Cornell University Library TG 145.M87 Designing and detailing of simple steel 3 1924 004 638 874 CORNELL UNIVERSITY LIBRARY Given to the COLLEGE OF ENGINEERING by the Dept. of Machine-Design. ^^1 Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004638874 DESIGNING AND DETAILING OF SIMPLE STEEL STRUCTURES IIIIII[.IIIIIIIIIIIJ !^ Qraw-MlBook Gx Irm PUBLISHERS OF BOOKS F O R^ Coal Age ^ Electric Railway Journal Electrical World v Engineering News-Record American Machinist v The Contractor Engineering S Mining Journal ^ Power Metallurgical S Chemical Engineering Electrical Merchandising IffiflfngmfflfnfffMffiiffff^^ DESIGNING AND DETAILING OF SIMPLE STEEL STRUCTUEES BT CLYDE T. MORRIS, C.E. PBOPHSSOH OF STBTjCTURAL BNCHNEBBING, OHIO STATE UNIVEBSITT, MBMBBB OF THE AMBEIOAN SOCIETY OF CIVIL ENOINEEES, MEMBER AMEBICAM SOOIETT FOR TESTINQ MATERIALS, MEMBER SOCIETT FOB THE PROMOTION OF BNeHNEBRIHO EDUCATION Third Edition Revised and Reset Second Impression McGRAW-HILL BOOK COMPANY, Inc. 239 WEST 39TH STREET. NEW YORK LONDON: HILL PUBLISHING CO., Ltd. 6 & 8 BOUVEBIE ST., E. C. 1914 COPTBIGHT, 1914, BY THE McGRAW-HILL BOOK COMPANY, Inc. COPYBIGHT, 1909, BY CLYDE T. MORRIS PEEFACE TO THIRD EDITION After four years use in the class room, the author has decided that the arrangement of the chapters could be improved and as he wished to include some additional material in the book, he has taken this opportunity to change the order of presentation of the different topics. The whole book has received careful revision and several of the chapters have been partially rewritten. A new chapter on highway bridges has been added together with a reprint of the Specifications for Steel Highway Bridges of the State Highway Department of Ohio. About half of the figures in the book have been redrawn and a number of new figures added and such errors as have been discovered in the text have been corrected. Clyde T. Mobbis. Columbus, Ohio, March, 1914, PREFACE TO FIRST EDITION The object sought in this book is to collect from the many larger and more exhaustive works on structural steel design, those parts which are applicable to simple structures, and which can be taken up in technical schools in the limited time usually allotted to the subject; and at the same time, to show by general cases and specific examples how the simple laws of statics may be applied to the details of steel structures with the object of producing details which are in accord with the stresses they have to transmit. Tl PEEFACE TO FIRST EDITION It is presumed that the student has already finished a course in stresses, and little time is given here to the methods of calcu- lating the primary stresses in structures. An effort has been made to make the nomenclature, through- out, conform to that used in " Stresses in Structures," by Prof. A. H. Heller, and a table is given so that the meaning of any letter or character in any formula can be at once determined by reference to it. In some cases where reference is made to another book, and a formula is taken bodily from it, the nomenclature of the original author is retained and the meaning of the letters given in connection. Cross references to other articles in this book are indicated by figures in parentheses giving the article number, thus (14). References to other works on the subject are given in foot notes. The author wishes to acknowledge his indebtedness to Mr. C. C. Heller for the privilege of using various manuscript notes and sketches, left at his death by Prof. A. H. Heller, which have formed the basis of many of the articles in this book. It is hoped that by the illustrations given and the methods employed, the reasons will be made apparent for many of the details conmionly employed in structural* work, and which are many times put in by " rule of thumb " and too often without due consideration of the stresses they have to carry. Clyde T. Moreis. Columbus, Ohio. AprU 6, 1909. NOTATION A = total area of cross-section (square inches). Ap^Mei area of one flange. A.„ = gross area of cross-section of web = th. a — distance shown in the figure. b = distance shown in the figure. C = centrifugal force per pound. C Ci C2 C etc = Constants of integration. c = distance shown in figure. D = direct stress. D.L. = dead load or dead load stress. d = distance from neutral, axis to a parallel axis. = depth between centers of gravity of the flanges of a girder. = depth between centers of chords of a truss. iJ = modulus of elasticity. e = distance shown in the figure. = eccentricity of application of load. jff= horizontal reaction. A = depth of the web of a girder (inches). Z= moment of inertia. k = distance shown in the figure. fci = distance between centers of bearings at the top of post. ^2 = distance between centers of bearings at the bottom of post. L= total length. L.L. = live load or live load stress. h h etc. = partial lengths. ilf= moment about any point or bending moment. iV= number of panels. P= concentrated load or force. 2?= panel length. i2= reaction. = resultant of two or more forces. viu NOTATION r= radius of gjTation. /S = shear. s=uiiit stress. si = maximum unit stress in extreme fiber. P Se=imit stress in compression =—. A Sp = dead load unit stress. sx, = live load unit stress. S|=unit stress in tension. s^= working unit stress. < = thickness of web of plate girder. y = vertical reaction due to horizontal forces. V = distance perpendicular to the neutral axis. W = total uniform load. w=\oa,A per foot. e = angle shown in figure. = angle with the vertical made by a diagonal truss member. CONTENTS CHAPTER I FAoa Designing and Estimating 1 Art. 1. Classes of Structural Steel Work 1 2. Kinds of Shops 2 3. Proposals and Contracts 2 4. Designs and Estimates 3 5. Time Savers 8 6. Order of Estimating 9 7. Specifications 13 8. Stress Sheets and General Plans 14 CHAPTER II Riveting 16 9. Dimensions of Rivets 16 10. Rivet Holes 17 11. Driving Rivets 18 12. Proper Sizes of Rivets ." 20 13. Spacing of Rivets 20 14. Kinds of Joints 22 15. Theory of Riveting 23 16. Requirements for a Good Riveted Joint 27 17. Design of Riveted Connections 28 18. Examples of Riveted Joints 30 19. Net Sections of Tension Members 35 20. Eccentric Stresses in Riveted Connections 40 21. Showing Rivets on Drawings 43 CHAPTER III Mill Buildings 45 22. Roofs 45 23. Construction 45 24. Roof Coverings 45 25. Types of Trusses 46 26. Building Construction 48 27. Loads 50 28. Stresses 52 29. The Design of a Building 53 ix X CONTENTS Art. fAOB 30. Purlins 53 31. The Trusses 57 32. Buildings with Columns 61 33. The Detail Drawings 65 CHAPTER IV Plate GraDEB Bridges »...-...- 72 34. Construction and Uses 72 35. Stresses in Girders 73 36. The Web 73 37. The Flanges 75 38. Economic Depth 76 39. Stiffeners. 78 40. Web Splices 79 41. Flange Riveting 80 42. Flange Splices 83 43. Design of a Stringer 84 44. Design of a Deck Plate Girder Bridge 90 45. Through Plate Girders 113 CHAPTER V Pin Connected BmDGEa 115 46. Construction 115 47. Types of Trusses 115 48. Loads 116 49. Tension Members 117 50. Compression Members 119 51. Lateral Systems 124 52. Design of a Pin Connected Railway Bridge 125 63. Dead Load 125 54. The Depth 125 55. Stresses 127 56. Design of Tension Members 129 57. Design of Compression Members , 133 68. Design of the End Posts 140 59. The Portal Bracing 144 60. Design of Floor Beams 146 61. Top Lateral Bracing 151 62. Bottom Lateral Bracing 152 63. Shoes and Rollers . .'. 153 64. Estimate and Stress Sheet 154 CHAPTER VI Details op Pin Connected Bridges 159 66. Detail Drawings 159 66. Pins 159 CONTENTS xi Art. page 67. Calculation of Pins 160 68. Camber 167 69. Details of a Riveted Tension Member 168 70.- Location of Pins in Top Chord and End Posts 171 71. Lacing of Compression Members 173 72. Details of the Floor Beams 177 CHAPTER VII Highway Bridges 182 73. Kinds of Bridges 182 - Y4. Flooring Materials 183 76. Loads 184 76. Impact 185 77. Distribution of the Load 186 78. Calculation of Joists 186 79. Types of Steel Highway Bridges 191 CHAPTER VIII 'Manufacture and Erection 193 80. Shop Operations 193 81. Erection 194 82. The Drafting Department 195 83. A Draftsman's Equipment 196 84. Ordering Material 200 85. Shop Drawings 203 86. Order of Procedure for a Pin Connected Bridge 211 87. Order of Procedure for a Plate Girder Bridge 213 88. Shop Bills 216 89. Shipment 218 90. Materials 219 91. Inspection 224 Appendix 225 General Specifications for Steel Highway Bridges, 1911, State Highway Department of Ohio ,,,,,,, 225 DESIGNING AND DETAILING OF SIMPLE STEEL STEUCTUEES CHAPTER I DESIGNING AND ESTIMATING 1. Classes of Structural Steel Work. Ordinarily the term " structural steel " covers only the rolled steel used in structures, and does not include any castings or machinery; but in many classes of work, machinery is so intimately connected with the structure as to render the separate design of the two impossible. The field of usefulness of steel in structural work is being constantly extended, and the problems of its design becoming more complex, especially for work in the more populous districts of the country. The following is a list of the more important kinds of struc- tural steel work: Bridges for steam and electric railways and highways, I-Beam spans. Longitudinal trough floor spans, Through and deck plate girder spans. Combination bridges (wood and steel), Simple truss spans, Draw-bridges (swing, lift, rolling, bascule, etc.), Viaducts or trestles, Elevated railways, Arch bridges. Suspension bridges. Turntables for locomotives, Trainsheds, Steel mill and factory buildings, 2 KINDS OF SHOPS Abt. 2 Steel roof trusses, Grandstands, . Steel work for tall office buildings, Stand pipes and elevated tanks and towers, Steel canal lock gates, Traveling crane girders. Ore conveyor bridges. Car unloaders. Bins for ore, coal, coke, grain, etc. 2. Kinds of Shops. It may be said that no single plant in this country is well equipped for turning out all of the differ- ent kinds of structures enumerated in the preceding article. Some are confined to the manufacture of railway bridges, heavy highway bridges, and heavy building work, some to highway bridges and light building work, some to steel work for build- ings, some shops are not equipped to make pin connected work and others cannot do girder work economically. Some shops are not fitted to handle reamed work. (10). These facts are sometimes emphasized by the manufacturer in order that he may be allowed to make his own designs, but this should not be given too much weight by the purchaser, as all the usual forms of details can be executed in any shop fitted for the particular kind of work under consideration and there will seldom be any difference in price to the purchaser, unless the form of detail is an unusual one. 3. Proposals and Contracts. The requirements of vari- ous purchasers in regard to proposals and contracts are not at all uniform. The law requires that public officials advertise for proposals on public work, and any manufacturer who meets the requirements must be allowed to bid. The laws differ in the various states. Private corporations, companies, and individuals do not usually advertise for bids, but invite proposals from such manufacturers as they desire to compete for the work. They very seldom require the deposit of a certified check with the proposal to insure the signing of a contract by the successful bidder, or the furnishing of a bond to insure the fulfillment of the contract. The certified check and bond are usually required on public work. If the purchaser does not furnish a design or plans of the Art. 4 DESIGNS AND ESTIMATES 3 work, each manufacturer submits his own design with his pro- posal. This may be in accordance with specifications of his own or with some standard specifications. The letting of, the contract then becomes a question not only of the lowest bid but also of the most desirable design. Usually the manufacturer submits only a stress and section sheet, commonly called a strain sheet, but sometimes " show " plans, showing the general appearance of the structure and some details of construction are also sub- mitted with the strain sheet. Show plans are frequently nothing more than ornamental drawings on which the lettering and shade lines play an important part. Railroads and the more populous counties and large cities have bridge engineering departments which prepare plans for their bridges. These, together with standard specifications, are submitted to the contractors who then all bid on the same plan. As a rule this method is more satisfactory than the other because the purchaser's engineer has the purchaser's interests uppermost in his mind and also he can usually devote mor- time to the study of peculiar conditions surrounding a particular job than can the contractor's engineer, who must limit the time spent on the design because there is no assurance that the cone tractor will secure the work. 4. Designs and Estimates. When an improvement is con- templated the purchaser should employ someone who is competent to prepare plans and specifications and estimates of cost of the proposed work. Also, before making a proposal, the manufacturer must make an estimate of cost, and if no plans are submitted by the purchaser on which to base the proposal, he must also prepare a design and plans to accompany his bid. In either case the method of procedure in making the designs and estimates will be essentially the same. In the case of the manufacturer this work is done by the estimating department. Designs and estimates must frequently be prepared upon the shortest notice by the contractor's estimating department, and in any case they must be completed before the time set for receiving bids. Certain methods of doing the work of the estimat- ing department are of the highest importance, as they save time and reduce the hability of errors. Proposals for bridge work are asked for either " lump sum " or per pound. In case a lump sum price is required a very care- 4 DESIGNS AND ESTIMATES Art. 4 ful estimate is necessary. Usually when a pound price is given, only an approximate estimate is made to give a general idea of the various quantities of materials involved. The estimate of cost includes such items as the following: Material, Steel from the mill (various shapes take different prices), Eye-bars, Castings, In case these are not manufactured Buckle plates, by the contractor in question. Hand railing, etc. ^ Labor of manufacture, Shop labor, Drafting, General expense. Freight, Haul, Erection (staging and false work) Painting, Lumber, Sub-contract work as paving, masonry work, etc. Before the cost estimate can be made, of course the various quantities of material required must be determined. The data furnished for making the design, are frequently very meager but usually include specifications, profiles and maps of the location. Before starting on a design and estimate, the first thing the designer has to do is to familiarize himself with the require- ments and conditions to be met. Of these requirements the specification is often the only one of importance, although in some cases other matters may demand more study. The specifi- cation is a guide giving the kind of material to use, the loads to be assumed as acting on the structure, the unit stresses allowed, the kinds of details desired, the quality of the workmanship, etc. These will be discussed more fully in Art. 7. If the design is to go in competition with others it is important that it be an economical one, that is, the weight must generally be as small as possible and still meet the requirements of the specifications. This is of course important to the purchaser in any case. Designing of structures is not such an exact science that it may be said that all material in excess of what is required Art. 4 DESIGNS AND ESTIMATES to take the calculated stresses is wasted, but the lightest struc- ture is generally the cheapest and usually the price is the most important determining factor in selecting a design. E^rch case must, however, be treated according to the peculiar conditions surrounding! it. Only engineers of experience can design really economic structures. This question is an important one because it is a matter of producing a. structure to perform a certain function safely and at a minimum cost. No two estimating departments use exactly the same methods. The following will give the essential points. In order that the important requirements of the specifica- tion may be easily found they may be underscored on the first Sheet I^.. FORM No. 3 THE OHIO STATE BRIDGE CORAPANY : ^ ' MEM. Nd. SIZE LMflth w*- - ,, , WEIGHTS 1 TOTAL P. Fl. / 1— — ' LXX-L-t— J Fig. 1. reading, or an abstract made omitting such parts as are common to all specifications and such parts as do not affect the design. If a blank form is used for this abstract it will be better for reference. Calculations should be kept in some permanent form for future reference, the name of the structure and the date being prominently indicated. The information used in making estimates of weight and cost, and stress and section sheets, is set down on blank forms called estimate sheets. If the'' estimate is from plans giving more or less detail, a form like Fig. 1 may be used. If a design is made in connection with the estimate, blanks like Figs. 2 and 3 are used. The usual size of these is 83 X 14 inches. On the form shown in Fig. 2, in the space at the top, should 6 DESIGNS AND ESTIMATES Art. 4 be shown a single line diagram of the structure, properly lettered. THE OHIO STATE BRIDGE COMPANY vanH N». Span C. to C. Estimated) (Steel DL oer ft. 1 | Floor & Total Steel Steel peril ToUl Lumber Roadway. Pane Depth C s at ( Track Sidewalk .... tn C. Total Capacity Tru«ses UDltth of Dial " LL _ SpeclAcatlons S«, T,. ■ EH DL Strtu IL SIrau IWII .Ota] Slou UnH IRK' SIrau fllraa ■ATERIU Actual Araa No. Pci. p. H. UngtK WEIGHT 1 -1- ; \± ; The form shown in Fig. 3 is to be used in connection with this one. Fia. 2. Sheet No.. THE OHIO STATE BRIDGE COMPANY ...... Rrtlmntt tor ____ ■EM DL Stmt LL Stmi Impact Total SIfBM Un)l Rtq. Etrtu Aria ■ATERtU Actual No. Ana P». Wl. P. Ft. Langtb WEIGHT 1 1 .. 1 This form is used in connection with the one shown in Fig. 2. Fia. 3. (For example see page 154.) This form also has places for the principal data upon which the design is based, stresses, make Art. 4. DESIGNS AND ESTIMATES 7 up and areas of members and their estimated weights. This form is used for sheet No. 1 of the estimate. For the following sheets the form of Fig. 3 is used, which is similar to the lower part of Fig. 2. An estimate should give within a few percent, the actual quantities of the various materials which will be required to make the structure. An estimator must, therefore, not only- know how to obtain the weights of main members, but he must be thoroughly familiar with detailing. Unless the estimate is made from plans giving details, or is for a plate girder bridge, or some such simple structure, the details are not all set down, but are lumped as a percentage of the main parts. A convenient way of doing this, for pin con- nected trusses, is to make the details of each member, a per- centage of the rest of the member, and for riveted trusses, a percentage of the balance of the whole truss. Of course these percentages will vary with the specifications and form of truss, and must be determined by making an estimate of the details, or by taking them from previous estimates in which the details have been estimated. An estimating department accumulates, in time, many valuable tables, such as tables of standard connections, joists, rivet and pin values, portal stresses, properties of columns, moment tables, etc., which save much time. Much valuable information is given in the handbooks published by mills rolling structural steel shapes. Those gotten out by the Carnegie Steel Co. and the Cambria Steel Co. are the most complete. Since they give the properties of all rolled shapes, one of them is indis- pensable in making designs and estimates. Combinations of shapes are frequently used for compression members and girders. Since it is necessary to know the radius of gyration or moment of inertia of these and the location of the neutral axes, and since calculating these involves considerable labor, there should be some systematic method of making the calculations and of preserving the results for future reference. There are several sets of tables published, giving the properties of builtup sections, and one of these will be a great help in designing.^ 1 "Osbom'a Tables," by Frank C. Osborn. "Properties of Steel Sections," by John C. Sample. "Godfrey's Tables," by Edward Godfrey. 8 TIME SAVERS Art. 5 6. Time Savers. Besides the books and tables above referred to there are several instruments, the use of which will save much time and mental effort and reduce mistakes to a minimum. The most important of these is the slide rule. It is, in fact, indispensable in this sort of work. Thacher's cylindrical slide rule or the Fuller rule are more accurate than is necessary for the ordinary work of the estimating department. A rule which will give results with a maximum error of one in two hundred is sufficiently accurate for all ordinary purposes. The Thacher rule is, of course, very convenient when more refined work is desired. It will give results with a maximum error of about one in ten thousand. The ordinary ten-inch Manheim rule will answer very well, but one which will give the product of three numbers at one setting is very convenient. In getting weights, the number of pieces, the weight per foot and the length are multiplied together. There are several rules on which this operation can be performed at one setting. The " Duplex " rule is one. This rule is ten inches long and the setting is made on one face and the result read on the other by means of a runner. On the "Engineer's Slide Rule " the entire operation is performed on one face at one setting. This rule is twenty-four inches long and has no runner. The great advantage of this rule, aside from its three multiple feature, is the ease with which it may be read. There are only a few more divisions in the twenty-four inches than are given on the other rules in ten inches, and consequently the continued use of the rule is not nearly so trying on the eyes. The degree of accm-acy is not much greater than that of the ten-inch rules. The maximum error of operations on the three multiple face is about one in two hundred. On the other face of the rule is an ordinary slide rule with scales twenty-four inches long, which gives results within one in five hundred with the same ease on the eyes. Care should be taken to select a rule which works easily but not loosely, and one in which the graduations on the slide cor- respond with those on the rule. The trial of a few simple num- bers will be a sufficient test of its iaccuracy. For instance, when the 1 and 2 are set opposite the following multiples should also read exactly opposite: 2 to 4, 2.5 to 5, 3 to 6, etc. A rule with a white celluloid face is preferable. Art. 6 ORDER OP ESTIMATING 9 The scales on the slide rule being logarithmic, problems involving multiplication, division, powers and roots can be solved by its use. The books of instruction, which accompany the rules, explain their use fully, but the method of operation can easily be discovered by trial with simple problems. Some definite method of operation should be adopted and always followed, to save time, so that it will be unnecessary to reason out the process each time a multiplication is performed. Most problems may be ax resolved into the simple form of — = Ans., and for these the following simple rule is convenient: "Keep the DIVISOR on the SLIDE and read the ANSWER on the OUTSIDE." Of course, any one of the three factors may be unity, which pro- vides for simple multiplication and division. The decimal point is best located by inspection after the result has been set down. If many estimates are made in one office, it should be pro- vided with some kind of an adding machine. There are several such machines manufactured in this and other countries. An elaborate machine, such as is used in banks and clearing houses, is not necessary. The " Computometer " is an excellent ma- chine but is somewhat expensive. A small instrument like the " Rapid Computer " is not so expensive and will answer very well. 6. Order of Estimating. It is, of course, very important that all multiplications and additions be correct within certain limits, and every check possible should be employed. It is also very important that no omissions are made. The best way to insure reliable results and at the same time secure speed in esti- mating, is to follow some fixed order of performing the work and some definite form of setting it down. The following forms have been used by the author and will serve as illustrations: 10 ORDEK OF ESTIMATING Akt. 6 ORDER OF ESTIMATING RAILWAY BRIDGES Truss Memb.-Web Diag. Web Vert. Bot. Chord Top Chord Total Truss Memb. Pins, Pin Nuts. Shoes & Mas. Pis. Rollers & Frames. Int. Floor Bms. End Floor Bms. Int. Stringers. End Stringers. Stringer Pedestals. Stringer Cross Frames. Stringer Laterals. Bottom Laterals. Top Laterals. Portals — ^Rods — Knees. Top Struts. Sub Struts. Sway Rods — ^Knees. Top & Bot. Struts-Deck Br. Bot. End Struts. Longitudinal Struts. Castings; Lead. Bolts & Spikes. Timber Furnished by. Placed by. Tie Plates. Specifications. Paint^Shop, Field. Material. Reaming. Inspection by Transportation. Haul. Removal. Erection. Bid f. o. b. or Erected. Certified Check. Bond. Penalty. Time of Completion. Bid Due. Substructure. ft. B. M. Total Iron & Steel. Akt. 6 ORDER OF ESTIMATING 11 ORDER OF ESTIMATING HIGHWAY BRIDGES. Trass Memb.-Web. Diag. Web Vert. Bot. Chord Top Chord Total Truss Memb. Pins, Pin Nuts, Shoes & Mas. Pis. Rollers & Frames. End Fl. Bms. 1 Hanger Pis. Int. Fl. Bms. J Lat. Con. &c. Sidewalk Brackets. Fl. Bm. Hangers. Bot. Laterals 1 Connections, Top Laterals J Pins, &c. Portals — Rods — Knees. Top Stmts. Sub Struts. Sway Rods — ^Knees. Fl. Bm. Knees — Low Trusses. Top & Bot. Strats-Deck Br. Bot. End Stmts. Longitudinal Struts. Steel Joist — I Bms. Facia, Curbs. St. Ry., Exp. Joints. Castings. Bolts & Spikes. Total Iron & Steel. Lumber Buckle Pis. St. Ry. Rails-furnished by. Laid by. Hand Railing. C. I. Newel Posts. Cresting, Ornaments. Latticed Hub Guard. Wood Fence. Paving-Roadways & S. W. Specifications. Paint— Shop, Field. Material. Reaming. Inspection by. Freight. Haul. Removal. Erection. Bid. f. o. b. or Erected. Certified Check. Bond. Penalty. Payment. Time of Completion. Bid Due. Substructure. ft. B.M. 12 ORDER OF ESTIMATING Akt. 6 ORDER OF ESTIMATING STEEL BUILDINGS. Trusses — Main, Vent., Knees. Lean-to. Special. Hip & Yalley Rafters, etc. Columns — Main. Clearstory. Crane. Lean-to. End. Floor. Struts — Latticed Eave. Side, End, Vent. Special. Ties — ^Bottom Chord. Special. Ventilator Knees. Roof Purlins — Main, Vent. Lean-to, Special. Purlins — Side. End, Gable. Finish Angles — Main Roof. Vent. Roof. Lean-to Roof. Rods — Rafter, Main, Vent., Lean-to. Bottom Chord. Side Sways. End Sways. Sag Ties. Anchor Bolts — Bolts, &c. Crane Girders — Brackets. Floor Girders — Joist. Floor Plate. Stairs — ^Tracks for Doors, &c. Crane Rail-CUps & Fastenings. Corrugated Iron — Roof. Sides. Ridge Cap — Flashing. Gutters — Down spouts. Slate, Felt, Tin, Cornice, &c. Louvers. Wood Purlins, Nailing Strips. Sheeting ft. B. M. Skylights — No. & size — Glazing. Windows — No. & size — Glazing. Doors. Door Frames— Window Frames. Skylight Frames. Railings. Circular Ventilators. Brick Walls & Foundations. Specifications. Materials. Paint — Shop, Field. Freight. •Haul. Removal. Erection. Bid f. o. b. or Erected. Certified Check. Bond. Penalty. Time of Completion. Bid Due. Total Steel in Bldg. Art. 7 SPECIFICATIONS 13 7. Specifications. A specification is a set of rules for the guidance of the designer, the draftsman, the rolling mill, the shop, the erector and the inspector. It is a part of the contract ^ and all work is gotten out in accordance with some specification, and for bridges, generally in accordance with some standard specification. There are a number of bridge specifications which are pubhshed in pamphlet form for general use. The following are some of the most used specifications for steel railway bridges: " General Specifications for Steel Railroad Bridges " of the American Railway Engineering Association. " General Specifications for Steel Railroad Bridges and Viaducts," by Theo. Cooper. " General Specifications for Railway Bridges," by Ed\idn Thacher. " General Specifications for Railway Bridge Superstructures," by The Osborn Engineering Company. " General Specifications governing the Designing of Steel Railroad Bridges and Viaducts," by J. A. L. Waddell. The general specifications for highway bridges usually include specifications for electric railway bridges because bridges fre- quently serve both purposes. The following are some of the more important of these: " General Specifications for Steel Highway and Electric Railway Bridges and Viaducts," by Theo. Cooper. " General Specifications for Highway Bridges," by Edwin Thacher. " General Specifications for Highway Bridge Superstruc- tures," by The Osborn Engineering Company. " General Specifications governing the Designing of Highway Bridges and Viaducts," by J. A. L. Waddell. Most railroads have standard specifications of their own. Manufacturers also have specifications which they use when no other is designated. The " Manufacturers' Standard Specifica- tions," given in the various rolling mill hand books, cover only the material as rolled. Specifications for bridges carrying electric railways, adopted ' See " Engineering Contracts and Specifications," by J. B. Johnson, for a complete discussion of the subject. 14 STRESS SHEETS AND GENERAL PLANS Art. 8 by the Massachusetts Railroad Commission, have been written by Prof. Geo. F. Swain. The building codes of the various large cities are supposed to govern the design and erection of all buildings within their limits, but many of these are antiqua-ted and cannot be applied to modern types of construction. " General Specifications for Structural Work of Buildings " by C. C. Schneider, covers all types of modern building construction. " General Specifications for Steel Roofs and Buildings," by Chas. Evan Fowler, refers only to mill building construction. There are many points of similarity in all specifications, especially with regard to certain details. The tendency in the future will, no doubt, be towards more uniformity in all require- ments for structures of the same kind. There is no more profitable study for the beginner, than the study of a number of standard specifications.^ They give, among other things, the types of bridges to be used for different spans, clearances required, con- struction of the floor, loads to be used in calculating stresses of all kinds, unit stresses which must not be exceeded, details of construction such as lacing for compression members and rollers for expansion bearings, kind of workmanship required, quality of gteel and timber to be used, requirements as to paint- ing, inspection, testing, etc. 8. Stress Sheets and General Plans. These are made on tracing cloth and of some standard size. Each company usually has at least two standard sizes of drawings. The common sizes are 8i in.X14 in., 11| in.XlS in., and 24 in.X36 in. The stress sheet should show, on a single line diagram, stresses, make up of each member and its area, principal dimensions such as span length, panel lengths, depth and width, and com- plete general data. live and dead load stresses should be given separately if the unit stresses are different. The maxi- mum shear and maximum moment should be given for plate girders. It is also well to specify the pitch of rivets in the flanges of girders, and the number of rivets required in the end connections of floor beams and stringers. (See stress sheets Figs. 32, 55, and 69, pages 62, 112 and 158. ' For a comparison of the main features of a number of railway bridge specifications, see an article by Prof. A. H. Heller in Engineering News, Vol. 50, page 444. Art. 8 STRESS SHEETS AND GENERAL PLANS 15 Full general data should be given for reference. Under this head are included the specifications governing the design, the kind of steel, the location of the structure, the live and dead loads assumed, the grade, the alignment, the skew (if any), the construction of the floor, the distance from masonry to bridge seat, etc. For bridges, the diagrams usually include an elevation, a half or full view of the upper and lower lateral systems, and end elevation and a cross section. General plans may be simply " show " plans or plans giving more or less detail. The latter sometimes show practically every- thing except the rivet spacing and lengths of details. CHAPTER II RIVETING /id^i' Rivets are used not only to connect members of riveted structures together; but also in all sorts of steel structures, to join parts of members built up of plates, angles, channels, etc., and for connecting details, such as pin plates, lacing bars and batten plates. 9. Dimensions of Rivets, Rivets are made in a machine, which upsets one end of a hot bar of steel or iron, forming the head, and cuts off enough of the bar to make a rivet of the desired length. The size of a rivet is designated by the diameter of the shank, and its length under head, thus | in.X3i in. " Button heads," which are hemispherical are used where there- is room for them. Their size de- pends upon the diameter of the rivet. Fig. 4 shows about the proportions which are used in structural work for " button heads " and countersunk rivets. Fig. 5 gives the standard heads used by The American Bridge Company. It will be noted that the heads do not have spherical surfaces before driving. The cups on the riveting machine are sup- posed to have hollow spherical surfaces, so that the pressure will at first be concentrated on the center of the head when the rivet is being driven. This aids in upsetting the body of the rivet so that it will fill the hole. The grip of a rivet is equal to the sum of the thicknesses of the pieces joined. The distance between the heads of a rivet will usually exceed the grip, on account of the roughness of the surfaces of the parts joined. Allowance is made for this in the length of the rivet used, which must be long enough so that 16 t_ _i — J Fig. 4. Art. 10 RIVET HOLES 17 there will be sufficient metal to fill the hole and form the head. A table of lengths required for different grips is given in the ^ i r?-^ rJJL, 4' rJ^ k3 4 ^ Q BUTTON HEADS . COUNTWiSUNK HEADS Fig. 5. mf^r. ■^■' (See hand-books published by the various steel companies. " Cambria," page 294.)i 10. Rivet Holes. Holes for rivets are either -punched, sub- punched and reamed or drilled. When reaming is required, the amount varies with different specifications from | in. to i in. That is, the diameter of the hole punched is from | in. to J in. smaller than the finished hole. The object of reaming is to remove the material surrounding the hole which is more or less injured in punching, and to insure a better fit and matching of holes. The injury done in punching is greater in thick material than in thin, and in medium steel than in soft steel. Hard steel is seldom used in structural work. Where metal is used of greater thickness than the diameter of the rivets, it is usually drilled. Also some specifications require that all holes shall be drilled in certain cases. The common practice is to use " punched work " for buildings and ordinary highway bridge work, with both soft and medium * Ail references are made to the 1912 edition. 18 DRIVING RIVETS Art. 11 Fig. 7. steel. For railway bridges the practice differs very much on different roads. IFsually soft steel over | in. thick, and all medium steel is required to be reamed. It is probable that the development of manufacture will be toward drilling all holes, which would assure a fit and matching of parts which cannot be attained with punched work. Even if it were possible to do pimching accurately, the matching of holes would be difficult to attain because punching causes a piece to stretch, and the amount of stretch depends upon the thickness of the metal and the number of holes. For this reason, as shown in Fig. 7, it is necessary to ream all holes after the pieces are assembled, so that the rivets may be entered. This is usually done with a hand pneumatic reamer. This reaming does not produce "reamed " work, as only part of the injured metal around the hole is removed. Forcing round tapered pins, called " drift pins," into the holes with sledges, instead of this reaming, is not allowable because it injures the metal. The use of drift pins however in assembling is not only permissible but is absolutely necessary. 11. Driving Rivets. Rivets are driven hot, and may be driven in three ways; by power riveting machines, by pneumatic hand hammers, or by hand. Wherever it is practical, rivets are driven by power riveters, because these produce better results at a less cost. Power riveting machines are of two kinds, direct and indirect acting. The direct acting are the most satisfactory, as the full pressure may be held on the rivet as long as desired. In these machines the ram moves in the line of the final pressure throughout the stroke. In the indirect acting machines, the cups are held in jaws which are pivoted in the middle, the power being applied at one end of the arm and the rivet driven at the other. This causes the cup to rotate in the arc of a circle. Consequently the cups must be changed every time the grip of the rivet changes or else a lop-sided rivet head would result. Machines using compressed air are the commonest, and are called air riveters. They are used as portable machines, being hung from cranes running on overhead tracks in the shop, and do very good work if of proper capacity and if the air pressure Aet. 11 DRIVING RIVETS 19 is sufficient. A shop doing girder work should have a machine which will exert a pressure of from 50 to 60 tons. Hydraulic machines are the simplest and most reliable, but they must be used as stationary machines. Steam machines are also station- ary, and these machines are therefore better adapted to riveting light pieces than large and heavy ones. Rivets which must be driven in the field are usually driven by hand, but on large jobs power is sometimes used. There are generally a few shop rivets in every structure which cannot be driven by machine without taking the piece back, after an inter- mediate operation, like planing, has been performed. Such rivets are also usually driven by hand or with pneumatic hand hammers. The use of the pneumatic hammer reduces hand riveting to very small proportions. This hammer strikes very rapidly. The blows are comparatively light ones, but very good rivets can be driven with it. Pneumatic hammers are often used for field riveting. Rivets driven by power riveters or pneumatic hammers, through several thicknesses of plates, which are then planed off to the center of the rivet, will show so tight that it is difficult to see the line of demarcation between the rivet and the plates. In hand riveting the end of the shank is hammered with hand hammers until it is upset roughly into the form of a head. A " snap," which is a hammer with a cup shaped face, is then held over it and struck with a sledge until the head is properly formed and the rivet is tight. The rivet is held in place while being driven by a " dolly," which is a steel bar with a cup shaped face which fits over the head of the rivet. The heating of rivets is important, because overheating, or " burning " is injurious, as well as doing work on them at a " blue heat." The range of temperature at which wrought iron may be worked without injury, is greater than for steel, and therefore some specifications require that field rivets shall be of wrought iron. If a rivet is not properly heated it is almost certain to be a bad one. There are also times in a shop, when there is an unusual demand for power, and the pressure used for driving the rivets runs too low. A loose rivet may be discovered by striking the rivet head a sharp blow with a light hammer specially made for the pur- 20 PROPEK SIZES OF RIVETS Aht. 12 pose. An experienced inspector can detect loose rivets by the jar on the hand and the sound produced, even when no move- ment can be seen. Sometimes attempts are made to deceive inspectors by caulking the heads of loose rivets or by giving them several sharp blows with the riveting machine. 12. Proper Sizes of Rivets. The usual sizes of rivets, which are seldom departed from in structural work are | in., f in., f in. and | in. Rivets larger than | in. in diameter can not be driven tight by hand, and in shops, it is not always possible to obtain sufficient power to drive them satisfactorily. It is a common rule not to use a rivet diameter smaller than the thickness of the thickest plate through which it passes, because, although somewhat thicker plates can be punched, it is often expensive work on account of the breakage of punches. If thicker metal is used it must be drilled, and the result is that metal of greater thickness than about f in. is avoided. Tables giving the maximmn size of rivet which can be driven in various sizes of structural shapes, and the location of the most desirable rivet center lines or " gages," are found in the hand- books published by the various steel companies.^ Generally it is best to use the largest size of rivet allowable in each piece, unless this would result in a number of sizes in one member, which would cause extra handling in the shop. Usually-but one or two different diameters of rivets are used in an entire structure. When two different diameters of rivets are used in one member, the change should be made in such a manner that the two sizes of holes do not both come in any large pieces, as this would necessitate extra handling in punching. Although a I inch rivet may be driven in a 3 inch leg of an angle, a 3j inch angle should be used to make an important connection with I inch rivets. 13. Spacing of Rivets. Rivets are spaced according to practical rules which are almost universal. It is evident that rivet holes might be punched so closely together that the metal between them would be injured to such an extent that it would be of very little value. On the other hand the rivets might be so far apart that the parts joined would not be in close contact between rivets, leaving a space for water and dirt to lodge, causing rust which would buckle the parts and might develop 1 See " Cambria," pages 44, 45, 46 and 298. Art. 13 SPACING OF RIVETS 21 mm.- ^A^!%.-t high local stresses. Rivets might also be placed so near the edge of a piece that the metal would tear out. By " 'pitch " of rivets is usually meant the distance center to center, parhllel to the line of stress, whether the rivets be in the same or in different rows. End distances are parallel to the line of stress and side distances are perpendicular to it. In Fig 8, p = pitch. e = end distance. s = side distance. d = diameter of rivet, t = thickness of outside plate. The following table gives the usual specified limits for rivet spacing, and Fig. 8 explains the terms used. ©- ^ e^^o- o}/^, max. p= 6' or /6t Fig. 8. d d ■SS JS a 8 ^ ?^ a 1(3.3 in. Dist. Cen. to C Specified Inches. S3 .lis OS'S ■§^.3 .SS s ■OCOhH gs III o, g g^.S Sr& ga H 1^.5 m ^Slg d Sd & g D «d w «d 63 \ 14 1\ .a 1 li 1 lor If 1 U 2i ■o u IJ H li 2J 2i o 1-1 n 14 14 14 \ 21 3 1-H n 14 If 14 The minimum pitch in a double line may be less than in a single line, so long as the distance center to center of holes in any direction is not less than the minimum distance specified. It is not the usual practice to use the least allowable pitch unless there is a good reason for not avoiding it. For the maximum pitch 16« requires 4 in. for J in. plates and 5 in. for ^ in. plates. It is not good practice to exceed these pitches, but in some classes of work 6 in. is used as the maximum pitch for all thicknesses of plates. In the best classes of work, no metal is used in impor- tant parts, less than f in. thick, in which case 16« = 6 in. The maximum pitch allowed perpendicular to the line of stress is usually about twice that allowed parallel to it, but this 22 KINDS OF JOINTS Art. 14 is rarely used except in cover plates of compression members, in which case 404 is sometimes allowed. At the ends of compression members, the pitch is usually 3 in. and should not exceed four times the diameter of the rivet for a distance equal to about twice the depth of the member. This is to insure a uniform distribution of the stress to the sev- eral component parts of the member. The end distance should never be less than I5 times the diameter of the rivet, and it is usually specified 2 diameters. It should never exceed 8 times the diameter of the rivet. In the location of rivets it is important to provide clearance for the riveting tool. This has a diameter about f in. greater than the diameter of the head of the rivet, so that from the center of the rivet to the clearance line, the distance should be ^ ^7- FiG. 9. Fig. 10. at least one-half the diameter of the rivet head plus f in. In special cases a riveting tool with one side cut off, requiring a clearance but little greater than half the diameter of the rivet head, may be used. Some shops have multiple punches, which punch a number of holes at one operation, and are usually used in connection with a spacing table. Certain parts are punched on these punches and are not laid out by templet. There are hmitations to the spacing which the table can make, and these must be kept in view in making the shop drawings. 14. Kinds of Joints. Figs. 9 to 14 show different kinds of riveted joints in plates, and different arrangements of rivets. It is evident that a lap joint is much weaker than a butt joint with two splice plates. In a lap joint there is a moment, having a lever arm equal to the sum of half the thicknesses of the plates. // there were no deformqtion, the resulting unit bending stress Abt. 15 THEORY OF EIVETING 23 in the plate would be three times the unit stress due to direct stress, but as the joint deforms the center lines of the plates ap- proach each other, as shown in Figs. 9 and 10, and the moment is reduced. The bending of the plates will increase the tensile stress ;n,the rivets, and successive chants of stress, if great enough .-wrould loosen them. y Bujtt joints with two splice plates should be used whenever possible. 15. Theory of Riveting. In spite of their importance, there is no rational working theory for designing riveted joints and ^p/icep/afeo^ f^ FlQ. 11. Fig. 12. Fig. 13. m ^^ fT\ (T* r\. 137 — yy vy — 137— "07 Fig. U. connections under stress. Therefore certain assumptions are usually made, which ordinarily Tender the design of riveted con- nectionp a very simple matter. In a, steam boiler or standpipe ^ the important point is to get a iij§ximum efficiency of the joint, which requires that we have tbe.same factor of safety in the net sections as in the rivets. This subject will not be considered here. In steel buildings and- bridges it is simply a- question of having, at any point, a sufficient number of rivets and a sufficient net area to take care of the stress at the point. > For the design of standpipes, see Johnson's " Modem Framed Structures," Chapter XXVII, 8th edition. 24 THEORY OF RIVETING Art. 15 The following assumptions are made in designing riveted joints: 1. That all rivets completely fill the holes into" which they are driven. 2. That the rivets in a compression member take the place of the metal punched out, but that in a tension member the section is weakened because the net section through the rivet holes is less than the gross section. 3. That a rivet cannot safely carry a tensile stress, that is a stress pulling against its head. 4. That the friction between the parts joined should be neglected. 5. That the bending stress in the rivets may be neglected. 6. That the net section of a piece of steel will offer the same resistance per square inch as the gross section. 