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Les diagrammes suivants illustrent la mdthode. 1 2 3 32X 1 2 3 4 5 6 I] 13.1 THE DESIGNING OF ORDINARY IRON HIGHWAY BRIDGES, BY J. A. L. WADDELL, C. E., B.A.Sc, Ma.E., '^"'■'^r^i'lT' ^'"^""'-'=''' "^'ANSAS CITV, MO.; ALSO ENGINEER IN CHARGE OF THE WESTERN 0FP1CK OF THE IHOiNlX BRIDGE COMPANY AND THE PHCENIX IRON COMPANY; FORMERLY PROFESSOH OF CIV.I. ENGINEERING IN THE IMPERIAL UNIVERSITY OF JAPAN MEMlfER OF ^hI AMERICAN SOCIETY OF CIVIL ENGINEERS, AMERICAN SOCIETY OF MECHANIcIl ENGINEERS, LA SOClfiTlt DES INofeNIEURS CIVILS, PARIS, RENSSELAER SOCIETY OF ENGINEERS, ENGINEERS* CLUB OF PHILADEI PHIA WESTERN SOCIETY Or KNGINEEHS. AND FNGINEERs' CLUB ' OF KANSAS l(. ASSOCIATE MEMlUiR OFIHE INSTITUTION F CIVIL ENGINEERS, LONDON, AND HONORARY MEMBEk OF THE KOGAKU KYOKAI (JAPANESE ENGINEERING SOCIETY). FJFTH EDITION. SECOND THOUSAND. NEW YORK : JOHN WILEY & SONS, 53 East Tenth Street. 1894. Copyright, 1884, By J. A. L. WADDELL. 1 i: c tl a \\ h. tt hi th si; sti ec th; ml bri to oth ser tha A PREFACE. This work is principally a compilation of the results of inve:tigations made by the author during the last three years, and presented in a number of papers to the various American engineering societies. Sev- eral port.o.. of the book, including many of the tables, are new. as th.s ,s the first systematic treatmeni. by the author, of bridges for cities and manufacturing districts; the previous papers havmg dealt especially w.th those for country roads. In ..aking this compilation, the author has been governed by no blind adherence to what he has alrea'dy writ- ten but as made changes wherever they have appeared to be advisable One o the ch.ef objects of this work is to reduce the labor of iron h.g way bndge designing to a minimum, for which purpose every thing that cou d be so arranged has been tabulated. Not only are the exact sues of h.p verticals joists, floor beams, beam hangers, lateral rods and truts, portal rods and struts, vibration rods, intermediate struts, lattice bars, stay plates, etc.. given for all practical cases, but also the most economic d„.ensions of panels and trusses, and dead loads, so exact ha by the,r use all necessity for a second trial is avoided. These 2^ .t IS hoped, will prove useful to those in the actual practice of ndge des,gnu.g. enabling them to greatly reduce the time required to make diagrams of stresses and sections and estimates of cost The other^tables. although they do not give final result, should also be of The value of the book may appear to some readers to be limited, in that ,t treats of only the Pratt and Whipple systems; but it must be IV PREFACE. reineml)ered that at least ninety per cent of all American iron highway- bridges are built on these systems. This fact alone ought to prove conclusively that they are the best type of bridge. Moreover, the author has demonstrated, in a paper entitled " Economy in Struts and Ties," published last year in the " Canadian Magazine of Science," and copied in the " American Engineer," by a method entirely practical, that for economy the web compression members of trusses should be vertical, or nearly so ; thus showing, that, of all the ordinary types of truss, the Pratt or Whipple is the best. Through bridges and pony trusses, both having inclined end posts, have alone been treated at length ; for highway deck bridges are un- common, and inclined end posts not only are more economical than vertical ones, but are also superior to them because they produce tensile stresses in the end panels of the bottom chords, thus ailding to the rigidity of the structure. The work is written for engineers, students, and, to a certain extent, county commissioners. It is not intended, though, to be used by itself as a text-book on bridges, dealing, as it does, with only one general style of triiss, but to supplement the books generally used by classes in engineering schools. It is essentially a treatise upon bridge designing, and not one upon stresses : nevertheless, it has been found necessary to discuss the latter subject in order to make the work comjjlete. The author would refer those who wish to study concerning stresses to Burr's " Stresses in Bridge and Roof Trusses," Bovey's "Applied Mechanics," and I)u Bois' " Strains in Framed Structures." For county commissioners. Chapters IV., XIV., and XVII., Tables I.-V., XV.-XXV., XXX.-XXXIII., and XXXVIII., and parts of Chap- ter II., will be found very useful ; containing, as they do, directions and data for making estimates of cost, and means of proving whether either designs or finished structures have or have not in many particulars sufficient strength. Those portions of the "General Specifications" in Chapter II., relating to quality and tests of materials, workmanship, painting, etc., have been taken from standard specifications too numerous to permit PREFACE. of their autliority being here quoted : nevertheless, the author must atkiu)wlf(Igf that he has received considerable assistance from a pa])or by Mr. 1'. F. Brcndlinger published in No. 4, vol. iii., of the "Proceed- ings of the Engineers' Club of Philadelphia," treating of some railroad- bridge specifications prepared by Theodore Cooper, C.E. He wishes to acknowledge also, with many thanks, the valuable aid rendered him by his assistants, Messrs. Y. Nakajima and T. Fukuda, in preparing drawings, and checking tables. J. A. L. W. ToKio, Japan, February, 1884. foil OVf to the nur but will 1 has eac est brie ma) A to a reas Ii men deta on. tion. seve; prev PREFACE TO SECOND EDITION. Although the first edition of this work was issued only three or four months ago, it has had the opportunity for receiving a thorough overhauling by a class of half a dozen students, who were requested to take special pains to point out errors. A few were found; but they are of small importance, being principally typographical or numerical. It is thought that all have been discovered and corrected, but it is possible that others may exist : so, if any reader find any, he will confer a favor upon the author by informing him of the same. The correctness of the weights of iron in Tables I., II., and III., has received additional confirmation from the same class of students, each student having made a complete design for a bridge. The great- est variation found was less than one-half of one per cent. As the bridges varied in class, span, and width of roadway, one being on a skew, and two having sidewalks, it is fair to conclude that the tables may be relied upon as correct for all cases. A slight change has been made in Chapter V., near the end, in respect to a statement concerning stresses in the posts of deck bridges ; but, for reasons there stated, the formula has not been altered. In a review of this treatise, by " The American En^neer;' there was mentioned the fact that double beam hangers are not a satisfactory detail, because of the unequal distribution of the floor-beam load there- on. In the addenda is described a detail which will remove the objec- tion. There are given also in this part of the work, and on Plate VIII., several other details that will be found to be improvements upon those previously described. ,, vm i'Ri:rACE TO sEco.xn edition. About July I, tlicre will be issued by the University of Toklo, In the form of the usual "Memoir," a treatise of the author upon "A System of Iron Railroad Bridges for Japan," which will be found to contain a nun )er of important matters respecting the designing of railroad- bridges, that have not hitherto received proper attention. The book is not for sale ; but there will be alwut two hundred copies distributed in America among engineers, colleges, public libraries, etc. The author wishes to express his thanks to the profession for the favorable reception given to his fust edition. J. A. L. W. ToKio, Japan, May 6, 1885. PREFACE TO THIRD EDITION. It is with considerable regret that the author allows this edition to go to press without making a single change or addition, more especially because his practice in bridge designing has lately been modified. Time will not permit of his rewriting the work for a year or two at least, so it will have to remain as it is for the present. The changes which he would like to introduce in the text are not in principles, init in methods and details of design ; American practice having changed somewhat since thj book was first written. These points s^'ll all be covered by some general specifications, which the author expects to issue in a few months. They will probably be for sale, and advertised in " Engineering Neros." The priiuii)al changes in his methods are the following : — I St, For long spans it is better to use the Pratt truss, with halved panels, instead of the Whipple truss. In spans exceeding two hundred feet, it is economical to make portions of the top chords inclined. For short spans it is, in general, well to use rolled beams up to twenty feet, plate girders from twenty to forty feet, triangular riveted girders from forty to sixty-five feet, pin-connected pony trusses from sixty-five to ninety feet, and pin-connected throug'^ or deck truss bridges from ninety feet upward. 2d, Tlie batter braces (or, as they are now being generally termed, the inclined end posts) are hinged at hip and pedestal. 3d, Floor beams are riveted to posts as near the lower chords as possible, and the lateral rods are attached to the lower part of the beams. The wooden shims over beams are retained for the purpose of spiking the joists thereto. ix PREFACE TO THIRD EDITIO.W 4th, Filling-plates under floor beam stiffeners are no longer necessary, as it is now very easy to Ijend the ends of the angles to fit around the' flanges of the beams. It is permissible to stagger intermediate stiffeners. End stiffeners should be figured for the total shear, using an intensity of three tons for bridges of Class A, and three and three- quarter tons for bridges of Classes B and C. 5 th, Upper lateral and portal struts are made of four angle -irons, with a single system of lacing-bars. These struts are rigidly connected to top chords or inclined end posts by riveting. 6th, End lower lateral struts can, in general, l^e made of single angle-iron of large size. It is preferable to use one of these struts at each end of every span. They can be riveted to the pedestals by means of a connecting-plate at each end. 7th, Lacing is used everywhere instead of latticing. 8th, Rivets are figured for shear and bearing, not for bending. 9th, In many cases flattened heads may be used to advantage, instead of countersinking the rivets, the thickness of the heads being three-eighths of an inch. lotli, Lateral rods are attached at each end to top chord by means of three short pieces of angle-iron, through one of which the rod passes. Tlie adjustment is made by a nut at each end, which bears against the last mentioned angle-iron. nth, In top-chord splicing, reliance is placed upon the abutting ends of the chord sections. The splice is made about fifteen or eighteen mches from the panel point on the side towards the nearer pier, and there are only two vertical rows of rivets in the splice i)late on each side of the joint The shop practice of first-class bridge companies has improved so much during the past five years, that it is now legitimate to rely upon abutting ends for this detail. Never- theless, the author would prefer to hinge the top chord at each panel point, for in this case there can be no doubt as to how the stresses travel. The same cannot be said for any other style of connection. 1 2th, When a bridge is sufficiently heavy, it is well to build the toj) chords and inclined end posts of plates and angles, using small, lioht PREFACE TO THIRD EDITION. XI angles above, and large, heavy angles below, so as to bring the centre of gravity of the section to the middle of the vertical plate. 13th, For hip verticals it is preferable to use a strut of two channels similar to the posts, but not so efficiently laced, as the member acts only in tension. Channels provide greater rigidity than do eye-bars. 14th, In proportioning compression members, Thacher's formula is used instead of that of the late C. Shaler Smith. It is the following : — / = 9,000 — 30 - for O D 9,000 - 35- for D O 9,000 — 40- for O O r where / is the intensity of working stress in pounds, / the un.supported length of strut in inches, and r the radius of gyration of section in inches. The above formula is for bridges of Class A. To use it for Classes B and C, multiply/ by \ ; and to use it for lateral struts, multiply / by |. In the latter case, however, considerations of rigidity generally necessitate the use of greater sectional area than the stress would call for. 15th, In order to be in accordance with modern practice, floor beams should be proportioned by neglecting the resistance of the web to bentling, and using an intensity of five tons for finding the ttct area of the bottom flange in bridges of Class \, and six tons for bridges of Classes B and C, then making tlie upper flange of the same section as the lower, taking care, however, to have the ratio of unsupported lengtii of beam to width of flange not greater than thirty. In the author's opinion this method is not so rational as the one which he used formerly, but it is more easily applied and gives about the same results. Strictly speaking, the web of a built beam does aid the flanges to resist bending; but, in truth, the designing of built beams and girders pertains less to science than to rule uf tiiumb. Xll PREFACE TO THIRD EDITION, 1 6th, Bent eyes on rods are no longer allowed, i7tli, In every thing relating to quality of material, workmanship, inspection, and tests, the Manufacturers' Standard Specifications are to be followed. The author trusts that the preceding lemarks, together with his new specifications, will keep his book from becoming antiquated until he can find time for re-writing the whole treatise. J. A. L. W. Kansas City, Mo., July i6, 1887. PREFACE TO FOURTH EDITION. Again with great regret does the author permit this work to reach another edition without receiving a thorough revision, amounting, in fact, to a complete re-writing of the book. The past year has been such a busy one, that it was impossible for him to spare the necessary time. The new specifications promised in the last preface have been issued, and are now on sale by Mr. A. C. Stites, Walworth Building, Kansas City, Mo., the price being twenty-five cents per copy. The author would advise that these be used in connection with this book, and that, where they conflict, the new specifications be followed. It will be seen that the latter contain considerably more than mere si)ecifications, being a systematic attack upon the present methods of tlesigning, letting, and building highway bridges. The pamphlet is being well advertised and distributed aniong county commissioners ; and the author is sparing neither time, trouble, nor expense to accomplish the reform which he deems so necessary. The re-writing of this treatise has already been begi;n ; but there is no telling when it will be completed, for the author's spare time is very limited. He hopes, however, that it will be be finished before a fifth edition becomes necessary. J. A. L. W. Kansas City, Mo., April u, 1888. CONTENTS. Chapter. , , Page. I. Introduction •••••••• I II. General Specifications .... III. List of Members 28 IV. Live AND Dead Loads. — Wind Pressure .... ,2 V. Stresses in Trusses . 