posts of Pratt trusses are often made of two channels latticed. When single latticing is used on opposite faces of a member the bars should alternate, as shown in Fig. 129. Batten plates and lattice bars should be so placed that ample room is left for driving all field rivets. One or two bars may have to be shipped bolted, as in Fig. 129, so they may be removed temporarily to facilitate driving the rivets. For the design of lattice bars, see page 216 : 4; for the spacing of them, see page 70 : 1. 5. Milling. — The ends of chord members and end posts are milled. This is especially important in trusses with riveted joints in order that stresses can be transmitted by direct bearing. At pin-connected joints clearance of about | is left between the milled surfaces to permit inde- pendent action of the members about the pins. When the members are not in the same straight line a mitered joint is used, the milled surfaces bisecting the angle between members. The slope of each mitered joint should be given to the nearest 32nd of an inch instead of the usual 16th, and also the corresponding angle should be expressed in degrees and minutes to facilitate the setting of the milling machines in the proper position. 6. Splices. — The riveted chords of parallel chord trusses are usu- ally spliced independently of the gusset-plate connections of the web members, in order to avoid complications which might arise if the web members and the floor beams were connected at points where the chords change section. The splices are placed as near the gusset plates as feasible, and logically on the sides of the smaller stresses (Figs. 124 and 124 PART II — STRUCTURAL DRAFTING ISpPIMh 'l-3"(bolt toship) ih- n 4-5,1" 7S3-I-9" /2e/'6"'/8-0" .3@4-W' /-5j" fS/j" 3@4-R}" l2®l-6"'l8-0" 24LanBars2i'h2-3i"croc. 24LanBarsZ^i'2-3i"c.to c. -a ZLatt.Barsh /-2".3e-93B33 I TOP CHORD &V-3» I „ „ Ul-^i- RIVETS i TOP CHORD /SOfT.SJ. THRO muss BRIDGE M/SSACHUSETTS R.R. BOSTON, MASS. DNIVERSITY BRIDGE COMPANY IN CHAHGE rig W.J. B. ^^ MADE RV GAK. JO. 2Q^ 14 1 26 Fig. 124. Top-chord Member for Riveted Truss Shown on Next Page. CHAPTER XXI BRIDGE TRUSSES 125 Sp, PI, 12.x J x 2-e"pc {bolt to ship) 2-0 pd {ban to ship) 2 Sp, PJ s. I4xil/^nt INCHARQE OE.._i!'^'i/'_S' M»DE By.AM:.iOj22lM_ P-JSi CH'K'D BY «■ Oi.'l. J0l3g[l^. Fig. 125. Bottom-chord Member for Riveted Truss of a Railroad Bridge. 1126 PART II — STRUCTURAL DRAFTING 1 2^^sUi ,/i/r b.tob . Ls 2k. nt '\i^ -?,i 9K sf'M M -■i« 1 ■ 1 si ' i % ^^ = 5 i *(S| --L jr :^ *o, H ; . : TO t I ^ , i: -. •*• 1 i\ ® . |bi 5 - ■ -^ ■ @ -en J li2-3*plA ■• ' 2 l ^ls, 2efxTpx 3-8*pc,^ 2 Pis. W xS X A-fi'pd 20xJJ \2-j4pf'' ' ' g Pis. 24 » fT^-si'pg ,2 Pis, 22ixAx Y-zi'ph' * ' 2 Pis. IS xi' 3-IOs^b k REQUIRED 1 2 End Posts EP' 2 „ EP'- IS bars 5 ii~r* 2 -S's, to c. jia Rivets -j Holss'A END POSTS 200 FT, S. T. THRO. PIfi CONK SPAN NEW JERSEY R.R.' TRENTON, N-J- UNIVERSin BRIDGE COMPANY -rrf"??"-. PLANT IN CHARGE Ot-_?i^l^l ,^_ «WBBX.-Bi.TM:MZljA. p. OH'K'D BY. W-Sj.JMIpJli ^ 17B Fig. 127. End Post for Pin-connected Truss Shown on Next Page. 128 PART II — STRUCTURAL DRAFTING REQUIRED 1 2 Top Chords UI-2'' 2 „ UI-2'- 8 Splice Plates SPI TOP CHORDS 200 FT. S. T. THRU PIN CONN. SPAN NEW JERSEY R.R. TRENTON. N.J. 'i / r\ IKK X \A K ^ 7 panels ®28-er=200-ok e. to c. end pins fi/Vets ^ Holes U UNIVERSITY BRIDGE COMPANY _ Trenton plant n< CHARGE OF_?'_^'_Qr ,-^t- M«DE BY C, T^B.il/3/14 r i2_ cwK-0 By 3JjjyMI±. ^ Fig. 128. Top-chord Member for Pin-connected Truss of a Railroad Bridge. CHAPTER XXI BRIDGE TRUSSES 129 ) 34-0 c.to c. pins 4®e=2-0" 4i a®3=g-'0" ^ ja =1 6 9®3=2-'3" 6®6=3-0" 3 3, -Rivs^ cak and chlpbea Shop rivets in far side 25'3i" l^iM .AJ,A.2' d 5J5l^ 2-64 , near side A^ l(^ 6-0 — © — o- 2-l5\S 40*^35' 4i" 2 Pis. 12x^x2 5'5i" 4@3=l'0"3i 26®8=l7-'4" 4®3 = l^0" 7®8-4'8" 4®3=l'0" — -y T^^r ^^lar — — l^ Ijpc pin Hoie ei+i •i~ en 2 Ls4x3i%^x e'-5" aa"*'- I Web lix §x e's'pf 66 Latt. bars 2-^xfx II ^c.to c Note: -Vertical posts are preferably drawn vertically when size of sheet permits. REQUIRED 2 Pests L2-U2'> 2 Posts L2-U2<- Rivets -f Holes if INTERMEDIATE POSTS 200 FT. S.T. THRU PIN. CONN. SPAN NEW JERSEY R.R. TRENTON, N.J. UNIVERSITY BRIDGE COMPANY Trenton pr ^mt m CHARQE np C. M.D. MADE m_E.AS!-JI^/i... n 1^ OH'K-D Bt.M^HjPUI/J2/±_ " 3 Fig. 129. Posts for Pin-connected Truss Shown on Preceding Page. 130 PART II — STRUCTURAL DRAFTING 125). Inclined top chords must be splice^ at the panel points; this usually necessitates the use of splice plates cut with reentrant angles (Fig. 128), although these should be avoided if possible on account of difficult shop work (page 76 : 1, IX (4)). For determining the size of splice plates and the number of rivets required, see page 270 : 2. 1. Reinforcing Plates. — Channel webs and the web plates of buUt members are seldom thick enough to transmit the proper stresses to pins. The webs of pin-connected members may be reinforced by aux- iliary plates to furnish sufficient bearing area on the pins. When the ends of two compression members bear on opposite sides of a pin, extra plates should be added, or one of the reinforcing plates on each side of each member should be extended, to surround the pin; these plates should not be riveted to the other member (Fig. 127). To avoid inter- ference, these plates may be placed outside of the webs on one member and inside on the other. The purpose of these plates is to hold the members in position during erection and also to keep water out of the joints. For determining the size of reinforcing plates and the number of rivets required, see Chapter XLII, page 284. 2. It is often necessary to use countersunk or flattened rivets to pre- vent the interference of different members during erection. Shopmen are accustomed to look for such rivets in certain usual places so it is sufficient to show them by the proper conventional sign (page 40 : 6). When rivets are countersunk or flattened in unusual places, or when they are so inconspicuous on the drawing that they are likely to be over- looked, a note should be added, as explained on page 40 : 6. Some of the more usual places where the rivets must be countersunk or flat- tened are: (a) in the main plates of the shoes which bear upon the rollers or bed plates; (6) in chords, posts, or shoes, to allow for eye-bar heads, for pin nuts, or for- the overlapping reinforcing plates mentioned in the preceding paragraph (Fig. 127) ; (c) in reinforcing plates or fillers under splice plates (Fig. 128) ; (d) in the top of the end post under the connection of the portal bracing in order to reduce the number of field rivets (Fig. 127) ; (e) in posts where rivets are required in addition to the field rivets of the floor-beam connections (Fig. 129). Field rivets should be so spaced that they need not be countersunk; thus in Fig. 128, ample clearance is allowed for placing the pin nut in position. The rivets which hold the angles and the reinforcing plates to the web plates are countersunk underneath the splice plate so they can be driven in the shop; note the manner of indicating these rivets by broken lines to show that they are countersunk back of the plate instead of in the plate. 3. Protection from the Weather. — Joints may be partially protected from the weather by splice plates or by reinforcing plates as described in the preceding paragraphs. Joints which are made at the upper panel points may be protected on top by making the connection plates for the top lateral bracing extend entirely across the chords. Care must be taken not to interfere with the free action of a pin-connected joint by riveting these plates to both members. Bottom chord members and joints should be so arranged that no rain pockets are formed. Drain holes should be provided in the larger bracing plates to prevent the accumulation of water (Fig. 125). 4. Clearance should be allowed to facilitate the erection of web members between the gusset plates which are attached to the chords. The out to out dimensions of the web members should be made | less than the clear distance between the plates. 5. The method of holding a " counter " in the proper position on the pin by means of a notched plate is illustrated by plate pd, Fig. 129. CHAPTER XXII COLUMNS Synopsis: Specific suggestions with illustrations are given for making working drawings of columns for different types of structures. 1. Steel columns form the principal supports of all steel structures other than bridges and similar spans which rest directly upon masonry. They may be of many different forms according to the type of structure. A few typical columns of office-building and mill-building construction have been selected for illustration. Many mill buildings and similar structures have unusual or complicated connections so that it is difficult to proceed with the drawings of the columns until after the drawings of the connecting members have been carried far enough to determine the column connections. When possible it is usually simpler to postpone the column drawings until all connecting members have been drawn. The available time is seldom sufficient to permit this method, however, because the columns are the first members to be erected. The drawings for the columns must logically be among the first drawings sent to the shop, and connections for other members must frequently be provided before the drawings of those other members have been made or even begun. It is often necessary to make a layout of the more unusual connections to determine the necessary dimensions to be used on the column drawings. These layouts may later be used by the draftsmen who make the drawings of the connecting members. Many types of connection recur so frequently that standards are prepared in the draft- ing rooms of the larger structural companies. These standards simplify the work of the draftsmen and in many cases they simplify the work of the templet makers. In fact, wooden templets for typical connections may often be preserved for future use to save making new ones for sub- sequent contracts. 131 2. It is desirable to draw all members in the same relative position on the sheet which they are to occupy in the finished structure. Thus, columns are preferably drawn with their longer axes vertical, as in Fig. 137. This is not always feasible on account of the multiplicity of details, for more space is available if they are shown with their longer axes hori- zontal (i.e., lengthwise). When the columns are drawn horizontally it is customary to show the base or bottom end of the column at the left as in Figs. 133 and 135. It is unnecessary to draw the full length of a column to the same scale as the details. The most common scale used for the details is |" = 1'. The extreme length of the column is made to suit the available space on the sheet allowing for the necessary views and dimension lines. The details are then placed at approximately propor- tional distances apart regardless of scale. No breaks in the views need be shown unless the drawing can be made clearer thereby. 3. So many different types of columns * are used by different designers it is impossible to show them all. Perhaps the three most common types are the plate and angle, the plate and channel, and the Bethlehem H-sec- tion. The drawings for the H-section are comparatively simple since the main section is rolled complete and no continuous lines of rivets are required unless cover plates are used. The connections are similar to those of other columns and it seems unnecessary to illustrate them here.f * See Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Co. Inc., New York. t For typical connections see the "Catalogue of Bethlehem Steel Shapes," Beth- lehem Steel Co., South Bethlehem, Pa. 132 PART II — STRUCTURAL DRAFTING The plate and channel columns are used for office-building construction. The upper sections are often made of channels with lattice bars, the bars being replaced by cover plates in the lower sections. As the loads increase, the thickness of the plates and the weights of the channels are increased and if necessary the width of the plates and the depth of the channels as well. The plate and angle column is used most exten- sively for mill-building construction; it is also used for office buildings. Very light sections are made of four angles latticed, but usually soHd web plates are used instead of the lattice bars. For very heavy loads larger angles are used with cover plates riveted to their outstanding legs. 1. Typical plate and channel columns are shown in Fig. 133. They are detailed for the conditions shown in the diagram of Fig. 158 and in the corresponding column schedule of Fig. 160. The views of the different faces are often lettered for convenience in the identification of the details. The dashed lines of the channel flanges in Faces A and C need not be drawn full length if the drawing is equally clear without. Since considerable time is required to draw so many long dashed lines it is well to omit portions of them whenever feasible. Colmnn AB\ shows the base angles which connect to the cast-iron bases. At the top, splice plates and angles are provided to connect to the superimposed column section composed of channels of the same depth and cover plates of the same width The lower end of the connecting column would be similar to the lower end of Colunm EF 27, differing only in dimensions since the colmnn is of a different size. The ends of office-building columns are milled so that the loads may be transmitted by direct bearing (page 31 : 1). A more complex splice is required where the depth of the channels and the width of the cover plates change. Such a splice "is shown on the column schedule (Fig. 160) ; it is described more fuUy on page 276: 4. Provision for a similar splice is made at the top of Column EF 27. The projecting corners at the top of the splice plates need not be cut (Fig. 277 (a) ) if they are to be concealed by the fireproofing. For the size of the fillers and the reinforcing plates and the number of the rivets see page 276 : 4. The spacing of the channels and the gages are given on pages 300 and 301. Note that for a given depth of channel the distance out to out of web faces and the distance between rivet lines are constant, while the distance back to back of webs and the gages vary with the weight. This is so arranged in order to standardize the splice plates and the beam connections and also to reduce the number of different lengths of beams. 2. The important dimension is the finished length and this is prefer- ably made conspicuous. Since all elevations on the diagrams are referred to the finished floor line it is important to show each floor line on the column drawings and to give the story heights. The beam details are located with reference to these floor Unes and the rivets which fasten the cover plates to the channels are then dimensioned to fill in the spaces between the details. Close spacing of four diameters is used at both ends of the column (page 69 : 1 (cQ) and near the beam connections. Six inch spacing is allowed as a maximum for the remaining distances. 3. Typical symmetrical beam connections are shown on Column EF 27, and special eccentric beam connections on Column AB\. The whole load from each beam is carried by the seat; the top angle serves to prevent the beam from overturning and to help transmit the wind stresses in the structure. The top angles are left bolted so that they may be removed to facilitate erection. They are placed j" higher than the theoretical top of the beam to provide for the spreading of the flanges of the beam while cooling on the rolls during their manufacture. Note that after the cover plates have been riveted to the channels a box section is formed, the inside of which is inaccessible. In order to provide for the temporary removal and the restoration of the bolts in the top angles of the connections on the charmel webs the bolts must pass through the whole column. Unless a similar angle is required directly opposite, a special note must appear to assure the punching of holes in both channel webs for through bolts (face D, ABX). The top angles on the cover plate faces are made sufficiently long to permit the use of short bolts through the channel flanges. If shorter angles were used, the necessary through bolts would often interfere with those through the charmel webs. The rivets in the channel webs and some of those in the cover plates are inaccessible after the column is assembled; thus, the rivets in the seat angles, stiffening angles, reinforcing plates, and fillers under splice plates, must be driven before the cover plates and channels are bolted together. Special gages are used in the 6" legs of the seat angles to conform to the spacing of the rivets in the channel flanges. The CHAPTER XXII COLUMNS 133 §r \ '$7'2 Face A \Faqe C opposite ^ 12 Azthru.SbltshlO Faces B and D r-z" ^ [j, loi M ^Zi-IO \ 2Sp.PIs.l4'i'^l-6fcb \2L^3'3'k-7iad ICapPl.Hl'i'l'oi I bolt for shipment J /5"J Tiers £ and F ■il 4 111 m Ms f Column Mati(EF27 COLUMIVS T'-MiMIO'k'Pl' „,y^^S% ~ TYPICALOFFICEBUIlDIIVe HOLES g Fig. 133. Typical Office-building Columns. 134 PART II — STRUCTURAL DRAFTING bottom ends of stiffening angles need not always be cut back as shown. If concealed by the regular fireproofing or by walls or partitions they may be cut square. The draftsman must be familiar with the methods of erection in order to determine wiiich rivets, if any, should be flattened or countersunk to facilitate the insertion of the beams (see Column EF 27). 1. Sectional views are drawn for each tier of beam connections in order to show the holes in the outstanding legs of the angles. The section is sometimes taken between the top and bottom angles, but more often above the top angles as shown in Fig. 133. In order to draw attention to the fact that the holes should be made in both the seat and the top angles, the holes are often shown in the other views as weU (page 40 : 6). 2. Fig. 135 illustrates a typical mill-building column drawn for the conditions shown in the plans and diagrams of Figs. 155 and 156. The lower part of the column is made wider than the upper in order that the crane loads may be transmitted to the column base more directly. The width of the lower section is usually made so that the outer face of the cover plate or channel comes directly under the center of the girder. Seat angles and stiffeners are used to provide a suitable girder seat as shown. The girder is secured against overturning by means of a dia- phragm. The end stiffeners of the crane girder shown in Fig. 103 are arranged to coimect to a diaphragm similar to that shown in Fig. 135. Holes are provided in the channel web for the girder knee brace shown in Fig. 140. 3. Connections. — At the top of the column a connection is provided for the roof truss shown in Fig. 116. The web plate of the upper section of the column is connected to the web plate of the lower section by means of splice plates designed to develop the full strength of the upper web (page 276 : 2). The outer angles are continuous, and the shorter angles of the upper section extend downward far enough so that they may be fully developed by rivets which connect them to the lower web. Holes are provided in the outstanding legs of the continuous angles for the girts and struts indicated on the erection diagram (Fig. 156) and detailed in Fig. 147. It is customary to punch these holes in both sides of the end columns the same as in the intermediate columns, although the side girts do not extend past the center lines. These extra holes may not all be used, although as far as possible the girts on the ends of the building are arranged to connect to them. The cost of punching a few unused holes does not greatly exceed the cost of omitting them because of the time required to make and to follow special notes, and furthermore, the wrong holes might be omitted. In case the building is later extended the extra holes may be used. The bottom strut at the end of the building (.S 7 Fig. 140) connects to the flange of the channel of Column C 1 instead of to the outer angles to make a more rigid connection and to reduce the lengths of the struts and the diagonal sway bracing. The sway bracing connects to the top of Column C 1 on the inner face by means of a bracket (D 13, Fig. 140). 4. A typical column base as described on page 290 : 1 is illustrated in Fig. 135. An excessive number of coimtersunk rivets in the base plate and the cap plate should be avoided. It is usually impractical to swing a long column around so that these few rivets can be driven by machine and consequently they must be driven by hand riveters. Since these rivets do not have a very important function their number should be reduced to the minimum. Holes for anchor bolts are made -f^" or f " larger than the diameter of the bolts to facilitate placing the columns in position when the bolts are set first, or drilling holes in the masonry for the bolts after the steel is in position. 5. Milling. — A column which supports crane runway girders is in- variably milled at the base and at the crane seat in order that the crane loads may be transmitted largely by direct bearing. The web plate is not always milled at the seat along with the angles and channel because of practical difficulties. 6. Most of the vertical dimensions to the bottom of the column extend only to the upper face of the base plate instead of to the extreme bottom. In this way the dimensions best serve the templet maker and the inspectors who use them before the base plate is in place. In some companies, however, the dimensions extend to the extreme bottoms of the column bases. Draftsmen must be particularly careful to give due consideration to those dimensions which may be affected by the thickness of the base plate. When many different connections appear on a single face of the column, as in the outer face of C 1 and C 2, "extension figures " should be given from each connection to the base plate, in addition to the dimensions from one connection to the next. The extension figures are CHAPTER XXII COLUMNS 135 SASi /p/./a'i'S'o'ca /P/./8''i''/-0"pa 2Fjl/s6xi>'l-7i"fa /P/./8'i'/-0"pb /L6'4'i'/-6'^ac REQUIRED 1 2 COLUMNS C/" 2 c/'- 8 ., C2 COLUMNS FU/^N/ICE BU/ID/JVG. METROPOUrAN STEEL CO. BOSTON, MASS UNIVERSITY BRIDGE COMPANY WORCESTERfyKm IN CHARGE OF fl^-G.O. HOLBS'iumESSmTED ^„.„,„ ^^ H. T.B. 8/2//)B RIVETS i) C^ Fig. 135. Typical Crane Column for a Mill Building. 136 PART II — STRUCTURAL DRAFTING convenient for the templet makers and the inspectors so that they can locate all the connections with a single setting of the tape. The figures are of convenience also to the draftsmen and checkers when referring to a drawing to obtain differences in elevation between connections. When making the drawing the draftsman should record the extension figures for each connection as soon as that connection is detailed. The dimen- sion should extend preferably to the point dimensioned on the diagram, as for example, the back of a girt or a strut angle. Similar connections may then be detailed before other types of connection are designed, and later the other types may be inserted in the proper places. After all connections are located the distance from one connection to the next may be found simply by subtracting the corresponding extension figures. Some companies require a complete line of dimensions from center to center of holes, but this seems unnecessary, particularly when there are comparatively few holes in each group. If the groups are located as shown in Fig. 135 the dimensions can often be taken directly from the diagram, and if the shopmen are forced to use these dimensions instead of calculated distances between adjacent holes one source of error is eliminated. 1. Standard gages in column angles are not used in all cases. In the outstanding legs of the main angles and of the angles in the diaphragm and similar places it is desirable to make the distances from center to center of holes a multiple of J" or preferably |". Thus the use of six- teenths and eighths in the main dimensions of connecting members is avoided. The gages in the angles may result in sixteenths or eighths, but the use of small fractions is confined to relatively few dimensions. Similarly, if girts or other members connect to column angles of different sizes, more members may be made ahke if the gages in the column angles are made the same. For example, the gages in 5 and 6 inch legs may be made equal, and those in Sf and 4 inch legs also. A single rivet line is usually used iu each leg, even if -5 or 6 inches. 2. Two other types of mill-building columns are shown in Fig. 137. Column C 3 is a column for the gable end of the mill building illustrated in Fig. 156. The end truss is made similar to the intermediate trusses and is designed to spnn the full width of the building without iutermedi- ate supports. The chief function of the gable column is to support the end framing (girts, struts, etc.) below the bottom of the truss. The upper end of the column is supported laterally by being coimected to the roof truss at a point where the truss is braced in the plane of the bottom chord; but in order to avoid stresses for which the truss is not designed, the connection angles at the top of the colmnn are provided with vertical slots to permit the free deflection of the truss. The base is designed to transmit the whole load through rivets so that it is unneces- sary to mill the column. In general, a column is not milled unless the load is more than about 40,(X)0# or imless the column is to support a crane or other moving load. Holes are provided in the outstandiog legs of the column angles for girts and struts as in the columns of Fig. 135. 3. Columns C 4 and C 5 are light latticed columns with provision for a roof truss connection at the top. An eccentric beam connection is inserted between the two groups of lattice bars. Connections for light lean-to rafters and for girts are shown in the outer faces. Sep- arate views of these faces are dravm for the two colmnns in order to show the differences clearly. When lattice bars are placed between the angles as in this type of column the distance between angles is not constant; the distance may be determined by the thickness of the plates as pa or pb, by the thickness of a single lattice bar, or by the thickness of two overlapping bars. Consequently either the gages in the angles or the distance between holes must vary. Usually it is desirable to maintain a constant distance between holes so that like members may be connected at different parts of the column. Rather than to dimension each group of holes separately it is well to omit the gages altogether and to let the templet maker make proper provision for the variation; then the distance between holes need be dimensioned only once for each view. For the size of lattice bars and battep plates see page 216 : 2-3. No tie or batten plate is needed at the top because the heel plate of the roof truss will serve the purpose after it is in position. CHAPTER XXII COLUMNS 137 BASE I -PI. I4xfx l'-l"oa 2 Uex B 'Ik II >s 2 Fillip xfxSfa REQUIRED 2 Columns C3R 2 " C3L 8 " 04 2 " CSR 2 " C5L BASE I PI. Mx^x 1^3'ob I PI. I2xlx9pa 2Ltex6xLx ll^ao 2niiiex±xeft> Rivets -f Holes i^unless noted COLUMNS TYPICAL MILL BUILDING Fig. 137. Typical Light Columns for a Mill Building. CHAPTER XXIII BRACING SYSTEMS Synopsis: A discussion of the types of bracing used under different conditions, with illustrations. 1. Some system of bracing is usually required to secure a structure against forces which tend to distort or overturn it. These .forces may result from the wind, from moving loads, or, during erection, from der- ricks or travelers. Diagonal bracing is the most effective but it cannot be used where it would interfere with the use of the structure, as for example across doorways. When it is not feasible to place diagonals entirely across the panel to be braced, special brackets, knee braces, or portal struts may be employed. In some structures the riveted joints may give ample security so that no special bracing is required. In other structures only temporary bracing is required during erection, as for example the bracing between steel columns which are later to be imbedded in solid masonry walls. 2. Bracing systems with full diagonals may be considered as trusses and so designed. The chord stresses of these trusses are taken by the members to which the bracing connects, as for example the columns, the girders, or members of other trusses. The "posts" or transverse compression members may be either special struts or else members which are already provided, such as floor beams, cross frames, or pur- Uns. The diagonal stresses in any panel may be resisted by a single member placed along either diagonal of the panel; if in one position it will be in tension but if in the other position it will be in compression. Usually these diagonal members are designed for tension and are placed accordingly. To provide for forces which might cause a reversal of stress, members may be placed along both diagonals to form "cross bracing; " only the diagonal which is in tension is considered to act at 138 any one time. The sizes of the members and the number of rivets are often standardized for similar conditions in order to simplify the design. 3. Bracing systems with full diagonals should be statically complete; that is, diagonals should not be used unless they are supplemented by the proper struts. Special struts are not always required; for instance an eave strut of a mill building may serve as a girt, as a purlin, and also as the end strut of the bracing in three different planes, viz: the vertical sway bracing between columns, the horizontal bracing between the bottom chords of the trusses, and the bracing parallel to the plane of the roof between the top chords of the trusses. 4. The lines of stress of all members which are connected by a single gusset plate should meet approximately in a common point to minimize the secondary stresses. Adherence to this rule is seldom strictly en- forced, however, because a slight deviation will permit the use of an auxiliary system of working points, as explained on page 108 : 5. A plate which connects only a single diagonal to another member should be so arranged that the line of action (rivet line) of the diagonal will fall within the group of rivets which connect the plate to the other member, in order to reduce the eccentricity. See Fig. 140. 5. Arrangement. — The drawings for cross bracing are usually so made that the diagonals are shown in the proper relation to each other and to the members to which they connect. The system of working lines can then be easily checked, and the connections to other members may be readily compared with the drawings of the corresponding mem- bers. The centers of the end holes in the diagonals are usually chosen CHAPTER XXIII BRACING SYSTEMS 139 as working points. The system of working lines may be plotted to a smaller scale than the details in order to save space; some of the simple diagonals or struts may be shown separately for the same reason. In the simplest form of cross bracing the diagonals are so turned that they may pass each other without interference, as shown in the cross frames, Fig. 142. More frequently the outstanding legs of the two arigles are made to face the same way even though one angle has to be cut and spliced at the intersection. In this position they occupy less space and they are less liable to interfere with other members; it is often necessary to turn them this way to obtain the desired clear open- ing without increasing the height or width of a structure. 1. Initial Tension. — Diagonal bracing must be tight in order to be most effective. A long diagonal will sag under its own weight during erection unless it is drawn tight before it is bolted or riveted. Con- siderable racking of the structure could take place without removing this sag or stressing the member. In order to make a structure more rigid by causing the diagonals to act at once, the length from center to center of the end holes is made less than the calculated distance. The member may then be drawn into position for bolting or riveting by driving a tapered drift pin into the holes. Since the holes are punched -iV" larger than bolts or rivets the member should be shortened iV" to take up the "play " in the holes and at least another ^" to overcome inaccuracies in punching and other factors. Tightness is thus insured even though a certain amount of initial tension may result. The total amount to be deducted from frhe calculated distance from center to center of end holes should be either |" or j%", whichever will make the main dimension a multiple of |". In this way the half lengths will be expressed in multiples of xV", and 32nds will be avoided. Sometimes the amount deducted is noted, as in T 1, Fig. 143. The chief benefit of such a note is to give assurance that provision has been made for some deduction. No deduction should be made for comparatively short stiff members such as the diagonals in the cross frames or the lateral bracing between the girders of a deck railroad bridge, because it would be diffi- cult to connect them. 2. Connections. — The diagonals and the connection plates are usu- ally shipped separately although some of the smaller plates may be fastened to the angles. The bracing for all bridges and many buildings are fully riveted in the field. The bracing for parts of some buildings may be bolted if the specifications will permit. When the field connections are to be bolted, similar shop connections may be bolted also (Fig. 140) ; if there are other shop rivets to be driven in the same member it is about as cheap to use rivets instead of shop bolts in the end connections. 3. Special gages are often used in bracing angles. The rivet line of a single angle is used as the working line. If this working line is placed in the center of the leg the connections may be detailed to better ad- vantage. The clearances on opposite sides are thus made more nearly equal regardless of which way the angle is turned when erected. In angles with legs less than 3" standard gages should be used to allow greater driving clearance for the rivets or bolts. 4. Typical illustrations have been selected to show the common forms of bracing used in different structures. The general arrangements are shown in the erection diagrams of Chapter XXV (page 151), but the details are shown in the drawings of this chapter. 5. A mill building can have no system of bracing which obstructs the interior and prevents the free movement of cranes or other objects. Cross bracing is commonly used in the sides, the ends, and the roof, while knee braces are used to stiffen the connections of the intermediate trusses to the columns. Angles are used as diagonals in the plane of the bottom chords of the roof trusses, and in the vertical sway bracing between columns, both on the sides and on the ends. Rods are used as diagonals in the planes of the top chords of the trusses, and in the sides and the tops of the monitors. The end panels of the building are usually fully braced in all these planes. See Fig. 156. Only every third or fourth intermediate panel is similarly braced with diagonals although the struts extend the full length of the building. The struts in the braced panels are usually heavier than those in the unbraced panels. In the plane of the bottom chords additional diagonals are so placed as to form a large system of cross bracing which extends the full width of the building. Vertical bracing is sometimes used between trusses at the center. 6. Fig. 140 shows the bottom chord bracing and the end sway bracing for the mill building represented in Fig. 156. The working lines are 140 PART II — STRUCTURAL DRAFTING 114-3' !k'l9''Zi'ljS •=g?i u... g ^ 24-4" f9-0" D'7 D6 Co/Truss^ 43~ M, P n-o^' iii §k. M /S-'4£' Fl ^ n5i'3'l'l'2'(cutfrom6C} / -iw Botfof Truss 2-5i' . 1 . l4-5i" /S'/j ' 17 -6i" 3L 1$ 4-3 R£OU/RED 4 D/AGOmiS Dl 4 „ DZ 4 D3 3 D4 3 DS 3 D6 4 D7 4 T/ES D8 Z D/AGOJV/^LS D/Z" z D/Z^ z D/3" z D/3'- 4 0/4 4 STRUTS S/ Z S?" Z „ S7'- 10 /<-/\f£EBRAClS A/** 10 H a /(/>■ 12 PLATES Ml 4 M2 4 M3 4 „ m^ RIVETS i ffix£slii/mssma> WASHERS Zi" ,i Spac/nff nolffiven '2z BRAC//VG FURMCE BU/LD//VG Jtf£T/iOPOUTAIYSTF£l CO. BOSTOAf. MASS. UNIVERSITY BRIDGE COMPANY yyo8ccsT£R. plant - CHARGE OF M-G.O. ^ M»DE Bv .A.S.D.'/i2/ia I . 1776 C.W.B.^/is/ia Fig. 140. Typical Bracing for a Mill Building. CHAPTER XXIII BRACING SYSTEMS 141 referred to the working lines of the trusses and columns for convenience in checking the field connections. The working lines through the end holes of the diagonals are placed to make the clearances on each side approximately equal, as explained on page 77 : 1. The main dimensions of the diagonals between end holes are made less than the calculated distances, as explained on page 139 : 1. For the sake of appearance, the corners of all plates should be concealed by the angles. They should preferably be made to fall at the edges of single angles, but this is not of sufficient importance to justify any increase in the size of the plate. The comers of diagonal cuts can be shown at the edges of angles drawn in position, or dimensions can be given if the angles are not in place. On account of the difficulty of holding narrow plates in the shears while long diagonals are being cut, the comers of splice plates such as pa or pb are often cut at 45° instead; these cuts are shown but not noted. 1. Unsymmetrical bracing is illustrated by the end sway bracing of Fig. 140. The bottom strut S 7 connects to the flange of the channel of C 1 (Fig. 135). The roof truss serves as the top strut, the bracket at the top of D 13 being connected both to the truss and the column; note that the angle which connects to the truss is cut to clear the fillet of the angle ma (Fig. 116). After the working points have been located, the length and the slope of each diagonal can be found in the usual man- ner. The position of the intersection of the diagonals relative to the lower working points can be found by solving the triangle of which these three points are the vertices. The angles may be easily determined and the horizontal side is known. The remaining sides may be found by equating the ratios of the sides to the sines of the opposite angles. For example, the angles are determined from their cotangents as fol- lows: log 14' 5i" = 1. 15949 log 15' 4f" = l.' 18740 log 21' 2|" = 1 . 32651 log 21' 6i" = 1 . 33328 log cot =9.83298 log cot =9.85412 angle = 55° 45' angle = 54° 27' third angle = 69° 48' = 180° - 55° 45' - 54° 27' The remaining sides are found as follows: log 14' 51" = 1.15949 log sin 55° 45' = 9.91729 colog sin 69° 48' = 0.02757 1.10435 length = 12' 8f " logl4'5i" = 1.15949 log sin 54° 27' = 9.91041 colog sin 69° 48' = 0.02757 1.09747 length = 12' 6^-g" These lengths should be reduced by tV" because the total lengths have been shortened |" to insure tightness (page 139 :l). 2. i?^ 1 is a typical knee brace to connect a crane girder to a column. Two types of connection are shown, one at the top and the other at the bottom; note that in each type the line of action falls well within the group of rivets (page 138 : 4). 3. Typical bottom lateral bracing for a through girder bridge is shown in Fig. 142. The plates are connected both to the girders and to the floor beams. Small angles ma are used to connect the diagonals to the bottom flange angles of the stringers; this is done to prevent longi- tudinal movement of the stringers due to traction and braking stresses. The bottom lateral bracing of a truss bridge is similar to that of the girder bridge except that it is usually made heavier because of the in- creased span. The single angles are often replaced by double angles. 4. The top lateral system of a through truss bridge cannot be made a complete system of cross bracing extending down the inclined end posts to the supports because a clear passageway must be maintained at the ends of the bridge. Cross bracing is used in each panel of the main top chord, but a portal strut is used to transmit the corresponding stresses to the end posts which act as girders in carrying these stresses to the supports. The portal struts and the intermediate struts or sway braces are made as deep as the required clearance will allow; in general they are made much heavier than they were a few years ago, to give greater rigidity, particularly in railway bridges. The intermediate sway braces are usually made of four angles latticed, as SB 1, Fig. 143; more elaborate bracing is used in bridges with inclined top chords because of the greater depth available. Many different types of portal struts are used, as for example the solid web type, PS 1, Fig. 143, or the latticed type. Fig. 149. Since the portal strut is in an incUned plane, the outer angle at the bottom forms a trough which should be provided with 142 PART II — STRUCTURAL DRAFTING 1^^^ 7-0" c. toe. Girders •^^ ^E A t'4@3i-/-3" Njc: ^'^■93{4i "^ - ^^ 1 /l6'4'S»6-6i"yya \4s3\=/-3 /i6'4'l'6'6i'w6 5-3i- fUUi ^l r^sf "s'^'"' ^ k^ Jm^ -mis' A^^ ^ „— s: — • — 4 • — • — 6-3i" n! jA \3i'3i4'6-6i' wd , ^ r3-7m'c.foc.f.B. f/-//i" S N^I/1^l\^\l^1i/|^ aiv£TsS MOLES '4 BRAC/JVG TYP/CAL e/RDER BR/D6ES Fig. 142. Typical Bracing for a Girder Bridge. CHAPTER XXIII BRACING SYSTEMS 143 Fig. 143. Typical Top Lateral Bracing for a Railroad Truss Bridge. 144 PART II — STRUCTURAL DRAFTING drain holes to prevent the accumulation of water. The comers of some of the angles of a portal may be cut at 45° if the appearance is improved thereby. The intermediate top struts or sway braces can usually be made deeper than the top chords; lattice angles are used when the depth is too great for the use of lattice bars. The connection plates at the ends (p/) must be cut out to clear the angles of the top chords; this is one of the few places where reentrant cuts are used. Such cuts are usually made by punching a series of connected holes the same size as the rivet holes, and then chipping off the remaining points with a pneumatic chisel. A small curve is drawn at the vertex of the reentrant angle to show that it is unnecessary to chip out the extreme corner to form a right angle. The top laterals or diagonals are composed of one or two angles in the lighter bridges and two or four angles latticed in the heavier bridges. The latticed members connect to plates which are fastened to the tops and the bottoms of the chords; the depth is thus determined by the depth of the chord members, being made -^^" or \" less than the clear distance between the lateral plates^. The upper lateral plates which serve to cover joints in the chords extend the full width of the chords; other plates connect to, the inner side only. Plate P 6 connects to the chord U 1-3 (Fig. 124), and to the top of SB 1. P 7 connects to the_ upper face of the angle on the bottom of the chord and to the vertical plate of SB 1. The diagonals fit between these plates. Plate P 4 connects to the top of the chord and it is bent up to connect to the top angle of the portal strut PS 1. The holes in the bent up portion should appear as ellipses instead of circles, but on account of the difficulty in drawing small ellipses, circles are sometimes used when no misunderstanding is likely to result. P 5 connects to the bottom angle of the top chord, to the vertical face of the end post, and to the end plate of the portal strut PS 1. The angles on this bent plate are not shown in true projection because the drawing would be made un- necessarily complicated. The bend in the plate is clearly shown and dimensioned. If the holes in the angles mh were to be shown accu- rately as circles two additional views would be required. It seems equally clear and more convenient to draw the top view of the angles directly above the elevation and to show them conventionally by three lines to faciUtate dimensioning the rivets and holes; confusion would result if both the rivets and the holes were shown in this view in exact orthographic projection. Care should be taken, however, to give dimen- sions only in the views where the corresponding distances are shown in true projection. 1. Brackets. — The compression chords of bridges where no top laterals can be used must be braced in some other way to give inter- mediate support to the compression members to prevent them from buck- ling. "Pony trusses " are trusses which are not deep enough to permit the use of overhead bracing. They may be braced by means of brackets such as that shown in Fig. 144. Similarly, the compres- sion flanges of through plate girder railroad bridges are braced transversely by nieans of brackets or deep gusset plates at the con- nections of the floor beams to the girders, as shown in Fig. 99. Through plate-girder highway bridges are braced in much the same manner except that it is impractical to use as wide plates on account of the en- croachment upon the clear roadway. The narrower plates are sometimes supplemented by other plates or brackets on the outside of the girders. 2. Deck plate girder bridges are braced vertically by means of cross frames such as shown in Fig. 142. The frames at the ends of the bridges {CF 1) are made heavier than the intermediate ones {CF 2). The cross frames are connected to the stiffening angles of the girders and also to the plates of the lateral bracing which are attached to the under sides of the top flanges. The key plan in Fig. 142 shows a typical layout of the lateral bracing, single angles being used for the diagonals and also for the struts between the cross frames. This lateral bracing is often drawn on the sheet with the girders so that the connection plates can be shown in position, in order to save the duplication of many of the dimensions. The spacing of the holes in the cross frames and the stiffen- ing angles should be so arranged that a clearance of ^V" is allowed I ^ 04\ Vl ) I'f'i : f is"i i • ^^Pla^ Fig. 144. CHAPTER XXIII BRACING SYSTEMS 145 between the tops of the cross frames and the lateral plates; in case the cross frames connect to bottom lateral plates as well, ^" clearance is allowed at the bottom and 5" at the top. 1. The wind bracing of an office building depends upon so many factors that it is impossible to discuss it comprehensively here.* The form of the building, the number of floors, the number * See Fleming's "Six Monographs on Wind Stresses," Kirkham's "Structural En- gineering," or Ketchum's "Structural Engineers' Handbook," all published by McGraw- and the position of the partitions, and the position of the doors and windows, are points to be considered in selecting the form of bracing. Diagonal bracing, portal bracing, knee bracing, and brackets are the more common types. Typical brackets for connecting oSice-building beams and girders to columns are illustrated in Fig. 145. Hill Book Co. Inc., New. York; also Burt's "Steel Construction," American Technical Society, Chicago. Fig. 145. ,, CHAPTER XXIV MISCELLANEOUS FRAMING Synopsis: Girts, struts, plate work, and skew work. 1. Illustrative Drawings. — In this chapter are given a few miscellane- ous drawings to supplement those of the preceding chapters. Taken as a whole, the drawings in this book have been chosen to illustrate different types of members and different methods of detailing. No attempt has been made to show the working drawings of complete structures, although in some cases several different members of the same structure are shown. It is felt that there are enough drawings to illustrate the fundamentals of structural drafting, and at the same time to show many of the more common kinds of connection. 2. In Fig. 147 are shown some of the girts and struts of the mill build- ing of Fig. 156. F 7 and F 8 are typical intermediate side and end girts, with holes in the outstanding legs for bolting the window frames in posi- tion. The side girts in the end panels are the same as in the intermediate panels, but the end girts which connect to the comer columns are made long enough to support both the side and the end corrugated steel at the comers. Thus i^ 9 is an end girt which connects to the inside face of the outer angles of column C 1 (Fig. 135), and extends beyond the column until it is flush with the outer edge of the side girts. If possible the con- nections for these end girts are made so that the holes in the comer columns are spaced the same as in the intermediate columns; this not only simplifies the drafting and the shop work but it also facilitates future extension of the building. F 10 is an intermediate support for the louvres; it connects to the purlins which are attached to the side of the monitor (Fig. 117) as indicated in the side elevation. Fig. 156. M 5 is a hanger or sag bar which is used in place of a sag rod to support a long girt wherever a window prevents the use of a rod. 146 3. /S 2 and S 3 are typical eave struts ; they serve as girts and as purlins to support the corrugated steel, as well as struts for three differ- ent systems of bracing (page 138 : 3). Each channel is stiffened by an angle which extends the full length between the connection plates. Holes are provided in jS 2 for the sway bracing which, at the bottom, connects to the strut S 4 shown below. S 4, iS 5 and S 6 are typical two-angle struts used in the sides and the ends of the building; they serve also as girts. 4. Fig'. 148 shows a drawing of some of the steel plates of a roof for a cast house around a blast furnace. This is not as common an application of plate work as floor plates or the plates in a tank, but in simple form it illustrates the method of dimensioning. In tank work the rivets must be placed closer together and the outer edges of the overlapping plates must be beveled for calking, in order to make the joints watertight (page 69 : 1). 5. Skew Work. — Some of the connections encountered in structural work require more than ordinary computation in determining the proper angles and dimensions. Common examples of this class of work are hip and valley roof construction, skew portal bracing, bins, chutes, hoppers, etc. The details and the corresponding calculation for the construction of different types of intersecting roofs have been so fully treated by the author in another volume * that they are not even summarized here. A complete mastery of that book should enable the draftsman to apply the principles to the solution of other problems of a similar nature. One form of skew portal is illustrated in Fig. 149; it is designed to connect to * "Hip and Valley Rafters," John Wiley and Sons, Inc., New York. CHAPTER XXIV MISCELLANEOUS FRAMING 147 \ p. . 1 ■ . , > — » • — ' f • • — ' — 1 >- 1 L-ok ', 3 2-e"=7-e" 1-3". l-3'\ 3 ® 2-8=7-6" l-sil'F 8 T* ' - fl 1 H^;^ '^ . V (O. / Pl.S xf^KBi-ps" Ibolt^lli'- '■-/ I L4naxf-^xlB'-7"for FT pa \. J 1 L4x3x^x 20-5 f for F8 1 bolt 'Z l9-4i- J F8 Ij 20-3" &^. 3 rt 'Face of Col, r ! ^d — — — J; o ■ • ' t T u J 3 ht 4-2" 2-e" 2-S" 1^3" 1^3" 2-6" 2-8" l-Oi " h '" jC °>it d 2 1 4 \ -1 |— ^ ^1 — (^ i~ ' — ^ f L<-^ 1 L4x3xf,x I7-8^'F9 pe\. S L ex4xfxSma ^ i bolt 2 bolts j- xlJ- , , * ' 17-21" '? Top of u > : IS. -% J '' \ > = *o (3 <4>ii CV3 Oi -J II K. , 1 L -1 Bott. of U ■I/ 24 /)0 cut on n pb for S2 i) po for S3 I PI. l3xf}X l-7'pb for S2 \l PI, 13 xix l'-7"pc for S3 / \j^.'Holea i/i pb only line \lOi: K: ^4 A — Holes In pd only pe oj/t on this line irXT^ — S4, S5 SB X ?i 2i I PI. 13 X fix 1-4 pd for S4 I PI, I3x^xl-4pe for S5, S6 / lie X 4 XT X 19-7" (.„. lLex4xix is'-ioi'i ■ I LBx 4x -ix 20'-5ii<,f, ILex4x 'fx 19^9" y^ Stitch rivets abt. 2'-6"sp3. SS ± l9-4i" 20-3" pd for S4 pe for ss; se REQUIRED 1 40 eirts F7 8 F8 8 ■' Fa" 8 " F9'- 20 Hangers FIO 32 " MS 4 Struts S2 6 " S3 4 tf S4 e S5 2 se Spacing notglvei) =2y- Rlveis-lr Holes j^unfess /ii Wask - ' ' fers 24- X— •« IS wted GIRTS, STRUTS ETC. FURNACE BUILDINQ METROPOLITAN STEEL CO. BOSTON, MASS. UNIVERSITY BRIDGE COMPANY \^orcester p| j^^t IN CHARGE OF ^' ^' 0- MADE HY A.S.D. 8/15/18 r>_ CH.K'o ry C.W.B. 8/18/18 t> Fig. 147. Typical Girts and Struts for a Mill Building. 148 PART II — STRUCTURAL DRAFTING •+.E li-' FIII4xTif5-e"MS 6@I-0=S'-D" 5-6" ni/4xfex3-3TM7 ■4'} -imi 4^ ^ P/O pi,tr>^^u lrS>J62!; pa PIO pa S2 PIAN or MO/VITOR S3 S3 S3 S2 ^^W ^/'^ P2 H->^ P3j> ( ® P2 j P/'- \ fifi® P5 1 /; ^ ^>^ ^ pa pa ^iy ^ X^ _25«C 55C sati -4g7 VJ PLArV or ROOF _m S3 JET \r7 [F7 \r7 _S5 PB\ S3 \TT in. \I1. \r7 ss [p& S3- HZ. J£7 L£Z. \r7 ss s® 20-0"' wo' 0" '^^.:nL^I% ^U^ \^>'^^l^l-^^\ n^n^i ¥^ T T -'jML ^33^i 17V' Drill holes in Field for Crane Stops CSI £lev. oF lopofra/l-161'O" /TVs' i- % 61 33-Ok" » Gl U 33-oi" e\ elevatioitofthe top of a beam abone or ' below the finished floor fine. ilori) TYPICAL BUt»-COHn£CTtON GENERAL NOTES All rivets and bolts ^ "^ All field connections wifhm 2-0"of columns toberivetee/: alf others to be bolted. PARTIAL PLAN 2 dP FLOOR - 'B' TIER TYP/CAL OFF/CE BU/LDf/VG. Rg. 158. Partial Floor Plan for an Office Building. CHAPTER XXV ERECTION PLANS AND DIAGRAMS • 159 59 and 61 are billed. The relative elevations of ull beams and tie rods should be indicated. A general sketch may be drawn for most beams, while the elevations of the tops of exceptional beams above or below the finished floor line may be indicated by dimensions in parentheses. The type of connections for beams to beams and beams to columns should be determined and preferably shown on the plan. Since the lengths of the beams which connect to the columns depend upon the sizes of the columns it is convenient to place near each column small figures to indicate the distances from the center of the column to the outer faces. Thus for the channel columns shown, one figure gives the distance from the center to the outer face of the channel (constant for a given depth of channel), and also the distance from the center to the outer face of the cover plates (varies with the thickness of the plate and also with the depth of chan- nel). After these figures are completed and the type of connection determined, the length to be ordered may be placed on each beam. The experienced draftsman can now quite easily assign to the beams the numbers of the identification marks. The floor number or letter of the complete identification mark (see page 81 : 5), is given once for all in the title and need not be repeated on each beam. The lengths of tie rods should be indicated on the plan. Some companies assign a letter with consecutive numbers to the rods, as X 1, X 2, etc. A better method is illustrated in the plan shown, where the identification mark in the circle is the length of the rod in inches. See page 82 : 3. It is unnecessary to mark every rod on the plan when a single mark be- tween continuous lines of beams will suffice. 1. Plans for different floors may be combined when quite similar. The column dimensions and beam lengths may differ but these differ- ences may be indicated without drawing separate plans. Ordinarily, separate plans are drawn for the first and second floors and the roof, the intermediate floors being combined in a single plan. 2. A column schedule is often prepared for use in the drafting room, although it is not indispensable to the erector. One form of column schedule is shown in Fig. 160. One space is laid off horizontally for each column, and the story heights are plotted and dimensioned verti- cally. Heavy lines are drawn to indicate the milled ends of the column sections at the spHces and at the extreme bottoms. The line at the bottom is shown broken, when the column bases are not all at the same elevation. The component material for each section is given, and also any fillers required at the splices. The cap plates are indicated clearly by shaded spaces so that the proper main material will be ordered short to allow for the thickness of the cap plates. The reinforcing plates may be given just below the cap plates. The loads or the column areas are sometimes given, but this is usually unnecessary. If one whole column from basement to roof is like another in section and in length, it may be referred to the other in order to avoid needless duplication. A typical column splice is often shown on this sheet so that it may be approved before the detailed drawings are far advanced. The column schedule may be made to serve as an index to the drawings upon which the different columns are detailed; the drawing number may be placed at the top of each rectangle as shown. 3. A tabular record of drawings is usually made for each contract. This provides for the initials of the draftsman and the checker for each drawing with dates showing when the drawing is completed and checked. Dates are recorded to show when prints are sent for approval and when approved, and when prints are issued to the different shops, to the inspector, to the erector, and to others interested. These tabular records are arranged to give the necessary information regarding sheets, but they do not give complete information regarding the members. In office- building work especially there are so many similar drawings, such as columns and beams, that it is difficult to make sure that the drawings are prepared in a logical order unless supplementary records are kept. On account of limited storage facilities near the site of an ordinary office building all material must be shipped as required. The squad foreman should guard against having the roof beams and columns detailed while some on the first tier remain untouched. Blueprints of the plans and the column schedule may be used to excellent advantage as progress record sheets, as explained in the following paragraphs. 4. Progress Record for Beam Drawings. — A blueprint of one of the floor plans is assigned to a draftsman who is to prepare the working drawings of the beams. As the drawing for each beam is completed, the draftsman should mark the plan with a distinctive color, say yellow. An ordinary check mark is not sufficient to clearly show his progress. 160 PART II — STRUCTUEAL DRAFTING Top oflO"ls 1 2 3 4 5 26 27 28 29 30 \ 31 32 35 54 35 55 57 58 59 60 CJS^^ : I Roof *;/? ^10 in 10 ^10 t-.II'dS // II II %if~^ II II // // // // // II II II Roof -te- en ■'/?" r/er 2-^, 5 -a 2^ :,& "3 ^ u '2» S| -J -S 7^ c!l IN ^4 1 illers « 1 = t 03 CO cts CO CO CO CO c:^ ^ t-^ *-!= J "N ^-1= 03 •a i O C:> O O O t> O o <;j 3rd Floof "C" Tier ~o « -O ^ s-.^- Aj m / FT V V / "A" Tier 'A, Cjrb <^ « A\ / \ ic Basement ..\ Floor -r <^ 'l 01 Floor 1 vi Top of CI. Bates 1 2 3 4 i'ff 27 28 29 30 31 3^ 53 5ff 57 58 59 60 5 3 4 3 5 lndfcates^"Cap Piste rm I ii I Ml Li | oi | o otor — ^""6™- "•I Wl Plate- ol n i"ii 1 ■I Il I JLi Plate ^Finished Floor I Reinforcing^ Plates ;o"i3 Typical Column Splice PARTIAL COLUMN SCHEDULE TYPICAL OFFICE BUILDING Fig. 160. Partial Column Schedule for an Office Building. CHAPTER XXV ERECTION PLANS AND DIAGRAMS 161 He should draw the crayon the full length of the beam so as to completely obscure the white line on the blueprint. In this way the whole tone of the print is changed from white to yellow, and the squad foreman or the chief draftsman can tell at a glance without interrupting the draftsman what proportion of the beams are detailed. Furthermore, when the draftsman has completed the drawings he can scan the print and easily detect any beam which he may have overlooked because a lone heavy white line will stand out conspicuously among the yellow lines and the fine white dimension hues. It is desirable to have all beams on one plan detailed by one man in order to insure uniformity of details and to avoid duplication. If the available time will not permit this, the work may be assigned to more than one draftsman, but the division should be made definite so that no beam in one portion is like any beam in the other portion. This may often be accomplished by assigning the wall beams to one man and the intermediate beams to the other. If a plan represents one or more floors, the beams for all the floors are usually drawn at the same time. Many of the beams may be combined upon the same sketch provided different marks are assigned the beams of different floors as in C 17, D 17, etc.. Fig. 92. Another blueprint of each plan is given to the checker who marks the beams as he checks the corresponding drawings. He uses a different color of crayon, say red, but he marks the plan in the same manner as the draftsman in order to obscure the white lines of the beams. 1. A print of the column schedule may be used for a progress record for the columns. All records for one contract should be made upon the same print. This may be posted upon the wall if accessible space is available or it may be filed near the squad foreman's desk. It is con- venient to have this record near the tabular record of drawings, for the two are frequently used together. Almost any amount of information can be recorded upon the print of the column schedule to satisfy the requirements of the men in charge of different drafting rooms. Sig- nificant colors and arrangements may be used for different needs. Yel- low and red are most distinctive while green, brown, or black may be used when additional colors are desired. The following suggestions may be used as a guide. Each column section is represented by a rec- tangle bounded by adjacent vertical lines and heavy horizontal lines (see above). Any system of marks should be confined to one of these rectangles, the other rectangles being marked similarl3^ The draftsmen should use the same color of crayon (yellow) as in beam work. In order to indicate that he is working upon a certain column or group of columns a draftsman should draw a diagonal line across the rectangle of each column of the group so that no one else will duplicate his work (see column AB 31, Fig. 160). When he has completed the drawing and it is ready to be checked he draws the other diagonal {AB 32). The checker adds a red circle or oval to each column as soon as it is completely checked {AB 33). A green vertical line may be drawn through the center of the rectangle when prints have been sent for approval {A B 34) and a horizontal brown or black line may be drawn across the center of the rectangle when prints have been issued to the shop {AB 35). Other records may be made by means of horizontal lines drawn across the rectangle above or below the center, using any of the above colors pro- ^•ided all horizontal lines with different significance are of different colors. By drawing the lines entirely across each rectangle continuous lines are formed when all the columns are marked. This simplifies the detection of any omissions because a break in a continuous hne is conspicuous. CHAPTER XXVI MATERIAL ORDER BILLS Synopsis: Preliminary lists of material are usually prepared in the drafting room for each contract before the drawings are made. These order bills are sent to the Order Department where the material is ordered from the roUing mills. 1. Purpose. — The chief function of a structural steel company is to build structures from steel which is already rolled into common com- mercial shapes. The drawings show how such shapes are cut, punched, and combined to make members which are subsequently connected to form complete structures. Some companies have their own rolling mills but most companies procure their steel shapes elsewhere. In either case the material must be ordered from the rolling mills. Usually it takes so long to have an order filled that it is impractical to wait until the working drawings are made before placing the order; often both the drawings and the templets can be made during the interval that elapses between the placing of the mill order and the delivery of the material. It is therefore imperative that all important material be ordered as soon as possible after a contract is made. 2. The original lists of material are prepared in the drafting room by men who are familiar not only with drafting room methods but also with the requirements of the Order Department. On these lists the material is classified according t» types of members, as for example, columns, trusses, beams, etc. In the Order Department new lists are prepared to meet the requirements of the rolling mills. On these lists the material is summarized and reclassified according to sections and lengths and an item member is assigned to each different item. Short plates and angles are usually ordered in multiple lengths to be cut to the desired lengths after they are received. Most companies carry a certain amount of material in stock for immediate use. The stock yard is under the 162 jurisdiction of the Order Department, where the necessary material is ordered to keep the yard supplied with the desired amount of stock. All additions and subtractions should be so recorded that one can tell at any time just what material is in stock. In the Order Department it is determined whether an item shall be taken from stock or ordered from the mills. 3. Methods. — When market conditions are such that there is likely to be considerable delay in filling an order it is especially urgent that all main material be ordered at once. Capable men are assigned to this work in order that it may be done as efficiently and expeditiously as possible. These men can often foresee the details of construction with sufficient accuracy to enable them to order much of the material by referring to the design sheets. In more complex work they may have to lay out some of the details which determine the lengths of main material. The lengths of angles of light trusses may often be deter- mined with sufficient accuracy for ordering by scaling a drawing without stopping to calculate the lengths. For this purpose a draftsman begins a working drawing; he lays down the working fines to scale and draws the outUnes of the angles. The angles are usually ordered about If" longer than the scaled lengths, to provide for inaccuracies. After the lengths are scaled the drawing may be laid aside until later, if desired. The beams and columns of office buildings can be ordered more satis- factorily after the erection plans and the column schedules have been prepared, as explained in the preceding chapter. CHAPTER XXVI MATERIAL. ORDER BILLS 163 1. Miscellaneous material other than structural steel shapes should also be ordered as early as possible so that all wUl be available when needed. Some of the more common examples of such materials are: eye bars, rails and rail fittings, pins, forgings, castings, pipe, corrugated steel and other roof and side coverings, lumber, windows and doors, and hardware. 