7. That the stress is equally distributed over the net sec- tion of the pieces joined in tension. 8. That the stress is equally distributed over all the rivets of a joint. As stated above, these assumptions are not rational, but nevertheless they are universally used in designing riveted con- nections because they give results which are consistent with the results of tests. These assumptions are largely interdependent and will be considered in detail. If a riyet were perfectly driven, and the hole completely filled when the rivet was hot, it would contract in diameter in cooling. This contraction precludes an intimate contact between the rivet and the walls of the hole} Regardless of this fact it is the universal practice to propor- tion compression members for gross section, and tension mem- bers for net section. An allowance should, however, be made in compression members, for open holes, or holes for loose fitting bolts or pins. The allowance to be made in tension members will be treated in Art. 19. 'Coincident with the contraction in diameter while cooling, the length between heads tends to decrease, and a tensile stress ' According to experiments by M. Considere in 1886, the space between the rivet and the side of the hole, varies from 0.002 to 0.02 inch. See Bulletin No. 62 American Railway Engineering Association, page 149, Art, 15 THEORY OF RIVETING 25 is set up in the rivet. In addition to this stress, the metal ■«srhich is being riveted together is compressed by the enormous pressure exerted by the riveting machine, and when this pressure is re- lieved, the metal tends to resume its unstrained form, and exerts a tensile stress on the rivet. This initial tension tends further to reduce the diameter of the cold rivet and cause a greater clearance between the rivet and the walls of the hole. The amount of the initial tensile stress on the rivet is a very uncer- tain quantity. It sometimes requires a very little pull on the head of a rivet to break it off. This is probably in part due to the heat treatment which it has received, making it nonhomo- geneous. Nearly all specifications prohibit the use of rivets in direct tension, but they are nevertheless so used in certain con- nections, because the construction is usual and simple. In these connections there are usually stresses acting at right angles to each other, such as a shearing and a tensile stress. Bolts might be used to take the tension and rivets to take the shear, but rivets are generally used throughout. Experiments indicate that the clearance between the rivet and the walls of the hole, allows a slip to take place when the friction between the parts is overcome.^ Therefore friction is the resisting force in a riveted joint, so long as the stress is not great enough to produce slip. With good riveting and ordinary working stresses there is probably no slip,^ nevertheless rivets are calculated to resist shearing off. If a proper working^ stress is used, the shearing strength of a rivet is a proper measure of the friction produced, because the friction depends upon the tension in the rivet, and that, as well as the shearing strength, depends upon the area of the cross section. In good work the slip is so small that a joint may safely be strained beyond the slipping point, if the stresses do not alternate in direction.^ Practically, it is considered of great importance, that the rivets should completely fill the holes into which they are driven. Since this is impossible it is not of so much importance so long as sufficient friction is produced between the parts joined. As ' See Johnson's " Materials of Construction," Article 375, also pages 3 and 4 of Bulletin No. 62 American Railway Engineering Association. ' Experiments indicate that slip occurs at a stress of from 11500 lbs. to 21900 lbs. per sq. in. of rivet cross section. ' See Bulletin No. 62 Am. Ry. Eng. Assoc, pages 3 and 4. 26 THEORY OF RIVETING Art. 15 it requires great pressure to make a hot rivet fill the hole, espe- cially when the holes in the parts joined do not come exactly opposite to each other, (see Fig. 7) this pressure is useful in bringing the parts into intimate contact, which is necessary to develop the friction. If no slip occurs, the only bending stress in a rivet is due to elastic deformation, if any at all occurs. The longer the rivet the less the bending stress. " Usually specifications require that the grip of a rivet shall not exceed from four to five times its diameter, on the supposition that the rivet transmits the stress. This requirement is necessary, because if the grip is great and the number of pieces to be riveted together is large, the pressure exerted by the riveting machine is not sufficient to bring the pieces into intimate contact and thus develop the friction. When rivet holes are punched, some of the material imme- diately surrounding the hole is injured, also a riveting machine exerts an enormous pressure on the metal near the rivet, and may overstrain it. These might tend to reduce the permissible unit stress in tension on the net section, ^ but experiments show that where the section is suddenly reduced, as in a notched bar or in a section through rivet holes, the ultimate strength per square inch is increased by an amount which will more than equal the reduction due to injury.^ If then the distribution of stress over the net section through the rivet holes is uniform, as per the 7th assumption, there is no reason why the allowable intensity of stress should not be as great as for a section without rivet holes. If, however, the stress is unequally distributed, the maximum intensity will be greater than the 7th assumption will give. There are a number of causes producing non-uniform dis- tribution of stress over the net section through rivet holes. If two plates in tension be joined by several rows of rivets, and there is no slip, the stress is transmitted from one to the other by means of the friction at their surfaces of contact. This friction is greatest under the rivet heads, because the friction is produced by the tension in the rivets. Therefore the intensity ' See Proceedings of the Institute of Mechanical Engineers, August, 1887, page 326. 'See Proceedings of the Inst, of Mech. Eng., October, 1888, also see Heller's " Stresses in Structures," Art. 13. Art. 16 REQUIREMENTS FOR A GOOD RIVETED JOINT 27 of stress is greater under the rivet heads than half way between them. If the stress is tensile in the plates joined, the uniform distribution of stress will be interfered with, as in a notched bar.^ The result is, no doubt, a somewhat greater intensity of stress near the rivet holes than half way between them. If the stress is not equal on all the rivets in a cross section, as per the 8th assumption, there may be a large variation in intensity of stress over the section. On this account the rivets in a joint should be symmetrically disposed about the center lines of stress, and eccentric stresses avoided wherever possible. If any of the rivets are defective, the result may be the same as that of an unsymmetrical distribution. If the friction which is produced by the rivets is greatest under the rivet heads, the stress is transferred from one plate to the other in a series of increments. The stress in one plate increases, while that in the other decreases. The result is that the intensitj'' of stress in the two plates at a cross section is not equal, and this tends to cause one plate to deform more than the other and thus throw more stress on the rivets at one end of the joint in one plate and upon those at the other end in the other plate. But the plates cannot deform unequally as long as there is no slip, so there is no reason why there should not be a uniform distrubution of stress over the rivets, as long as they are all in the same condition. This would require perfect work- manship. 16. Requirements for a Good Riveted Joint. From the discussion in Art. 15 the following conclusions may be drawn: A good riveted joint, 1. Should be as compact as possible, in order to render the uniform distribution of stress more certain. 2. Should not be very large, because the workmanship cannot be perfect, and there is the greatest danger of uneven distribu- tion of stress in a joint having the largest number of rivets. With- part of the rivets in a joint defective there may be eccentric stresses and overstrain, causing a redistribution of stress and probably, overstrain in other members. 3. ^Shmild have its rivets arranged symmetrically about the center tines of stress. ' See Proceediiigs of the Inst, of Mech. Eng., October, 1888, also[ see Heller's '< ^tr«saes;in. Str«cturp»," Ait.i 13. 28 DESIGN OF RIVETED CONNECTIONS Art. 17 4. Should have provision for unavoidable eccentric stresses (see Art. 20). 5. Should have rivets of good material, properly driven, under uniform conditions. 6. Should have a sufficient number of rivets so that there will be no slip if the stresses alternate in direction. 7. Should not have rivets in direct tension. 17. Design of Riveted Connections. Riveted joints in structural steel work are always designed upon the sujjposition that the rivets carry the stress according to the assumptions given at the beginning of Art. 15. According to these assumptions a joint may fail in the follow- ing -ways: 1. By tearing the parts in tension through a line of rivet holes. 2. By tearing out the metal between the end of the piece and the last rivets. 3. By shearing the rivets on one cross seetion. 4. By shearing the rivets on two cross sections. 5. By crushing the rivet on one or more of the pieces of metal joined. Provision against tearing through a line of rivet holes in tension members, will be treated in Art. 19. The end distances usually specified and which are given in Art. 13, provide against tearing out at the ends. If there is a tendency to shear off a rivet on one cross sec- tion, it is said to be in single shear, as in Figs. 9, 10 and 11. If there is a tendency to shear the rivet on two cross sections, it is said to be in double shear, as in Figs. 12, 13 and 14. It is evident that if two plates be joined together, one of them might be so thin that the rivet would be crushed where it bears on the plate before sufficient stress is developed to shear the rivet off. As the safety against crushing depends upon the area of pressure or bearing, and this depends upon the thickness of the plate, a rivet is said to be in bearing on the plate. Rivets are therefore proportioned for single shear, double shear or bearing. It is possible to have all of these to consider in a single joint. In a lap joint the rivets are in single shear or bearing, depend- ing on the thickness of the plates. In a butt joint with two Art. 17 DESIGN OF EIVETED CONNECTIONS 29 splice plates, the rivets are in bearing or double shear. The bearing may be either on the splice plates or on the main plate. The splice plates should always be made thick enough so that the bearing will be on the main plate. That is, each splice plate should be more than half as thick as the main plate. There is no very definite relation, generally recognized, between the working stresses in tension, shear, and bearing. The working stresses for rivets should depend on experiments. Many specifications give a shearing unit equal to about three- fourths of the tension unit and a value in bearing double that in shearing .'• The value of a rivet in single shear is simply the product of the area of its cross section, by the working unit stress in shear. Thus the area of cross section of a f in. rivet is 0.44 sq. in. and its value in single shear at a shearing unit of 7500 lbs. per sq. in. is 7500X0.44 = 3300 lbs. The value of a rivet in double shear is twice its value in single shear. The value of a rivet in hearing is taken as the product of the area in tearing by the working unit stress in bearing. The area in bearing is assumed to be the diameter of the rivet multiplied by the thick- ness of the piece against which it bears. Thus the value of a I in. rivet in bearing on a | in., plate at 15,000 lbs. per sq. in. is iXfX 15,000 = 6562 lbs. In designing riveted joints the strength of a rivet is always figured at its diameter before driv- ing. Tables of values of rivets in shear and bearing for several different working stresses, are given in " Cambria," pages 292 and 293. On account of the inferiority of field driven rivets an excess of from 25% to 50% over the requirements for power driven rivets is usually specified. The frictional resistance is much less with hand driven than with power driven rivets. The value allowed for rivets with countersunk heads varies with different specifications. If the metal, in which the counter- sinking is done, is thick enough to give sufficient bearing below the countersunken part to develop single shear in the rivet, no reduction need be made from the value used for rivets with full heads. No reduction is usually made when the heads are only flattened. Rivet heads | inch or less high are countersunk. ' For experiments on the ultimate resistance of steel and iron plates in bearing see Johnson's " Materials of Construction," Chapter XXVI. 30 EXAMPLES OF RIVETED JOINTS Art. 18 18. Examples of Riveted Joints. A few examples of the usual forms of riveted joints will now be taken up. In all of the examples in the remainder of this chapter we will assume the following data: Allowed shearing on rivets 7500 lbs. per sq. in. Allowed bearing on rivets 15,000 lbs. per sq. in. All rivets | in. in diameter. The values of rivets in single shear, double shear, and bear- ing, may be taken from " Cambria," pages 292 and 293. Fig. 9. The rivets in this single lap joint will transmit 3X4510 = 13,530 lbs. in single shear, but if either of the plates be less than f in. thick the value of the rivets in bearing on the plate will be less than the single shear value, and the amount of stress which the joint will transmit, will be less than 13,530 lbs. If the plates are -ig in. thick, the rivets will transmit only 3X4102 = 12,306 lbs. The zigzag line in the table in " Cambria," as explained at the bottom of the page, separates those bearing values which are less from those which are greater than single shear values. Fig. 13. In this butt joint with two splice plates it is evi- dent that the stress must go from the main plate on one side of the splice, to the rivets on that side, from these to the splice plates, from the splice plates to the rivets on the other side, and through them to the other main plate. The rivets are in double shear if the plates are thick enough. From " Cambria " we find that the value of a | in. rivet in bear- ing on a ^ in. plate is equal to its. value in double shear. If therefore the main plate is Ji in. thick or thicker, and the thick- ness of each splice plate is sufficient to develop single shear in the rivets (f in. or more), the rivets of the joint will transmit 7X9020 = 63,140 lbs. If the splice plates are only ^ in. thick, for example, the rivets will transmit only 14X4102 = 57,428 lbs. As stated in Art. 17, the sum of the thickness of the splice plates should always be greater than the thickness of the main plate. Fig. 15 shows the lower end of a post which resists, through the pin, the vertical component of the stress in the diagonal tension member. The post consists of two channels 12 in.X25 lbs. The pin bears against the post in an upward direction, and it is necessary to reinforce the webs of the chan- Art. 18 EXAMPLES OE KIVETED JOINTS 31 nels in order that the pin shall not crush them. Pins are figured in shearing, and bearing, exactly similar to rivets, and usually the same unit stresses are used. Pins must also be figured in bending, and this will be treated in Chapter VI. Assuming the total stress on the post to be 175,000 lbs., the stress in each channel will be 87,500 lbs. The thickness of bearing on the pin, required to take this stress will be ^ =1.30 in. The total thickness of pin plates required is 1.30 in. minus the Fig. 15. thickness of the channel web, which is 0.39 in. (See " Cambria," p. 162.) The pin plates must then be 1.30-0.39=0.91 in. thick or say ff in., and may be made up of one xs in- S'^d one I in. plate as shown. Enough rivets must be put through the pm plates to carry the stresses which they get from the pin to the web of the chan- nel. The total stress 87,500 lbs. from the pin, is distributed over 1^ inches thickness of bearing as follows: f in. channel web carries 5^X87,500=25)000 lbs. I in. pin plate carries ^X 87,500 = 25,000 lbs. ■fg in. pin plate carries ^ X 87,500 = 37,500 lbs. Total = 87,500 lbs. 32 EXAMPLES OP KIVETED JOINTS Art. 18 There must be enough rivets through each pin plate to transmit its proportion of the stress to the channel web, and there must be enough rivets through the channel web to trans- mit to it all of the stress from both pin plates. For that portion of the web which has a pin plate on each side, the rivets will be in bearing on the web, if the web is not thick enough to develop double shear in the rivets, and each rivet will transmit from each pin plate, one half the value of a rivet in bearing on the web. Therefore the number of rivets required through the thinner pin plate, will be found by divid- ing the stress carried by this plate, by one half the bearing value of a rivet on the web. -=11 rivets required through the f-in. pin plate. 1X4920 These 11 rivets will transmit the same amount of stress to the web, from the thicker plate on the other side of the web as from the thinner plate. In addition to these 11 rivets, there will be required through the thicker plate sufficient rivets to transfer the difference between the stresses in the two pin plates, to the web by single shear on the rivets. 37500 - 25000 = 12500 lbs. ^^^P = 3 rfvets 4510 required through the ^ in. pin plate, in addition to the 11 rivets through both. It js better to have the pin plates on opposite sides of the web as shown, but if necessary, both plates may be put on the same side, in which case the number of rivets required through each would be determined by single shear, and these numbers would have to be added together to determine the total number required through the web, as none of the rivet values would be determined by bearing on the web, unless the web were not thick enough to develop single shear in the rivets. In this example, the rivets below the pin have been counted, but it is evident that they can get no stress except by tension in the pin plates. No more stress can be transmitted to these rivets than can be carried by the net area of the pin plates at the sides of the pin hole. • Art. 18 EXAMPLES OF RIVETED JOINTS 33 Also usually, some of the rivets at a joint like this, have to be countersunk on account of clearances, in which case their values must be reduced according to the specifications used as stated in Art. 17. Fig. 16 shows the top chord of a bridge at the hip joint. The chord section is made up as follows: Cover Rate 22"x^" (^Q)Q>(S)Q>Q)Q)Q> Q G> Q Q Q G> Q Q Q Q G> Q fir —jn a„ i - 2& i6^>i^"outsMe j -2^/6""^ Inside f-2^ I l'*§ Outside 2ls4">'3i'>^f" 0^®^Q i gLQ^O^© Q Batten or Stay Plate Q O O O O OJO \ ^"Web^ ^'jatvP/ateJ' !0 O O O O 0!0 Fig. 16. 1 cover plate, 22 in. X | in. 2 web plates, 18 in.Xi^ in. 2 top angles, 3§ in.X3J in.Xf in. 2 bottom angles, 4 in.X3-^ in.Xf in. We will assume a stress in this chord section of 420,000 lbs., and that the pin is 6 in. in diameter. This then will require 34: EXAMPLES OF RIVETED JOINTS Art. 18 a bearing on the pin of ^ ?r^L =4-67 inches, or say 2| inches 6X15000 on each side. This bearing thickness may be made up as follows: Web plate ^in- Inside pin plate f in. Outside pin plate f in. Outside pin plate i^ in- Total, 2f in. =11 in. The stress will be distributed over the plates as follows: ^ in. web plate, ^X 210,000 = 49,740 lbs. f in. inside pin plate, |fX 210,000 = 66,320 lbs. f in. outside pin plate ^X 210,000 = 55,260 lbs. ^ in. outside pin plate ^X210,000 = 38,680 lbs. Total =210,000 lbs. The rivets in that portion of the web, covered by pin plates on both sides, will be in bearing on the web, the web not being thick enough to develop double shear in the rivets. The bearing value of a rivet on the xs in- 'web is 7383 lbs. The number of rivets required in the ys in. ou1;pide pin plate will be ^ - P„ = ll rivets. The number required in the f in. inside ^X lOOO pin plate will be ^ -„„„ = 18 rivets. More rivets than required 2 X lOOO are used in each of these plates, to insure a distribution of stress to the upper and lower rivets, and to give such an arrangement as will put the center of gravity of all the rivets as near as possible to the center line of stress. The nmnber of rivets through the outside pin plate between the angles, is determined by the single shear value of a rivet and 55260 is equal to -tfttt = 13 rivets, all of which must be placed beyond the rivets required by the other two pin plates. Strictly, the rivets passing through the top and bottom angles are in double shear, instead of bearing, because the angles Art. 19 NET SECTIONS OP TENSION MEMBERS 35 and web are both a part of the main chord section, and are held together by rivets beyond the pin plates. These together make up a thickness more than great enough to develop double shear in the rivets. A filler J in. thick will be required in this case, under the ^ in. outside pin plate, on the top angle. This filler, of course, takes no stress. One outside pin plate, and all inside pin plates, should take rivets through the angles, in order that the stress may be dis- tributed over the entire chord section, and to the top plate in particular. This even distribution of the stress requires that the rivets in the ends of compression members, for a distance equal to about twice the depth, should be spaced closely together, as stated in Art. 13. The design shown in Fig. 16 is not according to the best prac- tice as the pin plates do not extend far enough back from the pin to perfectly distribute the load over the entire section. No pin plate should be shorter behind the pin than its width and some of the pin plates should extend at least double the width of the member back of the pin.^ Here, as in Fig. 15, some of the rivets usually have to be countersunk and their values must be reduced accordingly. 19. Net Sections of Tension Members. In a tensjon mem- ber it is not only necessary to have, in a connection or splice, a sufficient number of rivets, but there must also be a sufiicient net area in the parts joined, and in the pieces joining them, to safely carry the stress. Therefore in tension members of a structure with riveted connections, there must be an excess of material, because the joints at their ends, and any splices in them, cannot be made as strong as the body of the member. Fig. 17 shows a simple tension splice, so made that the net area is as great as possible, and the waste therefore, as small as possible. If the stress to be transmitted across the joint is 65,000 lbs., it will require „-„- =10 rivets in bearing on the |-inch plate on each side of the splice. For getting net areas, the size of the rivet hole is always 'See Eng. News, Vol. 58, page 685 (December 26, 1907) and Vol. 65, pages 324 and 328, (March 16, 1911.) 36 NET SECTIONS OF TENSION MEMBEKS Art. 19 taken as | in. larger than the rivet, or 1 in. in diameter for a |-in. rivet. At the section AB, the net width of the main plate is 11 in. The net area therefore is 11X| = 5.5 sq. in. If the allowed unit stress in tension is 12,000 lbs. per sq. in., this net area will transmit 5.5X12,000 = 66,000 lbs. Therefore there is sufScient net area at AB. At the section CD the net area is 10X| = 5.0 sq. in., which at 12,000 lbs. per sq. in. is good for 60,000 lbs. The rivet at T has reduced the stress carried by the main | in. plate at CD to 65,000-^X65,000 = 58,500 lbs. There is then a little more net area on the line CD than is necessary to carry the stress. The stress carried by the main J in. plate at EF is 65,000-3X6500 = 45,500 lbs. The net section is 9X| = 4.5 G E C A H F D B '}\'}\'\\ Fig. 17. sq. in., which is good for 54,000 lbs. In like manner the stress in the main plate at GB. is 65,000-6X6500 = 26,000 lbs., while the net section at GH is able to carry 8 X§X 12,000 = 48,000 lbs. The net area of the splice plates at any section must also be sufficient to carry the stress in them, without exceeding the allowed tension unit. At GE. the stress in the two splice plates is 65,000 lbs. This will require a net area of = 5.42 sq.in. 12000 The net width of the plates at the point is 12—4 = 8 in., which 5.42 will give a required thickness of the two splice plates of -^ = .68 o in. and hence each plate will have to be f in. thick. The stress carried by the splice plates at EF is 65,000— 4 X 6500 = 39,000 lbs. The required net area is ='i.2'b sq. in., Art. 19 NET SECTIONS OF TENSION MEMBERS 37 3 25 which will require a net width of -—-^^A.^Z in., or a gross width of 4.33+3 = 7.33 in. The width of the splice plates may be reduced here some, but not in this case to the limit of 7.33 in. because this would not give sufficient edge distance beyond rivets K and L. In figuring these net areas, only square sections have been taken. It is obvious that if the lines of rivets GH and EF for instance, are close enough together, the zigzag section GKMPNLH will have less net area than the square section GH. Experiments have been made on steel plates which seem to indicate that rupture will take place on the zigzag line unless its area exceeds the area on the square section by at least 30%,^ and some specifications require net sections to be figured on this basis. Other and later experiments seem to show that rupture is equally probable on square or zigzag sections if the net areas are equal .^ None of these experiments may be a good guide, because there is no doubt an entirely different distribution of stress after the elastic limit is exceeded than before, on account of the unequal deformation and distortion produced. This is a difficult matter to investigate theoretically, and until further experiments are made, it is well to be liberal in allowances for rivet holes. In Fig. 17 the distance between the rivet lines GH and EF which would be necessary to give 30% excess to the zigzag line GKLH over the square section GH, is nearly 3 in., and if the transverse spacing were greater, this longitudinal distance would also have to be larger. In nearly all cases in practice, the least area is taken, whether it be zigzag or square section, and no attention is paid to the 30% rule, unless specially required by the specifications. Some specifications give a simple rule like the following: " The number of rivet holes to be allowed for in getting net section shall be the greatest number whose centers are If in.^ or less from any possible square cross section." According to this rule the rows of rivets would have to be more than 2f in. apart, if the holes in but one row were to be deducted. This > See articles by Prof. A. B. W. Kennedy in Trans. Inst. Mech. Eng., 1881, 1882, 1885 and 1888. 2 See Engineering News, May 3, 1906, Vol. LV, page 488. • Various specifications give the distance from If in. to 21 in. 88 NET SECTIONS OF TENSION MEMBERS Art. 19 rule is not a safe one to follow in all cases, as will be seen later. A common case is that of an angle, which may be considered like a plate developed, as in Figs. 18, 19 and 20. The width of the plate will be equal to the sum of the legs of the angle less its thickness. There are four cases according as the angle has one, two, three, or four lines of rivets. In getting the net area of an angle with one line of rivets, allowance is made for the area cut out by one hole; with two lines for one or two holes; with three lines for one, two, or three holes, and with four lines for one, two, three or four holes, depending upon the pitch and arrangement of the rivets. Fig. 18 represents a piece of an angle with one line of rivets in each leg in which the stagger of the holes in the two legs is 1| in., and A/wte3j^^j<£_A Fig. 18. according to the practical rule above, the net section is equal to the gross section, less the area cut out by two holes, or 2.75 — 2X5 = 1.75 sq. in. It is evident that the holes cut out a large percentage of the material. The square section on AE has an area of 2.75—1X1=2.25 sq. in., while the zigzag area ABCD is (3.47- 1+2X|)X| = 1.98 sq. in., showing a deficiency in place of an excess in the zigzag area. By working the problem in the other direction we can easily find the stagger of holes necessary to give us either an equal area or a 30% excess on the zigzag line, over the square section. In the case of Fig. 18, it would require the stagger to be at least 4j^ in. in order that only one hole need be deducted according to the 30% rule. This would make the holes in one line at least 8J in. apart. The following table gives the necessary stagger of rivets in several sizes of angles with one line of rivets in each leg, to give Art. 19 NET SECTIONS OP TENSION MEMBERS 39 an equal area and 30% excess area on the zigzag section, com- pared with a square cross section through one hole. By this table we see that the areas given by the practical rule are not always safe. Size of Angles in Inches. GAee g Inches. Size of Rivet in Inches. Area through 1 Hole. Stagger for Equal Area in Inches. Area plus 30% Stagger for 30% excess Area in Inches 2X2Xi 2iX2^Xi 3X3X1 3|X3|Xi 4X4Xi 1* If If 2 2i t 1 f 0.75 0.97 1.73 2.75 3.25 1.89 2.26 2.69 2.83 3.00 0.98 1.26 2.25 3.67 4.22 3.04 3.78 5.53 5.05 5.68 In Fig. 19 the net area on EG is 4.5-1X^ = 4.0 sq. in. The net area on EFCD is 1(3.81+1.5+4-2) = 3.65 sq. in. The /i/7a/e6'3i"x-^" Fig. 19. net area on ABCB is 1(6.18+1.5+1.5-2) =3.59 sq. in. The net area on ABFCD is 1(3.81+1.5+3.91+1.5-3) =3.86 sq. in. Failure would doubtless take place on ABCD still, according to the 30% rule, three holes would have to be deducted. This would give a net area of only 4.5—3X^ = 3.00 sq. in. The best modern practice does not require the use of the 30% rule. In Fig. 20 the area on AF is 5.75-1X^ = 5.25 sq. in. The area on ACG is ^(4+6.19+1.5-2) = 4.84 sq. in. The area on ACDE is Kl-5+3.9+6.19+1.5-3) = 5.04 sq. in. The area on ABCDE is 1(1.5+3.9+3.81+3.9+1.5-4) =5.31 sq. in. The area on ADE is Kl-5+8.63+1.5-2Xl)=4.81 sq. in. The 40 ECCENTRIC RIVETED CONNECTIONS Art. 20 weakest section is ADE on which the net area is 4.81 sq. in. According to the 30% rule four holes would have to be deducted from the square section giving an effective area of only 3.75 sq. in. If the 30% rule were followed it would make it necessary to make allowance for at least two holes in any angle having rivets in both legs if the maximum pitch of 16< or 6 in. were not exceeded. (13.) In order to provide against undiscovered defects in work- manship and material, it is well to make a liberal allowance in Fig. 20. calculating net areas, especially where stresses are eccentric, as they usually are in angles.' Practice is not at all umform on this point. 20. Eccentric Stresses in Riveted Connections. When the center lines of stress in a connection do not intersect at the center of the group of resisting rivets there is a moment on the connection as well as the direct stress, and the connection is said to be eccentric. This eccentricity should be avoided wher- ever possible. Eccentric connections are frequently put in by careless or inexperienced draftsmen where by a little thought ' See Engineering News, Vol. LVI, page 14 (July 5, 1906) for an account of experiments by Prof. Frank P. McKibben, which show that the eccentricity of stress in angles causes rupture to occur at about 80% of the ultimate strength of test pieces cut from the same material. Art. 20 ECCENTRIC RIVETED CONNECTIONS 41 they could be avoided. Fig. 21 shows such a connection and Fig. 22 shows how the eccentricity could be avoided. When it is necessary to use an eccentric connection, the stresses on the rivets should be carefully calculated to see that allowable unit stresses are not exceeded. Eccentric connections usually cause bending moments in T Fig. 21. the members connected and may cause overstrain if not properly taken care of. It is evident that a single lap joint like Fig. 9, is eccentric. The forces form a couple with a ^ -^ . lever arm equal to half the sum I - I (D Q 1^^ Q \ | of the thicknesses of the plates ' 'v^ V.*©^ \ joined, tending to bend the plates and the rivets (14). The plates are therefore subjected to a bend- ing and a direct stress. In a butt joint with two splice plates, Fig. 22. (Fig. 12), there are no eccentric stresses in the plates joined, but there are in the splice plates. The stresses on the rivets of the joint shown in Fig. 21 may be calculated as follows: Two equal and opposite forces P' and P" may be inserted at the center of the resisting group of rivets without changing the equilibrium. That is the single force F, of 16,000 lbs., may 42 ECCENTRIC RIVETED CONNECTIONS Aet. 20 be replaced by an equal force P' parallel to it, and a couple P"P whose moment is 16000X3.18 = 50,800 in. Ibs.i The direct stress on each rivet due to P' will be — ^ — =4000 4 lbs. To resist rotation about the center of gravity of the group of resisting rivets, each rivet acts in a direction perpendicular to its lever arm and thus takes an additional stress in proportion to its distance from the center of gravity of the group. If S be the stress on each outermost rivet, due to the moment, the equation of moments will be, 2X4.55+2X1.5^ -8=50,800 in. lbs., from which we get S=5080 lbs. The maximum stress on each outer rivet will be the resultant of 4000 lbs. and 5080 lbs., which may be obtained graphically as shown in Fig. 21. The resultant for the two outer rivets will not be the same, because the stresses due to the tendency to rotate act in opposite directions. If the greater of these result- ants exceeds the allowed stress on one rivet, more rivets must be used. The resultant for rivet A is 8370 lbs., and is the greater as would naturally be. expected. It is more than double the stress (4000 lbs.) that it would receive if there were no eccen- tricity as in Fig. 22. Figure 23 shows another common form of eccentric con- nection. The direct stress on each rivet is — 5 — =2500 lbs. o The total moment is 20,000X5.66 = 113,200 in. lbs. Writing the equation of moments we have 4X7.5(S+4X6.17^-S= 113,200 in. lbs. Solving, we get /S = 2250 lbs., which is the stress on A, B, C, or D due to the moment. These stresses act in the direc- tions shown in the figure, which also shows the direct stress on each rivet. Finding graphically, the resultants of the two forces which act on each outer rivet we have for A 400 lbs., for B 3100 lbs., for C 4750 lbs., and for D 3600 lbs. 1 This is an abstract proposition. See Rankine's " Applied Mechanics," Art. 42, also Heller's " Stresses in Structures," Art. 34. Art. 21 SHOWING RIVETS ON DRAWINGS 43 It is seen from these examples, that if the connection is eccentric, the rivets are not equally stressed, and that simply taking into account the direct stress will often give results far from the truth. In laying out a joint in which several members connect, rivet lines are often taken in place of center of gravity lines. 3tSj23 Fig. 23. This is permissible only when the resulting eccentric stresses come within proper limits. If the rivets in a joint are not sym- metrically arranged about the neutral- axes of the members, there will be eccentric stresses. An angle connected by one or both legs forms an eccentric connection which cannot be avoided. (See foot note, page 40.) 21. Showing Rivets on Drawings. In general only rivet heads in plan are shown on drawings. They should always be 44 SHOWING RIVETS ON DRAWINGS Art. 21 drawn to scale. Where there is any possibility of interference the rivet heads may be shown in elevation as well as in plan. In such cases the heads are sometimes only drawn in pencil to determine the clearance. In certain locations there is not room enough for a full head, therefore rivet heads may be flattened or countersunk as shown in Fig. 24. By this means heads may be made flush with the metal through which they are driven, or be made | in., J in. or f in. high. The usual symbols indicating these various kinds Shop ffii/e/s P/am Ceim/ia:si//?/r amf | Coi/ntersunk not. F/aftef2ea F/af/isnei/ kl II ^1 II II Tf^W \^ %_M. I II H-0 Mci)(DCl)( i )(DC|l)(i)(llD|) Fi'e/i/ ff/Ve/s f/o/n . COcmTersiffi/t ane^_ | Coi/n/s/svnfr not I . F/o^eneaf F/affemi^ Fig. 24. of heads are shown in Fig. 24, which also shows how open holes (into which rivets are to be driven in the field) are indicated. This is called the Osborn system of symbols, and is practically universal in this country now. All the rivets in a member need not be shown on a drawing, but all of the rivets at the joints should be drawn in. The inter- mediate portions of the members are frequently omitted and the spacing indicated as so many spaces at so much. In this case the spacing so given should tie up two definitely fixed points at the ends. CHAPTER III MILL BUILDINGS 22. Roofs. The roofs of buildings in which it is not desirable to have walls or columns at frequent intervals, are supported by means of trusses which are carried either on the walls or on columns placed at the sides. These trusses may be made either of steel or a combination of wood and steel. Steel trusses are usually used in mill and factory buildings and in fireproof build- ings. In the latter the steel must be protected by some method of fireproofing as the steel by itself is not a fireproof material. Combination trusses are sometimes used in forge shops and foun- dries where the sulphurous gases in the atmosphere would quickly corrode steel. The steel parts (tie rods) of a combination truss are usually round or square rods and thus present a minimum surface to the action of corrosive gases. Combination trusses are also frequently used in large public buildings and churches where fireproof construction is not deemed essential. 23. Construction. The roof trusses are placed transversely of the building, their distance apart (see Art. 26) depending on the length of span, type of construction of the building in general and the kind of roof covering. The upper inclined members of the trusses, parallel to the slope of the roof are called rafters. (See Fig. 36.) Longitudinal beams extending from truss to truss are supported by the trusses at intervals along the rafters. These are called purlins, and they carry the roof covering, either directly or by means of boards, called sheet- ing or sheathing, running transversely to the purlins (up and down the roof) or diagonally across them. 24. Roof Coverings. For mill buildings, the commonest kinds of roofing are currugated steel or iron, slate, tile, tin and various patent sheet metal roofs, tar and gravel and similar patented combinations. The corrugated steel or iron is usually fastened directly to 45 46 TYPES OF TRUSSES Art. 25 the purlins by means of clips.^ Slate is usually nailed to sheet- ing boards with a layer of roofing felt between, although some- times heavy slate is fastened directly to small purlins placed about 10-| inches apart. Tile is usually fastened directly to angle purlins spaced about 13 inches apart, without any sheet- ing. Tin, and simihr types of roofing are laid on sheeting with roofing felt between. Tar and gravel roofs are laid on wooden sheeting or sometimes on reinforced concrete slabs. The main function of a roof is to shed water, and in order to do this without leakage, it must have a fall or slope. The amount of slope required depends upon the kind of roof, covering. The pitch of a roof is the ratio of its rise to its span. Thus for a 60 ft. span, if the rise is 15 ft., the pitch is J, if the rise is 20 ft. the pitch is |. The least pitch advisable to use with corrugated steel, slate or tile is about J, that is a fall of about 6 inches per foot, and this is the pitch used for most mill and factory buildings. Tin and similar roofs with water tight joints may have a fall of as little as | inch per foot. Tar and gravel roofs should have a fall of from f in. to 2 in. per foot. 25. Tjrpes of Trusses. It is only in unusual structures such as train sheds, exposition buildings, grand stands, etc., that the span of a roof truss exceeds 100 ft. The slope of the roof and local conditions such as required clearances, ventila- tion, light, etc., will usually determine the general outline of the truss. Any type of bracing may then be selected to suit the materials of construction.^ For roofs of ordinary pitch and span, tne Fink truss is by far the commonest type. Fig. 25 (a), (b), (c) and (d) shows several modifications of this form of truss, to suit spans of vary- ing length.- For sake of economy in the rafters it is not desirable to have many loads coming on them from the roof purlins, between panel points, hence the advisability of increasing the number of panels as the span increases. For combination trusses of wood and iron, one of the forms shown in Fig. 25 {g) and (h) is used. In these trusses the ^ See " General Specifications for Steel Roofa and Buildings," by C. E. Fo\vler, Figures page 17. 2 See Heller's " Stresses in Structures," Art. 117. See Ketchum's " Steel Mill Buildings," page 146. Art. 25 TYPES OF TRUSSES 47 diagonal compression members and the top and bottom chords are made of wood, and the vertical ties are rods. For flat roofs some form of truss must be used similar to Fig. 25 (/), Qi) and {l), in order to gain sufficient depth at the center to give economic chord sections. Another type of roof which is rapidly coming into favor is the "savytooth" roof, shown in Fig. 25 (k). The plane of the steeper rafter is glazed, and this side is made to face the North if possible. By this arrangement the floor below is lighted by (a) Fink Trusses (b) (c) Compound Fink Trusses fifj (e) Pratt Trusses (f) (g) Howe Trusses (h) .- which weighs 19.1 lbs. per foot. The most economical section in this case is the channel, also channels are more easily placed in the field than the other shapes as they can rest against the purhn clips (see Fig. 27) until riveted in place, so we will use the channel purlins. To prevent the purlins sagging and to take the component of the load parallel to the roof, sag ties are inserted at intervals not exceeding about thirty times the width of the purlin. These are usually made of round rods, threaded. at the ends, which are run through holes in the purlin webs with nuts to hold them in place. The two ridge purlins are tied across the ridge as shown in Fig. 28 and when the roof is symmetrical the loads on the two sides balance each other. Thirty times the width of the purlin flange in this case is 30X2.26 = 67.8 inches. There will then be required, three lines of, sag ties in each bay, dividing the purlins into four equal parts. The component of the purlin load parallel to the roof is 1620 sin 26° 34' = 725 lbs. per purlin, there are 10 purlin spaces 56 PUELINS Art. 30 on each side of the roof so the component of the stress parallel to the roof in each of the ties across the ridge will be iX 10X725 = 1810 lbs. Then the stress in this ridge tie = 1810 sec. 26° 34' = 2025 lbs. and the required area will be (Spec. Art. 13) 2025 = .12sq.in. 17000 This net area must be provided at the root of the thread on the s ! Normal Wnd Load i Fig. 28. rod. This will require a |-inch round rod. (See " Cambria," page 302.) These ties are usually made f-inch rods and we will follow the custom and use that size. The roof load going to the ridge purlins is only half as much as that carried by the other purlins, but in addition to this they must take the normal component of the stress in the riSge ties. Fig. 28 shows the arrangement of the purlins at the ridge and the arrows indicate the loads which one of them has to carry. /53S ,-^ Distribute loaef ^ \ c ^'-''' . - ^'-^' ,r ^-«'"> , S-0" , Art. 31 THE TRUSSES 57 Normal wind load =iXl620= 810 lbs. Normal comp. of vert. load = JXl450= 725 lbs. Total normal distributed load = 1535 lbs. The normal component of the stress in each ridge tie is 2025 sin26°34' = 905 1bs. at each tie connection. Fig. 29 shows the distribution of the normal loads on the ridge purlin. The maximum normal moment is 12,890 ft. ^^ ^^ ^"^^ lbs. and the required section modulus is 10.32. This re- quires the use of 8 inch chan- nels 181 lbs. for the ridge „ ,. * ^ Fig. 29. purhns. We can now make an estimate of the weight of the purlins to see how it compares with the original weight assumed. One regular purlin weighs 11^X20 = 225 lbs. 20 purlins = 20X225 = 4500 lbs. per bay. The two ridge purlins weigh 2X18|X20 = 750 lbs. per bay. The sag ties = 2X3X46 ft. = 276 lin. ft. per bay and 276X1.04=287 lbs. per bay. To this must be added about 10% for laps and nuts' making 320 lbs. per bay. The total weight of purhns and ties per bay is 4500-|-750-|-320 = 5570 lbs. This is distributed over 81X20 = 1620 sq. ft., making the 5570 weight per square foot = yf^= 3.4 lbs. Our original estimate was three pounds. 31. The Trusses. For the purlin spacing which we have, no two panel loads on the truss will, in general, be the same, but it is sufficiently close to assume them equal when getting the stresses in the truss. For simple trusses resting on walls a vertical equivalent is usually used in place of the normal wind load. This equiv- alent load is assumed as acting over the entire roof and gives results which are safe and which are close enough for ordinary cases. (See Spec. Art. 6.) An approximate weight for our trusses may be calculated from the formula given in Art. 9 of the specifications. 0.04 58 THE TRUSSES Art. 31 X80+0.4 = 3.6 lbs. per sq. designing the truss then is ft. The total load to be used in f, / Covering tl4.i.w^\ Purlins.. A ". . . 2.0 lbs. per horiz. sq. ft. Purlins 3.4 lbs. per horiz. sq. ft. Trusses 3.6 lbs. per horiz. sq. ft. Snow 15.0 lbs. per horiz. sq. ft. U«^ Equivalent wind 15.0 lbs. per horiz. sq. ft. Total 39.0 lbs. per horiz. sq. ft. Fig. 30. Mem Stress BC CD DE ab be as. Bb Cc DisLt. 6C Cc/ cd c/£ } -S4,(,00 -46,6d0 -3/.200 f 7,opo HOO0 7,000 - 7,600 - 7,800 -/3,600 -Z3,400 a ISflOO /Sfioo 7,900 6,SS0 7,900 /S^OOO ffeq-. Benc/mq-'\ , , anefOmeefK Zh 6'-3i 'i Stress I 3^64 SIZ 0.8$ Z/4 OSZ O^Z 104 /.S6 7K!a^r/a/ asecf T Zls3i'-3i''i§' i'ffiy. JL ZI±3lZh''A Z is Z'^ > 4 r -ir Zli Z'Z'4 ^7?tV zi±zi''r4' '. '. A ZUz"'Z'''^' ^1 0.6/ 035 a6i\ //.3 //.3 //.3 OSS //.3 S6 f/.3 3.6 waaz 3.7/Akl 2.27' 7.86 Z64 /.88 /.som. The panel load per truss will be 1X80X20X39 = 7800 lbs. By means of the table on page 13 of the specifications, we find the following stresses for a panel load of 7800 lbs. (Note that the lettering of the truss in the specifications is not the same as used here.) The tension members may be proportioned first. The small- est angle allowed is 2 in.X2 in.Xi in-, (Spec. Art. 64,) and all members should be symmetrical (Spec. Art. 39 and 40). Therefore the smallest member allowed will be 2Ls 2"X2"X5". The largest rivets allowed in these angles are f in. (See " Cam? Art. 31 THE TRUSSES 59 bria," page 46.) The ^ross ar ea> 2X0.94 = 1.88 sq. in. The net area is 1.88-2XiX(f+i) = 1.88-0.38 = 1.50 sq. in. This will answer for bC, Cd and cd, but cd and dE are usually made continuous and should therefore be the same size. 2Ls 2§"X2"X|" will answer for these, the net area being 2Xl.07-2XiX(f+i) = 1.76 sq. in. For light trusses ah and be are also also usually made continuous. The sizes of the other tension members are easily determined, as shown in the table above. We will try to make each of the compression members of two angles. These will be back to back, and will be far enough apart to admit the connection or gusset plates between them at the joints. We will try to make all gusset plates f in. thick. The radius of gyration for the various sizes of angles may be taken from " Cambria," pages 181 to 183. The least width of com- pression member allowed is ^ of the length (Spec. Art. 59), therefore 2''X2"Ls cannot be used in compression members whose length is greater than 100 in. =8.3 ft. For Bb and Dd we will try 2Ls 2"X2"Xi". The least radius of gyration is 0.61. The maximum allowed unit stress is, 12500-500^ = 7900 lbs. per sq.in. The required area will be =qjrir = 0.89 sq.in., while the actual area ia 1.88 sq. in., and therefore Bb and Dd may be made of 2Ls 2"X2"Xi"- For Cc the least. allowable width of member will be 1L3X12^2 ,^ in. 5U The least angles that can be used will be 2Ls 3"X2^"Xi" unless " special " angles are used, which usually take longer for delivery from the mills and might thus delay the work. The table of column unit stresses on page 15 of the specifications may be used instead of applying the column formula each time. Trying 2Ls 3"X2^"Xs" for Cc, the least radius of gyration =0.95' jj i=i^ = 11.9. Allowed unit stress from table = 6550 lbs. r 0.95 60 THE TEUSSES Art. 31 Fig. 31. per sq. in. The required area=-^^r(r=2.14 sq. in. The actual area = 2X1.32 = 2.64 sq. in., which is sufficient. The rafter should be made continuous from eave to ridge, if this length is not too great, say over 60 ft. It must be proportioned for di- rect compression and bend- ing.i The maximum com- pression occurs in aB, and the bending in this case is also a maximum in this panel, or nearly so. aB is loaded transversely by the purlins, as shown in Fig. 31. Considering the member as a simple beam supported at a and B, the maximum moment will be 2509X3.55 = 8907 ft. lbs. The rafter is not really in the condition of a beam simply supported at the ends, nor are the ends fixed, because the con- nections are elastic. The actual moment lies somewhere between that for the two conditions of free and fixed ends, (Spec. Art. 16) and may safely be taken as f of the moment for a simple beam. We have then M = | X 8907 = 5567 ft. lbs. = 66,800 in. lbs. This is the positive moment under the load nearest the middle. There is also a negative moment at each support which may be assumed to be equal to the same amount. The maximum fiber stress will be the sum of the two fiber stresses due to direct stress and bending. P Mv Smax.