38 VI. Stresses in Lateral Systems and Vertical Sway Bracing . 48 VIL Remarks concerning Main Members Vin. Proportioning of Main Members of Trusses, Lateral' Sys^ TEMs, AND Sway Praclng . ^ 00 IX. Proportioning of Floor System ^ X. Theory of Pin Proportioning g XL Practical Method of Pin Proportioning g. XIL Riveting 90 Xin. Proportioning of Other Details XIV. Bills OF Materials AND Estimates OF Cost . ... 114 XV. Economy 120 XVI. Complete Design for a Bridge ,,5 XVIL Bridge Lettings 157 XVIII. Working-Drawings 172 XIX. Order Bills and Shipping Bills jg, XX. Erection and Maintenance j_g APPENDIX I. A Neglected Consideration in Highway-Bridge Designing . 215 APPENDIX II. Demonstration of Formula for Floor Beams . 219 APPENDIX III. Method of Finding the Length of the Long Diagonals in a Double-Intersection Bridge . . ,21 ADDENDA ... GLOSSARY OF TERMS . * "5 INDEX 233 . . . 247 INDEX OF TABLES. i.-iii. IV., V. VI.-VIII. IX. X., XI. XII. XIII., XIV. XV.-XVIII. XIX.-XXI. XXII.-XXIV. XXV. XXVI., XXVII. XXVIII. XXIX. XXX. XXXI. XXXII., XXXIII. XXXIV., XXXV. XXXVI., XXXVII. XXXVIII. XXXIX. XL. XLI. XLII. Dead Loads. Economic Depths and Tanel-Lengths. Sizes of Hip Verticals. Working Tensile Stresses and Initial Tensions. Intensities OF Working-Stresses for Channel Struts, Working Bending-Moments and Shearing-Resist- ances for Tins. Working Loads for Wooden Beams. Amounts of Lumher per Panel, Sizes of Joists, etc. Sizes and Weights of Floor-Beams. Sizes of Beam-IIangers. Sizes of Portal, Lateral, and Intermediate .Struts, and of Upper Lateral, Lower Lateral, and Vibra- tion Rods. Thicknesses for Pin-Bearings. Dimensions of Union Iron Mills' Channel-Bars. Lengths of Lattice-Bars, Weights per Foot of Same, ETC. Sizes of Lattice-Bars. Sizes of Lacing-Bars. Sizes of Stay Plates. Permissible Pressures on Rollers. Working Bending-Moments and Bearing-Pressures FOR Rivets. Laisor in Erection. Working Loads for Falsework Pillars. Working-Loads for J-Beam Struts. Stresses in Single-Intersection Trusses. Stresses in Double-Intersection Trusses. XV INDEX OF PLATES. I. Isometric Drawing of a Bridge with Names of Main Members. II. General Descriptive Plate of Details. III. Details for a Pony Truss-Bridge. IV. Details for a Single-Intersection Through City Bridge with Two Sidewalks. V. Diagram of Stresses and Sections. VI. Working-Drawings for a Bridge. VII. Working-Drawings for Falsework. VIII, Details Illustrating the AnnENDA. xvu CO I th( bri gix be not to ore] nee ger latt stn ten of V str€ can bcii size THE DESIGNING or ORDINARY IRON HIGHWAY-BRIDGES. CHAPTER I. INTRODUCTION. That many bridge designers will have fault to find with the contents of this book goes without saying, but it will be found that the principal objections will come from those who design the lightest and poorest structures. The weights of iron in the bridges here treated are probably from twenty to fifty per cent greater than those in the bridges ordinarily built ; but it is to be remembered that most American iron highway-bridges are not what they ought to be, and that the author has endeavored to design structures first-class in every respect. The principal differences between these bridges and those ordinarily built are the stiffening of the end panels wherever necessary ; the use of C. Shaler Smith's formula, involving, as it generally does, an increase of sectional area ; the peculiar lower lateral system, which avoids using the floor beams as lateral struts ; the large lateral rods employed ; the allowance for initial tension in all adjustable rods; the variation of the intensity of working-stress for main diagonals ; the assumption that all stresses at joints in top chords and at upper ends of posts are carried by the connecting plates and their rivets, no reliance bemg placed upon the abutting ends of channels ; the limiting sizes of the sections of iron employed ; and the unusual strength O/WJAAKy JKOA' JiiuliWAV-nKIDuES. of the upper lateral and portal struts, especially when no verti- cal sway bracinj; is usctl. On the other hand, those who wish to proportion bridges by the latest theories may object to the employment of C! Shaler Smith's formula (which fails to take into account the radius of gyration of the section) and to the non-employment of the results of Wohler's and Weyrauch's recent investigations con- cerning intensities of working-stresses. To the first objection, the author would reply, that designers of ordinary highway- bridges cannot afford the time to spend at least fifteen minutes in obtaining the theoretically best intensity of working-stress for each strut, but must have for this pur|)ose tables which will ^ive the intensities without calculation : besides, the best theoretical intensity is merely approximate. To the second objection, he would reply, that the results of the investigations rcfeired to have not yet been generally adopted, and that the variation of intensity of working-stress for the main diagonals used in tiiis treatise is, in his opinion, for ordinary highway-bridge design- ing, a sufficient concession to the general correctness of the theory of those writers. The units used throughout this work are as follows : the American ton (two thousand pounds) for the units of weight and stress, the foot for the unit of length, and the square inch for the unit of area. It is presupposed that the reader, if he intend to design, or even study the designing of, iron bridges, has procured a copy of Carnegie's " Pocket-Companion," the most useful little book of its kind for bridge builders that has ever been printed : so the tables therein are here referred to, instead of being repro- duced. The sections of iron employed arc those rolled at the Union Iron Mills, for the reason that not only is there more iron rolled in these mills than anywhere else in America, but the proper- ties of the sections arc tabulate'' n a mnch more convenient form than are those of any othe* n;il'<. The author intended to prepare a table of channels ,i ! by the New-Jersey Steel and Iron Company of Trenton, N.J., similar to Table XXVIII. ; but the information in that company's pocket-book is not II IK) vcrti- CSS of the OA'D/A'Afiy /A'ox nn;n\\'Av-niuiH;Es. 3 complete enou-h to enable him to tabulate the thicknesses of the webs. Anyone intending to desijrn bridges according to the method herein proposed should thoroughly acquaint himself with the numbers and uses of the different tables, so as to turn to the one required without delay. He should also become posted on the contents of Chapters VII.-XIII., so as not to have to refer to that part of the book, turning to Chapter II. to refresh his memory concerning intensities of working-stresses, limitations. etc., while designing each main member and detail. After a little practice, one will become acquainted with the method, when it will be necessary to refer to the tables only. If a designer be in doubt about how to proportion any main member or detail, he can at once find out the method by look- ing in the Inde.x, under the head "Proportioning," where he will see the numbers of the pages on which the proportioning of this member or detail is treated. Any intelligent man who is not an engineer can make an approximate estimate of what a first-class iron highway-bridge ought to cost, by finding the required weight of iron from one of Tables I., II., or III., modifying it, if neces.sary, in the manner explained in Chapter IV. ; and the required amount of lumber from one of Tables XV., XVI., XVII., or XVIII.. ascertaining the prices of iron per pound, and lumber per thousand feet° delivered at the nearest railway-station or seaport, and filling out the form for an estimate of cost given on p. 1 16. By refer- ring to the Index, under the heading "Cost," he can ascertain where approximate data for all bridge-building expenses can be found. No special treatment is here given for skew bridges ; for none is needed, the methods for designing them being precisely the same as those for other bridges. On account of the obliquity, the working drawings for the lateral bracing and sway bracino- are a little more complicated. Whenever it is convenient to do so, the panel lengths should be arranged so that the shoe of one truss comes opposite to the first panel point of the other truss, in order that the floor beams may be at ri-ht angles to the planes of the trusses, both for economical reasons, and to ORDIXARY IRON HIGHV'AY-BRIDGES. avoid using single beam hangers. This arrangement can often be made by shortening the panel length a little, and, if it be allowable, slightly changing the angle of the skew. Even if it be impracticable to make this arrangement, it is usually better, in skew bridges, to advance the ends of the floor-beams at one side of the bridge, by one or even two panel lengths, if, by so doing, the floor beams be shortened. ORDINARY IRON HIGHWAY-BRIDGES. CHAIT'ER II. GENERAL SPECIFICATIONS. This chapter, at first thought, may appear out of place ; for it is really a n'siivic of the whole subject of iron highway-bridge designing. It is placed here in order to be of easy reference. Students, and those unacquainted with bridge designing, are advised to omit these specifications, and to return to them after having read through Chapter XIII. Classification. — Highway-bridges maybe divided into three classes ; viz., Class A, which includes those for cities and their suburbs that are subjected to the continued dL\)X)\\c:xt\on of heavy loads ; Ciu.is B, which includes those for cities and their suburbs, or manufacturing districts, that are subjected to the occasional application of heavy loads ; and Class C, which includes those for country roads, where the traffic is lighter. Live Load. — The live loads for bridges of the different classes are to be taken from the followins table: — SPAN IN FEET. Moving Load per Square Foot of Floor. Classes A and B. Class C. to 50 50 to I 50 I 50 to 200 200 to 300 300 to 400 100 pounds 90 pounds 80 pounds 70 pounds 60 pounds 80 pounds 80 pounds 70 pounds 60 pounds 50 pounds The live loads for joists, floor beams, beam hangers, and hip verticals, are to be one hundred (100) pounds per square foot of floor for bridges of Classes A and \\, and eighty (80) pounds per 6 OKD/A\l/n- /J^O.y JIIullWA V-B RIDGES. square foot for bridges of Class C, irrespective of the length of bridge. DiacfLoad—Tho dead load is to include the weight of all the iron and wood in the structure, excepting that of those por- tions resting directly on the abutments, whose weights do not affect the stresses in the trusses ; also, if necessary, an allow- ance for snow, mud. paving, or any other unusual fixed load that may ever be placed on the bridge. Pine-lumber is assumed to weigh two and a half (2.1) pounds per foot, board measure ; and oak-lumber, fotir and a third (4^) pounds per foot, board measure. : Should, in any biidge of or below one hundred (100) feet span, the calculated dead load differ more than eight (8) per cent from that assumed, or in any bridge from one hundred (100) to two hundred (200) feet span, more than six (6) per cent, or in any bridge exceeding two hundred (200) feet span, more than four (4) per cent, the calculations of stresses, etc., are to be made over with a new assumed dead load. IViiui Prcssiin:— The wind pressure per square foot i.s to be assumed as forty (40) pounds for spans of one hundred (100) feet and under, thirty-five (35) pounds for spans over one hun- dred (100) and not greater than one hundred and fifty (150) feet, and thirty (30) pounds for all greater spans. For bridges in unusually exposed situations, these pressures are to be increased by ten (10) pounds per square foot. The total area opposed to the wind is to be determined by adding together the area of the vertical projection of the floor and joists, and twice the area of the vertical projection of the windward truss, hand rail, hub plank, guard rail, and ends of floor-beams. Laigt/t of Span. — The length of span is to be understood as the distance between centres of end pins for trusses, and between centres of bearing-plates for all beams and girders. Umitiiii; Lengths of Span for Different Clear Roadzvavs. — The greatest lengths of span for the different clear roadways are to be one hundred and forty (140) feet for twelve (12) foot roadways, one hundred and ninety (190) feet for fourteen (14) foot roadways, two hundred and sixty (260) feet for sixteen ORDINARY IROX HIGHlVAY-liRlDGES. 