2. The material order bills are divided into two parts. The first part is the main list of material and the corresponding description which are made in the drafting room in accordance with this chapter. The original sheets are written with copying pencils; these originals are sent to the V Order Department. A carbon copy is also made for use in the drafting room. After the corresponding mill orders are written in the Order Department, the second or central part of the original bills under "Mill Order" (Fig. 163), is filled in by the Order Department; copies of the sheets are then made in a copying press, and the originals are re- turned to the drafting room. The central portion shows the item numbers and other information required by the men who itemize the shop bills (page 169 : 1). Nothing but the item number is given unless the number of pieces, the section, or the length differ from those shown in the main part of the bill; all the differences are recorded. The sec- tion seldom differs except for material to be planed or recut at the shop. The length may differ by a small amount recorded in the column headed " + ins.," or by a large amount when material is in multiple lengths. The number of pieces may differ when pieces are ordered in multiples (item 31, Fig. 163), or when similar items are combined (item 1). In the latter case, the number of pieces and the length are recorded oppo- site the first item, the others being referred to this by the words "see above," or "see page "; the item number is repeated. 3. Each draftsman must make his drawings conform to the material ordered, and he roust report any instance where this is not feasible. Slight variations are of less consequence when the material is taken from stock or cut from the multiple lengths than when the material is cut to the desired lengths at the mill. The draftsman should, therefore, consult the original bills after they are returned"; the car- bon copies are used only while the originals are held by the Order Department. UNIVERSITY BRIDGE COMPANY ^,.,,.,._I_YPICAL OFFICE BU/LDIA/G ~ /•?'' S/f/PME/Vr_,,,,„^ ^^^ MATERIAL ItrLL ORDER orscRiPTroN no, Of .,„... + .1"/. .,„... ...... .... h. "■ .... Is/. Ti^r Cv/iXrAn.s- AL' 2 10 IS/ /5 # 29 S % ?9 si 4 1 Co/./ 2 P/s /2 ;S 29 .5 4 29 H 32 \ 6 10 IS/ 25* 29 S 29 si 3 Co/3.2.3.4 6 P/s 12 i 29 5 '. 29 si 34 2 Iff I& 25* 33 8 i 33 *? 2 Co/.S 2 % 12 i 33 8 i 33 si 33 24 12' iSj 30» 29 S 4 30 29 ^i 1 Co/s. 26-29, 32-3S S6-S9 24 P/s /4 % 29 5 '. 29 si 30 6 )2' IS/ ■30 # 29 5 i se9 Mve / Co/s.30. 3/ 60 6 P/s. /4 lA 29 S i 29 si 29 /O /4 ^ / ei ? 39 o 3/ Sp/lces /0"Co/s. 30 „ 14 ^ 2 0^ . /2" .. 2rni F^ooY BoeAnis ■ -B r/L 1 3 18 Is S5* // 2 /o Beam 1 3 /Sis 42^ 16 2 // .. 2.3 8 /sr 42^ /6 oi /2 „ 7 I 12' 7^ 16 2 /3 .. 4 6 10' T 25* /5 7 /4 ., 4/ 14 do /4 // /S .. S4 3 do /4 3i /6 ., 42 9 do /4 3 /7 .. S3 2 9' Is ?f # /4 // /a .. 52 2 a- Ts /a^ 14 /7 /9 ., S/.60 2 9' IS/ isk"^ f4 4 20 „ 40 2 8" iS/ '4 * /4 4 2/ .. SO S9 I 3' ISJ i,iif 8 4 22 „ 6/ i' f 209/ n. Ghf.t fJ ISO \ a FB IS6 40 IS 4 3 19 7 FT 72 {A' 48 8 /-* 4 3 2dsi F8 7.2 1 r&. 47 96 Pk 5 l?y flf pa6 Bo/fcomp/eh S.3\\\\ e 20 a 72 96 i b?//\s li L S m Girts 8-FS'^8F9' 16 L^ 4 3 17 8i 72 '26 49 76 L^ 6 4 S ma6 Bo/fcompleti 12.3 15 30 o 41 16 Pk 5 Si na6 5.3 i 4 20 o 72 48 # bc/rs li i 2 S im ZO us. 4 3 ^ .5- 6^ F/O 72 f) 27 8i 60 i 32 Bcin^ 4 i 5 8i A^S 1.9 n 22JOt 64 [ 4 Sl-ri/t^ S2 \ 6 S3 /O 9' i£i '^ /9 7 25J 40 lO L^ 5 \3f 17 4 8.7 ISI 4f> 8 Pk. 13 / 7 pb6 on S2 13.8 T 30 o 70 12 , 13 / 7 oc6 on S3 13 8 , m 30 o 70 1 ' c. 1 m 4 Strhfi S4 tP 6 ft SS sl/p 2 If S6 5t3& lO Z« 6 4 i 79 7 S4.S5 123 #173 1 — 44 10 L^ 6 4 i 18 loi n * i! 45 2 Z-r 6 4 \ 20 si S6 12.3 495 42 e 6 4 f9 9 „ 43 8 PA 13 1 I 4 m/6 on S4 13.8 3.7 1 30\0 70 16 13 16 t 4 pe6 . S5.S6 13.8 ! 37 3o\o 70 7Z X ^ ® 1 M U S BILL HADE Br _ C.'S.T. ^DATE 8/27/18 CONTftACT N0_^-7 7^ DRAWMCNa-^ -.BILL CHECKED BY A.S.D. ..Lk-nj3/30/ 18 _shEET (iUHBEB S^ ^_ 1 ^.^ J Fig. 168. Typical Shop Bills. CHAPTER XXVII SHOP BILLS AND SHIPPING BILLS 169 168 is included all the material required in making the two chord members of Fig. 124. When only part of a member is shown on the drawing all notes which affect the bill of material must be carefully considered. Thus for a member marked "Symmetrical about the center line " much of the material billed on the drawing should be doubled. When more than one drawing is made on a sheet the members should be grouped on the shop bill in the same way they are grouped on the drawing, as illustrated in Fig. 168, which shows the shop bill for the girts and struts of Fig. 147. One or more blank lines should be left to separate the groups and to provide a space for the total weight where necessary (page 170 : 1). The number, the name, and the mark of each different member should be printed prominently at the head of each group without regard to the vertical lines. Usually only one mark is put on a line, a,s F 7 and F 8, or S 4, iS 5 and »S 6 (Fig. 168), although two may sometimes be combined as F 9^ and F 9^, if it is desired to save space. Members which are com- posed of single pieces may be billed on a single line, as F 10 or Af 5 (compare page 173 : 1). Fine vertical lines are printed under "sections " as an aid to uniformity in billing. With these lines it is unnecessary to use crosses. All four columns are used for angles but the second one need not be used for plates. For beams the sign (#) may be placed in the last column. The material should be listed systematically, beginning with the main material. The details should be grouped as on the drawing, beginning at the bottom or left hand end of a member and proceeding toward the other end. The washers and bolts for any member should be the last items to be billed. Each item which is not common to all the members of a group should be so noted, as in Fig. 168. Similarly, notes should appear opposite each item which is "Milled " or "Finished " (abbreviated "Fin "), "Bolted complete," or "Bolted for Shipment." Assembling marks should be recorded in a special column headed "Piece Mark." Permanent bolts are usually' Usted on the drawing, hence they are billed as a matter of course. Temporary bolts used to hold loose pieces in position during shipment are usually of odd lengths picked up in the shop; these are not always listed on the shop bill, but they should be so listed for a "pound price " contract. It is usually sufficient to bill all temporary bolts as 3 inches long; in this way an average weight is provided for without undue investigation of details which would be inconsistent with the usual shop practice. The column headed " + ins." is used only when the material is ordered directly from the shop bills instead of from preliminary order bills, as for example, when shop bills are written for drawings made by a consulting engineer. In this case the complete shop bills can be prepared as quickly as preliminary bills; the latter may be dispensed with and much duphcation may be thus avoided. The use of this column on the shop bill is then the same as on the material order bill (page 164 : 6) . 1. Itemizing. — The second part of the shop bill shows the ordered material from which the yard men should select the steel for the different component parts of a member. All material which is ordered specially for a contract has the contract number and an item number painted on the steel. This item number appears on the prehminary material order bill (page 163 : 2) and it is transferred to the shop bill to indicate the proper assignment of material. The term "Itemizing" is applied to the preparation of this part of the shop bill. The best results are ob- tained if one man itemizes all of the shop bills of a single contract, or at least of a definite portion of it; this man should be conversant with the practice of the Order Department. Opposite each component part of a member should be placed the item number of the material from which it is taken, and suitable notation should be made on the material order bill so that the same pieces will not be used again. The other columns under "Mill Order " are not necessarily used in all cases. In general the number of pieces need not be given unless the material is to be ordered from the shop bill instead of from a material order bill, in which case the order department takes care of the whole Mill Order and no itemizing is done in the drafting room. The section need be entered onlj' when it differs from that listed in the main part of the bill. For example, an angle which is to be cut from another size should be so noted on the drawing, as l£,5ix3xfx l'-2 (cut from 6 X 3), illustrated in the bracket on D 13, Fig. 140; in the main part of the shop bill it should be billed 5J X 3 X f and the original biller should record 6 X 3 X | in the corresponding place under the Mill Order. The itemizer then provides for the 6 X 3 X | angle. Similarly, plates may be cut from other sizes. Sometimes small plates are changed so that the length becomes the width, as for example, a plate billed 6 X 170 PART II — STRUCTURAL DRAFTING 5 X I'-O may be itemized as a 12 X i X 6 plate. Plates which are ordered as sketch plates (page 165 : 2), should be noted as in Fig. 168. The length need be given only when it differs from the length billed in the main part of the bill. This may differ by only a fraction of an inch, as in material to be milled (page 165 : 1), or by a large amount when ordered in multiple lengths (page 165 : 2). On account of differ- ent grouping on the shop bill and the order bill the number of pieces will often differ. Sometimes more than one item number will have to be placed opposite a single entry on the shop bill, the number taken from each being recorded under "No. of Pieces." More frequently the number of pieces listed on the shop bill will be less than the number on the order bill; care should be taken to make the proper record on the order bill so that the same pieces will not be reassigned. Beam sepa- rators or other materials which are assembled in the shop with the beams or other members, should be billed with them in accordance with the drawings. When these materials are made from combination bills they should be itemized on the latter; to save duplication they should not be itemized on the shop bill but reference should be made to the combina- tion bill, as in Fig. 172. All material that is not provided for on the order bill should be itemized by the order department. Presumably this material will be taken from the plant stock, because care should be taken to write advance orders for all material which cannot be found in stock. Material taken from stock has no item number, but it is indi- cated by the capital letter S instead. No length need be recorded for stock items, but the section should be indicated if it differs from the billed section. 1. When a contract is based upon a certain price per pound, the payments are determined by the calculated weight. The scaled weights are used as an approximate check. For each contract the method of computation should be agreed upon, but undue refinements should be avoided. Usually the weights are determined from the material sum- marized on the main part of the shop bills; to these are added the weights of the heads of the shop rivets. Thus no deduction is made for comers cut off (except for plates ordered by sketch), nor for holes for field rivets or pins; the holes for shop rivets are filled by the rivet shanks so that the weight is not affected. The weights are expressed to the nearest pound; when members are composed of a large number of com- ponent parts it may be necessary to carry the partial weights to one decimal. The weights are recorded in ink on the shipping bills, each weight being for a single member. The shipper weighs each car load and compares the weight with the sum of the calculated weights of the corresponding members; since the number of members shipped on one car seldom equals the total number of members which are ahke, the weight of a single member is more useful than the total weight would be. The shop bills are used for convenience in determining the weights of members; these weights are ultimately transferred to the shipping bills. The weights on the shop bills are used simply as a means toward this end, and for this reason it is unnecessary to ink them; in fact all necessary prints of the shop bills may be made before the weights are added. Usually the weights are computed and checked by young men who specialize in that work, although the draftsmen are sometimes asked to help. Most companies have exhaustive tables to facilitate this work. In computing the weight of one member, the weight of the corresponding number of component parts should be found. Thus for each girt, F 7 ot F 8 (Fig. 168), there are two plates and two bolts; the weights should be entered accordingly. Usually the first step in com- puting weights is to determine from the tables the weights per foot for different sections. These weights may be recorded in the column pro- vided for that purpose; the weights of I-beams and channels are given in the main part of the shop bill so they need not be repeated. The weight of each item is the product of three factors, viz: the weight per foot, the length in feet, and the number of pieces per member. The order in which these factors are multiplied depends upon the method used and upon the factors themselves; it may be more convenient to multiply the length by one of the other factors before the inches and fractions are converted to decimals of a foot. The weights should be placed in the spaces provided for them; fine vertical lines are printed on the forms to simplify the alignment of figures for totaling. When all members of a group weigh the same, a line can be drawn under the weight of the last component part and a single total can be recorded in the blank space between groups, as for F 9. When the weights of the members of a group differ, each must have its own total; to save space CHAPTER XXVII SHOP BILLS AND SHIPPING BILLS 171 each total may be recorded opposite the mark of the proper member, as for F 7 and i*' 8 or for S 4, S 5 and S 6. Care must be taken to in- clude in these totals only the weights of the component parts which form the corresponding members. The weights of the rivet heads should not be overlooked. Since they do not appear on the shop bill they must be counted from the drawings and their weights must be entered upon the shop bill, as in Fig. 168. In counting shop rivets special attention should be given to symmetrical notes, and to group spacing; each rivet has two heads. The weights of 'rivets and bolts are given on page 304. The weight of a bolt or a rivet may be obtained by the proper combination of the weights of the head, the nut, and the shank of proper length. The weights of standard connection angles for beams include the weights of the shop rivet heads. 1. A shipping bill is a summary of members in the form in which they are to be shipped. It is made primarily as a check list for the shipper. All members which bear the same shipping mark should be billed on the same line, but different marks should be listed separately. In each case the number, the name, the mark, and the shipping dimensions should be given; the weight is given only when required (page 170 : 1). The sheet number of the drawing is also recorded. A portion of the bill is printed black so that white spaces will be left on the blue prints for the convenience of the shipper in making records of shipments. The shipping dimensions are usually given to the nearest inch (or half- inch). The extreme "box dimensions " are given, i.e., the three dimen- sions of a box which would contain the member. The length is given in feet and inches but the other two dimensions at right angles to the length and to each other are expressed in inches, the larger of the two being given first. In case these dimensions do not fairly represent a large member, a. freehand sketch with auxiliary dimensions may be drawn in the column headed "Remarks," as shown in Fig. 171. Mem- bers should be listed preferably in about the order in which they will be erected. When part of a structure is to be completed before the rest is begun, the material should be billed and shipped accordingly; the shipping bills should be marked with the shipment, as for example, "First Shipment." The last page for any shipment should be marked "Complete." Shipping bills are numbered consecutively, usually with ■"™"°^ UNIVERSITY BRIDGE COMPANY ..m^...J60n.SXTHRU,_rRUSS,BRLDGE_ ,„,„,„„ .,^ ...„. DtSCHIPIION II ■HI.HCNTI 1 IMMI .... ■.V ""■".«»"."*'"' ..... ?.■;•,:■.';,■.' \\fs.';.\ •■■■ | .....—" .Nl. 4 Toplaferals r/ 6 20'^ a 28 // /[3[3i/|a^H^^^^a 4 T2 2/'/0 rs 'oi Itm^I^HHHI^HI 4 T3 20*8 13 ffi y«[7llH^H^^^HI 2 P/ates P4" as'i 2 /i Benf KrN^^^I^^H Z P4L 35 xi 2 li 1/ m; ^I^H^^^I 2 PS" 20 '12 3 o '/'.^/Wmijuiiii 2 f^ PS'- 20<'f2 3 o_ '''^^■^n^n 6 P6 M" i 2 7i '^''^H^H^^H e P7^ 14*4 / 4 .^^H^a^^B 6 P7^ 14*4 / 4 i^n^^^B 3 Swav Brace. SB 1 72*IOi 14 9 lr--H 'll ^i^p^B^m^^m 2 Portals P.fl 96 *l2i m O ^^^ ' ''"'lijraiin 4 Posts U-UI S 16 *l4i 28 5 ^^■^J^IBffiBHiMl 4 L2-U2 „ is*r3 28 H ••?:6ti HSBjBliiHi^B 4 Diaaona/sL2-lJI /4 *l2i ?6 ^7 1 4^?\?S^^^S^^^ njpp^g^nmn] liifiij^dUlilllfl iHUsillBfilHd |B9iaHH|B ||Ui|i|iHII|||l IHfiBijjjjmBEl ^B^n^^H IHjyiiijIimiUjjIII IHhUUHIUHIjI < ^^■^a^^H ' lUtbBLmUlUBdl I^H^^^^^B H^nnRHi 1 i 1 HU^myi^H I^B^B^^^I 1 ■BEHlHEB i UnJiAl^^UIUIIU kdyil^H|UI i BILL MADE Bt. ^»-^' ^- - ^JMt- ^^ / ^O / ^4 CONTRACT NO, ^^ BILL CHECKED BY _^li^^,i- ^ihl^^jJ^/M: SHEET NUMBER R3 Fig. 171. Typical Shipping Bill. a distinctive letter as R 1, R2, etc. Bills for different shipments may be numbered in different series as ii 101, R 102, etc., for 1st shipment and R 201, R 202, etc., for 2nd shipment. 172 PART II — STRUCTURAL DRAFTING "™" UNIVERSrTY BRIDGE COMPANY ^..^...^lAFT_BWIPim^__2^0FLPJ3R BEAMS. „„„™ s„,p..= .,a MMBCII i.AICH.4< SHIPKENIS ,"",'. "■• .... ':: "■"," ""■'■ -:.";- ,* ..„ "•'" .... ■.•.°.l -■ |. -...■..■. 2 Beams B7 S3 — JT its' — ~ — — / „ 88 — / „ B9 „ 4 /o Ts C 25 4 * J. '6 ki :: fl S L^ 'r W - s - — 1 _ 6 Beams B/0 f3 ~ - '/9 lo 4- 8/r - S/_"" V ' y /O 2n /_5 LS 4 42 I 4 18 IP. \fi\?i s f? 20 ^0 /O 2? s' I2_ 3_ /li m'v I4r. h#' \ 1 0Pt^ 6 Beams 8/2 83 6 fO Is 25 f W // Z73\ 9 — - 1 B1LL-.be BY C.W. j,„,6 1/25/74 „„„.„.,. 6693 1 j,L, .-,«.,... IV. 3. r. ..„3/3a//4 „.„„„„„. QR z" 1 '"" UNIVERSITY BRIDGE COMPANY ZSJrA: BRANCH sT.uc,u« OFHCf BU/ID//VG - 2"!fAiVD 3^f^ FWOfl ^BEAMS .„„,.„ sh,.p.h=..ll HFMBCR N«TERI>L HILt ORDCn ,.....„ "" .... ".: "c" ..„,.. iraciH + ■I.S-I MLC V IMKI z 1 i -- — ' :"! - 1 1 — j • 1 1 1 1 T — 1 BiLL».D,.v ABC. ..„fi//7///l imn 1 _B>UL CHECKED BY V- C . r....e/20/M _ CD .^ 'I Fig. 172. Typical Shop and Shipping Bills. CHAPTER XXVII SHOP BILLS AND SHIPPING BILLS 173 1. Shop and Shipping Bills are often combined on the same form, as in Fig. 172. This is done when the shop bill for each member of a drawing occupies only a few lines, i.e., when each member is composed of but few different parts. These simple shop bills may be arranged to give the necessary information to the shipper so that special shipping bills need not be prepared. It would not be feasible to use combined forms for complex members because the shipping data would be obscured by the details, and the shipper would be burdened with an unneces- sarily large number of pages. Usually the combined shop and shipping bills are used for beam work and other simple work drawn on small sheets or printed forms (except those mentioned in the following para- graph); they are sometimes used for simple members drawn on large sheets. For example, the girts and struts of Fig. 147 might be billed on such a form instead of as in Fig. 168. In the combined form the number, the name, and the mark are listed in columns as in shipping bills, except that they are grouped as on the drawing. The remainder of the bill, except the shipper's record, is similar to the shop bill form. The bill of material may be started on the same line as the mark, unless members which bear different marks are grouped together; in this case, it is better to begin on the line below the last mark to avoid the confusion that might arise if part of the material were billed opposite one of the marks. Blank lines should be left between groups. In some work such as structures intended for export, the extreme shipping dimensions are given opposite each mark, just above the detailed list of material. The billed length of a beam is the length which appears on the drawing along with the depth and the weight — usually the ordered length. 2. Shop and shipping bills are sometimes combined with the drawing, as illustrated in Fig. 175 (a) and (6). The bill portion of these combina- tion sheets is much the same as for shop and shipping bills explained in the preceding paragraph. CHAPTER XXVIII MISCELLANEOUS DRAWINGS AND LISTS Synopsis : Some of the more simple drawings may be combined with the correspond- ing shop and shipping bills on the same sheet; the use of these combination sheets is illustrated. The method of listing field rivets and bolts is explained also. 1. Much of the miscellaneous material used in steel construction is drawing of one of these pieces is printed on each form with blank dimen- of such a nature that comparatively little information need be given on the drawings. This may be because there is little or no shop work to be done, or because most of the shop work is to be carried out according to fixed standards which need not be dupUcated on the drawings. Such material is usually drawn on a combination sheet of the general form shown in Fig. 175 (a) or (6). The use of such forms* reduces the number of sheets and saves duplication, because a working drawing, a shop bill, and a shipping bill are all contained on the same sheet. These sheets are used for rods, anchor bolts and washers, bearing plates and anchors, rollers, crane stops, castings, forgings, etc. Standard castings such as beveled or "O.G." washers, separators, or rail clamps may be listed without a drawing if reference is made to a standard pattern nimaber. When beam separators are to be assembled in the shop and shipped with beams in the form of beam girders, a note to that effect should be placed on the preliminary bill or combination sheet from which they are made so they will not be shipped separately. Reference to this sheet should be made on the shop bUl, as shown in Fig. 172. Castings and forgings should be listed on separate sheets for they are made in different departments. 2. Special printed forms are used by many companies to simplify the drafting. Such forms are commonly used for crane rails, eye bars, loop rods, pins, clevises, tumbuckles, corrugated steel, etc. A general * See footnote, page 83 sions to be filled in. The forms may be so arranged that the different variables may be recorded in tabular form; in this way similar pieces in any contract may be listed upon the same sheet conveniently. 3. The use of a combination sheet with a comparatively large space for the drawing is shown in Fig. 175 (a) which illustrates a typical cast- iron base t for an ofiice-building column. The tabular portion is arranged as a combination shop and shipping bill (page 173 : 1); not all of the blanks are required for castings. Note that the tops of these cast bases are finished to furnish uniform bearing for the columns. Holes are drilled in the tops for the bolts which hold the columns in place during erection; it would be impracticable to punch holes or to drive rivets in cast iron because of the danger of cracking the casting. Cored holes (cast in place) are sometimes used for bolts, but they should be made f inch larger than the bolts to allow for irregularities in the casting. Holes are cored in the bottoms of large cast bases to permit the more even distribution of grout which is poured after the bases are in place. 4. The use of a combination sheet arranged for a large number of items with comparatively small drawing space is shown in Fig. 175 (6). This illustrates the rods for the mill building shown in Fig. 156. It is perhaps necessary to show more complete drawings for some rods, and t For a table of dimensions of the American Bridge Company's standard cast-iron bases, see Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Co., Inc., New York. 174 CHAPTER XXVIII MISCELLANEOUS DRAWINGS AND LISTS 175 UNIVERSITY BRIDGE COMPANY ^.-..^. _ fJ^JL-. BRANCH 4-0 ■■ ^SKrrCH,SKOPAtfD SHIPPING BILL Holes in top j§ dril/ed i Cor^l" ^ ildramJioleS ^core '^Bottom not finished "* I' o/towed tor grouting Bases CBI Ccst'rcn 3250 C.X BASES BILL MADE BY S.-Jh.±: XiKl^—^LCJ^ ^CONTRACT H0.^^°OO_^ BILL CHECKED DY QlJl^l OK\t^^^IPL.{^ .SHEET NUMBEB Kj.L Fig. 175 (a). Combination Sheet with Drawing. UNIVERSITY BRIDGE COMPANY ........mmCLE BU/LD,NG ___ ,„ ^ 1 HATIRUL Tl .,u.,„u 1 IHIFHIHTI \ PItCI .... ...„., R MIT. e^LC. 1... ".. " "«" "V. ..... ... 1 1... „.. b'l »»!..... ...... 3itif a?/ B XI nw//?fl*/-te 8 70 SO Hi -» 1- 8 X2 „ „ Hb 4 61 51 32 Hex.nuts ,T 2o-3y'3-"mf\j6 X3 "SmyRodS* 20 4 32 52 bbII^sB 3g-J "Q^ ^ 32 Hex.nuts ,"? bIHU^H ~ ^^^^^H B^S^^H „ /O' 2phreaa S X4 SoaBotid'^ 1 4 2 .V B^B^^H ^ " N Vi. he 10 Hex.nuts S\ B^B^^^H < B^SSBB SSB^^S iO xs SaaRo(ls$''t> 6 3 "7 ~ ' s B^S^^S 20 Hex nuts V B^B^^S ^SI!^^S B^B^B^ 6^5'2i-,h^ 10 X6 ^a^Rodsn'^ 6 a \\\ i7 .9 BBB^^S '^ X7 10 X7 6 ^ li 7 9 bbubIbMI 6-8" ' 40 Hex.nuts 9 S^P^^B — fa^^— 1 3'threao 10 S ~ "~ "~ " ^s m ___ aiu»Ai.E.Y_ A.B.D. j,^^9-IO-ta -CONTRACT NO r776 RODS CHEC ,„„ H.T.B. ^^„9-is-ie on C 2 — — Fig. 175 (6). Combination Sheet with Small Sketches. some companies require them for all rods; but usually sufficient informa- center lines. Main diagonal rods are marked in the usual manner with tion can be given if the rods are shown conventionally by single lines, a letter X followed by a specific number (page 80 : 7). It is imprac- as in the figure. It is assumed that dimensions are taken along the tical to paint the mark on each individual sag rod or tie rod; they are 176 PART II — STRUCTURAL DRAFTING UNIVERSITY BRIDGE COMPANY ^,„,„. FUffJVACE BU/LDinrG rREcropinsr HO. or fi£ces OIAM. KIVCTS BOITS emp MeiUBOiS CONNECTED •B fe L£/mM HEAD NUT WASHERS 60 1" z? /i K/ fo- Co/s 40 3 i?n 2i i • . Girders /IZ li Hex. Hex. ik r7.F8.r9 to Cols riz 2 1 32 /^ \ F9 ro Co/s. 40 n 1 FfO fo Pur/ins 64 I? 1 MS fo Girts. 60 I? jg S 2, S3 to Co/s. 60 li ^ 96 li ^ S4.S5.S6 fo Co/s. 4S z rA 1 BILL HADE n A-^^f^ OATE- 9Z/4//8 ^o»™cT«o 1776 9/Z0//8 j«n™.,o,EF/ Fig. 176. Erector's List of Field Rivets and Bolts. usually shipped in bundles and the bundles are marked. In case rods become mixed before they are used, the erector must identify them by direct measurement. If a rod is indicated on the erection diagram by an X and a number, the erector must refer to a list of rods to determine the proper length; this extra step may be avoided except in the case of bent rods, if all straight tie rods and sag rods are marked according to their lengths. Thus, on the diagram the length in inches of one rod in each panel may be inscribed in a circle, as shown in Fig. 156 or Fig. 158; the circle is used to distinguish these marks from others. Since the tie rods or sag rods of a given structure are usually of the same diam- eter, the erector simply needs to know the required lengths; it is more convenient for him to find the lengths where the rods are shown on the diagrams, than to have to refer to a separate list. The lengths of tie rods and sag rods are usually made in multiples of 3" in order to reduce the number of different sizes; in determining the lengths, use may be made of the dimensions on page 316. For the weights of rods see page 315. 1. A summary of field rivets and bolts must be prepared for each contract in order that the proper number of each size may be shipped to the site for use in erection. Before this summary can be made, a detailed "erector's list " must be prepared to show the number and the size of the rivets to be used in each connection. To have each connec- tion provided for once, and only once, it is well to have one man hst the rivets for a whole structure or for a definite portion of it; he should work systematically to avoid duplication. Perhaps the best plan is to take one sheet at a time, and to Ust only those rivets by which each member on that sheet is connected to the swp-porting members. The rivets for all members which bear the same shipping mark should be listed together, and the rivets for similar members may be combined whenever this can be done conveniently without adding to the burdens of the erector. 2. A typical erector's list of field rivets and bolts is shoivn in Fig. 176; this provides for the connection of the knee braces in Fig. 140 and of all the members in Fig. 147 to the columns of Figs. 135 and 137. The erection diagram of Fig. 156 should be used as a guide in determining the relative positions of the members. A rivet is made with one head in place. The shank should be long enough to extend through the parts to be connected far enough to provide sufiicient metal for the forma- CHAPTER XXVIII MISCELLANEOUS DRAWINGS AND LISTS 177 tion of the second head and for the upsetting of the shank to fill the enlarged hole (page 30 : 4). Rivets commonly used in structural work are either "button head" or "countersunk" (page 40 : 6); both heads may be alike, or one may be button and the other countersunk. The length of a button head rivet is measured from the under side of the head ; the length of a countersunk rivet is the extreme length overall. The "grip " of a riyet is the total thickness of metal through which it must pass, i.e., the sum of the thicknesses of the parts connected. The length of a rivet is the sum of the grip and the extra length required for upsetting. The thicknesses of I-beam and channel flanges at the rivet lines are shown in the tables on pages 298 to 302. The lengths of rivets vary slightly according to the shapes of the heads adopted as standard by different companies. Tables are used to determine the proper lengths of rivets for diflferent grips.* These tables are usually arranged for grips varying by eighths of an inch. The grips for both rivets and bolts are usually recorded to the nearest sixteenth, but this is unnecessary unless one is likely to be substituted for the other; for rivets, grips in sixteenths should be increased -^ before the lengths are found. Care should be taken to differentiate between countersunk and button head rivets; more metal is required to form a button head than a countersunk head. It is well to record the lengths of all countersunk rivets as soon as the grips are recorded, being careful to place them in the proper column. It is usually more convenient to omit the lengths of button head rivets until one or more pages of the erector's list are otherwise complete, when they can all be recorded. The bolts are Usted upon the same form as the rivets, but the style of head (button, square, or hexagonal) and the style of nut (square or hexagonal) should be indicated as shown. The length of a bolt is measured from the under side of the head; it should be a multiple of J inch. A bolt should extend from tV to \ inch beyond the nut to insure the full bearing of all the threads in the nut. The thickness of a nut is the same as the diameter of the bolt with which it is used. When washers are used, a bolt should be made correspondingly longer. * The standards of the American Bridge Company are given in the "Pocket Com- panion" of the Carnegie Steel Company, and in Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Co., Inc., New York. UNIVERSITY BRIDGE COMPANY „„„„,,„ FURNACE BU/LD/NG FtELD RIVETS AND BOLTS HOOF PIECES DIAM. RIVETS BOLTS REMARKS '""'^ VFKHT .«.f.i™ w fe lEtKSTH HEAD NUT WASHERS TAL ;;,",'. 1 ■>". 1 ««.••»" 75 4 2i 3^blHHl|||||H 60 „ 3, 3?^^^^^^! 140 i ^^ ^^HM^^H ^HHHH^^B ^^^^I^^^H 400 ^ li Hex. Hex. rpH^I^^^^^H /to /i r ^i/i^i^^^^^^H /70 2 kpN^I^^^^^h I^I^^^^^^H £ri L Fig. 190 W. UC (—3 = Rl B — U{B-X) (B-X) uc(l-x-^ L ''" "' 2 This may be reduced to this form: 5C2 W = Mb at a distance B from Rl- .[.c-ff-f.(,-f)x^f]. BC 2L 2 ^ l^ - L The value of X which will produce the maximmn bending moment may be foimd by difl'erentiating this expression with respect to X, and placing the first derivative equal to zero, thus: u (b BC L X] 0, whence B - BC If we substitute this value of X in the last expression for bending mo- ment we have: CHAPTER XXX SHEAR AND BENDING MOMENT 191 U-f-f.(.-fy-(^'] U \ BC - ^^ - ^ + f J3 which may be reduced to this form: -('-!)(-©• The value of C which will produce the maximum bending moment may be found by differentiating this expression with respect to C, and placing the first derivative equal to zero, thus: UB (l - f ) (l - ^) = 0- whence C = L. If we substitute this value of C in the last expression for bending moment we have: -('-f)(-.^. or UL 2 [B - -j-j. (Compare page 188 : 2.) The value of B which will produce the maximum bending moment may be found by differentiating this expression with respect to B, and placing the first derivative equal to izero, thus: UL 2 1 ?) = 0. whence 1. Live-Load Bending Moment — Simple Beams. — Concentrated Loads. The maximum bending moment at any point of a simple beam for a system of moving concentrated loads mil occur when one of the concen- trated loads is at that point. The maximum bending moment due to two loads will occur when the larger load is placed at the given point with the other load on the longer segment as near the first load as possible. The placement of more than two loads to give the maximum bending mo- ment is not so simple. Often two or three different loads in turn must be placed at the point, and the corresponding bending moments must be computed and compared. The following criterion must be satisfied by the critical load which is placed at the given point: the average load on one segment should be greater than the average load on the whole beam when the critical load is considered on that segment, but less when it is considered on the other segment.* The average load is the sum of the loads on a segment, or whole beam, divided by the corresponding length. Often more than one load will satisfy this criterion. It is sometimes possible to tell by inspection that one of two wheels is the critical wheel; in this case it is unnecessary to apply the criterion. The greatest bending mo- ment that can occur on a simple beam for a series of moving concen- trated loads will be found near the center of the beam, but not as a rule at the center. The absolute maximum bending moment, or maximum of maxima, will occur under one of the concentrated loads when the center of the beam is midway between that load and the center of gravity of all the loads on the beam. The critical load is always one of the two loads ad- jacent to this center of gravity, usually the nearest load. The relative position of the center of gravity will often change when the loads are moved, because one or more loads may come on one end of the beam while others may 2 move off the other end. Enough trials must be made to make sure that the bending mo- ment under one load is greater than under either adjacent load when each is placed for the maximum. For special suggestions for ^S- 191- placing the concentrated wheel loads of Cooper's conventional locomotives, see page 195 : 1. To prove that the maximum bending moment on a simple beam will occur when the critical load P (Fig. 191) is placed as far on one side of the center of the beam as the center of gravity of all the loads on the beam is on the other side, let Y represent the distance from P to the center of gravity of 11 the loads Q, X the distance from P to the center of gravity of all the loads N on the left segment, and B the distance from P to the reaction Rl. Then Q{L-B - Y) „ Q(L- B - Y)B ,,^ ,, , ,- J = Rl, and = NX = the bending moment under the load P. The value of B which will produce the maximum bending moment may be found by differentiating this expression with' respect to B, and placing the first derivative equal to zero, thus: * For derivation see Marburg's "Framed Structures and Girders," Part I, McGraw- Hill Book Co., Inc., New York. 'JL p o n n n o o Rl / f R« B I * 192 PART III — THE DESIGN OF DETAILS Q(L - 2B - n ^ p^ ^^^^^^ L-2B-Y = 0, or 5 = ^ - J. 1. Elustrative Problem — Txco Concenlrated Live Loads. — (See page 195 : 1 for more than two loads.) To find the maximum bending moment on a 20-foot beam due to two concentrated live loads of 8000# and 6000jf respectively, spaced 7 feet sooo 6000 apart. The distance from the larger load to -Q — - — O ■^^ . the center of gra^'itJ' may be found by mo- \o^-=S350 Fie 192 id) "' i^6°^> taking the point of moments under the larger load. The sum of the moments of the loads taken separately must equal the moment of the sum of the loads (i.e., the resultant)', thus: 6000 x 7 = (6000 + 8000) X, whence X = 3 feet. The 8000 load should be placed IJ feet from the center of the beam, as shown in Fig. 192 (a). The reaction may be found either from the original two loads or from the resultant thus: or 5950# = (8000 X llj + 6000 x 4|)- 20 = Rl 5950# = 14,000 x 8| -^ 20 = i2i The maximum bending moment under the larger load is 50,580#ft. = 5950 X 8|. 2. Bending Moment — Simple Beams. — Combined Loads. Con- centrated loads exist only in conjimction with imifomily distributed loads. The latter may be due simply to the weight of the beam itself, or to track or floor loads as well. The maxi- mum bending moment for the unif ormly distributed load is at the center, but the maximum for moving concentrated loads is usually at another point. The maximum for the combined loads ^"ill not be found at either of these points but somewhere between them. This may be shown graphically by plotting the moment diagram for the imiforml}' distributed load above a base line and that for the concentration loads below the line, as in Fig. 192 (6) . The longest ordinate m from one curve to the other represents the maxi- mum total bending moment. The position of this point of moments is Fig. 192 (6). in the section for which the shear is zero; this may be found either alge- braically or graphically. However, it is seldom necessary to locate this point because at least one of the moment curves is nearly horizontal between the two points of maximum bending moments. It is customary to combine the maximmn bending moment due to moving concentrated loads with the maximum due to imiformly distributed loads, although they do not occur at the same point. The shght error is on the side of safety. The maximum bending moments due to fixed concentrated loads and imiformly distributed loads should not be combined unless they occur at points so close together that the excess wiU not be too great. 3. Live-Load Bending Moment — Cantilever Beams. — The maxi- mum bending moment for a beam supported at one end only will occur at the edge of the support when the loads are placed as far from the sup- port as possible. For beams which overhang one or both of two supports there will be a maximum positive and a maximum negative bending moment. One will be found at one of the supports when the overhang- ing end is fully loaded, the loads being placed as far from the support as possible The other maximum for fixed loads will occur at that sec- tion between the supports for which the total shear is zero; the maximum for five loads will occur midway between the supports when only the portion of the beam between the supports is loaded, the cantilever end being empty. The point of contraflexure is the point at which the bend- ing moment is zero. Typical shear and moment diagrams are shown in Fig. 193. Positive bending moments have been plotted downward ^o represent more nearly the direction in which the beams bend. 4. Restrained beams and continuous beams are not treated here because the structural draftsman is seldom called upon to design them. Beams and girders with end connection angles are in a measmre restrained or " fixed " at the ends. The amount of restraint depends so largely upon the eflBciency of rivets in tension and upon the rigidity of the sup- porting members that it is customary to design such beams as simple beams. Even beams which are inserted into masonry walls are not always suiBciently imbedded to insure a fixed condition, except such beams as lintels, which support masonry walls over openings. It is safer to design these beams as simple beams than to place so much dependence upon the masons. Office-building beams are often so braced to the CHAPTER XXX SHEAR AND BENDING MOMENT 193 columns that they must be designed as fixed beams, but these and similar beams are usually designed in the Designing Department and therefore are beyond the scope of this book.* Beams which have more than two supports are statically indeterminate. Their use is not recommended Ordinarily. If desired these continuous beams may be designed by the Ghsar Diagram ::5^ ^Qffr.Diagram Fig. 193. S/isar DIagrsiB " Theorem of Three Moments " *, but the Ughter beams (such as purlins) which extend over three supports primarily to give rigidity to a structure are more often designed as simple beams. 1. Conventional Wheel-Load Systems. — ^The floor systems (beams, stringers and floor beams) and the main girders of railroad bridges are usually designed to support a specified live load of two freight locomo- tives with concentrated wheel loads followed by a uniformly distributed train load. For very short spans an alternate loading of the two driving axles of a passenger locomotive is specified. Formerly ahnost every railroad specified a different locomotive until Theodore Cooper proposed his system of conventional engine loads for the sake of uniformity. He classified his engines according to the axle loads, the spacing between loads being the same for all engines. As the specified axle loads have increased considerably since his system was adopted, the spacing between * See Kirkham's "Structural Engineering," McGraw-Hill Book Co., Inc., New York; Fuller and Johnston's "Strength of Materials," John Wiley and Sons, Inc., New York, and others. loads is less than for actual locomotives. The difference in results is on the side of safety (except for cantilever bridges and turntables) and Cooper's Loadings are quite generally specified. The engines are classified ac- cording to the axle loads on the driving wheels, and all other axle loads vary proportionately. The axle loads on the drivers of an " E60 " load- ing are each 60,000 pounds, and the train is 6000 pounds per linear foot of track. Similarly, the corresponding loads of an " E40 " loading are 40,000 and 4000, and the shears and bending moments for E40 are four- sixths (two-thirds) of the corresponding shears and bending moments for E60. This relation makes it possible to prepare a table of shears and moments for one class of loading and to use this table in getting shears and bending moments not only for that class but, by proportion, for other classes as well. Such a table t is given on page 318. E60 loading is chosen in accord with the more recent specifications of the leading rail- road companies. In the table the axle loads per track have been divided by two to give the wheel loads per rail, and all shears and moments result accordingly. This usually corresponds to the loads supported by one stringer or girder. When two stringers are used under each rail these values must be subdivided again. Shears and moments are taken as if the loads were apphed directly to the stringers or girders, although as a matter of fact the loads are traiismitted to them through the track (i.e., the rails and the ties). The distances between wheels have been 1" plotted in the table to a scale of r^ = 1'. The number of wheels which may come on a given span may best be determined by plotting the length of the span along the edge of a strip of paper to this scale and then sliding the strip along the diagram. The significance of the different values is explained in the table. Students should verify enough values for shears, moments, and positions of centers of gravity to enable them to understand their full meaning. The use of the table is illustrated by the solution of the typical problems which follow. 2. Maximum Shear on Beam — Cooper's Loading. — The loading which will cause the maximum shear on a simple beam depends upon t Numerical values for shears, bending moments, floor-beam reactions, etc., are tabulated in Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Co., Inc., New York. 194 PART III — THE DESIGN OF DETAILS the span. For spans up to 12.5 feet the special loading of two 37,500# wheel loads 7 feet apart should be used. For longer spans (except those between 23.0 and 27.3 feet) the maximum shear on the beam will equal the left reaction (when the engines face toward the left as in the diagram) when the first driver (wheel 2) is placed at the left end. For spans be- tween 23.0 and 27.3 the maximum shear on the beam will equal the right reaction when wheel 5 is placed at the right end. This is due to the effect of wheel 1, which in this case is on the beam. Illustrative Problem — General Case. — To find the maximum shear on a 74-foot deck girder for Cooper's E60 loading. The figures printed along the vertical fine under wheel 2 give the distances from that wheel to the wheel over the corresponding vertical of the zigzag hne. The distance to wheel 14 is found to be 71 feet, and thus with wheel 2 at the left end, wheel 14 is 3 feet = 74-71 from the right end. The moment of these loads about Rr is equal to the moment about wheel 14 plus the product of the sum of the loads by the additional lever arm. (This may- be proved as on page 189 : 1.) The moment of wheels 2-14 about wheel 14 is foimd by following down the vertical line under wheel 14 to the heavy vertical line in the moment table, then toward the left to the number just to the right of the hne through wheel 2, viz.: 11,900 thousand pound-feet. The sum of loads 2-14 is found simi- larly in the shear table to be 333 thousand pounds. The total moment is then 12,900 = 11,900 + 333 x 3 in thousands of pound-feet. The maxi- Tniim shear is equal to the reaction Rl which is this total moment divided by the span, or 174 thousand pounds = 12,900 -^ 74. Illustrative Problem — Special Case. — To find the maximum shear on a 24-foot stringer for Cooper's E60 loading. If wheel 2 were placed at the left end, wheel 6 would be at Rr and only the four drivers would be on the span. (The distance 24 feet from wheel 2 to wheel 6 is not dupli- cated in the table because it is the same as from wheel 11 to wheel 15.) For beams between 23.0 and 27.3 feet long the maximum shear will equal the right reaction Rr when wheel 5 (or 14) is placed there, since not only the four drivers but the pilot wheel 1 (or 10) comes on the span. The parts of the shear and moment tables at the right of the zigzag hne should be used in much the same way as the parts at the left. Thus, the dis- tance from wheel 10 to wheel 14 is found to be 23, the sum of the loads 135, and the moment I860; Hence, the maximum shear = i^K = 83 = (1860 + 135 X 1) -> 24 in thousands of pounds. 1. Maximum Shear for Any Section — Cooper's Loading. — The loading which will cause the maximum shear for any section of a "simple beam depends upon the relative lengths of the segments. When the longer segment does not exceed 12.5 feet the special loading of two 37,500# wheel loads should be used. When the longer segment is between 23.0 and 27.3 feet and the^shorter segment not over 9 feet, the maximum shear for the section will be foimd when wheels 1 to 5 are on the longer segment with wheel 5 next to the section, no load being on the shorter segment. For all beams over 34.5 feet long the maximum shear for any section will be found when the longer segment is fully loaded and wheel 2 is next to the section (wheel 1 being on the shorter segment if the latter is more than 8 feet long). See Fig. 194. For all other spans the maximum shear for any section will be found when the longer segment is fully loaded and when r — Q — Cp O OO Q O . either wheel 2 or the first wheel of the special ' y- -^g^ loading is next to the section, depending upon the relative lengths of the segments. The shear for any section is not necessarily equal to the reaction, for when wheel 1 is on the shorter segment it must be deducted. Illustrative Problem. — - To find the maximima shear for a section 10 feet from the end of a 30-foot stringer for Cooper's E40 loading. The effects of two loadings must be compared because the beam is less than 34.5 feet long. Placing wheel 2 (or 11) next to the section, we find that wheel 5 (or 14) is 5 feet from the right end. The left reaction due to this position of wheels 1 to 5 is 64 = (1250 + 135 x 5) ^ 30 for E60, and the corresponding shear is 49 thousand pounds = 64 - 15. Placing the first 37,500# wheel of the special loading next to the section, we find the shear, which is equal to the reaction, is only 41 thou- sand = 37,500 (13 + 20) -^ 30. The maximum shear for E40 is there- fore 33 = 49 x f . • 2. Maximum Floor-Beam Reaction — Cooper's Loading. — In design- ing a through railway bridge it is necessary to determine the maximum concentrations on the floor beams. These are used in designing the floor beams and the girders and also the connections of the stringers to the CHAPTER XXX SHEAR AND BENDING MOMENT 195 floor beams and the floor beams to the girders. The concentration on an intermediate floor beam at each stringer point is equal to the right- hand reaction of one stringer plus the left-hand reaction of the adjacent stringer. The loads should be placed to make this suvi a maximum, but they cannot be placed to make both reactions maximum at the same time lest the engines overlap. The maximum concentration or " floor-beam reaction " will be found when one of the inner drivers of the second engine (wheel 12 or 13) is placed directly over the floor beam. It is usually necessary to try both wheel 12 and wheel 13 over the floor beam in order to ascertain which will give the larger floor-beam reaction. A criterion is sometimes used to determine which wheel to place over the floor beam. There is not much advantage to be gained by its use because both wheels 12 and 13 often satisfy the criterion and both must be tried the same as if no criterion were used. Care should be taken that the load over the floor beam is considered once, but only once, in finding the floor-beam reaction. It may be included in the right reaction of the left-hand span, or in the left reaction of the right-hand span, or 2n 8 OsOsOiOs it may be considered independently. t 15 {^ IS J Illustrative Problem. — To find the maximum Fie 195 (a) floor-beam reaction at each stringer point in a bridge with 15-foot panels, center to center of floor beams, for Cooper's E60 loading. Placing wheel 12 over the floor beam, as in Fig. 195 (a); the reaction at this floor beam may be found from the table as follows: 22.0 = (240 + 45 X 2) -f- 15 = i2B 30.0 = (150 + 60 X 5) ^15 = Rl 30 . = load at floor beam 82 . = total floor-beam reaction in thousands of pounds. This result may be obtained without the table by combining the lever arms of equal loads for both spans, thus: 82.0 = [15.0 X 2 + 30.0(10 + 15 + 10 + 5)] -^ 15. Similarly, by placing wheel 13 over the floor beam another value is ob- tained which in this case is smaller (81.3). 1. Absolute Maximum Bending Moment — Cooper's Loading. — The maximum bending moment for a simple beam not over 11.4 feet long will occur at the center when one of the two 37,500# wheel loads Is placed at the center. For any simple beam or girder from 11.4 to about 90 feet long the absolute maximum bending moment will occur under one of the inner drivers of the second engine (wheel 12 or 13) when the dis- tance between this driver and the center of gravity of all the loads on the beam is bisected by the center of the beam (page 191 : 1). The critical wheel will be adjacent to the center of gravity, usually the wheel nearest the center of gravity. The first engine will have an equal efl'ect for spans up to about 50 feet, but never a greater effect. For girders longer than about 70 feet a portion of the uniformly distributed train load must be considered. The relative position of the center of gravity then changes with every movement of the loads, and more trials are usually needed to determine the proper position of the loads. For girders longer than about 90 feet the critical wheel should be determined from the criterion (page 191 : 1). Illustrative Problem. — To find the maximum bending moment on a 40-foot girder for Cooper's E50 loading. By plotting the length to a 1" scale of -7^ = 1' (40 -r 16 = 2i inches) on the edge of a strip of paper and sliding it along under the wheels in the table to include different com- binations of wheels, it is found that the inner drivers 12 and 13 are brought in the vicinity of the center when wheels 10-16 are on the girder. The position of the center of gravity of these wheels may be found from the corresponding wheels of the first engine (wheels 1-7) to be 0.4 of a foot to the right of wheel 13. The critical wheel is always adjacent to the center of gravity, and for spans less than 90 feet it is one of the inner drivers; in this case, therefore, the maximum bending moment will occur under wheel 13 when it is placed 0.2 foot = 0.4 -^ 2 to the left of the center of the span, as shown in Fig. 195 (6), wheel 16 being 1.2 feet from the right end. For E60 loading, the moment of all wheels about wheel 16 is 3230 thousand pound-feet, and the sum of the loads 10-16 is 174 thousand pounds. The left reaction is 86 thousand pounds = (3230 + 174 X 1.2) -^ 40. The bending moment under wheel 13 is 980 thousand pound-feet = 86 X 19.8 - 720, the value 720 being" the NX // /2 13 14 o o o o 19.8 20.2 15 le o q Fig. 195 (6). 196 PART III — THE DESIGN OF DETAILS moment of wheels 10-13 taken directly from the moment table. The bending moment for E50 loading is f of 980 or 820 thousand pound-feet. In the use of the table, consistent accm^acy should be used. 1. Maximum Bending Moment at Any Point — Cooper's Loading. — The maximum bending moment at any point of a beam or girder wUl occur when the critical wheel is placed at that point. For spans up to 100 feet the critical wheel will be either wheel 12 or wheel 13, although in some cases the maximum moment wiU occin: when the engines face the longer segment instead of the shorter. For spans over 100 feet the critical wheel * should be found from the criterion on page 191 : 1. 2. Through Girders — Cooper's Loading. — The hve loads in a through bridge are appUed to each girder in the form of concentrated loads at the floor-beam connections. The action of the wheel loads may be best shown by sketching the stringers as if they rested on top of the floor 4 n 5 n 6 2n II 12 13 14 IS IB ^n 5 n f HHMHMMKM .Tle3 ^ Stringers Floor Beams -Slrder Fig. 196. beams, and the floor beams as if they rested on top of the girders, as in Fig. 196, although in reahty web connections are used and the trains pass " through " the bridge between the girders. The end stringers may rest directly upon the abutments or they may be connected to end floor beams; in either case the effect upon the girder is virtually the same, except for the details at the ends. If the bridge supports a Single straight track, each floor beam is symmetrically loaded and the corresponding girder load (for hve loads) is numerically equal to the floor-beam reaction. The maximum floor-beam reaction cannot occur at more than one floor * The critical wheels for different segments are indicated in a table in Ketchum's " Structural Engineers' Handbook," McGraw-Hill Book Co., Inc., New York. beam at the same time, and it is necessary to so place the loads that the bending moment at the floor beam nearest the center of the girder will be a maximimi. It so happens that the bending moment at any panel point is the same as if the wheel loads were apphed directly to the top flange of the girder, and hence, the position of the loads which will cause the maximum bending moment at any floor beam is found as in the pre- ceding paragraph. The bending moment at this point may be found as in a deck girder or else from total concentrated loads obtained by com- bining the different floor-beam reactions with the corresponding dead loads (page 225 : 1). The maximum shear in the end panel will occur when the loads are placed to give a maximum bending moment at the first floor-beam point. Illustrative Problem. — To find the maximiun bending moment on a girder of a through railway bridge of four 15-foot panels for Cooper's E60 loading. The maximum bending moment will occur at the center floor beam when the critical wheel (either 12 or 13) is placed at that point. Let us assume that wheel 12 is the critical wheel f and that the loads are placed as in Fig. 196. The floor-beam reaction at the center floor beam is 82,000# as determined on page 194 : 2. In a similar manner the corresponding floor-beam reactions at the first and third quarter points are found to be 39,900# and 52,100# respectively. The bending moment for these loads combined with impact and dead loads is found on page 225 : 1, and the shear on page 250 : 3. 3. Trusses — Cooper's Loading. — Trusses may be designed for Cooper's loading or for equivalent uniformly distributed loads. The table on page 318 may be used to advantage in finding the hve-load stresses in trusses, but the placement of the loads is beyond the scope of this book.J t Both positions should be tried to determine which causes a maximum. In this case a sUghtly greater bending moment is found when wheel 13 is placed at the center, but the difference is so small it is disregarded in order to simplify different steps in a series of problems based upon the values given here. t See Marburg's "Framed Structures and Girders," Part I, McGraw-Hill Book Co., Inc., New York. CHAPTER XXXI THE DESIGN OF BEAMS Synopsis: Beams are proportioned according to the bending moment and shear determined from the external forces. The shape and the size of the cross section are designed with due regard to bending, shearing, buckling, bearing, and deflection. 1 . General. — Most structures are designed in a Designing Depart- ment, although draftsmen are often called upon to design beams. Every draftsman should be familiar with the methods of design if for no other reason than to design the connections properly. The general arrange- ment of the beams in a structure is usually determined in the designing room. Beams which support machinery, tracks, runways, walls, etc., must be located to meet the given conditions. Beams near openings in floors or walls must be placed in the proper relation to these openings. The spacing of floor beams and roof beams or purlins in buildings de- pends upon the type of flooring or roofing and upon the superimposed loads. The type and the length of a beam, the form of loading, the mag- nitude of the loads, and the distance between beams all have their effect upon the shear and bending moment, as explained in the preceding chapter. After these are once determined the design of the beam, or the determination of the proper cross section, is the same for all, regard- less of the sign of the shear or the bending moment. 2. Points Considered. — Beams should be designed to give proper resistance to bending, shearing, buckling, and deflection. Beams which rest upon other beams or walls must have sufficient bearing area (page 203 : 1). Beams are usually designed first to resist bending, and then the resistance of the resulting beam to vertical and horizontal shear is in- vestigated. Beams seldom buckle except under a heavy concentrated load; this part of the design will be discussed under grillage beams (page 293 : 3). The amount of deflection is usually immaterial unless the beam is to support plastered ceilings, shafting, or machinery; when necessary, the deflection should be determined as on page 203 : 2. 3. Effects of Bending. — When a simple horizontal beam is loaded it sags, deflects, or bends downward. The horizontal fibers in the lower part of the beam are lengthened, while those in the upper part are shortened; between these two parts is a neutral surface in which the fiber lengths remain unchanged. Beams are designed upon the assump- tion that all points which lie in a transverse plane before a beam is bent remain in a plane after the beam is bent. In any fiber the " strain " or the change in length is proportional, within the elastic limit, to the " stress " or internal force which causes the strain, according to Hooke's law. The unit stresses used in the design of beams are well within the elastic limit (page 10) and this relation has been found by experi- ments to be true. It follows, therefore, that the horizontal fiber stresses are proportional to the distances of the fibers from the neutral surface. Stresses which tend to lengthen the fibers are called tensile stresses and the fibers are said to be in tension; similarly, compressive stresses tend to shorten the fibers which are in compression. When a beam is con- sidered cut by an imaginary transverse section plane the external forces acting upon either segment are not in equihbrium by themselves but they are held in equilibrium by the internal forces acting in the fibers which are cut by the section plane. The intersection of the neutral sur- face by this section plane is termed the neutral axis of this cross section; this neutral axis passes through the center of gravity of the cross section. 197 198 PART III — THE DESIGN OF DETAILS For convenience let us consider a simple horizontal beam with vertical loads. This simplifies the phraseology and covers the great majority of beams; the principles can be readily adapted to other conditions. The internal force in each fiber cut by the section plane may be resolved into horizontal and vertical components, the latter aU acting in the same direction. The sum of the vertical components must equal numerically the shear on the segment, because the algebraic sum of the vertical com- ponents of these internal forces and the vertical components of the external forces (i.e., the shear, page 184: 1 ) must equal zero in order to satisfy the V equation of equUibrium. In like manner the H equation is satis- fied when the algebraic sum of the horizontal components of both ex- ternal and internal forces equals zero; since there are no horizontal components of external forces it follows that the svun of the horizontal compressive stresses above the neutral axis must equal numerically the sum of the horizontal tensile stresses below the neutral axis. In order to satisfy the M equation the resisting moment or the smn of the moments of the stresses in the fibers cut by the section plane must equal mmieri- caUy the bending moment or the sum of the moments of the external forces acting on the segment (page 184 :2). Since the point of moments is taken in the section plane (page 184 : 2), the lever arm of the vertical components of the internal forces is zero, so only the horizontal compo- nents need be considered. The significance of these points will now be discussed in detail. 1. Resisting Moment — Theory. — A portion of a beam cut by a vertical section is shown in Fig. 198, the right-hand portion of the beam being removed. The inchned line shows the relative position, greatly exaggerated, of the same section after the beam is bent. The arrows indicate the horizontal components of the stresses in the. fibers cut by the sec- tion, being proportional to their distances Kg. 198. from the neutral axis. The vertical com- ponents are not shown because they do not enter into the resisting moment (see preceding paragraph). The fiber which is farthest from the neutral axis (either in tension or compression) is stressed the most and consequently its strength determines the strength of the beam. The unit stress in this extreme fiber must not exceed the allowed vmit stress for bending. Let / = the allowed stress in the extreme fiber, in pounds per square inch, a = the area of each fiber, in square inches, c = the distance from the neutral axis to the extreme fiber, in inches, and X = the distance from the neutral axis to any fiber, in inches. Then fa = the striess in the extreme fiber, ■^ — = the stress in any fiber at a distance x from the neutral axis, fax^ - — = the moment of this stress, c fax^ f S — - = - S ax^ = the sum of the moments of the stresses in all the c c fibers in the cross section, i.e., the resisting moment. But the expression xax^ is generallj^ recognized as the moment of inertia * of the cross section represented by /, therefore — = rriR = the general expression for the resisting moment of any homo- geneous beam. 2. In the above expression for resisting moment the unit stress / de- pends upon the material of which the beam is to be made. Values for / must be taken from the specifications which govern any specific design. For convenience, the values recommended by the American Railway Engineering Association for wood are given on page 320 and for steel on page 317. The values for wood are for a better grade of Imnber than is often used and the values allowed by the building laws of many cities are correspondingly lower. The unit stresses for steel have been quite generally adopted, although higher values are allowed for higher grade steel used in large bridges. These values for / are intended only for beams which are properly stayed against lateral flexure (page 201 :2). * See Kirkham's "Structural Engineering," McGraw-Hill Book Co., Inc., New York, or almost any book on the Calculus or Mechanics. For a proof without the Calculus, see page 199 : 3. CHAPTER XXXI THE DESIGN OF BEAMS 199 1. Section Modulus. — The / and the c in the expression for resisting moment both depend upon the form of the cross section of the beam. Values of - may be tabulated for different cross sections regardless of c the unit stress. This v quantity - is called the " section modulus " and is often represented by the letter S. In this book the lower-case letter s will be used consistent with the adoption of lower-case letters for units which involve inches, and capitals for those which involve feet. Hence TTiR = fs. The section moduli for different sections are found in the com- mon handbooks of the steel manufacturers and also in the tables at the end of this book, as explained below. 