= T+-7-- (See Spcc. Art. 16.) In applying this equation the distance v must be taken as the greatest distance from the neutral axis to the outside fiber as the bending moment is both positive and negative in the length of the member. ' For a complete discussion of this subject see Heller's " Stresses in Struc- tures," Art. 111. Akt. 32 BUILDINGS WITH COLUMNS 61 Wewilltry2Ls6"X3|"X4". Z=2><^16J9=33.18. f = 3.92. A =2X4.5 = 9.0. s = 66800X3.92 61100 33.18 "•" 9.0 = 7891+6789 = 14,680 lbs. per sq. in. The allowed fiber stress is 15,000 lbs. per sq. in., therefore these angles are large enough. If the next size smaller angle be tried it will be found too small. The lateral struts do not carry much stress, and their size is determined by Art. 59 of the specifications, which requires that their least width be not less than ^ of their length. This requires the use of members not less than 4.8 in. wide. The most economical section will be 2Ls5"X3"X^", the longer legs being back to back. The ridge strut is usually made the same for all bays. The bottom chord ties take no definite stress, but should not be less than one angle 3i"X3"XA" with the 3| inch leg vertical. All the laterals may be | in. round rods. The vertical member of the truss at the middle takes no stress, but keeps the lower chord from sagging. Having completed the designing of the members, the stress sheet and estimate of weight may be made. The stress sheet is usually a fine diagram as shown in Fig. 32, on which are written the stresses and sizes for all of the members, as well as the general dimensions of the building. The estimate of weight is_ given in Fig. 33. 32. Buildings with Columns. When the roof trusses are supported on columns, the wind stresses in them are affected by the thrust of the knee braces which give the building trans- verse stability. (See Fig. 26.) The stresses in the truss and knee braces would not be changed if the columns were replaced by trussed members as shown by the dotted lines in Fig. 34. The wind stresses in the truss and knee braces may be found graphically by using these auxiliary members. Theoretically the points a and a' should be taken at the points of contraflexure in the columns.^ The location of these depend upon the degree of fixity of the ends of the columns, and cannot be determined without making assuniptions which are ' See Heller's " Stresses in Structures," Art. 153 to 165 for a complete discussion of stresses in portal bracing. 62 BUILDINGS WITH COLUMNS Art. 32 40004^0,1-19 s I 111 «*4 5.^ TfofSMe/per,Siffi: = - /.H /He ■J ^ 748 pft /; f7t?< S5 '■imated for Dead Load = J-f 4 = 70' It Fig. 33. 64 THE DETAIL DRAWINGS Art. 33 not warranted by the conditions.^ The bases of the columns are usually not leveled and set true enough to give a guarantee that the lower end of the column would be fixed, and the elasticity of the connection at the top will not permit of the assiunption of fixity there. The stresses will be largest when the points a and a' are taken at the bottoms of the columns, and this is the usual assumption. P', Fig. 34, is the wind load on the upper half of the wall when the wall is supported laterally by the columns. The wind on the lower half of the wall is assumed to go directly to the foundations. H and H' are assmned equal if the columns are alike, and V and V may be found by statics. Maximum. Mem. Dead Load. Snow Load. Wind, Left. Wind, Right. Comp. Tens. aB +14.1 +23.5 +44.0 -13.1 +81.6 BC +13.3 +22.1 +44.0 -13.1 +79.4 CD +12.5 +20.8 +24.3 + 3.6 +57.6 DE +11.6 +19.4 +24.3 + 3.6 +55.3 ah -12.6 -21.0 -12.2 - 4.0 -45.8 be -10.8 -18.0 -19.6 + 8.0 -48.4 ce - 7.2 -12.0 - 1.4 - 1.4 -20.6 Bb + 1.6 + 2.7 + 4.0 + 8.3 Ce + 3.2 + 5.4 +16.3 - 8.4 +24.9 - 5.2 Dd + 1.6 + 2.7 + 4.0 + 8.3 bC - 1.8 - 3.0 -22.7 -27.5 Cd - 1.8 - 3,0 - 4.6 - 9.4 cd - 3.6 - 6.0 -18.2 + 9.4 + 5.8 -27.8 dE - 6.4 - 9.0 -22.6 + 9.4 + 4.0 -37.0 Ee If the trusses of the building of Art. 29 be supported on columns 25 ft. high with knee braces connected 8 ft. below the tops of the columns as shown in Fig. S4, the stresses in the trusses will be as given in the table above. This may be com- pared with the table of stresses given in Art. 31. The maximum moment in the columns will occur at the knee brace connection and equals He. The columns must be designed P Mv so that the maximum fiber stress, -jH — y-, does not exceed the /A I unit allowed by the specifications. ^See article by the author in Engineering News, Nov. 2, 1911. Art. 33 THE DETAIL DRAWINGS 65 33. The Detail Drawings. Drawings giving more or less detail are sometimes made by the purchaser's engineer to accom- pany the stress sheet, but the detail shop drawings are almost always made in the structural contractor's office. These should be submitted to the purchaser's engineer for approval. Fig. 36 is a shop drawing for the trusses designed in Art. 31. The methods for proportioning the details will now be given. To avoid eccentric stresses (20) the center of gravity lines of all members coming together at a joint should intersect in a point. This is usually not practical in roof trusses because it would unnecessarily complicate the drawings and templet work. Instead of using the gravity lines as center lines, the rivet gage lines are usually used. For members composed of Fig. 34. 2Ls 2"X2"Xi" the gravity line is 0.59 in. from the backs of the angles while the rivet line is l\ in. out. This makes the eccen- tricity of the connection 0.535 in. For a member composed of 2Ls 3i"X3§"Xf' the eccentricity is 2.00-1.01 = 0.99 in. For an angle having two gage lines, the center should of course be taken on that line which is nearest the gravity line. For a member composed of 2Ls 6"X3i"X§" the center of gravity is 2.08 inches from the back of the shorter legs. The rivet lines may spaced 2" and 4J" from the back, in which case the inside line should be used as the center line. In roof trusses it is the common practice to have the center lines of the members intersect in a single point at each of the joints except the shoe joint a. (See Fig. 36.) The reason for making an exception of this joint is that in order to take the 66 THE DETAIL DRAWINGS Akt. 33 reaction, the end of the truss must have an appreciable depth. This result is usually accomplished by making the intersection of the center lines of the rafter and bottom chord come at some little distance beyond the center of the bearing plate, as shown in Fig. 36. To facilitate, the driving of the rivets in the shoe plate and in the purlin connection the depth at the end should be ahout 6 inches. The distance from the center of the bearing to the intersection is usually made such an amount as will avoid odd fractions of an inch in the center lengths. Having determined this point by scale, the slope of the -La^ra/ Conn. P/afs Fig. 35. center line of the rafter is made exactly 6 in. vertical to 12 in. horizontal, for a 5 pitch roof. This method of detailing the joint at the shoe, while the most common is not the best, as it introduces eccentric stresses into the members, causing bending in them and twisting on the rivets of the joint. A better but slightly more expensive detail, is shown in Fig. 35, in which the center hues of the stresses at this joint intersect in a single point. The truss outline and the details are not drawn to the same scale. This amounts to drawmg the detail of each joint sepa- rately and then assembling the joints into the form of a truss. Art. 33 THE DETAIL DRAWINGS 67 It is not necessary to show the members broken between joints, although the, distances are not to scale. Any rivet spacing between panel points cannot be drawn to scale, but it is not necessary to show all the rivets if the figures locating them are properly given. The scale for details is usually 1 in. or 1| in. per ft., depending upon the available room. The larger scale is easier to work with, especially for the beginner. The scale for the center lines should be so selected that there will be sufficient room for the elevation of half the truss, the dimension lines, the top view of the rafter and the sectional view of the bottom chord, with all connections for purlins, laterals, etc. The scale for the details must be decided upon first. A sample drawing should be consulted and studied, and if necessary pre- liminary sketches made of the lateral connections. Compact- ness is desirable, but crowding, especially of dimension lines, should be avoided. Usually the scale for the outline should not be less than one half that of the details. Usually on the same sheet with the truss there is put a dia- gram of the roof showing the location of trusses, bracing, etc., similar to Fig. 32. This is called an erection diagram. In a building with steel columns and other steel work, the erection diagram usually occupies a sheet by itself. Sometimes there is also sufficient room on the sheet with the truss drawing for drawings of struts, purlins, etc. After the scales have been determined, one half the dis- tance between the intersections of the center lines of the rafters and bottom chord (40' lO^" in our case) is laid off horizon- tally to the smaller scale chosen for the outfine, and one half of this distance, if the roof .has i pitch, (20' 5|") is laid off vertically at the right end, this being the rise of the center line of the rafter above the bottom chord. Now the hypotenuse of the right triangle is drawn, which is the center line of the rafter. This center line in then divided into four equal spaces and the center lines of the members Bb, Cc and Dd are drawn perpendicular to it. The intersections of Bb and Cc with the bottom chord determine points b and c, and of Dd with cE, point d. The length of Cc is twice that of Bd and Dd, and equals aB. The lengths of ab, be, bC, Cd, cd and dE are equal. Thus it is seen that the center lengths are very easily determined, as given in Fig. 36, from right triangles. 68 THE DETAIL DEAWINGS Aet, 33 Joint a. Fig. 36 is a shop drawing of the truss. The forces acting at joint a are the rafter stress, the bottom chord stress, the purlin load and the reaction. There must be enough rivets in the joint to safely transmit these forces. To avoid chang- ing punches (12) the rivets will be made f in. throughout. (Maxi- mum size for a 2 in. leg.) Joint a has larger stresses than any other, and if | in. connection plates were used throughout it would result in a large gusset here, consequently, (16) we will use a I in. gusset plate at a and make all the others f in. The rafter stress is 61,100 lbs. The value of a f in. rivet in double shear is 6136 lbs. (This value is less than the bearing value on a I in. plate.) The number of rivets required in the rafter coimection = -;TTTr7r = 10 rivets. We will have to add an 6136 extra rivet to transfer the purlin load, this makes 11 rivets. The rivets immediately over the bearing plate in the bottom chord must transfer the vertical component of the rafter stress and the purlin load to the bottom chord angles which rest on the bearing plate. The amount of this reaction will be 4X7800=31,200 lbs., 31200 and the number of rivets required „^„„ =5. In addition to 6136 these we must have in the bottom chord sufficient rivets to trans- 54600 fer the bottom chord stress, 54,600 lbs. This requires =9 DioO rivets, making a total of 14 rivets in the bottom chord connec- tion. If the reaction acted equally on all the bottom chord connection rivets at this point, the connection would only have to be proportioned for the resultant of the two stresses V54600H31200^ = 62,900 lbs. and the rivets required would , , 62900 11 . , only be= „,„„ =11 rivets. 6136 It is not good practice to put the rivets closer together than 2f in., and they must not come nearer the edge of any piece than Ij in. (13). Care must be exercised to see that the rivets in opposite legs of angles stagger so that one rivet head does not interfere with the driving of the other rivet. Joint C. At this point the components of the stresses in bC and Cd, parallel to the rafter, balance each other in the plate Art. 33 THE DETAIL DKAWING8 69 and require no rivets in the rafter. The components perpen- dicular to the rafter must be transmitted to Cc. Their sum is 7000 lbs., which may be gotten by laying off the stresses and scaling the components parallel to Cc. The balance of the stress in Cc ( = 7000 lbs.) comes directly from the rafter. These together require ...q-. =3 rivets in bearing on the |-in. gusset plate. There must be a sufficient number of rivets through the rafter angles to transmit the 7000 lbs. More are put in here so as not to exceed the maximum allowed pitch. It will be noted that the rivet spacing dimension line for each member starts at the center. A connection by a single rivet should never be used, and preferably at least three rivets should be used in any connection. Joint c. A splice is made here in the bottom chord because it changes section, and it is made a field splice because the truss is too large to ship in one piece. Each truss is shipped in four pieces. The middle section of bottom chord and the vertical member Ee are two of these. The greatest depth of any piece will then be over 12 ft. at Cc, and this cannot be handled by all railroads. The horizontal components of Cc and cd act toward the right and their sum, equal to 15,600 lbs., must be transmitted to be. (15,600 lbs. is the difference in the stresses in be and ee.) This requires ^-„„„ =4 rivets in bearing on the f-in. gusset 31200 plate. The bottom chord splice will require „„„„ =11 rivets in single shear. We must have 11 rivets on each side of the splice, in the splice plate, which also acts as a connection for the bottom chord rods, strut and tie. The three rivets through ee and the gusset plate are not counted as a part of the splice (Spec. Art. 38) but are put in because there should be a connection between the vertical as well as the horizontal legs of the angles. The splice plate should have as much net section as the angles of ce. Even with the minimum thickness of plate allowed there is a large excess in this case. ! Lateral Connections. The lateral connections should be suffi- cient to take the full value of the area of a f in. rod at 18,000 lbs. per sq. in. (Spec. Art. 13.) We have then 0.44X18,000 = 7900 lbs. 70 THE DETAIL DRAWINGS Art. 33 If we use a If in. pin for the lateral rods which have forked loops, the allowed bearing pressure of the pin on the | in. plate will be I X 11X25,000 = 10,900 lbs. It is very essential that clearance be provided where two members come together, except where tight joints are required, as in the bottom chord splice and at the ridge. The usual mini- mum clearance of members is | in. Rivet holes are made ^t i^^- larger in diameter than the size of the rivet to be used. In roof work for lateral connections, pin holes are usually punched, and are made ^ in. larger than the pin. Sizes of all rivets and holes must be plainly marked on the drawings. The exact length of each piece must be given with its other dimensions. The length should invariably be given last. The width of a plate should be given first and the longer leg of an angle should be given first, thus, l-15"X|"Xl' 7i", 2Ls 4"X3"X A"><21' 7J". The width of a plate should always be given in inches, and should not contain a fraction less than i in. For the use of the templet maker, the bevel of each inclined line of rivet holes should be given. The longer dimension of the bevel is usually made 1' 0". All dimensions, other than the widths of plates, of one foot or more should be given in feet and inches, and not in inches alone, thus 1' Ij^" and not ■L"16 • While no dimension is ever to be taken by scale, off a shop drawing, it is nevertheless essential to draw by scale. This can not be done unless the drawing is worked up in a logical man- ner. A draftsman who makes many erasures will seldom become interested enough in his work to be a success. Rivet heads and rivet holes should he drawn to scale. Accuracy is essential, but no smaller fraction than ^ of an inch is ever used in structural work. If a line of spacing should add up 10' 6is", 10' 6i" will not answer. All spacing must be continuous from center to center, and the different sets of spacing should be kept separate and in straight lines if possible, not offset lines. First we have the general dimensions such as span and length of rafter, center to center; second, we have the distance center to center for each member; third, we have the rivet spacing which must be con- Fig. 36. (.Baween pp. 70-71) Aet. 33 THE DETAIL DRAWINGS 71 nected with the centers; and fourth, we have the open holes, which should be connected up for the benefit of the inspector. If there are holes in both legs of an angle, there must be two lines of spacing. Each rivet hole must be located definitely, cuts on plates shown, and bevels of center lines given. The gages of all rivet lines must be given. The good appearance of a drawing goes far to inspire con- fidence in its accuracy. It should be workmanlike. The appear- ance of a drawing depends largely upon the lettering and gen- eral arrangement. Except in the title, the letters should all be free hand and of a plain style. The figures should be par- ticularly clear. Figures and letters should not all be the same size. The dimensions of a main member should be in larger figures than those for a detail, and center distances larger than rivet spacing. It is essential that the sizes of plates, angles, etc., be in the best possible place for them. Shop men are not supposed to be able to read a drawing as readily as a draftsman or templet maker. To become a proficient letterer, persistent practice is necessary, and will work a wonderful improvement in any man's work. The title and sheet niunber should be in the lower right hand corner, if possible. The name of the draftsman and the date when the drawing was finished, should appear in the title as well as a statement of what is shown on the drawing. CHAPTER IV PLATE GIRDER BRIDGES 34. Construction and Uses. A plate girder is a built up I-beam. It consists of a single web plate ^ and two flanges (top and bottom) riveted together. Each flange may be composed of two angles, two angles and one or more cover plates, two angles with side and cover plates or, in very heavy girders, four angles with side and cover plates in various combinations. Fig. 37 shows some common flange sections. Types (e) and (/) are P^P (c) id) Fig. 37. (e) (f) frequently used for crane girders where a load is applied along the edges of the flange. Plate girders are used in buildings and bridges where some- thing larger than a rolled I-beam or I-beam girder is required. In buildings they are used for floor and crane girders and in bridges, for stringers and floor beams, and for the girders of plate girder bridges. Plate girder bridges are seldom built for spans of more than 100 ft., though some have been built over 130 feet long. The railways use them almost exclusively for spans from 30 ft. to 100 ft., when steel bridges are used, and many of the better class of highway bridges of these lengths are plate girders. A plate girder bridge is usually considered to be the most durable kind of metal bridge. 1 Wien two web plates are used a few inches apart, it is called a "box girder." 72 Art. 35 STRESSES IN GIRDERS 73 35. Stresses in Girders.^ A plate girder is treated as a solid beam and the stresses are investigated by the method of sections,^ the stresses acting upon a cross-section being the ones usually, found. The loads, including the weight of the girder itself, which a girder carries, together with the reactions produced by them, are usually a series of forces parallel to the cross section of the girder. (Vertical loads on a horizontal beam.) These forces produce a shear at the section equal to the algebraic sum of all the forces on one side of the section, and a bending moment equal to the moment of all the forces on one side of the section about the section. These are resisted by a shearing stress S at the section and by the moment of a couple. This resisting couple is produced by the compressive stresses on one part of the section and the tensile stresses on the other. These are shown in Fig. 38, F being the e ■!mi(Ay//4 R \f « Neutra/ A jf/s Sfress intensifit Fig. 38. resultant of all the compres- sive stresses and F' the re- sultant of the tensile stresses on the section. The lever arm of this couple is d, the dis- tance between these result- ants, and the moment Fd must equal the bending moment of the external forces if we are to have equilibrium. The inten- sities of the compressive and tensile stresses vary uniformly from zero at the neutral axis to a maximum intensity at the top and bottom. Since the greater part of the area of the cross section is in the flanges and the intensities are greatest at the top and bottom, the resultants, F, come near the top and bottom of the girder, making d large. Fd is the moment of resistance, and it is well to remember that it is equivalent to the moment of a couple, and that hath the web and flanges resist bending. 36. The Web. It is not knoMTi just how the shearing stresses are distributed over an I cross section. We know that their intensities must be zero at the upper and lower edges of the ' See Heller's " Stresses in Structxires," Art. 75, page 111. " See Heller's " Stresses in Structures," Art. 64, page 85. ^* THE WEB Art. 36 girder, and are a maximum at the neutral axis.i The law of variation between these extremes depends upon the cross sec- tion. For an I cross section, the usual assumption that the shearing stress is uniformly distributed over the area of the web only, will give an intensity of shearing stress which will usually be greater than the actual maximum.^ The flanges form a large part of the cross section and must carry considerable shear. It is therefore always assumed that the web carries all of the shear ^ and that its intensity is uniform. A^ = ht = ^ (1)* s. Equation (1) will determine the minimum area of web per- missible. Its thickness is never made less than J inch and seldom less than f inch. It must be made thick enough to give sufflcient bearing for the rivets which connect the flanges to it, and this consideration frequently determines its thickness.^ The depth, h, is determined by considerations of economy as explained in Art. 38, or by local conditions. When there are splices in the web, it is not strictly correct to take the gross area as effective in resisting shear. It may be . assumed that the rivets of the first row in the splice take up one half of their proportion of the shear on one side of the plane through the center of the row. (15.) Then the net section of the web through this row should be sufficient to take the balance of the shear. This would make equation (1) read as follows: (SmsB — I Value of rivets in row _ ih-holes)t . . (2) Formula (2) is not used in practice, and the difference in the result by the two is usually small. ' For a discussion of this subject on the assumption that a sudden change in width of the cross section has no effect upon the distribution of the shearing stress, se^ Johnson's " Modern Framed Structures," Chapter VIII, Art. 130, page 145. See also Rankine's " Applied Mechanics," Art. 309, page 338. ' See Heller's " Stresses in Structures,'' Art. 71, page 105. ' When the flanges are inclined, they carry a part of the shear. * See Heller's " Stresses in Structures," Eq. 33, page 111. » See an article by C. H. Wood in Eng. News, Aug. 6, 1908. Art. 37 THE FLANGES 75 The web resists considerable bending moment, as will be seen if the formula, M=j, (3)1 is considered. If, for example, the moment of resistance of the web is 4" of the total moment of resistance of the cross section, the web will resist ^ of the total bending moment and the flanges will resist f of it. The resultant of the two kinds of stresses caused by shear and bending, in the web is never calculated, but to compensate for this, it is often assumed that the flanges take all the bending stresses, which, of course, has the effect of making them larger and thus reducing the stress in the web. But if it be remembered that the shear is not a maximum where the bending is, it will be seen that, theoretically, this increase of flange section is not necessary. 37. The Flanges. The bending stresses in a girder may be provided for by making the cross section such that the extreme fiber stress, given by equation (3) will not exceed the maximum allowed unit. This, however, involves much labor, as there are no complete tables of section moduli of plate girders as there are of I-beams, and the solution, involving the two unknown quantities / and v, must be by trial. When the flanges are alike, as they usually are, the solution is very much simplifled by making two assxmiptions:^ " 1. The stresses in the flanges (tension and compression) are uniformly distributed over their areas and their resultants, (F, Fig. 38) therefore, act at the center of gravity of these areas. " 2. That the depth of the web h, may be set equal to d, the distance between the centers of gravity of the flanges." Granting these, it is easily shown that the moment of resistance of the web is equal to the moment of resistance of | of the web area, concentrated at the center of gravity of each of the flanges. ' For derivation see Heller's " Stresses in Structures," Art. 66, page 89, or any book on Mechanics. ' See Heller's " Stresses in Structures,'' Art. 75, page 111, for a complete discussion. 76 ECONOMIC DEPTH Art. 38 Then we have Equivalent flange stress = -j (4) •-, . , r, Equiv. flg. stress ,_. Equivalent flange area = , . . (5) Reqd. flange area proper (net area one flange) = equiv. flg. area— | Aa . (6) If, for any reason, there are vertical lines of rivet holes in the web, its moment of resistance is decreased, and this is some- times taken into account by modifying Eq. (6) as given in equa- tion (7) below .^ Reqd. flange area proper (net area one flange) = equiv. flg. area— |^k,. . (7) The effect of the rivet holes on the moment of resistance of the web may be easily calculated. Some specifications require that all of the bending stresses shall be considered as being resisted by the flanges, in which case the equivalent flange area as given by equation (5) becomes the required net flange area proper. Since d, the effective depth, cannot be calculated until the flanges are known, an approximate value must be used on the first trial. Two or three trials will usually give a flange which is practically exact. In equation (5) the working stress for the tension flange is used, thus giving the required net area of that flange. (See Art. 19 for allowance to be made for rivet holes.) The top flange is usually made the same as the bottom flange (gross areas alike) but it must be held so that it will not buckle sidewise.^ (See Arts. 43 and 44.) 38. Economic Depth.^ The most economical depth of a plate girder is usually the least weight depth. It depends upon ' See " Specifications of the American Railway Engineering Association for Steel Railroad Bridges," 1910, Art. 29. 2 See " Spec, of the Am. Ry. Eng. Assoc," Arts. 30 and 80. Also Cooper's " Spec, for Steel Railway Bridges," 1906, Art. 79. ' See Johnson's " Modern Framed Structures," Art. 285, page 332. Art. 38 ECONOMIC DEPTH 77 a number of conditions and may be easily calculated, theoreti- cally, when these conditions are known. The calculated, economic depth is seldom used exactly, on account of local conditions and practical limitations, and is to be regarded merely as a general guide. A variation in depth of as much as 10% or 15% will usually not change the total weight of the girder appreciably. Formulas will now be deduced for the economic depth for the following three conditions as to flange section: (a) When ^ of the web area is considered in each flange. (b) When | of the web area is considered in each flange. (c) When none of the web area is regarded as flange area. The girder will be assumed of constant cross section from end to end. (a) When | of the web area is regarded as flange area. The gross area of the cross section of the girder = ht+2AF+nvet holes. M From equations (4) and (6), -^f^-i — idt, and then we have, setting h = d, A=dt-{--^ ^dt+rivet holes. The gross area of the flanges may be taken as 15% greater than the net area, which gives: 2.3M A=0.617dt+ dst As the weight varies directly with the cross section, for a least weight depth we may differentiate this expression with respect to d and set the -first derivative equal to zero. from which and ^ = 0.6m-?:^=0, dd Std^ ,„ 2.3M d'' = 0M7s,t 78 STIFFENERS Art. 39 (6) When | the web is taken as flange area, equation (8) becomes ^=i-8Qa/| (9) (c) When no web is considered as flange area, equation (8) becomes ^ = 1-52^ (10) When the flange section is not constant for the entire length of the girder, the economic depth will be somewhat less than that given by the above formulas, and will vary with the propor- tion of cover plates, stiffeners, and web splices. The following equation will give the least weight depth as close as a general formula can give it. ^-nS- (") 39. Stiffeners. The lines of maximum compression in a plate girder web, cross the neutral axis at an angle of 45° and extend downward toward the supports from the middle.^ The tendency of the web plate to buckle under these compressive stresses is, in part, resisted by the equal tensile stresses at right angles to them. Just what the resulting effect on the web is,, is not well understood, but when the ratio of the depth of the web to its thickness is great (exceeds about 50 or 60) it must be stiffened. Of course the requirement of stiffeners depends upon the amount of shear at the point .^ Stiffeners are placed vertically on account of ease of manu- facture. They would, perhaps, serve their purpose better if placed parallel to the line of the compressive stresses, but if placed vertically and not more than the depth of the girder apart, or 5 or 6 feet for deep girders, they will prevent any buckling of the web. There is no rational method of determining the size of these stiffeners. Some specifications^ give column formulas for this ' See Heller's " Stresses in Structures," Art. 73, page 109. Also see Johnson's " Modern Framed Structures," Art. 130, page 147. " See Cooper's " Specifications for Steel Railway Bridges," 1906, Art. 47. See also " Spec, of the Am. Ry. Eng. Assoc," 1910, Art. 79. TIT Art. 40 WEB SPLICES 79 but there is no rational basis for it. Experience only determines their size and spacing. Sometimes fillers are put under the stiffeners, between the flange angles, and sometimes the stiffeners are " off set " or " crimped " over the flange angles as shown in Fig. 39. Fillers should be used under stiffeners bear- ing concentrated loads, or where there is anything connecting to the girder by means of the stiffener. Stiffeners should be placed at the ends of a girder, to transmit the end reaction from the web, and at all points of concentrated loading. Stif- feners should bear tightly against the horizontal legs of the flange angles at all points of concen- r^ 39. trated loading, as the load must be transmitted to the stiffener by direct bearing upon its end, and from the stiffener, by means of rivets, to the web. The outstanding leg of the stiffener should not project beyond the edge of the flange angle, and the other leg need only be large enough for the rivets. 40. Web Splices. For small girders, such as stringers and floor beams, the web plates can usually be obtained from the mills in one piece, and no web splices are necessary. When, however, the size of the girder is increased, the web plates can- not be obtained in single lengths and must be spliced.^ The stresses carried by the web at the point must be trans- ferred through the splice plates from one web plate to the other. If no bending moment is regarded as being carried by the web plate, only the shear has to be provided for, and the calculation of the rivets is a very simple matter. In this case a splice similar to that shown in Fig. 40 is used. The rivets are usually not spaced over 5 inches apart, and usually two rows are used on each side of the splice, although this often gives an excess of rivets. Two splice plates should always be used and their combined thickness should be greater than the thickness of the web. A pair of stiffeners is usually placed over the splice. When a part of the bending moment is regarded as being carried by the web, the web splice must be designed to provide ' For maximum sizes of plates which may be obtained, see " Cambria," page 28. These limits vary considerably with different mills. 80 FLANGE RIVETING Art. 41 t 1^ SI (K) <)() OO <)<) OC) (X) ()<) OO OO OO OO OO ()0 OO OO OO OO OO OO SJSS'xd'x^' N lo I for this stress in addition to the shear. The simplest form of web spUce to calculate, in this case, is that shown in Fig. 50, in which the plates FG, near the flanges, are assumed to take care of the bending moment in the web, and the vertical plates HK, are assumed to take all the shear. These assimiptions give an excess of plate and of rivets, but a rigid calcu- lation would make a splice of practically the same cost. See Art. 44 for the design of such a splice. In order that the allowed unit stress in the flange proper may not be exceeded, it is necessary to reduce the allowed unit stress in the splice plates FG, in propor- tion to their distance from the neutral axis. The entire solution must, in any case, be by trial. The form of splice shown in Fig. 40 may be used in place of that of Fig. 50, but the rivets must be calculated so that the resultant of the horizontal and vertical stresses (due to moment and shear) in the outermost rivets will not exceed the allowed stress on a rivet. (20) This would also be the exact method of calculating the rivets in Fig. 50. In Fig. 40 the splice plates act as a beam 8' 7|" deep to carry the web bending mcftnent, and the extreme fiber stress in them must not exceed the unit stress in the girder at an equal distance from the neutral axis. If the rivets through the web in the outer rows have a small pitch, one-eighth of the web area may not be available as flange area (37). 41. Flange Riveting. The stress in the flange of a girder, at the end, is zero, and it increases to a maximum somewhere between the supports (for a girder supported at the ends). The increase of the flange stress is due to the addition of the hori- FiG. 40. Art. 41 FLANGE RIVETING 81 zontal shears from the web,^ and the rivets connecting the flange to the web at any point, must be sufficient to transmit this horizontal increnient. Fig. 41 shows any part of a girder, supported in any man- ner. M and S are the known moment and shear at the section AB, then Mx = M+S{x-m)-Piix-a)-P2{x-b)-Ps{x-c). Differentiating with respect to x, -^ will give the rate of increase of the moment along the girder. dx '■ = S-Pi-Po-P3 = S^ The flange stress at any point is —f and, therefore, the rate of increase of the flange stress will be dMx . ,_Sx dx ' d' (12) or, in words, the increase of the flange stress per inch will be equal to the shear at the point divided by the effective depth of the girder in inches and sufficient rivets must be pro- vided, connecting the flanges to the web, to transmit this incre- ment. Then, to obtain the maxi- mum permissible rivet pitch in inches at any point, the value of a rivet must be divided by the increment per inch. (If there is no vertical load on the flange.) In a girder whose cross section is constant from end to end, and in whose design a part of the web has been considered as flange area, the pitch of the rivets may be increased because the part of the flange stress which is carried by the web does 1 See Heller's " Stresses in Structures,'' Arts. 17 and 70. 82 FLANGE RIVETING Akt. 41 not have to be transmitted by the rivets. Since the flange stresses are directly proportional to the flange areas, we have from equation (12) when one-sixth of the web is regarded as flange area, Increment of stress in flange proper = -jX . .i. , • • (13) a JiF-\-^Ji-w or when one eighth of the web is regarded as flange area, S A Increment of stress in flange proper =-jX ^ , i x • • • (14) a Ji.F-\--§Aw In a girder with cover plates which do not extend the full length of the girder, and in whose design a part of the web has been regarded as flange area, equation (13) or (14) may be used for that portion of the girder at the ends, whose cross section is constant, but when, passing toward the middle, the first increase in flange section is made by the addition of a cover plate, the flange angles and the part of the web considered as flange area have already received their maximiun allowed stress (see Fig. 48) and, therefore, all of the flange stress increment must go into the cover plate and enough rivets to transmit it must be provided, both through the angles and web, and through the cover plate and angles. So far we have considered only the flange stress increments as affecting the pitch of the rivets. If there are any loads resting upon the flange of the girder, they must be transmitted to the web, and since the web plate is not flush with the backs of the angles, the rivets in the flange must perform this duty unless the load is carried directly by stiffeners. The top flange of a deck plate girder is a case of this kind, and the resultant of the two stresses (vertical and horizontal) on a rivet must not exceed the allowed rivet value. Usually only three or four different groups of rivet pitches are used in the half length of a girder. The pitch need be figured only at three or four points and then a curve can be drawn through these, which will give the pitch at any other point with sufficient accuracy. See Fig. 43 and Fig. 49. The riveting in the two flanges is always made the same when possible, although this gives an excess in the bottom flange. Art. 42 FLANGE SPLICES 83 Sometimes the pitch of rivets in the flange angles will deter- mine the width of the vertical leg of the angles which may be used. For instance, if 2Ls 4"X4" would answer for the flange of a stringer, and it was found that the pitch of rivets required was less than the minimum allowed in a single line, (13) an angle with a vertical leg wide enough for two gage lines would have to be used. Sometimes the thickness of the web plate will have to be increased over that which would be required to resist the shear, in order to provide sufficient bearing area for the flange rivets, so that they will not have to be spaced closer together than the minimum allowable pitch. Also the web must be thick enough so that there is sufficient net area, horizontally between the flange rivets, to carry the horizontal increment of flange stress. These considerations sometimes make it necessary to use a thicker web plate at the ends of a girder than in the middle.^ 42. Flange Splices. There are two conditions which may make it necessary to splice the ilange of a plate girder even if the girder is not going to be shipped in more than one piece. These are, 1st. The flange angles may be so heavy that they cannot be obtained in one piece, of the length required. 2nd. When the girder is for a through bridge, frequently the upper corners are rounded for appearance, and the top flange angles and one cover plate run down the ends of the girder. In this case, the flange is spliced near the ends, so that the long pieces will not have to be handled in the blacksmith shop in heat- ing, b'ending and annealing. The flange splices should always be made as near the ends as possible, where the flange stress is least; and the joints in the component parts of the flange should break joints. The splices are made by means of splice angles cut and ground to fit the inside of the flange angles and by splice plates on the top. The net section of the splice plates and angles does not have to equal the entire net section of the flange cut, unless the entire strength of the cut portion is required at the point of splice. The size of the splice plates and angles and the num- ber of rivets required are determined by the proportion of the actual stress at the point, carried by the part cut. 1 See an article by C. H. Wood in Eng. News, Aug. 6, 1908. 84 DESIGN OF A STRINGER Art. 43 To illustrate the application of the principles set forth in this chapter, the design and methods of calculation for a stringer and a deck plate girder bridge, will now be given. 43. Design of a Stringer. The stringer of a railroad bridge is the simplest form of plate girder. We will assume the follow- ing data: Panel length 27' 0", Stringers 6' 6" center to center, Loading Cooper's Class E 40, Specifications, Cooper's 1906 for Railway Bridges, material medium steel, except rivets. The design of any structure should commence with that part which carries the load directly, and proceed in order, to the foundations. Hence the first part of our structure to be designed is the ties, next the -stringers, the floor beams, the trusses and last the foundations. Sections 12 to 15 of the specifications will govern the design of the ties. The dead load on a tie consists of the rails, guards, and the tie itself. These may all be considered as concentrated at the rails without appreciable error. Dead load concentrated at each rail. Rails. (Spec. § 23) ^> ,Sff' Fig. 46. wheel 12 is on the other. Then from Fig. 46 we can write the following equations: Wa+wx "^ 2' 40+a;=50-|-. Ma = Moment about A of all loads to the left of ^4, on the span. T7x = Sum of all loads to the left of A, on the span. w = Uniform load per lineal foot. Substituting in the above equations and solving for e and x, we get 6 = 0.2 ft. a; = 9.9 ft. Having determined the position of the loads, the calculation of the moment is a simple matter. The work may be greatly facilitated by the use of a moment table if one is available. 'See Heller's " Stresses in Structures," Art. 134, page 260. *See Heller's " Stresses in Structures," Art. 144, page 269. Art. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 93 The maximum live load moment in the girder is 4,025,000 ft. lbs. The maximum live load end shear will occur with wheel 2 at the end of the girder, and is 187,500 lbs. The equivalent uniform load for moments is determined 7*2 by setting the maximum live load moment equal to -5- and o solving for w. 4,025,000= "Xi"T 10=3220 lbs. per lin. ft. of girder. The equivalent uniform load for shears is obtained by setting the maximum live load end shear equal to -^ and solving for w. 187,500=H>^ w; = 3750 lbs. per lin. ft. of girder. These equivalent uniform loads may be taken from the curves of Fig. 56. From these equivalent uniform loads, the stress at any point can be obtained with sufficient accuracy. The uniform load moment varies as the ordinates of a para- bola, and can be scaled from a diagram drawn as shown in Fig. 48. The shears will now be figured from the equivalent uniform load at the sixth points 16f ft., 33| ft., and 50 ft. from the end. For location of points A, B, C and D see stress sheet, Fig. 55. Live load shear B,tA = — ^- ^ — = 187,500 lbs. Live load shear at 5 =^^^^^^^|^ = 130,200 lbs. Live load shear at C = — innyo ~^^>^QQ ^^s. Live load shear at 1) = ^^^^^"'^^"^ = 46,900 Ibs.i ' The live load shear at D calculated from the actual wheel loads is 49,200 lbs., or 4.9% greater than that given by the equivalent uniform load. 94 DESIGN OF A DECK PLATE GIRDER BRIDGE Akt. 44 ' To each of the stresses thus far determined, must be adaed the impact stress as determined by the formula given in the specifications, § 9, . o 300 L+300' Summary of Stresses. Maximum live load moment =4,025,000 ft. lbs. T , 4025000X300 onioor^t^ lu ' Impacts ioo_[_3oo =3,018,800 ft. lbs. T^ ,, , 1976X100X100 iooKnnr>f+iu Dead load = 5-— r = 1,235,000 ft. lbs. oX^ Total maximum moment = 8,278,800 ft. lbs. Live load end shear = 187,500 lbs. J . 187500 X300 i^ncnniu Impacts ^Qp^3QQ =140,600 lbs. ^ ,, , 1976X100 AnA^mu Dead load = -. = 49,400 lbs. 4 ' Total end shear =377,500 lbs. Live load shear at 5 = 130,200 lbs. , , 130200X300 monnAiu Impact = g3,_^3Q^ =102,000 lbs. D.L. =49400-^X49400 = 32,900 lbs. Total shear at 5 =265,100 lbs. Live load shear at C = 83,300 lbs. , , 83300X300 aoonc^^u Impact= gg,_^_3^Q = 68,200 lbs. D.L. =49400-1x49400 = 16,500 lbs. Total shear at C = 168,000 lbs. Live load shear at D = 46,900 lbs. T ^ 46900X300 .noAnlu Impact = CQ I qoo = 40,200 lbs. Dead load shear = 000 lbs. Total shear at D = 87,100 lbs. Art. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 95 Depth. The economic depth (38) can now be figured from equation (11). Assuming the web to be f inch thick, , / 12X8278800 ,-^ „ . , ^^V 16000X1 =^28.7mches. Section 29 of the specifications directs that the thickness of the web shall not be less than 1/160 of the unsupported dis- tance between the fiange angles. If we used a f" web plate, the unsupported distance between the flange angles could not exceed 160Xf = 60 inches, making the total depth of the girder not over 76 inches if we used 8"X8" flange angles. This would evidently be too shallow for economy . . We will try | inch web plates, these according to § 29 of the specifications, may be made 96 inches deep if we use 8 inch flange angles. „ . , ,, ./12X8278800 ,„ . . , Economic depth =y icnnnv^ =111.4 mches. The web will have to take the shear (36) without exceeding a unit stress of 10,000 lbs. per sq. in. on the gross section (Spec. 18). The required area of the web is 377500 „___ = 37.75 sq. m. 10000 Using a depth of 96 inches, the area of the web will be 96X| =48.0 sq. in. The cost per pound of plates increases very rapidly as the width increases after 100 inches is passed, until at 130 inches wide the cost has reached about 40% excess per pound over the cost of plates 100 inches and less in width. We will use web plates 96" X I". Flanges. For a first approximation, the effective depth of the girder (distance between centers of gravity of flanges) may be assumed as 8 ft. This gives an approximate maximum 8278800 flange stress = ^ = 1,035,000 lbs. and a required net area =■'^1^ = 64.7 sq. in. According to §29 of the speci- loUUU 96 DESIGN OF A DECK PLATE GIRDER BRIDGE Art. 44 fications one-eighth of the gross web area may be regarded as flange area. The following flange section will be tried. 