7 (16) foot roadways, and three hundred and fifty (350) feet for eighteen (18) foot roadways. By clear roadway is meant the tlistance between the innermost portions of the opposite trusses, measured in a direction perpendicular to their planes. Limit of Char Hcadivay. — The least allowable clear head- way is to be fourteen (14) feet, unless some local consideration cause it to be increased. \\y clear headway is meant the ver- tical distance between the upper face of the flooring and the lowest part of the portal or overhead bracing. Styles of Bridges for Different Spans. — Spans of and belo>v twenty (20) feet are to consist of rolled beams ; spans from twenty (20) to forty (40) feet, of riveted plate girders or trussed beams ; spans from forty (40) to si.xty-five (65) feet, of stiffened pony trusses or stiffened deck bridges, unless the weight of bridge be great enough to admit of the use of eye bars for the bottom chords ; and spans above sixty-tive (65) feet, of pin- connected through or deck truss bridges. Limiting Depth of Pony Trusses. —T\^ii greatest allowable depth, measured from centre to centre of chords, for pony trusses without exterior side bracing, is to be six (6) feet ; and that for pony trusses with exterior side bracing, nine (9) feet. Vw bridges with sidewalks, in which it is inconvenient to use exterior side braces, the depth may be increased to eight (8) feet, provided that the width of the top chord plate be double the dejith of the top chord channels, and that the channels comjiosing the posts and hip verticals be splayed outwartlly so as to be separated in the clear at their feet by at least twenty- four (24) inches. Limiting Slope for Batter Braces of Pony Trusses.— i:\\<t least allowable slope for batter braces of pony trusses is to be two and a quarter {2]) horizontal to one (1) vertical. Side Fumes. — The least allowable batter for side braces in pony-truss bridges is to be five (5) inches to the foot, and all sitle braces are to be made to resist both tension and compres- sion. In no case is a side I'race to have less strength than that of a 2^" X 2»" 5-lb. angle-iron. Limiting Length of Span for Double Interseetion Btidges. ~ The least allowable length of span for double intersection bridges is to be taken from the fdlldwin-" table: — ORDINARY IROX HIGniVAY-BRinGKS. CLEAR ROADWAY. I.i.MiTJNc; Lkni;tiis. Class A. Class B. Class C. 14' 16' 18' 20' 22' 24' i6s' •55' 150' 145' 140' 140' 175' 165' 160' 155' ISO' •45' 180' 170' 165' 160' ■55' 150' Limiting Sizes of Sections. — No rods less than three-quar- ters (|) of an inch in diameter are to be used in a bridge. No channels less than five (5) inches in depth are to be used for upper chords, batter braces, or posts, or less than four (4) inches in depth for other members. No flat bars less than one-half {I) inch thick, or one and a half (i^) inches wide, are to be used for diagonals or chord bars ; nor any iron less than one-quarter (|) of an inch thick anywhere in a bridge, excepting for filling plates. Expansion. — All spans are to be provided with some means of expanding and contracting longitudinally, with a variation in temperature of one hundred and fifty (150) degrees Fahrenheit. Spans of over seventy-five (75) feet are to have at one end nests of turned wrought-iron friction rollers, running between planed surfaces. Anchorage. — At least one end of every bridge must be anchored to the foundations. If the overturning moment of the greatest assumed wind pressure be more than half the resisting moment of the weight of the bridge, the latter must be anchored at the roller end also, but in such a manner as not to interfere with the expansion. Sliding. — At the roller end of a bridge, if the frictional resistance to the sliding of the shoe in the direction of the axes of the rollers be not more than double the tendency to slide produced by the wind pressure, a resistance equal to the differ- ence between this tendency and the frictional resistance with a factor of safety of four (4) must be provided. ORDINARY IRON HIGHWAY-BRIDGES. g CiHitii/iioiis Sfaiis. — Except in the case of swing bridges or cantilevers, consecutive spans are not to be made continuous ■over the points of support. Camber. — The cambers for bridges of the different spans are to be taken from the following table : — Si'AN IN Feet. Camber in Inches. Si'AN IN Feet. Camber in Inches. 40-60 I.O 180-220 3-S 60-80 'S 220-250 4.0 ,So-ioo 2.0 250-280 4-5 100-140 2.5 280-300 5.0 1 40- 1 So 3-0 Vertical Sway Bracing. — \n all deck bridges, and in all through bridges where the depth from centre to centre of chords is twenty-four (24) feet or over, vertical sway bracing is to be used. Portal and Lateral Struts. — Portal and lateral struts are to be proportioned to resist the compression produced by the wind pressure and the initial tensions in all the rods meeting at the end of the strut. If the strut be also subjected to bending, then to the area necessary to resist compression must be added sufficient area to resist the bending ; the intensity of working bending-stress being taken equal to six (6) tons. Effect of Wind on Posts and Batter Braces. — But the effect of the wind on the posts and batter braces is not to be considered to occur when the bridge is fully loaded : so, unless the stresses produced thereby exceed the product of the live load stresses by the ratio of seven and a half (7.5) to the intensity of working tensile stress for the bottom chord, the effect of the wind on these members may be neglected. Effect of Wind Pressure on Bottom Chord Tension. — For the same reason, the sectional area of the bottom chord need not be increased to resist the tension caused by the wind, unless the latter exceed the product of the live load stress by the ratio of seven and a half (7.5) to the intensity of working tensile stress for chord bars. 10 ORDIXARY IRON HIGHU'A Y-li RIDGES. Initial Tension. — To allow for the stresses caused in adjusta- ble members by the screwing up of the turn buckles or sleeve nuts, the stress in each such member is to be increased by the amount given in the following table :■ iMA.MiniCU (IK Kl>I>. Inhial Tension. DlAMETKR (IK R(ll). Initiai, 'Iensiiin, 1" 0.50 ton ■1" 2.25 tons r 0.75 ton If 2.50 tons I" 1. 00 ton •r 2.75 tons li" 1.25 ton 2" 3.00 Ions li" 1.50 ton ^-^' 3.25 tons If" 1.75 ton 2f' 3.50 tons li" 2.00 tons 2a" 375 t<"i^ Square or flat bars are to receive the allowance for round rods of equal sectional area. Conncctioti for Lateral Systems. — Whenever it be possible, the lateral rods of both upper and lower systems are to be connected directly to the chord pins. But, if the rods exceed one and three-quarter (i|) inches in diameter, bent eyes are not to be employed. Lower lateral rods are not to be attached to the floor beams. To make them clear the joists, wooden lateral struts resting on the floor beams, and having wrought-iron jaws at their ends attached to the chord pins, are to be employed for the joists to rest upon. These wooden struts are to be bolted about every two feet through the upper flange of the floor beam by five-eighth {\) inch bolts, care being taken to stagger the bolt holes, and to avoid placing a bolt at the middle of the beam. Should the sizes of the lateral rods be such as to prevent the use of bent eyes, pins dropped vertically through the jaws are to be employed. Stresses in End Lower Lateral Stmts. — In figuring the stress in a lower lateral strut at the roller end of a l^ridge, the stress caused by the wind pressure is to be added to the trans- verse component of the initial tension in the end lateral rod. ORDINARY IRON HIGHIVAV-URIDGES. I I lAI. 'i'ENSlON. 25 tons 50 Ions 75 tons 00 tons -5 tons 50 tons 75 tons round rods ai.d Irom the sum is to be subtracted the product of the press- lire on the windward shoe, when the bridge is empty and sub- jected to the greatest wind pressure, l)y the co-efficient of iron upon iron, which is about 0.25 for this case. Stiffened End Panels. ~\l, in the end panel of a bridge, the longitudinal component of the greatest allowable working^stress (including initial tension) in the lower lateral rod exceed the tension in the lower chord of that panel, caused by the dead load alone, when the bridge is subjected to the greatest wind p--jssure, the bottom chord of that panel must be made to resist both tension and the excess of compression. Where two chan- nels are employed for the lower chord section, the effective area of tie webs alone must be counted on to resist tension. Where the sriffening is obtained by trussing the inner chord bars, the intensities of working tensile stress to be employed for the net section of those bars arc four (4) tons for bridges of Class A, and five (5) tons for those of Classes B and C. Top-Chord and Battcr-Bracc Sections. — The top chords and batter braces shall consist of two channels, with a plate above, and latticing or lacing below. The top plate must be of the same section, and the chord channels of the same depth, from end to end of span ; the increase in chord section towards the middle being ojjtained by thickening the webs of the chan- nels. Post 5<v7/,vAv. — Posts arc to consist of two channels, with latticing or lacing on each side. The upper ends may be either rigidly attached to the chords, or may be hinged on the pins ; preference being given to the latter method. Portal and Upper Lateral Stmt Seetions. — Portal struts anrl upper lateral struts are to be formed of two channels, latticed o-- laced, and rigidly attached at their ends to the batter braces or chords. IVorkin^^r Tensile 5/;r...r.x - Except for the case of trussed bars, mentioned under the divisions " Stiffened I-:nd Panels " and "Stiffened Hip Verticals," the intensities of working-strosses for iron in tension in the various members are to be as given in the f'.>llowing table : — ORDLXARV IRON HliiH WAY-BRIDGES. MEMBERS. Lower chord bars and end main diagonals . Middle panel diagonals, counters, and hip verticals Flanges of rolled beams Flanges of built beams (net section) . . . Lateral and vibration rods Beam-hangers Intensitiks i)F W'okkinc.-Strkss. Class A. Classes B and C. 5.00 tons 4.00 tons 5.00 tons 4.00 tons 7.50 tons 3.00 tons 6,25 tons 5.00 tons 6.00 tons 5.00 tons 7.50 tons 4.00 Lons The intensities of working-stress for main diagonals inter- mediate between the counters or middle panel diagonals and the end diagonals lie between four (4) and five (5) tons for bridges of Class A, and between five (5) and six and a quarter (6|) tons for those of Classes B and C; the amounts being directly interpolated according to the position of the panel. Working Compressive Stresses. — For struts composed of two channels with plates, or lacing, or latticing, the following for- mulas are to be used in finding the intensities of working compressive stresses. For chords, batter braces, and posts in bridges of Class A, / I + H^ P = 4 + 20 and for all other cases, / 1 + / = 4 + C 30 H = p being the intensity of working-stress, and length of strut least diameter of stmt' f 19.25 for two fixed ends (1 end and one hinged end .yo • /= I 19.25 for one fixed end and I 18.90 for t\\(i liin:j:cil rnds, OND/X.IKV nWN HlGHWAY-liRlDGES. 13 'iiukinc-Stress. Classes B and C. 6.25 tons 5.00 tons 6.00 tons 5.00 tons 7.50 tons 4.00 ions and [5820 for two fixed ends. C -■- \ 3000 for one fixed end and one hinged end [ 1900 for two hingctl ends. Where I-beams are employed for intermediate struts or end lower lateral struts, the working-stresses arc to be taken from Table XL. For the flanges of rolled beams, the intensities of working compressive stress are to be taken equal to five (5) tons for bridges of Class A, and six (6) tons for bridges of Classes H and C. For the flanges of built beams, the corresponding inten- sities are to be four (4) and five (5) tons respectively on the gross section. Working Bcnding-Strcsscs. — The intensities of working bcnd- ing-stress on pins arc to be seven and a half (7.]) tons for bridges of Class A, and nine and three-eighths (9|) tons for those of Classes B and C. For pins belonging wholly to the lateral systems of bridges of either class, the intensity of working bending-stress may be taken equal to eleven and a quarter (I i|) tons. The intensities of working bending-stress for rivets are to be seven and a half (7.]) tons for bridges of Class A, and nine and three-eighths (9'^) tons for those of Classes V> and C. The latter intensity is also to be used for the lateral systems of bridges of Class A. Where steel pins are employed, the intensity of working bending-stress must not be taken greater than twelve (12) tons for bridges of Class A, or fifteen (15) tons for those of Classes B and C, unless special experiments on the steel used show an ultimate bending resistance greater than si.xty (60) tons per sc|u:He inch ; in which case a factor of five (5) may be used for bridges of Class A, and a factor of four (4) for those of Classes B and C. As before stated, the intensity of working bending- stress for channels in portal and lateral struts is to be six (6) tons. Working Bcaring-Strcsscs. — The intensities of working bear- ing-stress for pins and rivets, measured upon the projection of the semi-intrados upon a diametral plane, are to be six (6) tons for bridges of Class A, and seven and a half (7.