2. Units. — An expression for resisting moment may be equated to an expression for bending moment provided they are in the same units, fl ' thus : Mb = Mr or ms = fUR whence ms = — ■ Beams are usually of constant cross section and they are therefore designed for the maximum bending moment. If a beam is of variable cross section, such as an I-beam with plates riveted to the flanges along the central part of the beam, the resisting moment at any section must satisfy the maximum bending moment that can occur at that section. In the above equation, or " flexure formula " as it is sometimes called, there can be only one un- known quantity but that may be on either side of the equation. If the section modulus ( s = - j is unloiown the problem is one in design, other- wise it is one in investigation. In design it is desired to find the shape and size of a beam which will meet given requirements. In investigation it is desired to find how great a load a given beam will support, how great a distance the beam will span, how far from the support a given load may be placed, or how great a unit stress is developed. The usual units for bending moments are pound-feet (page 184 :2), while those for resist- ing moments are pound-inches (compare page 3:2). These must be made identical before they are equated, the value in pound-feet being multipHed by 12 to give pound-inches. Lack of care on this point accounts for the majority of all mistakes in the design of beams by beginners. A convenient method of determining the resulting unit of any expression such as that for resisting moment is to substitute the units of the component parts in the expression, and cancel like quan- tities which occur in both the numerator and denominator. This can be quickly done and it is less confusing than to combine the units and the numerical values in the same expression. For example, in the expres- fl sion - , / is in pounds per square inch, 7 is in inches to the fourth power, and c is in inches. The resulting unit is pound-inches, found as follows: # .... 1 , , , #in. in. in. in. r,- -, , ,. •■ r . — -. — X in. in. in. in. x ■— or better —. — ; — -. . similarly , the umt of in. in. in. in. in. in. section modulus is inches cubed, so the unit of fs is pound-inches thus: . ' . - — '-. This method can be applied in like manner to expressions in. in. for bending moment. 3. Rectangular Beams. — The moment of inertia of a rectangle is bd^ . . . . "TT where d is the dimension at right angles to the neutral axis and b the 1^ dimension parallel to this axis, both in inches. The distance c from the neutral axis to the extreme fiber is ^ because the neutral axis through the center of gravity passes through the center of the rectangle. Sub- stituting these values in the general expression, we find the resisting fbd^ moment of a beam of rectangular cross section to be -^, whence the section modulus is M2 6 ■ This expression for resisting moment may be derived independently without the use of the Calculus. The forces above the neutral axis (Fig. 198) may be replaced by a single resultant force. The unit stress at the extreme fiber is / and at the neutral axis zero. Be- tween these two the forces vary directly with the distance from the neutral axis (page 198:1). For unit breadth the sum of these forces is equivalent to the area of a triangle the base of which is /, and the altitude k- For a beam of breadth h the magnitude of this resultant compressive force 1 J is ^Xf X ^ xh which acts at the center of gi^avity of the triangle or 200 PART III — THE DESIGN OF DETAILS - X ^ below the top of the beam. Sunilarlj', the forces below the neutral axis may be replaced by a single resultant tensile force equal in magni- tude to the resultant compressive force and acting at a corresponding distance above the bottom of the beam. These two equal and opposite forces form a " couple," the moment of which about any point of mo- ments is equal to the product of one force and the perpendicular dis- tance between the two forces. This moment is the resisting moment of the beam and is equal to ^fbd x id -2x3) = -^. This expression applies to homogeneous beams only; it does not apply to compoimd beams, such as reinforced concrete beams. Most of the homogeneous rectangular beams which are designed by the structiu-al designer are wooden beams. These beams are quite often designed according to nominal dimensions, but it seems wiser and more logical to use the actual dimensions which in many cases are considerably less. This depends upon the custom followed in the saw mills of the different loeahties. By some the full nominal dimensions are furnished, while by others the width of each saw cut is deducted. If beams are planed, further deduc- tion is made. The designer should be cognizant of the customs of the limiber inilla which are most hkely to furnish his material. In the absence of further information the following quite common grading rules may be used: rough sawed beams must be accepted if not more than J" scant on each dimension, as 5f x llf ; surfacing or planing removes an addi- tional I" for each face surfaced, as 5f x llf if surfaced on one side and one edge (indicated SISIE), or 5§ x II5 if surfaced on all four sides (indicated S4S). Tables of section moduh for both nominal and actual dimensions are given on page 319. In each case the beam is known by its nominal size and is so referred to. In general there will be several different sizes of beams which will furnish a required section modulus, unless one dimension is determined by fixed conditions, as for example, when a beam must be of the same depth as another similar beam. In ease a table of section moduh is not available, a value of d (or b) must be assumed and the corresponding value of b (or d) calculated. Several trials may be made before a properly proportioned beam results. A knowledge of the stock sizes of the locahty wUl assist in the selection of the beam to be used. The position in the structure, the method of support, and the tendency to overturn or to buckle transversely must all be considered. The deeper beams deflect less, are stiller, and ha%'^ a smaller cross section for the same strength, but they are more Uable to overturn and they may not have sufficient bearing area to properly distribute the loads (page 203:1). In general the depth should be from Ij to 2 times the breadth. ird* d 1. For cylindrical beams of circular cross section I = -^, and c = ^ 32 where d is the diameter in inches. The resisting moment tkr = = 0.098/d' and the section modulus « = ^ = 0.098d'. 2. Steel Beams. — In determining the moments of inertia of I-beams, channels, angles, and other structural shapes, the curves are neglected. It is unnecessary for the designer to use the cumbersome expressions * for. the moments of inertia of these cross sections because numerical values for I and for s about axes perpendicular to each other are tabu- lated in the common handbooks and in this book (pages 322 to 326). I-beams and channels are regularly placed with their webs parallel to the apphed forces. In the selection of a steel I-beam or channel to satisfy a given section modulus, preference should be given to the weights printed in larger type because these sections can usually be obtained more readily from the mills. Furthermore, it will happen frequently that these beams will weigh less per foot and therefore cost less than some other sizes of the same strength. Sometimes beams must be of the same depth as some other beams, and it is usually of advantage to reduce to a mini- mum the mmaber of different sizes of beams for any one contract. The practical designer should keep posted upon market conditions and know which sizes are most easily and quickly obtained. 3. Every beam must be self supporting, and this fact must be con- sidered in the design. Since the weight of a beam is not known imtU after the beam is designed, the weight must be assumed and the corresponding bending moment must be combined with the bending moment for the other dead and hve loads. This is simpler than to attempt to carry the * These expressions are given in the Handbook of the Cambria Steel Company. CHAPTER XXXI THE DESIGN OF BEAMS 201 weight of the beam in terms of the unknown dimensions. After the size of the beam is determined the actual weight should be compared with the assumed weight and the design should be corrected accordingly, if necessary. Usually the bending moment due to the weight of the beam forms a small portion of the total bending moment, so that a slight discrepancy does not matter. Whether or not the difference in weight is great enough to affect the design can usually be told by inspection. It does not take much experience to enable one to estimate the weight more closely than if neglected altogether and there is a good chance of one's guessing accurately enough to make a redesign unnecessary. In estimating the weight of a wooden beam it is usual to allow 3J, 4, 4|, or 5 pounds per foot board measure, the last two being for creosoted wood. One " foot board measure " (Ft.B.M.) is one-twelfth of a cubic foot, as in a board one foot square and one inch thick. To obtain the number of feet board measure in a piece of timber take two dimensions in feet and one in inches. Four pounds per foot is an average value for struc- tural timber. If the dimensions of the cross section (6 and d) are taken in inches the weight of a beam per linear foot is 4 x 1 X t^ or -^. Upon this basis the weights in the last column on page 319 are obtained. 1. A beam is weakened by holes. — The size of the beam is determined by the maxunimi bending moment. Since a beam is generally of uniform cross section throughout its length there is an excess in area except near the point of maximum bending moment. Where this excess is large, as for example near the ends of a simple beam, holes may be safely punched or bored. AVhen holes are required in wooden beams or in the flanges of steel beams where the bending moment is nearly maximmn their effect should be considered. The moment of inertia of the net section should be used. Tliis may be found by subtracting the moment of inertia of the holes from the moment of inertia of the cross section about the same neutral axis. 2. Lateral Supports. — Steel beams are designed for the usual unit stress of 16,000#/sq. in. in bending only upon the assumption that they are properly stayed laterally so that the compression flanges will not buckle. Such lateral support may be furnished by wooden flooring or sheathing, by any form of solid floor construction, by masonry walls. by tie rods, by special struts, by lattice bars or tie plates, by separators, diaphragms, etc. In the absence of some such support the allowed unit stress should be reduced according to the ratio of the distance ([) between lateral supports to the extreme width of member (6). The American Railway Engineering Association specifies that the maximum stress in the compression fibers must not exceed 16,000 — 2OO7. For the sake of comparison, numerical values are tabulated below for this reduction formula, and also for the formulas recommended by R. Fleming * of the American Bridge Company, by the Carnegie Steel Company, and by the Cambria Steel Company. No value should exceed 16,000. Unit Stresses tor Beams without Lateral Support Ratio b A.R.E.A. 16,000-200^ FJeming 19,000 - 250 J Carnegie 19,000 - 30o[ Cambria 18,000 P ^ "*" 30006 » 6 10 15 20 25 30 35 40 15,000 14,000 13,000 12,000 11,000 10,000 9,000 8,000 16,000 16,000 15,250 14,000 12,750 11,500 10,250 9,000 16,000 16,000 14,500 13,000 11,500 10,000 8,500 7,000 16,000 16,000 16,000 15,880 14,900 13,850 12,780 11,740 3. Beams which are subjected to a lateral thrust should receive special consideration. For example, a floor beam next to an elevator shaft or other opening may receive the thrust from a brick or tile floor arch on one side only. Intermediate beams have the thrust of one arch largely counterbalanced by that of the arch on the opposite side. The thrust of an arch at the ends of the arch span is equal to the maximum total compressive stress and this must be counteracted by the tension in tie rods or by the lateral resistance of the beams. Concrete floor slabs are usually reinforced so that no thrust on the beam need be considered. In deriving an expression for thrust in pounds per Unear foot of beam * Engineering News, April 6, 1916. 202 PART III — THE DESIGN OF DETAILS let us assume an equal tension T in the tie rods, also in pounds per linear foot of beam. These equal forces constitute a couple, and the perpen- dicular distance between them is the effective depth of the arch h in inches. The resisting moment Th must equal the bending moment on the arch due to a vertical load of U' pounds per square foot for a span of X feet center to center of beams, thus: Th = 12-^ l-^V whence the 3 U' X^ thrust T = — ^T — ■ For fiat arches commonly used, the effective depth may be taken 2.4" less than the depth of the arch. A beam without lateral support must be designed so that the combined fiber stress due to vertical bending and to lateral bending will not exceed the allowed stress per square inch (16,000). A beam somewhat larger than the size required for vertical forces alone should be assumed and then investi- gated. The fiber stress due to vertical' forces may be found by equating the bending moment of vertical forces to the resisting moment and solv- ing for /, the section modulus of the assumed beam being known. Simi- larly, the fiber stress due to lateral forces may be found, the bending moment being found for the uniformly distributed thrust T (see above) and for the proper length between supports. The section modulus must be taken about an axis parallel to the web. Values for this S2 for channels are given on page 323. Values for I-beams may be obtained from 1 2 (page 322) and from c which is one-half the flange width. (Note that c for channels is the distance from the center of gravity to the further edge of the flange.) If a beam is supported by tie rods it becomes a con- tinuous beam. By the Theorem of Three Moments an expression * may be found for the maximum lateral bending moment in terms of the thrust T and the panel length B between rods. If only one rod is used in the center of the span L, the bending moment is" 8 if two rods are used making three equal panels of B feet the bending moment is TB^ 10 ' rods are used making four equal panels the bending moment is if three 28 ■ * See Johnson-Bryan-Tumeaure's "Modern Framed Structures," Part II, John Wiley and Sons, Inc., New York. See also footnote, page 193. 1. Shear. — After a beam is designed to give proper resistance to bending, its resistance to shear should be investigated. The size of the beam wiU seldom be increased as a result of this investigation, neverthe- less it should be disregarded only by a man of experience when he is con- fident that no increase will result. The intensity of vertical shear at any point of a beam is equal to the intensity of horizontal shear at the same point,t much as the vertical and the horizontal water pressures at any point in a tank of water are equal. This intensity is not uniform through- out the cross section but is zero at the extreme fibers and maximmn at the neutral axis. The maximum shear intensity in any beam should not exceed the allowed unit stress either in horizontal shear or in vertical shear. For steel the allowed stresses are equal, but for wood the value specified for the " longitudinal shear in beam " is considerably less than for the transverse shear. For any cross section of a rectangular beam the maximum shear intensity is three-halves of the average shear in- 3F tensity, or i; = ^7-^, in which v = maximum horizontal or vertical shear intensity in pounds per square inch, V = maximum shear for the section in pounds, b and d = the breadth and depth of the beam in inches. This ex- pression may be derived in the following manner. In Fig. 198 are shown the horizontal forces acting in the fibers of a beam cut by a transverse section. Let a similar section be passed at a small distance x from the first section. Let /i = the unit stress in the extreme fiber at the first section, /2 = " " " " " " " " " second " c = ^ = the distance from the neutral axis to the extreme fiber. mi = fis = the bending moment at the first section, ms = fiS = " " " " " second " wia = mi + Fa; (page 189 : 1), the shear virtually being constant between sections, s= -g- (page 199:3). fi -fi = the increase in stress in the extreme fiber within the distance x. t See Kirkham's "Structural Engineering," McGraw-Hill Book Co., Inc., New York, Fuller and Johnston's "AppUed Mechanics," Vol. II, John Wiley and Sons, Inc., New York, or similar books. CHAPTER XXXI THE DESIGN OF BEAMS 203 There is a proportionate increase in every fiber between the extreme fiber and the neutral axis. The longitudinal shearing stress at the neutral axis for the distance x per unit of breadth is the sum of the increases in stress in all these fibers. This sum is equivalent to the area of a triangle of which the base is U - /i and the altitude ^. The shearing stress per square inch or the shear intensity is equal to this sum divided by x, or IhcPx 2hd' The general expression* for the shear intensity at any point of a beam Vq . . of any cross section is ?> - -jr, in which q = the statical moment about the neutral axis of that portion of the cross section between a horizontal plane through the extreme fiber and a horizontal plane through the given point, and b = the breadth of the beam where cut by the latter plane. The statical moment is the product of the area of the portion of the cross section referred to by the distance from its, center of gravity to the neutral axis. Thus the expression for the maximum shear intensity at the center of a rectangular beam may be found from the general expression as follows: V = -. bd d F X-2 X I 6# 12 X 3F 2bd' For beams of circular cross section the maximum shear intensity is four-thirds of the average intensity or V = r- — - = - — - in which d and r = the diameter and the radius of the beam in inches. For I-beams and channels there is no convenient expres- sion for the maximum shear intensity, nor can the intensity be found without considerable computation. f For all practical purposes, however, it is sufficiently accurate to use an approximate method which can be applied much more easily. The web must furnish most of the resistance * See Fuller and Johnston's "Applied Mechanics," Vol. II, John Wiley and Sons, Inc., New York. t See Fuller and Johnston's "Applied Mechanics," Vol. II, John Wiley and Sons, Inc., New York, or the Carnegie Steel Company's "Pocket Companion." to shear because the flange areas are concentrated near the extreme fibers where the shear intensity is small. The maximum shear intensity for an I-beam or a channel may be found by dividing the maximum shear V by the area of the straight portion of the web between the flanges. This area is equal to the web thickness multiplied by the tangent dis- tance {d-2k from the tables) between the curved fillets. 1. Bearing. — A beam which rests upon its supports must have suf- ficient bearing area to properly distribute the pressure of the beam on the supporting wall, beam, or column. A beam which rests upon ma- sonry walls usually has a steel or cast-iron bearing plate to provide greater bearing area. The design of such a bearing plate is explained in Chapter XLIII, page 288. The bearing is not a determining factor in other methods of support for steel beams, such as connection angles with rivets. The bearing does play an important part in the design of wooden beams because it may determine the width of the supported beam or the width of the beam or column which supports it. The bearing area or the horizontal area of contact between a beam and its support must be large enough to prevent the fibers from crushing. The allowed pressure per square inch is the unit stress in " crusliing " or compression at right angles to the grain. The total pressure is equal to the maximxmi reaction which can be caused by the full dead load (including the weight of the beam) and the live load. The required bearing area is found by dividing this total pressure by the unit stress in crushing across the grain. The necessary length of bearing or the distance which the beam must project onto the support is found by dividing the bearing area by the width of the supported beam. If two beams are supported at the same point of a supporting beam, the width of the latter must be sufficient to furnish the proper length of bearing for both beams. Sometimes two narrow joists or beams overlap so that each may bear on more than one half the width of the supporting beam. 2. Deflection. — The amount of vertical deflection is an important consideration only in the design of beams which support tile or concrete floors, plastered ceilings, shafting, etc. If the deflection exceeds a cer- tain amount, unsightly cracks are liable to result in the floors or ceilings, and free action of the shafting or other moving parts may be impaired. Certain limiting ratios of the depth to the length of a beam can be found, 204 PART III — THE DESIGN OF DETAILS above which a beam will not have excessive deflection. By means of these ratios the designer can properly design beams without further investigation for deflection. Accordingly, the theory of the elastic curve wiU not be developed here,* but sufficient formulas will be given to enable the student to determine the amount of deflection in the average beam. In all of these expressions, L = the effective length of the beam in feet, I = the same in inches, P = the concentrated load in potmds, U = the unit load uniformly distributed in pounds per linear foot, W = the cor- responding total load uniformly distributed in pounds, I = the moment of inertia of the cross section in inches*, and E = the modulus of elas- ticity in poimds per square inch. The modulus of elasticity for steel is 29,000,000; values for different kinds of wood are given on page 320. The maximum deflection in inches at the center of a simple beam under bWl^ 4:5UL* a full load uniformly distributed is „. = , and under a single Pl^ 36PL3 load concentrated at the center is. The maximum de- end only under a full load unifoi-mly distributed is 48EI EI flection in inches at the free end of a cantilever beam supported at one Wl^ 216 UL* 8EI " EI ' PP 576PL* and under a single load concentrated at the free end is ^r^j^ = —^^ — ■ For beams with combined loads the deflection due to concentrated loads and imiformly distributed loads may be added. It has been determined experimentally that plaster will crack when the deflection is more than ■j^ of the span, and this value appears in many specifications. If we equate 12L ^ 45 UL* to or to 36PX» and eliminate U or P as explained 360 "" 2EI EI below, we can solve for the corresponding ratio of the depth to the length. By equating ttib = 2/7 12 UI/ \2PL or — : — to WlK = =^— = C 2// we find U 4/1 and P ML' By substituting these values above and also E = 29,000,000 * See Fuller and Johnston's "Applied Mechanics," Vol. II, John Wiley and Sons, Inc., New York; or Kirkham's "Structural Engineering," McGraw-Hill Book Co., Inc., New York. For diagrams by C. A. Ellis, see Engineering Record, Jan. 15, 1916. and / = 16,000, we can solve for -^ = t. In this manner we find that for simple steel I-beams or channels designed for a unit stress of 16,000#/sq. in. in bending, and a modulus of elasticity of 29,000,000#/sq. in., the de- flection wfll not exceed ^^ of the span if the depth is at least -^ of the span for a uniformly distributed load or at least ^ of the span for a single concentrated load at the center. In other words, the length in feet should not be more than two (or two and one-half) times the depth in inches. Other ratios can be derived in a similar manner as required. When a beam is subject to shocks or vibrations the depth should not be less than -^ the span. I-beam stringers for railway bridges should preferably have a depth not less than -^ of the span. When the depth cannot fulfill the above conditions the beam should be made enough stronger so that the deflection will not be greater than if a beam of the required depth were used. Roof purlins may usually have a depth of only ^ of the span because the maximimi load is seldom/ if ever, reahzed. 1. The principal points of this chapter are illustrated by the following tjrpical problems. First Problem — Wooden Beam. — Design a 12-foot Norway Pine beam for a building, to resist a bending moment of 12,600#ft. and a shear of 4,200#. 12,500#ft. = bending moment of superimposed loads 400#ft. = -^ X 6^ = bending moment due to weight of beam (6 X 12 assimied; see page 319 for weight) 12 X 12,900 = 1,200s (for unit stress in bending, see page 320) 129 = s. Counting the actual dimensions \" scant, this calls for a 6 X 12, the section modulus for a 5| x llf being 132. 4,200# = shear due to superimposed loads 150# = 24 X 6 = shear due to weight of beam cnji, ■ 3 X 4,350 " . ,. . . . 97#/sq. in. = 2 x 5 75 x 11 75 ^ "^^ ^" ^""^ shear mtensity (page 202:1). This is safely under the 150 allowed for longitudinal shear in beams (page 320). 3-3" = 230 X 5 75 ^ *^^ length of bearing required. CHAPTER XXXI THE DESIGN OF BEAMS 205 Second Problem — Wooden Beam. — Design a Long Leaf Yellow Pine 12 x 12,800 = 16,000s (for unit stress in bending, see page 317) (abbreviated LLYP) Highway bridge beam 20 feet long to support a uniformly distributed load of 250#ft. 8 X 12 30#/ft. = — ^ — = weight of beam 8 X 12 assumed (page 200 : 3) 14,000#ft. = ?^_±250 ^ ^Q, ^ ^^^^j ^^ 12 X 14,000 = 1,630s 104 = s which calls for a 6 X 12 or an 8 X 10 although both are large. 9.6 = s. Either a 7" I 15# (page 322) or a 9" U 13J# (page 323) can be used. Note that an 8" LJ 16j# is strong enough, but it weighs more and is not so readily obtained (page 200 : 2). 4,200# = shear due to superimposed loads 90# = 15 X 6 = shear due to weight of 7" I 15# 4,290 3,270 = .25(7 - 2 X I) = shear intensity which is safely under the -Since a 6 X 10 is nearly large enough it should be tried because the 10;|^00#/sq. in. allowed for beam webs as well as for girder webs (page reduced weight may reduce the section modulus sufficiently. 20 = — r. — = revised weight 4 = (30 - 20) 10^ X 12 317). Fourth Problem — Investigation. — Find the safe load concentrated at the center which a 15" I 42# 30'-<)" can support. Also find the maxi- mum deflection. The section modulus is 58.9 in.' and the unit stress = the reduction in s. 2 X 1630 100 = 104 - 4 = the revised section modulas. A 6 X 10 can there^ fore be used. 2,700# = (20 + 250)10 = maximum shear. 68#/sq. in. =-;r — -^ — — = maximum shear intensity which is safely under *'^® beam is -2" X 15 . Hence ^ X O X JLU 2 .. ^^^) = 16, 9,840# = P. is 16,000#/sq. in. The reaction for a load P at the center is -^ and the p bending moment x- x 15. The bending moment due to the weight of 42 1.2" = the 150 allowed. 45 X 270 X 20^ ^hVU 2 X 1,610,000 X 500 1E1 the maximum deflection. 12(|xl5 + ?Xl5M 000 X 58.9 ^ , ^ ^ . , n^„ 36 X 9,840 X 30' Z^PU , „ ^. , , . x j , , Third Problem — Steel Beam. — Design a steel beam to satisfy the -75" = 29 000 000 X 442 " ~£7~ " deflection due to concentrated load. 45 X 42 X 30* conditions of the first problem above. 12,500#ft. = bending moment of superimposed loads 300#ft. = Jjj^ X 6^ = Mb of assumed weight of beam •^^ 2 X 29,000,000 X 442 .81" = total deflection. 45C^* 2EI = deflection due to weight of beam. CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS Synopsis: The principles of design are given for the more common types of tension and compression members and for lattice bars. No 'attempt has been made to cover the practical points which must be considered in the design of a complete structure. 1. The structural designer must take into consideration many practical points. He must not design each member independently of other mem- bers, but he must so proportion all the members that they will form the best complete structure. He must consider not only the strength and the appearance of each member, but he must also anticipate the details so that the member can be fabricated and connected to other members to the best advantage. The design of complete structures is outside the scope of this book,* but the fundamentals of design are here given inasmuch as the draftsman is often called upon to design simple members. 2. A tension member is designed to transmit tensile stresses in a direc- tion parallel to its principal axis; the stresses which are transmitted by a tension member tend to elongate that member. A compression member is designed to transmit compressive stresses in a direction parallel to its principal axis; the stresses which are transmitted by a compression member tend to shorten that member. Sometimes forces are appUed to either tension or compression members which tend to bend them trans- versely. Such members must be designed for stresses due to both bending and direct tension or compression. , * For more complete treatises see Johnson-Bryan-Turneaure's "Modern Framed Structures," Vol. Ill, John Wiley and Sons, Inc., New York, for bridges and roof trusses; Ketchum's "Mill Buildings," McGraw-HiU Book Co., Inc., New York, for mill building construction; Burt's "Steel Construction," American Technical Society, Chicago, for office building construction; Kirkham's "Structural Engineering," McGraw-Hill Book Co., Inc., for bridges, mill buildings, and office buildings; and Kunz's "Design of Steel Bridges," McGraw-Hill Book Co., Inc., for viaducts, movable bridges, arches, canti- levers, etc. 206 3. The area of cross section is an important factor in the design of either a tension or a compression member, whUe the form of cross sec- tion is of special importance in a compression member. A tension member is equally strong whether the cross section is in the compact form of a circle or rectangle, or in the more open form of a hoUow pipe or similar section, provided the area is the same. A compression member, on the other hand, is stronger if the metal is distributed so that the member is less hkely to buckle or bend imder compression. Thus a small rod would not resist so much compression as would a hollow pipe contain- ing the same amount of metal. Cast iron columns, for example, are made hoUow for this reason. 4. Effect of Rivet Holes. — A tension member is weakened by having holes punched in it for rivets. A compression member is not weakened in the same manner, provided the rivet holes are completely filled with either shop or field rivets. The reason for this difference is that the rivets are in contact with the metal surrounding the holes, but they are not attached to this metal. The rivets in the holes can therefore transmit compressive stresses from one side of the hole to the other much as the original metal would, but the rivets cannot prevent the member from pulling away from them when the member is subjected to tensile stresses. Rivets are compressed in driving, so the effect of cooling is to reduce the resulting pressure in the rivets rather than to shrink them so they are no longer in contact. Bolts, however, do not completely fill the holes. Any bolt holes, or holes left open, should be considered in determining the effective area of a compression member, provided they occur where CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS 207 there is considerable tendency to buckle. In a tension member it is assumed that the total stress is distributed uniformly over the net area; in a compression member it is assumed that the total stress is distributed uniformly over the whole gross area, except as provided in the preceding sentence. These assumed conditions are not always fulfilled, particu- larly when the end connections are not properly designed; but the assumptions have proved sufficiently accurate for the design of such members as are discussed in this chapter. TENSION MEMBERS 1. A tension member must be so designed that it is strong enough at its weakest point to carry the total stress. Some of the lightest tension members are made of round or square rods. Different methods are employed for fasteniijg these rods to other members, as illustrated on page 316. 2. A loop rod is made by bending the end of a rod back upon the rod and forging it to form a loop (page 316). The loop is shaped to fit around a pin such as a cotter pin (Fig. 279) or a larger pin (Fig. 278 (6)). The loops are made stronger than the main part of the rod, so that the designer simply has to determine the size of the rod. Both round and square rods are used for loop rods. The required area of cross section is found by dividing the total stress by the allowed unit stress. From the table on page 315 the diameter of a commercial size of round rod may be selected with an area (second column) which equals or exceeds the required area. The size of a square rod may be found by taking the square root of the area or by using tables of square rods found in the handbooks of the different steel manufacturers. The sizes most used are multiples of ^". 3. A clevis is a forging made with two loops between which a con- necting plate is inserted and held in place by a cotter pin. The clevis is made to screw on the end of the rod like a nut, a right-hand thread being used at one end and a left-hand thread at the other so that when the rod is turned it is tightened. Clevises are used less frequently than formerly because of the relatively high cost. 4. The form of rod most used is the round rod threaded at the ends for nuts, as shown in the different types of connection on page 316. The effective area of the rod is reduced when a thread is cut and a corre- spondingly larger rod must be used so that the least area at the root of the thread will be sufficient. In most cases a larger rod is used for the entire length. The ends of some of the longer rods are upset in the forge shop to a larger diameter so that after the threads are cut the strength at the ends is slightly greater than the strength of the main portion of the rods. The diameters and lengths of standard upset ends are given on page 315. The design of an upset rod is the same as for a loop rod, only the main portion of the rod being considered. The table of root areas for the upset ends may be used in the design of rods which are threaded without being upset. For example, let us design a rod to carry a stress of 7,500# at a unit stress of 16,000#/sq. in. The net area must be at least 0.47 sq. in. = 7500 -^ 16,000. The diameter of a rod with a root area of 0.55 is 1", which must be used as the next smaller rod has a root area of only 0.42. Note that a loop rod or an upset rod used under these conditions need be only |" in diameter for the gross area is 0.60. The asterisks indicate that rods less than 1" are not as a rule upset. The asterisks have no significance when the table is used for threaded rods not upset. In order to obtain the root area for any multiple of |" between f and 3 it becomes necessary to use the following values to supplement those in the table: Diam. of Area as Upset Root of Thread H 0.69 i| 2.05 2f 4.62 5. Eye bars are used for the tension members of pin-connected bridges. The ends are upset and punched, as shown in Fig. 40 (d), and then the holes are accurately bored to the proper size and at the proper distance apart. The heads are made the same thickness as the rest of the bar, and they are designed to fully develop the main body of the bar so that no bar tested to destruction should fail in the head. The design of an eye bar is therefore quite simple. Eye bars are usually arranged in pairs to keep the forces on the pins S3anmetrical. The depth or width of an eye bar is usually determined by the size of other eye bars and of other members 208 PART III — THE DESIGN OF DETAILS in the bridge. The thickness of each bar and the number of bars are determined by the required area of cross section, which is foimd by diA^ding the total stress by the unit stress. The thickness of each bar is usually between 1" and 2"; 2" is the maximum thickness, while the TniTiimnm thickness differs with different widths of bar and with different .sizes of pins as indicated in the handbooks of the steel manxifactm-ers. Between these limits the thicknesses vary by one-sixteenth of an inch. 1. Riveted Tension Members.^ — Tension members other than rods and eye bars are usually made of angles, channels, plates and angles, or plates and channels. One or two angles are used for the hghter mem- bers, as for example, those in latticed girders (Fig. 110), roof trusses (Fig. 116, or bracing (Fig. 140). Foiu- angles are often used, as in the diagonal of Fig. 143. The component parts of a member must be fastened to- gether to distribute the stress so that each part receives its share. Two angles are fastened at intervals by stitch rivets (page 69:4). Four angles may be fastened by batten plates, by lattice bars, or by continuous plates (Fig. 125, 122, or 126); continuous plates may be coimted as part of the effective cross section. 2. The strength of a tension member is proportioned to the least net area of cross section, as explained on page 206:4. Riveted tension mem- bers are usually connected to other members by means of connection plates, and the least net areas are most often fomid through the holes for the rivets which connect the members to these plates. The weakest section of an ordinary hght tension member is a cross section through the largest number of rivet holes. Compare page 209:1. The net area of this section is found by combining the net areas of the component parts. The net area of each part is found by subtracting the area of cross section of the holes from the gross area found from the tables. The area of cross section of a hole; is the area of a rectangle, not of a circle (Fig. 221) ; it is the product of the diameter of the hole and the thickness of metal. The diameter of the hole in designing is taken J" greater than the nominal diameter of the rivet. The hole is actually punched only -^" larger, but the metal aroimd the hole is damaged during the process of punching so that it cannot be counted upon to carry the full stress per square inch; the practically universal method of taking this into account is to deduct an additional iV", calling the hole i" larger than the rivet. The areas of holes are tabulated on page 303; these areas may be used in finding the net areas of angles, channels, or other shapes. The net areas and the strengths of tension members composed of two angles are given on page 327; the net areas and strengths of single angles may be found by dividing these values by two. The net area of a plate can be foimd more conveniently by multiplying the net width of the plate by the thickness, since both the area of the plate and the area of each hole are proportional to the thickness. The table on page 321 is arranged to give both net and gross areas of plates. The net area is foimd opposite the net width. Thus the net area of a 14" plate with two holes deducted for f " rivets is the same as the gross area of a 12^" plate. 3. Illustrative Problem. — Investigation. — Let us find the safe load of a section composed of 1 PI. 12 x f and 4Ls4x3x| with holes for f " rivets, arranged as in C 3, Fig. 137. Unit stress in tension = 16,G00#/sq. in. 8.60 sq. in. = 4(2.48 - | x |) = the net area of 4 Ls4 x 3 x f 3.84 sq. in. = (12 - 2 x |)f = the net area of 1 PI. 12 x | 12.44 sq. in. = total net area 199,000# = 12.44 X 16,000 = the safe load. The net areas should be indicated completely as shown for the sake of future reference; this is of special benefit in student work because the instructor can mark mistakes in such a manner that the student can tell whether he took the wrong number of holes, the wrong diameter, or the wrong thickness, or whether he took the wrong value from the tables or made an arithmetical mistake. Thus, in the first line are shown the number of angles, the gross area of one angle, the number of holes deducted from each angle (in this case 1), the diameter of the hole (|" larger than the diameter of the rivet), the thickness of the hole (should be the same as the thickness of the angles), and the description of what the result indicates, i.e., the net area of a given munber of angles of a certain size. The gross area is taken from the table on page 303 as is also the area of one hole, 0.33 = 1 X f . Similarly, in the second fine are shown the full width of the plate, the number of holes, the diameter of each hole, the thickness of the plate, and the description of the result. 4. The design of a riveted tension member is an indirect process because the area of the holes cannot be found imtil the thickness of the CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS 209 metal is known. After the required net area is found, the size of the section may be approximated and the corresponding actual net area may be determined; unless this actual net area equals or exceeds the required net area another trial should be made. The final section should be the smallest section which will satisfy the requirements. The follow- ing tjrpical problems illustrate the design of simple tension members. First Problem. — Design a single angle, with a row of |" rivets in one leg, to support a load of 30,000# at a unit stress of 15,000#/sq. in. 2.00 sq. in. = 30,000 -^ 15,000 = the net area required. The simplest method is to use the table of net areas for two angles (page 327) for a value equal to twice the required area. With one hole for a j" rivet deducted, the following sections will satisfy the requirements: 4 X 4 X tV, 3^ X 3i X I, 3 X 3 X i^, 5 X 3 X T^, 4 X 3 X f , 3| X 2i X A. If the unit stress were 16,000 the problem would be still further simplified, since the stresses could be taken directly from the table and it would be unnecessary to find the net area. Second Problem. — A hanger is composed of two 8" channels placed back to back with a space between them for the insertion of connection plates at the ends. They are riveted to the plates by f " rivets placed in three rows. The total stress is 100,000#, and the unit stress is 16,000#/sq. in. Design the member. 6.25 sq. in. = 100,000 -^ 16,000 = the net area required. The gross areas and web thicknesses of channels are found on page 323. Since the web thickness is not a multiple of yV" it is better to use the decimal; with a slide rule this is as convenient as to use the table of areas for rivet holes. (5.54 sq. in. = 2(3.35 - 3 X i X .22) = the net area of 2-8"L^ lli#) 6.46. sq. in. = 2(4.-04 - 3 X | X .31) = " " " " 2-8"LU 13f# The result of the first trial was too small, so the second trial was neces- sary. Two 8" LSJ 13J# would be used. It is a good plan to draw paren- theses around all trial designs except the one adopted. Third Problem. — Design a 12" splice plate, with four lines of f " rivets, to carry a stress of 65,000# at 16,000#/sq. in. 4 . 06 sq. in. = 65,000 -^ 16,000 = the net area required 8.50 in. = 12 - 4 X I = the net width of the plate i" = .48 = 4.06 + 8.50 = the thickness required. Note that the thicknesses of commercial plates vary by sixteenths, and unless the resulting thickness is a multiple of j\", the next higher value should be used. The length of the spUce plate depends upon the total number of rivets required (page 270 : 2). 1. The least net section is not necessarily a right section. Rivets in another line may be spaced so close that a member tested to destruc- tion would fail along a zigzag fine, as shown in Fig. 209. The relative strength cannot be judged by comparing the full net section along the zig-zag line to the net right section, because the unit stress along the inclined lines is not the same as along the transverse lines. The maximum diagonal tension may be computed from the normal and the tangential components of the longi- tudinal stress. The minimum stagger which can be used without maldng the strength of the member less than at the net right section is found when this maximum diagonal unit stress equals the unit stress on the net right section. This minimum stagger may be found from the diagram on page 305 for different diameters of rivets and for different distances between rivet lines. The diagram is plotted for the following equation: (g d + {2 Fig. 209. (I ~ ^) (^ + ^^' + ^•^') =9'+P-{d+^) Vg^ +p in which g = the gage or the transverse spacing from center to center of rivets (see the figure under the diagram), / = the minimiun longitudinal pitch or stagger from center to center of rivets, and d = the nominal diameter of the rivets. This equation is based upon theory * which has been substantiated by tests on riveted tension splices.f If practicable, the pitch should not be less than the proper value foimd from the dia- gram. Otherwise, a corresponding reduction in the net section must be made, as explained in the next paragraph. Unfortunately, the importance * Adapted from a similaj- expression derived by V. H. Cochrane in the Engineer- ing News, April 23, 1908. See also the Engineering News, May 6, 1915. t "Versuche im Eisenbau," Berlin, 1915. 210 PART III — THE DESIGN OF DETAILS of this requirement is not yet fully realized by all designers and writers of specifications. 1. Working Rule for Effective Net Section. — Obviously, holes that are staggered do not weaken a member as much as if the holes were all in the same right section. If a hole is as far from a given right section as the minimum stagger determined from the diagram (see preceding paragraph) it has no effect upon the strength; if the hole is placed in the right section the net section is reduced by the full area of the hole; if the hole is between these limits the net section is reduced by a fraction of the area of the hole. From the theory upon which the formula of the preceding paragraph is based may be found this fractional part of a rivet hole which should be deducted in order to give the actual effective net section.* This method is too cumbersome for general use, but approxi- mately the same results may be obtained by means of a practical working rule t which is recommended; all variations are on the side of safety. This rule is as follows: " The net section of a plate or shape shall be defined as the least section obtainable across the rivet holes, square or zigzag, taking every net distance in a diagonal direction at 85% of the value, except where 85% of the distance is less than the square projection, in which case the latter shall be used instead." The application of this rule may be illustrated by a 12 X 2 plate with holes for |" rivets, as shown in Fig. 209; the transverse spacing is 3" with IJ" edge distances and the longitudinal spacing or stagger is 2". The net area of a right section is 5.00 sq. in. = (12 — 2 X l)i; if the rivets were placed in the same row the net area would become 4.00 = (12 - 4 x 1)^. Since the stagger is less than the minimum of 2| foimd from the diagram on page 305 (for a gage of 3"), the effective net area must fall between 4 . 00 and 5 . 00 sq. in. The net area outside of the outer holes is 1.00 = 2(1| - f)J and the net area between the inner holes is 1.00 = (3 - 1)^. , The diagonal distance from center to center of holes is 3.60; this may be determined graphically from a full-sized layout, from the diagram on page 312, or from a table of squares. Eighty-five per cent of the corresponding net area is 1.11 =0.85(3.60-1.00)1; this is not less than the " square projec- tion " 1.00 = (3 - 1)J, so two such areas should be combined with the * Derived by T. A. Smith in the Engineering News, May 6, 1915. t Developed by D. B. Steinman, in the Engineering News-Record, June 14, 1917. net areas already foimd to make the total effective net area 4.22 sq. in. = 2 X 1.11 + 1.00 + 1.00.' It should be noted that the rivet spacing is a prerequisite to the application of this rule, and the designer must anticipate the details. He must assume the niunber of rivets in a right section and also the minimum stagger; these are sometimes apparent, but usually he must either specify them to the draftsman or else indicate the least net area for which a member is designed so that the draftsman can space the rivets accordingly. The design of some of the smaller members may be simplified by considering all holes in the same right section, unless they can be spaced at the minimum stagger determined from the diagram; if only one or two additional holes are involved, par- ticularly if the stagger is small, very httle metal is thus wasted. 2. In the preceding paragraphs, the least net section is considered to be found within the portion of a member which is subjected to the full stress. A smaller net section may be safely used near the ends of a member where part of the stress has been transmitted to the connection plates by means of rivets. In this way the size of the connection plates may be reduced. For illustration, let us consider the strength of the member LO-2 Fig. 125. The least net section designed to take the full stress is 30.12 sq. in. = 2(21 - 4 x 1)A + 4(3.25 - 1 x i) found through the four shop rivets (in each web) near the right end where the 14 x t^ fillers begin. In the connection at the left end of the member, the net area through the three field rivet holes at the right of the group must be sufficient to take the full stress also. A smaller net area may be used two spaces to the left of this section, because the stress has been reduced by the strength of ten field rivets in single shear or 60,100# (page 310). Two rivets in the bottom batten plate come within IJ" of this new sec- tion; the minimum stagger from the diagram is 2f", found for a gage of 3f = 2J + 2| - |. If these rivets are counted in the same right sec- tion, the net area is 28.00 sq. in. = 2(21 - 5 xl) tf + 2(3.25 - 2 x 1 X i) -h 2(3.25 - 1 X I). The difference in strength between this section and the main section is only 33,900# = (30.12 - 28.00)16,000; this does not exceed 60,100, so the arrangement of rivets is satisfactory. Had this value been shghtly in excess of the strength of the ten rivets, the net area should be found more accurately (preceding paragraph) before any change were made in the arrangement of rivets. In hke manner, the CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS 211 net section near the ends of a member may be reduced by changing the rivet stagger instead of the number of rivets. The minimimi stagger from the diagram should be used for one or two spaces from the edge of the plate where the stress is maximum (i.e., towards the center of the member), but the remaining spaces may be reduced. As before, the net section at any point must be sufficient to carry that portion of the total stress that is not already transmitted by rivets. COMPRESSION MEMBERS 1. The design of a compression member is an indirect process in which the form and the size of cross section are assumed, and the corresponding safe load is compared with the required stress. The result of the first trial furnishes a guide for the second assumption. The experienced designer can usually approximate the final section in his first assump- • tion. Men who have considerable designing to do are equipped with more or less exhaustive tables of safe loads of members of different cross sections for different lengths.* Tables for struts composed of one or two angles are given on pages 330 and 331. No such table should be used, however, until the underlying principles are clearly understood. 2. The strength or safe load of a compression member is found by multiplying the unit stress by the gross area of cross section, without deducting for holes which are to be filled by rivets (page 206:4). The unit stress is not a fixed amount as for tension members, but it varies with the length of a member and with the form and area of its cross sec- tion. A long member is more liable to bend or buckle than a short one of the same cross section. When the area of cross section is distributed, it is more effective in resisting compression than when the same amount of material is compacted (page 206 : 3) . The unit stress allowed in the design of a compression member is determined from a " compression formula," " column formula," or " reduction formula." These formulas are of two general types, but both depend upon the " ratio of slenderness " -, in which I = the unsupported length of member and r = the least r * See also Ketchum's "Structural Engineers' Handbook,'' or Sample's "Properties of Steel Sections,'' McGraw-Hill Book Co., Inc., New York; also the handbooks of the different steel manufacturers. radius of gyration (see below), both in inches. One type is the "straight line formula," as for example unit stress = 16,000 - 70-, which is the equation of a straight line. The other type is the " Rankine (or Gordon) formula," as for example, unit stress = '-^ , which is the equa- 1 + P 36,000r2 tion of a curve. Most specifications and building laws require the use of a formula of one of these types, but in many of them different nu- merical values are inserted in place of the 16,000 and the 70, or the 12,500 and the 36,000. The Rankine formula is used less commonly than formerly, because the straight line formula is more easily applied and gives results which are quite as satisfactory. The formula most com- monly used is undoubtedly the 16,000 — 70 -, with a maximum value of 14,000, which is recommended by the American Railway Engineering Association; this has been widely adopted. The unit stresses obtained from this formula for different values of I and r are tabulated on page 328. _ 3. The radius of gyration is the term appUed to the expression i/-, or / = ar^, in which a = the gross area of cross section, and / = the cor- responding moment of inertia. The unit stress for any compression member without intermediate support is determined by the least radius of gyration, which is found from the least moment of inertia. Because of the rectangular construction of most structural steel members, the least moment of inertia is found about one of two perpendicular axes (except for a single angle). Often the axis about which the moment of inertia is least may be selected by inspection; otherwise, the moments about both axes must be found and compared. Thus for example, the moment of inertia and the corresponding radius of gyration of a rectangle are obviously less about an axis parallel to the longer side than about an axis at right angles to it. Accordingly, a rectangular member would buckle first in a direction at right angles to this axis, as is apparent from the manner in which an ordinary yardstick bends when compressed. The least radius of gyration of a single angle is found about a diagonal 212 PART III — THE DESIGN OF DETAILS axis, as shown in the tables on pages 325 and 326. The radii of gyration for members composed of two angles are given on page 329. 1. The moment of inertia about any axis of a cross section composed of several parts is found by combining the moments of inertia of the component parts about the same axis, even though the parts are on oppo- ■site sides of the axes. The moment of inertia 7c of any component part about an axis through its own center of gravity is found from a table; the moment of inertia I a about any parallel axis AA is found by adding to this moment of inertia the product of the area of the compo- nent part by the square of the perpendicular distance between the axes, or Ia = Ic + ax^. The moments of inertia and radii of gyration about perpendicular axes through their own centers of gravity are given in the tables for the following sections:* I-beams, pages 322 and 324; channels, page 323; angles, pages 325 and 326. The moments of inertia of plates about the axis perpendicular to the longer dimension are given on page 320. Most of the values used in the design of simple steel members are included in this table. Other values may be found W . . . by proportion or from the expression --^, in which d is the dimension at right angles to the axis. In most designs the moment of inertia of a steel plate about an axis through its center of gravity parallel to the longer dimension is neghgible, but when this moment is transferred to a parallel axis, the product of the area by the square of the distance will be con- siderable. The distances from the, centers of gravity to the back of chaimels and angles are also given on the corresponding pages; these distances may be used in finding the perpendicular distances between parallel axes. Care should be taken to choose the values for the proper axis. For angles, the axis parallel to the longer leg is marked L-L, while that parallel to the shorter leg is marked S-S. The diagonal axis about which the I and r are minimum is marked M-M. The sub-letters L, S, and M are used to distinguish the corresponding values. It is often most convenient to find the moment of inertia I a of an unsymmetrical section about an axis A A through the center of gravity of one or more of its component parts (e.g., the center of webs), and theti to transfer * For special rolled column sections in the form of the letter H see the handbook of the Bethlehem Steel Company or the Carnegie Steel Company. this moment to a parallel axis through the center of gravity of the whole section, by subtracting the product of the total area by the square of the eccentricity (i.e., the distance between the two axes), or Ic = Ia - a^- In transferring moments of inertia from one axis to another there is often some confusion as to whether to add or subtract the product of the area by the distance between axes. It should be remembered that for any given area the moment of inertia is least about an axis through the center of gravity of that area. If this moment is transferred to a parallel axis it should be increased. Conversely if the moment about a parallel axis is known, the moment about the center of gravity may be found by sub- traction. The eccentricity of an unsymmetrical section may be found by equating the moments of areas. If a thin sUce were cut from a member it could be balanced on a thin support along the axis CC through the center of gravity. If the support were placed along any other axis AA about which the moment of inertia I a is known and from which the eccentricity is to be measured, the slice would tend to rotate about the support. This tendency is the same whether the section is considered as a whole or whether the component parts are considered separately. The product of the whole area by the eccentricity should equal the alge- braic sum of the products of every component area by the distance from its center of gravity to the axis A A. Note that the moments of the areas on opposite sides of the axis A A have opposite signs; when the algebraic sum is zero the eccentricity must be zero. Some of the quantities are used in finding both the eccentricity and the moments of inertia, and the computation may be simplified accordingly. 2. The forms of members depend upon so many practical considera- tions that they cannot be discussed here. Single and double angles are commonly used for light compression members. Larger sections are composed of channels or angles with or without plates. The component parts of any member must be held in the proper relative position by stitch rivets, tie plates, lattice bars, or continuous plates in order to properly distribute the stress. Otherwise each component part is free to buckle independently, and the strength of the member is no greater than the combined strength of the component parts taken singly. The ratio of slenderness for_any part of a member determined by the distance between tie plates or lattice bars must not exceed the ratio of slenderness for the CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS 213 entire member determined by its full length. This ^is usually provided for without special investigation by the usual method of spacing stitch rivets (page 69:4), or tie plates and lattice bars (page 70:1). The areas of continuous plates may be included in the effective cross section, but tie plates and lattice bars are not considered as part of the main section. The arrangement and the spacing of the component parts of a member have their effect upon the strength. To illustrate, let us con- sider the strength of two angles with unequal legs. If the member receives no intermediate support, the longer legs of the angles are placed together. This arrangement gives better distribution of metal because the radii of gyration about perpendicular axes are kept more nearly equal, and the least radius is larger than if the angles were placed with their shorter legs together. This is the usual arrangement for struts, bracing, and web members of latticed girders and roof trusses. In de- , termining the strength of a member with intermediate support, such as a chord member of a latticed girder or light roof truss* which is supported by web members, there are two different lengths to be considered. The unit stress is found from the greatest ratio of slenderness -, and not neces- sarily from the least radius of gyration. Since the length between lateral supports is usually greater than between panel points, the corresponding radius of gyration should also be greater in order to keep the ratios of slenderness more nearly equal, or at least so that the larger ratio is mini- mum. The angles of such members are thus usually placed with their shorter legs together. Each member should be analyzed in this manner. Certain practical hmitations are often specified for the thicknesses of different component parts of compression members. Common examples are (a) that the thickness of web plates must not be less than ^\ the dis- tance between the lines of rivets which connect the plates to the angles; (b) that the thickness of cover plates must not be less than ^\ the distance between the lines of rivets which connect them to- the angles or channels; and (c) that the thickness of the angles without cover plates must not be less than yV of the outstanding leg of one angle. 1. The following tjrpical problems illustrate the design or the investiga- tion of some of the more common compression members. First Problem. — Design a single strut 10 feet long to carry a stress of 50,000if at a unit stress of 16,000 - 70 -. The table of safe loads on page 330 is based upon this unit stress, so it may be used directly. Under the column headed 10 feet is found the stress 51,000 opposite a 6x6x5, which would be used. If such a table were not available, a table of properties of angles (page 325) must be used. Unless the designer is guided by experience or otherwise, he must assume a section and then investigate it. He may approximate the section roughly by dividing the given stress by a unit stress of 10,000#/sq. in. In this prob- lem the required area is approximately 5 sq. in., so a 6 x 6 x yV is investi- gated. The least radius of gyration of a single angle about a diagonal axis is 1 . 19 in. The unit stress is 8,940#/sq. in. = 16,000 - ^^ ^ ^^^ ^^ , which multiplied by the area 5.06 sq. in. gives a safe load of 45,200#. This is too small, so the next larger size is tried in a similar manner and found sufficient, the safe load being 51,100#. Second Problem. — ■ Find the thickness of two 5 x 3f angles to carry a stress of 75,000# at 16,000 — 70 - pounds per square inch. The angles are 11 feet long and connect to a J" gusset plate placed between them. If no other member is connected to this member in such a way as to give intermediate support to prevent its buckling in one direction, the longer legs of the angles will be connected to the plate and hence be parallel and 5" apart. The radii of gyration about both axes appear in the middle table on page 329. The approximate area of two angles is 7.5 sq. in. = 75,000 -H 10,000. From the areas of two angles in the above table this falls between ^V ^-nd 5 inch in thickness. The latter would have a 70 X 11 X 12\ ^, - ^-rj 1, the former only 70,000#, hence 2 Ls 5 X 3| x i would be used. If the angles were f " apart the safe load could be taken directly from the table on page 331. If neither of these tables were available the radii of gjTation would have to be found from the properties of angles (page 325). The radius about an axis parallel to the shorter legs is the same for one or two angles because the axis through the center of gravity of the member safe load of 80,000# = 8.00 16,000 - (l6,C 214 PART III — THE DESIGN OF DETAILS passes through the centere of gravity of each angle; thus both the mo- ment of inertia and the area are doubled and the radius remains un- changed. The moment of inertia about the other axis is 18.8 in^ ,= 2[4.0 + 4.00(0.25 + 0.91)^] and the corresponding radius is 1.53 in. = V'18.8 -=- (2 X 4.00). Third Problem. — Find the safe load of a 20-foot column composed of two 12 X ? plates and two 10" liJ 15#, 6" back to back, as 12 500 shown in Fig. 214 (a). The allowed imit stress = — 1 + P 36,000r2 6.00 sq. in. = area of one 12 x i (by inspection, or from page 321) 12 X I (page 320) 10"U15# 10" U15# about axis AA 10"U15# " " BB r MM t e 2 Kg. 214 (a). 72.0 in^ = I " 4.46 sq. in. = area " 66.9 in' =7 2.3 in^ = " " 0.64 in. = dist. from b. of web to c. of g. (page 323) 1,33.8 = 2 X 66.9 = J of 2 lU about AA 330.7 = 2 X 6.00(5.00 + 0.25)^ = Z of 2 Pis. about A A (neglecting the I about axis through c. of g. of PI.) 464.5 = total / about A A 122.8 = 2(2.3 + 4.46 x 3.64^) = / of 2 lU about BB 144.0 = 2 x 72.0 = 7 of 2 Pis. about BB 266.8 = total 7 about BB 12.7 in^ = 266.8 -^ 2(6.00 -I- 4.46) = the least r^ 232,000# = ^^'^In ^^'o?? = the total safe load. (20 X 12)' ■•■36,000 X 12.7 Note that when the compression formula contains r^ it is unnecessary to find r. Fourth Problem. — Find the least radius of gjrration for a top-chord section composed of 2 web plates 18x §, 1 cover plate 21 x |, two top' angles 3 x 3 x f , and 2 bottom angles 4 x 3x |, arranged as shown in Fig. 214 (6). It is con- venient to select all the necessary areas, moments of inertia, and distances to centers of gravity from the tables at the outset. The distances may be recorded directly upon the sketch. 9 . 00 sq. in. = area of one PI. 18 X 2 tc tt tl it a 91 w i 10.50 2.11 3.25 1.8 2.4 5.0 243.0 385.9 Fig. 214 (&). m' 4x3x4 3 x3 xf about axis through its c. of g. " 4x3x1 " 4x3xi PI. 18 X i •' 21 X 4 hor. axis through its c. of g. vert. " hor. " vert. " tc It a tt tt tt tt tt tt tt it tt 39.22 sq. in. = 2(9.00 + 2.11 + 3.25) + 10.50 = total area moment of cover plate " 2 top Ls 99.8 in^ = 10.50 X (9.25 +0.25) 35.3 " =2x2.11 x8.36 = 135.1 " =sum 54.7 " =2x3.25x8.42= " " 2 bottom Ls 80 . 