1 Web = 1X48 = 6.00 6.00 2 Ls 8"X8"Xf" = 26.48 26.48-6X1X1 = 21.23 l-20"Xf" = 15.00 15.00-2X1X1 = 13.50 l-20"Xf" = 15.00 15.00-2X1X1 = 13.50 l-20"Xf" = 12.50 12.50-2X1X1 = 11.25 Total gross area 74.98 sq. in. Total net = 65.48 sq. in. Qen CerTtfff^nn'ify If The net areas have been figured with two rivet holes out of the vertical legs of the angles and one out of each horizontal leg. (19.) To obtain this as a minimum net area the pitch of the rivets in the cover plates must never be less than about 2f inches. The location of the center of gravity of this flange is 0.24 inch from the backs of the angles as shown in Fig. 47, making the actual effective depth 96.25-2X0.24 = 95.77 inches. The actual flange stress then is 8278800X12 . ^07 onniK i- +v, - = 1,037,300 lbs.,makmg the v^r 47 • A 1037300 - . -„ J^i<3. 47. required area= -.cr.r.r. =64.83 sq. m. The flange section given above will answer. A reduction in the thickness of the outside flange plate to y€ inch will reduce the net area below that required. Length of Flange Plates. The required lengths of the flange plates may be calculated from the equation of the parabola, in this case, as we are using an equivalent uniform load for the moments, or their lengths may be determined graphically by drawing the parabola, as shown in Fig. 48. The graphic method is nearly always used, as the moment diagram is frequently not a simple curve. As the moments and required flange areas are directly pro- portional, (when the effective depth is constant) the areas will vary as the ordinates of a parabola also, and it is simpler to lay off areas as ordinates instead of moments. Any convenient scales may be chosen for lengths and areas. In this case the middle ordinate of the parabola is 64.83( = Reqd. net flange Art. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 97 area) and the curve may be drawn in any one of several ways, the method shown is a simple one. After the curve of required areas is drawn in, the net areas of the component parts of the flange are measured off on the center line and horizontal lines through these points represent the parts. The required lengths of the various pieces may now be scaled off directly. The flange plates are made 2 or 3 feet longer than the theoretic length in order to provide a few rivets through the plate near the ends so that the strength may begin to be effective where it is required, and also to compensate for the fact that the actual wheel loads give slightly larger moments near the ends than the equivalent uniform load. The effective Fig. 48. depth decreases a little toward the ends, owing to the omission of the flange "plates, and this will also make the flange stress a little greater there than is given by the parabola. For a sym- metrical girder, only one half the diagram need be drawn. The top flange plate next to the angles is nearly always run the full length of the girder, to cover the flange angles and to stiffen them near the ends, against the deflection of the ties. (See specifications § 78.) Scaling from the diagram. Fig. 48, the following are the required lengths of the flange plates: 20" Xf"- 76 ft. use 78 ft. 20"Xf"-61ft. use64ft. 20"Xf"-42ft. use44ft. 98 DESIGN OF A DECK PLATE GIRDER BRIDGE Akt. 44 Flange Riveting. The required pitch of rivets in the girder flanges will now be calculated at the end, sixth, third, and cen- ter points. The horizontal increment of flange stress at the end may be determined from equation 14. As the top flange carries the direct load of the floor and the live load, the required pitch will be smaller for it than for the bottom flange, so the bottom flange pitch need not be figured as the two flanges are usually- made alike. Horizontal increment = -7^?r;^r X . „ .. „ = 3560 lbs. per in. 92.58 47.48 The gross areas are used for proportioning the stress. Note also that the effective depth here is less than at the middle of the girder. The vertical load from the floor is 263 lbs. per lineal foot and the weight of the flange of the girder here is 141 lbs. per lineal foot, making a total dead load of 404 lbs. per lineal foot = 34 lbs. per lin. in. 25000' Live load (see Spec. §§5 and 31) =-^7r~ = ^^^ ^^^- P^^ ^^^- ^^^ Impact (see Spec. § 5) = 100% = 595 lbs. per lin. in. Total vertical load = 1224 lbs. per lin. in. The resultant stress on the rivets will be V (3560)2+ (1224)2 = 3765 lbs. per lineal inch. Required rivet pitch =-^=xp- = 2.79 inches. To find the horizontal increment of flange stress at B, C, and D, we must use equation (12) because the web is here carry- ing all the bending stress allowed, and all the increment goes into the flanges proper. Horizontal increment = =2834 lbs. per lineal inch. Vertical load (same as before) = 1224 lbs. per lineal inch. Resultant stress = \/l2242 +28342 = 3087 lbs. per lineal inch. Required rivet pitch = -^jr— = 3.40 inches. 1 It is a question of judgment with the designer, whether this figure should be multiplied by % or not. An engine which will give a maximum shear equivalent to E50 might have a heavier driver concentration. Art. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 99 168000 Horiz. increment at C- 95.77 = 1754 lbs. per lineal inch. Resultant stress = \/l2242+ 17542 = 2140 lbs. per linea inch. Required rivet pitch = -rrrrTr = 4-90 inches. Horiz. increment at Z) = 2140 87100 95.77' = 909 lbs. per lineal inch. Resultant stress = Vl2242+9092 =1524 lbs. per lineal inch. 10500 Required rivet pitch = 1524 = 6.89 inches. These rivet pitches are plotted as shown in Fig. 49 and the fi/yfr PITCHES Fig. 49. actual pitches used are made to come within the curve as shown by the stepped line. The required pitch of rivets through the flange plates is determined by the horizontal increment of flange stress alone. The total shear at the theoretical end of the first flange plate is 295,000 lbs. This gives a horizontal increment of „„ =3150 yo.oo 2X7216 lbs. per lineal inch and a required rivet pitch of „ =4.58 inches. As the maximmn allowed pitch is 6 inches (see specifi- cations § 39) it will not be necessary to calculate the pitch at any other points. The pitch of the rivets in the cover plates must bear some relation to that of the rivets through the verti- cal legs of the flange angles so that they will not interfere. 100 DESIGN OF A DECK PLATE GIRDER BRIDGE Art. 44 Flange Splices. (42.) About the maximum length of angle 8"X8"X|" which can be obtained in one piece is 90 feet, therefore the flange angles will have to be spliced. We will splice one angle of each flange about 25 feet from each end of the girder so that both angles of one flange will not be cut at the same point. At this point the flange angles are carrying the maximum allowed stress, and the total stress in one angle will be 10.61X16,000 = 169,800 lbs. To take this stress we will use a splice angle on the inside of the angle spliced and a plate inside of the other angle. The splicing material required, then, will be IL 8"X8"Xi6" cut down to 7"X7"Xt4" and ground to fit the fillet of the flange angle, and one plate 7"XH"- These will have an available net area of 10.53 sq. in. The length of the angles will have to be sufficient to take enough rivets to transmit 169,800 lbs., and one-third of this must be transmitted to the plate on the side opposite the angle cut. According to the specifications § 57, the rivets connecting this plate must be increased 66f % over the number required by § 18 for the angle in contact with the cut member. Stress in one leg of splice angle = — ^ — =56,600 lbs. o Rivets required in angle on side next to splice = = 7.85 66f%= 5.25 Rivets required in angle on opposite side =13.1 The rivet pitch at the splice may be made 3 inches, which gives us a splice plate 6| ft. long on the side opposite the spliee and an angle 4 ft. long on the side next to the splice. Stiffeners. (39.) The stiffeners must be proportioned accord- ing to specifications §§ 16 and 79. The end shear which must be transmitted by the end stiffeners to the abutment is 377,500 lbs. To take this load we will need ^^^^^-[-50% = 54 rivets. (See Spec. § 58.) This number can be put into three pairs of stiffener angles with a single line of rivets in each angle. The stress, then, on Akt. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 101 each pair of angles will be — ^ — =125,800 lbs. The outstand- ing legs of these end stiffeners must be as wide as the flange angles will allow, so we will try for these 2Ls 7"X3i"X§". The allowed unit stress is 16000-70^^ = 15200 lbs. per 4.24 sq. in., but 14,000 is the maximum, so the required area of one . , ,' 125800 _._ pan: of angles ^-r^jij^nr- =9.00 sq. m. We can, therefore, use for these stiffeners, 2Ls 7"X3§"X2" whose are|i is 10.00 sq. in. The minimum size of • angles allowed for the intermediate 96 stiffeners is ^+2 = 5.2 inches for the outstanding leg. (See Spec. § 79.) We will use for these 2Ls 6"X34"X|". The spacing of the intermediate stiffeners must not exceed the distance d allowed by the formula in § 79 of the specifica- tions, with a maximum of 6 ft. Required spacing at A =^f 12000 Zo") ^^^ inches. Required spacing at jB=^(i2000 — — ^jo — j =81 inches. Required spacing at C = ^( 12000 j^— j =106 inches. Required spacing at Z) = gQf 12000 ^- j = 127 inches. Web Splices. The total length of the girder is 103 ft. Plates 96" Xi" may be obtained 300 inches long (see "Cambria," page 28) or 25 ft. It will therefore be necessary to splice the web at at least four points, making it in five pieces. The arrange- ment of the lateral system will be more convenient if the web is spliced at five points, making a cross frame come at each splice. See Fig. 51. The end sections may be made 18' 2" long and the inter- mediate sections each 16' 8". TlfH WllUlW^^-U^ ■feilJ'SE:: of the cross frames uniform. 102 DESIGN OP A DECK PLATE GIRDER BRIDGE Akt. 44 The majdmum bending moment at the first splice B, is as follows: Dead load = 686,000 ft. lbs. Live load =2,236,000 ft. lbs. Impact =1,677,000 ft. lbs. Total =4,599,000 ft. lbs. The actual net flange area effective at this point is 40.73 sq. in., and therefore the bend- ing moment taken by the web here is ^^ X4,599,000 = 677,- 500 ft. lbs. At the splice this moment must be resisted by the splicse plates FG, and the stress in these plates due to 677500X12 the moment will be - 68 Fig. 50. = 119,600 lbs. The maximum allowed unit stress on the extreme fiber of the girder is 16,000 lbs. per sq. in., and the maxi- mum allowed unit stress on the splice plates FG will be proportional to their distances from the neutral axis of the girder, or, 34 48.9 X 16,000 = 11,125 lbs. per sq. in. and the required area in the splice plates will be ,,,„^ = 10.75 11125 sq. m. This will require 2 plates 12"XtI") (net area = 16.5-4X2XlXH = ll-00 sq. in.). The allowed stress on the rivets must be reduced propor- tionally to their distance from the neutral axis as was done Akt. 14 DESIGN OP A DECK PLATE GIRDER BRIDGE 103 with the fiber stresses, so the allowed stress on a rivet in these plates is, .-^X 10,500 = 7300 lbs. 48.9 The number of rivets on each side of the splice in these , , .„ , 119600 ,^ plates will be ^gQQ- = 17. The vertical splice plates to take the shear will require ,„e„p. =26 rivets on each side. The design shown in Fig. 50 has 26 rivets on each side. These figures are for the splice at B, but usually the same design is used for all the splices. It will be noted that the maximum shear and maximum moment have been used here as occurring simultaneously. This is on the side of safety, but a rigid solution would not give a splice appreciably smaller. A splice similar to the one shown in E*ig. 40 may be used and calculated as follows. Here the number of rivets must first be assumed and then the maximum stress in them calculated, to see that it does not exceed the allowed units. The splice, as drawn in Fig. 40, contains 40 rivets on each side, the vertical stress on each rivet, due to shear, is 265100 .„„_,. — r^ — = 6630 lbs. 40 The bending moment to be resisted by these rivets is, 677,500X12 = 8,130,000 inch pounds. The amount of stress on each rivet due to bending moment will be in direct proportion to its distance from the neutral axis. (20.) Calling the stress on the outermost rivet S, we have: 4>SX38+4;Sx||x34+4.Sx|^X30+ . . . =8,130,000, 104 DESIGN OP A DECK PLATE GIEDEE BRIDGE Abt. 44 or using the letter y to represent the distance from the neutral axis to the rivet, in each case, we have : ^ AS In this case 22/2 = 5320 and S=^^^^^^ = U,050 lbs. The resultant maximum stress on the outer rivet is V'66302+14,0502 = 15,535 lbs., which is in excess of the allowed unit, (10,500), and therefore the number of rivets would have to be increased if this type of splice were used in this girder. The splice plates must be strong enough, when considered as a beam 79| inches deep, to carry the web's proportion of the bending moment without exceeding a unit stress at the top and bottom, proportional to the distance from the neutral axis, 40 or J— ^X 16,000 = 13,090 lbs. in this case. In figuring the moment of inertia of the plates, the rivet holes should be deducted. Lateral Bracing.^ To provide for wind stresses and vibra- tions (see Spec. § 10) a lateral system must be put in the span. Sometimes two systems are used, one in the plane of each flange, and sometimes only one is used, in the plane of the top flange, and the forces from the lower flange are transferred to the upper system by means of cross-frames (see Fig. 53) at inter- vals. Cross-frames are also put in to stiffen the bridge, when two systems of laterals are used. They are usually placed from 15 to 20 feet apart, depending upon the width of the flanges of the girders. In a deck plate girder bridge, the lateral system is of the Warren, or sub-divided Warren type of truss with an even number of panels, so as to be symmetrical about the center line. The number of panels is so chosen that the laterals will be efficient, that is, so that they will not be inclined at too great 1 Strictly, these forces are perpendicular to lines drawn from the center of gravity of the entire group of rivets, to each rivet. ' See Heller's " Stresses in Structures," Chapter XIV. Art. 44 DESIGN OF A DECK PLATE GIEDEE BRIDGE 105 an angle with the direction of the wind. Also, the panels must be short enough so that the actual unit stress in the top flange of the girder will not exceed that allowed by the specifications §30. 1037300 The actual unit stress in the top flange is = 13,830 lbs. per sq. in. Equating this to the unit as given in § 30 and solving for Z, we get 13,830 = 16,000 -200^ = 16,000 -lOZ from which 10Z = 2170 and 11 = 217 inche&=18'l". The unsupported length of the top flange must not exceed this amount. We will divide. the span into 12 panels, using a single sys- tem in the plane of the top flange, and put in cross frames at every second panel point. This will make a cross frame fall at each web splice. This is not necessary, but a stiffener must be at each cross frame. As but one system of laterals is to be used, it must be pro- portioned to carry the entire lateral force. ^ From the speci- fication § 10 the load is 200-|-200-|-10% of 5000 = 900 lbs. per lineal foot of girder, and all of this is to be considered as a moving load. The stresses in the laterals will be alternately compression and tension, and will all reverse when the direction of the wind reverses. Laterals, however, are never designed for reversals of stress, (see Spec. § 22) so far as the reversal of the wind is con- cerned, because such reversals would occur only at long intervals. Since it requires more material to take care of the com- pression than the tension in a lateral, we are concerned only with the compressive stresses, and choose that direction of the wind which, for any particular lateral, will give compression in it. It will be assumed that the load is all applied at the windward panel points, although the live load is really applied at both girders. This assumption is on the safe side, and simpli- fies the calculation of stresses. On account of the cross frames, there are 12 panels on one side and six on the other. When the wind is blowing as indi- cated in Fig. 51, all of the panel loads will be equal and are • For the calculation of the stresses in lateral systems of bridges having curved track see Heller's " Stresses in Structures," Art. 166, page 304. 106 DESIGN OP A DECK PLATE GIRDER BRIDGE Art. 44 16.67X900 = 15,000 lbs. each. This direction of the wind will give maximum compressive stresses in BC, DE, and FG, and these will be as follows: Sec. e= 11.55 8 BC=2JXl5,OOOXsec.0=54,lOO lbs. Di; = Y-xl5,OOOXsec.6i = 36,100 lbs. FG= |Xl5,000Xsec.e = 21,600 1bs. When the wind blows in the other direction as shown in /SOOO .^.$33 Fig. 52. Fig. 52, the compressive stresses will occur in AB, CD and EF. The panel loads on the lateral system for full loading are shown. A5 = 40,420Xsec.6l = 58,500 lbs. CD = 27,430 X sec. e = 39,600 lbs. £?F = 16,950 Xsec.(9 = 24,500 lbs. According to the specification § 25, the unit stress for laterals may be increased 25% over that given for other members, and according to §74 the smallest angle allowed is 3J"X3"X|". It is usual, where possible, to make laterals of single angles. The least radius of gyration of a single angle 3|"X3"Xf" is 0.62." The unsupported length may be taken as the length between edges of flange angles, and in this case will be about 11.55-1.95=9.6 ft. = 115 inches. Aht. 44 DESIGN OP A DECK PLATE GIRDER BRIDGE 107 Section 20 of the specifications limits the length of com- pression members of the lateral system to 120 times the least radius of gyration. This will make it impossible to use a mem- 115 ber whose radius of gyration is less than ——=0.96. The smallest lateral permissible then is one composed of a single angle 6" X 6" X |". The allowed unit stress is, (16OOO-7O ^V.25 = 11,550 lbs. per sq. m. The maximmn total stress which can be put upon this member is 11,550X4.36 = 50,300 lbs. This will answer for members FG, EF, DE, and CD. 54100 Required area for 5C=:pj-^^ = 4.69 sq. in. Use for BC \L 6"X6"XA' 11550 Actual area =5.06 sq. in. Required area for A5 = -— ^ = 5.10 sq. in. Use for AB \L 6"X6"X5". Actual area =5.75 sq. in. The end cross frames must be proportioned to carry all the wind load to the abutment. It is usually considered that half of this goes through each diagonal to the supports, one diagonal being in tension and the other in compression. The total force acting at the top of the cross frame at A (see Figs. 51 and 53) is 43,300 lbs. Stress in top strut = 21,700 lbs; Stress in diagonal = 21,700 sec. 6 = 30,700 lbs. The diag- onal in compression is sup- ported at the middle in one direction by the tension diagonal, so an angle havmg unequal legs will be more economical than an equal legged angle for the diagonals. Fig. 53. 108 DESIGN OF A DECK PLATE GIRDER BRIDGE Abt. 44 Try IL 6"X3|" Xf". Allowed unit stress is 120 16000-70j-g|+25% = 14,590 lbs. per sq. in. 30700 Required area=Y2TQ^ = 2.11 sq. in. Actual area=3.43 sq. in. As this is larger than necessary we will try IL 5"X3"Xf"- The allowed unit stress is 13,440 lbs. per sq. in. 30700 Required area = r^jjn = 2.29 sq. in. Actual area = 2.86 sq. in. Use for diagonals IL 5"X3"Xf". For the top strut try IL 3i"X3J"X|". Allowed unit 21700 stress = 9000 lbs. per sq. in. Required area = ^x^ = 2.41 sq. in. Actual area = 2.49 sq. in. This is large enough so use for top and bottom struts IL 3^"X3|"X|". The amount of load transferred by the intermediate cross frames is only 3333 lbs., so the smallest angle allowed by the specifications will be sufficient. Use for the intermediate cross frames 3|"X3"X|-" angles. The number of rivets in the end connections of the lateral members is determined by the single shear value of a rivet. The laterals will be field riveted, so the value of a rivet will be 6013 lbs. -o . 58500 .„ . , j^j^ . 36100 „ . , AB requires „ = 10 rivets. DL requires „ = 6 rivets. r,^ . 54100 „ . ^ „„ . 24500 ^ . ^ BC requires „„ „ = 9 rivets. Lp requires „^ ■■ = 5 rivets. ^_ . 39600 - . ^ „^ .' 21600' ^ . ^ CD requires "TTTrrTT = 7 rivets. /'W requires ^„.n =4 rivets. 6013 6013 30700 End cross frame diagonals require -„^„ = 5 rivets. (Shop.) 21700 End cross frame struts require 791^ ~^ rivets. (Shop.) The intermediate cross frames will have to have all con- Art. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 109 nections made with 3 rivets each, to comply with the specifica- tions § 74. Shoes. The shoe should be of such design that it will dis- tribute the end reaction evenly over the masonry. For short spans it is customary to simply rivet a plate, not less than | SofeR.zo'-fa-o 3fek.g''i''3'-0' K — e — e— «--e — s- ■ vP O i O ite- Bracket b3'3'-i m, w' //o/e for^iP/n <5jRo//ers 6'i//i7/77.'/-9' <^M/%./7'i''3'0' 2 /7/tc/ior 3ofib /^esUrm //? e/'a^ono/^ 7^ Panel Load per Truss 0L ....... - Total %MV'I<>?SO. Steel per H.iSJS.. Toul Lumtwr... /3.3L+I77 M Ties e'>'/2'xl/^" /4'c.A>C Guan/s e'xS' 2G. 'rden' ^ifeb 6.°^ A4or 7ent • 2l?S"x8'x-S ^ea xo x-g 64^ ' /-20"x^'7ipfi///SafW ~~l r,n" A." 1 I ?/^ 8 4S0/O3.0 375S5 4a2Sf 30/as szm /-^o"xi o^t- 4- S/.o 90.i 'Ait'i. /-zo-'xV /3jSt £/.0 640 nC60 Bna She gr t/.2S AfefSSHt 42i 44.0 ltS.2 49.4 /87S /40fi 3m Sf?e. irai /m. 6^rx3i\-i" 24 /r." go iZ60 J Tyearc 7f2ai'Sp//c' /-'V/s ^si"xr 24 fO^t 6.7 '670 /6.S 83.3 68.2 M. Wff 2lS6°xS^"x4'CCr;m/:>) S6 //.7 8.0 use Shear erfCt nfer 2JS , 20 //.7 8.0 Ii70 o.° 469 40.2 87.1 y/5 30 3.7 4.7 iSC 20 2.Z 6.7 iOO 'eb^'^/h e_ 2.S. /J'x4' zo 76.6 4.7 2± /2"xit' /i.8"x8"xMT<:'^^7x7y 40 28.0 2.6 iOO F/a/'t^e 3s.a *c /-7"xjk" 76.4 6.S ff/v ^ils- '■% i/60 734 2 £r.ti Fn ime. C onn P/s //. S''x3-k"x^" 20'x4" 8£ /a4 8 \ 2SS 2° / /30\ Foj Ward ii'A 55 /ii/3C Aht. 44 DESIGN OF A DECK PLATE GIRDER BRIDGE 111 Sl^t No 2 THE OHIO Mad* hv STATE BRIDGE COMPANY CTM. „... II-IO-/3. EsL.t. (or. . i*Cf? 6i j^^.. S-fid^e NO 2(7 Norfhen? Div/sio/r ■ta OL Strew LL Streil Inpiil ToUl SIreif Unit Slrau Riq. Art! MATERIAL Reluil Ar«B Nd. Pel. Wl. p. Fl. Unglb WEtGHT ffra ^A /i>r vara liSliO .^ Wen ?(!V7'/; ?/sf rami s 7, \p& lot //.3r'<3'xr 10 73 7.3 i70 Oh '^ / L ti m // /O 7.6 /a° 760 Co 17m VaA ,/-/8"xr 20 23C 77 7S0 /?} ■eh 4Z -^ 90 2 220 u fem, s AB S8.S l/IIO S^' /Le'xe'x-i" S.7S 2 m 70.S 410 BC S4.' If 4,si //.e'xe'x^" S.06 2 172 70.S i60 CD 39.e II 3.se /L 6'x6'x-§" 4.36 2 /49 /as no Of: 36.1 9300 IS9 /C S'xS"x^' 4.19 2 m 70.5 iCO EF 24S u Z.64 /L S'x5''x 4' 3.61 2 /2.3 /0.5 Z60 FG 2/.e 6710 3.23 /L4'x4"x-^" 3.31 2 //.3 /O.S Z40 c 9nn. %. /-^4'-xr 2 30.t 2^ /60 /- " 6 „ 4S iiC /- 2o"xr 6 25.S 4.0 ilO /-/^"xf" 7 /s:3 7.S 166 /?/i^ '■fs 4%\ — /iO 3 780 40 ■yper Sho ?s /-20'x^7p/ar7ed^c^y 4 63.6 SO 770 2^e"x4"^i" ' 6 236 3.0 i70 2S.6"xr (^•<) 8 /0.2 2.5 ZOO 2^,rxr O) 8 78.7 /8 Z7C 4^S''x3"xf" /6 9.8 0.9 I4C /?n ?/s 4% — ^ SO Z 030 41 ■)yyer S/70 ?s /- jy S / Yfi/a^redfofJ 4 //^^ 3.0 /iiC ^i-^/2"x4^' r^t^J /6 25.- 2.3 /on 2^/7"xr 0') 8 28.9 2.3 ii(. 2/S6''x6''x:i' 8 ^.7 3.0 egt. 4^J"x3"xi' CtJ /6 F.z 2^ ...A7.C 4^ /2"x ^" C/ln) 16 75.3 0.7 I7(. Gu, Tfes 2^6'xr 8 70.^ 3.0 Z4C Mat P/ /-33'xJfW''"e'=^^0 2 '26.^ 3.0 76C 2/s4'^4'x^' 4 9.8 3.0 no ff/i> R* 4% — 200 S iSC ^/5 'o//er A/eJ ^s S/Foo/?i^s 6" ' /O 96.' 78 I7i0 J •del 'iars 2^4-^^^ 4 76S 3.0 go S ■i7V/ ^CXf3 20/" 4 2^' ^■° 10 7Z, ■pBt V/s /' /"yf^'J 20 /.O 20 / 870 M/si e//a 7eoi s 7 '•-ackbo/fs 3c 500 / 5 /03 iOO Toi 7/. >7e( /-^ i5oesc 112 DESIGN OF A DECK PLATE GIRDEB, BRIDGE Art. 44 . g I N ■51 h — n n <0 «i ■727 /^ -^z^ ^^w s Ik's. ill I ,6 § ,S (i I ■§ E;«'s'.-5 ft i: c{ '^ ^1 SI i 1 ^i ^ 5 i?^ ^ ts i§l !5 cf 1^ I II ' I III ■^^^ II II n Art. 45 THROUGH PLATE GIRDERS 113 i7750( 400 is .„„ -=944 sq. in. (See Spec. §19.) Using a shoe 3 ft. 944 long, it will require -5^ = 26.2 inches width. 00 The smallest rollers allowed are 6 inches in diameter (Spec. 0'7'7 Kf\f\ § 60 and 62) and it will require = 105 lineal inches of rollers under each bearing. (See Spec. § 19.) This will require five rollers each 21 inches long. The pin must be large enough to properly transmit the shear, and the required area is „ „„„ =15.7 sq. in. This ^ X iiwuuo requires a pin 4 J inches in diameter. The shoe must be strong enough to distribute the end reac- tion, as a beam, from the pin, evenly over the masonry, and must also be strong enough laterally to transmit the wind forces to the abutments. Fig. 54 shows a good design for the shoe. The estimate of weight can now be made upon forms as described in Art. 6, and if the actual dead load taken from the estimate does not differ enough from the assumed dead load to cause a change in the size of any of the members, the stress sheet may be drawn, as shown in Fig. 55. The difference in the actual dead load from that assumed is 1509 — 1450 = 59 lbs. per lin. foot. This would increase the 59 X 100^ maximum moment — ^ „ — = 36,900 ft. lbs., which would increase ■ jn 4..1. . 36900X12 .„ the required flange area at the center 95 77x15000 ^'Q-^^ sq. in., making the total required area 64.83+0.29 = 65.12 sq. in. The actual net area is 65.48 sq. in., so no change is necessary. The stress sheet will now be drawn up. (See Fig. 55.) 45. Through Plate Girders. In a through plate girder bridge, all of the live and dead load, except the weight of the girders themselves, is concentrated at the panel points; and the weight of the girders may also be considered concentrated at the panel points to simplify the calculations. The shears and moments are found, then, as for a truss bridge.^ » See Heller's " Stresses in Structures," Chapters XII and XIII. 114 THROUGH PLATE GIRDERS Art. 45 The flange diagram (similar to Fig. 48) will be polygonal, the area required at each panel point being calculated. The load on the masonry will equal the end shear of the girder plus the corresponding end reaction of the end floor beam (if an end beam is used). There is no vertical load on the flange rivets, and the pitch of the rivets will be constant between panel points because the shear is constant. There can be but one lateral system, ^ and this is made of the Pratt type with two diagonals in each panel. It 4s assumed that these diagonals take tensile stresses only; they are connected to the lower flanges of the stringers so as to take up the longitudi- nal force due to the application of the brakes on a moving train. This tractive stress would, otherwise, produce sidewise bending in the floor beams. The top flanges of the girders are supported at the panel points by means of solid web brackets extending down to the top of the floor beams, and made as wide as the specified clear- ance will allow. Sometimes through plate girder bridges have solid floors, in which case the moment and shear vary as for a deck plate girder. In this case no lateral system would be necessary. ' See Heller's " Stresses in Structures," Art. 151, page 275. CHAPTER V PIN CONNECTED BRIDGES 46. Construction. In a truss bridge, the loads are delivered to the trusses at the panel points only. In the ordinary bridge this is done by means of floor beams and stringers. The stringers carry the ties and rails direct, and are in turn sup- ported by the floor beams at the panel points of the truss. This construction causes the moment in the truss to vary uniformly between panel points and the shear to be uniform in each panel. (45.) 47. Types of Trusses. Pin connected trusses are nearly always of the Pratt or Baltimore type, because the pin connec- tion is not well adapted to members whose stresses alternate in direction. The tendency is toward long panels, that is, ordinarily from 20 ft. to 25 ft., because this gives few and heavy members both in the trusses and in the floor system, and these are cheaper to manufacture and give a stiff er structure under traffic. An odd number of panels is preferable to an even number, because the maximum moment will be less and because the structure may be made symmetrical about the center line with regard to field splices. The panel lengths must be chosen so as to give an efficient lateral system without increasing the width of the bridge beyond that required for clearance of the roadway. For a single track bridge this width is usually about 16 ft., depending, of course, on the width of the truss members. The economic depth^ (38) cannot be determined with any degree of certainty, but is usually taken at from one-fifth to one-sixth of the length of span. The deeper the truss is made the stiffer it will be and the less the vibratory stresses will be. 1 See " Stresses in Bridge and Hoof Trusses," by W. H. Burr, Art. 76, page 353. 115 116 LOADS Art. 48 It is found that considerable variation in the depth will effect the weight and cost but little. In through bridges, the depth must be made sufficient to allow efficient overhead bracing with- out interfering with the clearances required by the traffic, unless a pony truss is used.^ Pin connected pony trusses are not desirable because of the lack of efficient transverse bracing. 48. Loads.2 Most specifications give a series of wheel loads representing the weights of two locomotives, followed by a uniform train load which is to be used in designing the struc- tures. In bridges over 100 ft. long, if an equivalent uniform load is used which will give the same center moment in the span, the errors in the stresses will not be large. It will be necessary to use several different equivalent loads for different parts of the structure, as, for instance, one for the stringers, one for the floor beams and hip verticals, and one for the trusses. The labor involved in obtaining these equivalent loadings for the floor beams and stringers is about as great as it is to calcu- late the stresses directly, so the wheel loads are generally Used for these. An equivalent uniform load is usually used for the trusses (except the hip verticals). The stresses in some of the members will be too large and in some too small. The variation will usually be less than about 4% from the stresses obtained by using the actual wheel loads specifled.^ Fig. 56 shows the equiva- lent uniform loads for Cooper's E40 loading. Curves similar to this may be found in Johnson's " Modern Framed Structtires." Even if the exact loading specified should ever come upon the bridge, the stresses calculated from the wheel loads would not be the true stresses, because the track distributes the wheel loads differently from what we assvime, and the stringers are partially continuous while we assume them to be simply sup- ported at each floor beam. Besides, the impact or vibratory stresses cannot be estimated with less than a probable error > See Heller's " Stresses in Structures," Art. 113 and 151. 2 See Heller's "Stresses in Structures," Art. 119, 130 and'131. ' See Trans. Am. Soc. C. E., Vol. 42, pp. 189, 215 and 206. Also Johnson's " Modern Framed Structures," 9th Edition, Part I, Arts. 168 to 175. Also DuBois' " Stresses in Framed Structures." Abt. 49 TENSION MEMBERS 117 amounting to many times the discrepancy in the stresses obtained by the two methods. Numerous other methods of obtaining " equivalent " load- ings have been proposed, and it is probably due to the disagree- ment on this point that engine loads are still specified in all but a few specifications, and that some engineers still calculate all stresses from wheel loads. The dead load must be estimated. The weight of the floor (44) including rails, ties and guards for the ordinary floor con- struction, with stringers not over 6 ft. 6 in. center to center, will not exceed about 400 lbs. per linear foot of track. The weight of the steel work may be estimated approximately by comparison with some previously made estimates of similar structures, or may be taken from an empirical formula (44). After the design and estimate are completed, the dead load must be revised to agree with the final estimated weight, if the dis- crepancy is sufficient to change the size of any of the members (43) (44). 49. Tension Members. The tension members of pin con- nected trusses, except the hip verticals, and in some cases the counters and eiid panels of the lower chord, are usually made of eye bars. The counters and end panels of lower chord are fre- quently required to be made rigid members, to increase the stiffness of the bridge. The hip verticals should always be rigid members, because this gives a better connection for the floor beams at these points, and because it greatly reduces the vibration. Eye bars are forged, and the heads are made of such size that in testing, the bar will break in the body instead of through the head. Usually the net section through the pin hole is made about 25% in excess of the section through the body of the bar.i Eye bars should not be thinner than about f inch, and should not be too thick, say over about 2i inches. Thick bars will usually not show as high an ultimate strength as thin ones. The usual proportions of width to thickness he between 3 to 1 and 7 to 1. Built tension members, of course, contain more material than tension members of the same strength made of eye bars. 1 Sizes of eye bars as manufactured by that company axe given in " Cam- bria," page 317. 118 TENSION MEMBERS Art. 49 />(*• 3NoJ ''mku o^iisoNnoaNi <7m nt^iNn xfaTtmnas Art. 50 COMPRESSION MEMBERS 119 The net section through rivet holes (19) and through the pin holes must be carefully investigated. The most common form is an H cross section made of four angles latticed together, although two channels latticed are frequently used. Sometimes two eye bars are laced together with bent bars, but this does not give a member much stiffer than the plain eye bar member. The required net area of a tension member is obtained by simply dividing the stress in the member by the allowed unit stress in tension as given by the specifications. 50. Compression Members. The intermediate posts are usually made of two channels, either built or rolled, latticed together. Built channels are of course more expensive than rolled channels, on account of the extra punching and riveting. If the toes of the channels are turned in, the backs form plane surfaces to which connections may be more easily made than if the toes are turned out. The distance in the clear between the channels must be great enough to allow the entrance of the riveting tool between the lacing bars, and it is economical to place the channels far enough apart to make the ratio of the unsupported length to the radius of gyration in the two direc- tions equal.^ Local conditions frequently limit the dimensions of these members. Experiments show that a column will fail at an average unit stress over the entire cross section, which is less than the ultimate strength of the material in compression, and that the longer the column the less will be this average unit stress at failure. In other words, a column does not fail by compression alone but by a combination of compression and bending.^ This is taken into account in the design of compression members by the use of a " column formula," which gives us an average unit stress which it is safe to allow on the cross section and after this unit is determined the design of the compression member is as simple as that of a tension member, but the deter- mination of the average unit stress allowable, involves properties of the cross section of the member, so the solution must be by trial. Most column formulas take into account the slenderness of ' See " Cambria,'' page 195. * For an excellent article on Columns see editorial in Engineering News, January 3, 1907. 120 COMPEESSION MEMBERS Art. 50 the column by using the ratio L/r, in which L is the unsup- ported length and r is the least radius of gyration.^ This ratio is applied to the maximum allowed fiber stress in compression as a variable reduction factor. The column theory ^ assumes that the whole member acts as one piece. When the member is composed of two or more parts connected by stay plates and lacing, it is the function of these to hold the component parts of the member in line and to insure its action as a unit. Previous to the collapse of the Quebec Bridge in 1907, very few designers attempted the calculation of stresses in lace bars, or their rational design. They were put in by empirical rule and roughly proportioned to the size of the member according to the judgment of the designer.^ The failure of the Quebec Bridge was due directly to the weakness of the latticing of the lower chord compression mem- bers, and since that time much has been written on the subject and now most specifications require the calculation of the stresses in the lace bars.* A column under stress will deform into a curve with a point of contra-flexure near each end,^ the distance from the end depending upon the degree of fixity of the end. At these points of contra-flexure the bending moment is zero, and consequently the stress on the column cross section is uniform. Midway between these points the maximum bend- ing moment occurs, and the maximum unit stress in compression occurs on the concave side, there- fore in a distance equal to one half the length between the points of contra-flexure, the unit stress in the concave side of the column must change from the average to the maximum allowed. 1 See article by the author on " Fixed End Columns in Practice," in Engineering News, Nov. 2, 1911, Vol. 66, page 530. 2 See Heller's " Stresses in Structures," Chapter X. ' See Cooper's " General Specifications for Steel Railway Bridges and Viaducts," 1906, Section 97. * See Report of the Royal Commission on the Failure of the Quebec Bridge, Appendix No. 16, and also the attached Report by Mr. C. C. Schneider. See also " General Specifications for Steel Railway Bridges," 1910, of the American Railway Engineering Association, Sees. 47 to 50. ' See Heller's " Stresses in Structures," Fig. 137, page 178. Art. 50 COMPRESSION MEMBERS 121 Suppose a column to be made up of two leaves connected by lacing or otherwise. Let si = maximum allowed unit stress on the material in compression. p Sc = average unit stress over the cross section =-7-. A i'' = total change in stress in one leaf of the column in a distance I. /= change in the total stress in one leaf per unit of F length = y. Z=the least distance from the point of maximum bend- ing moment to a point of contra-flexure. L= total length of column. Ai = area of cross-section of one leaf. F=^Ai{si-So), (16) f=^l^^ (^^^ For a pivoted ended column L = 2l and for a square or fixed ended colvunn L = ^l. Any column in practice will lie somewhere between these two limits, and in any case eccentricities of manu- facture and loading may make I different than theory would indicate. Also this theory assumes that the rate of change of stress in the leaf is uniform, which is not true, therefore, to be on the safe side we will take L = Wva. all cases ; then ^ JAM-s.) ^^g^ Equation (18) gives the longitudinal increment of stress in one leaf per unit of length of column, and sufficient connec- tion must be provided between the leaves to transmit this stress (41). The values of si and Sc are taken from the column for- mula which is being used unless there is bending due to trans- verse loads (70). Professors Talbot and Moore, in a paper presented before the American Society of Civil Engineers, (Trans. Vol. LXV, 122 COMPRESSION MEMBERS Art. 50 page 202) give an extended account of experiments made at the Engineering Experiment Station of the University of Illinois upon steel, built-up, compression members. Concerning the stresses in lace bars they say, " The measurements indicate stresses in the lattice bars which would be produced by a trans- verse shear equal in amount to 1 to 3% of the apphed compres- sion load, or to that produced by a concentrated transverse load at the middle of the column length equal to 2 to 6% of the compression load." The theoretical bending moment which is taken into account by the column formula may be obtained by setting si—Sc=—r=-r-9 and M=-^-^ = Pt. from which P, the equivalent transverse load at the middle of the column length may be found. The lacing may be propor- tioned for the shear due to this load. When lacing is used the bars must be capable of taking their stress either in tension or compression. The top chords and end posts are usually made of two built or rolled channels, connected by a cover plate on top and by stay plates and lacing on the bottom. The cover plate being solid aids in taking compression, and its area is always considered in the effective cross section. The cover plate then' serves both as a part of the compression area and to tie the two leaves of the column together. A compression member with a cover plate on one side only is not symmetrical about its center of gravity, and the end connections must be designed to transmit the stresses to the cross section properly (18). The cover plates should always be made as thin as the speci- fications will allow unless they have some special duty to per- form, so as to keep the eccentricity of the section small. The unsupported width of plates in compression (distance between rivet heads) is usually limited by the specifications to 30 or 40 times the thickness of the metal. If a compression member is subjected to transverse loads, causing bending i in addition to the direct load (29), the maxi- ' See Heller's " Stresses in Structures," Art. Ill, page 190. Art. 50 COMPRESSION MEMBERS 123 mum fiber stress due to both must not exceed the maximum allowed imit compressive stress (si), and to be on the side of safety should not exceed a unit stress determined by a suitable column formula {se), because the accidental eccentricities may increase the bending due to the transverse loading. Horizontal and inclined compression members are in bending due to their own weight in addition to being in compression. In the top chords and end posts of bridges this bending moment is partially neutralized by lowering the centers of the end con- nections an amount sufficient to produce an upward bending moment due to the eccentricity of the compressive stress, equal to the downward bending moment due to weight. ■Pe=-g- and e=-gp (19) Equation (19) is generally used in practice to determine the eccentricity of the pins to compensate for the bending due to the weight of the member. Using this value of e would render the bending moment almost zero at the middle, but as the bending moment (Pe) due to the eccentricity is a constant, while the moment due to the weight is a maximum at the middle and zero at the ends, the use of this value of e produces a negative bend- ing moment at the end as great as the original moment due to the weight.! j^ jg better to use a smaller value of e as given by equation (20), ^ = iOP' ^2^) as this will give a less resultant maximum bending moment in the column. Another case in which compression members are subjected to both axial and bending stresses is the end posts of a through bridge with overhead bracing. The end posts must carry the wind load in bending from the portal to the abutments.^ This bending is in a plane perpendicular to that of the bending due to weight. The lacing and riveting of the cover plates of, the 1 See Article by Prof. J. E. Boyd in Engineering News for April 11, 1907, Vol. LVII, page 404. ' See Heller's " Stresses in Structures," Arts. 153 to 165 inclusive. 12i LATERAL SYSTEMS Abt. 51' end posts must be sufficient to transfer the increments of stress as determined by equation (17). 51. Lateral Systems.^ In a through bridge a lateral system is always provided in the plane of the lower chord and, if the head room permits, in the plane of the upper chord also. In a deck truss bridge, lateral systems should always be provided in the plane of both the top and bottom chords. Transverse sway bracing is always provided at each panel point. In pony trusses this consists of knee braces to the floor beams which transmit each panel load of wind from the top chord to the bottom lateral system. In truss bridges with two lateral systems (top and bottom) the transverse sway frames will trans- mit part of the load from the other lateral system to the one in line with the supports, due to the deflection of the end sway bracing. Thus in a through bridge, part of the top lateral load will be transmitted at each panel point to the bottom lateral system by the intermediate sway bracing. The amount of load thus transferred depends upon the relative stiffness of the various members concerned and on the stiffness of the portal bracing. It will usually be safe to assume that half of each top chord panel load is transmitted by the sway bracing to the bottom lateral system at that point. In double track bridges and in bridges on curves the transverse bracing is proportioned to carry part of the load from one truss to the other in order to equalize the deflections of the trusses under eccentric loadings.^ The lateral system is a horizontal Pratt truss in which the floor beams act as the posts and the chords of the main trusses act as chords. The diagonal members are put in in both direc- tions to provide for a reversal of wind. The top lateral system in a through bridge and the bottom lateral system in a deck bridge take the wind load on half the projection of the trusses. The end reaction of the top lateral system in a through bridge is conveyed to the abutment bjr means of portal bracing 1 See Heller's " Stresses in Structures," Chapter XIV. " See Johnson's " Modern Framed Structures," 9th Edition, Part I, Art. 191. See Cooper's " Specifications," Sections 109 and 110. See " Framed Structures and Girders," by Edgar Marburg, Arts. 246 and 247. Aht. 52 PIN-CONNECTED RAILWAY BRIDGE 125 between the end posts and by bending in these end posts.^ (50.) Provision must be made in all main truss members carrying wind stresses for these, in addition to the dead and live load stresses. The wind blowing upon the side of a train on a bridge tends to overturn it, and thus produces, a greater load on the leeward truss than on the windward. The effect on the top chord of a through bridge is very small because the leeward top chord would be in tension under the wind load alone, and in compres- sion due to the overturning moment. The bottom chords and web members should, however, be proportioned for this additional stress. (56.) 62. Design of a Pin-coimected Railway Bridge. To illus- trate the methods of solving the various problems connected with the design of truss bridges, the design for a through Pratt truss railway bridge will now be worked out. We will assume the following data: Span 189 ft. c. to c. of end pins =7 panels at 27 ft. Single track. Alignment tangent. Specifications Cooper's 1906 for Railway Bridges. Loading Cooper's E40. Material medium steel except rivets. 53. Dead Load. (48) The stringers will be spaced 6 ft. 6 in. c. to c, and the size of the tie may be calculated as was done in Art. 43. We will use 8"X8" ties 10 ft. long spaced 14 in. c. to c, guard rails 6"X8." The weight of the floor comes out somewhat less than 400 lbs. per lin. ft., but the specification § 23 directs that not less than 400 lbs. per linear ft. shall be used (43). The weight of the steel work may be approximately esti- mated from equation (15), w=7L+600 from which «) = 1923 lbs. per lin. ft. of bridge. The total dead load then will be 1923-F400 = 2323 lbs. per lin. ft. of bridge, one-third of which will be considered as acting at the top chord and two thirds at the bottom chord. 54. The Depth of the trusses (47) must be sufficient to allow the required head room and also an efficient portal. The depth of the floor system will govern this to some extent also. ' See Heller's " Stresses in Structures," Arts. 153 to 165 inclusive. 126 THK DEPTH Abt. 54 An estimate of the depths required for these various parts may be made and an approximate minimum allowed depth calculated in the form of a table. The stringer should be designed before this table is made up, as the depth of the truss does not affect it. We will use the stringer as designed in Art. 43, for this bridge. 