^) tons for those '4 ORD/XARV /ROX Hh'.IIWA V-liRllh'.ES. of Classes V> and C. I'or pins and rivets belonging; wholly to the lateral system of a bridge of any class, the intensity is to be taken equal to seven an'l a half (7^) tons. Sirjcs of rp/'cr Lntrnil Rods. — In bridges of less than two hundred {200) feet span, the stresses in the upper lateral system in through bridges, or the lower lateral system in deck bridges, usually call for sections of rods which are practically too small : therefore the inferior limits of the diameters of these rods in such cases are to be taken from Table XXV. Stiffened Hip W-rticah. — Hip verticals in three or four panel pony trusses are to be stiffened so as to resist compression. If the section employeil consists of two channels, the net section of the webs alone is to be relied on to resist tension. If it con- sists of two flat bars trussed, the intensities of working tensile stress on the net section are to be reduced to three (3) tons for bridges of Class A, and to four (4) tons for those of Classes H and C. Trussing. — Trussing is to be used only in the posts of pony trusses, where there is a great excess of strength, in the hip verticals of pony trusses, and in stiffening lower chord bars. Upset Ends. — Middle panel diagonals, counters, lateral rods, vibration rods, and all other adjustable rods, excepting beam hangers that have an excess of section, are to have their ends enlarged for the screw threads, so that the diameter at the bot- tom of the thread shall be one-si.xteenth (,";.) of an inch greater than that of the body of the rod, .square or Hat bars being figured as if of equivalent round section. Threads. — All threads, except those on the ends of pins, must be of the United-States standard. Miiiininin Dimensions of Chord and Batter-Brace Plates. — The minimum dimensions for the top plate in top chords and batter braces are to be taken from the following table. For five (5) and six (6) inch channels, the thickness docs not increase with the width. For seven (7) inch channels, the thickness should be increased to five-sixteenths (/',.) of an inch, should the width exceed fifteen (15) inches. For the other channels, should the width of plate exceed that given in the table by from forty (40) to seventy (70) per cent, the thickness must be s than two cral system ick bri(l};es, ,' too small : jsc rods ill ;inf; tensile bars bein<^ ONJJ/XANV /h-OX umilWA Y-liRinCES. IS Increased by one-sixteenth (j\,) of an inch, while, if it exceed by more than seventy (70) per cent, the thickness must be iiuToased by one-eighth (J) of an inch. Iii-rni i)K MiNIMlM MlNIMI'M l)i:nii (IP MiM.MI'M MiNlMIM ClIANNBL. s" Thickness. Width. Channel. Thickness, WlDlll, f 7" 9" A" \\\" 6" f 8" 10" A" I2V' 7" f 9" 12" i" IS" ,S" i" 10" 15" i" ■ 9" AAn' /'/-^Ax —Sizes of stay plates are to be taken f rom Tables XXXII. and XXXIII. Stay plates on latticed or laced compression members are to be i)laced as near the pin holes as possible. Latticing or lacing must never be used without stay plates at the ends. I.atticiiii:; (vui Laciiio; Inirs. — The sizes for lattice bars and lacing bars are to be taken from Tables XXX. and XXXI. The distance from the back of an end rivet hole to the end of the bar must not be less than one-half the width of the bar. The ends of the bars are to be semicircular, except when there are two rivets at each end, in which case they should be cut l)arallel to the channels. Inclination of Latticiiii^ and Lacing Bars. — Lattice bars shall ces will permit. make with each other, as nearly as circumstan angles of ninety (90) degrees ; and lacing ba rs, an<iles of SIX (60) degrees. ty Diameters of Rivets for Different Channels. — For attaching |)lates and Ltttice or lacl.-.g bars to the flanges of channels, the least diameters of the rivets to be used are to be taken from the following table ; and the greatest diameters must not exceed those there given by more than one-eighth (J) of an inch. Drptli of tliiinnel . . 4" 5" Di.imuter of rivets . , 4" J" 6" k" 7" 9 " V6 8" 1" 9" 10" 12" 11" 3" 16 1 % 15" 13" 16 Splice Plates.— The length of a splice plate is to be deter- 16 oRP/x.ih']' /A'o.v nhiiiW'A v-nh'/in;/:.s\ mined by the niinihcr of rivets necessary to transfer the stress from one main meniber to the other. The sum of the workinj; bearing resistances of all the rivets on either side of the joint must not be less than the stress in the main member upon that side. The rivets must also be fi^an-ed for beiulin};. When practicable, a splice plate must be placed on each side of every member where a joint occurs. The transmission of compressive stresses shall be considered as entirely throu^di the medium of the rivets and connectin^^ plates, and these must be proportioned accor(lin<;ly ; so that the area of the two sj^lice plates connecting two channel bars must be at least ecpial to that of the Iar},^er channel bar. Ki-i/z/o/rn/^i,'- J'^latis. — Simple re-enforcing plates, or plates riveted to webs at pin holes in order to compensate for strength lost there, or to provide additional bearing for the pins, must have as many rivets to attach tliem to the webs as will give bearing and bending resistances for the same, equivalent to at least the greatest stresses that can come upon the re-enforcing plates. Cover Plates. — Cover plates for top chords or batter braces are to have the same section as the chord or batter-brace |)late, the joints in which they cover, and enough rivets on each side of the joint to take up the greatest stress that could ever come U|)on the said chord or batter-brace plate. Extension Plates. — Ivxtension plates on the end of a strut, for the purpose of hinging the latter, are to have at least twice the sectional area of the strut from the pin-hole to the nearest edge of the stay jilate ; and the thickness must be great enough to give sufficient bearing upon the pin. The length of the extension plates is to be such as to allow of the use of a suffi- cient number of rivets to provide proper bearing and bending resistances for the same. Shoe Plates, Roller Plates, ami Bed Plates. — No shoe jilate is to have a less thickness than three-cpiarters {\) of an inch, and no roller plate or bed plate a less thickness than seven- eighths (^) of an incli. When nine (9) or ten (10) inch chan- nels are used for tlie batter braces, the thickness of the shoe plates is to be seven-eighths {\) of an inch. When twelve (12) r)A7>/.\. //T fNOX mcinVAV-nNlDC.KS. 17 considered iiuli rlKinm-ls are used for tlie l)atter braces, the thickness of the slioe plates, roller plates, and bed plates, is to be one (i) iiuh ; and, when fifteen (15) inch channels arc used, it is to be (Hie :'nd an eighth {\\) inches. Ik'd plates must be of such dimensions that the fjreatcst pressure on the masonry shall not exceed two hun.Ired (200) pounds per scpiare inch. Every bearinj; upon masonry must lie provided with cither a bed plate or a roller plate, well fastened to the masonry by bolts not less than one (1) inch in diameter; but, if the shoe plate i)e sufficiently large, it may act as a bed plate at the fixed i^mX (if tile span. Inam-llaiii^ir Plates. — Ream-hanger plates arc never to be made less than three-(piarters {%) of an inch thick, and their ru-eas are to be such that the hanger nuts will always have a full bearing thereon. The necessary thickness for a beam-han-er plate is to he determined by considering it as a beam uniformly loaded by the whole weight that comes on th,. luingers ; the length of said beam being the distance between the centres of the holes through whieh pass the ends of one hanger, and its width I)eing the extreme dimension of the plate, mc^isured par allel to the floor beam. The intensity of working-stress for ben.hng in the plate is to be taken equal to that used in pro- portioning the lloor beam. Rivctii,}^r, _ In ri,,ctcd work, all joints arc to be squarely and truly dressed, and the rivet holes must be accurately spaced No rivets with crooked heads, or heads not formed accurately on the shank, or rivets which are loo.se either in the rivet holes or under the shoulders, will be allowed in a bridge. Kivet holes in top-chord plates and batter-brace plates shall be spaced as nearly as practicable two and a half (2I) inches eenlre to centre near the panel points, and four (4) inches centre to centre elsewhere. No rivet-hole centre shall be less than one and a half (lU < lameters from the edge of a plate: whenever practicable, this distance is to be increased to two (2) diameters. The diameter of a hole shall never exceed that of the rivet by more than one-sixteenth {-^) of an inch. i8 OA'/)/A:iA'r /A'O.V IIlCUWAV-nRlDGES. When two or more thicknesses of plate are riveted together in compression memljers, the outer row of rivets shall not be more than three (3) diameters from the side edge of the plate. Rivet holes must never be spaced less than two and a haif (2},) diameters from centre to centre: it is preferable that this distance be increased to three (3) diameters when so doing will not cause inconvenience in designing. All the rivet holes of the respective parts of any structure must be made to exactly coincide, either b> drilling the holes full size through the connecting portions, after being put together, or by sub-punching the pieces separately, and after- wards reaming the combined rivet holes to proper size. In all cases the burrs must be removed by slightly countersinking the edges of the holes. All rivets in splice or tension joints are to be systemati- cally arranged, so that each half of a tension member or splice plate will have the same uncut area on each side of its centre line. No rivet, excepting those in shoe plates, is to have a less diameter than the thickness of the thickest plate through which it passes, nor in any case less than half (\) an inch. Built J/rw/v/x — The several pieces forming one built mem- ber must fit closely together, and when riveted shall be free from twists, bends, or open joints. Use of Balis.— Ihc use of bolts instead of rivets is to be avoided whenever practicable. Lateral Dracin^r for Plate Girders. —When a span consisting of plate girders is over fifteen (15) feet in length, the adjacent girders are to be braced to each other by diagonal angle irons attached to or near the lower flanges. There are to be, also, light bracing-frames at each end between adjacent girders, so placed as not to interfere with the expansion. When the si^an is over twenty-five (25) feet in length, the upper flanges of adjacent girders are also to be connected by diagonal angle-iron braces. In every case the joists are to be dapped at least an inch onto the girders, and every third joist resting on any girder is to be bolted through the upper flange. ORD/AARV IROX HlGHlVAY-nRlDGES. 19 Fonna/a jor Built Floor Bavus mid Plate Girders * — The tension flanges of built floor beams and plate girders are to be proportioned by the formula A = 8DT 6 + A", where A is the area of the flange, A' that of the web, A" that lost from the flange by a rivet hole, JFthe uniformly distributed load in tons, /. the length of the beam in feet betv jen centres of supjjorts, 7) the depth in feet between centres of gravity (,( flanges, and T the intensity of working tensile stress in tons. The same formula will apply to the compression flanges by making A" equal to zero. Stiffnnrs. — Built floor beams and plate girders must be stiff- ened by four (4) angle irons at each support, and by two (2) angle-irons at several intermediate points ; the distance apart of the stiffeners being made no greater than twice the depth of the beam when the ratio of thickness of web to depth of same is not less than one-eightieth {^^), and no greater than one and a half (I J) times the depth when this ratio is one over one hundred and twenty (y-|^). Distances for intermediate ratios arc to be interpolated. Tee-irons are not to be used as stiffeners. Stiffening angles, which must always be in pairs (one angle on each side of the web), must extend from the upper leg^'of the upper flange angle to the lower leg of the lower fla^nge angle, being made flush with the other legs of the flanges by filling plates. U'r/> Splices in Floor Beams and Plate Girders. — Wchs of floor beams and plate girders must be well spliced at all joints by a splice plate on each side of the web ; and joints must be located where the shear is not great. Limitiug Depths of Floor Beams and Plate Girders. — The depth of the web of a floor beam or plate girder must never exceed one hundred and twenty (120) times its thickness. • For proof of this formula, see Appendix II. 20 ORDLXARV IROX HIGHWAY-BRIDGES. Rivets in Flanges of Floor Bcmiis and Plate Girders. — In spacing the rivets in the flanges of floor beams and plate gird- ers, the flanges are to be divided into portions of about two (2) feet in length, the stresses in the flanges are to be found at each point of division, and there must be enough rivets between any consecutive points of division to take up the dilfercnce between the stresses at the points, providing that the rivets be not spaced more closely than two and a half (2i) diameters, nor more than six (6) inches apat. /y,,x _In welded heads, the length of metal behind the pni- hole must be at least equal to the depth of the bar or diameter of pin, whichever be the greater, unless the head be corre- spondingly thickened ; while in hammered heads the amount is to be the same as that above or below the pin hole. The least amount of metal in the heads across the pin holes is to be as given in the following table : — DIAMETER OF I'lN Metal in Head across Pin. WIDTH OF BAR Welded. Hamnicred. o.So 1.50 1.50 1.04 1.50 1.50 1. 12 1.50 I-S3 1.20 1.50 ,.56 1.28 1.50 1.60 1.36 1-55 1.72 143 1 .60 1.76 1.50 1.67 1.85 1.64 i.r,7 1-95 177 1.70 2.05 1.90 ..76 'Til In loop eyes the distance of the inner point of the loop from the centre of the pin must not be less than three (3) times the diameter of the pin. The loop must fit closely to the pin throughout its semi-circumference. Pin holes in eye bars shall be bored to an exact size and dis- tance, and to a true perpendicular to the line of stress. No error in the length of bar exceeding one sixty-fourth (,.'4) of an ORDINARY IRON II IGIIW AY-BRIDGES. 21 irdcrs. — In I plate <;-ird- bout two (2) be found at /ets between e (lilference he rivets be ) diameters, lind tlie pin- or diameter id be eorre- le amount is he pin holes mc h will be allowed, nor ROSS Pin. Hammered. 