4 " = algebraic sum of moments about centers of webs. 2.05 in. = 80.4 -^ 39.2 = e = eccentricity. 486 in* 948. 299 461 2194 165 2029 = 2 X 243.0 = 7 of webs about centers of webs = 10.50x9.502 or 99.8 x 9.50 = 7 of cover plate = 2(1.8 + 2.11x8.362) or 3.6 +35.3x8.36 = 7 of top Ls = 2(2. 4 + 3. 25x8. 422) or 4. 8 + 54. 7x8. 42 ^ j ^f bottom Ls = total 7 about axis through centers of webs. = 39.22 X 2.052 or 80.4 x 2.05 = total 7 about horizontal axis through c. of g. CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS 215 386 in^ = / of cover plate about vertical axis 882 " =2x9.00x (6.75 + 0.25)2= 7 of webs 283 " =2(1.8 + 2.11 X 8.142) = 7 of top Ls 483 " = 2(2.4 + 3.25 x 8.58=) = of bottom Is 2034 " = total I about vertical axis through c. of g. 7.2in.= V2029T39T2 = least radius of gyration. The table of squares (page 332) may be used to advantage in a problem which involves squares or square roots. MEMBERS WHICH RESIST BENDING AND DIRECT STRESS 1. Tension or compression members, such as the top or bottom chords of roof trusses or the end posts of bridge trusses, are sometimes subjected to transverse bending as well as direct axial stresses. They must be designed so that the combined stress in any fiber will not exceed the allowed unit stress.* The maximum unit stress due to bending occurs fl m the extreme fiber; it is found by equating the resisting moment — to the bending moment (page 199:2) and solving for /. In an unsym- metrical tension member the value c should be taken from the neutral axis to the extreme fiber in tension. The unit stress in direct tension is found by dividing the total axial tensile stress by the net area of cross section. The sum of the unit stress in du'ect tension and the unit stress due to bending must not exceed the unit stress in tension allowed by the specifications. In an unsymmetrical compression member the value c should be taken from the neutral axis to the extreme fiber in compression. The unit stress in direct compression is found by dividing the total axial compressive stress by the gross area of cross section. In a compression member the allowed unit stress is usually a function of the least radius of gyration. Opinions differ as to whether the least radius of gyration about either axis of symmetry or the least radius of gyration about an axis perpendicular to the plane of bending should be used. The use of the * Some designers use different unit stresses for bending and for direct stress and combine the resulting areas; see Johnson-Bryan-Turneaure's "Framed Structures," Vol. Ill, John Wiley and Sons, Inc., New York. former is often specified, particularly for bridges, but the resulting margin of safety is unnecessarily large when the direct stress is relatively small. It is better to consider two different allowed unit stresses in compression as explained below. This method of design has been used extensively in building work by engineers of repute with apparent satisfaction. (1) The unit stress which is determined by the least radius of gyration about an axis perpendicular to the direction of bending should not be exceeded by the sum of the unit stress in direct compression and the unit stress due to bending. (2) The unit stress which is determined by the least radius of gjTation of the whole member should not be exceeded by the unit stress in direct compression alone. If the radius of gyration used in (1) is also the least radius for the whole member, step (2) is unnecessary. Illustrative Problem. — Design a horizontal compression member 8 feet long which will support a load of 2000# at its center. The direct com- pression is 75,000# and the member is composed of two 6x4 angles, ^" b. to b., with the 4-inch horizontal legs along the top. Assume 2 Ls 6 x 4 x tV- From page 329 we find that the area =8.36, r = 1 . 92 about an axis perpendicular to the direction of bending, and r= 1 . 68 the least radius. From page 325 we find that 7=31.0=2x15.5 and c = 1.96 = the distance from the. neutral axis to the extreme fiber in compression. 4000#ft.= ^x4=jI/b. 8,970#/sq. in. = 75,000 - 8.36 = direct unit stress , „ 4000x12x1.96 3,040 12,010 12,500 12,000 - „ = unit stress due to bending = total unit stress = 16,000 :r-^^ = allowed unit stress (combined) 16,000 1.92 70 x 8 X 12 1.68 = allowed unit stress for com- pression alone. Since 12,010 is reasonably close to 12,500 (§" angles would be too small) and since 8,970 does not exceed 12,000, 2 Ls6 X 4 x tV would be used. 216 PART III — THE DESIGN OF DETAILS LATTICE BARS AND TIE PLATES 1. The design of lattice bars and tie plates or batten plates for com- pression members cannot be theoretically developed. Certain mini- mmn sizes based upon the experience of many years are demanded by the specifications in common use. These requirements often determine the sizes to be used, but the lattice bars must also be large enough to carry the stresses found by the method explained below. This method of design gives safe results for all members except those of xery large structures which should receive more careful consideration. Some recent colinnn tests seem to indicate that this method results in lattice bars about twice as strong as necessary. 2. A tie plate should be placed in the plane of even,- system of lattice bars as near each end of the member as possible, and wherever the lattice system is interrupted. The plates at the ends should extend longitudinally at least as far as the transverse distance between the lines of rivets which attach them to the member. Intermediate plates need be only one-half as large. The rivets in tie plates are usually spaced about 3" apart,. The thickness of tie plates should not be less than ^ of the distance between the rivet lines mentioned above. A plate provided for another purpose may sen-e also as a tie plate even though it is not placed in position before erection. Tie plates with or without lattice bars are used on tension membere to dis- tribute the stresses, although they do not need to be designed to resist buckling. 3. The minimum widths of lattice bars are commonly specified as foUows: 2i" for |" rivets, 2i" for |" rivets, and 2" for f" rivets. |" rivets are used for latticing flanges 3§" wide or over. One rivet is gener- ally used at each end unless the flanges exceed 5" in width, when two are used. Double lattice bars are used when the transverse distance between rivet lines exceeds 1' 3". The minimiun thickness of single lattice bars is :^ of the length from center to center of end holes; similarly the minim um thickness of double lattice bars is -^ of the same length. The table on page 315 shows the maximum lengths for different thicknesses for these ratios and for others which are sometimes specified. 4. Method of Design. — Compression members which are designed for a xmit stress of 16,000 - 70 - could be designed for 16,000 the same r as a tension member were it not for the tendency to buckle. It may be reasoned that the term 70 - represents the stress in the extreme fiber due to this tendency to buckle. It may fairlj' be assumed that in effect this is equivalent to the fiber stress caused by transverse bending forces unif ormly distributed, the member acting as a beam. The corresponding shearing stresses are taken either by contiuuous plates (as in a beam or girder) or by lattice bars (as the diagonals in a latticed girder). The stress in each bar may be found accordingly as foUows: TTT 2 TJJ^ Mb = — c — (P3^6 188 : 2) ; if we let R = -^ = the reaction or maxi- mum shear we have Mb = -j- whence ms = -r Also I = a?-2 (page 211:3), and /= 70 - (from above). r Substituting these values in rriB =— (page 199:2), we have K = . in which a = the total area of cross section, r = the radius of gyration about an axis perpendicular to the plane of the lattice bars, and c = the distance from this neutral axis to the extreme fiber. This shear is the transverse component of the stress in the lattice bar and from it the stress can be determined by multiplying by the cosecant of the angle which the lattice bar makes with the longitudinal axis of the member. If this angle 396 ar is 45°, the stress in the bar is . If a member is latticed in two planes, the bars in each plane are stressed only one half the above amount. Similarly, if a continuous plate is used on one side and lattice bars on the other as in chord members, the plate and the sj-stem of bars may each be considered to take one-half. Since lattice bars resist both tension and compression they must be strong enough for either. Thej' are designed for compression at 16,000 - 70 -, for this determines the size. r CHAPTER XXXII THE DESIGN OF TENSION AND COMPRESSION MEMBERS 217 Illustrative Problem. — Design the lattice bars for the top-chord sec- tion of the fourth problem on page 214. Since a cover plate is used on top, the bottom lattice bars need be designed for only half the bend- ing. From Fig. 214 (6) the distance between rivet lines is obviously more than 1' 3", so double latticing is required, and therefore the angle of inclination is 45° „, . , . ,.11 396ar- . The maximum stress m one bar is ;; x s X in 2 2 c which a = 39.2, r = 7.2 y1 ,andc = 11.25 = 6.75 + 0.50 + 4.00. / 2034 39.2'' Substituting these values and solving, we find the stress in one bar = 2480#. g" rivets should be used since the 4" angle exceeds 3|", and bars at least 2§" wide must be used. The length of each bar from center to center of end rivets is 28" = 1.41 x 2(6.75 + 0.50 + 2.50), and the minimum thickness is | = H. The area of a 2§ x § is 1.25, and the radius of gyration is 0.14 = load is 2500# = 1.25 fl6,000 / 2.5 x0.5« 12 x2.5 xO.5 , whence the safe 70 X 28' 0.14 )• This is greater than the required stress 2480, so the bars are satisfactory. CHAPTER XXXIII THE DESIGN OF PLATE GIRDERS Synopsis: Three methods of designing the main cross section of a girder are pre- sented and compared. The discussion of details, such as the lengths of cover plates, the spacing of flange rivets, and the sizes of stiffening angles and splices is left for subsequent chapters. 1. Plate girders are designed to meet a great variety of conditions, as explained on page 95 : 1. The common forms of cross section are shown in Fig. 95, the majority of girders being of one of the first two forms. In order to simpUfy the phraseology, most of this chapter has been written to apply to horizontal girders with vertical loads, each flange being composed of two angles, with or without cover plates. 2. Analysis of Forces. — The external forces which act upon a plate girder must satisfy the three equations of equilibrium (page 183:2). If the girder is cut by an imaginary plane, the external forces which act on either segment are not in equihbrium by themselves, but they are held in equilibrium by the internal forces or " stresses " acting in the fibers which are cut by the section plane. The vertical components of these forces are shearing stresses; these are resisted by the web, as dis- cussed in Chapters XXXIX and XL, pages 266 and 270. The hori- zontal components of these internal forces must satisfy the H equation of equilibrium provided the external forces are all vertical; thus the sum of all tensile stresses (which tend to elongate the girder) must equal the sum of all compressive stresses (which tend to shorten the girder) as in a beam. The sum of the moments of the external forces which act on the segment is the bending moment, and the sum of the moments of the internal forces cut by the section plane is the resisting moment; these two moments must be equal in order to satisfy the M equation of equilibrium. If the point of moments is taken in the section plane the moment of the vertical components of the internal forces is zero, and only the horizontal components need be considered. The section plane is taken at the point of maximum bending moment and the girder is designed to furnish the proper resisting moment by one of the methods described in this chapter. 3. The depth of a plate girder is often predetermined by specific re- quirements. Within practical hmits, flanges may be designed for any depth of girder; as the depth is increased the flanges become lighter, and conversely. The most economical depth is from one-seventh of the length for short spans to one-twelfth the length for long spans; in the absence of other data an average value of one-tenth the length may be chosen; the maximum depth is Hmited to about 10'-6" by the over- head clearance available during shipment. The depth of the web plate is usually made a multiple of 2", and preferably a multiple of 6"; the depth from back to back of flange angles i^ usually \" or |" greater than the depth of the web (page 95 : 3). 4. The thickness of the web plate must be such that the strength of the web is sufficient to transmit the shearing stresses, as explained on page 266: 3. The web plate must also be thick enough to furnish proper bearing for the flange rivets, as explained on page 255:2. The usual values are from 1^" to I" (page 266 : 3) with a minimum value equal to x^ of the ver- tical clear distance between flange angles. Usually a value is assumed with due regard to this minimum, then the flanges of the girder are designed, and finally the strength of the web plate is investigated. If necessary, these steps may be repeated until a satisfactory solution is obtained. 218 CHAPTER XXXIII THE DESIGN OF PLATE GIRDERS 219 1. The flanges of comparatively light girders are composetl of two angles each. Cover plates are added to the flanges of heavier girders "to provide additional flange area where needed; the cover plates, unlike the angles, need not extend the full length of the girder, but they may be cut off at points beyond which the remaining area is sufficient to carry the reduced flange stress, as explained in Chapter XXXVIII, page 259. It is not practical to use cover plates unless the outstanding legs of the flange angles are at least 5 or 6 inches; the cost of using heavier angles would be less than the cost of using cover plates on account of the extra punching and riveting. Additional angles or vertical plates may be used in the heavier girders, as shown in Fig. 95, c, d. 2. Flange angles with unequal legs should be used whenever prac- ticable; angles with equal legs less than 6 inches are seldom used. 6x6 angles are used when 6 X 4 x f angles are not large enough, or when the .flange rivets in the web legs must be staggered to meet the requirements of Chapter XXXVII, page 241. 8x8 angles are reserved for very heavy girders; they are not used without cover plates. When unequal legs are used, the shorter leg is riveted to the web plate and the longer leg is outstanding. In this position the center of gravity of the flange is nearer the back of the angle and hence farther from the neutral axis; the resisting moment is thus made correspondingly greater (why?). The lateral stiffness is also increased by placing the longer legs horizontally. 3. The cover plates are made wide enough to fully cover the angle; plates of commercial widths will usually project beyond the angles. 18" plates (or 17) are used with 8" angles, 14" plates (or 13) with 6" angles, and 12" (or 11) plates with 5" angles. It is convenient to find the total thickness of cover plates as if there were only one plate on each flange; this total thickness may then be subdivided into the proper number of plates. No plate should be thicker than f" nor less than the minimum thickness of metal allowed (usually f"). Usually the number of plates used is the smallest which will meet these requirements so that the cost of handling and punching extra plates may be saved. Full-sized holes cannot be punched satisfactorily in metal thicker than f"; they must be either drilled or sub-punched and reamed (page 30:2). The cover plates should be made approximately of equal thickness, but they may differ by tV" when the total thickness is not an exact multiple of the number of plates. When plates of different thickness are used, the thicker plates should be nearer the angles. 4. Distribution of Area. — The net area of the flange angles should preferably be as large as the net area of the cover plates. In other words, the net area of the angles should be 50 % of the area which remains after the portion (if any) of the web plate counted as flange area is deducted from the total net area required. This requirement is often specified in order -to overcome the tendency of a few designers to put considerably more than 50% of the area into the cover plates to save metal; this tendency might result in angles which are too weak to transmit the cor- responding stress from the web plate to the cover plates. The auth9r has seen recently a flagrant violation of this specification in an existing main-line railroad bridge in which cover plates about 6" thick are connected to the web by 6 X 3| X i flange angles. In some of the very heavy girders it is impossible to obtain angles which are large enough to furnish 50% of the area mentioned, but the specifications provide for this contingency by allowing " the largest size of angle " to be used. In case no clause appears in the adopted specifica- tions * regarding the relative distribution of area, it is the common prac- tice to make the area of the angles 50 % of the net area remaining after I (or other portion) of the area of the web plate is deducted, provided the angles are no thicker than |". Thus, 6x6x1 angles are often used even though the cover plates are of somewhat greater area; this is done so that the rivet holes in the angles may be punched (see preceding paragraph). 5. The Compression Flange. — It is desirable from the standpoint of fabrication to make both flanges of a plate girder alike. Unless the top flange is braced transversely to prevent buckling it may have to be made of a different cross section. The flange stress is the same in the compression flange as it is in the tension flange as will be seen later (page 221 :2). The allowed unit stress is less in compression than in tension, but the effective area is greater because no deduction need be made for rivet holes. The tension flange is usually designed, and the * For example, the "Specifications for Steel Railway Bridges," of the American Railway Engineering Association, Chicago. 220 PART III — THE DESIGN OF DETAILS compression flange is made like it unless the compression flange is found not to have the proper lateral stiffness; the compression flange should never be made of smaller gross area than the tension flange. The com- pression flanges of bridge girders are usually braced at intervals either by lateral bracing (Fig. 142) or by gussets at the floor beam connections (Kg. 99); in the majority of cases the two flanges may be made ahke. The compression flanges of crane-runway girders are sometimes latticed to other girders (page 112 : 6), in which case the flanges may be made alike; otherwise the top flange must often be made heavier or wider, as shown in Mg. 95 (e) and (/). After the tension flange of a girder is designed, the strength of a like compression flange should be investigated. The allowed unit stress is based upon the ratio of the width of the flange to the imsupported length. The specifications recommended by the American Railway Engineering Association state that the unit stress per square inch of gross area of the compression flange must not exceed 16,000 — 200 7 when angles alone or angles with cover plates are used, or 16,000 - 150 r when angles with channel covers are used; b = the extreme width of flange in inches, and I = the distance in inches between lateral supports. If the compression flange is not braced, I = the full length of the girder. The thickness of flange angles used without cover plates should not be less than one-tweKth the length of each outstanding leg. 1. Three Methods of Design. — The flanges of a plate girder may be designed by any one of three methods, viz. : Case A, in which the flange angles and cover plates are assumed to resist the entire flange stress due to bending moment; Case B, in which the resisting moment of the web plate is considered; and Case C, in which the moment of inertia of the net cross section is used in much the same manner as in the design of beams. The method of Case C is given as an alternate method in the more modem specifications, but it is not recommended for general use on account of the somewhat indirect and laborious calculation involved. It is practical only when exhaustive tables are accessible, which give the moments of inertia or the section moduli of all types and sizes of girders, for different sizes of rivet holes. This method is an application of the general formula for flexure, ms = — (page 199 : 2) in which I = the moment of inertia of the net cross section. Theoretically the neutral axis is not at the center of the web because the tension half of the girder is weakened by the rivet holes, while the compression half is not. This refinement is not adopted ordinarily, but for convenience the upper half is considered like the lower half; that is, the moments of inertia of the holes in both flanges and in the whole web are deducted from the moment of inertia of the cross section (page 212 : 1). The method of Case B is meeting with most favor at the present time, and has been adopted quite generally. The results are obtained more readily by means of this method than by the more precise method of Case C, and they are very nearly the same. The assumption is made that the flange stress is imi- formly distributed throughout the whole flange, the resultant acting at the center of gravity of the flange. The effective depth is therefore the distance between the centers of gravity of the flanges; it cannot be ascertained definitely until the sizes of the angles and the cover plates are known. This necessitates a trial design, which makes the method somewhat more complex than that of Case A. Case B is treated more fuUy on page 223 : 1. The method of Case A is comparatively simple in appUcation, but it is not well adapted to the design of all girders for it would result in a waste of metal in some of the heavier girders. In this method the resisting moment of the web plate is neglected, but this is compensated for, in part, by the use of an increased depth (usually the depth of the web plate). The use of this method gives safe results; for girders without cover plates, or for girders with 6x6 angles and a single cover plate in each flange, the results are approximately the same as those obtained by the method of Case B or C. Until the effect of impact from moving loads is better understood so that different speci- fications are made more nearly uniform, and imtU there is a closer agree- ment between actual loads and those assiuned, the method of Case A should give consistently good results for the lighter girders, particularly, those mentioned in the preceding sentence. Case A is treated more fully below. 2. The degree of accuracy to be used in computation depends largely upon the precision of the given data. Usually loads are expressed to the CHAPTER XXXIII THE DESIGN OF PLATE GIRDERS 221 nearest hundred pounds, and bending moments to the nearest hundred pound-feet; bending moments which exceed 1,000,000 pound-feet may be expressed to the nearest thousand. In Case A the depth is taken to the nearest tenth of a foot, whereas in Case B the effective depth should be taken to the nearest tenth of an inch. Net areas should be expressed to the nearest tenth of a square inch; this gives consistent accuracy under usual conditions. Many designers carry net areas to hundredths, but this seems unnecessary; the results are usually identical whether tenths or hundreds are used, the difference in thickness never exceeding ^". The use of a slide rule is recommended for all computations. CASE A 1. This method is based upon the following assumptions: (a) that the web plate resists all the shearing stresses; (6) that the flange angles and cover plates carry the whole flange stress due to bending moment, the resisting moment of the web plate being neglected; (c) that the flange stress is uniformly distributed over the whole flange area, the allowed average unit stress being that speci- fied for the extreme fiber; and (d) that the effective depth is taken equal to the nominal depth of the girder, which is usually the depth of the web plate. 2. Theory. — A girder is designed so that the resisting moment of the horizontal forces equals the maximum bending moment, as explained on page 218 : 2. In the method of Case A, the resisting moment of the web plate is neglected; the web plate is virtually a rectangular beam in which the horizontal tensile forces and compressive forces are equal (page 197:3). From page 218:2 it is seen that the sum of all tensile forces equals the sum of all compressive forces, and it therefore follows that the total flange stress in the bottom (tension) flange angles and cover plates equals the total flange stress in the top (compression) flange angles and cover plates. Each of these flange stresses may be represented by a resultant force (F), aS" shown in Fig. 221 (a), and the total resisting moment is the product of one force F by the perpendicular distance between the two forces. (Two equal and opposite forces form a couple and the mo- ment is the same for any point of moments.) In this approximate method of Case A the distance between the resultant forces is taken for convenience as the nominal depth of the girder (usually the depth of the web plate Dw). This is generally in even inches and often in even half feet. The use of a fraction of an inch is not consistent with the assumptions upon which this method is based; if the depth between the centers of gravity of the flanges is to be used the girder should be designed by the method of Case B. In this method the depth is ex- pressed to the nearest tenth of a foot, so the resisting moment FDw in pound-feet is equated to the bending moment Mb in pound- feet, thus : FDw = Mb- The flange stress is equal to the unit stress multiplied by the net flange area, or F = fa. By substitution faDw = Mb, whence a Fig. 221 (a). Mb T^r— . Thus, if we jiJw divide the total maximum bending moment in pound-feet by the depth in feet and by the unit stress in pounds per square inch, we obtain the re- quired net area in square inches. The tension flange should be designed for this area in the same manner as a riveted tension member (pages 208 : 2 and 208 : 4) . The maximum number of holes in any one cross section is usually as indicated in Fig. 221 (b) for angles without cover plates, or as in Fig. 221(c) when cover plates are used; if more than one row of rivets is used in an angle leg the rivets are staggered. The amount of stagger should not be less than that specified on page 305 or else additional holes should be deducted. As a rule there is Uttle difficulty experienced in providing the proper stagger in either leg of the angles at the point where the bending moment is maxi- mum, but it is not usually feasible to attempt to make the rivets in one leg stagger with those in the other leg. The design of girders can best be illustrated by typical problems. The solution of the following problems Fig. 221 (6). Fig. 221 (c). 222 PART III — THE DESIGN OF DETAILS is adapted to the tables foimd in most handbooks. The solution may be simplified by the use of special tables in this book, as explained below. 1. Illustrative Problem — Case A. — Without Cover Plates. — Design an 18-ft. girder, composed of a 24 x f web plate and 6 x 4 Ls, to sup- Fig. 222. port a load which causes a bending moment of 260,000 #ft. and a unit stress of 16,000#/sq. in. Use I" rivets, 80#/ft. 3200/ ft, 263,200# ft 8.2 8.6 sq. m, sq. in 95#/ft 600#ft = 31 + 4 X 12 = approximate weight of girder (6 X 4 x f Ls assumed) = -^ X 9=^ = Mb due to weight (page 188 : 2) = 260,000 + 3200 = total Mb 263,200 areas given on page 327; thus, after the required net area (8.2) is found, the following angles with one f " rivet hole deducted from each angle may be selected: 6 x 4 x I, 6 X 3| x A, and 5 X 3J x |. The relative weights may be judged from the same table. When the usual unit stress of 16,000#/sq. in. is specified the problem may be still further simplified by the use of the stresses given in the same table; thus the flange stress may be found instead of the net area (131,600#=263,200-=-2), and angles selected to give an equal or greater stress (137,900 for 2 Ls6 X 4 x i). The computation should be arranged preferably as shown above, for reasons ^ven on pages 185 : 1 and 208 : 3. 2. Illustrative Problem — Case A — With Cover Plates. — Design the 60-ft. girder shown in Fig. 222 to carry a hve load of 6000#/ft. and a dead load of 200#/ft. in addition to its own weight. Use |" rivets, and a unit stress of 16,000#/sq. in. Assume a depth of one-tenth the span with a web plate 72 X T^ (page 218 : 3). 60-0 c to c. bearings 16,000 X 2 total net area required {Dw = 2 ft.) = 2(4.75 - I X i) = net area of 2 Ls6 x 4 x i = 31 + 4 X 16 = revised weight, using 6x4x5 angles 95 -80 2 600 X 9^ = increase in Mb = increase in net area, which is neghgible. 16,000 X 2 By inspection we can see that the next hghter angles would be too small. Therefore 2 Ls 6 X 4 x i would be used. If 6 X 4 angles were not specified, 6 X 3| or 5 X 3J angles might be tried to see if a reduction in the amount of excess area could be used in order to save metal. The solution of this problem can be simphfied by the use of the table of net 107#/ft. 116#/ft. 96#/ft. 300#/ft. 200#/ft. 6000#/ft. 6500#/ft. 2,925,000# ft. 30 . 5 sq. in. 15.9 sq. in. = weight of web plate (page 321) = 4 X 29 = weight of 6 x 6 x f Ls assumed (page 303) = 2 X 48 = weight of 14 x 1 cover plates assumed (page 321) = approximate total weight of girder assumed = other dead load = hve load = total load 6500 2 X^O^ 2,925,000 16,000 X 6 = 2(9.73-2x1 X J) total) Mb (page 188 : 2) = total net area required net area 2 Ls6 X 6 X | (50 % of CHAPTER XXXIII THE DESIGN OF PLATE GIRDERS 223 14.6 sq. in. = 30.5 — 15.9 = net area required in cover plates li" = 1.22" = 14.6 ^ (14 - 2 X 1) = total thickness of cover plates 360#/ft. = 107 +4x33 + 2x60 = revised weight 360 - 300 27,000# ft. 0.3 sq. in. = 2 27,000 X 30^ = increase in Mb increase in net area 16,000 X 6 li" =1.24" = (14.6 + 0.3) + (14 - 2 X 1) = revised thickness of cover plates (no change) f 2 Ls 6 X 6 X f ^'''l2Pls.l4xf This design compUes with the specifications that the net area of the angles should be as large as that of the cover plates, although the holes in the angles would have to be either drilled or sub-punched and reamed (page 30 : 1) . The net area of the angles will seldom equal the required 50%, so a slight excess will usually result; advantage may be taken of this excess by proportioning the cover plates for the remaining area instead of for the remaining 50%. The net area of the plate is propor- tional to the net width, as explained on page 208 : 2; the required thickness of plate is found by dividing the net area- by the net width. The com- mercial sizes of plates vary by sixteenths of an inch in thickness; when the required plate thickness falls between two sizes, the thicker one should be selected. If the total thickness of plate exceeds f " it should be sub- divided as explained on page 219 : 3; in this problem two f " plates are used. Note that two rivet holes are deducted from each flange angle when cover plates are used (page 221 : 2). The solution of this problem may be simplified by the use of the table on page 327 from which the net areas of angles may be found, and the table on page 321 from which the net areas of plates may be found. The net area of a plate of a given width is the same as the gross area of a plate whose width corresponds to the net width of the given plate; thus, the net area of a 14 x Ij plate is the same as the gross area of a 12 x Ij plate, the 12 being the net width after two 1" holes for |" rivets are deducted. Subsequent steps in the complete design of this girder are given on pages 248 : 1, 263 : 2, 264 : 3, 268 : 3, and 271 : 2.- CASE B 1. This method is based upon the following assumptions: (a) that the web plate resists all the shearing stresses; (6) that the web plate also resists part of the bending moment; (c) that the flange stress is uniformly distributed over the whole flange area, the allowed average unit stress being that specified for the extreme fiber; (d) that the resultant flange stress in each flange acts at the center of gravity of the gross area of the flange angles and cover plates, and that the effective depth is the distance between these centers of gravity of the two flanges. Note that (a) and (c) are the same as for Case A (page 221 : 1), but that (6) and (d) differ. 2. The application of this method involves two more steps than the method of Case A. The effective depth depends upon the position of the center of gravity of the flange; this cannot be determined until the approximate sizes of the angles and the cover plates are found in a trial design with an assumed depth. The resisting moment of the, web plate is considered; the web plate acts as a rectangular beam, but for con- venience an equivalent expression may be derived, so that one-eighth of the gross area of the web may be treated as flange area in conjunction with the net area of the angles and cover plates. Thus, the general method of solution is similar to that of Case A. 3. Theory. — The flange stress in the angles and cover plates of either flange may be considered as a single resultant force F acting at the center of gravity. The slight difference in the position of the centers of gravity of the net area and of the gross area of the angles and cover plates is negligible, so the gross area may be used for convenience. The resisting moment of the stresses in the flange angles and cover plates is Fdg (com- pare page 221 : 2), in which dg is the effective depth determined as explained in the following paragraph. Since the flange stress equals the unit stress multiplied by the net area of the angles and cover plates (if any), or F = fa', then the resisting moment Fdg = fa'dg. To this must be added the resisting moment of the web plate acting as a rectangular beam 224 PART III — THE DESIGN OF DETAILS (page 199 : 3) ; this resisting moment is iftd„^, where t = the thickness of the web plate (i.e., the width of the beam) and d^ = the depth of the web plate. In this method the effective depth, and the thickness and the depth of the web are expressed in inches, so the resisting moment in pound-inches must be equated to the maximum bending moment in pound-inches, thus: fa'd,, +^td^ = ms- Instead of using the resisting moment of the web plate in this form it is found to be more convenient to divide it by the effective depth and by the unit stress to give a quantity which can be combined with the net flange area of the angles and the cover plates to give the total net area, thus: a' 4- \ida \T] = <* = ~7T' In this expression the full gross area of the web plate is used, no allowance being made for rivet holes; but there will be holes in the web for the flange rivets, and usually for rivets in stiffening angles (page 266:2). There may be no stiffening angles exactly at the point of maximum bend- ing moment, nevertheless they may be placed where the moment is only slightly less. The position of the stiffening angles and the spacing of rivets cannot be determined until after the girder is designed, so it is unpractical to attempt to find the actual net area. Fiuthermore, the fraction of the web plate coimted as net area is small compared to the net area of the angles and cover plates, so a slight variation will have comparatively little effect. For convenience, a general method is used which provides for rivets under average conditions. Thus if we consider \" rivets to be spaced 4 inches center to center, it means that a 1" hole is deducted every 4 inches, leaving 3 inches of metal between; thus the net area of the web plate is f of the gross area. The effect of this is to multiply the fraction \ in the expression given above by f making \. In view of the approximation resulting from the assump- tion of the size and the spacing of the rivets, it is consistent and on the side of safety to call t- equal to imity. Our revised formula then becomes a! -f- \\dw = a or a' = a — ^td^. Thus, from the total net area required we subtract one-eighth of the gross area of the web, leaving the net area to be taken by the angles and cover plates. 1. The effective depth is expressed to the nearest tenth of an inch. The distance from the center of gravity of the gross area of the flange angles and cover plates to the back of the angles is found,* then twic« this distance is subtracted from the deptti of the girder from back to back of angles to give the effective depth. The depth from back to back of angles is not the same as the depth of the web plate, but is usuaUy J" greater imless the upper edge of the web plate is unprotected from the weather when it is only \" greater (see page 95 : 3). Since the effective depth cannot be determined accurately imtil the sizes of the angles and the cover plates are known, it is necessary to make a trial design with an assumed depth. No convenient rule can be given for selecting the proper depth to use, but an experienced designer is guided by the results of previous designs. In the absence of more definite information the fol- lowing guides may be used. For girders without cover plates the problem is comparatively simple because the distance from the center of gravity to the backs of the angles does not vary greatly for different thicknesses unless the size of leg changes. Thus, if the size of the legs is determined or assumed, the distance from the center of gravity to the back of an angle of intermediate thickness may be taken from the table on page 325, and a close approximation of the effective depth may be obtained. If angles of imequal legs with cover plates, or if equal-legged angles with more than two cover plates are used, the trial depth should be taken equal to the depth of the web plate; but if equaJ-legged angles with only one or two cover plates are used, the depth should be about 1" less than the depth of the web. From the sizes of the angles and cover plates found as a result of the trial design the corrected effective depth should be foimd to the nearest tenth of an inch. The bending moment due to the weight of the girder should be revised also, and a second solution of the problem should be made. If the sizes of the angles or cover plates differ from those found in the trial design the corresponding effective * For convenience the point of moments is taken at the back of the angles. The difference between the product of the gross area of the angles by the distance to the center of gravity of the angles and the product of the gross area of the cover plates by one-half the total thickness of cover plates, is divided by the sum of these gross areas; the resultant distance is measured toward the angles or toward the cover plates according to which of the above products is larger. CHAPTER XXXIII THE DESIGN OF PLATE GIRDERS 225 depth should be determined; a third design is. not necessary provided the corrected effective depth does not differ from the depth used in the second design by more than 0.1" for girders less than 3 ft. deep nor by more than \" for deeper girders. 1. Illustrative Problem — Case B. — Design the girder shown in Fig. 225, for a 60-foot single-track through railway bridge to support Cooper's E60 live load, using the specifications of the American Rail- way Engineering Association. We will use |" rivets, and assume a 72 Xy^ web plate (see page 218 : 3). The length is divided into four equal panels of 15 ft., and the width of the bridge from center to center of girders is 14' 6". The total dead load of the track _ is taken as 450#/ft., including the rails, the ties, the guard rails, the splice bars, the fastenings, etc. The design of the stringer and floor beam naturally pre- cedes the design of the girder ; we will assume that these have been designed and that the weights have been deter- mined to be 150#/ft., for each stringer and 175#/ft. for each floor beam. The maximimi concentrated live loads trans- mitted from the floor beams to this girder were found on page 196 : 2 to be 39,900#, 82,000#, and 52,100, respectively; to these should be added the corresponding impact allowance for the effects of moving loads, and also the dead loads, to give the total concentrated loads. The bending moment due to these concentrated loads should be increased by the bending moment due to the assumed weight of the. girder itself which is uniformly distributed. The allowance for impact stresses is provided for in the specifications in the form of a percentage of the live load. In the A.R.E.A. specifications mentioned above this percentage is deter- mined from the expression * j — „„,, , in which L is the length of track in Li + oUU 30,000 , , , , , . . . . , * A change to „„ r^rr. t » ^^ °^®° recommended but it is meeting with opposi- feet which must be loaded to cause the maximum live-load strain in the member. In this problem the maximimi bending moment in the girder will be found when the track is loaded for the entire length of the girder, hence the impact percentage is 5^. The solution follows: 6900# = f-2~ + 150 jl5 + 175 X — ^ = dead load at each panel, due to track, stringers, and floor beam 80,100# = 39,900 ^1 +1^] H- 6900 = total load at 1st panel point Fig. 225. 157,200# = 82,000 (l -\-^^ + 6900 = 102,400# = 52,100 (1 +1^) + 6900 = " n (( a 2nd 3rd 164,300# = (80,100 X 3 + 157,200 x 2 + 102,400 x 1) - 4 = left-hand reaction 3,728,000#ft. = 164,300 x 30 - 80,100 x 15 = Mb due to cone, loads (Fig. 251 (a)). 370#/ft. = 107+4x29+2x71 =approx. weight of girder (6x6xi Ls and 14 x li cover plates assumed) 30,000 + L' tion and it has not yet been adopted. 167,000#ft. 370 X 30^ = Mb due to weight of girder 226 PART III — THE DESIGN OF DETAILS 3,895,000#ft. = 3,728,000 + 167,000 = total Mb 40 . 6 sq. in. = 3,895,000 X 12 16,000 X 72 3.9 sq. in. = i x72 XtV = total net area required (dg assumed 72") the gross area of the web 36 . 7 sq. in. = net area required in angles and cover plates 13.9 sq. in. = 2(8.44 - 2 X 1 X I) = net area 2 Ls6 x 6 x f (see 303) 22 . 8 sq. in. = balance required in cover plates = 1.90" = 22.8 H- (14 - 2 X 1) = thickness of 14" cover plates 2 X8.44 X 1.78 -27.13 x 0.97 page 1 1 5 0.09" = distance from back of 16.88 + 27.13 angles to center of gravity (Fig. 226) 72.3" = 72 + 0.5 - 2 X 0.09 = effective depth dg 410#/ft. = 107 + 4 X 29 + 2 X 92 = revised weight of girder 410 185,000#ft. = -=- X 30^ = revised Mb due to weight of girder 3,913,000# ft. =3,728,000 + 185,000 = revised total Mb 3,913,000 X 12 40.6sq.in. = ^6 000x72.3 ( 2 Ls 6 X 6 X i Use \ 1 P1.14 X +i l2Pls.l4x| = revised total net area c, of Pis: A, of pis. =2 A 13 Fig. 226. Note that the revised total area is the same as the first total, so no further revision is necessary; this is because the increase due to increased weight happened to compensate the decrease due to the larger depth. Had there been a difference in area, the balance (22.8) required in the cover plates could have been changed by a Uke amount and the cor- responding thickness could have been found. For comments upon the arrangement see pages 185 : 1 and 208 : 3. For suggestions upon the solu- tion see page 222 : 2. Subsequent steps in the complete design of this girder are given on pages, 226 : 1, 250: 3, 262 : 1, 265 : 1, 269 : 1, and 273 : 1. 1. Railway bridges and viaducts are subject to lateral forces due to the effects of the rocking or " nosing " of the locomotives, and of the wind pressure both upon the structures themselves and upon passing trains. These lateral forces are often treated together. They act hori- zontally and they are resisted by the bracing systems. The effects of the train are most severe upon the " loaded chords," i.e., the top flange of stringers and deck girders, or the bottom flanges of through girders. The American Railway Engineering Association specifies a lateral force of 200#/ft. on the unloaded chord, while on the loaded chord this is increased by 10% of the specified train load which follows the engines; both are considered as moving loads. The bending moment due to these lateral forces cannot be combined with the bending moment due to the vertical forces because they act in different planes; but the correspond- ing flange stresses or flange areas can be added. The lateral bracing forms the web system of a horizontal truss, the chords of which are the flanges of the girders. By the method of sections the stress in one of the chords at the center is found by dividing the sum of the moments of the external forces on one segment by the depth of the truss, i.e., the perpendicular distance between girders. The sum of the moments is equivalent to the bending moment of the uniformly distributed lateral forces, even though the forces are concentrated at the floorbeams. Since the maximum flange stress due to the vertical forces, and the maximum flange stress due to the horizontal forces are not Hkely to occur simul- taneously, it is customary to neglect the latter unless the combined stress per square inch exceeds by more than 25% the unit stress allowed for vertical forces alone. When the combined stress does exceed this amount the flange should be strengthened. The effect of lateral forces upon the problem of page 225 : 1 should be considered as follows: 800#/ft. = 200 + 6000 X 0.10 = specified lateral force on bottom chord 360,000# ft.. 800 X 302 ^ ][fg (Jug tQ lateral force 1 . 6 sq. in. = 360,000 J. . 16 000 X 14 5 ^ corresponding net area required. This is less than 25% of the net area 40.6 which is required by the vertical forces alone; hence the combined unit stress will not exceed 16,000 X 1.25, and no change in section need be made. CHAPTER XXXIII THE DESIGN OF PLATE GIRDERS 227 1. The method of designing heavy girders with vertical flange plates, with four angles in each flange-, or with both, is similar to the method of Case B (page 223 : 3) only somewhat more complex. The effective depth is the distance between the centers of gravity of the gross area of the flange angles, the cover plates, and the vertical flange plates. One- eighth of the gross area of the web plate may be counted as flange area. It is assumed that only experienced designers will have occasion to design girders of this type, so that further comments would be out of place here. 2. Girders which support curved railroad tracks should be designed to resist centrifugal forces. These forces vary with the degree of curva- ture and with the weight and the velocity of the train. The forces are treated as uniformly distributed horizontal forces for which the hori- zontal bending moment and the corresponding flange stress or flange area must be found in the same manner as for lateral forces (see above). The flange should be designed for the sum of this area and the area found from the vertical forces, no increase in unit stress being allowed as for [772 lateral forces. The amount of centrifugal force is „„ r>n in pounds per 6Z.ZK linear foot applied at the top of the rails, where U = the equivalent uni- formly distributed live load which will produce the same live-load bend- ing moment used in the design, V = the velocity of the train in feet per second, and R = the radius of the curve in feet. The velocity is often, specified as 60 — 2|D miles per hour, where D = the " degree " of curva- ture in degrees. By substituting an equivalent expression in feet per second for F, and the approximate value of 5730 -^ D for R we obtain the following more convenient expression for centrifugal C/D(24 - BY force in pounds per Unear foot. If the length of the 13,700 span is long, or the degree large, it may become necessary to take into account the eccentricity of the load on the bridge whereby one girder receives more than one-half the load. This is treated more fully in books on Bridge Design.* * For example, Kirkham's "Structural Engineering," McGraw-Hill Book Co., Inc., New York; Waddell's "Bridge Engineering, " John Wiley and Sons, Inc. New York; or Marburg's "Framed Structures and Girders," Part I, McGraw-Hill Book Co., Inc., New York. CHAPTER XXXIV THE THEORY AND PRACTICE OF RIVETING Synopsis: A general discussion of the construction of riveted joints and of how their strength is determined. The application of the principles involved to typical problems is shown in subsequent chapters. 1. Rivets are used to connect the different members of a structure to one another and also to fasten together the component parts of each member. A rivet is composed of a cyUndrical shank with a head at one end. The holes in the parts to be connected are made -^" larger than the nominal diameter of the rivet shank so that the rivet may be inserted more easily. The length of the rivet must be greater than the thickness of the metal through which it passes, so that enough metal will protrude to form the second head. The rivet is heated, then put in position and " driven " until the second head is formed and the shank is upset to fill the enlarged hole, as explained on page 30 : 4. The parts connected are held in position by temporary bolts until rivets are driven in the remaining holes, after which the bolts are replaced by rivets. For this reason no piece should be connected by less than two rivets. Conditions sometimes justify the use of a single hoU but never a single rivet lest the piece become twisted during the process of riveting. 2. Shop and Field Rivets. — Rivets which are driven in the shop are more effective than those driven in the field. Shop rivets are usually driven by machines which develop sufficient pressure to insure complete upsetting. Field rivets must be driven by smaller machines or by hand. In the shop, the members are conveniently supported by skids, trucks, or cranes. In the field, the rivets must be driven at a disadvantage on accovmt of their comparatively inaccessible positions in the structure. It is customary to allow a smaller unit stress for field rivets, than for shop rivets. It is therefore imperative that the draftsman know which rivets are driven in the shop and which in the field. In general, shop rivets are used wherever possible because they are not only better, but they can be driven more cheaply. Field rivets must necessarily be used for connecting to each other members which are shipped separately, but shop rivets are used for holding the component parts of each member together. 3. Position in Member. — ■ Rivets are driven at right angles to the hne of the stress which they are to transmit from one part to another. The number of rivets required in an ordinary connection is found by dividing the total stress by the limiting value of one rivet. This limiting value will now be considered. 4. The design of a riveted joint is based upon several assumptions. Some of these are disputable, but the error in one assumption often tends to compensate the error in another, so that the results obtained are quite satisfactory. The usual assumptions are that: (a) the driven rivet completely fills the hole, (6) the effective area of a compression member is not reduced by the rivets, (c) the stress in a tension member is distributed uniformly over the net area of cross section, (d) the stress is equally distributed among all the rivets of an ordinary concentric joint, (e) the friction between adjacent parts is neglected, ( /) the bending of the rivets is ignored except for long rivets, and {g) rivet heads should not be subjected to tension. 228 CHAPTER XXXIV THE THEORY AND PRACTICE OF RIVETING 229 Assumptions (a), (b), and (c) are made in the design of tension and compression members (pages 206 : 4 and 211 : 2). Shop-driven rivets probably fill the holes because sufficient pressure is exerted to compress the rivets enough to overcome any shrinkage due to the rivets cooling. Field rivets do not so surely fill the holes but this fact is discounted in the specifications by allowing a lower unit stress. Inspectors should test each rivet with a hammer, and loose rivets should be redriven. A slight looseness probably would not impair the strength of a connection materially after the " initial slip " has taken place, unless subjected to alternate tensile and compressive stresses. That the stress is equally distributed among all the rivets (assimiption d) is impossible may be seen from Fig. 229 (a). This shows two bars fastened together by three rivets. The total stress is 18,000#. If the first rivet transmits a third moO' JOOO 12000 12000 6000 Fig. 229 (o). of the total stress from one bar to the other, then between the first two rivets one bar would carry 6000 and the other 12,000. Since the strain is proportional to the stress (page 197:3) the distance between rivets could not be kept equal in the two plates unless the area of each bar was changed at each rivet which would be impractical. This difference in distance would at once cause unequal distribution of the stress among the rivets. It is prob- able, however, that the average value of the rivets in a concentric connection is constant, and the allowed unit stress may be considered an average value. Eccentric connections must be treated differently, as explained in Chapter XXXVI, page 237. The friction between the adjacent parts of a riveted joint (assumption e) is considerable, especially when the rivets act in double shear and are machine driven. The. American Bridge Company has found from the tests on their standard beam connections (page 83 : 6) that when the web is enclosed between two connection angles, the value of each rivet is about 25% greater than when a single angle is used. This is on account of the friction. Except for these angles used under average conditions, it is common practice at present to ignore friction. The consequent increased efficiency compensates at least in part for the deficiencies due to the other assumptions. Although the effect of bending short rivets is disregarded (assumption /), the bending of long rivets must be con- sidered. It is unnecessary to design them as cylindrical beams as in the case of pins (Chapter XLI, page 278). More commonly the number of rivets is increased when the grip of the rivets (i.e., the thickness of the parts connected) is more than four times the diameter. The usual increase in number is 1 % for each additional sixteenth of an inch in the grip. See page 235 : 2 for the effect of loose fillers. The effect of axial tension on rivets (assumption g) is not well understood. Many engineers maintain that no dependence should be placed upon rivets in tension because the heads are liable to be pulled off. Others maintain that con- siderable tension can be resisted, and tests substantiate their claim, but the safe values to allow have not been definitely determined. It is better wherever possible to avoid connections in which rivets are subjected to axial tension. If this is impractical it is well to substitute bolts for the rivets, because they are stronger in direct tension. 1. A riveted joint is designed to resist the tendency to shear the rivets, and the tendency for the rivets to tear through one or more of the con- nected parts. The action of the shearing forces may be visualized by imagining a small hole bored through two overlapping steel plates and an ordinary wooden match stick driven through the hole. If one plate is made to slide along the other, the wooden match will be sheared off as if cut by shears. Similarly, if three pieces of cardboard are placed together with a wooden match passing through them, and the middle piece is slipped along the other two, remaining in contact, the match will tear through the cardboard. A riveted joint may fail, therefore, either in shear, by the shearing of the shanks of the rivets, or in bearing, by the rivets tearing through one or more of the connected parts. A tension joint 'may also fail in one of three other ways, 1st, in tension, by one of the parts tearing along the ^,„„.„..,„^^^^65.25 Dead Live Total End 17 = .56 x30 180 =6.0 X 30 197 3 2nd 14 =17-3 149 = 180 X (i^y 163 31 3rd 11 = 14 - 3 120 = 180 X i^y 131 4| 4th 8 =11 -3 95 = 180 X (t^t)'' 103 5f 5th 6 max. The use of the approximate method illustrated below would give the same results in this case because the total dead load is so small compared to the live load. „ „, 9190x65.25 .... . , " 6560 X 30 "" P "^ ^^ 3f = 3.04 X my = " " 2nd " 4i =3.04x(-V-)'-= " 5f = 3.04 X (-V^)2= " 3rd 4th CASE V — LOADS APPLIED TO THE FLANGE 2. How Applied. — One or more stiffening angles should be placed under each heavy concentrated load which rests on the top flange of a girder, in order to transmit the load to the web plate. The rivet pitch is then found according to the method of Case III. Obviously, stiffening angles cannot be used under moving concentrated loads or under either static or moving uniformly distributed loads. The only way in which these flange loads may be transmitted to the web plate is by means of the flange rivets. These rivets, therefore, must resist not only the same horizontal flange stresses which they would resist in case the same loads were apphed directly to the web, but they must resist also a vertical stress. This form of loading is very common. For example, the rails of crane runways rest directly upon the tops of the crane runway girders, and the tracks of railway bridges rest directly upon the tops of the stringers of through bridges and the tops of the girders of deck bridges. CHAPTER XXXVII RIVETS IN THE FLANGES OF PLATE GIRDERS 249 Similarly, masonry walls are often built upon the tops of girders. The ties of railroad tracks are so close together that they may be considered as uniformly distributed loads. In order that this vertical stress may be properly distributed among the rivets, the pitch should not exceed 4 or 4| inches; 4 inches is used' for crane runway girders, and 4^ for other deck loads. 1. Theory. — In order to combine the effects of both horizontal and vertical stresses on the rivets, they must be reduced to a common basis. For convenience, both the horizontal and the vertical components are found in pounds per linear inch of girder, measured horizontally. The resultant stress shows the maximum stress per linear inch to be resisted by the flange rivets. The rivet pitch in any panel is found by dividing the value of one rivet by the proper resultant stress, thus: P = resultant " The horizontal component per linear inch was found by the shear theory V on page 244 : 1 to be ;^ . It could be found by the bending moment dr theory on page 243 of the panel in inches, thus: VB 3 by dividing the stress per panel -jr- by the length VB ^ Y V Dr ■ l2Dr dr' The V and the dr are found in exactly the same way as if the loads were applied to the web, the shear being the only variable. The vertical component is usually constant throughout the full length of the girder. It may be composed of several parts, including the proper proportion of all loads which stress the rivets vertically, such as the maximum wheel load with impact or the maximum uniform live load, the dead load due to the track or other superimposed loads,* and the weight of the angles and cover plates of the top flange of the girder itself. Most of these loads are expressed in * Students should be cautioned against two common mistakes. The weight of track, including ties, service rails, steel and wooden guard rails and fastenings, is usually given in pounds per linear foot of track, and should be divided by 2 to give the weight per foot of girder. The weight of rails is given in pounds per yard and not pounds per foot. pounds per linear foot, from which the vertical component per linear inch may be found by dividing by 12. It would be impossible to transmit the whole of a heavy wheel load to the web through the single rivet directly under the point of contact of the wheel. This is unnecessary because the rail a,nd the top-chord angles acting as beams distribute the load among several rivets. It is customary to consider the load of a crane wheel to be distributed over 30 inches. In railway bridges it is commonly specified that the maximum wheel load is distributed over three ties. This amounts to about 36 inches, as for example, when 8-inch ties are separated by 6-inch spaces. The maximum wheel load of Cooper's loading is one of the heavy drivers except for short spans in which the maximum shears are obtained from the two special loads, in which case one of the special loads is used. The impact should be included; when this depends upon the loaded length of the track it is close enough to use the span length. The resultant stress per linear inch may best be determined graphically, either by means of the diagram on page 312 or by the use of a siraple graph constructed for each problem as follows: lay off two lines at right angles to each other, or use two edges of a rectangular sheet of paper; along one line lay off the constant vertical component; along the other hne lay off the different horizontal com- ponents; the resultants may be scaled without drawing the correspond- ing diagonal lines. 2. Loads are sometimes applied to the bottom flange. If the loads are divided between the two flange angles the problem is the same as for loads applied to the top flange. If, however, the loads are supported by one angle only, the vertical component tends to shear the rivets in single shear, while the horizontal component tends to shear them in double shear, although the bearing value in the web usually determines the limiting value. Obviously the resultant stress cannot be found from these two components as before. Perhaps the simplest treatment is to increase the vertical component by the ratio which the bearing value of a rivet bears to the single shear value, and then proceed as before, using the bearing value for r. 3. Illustrative Problem — Uniform Flange Loads. — The problem on page 248 : 1 would be modified as follows, if the load were apphed to the top flange instead of the web. 250 PART III — THE DESIGN OF DETAILS 6000#/ft. = live load 200#/ft. = superimposed dead load 130#/ft. = (360 — 107) H- 2 = weight of top angles and cover plates 6330#/ft. = total load per foot supported by the rivets 530#/in. = 6330 + 12 vertical component per linear inch. y The values of -r are found from the total shears given on page 248 : 1. the relation to V that the net area of the angles and cover plates bears to the total flange area including one-eighth or other portion of the web plate. Thus in finding the pitch in any panel, Panel V 65.25 9190 Pitch = 7- — - resultant Resultant _\/(gg^J+ 530^ End 2nd 3rd 4th 3020 2500 2010 3070 2560 2080 3 34 ^ 44 max. 1. Illustrative Problem — Concentrated Flange Loads. — See page 251 : 1. CASE VI— GIRDERS IN WHICH THE WEB IS CONSIDERED TO RESIST PART OF THE STRESS DUE TO BENDING MOMENT 2. Method. — ^ Probably the large majority of girders are designed according to the method of Case B (page 223 : 3) in which the resisting moment of the web plate is considered. In all these girders the rivet pitches should be determined accordingly. In this method of design a portion of the web plate (usually | of the gross area) is combined with the net area -of the flange angles and cover plates to form the flange area which resists the flange stress due to bending moment. That part of the flange stress which is resisted by the web plate requires no rivets. This is analogous to a simple rectangular beam. The flange rivets are required to transmit the remaining stress to the angles and the cover plates, and to provide for any vertical stress which may result from loads apphed to the flange. Thus the methods of the preceding cases may all be modified to apply to girders which are designed by the method of Case B by substituting for V a new value V. This affects the horizontal component of the stress in the rivets, but it does not affect the vertical component which remains the same as before. The new value V bears '"=^(1) in which V is the maximum shear used in finding the pitch according to the method of one of the preceding cases, V is the corresponding value used in the method of this Case VI, a' is the greatest net area of the flange angles and cover plates of one flange in the given panel, and a is the sum of a' and the part of the web plate considered as flange area, usually ^ of the gross area. The ratio — is not constant in a girder unless the same flange area is maintained throughout its length. When cover plates are used, the maximum section is furnished near the point of maxi- mum flange stress, but it is customary to cut off each cover plate at a point where the reduced area is sufficient to carry the maximimi flange stress which can occur at that point, as explained in the next chapter (page 259). Hence the lengths of the cover plates should be determined before the rivet pitches are computed. Since the ratio — increases with the area, the greatest cross section in any panel should be used; this will be found at the end of the panel nearer the center of the girder. If it is not feasible to determine the lengths of the cover plates before the rivet pitches are found, the maximum ratio found from the greatest flange area should be used throughout the whole girder. It is usually better to maintain the same pitch throughout a panel rather than to change it at the end of a cover plate because such a change would result in the use of a few spaces at a pitch smaller than the pitch either to the right or to the left. This should be avoided for the sake of appearance, particularly as long as very few rivets, if any, would be saved. If this greatest section extends for only a very small proportion of the panel length, the smaller area may be used, except for fixed con- centrated loads, because the shear at that end of the panel is less than at the be- ginning of the panel. 3. Illustrative Problem — Web Loads. — Find the rivet pitches in the girder designed on' page 225 : 1. The concentrated loads found on CHAPTER XXXVII RIVETS IN THE FLANGES OF PLATE GIRDERS 251 page 225: 1 are placed according to Fig. 251 (a) to give the maximum bending moment. This position also gives the maximum shear in the second panel = 84.2 thousand pounds = 164.3 - 80.1. The maxi- mum shear in the end panel is 194.7 thousand pounds, obtained when 80.1 157.2. 