1 s / \ C^arMi^ 5! \ u'-a- 1'^ ■\ \ Baseof^ff, — 1 is . FiQ. 58. Depth of tie over stringer 0';7|" (Spec. § 12) Depth of stringer 4''3|" Bot. of stringer to bot. of fl. bm 0' /Tf oB +/Z3/00 i-2SS4'00 i.264^00 + 3I300'' + 3I300 i5^e phrfa/ Be - 8Z/00 -/S2400 -/30000 * 2Z4M - 2Z4ao >^«fe/>i^y Cc/ - 4/000 -/Z/600 -/26/o<7 ± /4900 - J430P ^ a Oc^ - O - 73000 - T^Off^ i 3000 - aoet' // // O'c' * >f/ooo -S6SOO -34^500 t 4SOO - 4.Si>e te /, C'^ + ez/oo - /z/oo - 3600 t /^OO - /■SiX> ^j¥amJ>er Bh - 20S£>0 _ - 30/00 t 8000 - aa^o /^^yfetf/>^z/ Cc + -4/800 *■ 33000 f 96300 ? /utx? * J/40P U M £>c^ + /as^oo ■f^SiffSOO ¥^660i? f 630O +■ es^o *f Xf ab - 7B-fOO -/e47oo -/70600 - o t 2l?20t> - zezeo /^ ^ Jbc - 73400 -J647'^0 -/706£IO -^f^ t 20200 f /St zoo -ja/»Mt h^exceee&joi ccf -/JZ300 -ZT^SiPO -27-^^1!^ ^-/e3^oo -/3SOOO t 337"" -/697aa ,.■ M cfc/ -ASBSOO -.329,^00 -330/t>0 i /63ZOO * 4e4IX> -2t>36ae » ft a BC * /32300 *274-S^PO ¥Z74'Sri?o t '^J-^ J 337^^^ + 337tM> A^if/i?^M^i/ CO ^AS8800 «-3?$LSC!? ^■330/00 + Z7Zot> J jM>4^?e? * 27200 ff yf o6 * /SBSOO y3Z9-SOO +33a/l?0 *Z7Zot? f ■4a4^}o ■>■ Z72t>0 * •-' from the maximum live load moment for the span (48). This equivalent uniform load for a 189 ft. span is 4820 lbs. per lin. ft. of track. See Fig. 56. 2323X27 Panel load of dead load= Panel load of live load = 2 4820X27 =31,360 lbs. = 65,070 lbs. The table under Fig. 59 gives the direct stresses in all of the truss members due- to dead load, live load, and wind. The live load stresses calculated from the wheel loads are also given in a parallel column for comparison. The maximum error is seen to be in the end posts and amounts to about 3|%. 1 See Johnson's " Modern Framed Structures," Arts. 168 to 175. 128 STRESSES Abt. 55 The wind stresses in the chords from the lateral systems are gotten by assuming that the trusses are 16' 0" c. to c. This will not be far from right. According to specifications, § 24, 450 lbs. of the wind load shall be treated as acting on a moving train at a height of 6 feet above the base of rail. This gives a height of 6.0+4.58 = 10.58 feet above the pin centers. The horizontal force acting at this height (see Fig. 60) will be 450X27 = 12,100 lbs. per panel. _^Z^Asu X__ r /S.O ' ^•ssumei/ \ Fig. 60. The additional load on the leeward truss at each panel due to this overturning moment will be , 7 = 12100X10.58 16 = 8000 lbs. The additional stress in each member then will be the direct live load stress in the member, (figured for the equivalent uni- form load) multiplied by „-„-„ . The specifications § 39 direct that the stresses in the truss members due to wind may be neglected unless they exceed 30% Aet. 56 DESIGN OF TENSION MEMBERS 129 of the combined dead and live load stresses. Therefore we will have to consider the wind stresses only in the bottom chords. The- bending in the end posts due to the portal stresses will be " taken up in Art. 58. 56. Design, of Tension Members. The required net area for any tension member is obtained by adding algebraically, the areas required for dead load and live load stresses. (Spec. §§ 31 and 35.) There is also a limiting clause for counters. (Spec. §§ 50 and 51.) Since in these specifications, the dead load unit stress is just twice the live load unit, the same area will be obtained if the live load stress plus half the dead load stress be divided by the live load unit stress. From this relation we may derive an average unit stress which may be applied to the total dead plus live load stress in any member as follows : Let Spp = this average unit stress. Sx) = the dead load unit stress. Si = the live load unit stress. D = the dead load stress in the member. L = the live load stress in the member. iD+L D+L Si sw ' Sw = 2(D+L)Si D+2L 2si = 2sx, sw = Sd *z>- 1+K^ (21) It is not necessary to find this average unit stress except for those members in which the wind stress must be taken into account according to specifications § 39. The simplest members, those made up of eye bars, will be proportioned first. We will assume that we are limited in the choice of eye bars to those manufactured by the Cambria Com- pany, as indicated in their hand book, pages 316 and 317. 130 DESIGN OF TENSION MEMBERS Art. 56 Be Required D^L. area= onnnn ~ ^'^^ ^' '°" „ • , T T 182400 ,_„. Required L.L. area =^|jr^r^ = 18.24 sq. m. TotaI=22.35sq. in. This may be made up of 4 bars 6"XTf" (area =22.50 sq. in.) or 2 bars 7"Xlf" (area =22.76 sq. in.). The 6 inch bars are slightly more economical and will not require such large heads so we will use 4 bars 6"Xyf" for Be. Cd Required D.L. area = onmn" 2.05 sq. in, T, . , T T 121600 ,__ Required L.L. area = ^r^r^r^ = 12.16 sq. in. Total = 14.21 sq. in. This will require 2 bars 6" X li%" (area = 14.25 sq. in.) Dd' Required D.L. area =00 T> • J T T 73000 _ „ Required L.L. area= = 7.3 sq. m. This will require 2 bars 4"XTf" (area =7.50 sq. in.) or 2 bars 3"Xlj" (area = 7.50 sq. in.). The 3 inch bars cannot be used because, probably the size of the pin at d will exceed 5 in., which is the largest size that the table in " Cambria " gives for a 3 inch bar, so we will use 2 bars 4"Xyf"- An increase in live load of 25% or to E50, will increase the unit stress in this counter exactly 25% so § 51 of the specifica- tions is satisfied. D'c' Required D.L. area= „-,„„„ =2.05 sq. in. Required L.L. area= =3.65 sq. in. Difference = 1.60 sq. in. To comply with specifications § 51 an increase in live load of 25% must not increase the unit stresses more than 25%, therefore: Art. 56 DESIGN OF TENSION MEMBERS' 131 tj ■ A-r>T 41000 , „ . Required D.L. area = 2oooo+25% = ^-^* '1- '°- „ • , T T 36500+25% ^ „^ Required L.L. a,Tea, = ^QQ^Q_^^^^ = 3M sq. in. Difference = 2.01 sq. in. This will require 1 bar 1^6 in- square (area = 2.07 sq. in.). cd. The average unit stress allowable, as determined by equation (21) must be used here because the wind stress is more than 30% of the dead and live load stresses. (Spec. § 39.) 20000 .-,nA^>^u Sw = „-■ - = 11,940 lbs. per sq. in. ^406.8 11,940+30% = 15,520 lbs. per sq. in. Total stress in cd=132.3+274.5+169.7 = 576.5. T, . , 576500 ^^ , , Required area = YcEprr = 37.14 sq. in. This will require 4 bars 6"Xl^" (area = 37.50 sq. in.) or 2 bars 7"X1A" plus 2 bars 7"Xlf" (area = 37.64 sq. in.). The 7 inch bars will be better because the thickness is less, and this will give a less bending moment on the pin, and also probably the next chord dd' will necessarily be made of 7 inch bars, in which case the same dies may be used for making, all of the eye bar heads in the bottom chords, which would reduce the cost. dd' Total stress =158.8+329.5+203.6 = 691.9. Allowed unit stress = 15,520 lbs. per sq. in. Required area = -Y^^jr-= 44.58 sq. in. This will require 2 bars 7"Xlf" plus 2 bars 7"X1^"' (area = 44.64 sq. in.). According to the specifications § 10 the vertical suspenders and the two end panels of lower chord must be made rigid members. 132 DESIGN OF TENSION MEMBERS Art. 56 abc Total stress =79.4+164.7+101.8 = 345.9 Allowed unit stress = 15,520 lbs. per sq. in. „ . , 345900 „„„ Required area =—^^757^- = 22.29 sq. m. loozU This member may be made up of 4 angles and 2 plates laced together horizontally as shown in Fig. 61. We will use 4 angles 6"X3i"Xi", and 2 plates 14 inches wide by as thick as may be necessary to make up the required net area. To com- ply with specifications § 64 at least two rivet holes must be deducted from each angle (19). Fig. 61. Net area 4 angles 6"X3|"Xi" = 18.00- 8XlXi = 14.00sq. in. Required net area of plates = 22.29 — 14.00 = 8.29 sq. in. Equivalent net width of plates = 14 — 2X1 = 12 inches. 8 29 Required thickness of plates = ^^7^- = 0.69 inch. Use 2 plates 14" Xf". Total actual net area 4 angles 6"X3|"Xi" = 14.00 sq. in. net 2 plates 14" Xf"= 9.00 sq.in.net Total =23.00 sq. in. net It would be more economical to use four angles "without cover plates, but it is not well to use metal thicker than about I inch in a riveted tension member, besides, according to specifica- tions § 129, material over f inch in thickness in tension members must be reamed, which would increase the cost considerably. Bb will be made of two rolled channels, and will be made the same width as the intermediate posts Cc and Dd so that the floor beams may all be made alike. The allowed imit stresses are less for verticals carrying floor beams than for other truss members (Spec. § 31). T, • J T>. T 20900 , „, Required D.L. area = --^rT—= 1.31sq.m. TJ ATT 80100 ,_ _, Required L.L. area = -^tttt^ = 10.01 sq. in. Total = 11.32sq. in. Art. 57 DESIGN OF COMPRESSION MEMBERS 133 There will be pin plates on the webs of the channels for the connection at B, and stay plates riveted to the flanges near them. These will make it necessary to take at least 4 holes out of each channel as shown in Fig. 62. The member cannot be made of less than 10-inch channels or there would not be room for the floor beam connection. The lightest weight 10 inch channel cannot be used because specifica- tions § 82 requires that no metal less than | inch Fig. 62. thick be used, and the web of a 10" by 15 lb. channel is only 0.24" thick. 2 — 10" X 20 lb. channels is about the smallest section that can be used. The rivets in the flanges cannot be. larger than f", (see " Cambria," page 46), while it is desirable to have the rivets in the web |" for the floor beam connections. The net area then of the 2 channels 10"X20 lb. = 11.76-4Xi;VXi-4X0.38Xl=8.71 sq. in. As this is less than the required area we must use heavier channels. Try 2 channels 12"X25 lbs. Net area = 14.70^4X|X|-4X0.39Xl = 11.39 sq. in. These will answer. 57. Design of Compression Members. The least allowable section for a post is 2 channels 10"X20 lbs. (see Spec. §§ 35 and 82.) The greatest allowed length for a post composed of these channels is 100 times the radius of gyration (Spec. § 35) = 100X3.66 = 366 inches = 30' 6", which is less than the depth of our truss, so a larger section must be used. Try 2 channels 12"X25 lbs. Allowed length = 100X4.43 = 443" = 36' 11." Allowed unit stress for D.L. = 17000 -90- r = 17000- ^^^/^3^ ^^ = 9200 ^^^- P^"" ^^- '^- 134 DESIGN OF COMPRESSION MEMBERS Abt. 57 Allowed unit stress for L.L. =4600 lbs. per sq. in. Da liequired D.L. area ="5ofj?r= 1-14 sq. in. Tj . , T T 55800 ,„,„ iiequired L.L. area =-j^^ = 12.13 sq. in. Total = 13.27sq. in. Actual area = 2X7.35 = 14.70 sq. in., which is sufficient. Cc. The stress for this post is considerably greater than tor Dd, so we will try 2 channels 15"X33 lbs. Allowed D. L. unit stress = 10,850 lbs. per sq. in. Allowed L.L. unit stress =5,425 lbs. per sq. in. Required D.L. area = —r^^ = 3.86 sq. in. -n • J T T 93000 ,_,^ Required L.L. a,Tea, = -^j^ = l7.lQ sq. in. Total = 21. 02 sq. in. Actual area 2 channels 15" X33 lbs. = 2X9.90 = 19.80 sq. in. Try 2 channels 15"X40 lbs. Allowed D.L. unit stress = 10,650 lbs. per sq. in. Allowed L.L. unit stress = 5,320 lbs. per sq. in. ^ . ,T^T 41800 „_„ Required D.L. area= = 3.93 sq. m. ■D • J T T 93000 ,_,„ Required L.L. area =-^^^ = 17.48 sq. in. Total = 21.41 sq. in. Actual area 2 channels 15"X40 lbs. = 2Xll.76 = 23.52 sq. in., which is sufficient. In the above calculations for the posts we have assumed that the ratio of unsupported length to radius of gyration in the direction parallel to the webs of the channels was greater than that in the other direction (50). In order to make the posts safe according to the specifications, the distance between channels must be sufficient so that the allowed unit stress is greater than the actual. Art. 57 DESIGN OF COMPKESSION MEMBERS 135 The actual unit stress on Cc=-K;r-^ = bl^O lbs. per sq. in. From equation (21) the allowed unit stress = [17000-90^] /-V^ Equating these two units we get 1 = 10060-53.25-. 5730 = 10060 -53.25?^^^, from which r=3.1 in. This is asuming that the post is supported by sway bracing at an elevation of 21 ft. above the floor beam. (Spec. § 107.) The distance apart of the channels necessary to make the radius of gyration equal to 3.1 in. will now be calculated. r=^^, /=/.+Ad2, in which /„= moment of inertia of channels about their own center of gravity. d= distance from the center of gravity of the column to the center of gravity of the channel. -4 2X9.39+2X11.76X^^3 J 2X11.76 from which d2 = 8.81, d=2.97 inches. The minimum distance back to back of channels (toes turned in) then will be 2X2.97+2X0.78 = 7.5 inches, but Spec. §35 says that the least width of post permissible is 10 inches, so we will use this width. The post Dd and the hip vertical Bb will be made the same distance back to back in order that the floor beams may be made alike. The width of the top chord and end posts must be made the same throughout, and the depth of the two is usually made the same, although this is not absolutely necessary. 136 DESIGN OF COMPKESSION MEMBERS Art. 57 The width must be sufficient to^llow all of the web members to comiect to the pins inside of the top chord section. In some cases a pair of eye bars are allowed to connect to the pin outside the chord section, but this is unusual. There are more members connecting at B than at any other point, so the required width there will be determined. We can only estimate this width approximately at present. Width of Bh back to back of channels = 10" Pin plates on Bh say 2 — |" Bars Be 2-^" (2 outside chord) Webs of end posts say 2 — f" Pin plates on end posts say 2 — §" Top angles on end posts say 2—3" Clearances say _ 1 7// — ^i — 12 = 4" = 6" 11" Is Total =22i' m S -^^ In order to make sure that we have sufficient clearance we will make the cover plate of the chord 24 inches wide. The depth of the chord section must be made sufficient so that there is room between the pin and the cover plate for the connection of the members. The pin will be somewhat above the geometric center of the web plates because the center of gravity of the section will be above ^^' >| the center of the web. Assuming this eccentricity of the pin to be 1|" and that the radius te/^aoai!^ _4 "* of tli^ largest eye bar head is not ~^— over 7|", we have 9" as the half '■^ depth of the web required by the ^ — y sL=_i clearances. /•yf-' ,\ Fig. 63 shows about the dimen- FiG. 63. sions of the minimum chord section which we can use here. The specification §80 requires that the thickness of plates in compression shall not be less than ^ of the unsupported width, except for the cover plates of top chords and .end posts which are limited to ■^. The unsupported width of the plate is the distance between rivet heads. For the cover plate it Art. 57 DESIGN OF COMPRESSION MEMBERS 137 will be (9), 21|" - 1^" = 19if ". The minimum allowed thickness 19 8 of cover plate then will be ~77r=i"- The minimum allowed 13 3 thickness of web plate will be -~ =0.45", or say §" also. For the chord sections CD and DD we will try the following, which is about the least chord section allowable as we have seen : 2 web plates 18" X i" = 18.00 sq. in. 1 cover plate 24"X^" = 12.00 sq. in. 2 top angles 3"X3"Xf"= 4.22 sq. in. 2 bot. angles 4"X3"Xf"= 4.98 sq. in. Total =39.20 sq. in. We will now find the location of the center of gravity of the cross section by taking moments of areas about the upper side of the cover plate (see Fig. 63). Cover plate 12X 0.25= 3.00 Top angles 4.22X 1.39= 5.86 Web plates 18.00 X 9.62 = 173.25 Bot. angles 4.98X17.97=89.49 Sum =271.60 Distance of center of gravity from top of cover plate 271.60 39.20 = 6.93 inches. The distance of the center of gravity above the center of the web plate = 9.63 -6.93 = 2.7 inches. The least radius of gyration is required to be used in the determination of the allowed unit stresses. This will be about a horizontal axis through the center of gravity, and is equal to The moment of inertia about this axis must now be found.i 1 See Heller's " Stresses in Structures," Art. 67, page 92. 138 DESIGN OF COMPRESSION MEMBERS Art. 57 This is done by adding to the moment of inertia of each con- stituent part the product of its area by the distance squared, of its center of gravity from the center of gravity of the section. Cover plate ?^^2)!= o.25 12.00 X (6.68)2= 53547 Top angles 2 X 1.76 = 3.52 4.22 X (5.54)2= 129.52 Web plates ^^^i||^^= 486.00 18.00 X (2.70)2= 131.22 Bot. angles 2 X 1.92 = 3.84 4.98 X (11.04)2= 606.97 Total moment of inertia =1896.79 From which we get the radius of gyration about the hori- zontal axis through the center of gravity dead 1 from specifications § 35. 1896.79 „ _. . , ^^ = 6.95 mches. The allowed dead load unit stress is 20000-90 — = 15,800 ^ . ,^^ 158800 .__- Required D.Li. area= ^ro/^r. =10.05 sq. m. . 1 T T 329500 ,, „, Required L.L. area=-^Q^ =41.71 sq. m. Total =51.76 sq. in. The area of cross section must therefore be increased. We will try the following: 2 web plates 18"Xf" =27.00 sq. in. 1 cover plate 24" X|" = 12.00 sq. in. 2 top angles 3" X 3" X]^" = 4.88 sq. in. 2 bot. angles 4"X3"Xf" = 7.98 sq. in. Total =51.86 sq. in. Eccentricity=1.68 in. 7 = 2494. r = 6.93 in. Art. 57 DESIGN OF COMPRESSION MEMBERS 139 The change in the raditis of gyration is seen to be very small, and the corresponding change in the allowed unit will be very small, so this section will answer. BC. The section for this chord will lie somewhere between the two tried above, and therefore we may use the same allowed unit stresses. „ . jT^T 132300 _„_ Kequired D.L. area = „ = 8.38 sq. m. ■D • J T T 274500 „ . _. Required L.L. area = ^;^qj^ = 34.75 sq. m. Total=43.13sq. in. Pm. 64. Use the following section: 2 web plates 18" X -h" = 20.25 sq. in. 1 cover plate 24" X§" =12.00 sq. in. 2 top angles 3"X3"Xf" = 4.22 sq. in. 2 bottom angles 4"X3"XA"= 7.26 sq. in. Eccentricity =1.98 in. Total =43.73 sq. in. 7 = 2230. r = 7.14in. 140 DESIGN OF THE END POSTS Art. 58 BliP 58. Design of the End Posts. Before the end 'posts can be designed the stresses in them due to the -porial bracing must be determined. From Fig. 58 we see that we can make the vertical distance from the upper clearance line to the upper pin center 6 ft. 5 ins. Fig. 64 illustrates the method of determining the depth of portal which we may use. This may be laid out to scale and the depth scaled. For the purpose of calculating the stresses the depth does not have to be determined closer than the nearest 0.1 ft. In the following calculations of the stresses in the end posts and portal bracing due to wind, the methods and notation used in Heller's " Stresses in Structures," Arts. 153 to 165 inclusive, will be followed.^ The specifications § 106 direct that the portals be latticed and that they be rigidly connected to the end posts and top chords. The bearings of the ends of the posts upon the pins at the top and bottom will tend to hold the ends of the posts fixed in direction. The rigidly connected portal at the top will further tend to fix that end of the post; con- I 1 sequently the flexure lines of the \ MnfofConfmf/Xrej \ P^^*^ ^i^^ ^e somewhat as shown in \h — 1- T\^ \ ^^ exaggerated amount in Fig. 65. 1 \ ^ '^^^ degree of fixity of the bottom 1 depends upon the amount of the direct stress in the end post. If the moment, the direct stress multiplied by one half the dis- tance between the centers of the bearings of the end post webs on the pin (|fcD), exceeds the moment due to the wind forces when the ends are considered fixed (M2), the ends may be considered as fixed. Otherwise the ends will be only partially fixed. * See also Johnson's " Modern Framed Structures,'' Art. 186, or Marburg's " Framed Structures and Girders,'' Art. 239. Tm^ "Fia. 65. Akt. 58 DESIGN OF THE END POSTS 141 From Fig. 63 we may determine approximately that ki = k2 = about 17 inches. P= Panel load of wind load on top lateral system = 200 X 27 = 5400 pounds 12= Reaction of top lateral system on the portal =2P (there are 5 panels in the top lateral system) = 10,800 lbs. To test for the degree of fixity of the ends of the posts assume H=H'=^(R+P). (This is assuming fixed ends.) Then ff=i?' = 8100 lbs. The portal being rigidly connected to the end posts from B to F, fixes the tops of the posts, then the point of contra- flexure would occur midway between a and F or xi=x'i = 17.0 ft. Taking moments about the point of contra-flexure in one of the posts, ■2M=0=M2-Exi from which Ma =ffa;i = 8100X17 = 137,700 ft. lbs. = 1,652,400 in. lbs. Taking moments of all the forces about a in Fig. 65, V' = lUR+P)(a+d)-M2-M'2]^^{R+P){a+d-xi), and from vertical components equal zero F=-7' = ^(/2+P)(a+d-a;i)=j^X16,200X(43.0-17.0) = 26,100 lbs. The maximum stress in the end posts occurs in the leeward post when the live load is on the bridge and when the wind is acting. Dead load stress = 123,100 lbs. Live load stress = 255,400 lbs. Overturning tendency due to wind on train = 81,300 lbs. V due to wind on top lateral system = 26,100 lbs. Total maximum direct stress = 435,900 lbs. 142 DESIGN OF THE END POSTS Art. 58 The concurrent direct stress in the windward post will be 123,100+255,400-31,300-26,100 = 321,100 lbs. The moment of the direct stress at the bottom of the wind- ward post tending to fix the end is |fc2Z> = 321,100X^X17 = 2,729,400 in, lbs. As this is greater than the moment M2 tending to rotate the post at a, the posts will be fixed at the bottoms when the live load is on the bridge. The maximuln bending moment in the post occurs either at a' or at F', and is 1,652,400 in. lbs. We will try for the end posts the same section as was used for top chord sections CD and DD. The moment of inertia must be calculated for a vertical axis through the center of gravity, as the bending moment due to the wind is transverse. Area of cross section = 51.86 sq. in. Eccentricity = 1.68 in. I (horizontal axis) =2494; least r (horizontal axis) =6.93 in. / (vertical axis) = 3848. The average allowed unit stress for dead and live loads from equation (21) 17000-90^ ,„,„„ r 10460 „_ . . ,, '^= 255400 ^075 =^^^^ ^^'- P'"" '^- ''^• ■^378500 When wind stresses are added to the dead and live load stresses this unit may be increased 30%, (Spec. § 39), making it 8120 lbs. per sq. in. For this cross section the actual maximum fiber stress would be (50) P M»_ 435900 1652400X12.875 Smax-^+ J gj gg + 3g4g = 8405+5528 = 13,933 lbs. per sq. in. Therefore the section must be increased. As the moment of inertia increases when the area is increased, Art. 58 DESIGN OF THE END POSTS 143 we may arrive at -an approximate figure for the area by con- . sidering the equation above as follows : 8405 : s =13933 : 8120 from which v = 4900 lbs. This value of s^ assumes that in changing the section we have not changed the radius of gyration, and of course can be used only as a general guide. Using this value of s^ we find that the required area will , 435900 on • u ^ be ■„„„ =89 sq. m., about. 4900 It will be found by trial that this area cannot be made up without materially reducing the radius of gyration, and conse- quently the allowed unit stress, unless the width or depth of the section be increased. If the width were increased it would necessitate an equal increase in width of the top chord sections and add materially to their weight without increasing their efficiency. (See Spec. §§80 and 100), but the depth of the end posts may be increased somewhat without changing any of the top chord sizes. After several trials the following section was chosen: 1 cover plate 24"Xf " = 15.00 sq. in. 2 web plates 21" X I" = 36.75 sq. in. 2 top angles 3"X3"X|"= 6.72 sq. in. 2 bot. angles 4"X3"X|"= 7.98 sq. in. 2 side plates 15" X |" = 18.75 sq. in. Total =85.20 sq. in. The properties of this section are as follows: Eccentricity = 1.77 in. Area = 85.20 sq. in. '■ I (horizontal axis) = 4698. I vertical (axis) = 6424. r (horizontal axis) = 7.43 in. Allowed D.L. unit stress = 17,000-90- = 10,913 lbs. per sq. in. Allowed unit stress for D.L.+L.L. from Eq. (21) =6516 lbs per sq. in. Allowed unit stress for D.L. -l-L.L.+wind = 8468 lbs. per sq. in. 144 THE PORTAL BRACING Art. 59 435900 , 1652400X12.875 Max. extreme fiber stress = 85.20 ' 6424 5116+3312 =8428 lbs. per sq. in. 59. The Portal Bracing. The maximum stresses in the portal bracing will occur when there is no live load on the bridge. The direct stress then in the leeward post, assuming fixed ends as above, is as follows: Dead load stress = 123,100 lbs. Y= 26,100 lbs. Total =149,200 lbs. The concurrent direct stress in the windward post = 123,100 -26,100 = 97,000 lbs. The moment of the direct stress at the bottom of the leeward post tending to fix that end is §A;2D = 149,200X1X17 = 1,268,200 in. lbs. The moment M2 required to fix that end is 1,652,400 in. lbs. therefore the posts are only partially fixed at the bottoms. The tops are fixed by the construction. An approximate mean value of xi and x'l may be gotten from the equation _ P2Z) KR+py Neglecting V in the value of D, we get 8.5X123100 ,--. .„„. ,^ x„ = gjo^ = 129 m. = 10.75 ft. We may now get an approximate value for V. 1st Approx. V---V' = UR+P)ia+d-x„) ^ X 16,200(43 -10.75) =32,300 lbs. 16.15 2nd Approx. Z) = 123,100-32,300=90,800 lbs. 2nd Approx. D' = 123,100+32,300 = 155,400 lbs Art. 69 THE FOETAL BRACING 145 2ndApprox. ^2 = 8.5X90,800 = 771,800 in. lbs. 2nd Approx. M2'= 8.5X155,400 = 1,320,900 in. lbs. 2ndApprox. H' = i\R+P+^iM2'-M2)\ = 4(16,206+^^1^^X549,100) =9110 lbs. 2nd Approx. H=R+P-H' = 7090 lbs. 2nd Approx. xi=^= '^^^ = 109 in., = 9.08 ft. 2nd. Approx. a;i'=^=^^^ = 145 in. = 12.08 ft. 2nd Approx. V=-V' = ^UR+P)(a+d-xi)-H'{xi'-xi)\ =Y^ri6,200(43-9.08)-9110X3l =32,330 lbs. As this value of V does not differ materially from the first approximation the values of the other quantities are also deter- mined closely enough. Taking a section Im through the portal and a center of moments at the bottom flange Fig. 65, Stress in top &Singe= R+^P+H~^-V^ 24 Q2 r = 10,800+2700+7090 =^-32,330 1. The maximum compression in the top flange then will occur where x=0 and the maximum tension where x=b. Max. comp. in top flange = 33,100 lbs. (+) Max. tens, in top flange = 24,900 lbs. (— ) Taking the same section and a center of moments in the top flange Stress in bottom flange of portal =H j V -r. 146 DESIGN OF FLOOR BEAMS Art. 60 The maximum tension occurs where x = and the maximum compression where x = b. oo no Max. tens, in hot. flange = 7090 ^^ = 26,700 lbs. (-) Max. Comp. in hot. flange = 26,700 -32,330^^ = 31, 300 lbs. (+) The maximum shear at any section is y = 32,330 lbs. For the portal flanges the least allowable radius of gyration is j|qX14X12 = 1.4 inches. (Spec. § 35.) This radius of gyration is taken perpendicular to the plane of the portal. Try 2 angles 5"X3"X]^", 5 inch legs outstanding. Area = 2X2^41 =4.82 sq. in. gross; r = 2.47 in. The allowed unit stress = 13,000 -60- = 8920 lbs. per sq. in. T, , 33100 „_^ Keqd. area = -5^^ = 3.71 sq. m. These are large enough for the maximum compression stress. The required net area for tension = --^^r— = 1.48 sq. in. Actual net area = 4.82-2X 1^X1=4.20 sq. in. (|" rivets.) For the lattice of the portals we Will use angles spaced about as shown in Fig. 65. Any vertical section will cut four lattice angles, so we will consider the shear as equally divided among them. The secant of the angle of inclination of the lattice is about 32330 1.4, so the stress in each lattice angle = 1.4 X — j — = 11,300 lbs. tension or compression. The smallest angles allowable to use are 3"X2§"Xi^", (see Spec. § 83), which will be ample to take the above stress. 60. Design of Floor Beams. The weight of the beam itself is a imiform load, the weights of the floor, stringers and live Abt. 60 DESIGN OF FLOOR BEAMS 147 load form two concentrated loads on the floor beam 6' 6" apart Since the beam's own weight is a very small proportion of the total load, it will be considered as concentrated at the stringer connections also. The maximum live load concentration on the beam may be taken from the specifications, Table I, or calculated from the wheel loads. Live load at each stringer connection = 80,000 lbs. Dead load from floor =200X27 = 5400 lbs. Weight of stringers =165X27 = 4455 lbs. Weight of 5^ ft. of floor beam say = 945 lbs. Total dead load = 10,800 lbs. at each stringer. The distance center to center of trusses is 16 ft. If in. This is considered as the distance between supports of the floor beams. The distance between the center of the truss and the nearest stringer connection is 4' 9|". The moments on the floor beam are: Dead load moment = 10,800X4.82= 52,060 ft. lbs. Live load moment =80,000X4.82 = 385,600 ft. lbs. Economic depth from equation (10) (no flange plates) is 4 1.52-v/ .„r.r^^.,-i =55 inches. The depth assumed in the calculations for the depth of truss was about 13 inches more than the depth of the stringer, or 64J inches. (See Fig. 58.) It is desirable to have the stringer connection come between the flange angles of the floor beam rather than to have it lap over the vertical legs of these angles, in order to dispense with filler plates under the connection angles. For these reasons then we will use a web plate 64 inches deep. The maximum shear = 10,800+80,000=90,800 lbs. 148 DESIGN OF FLOOR BEAMS Art. 60 Using a f" web plate the unit shear =-2^ = 3780 lbs. per sq. in., which is safe. Assuming that the flange angles will be 6"X6", the effective depth will be about 61 inches. Approx. D.L. flange stress =■ ^r = 10,240 lbs. Approx. L.L. flange stress = ^3 = 75,860 lbs. Approx. D.L. required area = ^^rjrTj^ = 0.52 sq. in. Approx. L.L. required area =Yj™Tr= 7.59 sq.in. Total = 8.11 sq. in. 2Ls 6"X6"Xi^" = 10.12-4Xi^Xl = 8.37 sq. in. net. G inch rivets, no holes out of horizontal legs, two holes out of ver- tical legs, to comply with Spec. § 64.) The actual effective depth = 64.25- 2X1.66 =60.93 in. This will not change the flange stresses given above appre- ciably, so the flange as designed will answer. There must be sufficient rivets through the flange angles and web to develop the entire flange stress between the end of the beam and the stringer connection. This will require more rivets than would be given by the horizontal increment (41) because the flange angles cannot run to the theoretical end of the beam which is at the center of the truss. (See Fig. 80.) End Floor Beams are required by § 10 of the specifications, and it is always good practice to use them rather than to allow the end stringers to rest directly on the abutments. The end floor beam must carry the half panel load from the end panel of the bridge, and also the load from the short space between the end floor beam and the back wall, which is usually bridged by a cantilever bracket riveted to the beam opposite each stringer. This space will be about 2 ft. in our case. The dead load at each stringer connection will be Art. 60 DESIGN OF FLOOR BEAMS 149 Floor (13.5+2.0)200 = 3100 lbs. Stringer 15.5 X 165 = 2560 lbs. Floor beam say = 840 lbs. Total D.L. =6500 lbs. The live load reaction at the stringer connection must be determined from the actual wheel loads. The maximum reaction on the end floor beam will occur with the wheels placed as shown in Fig. 66. The reaction at a = & UJ ^7' 1785000 27 Fig. 66. = 66,100 lbs. 3 Dead load moment = 6500X4.82= 31,300 ft. lbs. Live load moment =66,100X4.82 = 318,600 ft. lbs. In order to simplify the connection of the end floor beam to the truss, it should be made as shallow as is consistent. We will therefore make the depth only sufficient to allow the stringer to enter between the horizontal legs of the flange angles. This will require a depth of about 521 or 53 inches. We will use a web plate 53" Xf". 72600 Unit shearing stress = -rQ-Q;^ = 3660 lbs. per sq. in., which is safe. The effective depth will be about 51 inches. Approx. D.L. flange stress = rr =7360 lbs. Approx. L.L. flange stress = ^ =75,000 lbs. • 1 T^ T 7360 . „_ Approx. required D.L. area = K7;pj^ = U.d7 sq. m. 20000 75000 7.50 sq. in. Approx. required L.L. area = „ Total = 7.87sq. in. 150 DESIGN OF FLOOR BEAMS Art. 60 If the required rivet pitch (41) is not too small for a single line of rivets in the flange, we may use unequal legged angles for the flange with the long legs horizontal, which will be more economical. Try 2Ls 6"X3i"x4". Net area = 9.00-2X§Xl=8.00 sq. in. (I inch rivets and no holes out of horizontal legs.) Actual effective depth =53.25-2X0.83 = 51.59. Actual D.L. flange stress = — ETTq — = 7300 lbs. Actual L.L. flange stress = — etTq — = 74,100 lbs. Actual required D.L. area = =0.37 sq. in. Actual required L.L. area =Tn7vY> = 7-41 sq. in. Total = 7.78 sq. in. This will not allow a reduction below the section assumed above. The number of rivets required to connect the flange angles to the web, between the stringer connection and the end of the beam will be the total flange stress 81,400 lbs. divided by the value of a |" rivet in bearing on the |" web. (See Spec. § 40.) TVT U f • ^ 81400 -, Number of rivets = „ „ =21. The distance from the stringer connection to the end of the beam will be about 3' 9". 45 Required rivet pitch=KT = 2.12 inches, which is less than should be allowed in a single line (13). (Spec. § 54.) Therefore 6"X6" angles must be used for the flange angles. Try2Ls6"X6'W'- Net area = 10.12-4Xi^Xl = 8.37sq. in. Actual effective depth = 53.25-2xl.66=49.93 in. Art. 61 TOP LATERAL BRACING 31300X12 151 Actual D.L. flange stress = Actual L.L. flange stress = Actual required D.L. area = 49.93 318600X12 49.93 7500 ' 20000 76600 = 7500 lbs. = 76,600 lbs. = 0.38 sq. in. Actual required L.L. area = r^rTr^ = 7.66 sq. in. Total = 8.04 sq. in. Use for flanges 2Ls 6"X6"Xi^". 61. Top Lateral Bracing. (51) The top lateral system is Fig. 67. a horizontal Pratt truss of five panels, with the portals at the ends acting as abutments. Panel load of wind load for top lateral system =200X27 = 5400 lbs. Sec = ^^ = 1.95. 16.15 The stresses are as follows: Diagonal BC = 2X5400Xl.95 = 21,100 lbs. Diagonal CD = lX 5400 X 1 .95 = 10,600 lbs. Diagonal DD = Strut CC = li X 5400 = 8100 lbs. Strut DD = 1X5400 = 2700 lbs. * Required area for diagonal BC = r^™ = 1.18 sq. in. To comply with specifications § 11 the lateral bracing must be made of shapes capable of resisting compression. It is not good practice to use angles smaller than about 3|"X3"Xi^" for these laterals. The net area of one angle 3|"X3" X A" = 1.94- 152 BOTTOM LATERAL BKACING Art. 62 2X^X1 = 1.32 sq. in., so that these angles will answer for all the diagonals. The size of the intermediate struts will be determined by §§ 35, 83 and 107 of the specifications. The unsupported length will be about 170 in. From Spec. § 35 the least allowable radius 170 of gyration =:72j^= 1.42 inches. This will require at least 2Ls3"X2i"X^", which are also required to comply with §83 of the specifications. Allowed unit stress = 13,000 -60- = 6000 lbs. per sq. in. T, . , 8100 , „_ Required area =^Trj:n^ = 1.35 sq. m. Actual area = 2X1.63 = 3.26 sq. in. These top strut angles are run over the top chords and o A c c/ d' C i} a' Fig. 68. riveted to the cover plates, and two other angles back to back are riveted between the intermediate posts as low down as the specified head room will allow (see Spec. § 107). These two struts are connected by diagonal lattice work of angles similar to the portal (see Fig. 65). 62. Bottom Lateral Bracing. The bottom lateral system (Fig. 68) must resist a static load of 150 lbs. per lin. ft. and a moving load of 450 lbs. per lin. ft. (Spec. § 24.) Panel load D.L. wind = 150X27 =4050 lbs. Panel load L.L. wind =450X27 = 12, 150 lbs. sec 0=1.95 (same as for top lateral system). The total stresses in the diagonals are as follows: Art. 63 SHOES AND ROLLERS 153 Diag. a&=4050X3Xl.95+12,150X 3X1.95=94,700 lbs. Diag. 6c=4050X2xl.95+12,150XVXl.95 = 66,500 lbs. Diag. cd=4050XlXl.95+12,150XV-Xl.95=41,700 lbs. Diag. dd=4050X0X1.95+12,150X fX 1.95 = 20,300 lbs. „ . , , 94700 _„. Required area ao = :r^,grT: = 5.2Q sq. in. ^ . , , 66500 „__ Required area oc=j^7rfrx = 3.70 sq. in. _ . , , 41700 -„- Required area cd = ^„„„„ = 2.32 sq. m. „ . , ,,, 20300 , ,„ Required a,iea da =:r^^r7r^ = 1.13 sq. in. To comply with § 33 of the specifications both legs of an angle in tension must be connected if the area of both legs is regarded as effective section, and therefore according to speci- fications § 64 at least two holes must be deducted from the gross section of each angle. Use for diagonal ab 2Ls 6"X3|"Xf". Net area = 6.86- 4X|Xl = 5.36sq. in. Use for diagonal be 2Ls 5"X3|"X^". Net area = 5.12- 4X^X1 = 3.87 sq. in. Use for diagonal cd IL 5"X4"X|". Net area=3.24-2xt XI =2.49 sq. in. Use for diagonal dd' XL 3^"X3"X3^". Net area = 1.94- 2X^X1 = 1.32 sq. in. The bottom flanges of the floor beams act as the bottom lateral struts, and the compression from the lateral forces tends to relieve the tension in them from vertical loads. 63. Shoes and Rollers. The end reaction will be 3§ panel loads of D.L.+L.L. = 3.1+96,430=337,500 lbs. According to specifications § 113 this will require 337500 ,„.„ • u ■ *!, - = 1350 sq. m. bearing on the masonry. The masonry plate may be made say 3' 6" long by 33 inches wide, giving a bearing area of 1386 sq. in. According to speci- 154 ESTIMATE AND STRESS SHEET Art. 64 fications § 114 the rollers cannot be made less than 5f inches in diameter. The maximum allowed pressure on the rollers will be 300X51 = 1725 lbs. per lin. in. Required length of rollers =-j;^^^ = 196 inches. This might be made up of 6 rollers 33 inches long, or 7 rol- lers 28 inches long. The details can not be worked out without detailing the end posts, end floor beams and shoes. 64. Estimate and Stress Sheet. The estimate of weight will now be given. The details can only be estimated approxi- mately until the detail drawings are made. Ordinarily the details are put in the estimate as a percentage of the main truss members, and an estimator of experience in detailing and estimating can choose his percentages so that the total error in weight will be very small. The stress sheet may now be drawn up. (See Fig. 69.) This is usually as much as is done until after the contract is awarded. The bridge company which fabricates the work makes the detail shop drawings, which are then approved by the railroad company's engineer. Art. 64 ESTIMATE AND STRESS SHEET 155 Sheet No. - /. THE OHIO Made by STATE BRIDGE COMPANY .£i.7r^ Date- Z-Z-'K.-^'S. — ^ ^ - Span Extreme /^■^■j^./S^. Sidewalk \/^a/fC. Capacity Trusses ^^G - . Capacity Floor t:^»^:.^9£€*. Spnn C. 10 c. .4isae 1 7 Ponds M^Ze'- Jeplh C. to C. .^^..^ 1 Length of DUg. r^6.SZ Estimated) (Steel DL per ft. ( I Floor & Trac Tola Panel l^ood per Truss DL s3 lA-6 Total Steel* Steel xKt n.i Total Lumber '•^AZa.. B C D DC- I 3' / \: K / \ TT ^//■//r^erj 6-6'c. 77es 8''8~''/c>-a /'oC. cr i h c d ef' c- 6- a Gua/ia^ ^''S" < y -^r X y^y >Pi« Slo ■41.S 8 i70 'Totat '.aw?' K 2^2r'^~ fi -44.« 4zx> 1 i 000 aB 2^/S--f (*S2 fl V.t AZ.O 1 C loo 2ii3''3'f~ 8 Ifsr 4Z.S 3 9/C Ze4'-^''f~ 8 1$.^ 42." 4 ito n<^ -SZ.I -ISi4 !Z.i • ^^6:i§~ f&fl ?z.s M /9./ 46.S li Zoo C^ ■'tl.o ■>?IA Hf-I P^6-./^' i»« fi ?4?. 4AS 3 000 Z3»" o -??« 73 ^^>#-.^- fijy. 7.t« a '?« ass 5 oflo D'c- *4lo -IfS 2"/ /^f./s /^: 7'rr 4 7' 49..S 1 390 Bh -.Z0.1 -fi"/ 'AV ZS/2~'2^*^ fi A(.f l/.-n ^ 7So 33.0 i (•00 Cc h4/.8 ttfc ?./yt Zli /S'^o"' 13.S fl 4fio 34.0 n fifio Oc/ f/as • TTfl 'in P It /!>" >.S>S* '47. fi ZJic 34o (, &ao abc ■ 79.-* -*w -iO/.X vr )^/^t:tBf-fk^ A /i!.f ?^o .1?? If^ Z6.0 1 Z 710 ^ZJf w % /fi 17'} Z6.0 1 450 cd -/32.3 -fY^'i -/ii.y T7ft l^JL 7'/^' Vi^ s mz 30.S 7 600 z^ r--/f' 8 ^71 3« ? ^Ho M' ■J£g^ ■M3A rzasi M^> r Z^7^/€" PtM ^ 'Iffy Jas 4 7Z0 Z^7i/Ji' 4 ^7f 3K5 o Z&3'^''^ 8 7.Z 26J> / SOO Z/i^k3~^' n 124 Z6jO 2 530 /^r >rt7/ a^ m 300 , " 156 ESTIMATE AND STRESS SHEET Art. 64 THE OHIO STATE BRIDGE COMPANY SlieetNo.^_ Made by Date __... Estln..!. Ior_ _ dScZ^SU ^'SS^'^^.&Z. '^SSsMglS! ^4=" MEH DL SlrHi LL Strait imput Talil Slr«u Unll SIreu ArM MATERIAL Actual No. Area Pes. wt. p. Ft. Length WE GHT at<^ vty. / 1 '2ea /-p^;i: ^ ios S3.0 iua Cann- asM- "(^1 V7(( Z^/S'i' w.ff 4 4S.9 g.lo i:2ia on z/^3'-j'',i' 4 S.3 K3.C 1760 Zli^.'-J'f' 4 Pt <'^ z IZiO 233 ?-'ro ■4A L^aa, ^ifffjr. W^fi 7^- «i g/y=J -7 ,0 '?-V F4 17-Z /s-.s \iZO '>>'nr, n(K<* A< rT"»r f ^Mei3^''s' 24 /S.3 6.0 iZOO ^^ •■, 7.^.3i^St^ ?4 S.Z ■sr.o .620 ^1 Mty /-/2''f Cfn) /?■ /S.3 ^.o .ne. 7/'A-<3i'-f 24- //■7 2.0 .Sic f?i\ 'fS *< .Hi /9 9fp ^y£ r^(^ / ^a ■/^f (7fn ! OLuL r'^ ^ /-^3'-^ r. 67fi iS.3 l&Zi A-/-, // ^//tfi. *>'' ^• ??* ZJiA~-g:^' 'WAi-f. 9^. fl /9,6 /S.3 lizi iSozt ^^ '= 7^A rv^ J' n. 'Iff, M Rh M' 2Z30 ti loo /*"" /f , *5;>»i qer. l^/> /-^r,f /4- Mio Z7o Itii: O/i./. ^am.- i?''^ o/f ^i'(;'<3i'-s^ "TvS^ 7^ 4.Z '22? i /-/Z'f C^r.) 42 a-j ZS I^OC Ri 'rft ?>< /zc ^ O'/O fn ifm ;/> 5 I'tiU ' Abt.64 ESTIMATE AND STBES8 SHEET 157 SkMNo. »3 tHE OHIO STATE BRIDGE COMPANY JHMle'llv n.*. '' nwi »•. » ^inute t<- ^^y?aC-3ZJ^ SU: ^jru^/y^.J<2Z^^e'^eiyz£}ji!r ... ■E. OL Slritl LL SlrtH I.Mcl rolal Ireu Unit Slran JS MATERIAL Actual Arts !'.. wt. p. Ft. Length WEIGHT SiL^^/ ^^ 34? 3gC ■ /^ '£2^ Tlr ^:ea. <■> aA 9f,r 'fiP ■^?f Pl^CiJi^f S^/ii-l ■f.-H fl //7 Sc fifi-i 3-7. ?/*.5-;.5*i^' -, .. "•fl fi ff 3ao 2 j5?o cc/ 4f7 •■ ?* // ^Z^%^ J .. ?4t ^ "0 30.0 1 3Zo d/ 703 „ /./3 /e-3^<%''S' . . /3r ^ fifi 30.0 ioa Cif/t •■P/^ /-36~'¥- r^TK) /p 4.Tt 4.0 Z Zoo ■4 J.O iSC V/ /-Al"-^' ^ ?3« (,.o Z3C „ /-/2''f' .«■ /.T- 6o li.o -./? /I3i~^3'^' /fi fti /^ l«^0 Rn i"A s ^/o /o 6oP / 7 ip/.t 'ftrn 'M //.as'^l^" /o /ifi 3Z.O 2 L( yO ^fV ^ flo z IFo / P ^^/ r/.^ *t-f^lf^ *3: loo* 4M^^^:'^' -2.1 7«o' l.a^/c,r /Z.3''2i'g' ?,(• "STx oo''^ i Q_00 ■ -/,' -o^* i coo ' ■ Tr/aK^Aa/As ^^^A^K _ •s fSf 959 ■ ■ ■ TSl', /.-= yh- /^ Mik MO - \- ■ - 158 ESTIMATE AND STEESS SHEET Art. 64 - CHAPTER VI DETAILS OF PIN CONNECTED BRIDGES 65. Detail Drawings. The design for the bridge and the stress sheet are usually worked out by the purchaser's engineer and submitted to contractors for prices, but sometimes the con- tractors are requested to submit designs with their bids (3). Frequently a general drawing showing more or less detail is submitted with the stress sheet. These drawings are not shop drawings. After the contract is awarded the detail shop drawings are made by the contractor and approved by the purchaser's engi- neer. (See Chapter VIII.) These detail drawings show the sizes and positions of all connections and details of members, together with the number and location of all rivets. The details must be so proportioned that the stresses will be safely and economically transmitted from member to member and finally to the abutments. 66. Pins. A pin is a beam which transmits the stresses at a joint. It is acted upon by forces in different planes, which produce bending moments and shears in it. It is usually convenient to resolve these forces into their vertical and horizontal components and get the bending moments in these two planes separately. The maximum bending moment at any point in the pin then is the resultant of the horizontal and vertical moments at that point. Likewise the maximum shear at any point is the resultant of the horizontal and vertical shears at the point. Since, in most cases, the maximum stresses in all of the members connecting to a pin do not occur under the same loading, the condition for a maximum moment in the pin is uncertain, and the moment must be calculated for the several conditions which give maximum stresses in the various members. In proportioning the pin for shear it must be remembered 159 160 CALCULATION OF PINS Art. 67 that the maximum intensity of shear on any cross section of a solid cylinder is equal to four thirds the average intensity.^ The bearing areas of the members on the pin must be suffi- cient so that the material will not crush (18). On this account it is well to have large pins, because the larger the pin the less thickness of pin plates required, and also there will be less danger of unequal distribution of stress to the different parts of a mem- ber. For example, if there are four bars in a panel of the lower chord, they should be stressed in proportion to their areas, but this will not occur if the pin should bend so as to relieve some of the bars of stress. On the other hand, the larger the pins the larger will be the diameters of the eye bar heads, and it is often difficult to find room for them, especially at the hip joint. The arrangement of the parts of the members on the pin is called the packing, and this should be such as to produce as small a moment as possible on the pin while at the same time insuring that the eye bars do not pull out of line in passing from joint to joint, more than about one-eighth of an inch per foot, and that the riveted members are of constant width throughout their length. The sizes of pins must be found by trial, since the moments depend upon the thickness of the bearings, and to get these we must first assume a diameter for the pin. 67. Calculation of Pins. A few of the joints of the truss designed in Chapter V will now be detailed to illustrate the methods. The Hip Joint. (B.) According to § 90 of the specifica- tions the least size of pin which may be used here is 0.8X6 = 4.8 inches, or say 4f inches. The allowed bearing pressure on one linear inch of this pin is 41X12,500 = 60,940 lbs. for live loads and 121,880 lbs. for dead loads. (See Spec. § 41.) Required bearing on end post aB ^ ^ 123100 , -, . ^■^- = 121886 = ^-^^ ""• J , 255400 .,_ . ^•^• = 60940-=^^ '''■ Total = 5.20 in. ' See Heller's " Stresses in Structures," Art. 71. Also Kankine's "Applied Mechanics," Art. 309. Art. 67 CALCULATION OF PINS Required bearing on top chord BC „ ^ 132300 . .. . D.L. = -^..^^^ = 1 .09 m. 161 121880 , T 274500 . .- . ^•^•=■60940" = *-^^ ^^• Total = 5.59 in. Required bearing on hip vertical Bb T.T 20900 _,_. D.L.=t;^t7^7;k = 0.17 in. 121880 T ^ 80100 . „_ . ^•^• = -60940 =1-^2 ^^• Total = 1.49 in. The bearing pressures on the eye bars of member Be is taken care of by complying with § 90 of the specifications. With these bearing thicknesses the spacing of the forces acting on the pin may be deter- mined approximately, as shown in Fig. 70. Sufficient clearance must be allowed between the different parts to allow them to be easily assembled. Fig. 70 shows a horizontal projection of the joint. In order to render the bending moment as small as possible (Spec. § 90) the eye bars should be packed as near their resistances as possible. The bending moments and shears will have to be calculated for two positions of the live load, one which gives maximum stresses in the top chord and end post, and one which gives a maximum stress in the diagonal Be. In figuring pins the same equivalent uniform loads may be used as were used in calculating the stresses in the members. It is a useless refinement in calculating pins, to figure the stresses Fig. 70.— Packing at B. 162 CALCULATION OF PINS Art. 67 by the actual wheel load method, even when the original stresses have been so figured. The algebraic sum of the horizontal and vertical components of the forces acting on the pin must always be zero. When the pins are symmetrically packed, as they always should be, the shear at the middle will be zero also and the moments on only half the pin need be figured. By keeping these facts in mind and putting down the stresses from the stress sheet, for those members in which the stress is a maximum, the others can usually be obtained without calculat- ing them from the loads. Usually the moments and shears on pins are calculated upon the assumption that the stresses in the members are concentrated at the centers of their bearing areas. This assumption is on the safe side, as the stresses are actually distributed over the' bearing areas and, generally, the moments produced by distrib- uted loads are less than those produced by the same loads con- centrated. Cooper's specifications, § 41, permits the calculation of the moments and shears on the assumption that the stresses are distributed uniformly over the middle half of the bearing areas. It is somewhat more laborious to calculate the stresses upon this assumption than upon the assumption of concentrated loads, and in practice the concentrated load method is almost univer- sally used. The moments and shears have been calculated by both methods for the pin at B and the moment and shear diagrams for the two methods are shown in Fig. 71. The dotted lines indicate the moments and shears figured by the concentrated load method and the full lines those calculated by assuming the pressure uniformly distributed over the middle half of the bearing. The calculation of the moments is best made in tabular form, remembering that the moment at any force is equal to the moment at the next preceding force plus the product of the shear by the distance between the forces.