1.50 1.50 '•S3 1.56 1.60 1.72 1.76 1.8s 1.9s 2.05 2.21 the loop from (3) times the <f to the pin size and dis- f stress. No irth (ji'^) of an # J variation of more than one thirty- secon.d {^.,) of an inch between the centre of the eye and the centre line of the bar. J'iiis. — Pins are to be proportioned to resist the greatest bending produced in them by the bars or struts which they connect. Steel pins are also to be proportioned for shearing. No pin is to have a diameter less than eight-tenths {-^^) of the depth of the deepest bar coupled thereon ; nor shall it vary from that of the eyes of the bars coupled theretc by more than one-fiftieth (r,^,) of an inch. The least allowable diameters for chord pins are two (2) inches for bridges of Class A, and one and a half {\l) inches for those of Classes B and C. The least allowable diameter for pins belonging wholly to the lateral systems of bridges of any class is one and a quarter {\\) inches. J'iii Baviiigs.— AW pin holes through webs shall be re-en- forced by additional material, so that the permissible pressure upon the bearings shall not be exceeded. Where a pin bears against a re-enforced channel bar, the web of the latter is not to be assumed to take any bearing-stress, unless the re-enforcing plates be riveted to it before the pin-hole be bored. Chord I\ickii/o^. — The lower chords are to be packed as closely as possible, and in such a manner as to produce the least bending-moments upon the pins. The various members attached to any pin must be packed as closely as possible, and all interior vacant spaces must be filled with wrought-iron fillers. Rxpaitsion Rollers. — Expansion rollers for bridges of Class A are to be proportioned by the formula / = 0.25^^7, and those for bridges of Classes B and C by the formula / = o.3i25V'^, where p is the working-load in tons per lineal inch of roller, and d is the diameter of the roller in inches. 22 OKD/XAKV /h'OX IIICinVA V-IIK/IHUCS. The least allowable diameters for rollers are one and three- quarters (\\) inches for bridges of Class A, and one and a half (I 1) inches for bridges of Classes H and C. The spaces between roflers must ne^■er exceed three-quarters (|) of their diameter. Ttini niickhs iiiid Slave Nuts. — All turn buckles and sleeve nuts must be made so strong, that they will be able to resist without rupture the ultimate pull of the bars which they con- nect, and without distortion, the greatest twisting-force to which they could ever be subjected. U-nuts are not to be used in any part of a bridge. Sizes of Xiits. — The dimensions of all scpiare and hexagonal nuts for the various diameters of rods are to be taken from Carnegie's "Pocket-Companion" (pp. 130, 13 1), excepting those nuts on the ends of pins which are subject to but a slight ten- dency to sheir the thread : in this case, these dimensions may be diminished, in direct [iroportion to this tendency, until the thickness reaches the limit of one-half (i) of an inch. Washers ami Xiits. — Washers and nuts must have a uniform bearing. Cast-iron washers must be used under the heads and nuts of all timber bolts, when the bearing is on the wood. Beam Ilai/oers. — Whenever possible, four (4) beam hangers per beam are to be used. The screw ends are to be provided with check nuts. y^,j,y. _ Great care must be taken, ii designing jaws for the ends of any strut, that they be so strong in every respect, that, when the strut is subjected to its ultimate load, it will fail near the middle rather than at the ends. Bnnkets. — Brackets, or knees, must be used to connect each overhead strut to the posts or batter braces. They should be of straight tee, angle, or channel iron : if made curved, no depend- ence is to be placed upon them, either for strength or stiffness. When there is no vertical sway bracing, each intermediate bracket must be proportioned to resist the compression induced in it by the wind pressure concentrated at the windward and lee- ward points of that panel of the top chords to which the bracket belongs; and each portal bracket, to resist the compression induced in it by one-half of the total wind pressure concentrated at the panel i)oints of the top chords. ^ 'i ■* OKD/XAK ) ■ /A'O.y I IK /// W.W '-H RIDGES. 23 ul IiL'xaL^onal taken from opting those a sliij;ht ten- ensions may :y, until the h. ve a uniform le heads and I wood, leam hangers be provided jaws for the respect, that, will fail near connect each J should be of d, no depend- I or stiffness. intermediate bsion induced ward and lee- h the bracket compression concentrated Cut tins; off the I'laiigcs of Cliatincls. — The llanges at the ends of channel bars must not be cut away, if it be practicable to a\()i(l doing so : if not, there must be sufficient re-enforcing used to make the strut as strong as it would have been with the flanges uncut. Sizes of /■'/ooriiig and Joists. — Pine flooring is to be at least tiirec (,^) inches thick, and oak flooring at least two and a half (j.i) inches thick. It is to be laid with close joints, anil well spiked to each alternate joist with two (2) seven (7) inch cut spikes. Consecutive boards should not be spiked to the same joists. Joists are to be proportioned by the formula, JF = ch where W is the safe uniformly distributed load in tons, b the hreadtli of the joist in inches, d the depth of same in inches, /the length in feet, and c — 16 for jjine and 1 1.5 for oak. Where the greatest load is a concentrated one, it is to be considered as supported equally between the joists directly under the wheels and those contiguous to the same ; i.e., the wheels on one side of a wagon are supposed to be placed directly over a joist, which joist is assumed to take half their load, the remaining half being equally divided between the two adjacent joists. All concentrated loads must be reduced to equivalent uniformly distributed loads in respect to deflection by multiplying them by one and si.\-tenths (1.6) before applying the formula. Wooden Hand Rails, etc. — Wooden hand railing is to be made of pine, the posts being 4" X 6" X 4', with two runs of 2" X 6" timbers — one on its flat, and the other below on edge to support the first for a hand rail — and one run of 2" X 12" hub plank. The latter and the lower run of 2" X 6" timber are to be let into the posts to their full depth, and spiked to the same with five (5) inch cut spikes ; and the posts are to be halved on the outer joists, to which each one is to be bolted by two (2) three-quarter (|) inch bolts. Guard rails are to be of C" X 6" pine, bolted to each hantl- 24 ORDINARY JRU.X lUCllW AY-BRIDGES. rail post, and to the floor once in, at most, cvc-ry five (5) feet, by three-quarter (|) inch bolts. When there are no wooden hand-rail posts, the guard rails must be bolted through joists placed symmetrically below them, care being taken that there be no bolt within two (2) feet of the middle point of any joist. The joints in the guard rails are to be lap joints, six inches long, and are to have a bolt passing through the middle of each lap. About every eighth or tenth plank, there is to be a crack left between flooring boards to let the water run through : this crack should be less than a quarter (|) of an inch in width. Should it be considered desirable to elevate the guard rails in order to let the air and water pass beneath, it is to be accom- plished by inserting hard-wood shims — one (1) fool long by two (2) inches deep, and six (6) inches wide — beneath the guard rails at each bolt hole ; the bolt passing through the middle of the shim, and each shim being fastened to the floor by four (4) five (5) inch cut spikes. Ii'ou Hand Railing. — Bridges with sidewalks v.-ill not require the wooden hand railing inside the trusses, but are to be pro- vided with a neat, substantial iron hand rail on the exterior of each sidewalk. It is to be rigidly attached to the floor beams and exterior sidewalk joists. Details not prcvionsly Mentioned. — Finally, as regards the proportioning of any structure, if cases should occur which are not covered by the preceding specifications, the following rule is in all such cases to be adhered to : " Details must always be proportioned so as to resist every direct and indirect stress that may ever come upon them under any probable circum- stances, without subjecting any portion of their material to a stress greater than tlie legitimate corresponding working-stress." Cast-iron. — No cast-iron is to be used except for washers for timber bolts, and for ornamental work and name plates. Name Plates. — The names of the designer and the manu- facturer of the bridge must be attached thereto in a prominent position and in a durable manner. Field Riveting. — I-'ield riveting must be done with the button OND/X.INV /KOX IIIGHU'AY-IiRinGES. !5 •egards the r which arc or washers 1 the button sett. The heads of the rivets must be hemispherical, and no rou<;ii edges must be left. Paiutiiii^. — i\\\ finished work, before leaving the shop, shall he thoroughly cleaned from all loose scale and rust, and covered with one good coat of pure boiled linseed-oil well worked into all joints and open spaces. In riveted work all surfaces coming into contact shall be painted before being riveted tofether. Ik'd plates, and all parts of the work which will not be acces- sible for painting after erection, shall have two coats of paint. i'ins, i)orcd jjin holes, and turned friction rollers, shall be coated with white lead and tallow before being shipped from the shop. After the structure is erected, the iron-work shall be cleansed from mud, grease, or any other objectionable material that may be found thereon, then thoroughly and evenly painted with two coats of jiaint mixed with pure linseed-oil, of a color pleasing to the eye ; the tension members being generally of a lighter shade than the compression members. Wherever it be possible to so design it, the iron-work must be made accessible to the paint-brush. Tititbcr.— KW timber is to be of the best quality, free from wind-shakes, large knots, decayed wood, sap, or any defect that would impair its strength or durability. Quality of Workmanship. — All workmanship is to be first- class ; abutting joints are to be truly planed and dressed, so as to insure a perfect bearing ; the pin holes in chords, batter braces, and posts, are to be bored as truly as is specified for the eye bars ; and there are no rough edges or corners to be left on the iron-work. 15ars which are to be placed side by side, or in similar posi- tions in the structure, shall be bored at the same temperature, and of such equal length, that, upon being piled on one another, the pins shall pass through the holes at both ends without driving. Whenever necessary for the protection of the thread, provision shall be made for the use of pilot nuts in erection. Quality ami Tests of Materials. — All wrought-iron must be tough, fibrous, and uniform in character. It shall have a limit of elasticity of not less than twenty-six thousand (26,000) pounds per square inch. 26 OA'V/X.lA'i' /A'O.V HlCllUAY-llRIDGES. Il: Finished bars must be thoroughly welded during the rolling, and free from injurious seams, blisters, buckles, cinder spots, and imperfect edges. lu)r all tension members the muck bars shall be rolled into flats, and again cut, piled, and rolled into finished sizes. They shall stand the following tests. Full-sized pieces of flat, round, or square iron, not over four and a half (4,}) scjuare inches in sectional area, are to have an ultimate strength of fifty thou- sand (50,000) pounds per scjuarc inch, and are to stretch twehc and a half (12.]) per cent of their whole length. Bars of a larger sectional area than four and a half (4^) square inches arc to be allowed a reduction of one thousand (i,ooo) pounds per square inch for each additional square inch of sec- tion, down to a minimum of forty-six thousand (46,000) pounds per square inch. Specimens of a uniform section of at least one (i) square inch, taken from bars of four and a half (4]) square inches sec- tion, and under, are to have an ultimate tensile strength of fifty-two thousand (52,000) pounds per square inch, and are to stretch eighteen (18) per cent in eight (<S) inches. Similar specimens from bars of a larger section than four and a half (4.^) square inches are to be allowed a reduction of five hundred (500) pounds per square inch for each additional square inch of section, down to a minimum of fifty thousand (50,000) pounds per square inch. Similar sections from angle and other shaped iron are to have an ultimate strength of fifty thousand (50,000) pounds per square inch, and are to stretch fifteen (15) per cent in eight (8) inches. All iron for webs of plate girders is to have an ultimate strength of not less than forty-six thousand (46,000) pounds per square inch of area of test-piece, and is to have a minimum elongation of ten (10) per cent in eight (8) inches. Rivets are to be of the best quality of double refined iron. The cast-iron must be of the best quality of soft gray iron. Test of Structure. — On the completion of the entire struc- ture, any bridge, after being in constant use for one day, may be tested by a load equal to that for which it was designed O/v'DLV.l/CV /A\hV n/GI/WA V-nN/DGES. 27 remaining upon it for at least one hour, then removed, and placed upon it again. The first removal of the loatl may show a little permanent set ; but, when the second load is ap|)lied, the total deflection must not be any greater than it was for the first loading, and upon its removal the bridge must return to the exact position which it occupied after the removal of the first loading. 28 ORD/XA N 1 ' //.'( ^\' ///( /// U'.n -/}N/1)(.;ES. CHAPTER III. T.IST OK MF:M1!KRS. In the followinj; list of momliors will be found the names of all the parts, both of wood and iron, in the bridj^es with wliich this treatise deals. Its use will be explained in Chapter XIV. It is inserted here so that those unacquainted with bridf;e designing; may inform themselves as to the names of all the parts of a bridge before proccedin<; farther. This they can do by consultinj;- the Cilossary, and referring; to the i)lates there indicated. The author would advise students, before proceeding to Chapter IV., to study closely Plates I. -IV., so as to obtain a general idea of how bridges are constructed. LIST OF MEMBERS IN A WROUGHT-IRON HIGHWAY-BRIDGE. M.MN PORTIONS. Channel Bars. — Top chords, batter braces, bottom chords, posts, upper lateral struts, end lower lateral struts, upper portal struts, lower portal struts, hip verticals in pony trusses. Plates. — Top chords, batter braces. I-Beams. — Floor beams, intermediate struts, end lower lateral struts, bottom chords. Bars and Rods. — Main diagonals, counters, hip verticals, upper lateral rods, lower lateral rods, vibration rods at portals, vibration rods on posts, chord bars. Angle Iron. — Side bracing, end lower lateral struts. Iron hand railing. Floor beams. DET.