102.4 15 [is I 15 I 15 \l64.3 l''5.4\ 157.2 102,4 102.1 IS \ 15 \ 15 [ 15 1194./ Fig. 251 (o) Fig. 251 (b). the loads are placed to give the maximum bending moment at the end of the first panel, which brings the maximum concentration at the quarter point, as shown in Fig. 251 (6). 9190# = r = value of one |" rivet bearing in a j\" plate at 24,o6o#/sq. in. 65.25" = 721 _ (2 x 2i + 2i) = d, ' 12,300# = 410 X 30 = end shear due to weight of girder 6,200# = 12,300 — 410 x 15 corresponding shear for second panel 37.1 13.9 + 8.2 + 7.5 + 7.5 ,. a' ^ , ^ 3.9 + 13.9 + 8.2 + 7.5 + 7.5 = ^^^^V^^'' ^"^ ^^""'^ 41.0 29.6^ 33.0 41.0 37.1 -7.5 7,5 ratio for end panel, see Fig. 262 183.0 29.6 33.4 37.1 (194.7 + 12.3) = F' for end panel in thousand pounds 81.8 =|Y^ (84.2 +6.2) = F' " 2nd 9.19x65.25 3i" = 6" max = 183.0 9.19x65.25 81.8 = pitch in end panel = " " 2nd " 1. Illustrative Problem — Flange Loads. — Find the rivet pitches in a stringer for the same bridge as the preceding problem. The stringer is composed of a 22 x | web and 6 x 6 X ri angles without cover plates. 13,130# = value of one |" rivet bearing in a |" plate at 24,000#/sq. in. 15" = 22i- - (2 X 2-1 + 2|) = dr (the web being flush with top angles) The panel length is taken equal to (/, . The dead-load end shear is 2800# = (Affi. + 150) 7.5, which is reduced by 500# = 375 x 1.25 per panel. The live-load shears for the first two panels are found by means of the table on page 318. The remaining live-load shears are maximum for the two special 37,500# loads spaced 7 feet apart, since the loaded segment does not exceed 12.5 feet (page 194:1). A single impact percentage determined from the span length may be used for each panel. The con- "' 14 2 14 2 The vertical component per hnear stant ratio — a 15.9 1.7 + 14.2 inch for the two end panels is 1650# ^Q'Q00x^*+^ + '%he50 being the weight of the top flange angles. the remaining panels is 2050# = 37,500 X 36 ' 12 The vertical component for 15 450 ^ 50 33 + 12 Panel End 2nd 3rd 4th 5th 6th Horizontal Component = ^7 615 \14.2 7140 = ( 60,000 X — + 2800 ■ - 15 315 / 15.9 615 \14.2 6240 = 52,500 x — + 2300 h- 15 * ' 315 /15.9 / 615 \14.2 5330 = 45,000 x — + 1800 .=- 15 \ 315 /15.9 / 615 \14.2 4580 = 38,800 x — + 1300 h- 15 \ olu I Id . y / 615 \14.2 3820= 32,500 x,;7i;+ 800);^-:;-=- 15 315 615 /15.9 \14.2 3080= 26,300 X; — + 300) 315 /15.9 -e-15 Vertical Component Resultant 1650 7330 1650 6450 2050 5710 2050 5020 2050 4340 2050 3700 Pitch = 13,130 resultant 11 2 21 2; 3 35- The rivet pitches are here determined up to the center in order to illustrate the method, although as a matter of fact they could not be used because the pitch in the end panel is less than the minimum of 2| found from the table on page 306. In this case the girder should be redesigned with either an increased web thickness or increased depth. 252 PART III — THE DESIGN OF DETAILS CASE Vn— BOX GIRDERS, CANTILEVER GIRDERS, AND GIRDERS WITH NON-PARALLEL FLANGES 1. A box girder may be considered as two or more girders, depending upon the number of webs (Fig. 95 (g)). The cross section is usually made sjTximetrical about a vertical axis. When there are only two webs each half of the girder will carry one-half the load, and one-half the total flange stress will be resisted by the angle (or angles) on each web together with one-half the cover plate. The flange rivets in each web must be proportioned for this half stress, according to the method of one of the preceding cases. If flange angles are used on only one side of each web, the rivets will be in single shear, and the corresponding rivet value must be chosen. Girders with three webs are usually designed so that the center portion carries one-half the total load. Thus there are two angles in each flange on the central web, but only one on each outer web. The central web should be thick enough to make the value of one rivet twice the single-shear value so that the rivet pitches in all three webs will be the same. Otherwise, the pitches must be determined separately. 2. In a cantilever girder the rivet pitches may be determined by the method of one of the preceding cases given for simple girders, but care must be taken that the proper shear is used. In determining the pitch in any panel, the maximum shear in the panel should be used. Sometimes this maximum will occur when the section is taken at the left end of the panel and sometimes when it is taken at the right end, depending on the position of the panel in the girder. See page 190 : 1 for the position of moving loads which will cause the maximum shears. 3. Illustrative Problem — Cantilever Girder. — Find the pitches of j" rivets in a 40-ft. cantilever girder which projects 10 ft. beyond one of two supports which are 30 ft. apart. The total static load is 4,000#/ft. including the weight of the girder. The girder is composed of a 36 x f web and 6x4 angles. The imit stress in bearing is 20,000#/sq. in. Assume the simplest case in which the load is applied to the web, and the resisting moment of the web is neglected. The shear and moment diagrams for this form of loading are shown in Fig. 193. The maximum bending moment occurs at the section for which the shear is zero, and the point of contraflexure is at the point where the bending moment is zero. The bending moment and shear, and hence the rivet spacing, are symmetrical between the point of con- traflexure and the supported end. The distance from the right support to the point of contraflexure is 26 . 6 found by equating to zero an expres- sion for bending moment in terms of the distance X. The point of contra- flexure is not much over a panel length from the left-hand support so the equal panels are laid off from the point of contraflexure and from the right-hand support as shown in Fig. 252 in order to make the rivet spacing symmetrical. If preferred, 12 3 4 S 6 7 8 8 7 8 5 i.t 2.e-2.eX I II. 2.5 2.5 2..5 2.6. * a2- WsTi ■>1.C' 30 mj 63,3 Fig. 252. the equal panels could be laid off from the left-hand support, but additional pitches would have to be cal- culated because the shears for the panels at the right would differ from those at the left. The cantilever end is divided into four equal panels. 5630/ = r = value of one f " rivet bearing in a f " plate 31.5" = 36| -2x2i = dr. Panel Shear = V (in thousands) Pitch = ^«^^«l-« 0-1 1-2 2-3 3-4 4^5 5-6 6-7 7-8 8-8 10.0 =4.0 x2.5 20.0 =10.0 x2 30.0 =10.0 x3 40.0 =10.0 x4 66.7 =106.7-40.0 53.3 =Br 42.9 =53.3 -4.0 x2.6 32.5 =42.9 -4.0 x2.6 22.1 =32.5 -4.0 x2.6 6 max. 6 max. 6 ^ 21 31 4i 51 6 max. The smallest space 2f is not less than the minimum 2| found in the bottom table on page 306 so the solution is satisfactory. 4. Girders with non-parallel flanges are used for turntables, sidewalk brackets, and other special work. The inclined flanges have vertical components which relieve the web plate of part of the shearing stresses, and the number of rivets must be increased accordingly. The formula CHAPTER XXXVIl RIVETS IN THE FLANGES OF PLATE GIRDERS 253 p = -r^, or a modification of it for conditions similar to those of the pre- ceding cases, may be adapted to girders with inclined flanges by substi- tuting V" for V, as explained below. The resulting pitch will be the distance altmg the flange and not necessarily horizontal. The pitch along the bottom flange will theoretically be the same as the pitch along the top flange even though the inclination is not the same. Sometimes for practical reasons, only the pitch of the rivets in the steeper flange is com- puted, the rivets in the other flange being placed in the same vertical lines even though more rivets are thus used. The pitch is usually changed at equal intervals. Since both V" and dr vary, the pitches should be determined at both ends of a panel and the smaller of the two should be used throughout that panel. The value of V" may be determined from the following expression : * M (tan a + tan P) V" = V dr in which V = the maximum shear for a given section, M = the cor- responding bending moment for the same section and for the same posi- tion of the loads, dr = the vertical distance between rivet lines at the given section, a and /8 = the angles of inclination of the bottom and the top flanges with the horizontal. The signs of the tangents given, above are based upon the flanges converging toward the end of the girder. In case either slope is reversed the corresponding sign of the tangent should be changed. If either flange is horizontal the corresponding tangent becomes zero. CASE vm— GIRDERS WITH VERTICAL FLANGE PLATES, AND GIRDERS WITH FOUR ANGLES IN EACH FLANGE 1. When Used. — Girders which carry heavy loads over long spans frequently require greater flange areas than can be furnished by two angles with cover plates. Similarly the use of a depth less than the most economical depth may necessitate the use of a more complex flange. * For derivation see Johnson-Bryan-Turneaure's "Modern Framed Structures," Vol. Ill, John Wiley and Sons, Inc., New York; or Waddell's "Bridge Engineering," Vol. I, John Wiley and Sons, Inc., New York. Various forms of flange are adopted to meet different requirements, as illustrated in books on girder design. Only two forms will be considered here, viz.: flanges with vertical plates between the angles and the web, and flanges composed of four angles. Vertical flange plates are often used in conjunction with the four angles, either between the angles and the web or outside of the vertical legs of the angles, or both, but any draftsman who is hkely to design the details for such a girder should be able to adapt the principles of this chapter to his needs. 2. Vertical flange plates which are placed between the flange angles and the web plate extend the entire length of the girder because it is impractical to make them shorter than the angles which Fig. 253. rest upon them. The rivets which pass through both the angles and the vertical plates (rows a and b, Fig. 253) must be considered separately from those which pass through the web and the vertical plates only (row c). The former transmit only that portion of the flange stress which is carried by the flange angles and the cover plates. This part of the stress tends to shear the rivets between the angles and the vertical plates, and the thickness of metal is sufficient to develop the full double-shear value of the rivets. The total stress carried by the angles, the cover plates, and the vertical flange plates tends to shear the rivets in aU rows between the vertical plates and the web, and the rivet value is usually Hmited by the bearing value in the web plate. For practical reasons it is customary to place the rivets in row c opposite those in rows a and b. The pitch in row c increases more rapidly than the pitch in rows a and b. If the pitch in rows a and b is found to be less than that in row c in the end panel it will also be less in the other panels, so it is unnecessary to determine the pitch in row c in every panel. Sometimes the pitch in row c will be twice as great as in rows a and b in some panels, and the rivets may be placed opposite those in row a only, as in Fig. 253, provided the 254 PART III — THE DESIGN OF DETAILS maximum value (usually 6") is not exceeded. The pitch in row c must then be determined in enough panels to find where the double pitch may begin. 1. Theory — Rivets in Angles. — The rivet pitch in rows a and b r"dr rivets in rows a and b is is determined from the expression p = Y"" in which r" = the double shear value of one rivet, dr = the mean depth between the rivet lines in the angles (rows a and b), and V" = that proportion of the maximum total shear V in the panel which the net area of the angles and the cover plates bears to the total net flange area in the panel, including the ver- tical flange plates. Since this proportion increases with the areas, both areas should be taken for a section at the end of the panel toward the center of the girder, although the maximmn shear is not found for the same section (compare page 244 : 3). The resulting pitch is the horizontal distance from a rivet on row a to a rivet on row b, the rivets being stag- gered. If three rows are used in each angle, the rivets in the middle row are usually staggered with the rivets in the top and bottom rows which are placed opposite. The pitch from a rivet in the middle row to the rivets in the other rows would be three-halves of the pitch found from the formula, dr being the mean depth of the three rows. If the loads are applied to the flange of the girder, a vertical component must be com- bined with the horizontal component as in the method of Case V (page 248 : 2). If the girder is designed according to Case B (page 223 : 3), the total net flange area mentioned above should include one-eighth or other portion of the web which is counted as flange area, as explained under Case VI (page 250 : 2). 2. Theory — Rivets in Vertical Plates. — The determination of the pitch of the rivets ia row c (Fig. 253) is based upon the difference between the total number of rivets required in rows a, b, and c, and the number required in rows a and b. The total number of rivets in all three rows . VB required in a panel of B feet is —tj- (compare page 243 : 3), in which V = the maximum total shear in the panel, r = the value of one rivet in bearing in the web (or double shear if less), and d' = the mean depth of aa + bb + cc the three rows of rivets or The corresponding number of V"'B r"dr (preceding paragraph). The number of rivets in row c is equal to the difference between these two numbers, and the rivet pitch is found by dividing the panel length by this difference. The panel length cancels out and the formula for the rivet pitch in row c is P = rd' r"dr If the loads are appHed to the flange of the girder, the same vertical component used in finding the pitch in rows a and b should be combined V V" with -p and also with — r- to give two resultants which should be used in place of the corresponding quantities in the above formula. If the girder is designed according to Case B, the V of the formula should be replaced by V as in Case VI (page 250 : 2) and the V" should be modi- fied as in the preceding paragraph. In case a deeper vertical plate is used with an additional row of rivets, the rivets would be staggered on the two lines, and the pitch of the staggered rivets would be found as before except the extra rivet line would have to be considered in deter- mining the mean depth d'. 3. Illustrative Problem — Girder with Vertical Flange Plates. — The points peculiar to this type of girder may be illustrated by finding the pitch in one panel where the maximum shear = 600,000#. The girder is composed of a 120 x f web, 6x6 angles, 14" cover plates, and 12 x |" vertical flange plates, with f " rivets. Let us assume that the resisting moment of the web is considered; that the ratio of the net area of the angles, cover plates, and vertical plates to the total net area including I the web is 0.8, or 7' = 0.8 F; and that the ratio of the net area of the angles and cover plates to this same total net area is 0.6, or V" =0.67. The depth back to back of angles is 10' 0|", the distance from the back of the angle to the first row of rivets a is 2|, from row a to row b is 2^, from row b to row c is 3, and from row c to row d (the additional row in the vertical plates) is 3. The mean depth dr of the rows a and b is 113?, and the mean depth d' of rows a, 6, c, and d is 107 . 6. From the last table on page 310, the value of one rivet in double shear r" = 12,030, and CHAPTER XXXVII RIVETS IN THE FLANGES OF PLATE GIRDERS 255 in bearing in the f" web plate r = 10,940. The pitch of the staggered 12 nQfi V 1 1 ^ 9fi nvets in rows a and 6 is 3| = q's x 600 000 '^^^ P'*''^ °^ *^^ ^*^S- gered rivets in rows c and d is calculated to be over the maximum of six inches, thus: 1 0.8 X 600,000 _ 0.6 X 600,000 10,940 X 107.6 12,030 x 113.25 Since 6" is less than 2 x 3f the double space cannot be used, and for practical reasons a pitch of 3f would be used, with the rivets in rows c and d opposite those in rows a and h. In case the load was appKed to the flange and the vertical component was 1000# per linear inch of girder, the above problem would be modified as follows. The horizontal component Y'" 3280 = 0.6 x 600,000 must be replaced by the resultant of this 113.25 force and the vertical component of 1000, or 3430. The horizontal + ^' AAca 0.8x600,000 ^, , J . XI- ,. . component -rr = 4460 = ' — must be replaced by the resultant of this force and 1000, or 4750. The rivet pitch in rows a and h would 12 030 then be ?>\ = ' , and the pitch in rows c and d would become which is over 6". A pitch of 2>\ would be used since 6" 4570 3430 10,940 12,030 is less than 2 x 3^. 1. When four angles in each flange are used, the rivets in the addi- tional angles are placed opposite those in the outer angles, as shown in Fig. 255, for convenience in spacing the rivets both in the drafting room and in the shop. It is therefore necessary only to determine the pitches in either the outer or the inner angles whichever is smaller. The rivets in the outer angles are proportioned for the entire vertical component due to any load which rests upon these angles, and for that portion of the horizontal stress which is carried by the outer angles and the cover plates. The rivets in the inner angles are proportioned simply for that part of the horizontal stress which is carried by the inner angles (unless there should be a vertical load applied to these angles). The depth dr should be the mean depth between the rivet lines in the angles in which the pitch is determined, the mean depth for the inner angles being considerably less than that for the outer angles. When cover plates are used, the limiting pitch is found in the outer angles, otherwise the pitches in both angles should be determined in one or more panels and the smaller values chosen. Fig. 255. THE DETERMINATION OF THE MINIMUM PITCH BASED UPON THE STRENGTH OF THE WEB 2. Importance. — One point of failure of plate girders is apparently overlooked by some designers, although it should receive the most care- ful consideration. The strength of the web plate between flange rivets may not be sufficient to transmit the full flange stress for which the flanges are designed and for which the rivet pitches are determined. If the rivet pitch which is determined by any of the methods of the preced- ing Cases happens to be less than a certain minimum, the web plate will fail along the line of rivets before the strength of the rivets is fully devel- oped, and the maximum safe load of the girder will be somewhat less than the required amount. The minimum space of " three diameters " (page 68 : 6 ) is so generally recognized as the smallest pitch allowed for rivets in a single line that no serious difficulty is likely to arise from the lack of further consideration of flange rivets which are placed in a single fine, although the minimum pitch is not exactly three times the diameter of the rivet for all unit stresses. A draftsman is quite liable, however, to use a smaller pitch for staggered rivets than is justified by the strength of the web plate. Although the minimum pitch for stag- gered rivets is somewhat less than " three diameters," it is not so much less as many designers and draftsmen suppose. It is important that no 256 PART III — THE DESIGN OF DETAILS pitch be less than the minimum determined by the strength of the web as explained below. 1. A table of minimum pitches for flange rivets is given on page 306. Values are shown for different sizes of rivets, for different web thicknesses, and for different unit stresses. Distinction is made also between rivets placed in single and double rows, and between those which act in single and double shear. It should be noted that the pitch varies with the web thickness only when the rivet value is Umited by either single or double shear, but the pitch is independent of the web thickness when the rivets are limited by the bearing value as. is more frequently the case. Values are given in the tables only for webs from ^" to f" thick, and no value is given which would provide less than the minimum clearance required in driving the rivets by machine. Since rivets are so commonly stag- gered on hues which are 2\" apart it hag seemed desirable to indicate all values which are less than the minimimi determined for this gage from the diagram on the page preceding the table. All values above the fine lines should be used only upon the assurance that the corresponding re- duction in the net flange area will not impair the strength of the girder. For example, this is true when rivets in both hues have been deducted in determining the net area used in the design of the flange, or when there is sufficient excess of flange area in the panel for which the pitch is de- termined as is quite often the case. 2. Unit Stresses. — The unit stress in shear is usually specified for the gross area of the web plate but seldom for the net area. In deter- mining the strength of the web between rivets the net area is used. In the tables two different imit stresses in shear on the net section of the web are used in conjunction with the common unit stresses for the rivets. Unless otherwise specified a unit stress of 13,000#/sq. in. may be used. This is about eight-tenths of the unit stress in tension of 16,000, which is a fair allowance. It is also about four-thirds of the unit stress in shear on the gross section of 10,033, which is consistent with the ratio used in allowing for rivets in the web plate in deriving the formula used for designing girders by the method of Case B (see page 223: 3). Incidentally, the use of 13,000 with the unit stresses for rivets as specified by the American Railway Engineering Association reiults in a minimum pitch in a single row of rivets of three diameters, as shown in the first table on page 306. 3. Theory. — The web plate must be strong enough to transmit the flange stress to the flange angles. The critical horizontal section is along the fine of flange rivets. When two lines of rivets are used, the critical section will be along the line nearer the center of the web. The web between adjacent rivets on the critical line must develop the strength of the corresponding number of rivets, i.e., one when a single line is used as in Fig. 257 (a) and two when the rivets are staggered as in Fig. 257 (6). The formulas upon which the values in the tables on page 306 are based depend upon whether rivet values are limited by bearing, or by single or double shear. The formulas for the minimum pitch for rivets in a single line and for staggered rivets are so similar that they are derived in parallel columns for the sake of comparison. Similar expressions for three or more hues of rivets may be derived in like manner as occasion demands. Let p = the minimum rivet pitch, measured parallel to the rivet hues from center to center of rivets, d = the diameter of the rivet, d + l = the diameter of the rivet hole used in designing (page 208:2), t = the thickness of the web plate (or the thickness of a single angle of a box girder if less than the web thickness), s = the unit stress in shear on the net section of the web plate, s' = the unit stress in shear on the rivets, and h = the unit stress in bearing. All units are inches or pounds per square inch. CHAPTER xxxvii RIVETS IN THE FLANGES OF PLATE GIRDERS RIVETS IN SINGLE LINE STAGGERED RIVETS 257 Fig. 257 (a). In Fig. 257 (a), the net area which resists horizontal shear in the space p is [p - (d + 1)3 1. This is multiplied by the unit stress s and equated to the value of one rivet. // the rivets are limited by the bearing value: [p-{d + l)y = dtb, or p=^ + (d + ^). // the rivets are limited by the single shear value: Fig. 257 (6). In Fig. 257 (6), the net area which resists horizontal shear in the space 2p is [2p - (rf + !)]<. This is multipUed by the unit stress s and equated to the value of two rivets. // the rivets are limited by the bearing value: [^ - (' + ^). ts = TrrfV or TTdV ■ + i^-t)- If the rivets are limited by the single shear value: 2ir d^s' 4, ' - '' 4fe // the rivets are limited by the double shear value: [p-[d + s)\'^-^' or p=^^ + (d + -j. [2p -(d + rivets an Ihe rivets are lit ts = 2dtb, or V db 1 r + 2 ts = or V Us "*" 2 If the rivets are limited by the double shear value: 2 X 27r dH' ts = or 7r*s' 1 / , 1\ ^ = Ws+2\^ + l} SUMMARY CASES I, U, III, and IV. Girders in Which the Loads are Applied to the Web and the Resisting Moment of the Web is Neglected. — The rdi- maximum pitch in each panel is found from p = ^^^ in which r = the limiting value of one rivet, rfr = the mean depth between the rivet hnes of the top flange and those of the bottom flange, and V = the maximum total shear at the beginning of the panel. No pitch should be more than 6" or less than the minimimi found from the table on page 306. The panel lengths are chosen approximately equal to the depth between rivet lines, although this may be varied somewhat to conform to the spacing of the stiffening angles. The pitch is also changed at the point of ap- plication of any fixed concentrated load. If there are no other loads besides the fixed concentrated loads except the weight of the girder, the pitch is changed only at these points of concentration. For girders which support moving uniformly distributed loads the intermediate pitches may be found from the pitch in the end panel as explained on page 247 : 3. CASE V. Girders in Which the Loads are Applied to the Flange and the Resisting Moment of the Web is Neglected. — The maximum pitch -, in which the resultant is found in each panel is found from p = ' rGSiHiSiiiu from horizontal and vertical components in pounds per linear inch. The , V horizontal component is -j found from the same values and at the same points as in Cases I-IV above. The vertical component is found from the loads which tend to shear the rivets verti{^ally, as explained on page 249 : 1. No pitcli should exceed 4|" (usually 4" for crane runway girders), or be less than the minimum found from the table on page 306. CHAPTER XXXVIII COVER PLATES Synopsis : The methods of finding the lengths of the cover plates of plate girders to be used under different conditions, and the determination of the rivet spacing in the cover plates. 1. Use. — Cover plates are often riveted to the flange angles of plate girders in order to furnish the necessary flange area when the angles alone are insufficient, as explained on page 219 : 1. The use of cover plates which do not extend the full length of the girder permits the reduction of flange area toward the ends of the girders to correspond to the reduction in the flange stress due to bending moment. LENGTHS OF COVER PLATES 2. Some cover plates extend the full length of the girder in order to furnish protection from the weather, or to give uniform bearing. On girders which are exposed to the elements, one cover plate of the top flange is made to extend the entire length to prevent the collection of water in the pocket formed between the angles above the edge of the web plate (page 95:3). Some specifications require that one of the bottom plates extend the full length also, particularly in bridges over salt water. This keeps the girder symmetrical about the neutral plane, although no harm can come from having an excess in one flange even though it is not balanced by an excess in the other. In crane runways the rails usually rest directly upon the top flanges of the girders, and in order to give proper bearing for the rails all the top cover plates, or the cover channel (Fig. 95 (e)), must run the full length. This is not required in the top flanges of deck railway bridge girders because the ties can be notched to make up for the variation in the thickness of the plates. 3. The theoretical length of a cover plate is determined from the curve of bending moments, but the actual length is usually made from two to three feet greater. (Compare pages 261: 2 and 262: 2.) This extension of one foot or more at each end permits the partial development of the plate by rivets beyond the point where the plate theoretically begins, thus insuring its action when needed. The extension also provides a safe margin for any inaccuracies in length due to scaling the graph or to calculation, and minimizes the chance of the girder failing at the end of a cover plate. 4. The graphic method of determining the theoretical lengths of cover plates will be explained first because it is more general in that it can be adapted to any condition of loading. The algebraic method is more con- venient than the graphic method upon which it is based, but it is Hmited to imiformly distributed or moving loads, as explained on page 263: 1. 5. For girders which are symmetrically loaded only one-half of the span need be plotted. This is true also for girders with unsymmetrical loads which may be reversed, as in bridges. For unsymmetrical fixed loads the full length should be plotted. Usually the curve of bending moments for a single position of the loads is sufficient, but for variable fixed concentrated loads more than one curve may be required, as ex- plained on page 261: 2. 6. The bending moments for a girder which supports a uniformly dis- tributed load vary as the squares of the distances, and the curve of mo- ments is a parabola. This is true for moving loads as well as for static 259 260 PART III — THE DESIGN OF DETAILS loads because the maximum bending moment at any point occurs when the load extends the entire length of the girder. The vertex of the parab- ola is at the center of the span where the bending moment is maximum. To any convenient scale, AB equal to the half span (or full span as ex- plained below) is laid off horizontally, and BC equal to the total maxi- mxmi bending moment is laid off vertically, as in Fig. 260. The vertical scale is different from the horizontal scale because the units are different. It is well to choose the scales so that the distance BC is no greater than D' E' r \ 2 / \\ ■ % ^ "^^.^ Fig. 260. Lengths of Cover Plates — Uniformly Distributed Loads. the distance AB and no less than three-quarters of AB. With the ver- tex at C a parabola* is drawn through A. The ordinate to the curve from any point between A and B represents the bending moment at that point. On any inclined hne through B is laid off BH equal to the total * Construction : Draw a vertical through A, and lay off AA'= BC. Divide AA' into any number of equal parts, depending upon the accuracy required. Connect each of these points with C. Divide AB into the same number of equal parts and drop a vertical through each point. The intersection of the first vertical with the first diagonal gives the first point on the parabola, etc. The points may be joined by means of a curved ruler. Only enough of the construction lines need be drawn to show the intersections. required net flange area for which the girder is designed. This is sub- divided so that BD is the actual net area of the two flange angles together with the portion of the web, if any, which is counted as flange area in the design, and DE, EF, FG, etc., are the net areas of the cover plates, the larger being nearer the angles. Usually the last point will fall a httle outside of the point H because of the excess in area which results from the selection of conunercial sizes. A hne is drawn from H to C, and hues parallel to this hne are drawn through points D, E, and F. These lines make proportionate intercepts on the line BC which show the portion of the maximum bending moment which is resisted by each of the com- ponent parts, since the net areas are directly proportional to the bending moments (page 221:2). Horizontal lines drawn through these new points cut the parabola at points where the corresponding net areas satisfy the bending moment. Thus, from A to D' the web and the flange angles are sufficient without cover plates; at D' the first cover plate be- comes necessary, but it is not fully developed imtil E' is reached, at which point the second cover plate begins; the third plate begins at F', etc. The theoretical length of the first (thickest) plate is twice the dis- tance from D' to B, the second twice the distance E'B, and the third twice F'B. By making AB equal to the whole span instead of one-half, the effect will be to change the scale so that the distances D'B, E'B, and F'B give the whole lengths of the plates without doubling. If the line BH is drawn so that the line HC will be horizontal, the parallels will be coincident with the horizontal lines which cut the curve, and the con- struction is simplified (see illustrative problem, page 262: 1). It is often more convenient not to pilot the bending moment, but to lay off the net areas along the hne BC and to draw the parabola through the new point C = H. The curve then represents net areas instead of bending moments, and the inclined Une is not needed. It is quite a common practice to draw the parabola to correspond to the point G of the actual area instead of point H of the required area. This gives safe results but inconsistent results, because the lengths of some cover plates may be increased a foot or more while others in the same girder are changed only shghtly. It is unnecessary to strengthen the flange throughout its length simply be- cause it happens to be impossible to find a commercial size which will satisfy the requirements at the center. If all other parts of the girder CHAPTER XXXVIII COVER PLATES 261 were strengthened in proportion it might be desirable, but even then a more equitable distribution could be devised. However, no great harm can come from the use of actual areas instead of the required areas, and in some cases it is more convenient. 1. The bending moments for a system of concentrated loads increases constantly between loads, and the curve of moments is a series of straight lines. Since concentrated loads are found only in conjunction with uni- formly distributed loads, the two curves must be combined. This may Fig. 261 (a). Lengths of Cover Plates — Combined Loads. be best accomplished by plotting one below and the other above a hori- zontal line so that the combined ordinates representing the total bend- ing moments may be scaled. Thus in (a), Fig. 261 (a), the parabola is drawn, through P and M so that NP is the maximum bending moment due to the uniform load, as in tke preceding paragraph. The bending moment due to the concentrated loads must be found and plotted at the point of application of each load, as UV and NQ. The total maximum bending moment for which the flanges were designed is represented by the maxi- mum combined ordinate PQ. This total bending moment should be subdivided in proportion to the resisting moments of the angles and web, and each cover plate, as in the preceding paragraph. This should be done along the edge of a separate card or piece of paper, as shown in (6), Fig. 261(a). This card can be made to slide over the graph of (a). Fig. 261(a), so that P' follows the parabola, and the hne P'Q' is kept vertical. In the position where R' falls in the lower curve at R, the vertical line marks the point where the first cover plate should theoretically begin, because the resisting moment of the angles and web P'R' satisfies the total bending moment P'R. Similarly, the second cover plate should begin where the total ordinate P'S equals the distance P'S', the third where the ordi- nate P'T equals P'T', etc. In case there is no other uniform load than the weight of the girder itself, the corresponding bending moment would be relatively so small that the parabola would be too flat to plot. In this event a single curve should be plotted from the total bending moments. Thus the bending moment due to the concentrated loads at the point of application of each load should be increased by the bending moment due to the imiform load at the same point. 2. For variable concentrated loads, fixed in position, the lengths of the cover plates are not always determined from a single position of the loads. Take, for example, the girder of a through rail- way bridge. The loads should be placed to give the maximum bending moment for which the flanges are designed (page 225 : 1), the total bending moment at each panel point should be found for this position of the loads, and the corre- sponding curve of bending moments should be plotted, as shown by the full line in Fig. 261 (6). The loads should then be placed to cause the maximum bending moment at one of the other panel points^ and the curve of aad Web Fig. 261 (b). Lengths of Cover Plates — Variable Concentrated Loads. 262 PART III — THE DESIGN OF DETAILS bending moments should be constructed for this position in the same manner, as represented by the dashed Hne. Similarly, a curve should be plotted for the position of the loads which causes the maximum bending moment at each other panel point. Since the hve loads may cross the bridge in either direction, the girder is made symmetrical and only one- half need be plotted. Each curve should be plotted for that half of the girder in which the larger bending moments occur. Each curve will be outside of all the other curves at least at one panel point. The maximum ordinate BC representing the maximum bending moment for which the flange is designed should be subdivided as before (page 259 : 6) to show the proportion of the bending moment which is resisted by each component part. The length of each cover plate is determined by drawing a horizontal hne through the proper point on the hne BC imtil it intersects the curve of bending moments which is farthest from the center. The bending moments due to the weight of the girder are usually so small that they can be combined with the bending mo- ments due to the concentrated loads which include other dead loads, hve loads, and impact. If there were additional uniformly distributed loads it might become necessary to plot the moment parabola separately, as explained in the preceding paragraph. There are so many steps to a problem such as described in this paragraph that inaccuracies in computa- tion and in plotting are Hable to accumulate. It is well, therefore, to be somewhat hberal in the amotmt added to the theoretical lengths in obtaining the practical lengths to be used. 1. Illustrative Problem — Variable Concentrated Loads. — Find the lengths of the cover plates of the girder designed on page 225: 1. The maximum total bending moment at the center was found on that page to be 3913 thousand potmd-feet, including 185 thousand due to the weight of the girder. The concentrated loads were placed as shown in Fig. 251 (a). The corresponding bending moment at the right-hand quarter point (which is greater than at the left-hand quarter point) is 2769 = 175.4 ,^ 410 ,- ,. X 15 + -2- X 15 X 45. The full line of Fig. 262 is plotted from these bending moments. With the loads placed for the maximum bending moment at the quarter point, as in Fig. 251 (6) (see also page 261: 2), the bending moment at the center is 3668 = 194.7 X 30 - 157.2 x 15 -|- 185, and the bending moment at the quarter point is 3059 = 194.7 x 15 -|- 138, the 138 being the bending moment due to the weight of the girder foxmd above. The dashed line is plotted from these bending moments. On the diagonal line are laid off the total net area 40.6 sq. in., the net area of the angles and J of the web 17.8 = 13.9 + 3.9, the net area of the 14 x H plate 8.2, and the net areas of the two 14 x f plates each 7.5. The total area 40.6 is swung about B as a center until it intersects a horizontal line through C. In this way the parallel lines become horizontal and coinci- dent with the horizontal construction hues which cut the curves, which may, therefore, be drawn directly from the points on the diagonal line eo-o *~ 30-0 30-0 ■ <^ ^ "^ s \ \ 43.2 ^ \, 5l \£> V 35.4 3 \ \\ 3 \ Fig. 262. to the curve farthest from the center line. In this case the lengths of all three cover plates are determined by the dashed line. Since the dis- tance AB was made the full length of the girder, the scaled lengths of the cover plates represent the full theoretical lengths. To these should be added about three feet to give the actual lengths to be used, thus: 46' 0" = 43.2 -h 2.8, 38' 6" = 35.4 + 3.1, and 24' 6" = 21.6 + 2.9. On the top flange the 14 x ii plate should extend the fuU length of the girder instead of 46' 0". 2. For a system of moving concentrated loads, such as Cooper's con- ventional engine loads, it is usually impractical to construct an accurate curve of bendmg moments because this would necessitate finding the CHAPTER XXXVIII COVER PLATES 263 maximum bending moments at short intervals, say equal to the depth of the girder. This would involve a different position of the loads for each bending moment. The resulting curve would approximate a parab- ola, and it is usually sufficiently close to consider it a parabola, provided a liberal amount is added to the length of each plate to overcome the discrepancy between the curves. Usually from 3 to 4 feet should be added to the theoretical length instead of from 2 to 3, particularly for the short- est plate when more than one are used. 1. An algebraic method is more convenient than the graphic method when the curve of bending moments is a parabola. No general algebraic method can be given for girders with fixed concentrated loads because the conditions are so varied. It is possible to compute algebraically the lengths of the cover plates for any specific case by a method adapted from the corresponding graphic method outlined in the preceding paragraphs, but this is not usually recommended for fixed concentrated loads. For ' either static or moving uniformly distributed loads the curve of maximum bending moments is a parabola, and for moving concentrated loads the curve approximates a parabola, as explained in the preceding paragraph. The curve of net flange areas is also a parabola since the net areas are proportional to the bending moments. The equation of a parabola referred to the origin at the vertex is X^ = 4PF, which shows that values of Y vary as the squares of the corresponding values of X, P being a constant. Hence, ^tf^ ^ -^ or X = Xi \/ -—r ■ Let us assume that the parabola in X\- Yi y Yi Fig. 260 represents net areas instead of bending moments, and that the line BH coincides with BC. Then BC is the total net area required, and the vertex C is the origin of the coordinates. Point A is the only other point on the curve for which the coordinates are known. Neglecting the signs because they do not affect the result, the coordinates of the point A are Xi = -^) and Fi = a, where L = the total length of the girder, and a = the total net flange area required. If for F we substitute a" = the ordinate from the origin to the horizontal hne which determines the length of any plate, then the corresponding value_of X will be one-half the theo- L /a" retical length of that plate, ox X = -^\/ — ■ On account of the usual - 2y a excess of the actual net area over the required net area, a" can be found best from a by subtracting the net area of the flange angles, the portion (if any) of the web considered as flange area, and the net area of cover plates between the angles and the cover plate the length of which is de- sired. For the plate nearest the angles, a" is equal to the net area left for cover plates, taken directly from the design of the flange. The a" for the next plate is found from this value by subtracting the net area of the first plate, etc. By doubling both sides of the equation, we have the total theoretical length of cover plate =V?' the result being in feet since L is in feet. 2. Illustrative Problem — Uniformly Distributed Loads. — Find the lengths of the cover plates of the girder designed on page 222 : 2. The total net flange area required is a = 30.5. The resisting moment of the web was neglected, and the net area of the angles was 15.9. The net area of each 14 x | plate is 7.5. The a' for the flrst plate is 14.6 taken from the design (30.5 - 15.9). The a' for the second plate is 7.1 = 14.6 - 7.5. The theoretical lengths are 41.5 = 60 1/30.5 and 28.9 = 60 1/30.5 The actual lengths would be 43' 6", and 31 ' 0" on the bottom flange. The longer plate on the top flange should extend the full length of the girder if exposed to the weather. MVETS IN COVER PLATES 3. Four points must be considered in determining the spacing of the rivets which fasten the cover plates to the flange angles of a plate girder. These rivets must (1) transmit that part of the total flange stress which is carried by the cover plates, (2) provide for the maximum increase in this flange stress, (3) develop the strength of each cover plate between the end of the plate and the end of the next plate, and (4) conform to the general rules for rivet spacing. The first and third points are satisfied when the second is provided for, and often all requirements are fulfilled when the rivets are spaced according to the usual rules for spacing, particularly those given on pages 69:1 (a), (b), (d) and 106:2. Some companies advocate placing the rivets in the cover plates opposite the flange rivets 264 PART III — THE DESIGN OF DETAILS through the web in order to simplify both the drafting and the shop work, but as a rule, the benefits derived do not justify the use of the large num- ber of extra rivets. 1. The rivets in the cover plates must carry that proportion of the increase in flange stress which the net area of the cover plates bears to the total net flange area. The total increase in horizontal flange stress V per linear inch at any point in the girder is j- (page 244: 1) in which V = the maximum vertical shear for a section at the given point, and dr = the mean depth of the girder between rivet lines in the vertical legs of the flange angles. The portion of this increase which is carried by the cover plates is — > in which ai = the net area of aU the cover plates at the given point and a = the total net flange area at the same point includ- ing any portion of the web counted as flange area. The maximum pitch of the rivets in the cover plates at any point is found by dividing r' = the value of one rivet in single shear by this increase, or P ar' dr This formula should be apphed at the theoretical end of each cover plate. The resulting pitches usually exceed 6", so that no further computations need be made. Should the pitches be considerably less than 6", pitches should be calctdated at every point, within the limits of the cover plates, where the pitches of the flange rivets through the web are determined (preceding chapter, page 241). The pitch in the cover plates will always exceed the corresponding pitch of the rivets through the web, but the excess is proportionately less near the center. If the rivets are to be placed opposite those in the web the pitch need not be computed, and if placed opposite alternate rivets in the web only enough pitches need be calculated to deternune where this double pitch is insufficient. 2. Each cover plate should be developed by rivets between the end of the plate and the end of the next plate. A plate which is fully developed by rivets should fail before the rivets when tested to destruction. A cover plate in tension is, therefore, developed when there are enough rivets to resist the maximum stress which the plate will carry. This is found by multiplying the net area of the plate by the unit stress in tension. Some designers claim that the plate should be developed beyond the theoretical end of the plate, but this is unnecessary, as shown by the curve of bend- ing moments in Fig. 260. From the end of the girder to the point 1 the entire flange stress due to bending moment is resisted by the angles and the web. At any point 3 there is an additional bending moment repre- sented by the distance 2-3. This increase is provided for by that part of the net area of the plate represented by the distance D-4, and the whole plate need not be developed until the point 5 is reached. The increase in flange stress is not uniform between these points 1 and 5, but ample rivets wiU be provided if the pitch does not exceed the amoimt determined by the formula of the preceding paragraph. Each plate extends one or more feet beyond the theoretical end, and the rivets in this extra length are spaced not over four diameters (page 69: 1 (d)). This insures the de- velopment at any point of at least as much of the plate as is required. 3. Illustrative Problem — Uniformly Distributed Loads. — Find the spacing of the rivets in the cover plates of the girder designed on page 222: 2. The theoretical lengths of the cover plates were found on page 263: 2 to be 41.5 and 28.9. The maximum shears in thousands of pounds for sections taken at the ends of the cover plates may be found from the maximum end shear of 196.8 (page 248: 1) by the approximate method m + 41.5 Y (page 247:3) to be 140.9 = 196.8 x /60 + 28.9Y 602 and 108.0 = 196.8 X / 60 + 28.9 y dr „„2 'The value of one rivet in single shear is r' = 7.22, and = 65.25. At the end of the first plate ai = 7.5, and a = 23.4 = 15.9 + 7.5, the resisting moment of the web being neglected. The maximum pitch determined by the method of page 264 : 1 is 23.4 X 7.22 X 65.25 7.5 X 140.9 which exceeds 6". The pitch at the end of the second plate is 30.9 X 7.22 X 65.25 15.0 X 108.0 ' CHAPTER XXXVIII COVER PLATES 265 which also exceeds 6". When the first pitch is so large, as in this case 10|", it is often unnecessary to find the pitch at the ends of the other plates. At the ends of these plates 3" spaces would be, used for about 1' 9" = 1| X 14" from the actual ends (page 69: 1 (d)), and 6" spaces would be used for the remainder. 1. Illustrative Problem — Concentrated Loads. — Find the spacing of the rivets in the cover plates of the girder designed on page 225 : 1. From Fig. 262 it is seen that the first two plates end in the first panel where the shear is nearly constant. The smaller pitch will be found in the second plate because the ratio — is less. This pitch should be found first for if it exceeds 6" it will be unnecessary to find the pitch at the end of the longest plate. The maximum shear in thousands of pounds for a section 41 X 35 4 at the end of the second cover plate is 202.0 = 194.7 + — ^ '-> where 194.7 is the maximum shear due to the concentrated loads (page 250 : 3) and the second term is a simplified expression equal to the weight of the girder (410#/ft) multiplied by one-half the length of the cover plate, which gives the shear due to the weight of the girder. The value of one rivet in single shear is r' = 7.22, and dr = 65.25. ai = 15.7 = 8.2 + 7.5, and a = 33.5 = 15.7 + 13.9 + 3.9. The corresponding pitch is 4f = — " ' — ^Tj^TTr^ — 10. / X ^0^.0 Similarly, the pitch at the end of the first cover plate is found to be over „„ 26.0 X 7.22 X 65.25 „, . , , .■ . ^^ ^ 6 = T-— f^ttttt; The maximum shear tor a section at the end 8.2 X 203.6 of the third cover plate is 88.6 = 164.3 - 80.1 + ^-^^ ^ 21.6 ^^^ ^^^ -. ., , . „„ 41.0 X 7.22 X 65.2 5 ^, ., , , ^, corresponding pitch is over 6 = j^^-j^ ^^-x ihe pitch at the beginning of the second panel would be greater than at the beginning of the third cover plate because the shear is only slightly greater, and the ratio — is considerably greater. 3" spacing would be used from the actual end of each plate for a distance of about 1' 9" (see preceding problem), and' 6" throughout the remainder of all the cover plates except that 41" must be used for the short distance from the 3" spacing at the end of the second plate to a point beyond the entire connection of the concen- trated load at the quarter point. CHAPTER XXXIX WEB STIFFENERS Synopsis: Stiffening angles are riveted to the web plate of a girder wherever the web plate is not strong enough to resist the shearing stresses. These stiffening angles may serve incidentally as connection angles. 1. The web plate of a girder is designed to resist all shearing stresses. The actual course of the diagonal stresses is not known, but the girder can be designed to resist the horizontal and vertical components of the shear- ing stresses, because these can be determined. The resistance of the web plate to the horizontal components was considered on page 255 : 2. The resistance to the vertical components only need be discussed in this chapter. 2. Vertical stiffening angles or " stiff eners," usually in pairs, are riveted to the web plate of a girder to assist in providing for the vertical shearing stresses when the web plate alone is not sufficient (page 266 : 3). Stiffen- ing angles are also placed at concentrated loads, serving either to connect these loads directly to the web, or else to transmit to the web any loads which rest upon the flange. Stiffening angles are used at each support to transmit the entire reaction, unless the web plate is connected directly to the angles of a colimm or other member. These stiffening angles may serve as connection angles when the girder is connected to the face of another member, or they may transmit the stress to the bearing when the girder rests upon the support. AH stiffening angles should be accu- rately cut so that they will fit tightly between the outstanding legs of the top and bottom flange angles. 3. The thickness of the web plate must be sufficient to satisfy several requirements. It should never be less than f " in a railway bridge, nor less than ^" in a highway bridge or other structure. Many specifications require that the thickness shall be at least y^ of the clear distance between 266 the flange angles, although this is not so general a requirement as some others. It is desirable that any plate over 7 feet deep shall be at least 1^" thick on account of handling in the shop. The area of cross section of the web plate at any point must be sufficient to resist the maximum shear for a section at that point. It is impractical to use more than one web thickness in any girder on account of the method of construction. Web plates are seldom thicker than 3^" or f " for it is better to xise reinforc- ing plates where the shear exceeds a certain amoimt than to use a heavier plate throughout the whole length of the girder. Unless reinforcing plates are used, the web thickness must be such that the product of the gross area of cross section (full depth times thickness) by the correspond- ing imit shearing stress will equal or exceed the maximum shear on the girder. The gross area is used, and the unit stress is specified for the gross section, because it is not feasible to determine the rivet spacing in the stiff eners before the web thickness is determined, and because the use of net areas would not affect the result appreciably. 4. End stiffening angles which connect the web to a supporting mem- ber need not be designed as a whole, because the stress increments are transmitted almost directly from the web through the angles to the sup- port, and at no point do the angles have to carry a large cumulative stress. The lengths of the legs are chosen to suit the conditions of each case, usuaUy from 3 to 6 inches. The thickness is usually f " for light girders, and j^" or 5" for heavier ones. The stiffening angles over the supports of girders which rest upon other members or upon masonry must be designed CHAPTER XXXIX WEB STIFFENERS 267 to transmit the entire reaction. Since the edge of the web plate is not flush with the backs of the bottom flange angles and can get no direct bearing, the entire maximum shear must be carried from the web plate to the outstanding legs of the flange angles by means of stiffening angles. These angles are sometimes placed at the extreme end of the girder as in (a), Fig. 267 (a), and sometimes so that the outstanding legs are at the center of the bearing plate, as in (6) , Fig. 267 (a) . Angles placed at the extreme end are not so likely to obtain full bearing upon the flange angles, because the latter may be cut short or damaged in cutting. When a girder rests on top of a column, or portion of a column, the outstanding legs of the stiffeners should be placed directly over part of the main column section if practicable. When the reaction is too large to be carried by one pair of stiffeners, two pairs are used, as in (c) or (d), Fig. 267 (a). When the angles Fig. 267 (a). (b) (c) (d) ■ Methods of Placing Stiffeners at the Ends of Girders. are placed at opposite ends of the bearing plate, as in (c), the pair nearer the center of the girder will get more than half the stress on account of the deflection of the girder. It is difficult to determine the propor- tion carried by each pair. Sometimes a beveled bearing plate is designed to give an equal distribution under a full load', but this result is diflJcult to accompUsh in practice. More frequently the larger pair is assumed to take two-thirds, and the end angles one-third. This uncertainty is over- come by placing the angles as in (rf). Sometimes more than two pairs of angles are required, as shown in Fig. 101. The stiffening angles over the support must be designed to transmit the reaction by bearing on the out- standing legs of the flange angles, which in turn transmit the load to the support. The strength of the stiffening angles acting as a compression member must then be investigated. 1. The stiffeners over the support must be designed for bearing. The angles are usually riveted against the vertical legs of the flange angles, and fillers are used between the top and bottom flange angles to fill the space between the stiffening angles and the web, as shown in Fig. 97. In order to place the stiffeners in this position the ends must be cut to clear the curved fillet of the flange angles, as shown in the enlarged sketch Fig. 267 (b). That part of the stiffeners which is cut back in this way cannot be counted in bearing, because the usual shop methods do not insure contact. Even if perfect contact were obtained, the value of the bearing upon the curved surface of the fillet would be questionable. The fillets of 6 x 4 and 6x6 flange angles are J" in radius, and those of 8 X 8 angles are f". Unless the stiffeners are more than ^" thicker than the radius of the fillets, the bearing of the web legs (i.e., the legs riveted to the web) must be ignored, and the portion of the outstanding legs beyond the fillets of the flange angles must carry the whole load. The necessary thickness of the angles is foimd by dividing the maximum reaction by the allowed unit stress in bearing, and again by the combined projections of the outstanding legs of the stiffeners beyond the fillets of the flange angles. If the thickness of the angles exceeds the radius of the fillet by more than ^" (to allow for inaccurate cutting), the bearing Pig. 267 (6). of the remaining portion of the web legs may be counted. The unit stress in bearing may be taken the same as the bear- ing value for pins and shop rivets (24,000#/ sq. in. according to the speci- fications of the American Railway Engineering Association). Some designers use a smaller unit stress and count both legs of the angles, but it is more logical to count only that portion which is sure to bear. The outstanding legs are less likely to buckle when designed in this manner. Some engineers design the stiffeners as compression members without considering bearing, with the result that the outstanding legs are often seriouslj' overstressed. It is better to design the angles for bearing, and then investigate their strength as a compression member. The lengths of the outstanding legs are usually made of the largest commercial sizes which will not project beyond the edges of the flange angles, but circumstances may justify cutting larger angles so that they will be flush with the edges of the flange angles. The web legs are shorter than the outstanding legs, standard angles being used. The thickness should not be less than f ", and if more than f " the angles must be sub-pimched or drilled. 268 PART III — THE DESIGN OF DETAILS 1. The strength in compression of the stiff eners over the support should be investigated. The stress in the angles is cumulative throughout the depth of the web, and the full stress acts only at the bottom. It is, there- fore, unnecessary to consider the full load acting at the top of the stiffening angles, but it is customary to consider the length of the compression mem- ber equal to one-half the depth of the girder. The radius of gyration is chosen for an axis through the center of the web, because the angles are restrained in the other direction by being riveted to the web. Only the area of the angles is considered, the included portion of the web being neglected. The usual unit stress in compression is used, as for example, 16,000-70-- r 2. There must be enough rivets in each pair of stiffening angles over the supports to transmit the whole stress taken by the angles. The rivets which pass through the flange angles should not be counted upon to take any of this vertical stress, because they are fully developed in transmitting the horizontal stress from the web to the flange angles. The rivets are driven in the shop, and the value of one rivet is Fig. 268 (a). hmited by the bearing in the web (unless the double-shear value is less). Rivets which pass through fillers are less effective than those which connect the parts directly, because the rivets are more hkely to bend. The usual specifications provide for this by requiring arbitrarily that the number of rivets be increased 50% when they pass through fillers. Whenever feasible it is well to increase the width of the filler so that some or all of the extra rivets may be used to connect the fillers to the web without passing through the angles, as shown in (a). Fig. 268 (a). When pairs of stiffening angles are close together these fillers may extend under both pairs, as in {b), Fig. 268 (a). These extra rivets should be spaced not more than twice the maximum distance allowed in the angles, which is sometimes specified 5" instead of the usual 6". If the grip of the rivets (i.e., the total thickness of the parts connected) exceeds four times the diameter, the number should be increased 1% for each additional sixteenth of an inch in the grip. (a) 3. Illustrative Problem. — Angles at Edges of Bearing Plate. Design the end stiffening angles of the girder shown on page 222 : 2, arranging them as in Fig. 268 (6). The outstanding legs of the flange angles are 6", so we will use 5 x 3§ stiffeners. The maximum end shear was found on page 248: 1 to be 196,800#, and two-thirds of this will be assmned to be carried by the inner pair of angles. If the angles are not thicker than the I" fillet, the length of bearing will be 9" ^ ing thickness must be 5" 8 2 X 196,800 2 (5 - 1), and the correspond- This is i" more than the 3 X 9 X 24,000 radius of the fillet, but if smaller angles were used they would not exceed the radius by more than ^" which is neghgible, so I" angles will be used. The two angles are separated by the ^" web and two |" flange angles. The haK depth of the girder is 3 ft. From the table on page 331, the safe load of 2 Ls 5 X 3i X f X 3' 0" is 132,000 when the least radius of gyration about an axis perpen- dicular to the web is used. A larger safe load determined by the radius about the other axis could be used, because the angles are restrained, but this value need not be found in this case be- cause 132,000 is equal to the necessary two-thirds of 196,800. The number of |" rivets bearing in the ■^" web plate, required in these stiff en- Fig. 268 (b). ing angles is 15 = 2 X 196,800 and the total number in the angles and 3 X 9190 ,, „,, . „ 2x196,800x1.5 „, ,^ . , , ,, ^ the filler is 22 = g v 9190 — ~" " should be used m the angles * exclusive of the two in the flange angles, and 7 additional rivets should be used in the fillers. The angles at the end of the girder carry only one-half the load of the angles just designed, so they need be only one-half as thick, the f " minimum being suflacient. The number of rivets should be 11 = 22 ^ 2, but four more are used so that the rivets line up with those in the other angles. * Two more than shown in Fig. 268 (6). CHAPTER XXXIX WEB STIFFENERS 269 1. Illustrative Prohlem — Angles at Center of Bearing Plate. — Design the end stiffening angles of the girder designed on page 225: 1. The maxi- mum end shear was found on page 250: 3 to be 207,000#. The effective length of bearing in two 5 x 3J angles is 9 = 2(5 - |), and the corre- sponding thickness would have to be 1" = 207,000 Since no such 9 X 24,000 angles are rolled, and since they would have to be drilled if available, four angles will be used, each |" thick, arranged as Lin Fig. 269. The safe load would be consider- ably greater than that shown in the table on page 331 (see preceding problem), but for two pairs of angles this is 2 x 108,000 so that no further investigation is required. The number of I" rivets in each pair of angles, increased 50% ^. t^u txu ■ -IT* 207,000 X 1.5 on account oi the fillers, is 17 * = — ^ — ^-7^7; — > t, ' 2 X 9190 exclusive of those through the flange angles. These are all placed through the angles, and spaced to line up with the rivets in the spUce plates. Fig. 273. Seven-inch fillers are used ex- tending under both pairs of angles. If wider fillers were used, the total number of rivets would be increased or else the maximum spacing would be exceeded. 2. Intermediate stiffeners are generally used at concentrated loads and at web splices. They are also used in the deeper girders to prevent the web from buckling under its shearing stresses. The more modern specifications require the use of intermediate stiffeners when the thick- ness of the web is less than -^ of the unsupported clear distance between the flange angles. Formerly some form of " buckle formula" (page 293: 3) was used to determine when stiffeners should be used. The sizes of intermediate stiffening angles are not designed, but they are usually fixed * Two more than shown in the figure. Kg. 269. by the standards of the different structural companies. The specifica- tions often require that the length of the outstanding legs should be at least 2" greater than ^V o^ the nominal depth of the girder. The inter- mediate stiffeners are usually made lighter than the end stiffeners, and often the legs are of the next smaller commercial size, excepting perhaps those which serve as connection angles for concentrated loads. The thickness of intermediate stiffening angles in railway bridges is usually I", although this may be increased in the heavier girders. The thickness of the intermediate stiffening angles in other girders is usually either T¥ or 8 . 