^ In making up the table always begin at the outside where the shear is zero and work toward the center where the shear is again zero. ' See any book on Mechanics. Art. 67 CALCULATION OF PINS 163 MAXIMUM STRESSES IN aB AND BC MOMENTS OF HORIZONTAL COMPONENTS Mem. Horizontal Component. Shear. Lever Arm in Inches. Moments. Increment. Total. Be - 40,700 - 40,700 2 - 81,400 BC +203,400 - 81,400 +162,700 i + 122,000 aB ■ -122,000 + 40,600 + 40,700 2 + 81,400 Be - 40,700 +122,000 000 2 000 Bb 000 +122,000 MOMENTS OP VERTICAL COMPONENTS Mem. Vertical Component. Shear. Lever Arm in Inches. Moments. Increment. Total. Be - 48,200 - 48,200 2 - 96,400 BC 000 - 96,400 - 48,200 3 i - 36,150 aB +144,600 -132,500 + 96,400 2 +192,800 Be - 48,200 + 60,250 + 48,200 2 + 96,400 Bb - 48,200 +156,650 The and is maximum resultant moment for this loading occurs at Bb V (122,000)2+ (156650)2 = 198,730 in. lbs. MAXIMUM STRESS IN Be MOMENTS OF HORIZONTAL COMPONENTS Mem. Horizontal Component. Shear. Lever Arm in Inches. Moments. Increment. Total. Be - 42,800 - 42,800 o - 85,600 BC +184,100 - 85,600 +141,320 3 4 +106,000 aB - 98,500 + 20,400 + 42,800 2 + 85,600 Be - 42,800 +106,000 000 2 000 Bb 000 +106,000 164 CALCULATION OF PINS Art. 67 MOMENTS OP VERTICAL COMPONENTS Mem. Vertical Component. Shear. Lever Arm in Inches. Moments. Increment. Total. Be - 50,500 -50,500 2 -r 101,000 BC - 000 -101,000 -50,500 f - 37,800 aB +il6,500 -138,800 +66,000 2 +132,000 Be - 50,500 - 6,800 +15,500 2 + 31,000 Bh - 15,500 + 24,200 The maximum resultant moment for this loading occurs at aB and is V (20400)2 + (138800)2 = 140,300 in. lbs. Then the maximum bending moment on the pin occurs under full loading and is 198,700 in. lbs. The maximum moment when figured by considering the pres- sures distributed over the middle half of the bearing areas is the same in this case. The effect is to round the apexes of the moment diagram. With an allowed fiber stress of 18,000 lbs. per square inch this will require a 4| inch pin, (see " Cambria," page 300) or exactly the size that was assumed. The maximum shear is materially different when figured by the two methods, in this case, because the bearing areas of the end post and the top chord overlap. The actual maximum shear is probably more nearly that given by considering the pressures distributed over the middle half of the hearing areas. At other joints the shears will usually be the same when figured by either method. The maximum resultant shear when the loads are considered distributed, occurs for full load, between members BC and aB and is \/(106060)H (96400)^= 143,200 lbs. This gives a maxi- 4 143320 mum required area of ^X q^^^ =21.22 sq. in. A 5i inch pin will answer. In a similar manner the pins at the other joints are figured with the following results; Art. 6 CALCULATION OF PINS 165 Hor/'zonfa/ //soo^ S-<5'-^(7^ ^^oyo,-? /220?0 Shear D/a^rnfm i Horizonta/ Op/nponehts Moment D/a^ram Horizonfa/ Compone, y/s SJyearDia^rcfm i Vertica/ Co/nponents /S66SO Moment Dia^nsrm if^ertica/ Components 166 CALCULATION OF PINS Art. 67 At a a 5f inch pin is required. At c a 5J inch pin is required. At d a 5| inch pin is required. It will make the shopwork and erection somewhat simpler Fig. 72. — ^Packing at a. Fig. 73. — ^Packing at c. Ill III ^^7t/^' <^yt Fig. 74. — ^Packing at d. Fig. 75. — Packing at C. if these pins are all made the same size, so we will use 5f inch pins at a, c, d, and B. No pin is used at h, but the bottom chord is run through continuously from a to c, and a riveted connection is. made at b between Bh and the chord abc. At C a 4| inch pin is required, and we will use the same size at D. Abt. 68 CAMBEK 167 Figs. 72 to 75 inclusive, show the packing at the various joints. 68. Camber. Camber is the slight arching of the bridge which is put into it for appearance. All bridges should be cambered ^ in order that they may not sag below a straight line under the maximum load and also to prevent the appearance of sagging at any time. A perfectly straight girder, when viewed from the side, will appear to be deflected downward. Trusses are cambered by making the top chord slightly longer than the bottom chord. The diagonals must be figured for this increased length. Some specifications give the amount of increase of length of top chord to pujb in, and others specify the amount of camber (middle ordinate to the curve) in the span. For a given increase of length of top chord, the amount of cam- ■7 a,ne/s af^7-Oi'-'/S9'-2^' Fig. 76. Increase in length of top chord =- ber will vary with the depth of the truss. The following formula is taken from Trautwine's " Civil Engineer's Pocketbook," page 607: D epth X camber X 8 Span All in feet or all in inches. Fig. 76 is an exaggerated diagram of the truss showing the camber. Specifications, § 120, requires that the top chord be made longer ^than the bottom chord at the rate of \ inch for each 10 feet. This will make each top chord panel 27' Of". The length of the diagonals will be \/(27' 0A")^+(32' 0")2=41" 10^". iSee Coopec's " Specifications," § 120. American Railway Specifications, § 77 and § 81. 168 DETAILS OF A RIVETED TENSION MEMBER Art. 69 From Trautwine's formula we can compute the camber which this will give the truss. 2|..^32Xl2XcamberX8_ Camber = 1.93 inches. 189 X 1^ 69. Details of a Riveted Tension Member. (19) A detail drawing of one end of the lower chord abc is shown in Fig. 77. PJJ6'''<£x4'-7\ „ , ,„ Fig. 77. The width of the member is determined by the packing at a and c as shown in Figs. 72 and 73. The maximum stress in the member is 345,900 lbs. (D.L.+L.L. +wind). The average allowed unit stress in tension is 15,520 lbs. per sq. in., and the required net area of the body of the member is 22.29 sq. in. (See Art. 56.) According to the speci- fications § 68 the net section through the pin hole must be one- third in excess of this amount, or 29.72 sq. in., and the least section back of the pin hole 60% of this, or 17.83 sq. in. The net section of the 2— 14"X|" plates through the pin hole is 2[2X2|+2V(2|)2-|-(4|)2-5f-2]f = 5.60 sq. in. Art. 69 DETAILS OP A EIVETED TENSION MEMBER 169 The balance = 29.72— 5.60 = 24.12 sq. in., must be made up of pin plates. The effective net width through the pin hole, of plates 16 inches wide is (see Fig. 77) : 2X3|+2V(2A)2+(4f)2-5f-2 = 9.46 in. Then the required thickness for pin plates 16 inches wide to take the tension is 24.12 „ .^ . ns ■ X. „ . „ = 2.55 m., or say 2f mches. This will require one pin plate 16" Xf" and one 16" XW on each side. The average allowed unit stress in bearing on the pin (D.L.+LX.+W.) =-?^^X 1.3 = 19,400 lbs. per sq. in. ^"'"406.8 (from Eq. (21) and Spec. § 39), and the allowed bearing pressure per linear inch of pin is 5|X19,400 = 111,550 lbs. None of the bearing plates can however be counted on to take more stress in bearing than they transmit past the pin hole in tension. The net area through the pin hole is as follows: 2-14"X f" = 7.46Xf = 5.60 sq. in. 2-16"X f" = 9.46Xli = 11.82 sq. in. 2-16"Xii" = 9.46Xlf = 13.01 sq. in. Total = 30.43 .sq. in. The stress transmitted by the 2— 14"Xf" plates past the pin hole will be proportional to the areas, and is ' ^■^^,X345,900=63,6501bs. 30.43 The stress transmitted by the other pin plates is 345,900-63,650=282,250 lbs. 170 DETAILS OF A RIVETED TENSION MEMBER Art. 69 Then the required bearing thickness of the 16 inch pin plates =????f^= 2.53 inches, therefore the 16 inch pin plates 111550 used are sufficient. 17 83 The required net length back of the pin hole =-51- =5-3 in. Og Allowing one rivet hole out this will require the pin plates to extend 5|+l+2| = 9i inches beyond the pin center. The stresses taken by the component parts of the body of the member will be in proportion to their gross areas because their deformations must be equal, and the connection must dis- tribute this stress properly to the component parts. The stress taken in the body of the member by 1— 14"X|" plate = ^^ X 345,900 = 63,700 lbs. Therefore 63,700-4X63,650=31,875 lbs. must be transmitted from each of the 14" Xf" plates to the 16 inch pin plates before the pin hole is reached. The stress transmitted past the pin hole by each of the 16 inch pin plates is as follows: 16" X f " plate = If X 282,250 = 67,200- lbs. 16" XH" plate =1^X282,250 =73,925 lbs. and sufficient rivets must be provided to transmit these stresses from these plates to the body of the member. The six countersunk rivets between the pin and the end of the angles may be considered as transmitting stress from the outside pin plate to the 14" Xf" plate so long as this does not raise the total stress in that plate above its proportion of the stress in the body of the member, 63,700 lbs. The value of the six countersunk rivets in the | inch plate is 6XfX4922 = 12,660 lbs. (Spec, §40). This would bring the total stress in the 14" Xf" plate at the end of the angles up to 12,660+1X63,650=44,490 lbs., which is less than 63,700 lbs., and therefore safe. Further rivets will be required in the outside pin plate to transmit 67,200 - 12,660 = 54,540 lbs. The rivets will be in single shear and the number required = -rjT~- = 10. Art. 70 PINS IN TOP CHORD AND END POSTS 171 The rivets to transmit the stress from the inside 16" XH" pin plate must be placed beyond those required for the outside pin plate. The number required = = 14. The required net area of the body of the member through the first line of rivets of the coimection plates is 22.29 sq. in., and the required net area on a zig zag line of holes = 1.3X22.29 = 28.98 sq. in. (Spec. § 64.) Assuming that a lacing rivet comes opposite the first rivet in the pin plate (which is not exactly the case here) we may write an equation as follows, and solve for the least allowable pitch of rivets in the connection plate at this point (19). Calling this distance x we have 28.98 = iX4(l§+H+V(2|)2+a;2+V(3i)2+a;2-3) +2Xf(2|+2|+5i+2V(2|)2+a;2-4) Solving we get a;=3| inches. JThis pitch may safely be reduced to 3 inches after the first line of rivets is passed, as the stress in the body of the member has been reduced by the value of the rivets passed. The lacing of a tension member does not have to comply with § 97 of the specifications, and may be put in according to the judgment of the engineer. 70. Location of Pins in Top Chord and End Posts. (50) The location of the pins in the top chords and end posts depends upon the location of the cen- ters of gravity of the sections and upon the amount of the displacement of - the pins necessary to compensate for the bending due to the weight of the member. The pin at the hip cannot be placed in the exact theo- ^ -p^^ ^g retical location for both the end post and top chord, and its location must necessarily be a compromise between the two. Fig. 78 shows the factors which must be taken into con- sideration in this problem. From § 43 of the specifications we 172 PINS IN TOP CHORD AND END POSTS Art. Id see that the bending moment due to the weight of the member need not be considered unless it increases the fiber stress more than 10% above the allowed unit. The weight of the end post wiU be as follows: 1 cover plate 24"X|" = 51.0 2 web plates 21"X|" = 89.2 2 side plates 15"Xf" = 63.8 2 top Ls 3"X3"xr = 23.0 2 bottom Ls4"X3"Xf" =27.2 254.2 Details say 10% = 25.8 Total =280.0 lbs. per lin. ft. The weight per linear foot horizontal will be 280 esc 6 = 434 lbs., and the bending moment due to the weight will be ^^^^^ = 39,550 ft. lbs. The maximum compressive fiber stress due to weight 39550X12X9.48 „„„ ,, • • ^i, . t *-i. = 7W7^ = 960 lbs. per sq. m. m the top of the cover 4698 plate. (See Art. 58.) The allowed unit stress for D.L.+L.L. is 6516 lbs. per sq. in., therefore the bending. moment due to weight must be considered in the end post. The maximum compressive fiber stress due to weight or to displacement of the pins may reach 651 lbs. per sq. in. The weight of the end section of the top chord is as follows; 1 cover plate 24" X |"=40.8 2 web plates 18" X A" = 68.8 2topLs 3"X3"X §" = 14.4 2 bottom Ls4"X3" X A" = 24.8 148.8 Details say 10%= 14.2 Total = 163.0 lbs. per ft. 163X27^ The bending moment due to the weight = 5 =14,880 o Art. 71 LACING OP COMPRESSION MEMBERS 173 ft. lbs. The distance from the middle of the web to the center of gravity is 1.98 in., and the moment of inertia about the hori- zontal axis is 2230. The maximum compressive fiber stress due to weight = 14880X 12X7.64 ^,„ ,, 22^0 = ol2 lbs. per sq. m. The average allowed unit stress for D.L.+L.L. from equation (21) is 9490 lbs. per sq. in., therefore the bending due to weight need not be considered in the top chord. The most desirable location for the pin will be obtained from equation (20) as follows: Fortheendposte=fg^ = 1.00in. For the top chord e = lgg^|^=0.36 in. For the end post the pin should be 1.77—1.00 = 0.77 in. above the center line of the web. For the top chord the pin should be 1.98-0.36 = 1.62 in. above the center line of the web. If X2 in Fig. 78 is made 8 in. to agree with the most desirable position for the top chord, from similar triangles Xi:x2 = di:d2 or a;i = 9.33 in., which would place the pin in the end post above the center of gravity. If xi is made 10§ in. to agree with the most desirable posi- tion for the end post, X2 = 9.00 in. This will place the pin f in. above the center of the web of the end post and f in. above the center of the web of the top chord. This location will be used. The pins at the intermediate top chord points are placed on the same center line as those at the hips, as they only have to transmit the increments of stress from the diagonals. Fig. 79 is a detail of the hip joint. 71. Lacing of Compression Members. (50) The lacing for the top chord will be calculated by each of the three methods given in Art. 50, so that the results may be compared. The lacing is in a horizontal plane to resist bending about a vertical 174 LACING OF COMPRESSION MEMBERS Art. 71 axis so we will have to use the radius of gyration about the vertical axis. \Open holes on inside ^for lateml connection . 6 6 d 15 .^'■»^V ^ ) O O O O ♦ f ffl^g-P'O o ^=g ^^^ 1 O O O O ♦ f nL.j C(n^rm4'>if Holes. fyrHrtal conneclion in inside iVebs only-^ Ml Fig. 79. For the top chord CD (which is the largest) the allowed unit stress for D.L.+L.L. from equation (21) is 20000-90- J g^g ^ = 11,940 -53.7- = 9920 lbs. per sq. in. (using the radius of gyration about the vertical axis) . Art. 71 LACING OF COMPRESSION MEMBERS 176 From equation (18) . 4X19.93X20 .-_,- Length of member covered by one lace bar (single lacing, Spec. § 97) = 22i cot 60° = 12.8 in. Longitudinal increment of stress taken by one bar = 497 X 12.8 X I = 3180 lbs. (Half is taken by cover plate.) The stress in one bar = 3180 sec 60° = 6360 lbs. Second Method. The total safe compressive load on the member is i^X 51. 86 =489,200 lbs. (See Art. 57.) The 1.d70 transverse shear equals 1 to 3% of this, which is 4890 to 14,680 lbs. o, . , i.^f4890 ^ Roo J 2825 Stress m one bar=§X| j^goQXcsc 60 =i g^ye- Third Method. i^=^=53.7^=2020, / An r -, 2020X51. 86X (8.61)2 M = ^21x12 " ' " ^ Transverse shear = |P= 3725 lbs. Stress in one bar =|X3725Xcsc 60° = 2150 lbs. From these calculations it is seen that the three methods agree fairly well. In the lattice it is safe to use the unit stresses allowed for latlral bracing. Specifications § 97 require the lattice for this chord to be 5 in. thick. Allowed imit stress in compression is 13,000-60- = 13,000-^^^=4520 lbs. per sq. in. ^ . , 6360 , ., Reqmred area ^iHon^ ^^' ™" 1 41 Required width =-^=2.26 m. 176 LACING OF COMPRESSION MEMBERS Art. 71 Use lace bars 3"Xf" for top chords to comply with speci- fications § 97. The lacing for the end posts can not be obtained directly from equation (18) because the end post carries transverse shear in addition to the direct stress. The total difference in extreme fiber stress due to colimin action is obtained from the column formula for D.L.+L.L.+wind. „ ,„,, 17000-90- -. From Eq. (21) ,,^ ^ X 1.3 = 13,200-69.8^- 1.675 r The values of L and r here must be taken about a vertical axis because we are figuring for the shear in that direction. The difference in unit stresses due to column action = 69.8 X n „a =3280 lbs. per sq. in. O.DO The difference in unit stresses due to transverse bending from Art. 68 = 3310 lbs. per sq. in. Total difference = 3310+3280 = 6590 lbs. per sq. in. Total stress to be transferred by the lacing and cover plate in a distance of 17 ft. (distance from end to point of contra- flexure) =6590X^1 = 6590X35.1 = 231,300 lbs. , 231300 „„. ,, . , Longitudinal increment of stress taken by one bar =1 134 X 12.8X1 = 7260 lbs. Total stress in one bar = 7260 sec 60° = 14,520 lbs. Using bars f in. thick, the allowed compressive unit stress is 4520 lbs. per sq. in. „ . , 14520 _-. Required area =-j^^ = 3.21 sq. in. 3 21 " Required width = -^Kc=5.12 in. Use lace bars 5"Xf " with two rivets in each end. Art. 72 DETAILS OF THE FLOOR BEAMS 177 For the intermediate posts Cc, the radius of gyration per- pendicular to the chanmel webs is 4.31 in., and the unsupported length in that direction about 21 ft. The allowed unit stress' for D.L.+L.L. = 10,060-53.25^ r = 69501bs. per sq. in. (See Art. 57.) From equation (18) we get . 4X11.76X3110 „-,, . , J = o^\/^'2 =580 lbs. per inch. The length covered by one lace bar (single lacing, Spec. § 97) is 3^ inches. Longitudinal increment of stress taken by one bar = 580 X 3| Xi = 1015 lbs. (Lacing on two sides.) Stress in one bar =1015 sec 60° = 2030 lbs. Specifications § 97 require that the lacing for this case be ■^ inch thick, but § 82 limits us to f in. fin "^7 Allowed unit stress =13,000 r7r^=9100 lbs. per sq. in. T> ■ A 2030 _„ Required area =0^^ = 0.23 sq. m. 23 Required width =-^=^=0.61 in. Specifications § 97 requires 2§ in. X| in. For post Dd specifications require lacing 2^"Xf". 72. Details of the Floor Beams. In all calculations relating to the floor beams, the span of the beam is considered as the distance between the center lines of the trusses. The ends of the floor beams must be cut away at the bottom to allow the connection of the diagonal and chord members on to the pin, and where this is cut away the cross section must be rein- forced sufficiently so that the maximum extreme fiber stress does not exceed that allowed by the specifications. 178 DETAILS OF THE FLOOR BEAMS Art. 72 O 1 o O o 1— t U5 ^ T-H o 1-H N -a T-l o i-H 00 1 ^ •"• (3 lO lO o t'' ^ CO w? Ol i M hIh »-4 •^ 3 a* w|h o rtln 00 I-H (N hIh 00 O) c to l> ^ "5 o lO g ►.[CO j-t & t-|oo S3 P. i-l«> p. »-l<» R H« to' l> »H rH i-H 3 tH z s o l-J as o" ci as lO b- (30 O IS \6 CO s as t^ m" as CD U3 lO to 1 8 iH lO o o g nn ■* o o lO o fO to lO in CM O o o P '"' WI-* -* a ml'^ i^ 00 o ■♦J mt to rt «i^ CD U3 m OS OJM UJ CM O i^ O CO i> oT p X ffi o ,rl ^ lO Oi 43 1 CD lO lO 1 W5 (N O > ^K a SIS tH (M M_ CD 1> OO" 0} SIS 1-*" CO in iH r-l rt .3 hIh lO ^ b- ^ O 00 lO CD CO a as CM rH O rH W lO rjT rh ift ■ CO 01 »0 CO O r» ifl CO r- ffl O owe id s ■s M to >0 »o b. o OS IS »!« w|« U5 CO t^ Ul|« O (N rti" s ■3 uloo TjT lo" to ■s islo CO ■* U5 CO to C (M Tjf to OS « lO iO r- o M 00 M CO CO -* CD O "O i-t N W b- CO O n 1 'IS »R O Oi t> lO lO to S •IS 0> iH N 1 •IS « OS to s •IS CO OS U3 eo" co" ff 5 s -^ ^ s ira CO o (N CD O (O lO >o 00 ■* o O U3 O o o o rn ^ a HlO rt|N ■*■ uS CD rH|N 00 OJ ^' ^ H|C< b- CO O CO -tf »o Eh Hit. O »D O CO CO ril H 3 ^ i H 02 o 1 b '"' 1 1 CO -^ r> CO CO Tt< rH W lO eo f^ Si Hs CI t- s to HS OS "3 CSl SH HS CO © 00 ^ HS M 00 CO -s, HS gg lo § Tff »o CD .2 CO Tji lO .2 b- 00 O) 3 CO eo ■* a cm" CO co' rr lO 00 o m CO 00 (M ^ o o Ui O o Ml« (N W IN Ol CO w|co fe CO o « n|« CM CO ^^^ n|« 00 W ID (N l> Oi n» lO to o -a ■* tP ui 3 1 CO eo -# ? CD i> oo' 1 1 CS) CO CO 1 CM (n" co" CO C^ i-H lO 00 o bO a »e .H O CO CO -^ -^ f^ "IS « cq i> (N CO CO 1 HS t- U3 CO cq ^ o U5 to !< -IS CO t> I-H (N oT co' 0) pq HS w -i "5. rt IN CM 1! O "3 O OJ « w lO l> O o o o d « hN rt M lO 00 (N t* rHl-a CS| to O H'M w o> to W hM l> 00 o H|-« lO t- o B g N CO CO cq (N CO Tf ^ lO rH M CM iH rH CO iJ >:* c, r:* (N O O e. r7* 00 CD to a. 3 rr* cq CD -«}* a 2 ,r* ^ C4 C4 OQ 1> O Tji e "S to 00 i-H c "E3 rH eo rH rH r-l (N c "a U3 I> OS t So ■* U3 t- « 0) ^-« r:* a ,-w r ^S CO ■^ »o 5 ="S U9 W O CQtO N CO ■*H i^iS CM CM CO as 5 S 5 £ s 5 5:: WW i-ta tH 1 IB WH»^ s ^« ^^ £ Ih ShpS^t 3" C r C i" c " C i" "" isa rt 1 i o 53^ ft s 1 PL4 CQ H4 § Art. 72 DETAILS OF THE FLOOR BEAMS 179 Fig. 80 shows a detail drawing of one of the intermediate floor beams and the lower end of the post with the connecting members. The cross section at the end has been reinforced by the addition of 2 plates 35"XiV" on the web, and by the bent flange angles at the end. Cooper's specifications § 40, require the use of a number of different unit stresses for rivets in various positions, and these must be kept in mind in detailing. The table below gives these values. The bearing values below the lower zigzag lines are less than single sheai:; between the upper and lower zigzag lines they are greater than single shear and less than double shear, and above the upper zigzag line they are greater than double shear. Neither the top nor the bottom flange angles extend to the theoretical end of the beam (center of the truss) and therefore the rivet pitch in the flanges cannot be calculated by the methods of Art. 41, but suflicient rivets must be put in between the stringer connection and the end of the flange angles to carry all the stress in the flange at the stringer connection. (60.) To get sufficient connection for the bottom flange the expedient is resorted to of riveting plates on top of the flange angles, to transfer a part of their stress to the web. The rivets through these plates and the angles are in double shear plus bearing on the web. The total flange stress to be transferred is 7500 lbs. D.L.+76,600 lbs. L.L. = 84,100 lbs. (See Art. 60.) The connection of the bottom flange as shown is good for the following stress: 16 rivets bearing on f in. web = 16X3938= 63,000 lbs. 6 rivets in double shear = 6X8659= 51,900 lbs. Total = 114,900 lbs. The connection of the top flange is good for 26 rivets bearing on f in. web = 26X3938 = 102,400 lbs. Rivets required for the stringer connection =-2^2=' =35. 180 DETAILS OF THE FLOOR BEAM« Art. 72 Art. 72 DETAILS OF THE FLOOR BEAMS 181 Rivets required for the end connection angles of the floor beam through the web = „^r» =11. oDoy Rivets required for the field connection to the post = oooc ~^^- Rivets required on each side of web splice =■^7^5^=23. CHAPTER VII HIGHWAY BRIDGES The problems met in highway bridge design are in many respects more difficult of satisfactory solution than those in railway bridges. There are many more uncertain features present. Chief among these is uncertainty as to the amount and position of the loads and their distribution through the flooring materials to the other parts of the structure. Notwithstanding this fact there is usually less time and thought devoted to the design of highway bridges, per dollar of expenditure, than there is to the design of railway structures. This is probably in part due to the lack of knowledge of the existence of these uncertainties, on the part of the public officials who have the design in charge, and in part to the more permanent and efficient organization in railway engineering departments. 73. Kinds of Bridges. The following points should be con- sidered in selecting the type of bridge to be used in any particular case: 1. Use, 2. Location, 3. Permanence, 4. Strength and rigidity,") 5. Economy, 6. Artistic effect. Most specifications for highway bridges give a list of types recommended for use for various spans.^ These recommended ' The " Standard Specifications of the State Highway Department of Ohio, for Steel Highway Bridges," are printed as an appendix to this book. See § 2. • See also " Standard Specifications," by John C. Ostrup, Art. 50. See also " General Specifications for Steel Highway and Electric Rail- way Bridges," by Theo. Cooper, 1909, § 2. 182 Abt. 74 FLOORING MATERIALS 183 types usually take into consideration only the questions of strength, rigidity and economy. Any person having authority in the selection of a design for a bridge should give due consideration to harmony with the surroundings, and artistic effect. If the location warrants it an architect should be employed to work in connection vnth the engineer, not called in after the design is completed, simply to design some ornamental railings or crestings. A structure which will fit in with the surroundings and be pleasing to the eye will frequently cost no more than some uncouth structure which will, forever be an eyesore.^ 74. Flooring Materials. The ideal bridge floor should be such that in crossing the bridge one would be unconscious of a change. The same surfacing that is used on the roadways approaching the bridge should be continued across it if possible. This, of course, is not always practicable, but in any case the joint between the floor of the bridge and the approach should be so constructed that a rut will not form at this point. The most common forms of flooring are: Plank on wood or steel joists, Creosoted wood block on creosoted plank, Reinforced concrete, plain or with bituminous surface. Macadam on reinforced concrete base, Brick, asphalt or block paving on a reinforced concrete or buckled plate base. Sufficient crown for drainage should be given to all water tight bridge floors and scuppers provided along the curbs to carry the water away, clear of the steel work. With plank floors on steel joists, nailing strips should be provided for securing the planking to the joists. Sometimes spikes are driven through the plank and simply clinched over the edge of the I-beam joists, but this is a poor connection as the spikes soon rust and break off leaving the plank loose. Fig. 81 shows two methods of putting on the nailing strips. The placing of the nailing strips at the side of the joist is somewhat preferable as it is easier to maintain a true surface to the road- way when the plank rest directly on the steel joists. The 1 See " Artistic Bridge Design," by H. G. Tyrrell and " Engineering Studies," by Charles Evan Fowler. 184 LOADS Art. 75 nailing strips should always be bolted to the steel joists at in- tervals not exceeding 4 feet. Wheel guards should be provided at the sides of the road- way and should be hook-bolted to the outside line of joists.^ The creosoted plank base for a creosoted wood block floor is put down with nailing strips similar to any plank floor. Tar paper and hot tar are used between the plank and the wood block.2 "Hook Bolts ylWiee/ Guard ^B/ocks atBo/ts ■Bolthead Countersimk ^Blocks att>o/is^A FiQ. 81. The traffic should never be allowed to come directly upon a reinforced concrete slab floor, as it soon wears into ruts, making a rough roadway and also weakening the slab. The surface of the concrete is sometimes protected with a coating of tar and gravel. This coating will require renewing about once in two years under ordinary country traffic. The cost of the treatment is small and the concrete is very effectively protected. ■Brick or Block Pa\//ngr /^SandCcfshlon III. 'i I I I ' l I , .J I 1.1- ..,J ,, .. _ i t Cdncrefe Bc7se Buckle Plates Peinlbrceef Concrete Base- Fig. 82. For short span bridges in the country, a macadam covered roadway on a concrete base makes a very satisfactory floor. Fig. 82 shows two types of paved roadways. 75. Loads. The selection of the proper live loads for which to figure highway bridges, and the assumptions as to their dis- •See Cooper's " Specifications for Steel Highway Bridges," § 21. See " Specifications of the State Highway Department of Ohio," § 40. ''See " Specifications of the State Highway Department of Ohio " §§ 22 to 36. Art. 76 IMPACT 185 tribution, are perhaps the most difficult problems in the design. Bridges, even in the most remote country districts, must be designed to safely carry traction engines or road rollers. The proper weight of engine to use depends somewhat upon the topog- raphy of the country. Engines used in level countries may be considerably heavier than those used in hilly countries. The weight of the engine is usually considered as two thirds on the rear axle and one third on the front. The loads given in most specifications^ consist of a road roller for the floor system and members carrying floor loads directly, and a uniformly distributed load for the girders or trusses. It is usually not considered probable that more than one road roller or traction engine will be on the bridge at the same time and consequently the uniform loads for which trusses are designed usually diminish as the span increases. When bridges carry electric cars in addition to the high- way traffic, the loading used for the car track should be con- sidered as acting simultaneously with any possible highway loading. 76. Impact. The moving loads are appUed to the bridge with more or less impact ^ depending upon the character of the load and the smoothness of the floor. Prof. F. 0. Dufour, in a paper entitled " Some Experiments on Highway Bridges under Moving Loads,"' read before the Western Society of Engineers, gives considerable data on the question of impact. The heavier loads, such as road rollers and traction engines, are usually slow moving and consequently produce a less per- centage of impact than the lighter loads, but the combined effect on the bridge (static load plus impact) is usually greater for the heavy loads. That is, the percentage to use for impact in con- nection with the usually specified loads, should be comparatively small. Prof. Dufour's conclusions point out this fact and state that with concrete floors on bridges the impacts observed were very small indeed, even when heavy loads were allowed to run over boulders as large " as two fists." On plank floor bridges the igee Cooper's "Specifications," §38. See "Specifications of the State Highway Department of Ohio, " §§43 to 48. » See " Specifications of the State Highway Department of Ohio," § 50. ' Journal of the Western Society of Engineers, June, 1913. 186 DISTRIBUTION OF THE LOAD Abt. 77 impacts observed were very much higher than on concrete floor bridges, due to the lighter dead load, less rigidity and more uneven surface. 77. Distribution of the Load. The distribution of the load through the flooring materials is even more difficult of satisfactory solution than the selection of the proper, loads to use or the treatment of impact. Prof. Dufour found that with reinforced concrete floors, the joist immediately under the load did not carry more than 20% of the load, the balance being distributed to the other joists by the concrete slab. This distribution would be very much less with plank floors and would probably vary with the ratio of thickness of slab to distance between joists. Experiments by the State Highway Department of Ohio indicate that the maximum load carried by a joist never exceeds 50% of the wheel load, when the ratio of slab thickness to slab span is greater than one eighth and the slab is continuous over 6 or more lines of joists. Cooper's specifications § 17, allows the joists of plank floor bridges to be figured for two thirds of the wheel load as long as the joists are hot spaced more than two feet apart. With wood block floors on plank it is safe to consider two thirds of the wheel load as going to one joist as long as the joists are spaced not over 2| feet centers. 78. Calculation of Joists. Investigation of existing structures will, in a majority of cases, show that the joists and floor beams are, relatively, the weakest points in the bridge. They should always be calculated to carry the specified roller load, and it should be borne in mind that they are the parts of the bridge which receive the greatest impact effect. If the roadway is wide enough (more than 20 feet) the pos- sibility of turning the roller on the bridge should be con- sidered. To illustrate the methods, the joists for an ordinary plank floor, country bridge, and for a paved floor city bridge will now be calculated. For the plank floor bridge let us assume a 16 ft. clear roadway, a 19 ft. panel length and the specifications of the State Highway Department of Ohio, Class D loading. (See §§ 1 and 48.) The plank will be 3 inches thick and we will use 2 lines of channels and 5 lines of I-beams for joists, arranged as shown in Fig. 81. Art. 78 CALCULATION OF JOISTS 187 This will make the joists about 2| ft. center to center. The dead load per joist will be as follows: Plank 3 inch = 3X2JX4| =33f lbs. per lin. ft. Nailing strips 3X6 = 1|X4|= 6f lbs. per lin. ft. Steel joists say =30 lbs. per lin. ft. Total dead load =70^ lbs. per lin. ft. Dead load moment = ^^^^ =3180 ft. lbs. 8 ' The live load consists of ten tons on two axles ten feet cen- ters. (See Spec. § 48.) Two thirds of this will be taken on the /go 55. cl ii « »i ' 9.S V Q 9.S mo Fm. 83. rear axle and one third on the front. If we consider that only two thirds of this goes to one joist, we get a loading per joist as shown in Fig. 83. This loading gives a maximum live load moment in the joist of 24,060 ft. lbs. The total moment for which to design the joist is Dead load moment = 3,130 ft. lbs. Live load moment = 24,060 ft. lbs. Impact Iy^XL.L. = 7,550 ft. lbs. Total = 34,790ft. lbs. T> • J .• ^1 34790X12 „„ . Required section modulus = — Jgooo — ~^^-^- 188 CALCULATION OF JOISTS Art. 78 Use 10 inch I beams, 30 lbs. for the intermediate joists. The outside joists are usually made of channels the same depth as the intermediate I beams. They do not carry as much load as the intermediate joists and therefore it is not customary to make any calculations for them. We will use 10 inch channels, 20 lbs. See specificatioas § 85. For the city bridge let us assvune a roadway wide enough so that a road roller could be easily turned on the bridge, a panel length of 19 ft. and Cooper's specifications. Class Ai (see Spec. §§ 16, 23 to 29 and 38). The floor will be of 4 inch brick on a IJ inch sand cushion on an 8 inch reinforced concrete slab resting on steel joists spaced 5 ft. center to center. The gen- eral arrangement is as shown in Fig. 82. » 6.0' % 1 1 ll.'f-*''.-''^'. ^1 k &s' 9.s' J /9.0' Fig. 84. The dead load per joist will be as follows: Brick 4 inch = | X 150 X 5 = 250 lbs. per hn. ft. Sand \\ inch =|X 100X5= 62 lbs. per lin. ft. Concrete 8 inch = |X 150X5 = 500 lbs. per lin. ft. Steel joist say = 55 lbs. per lin. ft. Total dead load =867 lbs. per lin. ft. 8fi7 V 1 Q2 Dead load moment =^^^^-^^^=39, 120 ft. lbs. o The live load consists of 24 tons on two axles 10 ft. centers. Two thirds of this will be assumed on the rear axle and the spacing of the wheels on the axle will be assumed at 6 ft. center to center. When the roller is turned across the roadway and it is assumed that the concrete floor distributes the load over the joists so that not more than 50% goes to one joist, the loading per joist is as shown in Fig. 84. Art. 78 CALCULATION OF JOISTS 189 190 CALCULATION OF JOISTS Art. 78 This loading gives a maximum live load moment in the joist of 41,260 ft. lbs. The total moment will be 41,260+39,120=80,380 ft. lbs. The required section modulus is — — = 74.2, XoUUU Use 18 inch I beams, 55 lbs. for the intermediate joists.. The outside joists will have to be built up to form a curb as Art. 79 TYPES OF STEEL HIGHWAY BEIDGES 191 shown in Fig. 82, or a concrete curb may be built resting on I beam joists. 79. Types of Steel Highway Bridges. The use of pony trusses for spans between 50 and 100 ft. is permissible in high- way bridge work in locations where plate girders would be difficult of transportation or erection. Pony trusses can also be built at a slightly less total cost than equivalent plate girder bridges. Pony trusses should always be riveted structvu'es and should have the top chord stayed by suitable knee braces at every panel point. Fig. 85 shows a design for a pony truss highway bridge with creosoted block or plank floor. The plate girder bridge is the most desirable form of steel bridge for spans up to about 80 ft. on account of its rigidity and durability. On account of the necessity of shipping the mina girders in one piece it is not well adapted to some locations. Fig. 86 shows a design for a plate girder highway bridge with concrete floor. Note the absence of joists, the concrete slab being carried directly by the floor beams. Fig. 87 shows a through riveted truss bridge with creosoted block floor. 192 TYPES OF STEEL HIGHWAY BRIDGES Abt. 79 CHAPTER VIII MANUFACTURE AND ERECTION 80. Shop Operations. Before taking up the subject of shop drawings, we will consider, briefly, the method of proceed- ure in the shop work and the erection. Thi? description will be general, as all classes of work are not handled alike and various plants differ somewhat in their equipment and methods. When the shop drawings on a contract are complete, blue prints of them and the accompanying bills of material are sent to the various departments of the shop. In the templet shop, a wooden ^ templet is made for each constituent piece of each dif- ferent member, excepting, of course, such parts as rods, eye- bars, pins, rollers, etc. This templet is of the exact length (or half length) of the finished piece, gives bevels and has holes at every point where a rivet hole is to be located. It is to be damped to the metal for the purpose of laying out the work to be done on each piece. Laying out directly upon the metal is seldom done because of the danger of making errors and ruin- ing the steel for the purpose for which it was intended. When the steel arrives from the mill it is unloaded at one end of the plant and marked with the contract number and sizes for future identification. Pieces of the same size are piled together and separated from other sizes as far as possible, so that any material can be gotten out easily at any time without handling other material which is not wanted. The unloading is usually done with a crane of some sort which deposits the material in the yard, or at some plants, in the shop. When enough material on any contract has been received from the mill and that contract is reached on the shop program, the material is run into the shop as it is needed, and usually continues straigl^t through to the opposite end of the plant where the finished product is loaded. ' Some shops are using paper mach6 for their large flat templets. 193 194 ERECTION Abt. 81 The first operation after the material is run into the shop is to straighten it so that the templet may be applied and that all pieces may be laid out accurately. This is done with presses, rolls and sledges. The next operation is laying out, that is, marking the lines on which the material is to be sheared, and with a center punch, which fits closely in the holes in the temp- let, the position of each rivet hole. Some material is sheared to length first and then laid out. From the shears or laying out skids, the material passes to the punches where all holes for rivets are punched. Next the various pieces which are to be riveted together are assembled and fitted, putting enough bolts through the rivet holes to hold the pieces in position until the riveting is completed. These bolts are taken out at the riveting machine as the riveting progresses. Before the pieces ^re assembled, such faces as will be inaccessible after riveting are painted, and before the riveting is done the holes are reamed out to correct inaccuracies in punching, or if reaming is required it is done at this time (10). Some pieces require planing, boring, chipping and hand riveting after the power riveting is done. After all the operations have been performed on a piece, it is run on to a scale and weighed by the shipper, who makes out a shipping bill. Having been weighed and inspected to see that it conforms with the drawing it is painted and loaded upon cars or stored to go out when wanted. All bending, forge work, upsetting, etc., are usually done in the blacksmith shop. Turning, planing (except rotary plan- ing) and all machine work are done in the machine shop. 81. Erection. Putting up the work in the field may be a very simple operation or one involving the use of a large plant and considerable risk, depending upon the character of the structm-e and its location. Bridges are usually erected on false work, which consists of wooden trestles, by means of a traveler or gallows frame, to which the tackle for hoisting all material into place is fastened. A gallows frame consists simply of two wooden posts connected together at their tops by a beam and braces. The posts usually rest upon temporary stringers outside of the fine of the girders or trusses. A traveler has four legs, at least, braced together longitudinally and transversely, allowing room enough under it Art. 82 THE DRAFTING DEPARTMENT 195 to erect the bridge inside of it. It runs on wheels so that it may- be moved lengthwise of the bridge as the erection progresses. Generally during the erection of railroad bridges the traffic must not be interfered with, but trains usually reduce their speed and run slowly over a bridge which is being renewed. The floor system is sometimes put in place before the trusses and blocked up somewhat higher than its final position. The trusses are erected begiiming at the center, putting up one half and then moving the traveler back to the center and working toward the other end. Enough bolts are put into the connections, which are to be riveted, to fill about two thirds of the holes. After everything is connected together, the bridge is " swung," that is, the blocking between it and the false work is taken out and it becomes self-supporting. Rivets for connections of tension members of trusses are driven before the bridge is swung and all others after it is swung. In the designing and detailing of steel structures it is important that the manner of erecting them be constantly kept in mind. Field splices must be placed in the proper positions, connections should be designed with a view to facility in making them under the conditions which obtain in the field; field rivets should be located where they can be easily driven; sufficient clearance must be provided at all joints. All pieces should have plain marks for identification and a good erection diagram, showing all marks, should be made.^ 82. The Drafting Department. The organization of the drafting department in various companies differs greatly. Usually there is a chief draftsman who has general supervision of all work and assigns the work to the various men under him, whom he deems best fitted to get out the drawings for it. Gen- erally a contract is given to a squad foreman, who has three or four men working under him and who directs the method of getting out the work, writes the order bills for the material, and sometimes makes some of the more complicated drawings. When the drawings are made and traced they are sent to a " checker," who is generally an old experienced draftsman, and he checks ' For detaOs of tools, tackle, traveler, false work, etc., see Chapter XIII in Du Bois' " Framed Structures," by John Sterling Deans, M. Am. Soc. C. E., and Appendix C in Johnson's " Modern Framed Structures." Eighth edition. 196 A DRAFTSMAN'S EQUIPMENT Art. 83 every dimension and size given on the drawing and marks such changes as are necessary, in pencil. The drawing is then cor- rected by the one who made it, and after being accepted and signed by the checker is ready to send to the blueprint room. The man who makes the drawing and the checker are held equally responsible for any errors. Drawing hoards should be used, as it is very inconvenient to have to remove a tracing from a table top in order to make a lay out or to work a short time on another drawing. The draw- ing boards should be of pine so made that they will not warp or split. They should have one true edge, preferably of hard wood, at the left hand end. T-squares should have rigid heads and true edges. The drawing table should be large enough to accommodate the drawing board, reference drawings, etc. It should, be at least six feet long, and supplied with a drawer for instruments, etc. It should be, preferably, adjustable as to height and slope of top. The stool accompanying it should be adjustable for height. The lighting of the drawing room should, of course, be the best possible. If artificial light is used at any time, it should be a diffused light reflected from the ceiling. A comparatively ' quiet, well ventilated, clean and orderly office will be conducive to good work and little friction. Unfortunately all of these reasonable conditions are not usually obtained. A suitable fiU^g system should be provided for all drawings and other data, preferably in a fireproof vault. 83. A Draftsman's Equipment. Shop drawings are the work- ing drawings used in the shop and give all details. Making shop drawings is the foundation upon which a bridge engineer's future advancement is based. A draftsman makes his own reputation. Conditions have been such in the past that advance- ment comes to the draftsman about as rapidly as he is able to take advantage of his opportunities. One who makes himself thoroughly acquainted with the theory of everything he does, one who is not afraid of a little work outside of office hours, who carefully studies and considers every piece of work entrusted to him, will not find the work growing monotonous. A reputation for making mistakes is perhaps the worst a draftsman can make for himself. The fact that every drawing is checked should Art. 83 A DRAFTSMAN'S EQUIPMENT 197 have no influence upon the amount of care bestowed on it. Errors will sometimes pass the checker and are expensive in nearly all cases. Errors are especially hable to occur when changes are made necessary after a drawing is made, either before or after it is checked. For this reason a draftsman should do everything according to some method. There is a best place to begin on a structure and a most logical order in which to work it up, not only each drawing but every detail. If this is followed very little erasing will have to be done, and everything will be better designed than if one detail is worked out regard- less of everything else and afterwards fudged to correspond with other requirements. After changes are made the drawing is usually out of scale, and not drawing to scale is usually con- ducive to. mistakes. Even rivet heads should be to scale. Every drafting room has some peculiar practices of its own, and it is generally the part of wisdom for a new-comer to conform with them as soon as he can find out what they are. A draftsman's outfit should include the following tools: 1st. Triangles, ruling pen, compass, bow pen, bow pencil, dividers large and small, pen knife, pen wiper, scales, oil stone, etc. 2nd. A copy of some rolling-mill's handbook. 3rd. Tables of squares and logarithms of dimensions in feet, inches and fractions. 4th. A copy of the office standards. 5th.. A five place table of the natural functions of angles varying by minutes. 6th. A five place logarithmic table of numbers and func- tions of angles. 7th. A slide rule. 8th. Reference books. 