\ILS. Stay Plates. — Top chords, batter braces, ends of posts, mid- s. ( >A-J)/X. IRV /A'O.V 1 Hi.: nil -A J -liKt IHlllS. -9 he names of s with which hapter XIV. with brid<;c »s of all the they can do plates there ■e proceeding; s to obtain a \Y-BRIDGE. ttom chords, upper portal isses. lower lateral u|) verticals, Is at portals, uts. )f posts, mid- dle of i)i)sts, bottom-chord channels, upper lateral struts, end lowrr latt'ral struts, up])er portal struts, lowrr portal struts. Ri-iiifoiriiii^ and Coiuuctiiii^ or SI'Hcl- /Wit^s. — Hip inside, Iiip outside, top-clinrd intermediate jiaml points inside, top-chord iiilerniediate panel points outside, holtoni-tliord struts at shoe, l)ottom-ch()rd struts at first panel points, shoe inside, shoe out- side, lower enils of posts insiile, lower ends of jiosts outside, mid- dle of posts inside, middle of i)osts outside, lateral struts U) to|) ihoids, up|)er portal struts to batter braces, lower portal struts to hatlL'r braces, portal struts to brackets and name plates, iiitennediate struts to posts, side bracinuj to floor beams, end lower lateral struts to pedestals. (\nrr P/atis. — Hip joints, joints at intermediate panel points of to|) chords. I'i/liiii^ Plates. — Hips, intermediate panel points of top chord, over end floor beams, between pedestals and lateral struts. ICxtension plates at upper enils of posts, shoe plates, roller plates, bed plates, beanvhanger jilates, name plates. /,(?(-///i,'- or Latticing. — Top-chord channels, batter-brace chan- nels, bottom-chord channels, post channels, upper lateral strut channels, end lower lateral strut channels, upper portal struts, lower portal struts, hip verticals in pony trusses. y'/v/.ovV/i,'-. — Hip verticals in pony trusses, lower-chord bars. /V//.S-. — Top chords, bottom cliords, middle of posts, lower lateral rod connection to jaws, vibration-rotl connection to upper portal and lateral struts, vibration-rod connection to lower portal struts, between floor beams and beam-hanger plates. Bolts. — Brackets to portal struts and lateral struts, brackets to batter braces and posts, name plates to jwrtal struts, vibra- tion rods to lateral struts, vibration rods to intermediate struts, bed plates to piers (anchor bolts), shoes to bed plates, expansion pedestal connection to bed plates, portal struts to batter braces, iiand-rail posts to joi.sts, lower lateral struts to floor beams, lower lateral struts to jaws, felly planks to floor and hand-rail posts. Brackets or Knee Braces. — Portal struts to batter braces, upper lateral struts to posts, intermediate struts to posts. Ornamental work at portals, beam hangers, expansion rollers, 30 ORDINARY IROX IllGllWlV-BRlDGES. roller frames, fillers for pins, turn buckles, sleeve nuts, ronnect- in^'-iiiord heads for bt)tl()ni chord channels, jaws for lateral and portal struts. Ati}^lc //vw. — natter braces to shoe plates, sides of roller plates, ends of roller plates. Picas of Chanmb. — Hearins for bent eyes of upper lateral rods, bearinj; for bent eyes of lower lateral rods, batter-brace connectioh o shoe plates. Kivif Heads. — Tlate to chord and batter-brace channels, lat- ticin-; or lacing to channels, latticing; to latticing, the various stay plates to channels, the various connecting and re-enforcing plates to channels, connecting plates to shoe plates, connecthig plates to intermediate struts, connecting plates to side bracing and floor beams, connecting plates at pedestals to pedestals and lateral struts, cover plates to chords, extension plates to posts, trussing to hip verticals and posts, trussing to chord bars, orna- mental work to portals, brackets to posts and batter braces, brackets to portal, lateral, and intermediate struts, components of jaws to each other, angle irons to shoe plates, angle irons to roller plates, the various pieces of channels to the parts which they connect. 5y,//vx — Flooring to joists, hand rails to posts, hub planks to posts, felly planks to flooring, joists to lower lateral struts, jaws to lower lateral struts. Waslicrs. — Hand-rail post bolts, bolts connecting lateral struts to floor beams, felly-plank bolts. ^\^/^/.s-. — On pins, on bolts, on beam hangers, lock nuts on beam hangers, pilot nuts. Details for a Built Floor Beam. — Web, upper-flange angles, lower-flange angles, top plate, bottom plate, stiffening angles, filling plates, re-enforcing plates at beam-hanger holes, rivet heads. Details for a Trussed Beam. — Rolled I-beam for upper chord, lower-chord bars, end diagonals, counters, I-beam posts, con- necting plates for posts to beam, re-enforcing plates at feet of posts, pin plates for end diagonal connection to beam, stiffeners at supports, pins and nuts on same, fillers, turn buckles or sleeve nuts, rivet heads. lateral struts lock nuts on 0/\/)/.y.lA-r /I'lKV Jl/UJ/lfA V-IiKUHiLS. 31 f.iniil'tr. — Joists, flooring, hand-rail pieces, hand-rail posts, lull) planks, felly planks or guard rails, lower lateral struts. es of roller DI/PAILS roR A SPAN COMI'OSED OK PI.ATK (ilROKKS. Webs, upper-flange angles, lower-flange angles, top plates, bdttoin plates, stiffening angles, filling plates, angles for lateral braces, connecting plates for lateral braces, shoe plates, bed plates, anchor bolts and nuts, rivet heads. 32 OKDL\AJ<]- JNO.X HluUWA V-HRlDuES. CHAPTER IV. LIVE AND DEAD l,( )ADS.— WIXD PUKSSURE. As stated in Cliaptor 1 1., lii^Ii\vay-liri(ls;os are divided into throe elasses, A, B, and C, whieh arc res])ectively for loeations where the loads are heavy and of frequent oecurrenee, loea- tions where the loads are occasionally heavy, and locations where the loads are li_nht. After deeidinj;' ui^on the lenfjth of sjian, width of roadway, and class of hridi;e for any location, the live load per s(|uare foot of floor is to be taken from the table on p. 5. The reason why lont; sj)ans maybe proportioned for lii;-hter loads than short ones is the very small probability of a loni;- span e\er beini;' covered bv the maximum loatl, while there is a chance of sucii ai. event takinj;' place in case of a short span. It can easily be seen, then, that, in all bridt^es of any hiirth of span, each jianel should be proportioned to sustain the maxi- mum load ; for it is possible to load one panel heavily without loadin^f any of the others. This panel excess will affect only the sizes of the joists, floor beams, beam hangers, and hip verticals. Sometimes the jxinel excess is sup})osed to exist when the bridt;e is partially or wholly covered by the movinj;' load, thus aflectin,<4' all the main membei-s of the trusses ; but this is too nnich letinement for highwav-bridt;e desii;-ninL;'. The dead load per lineal foot is to be taken from one of Tables 1., II., and III., if there be no special loadin<j: such as that tlue to snow, if the style of hantl railini;-, i;uard rail, etc., for the bridj^e to be designed, corresiiimd with that adopted in this work, if the wiilth of roadway correspond with one of those in the table, and if the length of the siian be exactly divisible (>A'/)/x.iA'y /A'o.v J //amy A y-/uu/)g/':s. Zl divided into ' for locations iirrcnce, loca- and locations 1 of roadway, d per sc|uare The reason ids than short n e\er Ikmiil;' lance of sucli of any hiii'ih ;ain the maxi- .'avily without le joists, floor nes the panel ■; partially or ;■ all the main ^'tinenient for from one of idinii; such as lard rail, etc., It adopted in 1 one of those actly divisible by Icn. If either or both of the last two conditions be not fulfdled, the dead load is to be directly interpolated ; then if there be any difference in the lumber, or any special loadin<,^. the effect of the chan.i^e or changes is to be calculated by the method to be explained presently. The weiurhts of iron and lumb LT given in Tables I., II., and III., are the results of calculations for the bills of materials of sixty bridges, so chosen in respect to length of span, and width e weights vary e most eco- (if roadway, as to indicate the laws by which th with these dimension.s. All the bridges are of th nomic (le \\\ th t ie (hm fiv e colunms un pth and panel length, corresponding in these respects ensions given in Table IV. The figures in the weights ems, and floor Jot, not includinj der each roadway gi\e respectively the of iron per lineal foot in the tru.sses, lateral syst system ; the weight of lumber per lineal fo was te; and the dead load per lineal foot, corrected for the small amount resting on the i)iers. To find the dead load for any span where there is to increased weight of floorinf:, or be an an additional load, find th value for the weight of lumber (proportioning the ioist methoi n\ WCl ■hs t en in Chapter IX., remembering that e new by the pine lumber wo pounds and a half per foot, board measure, and oak lumber four pounds and a thirtl), then that of the fl by the formula oor system where F' is the weight per foot of the floor system required, F that of tiie floor system given in the table, ami r (greater than unity) the ratio of total loads on floor beams in the two cases considered. Next assume T\ the new value for the weight T m the truss column, and find the ratio ;-' (greater than unity) of total loads per foot on trusses in the two cases ; then If the value of T' thus found agrees with that assumed, all right ; '1 not, It will be necessary to try again until it does agree. 34 ORDINARY IRON HIGHWAY-BRIDGES. Next add together the differences between T' and T, between F' and F, and between the weights of lumber per lineal foot. To the sum of these differences add the weight of snow or other special loading per lineal foot of bridge, and the dead load taken from the table. The final sum will be the dead load required. To find the dead load for a bridge with sidewalks, look in the table of the class to whicli the bridge belongs, and find the weights for a bridge of the same span and roadway without sidewalks, then estimate the increments of these weight." as follows : — First, the weight of lumber per lineal foot on the sidewalks is to be calculated ; and from it is to be subtracted twenty-four pounds, which is the weight per foot of the wooden hand rails, hub planks, and hand-rail posts (lumber not required when there are sidewalks). The difference will be the increment for the "lumber" column. The increment for the " lateral system " column will be zero : that for the " floor system " column can be found approximately by the formula / = 2bF where / is the increment required, F the weight per foot of floor system taken from the table, b the sum of the widths of the sidewalks, and /; the clear width of main roadway. The increment of the "truss" column is found by assuming the dead load required, and calling it W'l,. Let IVa = tlie dead load given in the table, p^ _ the live load per lineal foot on the main roadway, Pi, = that on the sidewalks ; then Let Pa + //;, T„ = the truss weii^lit from the table, 7), — the new iriiss weit;ht ; ORDINARY IRON HIGH WAY-BRIDGES. 35 then 1 roadway, s. Ty ^(- ^{ Pa\-P l,-^Wt)\ and the increment will be T/, — T„- Next add /F„, the three increments found, and the weight per lineal foot of the iron hand rails : the sum will be the dead load required. If it agrees with the assumed load IVt, all right ; if not, another trial for the new truss weight is to be made. There is one case in which this method would give too trreat a result : it is that of a pony truss with side braces, of which the only representative in the tables is the sixty-foot span. To apply the method to this case, it will be sufificiently exact to use the weight of floor system of the fifty-foot span, because the floor beams of the sixty-foot span project beyond the trusses. This change being made, the method can be otherwise followed exactly. The full double horizontal lines in Tables I., II., and III., divide the single from the double intersection trusses. All the bridges in Table III. lying to the left of the double vertical line which separates the twenty-two-foot and twenty- fnur-foot roadways, have stiffened end panels. The correspond- ing lines of division in Tables I. and II. separate the twenty-foot and twent}-two-foot roadways. The weights of iron in Tables I., II., and III., do not include tlw 'u'cig/it of the spikes. It is seldom necessary to make an allowance for snow load in bridges of Class C, but it may be advisable to do so in bridges of Classes A and B; for, after a heavy snow-storm, the travel nn country roads would be light, which would not necessarily the case in a city or its suburbs. The proper allowance snow load should be from ten (lo) to thirty (30) pounds er square foot of floor ; according to climate, locality, proba- bility of greatest live load occurring simultaneously with the .siKJW load, etc. As stated in Chapter II., the wind pressure assumed is forty (40) pounds per square foot for spans of one hundred (100) feet and under, thirty-five (35) pounds for spans between one hun- dred (100) and one hundred and fifty (150) feet, including the 36 ORDINARY IRON HIGHWAY-BRIDGES. latter, and thirty (30) pounds for all greater spans. It is true that actual wind pressures do occasionally exceed these amounts ; but in view of the fact that the chance of any one bridge ever being subjected to such pressure throughout its whole length is extremely small, and that it could receive once in a while a far greater pressure without suffering material injury if tlic bridge' be properly designed, it seems legitimate to adopt the pressures assumed. Moreover, when a highway-bridge is blown down, the actual loss is seldom much greater than the cost of a new bridge. Travellers can cross the stream at the nearest bridge above or below, until the structure be replaced. And the fall of the bridge need involve no loss of life : for, in the f^rst place, no human being would be likely to be upon it in such a storm ; and, in the second, if there were, he could not escape being dashed to pieces or blown off, even if the bridge were sufificiently rigid to withstand the pressure. With railroad-bridges, of course, it is a very different matter. The delay caused by the loss of such a bridge may be much more expensive than the replacing of the structure. Besides, railroad-bridges are subjected to the greatest wind pressure when covered by a train ; so that the fall usually involves the loss of human life. If the lateral systems of highway-bridges were ^o be made as strong as those of railroad-bridges, unstiffened eye-bars could be very seldom employed for the bottom chords ; because the compression there due to the wind pressure would be far in excess of the tension due to dead load (%ndc Appendix I.). Even with the pressures assumed, it is necessary to rely upon the stiffness of the joists to prevent buckling the bottom chords of at least two-thirds of the iron and combination highway- bridges in the United States. It is not necessary to add any area to the section of the bot- tom chords to resist the tension due to wind pressure, unless this tension exceeds that due to the live load multiplied by the ratio of the intensity f)f working tensile stress in lateral systems to that of working tensile stress in chords. Should it so exceed, the chords should he proportioned to resist the wind ORDLXARV IRON HIGHWAY-BRIDGES. 