3. The spacing of intermediate stiffeners should not exceed the maxi- mum allowed by different clauses in the specifications. The stiffeners at concentrated loads are usually fixed in position. In railway bridges, viaducts, and heavy crane runways, the clear distance between stiffeners should never be more than 6 feet, nor more than the clear distance be- tween the flange angles; it should not exceed jjr (12,000 — v), in which t = the thickness, and v = the maximum shear intensity, in pounds per square inch of gross section. This formula provides for closer spacing near the ends of the girder where the shear intensity is greater. In highway bridges and structures other than those mentioned above, the clear distance between stiffeners should not exceed 5 feet, nor the full depth of the web. 4. The number of rivets in intermediate stiffeners is not computed, but the rivets are made to line up with those in the stiffeners at the supports. This simplifies both the drafting and the shopwork, particularly when multiple plate punches are used. The full number is used in the stiffeners at concentrated loads and at splices, but in other stiffeners the alternate rivets may be omitted if the resulting spaces do not exceed the allowed maximum. Care should be taken to see that the number of rivets in stiffeners used as connection angles fully provide for the loads. 5. Intermediate stiffening angles which have no connections to the outstanding legs may be crimped, as explained on page 97: 1. Synopsis: The and column splices. CHAPTER XL SPLICES of typical splices is illustrated by different types of girder 1. Definition. — One member is usually connected to another by- means of connection plates or angles, but a member or part of a member is said to be spliced when the two similar segments are connected end to end in the form of a butt joint. A sphce becomes necessary when the de- sired length of material is not available, or when it is impracticable to ship a whole member in one piece. Whenever possible a splice should be avoided. 2. Design. — A splice should be designed to transmit the full stress in the part spliced. In a tension member or a light compression mem- ber the splice plates or angles should be designed to carry the full stress. This is not feasible in a heavy column or chord member, so part of the stress is transmitted by direct bearing, the ends of the two segments being "milled" or "faced" (page 31: 1) to furnish uniform bearing against each other, as shown in Figs. 124 and 133. The rivets in each half of the spHce plates or angles should fully develop that part of the stress which is carried by the corresponding plates or angles. Thus in a tension mem- ber, the combined net areas of the splice plates or angles should equal or exceed the net area for which the main member is designed, as illus- trated by the problems on page 208: 4, and the rivets which connect the splice plates or angles to each segment should develop the full strength of the main member. In a milled splice of a heavy compression member most of the stress is transmitted by direct bearing, but enough splice plates or angles should be used to hold the segments in the proper posi- tion and to transmit the stresses due to bending. 3. Three t3rpes of splice are selected to illustrate the principles em- bodied in the design of any ordinary splice. These three will be dis- cussed in the following order: a sphce in the web of a plate girder, a sphce in the flange of a plate girder, and a column sphce. WEB SPLICES 4. When Used. — The web plates of all girders over 40 or 50 feet long must be spliced because longer plates are not rolled. The extreme lengths of some of the deeper webs are less than 20 feet so that the webs of the longer girders must be sphced at several points. The number of sphces is determined by the maximmn rolled lengths * of the plates, but for convenience in handUng the plates in the shop no single plate should weigh more than 3000#. A splice should not be located at the point of maximum bending moment, except possibly in comparatively hght girders which would then require only one sphce. It is usually customary to locate each splice under a pair of stiffening angles. Not only is the splice thus stiffened, but the thickness of the fillers is reduced, and there is one less line of rivets to be driven. 5. The design of a web splice depends upon the method by which the girder is designed, because the sphce plates must transmit the web stresses. If the entire flange stress is considered to be resisted by the flange, and the resisting moment of the web plate is neglected (as in Case A, page 221: 2), the sphce is designed for shearing stresses only. If the resisting moment of the web is considered (as in Case B, page 223: 2), the splice must be designed for stresses due both to shear and to bending * See Ketchum's "Structural Engineers' Handbook," McGraw-ffiU Book Co., Inc., New York, or the handbooks of steel manufacturers. 270 CHAPTER XL SPLICES 271 moment. When there are more than two spUces in a girder, the one for which the shear is greatest is designed and the others are made hke it for practical advantages during fabrication. Sphce plates are placed on both sides of the web, and the thickness of each plate should not be less than f " in railway bridges or ^^" in other structures. 1. When the splice is designed for shear only the plates extend the full depth between flange angles, except for a clearance of J" (or less) at each end, being the same length as the fillers (page 96:4). The.net area of the two splice plates in a vertical cross section should be as great as the net area of the web plate, but for all practical purposes it is close enough to compare the gross areas since the proportions are so nearly identical. The width of the splice plates is determined by the spacing of the rows of rivets which often depends upon the size of the superimposed stiffening angles. A space of from j" to J" is usually left between the two sections of the web (page 96:2). At least two rows of rivets are com- monly used in each half, even though one row would satisfy the con- ditions. Usually the rivets in the inner rows are spaced like those in the intermediate stiffening angles (page 269: 4), but those in the outer rows are spaced twice as far apart. After the rivets have been located in this manner their resistance to shear should be investigated. The shear, or the algebraic sum of the vertical external forces on one side of the splice, is positive, while the shear on the other side is of equal magnitude but negative, in order to satisfy the V equation of equilibrium. Since the shearing stresses are transferred from one segment of the web to the other by means of the spUce plates and the rivets, the effect is the same as if the maximum shear V were a single resultant force acting upward at the center of gravity of the group of rivets in one-half the splice, with an equal downward resultant force acting at the center of gravity of the rivets in the other half. A couple is thus formed, the moment of which is the product of a single force V by the perpendicular distance between the two forces. This moment tends to cause rotation of the spUce plates, and the sphce is a double eccentric connection. The rivets in each half of the sphce must not only satisfy the maximum ver- tical shear V, but they must resist one-half of this moment accordmg to the method of eccentric connections, page 237 : 2. Should the strength of the rivets prove to be insufficient, the number in the outer row may be increased by one or more, the number in the inner row may be made the same as the rivets in the end stiffeners if not already the same, the rows may be spread slightly, or the number of rows may be increased. 2. Illustrative Problem — Web Splice for Shear Only. — Design a sphce for the web at the quarter point of the girder shown on page 222 : 2. The maximum shear for a section at the quarter point in thousands of pounds may be found from the maximum end shear by the approximate method (page 247 : 3) to be 110 . 7 = 196 . 8 X (1)^- The length of the splice plates is 60" = 72.5 - 2(6 + i), and the thickness of each plate is found by equating the gross area of two splice plates to the gross area of the web plate thus: 2 x 60i = 72 x t\; this gives a value for t less than the minimum, so f" plates are used. The minimum number of rivets is as shown in Fig. 271, the spacing in the intermediate stiffeners being the same as in the end angles shown in Fig. 268 (b) because the double pitch would exceed the maximum allowed. Since the inner row has approximately twice as many rivets as the outer row, the center of gravity may be taken one-third of the distance from the inner row to the outer row. The distance from this center of gravity to the center of the splice is 3" = 1 + 2, which is half the distance between the centers of gravity of the two groups of rivets. The half moment of the couple is then 332,100#/ in. = 110,700 x 3. The sum of the squares of the horizontal and vertical distances to the rivets is 6670 = 7 X 2^ + 13 x P + 4(91^ + 19^ + 284^) + 2(4f2 +1412 + 23|^). The coordinates of the rivet farthest from the center of rotation are Xm = 1, and ym = 28 J. The horizontal component of the shearing I-* , ^= = — — — \ ~tf -~ \ , ' 1 ' . ' B 1 ■0^1 ^ 1 ^1 m \ \ I ( \ I \ H " Ik \ ~os / 1 ■Uwo (l( ^ \ Mn-^=^ ® \ n .-In ES II M.jXjCV, , ( < Q •NCMCM ^ lng Nut Fig. 278 (o). Fig. 278 (b). with a special head at one end and a hole for a "cotter" at the other (Fig. 279) or with cotters at both ends. The larger bridge pins are turned cylinders with threaded ends of reduced diameter upon which pilot nuts and driving nuts (Fig. 278 (a)) are screwed for use in erection. These pins are driven cold without upsetting, the holes in the members being from ^" to ^" larger than the diameters of the pins. The pins are held in position by recessed nuts called "Lomas nut" or nuts with washers (Fig. 278 (6)) which replace the temporary driving and pilot nuts. Pins over 10" in diameter may have caps instead of nuts, held in place by small rods passed through holes in the pins. 278 2. Pins are designed as cylindrical beams to resist both bending and shear. Usually the size of the pin will be determined by the bending moment, but the strength of the resulting cross section should be in- vestigated for it may be necessary to increase the size of the pin as a result. Each member which bears upon a pin must furnish sufficient bearing area to properly distribute the stress in that nember. This bear- ing area is the product of the diameter of the pin by the thickness of the metal which bears upon the pin (compare page 230 : 3). The bearing area of riveted members may be increased by the use of reinforcing plates, as explained in the next chapter (page 284), but when this is not feasible the minimum diameter of the pin may be determined by the bearing in some member. Thus the minimum diameter of pin used in any eye bar may be found by dividing the total stress in the bar by the thick- ness of the bar and by the unit stress in bearing. Often a minimum of 5" or eight-tenths of the width of the eye bar is specified for bridge work. 3. Application of Forces. — ■ For convenience in finding the bending moment on a pin it is usually assumed that the force due to the stress on a member or part of a member acts upon the pin as if concentrated at the center of bearing, i.e., the center of the surface of contact. This assumption is on the side of safety, and the sUght increase in the size of the pin is relatively unimportant. The bearing may depend not only upon the thickness of the main part of a member, but also upon the thick- ness of any reinforcing plates which may be needed (see above). Since CHAPTER XLI PINS 279 the bearing depends upon the diameter of the pin, the two are interde- pendent and either the thiclcness or the diameter must be first assumed and later verified. In this chapter the plate thickness is assumed to be correct. In the case of a small pin for a clevis or a loop-rod, all forces lie in the same plane, and the bending moment is found as in a simple beam. At a joint in a bridge truss, however, the forces are not con- fined to a single plane, and the position of the point of maximum bending moment is not so apparent. 1. Design for Bending. — As in the design of other beams, the maxi- mum bending moment is equated to the resisting moment. For a beam of circular cross section the resisting moment is 0.098/d', where / is the unit stress in bending and d the diameter (page 200:1). The unit stress. in bending is usually about 50% greater than for other beams, 24,000#/sq. in. being specified by the American Railway Engineering Association. ,In order to facilitate the designing of pins, a table of resisting moments for different values of / and d is shown on page 333. 2. Investigation for Shear. — In determining whether a pin designed for bending has sufficient area to resist the shear, it should be remem- bered that the intensity of the shearing stress is not uniform throughout the cross section, but is greatest at the neutral axis. The maximum shear 4F 167 intensity is four-thirds the average intensity, or r — ^ = -^—r^, where V is the maximum shear, r and d the radius and the diameter, respectively, of the pin (page 202 : 1). This maximum shear intensity must not exceed the allowed unit stress in shear, which is usually the same as for shop rivets and usually one-half the unit stress in bending or bearing. 3. Illustrative Problem. — Co-planar Forces. Design a pin to fasten a 1" square loop-rod between two |" plates, as shown in Fig. 279. The stress in the rod is 16,000#, and the 16 X 8,000 3 T my , which is safely under the 10,000 ^^t: M= Fig. 279. U— ffiooo stress in each plate is one-half this amount. The distance from the center of bearing of the rod to the center of bearing of one plate is f" = Kl + 2), and the maximum bending mo- ment on the pin at the center is 6000#in. = 8000 X f . Using a unit stress in bending of 20,000#/sq. in., the required diameter of the pin may be foimd from the table on page 333 to be IJ". The maximum shear in- tensity is 6000#/sq. in. allowed. 4. Not every pin in a truss need be designed because it is impractical to use so many different sizes. It is preferable to make several pins alike in order to reduce the number of different eye bars to be made and the number of different pin holes to be bored. It is customary to calculate the size of the pins at the shoe (Fig. 290), at the hip, at the top-chord joint next to the hip, and at the bottom-chord joint nearest the center. Except for very long spans, the remaining pins in the bottom chord may be made like the central pin, and the remaining top-chord pins may be made like that in the joint next to the hip. Often the lower pins can be made like the upper ones. 5. The arrangement of the different members on a pin has its effect upon the size required. The arrangement is usually termed the "pack- ing." Sometimes the results of two or more different arrangements must be compared in order that the best one may be selected. The packing on a pin is made symmetrical, and therefore members which are composed of eye bars should have an even number of bars, and riveted chord members and posts should have two or more webs. A single stir- rup or small counter is sometimes placed at the center. The bars of diag- onals are usually placed next to the posts in order to reduce the bending moments. No two eye bars of a single member should be placed in con- tact as it would be impossible to paint between them. Unless a bar of an opposing member is placed between two bars of one member, the latter should be separated on the pin by a collar at least 1" wide. The pin is thus lengthened 2", but the diameter may often be reduced considerably. Unless the bars on a pin are within |" of each other, the space between them should be filled with a washer or collar in order to maintain the proper spacing of the bars in accord with the design. In determining the distances from center to center of bearings used in com- puting the bending moments, an allowance of at least yV" should be made between adjacent bars to allow for paint, for scale, and for variation in thiclcness. A clearance of j" should be left between the bars and the built members, due allowance being made for the heads of rivets in rein- forcing plates or other component parts. It is often necessary to flatten 280 PART III — THE DESIGN OF DETAILS or countersink these rivets. The flanges of channels or angles are often notched to clear the bars, provided the webs are properly reinforced. The pacldng at one pin is dependent upon that at the adjacent pins be- cause the bars should be kept approximately parallel. A bar should not slope more than ^" per foot. If it is necessary to use a greater slope the bars should be bent to furnish better bearing on the pins. 1. Since the forces which act upon a pin in a truss do not lie in the same plane, each force should be resolved into horizontal and vertical components. The position of the point of maximum bending moment is usually not apparent, so it becomes necessary to find the bending mo- ment due to the horizontal components, and that due to the vertical components at each point of concentration. The resultant bending moment at each point will be the square root of the sum of the squares of the horizontal and the vertical bending moments at that point. Care must be taken not to combine the horizontal bending moment at one point with the vertical bending moment at another. The maximum bending moment on a pin will often occur at a point where there is no vertical bending moment. The use of the table of squares on page 332, or the diagram on page 312, is recommended in finding the resultants. 2. The forces which act upon a pin must be selected with great care. The values on the stress diagram show the maximum stresses for which each complete member is designed, but these maximum stresses do not occur in all members of a truss simultaneously. The maximum chord stresses are found when the truss is fully loaded, but the maximum web- member stresses are found when the truss is only partially loaded. Care should be taken to use either the maximum chord stresses and the cor- responding stresses in the web members, or conversely, the maximum stresses in the web members and the corresponding chord stresses. As a rule, the first condition will govern the size of the pin at the shoe and at the hip, the second condition will govern the size of the remaining top-chord pins, but either condition may govern the size of the bottom- chord pins. Counters are not stressed when the main diagonals are stressed, but they must be considered in packing the pin because they will cause increased lever arms which will affect the bending moments. The stresses which act upon a pin at any one time must be in equilibrium. To insure this, only the maximum chord stresses or the maximum stresses in the diagonals should be taken from the stress diagram, and the other stresses should be computed to correspond. It is well not to use the stress in a post as given on the diagram because the stress on the pin may differ on account of the method of supporting the floor beam. In a bottom-chord joint governed by maximum chord stresses, these chord stresses are taken from the diagram and divided proportionately among the component parts of the members. A sketch is drawn showing all of these horizontal forces and the horizontal components of the forces in the component parts of the diagonals. The proper magnitudes of the latter forces may be determined from the H equation of equiUbrium. The vertical components may be determined from these horizontal com- ponents, and the corresponding forces in the component parts of the post may be found from the V equation. Similarly, in a top-chord joint the maximum stress in the diagonal is taken from the diagram, and the corresponding stresses in the other members are computed. In case the adjacent top-chord members are in the same straight line, only the differ- ence in their stresses need be foimd, since the members bear on opposite sides of the pin and cause no bending. 3. Computation. — Since the forces on a pin are symmetrically placed, it is necessary to determine the bending moments on only one-half of the pin, care being taken to count only one-half of a force at the center. The bending moment at one point may be best found from the bending mo- ment at the preceding point by adding algebraically the product of the shear for a section between the points by the distance between the points (page 189 :1). It is convenient to arrange the computation in tabular form as shown in the problems which follow. When finding the result- ant bending moment from the two components it should be remembered that the horizontal bending moment is constant between the horizontal force nearest the center and the corresponding force on the opposite side of the center. This should be obvious because the shear is zero. The actual position of the bars on a pin may vary shghtly from the spacing used in the design, and it is therefore consistant to use lever arms to the nearest \", and_ shears and bending moments to the nearest thousand pounds or pound-inches. 4. Illustrative Problem. — Bottom-chard Pin. Design the pin at the joint LZ of the truss shown in Fig. 281 (a). Let us assume that the size of CHAPTER XLI PINS 281 the pin will be determined when the chord stresses are maximum, and that the arrangement of the bars can be selected without regard to the other joints of the truss. Let us assume also that the reinforcing plates . Z-Js"\li33* 2-^ reinforcing l-Z 4 bars s'x ij^" 1-3 4 h^rs 8"x lis" 1-4 7paneis e 28-e'=l99'-e" Fig. 281 (a). on the post have been determined from an assumed size of pin, and that the resulting size is the same as assumed. The results of the two ar- rangements shown in the figures will be compared. In both arrange- ments the bars of the main diagonal are placed next to the post, and the counters between the diagonals and the chord bars. Inclined bars may be differentiated from the horizontal bars by section lines as shown. The smaller chord bar is placed at the end, and the other chord bars are alternated in the first arrangement, or placed as shown in the second arrangement with a 1" collar between the two larger bars. The stress in thousands of pounds in each of the four 8 x IfJ bars is 217 = 868 h- 4, and in each of the 8 x Iff bars is 247 = 986 ^ 4. In order to satisfy the H equation, the horizontal component in the main diagonal must be 60 = 2 X 247 - 2 X 217. The corresponding vertical component is 34 71 = 60 X 7^5-T, and the force in one-half the post must be the same, zo.o These forces are shown in the small sketches, together with the lever arms which are found as follows: 1 tir \{m + lit) + tV 2f" = §(1H + li) + ItV + 2 X tV \\" = \{\\ + 2 + rg-) + 4 l^the rivets being countersunk) 3" = li| + l+A First Arrangement 217* 1 »,•.-- ■►-i„' £17*— 2 ■ 3 -=-j •nK 60* — i 247 ■24? Fig. 281 (b) Horizontal Components Point of Momenta Vertical Components Shear Lever Arm Product Bending Moment Shear Lever Arm Product Bending Moment lOOOif In, 1000# in. 1000# in. 1000# In. 1000# in. 1000# in. -217 + 30 -187 + 60 n n n 2| -407 +56 -351 +165 -407 -351 -702 -537 -537 1 2 3 4 5 -71 H -89 -89 The maximum bending moment for this arrangeme nt is 702 at point 3, since this is obviously greater than the resultant V'537^ + 89^ at point 5. It is unnecessary to carry the solution further until the results of the second arrangement are obtained. 282 THE DESIGN OF DETAILS Second Arrangemeni S'i li- 2l7-<^-, 1 2 217-^^ 3~ 1 Fig. 282( a) Horizontal Components Point of Moments Vertical Components Shear Lever Ann Product Bending Moment Shear Lever Arm Product Bending Moment 1000/ In. 1000#m. 1000# in. 1000# In. 1000#in. 1000#in. -217 + 30 +277 + 60 1| 3 1- 2* -407 + 90 +519 +165 -407 -317 +202 +367 +367 1 2 3 4 5 -71 H -89 -89 The maximum bending moment for this arrangement is 407 at point 1, since this is more than the resultant Vse?^ + 89^ at point 5. This ar- rangement gives a smaller bendiog moment and is therefore adopted. Using a unit stress in bending of 24,000#/sq. in., we find from the table on page 333 that a 5f" pin is required for a bending moment of 407,0(X)# 16 X 277 000 in. The maximum intensity of shear is 14,200 = g ^ .^3^2 " This exceeds the allowed value 12,000, so the diameter must be increased to 6i"=|/ 16 X 277,000 . This is less than the diameter required to satisfy 3 TT 12,000 the bending moment of the first arrangement and hence is used. In neither arrangement does the presence of the count.er increase the size of the pin. If the maximum bending moment was fotmd at point 4 or 5, it might be de- sirable to place the covmters between the channels of the post, cutting the flanges if necessary, in order to reduce the lever arm between points 3 and 4. 1. Illustrative Problem. — Pin at Hip. Design the pin at the joint C/l of the truss shown in Fig. 281 (a). Let us assume that the reinforcing plates on the members which meet at this point have been designed from an assumed diameter of pin which proves to '^^"\'J_^f""^ r T ^°^ , ^center of bearing UI-2 be correct, and that the arrangement on the pin is as shown in Fig. 282 (6). The outer reinforcing plate of the top chord and the inner plate of the end post are extended to hold the pin in position against shock and to protect the joint from the weather. The centers of bearing of these two mem ers are therefore not quite opposite. The diagonal is placed between the end post and the hip vertical with ample clearance for countersunk rivets in each so the rivets need not be chipped. As a rule only the full load which causes maximum stresses in the end post, the top chord, and the hip vertical need be considered. From the panel lengths and depths the lengths of the members may be calculated, and the components of the maximum stresses in these members may be found by proportion, thus: Fig. 282 (6). Horizontal Components 28.5 41.4 28.5 28.8 LI C/1 = Vertical Components EP = 606 = 881 X L/1-2 = 866 = 877 X EP = 638 = 881 X C/1-2 = 120 = 877 X LI [71 = 244 30.0 41.4 4.0 28.8 CHAPTER XLI PINS 283 Since each of these members bears upon the pin at two points of con- centration the above vahies should be divided by 2, and recorded on the sketch as shown. The corresponding components in each bar of the diagonal L2 f/1 may be found from the H and V equations of equilibrium. From the bending moments tabulated on this page the maximum bend ing moment is found to be 1 154 /sq. in. this requires an 8 V7202 + 902= at point 3. At 24,000# and the maximum shear intensity is 11,600/ = than the allowed 12,000. pin. The maximum shear is 437 = V4332 + 60^, 16 X 437,000 SttS^ which is less 303- -433 130 eo- Fig. 283. 319 ■137 ■122 Horizontal Components Point of Moments Vertical Components Shear Lever Arm Product Bending Moment Shear Lever Arm Product Bending Moment lOOOif In. lOOOi? in. lOOOi? in. lOOOif In. 1000# in. lOOO; in. -433 -130 n -379 -341 -379 -720 -720 1 3 +60 -259 -122 7. +53 -680 -275 +53 -627 -902 CHAPTER XLII REINFORCING PLATES Synopsis: The webs of riveted members of pin-connected trusses must be reinforced at the ends in order that they may properly transmit the stresses to the pins. The method of designing reinforcing plates is here shown. 1. When Used. — Reinforcing plates are used to strengthen the weaker parts of members in order to fully develop the strength of the remaining parts. Usually such reinforcement occurs at the ends of the members. Reinforcing plates are used on girder webs (page 266: 3), at the splices of certain ofHce-building columns (page 276:4), at the joints of pin-connected trusses, and at similar places. The method of designing the reinforcing plates of pin-connected riveted members is illustrated in this chapter- These plates are often termed "pin plates" and their design typifies the design of all reinforcing plates. 2. Type of Member. — A compression member in the chord of a simple pin-connected truss is usually composed of two channels with one cover plate (Fig. 122), or of two or more web plates with angles and one or more top cover plates (Fig. 128). A compression web member is often composed of two channels. Each end of these members bears against a cyhndrical pin which is located at or near the center lines of the webs. Since no other part of the member bears against the pin the whole stress must reach the pin through the webs, which must be reinforced to fur- nish the necessary bearing. Most of the tension members of a pin-con- nected truss are composed of eye bars and these need no reinforcement. A riveted tension member is often used in the two end panels of the bot- tom chord to provide for a reversal of stress. 3. Method of Design. — All reinforcing plates must be designed to furnish the necessary bearing area for the pin. This part of the design consists in finding the thickness of the plates and the number of rivets 284 required to fasten them to the webs. The width of the plates is usually made as large as the available space will accommodate, and the length depends upon the number and the spacing of the rivets. The size of the pin must either be predetermined or assumed (see page 278: 2). The rein- forcing plates for a pin-connected tension member composed of channels or plates and angles must not only provide the proper bearing, but also the necessary net section. To prevent failure at the pin, the net section through the pin hole must exceed the net area for which the main mem- ber is designed. The amount of this excess is usually specified as 25%. The location of the rivets in the reinforcing plates of a tension member must receive special consideration. Provision must be made to properly reinforce a member which is weakened by having part of the flanges cut away for clearance. 4. Design for Bearing. — One-haK the total stress in a member with two webs is imparted to the pin through each web and its reinforcing plates. When there are more than two webs, the proportion will be approximately equal to the relative cross-sectional areas included be- tween lines drawn midway between the webs. The bearing area of each web and its reinforcing plates is found by dividing the corresponding stress (one-half or other portion of the total stress) by the unit stress allowed for bearing. The combined thickness of the web and its rein- forcing plates is found by dividing this area by the diameter of the pin (compare bearing on rivets, page 230:3). The web thickness is ded acted from this combined thickness, leaving the required thickness of the rein- CHAPTER XLII REINFORCING PLATES 285 forcing plates, which should be increased to the nearest commercial size (a multiple of xV")- The total thickness may be subdivided into as many- parts as are best suited to particular conditions. It is usually desirable to place part of the plates on each side of the web to make the rivets more •effective. No single plate should exceed f " on account of punching. 1. The nxunber of rivets in the reinforcing plates should fully develop the plates. If the plates are all on one side of the web, the rivets act in single shear, but if part of the plates are on each side, the rivets act in double shear. The limiting value of each rivet must be selected with care because often the bearing value in a channel web is less than the single-shear value, or the bearing value in a heavy web is more than the double-shear value. For the value of countersunk or flattened rivets, see page 231 : 2. The bearing value in webs which are npt multiples of ^" may be fotmd by multiplying the decimal thickness by the rivet diameter and by the imit stress in bearing. This should be necessary only when the number of rivets is large; it is usually close enough to roughly inter- polate a value from the tables, or to use a value given for the nearest iV"j preference being given to the lower of two. values. The developed stress in the plates is the product of the total thickness of the reinforcing plates by the diameter of the pin and by the imit stress in bearing. This value should be used to find the total number of rivets when the plates are all on one side of the web or when the plates are about equally divided on opposite sides. The rivets should distribute the stress proportionately among the component parts of the member as far as practicable. Thus enough rivets should connect the reinforcing plates to the bottom angle to develop the stress in the angle, and rivets in the top angle should develop the angle and part of the cover plate.* See Fig. 128. When more than one plate is used on the same side of the web, or when the plates on opposite sides differ considerably in thickness, the plates may be made of different lengths because it is unnecessary that they contain the same number of rivets. The stress in each plate is propor- tional to its thickness and equal to the product of the thickness by the diameter of the pin and by the imit stress in bearing. The plates on opposite sides of the web may be considered separately. There must * For illustrative problems see Johnson-Bryan-Turneaure's "Modern Framed Structures," Part III, John Wiley and Sons, Inc., New York. be enough rivets through the outer plate to develop that plate, there must be sufficient rivets through the two outer plates to develop both plates, and so on, the number in the plate next to the web being deter- mined by the stress in all the plates on that side of the web. The rivets do not all have the same limiting value, however. Those which pass through plates on only one side of the web may be counted in single shear, imless the bearing value in a channel web is less. One-half the value of the rivets which pass through plates on both sides of the web may be counted in developing the plates on each side. This will be one-half * the bearing value unless the thickness of the web, or the web and the angles through which part of the rivets may pass, is great enough to develap double shear, in which case the half value equals the single-shear value. The thicker plate should be placed next to the web. Each plate is cut at right angles to the axis of the member. The length of each plate should be as great as the width, or at least three-quarters of the width, in order to fully develop the rivets near the edges. In bridges it is cus- tomary to let a thin outer plate extend around the pin, as in Fig. 127, in order to cover the joint between members and to hold the members in position during erection. Rivets in tension members, and ia com- pression members where the pin is not at the extreme end, should meet the added requirements of page 286:2. 2. Illustrative Problem. — Compression Member. Design the rein- forcing plates at the end of a compression member composed of two 12" \±i 30# and one cover plate 14 x f . The maximum stress in the whole member is 342,000#. Use a 4" pin and f " rivets, with a unit stress in bearing of 24,000#/sq. in. 171,000# = 342,000 -^ 2 = stress in each web and its reinforcement 171,000 1.78" = = combined thickness of web and plates 1 5 " 4 X 24,000 1 . 27" = 1 . 78 - . 51 = thickness of reinforcing plates 126,000# = li^ X 4 X 24,000 = developed stress in plates. Part of the plates should be placed on each side of the web, preferably, the inner ones extending the full depth of the channel, the outer ones * More strictly, the bearing value is divided in proportion to the relative thickness of the plates on the opposite sides of the web, but this is usually not necessary, and it is not consistent with the usual method of designing riveted joints. 286 THE DESIGN OF DETAILS being limited to 10" to clear the flanges. If the plates are about equally divided, as shown in Fig. 286 (a), the rivets are limited by the bearing in the i" channel web, and the total number required is 14 = 126,000 + 9000. If a Jg" plate is used on the inside and two I" plates on the outside, as shown in Fig. 286 (6), the rivet value counted on each side of the web is 4500 = 9000 -=- 2 where plates are on both sides, and 5300 The number required in the outer f" plate The nimiber required in the ^^" plate is 12 2-12 tsi 50 2 Pls.lO;'xfxl'-3",] 2 Pls.12 i Hx 1^3/ Fig. 286 (a). where on only one side, . I X 4 X 24,000 ^^ ^ " 4500 9 V 4 V 24 000 = ^^ tpt:^^ — '- These 12 rivets provide also for an equal stress in 4500 the two I" plates so that the additional number in single shear is 4 (3 9 ■) 4 y 24 000 = — — \,„^^ '- Since 12 rivets cannot be arranged to advantage 5o00 14 are used in the ■^" plate. By this arrangement it is unnecessary to use 16 = 12 + 4 rivets in the other |" plate because by extending the inner plate all rivets pass through plates on both sides, and 14 in bearing are sufficient for the total stress, as foimd above for two plates. 1. Design for Tension. — The rein- forcing plates of pin-connected tension members are designed for bearing, as on page 284:4, but they must also satisfy another requirement. The pin tends to tear out toward the end of the member, and unlike a compression member the whole bearing is on the outer half of the pin. As far as bearing is concerned the rein- forcing plates could be placed entirely beyond the pin, where they would act as in a compression member, but the strength of the main member at the pin would not be sufficient to transmit the stress. This ; P/.M/f 2-12"^^^ 30* i2 Pla.lO"xf'i< l'-3" O O do 0f^2PI^-l2"''A"''l-3" 2 Pls.W'xi xl'-2" O O Oii.O\ 7 m Fig. 286 (6). part of the member must be reinforced, and logically the same reinforc- ing plates are extended for this purpose. The plates should be made thick enough for tension as well as for bearing. According to a common clause in the specifications, the total net area of cross section through the pin hole of a tension member must exceed by at least 25% the net' area for which the main rriember is designed. The latter net area is usually found through that row of rivets in the reinforcing plate which is nearest the center of the member (page 208: 2). Furthermore, the mem- ber must extend beyond the pin far enough so that the net area of cross section between the pin and the end of the member, parallel to the axis, should not be less than the net area of the main member. In determin- ing the net area at the pin, the diameter of the hole is taken equal to the nominal diameter of the pin, although it is from ^V" to ^V" greater. Due allowance should be made for any reduction in area on account of flanges of channels or angles being cut to clear eye bars or other members. 2. The rivets in a tension member should satisfy other requirements in addition to those on page 285: 1. When the thickness of the reinforcing plates determined by the net area exceeds that required for bearing, the rivets should fully develop the strength of the plates in tension. Other- wise the total number of rivets is found as on page 285 : 1. The rivets which connect the reinforcing plates to the end of a compression member are naturally all placed on the side of the pin nearer the center of the mem- ber. This is. often necessarily true because the member cannot extend beyond the pin without interfering with an opposing member. In a tension member the rivets must be divided. Enough rivets must be placed in the plates between the pin and the center of the member to transmit the tensile stress in the plates which is required to develop the necessary net section at the pin, as explained in the preceding paragraph. But no more rivets should be so placed than can be developed by the actual tensile strength of the plates at the pin. Between these minimum and maximum values the number of rivets on the side of the pin toward the center of the member is chosen, and the balance of the total num- ber is placed between the pin and the end of the member. When rivets are placed on both sides of the pin in a compression member the distribu- tion should be determined in a similar manner. CHAPTER XLII REINFORCING PLATES 287 1. Illustrative Problem. — Tension Member. Design the reinforcing plates at the end of a hanger composed of two 8" LU 13f#, from which a load of 110,000# is suspended by means of a 3" pin, as shown in Fig. 287. Use a single 6" plate on each channel, f" rivets, and a bearing value of 20,000#/sq. in. 55,000# = 110,000 -^ 2 = stress in each web and its reinforcement 55,000 o o o o o o o o o o o ) ^1 0.92" 3 X 20,000 f" = 0.61" = 0.92-0.31 4.38 sq. in. = (4.04-2 x : combined thickness of web and plates = thickness of reinforcing plate required for bearing I X . 31)1 . 25 = net area re- quired at pin = 0.42' Fig. 287. 21,000# 30,000# = [4.38 - (4.04 - 3 X 0.31)] + (6 - 3) = thickness of reinforcing plate required for tension 37,500# = f X 3 X 20,000 = developed stress in bearing (6 - 3) X tV X 16,000 = developed stress in tension (6 - 3) X I X 16,000 = strength of plate in tension 9 = 37,500 -^ 4420 = total number of rivets 5 = 21,000 s- 4420 = minimum number of rivets above the pin 6+ = 30,000 -V- 4420 = maximum " " " " " " The thickness required for bearing exceeds that required for tension and a 6 X I plate is used. In order to develop this plate in bearing a total of 9 rivets must be used. In order to develop the required stress in ten- sion at least 5 rivets must be placed above the pin (toward the center), but not more than 6 can be so placed without over stressing the plate in tension. This maximum number falls between 6 and 7, so the smaller number is used. At least 5 and not over 6 rivets should be placed above the pin, the remainder being placed below. Since the rivets are placed in two rows, 6 are placed above and 4 below, an extra rivet being used in order to keep the member symmetrical. The length of the member below the bottom of the pin should be at least 3f" = — — „„„!.„.■ — so that the net area will equal that of the main member. If the thickness of the plate required for tension had been greater than that required for bearing, the total number of rivets and the maximum and minimum numbers above the pin would be identical, and all the rivets would be placed above the pin. In this case, a few extra rivets would be used below the pin to hold the plate in place. CHAPTER XLIII BEARING PLATES AND COLUMN BASES Synopsis: Wherever structural steel is supported by masoiu'y, some provision must be made to distribute the load over the proper area. The design of simple bases is dis- cussed in this chapter. 1. T3rpe. — Loads from steel beams, trusses, or columns which rest upon masonry must be distributed over a sufficient area so that the al- lowed bearing value of the masonry will not be exceeded. Simple rec- tangular plates of steel or cast iron are used under the ends of beams, roof trusses, and some of the lighter girders. Cast-iron pedestals are used under the heavier girders. Plate and angle shoes with expansion rollers support bridge trusses. Cast-iron bases or steel slabs, in con- junction with grillage beams or reinforced concrete piers, are used under ofiice building columns, while other colmnns are provided with bases built of plates and angles. 2. Size of Bearing Plate. — Standard bearing plates are used at the ends of wall-bearing I-beams and channels under usual conditions for the sake of simpHcity. The sizes of these plates are given in the tables of I-beams and channels, pages 298 to 302. Special plates should be designed for beams with relatively large reactions, for roof trusses, and for light plate girders or latticed girders. The required area of the plate is equal to the maximmn reaction divided by the bearing value of the masonry. The allowed pressure per square inch varies with the differ- ent specifications and with the kinds of masonry. Usual values for con- crete are from 400 to 600 pounds per square inch, the latter value being specified by the American Railway Engineering Association. For brick, the values are about one-half as large. The shape of the plate which will best meet the requirements depends upon several factors. The best distribution on the masonry is effected when the two dimensions of 288 the plate are approximately equal, but this is not always feasible. The thickness of the plate depends upon the distance the plate projects be- yond the edges of the beam, and this should be kept as small as practical. Usually the plate does not extend beyond the end of the beam, and the shorter dimension of the plate determines the amount the beam pro- jects upon the supporting wall. If this is too large, the length of the beam is unnecessarily long, and if too short, dangerous cracks may develop in the wall. The bearing plates of light trusses and girders are usually anchored to the masonry, and the plate must be long enough to provide the necessary edge distances beyond the bolt holes when the anchor bolts are placed far enough from the edges of the angles to permit the turning of the nuts. It may seem wise at times to make the area of the plate somewhat greater than that required, but the thickness may be made correspondingly less because the developed unit pressurie on the masonry is reduced. 3. The thickness of a bearing plate should be such that the bearing value of the masonry may be developed at every point. The thickness is deter- mined by the maximum projection of the plate beyond the edge of the superimposed metal. This portion of the plate is treated as a cantilever beam with a uniformly distributed pres- sure on the under side equal to the developed bearing pressure on the masonry. The maximum bending moment on this portion of the plate occurs at the edge of the superimposed metal. An expression for the thickness may be derived, as follows (see Fig. 288) : 4 il Fig. 288. CHAPTER XLIII BEARING PLATES AND COLUMN BASES 289 Let b = the developed unit stress in bearing on the masonry, i.e., the total load divided by the area at the plate, in pounds per square inch, / = the allowed unit stress in bending on the extreme fibers of the plate, in pounds per square inch, p = the projection of the plate beyond the superimposed metal, in inches, c = the width of the portion of the plate considered, in inches, t = the required thickness of the plate, in inches. Since the pressure and the resisting moment are both proportional to c, its value does not affect the result. he = the pressure per linear inch, uniformly distributed, p6c X ^ = the maximum bending moment in pound-inches (page 187: 1), \fcP = the resisting moment in pound-inches (page 199:3). By equating the resisting moment to the bending moment and solving, we have t=v 36 .^ * Fig. 289 (a). The diagram on page 316 gives values for / to correspond to different values of p and 6 when / = 16,000#/sq. in. For cast-iron plates / is usually about 3000#/sq. in. When the load is appUed to the plate by means of angles, as in the case of a roof truss or light girder, the combined thickness of the angle and the plate must be sufficient to prevent bending at the edge of the vertical leg of the angle. This combined thickness t' may be found from the above formula by tak- ing p equal to the distance from the edge of the plate to the vertical leg of the angle, as shown by p'. Fig. 289 (a). The fillet of the angle is usually neglected. If the thickness of the angle is fixed, the thickness of the plate should be the greater of two values, one the thick- ness t required at the edge of the angle, and the other the difference between the combined thickness t' and the thickness of the angle. 1. Illustrative Problem. — Bearmg Plate. Design a bearing plate for a roof truss which rests upon a brick wall, as in Fig. 114 {d). The bottom chord angles are 5 x 3§ X f , and they are separated by a f " heel plate. The maximum reaction is 33,000#, and the allowed unit stress on the brick wall is 300#/sq. in. The required area, 110 sq. in. = 33,000 H- 300, would be satisfied by a plate 10" x 11". If f" anchor bolts are used, the holes should be punched about 2" from the edges of the angles to allow for turning the nuts. With an edge distance of about li", the length of the plate must be about l'2i" = f + 2(3i + 2 + 1|). Probably it would be better to increase the area accordingly, rather than to reduce the 10" bearing of the truss. The effect of this in- crease would be to reduce the developed bearing value 6 to 228#/sq. in. = 33,000 -=- (10 X 14.5). The projection beyond the angles is p = 3^" = 1(141 - f) - 3i, and the projection beyond the vertical legs is V' = 6fff" = i(14| - I) - f . From the diagram, the corresponding thickness of the plate alone is < = f ", and the combined thickness of the plate and the angles is <' = If". Since the chord angles are only |" thick the plate must be at least 1" = If - |, and since this exceeds the first value the size of plate adopted is 10 x 1 X 1'2|". 2. Expansion. — At one end of a span, two plates may be used in- stead of one to allow free expansion or contraction under temperature changes. A "masonry plate" rests upon the masonry, and a "sole plate" is riveted to the girder or truss, the surfaces of contact being planed. Slotted holes for the anchor bolts are provided in the upper plate. The combined thickness will be somewhat greater than the thickness of a single plate, because each plate is designed to resist its proportion of the total bending moment. Thus if the two plates are of equal thickness, each would be about 0.7 = Vf of the thickness required for a single plate. 3. Pedestals and Shoes. — Bridge girders are commonly supported by cast-iron or cast-steel pedestals, as shown in Fig. 289 (6). These pedestals are fastened to the masonry by anchor bolts, and the girders are bolted to them. Slotted holes are provided in one end of girders up to about 60 feet in length to allow for expansion, the top of the pedestals and the bottoms of the bearing plates on the girders being wMmym I wMvy/mm/m Fig. 289 (6). Cast Pedestal for Bridge Girder. 290 PART III — THE DESIGN OF DETAILS I ■I planed. Segmental rollers are placed under the pedestal at one end of girders over 60 feet long. Special hinged shoes or rockers are used at the ends of some of the longer girders to pre- vent unequal distribu- tion of the load upon the masonry as the girders deflect. Similar hinged shoes are used at the ends of bridge trusses, and roller nests are placed imder the shoes at one end, as shown in Fig. 290. For the design of shoes and rollers consult books on Bridge Designing, par- ticularly those Usted below.* 1. Column bases are of two main types which for convenience will be designated according to the principal structures in which they are used, viz.: mill buildings and office buildings. In the former the loads are transmitted largely by rivets, whUe in the latter by direct bearing. In mill buildings the column loads are comparatively hght, and the bases must be anchored to the masonry piers to prevent lateral displacement by accident, and to resist the overturning effect of the wind. Cross bracing can be used only at the ends of a mill building, and the wind pressure on the sides must be resisted largely by the columns acting as beams fixed at the lower ends. The effect of this, combined with the effect of eccentric loading on the column, is to cause vmequal distribution of the load on the masonry, and the area of the base must be so propor- tioned that at no point will the allowed bearing pressure be exceeded. * Waddell's "Bridge Designing/' Vols. I and II, John Wiley and Sons, Inc., New York, and Skinner's "Details of Bridge Construction," Vol. Ill, McGraw-Hill Book Co., Inc., New York. Fig. 290. Typical Bridge-truss Shoe with Jlollers. The pressiu-e near One edge of the base may be very small, in fact the upward forces due to wind may exceed the downward forces due to the direct load so that it is necessary to anchor the base to the masonry. In order to make the anchor bolts effective, the base must be securely riveted to the column, and for this reason it is usually built of plates and angles. For hght columns, such as shown in Fig. 137, these rivets are designed to transmit the whole column loads. Columns which support crane run- ways or other moving loads, and columns in which the load exceeds 40,000 poimds are milled so that a portion of the loads are transmitted by direct bearing. A typical crane-girder colmnn base is shown in Fig. 135. In office buildings there are intermediate columns which are rigidly con- nected at each floor, and the principal wind stresses which reach the basement columns are vertical. The uplift on the windward columns is usually less than the vertical dead loads so that anchors are not re- quired except in tall narrow buildings or towers. From the nature of the building there is shght chance of displacement of the column bases by accident. The bending stresses are small compared to the total loads, and the pressure on the bases is distributed more uniformly than in mill buildings. Cast-iron or cast-steel bases,* such as shown in Fig. 175 (a), are commonly used in office-building construction. The bottoms of the columns and the tops of the cast bases are both planed so that practically the entire column loads are transmitted by direct bearing without rivets. Light angles are usually riveted to the end of the colmnn, as in AB\, Fig. 133. and these angles are bolted to the cast bases to prevent displace- ment during erection. The cast bases are grouted on top of reinforced concrete piers or grillage beams, as explained in the next chapter (see Fig. 291), and then they are imbedded in concrete. Column bases are usually standardized by structural companies so that it is unnecessary to design each base. Furthermore, the design depends so much upon the wind stresses, that it seems unwise to attempt further explanation here.f * For dimensions of American Bridge Company's standard cast bases see Ketchum's "Structural Engineers' Handbook," McGraw-Hill Book Company, Inc., New York. t For the design of mill-building column bases, see Kirkham's "Structural Engineer- ing," McGraw-Hill Book Co., Inc., New York; for the comparison of different methods of designing anchor bolts, see articles by R. Fleming and E. Godfrey in the Engineering News, April 30, 1914, and May 7, 1914; for the design of cast bases for office buildings, see Blurt's "Steel Construction," American Technical Society, Chicago. CHAPTER XLIV GRILLAGE BEAMS Synopsis: When it is impractical to extend foundations for heavily loaded columns to bed rook, the footings may be spread over the proper area of soil within a compara- tively small depth by means of grillage beams imbedded in concrete. 1. When Used. — In providing suitable foundations for office build- ings it is often impractical, if not impossible, to extend the footings to bed rock. When the footing of an average office-building column bears directly on the soil a large bearing area is required because of the com- paratively small pressure allowed on the soil. If an ordinary masonry pier were designed to satisfactorily distribute the load from the small area at the column base to the large area required on the soil, the pier would be so deep that the cost of the excavation and of the masonry would be prohibitive. The same results may be obtained in much less depth by the use of either steel grillage beams or reinforced concrete slabs. The design of reinforced concrete footings would be out of place in this book. Grillage beams are still in common use since reinforced concrete footings have not yet met with universal favor for various reasons, among them being the uncertain effects of electrolysis and corrosion upon the comparatively small steel areas in the reinforcing rods. 2. Arrangement. — Grillage beams are arranged in tiers, as shown in Fig. 291, the beams in one tier being placed at right angles to those in the next tier. The bottom tier rests upon a concrete mat about 12 inches thick. Concrete is placed between the beams of each tier, and ultimately the whole footing, including the cast-iron base, is imbedded in concrete at least 4 inches thick to hold the parts in position and to protect the steel against fire and corrosion. The concrete between the beams acts as inverted arches to complete the bearing area of the tier. The maximum distance in the clear between the beams should be such that the full pres- sure on the concrete is transmitted to the beams. Unless this clear dis- tance between the edges of the flanges exceeds about one and one-half times the width of each flange it is unnecessary to investigate the strength Fig. 291. Grillage Footing (Concrete Filling Not Shown). of the arch.* The spacing of the beams is usually determined by the number to be placed within a given distance. The distance between * For the method of investigation, see page 201:3. 291 292 PART III — THE DESIGN OF DETAILS flanges should be at least 2f or 3 inches to permit the placing and the tamping of the concrete. Since it is difficult to insure uniform bearing between the beams of successive tiers when they are placed in contact, a space of about J inch is usually left for grouting. Similarly, if the unit load is not too great, grout is used between the upper beams and the cast base. This facilitates placing the base truly horizontal . and at the proper elevation. The allowed pressure on the grout is about 35 tons per square foot, or 500 pounds per square inch. If the column load divided by the area at the bottom of the cast base exceeds this amount, the base must be placed in direct contact with the beams, the bottom of the base being planed. This requires extreme accrracy in setting the beams to furnish uniform bearing for the base at the proper elevation. 1. Tie Rods. — Grillage beams are held at uniform distances apart by means of rods and separators. When it is not feasible to use beams with webs thick enough to withstand the tendency to buckle, cast-iron separators or stiffening angles may be used to stiffen the webs. Usually, however, pieces of gas pipe are placed between the webs. Three-fourths inch rods extend through all the beams of each tier, passing through the separators (Fig. 291). Enough rods should be used to resist the thrust of the concrete arches between the beams (preceding paragraph). It is seldom necessary to calculate this thrust. Usually rods are placed about 6 inches from the ends of the beams, and the remaining spaces are sub- divided so that the rods are not more than 5 or 6 feet apart. In the smaller beams the rods are placed centrally in the webs; in beams 12 inches or more in depth the rods are used in pairs, the vertical spacing being the same as for cast-iron separators (page 316). 2. The loads for which grillage beams are designed 'are determined by one of several methods.* A grillage foundation will settle as the loads are apphed; this cannot be prevented. It is important that the settle- ment be imiform throughout the structure to prevent cracks in the walls and floors. Under Uke soil conditions this means that the unit pressure must be the same for all footings. Some engineers design each footing for the total dead and Hve load, while others design the footing for the critical column and proportion the others from this one according to the * For comparison, see Jaooby and Davis' "Foundations of Bridges and Buildings," McGraw-Hill Book Co., Inc., New York. ratios that the dead loads bear to the dead load of the critical column, maintaining that the settlement will be proportional to the dead loads because they act at a maximum constantly. The critical column is the one which has the largest ratio of dead load to live load. Other engi- neers consider one-half (or other fraction) of the Uve load in conjunction with the dead load in determining the ratios. The Uve load on the base- ment column is not the sum of the maximum hve loads from each floor, but a certain percentage of this sum depending upon the height of the building.f 3. The allowed bearing pressure should be determined by tests made upon the actual material at the site. Records of tests made for nearby buildings are sometimes available. Average values for different charac- ters of soil as specified in dififerent building codes are tabulated in both of the books just referred to. These values are usually expressed in tons per square foot. They may be converted into pounds per square inch by multiplying by 13 . 89 = 2000 -=- 144, or approximately by mul- tiplying by 14. 4. The extreme dimensions of the concrete mat are determined by the area found by dividing the total load by the allowed pressure on the soil. The most desirable shape of mat is a square, but it is not always possible to use a square of sufficient proportions without extending beyond the building lines or interfering with other foundations or pits. Usually a rectangular mat will prove satisfactory. In case it is impracticable to center the grillage under the column, the eccentricity may be overcome by means of a cantilever girder J which extends under an adjacent column. The extreme dimensions of the bottont tier of beams may be made less than the corresponding dimensions of the concrete mat, because the mat itself may be considered to partially distribute the load. The re- sisting moment of the concrete depends upon the tensile strength in the extreme fiber; this is variable and very small. A projection of 6 inches on each side of a mat 12 inches thick is considered safe, but an increase in this amount would be inadvisable. It may be found that when a t See copies of the building laws of different cities, or Ketchum's "Structural En- gineers' Handbook," McGraw-Hill Book Co., Inc., New York. t See Kidder's "Architects' and Builders' Pocket Book," John Wiley and Sons, Inc., New York. CHAPTER XLIV GRILLAGE BEAMS 293 projection of one-half the depth of the mat is used, the tensile stress in the extreme fiber is three-fourths of the bearing power of the soil.* 1. Method of Design. — Grillage beams must be designed to resist bending, buckling, and shearing. The depth of a beam is usually deter- mined by bending, and the web thickness either by bending or buckling. The upper beams are first designed for bending and then their strength is investigated regarding buckling and shear. It may not be necessary to consider either buckling or shear in the design of the lower tiers. Many different arrangements of grillage beams may be designed to satisfy given conditions, because the beams of the different tiers are interdependent. The best arrangement may be selected from the results of several differ- ent designs, with due consideration of the comparative costs. Usually two or three tiers will suffice. The extreme width of the top tier of beams is equal to the corresponding dimension of the column base. The length of the beams in one tier is equal to the extreme width of the next tier be- low. If only two tiers are used, the length of the top beams is equal to the extreme width of the bottom tier. If it is impractical to make the top beams so long, an intermediate tier is used, the length of which is equal to the width of the bottom tier. The width of this intermediate tier, equal to the length of the top tier, is made such that the top beams have equal strength in resisting bending and buckling. 2. Design for Bending. — The number of beams to be used in any tier is unknown. For this reason it is convenient to compute the total bending moment on all the beams in the tier, and from this bending mo- ment find the combined section modulus. The proper numbers of beams of different sizes may then be found which will furnish the required sec- tion modulus, and the best combination may be selected. The total downward load on each tier of beams is equal to the column load W. It is uniformly distributed throughout the central portion of all the beams for a distance L' equal to the extreme width of the superimposed tier of beams, if any, or to the width of the column base. The beams are sup- ported by upward forces of the same total magnitude (yV) but these forces are uniformly distributed throughout the entire length of the beams L. The weight of the beams may be neglected. The maximum bending * As in the design of bearing plates (page 288: 3) t = p l/y, whence / = Jb if « = 2p. moment will occur at the center. An expression for the maximum bend- ing moment for all the beams in the tier may be found by the method of page 187 : 1 . The downward forces at the left of the center may be replaced W . L' by a single resultant force of -^ acting at a distance of — from the center. w Similarly, the resultant of the upward forces is -^ but it acts at a distance L . . W L W L' of -T- from the center. The bending moment is -^r X i ^ X —r, or 4 . 2 4 2 4 ^ (L - L') = Mst or f (Z - I') = ma The combined section modulus of all the beams in the tier may be found by dividing this bending moment by the allowed unit stress in bending. The section modulus should be equaled or exceeded by the product of the number of beams and the section modulus of a single beam. 3. Investigation for Buckling. — The portions of the beam webs di- rectly below the superimposed load act as columns and they should be of sufficient thickness to prevent buckling. The usual column formulas (page 211:2) in terms of I and r are inconvenient, but they may be con- verted into equivalent formulas in terms of d and t, where d is the depth of the beam and t the web thickness. The effective length I may be safely taken as 0.825d which is slightly greater than the average tangent distance between the curved fillets connecting the flanges to the web. The formula for unit stress is independent of the area of cross section of the column so we may assume a portion of beam x inches in length. The area of cross section of the column is then tx and the least moment of inertia xf is rr^, whence the least radius of gyration r \/lW 12te V\2 Substituting these values for I and r in the column formula 16,000 - 70 - we have 16,000 70 x0.825d VT2 t or t Note that the bending moment is a function of the projection of the beam beyond the superimposed load. The bending moment is equivalent to the bending moment at the center of a simple beam under the same total load, uniformly distributed, for a span equal to this projection {L-L'). 