9th. The following which are usually supphed by the office: drawing tables, drawing boards, T-squares, erasers, soap- stone, pencils, pens, tacks, tracing cloth, drawing paper, ink, and chalk. The drawing instruments should be of the best quality. Loss of time due to poor instruments is inexcusable. Triangles should be transparent and not less than i^ inch thick. A 5 in. or 6 in. 45 degree triangle and an 8 in. or 10 in. 30-60 degree triangle will be found convenient. For some classes of 198 A DRAFTSMAN'S EQUIPMENT Art. 83 work a quarter pitch triangle (slope 1 in 2) and a small triangle that will fit the standard bevel of the flanges of I beams aiid channels (1 in 6) will save time. The ruling pen should be of a kind that is easily cleaned because the ink used dries rapidly. There are pencil sharpening machines which do very good work. If there is not one conveniently located in the office, a sharp pen knife can be made to do good work in connection with a piece of sand paper or a file for sharpening the lead. A draftsman who wishes to make a workmanlike drawing will not work with a blunt pointed pencil. The architects' scale is used for all shop drawings. This is a scale of feet and inches. Scales should not be over 6 inches long for detail work and preferably have white celluloid faces. A long scale necessitates moving the T-square and triangles too much. A 12 inch decimal scale for longer dimensions and graphic calculations should also be provided. A triangular architects' scale is usually divided into the following scales per foot: ^in., | in., ^ in., Jin., fin., § in., f in., 1 in., 1| in., 3 in. and 12 in. or full size. As most of these scales are used infrequently, it is more convenient to have two flat scales cover- ing the more often used scales. One divided into scales of | in., J in., I in. and 1 in. per foot and another divided into f in., f in., 1| in. and 3 in. per foot will answer most purposes. A scale of IJ in. per foot makes a very nice scale for some classes of work but it is not a standard .scale. The scale of J in. per foot is much used by architects. A good pencil eraser, one that will not " smear," is, of course, necessary. Ink on tracings should be erased with a rubber ink eraser although a steel eraser (knife) may be used occasionally. To prevent ink " rimning " and dirt accumulating on the spot which has been rubbed, the tracing cloth should be rubbed with soapstone. To confine the rubbed surface within the required limits, it is convenient to have a thin metal erasing shield with holes and slots of different sizes. The ink should be waterproof India ink of good quality. For drawing lines on detail paper a 6H pencil should be used, because it does not require such frequeilt sharpening as a softer pencil. For putting in dimensions and figures a 4H pencil will be about right. On tracing cloth a SH pencil will work best, and a soft pencil is needed for scratch figuring. Art. 83 A DRAFTSMAN'S EQUIPMENT 199 A pen must be " broken in " before good lettering can be done with it. After it has been used for some time the point becomes blunt and may be improved by using a knife on it as on a pencil in sharpening it. The rolling-mill hand books contain much information of use to the draftsman, and he should know what may be found in them. The pages most frequently referred to should be indexed for quick reference in some manner similar to a ledger index. The principal shapes rolled by the various mills are all alike and in accordance with the standard adopted by the Manu- facturers' Association. All properties of these shapes are given in the hand books. The American Bridge Company's Stand- ards give much other valuable information. Each office usually has a set of standard tables and draw- ings. Many of these are of general value, but some correspond with certain local shop practices. Tables of squares and logarithms of dimensions in feet and inches are in constant use, and are a much greater help than would appear on first thought.^ In working with right angle triangles, only the table of squares is necessary. The table of logarithms is not used so often, but when there is use for it it saves much time. These tables give results to the nearest 1-32 of an inch, and this is the smallest fraction ever used on struc- tural steel drawing^. The above tables, together with a good table of the natural functions of angles such as is given in " Trautwine's Pocket- book," and a five place table of logarithms such as Gauss' or Jones' will enable the draftsman to solve all problems in men- suration which may arise, if he is thoroughly familiar with the fundamentals of geometry and trigonometry. The draftsman should be familiar with the use of the slide rule, and should use it to calculate pins, rivets, bearings, etc. (5). If the office is provided with a Thacher cylindrical rule it may be used to good advantage in calculating the dimensions • " Tables of Squares," by John L. Hall and " Buchanan's Tables of Squares," by E. E. Buchanan, give the squares of dimensions under 50 feet, expressed in feet and inches. Tables by Thos. W. Marshall give the loga- rithms of the same quantities. " Smoley's Tables of Squares and Loga- rithms," by Constantine Smoley, give both the squares and logarithms of these dimensions in parallel columns. 200 ORDERING MATERIAL Art. 84 in oblique triangles, and will give results within ^ of an inch so long as none of the lengths involved exceed about 30 feet. A note book is very convenient for keeping calculations which one may wish to refer to again. Many figures which a draftsman makes will be on scratch paper, but all figures which may be needed for future reference and for consultation when the changes made by the checker are gone over, should be kept in a permanent and methodical form. A careful man will find satisfaction in seeing how he made a mistake, and this record will also be valuable in giving reasons for certain things he has done, and prevent his being misled by some one who, perhaps, has not considered all the conditions. A draftsman should have at hand reference hooks in order that he may look up any point in theory with which he is not familiar. A few may be mentioned here but, of course, for structures out of the ordinary special works should be consulted. The most useful are: Johnson's " Theory and Practice of Modern Framed Struc- tures," Heller's " Stresses in Structures," some good work on the strength of materials, Wright's " The Designing of Draw Spans," Tyrrell's " Artistic Bridge Design," Merriman and Jacoby's " Bridge Design " (Part III of Roofs and Bridges), Kent's " Mechanical Engineer's Pocketbook," Trautwine's " Civil Engi- neer's Pocketbook," Engineering News, etc. Access to the Transactions of the American Society of Civil Engineers, and of other engineering societies will be valuable. An individual card index should be kept in order that any subject may be looked up when occasion requires. 84. Ordering Material. As soon as a contract has been secured and entered, complete data relating to the construction are turned over to the drafting department. The first thing to be done by this department is to prepare a list of the material required, which is called an " order bill." The draftsman to whom this is entrusted should first carefully examine all data. If any necessary information is found lacking at any point in the progress of the work, it should be promptly reported. Care should be taken to include everything in the order bill that will be required to make the structure, unless upon inquiry it is found that certain materials may be ordered later. Since the order bill must, in general, include all details such Art. 84 " ORDERING MATERIAL 201 as pin plates, batten plates, lacing bars, rollers, pins, eye bars, rods, timber, lead, corrugated iron, windows, doors, crane run- way rails, etc., it is necessary to proportion all details, to calcu- late pins, rivets, bearings and connections, and to determine clearances, splices, etc. In some cases considerable drafting will be required, but not nearly so much as will be necessary to make complete detail drawings. In general, this preliminary drafting should be done so that after the order bill is complete the drawings may be developed into final shop drawings. This method will save much drafting, which is expensive work. In order to expedite the placing of the orders for the material at the mills, no more drafting than necessary should be done. It may be supplemented by free hand sketches and notes, which should be preserved with other data for reference by the checker and draftsman making the shop drawings. For a contract of any magnitude the order bills would be gotten out in sections; those parts which will be needed first should be gotten out first. In any case, the first attention should be given to the kind of material which will -be most difficult to get promptly. However, time spent upon a consideration of the entire con- tract in all its bearings, and especially with regard to duplica- tion of parts, is never wasted. The order bills are checked and a copy sent to the order department. The originals are retained for the guidance of the draftsmen who make the shop drawings. The element of time is so important that most companies do not make blue prints of the order bills, but use some more rapid duplicating process. The order department makes up a " mill order " from the order bills, bringing together all items of the same kind and combining some of the shorter lengths into long lengths (mul- tiple lengths) to be sheared to the proper lengths at the shop. Some companies keep more or less material in stock in order to be able to make prompt deliveries of certain classes of work. In this way considerable waste (short pieces) accumulates, which must be appUed on contracts whenever an opportunity offers. It is the duty of the order department to keep track of the stock, to keep up the supply of stock sizes, and not to allow an accumulation of waste. When stock material is applied to a contract it should be so marked, in order that it may be 202 ORDERING MATERIAL Art. 84 reserved. The shop, bill generally shows what items are to come from the mill and what items from stock. Stock material cannot always be used on contracts, as some specifications require a different quality of material from that carried in stock and require inspection at the mills. The importance of avoiding errors and omissions in the order bills is apparent, since they may cause serious delay to the entire work. In making up the order bill, it should be remembered that odd sizes of angles and other shapes should be avoided in order to get prompt delivery from the mill; J inch extra material should be ordered for all tool finished (milled or planed) sur- faces, except for the flat surfaces of plates for which ^s i^i- or I in. extra should be ordered, depending upon the size of the plate. Stiffener angles which are to be crimped or offset, are usually ordered as long as the depth back to back of angles of the girder to which they belong. The length of bent angles and plates is taken on the center of gravity line. Other material is ordered the exact length required (avoiding smaller fractions than eighths of an inch) and usually comes a little longer so that it may be sheared to the finished length. Plates are of two kinds, " sheared " and " universal mill." The former have sheared edges and the latter rolled edges. The maximimi width of universal mill plates varies from 20 in. to 48 in., depending upon the mill where they are rolled. In the rolling mill hand books will be found tables showing the maxi- mum length to which plates' of various widths and thicknesses can be rolled. Plates up to 7 in. in width are called bars. Flange plates for plate girders are usually obtained as long as wanted, but web plates must be spliced. It is usual to order web plates of a width J in. less than the depth back to back of angles, and to allow I in. clearance between their ends. It is permissible to order odd shaped plates sheared to the dimensions wanted, as shown by a sketch. Angles may be obtained in single pieces up to about 90 feet long, provided that they do not weigh more than about 3000 lbs. apiece. Special sizes should be avoided on account of slow delivery. The order bill should indicate the kind of material (soft or medium steel) and the specifications governing its quality and inspection. Art. 85 SHOP DRAWINGS 203 85. Shop Drawings. Drawings should be made on the dull side of tracing linen, because they will not lie fiat when made on the smooth side. An experienced draftsman will work directly on the tracing cloth and this cannot be done except on the dull side. Drawings may be fastened to the board with thumb tacks, but it will be foimd more satisfactory to use very small carpet tacks, tacking the four edges like a carpet so that the drawing will be stretched and present as smooth a surface as possible. Changes in temperature and moisture of the air may sometimes necessitate restretching. The drawing should be covered up at night with a heavy cloth or a piece of table oil cloth. If the drawing is made on the tracing linen direct, the principal lines may be inked before the drawing is completed in pencil. This will bring out the main parts and make it more satisfactory to work with, especially if there is much work on the drawing, as the lines are liable to become faint from rubbing over them. It is, however, safer for an inexperienced man to make a complete pencil drawing before doing any inking. In order that the tracing cloth may "-take " the ink it is necessary to rub it with pulverized chalk, fuller's earth, or blotting paper. This is especially necessary during cold and damp weather. The draftsman should not get the idea that the appearance of a shop drawing is of no importance. A drawing should have a workmanlike appearance or it will not inspire confidence in its correctness. The general arrangement and the lettering are the main features so far as appearance is concerned. All lettering should be free hand and the draftsman should, at the beginning, practice with exceeding patience some simple style of lettering. The style used in the drawings published in the Engineering News is a very good one to follow. A very important point is to have the letters and figures of different sizes, depending upon their importance. The sizes of materials should be more promi- nent than the rivet spacing, and center lengths than secondary dimensions. There is also a best position for each dimension. The letters and figures should be made as carefully as is con- sistent with rapidity. It is only practice, persistent and patient, that can make a good letterer. Not all can hope to become equally proficient, but all can improve. 204 SHOP DBA WINGS Art. 85 The general appearance of a drawing depends very much upon the general arrangement, the scale, and the relative sizes of letters. A drawing may cover practically all the available space within the border Unes, if there is no evidence of crowding anywhere, and if the various parts or pieces represented stand out clearly so that the different views of the several pieces can not be confused. There is an advantage in compactness, but clearness is the first consideration. Not every one who uses a drawing can read it as readily as the man who made it. He should make it so plain that it will explain itself and that only gross negligence will allow anyone to make a mistake in using it. The object should be, not to make it " good enough " but to make it first class. The length of a structure, like a truss, seldom determines the scale of the drawing. Usually the available width of a sheet determines the scale to be used. If the structure is too long to show on one sheet to this scale two or more sheets may be used. The center line diagrams of trusses are usually drawn to a smaller scale than the details, say J in. or f in. per foot while the details would be 1 in. or 1§ in. per foot. In this case, of course, there is a part of the member near the middle which is cut out and which need not be shown, but the spacing of rivets, etc., is indicated. True projections are not always made if they do not serve to make matters clear. Bottom views are seldom made but sections instead, placed below the elevation. The top view should always be above the elevation. A half top view and half section are sometimes made together when symmetry will allow. A single view or two views will sometimes suffice, especially if it is a construction with which the shop is familiar. There should be no more drafting than is necessary for clearness. Drawings should have one or two plain border lines. If two are used the blue prints may be trimmed to the outer one. (See Fig. 88.) In some drafting rooms an outfit for printing titles on tracings is used; in some rubber stamps are used. Printing is the most satisfactory method when the number of drawings tm'ned out is large. Titles should correspond with some stand- ard as indicated in Fig. 88. The title should, when possible, be in the lower right hand corner. When necessary it may be divided in two parts placed side by side. A supplementary Art. 85 SHOP DRAWINGS 205 36- 3S-i THE OHIO STATE BRIDGE CO. COLUMBUS, OHIO Bridge No.34 Western DkQ.R.&M.Ry. I Through Truss 5pan-DoubleTnd<.5kew ia6'-6"C.toC. Floor Beams Stringers and Portals. In Charge of Smith Drawn by AJ.K 7-1-07 Revised 6-6-07 Checked l>y ^^7-84-07 Revised 8-7-07 Shop Bills Nos. I.Z.3&. 4 CONT. NO. 746 (^ ■/^/y? S/i/e Prmt on th/'s Line) (Thm 7ri7C//7ff on tftis Line) Fig. 88. 3^ _25i_ 55 Specif /caf/orts- Cooper'.sRu. /SO/. MaTer/a/^off 0.//.^5reel. Wi^ets §; '//a/ea^ 1/n/e.ss o//ierwiee no&c/. /7ca/7ii/ja - nor?e. /-'/am'nar^/jeamc/ 4^-j3_ 1_ o^.3-JzO:A. SAyie^ffre_MiJ6.-6i£La£M^^ D™»ioe no. -/^- Skl, No. Pci. Kin. SIZE Wl. P. Ft. DESCRIPTION FInlihed Unglh OrderBd Length REMARKS -^ T^fA rm. w>CAoraL ^'-3ir-f as 7a^ M 2/-3£ 7./-SS ^ fl li "■'§' n 7 Bo^. U Z/-9£ 2l-9i' ^ P A. /6--f' A^As ?J-9£ 2/-9£ tt a ^ 3-i /ii^A . yiAop /-o" /£-£>" A?/.. . 4 J- 2'/' /^-a~ M/ . .. 4 ^. /jS'f /^/7^n fiVs. p-oi' /?--^* Af.L. .. fifi A Zii'¥ LoM-ftT * ^ ^fock Wi^*--/.^^ z Tntf rm. ^of^/jont t'jf. ff. /DO. a i^ 2S-'¥ C^,r^rfV. 24'3k 24i^ f7K>r/7ea'ie Fig. 94. lowing information should also be put on a bill sheet and sent with the shop bills: Contract No. Description Location Date to Ship Inspected by Erected by Ship to Shop Paint Field Paint Lumber furnished by Penalty In general, the drawings should show everything complete. 218 SHIPMENT Akt. 89 but the drawings of the forge work, machine shop work, and miscellaneous details are often made on bill sheets. 89. Shipment. Field splices and connections are often determined by the limitations of transportation facilities. These should be determined at the outset. Some routes can take care of pieces of greater extreme dimensions than others. Tvmnels often limit the width of the loading and overhead bridges, .the height. Sharp curves have an important bearing on loading long pieces, especially girders. It should be remembered that a piece extending over two or more cars, swings away from the center line of the track on a curve, requiring more clearance than on a straight track, and that a car on a curve is inclined toward the inside of the curve. Ordinarily, pieces about 10 feet high can be transported on the railroads, bjit the width at the top is usually limited to about 6 feet. The greatest width of a steel car is 10 feet 2 inches. Pieces 10 feet or more in width can be transported if they are not too high or too long. The question of weight is not generally an important one, except that cars of proper capacity must be used so that no truck will be overloaded. It is allowable to put two thirds of the nominal capacity of a car on one truck. For export shipment special instruction must be obtained on each job as to maximum lengths, weights, etc. Pieces for export work must, in some cases, be so small that they can be trans- ported on pack animals. A thorough and simple system of marking is necessary. Instead of marks, colors are sometimes used. The question of cost of freight is sometimes an important one, and may determine the maximum length of a piece. If the total weight of a contract is less than a car load, so far as cost of transportation is concerned, no piece should be longer than a car length. There are two kinds of freight rates, " car load " and " less than car load " (C. L. and L. C. L.), the latter being the higher. The minimum car load is generally 30,000 lbs.; the minimum for two cars is 40,000 lbs. ; and 20,000 lbs. is added for each addi- tional car. Therefore if any piece extends from one car over part of another, freight must be paid on at least 40,000 lbs., no matter how much less the shipment weighs. In case of a girder extending over three cars, the minimum amount charged would be on 60,000 lbs. Art. 90 MATERIALS 219 90. Materials. The materials used by the structural engineer are wrought steel, wrought iron, cast steel, cast iron and timber. Cast steel and cast iron are used for the machinery of draw bridges. Except in special cases of columns for buildings, and pedestals, and for small details like washers, ornaments and separators, cast iron has passed out of use entirely in structural work. Cast steel is sometimes used for shoes of bridges. Timber is used for the compression members in combination bridges and roof trusses, and for the floors of bridges. Wrought iron is used for rods which must be welded, — rods with loop eyes, or forked heads. In the best classes of work welds are entirely avoided. Welds in steel are not considered reliable. The qualities of the materials required are given in the specifications governing the work. We shall consider structural steel more in detail. At present three kinds of steel are commonly specified, viz., " rivet steel," " soft steel " and " medium steel." Of these, rivet steel is the softest and medium steel the hardest, or the steel of greatest ultimate strength. " Hard steel," or steel having an ultimate strength greater than 70,000 lbs. per sq. in., is seldom used for bridges or buildings. There is at present a movement toward the adoption of a single grade of steel for all structural purposes.^ This would simplify the steel maker's work, and no doubt result in a more uniform and a cheaper product. The quality of steel is determined by analysis and test. There is considerable uniformity in the requirements of various specifications. These may be enumerated as follows : Chemical Requirements. Percentage of phosphorus, sulphur, manganese, silicon, carbon, copper and arsenic. Physical Requirements. Process of manufacture, uniformity, finish, heat treatment, ultimate strength, elastic limit, elonga- tion, reduction of area at point of fracture, appearance of frac- ture, bending, bending, after quenching, punching, drifting of punched holes, variation of cross section and full sized tests. Chemical analysis determines the amounts of the impurities in steel. All elements except iron and carbon may be called impurities. Since it is practically impossible to eUminate all •See Bulletin No. 62 American Railway Engineering and Maintenance of Way Association. 220 MATERIALS Abt. 90 the phosphorus and sulphur, a small percentage of manganese is considered advantageous. In order to meet the physical requirements the mianufacturer must limit the amount of all impurities, and of the carbon. All specifications, however, limit the amount of phosphorus allowed, since this element renders the steel brittle or " cold short " while it, at the same time, hard- ens it. Some specifications also specify maximum allowable percentages of sulphur, manganese and silicon. The maximum allowable amount of phosphorus in steel depends upon its mode of manufacture. It is usually about 0.04% for basic open hearth steel and 0.08% for acid open hearth and Bessemer steels. Carbon has the greatest influence upon the ultimate strength or hardness of steel. Phosphorus, manganese and sulphur make steel harder and also reduce its ductility. Basic open hearth steel will, in general, have about the fol- lowing ultimate strengths, depending upon the percentage of carbon: 65,000 lbs. per sq. in. with 0.10% carbon. 60,000 lbs. per sq. in. with 0.15% carbon. 65,000 lbs. per sq. in. with 0.20% carbon. 70,000 lbs. per sq. in. with 0.25% carbon. The elastic limit will be about 0.6 of the ultimate tensile strength. There is no rigid line separating the different grades of steel, but steel having less than 0.15% carbon is generally soft steel, and with more than 0.30% carbon, hard steel, the intermediate grade being medimn steel. These grades are usually defined by their ultimate strength. Process of Manufacture. Steel is made by the Bessemer or open hearth process. Open hearth steel is now used for all important bridge and building work. It is almost invariably required when a regular specification governs the work. Bessemer steel is not so uniform in quality as open hearth steel and is, therefore, not so reliable a material. It is made in a converter, by blowing a blast of air through molten pig iron until the carbon and silicon are all burnt out. Ferro-manganese is then added to recarbonize the metal the required amount and to absorb the excess of oxygen, which would make the steel " rotten." From the converter the metal is poured into a ladle Aet. 90 MATEKIAL8 221 and then into moulds. Here the metal is allowed to solidify, producing ingots. The ingots are reheated and then rolled into slabs, blooms and billets of various sizes, depending upon the final form into which thej' are to be rolled. Open hearth (Siemens-Martin) steel is made in an open hearth furnace and is of two kinds, acid and basic. The use of the latter predominates. Add steel is made in a furnace having a hning of a refrac- tory silicious material which has an acid reaction. Basic steel is made in a furnace having a lining of magnesite or dolomite, which has a basic reaction. The raw material in either case is pig iron, now usually charged in a molten state. If the pig iron contains larger percentages of phosphorus and sulphur than are allowed in the steel, these must be reduced. Since they have a great affinity for iron, some reagent must be introduced in the molten metal which has a greater affinity for them. For this purpose a basic material must be used, since they form acids when oxidized. The material employed is lime charged in the form of limestone. This cannot be used in an acid lined furnace because it would form a flux with the lining. In the acid process, therefore, the percentages of phosphorus and sulphur in the raw material must not much exceed what is allowed in the finished product. This process requires a better grade of pig iron than the basic process. In the open hearth basic process, large quantities of oxide of iron in the form of iron ore or mill scale, are charged into the furnace, together with limestone and molten pig iron. The lime which is formed, combines with part of the phosphorus and sulphur, reducing the percentages of these to minute quantities, while the oxide of iron serves to burn out the carbon, manganese and silicon. The desired amounts of carbon and manganese are then added. As in the Bessemer process, the steel is made into ingots, billets and slabs, and is finally rolled into the desired shapes. Upon the care with which all of these processes are carried^ out depends the uniformity and finish of the rolled steel, as well as its quality to some extent. Lack of uniformity may be due to unequal heat treatment, unequal working or to segregation in the ingot, producing a steel of variable composition. If a piece of steel is not uniformly treated and cooled there may be internal 222 MATERIALS Abt. 90 stresses in it, hence it is required that pieces which are heated in working as eye bars, for example, must be annealed. The hotter a piece of steel is heated, the coarser grained it will be and the more rapidly it is cooled, the harder it will be. Rolling and ham- mering steel increases its density and strength, but working it at a blue heat may crush the grain, which is very injurious. Rough iron cracks are indications of " red shortness " or burning. Other surface defects are easily discovered on close inspection. Defects due to bad heat treatment, improper working, excess of impurities, etc., are discovered by chemical analysis and physical tests. Tests are made of material from each heat, melt or blow. Specifications allow a range of ^000 to 10,000 lbs. per sq. in. in the ultimate tensile strength of any particular grade of steel, but they do not all agree as to the hmits. Depending upon the specifications, soft steel may include steel having an ultimate strength as low as 52,000 lbs. per sq. in. and as high as 62,000 lbs. per sq. in., medium steel as low as 60,000 and as high as 70,000 lbs. per sq. in., and rivet steel from 48,000 to 58,000 lbs. per sq. in. The ultimate strength, elastic limit, elongation and reduc- tion of area are determined from test pieces cut fron" the finished material. It is usually required that the elastic limit must not be less than one half of the ultimate strength. As it is not diffi- cult to obtain an elastic limit equal to 0.6 of the ultimate strength it would be well to specify, as is sometimes done, a minimum for the elastic limit. Thus, if the ultimate may vary from 60,000 to 68,000 lbs. per sq. in., the minimum elastic limit might be fixed at 32,000 lbs., for example, and then steel having a greater ulti- mate than 64,000 lbs., would have to have an elastic limit of at least one half the ultimate. In this case the unit stresses could be based upon an elastic limit of 32,000 lbs. In commercial testing, the elastic limit is determined by the drop of the beam of the testing machine, that is, it is really the yield point.^ It is important that steel be ductile and not brittle. For determining ductility, the tension piece is measured after rup- ture to determine the stretch in an original length of eight inches, and the reduction of area at the point of fracture. The deter- mination of the latter is not important and is usually omitted. 'See Heller's " Stresses in Structures," Art. 21. Abt. 90 MATERIALS 223 In a general way, the elongation in eight inches is about 30% for good steel having an ultimate strength of 56,000 lbs., per sq. in., and 25% for 65,000 lb. steel. This is for standard test specimens having an area of cross section of not less than | sq. in. The usual requirements are 25% for soft steel and 22% for medium. Pin material is only required to have an elonga- tion of 16% or 17%, and eye bars, when tested full size, 10% in the body of the bar. The percentage of reduction of area is about 1.8 to 1.9 times that of the elongation. The appearance of the surface of the fracture is always noted in 'testing steel. If it shows defects such as blisters, cinders, spots, cracks or lack of uniformity of color, it is not a desirable product. The fracture of good material is described as " silky," and has a " uniform, fine grained, structure of blue steel gray color, entirely free from fiery ' luster ' or a ' blackish ' cast." If the fracture is granular and has a " fiery " luster it indicates over heating. If the fracture is dull or " sandy," the steel is impure, or worked cold, and should be rejected. The bending test requires that the test piece shall bend cold without sign of fracture. For soft steel it must bend fiat on itself, and for medium steel, to a curve whose diameter is from one to three times the thickness of the piece tested. Some speci- fications require this bending test to be made upon pieces which have been heated and quenched in water. A punching test is sometimes specified. This requires that the walls between the punched holes shall not break down except when they are less than J inch thick. The drifting test requires that the ductility of the metal must be such that a punched hole will stand drifting until its diameter is increased from 33f to 100% without cracking the edges. Pieces of large cross section are apt to be " piped," that is, they are not solid. This is due to bad working or unequal cooling, and occurs particularly in pins. It is usually specified that the larger sizes of pins (say over 4^ inches) must be forged from blooms having a sectional area of about three times the area of the pin, in order that the material may be sufficiently worked to make it sound. Full sized tests are usually confined to eye bars. Some 224 INSPECTION Art. 91 reductions in requirements of ultimate strength and elongation are made from those required for small test pieces, because pieces of large cross section do not test as high as those of small cross section. 91. Inspection. If an inspector is employed on a contract, his duties may relate to material, shop work and erection. On some classes of work the purchaser employs no inspector. The manufacturer has all work inspected as to dimensions, to avoid trouble in erection. In some cases reports of tests of material are furnished by the rolling mill, which conducts a testing department for this and other purposes. An inspector is most frequently employed to make tests of the steel, at the mill, as it is rolled. The shop work is also inspected for the best classes of work, but in comparatively few cases is the field work inspected by a regular inspector. The large railway companies have inspectors in the mills, the shop, and the field. The inspection of material includes tests, analyses, surface inspection, measuring sizes, etc., of steel, lumber, paint, etc. A shop inspector should see that no material is injuriously treated, that reaming of rivet holes is properly done, that all parts are made in accordance with the drawings, that rivets are good and. tight, that members are straight, that no work is ragged or unfinished, that painting is done in accordance with the specifica- tions, and should make reports of progress. The field inspector should see that no part of the structure is injuriously treated, that no members are interchanged, that all field driven rivets are good, and that' the painting is properly done. Rare qualifications are required for a good inspector. He must serve his employer honestly and avoid friction with the contractor. GENERAL SPECIFICATIONS FOR STEEL HIGHWAY BRIDGES 1911 OHIO STATE HIGHWAY DEPARTMENT COLUMBUS, OHIO 225 SPECIFICATIONS FOR BRIDGE SUPER- STRUCTURES. GENERAL Classification. 1. All bridges under these specifications will be divided into four classes: (45 to 48) Class A — ^Bridges for city traffic. Class B — Bridges for suburban or interurban traffic with heavy electric cars. Class C — ^Bridges for country roads with Ught electric cars or heavy highway traffic. Class D— Bridges for country roads with ordinary highway traffic. Type. 2. The following types of bridges are recommended: For spans up to 6 ft., concrete, stone or pipe culverts. For spans from 6 ft. to 15 ft., reinforced concrete slabs, reinforced concrete beams with slab floor, rolled steel beams cased in concrete with slab floor, or rolled steel beams with plank floor. For spans 15 ft., to 25 ft., reinforced concrete beams with slab floor, rolled steel beams cased in concrete with slab floor, or steel beams with plank floor. For spans from 25 ft. to 40 ft., steel plate girder bridges. For spans from 40 ft. to 80 ft., steel plate girders, or riveted truss bridges. For spans from 80 ft. to 120 ft., riveted truss bridges. For spans over 120 ft., riveted or pin-connected truss bridges. Span. 3. In calculating the stresses, the length of span shall be understood to be the distance between centers of end pins for trusses, center to center of trusses for cross floor beams, centers of bearings for all longitudinal beams and girders, and the width of clear opening plus the depth of slab, for rein- forced concrete slabs. Clearances. 4. All through bridges carrying electric cars, shall have a clear headroom above top of rail, of at least 15 ft., for a width of 6 ft., over the center of the track. Where the track is straight there shall be a clear width of at least 6J feet on each side of the center Une of track at a height of 1 ft., above the top of ran. Where the tracks are curved, the additional clearance shall be 227 228 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES computed by assuming the extreme length of car as 45 feet, width 8 ft. and distance between centers of trucks 20 ft. 5. For bridges without electric cars, the clear head room above the floor shall be at least 12J ft. and preferably 15 ft. Roadway. 6. The clear width of roadway shall in no case be less than 16 ft., and for bridges carrying electric cars there shall be a clear width of at least 12 ft. from the center line of track on one side of the track. General Proportions. 7. The width center to center of girders or trusses shall in no case be less than one-twentieth of the effective span. The depths of trusses or girders shall preferably not be less than the following: For roUed beams, one-twentieth (1-20) the span. For plate girders, one-twelfth (1-12) the span. For riveted trusses, one-tenth (1-10) the span. For pin-connected trusses, one-eighth (1-8) the span, In truss bridges the inclination of the diagonals with the vertical shall be preferably less than 45°. Foot Walks. 8. Where foot walks are required, they will generally be placed outside of the trusses or girders and supported on over-hanging brackets. -•Railings. 9. A handrailing 3j ft. high shall be placed on each side of the bridge except where plate girders serve the same purpose. Where the handrailing- is of rolled steel or cast iron it shall be of pleasing design and shall be rigidly attached to the superstructure. Trestles. 10. Where trestles are used, each trestle bent shall, as a general rule, be composed of two supporting columns, and the bents united in pairs to form towers; each tower thus formed of four columns shall be thoroughly braced in both directions, and have struts between the feet of columns. (53) (108) Trestle towers. 11. Each tower shall have sufficient base, longitudinally to be stable when standing alone without other support than its anchorage. (108) 12. Tower spans for high trestles shall not be less than 30 feet. Approaches. 13. AU floor timbers, rails, guards and handrailings shall extend over all piers and abutments and shall make suitable connection with the embank- ments at either end of the structure. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 229 Approval of plans. 14. The contractor shall not, except at his own risk, order any material, or commence any work until after the shop drawings have been approved by the State Highway Commissioner or his Deputy. After approval, the contractor shall furnish the State Highway Department and the County Surveyor, without charge, with as many sets of the shop drawings as they may require. 15. The contractor shall check all leading dimensions and clearances as a whole and in detail, the fitting of all details, and become responsible for the exact position and elevation of all parts of the work; and the approval of the working drawings shall not reheve the contractor of this responsibiht Anchor bolts. 16. The contractor for the metal work shall furnish the requisite anchor bolts to the sub-structure contractor with a masonry plan showing their location, in time that they may be built into the masonry. Name plates. 17. One or more cast iron name plates of an approved design, giving the date of construction, the names of the County Commissioners, the County Surveyor, the State Highway Commissioner, the Contractor for the Super- structure and the Contractor for the Substructure, shall be securely bolted to the superstructure at the point or points specified. FLOORING MATERIALS Paved floors. 18. Pavements consisting of stone blocks, paving bricks, asphalt, etc., may rest on a reinforced concrete slab, or on a concrete bed resting on buckled plates as directed by the Highway Department. Buckled plates. 19. When buckled plates are used they shall not be less than 6-16 inches thick and the concrete bed shall not be less than 3 inches thick for the road- way and 2 inches thick for the foot walks over the highest point. The buckled plates shall be placed with the buckle down and each buckle shall be provided with a drain hole., (128) (129) Pavements. 20. When asphalt, brick or stone pavements are used, they shall be put down according to the specifications of the State Highway Department. Scuppers. 21. Scuppers must be provided at frequent intervals along the curbs or wheel guards for drainage and for passing the sweepings and snow, clear from contact with any parts of the trusses or floor system. Wood block. 22. Creosoted wood block pavements may be laid on a concrete base or on creosoted plank as directed by the Highway Department. 230 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES Sand cushion. 23. When a concrete bed is used, the wood blocks shall be laid on a one- inch sand cushion. Sub-floor. 24. When a creosoted plank sub-floor is used under a wood block pave- ment, the planks shall be laid tight and coated with a layer of paving pitch, or coal tar known as Distillate No. 4, heated to 240° Fahr. Upon the hot tar shall be laid one layer of three-ply tarred roofing felt of a quaUty acceptable to the engineer. Another coating of hot tar shall be applied on top of the paper and the blocks laid in this coating while it is hot. Laying. 25. The blocks shall be laid with the grain vertical in courses trans- versely of the roadway. They shall be laid to break joints at least three inches in consecutive courses. Filler. 26. After the blocks are laid the joints shall be filled with coal tar, Distillate No. 6, heated to 320° Fahr. and thoroughly broomed into aU joints while hot and then the whole pavement covered with a J inch layer of clean coarse sand. Timber. 27. The paving blocks shall be yellow pine 90% heart, sawed into rectangular blocks 3 inches thick, 6 to 10 inches long of the depth shown on the plans. 28. All other creosoted timber must be good long leaf yellow pine, free from large loose or rotten knots, must be sawed true and out of wind, and must be free from wind-shakes or other defects which would injure its quaUty. Treatment. 29. When creosoted timber is specified, it must be sized and cut to the dimensions given on the plans before the creosotingis done. 30. The timber and paving blocks to be treated shall first be subjected to a steaming and vacuum drying process to remove the water and sap and to open the pores of the wood, after which they shall be impregnated with creosote oil as specified below. Steaming and drying. 31. The timber and blocks shall be placed in the steaming cylinder and a 30-lb. steam pressure shall be appUed and maintained in the cylinder for 4 hours, during which time the temperature must be maintained above 250° Fahr. After the steaming it shall be allowed to cool down for one hour. Vacuum. 32. The material shall then be put under a vacuum of 24 inches or less and subjected to a temperature of 240° Fahr., until moisture and gases cease to come from the cylinder. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 231 Application of oil. 33. At the end of the drying, the creosote oil shall be admitted to the cylinder while the timber is still under the vacuum, and a pressure of 100 lbs., per sq. in. shall be applied and maintained until the required amount , of oil has been forced into the timber and blocks. The oil shall be at a tem- perature of 200° Fahr., when admitted to the cylinder and so maintained throughout the time of impregnation. Oil. 34. The creosote oil shall be a dead oil of coal tar, commonly known as creosote, and shall have a specific gravity of not less than 1.02 or more than 1.10 at 68° Fahr. It shall at no time contain more than 2% of water, and if at any time water in excess of this amount is found in the oil, operations shall cease until the surplus water has been removed by distillation or otherwise. Amount of oil. 35. The timber and blocks shall receive not less than 16 lbs. of oil per cu. ft. Tests. I 36. The quantity of oil forced into the timber shall be determined by weighing marked pieces selected as representing the average green timber before the charge is dried and finally reweighing them after the application of the-oil. From these weights the average amoimt of oil used in the whole cyUnder load shall be determined. Plank floor. 37. For bridges with a plank floor the plank shall not be less than 2| inches thick, laid with J inch openings and spiked to each supporting joist, if wood joists are used, or to 3 inch nailing strips securely bolted to the steel joists. When this is covered with an additional wearing floor (38) it must be laid diagonally with J-inch openings; all planks shall be laid with the heart side down. The floor plank must have a thickness in inches at least equal to the distance apart of the joists in feet. The floor planks must bear firmly upon all joists. Wearing surface. 38. Where specified, an additional wearing floor IJ inches thick of white oak plank shall be placed over the above. (37) Walks. 39. The foot-walk plank will be 2 inches thick and not over 6 inches wide, spaced with |-inch openings. Guards. 40. There will be a wheel guard not less than 4 in. X6 in. on each side of the roadway to prevent the hubs of wheels from striking any part of the bridge. It shall be blocked up from the floor to admit drainage and cir- 232 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES culation of air and shall be secured by | in. hook bolts with washers under the nuts, to the steel joist, or if wood joists are used, by f in. lag screws with washers, at intervals of not over 4 ft. Wood joists. 41. When wood joists are used they will lap by each other so as to have full bearing on the floor beams, except the outside lines under the wheel guards, which must be butted over the floor beams. Their scantling will vary in accordance with the length of panels selected, but shall not be less than 3 inches or one-fourth of depth in width. When joists are spaced not over 2J feet centers, one joist shall be considered as carrying only two-thirds of the concentrated live load. (49) Timber. 42. The timber, unless otherwise specified, shall be strictly first class spruce, white pine, uouthern yellow pine, or white oak bridge timber, sawed true and out of wind, fuU size, free from wind shakes, large or loose knots, decayed or sap wood, worm holes, or other defects impairing its strength or durability. It will be subject to the inspection and acceptance of the Engineer. LOADS 43. All parts of the structure shall be proportioned for the maximum stresses produced by the dead load, temperature, wind, traction and by any one of the Uve loads given below as specified. (1) Dead load. 44. The dead load shall comprise the actual weight of the completed structure. The dead load used in figuring stresses must not vary more than 5% from the actual estimated weight made from the completed design. In estimating the dead load the following unit weights shall be used: Timber untreated 4j lbs. per ft. B. M. Timber creosoted - 5 lbs. per ft. B. M. Concrete plain - 140 lbs. per cu. ft. Concrete reinforced 150 lbs. per cu. ft. Asphalt - 155 lbs. per cu. ft. Brick . . - 150 lbs. per cu. ft. Macadam - - 100 lbs. per cu. ft. City bridges. 45. Class A. City Bridges. For the floor and its supports, on each street car track or on any part of the roadway, a concentrated load of 24 tons on two axles 10 ft. centers and 6 ft. center to center of wheels, with f of the load on one axle (assumed to occupy an area 12 ft. X20 ft) and upon the remaining portion of the floor including foot walks, 100 lbs. per sq. ft. For the trusses for spans up to 100 ft., 1800 lbs. per lineal ft. of each car track (assumed to occupy 12 ft. in width) and 100 lbs. per sq. ft. on the remaining floor surface, with a minimum live load of 2200 lbs., per lineal SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 233 ft. of bridge; for spans of 200 ft. and over, 1200 lbs. for each lineal ft. of track and 80 lbs. per sq. ft. of floor, with a minimum live load of 1600 lbs. per lineal foot of bridge; proportionally for intermediate spans. Suburban and interurban bridges. 46. Class B. Suburban and Interurban Bridges. For the floor, and its supports, on any part of the roadway a concentrated load of 15 tons on two axles 10 ft. centers and 6 ft. center to center of wheels, with f of the load on one axle (assumed to occupy an area of 12 ft. X 20 ft.) and on each street car track a concentrated load of 24 tons on two axles 10 ft. centers with f of the load on one axle, and upon the remaining portion of the floor including footwalks 100 lbs. per sq. ft. For the trusses of spans up to 100 ft., 1800 lbs., per lineal ft. of each car track and 80 lbs. per sq. ft. of the remaining floor surface, with a minimum live load of 2000 lbs. per Un. ft. of bridge; for spans of 200 ft. and over, 1200 lbs. per Uneal ft. of each car track and 60 lbs. per sq. ft. of the remaining floor surface with a minimum live load of 1500 lbs. per lineal foot of bridge; proportionally for intermediate spans. Heavy country bridges. 