37 stress plus the dead-load stress multiplied by the aforesaid ratio, using an intensity of seven and a half (/.]) tons, or, in case of stiffened eye-bars, six and a half (6^) tons. This ex- cess should be looked for in narrow bridges in unusually exposed situations, in the design for which the wind pressure has been increased ten (lo) pounds per square foot. I-\)r this same reason, of there being no probability of a live l(md remaining upon a highway-bridge during a heavy storm, the effect of the wind upon posts and batter braces may be neglected, unless the stresses produced thereby exceed those due to the live load multiplied by the ratio before mentioned ; in which case the wind stresses should be multiplied by the reciprocal of this ratio, and to the product should be added the dead-load stresses, in order to find the greatest stresses for which to ])roportion these members. As before, this excess is to be looked for when the assumed wind pressure has been increased by ten (lo) pounds per square foot: it will probably be only the lighter posts that will be so affected. l^ut the bending effect of the wind pressure upon portal and latL'ral struts, when no vertical sway bracing except brackets is used, should always be provided for. The author believes, that, instead of designing highway- bridges in ordinarily exposed situations to resist the greatest recorded wind pressure in the district, it is better to run a little risk of losing a structure than to make all the britlges so much more expensive. Nevertheless, he wishes it to be distinctly understood, that, in advocating the adoption of com- paratively low wind pressures, he does not countenance the buikling of such miserable apologies for lateral systems as one rinds in the majority of highway-bridges. 38 ORDINARY IROX HIC-lIW'AV-liRIDGKS. CHAPTER V. STRKSSKS IN TRUSSES. The length of span having hecn decided by considerations of both necessity and economy {vide Chapter XV.), and the width of roadway by the requirements of travel, there remain to be determined, before making out the diagram of stresses, only the style of intersection, panel length, and depth of trusses. These matters are fully treated in Cluipter XV. Meanwhile, the style of intersection may be settled by remembering that the single is more expensive than the double, and that the inferior limits of the latter for the different classes of bridges and differ- ent clear roadways are given in the table on p. 8. The most economic panel lengths and depths of truss for locations wliere long timber is expensive, and, in fact, for nearly all locations, are to be taken from Table IV. For locations where long tim- ber is very cheap, there can be made a little saving in the iron-work by using Table V. instead of Table IV. As is customary in figuring stresses, uniformly distributed loads are to be considered as concentrated at the panel points; and the half-panel load at each end of the truss is not supposed to produce any stress in any member of the truss. The first step in making a diagram of stresses is to fill out one of the following tables of data : — Single Intersection. 11 — d = diag. = sec Q = iLMM.E ISTEUSECTION. Doi'Fii.E Intersecticin, ;n Number of Panels. odd Number of I'.uicls. n — n = / = / = d=. d = short diag. = short diag. = long diag. = long diag. = OKJ)/XAKV /NOX lllClllVAY-nRIDGES. 39 Doi'dLlv iNTKHMiCTlON. DoimtR iNTF.RSKCTinN SlMiLE iNTEK-iKCTlON. Even Niinitjcr of i'aiicls. Odd Number of I'anek tan B = sec a = sec a = ; w =■ tan u = tan a = IV, = sec ft = sec ft = IV" = 70 = TV = IV' = ^F,= PV,= I JF" = IV" = n IV' = IV = - w sec = w I 1 ~ 7V = n n\ sec = U/;sec6 = I - 70 sec « = n ' '/r"tane = ^ /F" tan 6 = ?Fj sec « = I U\ sec « = I - IV sec « = 11 - 7S.I sec i8 = Uv, sec« = IV, sec j8 = \ n\ sec /3 = - 7v sec fl = ]V" tan <« = ^ff'tan« = n ' sec /3 = -■ W" tan « = is to fill out where ;/ is the number of panels in the span, / the length of each panel, d the depth from centre to centre of chords, b the inclination of the diagonal ties in the single-interspction truss to the vertical, a' the live panel load in tons on one truss (i.e., one-half the ]:)roduct of the live load per foot by the panel length, or one-half the product of the clear roadway by the l);incl length by the live load per square foot in pounds, all divided by two thousand), W, the panel dead load on one truss, W" — III + //'j, IV" the portion of H\ concentrated at the upper panel point, « the inclination of the short diagonal ties in double- intersection trusses to the vertical, and ft the inclination of the long diagonal ties in same to the vertical. The value of If" is usually between one-foiuth and one-third of /f'j: by taking it always eqtial to one-third of Jl\ a small error on the side of safety will be made in designing short spans. Having filled out the table of data, the next step is to draw a 40 ORDINARY IRON H/GHWAY-nR/DGES. skeleton diagram large enough to contain all the stresses and sections. It is not necessary that the diagram be drawn to scale ; but the ratio of panel length to depth of truss on the diagram, for the sake of appearance, should not vary too greatly from the ratio of the actual values of these dimensions. A panel length of an inch and a half, and a depth of two inches and a half, are about as small dimensions as will be found con- venient. At each lower panel point write lightly in pencil, so th^t it can be afterwards erased, the number of the panel point, begin- ning with zero at the right-hand end of the span. It is well known, and will be accepted here without proof, that the greatest stresses in the chords and batter braces occur when the bridge is entirely covered by the moving load ; that the greatest stress in any diagonal exists when the live load extends to its foot from that end of the bridge towards which the diagonal points in a dimiiu'a ni (Xnccixon ; that the greatest stress in any post occurs when the main diagonal (or, if there be none, when the heaviest counter) attached to its up[)er end receives its greatest stress ; and that the two diagonals of a panel cannot at the same time be subjected to the same kind of stress, excepting, of course, the initial tension. It is apparent that when the greatest stresses in all the diagonals sloping upward in one direction, and in all the posts and chord panels on one side of the central plane, are found, the greatest stresses in the diagonals shjping in the opposite direc- tion, and in the |)osts and chord panels on the other side of the central plane, can be immediately written. This fact is so well known, that, in making a diagram of stresses, it is usual to write the stresses on only one-half of the members of the truss. First let us take a single-intersection through-bridge. The greatest stress in any diagonal sloping upward from right to left can be found by the formula -(// + I ) sue & + { // 2 /I \ 2 ')'K sec 9, where ;/ is the number of the j^anel point at the foot of the diagonal. This formula is ai)plicable to counters as well as to ORDINARY IRON HIGHWAY-URIDCEs. 41 main {liayonals. If the stress should come out negative, it shows tiuit no counter is needed in the panel considered. It is also applicable to the batter brace by putting (// — i) for ;/. The stress in any post can be found by the formula u liere ;/ (not less than "^ is the number at the foot of the post. The stress in any panel of the top chord is given by the formula c z=. "'(^ ~ ^0 W" tan 6, wliere ;/ (not greater than -^ is the number at the end of the panel nearest to the centre of the bridge. The stress in any panel of the bottom chord, except the one at the end of the span, is given by the formula r=l^jH^Zl^_L),r'tan^. ;/' having the same value as in the last formula. For the end panel, the stress is the same as for the second panel. As the values of '^, ^ sec ^, and //; sec ^, are given in the table of data, the substitution in these formulas is a very simple matter. ' ' The stress in the hip vertical is tc + .1 (weight of floor beam plus a panel weight of lumber), neglecting the weight of the Dcam hangers, end lower chord bars, etc., which is not worth considermg. It is not necessary to calculate this stress ; for the section required, or the size of the square bars, if that shape be employed, can be taken immediately from one of Tables VI., VII., or VIII. Some engineers may object to using formulas for figuring stresses : if so, the following method will give the same results lor single-intersection bridges. 42 OA'/)/.\:iA'i- fh'(h\ //A/////'./ J'-/.'A'//>(;a\v. I'ass ;i vcMtical plane through the middle point of the bottom ehoni • all ihe dead loads to the ri-ht of this plane may be c.nsidered to k<> to the li-ht-haml pier, and all to the left of the plane to the leftdianii pier. Shonld there be a post at the middle of the brid-e. the wei-ht at the foot is to be e.msidere.l as halved, one-half goin- to each pier. Then the stress m any main diagonal of the left-hand half of the bridge is to be f.mnd by eommencin- at the ri-hthand end, and a.ldin- the nimd.ers at the panel points until the foot of the diagonal eonsidered is reached, multiplying the sum by Sc sec ^, and to the product adding the number of panel dead loads between the central plane and the panel point at the foot of the diagonal considered (including the one at this point) multiplied by \\\ sec b. Vox instance, in a ten-panel bridge, the stress in the end main diagonal, the number at its foot being eight, will be lO (I + 2 + 3 + etc. . The stress in a counter on the right-hand half of the bridge will be found bv adding the numbers at the panel points until the foot of 'the counter considered is reached, multiply ing the sum by - «- sec /^ and from the product subtracting the dead-load stress of the main diagonal which crosses the coun icr Thus, in the ten-panel bridge, the stress in the second counter from the centre in the right-hand half of the span, or the one at the foot of the third panel point, is The greatest stress in any post is found by adding W to the vertical component of the greatest stress in the main diagonal attached to its upper end ; thus, in the same bridge, the stress in the first post from the left-hand end, or the one at the eighth panel point, is (x + . + 3-fctc.... + 7)"+(Jf + O^J^+^^'- ()A'/)/A:iA'y /NOX niCIIW.lY-lil^lDCES. 43 For the case of a middle post, the stress in one of the coim- tiTs at the upper ^wA must be substituled for that of tlic .uaiii (lia-onal ; thus, in the same bridge, the stress in tiie middle post is (I + 2 + 3 + 4),^ -\W, + W'. btractiiii; tlie The stresses ni the chords are to be found by the follow-in- nu'thod : — I'ass a plane throu{,^h the foot of the post at or nearest to the mi. Idle of the truss, and take the centre of moments at this loot. I-rom the moment of the re-action at the nearest end of the l.ridj^a" subtract the sum of the moments of the pane 1 loads (//'") lyinj; between the centre of u mci.ts and this end, and divide the dilTerence by the depth of the truss. The result will be the stress in the panel of the top chord nearest the centre of the brid^^e : it will be some multiple of //'" tan e. The stress in tiie panel of the bottom chord immeuiately below will be equal to the one found, less the horizontal com- |)oncnt of tile luaiit diagonal of the panel, when the brid<;e is covered by the moving load. This horizontal component" will be zero for a truss with an odd number of panels, anti .i //'" tan lor a truss with an even number of panels. The stress in the ne.xt panel of the bottom chord towards the nearest end of the bridj^e Is found by subtracting from the one already determined tlie horizontal component of the stress in the main diagonal at the panel point between the two panels considered ; the bridge, as before, being fully loaded. This com- ponent is a multiple of W" tan 6. In this way can be found all the stresses in the panels of the bottom chord, the correctness of the work being checked by seeing if the stress in the end panel be equal to the re-action multiplied by tan (i. If so, the remaining upiier-chord stresses mav be at once written by mspection; for the stress in the ;/th panel of the top chord, counting from the nearest jjier or abutment, and supplying the missmg panel at the end, is numerically equal to that in the {it-\- i)th panel of the bottom chord. It seems almost unnecessary to state, that the stresses in the 44 oNn/XAKV //COX ///<;// ivA y-/i/c//Hi/-:s. top chords, hatter hraccs, and posts, arc compressive, and those in liottom chords, main diagonals, counters, and hip verticals tensile. Next let us consider the double-intersection truss. The formulas for this case are so complicated that it is better not to employ them. The simplest method is to draw a skele- ton diagram, and number the panel points, as in the single-inter- section truss. The double-intersection truss really consists of two trusses, as may be seen in the accompanying diagram. D II i:t 11! 