294 PART III — THE DESIGN OF DETAILS 16,000 - 200 - = the allowed unit stress per square inch of web section under direct load. Compare page 201 : 2. This web section is the product of the number of beams in a tier by the thickness of the web and by the distance (in inches) over which the super- imposed load is distributed. By some companies this distance is in- creased by one-quarter or one-half the depth of the beam, part of the web beyond the load being considered effective. 1. Investigation for Shear. — The maximum shear on a grillage beam will occur at the outer edge of the superimposed load. Its magnitude may be found by multiplying the distance (in inches) which the beam projects at each end beyond the superimposed load by the upward force per linear inch of beam. This upward force is found by dividing the total column load by the number of beams in the tier and by the length of each beam. The maximum intensity of shear per square inch is found by dividing the above magnitude by the area of cross section of the portion of the web between the flanges (page 202: 1). This intensity of shear should not exceed the unit stress in shear allowed by the specifica- tions, as for example 10,000#/sq. in. 2. Illustrative Problem. — Design a grillage footing for a column load of 400,000#, using the following unit stresses Sr/sq. ft. = 42#/sq. in. = allowed bearing value on soil 500//sq. in. = " " " " grout 16,000#/sq. in. = unit stress in bending 10,000#/sq. in. = " " " shear 16,000 200-#/sq.in. = " buckling. Assuming that a square footing can be used, each side of the 12" con- crete mat should be 98" = A/ — jo — > ^^^ allowing a 6" projection be- yond the beams, the length of the bottom beams is 86" = 98 — 2x6. Each side of a square cast-iron base should be 28 /400,0C "^ 'V 500 000 . if grout is to be used. Many companies make their bases in multiples of 3" to minimize the number of different patterns. We will use a 30" square base. First Arrangement — Two Tiers If two tiers of beams are used as in Fig. 291, the length of each is 86". The load on the upper tier will be distributed over 30", the width of the 400,000 column base. The total section modulus is 175 = 8 (86 - 30) ^ 16,000. We can use either 4 - 15" Is 42#(s = 236) or 4 - 12" Is 40#(s = 179). The clear distances between flanges are 2.7" = (30-4 X 54) -4- 3, and 3.0" = (30 - 4 x 5^) 4- 3, respectively. Smaller beams need not be tried because more than four would be required and the space between flanges would be too small. The 12" Is 40# are chosen because they are lighter, and the webs are less liable to buckle. The direct stress which tends to buckle the webs is 7200#/sq. in. = ^ — —r^ 4 X oU X U.4d which is safely imder the allowed imit stress of 10,800#/sq. in. = 16,000 200 X 12 The maximum shear intensity is 7700#/sq. in. 0.46 400,000 X i (86 - 30) which is less than the 10,000 allowed. The 4x86(12-2x11)0.46 beams selected are therefore satisfactory. The total section modulus for the beams in the lower tier is the same as for those in the upper tier, since both I and V are the same. The conditions are fulfilled by any one of the following combinations: Number of Beams Size Section Modulus Total Weight per foot Clear Distance between Flanges 5 7 8 10 13 12" I 31i# 10" I 30# 10" I 25# 9" I 21# 8" I 18# 180 188 195 189 185 158 210 200 210 234 15.3" = (86 -5 X5.0) ^4 8.7" = (86 -7 x4.8) *6 6.9" = (86 -8 X4.7) ^7 4.7" = (86 -10 x4.4) -^9 2.8".= (86 -13 X4.0) -:-12 The 5-12" Is 31^" are the lightest and they involve the smallest number of pieces to be handled, but they are too far apart. The 7-10" Is 30# are also too far apart, and they weigh more than the 8-10" Is 25#. The latter best meet the requirements and they are strong enough to resist both buckling and shear because g^^M^^< ig^ooo - —^ and CHAPTER XLIV GRILLAGE BEAMS 295 400,000 X I (86-30) 8 X 86(10-2 X 1)0.31 arrangement is 2580 < 10,000. The total weight of the beams for this = (4 X 40 + 200)86 ^ 12. Second Arrangement — Three Tiers It is obvious that the upper-tier beams will be smaller than those in the first arrangement because they are shorter. In order to make the beams of equal strength in resisting bending and buckling, let us first design them to resist buckling and then determine their proper length. The safe loads of different sizes of beams are as follows: Number of Beams Size Safe Load Determined by Resistance to Buckling 4 4 4 10" I 25# 9" I 25# 8" I 20J# 355,000# = (l6,000 - ^°^^^^°) 4 x 30 x 0.31 570,000# = (l6,000 - ^^^) 4 X 30 X 0.41 499,000#= (l6,000 - ^^^) 4 x 30x 0.36 The safe load of the 10" Is 25# is less than 400,000# so they cannot be used. 4-10" Is 30# would be sufficient but these would weigh more than the 4-9" Is 25# so they need not be investigated. 5-8" Is 18# would be sufficient but they would weigh more than 4-8" Is 20J#. The latter are the lightest beams which will satisfy the conditions. The distance between flanges is 4.5" = (30 -4x4.1) -^ 3. The safe length of these beams in bending may be found by equating an expression for vib to mr 400,000 thus: 8 (Z - 30) = 4 X 15.2 X 16,000, whence I = 49.5" or say 49". These beams are also strong enough to resist the shear, because 400,000 X f (49 - 30) 4x49(8-2x1)0.36 < 10,000, hence 4-8" Is 20i# are selected. The total section modulus for the middle tier is the same as in the bottom tier of the first arrangement, because the I and the I' are the same. The beams may be selected from those shown under the first arrangement, but the same ones cannot be used because they would be too close together. Either 5-12" Is 31i# or 7-10" Is 30# could be used, the former being lighter. The distance between flanges is 6" = (49 - 5 x 5.0) -r- 4. These 12" beams are strong enough to resist both buckling and sheai because 400,000 < 16,000 200 X 12 5 X 30 X 0.35 The total section and 400,000 X J (86 -: 30) 0.35 modulus for the 5x86(12 beams in -2x11)0.35 116 = 400,000 8 (86 - 49) -^ 16,000. The < 10,000. the bottom tier is following beams give the re- quired section modulus: Number of Beams Size Section Modulus Total Weight per foot Clear Distance between Flanges 7 9 11 9" I 21# 8" I 18# 7" I 15# 132 128 114 147 162 165 9.3" = (86 -7 x4.4) -i-6 6.2" = (86 -9 X4.0) -i-8 3.9" = (86 - 11 X 3.7) -H 10 Either the 8" or the 7" beams are satisfactory, but the 9" beams would be too far apart. The 9-8" Is 18# are chosen because they are fighter. It is usually unnecessary to investigate the strength of the bottom beams for buckling or for shear, because of the relatively large nmnber. The total weight of the beams for this arrangement is 2630# = (4 x 201 X 49 + 5 X 31§ X 86 + 9 X 18 X 86) H- 12. This is only slightly more than the weight of the beams for the first arrangement but there are four more beams to handle, and the depth of the excavation and the amount of concrete is more. This can be shown roughly by comparing the ex- treme depth of steel allowing 1" between tiers for grouting, thus: 23" =12 + 1 + 10 for the first arrangement and 30" = 8 + 1+12 + 1+8 for the second. In general two tiers are preferred to one, and the first arrangement would be used, as shown in Fig. 291. TABLES AND DIAGRAMS For Description, see pages 334-338. 298 WEIGHTS AND DIMENSIONS OF CARNEGIE I-BEAMS AND AMERICAN BRIDGE COMPANY CONNECTION ANGLES. 1 IF THICKNESS OF WEB OR WIDTH OF FLANGE IS MOJ^E THAN ^ ABOVE AN EVEN SIXTEENTH. THE NEXT HIGHER SIXTEENTH IS GIVEN IN THE TABCE BELOW. r=. THE MAXIMUM SIZE OF RIVET OR BOLT USED IN THE FLAMGE P= THE SIZE OF SEARING PLATE. THE WIDTH OF PLATE IS THE LENGTH OF BEARIHG. USE 4"rIVETS in the CONNECTION ANGLES THE WEIGHTS OF CONNECTION ANGLES INCLUDE THE HEADS OF SHOP RIVETS. 1 - 1 y L wS~ Oi u ( k (TO END OF FILLE 1 \ 1 T) r = GRIP IT SIZE WEIGHT FLANGE WEB 9 k r t fa P CONNECTION ANGLES SIZE WEIGHT FLANGE WEB S /{ r t c b P CONNECTION ANGLES 27 90 * 9 .52 9 16 5 3i 1 ^ 10 24 It to 12 55 51 .82 1 1 3 If- f 11 16 4 2h 1 " ff \ 27 1 IC— n 1 24 115 8 .75 t 44 IJ 1 li 10 2f F U 3 50 54 .70 hr fo 3i ^ -7 110 7}| .69 11 fo 21 45 51 .58 9 16 1 Sfs i) «^- i V 105 71 .63 f 1 2f6 40 54 .46 4 5 10 24 K rr^l 100 n .75 f 4 1| 1 i 1^ 2f ¥ 35 54 .44 16 24 14 f A f6 34 95 7f„ .69 t T 16 21 Li 314 5 .35 f i 31 2Lali4i,l 18}- WT.=n 90 n .63 f 1 2f6 \ 2U4i4x3xl-8j" WT. = 46 28 * 6 .38 1 34 14 4 ^6 f« 21 85 7^0 .57 D 16 1 2f6 10 40 54 .75 4 34 1 4 4 ii, 2f 00 80 7 .50 i fc 24 \ \ "■ Fi •- E M 35 4{^ .60 f 1 2ife 74 * 9 .48 i 5 2 1 16 -a. ic 24 30 4il .46 4 fi- le 24 21 60i* H .43 f. 44 If 1 9 IS i 2fo 25 4^ .31 10 i 2i^ 20 100 7fo .88 i 4 14 1 ■ft i 2^ r 32i* 54 .25 i 3 14 4 f 10 21 95 n .81 \l 4 2fe 9 35 4t .73 4 -24 1 4 £ J. 10 2f 00 =tF-^ ,J5^ r^" \ \ ZLBlxliiil-'s}" WT.=39 ^ 1 4* j-.^ 90 n .74 i 15- 2* 30 41 .57 IG 1 2^6 ^1 85 ^k .66 16 1 2ife 35 4ii .41 if i 3i\ ' «^j 1 80 7 • 60 i f 2ii, 21 41 .20 ^ fo 31 2L«6i.lif jiBj- WT.= 13 h M 75 64 .65 ^ 34 14 1 * 1 2i^ § D 8 254 41. .54 y 16 3i i f fa 5 10 24 o «*» 00 70 6?„ .58 M 4 2fe 23 4^ .45 10 A 24 65 Ci .50 i 16 2^ M f 304 44 .36 1 i 2fr 18 90 7i .81 t 4 If i ^ 4 2fo 18 4 .37 * i'o 31 85 7fo .78 4 10 21 174* 5 .22 4 34 1 1 f 16 2i 80 7i .04 # f 2f6 7 30 sl .46 4 3} i 1 ■1 5. 16 34 75 7 .56 16 1 2,^, 174 3f .35 6 i 2& 70 6i .72 i 3i li 4 11 16 10 2f 15 3!1 .25 i ^ 34 65 OS .04 1 1 3f„ 6 17i .48 4 2 f 1 f 5 le 24 "o 60 64 .56 * f 2f6 14i Sh .35 1 i 2^ 55 6 .46 i 16 24 SF" 12i 31 .33 i il 3ft 48 * 7i ■ 38 1 4 1* 1 4 i 3i°6 15ri8'.'20"l T f- i 6 144 Siir .50 4 If 4 4 10- 5. 10 34 1 s d& 1 m { 15 75 6fe .88 1 Si H 4 * 4 2^6 134 3^ .36 f i 2^ 91 & 6 iltr^ 70 6S .78 if 10 n i h 1 — ^ 94 3 .31 i 16 3ft »i.^^-«t 1 65 6i .69 11 16 # 21 2 Uijja^-L iii WT. =ja 4 104 2J .41 vf 14 i 4 S i 2f„ ^2 lEei6ifi3 WT.= 41 „ » „>' 2LB6mfx3WT.=7f fOR 6,6,7 lL6i6i}i2 WT.=si „_ ,r„ 2I.a6ili|x2WT.=5f F0H3,1 60 6 .59 f « 2fc 94 oia '-16 .34 f i 3f, 55 54 .66 11 To- 3 li 4 4 f 3f6 1-1 M 1-1 84 24 .26 4 3 16 2ft 50 &M .56 ts f 3^ 74 21^ .19 _3_ a 2ft 45 5^ .46 4 5 10 24 3 74 3^ .36 « Ifo 4 4 i i 21 42 5i .41 7 16 i 2i^ 64 3n .26 i il, 2ft 37 i* 6f .33 « 34 If i f6 i 2^ 54 2^ .17 1 4 2|i *i >u PPLE MEN1 rARY BEA M ■"" "— 299 WEIGHTS AND DIMENSIONS OF STANDARD I-BEAMS* AND LACKAWANNA CONNECTION ANGLES }\ P /(■(TO END or FILLET) IF THICKNESS OF WEB OR WIDTH OF FLANGE IS MORE THAN n ABOVE AN EVEN SIXTEENTH, THE NEXT HIGHER SIXTEENTH IS GIVEN IN THE TABLE BELOW. r°THE MAXIMUM SIZE OF RIVET OR BOLT USED IN THE FLANGE. p= THE SIZE OF BEARING PLATE. THE WIDTH OF PLATE IS THE LENGTH OF BEARING. USE TWO CONNECTION ANGLES WHERE POSSIBLE. f'RIVETS IN ANGLES. THE WEIGHTS OF CONNECTION ANGLES INCLUDE THE HEADS OF SHOP RIVETS. SIZE WEIGHTFLANGE WEB CONNECTION ANGLES SIZE WEISHTFLANGE 3 ia CONNECTION ANGLES 24 20 18 105 n ,63 100 7f ,75 95 69 90 ,68 85 'l6 ,57 80 .50 100 '10 95 7i .81 90 7i .74 85 7^ Mfi ,66 80 ,60 75 .65 70 61S .58 65 &i 50 70 Gi ,72 65 6^ ,64 60 6i- ,56 55 .46 51 2 10 5i I CONST. ) JDIMENS.I ( SYSTEM) H 5i 3 16 5rc 2 10 55 83 50 5 + .70 12 45 58 40 5i ,46 35 .44 at (STANDARDlV^U Hi „1 } CONN. 5. r,. ■'^ ( ANGLES f "o" 2L84ilx t xlV WT=32 35 40 5^ 75 1| Si. 10 35 60 30 4tj ,46 2fr 25 31 5i 2^ < CONST, 1 'j DIMENS.V ( SYSTEM ). 3^ 5m H 85 ,73 80 4i 57 35 41 21 41 29 35^ ,54 (STANDARD) i CONN. >■ ( ANGLES ) 33 .45 30 i 3fo 2Lb1 X 4i i xl'ai' WT = 27 4i 36 18 ,27 91 30 8^ 46 171 8f ,35 H 15 ,25 1-5 10 2il •^ 18 2 IB 2! 2i 2i o IC 2i 2^ 3| li 2i 2| 4| Mo lL6x 6xf hTJ WT=11 2L88X 4 I f TLli WT = 17 ^10 3tc 2i 5? 3 10 ' 10 2f 3i 5^ -» 10 3 10 4 10 3i^ 2}2i( CONST ( CONST, ) ,1 Jdimens.I in ( SYSTEM )|,L|H 3f o i ^10 ITS' n 5w 9-L 2i 3i ■*io 3^ 34 3i 4^ 3i 3 10 ILOxOifiS WT= 7 SLsOili t z5 WT^U 4f 34 15 100 OlO 1,18 17i ,48 95 rU 010 1.09 li 90 ,99 3f 5f 14 f ,85 3i 3i 5i Sf 121- 33 41 85 61 ,89 ^10 80 610 81 5 i> To 75 61c ■^10 5t 70 78 65 6i .69 H oA As 60 .59 31- 5i 3 10 55 .66 5iir 2 To 3 10 3l 14 f 50 13 i QIC 2l 3i 86 j-i 9f .31 4| 10 41 1- ■ilO o A ^ 10 9i oia. ■^ 10 .34 50 5il 56 45 5ig .46 5li! 2:gr 2i *io J32,l^ TL6r 61 t;i0'10' WT=14 2L8ei4.i t lO'lO' WT=22 .36 li 4i 2 10 '^ 10 * 7i 7i oil ■» 10 19 STANDARD 1L6x0.t|x21 WT=4)„, .., . 2Ls6x4xj. x2J WT=6( ' ILOsOxfxl} Wf =3i„. .■..- 2La6It^J il} WT=4t " 411 16 86 2i H 26 Ifo 42 5l .41 4l6 2ft 51 3f 17 41- 2 10 2 16 ^ 18 3| 2^ H^BASED UPON THE STANDARDS OF THE CAMBRIA, LACKAWANNA, ^PJIOENIX ANB JONES AND CAMBRIA CONNECTION ANGLES AND Z' PHCENIX CONNECTIONS ANGLES ARE SIMILAR TO THOSE ON THE OPPOSITE PAGE. J-AUGJULUN STEEL COMPANIES. + SPECIAL 4:CAMBRIA 8'1's WEIGH 25^ ,22|,20^ .AND 18. 300 WEIGH1 rs AND DIMENSIONS OF CARNEGIE CHANNELS AND AMERICAN BRIDGE COMPANT CONNECTION ANGLES IF THICKNESS OF WEB OR WIDTH OF FLANGE IS MORE THAN^ABOVE AN EVEN SIXTEENTH .IKE NEXT HIGHER SIXTEENTH IS GIVEN IN THE TABLE BELOW. r = THE MAXIMUM SIZE OF RIVET OR BOLT USED IN THE FLANGE. P =THES1ZE OF BEARING PLATE. THE WIDTH OF PLATE IS THE LENGTH OFBEAAING. USE TWO CONNECTION ANGLES "WHERE POSSIBLE. fVlVETS IN ANGLES. THE WEJGHTS OF CONNECTION ANGLES INCLUDE THE HEADS OF SHOP RIVETS. in z < z o 5 w z z 8 1 " — ' 4 H M r hi 1£ ■S T =?. " -Q »-^ ►- »- t t = =- 3 ESS Lii. ?s .-9 h::=*l 1 HH ny -u iS3 ^- 3l /^ij^ 'i-;-ii- t"! »( CO <« ' « M f=asi 03 m « M 1 -Q M HS H f '1 ¥ '^ M M M M X M M H H ■^ 5 £ =a J y -^s rH N -H IN ex. „?;l X X X ST ^o-jxi^ei „0-,TX*XBT „0;T:xf x8 „0-,Is:| xg ,,8,0x1 X 8 „9,0xf xg „t-,0 X t X ^ -Q MS =13 HS (N HS « -IS « -IS en -IS -.IS CM -IS -1=. -IS IM -IS -.|e. «|=0 o|« C5 HS (N IN -IS (M .OIOO IN UJ|« n|-l T-l « 1-i ~o TT 10 6 tot •"> *8 OT •JO 8 fgJofg "b e-l" a|s sts «.]« ^1=. „|0i ,^i« «!■. «l« -IS -l~ -IS C^IU sIS -IS HS «|co H- «l* ol» —IS "IS sis ^» «|oo ■=IS SIS -IS -,:« «|" "IS Sis isjao „|=. H" "IS o|«> ^i« H" «H. -IS -IS ,^1^ OIIOO "IS h|* -IS "IS -M o .Hlo. HS »l» "IS .-1^ - •M lo|« ais "IS -IS -|» -.|« «1« -IS m|=o HS 05|«l nloo n|«. «|«. n|« nl" "IS "IS "IS -1« ■o J ^ nH „i^ t>|eo ^l« MM «i-*i «|* 05|-« »»l* H-* "|-» Ml-H .=!« o|« "1- «=:« Ho. H|0. ^10, Ol|» -IS N§ ^ -i JC v.-J.- m|oo - T-l ,-|» t-|oo t-l« H» t-|« t-l« «M «l-» «N «i* laloo ^« .o|» * CO "IS CO "IS CO -IS CO S|S "Is CO -IS CO IN Ml* IM ,=l« sis IN sis -Is (N (N -Is -IS IN -,l* IN -IS (N ■nlS en Hs C<1 - < S xu ISS « O > H X *=' 2 f* J S 5 « lu o K L. b. h- 2 ,j O X O < < Ul .J o Sum! o P 1 1 s s o 5 Ul u a SI X S X H >- * p CO H CO Ul u U. Ill II --fOT HS SIS S!? als «w >*» «(s ^ •rfS "i? •=« i« //0/Tx:f xgx H^ ^^ ^OX «> ?8 «H ^^ //O/X^fxrg •fe^ss-fg «H Sis »J3 «!S m;s grog ^ rt« •H^ ^ ^ «(S gxfxg sp t «(S ■Eiio-fe «is -HS "(5 0© !*■ * »ia •JS »is ^ dS -W ^OD^ >=K cP «K «(S ^te ^?^? » i » » p "5 ^ = ,3 " ■J-.- J J J .3 rt 0« rt M. 9X^X9 •* H2 «K ■« -<= T-^ iH tH ^ SXOf »*> -nB =!|S ■=(S -« «e EtS »fS 4S "« MS •+» ^ r+« ^ Sfcs ■H3 «(S -t" ■^ * BASED UPON THE STANDARDS OF THE CAMBBIA, LACKAWANNA. PHOENIX, AND JONES AND LA.UGHUN STEEL COMPANIES. CAMBRIA CONWBCTION ANGLES AND PHOENJX CONNECTION ANSLES ARE SIMILAR TO THOSE ON THE OPPOSITE PAGE. 302 WEIGHTS AND DIMENSIONS OF BETHLEHEM I-BEAMS AND GIRDER BEAMS 1 Hto end of fillet) C=i WEB+n IF THICKNESS OF WEB OR WJDTH OF FLANGE IS MORE THAN^ABOVE AN EVEN SIXTEENTH. THE NEXT HIGHER SIXTEENTH IS GIVEN IH THE TABLE BELOW. r =■ THE MAXIMUM SIZE OF RIVET OR BOLT USED IN THE FLANGE. P= THE SIZE OF BEARING PLATE, THE WIDTH OF PLATE IS THE LENGTH OF BEARING. USEiRlVETS IN THE CONNECTION ANGLES. THE WEIGHTS OF CONNECTION ANGLES INCLUDE THE HEADS OF SHOP RIVETS. 303 WEIGHTS, AREAS AND GAGES OF ANGLES STANDARD GAGES SPECIAL (SEE NOTE BELOW) BDOPTED 1910 BY ASSOCIATION OF AMERION STEEL. MANUFACTUR^as EQUAL LEGS SIZE 8x8 6x6 4x4 U2X02 3x3 2x2 THICK- NESS WEIGHT PER FT. 1 6G.9 M.O 61.0 18.1 t6.0 Vt.O 38.9 35.8 32.7 !g.6 26.1 37.t 3S.3 33.1 31.0 28.7 26.5 21.2 21.9 19.6 17.2 11.9 18.5 17.1 15.7 11.3 12.8 11.3 9.8 8.2 13.6 12.1 11.1 9.8 8.6 7.2 9.1 8.3 7.2 6.1 ■1.9 6.8 5.9 5.0 4.1 3.1 1.7 3.9 3.2 2.1 AREA 10.73 15.87 16.00 11.12 1.3.23 12.31 11.11 10.53 9.01 8.68 7.76 11.00 10.37 9.73 9.09 8.11 7.78 7.11 6.13 6.75 6.06 1.30 6.11 6.03 1.61 1.18 3.75 3.31 3.98 3.62 3.2s 2.87 2.18 2,75 2.13 2.11 1.78 1.11 2.00 1.73 1.17 1.19 0.90 1.36 1.15 0.91 0.71 UNEQUAL LEGS SIZE 6x4 6x3| 5x32- 5x3 4x3 3ix3 3^x2i 3x2i 2ix2 THICK- NESS ^ ^ II "13" li. ^ . 10 WEIGHT PER FT. AREA 37.2 25.1 J3.6 21.8 20.0 18.1 16.2 11.3 12.3 25.7 21.0 22.1 20.0 18.9 17.1 16.3 13..5 19.8 18.3 1C.8 15.2 13.0 12.0 10.1 J7.I 15.T 11.3 12.8 11.3 9.8 8.2 13.6 ,12.1 11.1 0.8 ll.l 10.2 9.1 7.9 0.6 9.1 8.3 7.2 6.1 1.9 7.6 0.0 5.6 1.6 5.3 1.5 3.3 2.8 7.98 7.17 6.91 0.10 5.83 6.31 4.75 1.18 3.61 6.50 6.06 6.5B 5.03 4.50 3.97 3.12 6.81 5.37 1.92 -1.17 1.00 3.53 3.05 2.50 6.03 1.01 1.18 3.75 3.31 2.86 2.10 3.98 3.62 3.25 2.87 2.18 2.09 3.31 3.00 2.00 2.30 1.93 2.13 2.11 1.78 1.11 2.21 1.92 1.02 1.31 1.55 1.31 1.06 0.81 ^ *NOT ROLLED BY ALL THE LEADING STEEL COMPANIES ■!■ ROLLED ONLY BY ONE OR TWO COMPANIES LEG a 24 2* 2i RIVET li 4i 3i 2i 2i' If If If li li H" 2i' li < < ? fc «»■ i o o o u u U o U) Ui lij in z 5 ■1 g i S a It 0! g op 9x X •«■•»-*« -J.- AREAS OF RIVET HOLES THICK- NESS 01 METAL DIAMETER OF HOLE (diameter or rivet +-|') 1.25 1.21 1.17 1.13 1.09 1.05 1.02 .98 .91 .00 .86 .82 .78 .71 .70 .60 .03 .59 .55 .61 .17 .13 .39 ■ .35 .31 .27 .23 .20 .16 .12 1.50 1.15 1.11 •1.36 1.31 1.2T 1.22 I.IT 1.13 1.03 1.03 .98 .91 .89 .81 .80 .75 .70 ,66 .61 1.76 1.70 l.Cl 1.59 1.63 1.47 1.12 1.37 1.31 1.26 1.20 1.15 1.09 1.01 'i 2.25 rt.18 2.11 2.01 1.97 1.90 1.83 1.70 1.09 1.02 1.55 1.18 1.11 1.31 1.2T 1.20 1.13 1.05 .98 .91 .81 [70 .63 .50 .49 .42 .3.) EQUAL LEGS SIZE 5x5* ■I- 4x4 * ■I- * ■I- I + 34X04!]! ■i- + 3 X 3' ■I- 't ■I- ^4X^4-^ + •I- 2^x21, 2^21; 2x2 THICK- WEIGHT ,pp. NESS PER FT. ""■=•" * 27.2 25.1 23.6 21.8 20.0 18.1 16.2 11.3 12.3 10.3 21.2 19.9 6.6 18,3 17.1 16.0 11.8 5.8 3.6 11.7 13.6 12.5 11.4 10.2 9.1 1.9 0.6 5.1 3.1 11.5 10.1 3.7 2.6 '8.6 7.6 6.0 6.6 .1.5 3.1 2.3 7.7 .2.1 6.8 6.1 5.3 4.6 3.6 6.0 6.3 9.00 8.60 ■7.98 7.10 6.94 6.10 6.86 6.31 4.75 1.18 3.61 3.03 0.23 6.81 1.01 6.36 5.03 4.09 4.31 1.09 1.07 4.31 1.00 3.07 3.31 3.O1I 2.05 2.30 1.93 1.56 0.99 3.36 3.00 1.09 0.73 2.50 2.21 1.92 1.02 1.31 1.00 0.07 1.2) 0.61 2.00 1.T8 1.55 1.31 1.06 0.81 0.5-5 1.75 1.50 0.48 UNEQUAL LEGS ciyr THICK- WEIGHT S'ZE HESS PER FT, AREA 8x6 8x3 7x3i 6x4' 6 x3^* 5x4 5 X 3^* 5x3* li is- 19.3 10.8 11.2 41.7 39.1 36.5 33.8 31.2 28.5 25.7 23.0 20.2 35.7 33.7 31.7 29.6 27.5 25.3 23.2 21.0 18.7 10.6 32.3 30.5 28.7 26.8 21.9 23.0 21.0 19.1 17.0 15.0 13.0 30.0 28.0 28.9 27.3 9.8 24.2 22.7 21.1 19.6 17.8 16.2 11.5 1'2.8 ILO 9.3 21.2 22.7 21.3 21.2 19.9 J8.5 14.49 13.75 13.00 12.25 11.18 10.71' 9.91 9.16 8.36 7.66 6.75 6.93 10.50 9.90 9.30 8.68 8.06 7.43 0.80 6.15 6.60 4.84. 9.50 8.97 8,42 7,87 7.31 6.75 6.17 6.59 5.00 4.40 3.80 9.00 8.60 8.50 8.03 2.87 7.11 0.65 6.19 5.72 6.23 4.75 4.25 3.76 3.23 2.T1' 7.09 6.67 6.26 6.23 6.81 6.41 1.91 SIZE 4ix3: 4x3i 4x3* 3k3' 3|x2|* 3 X 2i' 3x2 2ix2: THICK- WEIGHT NESS PER FT. AntA ; i 18.6 17.3 16.0 11.7 13.3 11.9 10.0 9.1 19,8 18.S 17.3 10.0 11.7 13.3 11.9 10.0 9.1 ■7.7 6.2 18.3 17.1 16.0 11.8 5.8 10.8 15.8 11.7 13.6 12.6 6.1 13,1 12,5 11,5 10,1 10,1 9,5 5.9 5.0 1.1 3.1 6.8 0.1 NOTE- BASED UPON STANDARDS OF THE CARNEGIE, CAMBRIA. LACKAWANNA, JONES AJND LAUGH PHOENIX SECTIONS ARE SIMILAB. LIN, AND PENNSYLVANIA STEEL COHPANIES, 304 RIVETS AND BOLTS WEIGHTS AND DIMENSIONS OF RIVETS SHAPE < z taJ S X in u RIVETS SHOOLD NOT BE COUNTERSUNK IN PLATES THINNER THAN THOSE GIVEN IN TABLE SHANK X z S2 5.6 8.7 12.5 17.0 22.3 BUTTON HEAD 1^ li li ■•■16 1| 1* HO xo ID — 5.0 9.7 16.0 24.0 35.0 C'S'KHEAD ■1-16 1-i ^16 WEIGHTS AND DIMENSIONS OF BOLTS MANUFACTURERS STANDARD SHANX J. 2 X z s2 5.6 8.7 12.5 17.0 23.3 HEXAGONAL HEAD lf« li _l Q li li If h- o X o o — g Q. 5.1 10.0 17.3 37.4 42.0 HEXAGONAL NUT us o < 1^ li 1-6- It 1^ 1^ 1^ li 3 16 I- S X o o — nS S a. 9.9 19.5 34.5 45.3 57.5 SQUAREHEAD li ii 1-fr 1-2- 116 o — lg > Q. 5.9 11.5 19.9 1| 3L1 3r 47.3 SQUARE NUT It li H 3 I s S ° : 2 o - > Q- 1^ 11. I16 2i 33.0 41.0 3i 61.3 2# 95.3 RIVET CODE SHOP RIVETS nsri o p .0; EXPLANATION FITLL BUrrON HEADS, BOTH SIDES coontersunk and chipped, near side countersotfk and chipped, far side countersunk and CHIPPED, BOTH StDES COUNTERSUNK BUT NOT CHIPPED, NEARSIDE>'+ u COUNTERSUNK BUT NOT CHIPPED, FAR SIDE >0 COUNTERSUNK BUT NOT CHIPPED, BOTH S;iDE§J < FLATTENED TO -^° HIGH, NEAR SIDE' FLATTENED TO ^ HIGH, FAR SIDE FLATTENED TO -1-° HIGH, BOTH SIDES FLATTENED TO |° HIGH. HEAR SUIE ELATTENED Tof HIGH, FAR SIDE FLATTENED T0|° HIGH, BOTH SIDES STITCH RIVET WITH WASHER FIELD RIVETS ^ CLEARANCE FOR MACHINE DRIVEN RIVETS MINIMUM RIVET STAGGER"/) "FOR USUAL VALUES OF"c"AND THE FOLLOWING VALUES OF"; t: "t CKIMPED ANGLE It n USUAL VALUES OF"C "GIVEN IN TABLE.IN EXTREME CASES"C"MAY BE TAKEN-|^'+ ONE HALF DIAM.OF HEAD. lA ^h li 15. li 1-^ JL III 1^ li\ li a 1-S- Is life li •I 16 li li il6 lis lli li U li 3^ 2i 3i» DIAMETER 1- i 1 i 8 1 THREE DIAMETERS 11 li 1^ H sf 3 USUAL MINIMUM li a 2 H 2f 3 PREFERRED ih ii- 3i- 21- 3 3i MINIMUM RIVET SPACING "/77" E. ^ SEE ALSO FOLLOWING PAGE. MAXIMUM RIVET SPACING I — tn :^=^ — X — c } 1 \ — t"-fi S= ^H '- J_ P ' ' THE RIVET PCrCH"p"OR THE SPACING MEASURED PARALLEL TO THE LINE OF STRESS, SHOULD NOT EX- CEED 6"0R 16 i^ FOR J"ORf "rivets. OR 44"0R 16 t F0R|"RIVETS, WHERE t IS THE THICKNESS OF THE THINNEST OUTSIDE PLATE. INGIRDERS OR STRINGEliS WHICH SUPPORT MOVING LOADS APPLIED TO THE FLANGES, A MAXIMUM PITCH OF 4"0R 4i"lS OFTEN SPECIFIED. THE MAXIMUM PITCH AT THE ENDS OF COMPRESS- ION MEMBERS IS FOUR DIAMETERS FOR A DISTANCE OF ONE AND ONE HALF TIMES THE WIDTH OF THE MEMBER. THE MAXIMUM RIVET SPACING"lr"MEASURED PER- PENDICULARLY TO THE LIN£ OF STRESS IS 40 t. EDGE DISTANCE"e" Zle ZSe "|S DIAMETER EXTREME MINIMUM USUAL MINIMUM PREFERRED MAXIMUM 11 11 11 H il li 8 ik If: 5"OR8t(SEEABOVE) eiVET SPACING « 305 MINIMUM RIVET STAGGER 4 5 1" 9. GAGE OR TRANSVERSE 4 5 6 DISTANCE BETWEEN RIVET LINES ' k^ USE THE CIRCULAR ARCS TO DETERMINE THE MINIMUM STAGGER(f) WHICH y WILL MAKE THE DISTANCE C.TO C. HOLES. (/i) EQUAL TO THE USUAL MINIMUM i_ SPACING(m)GIVEN ABOVE. USE THE OTHER CURVES TO DETERMINEJHEMINIMUM STAGGER (f) WHICH CAN BE USED IN A TENSION MEMBER WITHOUT REDUCING THE AREA OF CROSS SECTION BY THE AREA OF AN ADDITIONAL RIVET HOLE * ON THIS PAGE ALL DIAMETERS ARE RIVET DIAMETERS AND ALL DIMENSIONS ARE IN INCHFS. 92 306 MINIMUM PITCHES FOR FLANGE RIVETS UNIT STRESSES POUNDS PER SQUARE INCH RIVETS IN A SINGLE LINE 1 RIVETS STAGGERED IN TWO LINES SINGLE SHEAR DOUBLE SHEAR SINGLE SHEAR DOUBLE SHEAR X-Aii tV i A 1 a i 4 or under A n S a * Xa '■ A 1 t'j s H ior under A \ ii 1 % IH u lA lA lA lA lA ift n If IH lA u % 1ft 1* lA lA 1ft 1ft lA li 11 1ft 1ft 1} SHEAR ON WEB (NET SECTION) s = 13,000 2A 21 2 2i 2i IH 2i If 2 If li If IH i; IH 2i 2f 2i 2f 2ft 2f 2A 2f 2 2i If 2i 2 lA If 1ft IS 1ft n Ift If 1ft If IH IH 21 If 21 If 21 1ft 2 2S SHEAR ON RIVETS s' = 12,000 BEARING IN WEB b = 24,000 1 3 3 2H 2A 2A 2ft 2ft 2A 3 3 3 3 3 1 2ft 2ft 21 2 ij 11 If 2A 2ft 2ft 2A 2ft IM 3 A 3ft 3A 3; 2f 2J 2f 2i 3A 3ft 3ft 3A 3ft x'A 2H 2H 2H 21 21 21 2 2H 2H 2H 2H 2H 1)4 3tt 3H 3H 31 3i 3ft 3ft 2J 3H 3H 3n 3H 3H 1)4 3 3 3 2H 2H 21 2f 3 3 3 3 3 % ItV lA lA lA lA lA 1ft lA IH IH Ift 11 1ft % 1ft 1ft 1ft 1ft lA lA 1ft lA 1ft lA 11 1ft SHEAR ON WEB (NET SECTION) SHEAR ON RIVETS s = 13,000 s' = 11,000 % % 2A 2i n 2i 2A ll 2 If Hi If lit If If IH 2i 2J 2i 2i 2A 2i 2 2i u 2f If 2 Ift u 1ft Hi u li 1} lA u If u If iH IH 2 2 1ft 2 1ft 2 BEARING IN WEB b =22,000 1 2H 2ii 21 2A 2A 2A 2J 2 2H 2H 2H 2H 2H 1 21 2i 2A If If IS 1ft 2i 21 21 21 21 i'/s 3i 3i 3i 2H 2f 2f 2f 2f 3i 3i 3} 3f 3} I'yi 2i 2i 2} 2ft 21 U If 21 21 2i 21 21 i'4 3J 3i 3J 3 A 31 3ft 2J 2i 3i 3J 3i 3J 3i 1)4 2H 2H 2H 21 2ft 2i 2ft 2H 2H 2H 2H 2H SHEAR ON WEB (NET SECTION) SHEAR ON RIVETS s = 12,000 s' = 12,000 % % If 2A 2i lA 2A 21 lA 1? 2| lA If 2ft lA IH 2A 1ft If 2 lA If If lA If IH 2 21 2J If 2i 2J n 2ft 21 If 2ft 2} 1ft 2ft 2S % % u If 2i lA If 2i 1ft 1ft iL 1ft 1ft 2H 1ft U 1ft lA 11 U 1ft u If If 11. IH 21 If If 21 u 21 1ft If 2J IH 21 BEARING IN WEB b = 24,000 1 3} 3i 2H 2H 2A 2f 2i 2ft 3S 3i 3f 3J 3i 1 2ft 2A 2f 2i 2 IH IH 2ft 2ft 2ft 2A 2ft 1'^ 3i 3J 3i 3i 3 2f 2H 2ft 3i 3J 3i 3J 31 1% 2i 2} 2J 2f 2} 21 2ft 21 2i 21 2i 21 1% 3J 3J 3J 3ii 3A 3f 3ft 3 3f 3J 3J 3{ 3J 1)4 3ft 3A 3ft 3f 2f 2H 21 3ft 3ft 3ft 34 3ft % m li lA lA lA lA lA lA H U IH 1ft U % 1ft If 1ft 1ft 1ft lA 1ft 11 If 1ft 1ft U SHEAR ON WEB (NET SECTION) SHEAR ON RIVETS s = 12,000 s' = 11,000 2A 21 2i IH 2i IH 2J If 2 U n If lit If IH 2i 2f 21 2f 2ft 2f 2ft 2f IH 2i u 2i 2 If If 11 If U U U If u If IH lit 21 21 IS 21 2 21 BEARING IN WEB b =22,000 1 2tt 2n 2« 2A 2A 2A 2ft 2 2H 2H 2H 2H 2H 1 2f 2| 21 2 If U If 2f 2f 2f 2f 2f IM 3A 3A 3ft 3A 21 2i 2ft 2i 3ft 3ft 3ft 3ft 3ft IM 2H 2H 2H 2A 21 2i IH 2H 2H 2H 2H 2H l!4 3H 3H 3H 3| 3f 3ft 3 2! 3H 3H 3H 3H 3H 1)4 3 3 3 2H 2H 21 2A 3 3 3 3 3 % lA lA lA lA lA lA 1ft lA IJ IH 1ft U lA % 1ft lA 1ft lA 1ft 1ft lA If 1ft 1ft u 1ft SHEAR ON WEB (NET SECTION) SHEAR ON RIVETS s = 12,000 s' = 10,000 % % 2 A 2A 2f 2A If 2 If n If IH If IH If Hi 2f 2A 2i 2A \ 2ft 2A IH 2ft If 2f % If IH lA 1ft JH U 11 11 If U If 11 If IH IH IH If IH IH 1ft IH BEARING IN WEB b = 20,000 1 2H 2}i 2f 2A 2ft 2A 2ft 2 2H 2H 2H 2H 2H 1 2i 21 2ft 1} li If li 21 2} 21 21 21 i% 3J 3J 3J 2}i 2i 2A 2A 2} 3f 3f 3f 3f 31 1)^ 2J 2i 2i 2ft 2i IH IH 21 2i 2i 21 21 l'4 3A 3A 3 A 3A 3A 3 2J 2} 3A 3A 3A 3ft 3A 1)4 2? 2} 2J 21 21 2A 2A 2} 2f 2} 21 2! NO VALUE GIVEN IS LESS THAN THE MINIMUM SPACING FOR MACHINE DRIVEN RIVET VALUES ABOVE THE SHORT FINE LINES ARE LESS THAN THE MINIMUM STAGGER FOU FOR THE MINIMUM STAGGER FOR OTHER GAGES, SEE DIAGRAM. 5, EOUA ND FRO . TO THE DIAMETER OF THE RIVET HEAD PLUS f- \A THE DIAGRAM ON THE PRECEDING PAGE FOR GAGE » = ll". MULTIPLICATION TABLE FOR RIVET SPACING 307 o < Q. PITCH OF RIVETS IN INCHES VI 111 o £ 2 n li If Ih If li If 2 2f 2i 2f 4 2f 2i 2f 3 Si si 3f si Si 4 a a 4i 5 Si 6i 6f 6 2 21 2i 2} 3 3} 3} 33 4 4} 4} 4} 5 5} 6} Si 6 6} 6} 6} 7 7} 8 8} 9 9} 10 10} U 11} 1-8 3 3i 3} 4i 4} 4} 51 51 6 6} 6i 7} 7} 7} 81 8} 9 9} 9i 10} 10} 11} 1-0 1-0} 1-1} 1-2} 1-3 1-3} W} 1-5} 1-6 3 4 4} 5 5} 6 6} 7 7} 8 8} 9 9} 10 10} 11 11} 1-0 1-0} 1-1 1-1} 1-2 1-3 W 1-5 1-6 1-7 1-8 1-9 1-10 1-11 2-0 4 5 51 6i 65 7} 8} 8i 9§ 10 10} 111 11} 1-0} 1-1} 1-li 1-2} 1-3 1-3} 1-41 1-4} 1-5} 1-6} 1-8 1-91 1-lOj 1-11} 2-1 2-2} 2-3} 2-4} 2-6 5 6 6} n 8}. 9 9i 10} 111 1-0 1-Oi 1-1} 1-2} 1-3 l-3i 1-4} 1-5} 1-6 l-6i 1-7} 1-81 1-9 1-10} 2-0 2-1} 2-3 2-4} 2-6 2-7} 2-9 2-10} 3-0 6 7 7J Si 0} 10} 11} 1-0} 1-1} 1-2 1-2} l-3i 1-1} 1-5} 1-6} 1-71 1-8} 1-9 1-9} 1-ioi l-llf 2-0} 2-21 2-4 2-5i 2-7} 2-9} 2-11 3-0} 3-2} 3-41 3-6 7 8 9 10 11 1-0 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-10 1-11 2-0 2-1 2-2 2-3 2-4 2-0 2-8 2-10 3-0 3-2 3-4 3-6 3-8 3-10 4-0 8 9 lOi Hi l-Of 1-1} 1-2} l-3i 1-4} 1-6 1-7} 1-8} 1-0} 1-10} 1-11} 2-Oi 2-1} 2-3 2-4} 2-51 2-6} 2-7} 2-9} 3-0 3-2} 3HI} 3-6} 3-0 3-11} 4-1} 4-3} 4-6 9 10 Hi 1-Oi 1-li 1-3 Wi 1-5} 1-6} 1-8 1-91 1-10} 1-1 li 2-1 2-2} 2-3} 2-4} 2-6 2-71 2-8} 2-9i 2-11 3-1} 3-4 3-6} 3-9 3-11} 4-2 4-4} 4-7 4-9} 5-0 10 11 l-Oi 1-li 1-3} 1^} 1-5} 1-71 1-8} 1-10 1-11} 2-OJ 2-2} 2-3} 2-4} 2-6} 2-7} 2-9 2-10} 2-11} 3-1} 3-2} 3-51 3-8 3-10} 4-1} 4^1 4-7 4-9} 5-0} 5-3} 5-6 11 12 i-ii 1-3 1-4} 1-6 1-7} 1-9 1-10} 2-0 2-1} 2-3 2-4} 2-6 2-7} 2-9 2-10} 3-0 3-1} 3-3 3^} 3-6 3-9 4-0 4-3 4-6 4-9 5-0 5-3 5-6 5-9 6-0 12 13 l-2i 1-41 1-5J 1-7} 1-9} 1-10} 2-0} 2-2 2-3} 2-5} 2-6} 2-8} 2-10} 2-11} 3-li 3-3 3-4} 3-61 3-73 3-9} 4-0} 4^ 4-7} 4-10} 6-H 6-6 5-8} 5-11} 6-2} 6-6 13 14 1-3J 1-5} 1-7} 1-9 1-ioi 2-0} 2-2} 2-4 2-5} 2-7} 2-91 2-11 3-OJ 3-2} 3-4} 3-6 3-7} 3-9} 3-11} 4-1 4-4} 4-8 4-11} 5-3 5-6} 5-10 6-1} 6-5 6-8} 7-0 14 15 l-4i l-6i l-8i 1-10} 2-0} 2-2} 2-4} 2-6 2-7J 2-9} 2-llj 3-1} 3-3} 3-5} 3-7} 3-9 3-10} 4-Oi 4-2} 4-4} 4-8} 5-0 6-3} 5-7} 5-11} 6-3 6-6} 6-10} 7-2} 7-6 16 16 1-6 1-8 1-10 2-0 2-2 2-4 2-6 2-8 2-10 3-0 3-2 3-4 3-6 3-8 3-10 4-0 4-2 4^ 4-6 4-8 5-0 5-4 5-8 6-0 6-4 6-8 7-0 7-4 7-8 8-0 16 17 l-7i 1-91 1-llt 2-1} 2-3} 2-52 2-7} 2-10 3-0} 3-2} 3-4} 3-6} 3-8} 3-lOi 4-0} 4-3 4-6 J 4-7} 4-9} 4-U! 6-31 5-8 6-0} 64} 6-8} 7-1 7-5} 7-9} 8-1} 8-6 17 18 l-8i 1-10} ^-0} 2-3 2-5} 2-7} 2-9i 3-0 3-21 3-4} 3-6} 3-9 3-11} 4-1} 4-3} 4-6 4-8} 4-10} 5-Oi 5-3 5-7} 6-0 6^} 6-9 7-1} 7-6 7-10} 8-3 8-7} 9-0 18 19 l-9f 1-iU 2-2} 2-4} 2-6} 2-91 2-111 3-2 3-43 3-6i 3-9} 3-11} 4-1} 4-4} 4-6} 4-9 4-lli 5-li 5^} 5-6} 5-11} 6-4 6-8} 7-1} 7-6} 7-11 8-3} 8-8} 9-11 9-6 19 20 1-lOi 2-1 2-3} 2-6 2-8} 2-11 3-1} 3-4 3-6} 3-9 3-115 4-2 4-4} 4-7 4-9} 5-0 6-2} 5-5 6-7} 5-10 6-3 6-8 7-1 7-6 7-11 8-4 8-9 9-2 9-7 10-0 20 21 1-iH 2-2} 2-4} 2-7} 2-10} 3-Oi 3-3} 3-6 3-81 3-11} 4-1} 4-45 4-7} 4-9} 6-0} 5-3 5-6} 5-8} 6-10} 6-1} 6-6i 7-0 7-51 7-10} 8-3} 8-9 9-2} 9-7} 10-0} 10-6 21 22 2-OJ 2-3} 2-6} 2-9 2-11} 3-2} 3-5} 3-8 3-10} 4-1} 4^1 4-7 4-9} 5-0} 6-3} 5-6 5-8} 5-11} 6-21 6-5 6-10} 7-4 7-9} 8-3 8-8} 9-2 9-7} 10-1 10-6} 11-0 22 23 2-lJ 2-4J 2-71 2-10} 3-li 3-41 3-7} 3-10 4-0} 4-3i 4-6} 4-9} 6-0} 5-3} 5-6} 5-9 5-11} 6-2} 6-5} 6-8} 7-21 7-8 8-1} 8-7} 9-1} 9-7 10-Oi 10-6} 11-0} 11-6 23 24 2-3 2-6 2-9 3-0 3-3 3-6 3-9 4-0 4-3 4-6 4-9 5-0 5-3 5-6 5-9 6-0 6-3 6-6 6-9 7-0 7-6 8-0 8-6 9-0 9-6 10-0 10-6 11-0 11-6 12-0 24 25 2-4i 2-7} 2-lOj 3-1} 3-41 3-7i 3-10} 4-2 4-5} 4-81 4-11} 5-2} 5-5} 5-8} 5-1 H 6-3 6-6} 6-9i 7-0} 7-3} 7-9} 8-4 8-10} 9^} 9-10} 10-5 10-111 11-5} 11-11} 12-6 26 26 2-5i 2-8} 2-lli 3-3 3-6} 3-9} 4-Oi 4-4 4-7} 4-10} 5-1} 5-5 5-8} 5-11} 6-2} 6-6 6-9} 7-0} 7-3} 7-7 8-1} 8-8 9-2} 9-9 10-3} 10-10 11^} 11-11 12-6} 13-0 26 27 2-6J 2-9i 3-1} 3^} 3-7} 3-11} 4-2j 4-6 4-9} 5-Oi 5-4} 5-7} 5-10} 6-21 6-6} 6-9 7-0} 7-3i 7-7} 7-10} 8-51 9-0 9-6} 10-1} 10-8} 11-3 11-9} 12-4} 12-11} 13-6 27 28 2-7J. 2-11 3-2} 3-6 3-9} 4-1 4-4} 4-8 4-11} 5-3 5-6} 5-10 6-1} 6-5 6-8} 7-0 7-3} 7-7 7-10} 8-2 8-9 9-4 9-11 10-6 11-1 11-8 12-3 12-10 1^-5 14-0 28 29 2-81 3-0} 3-3} 3-7} 3-11} 4-2} 4-61 4-10 5-1} 5-51 5-8} 6-0} 6-4} 6-7} 6-11} 7-3 7-6} 7-lOJ 8-1} 8-5} 9-0} 9-8 10-31 10-10} ll-5i 12-1 12-81 13-3} 13-10} 14-6 29 30 2-9i 3-1} 3-5} 3-9 4-OJ 4-4} 4-8} 5-0 5-3} 5-7} 6-111 6-3 6-6} 6-lOi 7-2} 7-6 7-9} 8-1 i 8-51 8-9 9-4} 10-0 10-7} 11-3 11-10} 12-6 13-1} 13-9 14-4} 15-0 30 li li If li If li 1| 2 2f 2i 2f 2| 2f 2f 2f 3 Si 3i 3f 3i Si 4 4i 4| 4i 5 6i 6i Si 6 308 1" RIVET VALUES SHEARING AND BEARING VALUES FOR |" RIVETS IN THOUSANDS OF POUNDS | r RIVETS BEARING VALUES TO THE LEFT OF THE DOTTED LINES ARE LESS THAN THE SINGLE SHEAR VALUES 8 "ivtio BEARING VALUES IN PLATES THICKER THAN THOSE GIVEN ARE GREATER THAN THE DOUBLE SHEAR VALUES SHOP RIVETS FIELD RIVETS BOLTS NO. OF RIVS SHEAR AT 12000 LBS./SQ. IN BEARING IN PLATE AT 24000 LBS./SQ. IN. NO. OF RIVS SHEAR AT 10000 LBS./SQ. IN BEARING IN PLATEAT20000 LBS./SQ. IN. NO. OF RIVS SHEAR AT 9000 LBS./SQ. IN BEARINGIN PLATE AT18000 LBS./SQ. IN. SINGLE DOUBLE A ' 1 1 ^ A f A SINGLE DOUBLE A i i A t A SINGLE DOUBLE A 1 1 1 4 A f A 1 3.7 7.4 2.8 \ 3.8 4.7 6.6 6.6 1 3.1 6.1 2.3 ; 3.1 3.9 4.7 5.5 1 2.8 5.6 2.1 • 2.8 3.5 4.2 4.9 2 7.4 14.7 5.6 : 7.5 9.4 11.3 13.1 2 6.1 12.3 4.7 ! 6.3 7.8 9.4 10.9 2 5.5 11.0 4.2 J 5.6 7.0 8.4 9.8 3 11.0 22 1 8.4 ; 11.3 14.1 16.9 19.7 3 9.2 18.4 7.0 : 9.4 11.7 14.1 16.4 3 8.3 16.6 6.3 : 8.4 10.5 12.7 14.8 i 14.7 29.5 11.3 : 15.0 18.8 22.5 26.2 4 12.3 24.5 9.4 ; 12.5 16.6 18.8 21.9 4 11.0 22.1 8.4 ! 11.2 ■ 14.1 16.9 19.7 S 18.4 36.8 14.1 : 18.8 23.4 28.1 32.8 6 16.3 30.7 11.7 ! 15.6 19.5 23.4 27.3 5 13.8 27.6 10.6 ! 14.1 17.6 21.1 24.6 6 22.1 44.2 16.9 22.6 28.1 33.8 39.4 6 18.4 36.8 14.1 ■ 18.8 23.4 28.1 32.8 6 16.6 33.1 12.7 ! 16.9 21.1 25.3 29.5 7 25.8 51.5 19.7 26.3 32.8 39.4 46.9 7 21.6 43.0 16.4 ■ 21.9 27.3 32.8 38.3 7 19.3 38.7 14.8 ; 19.7 24.6 29.5 34.5 8 29.5 58.9 22.5 30.0 37.6 45.0 62.5 8 24.5 49.1 18.8 26.0 31.3 37.5 43.8 8 22.1 44.2 16.9 22.5 28.1 33.8 39.4 9 33.1 66.3 26.3 33.8 42.2 60.6 59.1 9 27.6 56.2 21.1 28.1 36.2 42.2 49.2 9 24.8 49.7 19.0 26.3 31.6 38.0 44.3 10 36.8 73.6 28.1 37.6 46.9 66.3 65.6 10 30.7 61.4 23.4 31.3 39.1 46.9 64.7 10 27.6 55.2 21.1 28.1 35.2 42.2 49.2 SHOP RIVETS FIELD RIVETS BOLTS 1 NO. OF RIVS, SHEAR AT 11000 LBS./SQ. IN. BEARING IN PLATE AT 22000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 9000 LBS./SQ. IN. BEARING IN PLATE AT18000 LBS./SQ, IN. NO. OF RIVS. SHEAR AT 8000 LBS./SQ. IN. BEARING IN PLATE AT16000 LBS./SQ. IN, SINGLE DOUBLE A i i A 1 A SINGLE DOUBLE A ! 1 4 A f A SINGLE DOUBLE A i A f A 1 3.4 6.8 2.6 i 3.4 4.3 5.2 6.0 1 2.8 6.5 2.1 2.8 3.6 4.2 4.9 1 2,5 4.9 1.9 2.5 3.1. 3.8 4.4 8 6.8 13.6 5.2 ! 6.9 8.6 10.3 12.0 2 5.5 11.0 4.2 5.6 7.0 8.4 9.8 2 4,9 9.8 3.8 6.0 6.3 7.5 8.8 3 10.1 20.3 7.7 ; 10.3 12.9 15.5 18.0 3 8.3 16.6 6.3 8.4 10.6 12.7 14.8 3 7.4 14.7 5.6 7.5 9.4 11.3 13.1 4 13.5 27.0 10.3 : 13.7 17.2 20.6 24.1 4 11.0 22.1 8.4 11.2 14.1 16.9 19.7 4 9.8 19.6 7.5 10.0 12.5 16.0 17.5 5 16.9 33.8 12.9 : 17.2 21.5 25.8 30.1 6 13.8 27.6 10.6 14.1 17.6 21.1 24.6 6 12.3 24.5 9.4 12.5 15.6 18.8 21.9 6 20.3 40.5 15.5 20.6 25.8 30.9 36.1 6 16.6 33.1 12.7 16.9 21.1 26.3 29.5 6 14.7 29.6 11.3 15.0 18.8 22.5 26.3 7 23.6 47.3 18.0 24.1 30.1 36.1 42.1 7 10.3 38.7 14.8 19.7 24.6 29.6 34.5 7 17.2 34.4 13.1 17.5 21.9 26.3 30.6 8 27.0 54.0 20.6 27.5 34.4 41.2 48.1 8 22.1 44.2 16.9 22.5 28.1 33.8 39.4 8 19.6 39.3 16.0 20.0 25.0 30.0 35.0 9 30.4 60.8 23.2 30.9 38.7 46.4 64.1 9 24.8 49.7 19.0 25.3 31.6 38.0 44.3 9 22.1 44.2 16.9 22.5 28.1 33.8 39.4 10 33.8 67.5 26.8 34.4 43.0 51.6 60.2 10 27.6 66.2 21.1 28.1 35.2 42.2 49.2 10 24.5 49.1 18.8 26.0 31.3 37.5 43.8 SHOP RIVETS 1 FIELD RIVETS 1 BOLTS j NO. OF RIVS. SHEAR AT 10000 LBS./SQ. IN. BEARING IN PLATE AT 20000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 8000 LBS./SQ. IN, BEARING IN PLATE AT16000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 7000 LBS./SQ. IN. BEARING IN PLATEAT14000 LBS./SQ. IN. SINGLE DOUBLE A 1 A f A SINGLE DOUBLE A 1 4 A f A SINGLE DOUBLE A : i A f A 1 3.1 6 1 2.3 3.1 3.9 4.7 5.5 1 2.5 4.9 1.9 . 2.5 3.1 3.8 4.4 1 2.2 4,3 1.6 : 2.2 2.7 3.3 3.8 2 6.1 12.3 4.7 6.3 7.8 9.4 10.9 2 4,9 9.8 3.8 ' 6.0 6.3 7.6 8.8 2 4.3 8,6 3.3 : 4.4 5.5 6 6 7.7 3 9.2 18.4 7.0 9.4 11.7 14.1 16.4 3 7.4 14.7 5.6 ; 7,6 9.4 11.3 13.1 3 6.4 12,9 4.9 " 6.6 8.2 9.8 11.5 4 12.3 24.6 9.4 12.5 16.6 18.8 21.9 4 9.8 19,6 7.6 ; 10.0 12.5 16.0 17.5 4 8.6 17.2 6.6 ; 8.8 10.9 13.1 16.3 S 15.3 30.7 11.7 15.6 19.5 23.4 27.3 5 12.3 24,6 9.4 ; 12.5 ■ 15.6 18.8 21.9 6 10.7 21.5 8.2 J 10.9 13.7 16.4 19.1 6 18.4 36.8 14.1 ; 18.8 23.4 28.1 32.8 6 14,7 29.6 11.3 ; 16.0 18.8 22.6 26.3 6 12.9 25.8 9.8 ; 13.1 16.4 19.7 23.0 7 21.5 43.0 16.4 ; 21.9 27.3 32.8 38.3 7 17.2 34.4 13.1 : 17.5 21.9 26.3 30.6 7 15.0 30.1 11.5 ! 16.3 19.1 23.0 26.8 8 24.6 49.1 18.8 : 26.0 31.3 37.6 43.8 8 19.6 39.3 15.0 : 20.0 25.0 30.0 35.0 8 17.2 34.4 13.1 ! 17.5 21.9 26.3 30.6 9 27.6 56.2 '21.1 : 28.1 35.2 42.2 49.2 9 22.1 44.2 16.9 : 22.5 28.1 33.8 39.4 9 19.3 38.7 14.8 : 19.7 24.6 29.5 34.5 10 30.7 61.4 23.4 : 31.3 39.1 46.9 54.7 10 24.5 49.1 18.8 : 26.0 31.3 37.5 43.8 10 21.5 43.0 16.4 : 21.9 27.3 32.8 38.3 1" RIVET VALUES 309 3„ R.wp-ps SHEARING AND BEARING VALUES FOR f RIVETS IN THOUSANDS OF POUNDS ' BEARING VALUES TO THE LEFT OF THE DOTTED LINES ARE LESS THAN THE SINGLE SHEAR VALUES i" R'VETS BEARING VALUES IN PLATES THICKER THAN THOSE GIVEN ARE GREATER THAN THE DOUBLE SHEAR VALUES SHOP RIVETS FIELD RIVETS BOLTS 1 NO. OF RIVS SHEAR AT 12000 LBS./SQ. IN BEARING IN PLATE AT 24000 LBS./SQ. IN. NO. OF RIVS SHEAR AT 10000 LBS./SQ. IN BEARING IN PLATE AT 20000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 9000 LBS./SQ. IN BEARING IN PLATE AT 18000 LBS./SQ. IN. SINGLE DOUBLE A i i A f A i A SINGLE DOUBLE A i j A i A i A SINGLE DOUBLE A 1 1 ■ A f A i A 10 S.3 10.6 IS. 9 21.2 26.5 31.8 37.1 42.4 47.7 53.0 10.6 21.2 31.8 42.4 53.0 63.6 74.2 84.8 95 4 106.0 3.4 6.8 10.1 13.5 16.9 20.3 23.6 27.0 30.4 33.8 4.5 9.0 13.5 18.0 22.5 27.0 31.5 36.0 40.5 45. ; 5.6 ; 11.3 : 16.9 :22.5 !28.1 33.8 :39.4 45.0 ,60.6 56.3 6.8 13.5 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.5 7.9 15.8 23.6 31.6 39.4 47.3 55.1 63.0 70.9 78.8 9.0 18.0 27.0 36.0 45.0 64.0 63.0 72.0 81.0 90.0 10.1 20.3 30.4 40.5 50.6 60.8 70.9 81.0 91.1 101.3 1 2 3 * 5 6 7 8 9 10 4.4 8.8 13.3 17.7 22.1 26.5 30.9 35.3 39.8 44.2 8.8 17.7 26.5 35.3 44.2 53.0 61.9 70.7 79.5 88.4 2.8 5.6 8.4 11.3 14.1 16.9 19.7 22.5 25.3 28.1 3.8! 4.7 7.6 ! 9.4 11.3: 14.1 15.0 : 18.8 18.8:23.4 22.5! 28.1 26.3 : 32.8 30.0 ; 37.5 33.8:42.2 37 5 : 46.9 5.6 11.3 16.9 22.5 28.1 33.8 39.4 45.0 50.6 56.3 6.6 13.1 19.7 26.3 32.8 39.4 46.9 52.5 59.1 65.6 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0 8.4 16.9 25.3 33.8 42.2 50.6 59.1 67.5 75.9 84.4 1 2 3 4 5 6 7 8 9 10 4.0 8.0 11.9 15.9 19.9 23.9 27.8 31.8 35.8 39.8 8.0 15.9 23.9 31.8 39.8 47.7 56.7 63.6 71.6 79.5 2.5 5.1 7.6 10.1 12.7 15.2 17.7 20.2 22.8 25.3 3.4 6.8 10.1 13.5 16.9 20.3 23.6 27.0 30.4 33.8 : *^ 8.4 12.7 16.9 21.1 25.3 ,29 5 :33.8 38.0 42.2 5 1 10.1 15.2 20.3 25.3 30.4 35.4 40.5 45.6 50.6 5.9 11.8 17.7 23.6 29.5 35.4 41.3 47.2 53.2 59.1 6.8 13.5 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.5 7.6 15.2 22.8 30.4 38.0 45.6 53.2 60.8 68.3 75.9 SHOP RIVETS FIELD RIVETS BOLTS 1 » NO. OF RIVS SHEAR AT UOOO LBS./SQ. IN. BEARING IN PLATE AT 22000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 9000 LBS./SQ. IN. BEARING IN PLATE AT 18000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 8000 LBS./SQ. IN. BEARING IN PLATE AT 16000 LBS./SQ, IN. SINGLE DOUBLE A i A f A i A SINGLE DOUBLE A i 1 A 1 A i A SINGLE DOUBLE A i A f A h A 10 4.9 9.7 14.6 19.4 24.3 29.2 34.0 38.9 43.7 48.6 9.7 19.4 29.2 38.9 48.6 58.3 68.0 77.8 87.5 97.2 3.1 6.2 9.3 12.4 15.5 18.6 21.7 24.8 27.8 30.9 4.1 8.3 12.4 16.5 20.6 24.8 28.9 33.0 37.1 41.3 5.2 10.3 15.5 20.6 25.8 30.9 36.1 41.2 46.4 51.6 6.2 12.4 18.6 24.8 30.9 37.1 43.3 49.6 65.7 61.9 7.2 14.4 21.7 28.9 36.1 43.3 50.5 57.8 65.0 72.2 8.3 16.5 24.8 33.0 41.3 49.5 57.8 66.0 74.3 82.5 9.3 18.6 27.8 37.1 46.4 65.7 65.0 74.2' 83.5 92.8 1 2 3 4 B 6 7 8 9 10 4.0 8.0 11.9 15.9 19.9 23.9 27.8 31.8 35.8 39.8 8.0 15.9 23.9 31.8 39.8 47.7 55.7 63.6 71.6 79.6 2.5 5.1 7.6 10.1 12.7 15.2 17.7 20.2 22.8 25.3 3.4; 4.2 6.8! 8.4 10.1 ! 12.7 13.5 : 16.9 16.9 1 21.1 20.3 '• 25.3 23.6 J 29.5 27.0; 33.8 30.4 ; 38.0 33.8:42.2 5.1 10.1 15.2 20.3 25.3 30.4 35.4 40.5 45.6 60.6 5.9 11.8 17.7 23.6 29.5 35.4 41.3 47.2 53.2 59.1 6.8 13.5 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.5 7.6 15.2 22.8 30.4 38.0 45.6 63.2 60.8 68.3 75.9 9 10 3.5 7.1 10.6 14.1 17.7 21.2 24.7 28.3 31.8 35.3 7.1 14.1 21.2 28.3 35.3 42.4 49.5 56.6 63.6 70.7 2.3 4.5 6.8 9.0 11.3 13.5 15.8 18.0 20.3 22.5 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0 3.8 7.5 11.3 15.0 18.8 22.5 26.3 30.0 33.8 37.5 4.5 9.0 13.5 18.0 22.5 27.0 31.5 36.0 40.5 45.0 5.3 10.6 15.8 21.0 26.3 31.5 36.8 42.0 47.3 52.5 6.0 12.0 18.0 24.0 30.0 36.0 42.0 48.0 54.0 60.0 6.8 13.6 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.6 SHOP RIVETS FIELD RIVETS BOLTS 1 NO. OF RIVS SHEAR AT 10000 LBS./SQ. IN. BEARING IN PLATE AT 20000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 8000 LBS./SQ. IN. BEARING IN PLATE AT 16000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 7000 LBS./SQ. IN. BEARING IN PLATE AT 14000 LBS./SQ. IN. SINGLE DOUBLE A i A 1 A ^ A SINGLE DOUBLE A I 1 A i A i A SINGLE DOUBLE A i A f A i A 1 S 3 4 8 6 7 8 9 10 4.4 8.8 13.3 17.7 22.1 26.5 30.9 35.3 39.8 44.2 8.8 17.7 26.5 35.3 44.2 53.0 61.9 70.7 79.5 88.4 2.8 5.6 8.4 11.3 14.1 16.9 19.7 22.5 25.3 28.1 3.8 7.5 11.3 15.0 18.8 22.5 26.3 30.0 33.8 37.5 4.7 9.4 14.1 18.8 23.4 28.1 32.8 37.5 42.2 46.9 5.6 11.3 16.9 22.5 28.1 33.8 39.4 45.0 50.6 56.3 6.6 13.1 19.7 26.3 32.1 39.4 45.9 52.5 69.1 65.6 7.6 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0 8.4 16.9 25.3 33.8 42.2 50.6 59.1 67.5 75.9 84.4 1 2 3 4 6 6 7 8 9 10 3 5 7.1 10.6 14.1 17.7 21.2 24.7 28.3 31.8 35.3 7.1 14.1 21.2 28.3 35.3 42.4 49.5 56.6 63.6 70.7 2.3 4.5 6.8 9.0 11.3 13.5 15.8 18.0 20.3 22.5 3.0 : 3.8 6.0 : 7.5 9.0 I 11.3 12.0 1 15.0 15.0 1 18.8 18.0; 22.5 21.0:26.3 24.0 ; 30.0 27.0 ; 33.8 30.0 ! 37.5 4.5 9.0 13.5 18.0 22.5 27.0 31.5 36.0 40.5 45.0 5.3 10.5 15.8 21.0 26.3 31.5 36.8 42.0 47.3 52.5 6.0 12.0 18.0 24.0 30.0 36.0 42.0 48.0 54.0 60.0 6.8 13.5 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.5 1 2 3 4 5 6 7 8 9 10 3.1 6.2 9.3 12.4 15.5 18.6 21.7 24.7 27.8 30.9 6.2 12.4 18.6 24.7 30.9 37 1 43.3 49.5 56.7 61.9 2.0 3.9 5.9 7.9 9.8 11.8 13.8 15.8 17.7 19.7 2.6 5.3 7.9 10.5 13.1 15.8 18.4 21.0 23.6 26.3 3.3 6.6 9.8 13.1 16.4 19.7 23.0 26.3 29.5 32.8 _ 3.9 7.9 11.8 15.8 19.7 23.6 27.6 31.5 35.4 39.4 4.6 9.2 13.8 18.4 23.0 27.6 32.2 36.8 41.3 45.9 5.3 10.5 15.8 i21.0 26.3 31.5 36.8 42.0 47.3 52.5 5.9 11.8 17.7 23.6 29.5 35.4 41.3 47.2 53.2 59.1 310 1" RIVET VALUES i" RIVETS SHEARING AND BEARING VALUES FOR l" RIVETS IN THOUSANDS OF POUNDS Z" RIVETS BEARING VALUES TO THE LEFT OF THE DOTTED LINES ARE LESS THAN THE SINGLE SHEAR VALUES 8 "■•'^••' BEARING VALUES IN PLATES THICKER THAN THOSE GIVEN ARE GREATER THAN THE DOUBLE SHEAR VALUES SHOP RIVETS FIELD, RIVETS BOLTS NO. OF RIVS. SHEAR AT 13000 LBS./SQ. IN. BEARING IN PLATE AT 24000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 10000 LBS./SQ. IN. BEARING IN PLATE AT 20000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 9000 LBS./SQ. IN. BEARING IN PLATE AT 18000 LBS./SQ. IN, SINGLE DOUBLE i tk f A i A f SINGLE DOUBLE 1 4 A j i A i A 1 SINGLE DOUBLE 1 I A f A i A f 7.2 14.4 21.6 28.9 36.1 14.4 28.9 43.3 57.7 72.2 5.3 10.5 15.8 21.0 26.3 6.6 13.1 19.7 26.3 32.8 . 7.9 1 15.8 :23.6 .'31.5 :39.4 9.2 18.4 27.6 36.8 45.9 10.5 21.0 31.5 42.0 52.5 11.8 23.6 35.4 47.2 59.1 13.1 26.3 39.4 62.5 65.6 1 2 3 4 6 6.0 12.0 18.0 24.1 30.1 . 12.0 24.1 36.1 48.1 60.1 4.4 8.8 13.1 17.5 21.9 5.5 1 6.6 10.9 : 13.1 16.4 : 19.7 21.9 ! 26.3 27.3 ! 32.8 7.7 15.3 23.0 30.6 38.3 8.8 17.5 26.3 35.0 43.8 9.8 19.7 29.5 39.4 49.2 10.9 21.9 32.8 43.8 54.7 1 2 3 4 6 5.4 10.8 16.2 21.6 27.1 10.8 21.6 32.5 43.3 54.1 3.9 7.9 11.8 16.8 19.7 4.9 9.8, 14.8: 19.7: 24.6 : 5.9 11.8 17.7 23.6 29.5 6.9 13.8 20.7 27.6 34.5 7.9 15.8 23.6 31.5 39.4 8.9 17.7 26.6 35.4 44.3 9.8 19.7 29.5 39.4 49.2 10 43.3 50.5 57.7 64.9 72.2 86.6 101.0 115.4 129.9 144.3 31.5 36.8 42.0 47.3 52.5 39.4 45.9 52.5 69.1 65.6 ;47.3 ;65.1 :63.0 :70.9 178.8 65.1 64.3 73.5 82.7 91.9 63.0 73 5 84.0 94.6 105.0 70.9 82.7 94.6 106.3 118.1 78.8 91.9 105.0 118.1 131.3 6 7 8 9 10 36.1 42.1 48.1 64.1 60.1 72.2 84.2 96.2 108.2 120.3 26.3 30.6 35.0 39.4 43.8 32.8 J 39.4 38.3 : 45.9 43.8 i 62.5 49.2; £9.1 54.7 : 65.6 46.9 53.6 61.2 68.9 76.6 62.5 61.3 70.0 78.8 87.5 59.1 68.9 78.8. 88.6 98.4 65.6 76.6 87.5 98.4 109.4 6 7 8 9 10 32.5 37.9 43.3 48.7 64.1 64.9 75.8 86.6 97.4 108.2 23.6 27.6 31.5 35.4 39.4 29.6; 34.5; 39.4; 44.3; 49.2: 35.4 41.3 47.2 53.2 59.1 41.3 48.2 65.1 62.0 68.9 47.3 55.1 63 70.9 78.8 63.2 62.0 70.9 79.7 88.6 59.1 68.9 78.8 88.6 98.4 SHOP RIVETS FIELD RIVETS BOLTS 1 NO. OF RIVS. SHEAR AT 11000 LBS./SQ. IN. BEARING IN PLATE AT 22000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 9000 LBS./SQ. IN. BEARING IN PLATE AT 18000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 8000 LBS./SQ. IN. BEARING IN PLATE AT 16000 LBS./SQ. IN. SINGLE DOUBLE 1 4 A 3 8 A 1 2 A 5 8 SINGLE DOUBLE i A i f A i A 1 SINGLE DOUBLE i A f A i A 1 1 2 3 4 6 6.6 13.2 19.8 26.5 33.1 13.2 26.5 39.7 52.9 66.1 4.8 9.6 14.4 19.2 24.1 fl.O 12.0 18.0 24.1 30.1 7.2 14.4 21.7 28.9 36.1 8.4 16.8 25.3 33.7 42.1 9.6 19.3 28.9 38.6 48.1 10.8 21.7 32.5 43.3 54.1 12.0 24.1 36.1 43.1 60.2 1 2 3 4 6 6.4 10.8 16.2 21.6 27.1 10.8 21.6 32.5 43.3 54.1 3.9 7.9 11.8 15.8 19.7 4.9 J 6.9 9.8 ; 11.8 14.8; 17.7 19.7 ;23.6 24.6:29.6 6.9 13.8 20.7 27.6 34.6 7.9 15.8 23.6 31.6 39.4 8.9 17.7 26.6 35.4 44.3 9.8 19.7 29.5 39.4 49.2 1 2 3 4 5 4.8 9.6 14.4 19.2 24.1 9.6 19.2 28.9 38.5 48.1 3.5 7.0 10.5 14.0 17.5 4.4 8.8 13.1 17.5 21.9 5.3 10.6 15.8 21.0 26.3 6.1 12.3 18.4 24.5 30.6 7.0 14.0 21.0 28.0 35.0 7.9 15.8 23.6 31.5 39.4 8.8 17.5 26.3 35.0 43.8 6 7 8 9 10 39.7 46.3 62.9 59.5 66.1 79.4 92.6 105.8 119.1 132.3 28.9 33.7 38.5 43.3 48.1 36.1 42.1 48.1 64.1 60.2 43.3 50.5 67.8 65.0 72.2 60.6 69.0 67.4 75.8 84.2 67.8 67.4 77.0 86.6 96.3 65.0 75.8 86.6 97.6 108.3 72.2 84.2 96.2 108.3 120.3 6 7 8 9 10 32.6 37.9 43.3 48.7 54.1. 64.9 75.8 86,6 97.4 108.2 23.6 27.6 31.5 35.4 39.4 29.5 I 35.4 34.5 ; 41.3 39.4 ;47.2 44.3 ; 53.2 40.2:59.1 41.3 48.2 55.1 62.0 68.9 47.3 55.1 63.0 70.0 78.8 63.2 62.0 70.9 79.7 88 6 69.1 68.9 78.8 88.6 98.4 6 7 8 9 10 28.9 33.7 38.5 43.3 48.1 , 57.7 67.3 77.0 86.6 96.2 21.0 24.5 28.0 31 5 35.0 26.3 30.6 35.0 39.4 43.8 31.5 36.8 42.0 47.3 52.5 36.8 42.9 49.0 55.1 61 3 42.0 49.0 56.0 63.0 70.0 47.3 55.1 63.0 70.9 78.8 52.5 61.3 70.0 78.8 87.5 SHOP RIVETS FIELD RIVETS BOLTS NO. OF RIVS. SHEAR AT 10000 LBS./SQ. IN. BEARING IN PLATE AT 20000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 8000 LBS./SQ. IN. BEARING IN PLATE AT 16000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT 7000 LBS./SQ. IN. BEARING IN PLATE AT 14000 LBS./SQ. IN. SINGLE DOUBLE i A f A 1 2 A f SINGLE DOUBLE i A i t A i A i SINGLE DOUBLE 1 4 A i A i A f 6.0 12.0 18.0 24.1 30.1 12.0 24.1 36.1 48.1 60.1 4.4 8.8 13.1 17.5 21.9 5.5 10.9 16.4 21.9 27.3 6.6 13.1 19.7 26.3 32.8 7.7 15.3 23.0 30.6 38.3 8.S 17.5 26.3 35.0 43.8 9.8 19.7 29.6 39.4 49.2 10.9 21.9 32.8 43.8 54.7 1 2 3 4 5 4.8 9.6 14.4 19.2 24.1 9.6 19.2 28.9 38.5 48.1 3.5 7.0 10.5 14.0 17.5 4.4 : 5.3 8.8 : 10.5 13.1 : 15.8 17.5 ; 21.0 21.9 ; 26.3 6.1 12.3 18.4 24.5 30.6 7.0 14.0 21.0 28.0 35.0 7.9 15.8 23.6 31.5 30.4 8.8 17.5 26.3 35.0 43.8 1 2 3 4 5 4.2 8.4 12.6 16.8 21.0 8.4 16.8 25.3 33.7 42.1 3.1 6.1 9.2 12.3 15.3 3.8 7.7 11.5 16.3 19.1 4.6 9.2 13.8 18.4 23.0 5.4 10.7 16.1 21.4 26.8 6.1 12.3 18.4 24.5 30.6 6.9 13.8 20.7 27.6 34.5 7.7 15.3 23.0 30.6 38.3 10 36.1 42.1 48.1 54.1 60.1 72.2 84.2 96.2 108.2 120.3 26.3 30.6 35.0 39.4 43.8 32.8 38.3 43.8 49.2 54.7 39.4 45.9 52.5 69.1 65.6 45.9 63.6 61.2 68.9 76.6 52.5 61.3 70.0 78.8 87.5 69.1 68.9 78.8 88.6 98.4 65.6 76.6 87.6 98.4 109.4 6 7 8 9 10 28.9 33.7 38.5 43.3 48.1 57.7 67.3 77.0 86.6 96.2 21.0 24.5 28.0 31.5 36.0 26.3 ;31.5 30.6 ; 36.8 35.0 ; 42.0 39.4 : 47.3 43.8 : 52.5 36.8 42.9 49.0 65.1 61.3 42.0 49.0 56.0 63.0 70.0 47.3 55.1 63.0 70.9 78.8 52.5 61.3 70.0 78.8 87.5 6 7 8 9 10 25.3 29.5 33.7 37.9 42.1 50.5 58.9 67.3 75.8 84.2 18.4 21.4 24.5 27.6 30.6 23.0 26.8 30.6 34.5 38.3 27.6 32.2 36.8 41 3 45.9 32.2 37.6 42.9 48.2 53.6 36.8 42.9 49.0 65.1 61.3 41.3 48.2 55.1 62.0 68.9 45.9 53.6 61.2 68.9 76.6 a 1" RIVET VALUES 311 „ SHEARING AND BEARING VALUES FOR l" RIVETS IN THOUSANDS OF POUNDS BEARING VALUES TO THE LEFT OF THE DOTTED LINES ARE LESS THAN THE SINGLE SHEAR VALUES ^" R'VETS BEARING VALUES IN PLATES THICKER THAN THOSE GIVEN ARE GREATER THAN THE DOUBLE SHEAR VALUES SHOP RIVETS, 1 FIELD RIVETS BOLTS NO. OF RIVS SHEAR AT 12000 LBS,/SQ, IN BEARING IN PLATE AT 21000 LBS./SQ, IN, NO. OF RIVS SHEAR AT 10000 LBS./SQ. IN BEARING IN PLATE AT 20000 LBS./SQ. IN. NO. OF RIVS SHEAR AT 9000 LBS./SQ. IN BEARING IN PLATE AT 18000 LBS./SQ. IN. SINGLE DOUBLE t i A ^ A f « f SINGLE DOUBLE 1 . ft i A 5 tt 3 SINGLE DOUBLE 1 i A 1 2 A 1 a f 1 2 3 4 6 6 7 8 9 10 9,4 18,9 28,3 37,7 47.1 56.6 66.0 75.4 84.8 94.2 18.9 37.7 56.6 75.4 94.3 113.1 132.0 150.8 169.7 188.5 9.0; 10.5 18.0:21.0 27.0 :31.5 36,0 : 42,0 45.0; 52.5 54.0; 63.0 63.0 ; 73.5 72.0 ; 84.0 81.0 ; 94.5 90.0 ;i05.0 12.0 24.0 36,0 48,0 60,0 72,0 84.0 96.0 108.0 120.0 13.5 27 .0 40 .5 54 .0 67 .5 81 .0 94 .5 108 .0 121 .5 135 .0 15,0 30,0 45.0 60.0 75.0 90.0 105.0 120.0 135.0 150.0 16.5 33.0 49.5 66.0 82.5 99.0 115.5 132.0 148.5 165,0 18.0 36.0 54 72.0 90.0 108.0 126.0 144.0 162.0 ISO 1 2 3 4 S 6 7 8 9 10 7.9 15.7 23.6 31.4 39.3 47.1 55.0 62.8 70.7 78.5 15.7 31.4 47.1 62.8 78.5 94.2 110.0 125.7 141.4 157.1 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67,5 75,0 ; 8.8 ; 17.5 126.3 :35.0 ■ 43.8 52.5 ! 61.3 ; 70.0 ;78,8 ■87,5 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80,0 90.0 100.0 11.3 22,5 33,8 45,0 56,3 67,5 78,8 90,0 101.3 112 5 12.5 25.0 37.5 50.0 62.5 75,0 87,5 100,0 112,5 125,0 13.8 27.5 41.3 55.0 68.8 82 5 96.3 110.0 123.8 137.5 15,0 30,0 45.0 60.0 75.0 90.0 105.0 120.0 135.0 150.0 1 2 3 4 6 6 7 8 9 10 7.1 14.1 21.2 28.3 35.3 42.4 49.5 56.6 63.6 70.7 14.1 28.3 42.4 56.5 70.7 84.8 99.0 113.1 127.3 141.4 6.8 13.5 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.5 ; 7.9 : 15.8 : 23.6 : 31.5 39.4 47.3 ; 55.1 : 63.0 : 70.9 : 78.8 9.0 18.0 27.0 36.0 45.0 54,0 63,0 72,0 81.0 90.0 10.1 20.3 30.4 40.5 50.6 60.8 70.9 81.0 91.1 101,3 11.3 22.5 33.8 45.0 56.3 67.5 78.8 90.0 101.3 112,5 12,4 24,8 37.1 49.5 61.9 74.3 86.6 99.0 111.4 123.8 13.5 27.0 40.5 54.0 67.5 81.0 94.5 108.0 121.5 135.0 SHOP RIVETS FIELD RIVETS BOLTS NO. OF RIVS. SHEAR AT 11000 LBS./SQ. IN BEARING IN PLATE AT 22000 LBS./SQ. IN. NO. OF RIVS SHEAR AT 9000 LBS./SQ. IN. BEARING IN PLATE AT 18000 LBS./SQ. IN. NO. OF RIVS. SHEAR AT BOOO LBS./SQ. IN. BEARING IN PLATE AT 16000 LBS./SQ. IN, SINGLE DOUBLE 1 : A 1 A 5 S a 3 i SINGLE DOUBLE f ■ A 1 2 A f tt 1 SINGLE DOUBLE 1 i A r A 5 S a f 1 2 3 4 6 6 7 8 9 10 8.6 17.3 25.9 34.6 43.2 51.8 60.5 69.1 77.8 86.4 ■ 17.3 34.6 61.8 69.1 86.4 103.7 121.0 138.2 155,5 172.8 8.3 i 9.6 16.5 ! 19.3 24.8 : 28.9 33.0 ! 38.5 41,3 ; 48,1 49,5 i 57,8 57,8; 67,4 66,0 ! 77.0 74.3 ! 86.6 82.5 : 96 3 11. 22.0 33.0 44.0 55.0 66.0 77.0 88.0 99.0 110. 12.4 24.8 37.1 49.5 61.9 74.3 86.6 99.0 111.4 123.8 13.8 27.5 41.3 55.0 68.8 82.5 96.3 110. 123.8 137 5 15,1 30,3 45.4 60,5 75,6 90.8 105.9 121.0 136 1 151 3 16.5 33.0 49.5 66.0 82.5 99.0 115.6 132.0 148 5 65.0 1 2 3 4 6 6 7 8 9 10 7.1 14.1 21.2 28.3 35.3 42.4 49.5 56.6 63.6 70 7 14.1 28.3 42.4 56.5 70.7 84.8 99.0 113.1 127.2 141 4 6.8 13.5 20.3 27.0 33.8 40.5 47.3 54.0 60.8 67.5 : 7,9 : 15,8 123,6 :3i,5 > 39.4 47.3 ; 65.1 ;63.0 ;70.9 : 78,8 9.0 18.0 27.0 36.0 45.0 54.0 63.0 72.0 81.0 90,0 10.1 20.3 30.4 40.5 50.6 60.8 70.9 81.0 91.1 101.3 11,3 22,5 33.8 45.0 56.3 67.5 78.8 90.0 101.3 112.5 12.4 24.8 37.1 49.6 61.9 74.3 86.6 99.0 111.4 123,8 13.5 27.0 40.5 54.0 67.5 81.0 94.5 108.0 121.5 135.0 1 2 3 4 6 6 7 8 9 10 0.3 12.6 18.8 25.1 31.4 37.7 44.0 50.3 56.5 62.8 12.6 25.1 37.7 50.3 62.8 75.4 88.0 100.5 113.1 125.7 6.0 ; 7.0 12.0 : 14.0 18.0 121.0 24.0 !28.0 30.0 1 35.0 36.0; 42.0 42.0; 49.0 48.0 ; 56,0 54,0 ; 63,0 60.0 ; 70,0 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 80.0 9.0 18.0 27.0 36.0 45.0 54.0 63.0 72.0 81,0 90.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 11.0 22.0 33.0 44.0 55.0 66.0 77.0 88.0 99.0 110.0 12.0 24.0 30.0 48.0 60.0 72.0 84.0 96.0 108.0 120.0 SHOP RIVETS FIELD RIVETS BOLTS NO. OF RIVS, SHEAR AT 10000 LBS./SQ. IN. BEARING IN PLATE AT 20000 LBS./SQ. IN. NO, OF RIVS. SHEAR AT 8000 LBS./SQ. IN. BEARING IN PLATE AT16000 LBS./SQ. IN. NO. OF RIVS, SHEAR AT 7000 LBS./SQ. IN. BEARING IN PLATE AT 14000 LBS./SQ. IN. SINGLE DOUBLE 1 A 1 A f ii 3 4 SINGLE DOUBLE t 1 A 1 2 A f a f SINGLE DOUBLE f A i A f a f 1 2 3 4 6 6 7 8 9 10 7.9 15.7 23.6 31.4 39.3 47.1 S5.0 62.8 70.7 78.5 15.7 31.4 47.1 62,8 78.5 94.2 110.0 125.7 141.4 167.1 7.5 15.0 22,5 30,0 37,5 45,0 52,5 60.0 67.5 75.0 8 8 17,5 26,3 35.0 43,8 52,5 61.3 70.0 78.8 87.5 10.0 20.0 30.0 40.0 50.0 60,0 70,0 80,0 90,0 100.0 11.3 22.5 33.8 45.0 66.3 67,5 78,8 90,0 101,3 112,5 12.5 25.0 37.5 50.0 62.5 75.0 87.5 100.0 112,5 125.0 13.8 27.5 41.3 55.0 68.8 82.5 96.3 110,0 123.8 137.5 15.0 30.0 45.0 60.0 76.0 90.0 105.0 120.0 135.0 150.0 1 2 3 4 6 6 7 8 9 10 6.3 12.6 18.8 25.1 31.4 37.7 44.0 50.3 56.5 62.8 12.6 25.1 37.7 50,3 62.8 75.4 88.0 100.5 113.1 125.7 6.0 : 12.0 ! 18,0 : 24,0 ; 30.0 ; 36.0 ■ 42.0 ; 48,0; 54.0 : 60.0 ; 7,0 14.0 21.0 28.0 35.0 42 49.0 56.0 63.0 70.0 8,0 16,0 24,0 32,0 40.0 48.0 56.0 64,0 72.0 80.0 9.0 18.0 27,0 36,0 45,0 64,0 63,0 72,0 81,0 90,0 10.0 20,0 30,0 40 50,0 60,0 70,0 80.0 90.0 00.0 11,0 22,0 33,0 44,0 55.0 66 77,0 88,0 99,0 10,0 12.0 24.0 36.0 48.0 60,0 72,0 84,0 96.0 108 120.0 1 2 3 4 6 6 7 8 9 10 5.5 11.0 16.5 22.0 27.5 33.0 38.5 44.0 49.5 55.0 11.0 22.0 33.0 44.0 55.0 66.0 77.0 88.0 99.0 110.0 5.3 10.5 15,8 ! 21.0 '• 26.3 31,5 36 8 ; 42,0 ; 47,3 ; 52,5 1 6.1 12,3 18,4 24.5 30,6 36 8 42,9 49,0 55,1 61.3 7.0 14.0 21,0 28,0 35,0 42,0 49,0 56,0 63,0 70,0 7.9 15,8 23.6 31,5 39,4 47,3 55,1 63,0 70.9 78.8 8,8 17,5 26,3 35.0 43.8 52.5 61,3 70,0 78,8 87,5 9.6 19.3 28.9 38.5 48.1 57.8 67.4 77.0 86.6 96.3 10.5 21.0 31.5 42.0 52.5 63.0 73.5 84.0 94.5 105.0 312 GRAPHIC RESULTANTS-DECIMALS e 7 8 9 JO IT 12 13 14 15 16 17 e 8 9 10 II 12 13 14 IS 16 17 THE DIAGRAMS ON PAGES 312, 313, AND 314 ARE PRINTED WITH THE PERMISSION OF MR. C. K. SMOLEY. ALTHOUGH DEVELOPED INDEPENDENTLY THEY ARE SIMILAR TO DIAGRAMS IN SMOLEY'S "parallel TABLES OF LOGARITHMS AND SQUARES" COPYRIGHTED IN 1912 AND 1914 GRAPHIC RESULTANTS-INCHES AND FRACTIONS 313 C C C5 / 2 THE DIAGRAMS ON PAGES 312, 313, AND 314 ARE PR IN SMOLEY' 3 A- INTED WITH THE PERMISSION OF MR. C. K. 8 " PARALLEL TABLES OF LOGARITHMS AND 5 SMOLEY. SQUARES e 7 ALTHOUGH DEVELOPED INDEPENDENTLY THEY ARE SIMILAR TO DIAGRAMS " COPYRIGHTED IN 1912 AND 1914 314 GRAPHIC RESULTANTS -FEET AND INCHES e 7 8 9 10 'II 12 13 14 15 16 ir \ 2 3 4 5 6 7 8 9 10 II 12 13 14- 15 16 17 THE DIAGRAMS ON PAGES 312, 318, AND 814 ARE PRINTED WITH THE PERMISSION OF MR. C. K. SMOLEY. ALTHOUGH DEVELOPED INDEPENDENTLY THEY ARE SIMILAR TO DIAGRAMS IN SMOLEY'S "parallel TABLES OF LOGARITHMS AND SQUARES" COPYRIGHTED IN 1912 AND 1914 315 PURLIN CONNECTIONS, LATTICE BARS, AND RODS (AMERICAN BRIDGE COMPANY) PURLIN CONNECTIONS LATTICE BARS AREAS AND WEIGHTS OF RODS :^_ Purlin Gonnecthns are uau&llj bolted ANGLE PURLINS 3x2i 8x2i 3ix3i GAGE 9 DIAM. IN. Single Lattice MAXIMUM DISTANCE i; /j 4 .# 2 =■URLi^ DEPTH Use flonge connection with web connection for 8, 9, and 10 incfi ohanneis and for 6 inch Z~Bars. Omit flange connection for smaller sections. Purlin connections are usually bolted Ordinary Connection li2i 4 2iii CHANNEL AND Z-BAR PURLIN CONNECTION ANGLE 3x2i 8-ix2i 4x3 4x3 4x8 5x3i 5x3i 2 3i 3 3 8 3i 3i Strut Connection PURLJN CON^ECTION GAGE 'ILLER! GAGE DEPTH ANGLE f 9 ilea flange connection Instead ofweb connection for t-Beams 8 Inches or over. Ordinary Connections li2i4 2ili I-BEAM PURLINS 3ix3i 4x3 4x3 5xSi 2i THICKNESS t c=40 t 2'1" I'lOi" 1'8" iSi" 1'3" I'Oi" 10" c=50t 3'7i" 2'4i" 3'1" 1'9J" l'6i" l'3r' I'Oi" Double Lattice MAXIMUM DISTANCE c' 3 3i THICKNESS t c'=eo t 3'li'' 2'9f" 2'6" 2'2i" I'lOi" I'er is" 0=75 t AREA SO. IN. .20 .81 .44 .60 .T9 .99 1.23 1.48 1.77 2.07 2.41 2.76 8.14 3.55 3.98 4.43 WEIGHT PER FT. .7 1.0 1.5 2.0 2.7 8.4 4.2 5.1 6.0 7.1 8.2 9.4 10.7 13.1 13.5 15.1 UPSET END DIAM. 4 * \ * * * 2i 3i 2i n 3 AREA AT ROOT OF THREAD 4 4 4 4 4 4 4 4 44 4i 6 5 5i Si 6 6 .80 .42 .55 .89 1.05 1.29 1.62 1.74 2.30 3.65 3.03 8.43 3.73 4.16 5.11 5.43 3'lOf 8'6V' 3'li" 2'8r 3'44" I'llf; 1'6J" For f Rivets 3| ^J " ? " 3i , 5" , " « . 2'a _ c 2l . ;•) [• i)(^ o im U TC lua E" Purlin connections are usually bolted Strut Connections :(: SPECIAL 316 BEARING PLATES, SEPARATORS. ANCHORS AND ROD CONNECTIONS DIAGRAM FOR BEARING PLATES Projection of Plate "p". in Inches GOVERNMENT ANCHOR ANCHORS (AMERICAN BRIDGE COMPANY) ANGLE ANCHOR SWEDGE BOLT BUILT-IN ANCHOR BOLTS ^^^ 3X2X2X1 WEIGHT INCLUDES NUT 2 U e"x 4"x f-s'f 2|" Wt. with ^'boII 7* jRodI 9ig, Wt,= 3* li 0'9" I'O" I'O" I'S' WEIGHT 1.3 3.3 3.1 6.1 Wtien Distance c.to c. ofboflsU less than 6"use one washer for two bolts BEAM SEPARATORS (AMERICAN BRIDGE COMPAHY) I-BEAMS 34 20 18 10 WEIGHT C.TOC 105-115 90-100 80-85 95-100 75-90 65-70 90 80-85 75 65-70 55-60 75 65-70 55-60 43-50 45-55 31^-40 35-40 25-30 80-35 21-35 18-25^ 174-20 15 14f-17i 12^ 9i-14j 7i-94 5^-7^ ii a 3i Bi DIMENSIONS 8i 6i 54 fNCL. BOLTS SKETCH i>i »-L-| ■I ■s Cored Holes for§ Bolts ;•« — w — * S) I -g Cored Holes for^'Bofla Use I Gas Pipe ^ TIE RODS AND SAG RODS (AMERICAN BRIDGE CDMPASt) 2'^toll Jto lj ^r »!/. t^^^fi.^^hr. Mai=^^ L b , ] I to IB 150 110 100 95 90 75 70 60 65 SO 45 40 35 30 25 120 110 100 90 100 90 80 70 14.7 10.80 9.84 9.28 8.83 8.33 7.86 7.33 6.81 5.93 5.38 4.87 4.40 3.94 3.44 3.00 2.39 11.85 10.82 9.95 8.82 9.84 8.82 7.86 6.82 5.86 23.1 17.2 14.6 13.3 12.2 ll.l 10.1 9.1 8.2 7.4 6.6 6.7 5.0 4.3 3.6 3.0 2.5 1.8 18.9 16.7 15.1 12.6 15.1 12.5 10.2 8.3 6.5 6j- 5f 6fr 6f Ola 6 4§ 4-t- 4-fe 4+ 4* 3i 3lJ 3+ _M_ 6i- 5j- 6 5l 5i 4 + 6i Bf Bf b4 5 4« 4i 4* 4+ 4* 3* 3i 24 5i 44 4i 4 1 1 4t 2+ 2^} 2| 2-B 2i 2i 2i 2 + 2i 2 1* If i!! 2i 9.13. 2* 2fr 2i 9-6- * IS 2i 2t 1 Ji liu 1-J u 1-S, ll li llB li 1^ li 1* If li J la Is- Ifr li li + J. 2 1 2iJ 2i 2i 2i- 2i 2ft 2j- 2 16 2 li 1* li li 1* li If ] 3i Si 3 2& 2t 2 ft 2fr 2i 2i SPLICE BARS FOR CRANE RAILS f X2V 3 X i 3 X I 2| X i 2i xi 2ix-| 24- x i 2ixi 2ixi 2i XT. 2 ni 2 x| 2 xf lixi lixA lixft lixi l^xi 3 xl 21- xl 2ix J x2-'6" x2'6" x2-'6" X 2'8" x2-'6" x2-'6" X2'6" X2'6" xl'6" xl-'6" X 1'6" xl-'6" xl'6" xl'6" xl!3" xl^3" xl-3 x2'6" x2-'6" x2-'6" X 2-6" 3x5 2|x4 2i-x4 2 X i 2 x-ft X 2'6" X 2-6" X2!6" x2-'6" xl-'6" UNIT STRESSES FOR STRUCTURAL STEEL POUNDS PER SQUARE INCH RECOMMENDED BY THE AMERICAN RAILWAY ENGINEERING ASSOCIATION 1 6,000 =AXIAL TENSION, ON NET SECTION. 16,000-70-^, WITH A MAXIMUM VALUE OF I4,000 = AXIAL COMPRESSION, ON GROSS SECTION, WHERE I IS THE LENGTH OF THE MEMBER IN INCHES AND r IS THE LEAST RADIUS OF GYRATION. 16.000 = DIRECT COMPRESSION, ON STEEL CASTINGS. 16,0O0 = BENDING, ON EXTREME FIBERS OF ROLLED SHAPES, BUILT SECTIONS, GIRDERS, AND STEEL CASTINGS-NET SECTION. 24,000= BENDING. ON EXTREME FIBERS OF PINS. I2,000=SHEARING, ON PINS AND SHOP DRIVEN RIVETS. I0,000=SHEAR1NG, ON TURNED BOLTS AND FIELD DRIVEN RIVETS. 10,000=SHEARING, ON PLATE GIRDER WEBS-GROSS SECTION. 24,000 = BEARING,FOR PINS AND SHOP DRIVEN RIVETS. 20,000 = BEARING,FOR TURNED BOLTS AND FIELD DRIVEN RIVETS. 600=BEARING ON MASONRY. 600cf=BEARING ON EXPANSION ROLLERS PER LINEAL INCH WHERE d IS THE DIAMETER OF THE ROLLER. Rails 35^ and under HOOK BOLTS FOB CONNECTION TO I-BEAMS t BOLTS FOR 25-35* RAILS A" 4 " •' 40-55" 1." . B 60.100 " RAIL CLAMPS FOR CONNECTION TO GIRDERS CI. CLAMPS WITH ECCENTRIC WASHERS FOR ADJUSTMENT. THE BOLTS ARE OF THE SAME DIAMETER AS THE RIVETS IN THE GIRDER. SPLICE BARS FOR CRANE RAILS USE TWO BARS AS SHOWN ABOVE KEEP THE RAIL SPLICES AT LEAST 2-o"fROM the JUNCTION OF GIRDERS. i BOLTS FOR 25* RAILS " 30-35 " 40-65 " " 90-100'" CRANE STOP AMERICAN BRIDGE CO. w 318 SHEAR AND MOMENT TABLE FOR COOPER'S E60 LOAOrNG. ALL LOADS, SHEARS, AND MOMENTS ARE FOR EACH RAIL. HORIZONTAL DISTANCES ARE PLOTTED TO THE SCALE 1 1N. = 16 FT. THE VALUES GIVEN IN THE TABLE ARE FOR COOPER'S CONVENTIONAL E60 LOADING. VALUES FOR COOPER'S OTHER LOADINGS MAY BE OBTAINED FROM THOSE IN THE TABLE BY PROPORTION, AS FIVE-SIXTHS FOR E50,OR TWO-THIRDS FOR E40. FIRST ENGINE SECOND ENGINE TRAIN PILOT DRIVERS TENDER PILOT DRIVERS TENDER UNIFORM LOAD WHEEL LOADS ON EACH RAIL^^ f II II II 1 30.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0 r^r^r^/-\ ij^ ^^ rs^ ij:^ ,,,„ ^-^/^^/I^^^^ ')< 'X 'J^ '^ ■ 3.0 PER LIN. FT. IN THOUSANDS OF pound! CD W^V^VVV CO W ^' ) ^^ ) (^ WW WW W W W W ,. DIST. C. TO C. WHEELS IN FEET 8 . 5 5 ^ ,, 5 , . 5 . . 6 ,. 5 8 8 , 5 6 , . 5 9 « ■' , 6 ^ ^ 6 ^ 5 . 2.1 2.2 J J J L 0.4 J L 0.2 DISTANCES TO THE CENTERSl 1.04 2,4 J OF GRAVITY OF DIFFERENT COMBINATIONS OF LOADS, MEASURED FROM THE NEAR- EST LOADS. L L 0.34 ^ J L 2.2 2.2 J L 0.1+ L 0.2 J L ?-^,- J 0.8 J L 0.2 L 3.4 J 3<^ SHEARS 5o OF THE VALUE, AND OF gu^g'ALL LOADS BETWEEN S'-Z^THESB TWO. 22g 5 to ^ § fc R! Co to to S o ■* en c^ to o lo SHEARS EACH VALUE ON RIGHT OF ANY S 426 § 411 5 381 §55/ « 321 "^.291 ES 271? 7^,252 g 232? § 213 §/ss Sg/es ^138 S 108 S 78 ^ 5S.6 •n39 THE S 408.S 5 39lf § 361? SS 331? g 301? i 271? a 252 'S>232? B 213 ? 193? 'S,t78? ^148? 'S, 118? S 88? = 58.5 to 39 39 ^ VERTICAL OF THE ZIG- ZAG LINE IS THE SUM. IN THOUSANDS OF POUNDS, OF THE LOAD DIRECTLY OVER THIS VERTICAL, OF THE LOAD OVER THE FIRST LINE AT THE RIGHT OF THE VALUE, AND OF ALL LOADS BETWEEN THESE TWO. S 387 ^372 ^342 ^312 g 282 5 252 § 232? %2I3 ? 193? !S 174 S'59 ^129 S 99 S 69 ^^39 39 to 58? § 367.B § 352.1 R 322? g 292? § 262.^ n232p 5 213 :? 193? 5 174 fS IS4? ^139? ZI09.S 5 79? o> 49,5 39 •n 5S.5:; 78 S g 348 K 333 §503 5273 g 243 •^213 ^ 193? %I74 B 154? S I3S SI20 S90 •o 60 49? o> 69 Z fiS.5° 108 S Z 318 § 303 S273 ^243 B 213 g 183 S; 163? ^ 144 ^ 124? S 105 SSO w 60 60k, 79.5 3: 99Z //s.=S 138 § 2 288 ^273 ^243 B2/3 5 183 'Si 153 % 133? ^ 114 Si 94? 2 75 ^60 60^ 90S /09.5 S 129^ /4S.50 168 S8 S 2S8 ^243 B 213 ^ 183 5 153 ^ 123 Si 103? 5; 84 S 64? a, 45 60 w sog 120'ii /39.5 5; 159?^ 178?^ 198 o g 228 § 213 5 183 ^153 ^ 123 ^ 93 a 73? 2 54 CO 34? 45 CO 752 105-^ 135^ 154? S- '7'(f5 W3.s^ 213 « MOMENTS EACH VERTICAL OF THE ZIG- ZAG LINE CONTAINS THE POINT OF MOMENTS FOR ALL VALUES ON THE LEFT OF THIS LINE. EACH VALUE IS THE MOMENT, IN THOUSANDS OF POUND-FEET. OF ALL LOADS FROM THE POINT OF MOHENTSTO AND INCLUDINE THE LOAD OVER THE FIRST LINE AT THE LEFT OF THE VALUE. 24,500 22,900 19,900 17,000 14,300 11,700 10,200 8.790 7,500 6,310 6,5/0 4,160 2,960 1,910 1,010 605 293 97.5 MOMENTS 22,400 20,900 18,000 15,200 12,700 10,200 8,830 7,530 6,340 5,240 4,520 ' 3,320 2,270 1,370 624 312 97? , EACH VERTICAL 20,400 18,900 16,200 13,600 11,200 8,880 7,570 6,360 5,270 4,280 3,630 2,580 1,680 ■932 332 117 97? CONTAINS THE POINT OF MOMENTS FOR ALL VALUES ON THE RIGHT OF THIS LINE. EACH VALUE IS THE MOMENT, IN THOUSANDS OF POUND-FEET, OF ALL LOADS FROM THE POINT OF MOMENTS TO AND INCLUDING THE LOAD OVER THE FIRST LINE 18,100 16,700 14, too 11,700 9,470 7,370 6,180 5,090 4,110 3,230 2,680 f,8IO 1,090 518 97? 117 332 16,200 14,900 12,500 10,300 8,150 6,200 5,110 4,120 3,240 2,460 1,980 1,260 690 270 97? 312 624 13,100 11,900 9,780 7,800 5,970 4,290 3,370 2,550 1,850 1,250 900 450 160 176 449 839 1,330 11,500 10,400 8,410 6,680 4,900 3,370 2,550 1,830 1,230 720 450 150 ISO 423 794 1,280 1,870 10,100 9,030 7,200 5,520 3,990 2,6 m 1,890 1,260 765 345 160 ISO 460 821 1,290 1,870 2,560 8,770 7,810 6,130 4,600 3,220 1,990 1,370 842 432 120 150 450 900 1,370 1,930 2,620 3,400 6,950 6,110 4,670 3,380 2,240 1,250 780 410 166 240 630 1,170 1,860 2,480 3,210 4,040 4,980 VALUE. PROPERTIES OF WOODEN RECTANGULAR BEAMS 319 WEIGH1 PER FOOT OF LENGTH (4 LBS. PER FT B. M.) a z o 0. §SSE2 O OO CO M* CO ^ CO -o so b- b- OO so lO Tj* CO cq OS -efi Cl oa ssss CO cq o CO ss ^ ^ « O 00 t- S2S 00 t« lO (M OO CO L-s tP Irt ^ CO BOARD MEAS- URE PER FOOT OF LENGTH t}S U. CQ o o o o o o o o lO 00 o CO t^ O CO t— O CO O CO 1-^ CO O t^ CO o b- lO CS CO o o o o o o »o o CO l>- o co lo —( r- CO o t- O b~ CO O O L-D CO O eo cq 1-H 1-1 1-1 CO O I>- 1-i i-I O SS S2 »0 (N CS CO ■* CO CO ■—1 CO SO CO o C-» i-l 1-H i-t i-l 00 »0 ■-* CO C-i O tH ^ OS I^ •* CO cq cq ri o OO o ■* eo eq cq OO CO lO CO c] ei 1-1 lo Tt* ca (M 1-1 1-1 AREA OF CROSS SEC- TION IJJW u ?S §§ S 2 CO (N CS| (M §3s^ sss? O -* C^ O OO S ?3 3 S S^ SSSSS3 CO CO O tM -^ OS to -i^ 1-) M CO cq i-O CO lO -i^t CO £N ||gE2 03 CO O I* Tf< CO CO cq sss S^SS S^g? sss CD 1*1 00 »0 CM CO CM 1-1 1-1 1-1 CO eq 00 ^_1U1 5 < N Oz^; iii I o z sass X X X X aaaa aaaa XXXX aaa XXX to « (D (0 (0 (O CO XXXXX "* <* ^ XXX <# C3 C4 SECTION MODU- LUS s ul X o z istg 00 CO OO r~ Tj< CO 0 ■* CO t^ lO -..H CO g 2 3 CO OO O CO •o CO CO cq O M CO t— lO CO CO CSS I:}* CM i-i »-l OO OO CO O OO CM •-< 1-1 i-H t- in CO ACTUAL SIZE ¥ SCANT ul X o z r4|n hM r4n r«t t~ !>■ t- t- xxxx r^ lo CO ^ XXXX HM M)n *«* H« OS t- »o eo XXX lO W3 »0 .lo ^ XXXXX »0 CO ^ c? K" H« Hn H» mn Hn »o w3 >ra »« »n XXXXX CO CO CO CO CO XXXXX F*» F-W Hei --l CS t~ W3 Hn H« Hn r4n CO CO CO CO XXXX mn T*» cq i-i:m CO (M 1-1 Hln rim rW HM rH 1-1 1-4 1-4 XXXX Hjc Hn H« Hw XXXX r*» Hc» mw a> a XXX Hn Hn ntn CS t^ lO .4« Htn HlPi Htn XXXX ,*! HN ■*• W t- I^ XXX FL »o CO Hn i-On hM XXX F-lM CM uln lO lO »o iS" iO XXXXX- MIN F^n r4r< ?q r«4 lO CO Pq ^ r«< hM Htn CO CO CO XXX CO Cfl 11 SECTION MODU- LUS s Ul X o z SiSi Tt* CO « l-H to -^ CO 1-4 OO M In P S 2 (O to -5 CO CO - "■* 1-1 00 CD -H CO lO to ■* CO CM sss sss O OS -# 1-1 OS CO 1-1 1-1 1—1 OO eo •*< ACTUAL SIZE t" SCANT ul X o z t^ t>. t* t- XX XX t- lO CO 1-1 MW |«-> U^ HJB XXXX O? 1?^ S" m" XXX srs'2? llo ira WHO wKe hKo CO tH CI r- lO CO CO CO CO XXXX hHo WHO H«> uHto CO CT Cq »-« ^ ^ ^ ^ XXXX ■Am loM n)a xxa XXXX ■nia K>M tAd iB|4D CO OJ CM 1-1 grsrgr XXX OS i>. to Oi a> Oi a> XXXX C? C? M '^ •ma «)» wKo t~ 1^ t^ XXX nia mla irfa b- lO CO XXX C^ M T-l XXXXX XXX SECTION MODU- LUS s eft Ul X o z 1 SKS 2SSS; lO ■«tt< CO i-< 5Sg eo lo ■**< -«f CO CO W ■«* CO « S3 3 S " '- §I§|2 Sfepg M . t^ t^ t^ XXXX ST 3? SI?::!: Mt« MM HN nH I^ t~ t^ t^ XXXX OS 1^- «0 CO »9|« nh* M« t^ t^ l^ XXX nt* i-«^ B|» cq cq T-. »0 U? S? lO U5 XXXXX nl-x nl-n nH n|-« «j« •O CO 1-1 o t- m* nW nM nh* MM ui US uz ta tn XXXXX rHi nl-a nj-« rt« nN lO CO M M •-( rfr* nl-* MM MHl nW CO CO CO CO CO XXXXX nl-# nl-« m* «l-» nHi CO 1-1 C73 1>- lO CO CO CO CO XXXX nW «M Wi> «1* CO ca M i-( XXXX nt« «)* n'.5 nf« XXXX K a- ST s XXX c» I- lb p4« M-« *9t« nl4 O C» C?> OS XXXX r'-« ml* ■-'* •«■• CO (TJ W 1-1 XXX nW n|< «1« I- O CO nM «h* <«M 1^ t, r- XXX «|4 rti* nW c Hoi HcB i>. i>, r^ r- XXXX H OS t>- »0 CO M" H* M« r- t^ 1^- XXX H« H" H" i-No H» lO »<:> >o o lo XXXXX H« H« r-M) H«> M* ira CO .-< C» t^ He H« Ha r-|B Ha lo u3 m ^o to XXXXX H« H H« t-Wt CO .-1 O t^ l-O HB Ha HW H«> CO (N M r-l Ha Hm H OJ o> XXX 1-kD Ha r-is CI b- »o >-|a Ha Ha i-to 03 OS OS OS XXXX Ha t-So nhe H« CO CM Oq 1-1 I^ IT- l>- XXX t- O CO t-, c^ t^ XXX >-|« Ha Ha H« Ha lO lO lO i-O ifl XXXXX lO CO ST eq* i-i t-» H» Hm CO CO CO XXX Ha H" H* CO CM 1-1 XXXX t-» »-|a Ha Ha -^ CJ t^ »o XXXX CO m'STCh SECTION MODU- LUS s Ul X o z N -MJ to QO 1— SO m -^ OS oo t- S »0 Ttl CO C^ sss CO t^ C4 ■>• •-• so to S 9 CO CD r-l 00 t~- iO lo r^ ci_iu^iiix O Z i II < _JUJ JIUJ 1200 (1- 1300 (1- 1100 (1- 1000 (1- 1100 (1- 800 (1- 1000 (1- 1200 (1- 900 (1- 1100 (1- 900 (1- 1300 (1- ■l/Wd ■I /mi ■i/m ■i/m ■i/mdi ■i/m ■i/md ■i/m ■i/m ■i/md' ■i/m ■1/60 i 1500 (1- 1630 (1- 1380 (1- 1250 (1- 1380 (1- 1000 (1- 1250 (1- 1500 (1- 1130 a- 1380 (1- 1130 (1- 1630 fl- ■l/mi ■i/md ■l/BOd ■1/60 d ■1/60 d ■1/60 ■1/60 d ■1/60 ■l/Wd. ■1/60 ■1/60 1 ■1/60 i 1800 (1- 1960 (1- 1650 (1- 1500 (1- 1630 (1- 1200 (1- 1500 (1- ISOO (1- 1350 (1- 1650 (1- 1350 (1- 1950(1- 7/00 iJ 1/60 d 1/&M 1/60 d' ■1/60 ■1/60 d ■1/60 d ■1/60 d ■1/60 d ■1/60 ■1/60 d' ■1/60 d *USE THE VALUES OF "E" GIVEN IN THE BOTTOM TABLE FO OF BEAMS UNDER QUIESCENT OR LONG CONTINUED LOADS. UPPER TABLES WHEN THE LOADS ARE SUDDENLY APPLIED. R FINDING THE DEFLECTION USE THE VALUES IN THE MOMENTS OF INERTIA OF RECTANGLES INCHES' muTRAL MOMENTS OF INERTIA OF WIDER RECTANGLES MAY BE FOUND BY DIRECT PROPORTION t5 uuz WIDTH OF RECTANGLE (PARALLEL TO NEUTRAL AXIS) IN INCHES 0.2 0.6 1.3 2.6 4.5 7.1 10.7 15.2 20.8 27.7 36.0 45.8 57.2 70.3 16 85.3 106.7 17 102.4 127.9 18 121.5 151.9 19 143.9 178.6 20 166.7 208.3 21 192.9 241.2 22 221.8 277.3 23 253.6 316.8 21 288.0 360.0 25 325.6 406.9 366.2 410.1 457.3 608.1 562.5 682.7 818.8 972.0 1143 1333 1544 1775 2028 2304 2604 2929 3281 3659 4065 4500 0.2 0.7 1.7 3.3 6.6 8.9 13.3 19.0 26.0 34.7 46.0 57.2 71.5 87.9 457.7 612.6 671.7 636.1 703.1 853.3 1024 1215 1429 1667 1929 2218 2535 2880 3255 3662 4101 4573 5081 5625 0.8 2.0 3.9 6.8 10.7 16.0 22.8 31.3 41.6 54.0 68.7 85.8 105.6 128.0 153.6 182.3 214.3 250.0 289.4 332.8 380.2 432.0 488. 3 549.3 615.1 686.0 762.2 843.8 1024 1228 1458 1715 2000 2315 2662 3042 3456 3906 4394 4921 5488 6097 6760 0.3 1.0 2.3 4.6 7.9 12 18.7 26.6 36.6 48.5 63.0 80.1 100.0 123.1 149.3 179.1 212.6 250.1 291.7 337.6 388.2 443.6 604.0 669.7 640.8 717.6 800.3 889.2 084.4 1195 1433 1701 2001 2333 2701 3106 3649 4032 4557 5126 6741 6403 7113 7875 1.1 2 5.2 9.0 14.3 21.3 30.4 41 65.6 72.0 91.5 114.3 140.6 170. 