47. Class C. Heavy Country Bridges. For the floor and its supports, on any part of*the roadway, a concentrated load of 15 tons on two axles 10 ft. centers and 6 ft. center to center of wheels with f of the load on one axle, and on each street car track a concentrated load of 24 tons on two axles 10 ft. centers, with f of the load on one axle, and upon the foot walks 100 lbs. per sq. ft. For the trusses of a span up to 100 ft. 1200 lbs. per lineal ft. of each car track and 80 lbs. per sq. ft. of the remaining floor surface with a minimum Uve load of 1600 lbs. per lineal foot of bridge; for spans of 200 ft. and over, 1000 lbs. per Uneal ft. of each car track and 60 lbs. per sq. ft. of remaining floor surface, with a minimum live load of 1200 lbs. per lineal ft. of bridge; proportionally for intermediate spans. Country bridges. 48. Class D. Ordinary Country Bridges. For the floor and its sup- ports on any part of the roadway a concentrated load of 10 tons on two axles 10 ft. centers and 6 ft. center to center of wheels with f of the load on one axle. For the trusses of spans up to 100 ft. 80 lbs. per sq. ft. of floor surface with a minimum live load of 1200 lbs. per lineal ft. of bridge; for spans of 200 ft. and over, 60 lbs. per sq. ft. of floor surface, with a minimum Uve load of 1000 lbs. per Uneal ft. of bridge; proportionaUy for intermediate spans. Distribution. 49. Concentrated loads appUed through paving or macadam may be assumed to be distributed at an angle of 30° with the vertical. Street car rails may be assumed to distribute their loads over three ties. The width of tires on the wheels in the above loadings may be assumed at as many inches as the load on two axles is in tons. Isolated loads on concrete slabs 234 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES may be assumed to be distributed over a width equal to twice the depth of the slab, in excess of the actual width of the load on top of the slab. (41) Impact. 50. To compensate for the effect of impact and vibration the dynamic increment of the live load shall be added to the maximum computed live load stresses and shall be computed by the following formula: '-( I in which 300 +L/ /= the djmamic increment , /S=the maximum computed static live load stress L =the length of load necessary to produce the maximum static stress. Swing bridges. 51. For swing bridges and other movable structures the dead load stresses during motion shall be increased 25% as a djmamic increment. Wind loads. 52. To provide for wind and vibrations, the top lateral bracing in deck bridges, and the bottom lateral bracing in through bridge, shall be pro- portioned to resist a lateral force of 300 pounds for each lineal foot of the span; 150 pounds of this to be treated as a moving load. (Ill) The bottom lateral bracing in deck bridges, and the top lateral bracing in through bridges shall be proportioned to resist a lateral force of 150 pounds for each lineal foot. (Ill) For spans exceeding 300 feet, add in each of the above cases 10 pounds additional for each additional 30 feet. 53. In trestle towers the bracing and columns shall be proportioned to resist the following lateral forces, in addition to the stresses from dead and live loads: On the trusses loaded or unloaded the lateral pressures specified above; and a lateral pressure of 100 pounds for each vertical foot of the trestle bents. Temperature. 54. In steel structures variation in temperature to the extent of 150 degrees Fahr. shall be provided for. Centrifugal force. 55. For electric railways on curves the additional effects due to the centrifugal force of cars single or coupled shall be considered as a Uve load. It will be assumed to act 5 feet above base of rail, and will be computed for a speed of 60 — 2|Z) miles per hour, where Z)= degree of curve. Traction. 56. The stresses produced in the bracing of the trestle towers, in any members of the trusses, or in the attachments of the girders or trusses to SPECIFICATIONS FOR BEIDGE SUPERSTRUCTURES 235 their beaxinga, by suddenly stopping the maximum electric car trains on any part of the work must be provided for; the coefficient of friction of the wheels on the rails being assumed as 0.20. UNIT STRESSES AND PROPORTION OF PARTS 57. All parts of structures shall be so proportioned that the sum of the maximum stresses produced by the foregoing loads shall not exceed the fol- lowing amounts in pounds per sq. in. except as modified in paragraphs 66 to 70: Steel tension. 58. Axial tension on net section 16,000 Compression. 59. Axial compression on gross section of columns 16,000-70 — r With a maximum of 14,000 Where L is the length of the member in inches and r is the least radius of gyration in inches. Bending. 60. Bending: on extreme fibers of rolled shapes, built sec- tions, girders and steel castings; net section 16,000 On extreme fibers of pins 24,000 On extreme fibers of timber, yellow pine or white oak 1,800 White pine or spruce 1,500 Shearing. 61. Shearing: shop driven rivets and pins 12,000 Field driven rivets and turned bolts 10,000 Plate girder webs; gross section 10,000 , Bearing. 62. Bearing: shop driven rivets and pins 24,000 Field driven rivets and turned bolts 20,000 Expansion rollers; per Uneal inch OOOi Where d is the diameter of the roller in inches. On masonry 600 Concrete. 63. Unit stresses for concrete and reinforced concrete, see General Specifications for Concrete and Reinforced Concrete Structures of the State Highway Department. Limiting lengths. 64. The unsupported lengths of main compression members shall not exceed 120 times their least radius of gyration, and those for wind and sway bracing 140 times their least radius of gyration. 236 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 65. The lengths of riveted tension members in horizontal or inclined positions shall not exceed 200 times their radius of gyration about the hori- zontal axis. The horizontal projection of the unsupported portion of the member is to be considered as the effective length. Alternate stresses. 66. Members subject to alternate stresses of tension and compression shall be proportioned for the stresses giving the largest section. If the alternate stresses occur in succession during the passage of one series of loads, as in stiff counters, each stress shall be increased by 50% of the smaller. This increased stress shall be used in proportioriing the connections. Counters. 67. Wherever the hve and dead load stresses are of opposite character, only two-thirds of the dead load stress shall be considered as effective in counteracting the hve load stress. 68. For bridges carrying electric or motor cars counters shall be pro- vided and proportioned so that a future increase of 25% in the specified live load shall not in any case increase the allowed unit stress more than 25 per cent. Combined stresses. 69. Members subject to both axial and bending stresses shall be pro- portioned so that the combined fiber stresses will not exceed the allowed axial stress. (93) (112) Wind stresses. 70. For stresses produced by longitudinal and lateral or wind forces combined with those from hve and dead loads and centrifugal force, the unit stress may be increased 25 per cent over those given above; but the section shall not be less than required for live and dead loads and centrifugal force. (52) (53) Net section at rivets. 71. In proportioning tension members the diameter of the rivet holes shall be taken 1-8 in. larger than the nominal diameter of the rivet. 72. In proportioning rivets the nominal diameter of the rivet shall be used. Net section at pins. 73. Pin-connected riveted tension members shall have a net section through the pin-hole at least 25% in excess of the net section of the body of the member, and the net section back of the pin-hole, parallel with the axis of the member, shall not be less than the net section of the body of the member. Rolled beams. 74. Rolled beams shall be proportioned by their moments of inertia. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 237 Plate girders. 75. Plate girders shall be proportioned either by the moment of inertia of their net section; or by assuming that the flanges are concentrated at their centers of gravity; in which case one-eighth of the gross section of the web, if properly spliced, may be used as flange section. The thickness of web plates shall not be less than 1/240 of the unsupported distance between flange angles. 76. The gross section of the compression flanges of plate girders shall not be less than the gross section of the tension flanges, nor shall the stress per sq. in. in the compression flange of any beam or girder exceed 16,000 — 200( — ), where L is the unsupported length and 6 the width of the flange. Flange rivets. 77. The flanges of plate girders shall be connected to the web with a suflicient number of rivets to transfer the total shear at any point in a distance equal to the effective depth of the girder at that point, combined with any load that is applied directly to the flange. DETAILS OF DESIGN 78. All parts shaU be so designed that the stresses coming upon them can be accurately calculated. Camber. 79. All truss bridges shall be cambered an amount equal to one-six hundredth (1/600) of the span, and plate girders one-twelve hundredth (1/1200) of the span unless otherwise specified. Open sections. 80. Structures shall be so designed that all parts will be accessible for inspection, cleaning and painting. Pockets. 81. Pockets or depressions which would hold water shall have drain holes, or be filled with water-proof material. Symmetry. 82. Main members shall be so designed that the center of gravity will be as nearly as practicable in the center of the section, and the centers of gravity of intersecting main members of trusses shall meet at a common point. Counters. 83. Rigid counters are preferred; and where subject to reversal of stress shall preferably have riveted connections to the chords. Adjustable counters shall have open turnbuckles. 238 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES Coimections. 84. The strength of connections shall be suflBcient to develop the full strength of the member, even though the computed stress is less, the kind of stress to which the member is subjected being considered. Minimum thickness. 85. For main members and their connections no material shall be used of a less thickness than 5/16 of an inch; and for laterals and their connec- tions, no material less than J of an inch in thickness; except for lining or filUng vacant spaces. No bars shall be used with a net area less than f of one square inch. (93) Riveting. 86. The pitch of rivets in all classes of work shall never exceed six inches, or sixteen times the -thinnest outside plate, nor be less than three diameters of the rivet. 87. The minimum distance from the center of any rivet hole to a sheared edge shall be If in. for f in. rivets and 1| in. for i in. rivets, and to a rolled edge IJ in. and 1| in. respectively. The maximum distance from any edge shall be eight times the thickness of the plate, but shall not exceed 6 in. 88. The rivets used shall generally be j and | inch for the main mem- bers and the floor system. Long rivets. 89. Rivets carrying calculated stress and whose grip exceeds four diameters shall be increased in number at least one per cent for each addi- tional 1/16 in. of grip. Indirect connection. 90. Rivets carrying stress where the parts connected are not in direct contact, shall be increased in number over the number theoretically required, 25% for each intervening plate. Bolts. 91. When members are connected by bolts the holes must be reamed parallel and the bolts turned to a driving fit. All bolts must be of neat lengths, and shall have a washer under the heads and nuts where in con- tact with wood. Bolts must not be used in place of rivets, except by special permission. All nuts must be of hexagonal shape. 92. The pitch of rivets at the ends of built compression members shall not exceed four diameters of the rivets, for a length equal to one and one half times the maximum width of member. Compression members. 93. In compression members the metal shall be concentrated as much as possible in the webs and flanges. The thickness of each web shall not be less than one-thirtieth (1/30) of the distance between its connections to the flanges. Cover plates shall have a thickness not less than one forty- SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 239 eighth (1/48) of the distance between rivet lines and they shall not be thicker than | inch except when necessary to resist bending stresses or to comply with the above requirement. (85) Tie plates. 94. The open sides of compression members shall be provided with lattice and shall have tie plates as near each end as practicable. Tie plates shall be provided at intermediate points where the lattice ia interrupted. In main members the end tie plates shall have a length not less than the distance between the lines, of rivets connecting them to the flanges, and intermediate ones a length not less than one-half this distance. Their thickness shall not be less than one-forty-eighth of the same distance. Lattice. 95. The latticing of compression members shall be proportioned to transmit in a distance equal to one-fourth (J) the length of the column, the allowance for flexure provided in the column formula of paragraph 69 by the term 70—, and also any shear due to transverse loading. The thick- r ness shall not be less than one-fortieth (1/40) of the distance between rivets for single lattice or one sixtieth for double lattice with riveted intersections. The minimum widths of bars shall be If inches or one-sixth (1/6) the greater width of the members. Lattice bars with at least two rivets in each end shall be used for flanges 5 inches and over in width. 96. The inclination of lattice bars with the axis of the member shall not be less than 45 degrees, and when the distance between rivet Unes in the flanges is more than 15 in., if single rivet bars are used, the lattice shall be double and riveted at the intersections. 97. Lattice bars shall be so spaced that the portion of the flange included between their connections shall be as strong as the member as a whole. Faced joints. 98. Abutting joints in compression members when faced for bearing shall be spliced on four sides sufiiciently to hold the connecting members accurately in place. All other joints in riveted work, whether in tension or compression, shall be fully spliced. Pin plates. 99. Where necessary, pin-holes shall be reinforced by plates, some of which must be the full width of the member so the allowed pressure on the pins shall not be exceeded, and so the stresses shall be properly distributed over the full cross-section of the members. These reinforcing plates must contain enough rivets to transfer their proportion of the bearing pressure, and at least one plate on each side shall extend not less than six inches beyond the edge of the batten plates. 100. Where the ends of compression members are forked to connect to the pins, the aggregate compressive strength of these forked ends must equal the compressive strength of the body of the members. 240 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES Pins. 101. Pins shall be long enough to insure a full bearing on all the parts connected upon the turned body of the pin. They shall be secured by chambered nuts or be provided with washers if soUd nuts are used. The screw ends shall be long enough to admit of burring the threads. 102. Members packed on pins shall be held against lateral movement. Expansion. 103. Provision for expansion to the extent of I inch for each 10 ft., shall be made for all steel structures. Efficient means shall be provided to prevent excessive motion at any one point. End bearings. 104. All bridges over 100 feet span shall have hinged bolsters on both ends, and at one end nests of turned friction rollers or rockers running between planed surfaces. These rollers shall not be less than 3f inches in diameter for spans of 100 feet or less, and for greater spans this diameter shall be increased in proportion of 1 inch for each 100 feet additional. The rollers and bearings must be so arranged that they can be readily cleaned and so that they will not hold water. 105. Bridges less than 100 feet span shall be secured at one end to the masonry, and the other end shall be free to move longitudinally upon smooth surfaces. (160) 106. Where two spans rest upon the same masonry, a continuous plate, not less than f inch thick, shall extend under the two adjacent bear- ings, or the two bearings must be rigidly tied together. Wall plates. 107. Wall plates may be cast or built up; and shall be so designed as to distribute the load uniformly over the entire bearing. They shall be secured against displacement. Anchors. 108. Anchor bolts for viaduct towers and similar structures shall be long enough to engage a mass of masonry the weight of which is at least one and one-half times the uplift. (53) 109. Bridges on an inclined grade without pin shoes shall have the sole plates beveled so that the masonry and expansion surfaces may be level. Floor beams. 110. Floor beams shall preferably be square to the trusses or girders. They shaU be riveted directly to the girders or trusses or may be placed on top of deck bridges. Bracing. 111. Lateral, longitudinal and transverse bracing in all structures shall preferably be composed of rigid members. 112. All through bridges shall have latticed portals, of approved design, at each end of the span, connected rigidly to the end posts and top chords. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 241 They shall be as deep as the specified head-room will allow and provision shall be made in the end posts for the bending stresses from wind pressure. (93) (95) 113. When the height of the trusses exceeds 20 ft. an approved sys- tem of overhead diagonal bracing shall be attached to each post and to ^he top lateral struts. 114. Knee braces shall be placed at each intermediate panel point, and connected to the vertical posts and top lateral struts, for trusses 20 feet and less in depth. 115. Pony trusses and through plate or lattice girders shall be stayed by knee braces or gusset plates attached to the top chords at the ends and at intermediate points, and attached below to the cross floor beams or to the transverse struts. 116. All deck girders shall have transverse braces at the ends. All deck bridges shall have transverse bracing at each panel point. This bracing shall be proportioned to resist the unequal loading of the trusses. Diaphragms. 117. At aU points where floor beams, portals or other bracing connect with the posts of chords, proper diaphragms must be inserted to distribute the loads and forces over the full section of these posts or chords. 118. All members of the web, lateral, longitudinal or sway systems must be securely fastened at their intersections to prevent sagging and ratthng. Flange plates. 119. Where flange plates are used, one cover plate of the top flange shall extend the whole length of the girder. Stifieners. 120. There shall be web stiffeners, generally in pairs, over bearings, at points of concentrated loading, and at other points where the thickness of the web is less than one-sixtieth (1/60) of the clear distance between the flange angles. The distance between the stiffeners shall not exceed the clear distance between flange angles or a maximum of six feet. 121. Stiffeners at the ends and at points of concentrated loading shall be proportioned by the formula of paragraph 59, the effective length being assumed as one-half the depth of the girders. End stiffeners and those under concentrated loads shall be on fillers and have their outstanding legs as wide as the flange angles will allow and shall fit tightly against them. Intermediate stiffeners may be offset or on fillers and their outstanding legs shall not be less than 1/40 the depth of the girders plus 2 inches. 122. The webs of plate girders must be spliced at all joints by plates on each side of the web. The splice must be proportioned to transmit the resultant of the shear and the portion of the bending moment taken by the web. 242 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES Flange plates. 123. In girders with flange plates, at least one-half of the flange section shall be angles or else the largest sized angles must be used. Flange plates must extend beyond their theoretical length two rows of rivets at each end Lattice trusses. 124. In- lattice girders and trusses the web members must be double, and connect symmetrically to the webs of the chords. The use of plates or flats alone, for tension members must be avoided where it is possible; in lattice trusses, the counters, suspenders and two panels of the lower chord, at each end, must be latticed; all other tension members must be coimected by batten plates or latticed. Eye-bars. 125. The eye-bars composing a member shall be so arranged that adjacent bars shall not have their surfaces in contact; they shall be as nearly parallel to the axis of the truss as possible, the maximum inclination of any bar being limited to one inch in 16 ft. 126. In special cases, where floor beam hangers may be permitted, they must be rigidly attached to the trusses, and be so arranged as to stay the floor beams firmly against rotation or end motion. Pony trusses. 127. Pony trusses shall be riveted structures, with double webbed chords, and shall have all web members latticed or otherwise effectively stiffened. Buckled plates. 128. Buckled plates miist be firmly riveted to the supporting beams and be spUced at all free edges. Preferably they will be made in continuous sheets of panel lengths. They may be pressed or formed without heating. (19) 129. A buckled-plate floor, as specified, may be considered as the required lateral system of bracing at the floor level. WORKMANSHIP 130. All parts forming a structure shall be built in accordance with approved drawings. The workmanship and finish shall be equal to the best practice in modern bridge works. Material arriving from the mills shall be protected from the weather and shall have clean surfaces before being worked in the shops. Straightening. 131. Material shall be thoroughly straightened in the shop, by methods that will not injure it, before being laid off or worked in any way. Finish. 132. Shearing and chipping shall be neatly and accurately done and all portions of the work exposed to view neatly finished. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 243 Rivets. 133. The size of rivets called for on the plans shall be understood to mean the actual size of the cold rivet before heating. Reaming. 134. Steel may be used in tension without reaming of punched holes up to f inch in thickness and may be used in compression without reaming up to f inch in thickness. Punching. 135. Where reaming is not required the diameter of the punch shall not be more than 1/16 inch greater than the diameter of the rivet, nor the diameter of the die more than f inch greater than the diameter of the punch. 136. Punching shall be accurately done. Drifting to enlarge imfair holes wiU not be allowed. If the holes must be enlarged to admit the rivet, they shall be reamed. Poor matching of holes will be cause for rejection. 137. Where sub-punching and reaming are required the punched holes shall be at least 1/16 inch smaller than the nominal diameter of the rivet and the holes shall then be reamed to a diameter not more than 1/16 inch greater than the nominal diameter of the rivet. 138. Where reaming is required it shall be done after the pieces form- ing one built member are assembled and firmly bolted together. No inter- change of reamed parts wiU be permitted. 139. Reaming shall be done with twist drills and without using any lubricant. 140. The outside burrs on reamed holes shall be removed to the extent of making a 1/16 in. fillet. Assembling. 141. Riveted members shaU have all parts well pinned up and firmly drawn together with bolts, before riveting is commenced. Contact sur- faces are to be painted. (163) Lattice bars. 142. Lattice bars shall have neatly rounded ends, unless otherwise called for. Stiffeners. 143. Stiffeners shall fit neatly between flanges of girders. Where tight fits are called for, the ends of the stiffeners shall be faced and shall be brought to a true contact bearing with the flange angles. Fillers. 144. Web splice plates and fillers under stiffeners shall be cut to fit within I in. of flange angles. Web plates. 145. Web plates of girders which have no cover plates, shall be flush with the backs of angles or project above the same not more than J in. 244 SPECIFICATIONS FOE BEIDGE SUPERSTRUCTUKES unless otherwise called for. When web plates are spliced, not more than J in. clearance between ends of plates will be allowed. Floor beams and stringers. 146. The main section of floor beams and stringers shall be milled to exact length after riveting and the connection angles accurately set flush and true to the milled ends. Riveting. 147. Rivets shall be uniformly heated to a light cherry red heat in a gas or oil furnace so constructed that it can be adjusted to the proper tem- perature. They shall be driven by pressure tools wherever possible. Pneumatic hammers shall be used in preference to hand driving. 148. Rivets shall look neat and finished, with heads of approved shape, fuU and of equal size. They shall be central on shank and grip the assembled parts firmly. Recupping and calking will not be allowed. Loose, burned or otherwise defective rivets shall be cut out and replaced. In cutting out rivets great care shall be taken not to injure the adjacent metal. If neces- sary, they shall be drilled out. 149. The several pieces forming one built member shall bfi straight and fit closely together, and finished members shall be free from twists, bends or open joiats. Joints. 150. Abutting joints shall be cut or dressed true and straight and fitted close together, especially where open to view. In compression joints depend- ing on contact bearing, the surfaces shall be truly faced, so as to have even bearings after they are riveted up complete and when perfectly aligned. Eye-bars. 151. Eye-bars shall be straight and true to size, and shall be free from twists, folds in the neck or head, or any other defect. Heads shall be made by upsetting, rolling or forging. Welding wiU not be allowed. The forms of heads will be determined by the dies in use at the works where the eye- bars are made, if satisfactory to the engineer, but the manufacturer shall guarantee the bars to break in the body when tested to rupture. The thickness of head and neck shall not vary more than 1/16 in. from that specified. 152. Before boring, each eye-bar shall be properly annealed and care- fully straightened. Pin-holes shall be in the center line of bars and in the center of heads. Bars of the same length shall be bored so accurately that, when placed together, pins 1/32 in. smaller in diameter than the pin-holes can be passed through the holes at both ends of the bars at the same time without forcing. Pin-holes. 153. Pin-holes shall be bored, true to gages, smooth and straight; at right angles to the axis of the member and parallel to each other, unless SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 245 otherwise called for. The boring shall be done after the member is riveted up. 154. The distance center to center of pin-holes shall be correct within 1/32 in., and the diameter of the holes not more than 1/50 in., larger than that of the pin, for pins up to 5 in., in diameter and 1/32 in., for larger pins. Pins and rollers. 155. Pins and rollers shall be accurately turned to gages and shall be straight and smooth and entirely free from flaws. Screw threads. 156. Screw threads shall make tight fits in the nuts and shall be IT. S. standard, except above the diameter of If in., when they shall be made with six threads per inch. Annealing. 157. Eye-bars, all forgings and any pieces which have been partially heated or bent cold must be wholly annealed. Crimped stiifeners need not be annealed. 158. Steel castings shall be free from large or injurious blowholes and shall be annealed. Welds. 159. Welds in steel will not be allowed. Bed plates. 160. Expansion bed plates shall be planed true and smooth. Cast wall plktes shall be planed top and bottom. The finishing cut of the planing tool shall be fine and correspond with the direction of expansion. Pilot nuts. 161. Pilot and driving nuts shall be furnished for each size of pin, in such numbers as may be ordered. PAINTING Cleaning. 162. Steel work, before leaving the shop, shall be thoroughly cleaned and given one good coating of pure linseed oil, or such paint as may be called for, well worked into all joints and open spaces. Contact surfaces. 163. In riveted work, the surfaces coming in contact shall each be painted before being riveted,together. Inaccessible surfaces. 164. Pieces and parts which are not accessible for painting after erection, including tops of stringers, eye-bar heads, ends of posts and chords, etc., shall have an additional coat of paint before leaving the shop. 246 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 166. Painting shall be done only when the surface of the metal is per- fectly dry. It shall not be done in wet or freezing weather, unless protected under cover. Machined surfaces. 166. Machine-finished surfaces shall be coated with white lead and tallow before shipment or before being put out into the open air. Buckled plates. 167. Buckled plates shall have a thick and thorough coating of red lead and linseed oil before shipment. AU rivet heads and scarred places shall also be coated with this red lead as soon as practicable after erection. Field Painting. 168. After the steel work is erected it shall be thoroughly cleaned of all dirt, rust, scale, or grease and given two additional coats of paint as specified below. The first field coat is to be pure red lead and pure raw hnseed oil mixed in the proportion of 20 lbs. of lead to one gallon of oil. The second coat is to be a pure graphite, ground in pure raw linseed oil of color to be selected by the County Commissioners. The first coat must be thoroughly dry before the second coat is applied. ERECTION 169. The contractor, unless it be otherwise specified, shall furnish all staging and false work, shall erect and adjust all the metal work, and put in place all floor timbers, guards, etc., complete. Contractor's responsibility. 170. The contractor shall so conduct all his operations as not to inter- fere with the work of other contractors, or close any thoroughfare by land or water, except by written consent of the County Commissioners or other proper aiUhority. 171. The contractor shall assume all risks of accident to men or material prior to the acceptance of the finished structure. The contractor must also remove all false work, piling and other obstructions, or unsightly material produced by his operations. INSPECTION 172. The manufacturer shall furnish all facilities for inspecting and testing the weight and quality of workmanship at the shop where material is manufactured. He shall furnish a suitable testing machine for testing full-sized members, if required. 173. The purchaser shall be notified well in advance of the start of the work ia the shop, in order that he may have an inspector on hand to inspect material and workmanship. 174. When an inspector is furnished by the purchaser, he shall have fuU access, at all times, to all parts of the shop where material under his inspection is being manufactured. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 247 175. The inspector shall stamp each piece accepted with a private mark. Any piece not so marked may be rejected at any time and at any stage of the work. If the inspector, through an oversight or otherwise, has accepted material or work which is defective or contrary to the speci- fications, this material, no matter in what state of completion, may be rejected by the purchaser. 176. Complete copies of shipping invoices shall be furnished to the purchaser with each shipment. These shall show the scale weights of individual pieces. Final tests. 177. Before the final acceptance the Engineer may make a thorough test by passing over each structure the specified loads or their equivalent, or by resting the maximum load upon the structure for twelve hours. After such tests the structures must return to their original positions without showing any permanent change in any of their parts. MATERIAL Steel. 178. All steel must be made by the open hearth process. The phos- phorus must not exceed 0.08 of one per cent for steel made by the acid method, or 0.04 for steel by the basic method. 179. The steel must be uniform in character for each specified kind. The finished bars, plates and shapes must be free from injurious seams or flaws, cracks on the faces or corners, or other defects, and have a clean, smooth finish. No work shall be put upon any steel at or near the blue temperature or between that of boiling water and of ignition of hard-wood sawdust. 180. The tensile strength, elastic Umit and ductility shall be deter- mined by samples cut from the finished material after rolling. The sam- ples to be at least 12 inches long, and to have a uniform sectional area not less than J square inch. 181. Material which is to be used without annealing or further treat- ment is to be tested in the condition in which it comes from the roUs. When material is to be annealed or otherwise treated before use, the specimen representing such material is to be similarly treated before testing, for ten- sile strength. The elongation shall be measured on an original length of 8 inches. At least two test pieces shall be taken from each melt or blow of finished material, one for tension and one for bending. 182. All samples or full-sized pieces must show uniform fine grained fractures of a blue steel-gray color, entirely free from fiery luster or a blackish cast. Structural steel. 183. Structural steel shall have an ultimate strength, when tested in samples of the dimensions above stated, of 60,000 to 70,000 pounds per square inch, an elastic limit of not less than one-half of the ultimate strength, and a minimum elongation of 20 per Cent, in 8 inches. But for eye-bar 248 SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES material, not over 20 per cent, of the material must run below 62,000 or above 68,000 pounds per square inch. Steel for pins may have a minimum elonga- tion of 15 per cent. 184. Before or after heating to a low cherry red and cooling in water at 82 degrees Fahr., this steel must stand bending to a curve whose inner radius is one and a half times the thickness of the sample, without cracking. Eye-bars. 185. Eye-bar material, 1| inches and less in thickness, shall on te-st pieces cut from finished material, fill the above requirements. For thickness greater than IJ inches, there will be allowed a reduction in the percentage of elongation of 1 per cent, for each i of an inch increase of thickness, to a minimum of 18 per cent. No bars over 2 inches in thickness will be used, except by special permission. 186. Full-sized eye-bars shall show not less than 10 per cent, elonga- tion ih the body of the bar, and an ultimate strength not less than 56,000 pounds per square inch. Should a bar break in the head, but develop 10 per cent, elongation and the ultimate strength specified, it shall not be cause for rejection, provided that not more than J of the total number of bars tested break in the head. (151) 187. Full-sized material for eye-bars shall bend cold 180° to a curve, whose inner radius is equal to the thickness of the material, without fracture on the outside of the bend. Pins. 188. Pins over 7 inches in diameter shall be forged. Blooms for pins shall have at least three times the sectional area of the finished pins. Rivet steel. 189. Rivet steel shall have an ultimate strength of 48,000 to 58,000 pounds per square inch, an elastic limit not less than one-half the ultimate strength and a minimum elongation of 23 per cent, in 8 inches. 190. The steel for rivets must, under the above bending test, stand closing sohdly together without sign of fracture. When nicked and bent around a bar of its own diameter it shall break gradually and give a fine, uniform, silky fracture. Variation in weight. 191. A variation of cross-section or weight in the finished members of 2J per cent, from the specified size may be cause for rejection. 192. Steel castings will be used for drawbridge wheels, track segments and gearing. They must be true to form and dimensions, of a workman- like iSnish and free from injurious blowholes and defects. All castings must be annealed. M When tested in specimens of uniform sectional area of at least i square inch for a distance of two inches, they must show an ultimate strength of not less than 67,000 pounds per sq. in., an elastic limit of one-half the ulti- mate strength, and an elongation in 2 inches of not less than 10 per cent. SPECIFICATIONS FOR BRIDGE SUPERSTRUCTURES 249 The metal must be uniform in character, free from hard or soft spots, and be capable of being properly tool finished. 193. Except where cast steel or chilled iron is required, all castings must be of tough, gray iron, free from cold shuts or injurious blowholes, true to form and thickness, and of workmanlike finish. Sample pieces, 1 inch square cast from the same heat of metal in sand moulds, shall be capable of sustaining, on a clear span of twelve inches, a central load of 2,400 pounds, when tested in the rough bar. A blow from a hammer shall produce an indentation on a rectangular edge of the casting without flaking the metal. INDEX Adding Machines Angles — ^maximum lengths Bearing plates for plate girder Bending of chords due to weight Bolsters for plate girder Books of reference Bottom Lateral Bracing Box girders Building construction Buildings with columns Built tension members Butt joints Button head rivets Calculation of joists Calculation of pins Camber Chords — ^Design of — ^Location of pins Classes of structural steel work Clearances Columns — Mill buildings with — stresses in Compression and bending combined Compression members — Allowance for rivet holes . — Design of —Width of Contracts and proposals Corrugated iron or steel Countersunk rivets Countersunk rivet values Dead load — for plate girder bridge — of truss bridges Dead loads — Roof Art. Page 5 9 44 100 44 109 50 123 44 109 83 200 62 152 34 72 26 48 32 61 49 117 14 22 9 16 78 186 67 . 160 68 167 57 136 70 171 1 1 85 209 50 119 32 61 32 •62 50 119 50 119 15 24 57 133 57 135 3 2 24 45 9 16 17 29 63 125 44 91 48 117 27 50 251 252 INDEX Art. Page Deck plate girder bridge design 44 90 estimate 44 110 stress sheet 44 112 Depth of truss 54 125 Depth of trusses 47 115 Design of chords ~ 57 136 compression members 57 133 end posts 68 140 deck plate girder bridge , . . . 44 90 floor beam 60 146 mill building 29 53 pin-connected bridge 52 125 portal 59 144 riveted connections 17 28 roof purlins 30 54 roof truss 31 57 a stringer 43 84 tension members 56 129 Designing and estimating 4 3 Designing and estimating '. Chap. I 1 Detail drawings 65 159 Details — Duplication of 85 207 floor beams 72 177 hip joint 70 171 pin-connected bridges Chap. VI 159 a riveted tension member 69 168 Distribution of loads 77 186 Dolly 11 19 Drafting department 82 195 Draftsman's equipment 83 196 Drawing boards 82 196 instruments 83 197 pencils 83 198 room light 82 196 table 82 196 Drawings for roof trusses 33 64 Drawing of roof truss . . 70 Drift pins 10 18 Driving rivets 11 18 Eccentricity of pins in chord members 50 123 Economic depth of girders 38 76 girders 43 85 girders 44 95 trusses 47 115 Effective depth of plate girders 37 76 End floor beam 60 148 End posts — Design of 58 140 INDEX 253 Art. Page End posts — ^Lacing 71 176 Equivalent loads 48 116 Erection 81 194 Erection and manufacture Chap. VIII 193 Estimate for deck plate girder bridge 44 110 for pin connected bridge 64 154 of weight of stringers 43 89 Estimates of cost 4 3 Estimates — Forms of 4 5 Estimating and designing 4 3 Estimating and designing Chap. I 1 —Order of 6 9 — Order for highway bridges 6 11 — Order for railway bridges 6 10 — Order for steel buildings 6 12 Eye bars 49 117 Falsework 81 194 Field riveting 81 195 Field rivet values 17 29 Flange plates of plate girders 44 96 riveting in plate girders 41 80 riveting in plate girders 43 87 riveting in plate girders 44 98 sections 34 72 splices in plate girders 42 83 splices in plate girders 44 100 Flanges of girders 37 75 girders 43 86 girders 44 95 Floor beams — Details 72 177 —Details 72 180 —Design 60 146 Floor — Design of, for bridge 44 90 Flooring materials 74 183 creosoted wood block floor 74 184 macadam ,74 184 plank floors with steel joists 74 183 Freight 89 218 Gallows frame 81 194 General plans ■ • - 8 14 Girders Chap. IV 72 — ^Economic depth 38 76 —Effective depth 37 76 —The flanges 37 75 — Flange riveting 40 80 — Flange splices 42 83 — Maximum lengths 34 72 254 INDEX Art. Page Girders — Moment of resistance 35 73 — Shear distribution 36 74 — Stiff eners 39 73 — Stresses 35 73 — Stresses 43 gg — Stresses 44 93 —The web 36 73 — ^Web splices 40 79 Grip of rivets ,. 9 IQ Heating rivets 11 19 Highway bridges Chap. VII 182 — artistic effects in 73 183 Calculation of joists 78 168 Distribution of load 77 186 Flooring materials 74 183 Impact 76 185 Kinds of bridges 73 182 —loads 75 184 — Tsrpes of steel highway bridges 79 191 Hip joint — Detail of 70 174 pin 67 171 Impact .-. 76 185 Inertia — Moment of 57 138 Inspection 91 224 Intermediate posts — Lacing 71 177 Jack rafters 26 48 Joints — Butt 14 22 — Lap '. ; 14 22 Kinds of Highway Bridges 73 182 Lacing of compression members 50 122 compression members 71 173 Lap joints 14 22 Laterals — Bottom 62 152 Lateral bracing of plate girders 44 104 stringers 43 89 Lateral systems 51 124 Laterals— Top 61 151 Loads 48 116 Loads for highway bridges 75 184 Loads— Roof 27 50 Location of pins in top chord and end posts 70 171 Macadam floor 74 184 Manufacture and erection Chap. VIII 193 Materials 90 219 Material orders 84 200 Mill Buildings Chap. Ill 45 —Design of a 29 53 INDEX 255 Art. Page Moment in deck plate girder 44 92 Moment of inertia 57 138 Moment of resistance of plate girder 35 73 Net sections of tension members 19 35 Order of estimating 6 9 highway bridges 6 11 railway bridges 6 10 steel buildings 6 12 Order of procedure for a pin connected bridge 86 211 for plate girder bridge 87 213 Ordering material 84 200 Packing 66 160 Packing at various joints 67 166 Panel lengths 47 115 Pins 66 159 Pins— Calculation of 67 160 Pin-connected bridges Chap. V 115 —Design of 52 125 details of Chap. VI 159 —Estimate 64 158 — Order of procedure for 86 211 stresses 55 127 — Stress sheet 64 158 Pins — ^Location in top chord and end posts 70 171 Pin plates 18 31 Pin plates 18 30 Pitch ot rivets defined 13 21 Pitch of roofs 24 46 Plank floor on steel joists 74 183 Plans — General 8 14 Plans— Show 8 15 Plate girder bridges ^ Chap. IV 72 Plate girder bridges — Order of procedure 87 213 Plate girder design 44 90 Plate girders — ^Economic depth 38 76 — Economic depth 43 85 — Economic depth 44 95 —Effective depth 37 76 —Effective depth 43 87 —Effective depth 44 95 —Flanges 37 75 —Flanges 43 86 — Flanges 44 95 — Flange plates 44 96 — Flange riveting 41 80 — Flange riveting 43 87 — Flange riveting 44 98 256 INDEX Plate girders — Flange splices — Flange splices — ^Highway design — Lateral bracing — Maximum moment — Stiffeners — Stiffeners — Stiffeners — Stresses — Stresses — Stresses —Web —Web —Web — Web splices — ^Web splices Plates — Sizes of Pony trusses — design for highway Portal Bracing. Proposals and contracts Purlins — arrangement of, at ridge Radius of gyration Rafter design, for a roof truss Reaming Rivet holes — ^Allowance for in compression members in tension members Rivet pitch in flanges of girders Rivet spacing Rivet values — Cooper's Riveted joints — ^Alternating stresses — ^Alternating stresses — Assumption made in design of — Design of — ^Examples — Friction in — ^Kinds of — Manner of failure — Requirements for good — Slip in Riveted tension member details Riveted truss bridges — Design, highway bridge Riveting Chap. — Design of joints in a roof truss Art. Page 42 83 44 100 190 44 104 44 92 39 78 43 88 44 100 35 73 43 86 44 92 36 73 43 86 44 95 40 79 44 101 84 202 47 116 189 69 144 3 2 30 53 30 56 57 135 31 60 10 17 10 17 15 24 19 35 41 81 85 208 72 178 15 25 16 28 15 24 17 28 18 30 15 25 14 22 17 28 16 27 15 25 69 168 86 213 192 II 16 33 64 INDEX 257 Art. Page Riveting of flanges of plate girders 41 80 of flanges of plate girders 43 87 of flanges of plate girders 44 98 machines 11 19 of pin plates 18 30 of pin plates 18 31 — Theory of 15 23 Rivets — American Bridge Co.'s standard 9 16 — Bending in 15 26 — Button heads 9 16 — Conventional signs for 21 43 — Cooper's rivet values 72 178 — Countersunk 9 16 — Dimensions of 9 16 — Driving 11 18 — ^Field values 17 29 —Grip 9 16 — ^Heating 11 19 — ^Initial tension in 15 * 25 — ^Length required 9 16 — Shape of heads 9 16 — Proper sizes 12 20 —Spacing of 13 20 — ^Values of countersunk 17 29 — Working stresses 17 28 Rollers 63 153 Roofs 22 45 — Building construction 26 48 — Construction 23 45 — Coverings 24 45 —Dead load 27 50 —Design of 31 57 loads 27 50 pitch for various coverings 24 46 Roof purlins 30 53 — design of 30 64 rafters 23 45 — sheathing 23 45 — sheeting 23 45 truss drawings 33 64 truss drawing 33 70 trusses — Types of 25 46 Scales 83 198 for roof truss drawing 33 67 for shop drawing 86 212 Shear — Distribution over cross-section of girder 36 73 Shear in girders 36 74 258 INDEX Shear in girders Shear in girders Shipment Shoes for plate girder Shoes and rollers Shop bills Shop drawings drawings — Methods of working up . drawings — Notes on drawings for roof truss drawings for roof truss drawings — ^Titles on Shop operations Shops— Kinds of Show plans Signs for rivets on drawings Sizes of rivets Sizes of rivets SUde rules — Duplex — ^Engineer's —Fuller's — Manheim — ^Rule for operation of — Thaoher's — Three multiple Snap for rivet heads Snow loads Solid floors Spacing of rivets Specifications -for bridge superstructures. Splices in flanges of plate girders — ^Flanges of girders in webs of plate girders in webs of plate girders Steel — ^Aoid — ^Basic — ^Bessemer — ^Effect of carbon — Open hearth — Physical characteristics — Process of manufacture — Specifications for —Tests of Stiff eners Stififeners Art. Page 43 86 44 93 89 218 44 109 63 153 88 216 85 203 85 203 85 207 33 64 33 70 85 205 80 193 2 2 8 15 21 43 9 17 12 20 5 8 5 8 5 8 5 8 5 8 5 9 5 8 5 8 11 19 27 51 45 114 13 20 7 13 225 44 100 42 83 40 79 44 101 90 221 90 221 90 220 90 220 90 220 90 219 90 220 90 220 90 222 87 214 39 78 INDEX 259 Stiffeners Stiffeners Stiffeners — Crimped Stress sheets for deck plate girder bridge, for pin connected bridge. . . . for a roof Stresses in columns of mill buildings in girders in girders in girders in pin connected bridge in roof trusses in roof trusses in trusses of bridge due to wind . Stringer — Design — Estimate of weight laterals Structural steel — Classes of Templets Tension members —Built — Details of riveted -^Design of — Net sections Tension on rivet heads Tests of steel Theory of riveting Through plate girders Ties — Design of, for bridge Tie rods Time savers Titles on shop drawings Top chord — ^Lacing Top lateral bracing Tracing linen Traveler Trusses — Types of Tj^pes of plate girder flanges Types of roof trusses IVpes of steel highway bridges T3T)es of trusses Webs of girders of girders of girders — Moment of resistance — Moment of resistance Art. Page 43 88 44 100 39 79 8 14 44 112 64 157 32 62 32 62 35 73 43 84 44 92 55 127 28 52 28 52 55 127 43 84 43 89 43 89 1 1 80 193 49 117 56 129 69 168 56 129 19 35 15 25 90 222 15 23 45 113 44 107 22 45 5 8 85 205 71 173 61 151 85 203 81 194 47 115 34 72 25 46 79 191 47 115 36 73 43 85 44 95 36 75 37 75 260 INDEX Webs splices in plate girders . . . . splices in plate girders . . . . Wheel guards Width of compression members . Wind pressure 40 79 44 101 74 184 57 135 27 50