204. 243.0 285.8 333.3 385. 9 443.7 607.0 676.0 651.0 732.3 820.1 914.7 1016 1125 1365 1638 1944 2286 2667 3087 3649 4056 4608 5208 6859 6561 7317 8130 9000 0.4 1.3 3.0 6.9 10.1 16.1 24.0 34.2 46.9 62.4 81.0 103.0 128.6 158.2 192.0 230.3 273.4 321.6 375.0 434.1 499.1 670.3 648.0 732.4 823.! 922.1 1,029 1,143 1,266 1,536 1,842 2,187 2,572 3,000 3,473 3,993 4,563 6,184 6,859 6,591 7,381 8,232 9,146 10,130 0.4 1.4 3.3 6.5 11.3 17.9 26.7 38.0 52.1 69.3 90.0 114.4 142.9 175.8 213.3 255.9 303.8 367.2 416.7 482.3 554.6 633.7 720.0 813.8 915.4 1,025 1,143 1,270 1,406 1,707 2,047 2,430 2,868 3,333 3,859 4,437 5,070 6,760 6,510 7,323 8,201 9,147 10,160 11,260 H 0.5 1 3.7 7.2 12.4 19.7 29.3 41.8 57.3 76.3 99.0 125.9 157.2 193.4 234.7 281.5 334.1 393.0 458.3 530.6 610.0 697.1 792.0 895.2 1,007 1,128 1,268 1,397 1,547 1,877 2,262 2,673 3,144 3,667 4,245 4,880 6,577 6,336 7,161 8,066 9,021 10,060 11,180 12,380 0.6 1.7 4.0 7.8 13.6 21.4 32.0 45.6 62.5 83.2 108.0 137.3 171.5 210.9 256.0 307.1 364.5 428 500.0 678.8 665.6 760.4 864.0 976.6 1,099 1,230 1,372 1,524 1,688 2,048 2,457 2,916 3,430 4,000 4,631 5,324 6,084 6,912 7,813 8,788 9,842 10,980 12,190 13,500 0.5 1 8 4.3 8.5 14.6 23.2 34.7 49.4' 67.7 90.1 117.0 148.8 185.8 228.5 277.3 332.7 394.9 464.4 641.7 627.0 721.0 823.8 936.0 1,058 1,190 1,333 1,486 1,651 1,828 2,219 2,661 3,159 3,715 4,333 5,016 5,768 6,590 7,488 8,464 9,520 10,660 11,890 13,210 14,620 0.6 2.0 4.7 9.1 15.8 25.0 37.3 63.2 72.9 97.1 126.0 160.2 200.1 246.1 298.7 358.2 425.3 500.1 683.3 675.3 776.4 887.2 1,008 1,139 1,282 1,435 1,601 1,778 1,969 2,389 2,866 3,402 4,001 4,667 5,402 6,211 7,097 8,064 9,115 10,250 11,480 12,810 14,230 15,750 if 0.6 2.1 5.0 9.8 16.9 26.8 40.0 57.0 78.1 104.0 135.0 171.6 214.4 263.7 320.0 383.8 465.6 535.9 625.0 723.5 831.9 960.6 1,080 1,221 1,373 1,538 1,715 1,905 2,109 2,560 3,071 3,645 4,287 5,000 5,788 6,665 7,604 8.640 9,766 10,990 12,300 13,720 15,240 16,880 0.7 2.3 5.3 10.4 18.0 28.6 42.7 60.1 83.; 110.9 144.0 183.1 228.7 281.3 341.3 409.4 486.0 571.6 666.7 771.8 887.3 1,014 1,152 1,302 1,465 1,640 1,829 2,032 2,250 2,731 3,275 3,888 4,573 5,333 6,174 7,099 8,111 9,216 10,420 11,720 13,120 14,630 16,260 18,000 AREAS AND WEIGHTS OF PLATES 321 AREAS OF PLATES IN SQUARE INCHES WEIGHTS OF PLATES IN POUNDS PER LINEAL FOOT* | WIOTHi IN INS. THICKNESS IN INCHES WIDTH IN INS, THICKNESS IN INCHES | i A 1 A i A 1 tt 1 1 ts i a 1 lA ij lA 1.1 1 lA 111 lA 1^ lA If 114 ij m ll m 2 T A 1 Al 4 A 5 8 a i 1 if 1 f M 1 3 0.75 0.94 1.13 1.31 1.50 1.69 1.88 2.06 2.25 2.44 2.63 2.81 3.00 3.19 3,38 3,56 3.75 3.94 4.13 4.31 4,50 4.69 4.88 5,06 5.25 5.44 6.63 6.81 6.00 1 0,9 1.1 1.3 1.5 1,7 1.9 2,1 2.3 2.6 2.8 3.0 3.2 3.4 4 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.76 3.00 3.25 3.50 3.75 4.00 4.25 4,50 4,76 5.00 5.25 5.60 5.75 6,00 6.25 6.50 6.75 7,00 7.25 7.50 7,76 8.00 2 1,7 2.1 2.6 3,0 3,4 3.8 4,3 4.7 6.1 6.5 60 6.4 6.8 5 1.25 1.56 1.88 2.19 2.50 2.81 3.13 3.44 3.75 4.06 4.38 4.69 5.00 5.31 5,63 5,94 6.25 6.56 6.88 7.19 7,50 7.81 8.13 8.44 8.75 9.06 9,38 9,69 10,00 3 2.6 3.2 3.8 4.5 5,1 5.7 6.4 7.0 7.7 8.3 8.9 9.6 10.2 6 l.SO 1.8S 2.26 2.63 3.00 3.38 3.75 4.13 4.50 4.88 5.25 5.63 6.00 6.38 6.75 7,13 7.50 7.88 8.26 8.63 9,00 9.38 9.75 10.13 10.50 10.88 11.25 11,63 12,00 4 3.4 4.3 5,1 60 68 7.7 8.5 9.4 10.2 11.1 11.9 12.8 13.6 7 1.75 2.19 2.63 3.06 3.50 3.94 4.38 4.81 5.25 B.69 6.13 6.56 7.00 7.44 7.88 8.31 8,75 9.19 9.63 10,06 10,60 10.94 11.38 11.81 2.25 12.69 13.13 13,66 14,00 6 4.3 6.3 6,4 7.4 8.5 9.6 10.6 11.7 12.8 13.8 14.9 15.9 17.0 8 2.00 2.60 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8,50 9.00 9.60 10,00 10.60 11.00 11,50 12,00 12.60 13.00 13,60 14.00 14.60 16.00 15.50 16,00 6 5.1 6.4 7,7 8.9 10.2 11.5 12.8 14.0 16.3 16.6 17.9 19.1 20.4 9 2.25 2.81 3.38 3.94 4.50 5.06 5.63 6.19 6.75 7.31 7.88 8,44 9.00 9,56 10,13 0.69 11,25 11.81 12.38 2,94 13,50 14,06 14.63 15,19 16.75 16.31 16.88 17,44 18,00 7 6.0 7.4 8,9 0.4 11.9 13.4 14.9 16.4 17.9 19.3 20.8 22.3 23,8 10 2.50 3.13 3.75 4.38 5.00 5.63 6.25 6.88 7.50 8.13 8.75 9.38 10.00 10,63 11,26 1.88 12.50 13.13 13.76 14,38 16.00 15.63 16.25 16,88 17.50 18.13 18,76 19.38 20,00 8 6.8 8.5 10,2 11.9 13.6 15.3 17.0 18.7 20.4 22.1 23.8 25.5 27.2 lOi 2.56 3.20 3.84 4.48 5.13 5.77 6.41 7.05 7.69 8.33 8.97 9.61 10.25 10,89 11,.53 2.17 12.81 13.45 14.09 14,73 15.38 16.02 16,66 17,30 17.94 18.58 19,22 19.86 20,50 9 7.7 9.6 11,6 13,4 15.3 17,2 19.1 21.0 23.0 24,9 26.8 28.7 30.6 10 2.63 3.28 3.94 4.50 6.26 5.91 0.66 7.22 7.88 8.53 9.10 0.84 10.50 11.16 11,81 12.47 13.13 13.78 14.44 15,09 15.75 16.41 17,06 17.72 18,38 19.03 19,69 20.34 21,00 10 8,5 10.6 12,8 14,9 17,0 19,1 21.3 23.4 25.5 27.6 29.8 31.9 34.0 10 2.69 3.36 4.03 4.70 5.38 6.06 6.72 7.39 8.06 8.74 9.41 10,08 10.75 11.42 12,09 12.77 13.44 14.11 14.78 15.45 16.13 16,80 17,47 18,14 18.81 19.48 20,16 20.83 21,60 11 9,4 11.7 14,0 16,4 18,7 21,0 23.4 25.7 28.1 30.4 32.7 35.1 37.4 11 2.75 3.44 4.13 4.81 5.60 6.19 6.88 7.66 8.25 8.94 9.03 10,31 11.00 11.69 12.38 13.06 13.75 14.44 16.13 15,81 16.50 17,19 17,88 18.56 19.26 19.94 20,63 21.31 22.00 12 10,2 12.8 16.3 17,9 20.4 23,0 25.5 28.1 30.6 33.2 35.7 38.3 40.8 in 2.81 3.52 4.22 4.92 5.63 6.33 7.03 7.73 8.44 9.14 9.84 10,65 11.25 11,95 12.66 13,36 14.06 14.77 15.47 16,17 16.88 17,58 18,28 18,98 19.69 20.39 21,09 21,80 22,50 13 11,1 13.8 16.6 19,3 22.1 24,9 27.6 30.4 33.2 35.9 38.7 41.4 44.2 2.88 3.59 4.31 5.03 5.75 6.47 7.19 7.91 8,03 9.34 10.06 10.78 11.60 12,22 12.94 13,66 14.38 15.09 15.81 16,63 17.25 17,97 18.69 19,41 20.13 20.84 21.56 22,28 23.00 14 11,9 14.9 17.9 20,8 23.8 26,8 29.7 32.7 35.7 38.7 41.7 44.6 47.6 Hi 2.94 3.67 4.41 5.14 6.88 0.61 7.34 8.08 8.81 9.55 10.28 11,02 11.75 12,48 13.22 13.95 14.69 16.42 16.16 16,80 17.63 18,36 10.09 19,83 20.56 21.30 22.03 22.77 23.50 16 12,8 15.9 19.1 22.3 25.6 28,7 31.9 35,1 38.3 41.4 44.6 47.8 61.0 12 3.00 3.75 4.50 6.25 6.00 6.75 7.50 8.25 9.00 9.75 10.50 11.25 12.00 12,76 13.60 14.25 15.00 15.75 16.60 17.26 18.00 18.75 19.50 20,25 21.00 21.76 22.50 23.26 24.00 16 13.6 17.0 20.4 23.8 27.2 30,6 34.0 37.4 40.8 44.2 47.6 51.0 54.4 12i 3.06 3.83 4.59 5.36 6.13 6.89 7.66 8.42 9.19 9.95 10.72 11.48 12.26 13,02 13.78 14.65 15.31 16.08 16.84 17.61 18.38 19.14 19.91 20,67 21.44 22,20 22.97 23.73 24.60 17 14.5 18.1 21.7 25.3 28.9 32.5 36.1 39.7 43.4 47.0 50.6 54.2 67.8 12 12 3.13 3.01 4.69 5.47 6.25 7.03 7.81 8.59 9.38 10.16 10.94 11.72 12.50 13.28 14.06 14.84 15.63 16.41 17.19 17.97 18.76 19.63 20.31 21,09 21.88 22,66 23.44 24.22 25.00 18 15.3 19.1 23,0 26.8 30,6 34.4 38.3 42.1 45.9 49.7 53.6 57.4 61.2 3.10 3.98 4.78 5.58 6.38 7.17 7.97 8.77 9.56 10.36 11.16 11.95 12.75 13.55 14.34 15.14 15.94 16.73 17.53 18.33 19.13 19.92 20.72 21,62 22.31 23,11 23.91 24.70 25,50 19 16.2 20,2 24,2 28.3 32,3 36.3 40.4 44.4 48.5 52.5 56.6 60.6 64.6 13 3.25 4.06 4.88 5.69 6.50 7.31 8.13 8.94 9.75 10.66 11.38 12.19 13.00 13.81 14.63 15.44 16.25 17.06 17.88 18.69 19.50 20.31 21.13 21.94 22.75 23.66 24.38 25.19 26,00 20 17.0 21,3 25,5 29.8 34,0 38.3 42.5 46.8 51.0 55.3 59.5 63.8 68.0| 13} 13 3.31 4.U 4.97 5.80 6.63 7.45 8.28 9.11 9.94 10.77 11.50 12.42 13.26 14.08 14.91 15.73 16.56 17,39 18.22 19.05 19.88 20.70 21.53 22.36 23.19 24,02 24.84 25.67 26.50 21 17.9 22,3 26,8 31,2 35.7 40,2 .44.6 49.1 63.6 58.0 62.5 66.0 71.4 3.3S 4.22 5.06 5.91 6.75 7.59 8.44 9.28 10.13 10.97 11.81 12.66 13.50 14,34 15.19 16.03 16.88 17,72 18.56 19.41 20.25 21.09 21.94 22.78 23.63 21,47 25.31 26.16 27.00 22 18.7 23,4 28,1 32,7 37.4 42,1 46.8 51,4 66.1 60.8 65.6 70.1 74.8 13 3.44 4.30 5.16 6.02 6.88 7.73 8.59 9.45 10.31 11.17 12.03 12.89 13.75 14,61 15.47 16.33 17.19 18,05 18.91 19.77 20.63 21.48 22.34 23,20 24.06 24,92 25.78 26.64 27.50 23 20.0 24.4 29,3 34.2 39.1 44,0 48.9 63,8 58.7 63.6 68.4 73.3 78.2 U 3.60 4.38 6.25 6.13 7.00 7.88 8.75 9.63 10.50 11.38 12.25 13.13 14.00 14.88 16.75 16.63 17.50 18.38 19.25 20.13 21.00 21.88 22.75 23,63 24.50 25,38 26.25 27.13 28.00 24 20.4 25.5 30.6 35.7 40.8 45,9 51.0 66,1 61.2 66.3 71.4 76.5 81.8 m 3.56 4.45 5.34 6.23 7.13 8.02 8.91 9.80 10.69 11.68 12.47 13.36 14.25 15.14 16.03 16.92 17.81 18.70 19.59 20.48 21.38 22.27 23.16 24.06 24.94 25,83 26.72 27.61 28.50 25 21.3 26,6 31.9 37.2 42.5 47.8 53.1 58,4 63.8 69.1 74.4 79.7 85.0 U 3.63 4.53 5.44 6.34 7.25 8.16 9.06 9.97 10.88 11. 7S 12.69 13.59 14.60 15.41 16.31 17.22 18.13 19.03 19.94 20.84 21.76 22.66 23.56 24,47 25.38 26,28 27.18 28.09 23.00 26 22,1 27,6 33.2 38.7 44.2 49.7 66.3 60,8 66.3 71.8 77.4 82.9 88.4 U 3.69 4.61 5.53 6.45 7.38 8.30 9.22 10.14 11.06 11.98 12,91 13.83 14,76 15.67 16.50 17.52 18.44 19,36 20.28 21.20 22,13 23.06 23,97 24,89 26.81 20.73 27,66 28.68 29,50 27 23.0 28,7 34.4 40,2 45.9 51.6 67.4 03,1 68.9 74.6 80.3 86.1 91.8 16 3.75 4.69 6.63 6.56 7.50 8.44 9.38 10.31 11.25 12.1c 13.13 14.06 15.00 16.94 16.88 17.81 18.75 19,69 20.63 21.56 22,50 23.44 24,38 26,31 26.25 27.19 28.13 29.06 30.00 28 23,8 29,8 35.7 41,7 47.6 53.6 59.5 65,6 71.4 77.4 83.3 89.3 95.2 15 3.81 4.77 5.72 6.67 7.63 8.58 9.53 10.48 11.44 12.39 13.34 14.30 15.26 16,20 17.16 18,11 19.06 20,02 20.97 21,92 22,88 23.83 24,78 25,73 20.69 27.64 28.59 29.65 30.50 29 24,7 30,8 37.0 43,1 49.3 65.6 61.6 67.8 74.0 80.1 86.3 92.4 98.6 16 3.88 4.84 5.81 6.78 7.75 8.72 9.69 10.66 11.63 12.59 13,56 14.53 16,50 10.47 17.44 18.41 19.38 20,34 21,31 22,28 23,25 24.22 25.19 26,16 27.13 28.09 29.06 30.03 31.00 30 25,6 31,9 38.3 44.6 51.0 57,4 63.8 70.1 76.6 82.9 89.3 95.6 102.0 16 3.94 4.92 5.91 6.89 7.88 8.80 9.84 10.83 U.81 12.80 13.78 14,77 15,76 1C,73 17.72 18.70 19.69 20.67 21,66 22.64 23,63 24.61 25.59 26,58 27.56 28,55 29.53 30,52 31.50 31 26,4 32,9 39.5 46.1 52.7 59,3 65.9 72.5 79.1 85.6 92.2 98.8 105.4 16 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17,00 18.00 19.00 20.00 21.00 22.00 23.00 24,00 25.00 26.00 27.0028.00 29,00 30.00 31.00 32.00 32 27,2 34,0 40.8 47.6 54.4 61,2 68.0 74.8 81.6 88.4 95.2 102.0 108.8 let 4.06 5.08 6.09 7.11 8.13 9.14 10.16 11.17 12.19 13.20 14.22 16,23 16,26 17.27 18.28 19.30 20.31 21.33 22.34 23.36 24,38 25.3926.41 27.42 28.44 29,45 30.47 31.48 32.50 33 28,1 35,1 42.1 49,1 56.1 63,1 70.1 77.1 84.2 91.2 98.2 105.2 112.2 4.13 5.16 6.19 7.22 8.25 9.28 10.31 11.34 12.38 13.41 14.44 15,47 16,60 17,53 18,60 19.59 20.63 21.66 22.69 23.72 24,75 25.78 26.81 27.84 28.88 23.91 3U.94 31.97 33.00 34 28,9 36,1 43.4 50,6 67.8 66.0 72.3 79.5 86.7 93.9 101.2 108.4 115.6 16^ 4.19 5.23 6.28 7.33 8.38 9.42 10.47 11.52 12.56 13.61 14,66 16,70 10,75 17,80 18,84 19.89 20.94 21.98 23.03 24.08 25,13 26.1727.22 28.27 29.31 30,36 31.41 32.45 33.50 35 29,8 37.2 44.6 52,1 59.5 66,9 74.4 81.8 89.3 06.7 104.1 111.6 119.0 17 4.25 5.31 6.38 7.44 8.50 9.56 10.63 11.69 12.76 13.81 14.88 15.94 17.00 18,00 19.13 20.19 21.25 22.31 23.38 24.44 25,50 26.56 27.03 28.6929.76 30,81 31.88 32.94 34.00 36 30.638,3 46.9 53,6 61.2 68.9 76.5 84.2 91.8 99.5 107.1 114,8 122.4 18 4.50 5.63 6.75 7.88 9.00 10.13 11.25 12.38 13.50 14.63 15.76 16.88 18.00 19,13 20,25 21,38 2^.50 23.63 24.75 25.88l27.00l28.i3 29.25 30.38 31.60 32,63 33.75 34,88 36.00 37 31.5 39.3 47.2 55,0 62.9 70.8 78.6 86.5 94.4 102.2 110.1 117.9 125.8 19 4.75 5.94 7.13 8.31 9.50 10.69 11.88 13.00 14.26 15.44 16.63 17.81 19.00 20.19 21,38 22,56 23.76 24.94 26.13 27.31 28.50 29.69 30.88 32.06 33.25 34,44 35.63 36.81 38.00 38 32,3 10.4 48.5 50,5 64.6 72.7 80.8 88.8 06.9 IOj.O 113.1 121.1 129.2 20 21 5.00 5.25 6.25 6.56 7.60 7.88 8.25 8.63 9.00 8.75 9.19 9.63 10.06 10.60 10.00 10.60 11.00 11.50 12.00 11.25 11.81 12.38 12.94 13.50 12.50 13.13 13.75 14.38 15.00 13.70 14.44 15.13 15.81 16.50 15.00 15.76 16.50 17.26 18.00 16.26 17.06 17.88 18.69 19.50 17.50 18.38 19.25 20,13 21,00 18.75 19.69 20.63 21.66 22.60 20.00 21.00 22.00 23.00 24.00 21,25 22,31 23,38 24,44 25.50 22,50 23,63 24,75 25.88 27.00 23,75 25.00 26.25 27.60 28.75I3O.OOI3I.25 32..50 33.7535,00 30.25 37.50 38.75 40.00 39 40 41 42 43 33,2 34.0 34 9 41.4 42.5 43 6 49.7 51.0 52.3 53.6 54.8 58.0 59.5 61.0 62.6 64.0 66.3 68.0 69 7 74.6 76.5 78 4 82.9 85.0 87 1 91.2 93.6 95 8 99.5 102.0 104.6 107.1 109.7 107.7 110.5 113 3 116.0 119.0 122 124,3 127.5 130 7 132.6 136.0 139 4 AREAS OF PLATES IN SQUARE INCHES 22 23 24 5.50 5.75 6.00 6.88 7.19 7.50 65 16.50 20.63 s A i ft i s {i i if i n 1 35',7 36,6 44! 6 45.7 7l!4 73.1 80!3 82.2 89!3 91.4 98!2 100.5 nolo 118.8 125!o 127.9 I33!9 137,1 142;8 146.2 24.75 28.88 33.00 37.13 41.25 45.38 49.60 53.63 67.76 61.88 66.00 26 6.25 7.81 9.38 10.94 12.50 14.06 15.63 17.19 18.75 20.31 21,88 23.44 25.00 26.56 28.12 72 18.00 22.50 27.00 31.60 36.00 40.60 45.00 49.50 64.00 58.50 63.00 67.50 72.00 44 37.4 46.8 56.1 65.5 74.8 84.2 93.5 102.9 112.2 121.6 130.9 140,3 149.6 26 27 28 29 6.50 6.7S 8.13 9.75 11.38 13.00 14.63 16.25 17.88 19.50 21.13 22,75 24.38 26.00 27.63 29.25 18 19.50 24,38 29.26 34,13 39,00 43.88 48.76 53.63 68.50 63.38 68.25 73,13 78,00 45 38.3 47.8 57,4 66.9 76.6 86.1 95.6 105.2 114.8 124.3 133.9 143,4 153.0 8*44 io!i3 11.81 13! 50 15.19 16.88 18.66 2 J. 25 21.94 23,63 26.31 27.00 28.69 30.38 84 21.00 26,26 31.60 36,75 42,00 47.25 62.50 57.75 63.00 68.25 73.60 78,76 84,00 46 39.1 48,9 68,7 68.4 78.2 88,0 97.8 107.5 117.3 127.1 136.9 1466 156.4 7!oc s!7£ 10.50 12.25 14.00 15.76 17.50 19.26 21.00 22.76 24,50 26.26 28.00 29.75 31.50 90 22.50 28.13 33.75 39.38 45.00 50.63 66.25 61.88 67.50 73.13 78.75 84.38 90.00 47 40.0 49,9 69,9 69.9 79.9 89,9 99.9 109.9 119.9 129.8 139.8 149.8 159.8 7.2£ 9.06 10.88 12.69 14.50 16.31 18.13 19.94 21.75 23.56 25,38 27.1C 29.00 30.81 32.63 96 24.00 30.00 36.00 42.00 48.00 54.00 60.00 66.00 72.00 78.00 84.00 90.00 96,00 48 40.8|51.0 61,2 71.4 81.6 91,8 102.0 112.2 122.4 132.6 142.8 153.0 163.2 30 32 34 36 38 40 42 44 7.50 8.00 8.50 9.00 9.50 10.00 10.50 11.00 9.38 10.00 10.63 11.25 11.88 12.50 13.13 13.75 11.25 12.00 12.75 13.50 14.25 15.00 15.75 16.50 13.13 14.00 14.88 15.75 16.63 17.60 18.38 19.25 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 10.88 18.00 10.13 20.25 21.38 22.50 23.63 21.75 18.75 20.00 21.2a 22.50 23.75 26.00 26.25 27.60 20.63 22.00 23.38 24.75 26.13 27.50 28.88 30.25 22.50 24.00 25.50 27.00 28.50 30.00 31.50 33.00 24.38 26.00 27.63 29.25 30.88 32.60 34.13 35.75 26,25 28,00 29,76 31.50 33.25 35.00 36.76 38.50 28.13 30,00 31,88 33,75 35.63 37.50 39.38 41.25 30.00 32.00 34.00 36.00 38.00 10.00 42.00 44.00 31,88 34,00 36,13 38.25 40.38 42.60 43.63 46.75 33.75 36.00 38.26 40.50 42.75 45.00 47.25 49.50 102 108 114 120 25.50 27.00 28.60 30.00 31.88 33.76 35.63 37.50 38,26 40,50 42,75 45,00 44.63 47.25 49.88 62.50 51.00 54.00 67.00 60.00 57.38 60.75 64.13 67.50 63.75 67.50 71.25 75.00 70.13 76.60 74.2581.00 78.3885.60 82,5090,00 82.88 87.75 92,63 97,5C 89.25 94.60 99.76 IO5.O0 96.63 101.26 106.88 112.50 102,00 108,00 114,00 120,00 49 50 51 62 53 64 65 66 41.7 42.5 43.4 44.2 45.1 45.9 46.8 47.6 52,1 53,1 54,2 55,3 56.3 57.4 58.4 59.5 62,6 63,8 65,0 66.3 67.6 68.9 70.1 71.4 72.9 74.4 75.9 77.4 78.8 80.3 81,8 83,3 83,3 86,0 86,7 88.4 90,1 91,8 93,5 95.2 93,7 95.6 97.6 99.5 101,4 103,3 106,2 107.1 104.1 106.3 108.4 110.5 112,6 114,8 116,9 119,0 114.5 116.9 119.2 121.0 123.9 126.2 128.6 130.9 125.0 127.6 130.1 132.6 135.2 137.7 140.3 142.8 135.4 138.1 140.C 143.', 146.4 149.2 151.9 154.7 145.8 148.8 151.7 154.7 157.7 160.7 163.6 166.6 166.2 159.4 162.6 165.8 168.9 172.1 176,3 178.5 166.6 170.0 173.4 176.8 180.2 183.6 187,0 190,4 WEIGHTS OF PLATES IN POUNDS PER LINEAL FOOT*" i A i A i A f ii i a 7 8 # 1 £6 72 66.1 61.2 70.1 76.5 84.2 91.8 98,2 107.1 112.2 122.4 126.2 137.7 140.3 153.0 154,3 168,3 168.3 183.6 182.3 198.9 196.4 214.2 210.4 229.5 224.4 244,8 46 11.50 14.38 17.25 20.13 23.00 25.88 28.76 31.63 34.50 37.38 40.25 43.13 46.00 48.88 51.75 78 66.3 82.9 99.5 116.0 132.6 149.2 165.8 182,3 198.9 215.5 232.1 248.6 265,2 57 48.5 60,6 72.7 84,8 96,9 109.0 121.1 133.2 145.4 157.6 169.e 181.7 193,8 48 12.0C 15.0[ 18.00 21.0( 24.00 27.00 30.00 33.00 36.00 39.00 42.00 45.00 48.00 51.00 54.00 84 71.4 89.3 107.1 125.0 142.8 160.7 178,6 196.4 214.2 232.1 249.9 267.8 285,6 58 49.3 61,6 74.0 86,3 98,6 110,9 123.3 135.6 147,[ 160.2 172.f 184.! 197.2 60 125C 15 6c 18.75 21.8i 25.00 28.13 31.26 34.38 37.60 40.63 43.75 46.88 50.00 63.13 56.25 90 76.5 95.6 114.8 133.C 153.0 172.1 191.3 210.4 229.5 248.6 267.8 286.9 306,0 69 50.2 62.7 75.2 87.8 100,3 }m 125.4 137.9 150,5 163.C 175.5 178.5 188.1 191.a 200.6 204.0 62 isioo 16.25 19.50 22.75 26.00 29.25 32.50 35.75 39.00 42.25 45.50 48.75 52.00 55.25 58.50 96 81.6 102.0 123.4 142.8 163.2 183.6 201.0 224.4 244.8 265.2 285.6 306.0 326,4 60 51.0 63.8 76.5 39.3 102.0 ll^.O 127.5 140.3 153.0 165.8 64 66 68 60 13.50 i4.on 14.50 15.00 16.88 17.50 18.13 18.75 20.25 23.63 27.00 30.38 33.75 37.13 40.50 43.88 47.25 50.63 54.00 57.38 60.75 102 86.7 108.4 130.1 151.8 173.4 195.1 216.7 238.4 260.2 281.8 303.5 325.1 346,8 61 51.9 64.8 77.8 90.7 103.7 116.7 129.6 142.6 155.6 168.5 181.5 194.4 207.4 21. 0( 24., 5f 28.00 31.50 35.00 38.50 42.00 45.50 40.00 52.50 56.00 50.50 63.00 108 91.8 114.7 137.8 160.7 183.7 206.6 229.6 252.4 275.5 298.3 321.3 344.3 367.2 62 52.7 65.£ 70.1 92.2 105.4 118,6 131.8 144.9 158.1 171.S 184.5 197.1 210.8 oi'75 9.=i .^ft 29.00 32.63 36.26 39.88 43.50 47.13 50.75 54.38 58.00 61.63 65.25 114 96,9 121.1 145.4 169.6 103.8 218.1 242.2 266.4 290.8 314.9 339.2 363.4 387,6 63 53.6 66.£ 80.3 93.7 107.1 120.6 133.9 147.3 160.7 174.( 187.< 200.1 214.2 22!6026.26 30.00 33.75 37.50 41.26 45.00 48.75 52.50 56.25 60.00 63,75 67.50 120 102.0 127.6 153.0 178,5 204,0 229.6 255.0 280.5 306.0 331.6 357.0 382.5 408,0 64 54.4 68.C 81.6 95.2;ios,s 122,4 136,0il49,ti!103,a 176.8 190.4 204.0iziY.o 4 WE GHT = 3, 4X/ REA OR 12 CUB C IN CHE S OF ST ;el WEI GHS 3.4 POUNDS 322 PROPERTIES OF I-BEAMS IF THE THICKNESS OF THE WEB IS MORE THAN ^ BELOW AN EVEN SIXTEENTH, THE NEXT LOWER SIXTEENTH IS GIVEN IN THE TABLE BELOW /=THE MOMENT OF INERTIA OF THE CROSS SECTION ABOUT THE AXIS 1-1 S=THE CORRESPONDING SECTION MODULUS ABOUT THE AXIS 1-1 r = THE CORRESPONDING RADIUS OF GYRATION ABOUT THE AXIS 1-1 /!! = THE MOMENT OF INERTIA OF THE CROSS SECTION ABOUT THE AXIS 2-2 r2=THE CORRESPONDING RADIUS OF GYRATION ABOUT THE AXIS 2-2 c 1- c: 2 f 1 CARNEGIE I-BEAMS STANDARD I-BEAMS SIZE WEIGHT WEB AREA / 5 r h I'll SIZE WEIGHT WEB AREA / s IN.s r IN. IN.« IN. SIZE WEIGHT WEB AREA / s r IN, h 'z SIZE WEIGHT WEB AREA / s - I2 n IN. LBS./FT. IN. SQ.IN. IN,« IN.3 IN. IN.« IN. IN. LBS./FT. IN. SQ.IN. IN.» IN. LBS./FT. IN. SQ.IN. IN.4 IN.3 IN.' IN, IN. LBS./FT. IN. SQ.IN. IN.* IN.' IN. IN.* IN. 27 90* .52U 26.33 2958.3 219.1 10.60 75.3 1.69 12 55 50 45 40 .82 .70 .58 .46 16.18 14.71 13.24 11.84 321.0 303.4 285.7 269.0 53.5 50.6 47.6 44.8 4.45 4.54 4.65 4.77 17.5 16.1 14.9 13 8 10.1 9.5 1.04 1.05 1.06 1.08 0.9(1 1.01 24 105t 100 95 90 85 80 .63 .75 .69 .63 .57 .50 f 1 ft i 30.98 29.41 27.94 26.47 25.00 23.32 2811.5 2379.6 2309.0 2238.4 2167.8 2087.2 234.3 198.3 192.4 186.5 180.7 173.9 9.53 8.99 9.09 9.20 9.31 9.46 78.9 48.6 47.1 45.7 44.4 42.9 1.60 1.28 1.30 1.31 1.33 1.36 12 55 50 45 40 .82 .70 .58 .46 H ft ft 16.18 14.71 13.24 11.84 321.0 303.4 285.7 268.9 53.5 50.6 47.6 44.8 4.45 4.54 4.65 4.7? 17.5 16.1 14.9 13.8 1.04 1.05 1.06 1.08 24 115 110 105 .75 .69 .63 i i 33.98 32 48 30.98 2955.5 2883.0 2811.5 246.3 240.3 234 3 9.33 9.42 9.53 9.00 9.09 9.20 9.31 9 46 83.2 81.0 78.9 48.6 47.1 45.7 44.4 42.9 1.57 1.58 1.60 1.28 1.30 1.31 1.33 1.36 100 95 90 85 80 .75 .69 .63 .57 .50 } U 1 i 29.41 27.94 26.47 25.00 23.32 2379.6 2309.0 2238.4 2167.8 2087.2 198.3 192.4 186.5 180.7 173.9 35 31J .44 .35 A A 10.29 9.26 228.3 215.8 38.0 36.0 4.71 4.83 35 31J .44 .35 ft ft 10.29 9.26 228.3 215.8 38.0 36.0 4.71 4.83 10.1 9.5 0.99 1.01 28* [.28 J 8.15 199.4 33.2 4,95 12,6 1.24 20 100 95 90 85 80 .88 .81 .74 .66 ,60 } « i t ft 29.41 27.94 26.47 25.00 23.73 1655.6 1606.6 1557.5 1508.5 1466.3 165.6 160.7 155.8 150.9 146.6 7.50 7.58 7.67 7.77 7.86 52.7 50.8 49.0 47.3 45.8 1.34 1.35 1.36 1.37 1.30 10 40 35 30 25 .75 .60 .46 .31 ft ft 11.76 10.29 8.82 7.37 158.7 146.4 134.2 122.1 31.7 29.3 26.8 24.4 3.67 3.77 3.90 4.07 9.5 0.90 8.5 0.91 7.7 0.93 6.9 0.97 10 40 35 30 25 .75 .60 .46 .31 3 11.76 10 29 8.82 7.37 158.7 146.4 134.2 122.1 31.7 29.3 26.8 24.4 3.67 3.77 3.90 4.07 9,5 8.5 7.7 6,9 0.90 0.91 0.93 0.97 74' .48 IS 21.70 1950.1 162.5 9.48 61.2 1.68 21 aof .43|/sl 17.68 11235.5 117.7 8.36|43.5 1.57 9 35 30 25 21 10.29 8.82 7.35 6.31 111.8 101.9 91.9 84.9 24.8 22.6 20.4 18.9 3.30 3.40 3.54 3.67 7.3 0.84 6.4 0.85 5.70.88 5.2 0.90 20 100 95 90 85 80 .88 .81 .74 .66 60 i 1 29.41 27.94 26.47 25.00 23.73 1655.6 1606.6 1557.6 1508.5 1466.3 165.6 160.7 155.8 150.9 146.6 7.50 7.58 7.67 7.77 7 86 52.7 50.8 49.0 47.3 45.8 1.34 1.35 1.36 1.37 1.39 22i' .25 V 6.54 113.6 22.7 4.17 9,0 1.17 .57 .41 .29 la ft J i 9 35 30 25 21 .73 .57 .41 .29 H A i i 10.29 8.82 7.35 6.31 111. 8 101.9 91.9 84.9 24.8 22.6 20.4 18.9 3.29 3.40 3.54 3.67 7.3 6.4 5.7 5.2 0.84 0.85 0.88 0.90 75 70 65 ,65 ,58 ,50 ft i 22.06 20.59 19.08 1268.8 1219.8 1169.5 126.9 122.0 117.0 7.58 7.70 7.83 30.3 29.0 27.9 1.17 1.19 1.21 8t 25i 23 20i 18 .54 .45 .36 .27 i ft ft i 7.50 6.76 6.03 5.33 68.4 64.5 60.6 56.9 17.1 16.1 15.2 14.2 3.02 3.09 3.17 3.27 4.8 0.80 75 70 65 .65 .58 .50 f 22.06 20.59 19.08 1268.8 1219.8 1169 5 126.9 122.0 117.0 7.58 7.70 7.83 30.3 29.0 27.9 1.17 1.19 1.21 8 251 23 20i 18 .54 .45 .36 .27 I ft J 7.50 6.76 6.03 5.33 68,4 64.5 60.6 56.9 17.1 16.1 15.2 14.2 3.02 3.09 3.17 3.27 4.8 4.4 4.1 3.8 0.80 0.81 0.82 0.84 18 70 65 60 65 .72 .64 .56 .46 i ft 20.59 19.12 17.65 15.93 921.2 881.5 841.8 795.6 102.4 97.9 93.5 88.4 6.69 6.79 6.91 7.07 24.6 23.5 22.4 21.2 1.09 1.11 1.13 1.15 4.4 ' " 4.1 3.8 0.81 0.82 0.84 n 7A 18 90 85 80 75 .81 .73 .64 .56 i is 26.47 25.00 23.53 22.05 1260.4 1220.7 1181.0 1141.3 140.0 135.6 131.2 126.8 6.90 6.99 7.09 7.19 52.0 50.0 48.1 46.2 1.40 1.42 1.43 1.45 7 20 17J 15 .46 .35 .25 ft ft i 5.88 5.15 4.42 42.2 39.2 36.2 12.1 11.2 10.4 2.68 2.76 2.86 3 2 17^ .22 ft 5.12 58.4 14.6 3.38 6.2 1.10 2.9 0.76 2.7 0.78 7 20 m 15 .46 35 .25 ft i 5.88 5.15 4.42 42.2 39.2 36.2 12.1 11.2 10.4 2.68 2.76 2.86 3.2 2.9 2.7 0.74 0.76 78 15 100 95 90 85 80 I.IS 1.00 .99 .89 .81 ift ift 1 J 13 29.41 27.94 26.47 25.00 23.53 900.5 872.9 845.4 817.8 795.5 120.1 116.4 112.7 100.0 106.1 5.53 5.59 5.65 5.72 5.78 31.0 48.4 45.9 43.6 41.8 1.31 1.32 1.32 1.32 1.32 6 14J 12i .48 .35 .23 ft ft ft 5.07 4.34 3.61 26.2 24.0 21.8 8.7 8.0 7.3 2.27 2.35 2.46 2.40.68 2.10.69 1.9 0.72 70 65 60 65 .72 .64 .56 .46 20.59 19.12 17.65 15.93 921.2 881.5 841.8 795.6 102.4 97.9 93.5 88.4 6.69 6.79 6.91 7.07 24.6 23.5 22.4 21.2 1.09 1.11 1.13 1.15 6 m 14} 121 .48 .35 .23 ft ft 5.07 4.34 3.61 26.2 24.0 21.8 8.7 8.0 7.3 2.27 2.35 2.46 2.4 2.1 1.9 0.68 0.69 0.72 6 145 12i 91 .50 .36 .21 i ft A 4.34 3.60 2.87 15.1 13.6 12.1 6.1 5.4 4.8 1.87 1.94 2,05 1.70.63 1.5 0.63 1.2 0.65 48* .38 i 14.08 737 1 81.9 V.23 30.0 1.46 5 145 12i 9f .50 .36 .21 i ft ft 4.34 3.60 2.87 15.2 6.1 13.6 5.5 J2.1 4.8 1.87 1.04 2,05 1.7 1.5 1.2 0.63 0.63 0.65 75 70 65 60 .88 .78 .69 .59 i i H ft 22.06 20.59 19.12 17.67 691.2 663.7 636.1 609.0 92.2 88.5 84.8 81.2 5.60 5.68 5.77 5.87 30.7 29.0 27.4 26.0 1.18 1.19 1.20 1.21 16 75 70 65 60 .88 .78 .69 .59 t S H 22.06 20.59 19.12 17.67 691.2 663.7 636.1 609.0 92.2 88.5 84.8 81.2 5.60 5.68 5.77 5.87 30.7 29.0 27.4 26.0 17.1 16.0 15.1 14.6 1.18 1.19 1.20 I 21 1.02 1.04 1.07 1.08 4 94 Si 7J .41 .34 .26 .19 1 A i ft 3.09 2.79 2.50 2.21 7.1 6.7 6,4 6.0 3.6 3,4 3,2 3,0 1.52 1.54 1.59 1.64 1.0 0.57 0.9 0.58 0.9 0.58 0.8 0.59 4 m 9J 7i .41 34 .26 .19 s ft i ft 3. CO 2.79 2.50 2.21 7.1 6.8 6.4 6,0 3.6 3.4 3.2 3 1.52 1.55 1.59 1 64 1.0 0.9 0.9 ns 0.57 0.58 0.58 59 55 50 45 42 .66 .56 .46 .41 f 1 16.18 14.71 13.24 12.48 511.0 483.4 455.9 441.8 68.1 64.5 60.8 58.9 5.62 5.73 5.87 5.95 55 50 45 42 .66 .56 .46 .41 ft 16.18 14.71 13.24 12.48 511.0 483.4 455.8 441.8 68.1 64.5 60.8 58.9 5.62 5.73 5.87 5.95 17.1 16.0 15.1 14.6 1.03 1.04 1 07 1.08 3 n 6i Si .36 .26 .17 i i i 2.21 1.91 1.63 2.? 2.7 2.5 1.9 1.8 1.7 1.15 1.19 1.23 0.6 0.5 0.5 0.52 0.52 0.53 3 6i .36 .26 .17 S I i 2.21 1.91 1.63 2.9 2 7 1,9 1.8 1.7 1.15 1.19 1.23 o.e 0.6 0.5 0.52 52 37r .33 A 10.91 405.5 54.1 6.10 19.9 1.35 2.5 0.53 SUPPLEMENTARY BEAM. t SPECIAL. t CAMBRIA STS WEIGH 251, 22i, 201 AND 18. PROPERTIES OF CHANNELS 323 IF THE THICKNESS OF THE WEB IS MORE THAN ^ BELOW AN EVEN SIXTEENTH, THE NEXT 2 1_ LOWER SIXTEENTH IS GIVEN IN THE TABLE BELOW f / = THE MOMENT OF INERTIA OF THE CROSS SECTION ABOUT THE AXIS 1-1 jP r— ' s = THE CORRESPONDING SECTION MODULUS ABOUT THE AXIS 1-1 r = THE CORRESPONDING RADIUS OF GYRATION ABOUT THE AXIS 1-1 . —3 7 i=THE MOMENT OF INERTIA OF THE CROSS SECTION ABOUT THE AXIS 2-8 3— S2= THE CORRESPONDING SECTION MODULUS ABOUT THE AXIS 2-2 r 2= THE CORRESPONDING RADIUS OF GYRATION ABOUT THE AXIS 2-2 T~~l — t X 2 UJ III X X 1- h II II DISTANCE FROM THE BACK OF THE WEB TO THE CENTER OF GRAVITY DISTANCE BACK TO BACK OF WEBS WHICH MAKES h = h = il ,L J z .,^. 4 • NOT STANDARD FOR ALL STEEL COMPANIES SIZE WEIGHT WEB AREA SQ. IN. / 5 r h S2 ■ ■-a X z SIZE WEIGHT WEB ■AREA / s r '. s. fi X z IN. LBS. /FT. IN. IN < IN. 3 IN. IN.* IN.' IN. IN. IN, IN. LBS. /FT. IN. SQ. IN. IN," IN. 3 IN. IN,« IN.^' IN. IN. IN. 55 .82 \i 16.18 430.2 67.4 5.16 12.2 4.1 0.87 0.82 8.53 21i .58 ti 6.25 47,8 11.9 2.76 2.3 1.1 0.60 0.59 4.22 50 .72 U 14.71 402.7 53.7 5.23 11.2 3.8 0.87 0.80 8.72 185 .49 } 5.51 43.8 11.0 2.82 2.0 1.0 0.60 0.57 4.37 16 i& .62 f 13.24 375.1 50.0 5.32 10.3 3.6 0.88 0.79 8.92 8 16i .40 * 4.78 39.9 10.0 2.89 1.8 1.0 0.61 0.56 4.53 40 .52 J 11.76 347.5 46.3 5.44 9,4 3.4 0.89 0.78 9.16 13J .31 ■A 4.04 36.0 9.0 2.98 1.6 0.9 0.62 0.56 4.72 35 .43 A 10.29 319.9 42.7 5.57 8.5 3.2 0.91 0.79 9.42 Hi .22 A 3.35 32.3 8.1 3.10 1.3 0.8 0.63 0.68 4.92 33 .40 i 9.90 312.6 41.7 5.62 8.2 3.2 0.91 0.79 9.51 19} .63 * 6.81 33.2 9.5 2.. 39 1.9 1.0 0.56 0.58 3.48 50 .79 i 14.71 313.7 48.3 4.62 16.7 4.9 1.07 0.98 7.02 17i ,63 * 5.07 30.2 8.6 2.44 1.6 0.9 0.56 0.56 3.64 45 .68 a 13.24 292.9 45.1 4.70 15,3 4.6 1.08 0.97 7.22 7 14} .42 ■ft 4.34 27.2 7.8 2.50 1.4 0.8 0.57 0.54 3.80 13* 40 .57 A 11.76 272.2 41.9 4.81 13.9 4,3 1.09 0.97 7.44 12i ,32 ft 3.60 24.2 6.9 2.59 1.2 0.7 0.58 0.53 3.99 37 .50 1 10.88 259.8 40.0 4.89 13.1 4,2 1,10 0.98 7.56 9} .21 ft 2.85 21.1 6.0 2.72 1.0 0.6 0.59 0.55 4.21 35 32 .45 .38 ft 10.29 9.30 251.5 237.5 38 7 36.5 4.94 5.05 12.5 11 5 4,1 3.9 1,10 1,11 0.99 1.01 7.66 7.84 6 15i 13 .56 .44 ft ft 4.56 3,82 19 5 17.3 6.5 5.8 2.07 2.13 1.3 1.1 0.7 0.7 0.63 0.53 0.65 0.52 2.90 3.08 40 .76 1 11.76 196,9 32.8 4.09 6.6 2.5 0.75 0.72 6.60 35 .64 t 10.29 179.3 29.9 4.17 5.9 2.3 ■ 0.76 0.69 6,83 lOi .32 ft 3 00 15.1 5.0 2.21 0.9 0.6 0.53 0.50 3.29 12 30 25 .51 .39 i il 8.82 7.35 161.7 144.0 26.9 24.0 4.28 4.43 5.2 4.5 2.1 1.9 0.77 0.78 0.68 0.68 7,06 7.36 8 .20 ft 2,38 13.0 4.3 2.34 0.7 0.5 0.54 0.52 3.51 Mi .28 i 6.03 128,1 21.4 4.61 3,9 1.8 0.81 0.70 7.67 6 lU 9 6i .48 ,33 .19 ft ft ft 3.38 2.65 1.95 10.4 8.9 7.4 4,2 3.6 3.0 1.75 1.83 1.95 0.8 0.6 0.5 0.5 0.5 0.4 0.49 0.49 0,50 0.61 0.48 0,49 2.35 2.57 2.79 35 .82 18 10 29 115.5 23.1 3.35 4,7 1.9 0.67 0.70 5.17 10 30 25 .68 .53 i 8.82 7 35 103.2 91.0 20.6 18.2 3.42 3.52 4,0 3.4 1.7 1 5 0.67 0.68 0.65 0.62 5.40 5.66 7J ,33 ft 2.13 4.6 2.3 1.46 0,4 0.4 0.46 0.46 1.88 20 .38 i 5.88 78.7 15.7 3 66 2.9 1.3 0.70 0.61 5.97 4 6i .25 >, 1.84 4.2 2.1 1.51 4 0.3 0.45 0.46 1.96 IS .24 i 4,46 66.9 13.4 3 87 2.3 1.2 0.72 0.64 6.33 61 .18 ft 1.55 3.8 1.9 1.56 0.3 0.3 0.45 0.46 2.08 26 62 , 7.35 70,7 15.7 3.10 3.0 1.4 0.64 0.62 4.83 20 .45 I'm 5.88 60,8 13.5 3.21 2.5 1 2 0.65 0.58 5.14 6 .36 i 1,76 2.1 1.4 1.08 3 0.3 0.42 0.46 1.10 9 16 .29 t 4.41 50,9 11,3 3.40 2.0 1.0 0.67 0.59 5.49 3 5 .26 1 1.47 1.8 1.2 1.12 0.3 0.2 0.42 0.44 1.17 Ui .23 A 3.89 47.3 10.5 3.49 1.8 1.0 0.67 0.61 5.62 4 .17 4 1.19 1.6 1.1 1,17 0.2 0.2 0.41 0.44 1.29 324 PROPERTIES OF BETHLEHEM I-BEAMS AND GIRDER BEAMS, AND LIST OF SHIPPING MARKS :-U IF THE THICKNESS OF THE WEB IS MORE THAN ^ BELOW AN EVEN SIX' TEENTH, THE NEXT LOWER SIXTEENTH IS GIVEN IN THE TABLE BELOW / = THE MOMENT OF INERTIA OF THE CROSS SECTION ABOUT THE AXIS 1-1 S = THE CORRESPONDING SECTION MODULUS ABOUT THE AXIS 1-1 r = THE CORRESPONDING RADIUS OF GYRATION ABOUT THE AXIS 1-1 /2=THE MOMENT OF INERTIA OF THE CROSS SECTION ABOUT THE AXIS 2-2 rj=THE CORRESPONDING RADIUS OF GYRATION ABOUT THE AXIS 2-2 BETHLEHEM I-BEAMS SIZE WEIGHT 30 28 24 20 18 16 12 10 105 81 83 73 82 72 64 69 59 S4 52 481 71 64 54 46 41 SQ.IN, .50 36 32 2SJ 28J 23i 24 20 m m .25 AREA 35.30 26.49 24.80 24.59 21.47 24.17 21.37 20.26 18.86 17.36 17.40 15.87 15.24 14.25 20.95 18.81 15.88 13.52 12.02 11.27 10.61 9.44 8.42 8.34 6.94 7.04 6.01 5.78 5.18 IN.' 5239.6 4014.1 2977.2 2381.9 2240.9 2091.0 1559.8 1466.5 1268.9 1222.1 1172.2 883.3 842.0 825.0 798.3 349.3 286.7 229.0 198.5 186.7 174.3 156.0 146.7 126.9 122.2 117.2 8.1 91.7 88.7 796.2 664.9 610.0 484.8 456.7 442.6 269.2 228.5 216.2 134.6 122.9 85.1 60.6 67.4 106.2 88, 81, 64.6 60, 59.0 44.9 38.1 36.0 26.9 24.6 20.5 18.9 15.1 14.3 IN. 12.18 10.60 9.55 9.87 8.03 8.28 7.91 8.05 8.22 7.12 7.28 7.36 7.48 6.16 5.96 6.20 5, 6.16 6.27 IN.* 131.5 101.2 91.1 78.0 74.4 79.9 75.9 51.2 49.8 48.3 39.1 37.7 37.1 36.2 61.3 41.9 38.3 25.2 24.0 23.4 5.04 4.92 5.07 4.02 4.21 3.62 3.76 21.3 16.0 15.3 12.1 11.2 8.2 2.16 2.06 1.95 BETHLEHEM GIRDER BEAMS IN. LBS./FT, 30 200 180 26 24 15 12 180 166 160 150 140 120 140 112 92 140 104 73 70 55 32i SQ. IN. 58.71 53.00 62.86 48.47 9150.6 8194.5 7264.7 6562.7 46.91 43.94 41.16 35.38 41.19 32.81 2934.7 2342.1 27.12 41.27 30.50 21.49 20.58 16.18 12.95 11.22 9.54 5620, 5153.9 4201.4 3607.3 IN.» 610.0 546.3 12, 12.43 518.9 432.4 ,5 350.1 300, 1591.4 1592.7 1220.1 .4 212.4 7 117.8 432.0 170.9 293.5 234.2 176.8 72.0 48.8 38.0 28.6 11.72 11.64 10.95 10.83 10.10 10.10 8.44 8.45 6.21 6.32 6.41 5.12 5.17 4.34 3.90 3.46 IN. 630.2 433.3 533.3 371.9 435.7 314.6 346.9 249.4 182.6 331.0 213.0 123.2 3.28 2.86 3.18 2.77 3.05 2. 2.91 2.70 2.69 114.7 81.1 57.3 2.10 32.9 EACH MEMBER WHICH IS SHIPPED SEPARATELY SHOULD BE MARKED WITH A CHAR' ACTERISTIC LETTER OR LETTERS FOLLOWED BY A SPECIFIC NUMBER, THUS:B/*, LO 2 ALL MEMBERS WHICH ARE INTERCHANGEABLE, EXCEPT OFFICE BUILDING COLUMNS,* SHOULD BEAR THE SAME MARKS. MEMBERS WHICH ARE. EXACT OPPOSITES SHOULD BE MARKED RIGHT AND LEFT, THUS: C rS", C 78'-, THE ONE SHOWN ON THE DRAWING BEING THE RIGHT. IN ALL OTHER CASES, MEMBERS SHOULD BEAR DIFFERENT MARKS. THE MORE COMMON CHARACTERISTIC LETTERS USED FOR SHIPPING MARKS (ADAPTED FROM THE STANDARDS OF THE AMERICAN BRIDGE COMPANY) ARE GIVEN BELOW: — BUILDING WORK ANGLE BRACING D BEARING PLATES MP BUCKLED PLATES BP CAST BASES CB CASTINGS. MISCELLANEOUS, STANDARD A "■ ■ " SPECIAL H COLUMNS AND POSTS, MILL BUILDINGS, ETC. C OFFICE BUILDINGS • CRANE STOPS CS FLOOR PLATES FP GIRTS, AND PENT HOUSE FRAMING f GIRDERS, PLATE Gt LATTICED LG HOPPERS, BINS, AND CHUTES H I-BEAMS ANDCHANNELS,MILLBUILDINGS,ETC.S OFFICE " J KNEE BRACES K LINTELS L MISCELLANEOUSANGLES, PLATES,BRACKETS M PURLINS P\ RAFTERS R RAILINGS H RAILING POSTS P RODS, BRACING X " TIE AND SAG, LENGTH IN INS., THUS: @ SIDE WALL, PARTITION, & CEILING FRAMING F SMOKE FLUES SF SPLICE PLATES SP STRUTS S TRUSSES, COMPLETE .. T TRUSS MEMBERS AS FOLLOWS: — BRIDGE WORK ANGLE BRACING, BETWEEN STRINGERS.... D BOTTOM LATERALS L TOP " 7" BED PLATES, EXPANSION END RP FIXED END FP BRACKETS B BUCKLED PLATES BP CAST PEDESTALS CP CROSS FRAMES CF END POSTS EP FLOOR BEAMS F GIRDERS, PLATE fl " LATTICED LO KNEE BRACES K MISCELLANEOUS ANGLES M PLATES P PINS PANEL POINT LETTER RAILINGS R RAILING POSTS P ROLLER NESTS RN SHOES, EXPANSION RS FIXED FS SHOE STRUTS ES SPLICE PLATES SP STRINGERS S STRUTS, BOTTOM LATERAL BS TOP " TS PORTAL PS SWAY BRACING SB TRUSSES, COMPLETE T TRUSS MEMBERS AS FOLLOWS: — X ROOF ^ He K e ' H THE INTERSECTION POINTS OF TRUSSES SHOULD BE LETTERED, AND EACH SEPARATE MEMBER SHOULD BEAR THE LET- TERS AT THE ENDS. THUS: 60 2, EK /«. WHEN TRUSSES ARE SHIPPED IN SECTIONS, SUCH SECTIONS MAY BE MARKED PT (PART TRUSS), UNLESS SHIPPED IN HALVES, AS SHOWN IN THE FIGURE ABOVE. WHEN THE HALF AEG IS MARKED AH, AND THE HALF XEG IS MARKED XH, THE PEAK PLATE BEING SHIPPED ON THE AH HALF. THE UPPER PANEL POINTS OF A BRIDGE TRUSS SHOULD BE MARKED U7, U2, ETC., AND THE LOWER PANEL POINTS LO.LI, ETC, SO THAT L 1 IS UNDER U 1. THE END POST (LO-Ul) SHOULD BE MARKED EP, BUT EACH OTHER MEMBER SHOULD BEAR THE MARKS OF THE PANEL POINTS BETWEEN WHICH IT EXTENDS, THUS : — i 7-2, U 1-3. L 1-U 1. L2-U 1. THE MEMBERS OF THE LEFT HALF OF THE FAR TRUSS SHOULD BE DRAWN AND CON- SIDERED RIGHT.THE OTHERS BEING MARKED R AND L ACCORDINGLY, Each office building column should bear either the Numbers of the floors between which it extends or e^se the Letters of the floors which it supports. Thus: — Col. 13 (0-2) or AB 13- Col. 25 (5-6) or EF 25 Office building columns should be numbered consecutively on the plans so that no two bear the same mark, even though alike. The same number should be maintained from the basement to the roof, thus section GH 16 IS spliced to the top of section EFId. f Each office building girder should bear the floor number in addition to the mark, thus:— 67 (2nd Fl.) J Each office building beam should bear either the number or the letter of the floor for which it is intended, thus: — ^40 — I ST Fl. or /I 40; #1 5 — 8TH F|. or f 75' #30 — Roof or #30- PROPERTIES OF STANDARD ANGLES 325 EQUAL LEGS ? UNEQUAL LEGS i- ^ adopted 1910 by association of american Steel manufacturers ; /CENTER OF GRAVITY ADOPTED 1910 BY ASSOCIATION OF AMERICAN MANUFACTURERS STEEL iL-CEBTIROr GRAVITY k ^M S ^M SIZE THICK- NESS WEIGHT PER FT. AREA 's *S '■s X I'M SIZE THICK- NESS WEIGHT PER FT. AREA 's *,s 's X 'l "l ••l y •■m INCHES INCHES POUNDS SQ. IN. IN.* IN." IN. IN. IN. INCHES INCHES POUNDS SQ. IN. IN,* IN.3 IN, IN. IN.« IN.s IN. IN. IN. li 56.9 16.73 98.0 17.5 2.42 2.41 1.55 i 27.2 7.98 27.7 7.2 "ITSO'^ 2.12 9.8 3.4 1.11 1.12 0.86 lA 84.0 15.87 93.5 16.7 2.43 2.39 1.56 i% 25.4 7.47 26.1 6.7 1.87 2.10 9.2 3.2 1.11 1.10 0.86 1 61.0 15.00 89.0 15.8 2,44 2^37 2.34 1.56 1.56 i 23.6 6.94 24.5 6.2 1.88 2.08 8.7 3.0 1.12 1.08 0.86 IS 48.1 14.12 . 84.3 14^9 2.44 6x4 ^* s 21.8 20.0 6.40 5.86 22.8 21.1 5.8 6.3 1.89 1.90 2.06 2.03 8.1 7.6 2,8 2.5 1.13 1.13 1.06 1.03 0.86 0.86 8x8 45.0 13.23 79.6 14.0 2.45 2,32 1.56 ft 18.1 6.31 19.3 4.8 1.90 2.01 6.9 2.3 1.14 1.01 0.87 ii 42.0 12.34 74.7 13.1 2.46 2.30 1.67 i 16.2 4.76 17.4 4.3 1.91 1.99 6.3 2.1 1.16 0.99 0.87 38.9 11,44 69.7 12.2 2.47 2,28 1.57 ft ] 14.3 4.18 16.6 3.8 1.92 1.96 5.6 1.8 1.16 0.96 0.87 H 35.8 10.53 64.6 11.2 2.48 2,25 1.68 12.3 3.61 13.6 3.3 1.93 1.94 4.9 1.6 1.17, 0.94 0.88 32.7 9.61 59,4 10.3 2.49 2.23 1.58 i 25.7 7.56 26.4 7.0 1.87 2.22 6.6 2.6 0.93 0.97 0.75 A 29.6 8.68 54 1 9.3 2.50 2.21 1.58 }8 24.0 7.06 24.9 6.6 1.88 2.20 6.2 2.4 0.94 0.95 0.75 26.4 7.75 48.6 8.4 2.51 2.19 1.58 i 22.4 6.56 23.3 6.1 1.89 2.18 5.8 2.3 0.94 0.93 0.75 6x3^ 15 20.6 6.06 21.7 6.6 1.89 2.15 5.6 2.1 0.95 0.90 0.75 1 37.4 11.00 35.5 8.6 1.80 1.86 1.16 i 18.9 6,55 20.1 6.2 1.90 2.13 5.1 1.9 0.96 0.88 0.75 ii 35.3 10.37 33.7 8.1 1.80 1.84 1.16 ft 17.1 6.03 18.4 4.7 1.91 2.11 4.7 1.8 0.96 0,86 0.75 33.1 9.73 31.9 7.6 1.81 1.82 1.17 i 16.3 4.50 16.6 4.2 1.92 2.08 4.3 1.6 0.97 0.83 0.76 a 31.0 9.09 30.1 7.2 1.82 1 80 1.17 1.17 ft 13.6 3.97 14.8 3.7 1.93 2.06 3.8 1.4 0.98 0.81 0.76 28^7 8^44 28^2 6.7 1^83 178 i 11.7 3.42 12.9 3.3 1.94 2.04 3.3 1.2 0.99 0.78 0.77 6x6 a 26.5 7.78 26.2 6.2 1.83 1.75 1.17 \ 19.8' 6.81 13.9 4.3 1.55 1.76 5.6 2.2 0.98 1.00 0.76 ft 24.2 7.11 24.2 5,7 1.84 1.73 1.17 1.18 « 18.3 5.37 13.0 4.0 1.56 1.72 5.2 2.1 0.98 0.97 0.75 21.9 6.43 22^1 5!l 1.86 1.71 5x3^ ft* 16.8 15.2 4.92 4 47 12.0 11.0 3.7 3.3 1.56 1.67 1.70 1,68 4.8 4.4 1.9 1.7 0.99 1.00 0.96 0.93 0.75 0.75 19.6 5.75 19.9 4,6 1.86 1.68 1.18 i 13.6 4.00 10.0 3.0 1.68 1.66 4.0 1,6 1.01 0.91 0.75 i. 17.2 5.06 17.7 4,1 1.87 1.68 1.19 ft 12.0 3.53 8.9 2.6 1.59 1.63 3.6 1,4 1.01 0.88 0.76 14.9 4.36 15.4 3.5 1.88 1.64 1.19 t 10.4 3.05 7.8 2.3 1.60 1.61 3.2 1,2 1,02 0.86 0.76 ft 8.7 2.66 6.6 1.9 1.61 1.69 2.7 1.0 1,03 0.84 0.76 18.5 5.44 7.7 2.8 1.19 1.27 0.77 H 17.1 15.7 6.03 4.61 7.2 6.7 2.6 2.4 1.19 1.20 1.25 1.23 0.77 0.77 17.1 15.7 14.3 5.03 4.61 4.18 12.3 11.4 10.4 3.9 3.5 3.2 1.56 1.57 1.58 1.82 1.80 1.77 3.3 3.1 2,8 1.6 1.4 1.3 0.81 0.81 0.82 0.82 0.80 0.77 0.64 0.64 0.65 4x4 ft 14.3 4.18 6.1 2,2 1.21 1.21 0,78 5x3 12.8 3.76 9.5 2.9 1.59 1.75 2.6 1.1 0.83 0.75 0.65 12.8 3.75 6.6 2.0 1.22 1.18 0.78 ft 11,3 3.31 8.4 2.6 1.60 1.73 2.3 1.0 0.84 0.73 0.66 ft 11.3 3.31 5.0 1.8 1.23 1.16 0.78 \ 9.8 2.86 7.4 2.2 1.61 1.70 2.0 0.89 0,84 0.70 0.65 9.8 2.86 4.4 1.5 1.23 1.14 0.79 ft 8.2 2.40 6.3 1.9 1.61 1.68 1.8 . 0.75 0.85 0.68 66 ft 8.2 2.40 3.7 1.3 1.24 1.12 0.79 1 13.6 3.98 6.0 2.3 1.23 1.37 2.9 1.4 0.85 0.87 0.64 13.6 3.98 4.3 1.8 1.04 1.10 0.68 4x3 12.4 11.1 3.62 3 25 5.6 5.0 2.1 1.9 1.24 1.26 1,36 1,33 2.7 2,4 1.2 1.1 0.86 0.86 0.86 0.83 0.64 0.64 ft 12.4 3.62 4.0 1.6 1.05 1.08 0.68 9 8 2.87 4.5 1.7 1.26 1,30 2.2 1.0 0,87 0.80 0.64 05X02 11.1 3.25 3.6 1.5 1.06 1.06 0.68 8.5 2.48 4.0 1.5 1.26 1.28 1,9 0.87 0,88 0.78 0.64 ft 9.8 2.87 3.3 1.3 1.07 1.04 0.68 ft 7.2 2.09 3.4 1.2 1.27 1.26 1,7 0.74 0,89 0.76 0,65 8.5 2.48 2.9 1.2 1.07 1.01 0.69 11.4 3.34 3.8 1.6 1.07 1.15 2,6 1.2 0.87 0.90 0.62 ft 7.2 2.09 2.5 1.0 1.08 0.99 0.69 " i 10.2 3.00 3.6 1.5 1.07 1.13 ' 2,3 1,1 0.88 0.88 0.62 1 9.4 2.75 2.2 1.1 0.90 0.93 0.58 35x3 9.1 7.9 2.65 2.30 3.1 2.7 1.3 1.1 1.08 1.09 1.10 1.08 2.1 1,8 0,98 0.85 0.89 0.90 0.85 0.83 0.62 0.62 ft 8.3 2.43 2.0 0.95 0.91 0.91 0.68 6.6 1.93 2.3 1.0 1.10 1.06 1.6 0.72 0.90 0.81 0.63 3x3 ft 7,2 6.1 2.11 1.78 1.8 1.5 0.83 0.71 0.91 0.92 0,89 0.87 0.58 0.69 9.4 8 3 2.75 2 43 3.2 2,9 1.4 1.3 1.09 1.09 1.20 1.18 1,4 1,2 0.76 0.68 0.70 0.71 0,70 0.68 0.53 0.54 4.9 1.44 1.2 0.58 0.93 0.84 0.69 35x2^ i 7.2 2.11 2,6 1.1 1.10 1.16 1,1 0.69 0.72 0.66 0.54 ft ft ft 6.8 5.9 2.00 1.73 1.1 0.93 0.65 0.57 0.75 0.75 0.78 0,76 0.48 0.48 ^S 6.1 4.9 1.78 1,44 2,2 1.8 0.93 0.75 1.11 1.12 1.14 1.11 0.94 0.78 0.50 0.41 0.73 0.74 0.64 0.61 0.54 0.64 2^x2^ 5.0 4.1 3.1 1.47 1.19 0.90 0.85 0.70 0.55 0.48 0.39 0.30 0.76 0.77 0.78 0,74 0.72 0.69 0.49 0.49 0.49 3x2^ ^^! 7.6 6.6 5.6 4.5 2,21 1.92 1.62 1.31 1.9 1,7 1,4 1.2 0.93 0.81 0.69 0.66 0.92 0.93 0.94 0.96 0.98 0.96 0.93 0.91 1.2 1.0 0.90 0.74 0.66 0.68 0,49 0,40 0.73 0.74 0,74 0,75 0.73 0.71 0.68 0.66 0.52 0.52 0.53 0.53 4.7 1.36 0.48 0,35 0.59 64 0.39 *: 5 3 1.55 0.91 0,56 0.77 0.83 0.51 0,36 0.58 0.58 0.42 2x2 ft 3.9 1.15 0.42 0,30 0.60 61 0.39 2^x2 4 5 1.31 0,79 0,47 0.78 0.81 0,45 0,31 0.68 0.66 0.42 ft ^ 3.2 0.94 0.35 0.25 0.61 0.59 0.39 3.6 1.06 0,65 0.38 0.78 0.79 0.37 0.26 0.59 .54 0.42 2.4 0.71 0.28 0.19 0,62 0.67 0.40 ft 2,8 0,81 0,51 0,29 0.79 0.76 0,29 0.20 0,60 0.61 0,43 326 PROPERTIES OF SPECIAL ANGLES EQUAL AND UNEQUAL LEGS 1 UNEQUAL LEGS .^ • NOT ROLLED BY ALL THE LEADING STEEL COMPANIES FOR ADDITIONAL SECTIONS SEE PAGE 303 CEUTER OF GRAVITY -S • NOT ROLLED BY ALL THE LEADING STEEL COMPANIES FOR ADDITIONAL SECTIONS SEE PAGE 308 "v 1 CEBTER or QUI vmr X'^ SIZE THICK- NESS WEIGHT PER FT. AREA 's «S 's r 'l "i '■l y ru SIZE THICK- NESS WEIGHT PER FT. AREA '3 »S 's - 'l «X 'i y '■.Jlf INCHES INCHES POUNDS SQ. IN. IN.« IN.3 IN. IN. IN.* IN.3 IN. IN. IN. INCHES INCHES POUNDS SQ. IN. IN.' m.» IN. IN. IN.* IN.» IN. IN. IN. * U 28.9 8.50 18.7 5.5 1.48 1.69 0.C6 • 24.2 7.11 16.4 5.0 1.52 1.71 9.2 3.3 1.14 1.31 0.84 * 27.2 7.98 17.8 5.2 1.49 1.67 0.96 * i?f 22.7 6.65 15.5 4.7 1.53 1.68 8.7 3.1 1.15 1.18 0.84 * il 25.4 7.46 16.8 4,9 1.50 1.66 0.97 • 21.1 6.19 14.6 4.4 1.64 1.66 8.2 2.9 1 15 1.16 0.84 • 23.6 6.94 15.7 4.6 1.50 1.62 0.97 5x4 H 19.5 5.72 13.6 4.1 1.64 1.64 7.7 2.7 1.16 1.14 0.84 bxb H 21.8 6.40 14.7 4.2 1.51 1.60 0.97 17.8 5.23 12.6 3.7 1.55 1.62 7.1 2.5 1.17 1.13 0.84 20.0 5.86 13.6 3.9 1.52 1.48 0.97 ft 16.2 4.75 11.6 3.4 1.66 1.60 6.6 2.8 1,18 1.10 0.85 ft 18.1 5.31 12.4 3.5 1.53 1.46 0.98 14.5 4.25 10.5 3.1 1.57 1.57 6.0 2.0 1.18 1.07 0.85 16.2 4.75 11.3 3.2 1.54 1.43 0.98 ft 12.8 3.76 ■ 9.3 2.7 1.58 1.65 5.3 1.8 1.19 1.05 0.85 A 14.3 .4.18 10.0 2.8 1.55 1.41 0.98 11.0 3.23 8.1 2.3 1.59 1.63 4.7 1.6 1.20 1.03 0.86 12.3 3.61 8.7 2.4 1.56 1.39 0.99 5x3^: 22.7 6.67 16.7 4.9 1.53 1.79 6.2 2.5 0.96 1.04 0.75 4x4. a 19.9 5.84 8.1 3.0 1.18 1.29 0.77 H 21.3 6.35 14.8 4.6 1.54 1.77 5.9 2.4 0.97 1.02 0.75 6.6 1.94 3.0 1.0 1.25 1.09 0.79 5x3: 21.2 6.33 14.8 4.8 1.64 1.88 3.9 1.9 0.79 0.88 0.64 35x35 a 17.1 16.0 5.03 4.69 6.3 5.0 2.3 2.1 1.02 1.03 1.17 1.15 0.67 0.67 H 19.9 18.6 5.84 5.44 14.0 13.2 4.5 4.2 1.65 1.55 1.86 1.84 3.7 3.5 1.7 1.6 0.80 0.80 0.86 0.84 0.64 0.64 a 14.8 4.34 4.7 2.0 1.04 1.12 0.67 » 18.5 5.43 10.3 3.6 1.38 1.65 3.6 1.7 0.81 0.90 0.64 5.8 1.69 2.0 0.79 1.09 0.97 0.69 H 17.3 16.0 5.06 4.68 9.7 9.1 3.4 3.1 1.39 1.39 1.63 1.60 3.4 3.2 1.6 1.5 0.83 0.83 0.88 0.86 0.64 0.64 3x3* 11.5 3.36 2.6 1.3 0.88 0.98 0.57 4^x3 : 14.7 4.30 8.4 3.9 1.40 1.58 3.0 1.4 0.83 0.83 0.64 A 10.4 3.06 2.4 1.2 0.89 0.95 0.58 ft 13.3 3.90 7.8 2.6 1.41 1.66 2.8 1.3 0.85 0.81 0.64 2^x2^ 7.7 2.25 1.2 0.73 0.74 0.81 .... 0.47 ft 11.9 10.6 3.50 3.09 7.0 6.3 3.4 3.1 1.42 1.43 1.54 1.61 2.5 2.3 1.1 1.0 0.85 85 0.79 0.76 0.65 0.65 * 2ix2i: A 6.1 5.3 1.78 1.55 0.79 0.70 0.52 0.45. 0.67 0.67 0.72 0.70 0.43 0.43 ft 9.1 7.7 2.67 2.25 5.5 4.7 1.8 1.5 1.44 1.44 1.49 1.47 2.0 1.7 0.88 0.75 0.86 0.87 0.74 0.73 0.66 0.66 ft 4.5 1.31 0.61 0.39 0.68 0.68 0.44 \^ 18.5 5.43 7.8 2.9 1.19 1.36 5.5 3.3 1 01 1.11 0.72 3.7 1.06 0.50 0.32 0.69 0.65 0.44 17.3 5.06 7.3 2.8 1.20 1.34 5.2 2.1 1.01 1.09 0.72 * ft 2.8 0.81 0.39 0.24 0.70 0.63 0.44 ',i 16.0 4.68 6.9 2.6 1.21 1.32 4.9 2.0 1 02 1.07 0.72 2x2 ft 5.3 1.56 0.54 0.40 0.69 0.66 0.39 4x37 ft 14.7 13.3 11.9 10.6 4.30 3.90 3.50 3.09 6.4 5.9 2.4 2.1 1.23 1.23 1.23 1.24 1.29 1.27 1.25 1.23 4.5 4.2 1.8 1.7 1.5 1.3 1.03 1.03 1.04 1.02 0.72 0.72 * 1 44.2 13.00 80.8 15.1 2.49 2.65 38.8 8.9 1.73 1.65 1.28 ft 4.8 1.7 3.4 1.04 1.05 1.00 0.98 0.72 72 5S 41.7 12.25 76.6 14.3 2.50 2.63 36.8 8.4 1.73 1.63 1.28 9.1 2.67 4.3 1.5 1.25 1.21 3.0 1.2 1.06 0.96 73 39.1 11.48 73.3 13.4 2.51 2.61 34.9 7.9 1.74 1.61 1.28 ,"t 7.7 2.26 3.6 1.3 1.26 1.18 2.6 1.0 1.07 0.93 73 8x6 U 36.5 33.8 10.72 9.94 67.9 63.4 12.5 11.7 2.52 2.53 2.69 2.66 32.8 30 7 7.4 6 9 1.75 1 70 1.59 1 56 1.29 1 29 4x3 U 17.1 5.03 7.3 2.9 1.21 1.44 3.5 1.7 0.83 0.94 0.64 a 31.2 9.15 58.8 10.8 2.54 2.64 28.6 6.4 1 77 1 54 1.29 4.69 6.9 2.7 1.22 1.42 3.3 1.6 0.84 0.92 0.64 28.5 8.36 64.1 9.9 2.54 2.62 26.3 6.9 1.77 1.62 1.30 14.8 4.34 6.5 3.5 1.22 1.39 3.1 1.5 0.84 0.89 0.64 ft 25.7 7.56 40.3 8.9 2.55 2.60 24.0 5.3 1.78 1.50 1.30 * V3 15.8 4.62 5.0 3.3 1.04 1.23 3.3 1.7 85 0.98 62 6.75 44.3 8.0 2.56 2.47 21.7 4.8 1.79 1.47 1.30 35x3 • • 14.7 4.31 4.7 3.1 1.04 1.21 3.1 1 5 0.85 0.96 0.63 * 1 11 32.3 30.5 28.7 9.50 8.97 8.42 45.4 43.1 40.8 10.6 10.0 9.4 2.19 2.19 2.20 2.70 2.69 2.66 7.5 7.2 6.8 3.0 2.8 2.6 0.89 0.83 0.90 0.96 0.94 0.91 0.74 0.74 0.74 a 13.6 13.5 5.4 4.00 3.67 1.56 4.4 4.1 1.9 1.9 1.8 0.78 1.05 1.06 1.11 1.19 1.17 1.04 3.0 2.8 0.91 1.4 1.3 0.68 0.86 0.87 0.91 0.94 0.92 0.79 0.63 0.62 0.63 11 26.8 7.87 38.4 8.8 2.21 2.64 6.5 2.5 0.91 0.89 0.74 35x35 ■ti 13.5 3.65 4.1 1.9 1.06 1.27 1.7 0.99 0.69 0.77 0.53 7x35 24.9 7.31 36.0 8.2 2.22 2.62 6.1 2.3 0.91 0.87 0.74 11.5 3.36 3.8 1.7 1.07 1.25 1.6 0.93 0.69 0.75 0.53 a 23.0 6.75 33.5 7.6 2.23 2.60 5.7 2.1 0.92 0.85 0.74 ft 10.4 3.06 3.6 1.6 1.08 1.23 1.5 0.84 0.70 0.73 0.63 21.0 6.17 30.9 7.0 2.24 2.57 5.3 2.0 0.C3 0.82 0.75 3x2^ ft 9.5 2.78 2.3 1.2 0.91 1.02 1.4 0.83 0.72 77 ft ft 17.0 IS.O 5.00 4.40 26.4 22.6 6.3 5.7 5.0 2.25 2.25 2.26 2.55 2.53 2 50 4.9 4.4 4 1.8 1.6 1 4 0.93 0.94 96 0.80 0.78 75 0.75 0.75 76 8.5 7.7 2.50 2.25 2.1 1.9 1.0 1.0 0.91 0.92 1.00 1.08 1.3 0.6:^ 0.74 0.47 0.72 0.55 0.75 0.58 0.52 0.43 • 13.0 3.80 19.6 4.3 2.27 2.48 3.5 1.3 0.96 0.73 0.76 3x2 ft 5.9 1.73 1.7 1.5 0.89 0.78 0.93 0.94 1.06 1.04 0.61 0.64 0.42 0.37 0.56 0.56 0.56 0.64 0.43 0.43 6x4* 1 30.6 9.00 30.8 8.0 1.85 2.17 10.8 3 8 1 09 1 17 85 ft 5.0 1.47 1.3 0.66 0.95 1.03 0.47 0.33 0.57 0.52 0.43 u 28.9 8.50 29.3 7.6 1.86 2.14 10.3 3.6 1.10 1.14 85 4.1 1.19 1.1 0.64 0.95 0.99 0.39 0.35 0.67 0.49 0.43 * fii 3.1 0.90 0.8 0.41 0.97 0.97 0.31 0.20 0.53 0.47 ■ 44 6x3r 1 28.9 27.3 8.50 8.03 29.2 27.8 7.8 7.4 1.85 1.86 2.26 2.24 7.2 6.9 2.9 2.7 0.92 0.C3 1.01 0.99 0.74 0.74 2^x2: ft 6.8 6.1 2.00 1.78 1.1 1.0 0.70 0.02 0.75 0.76 0.88 0.85 0.64 0.58 0.46 0.41 0.56 0.57 0.63 0.60 0.42 0.42 TWO ANGLES IN TENSION 327 NET AREAS IN SQ. INS., AND ALLOWABLE TENSILE STRENGTH IN THOUSANDS OF LBS. AT 16,000 LBS. PER SQ. IN., FOR TWO ANGLES | EQUAL LEGS UNEQUAL LEGS | DIAM. OF HOLES Ve' LARGER THAN DIAM. OF RIVETS ONE HOLE IN EACH ANGLE DEDUCTED TWO HOLES IN EACH ANGLE DEDUCTED DIAM. OF HOLES Vb' larger THAN DIAM. OF RIVETS ONE HOLE IN EACH ANGLE DEDUCTED TWO HOLES IN EACH ANGLE DEDUCTED DIAM. OF RIVETS % % % 1 % % ya 1 DIAM. OF RIVETS % % % 1 % % Va 1 1 "^ ; w : t/) : w ■ to : . ia: . " *• ISO * UNIT STRESS EXCEEDS 14.000 POUNDS POUNDS AT 16,000- 70 //r THE RIGHT OF " ■• .. .. 160 SIZE THICK- NESS LENGTH OF MEMBER IN FEET SIZE THICK NESS LENGTH OF MEMBER IN FEET 3 4 6 G 1 ■> 8 9 10 1 11 12 13 14 IS 16 17 18 19 3 4 6 6 7 i 8 9 10 U lA 240' 228* 232 220 222 211 213 202 204 194 1^5 185 186 177 177 168 168 160 159 151 150 141 134 132 126 123 117 113 109 104 100 95 92 }l 104 98 96 90 89 83 81 76 73 68 65 61 58 54 50 47 143 216* 208 200 191 184 175 167 159 151 143 135 127 119 111 103 95 87 ^ 91 84 77 84 77 71 77 71 65 70 65 59 64 59 54 57 52 48 50 46 42 43 ■40 36 il 203* 196 188 180 173 165 157 150 142 135 127 119 112 104 97 89 82 6x4 8x8 190* 183 176 169 162 155 148 140 133 126 119 112 105 98 91 83 76 A 70 64 59 54 49 44 39 34 \l 178' 171 165 158 151 145 138 131 125 118 112 105 98 92 85 78 72 62 58 53 49 44 39 35 30 165* 159 153 146 140 134 128 122 116 110 103 97 91 85 79 73 67 A 55 51 47 43 39 35 31 27 il 152* 138* 146 133 141 128 135 123 129 118 124 113 118 108 112 103 107 98 101 92 96 87 90 82 85 77 79 72 73 67 68 62 62 57 il 47 95 44 87 41 79 37 70 34 30 27 45 42 23 '26" 62 53 A 125* 120 116 111 107 102 97 93 88 84 79 74 70 65 61 56 51 89 81 73 66 58 50 112' 152 107 144 103 136 99 128 95 120 91 112 87 104 83 79 75 70 66 62 58 54 50 46 6x3^ 15 * 83 77 70 76 70 64 68 63 58 61 56 51 54 49 45 46 43 39 39 36 33 96 88 80 72 64 H IM 136 128 121 113 106 98 91 83 76 68 61 A 64 58 62 47 41 35 30 1S5 128 121 114 107 100 93 86 79 72 65 58 57 52 47 42 37 32 27 6x6 i% 126 117 119 111 113 105 106 99 100 93 93 87 87 80 80 74 74 68 67 62 61 56 54 50 A 50 44 46 40 42 36 37 32 33 29 28 25 24 21 ii 108 102 97 91 85 80 74 69 63 57 52 46 73 67 60 54 47 41 34 98 93 88 83 78 73 68 63 58 52 47 42 « 68 62 56 SO 44 38 32 A 89 85 80 75 71 66 62 57 53 48 43 39 62 57 51 46 40 35 29 80 76 71 67 63 59 55 51 47 43 39 35 5x35 A ^ 56 51 52 46 46 42 41 37 36 33 31 28 26 24 A 70 67 63 59 56 52 49 45 42 38 34 31 A 45 41 37 33 29 25 21 4x4 A 60 69 64 59 53 48 57 63 59 54 49 44 54 57 53 49 44 40 51 51 48 44 40 36 48 45 42 39 36 33 30 27 .... 5x3 A iJ A ^ A 39 32 61 56 51 45 40 35 30 54 SO 45 41 36 32 27 47 43 40 36 32 29 24 25 21 22 18 28 25 24 21 19 18 15 45 42 39 35 32 40 37 34 31 28 34 31 28 26 24 41 37 34 31 27 ~34- 31 29 26 23 A 42 39 35 32 28 24 21 35 31 27 24 20 16 37 34 31 27 24 21 18 A 29 26 23 20 17 14 A A 31 49 44 28 44 40 26 39 36 23 21 IS 24 22 15 .... 4x3 A ^ A 48 44 39 35 43 39 35 31 38 34 31 32 29 26 23 27 25 22 20 22 20 18 16 34 31 29 27 05X02 40 36 32 28 24 20 30 27 23 20 17 14 A 35 32 28 25 21 18 A 25 23 20 17 15 12 31 28 25 22 19 10 A 40 35 31 26 22 h 26 32 23 28 21 13 16 16 13 35x3 A J 36 32 27 32 28 24 28 24 21 24 21 18 20 17 15 ::;; 24 20 3x3 h A ^ A 28 25 21 25 22 18 21 18 16 18 15 13 U 12 11 .... A 23 31 21 27 18 15 13 22 1» 17 21 15 18 13 11 11 9 " .... 05XZ2 A A 28 24 20 24 21 17 20 17 15 16 14 12 .... 14 19 16 13 10 j 16 14 12 10 25x21 A 16 13 11 8 A 25 21 18 14 A 13 10 11 8 9 7 7 5 3x2^ A A \ A * 21 18 15 15 13 11 8 18 16 13 15 13 11 12 11 2x2 A ^ A 13 11 9 7 — - — — r '..\\ 2-ix2 8 10 8 7 12 10 8 7 .... j .... 6 8 6 5 5 4 SIZE THICK- NESS 3 4 5 16 1 7 8 9 1 10 1 11 12 13 14 16 1 16 1 17 18 19 SIZE THICK- NESS 3 4 6 6 7 8 9 ~10 11 LENGTH OF MEMBER IN FEET' P 1 LENGTH OF MEMBER IN FEET TWO ANGLE STRUTS- SAFE LOADS 331 SAFE LOADS IN THOUSANDS OF POUNDS AT 16,000- 70 //r. for explanations SEE PRECEDING PAGE 1 1-1*11 5«RII^I ^?S"I ^^'^ ^^ •'O" ^^^ Ls OR OVER. AND Si/iXZyiXV*. AND 3'/2 X 2yi X S/^« =^f== k'N*Y"£.f^ATclll°A"R;*FSl3^^,^°3%"^^2.>^ A°n"d"2'1;^V^^^ a./xai^.X'/. AND 3./x2./.XV.. ^ _, W B. TO B. FOR ALL OTHER ANGLES '^ " I | LEAST RADIUS ABOUT AXIS AA ANY DISTANCE APART ? 't SIZE THICK- NESS LENGTH OF MEMBER IN FEET LENGTH OF MEMBER IN FEET | 3 4 6 6 7 8 9 10 11 12 13 14 L5 16 17 IS 19 20 21 91 84 77 70 3 4 6 6 7 8 9 10 11 12 13 98 92 87 81 74 68 62 55 48 14 76 72 66 60 55 49 43 6x4 6x35 5x31 5x3 4x3 3ix3 32-x22i 3x2i 2-ix2 18 A I'l H H A A kl A A A JJ A A A A A A A A A A ^ A A A A A 232* 217* 201' 186* 170* 154* 138* 121' 104* 216* 202* 187* 173* 158* 143* 128* 113* 97* 167* 154' 141* 128* 114* 101 • 87' 73* 141' 129' 117* 105 92 80 67 111 101 91 80 69* 59' 91 82 63 53 75 67 58 49 39 59 51 43 35 39 33 27 21 224* 210* 195* 179* 164 148 133 117 101 208 194 180 166 152 137 123 108 93 161 148 136 123 110 97 84 70 135 123 111 100 88 76 64 106 96 87 76 66 56 86 77 68 59 50 71 63 55 46 37 55 48 40 33 36 31 25 19 216 202 188 173 158 143 128 112 97 199 186 172 159 145 131 117 103 89 154 142 130 lis 105 93 80 67 128 117 106 95 83 72 60 100 91 82 73 63 53 81 72 64 56 47 67 69 51 43 35 51 44 37 30 33 28 23 17 208 195 181 166 152 138 123 108 93 191 178 165 152 138 125 112 98 85 148 136 125 113 101 89 77 64 122 111 100 90 79 68 57 95 86 78 69 60 50 75 68 60 52 44 63 55 48 41 33 47 41 34 28 29 25 20 16 200 187 174 160 146 132 118 104 89 182 170 157 145 132 119 106 94 81 142 130 119 108 96 85 73 61 115 105 95 85 75 64 54 89 82 73 65 56 43 70 63 56 49 41 58 52 45 38 31 42 37 32 26. 193 180 167 154 140 127 113 99 86 173 162 150 138 125 113 101 89 76 135 124 114 103 92 81 70 68 109 99 89 80 70 60 50 84 77 69 61 63 43 65 58 52 45 38 54 48 42 35 28 185 173 160 147 134 121 109 95 82 165 ■ 154 142 131 119 107 96 84 72 129 118 108 98 87 77 66 55 102 93 84 75 66 !? 78 72 65 57 50 42 177 165 153 141 128 116 104 91 78 156 146 134 124 112 101 90 79 68 123 113 103 93 83 73 62 52 95 87 78 70 61 52 44 73 67 60 53 46 39 169 158 146 134 122 110 99 86 74 148 138 127 117 106 95 85 75 64 116 107 97 88 78 69 59 49 161 150 139 128 116 105 94 82 71 139 130 119 110 153 143 132 122 110 100 89 78 67 146 1 136 1 126 1 115 1 J8 130 28 121 18 112 39 102 98 93 39 84 79 75 39 65 59 66 122 114 114 106 98 901 81 73 65 56 48 88 82 74 68 .... 72 65 59 53 47 40 34 29 106 99 01 83 75 67 60 62 45 66 59 99 91 84 77 63 62 55 48 41 219 206 191 176 161 146 .131 116 100 200 188 175 162 148 134 121 107 92 156 U4 132 121 108 96 33 69 130 119 108 97 86 74 63 104 95 85 75 65 55 88 79 70 61 51 68 60 53 45 36 207 194 180 167 153 139 124 110 95 187 175 163 151 139 126 113 100 86 146 135 121 113 101 89 78 65 119 109 99 90 79 69 68 96 88 79 70 60 61 81 73 65 56 47 62 55 48 41 33 50 44 37 30 32 27 22 17 196 183 170 157 144 131 117 104 90 173 193 151 140 129 117 105 93 80 136 126 116 105 95 84 72 61 109 100 91 82 73 63 53 88 80 72 64 56 47 75 67 60 52 44 55 49 43 36 30 45 40 33 27 ■183 171 160 148 135 123 110 97 84 160 150 140 130 119 108 97 86 75 126 117 107 98 88 78 67 57 98 90 82 74 66 67 48 80 73 66 69 51 43 68 62 55 48 40 171 160 149 138 127 115 103 91 79 146 138 128 119 110 99 89 79 69 116 107 99 90 81 72 62 53 159 149 139 129 118 107 96 85 74 147 137 128 119 109 100 90 79 69 134 126 118 110 100 92 83 73 64 122 115 108 100 92 84 76 67 68 110 103 97 91 83 76 69 61 53 61 56 50 45 40 66 61 57 53 48 42 37 32. lbs 96 87 78 70 61 62 97 90 82 75 67 60 53 46 39 78 71 64 58 51 44 38 31 104 94 84 74 63 131 122 112 103 93 84 74 65 56 103 95 86 78 69 61 52 43 132 125 116 108 119 112 104 97 90 82 74 66 67 96 89 82 75 68 60 62 44 122 T 114 1 104 96 86 78 69 60 14 m 36 93 37 89 39 82 30 73 72 66 34 58 i6 61 17 43 lbs 100 93 87 80 73 66 59 51 86 80 74 91 87 81 76 71 64 58 52 46 76 71 66 60 65 48 42 36 '27' 23 '33' 30 26 22 90 80 70 60 100 90 82 73 63 106 98 91 83 75 66 67 48 55 110 101 92 83 74 65 65 46 97 80 81 73 31 86 33 77 J5 70 38 63 6^ 61 54 47 40 65 56 48 40 W 66 )2 48 15 41 S7 34 33 66 57 51 50 .... a .... 39 .... 33 .... !7 .... 16 .... 12 .... 38 .... 34 .... 30 .... 25 .... 89 81 72 65 57 49 40 68 62 56 49 43 36 82 75 67 60 52 45 37 62 57 62 46 40 34 69 61 64 48 41 34 57 62 47 42 36 31 39 35 31 28 23 33 29 26 22 17 63 56 49 43 37 31 51 47 43 38 33 28 83 81 74 67 77 71 65 69 63 46 39 64 59 63 48 41 35 65 50 45 39 33 ■ 67"' 61 57 62 46 40 34 57 52 47 42 37 31 49 44 40 ■■■57 52 48 44 40 34 29 49 45 40 36 32 27 42 39 35 31 26 60 51 44 72 60 60 53 46 39 62 56 50 44 37 60 54 54 49 44 38 32 46 40 35 30 24 4 C O o O" o o xe DrMEx?io^"S, 106:6 Reference Lines, 107:1 References, cross, 2:3 to otha drawings, 53:1 Reinforced Concrete Foot- es-gs. 291:1 Reinfohcing Plates, bridges, 130:1 design, 2S4:3 bearing, 2S4:4 tension, 2S6:1 rivets, 2So:l, 2S62 columns, 276:4 when used, 130:1, 2S4:1 Representation, conventional, 38:3 Required Lists. S1:1 Resistance of web plat«, 223 :3 Resisting Moments, beams, 198:1 girders, 2182 pins, table, 333 RESTR-iixED Beams, 192:4 Resttltants, diagrams, 312. 313, 314 Reatsions of drawings, 182 :4 Ridge STRirrs, 118:5 RkShts an-d Lefts, 812 Ri^-ets, 228:1 assumptions in design, 228:4 axial tension, 228:4 \ beam connections, 2342. 235:1 bearing, 230:3 bearing values, tables, 308-311 incl. bending, 228:4 code, 304 covmtersunk, bridge trusses, 1302 column bases, 134:4 driving, 30:4 how shown, 40:6 value, 2312 Rivets (Ckmtinued) cover plates, I developed plate, 2642 I flange stress, 264:1 ^ pointsconsidered,1062,263:3 ^ critical, 237:3 ^ design, 229:1 diameter, nominal, 230:1 J distribution of stress, 228:4 , double shear, 2302 , double-shear values, tables, I 30S-311 incl. j driving, 30:4 I driving clearance, 73 .5 ; table, I 304 J eccentric connections, see I "eccentric connections" I edge distance, 69:3; table, 305 r field, 2282 erector's lists, 1762 grip, 1762 length, 1762 number, 177:1 summary, 177:1 ; fillers, 232:1, 2352 flange, sff "flange rivets"' flaUened, 40*, 130:2. 2312 floor-beam connections, 236:1 gages. 68:5, 106:3 gusset plat€s, 2332. 3 heads, shape, 30:4 table, 304 weight. 170:1 holes, sff "holes" how billed, 45:4 how dimensioned, 492 how made, 31 :6 how shown, 40:6 indirect, 232:1 inspection, 31:3 limiting value, 231:1 list, 176:1, 2 INDEX 349 Rivets (Continued) ; loose, 31:3 l maximum spacing, table, 305 minimum spacing, tables, 305, 306 minimum stagger, diagram, 305 more than one used, 228:1 nominal diameter used in de- sign, 230:1 noting size, 52:4 ■number, 231:1 pitch, 68:1 position in member, 228:3 reinforcing plates, 285:1, 286:2 shank, 30:4 shear, 230:2 shop, 30:4, 228:2 single shear, 230:2 single-shear values, , ;tables, 308-311 incl. spacing, 68:1 ^ ccjntinuous, 70:4 cover plates, 69:2 maximum, 69:1, table 305 I n linimum, 68 :6, table 305 n lultipUcation table, 307 I (tactical points, 70 :2 1 Tiles, 68:2 ! rtitch, 69:4 I subdivisions, 50:2 uninterrupted, 49:5 usual, 70:3; table, 305 sp lice plates, see "splices" st a ggered, 49 :2 f ,tlffeners, 96:3, 268:2, 269:4 stitch, 69:4, 112:4, 1182 strength, in bearing, 230:3 in shear, 230:2 stringer conneotions, 235:2 unit stresses, 350 ;2, 3 use, 228:1 Rivets (Continued) values, tables, 308-311 incl. weight, 170:1 when inked, 60:3 Rivet Lines, 37:1, 49:2 Riveted Joints, design, 229:1 Riveted Tension Members, see "tension members" Riveters, 30:4, 60:3 Riveting, 30:4 Rockers, 289:3 Rods, bracing, 119:2 design, 207:2, 3, 4 drawing, 150:1, 174:1, 174:2, 4 how billed, 44:4 how shown, 39:2 lengths, 174:4 marking, 174:4 sag, 166:1, 174:4 tables, 315 tie, 166:1, 174:4 Rod Connections, 316 Rollers, 174:1, 289:3 Rolling Steel, 23:3 Rolls, effect of spreading, 25:1 finishing, 23:3 roughing, 23:3 straightening, 29:1 Roof Plates, 146:4 Roop Trusses, arrangement on sheet, 115:1 bottom-chord bracing, 119:3 camber, 113:2 center hanger, 118:3 flat, 113:1 form of members, 115:3 future extension, 119:4 gable girts, 119:5 gusset plates, 118:1 heel plates, 114:3 louvres, 119:6 Roop Trusses (Continued) peak plates, 118:5, 234:1 pitch, 114:1 purlin connections, 119:1 purlin spacing, 114:2 ridge strut, 118:5 rod connections, 119:2 saw tooth, 113:2 scale, 115:2 sections for shipment, 118:4 shipping marks, 82:2 stitch rivets, 118:2 supports, 114:3 types, 1132 use, 113:1 working lines, 115:2 Root Areas, 207:4, table, 315 Rotary Planer, 31:1 Rotation, center of, 237:3 Roughing Rolls, 23:3 Rule, bending moment, short-cut, 188:2 eccentric connections, 238:1 net section, 210:1 rivet spacing, 68:2 Ruling Pens, care, 56:3, 57:1 cleaning, 56:3 filling, 56:3, 58:8 lettering with, 57:3 setting, 58:9 sharpening, 57:1 stopping, 58:7, 59:1 use, 56:3 RuNWAT Beams, ordering, 164:7 Safe Loads, anglfes, tables, 330, 331 compression members, 211:2 Sag Bars, 146:2 Sag Rods, 146:2 drawing, 174:4 Sag Rods (Continued) holes, 91:1 marking, 174:4 ordering, 166:1 spacing in purlins, 91 :1 table, 316 Saws, cold, 28:1 Saw-tooth Truss, 113:2 Scale, of drawing, 35:3 bracing systems, 138:5 roof trusses, 115:2 use, 35:3 Scale Guard, 35:3 Schedule, column, 159 a, 161:1 Scope of this book, 1 :1 Scratchbr, avoid use, 63:3 Seat, erection, 73:2 Seat Connection, beams, 73:2 design, 235:1 girders, 134:2 independent, 232:2 Section, for shear, 184:1 least net, 209:1 net, at ends of tension mem- bers, 210:2 roof trusses, 118:4 Section Lines, 37:2 Section Modulus, 199:1 tables, angles, 325, 326 Bethlehem beams, 324 channels, 323 I-beams, 322 rectangular beams, 319 Sectional Views, 37:1, 134:1 Segment of beam, 183:4, 184:4 Selvage Edges, 55:5 Separators, beams, 91:5, 174:1 grillage, 292:1 Separators (Continued) table, 316 Setting of pen, 58:9 Shade Lines, 38:2 Shank, rivet, 30:4 Shape of cross section, 26:1 Shapes most used, 38:4 Sharpening ruling pen, 56 :3 Shear, 183:1 arrangement of computation, 185:1 combined loads, 188:1 concentrated loads, 186:1 Cooper's engine loading, 193:1,2, 194:1; table, 318 definition, 184:1 design for, beams, 292:1, 294:1 girders, 218:2 double, 230:2 forces considered, 183:4 formulas, 184:3 intensity, 202:1 longitudinal, 202:1 live-load, cantilever beams, 190:1 live-load, simple beams, 189:3 pins, 279:2 principles, 183:2 reactions, 185:2, 194:2 relation to bending moment, 189:1 rivets, 230:2 signs, 6, 183:3 single, 230:2 sketches, 184:4 uniform loads, 187:1 values for rivets and bolts, tables, 308-311 incl. Sheared Plates, 25:3, 165:2 Shearing, 28:1 Shearing Stresses in web, 266:1 350 INDEX Shears, 28:1 Sheet Numbers, 54:5 assembling marks, 80:3 Shield, erasing, 63:4 Shipments, order bills, 164:1 Shipping, 31:5, 118:4 Shipping Bills, 171 :1 when made, 22:1 Shipping Marks, 80:6 bridge trusses, 82:1, 123:1 component parts, 80:7 list, 324 marked conspicuously, 81:1 members combined, 81 :3 ofiBce buildings, 81 :5 opposites, 81:4 rights and lefts, 81 :2 roof trusses, 82:2 tie and sag rods, 82:3 use, 52:5, 80:6 Shoes, bridge, 289:3 Shop Bills, arrangement, 167:4 bolts for shipment, 167:4 calculated weights, 170:1 component parts, 167:3 form, 167:2 itemizing, 169:1 notes, 167:4 numbering, 167:2 use, 167:1 weights of rivet heads, 170:1 when made, 22:1 Shop and Shipping Bills, 173:1 combined with drawing, 173:2 Shop Methods, 27:2, 3 Shop Rivets, see "rivets" Shrinkage Scales, 31 :6 Signs, conventional, 43:2 of forces and moments, 6, 183:3 Simple Beams, 83:1 Single Punch, 29:5 Single Shear, 230:2 Single Latticing, 70:1 Size, 46:1 bearing plates, 288:2 drawing, 35:4 holes, noting, 52:4 pin holes, 123:3 rivet holes, 30:4 Sketches, forces, 184:4 members, 35:1 Sketch Plates, ordering, 165:2 Skews ACK Angles, 94:3 Skewbacks, 94:3, 316 Skew Connections for beams, 94:5 Skew Portals, 146:5 Skew Work, 146:5 Slag, 23:1 Slbnderness Ratio, 211:2 Slope, calculation, 76:2 how dimensioned, 50:7 roof, 114:1 Soaking Pits, 23:3 SoAPSTONE, 29:2 Soil, bearing, 292:3 Spacing, lattice bars, 70:1 purlins, 114:2 rivets, 68:1 continuous, 70:4 cover plates, 69:2 flange, see "flange rivets'' maximum, 69:1; table, 305 minimum, 68:6; table, 305 multiplication table, 307 practical points, 70:2 stitch, 69:4 stiff eners, 96:3, 268:2, 269:4 usual, 70:3 Spacing Rack, 29:5 Specifications, 68:4. 164:3 Spiking Pieces, 91 :3 Splice, Splices, 270:1 bridge members, 123:6 columns, 276:2, 3, 4 design, 270:2 girders, field, 275:1 flange, angles, 274:2 cover plates, 274:1 curved ends, 274:3 when used, 273:2 where placed, 273:2 web, design, 270:5 moment, 272:1, 2 shear, 271:1, 272:2 when used, 270:4 where placed, 270:4 indirect, 274:2 raUs, 317 types, 270:3 use, 270:1 Splice Angles, 274:2 Splice Plates, 270:2 Sponge Eraser, 56:2, 64:1 Squad, 20:4 Squad Foreman, 20:4 Squares, table, 332 Staggered Rivets, how dimensioned, 49:2 minimum, diagram, 305; table, 306 Standard Bearing Plates, table, 316 Standard Connection Angles, tables, 298-302 incl. Standard Gages, 68:5, 132:1, 136:1 tables, angles, 303 channels, 300, 301 Standard Gages (Continued) tables (Continued) I-beams, 298, 299, 302 Standards, rails, 44:7, 68:3 Static Loads, 189:2 Steel, manufacture, 23:2 ruling, 23:3 unit stresses, table, 317 Stipfenebs, or Stiffening Angles, columns, 132:3, 134:2 cutting, 29:4 girders, end, 266:4 design for bearing, 267:1 gages, 106:3 length, 96:1 position, 266:2 rivets, 268:2 strength in compression, 268:1 intermediate, crimping, 29:4 97:1, 269:5 rivets, 96:3, 269:4 spacing, 269:3 when used, 269:2 grillage beams, 292:1 ordering, 165:1 outstanding legs in contact, 106:4 Stiffening Girders, 112:6 Stitch Rivets, 69:4, 112:4, 118:2 spacing, 69:4 Stock Yard, 28:1 Stove, 23:1 Straight-edge position, 58:5, 6 Straightening Rolls, 29:1 Straight-line Formula, 211:2 Strain, 197:3 Strength of, compression members, 211:2 Strength of (Continued) . countersunk rivets, 231 :2 flattened rivets, 231 :2 rivets in bearing, 230:3 > rivets in shear, 230:2 single angles in compression, table, 330 two angles in compi'ession, table, 331 two angles in tension, table, 327 web plates, 255:2 Stresses, combined bending and axial, 215:1 compressive, 197:3 flange, 221 :2 horizontal, 221:2 plate gu-ders, 221:1, 2, 223:1 tensile, 197:3 unit, see "unit stress" vertical, 248:2 Stress Sheets, 20:3 Stringer Connection, dtieign, 235:2 Stroke, continuous, in inldng, 58:8 Structural Draftsman, 1£I:1 Structural Drawings, 33 : 1 appearance, 55:1 elements, 33:7 method of making, 36:1, 65 '.1,3 Structural Shapes, 38:4 Structural Shop, 19:5 Structural Steel, 23:2 Struts, bracing systems, 138:3 collision, 120:2 eave, 138:3, 146:3 portal, 141:4 ridge, 118:5 top, 141:4 Stub Pens, 57:3 INDEX 35} Students' Drawings, checking, 182:2 Subdivisions, rivet spacing, 50:2 SuB-PBATT Truss, 120:2 Sub-punching, 30:2 Sum of dimensions, 50:2 Summary, assembling marks, 80:5 field rivets and bolts, 177:1 flange rivet spacing, 257 Supplementary Dimension Lines, 50:1 Surface of Tracing Cloth, prepared, 56:2 restored, 63:6 Sway Bracing, 141:4 SwEDGE Bolts, 152:3, 316 Symmetrical Gusset Plate, 234:1 Symmetrical Loads, 185 :2 Symmetrical Members, 34:5 ' Systems of bracing, 138:1, 2, 3 T, or Tee, how billed, 44 :5 how shown, 40:1 Tables, arrangement, 1:1 description, 334-338 incl. Tacks, 56:1 Tank Work, 146:4 Templets, 27:5 Templet Shop, 19:4, 27:5 Tensile Strength of two angles, table, 327 Tension, initial, 139:1 on rivets, 228:4 Tension Members, cross section, 206:3, 208:2 design, 206:2, 207:1 effect of rivet holes, 206:4 eye bars, 207:5 'Xension Members (Continued) reinforcing plates, 286:1 riveted, bending and tension, 215:1 design, 208:4 net arcti, 208:2 at ends, 210:2 least, 209:1 working rule, 210:1 size of rivet holes, 208 :2 rods, 207:2,3, 4 Tests for students, 182:2 Theorem of three moments, 192:4 Thickness, bearing plates, 288:3 girder webs, 266:3 metal, compression members, 212:2 Through Bridge, 120:2, 152:1 Through Girders, bending moment, 196:2 Ties, cut for curves, 97 :2 Tie Plates, size, 216:2 use, 208:1, 212:2 Tie Rods, design, 201 :3 drawing, 174:4 grillage beams, 292:1 holes, 90:2 marks, 82:3, 174:4 ordering, 166:1 spacing, 90:2 table, 316 Tight Fits, 72:3 Timber, unit stresses, table, 320 Title, component parts, 54:2, 3 smaller drawings, 54:4 when inked, 61:1 where placed, 54:1 Top Angles, 89:2, 132:3 Top Lateral Bracing, 141 :4 Top View, 34:1 Tracers, 36:1, 65:2 Tracing, nee "inking" Tracing inverted when com- pleted, 61 :2 Tracing Cloth, care of, 55:3 drawing directly in ink on, 65:1,3, 66:4 dull side used, 55:4 preparation of surface, 56 :2 selvage edges removed, 55 :5 stretching, 56:1 surface restored, 63:6 Tracing Cloth Powder, 56:2 Track, 225:1 Travelers, 20:1 Trusses, bridge trusses, see "bridge trusses" roof trusses, sec "roof trusses" Type used in this book, 2 :4 Types of, bearing plates, 288:1 columns, 131:3 latticed girders, 108:2 layout, 75:4 members, bridges, 123:4 roof trusses, 115:3 plate girders, 95:2 trusses, bridges, 120:2 roofs, 113:2 Uniformly Distributed Loads, bending moment, 187:1, 188:2 cover plates, 259:6 flange rivets, 244:2, 3 short-cut rule for bending moment, 188:2 Units, bending moments, 3:2, 184:2 design of beams, 199:2 working, 34:6 Unit Stress, bearing, 230:3 bending, 198:2 bolts, 230:4 compression, 211:2 rivets, 230:2,3 shear, 230:2 steel, table, 317 wood, table, 320 Universal Mill (U.M.) Plates, 25:3 ordering, 165:2 use in girders, 97:2 Unsymmetrical Bracing, 141:1 Unsymmetrical Members, 212:1 U-Plates, 316 Upset Rivets, 30:4 Upset Rods, 207:4; table, 315 Valley Roof Construction, 146:5 Values op Rivets, bearing, 230:3 interpolation, 231:1 limiting, 231:1 shear, 230:2 tables, 308-311 incl. Variation, mill, 25:2, 88:1 Vertical Flange Plates, 227:1 \'ertical Flange Stress, 248 :2 Views, 33:3, 4, 34:1, 121:3 distance between, 34:2 sectional, 37:2, 134:1 Visible Edges, 37:1 Wall Plates on beams, 94:2 Warren Truss, 108:2, 120:2 Washers, beveled, 174:1 how billed, 45:3 how shown, 41 :3 O.G., 174:1 Web Connections for beams, 83:6, 234:2 Web Plates or Webs, beams, 202:1, 293:3 compression members, thick- ness, 212:2 plate girders, 96:2 design, 218:4 length, 96:2 resistance, 223:3 shearing stresses, 266:1 splice, see below thickness, 266:3 weights, table, 321, Web Splices, design, 270:5 moment, 272:1, 2 shear, 271:1, 272:2 when used, 270 :2, .4 where placed, 270:4 Web Stippeners, see " stiff en- ers" Weights, beams, assumed, 200:3 calculated, 170:1 tables, angles, 303 Bethlehem beams, 302 bolts, 304 channels, 300, 301 I-beams, 298, 299, 302 plates, 321 rails, 317 rivets, 304 rods, 315 Wheel, critical, 191:1, 195:1 Wheel-load Systems, 193:1 Wide Lines, inking, 59:3 352 INDEX WioTHS of cover plates, 219:3 Wind Bracinq, 138:1, 145:1 Wood, unit stresses, table, 320 weight, 200:3 Wooden Beams, actual sizes, 199:3 design, 199:3 properties, table, 319 shear intensity, 202:1 WoBKiNQ Drawings, 33:1 Working Lines, 37:1 bracing, 138:4, 5 layouts, 76:1, 2, 77:1 trusses, bridge, 121:3 roof, 115:2 Working Rule, ^ eccentric connections, 238:1 net section, 210:1 Working Units, 34:6 Yard, receiving or stock, 28:1 Z-BAHS, how billed, 44:6 how shown, 40:2