11 Id 1) a j ;■ » :< i :i j i u Ah NlxM /I A - fig. 3 IBM n 10 n i i i a Such a division is necessary in order to calculate the chord stresses when the truss contains an odd number of panels. This is accomplished by finding, by the method of moments already explained, the chord stresses in each of the trusses shown in Figs. 2 and 3, and then combining them. Thus the stress in panel 9-10 of the lower chord in Fig.i is equal to that in panel 9-1 1 of Fig. 2, plus that of panel 8-10 of Fig. 3. The live-load stress in any diagonal sloping upward from right to left is found by noting whether the number at its foot be" odd or even, then taking the sum of the odd or even numbers, from one or two up to the number at the foot of the to IV diagonal, and multiplying the sum by - sec a, or - sec [i, as the case may be. The stress due to the dead load is found by taking the sum of the same numbers, and from it subtracting the sum of the odd or even numbers from one or two up to n — (//' + 2), where ;/ is the number of panels in the span, and // is the number at the foot of the diagonal considered. Whether the odd or even OA'/>/.\:iA'y /A'6».v ///(,// n: I y-/,'/://h;/:s. 45 iiiimhns should he taki-n can he ascertained hy followinf? out towards the left the system to which the dia^a)nal helon;;s : if the system contain the short (lia;j;onal at tli.it end, then th.- even nimihers arc to he taken, otherwise the odd ones. The difference thus found, multiplied hy " ' '*'''-'" or ^^'''■' /^, '/ // as the case may he, will f,Mve the dead-load stress in the dia;;onal. Thus, in the diagram, the dead-load stress in the main diago- nal at the panel point lo is [(2 + 4 4- etc. + io)-(i +3)]-- /F, sec /3 As in the case of the sinp;le intersection, the stress in a main (liaj;-onal is equal to the simi of the live and dead load stresses ; that in a counter, to the difference hetvveen its live-load stress and the dead load stress of the main diaj,fonal crossin^^ it at the middle of its len-^th ; that in a post, hy the sum of //" and the vertical component of the Kix-atest stress in the main dia-onal (or, if there he none, that in the principal counter) attached to its upper end. As the hatter hraces helong to hoth systems of triangulation, their stresses are the sum of the stresses found hy each system, or hy the formula C=[r + 2 + 3 -f- etc + (n - ,)]l^:±i51i££i.\ If the numher of panels he even, the calculation for the dead- load stresses may he much simpliiietl hy coinitin-; the numher nf panel jjoints on the system considered lyin^ hetween the central plane and the panel point at the foot of the diagonal, inchuling the latter, rememherin-,- th.at the load at the middle panel is halved, and multiplying the result hv Jl\ hcc a, or /r, sec/i. The finding of the chord stresses is .also simplified when there is an even numher of ixmels ; for they can then he calcu- lated hy the method explained for the single-intersection truss. In every douhle-intersection truss, there is neces.sarily a little amhiguity ; for it is possihle that the whole of the load con- ■} 1* 46 ORDLXARV IROX IIIGIIWAY-BRIDGES. centrated at the first panel point docs not travel by the sys- tem of odd numbers ; but this ambiguity is a matter of small moment. The only difference between the stresses in a deck bridge and those in a corresponding through bridge will be in the posts, the stresses for which are to be found by letting the live load extend from the farthest end of the bridge to the top of the post ; so that the post will no longer take its greatest stress with the main diagonal attached to its top, but with the one attached to its foot. The formula for post stresses in single-intersection deck bridges is, therefore. C = t>'{jl' - I)+ 2 'i{^\ + [,,'-.'i±iyv,+w'.* To find the stress in a post of a double-intersection deck bridge, add ic, U", and the vertical component of the greatest stress in the principal diagonal attached to its upper end.* In designing bridges where there is an assumed snow load, tlie counter stresses, and the post stresses produced by the counters, should be figured without the snow load ; because, the greater the dead load, the less the counter stresses, In Carnegie's "Pocket-Companion," pp. 141-143. ^'ViH be found tabulated the numerical co-efificients for the stresses in single- intersection trusses having from three to twelve panels, and in double-intersection trusses having from eleven to twenty panels. The panel dead loads are supposed to be concentrated^on the " * This method of finding post stresses is not exact, but gives an error on the side of safety, varying from "- at the centre to zero at the ends of tlie span : it assumes the total panel load «■ to pass down the i^ost before being divided into the portions which i>ass to nglit and left, when in fact the portion going to the farther end passes down the main diago- nals as compression. Tlie formula was uriginally obtained under tlie false assumption ; but it has been retained for the following reasons : — ist, There is a certain amourt of shock accomjianying the application of the panel live load on the post ; 2d, The load w comin^^ from the floor beam is applied to one side of the axis of the post, and consequently tends to produce a slight bending thereon ; 3d, The distribution of the excess of stress is favorable, being greatest for the light jxjsts near the middle of the span, and smallest for the heavy ones near the ends. ORDIXA R Y IRON HIGH WA J -BRIDGES. section deck 47 bottom chords in through bridges, which will cause an error on the side of danger in the post stresses : this fact is pointed out on p. 141. A slight difference will be found between the co- efficients there given for the diagonal and chord stresses of double-intersection trusses having an odd number of panels, .uul those obtained by following the method indicated in this chapter. The latter will give stresses slightly in excess of those in the "Pocket-Companion;" but the difference is so small, that it is scarcely worth mentioning. Had the engineer who ijrepared the tables been a believer in the use of long panels, he would have commenced his douWe-intersection trusses with seven panels instead of eleven. Tables XLI. and XLII. give the stresses for all bridges treated in this work. rsection dec) ion of tlie panel live Ic of the axis of tlie 48 ORDLXAKY JRO.X HlGlilVA V-BRWGES. CHAPTER VI. STRESSES IN LATERAL SVSTEALS AND SWAY BRACING. The wind loads concentrated at the panel points are deter- mined by imagininjj; a horizontal plane passing through the middle of the truss, and supposing that the pressure on all the exposed surface of the bridge above this plane is concen- trated at the upper- panel points, and all below this plane at the lower-panel points. This may be a correct assumption, or may not ; but it is as likely to be correct as any other. Where vertical sway bracing is used, the di\'ision of wind pressure becomes still more ambiguous ; but, as before, the same assumption is as likely to be correct as any other. In calculating the area opposed to the wind, the area of the vertical projectit)n of one truss, hand railing, including hub plank, guard rail, and the rectangles described about the windward ends of the floor beams, is to be doubled, and to this is to be added the area of the vertical projection of the floor and joists. As the windward hand rail would probably fail under high pressure, the total area thus found is somewhat in excess ; but such a failure should not be depended upon when the wind is considered to strike the bridge suddenly. For spans of and under two hundred, or sometimes even two hundred and thirty feet, the sizes of the upper lateral rods are not to be determined by the effect of the wind pressure, as this method would make them smaller than experience would indicate to be necessary for rigidity. The sizes to be used can be found in Table XXV. The wind stresses on the lateral systems are to be calculated for a moving load, instead of one upon the whole bridge ; because this method causes the rods towards the centre of the span to IRACING. s are deter- ;hrough the ^sure on all ; is concen- plane at the u nipt ion, or cr. ion of wind before, the her. area of the :luding hub about the and to this of the floor under high e.xcess ; but the wind is pans of and d and thirty ' determined would make le necessary rable XXV. le calculated Ige ; because the span to o/wj.v.iA'i- /AU)x uicnwAv-nRincEs. 49 he somewhat increased in diameter : besides, it is possible for a portion only of a structure to be subjected to wind pressure- the rest being protected by a hill, a building, or some other neighboring object. Without making any appreciable error, the wind pressure, for the purpose of simplifying calculation, may be considered as equally distributed between the two sides of the bridge, althou-h the windward side does receive the larger share. " The stress in any diagonal can be found by the formula ^ _ !i'(?i' + i) 7o sec e and that in any strut, except at the end of the lower lateral system, by the formula C = n\n ~ \) + n 271 •70, wiiere r.' is the sum of the pressures at a wind lanel point, // the number of panels in th ing in the two lackiu"; at th ivard and leeward e wind bracing, count- e ends of the upper lateral brae m-r in through bridges, ;/ ("not less th lan D th e number at the lee- ward end of the diagonal, or at eitl panel pom ler end of the strut, the ts being marked as directed in the last chapter, and 't the angle that the diagonals make with th 1 he stresses in the diagon tension, or, what is the same e struts. al s are to be th increased for initial )e taken from Tabic IX. mg, the W(jrking-stresses are t T atl( le ellect of the initial tei led to the stresses in those member sions on the struts is also to bi The method of calculating the st resses in the vertical sw bracing is as follows. It is essentially that of Profe< ;i\'en in his treat In 1-ig. I, let J' be the se on " Stresses in Brids ay ssor Burr, as ;eand Roof Trusses." at the upper ])anel point on on pressure supposed to be concentrated wliic'h CO e side of the brid- mes upon a panel length of lop chord, area o| the diaironals :e'. It is that one-haif the tiun of the post above the plane A/> meetmg at the panel point and th por- so OA'D/.V.I A" 1 • /A'OA I i lull II :n -JIKJDGES. Let P' be the pressure concentrated at one end of the inter- mediate strut /A'. It is that which comes upon the portion of the post between the planes AB and CD, the latter passing halfway between the intermediate strut and the bottom chords. If the interme- diate strut be at the middle of the post, and if the main diagonals and counters be coupled on a pin at this point, it would be necessary to divide the pressure upon ■ w**H the diagonals between the upper, middle, and lower points of the posts ; the middle taking one-half, and the others one-quarter each. Let d = the depth of the truss, /= the vertical distance between the upper lateral and interme- diate struts, d = the perpendicular distance between centres of trusses, and 6 = the ancle made bv the vibration rods with the vertical. The pressures concentrated at the lowest points of the posts do not affect the vertical sway bracing, so are not considered. The total pressure, 2{P + /") = //, is assumed to be ec|ually resisted by the feet of the posts. It is possible that this assumption is incorrect, for one foot may resist more than the other ; but, when it is remembered that perhaps the whole of the force 2P passes through the upper lateral system to the pedestals at the feet of the batter braces, it will be conceded that the assinnption is not upon the side of danger. If the whole of 2{P -f P') were to be resisted by the feet of the posts, th(! functions of the upper lateral system would be rather limited, the whole of the wind pressure upon the sliuc- ture being carried by the lower lateral system, which is highly improbable. But, whether the wnnd pressure upon the upper part of the trusses be carried by the ujiikt or by the lower lateral bracing, it is better, as far as the vertical sway bracing is concerned, to pro- portion the latter under the suj^position that the pressures at the upper panel points are carried thereby to the feet of the posts. ORDIXARY IKOX UIGHWAV-IiRlDGES. 5' ral and interme- Taking the centre of moments at E, the moment of the pressure is 2Pd+ 2P\d-f), : which can be resisted only by the moment of a released weight /'upon the foot at /^; thus, 2Pd^2P\d-f)=.Vb, and y_ 2d{P^P')-2P'f b This release of weight V must pass up the vibration rod KG, causing a tension therein equal to ,. „ 2d{P+ P') - 2P'f Fsec 6 = ^ ^' Z. sec 6, To find the stress on the strut /A', pass a plane through the sway bracing, cutting GI/, GK, and /A' {/// not being strained); take the centre of moments at G, and consider the forces act- ing on the left side of the truss ; then the moment of the stress In JK will balance the moments of P' and i//, thus, (Ml = \Hd-P'f d,^ ^~^-^=jr{P^P')-P', to which must be added the horizontal component of the initial tension in///. {JK) represents the stress mJK. The stress in the upper lateral strut GH is that due to the wind pressure, considering it as a portion of the upper lateral system plus the sum of the horizontal components of the initial tensions in the three rods meeting at one of its ends. If G/I be considered as a portion of the vertical sway bracing, its stress may be found by passing a jilane, as in the last case! and taking the centre of moments at K, considering the external fcrces acting on the left-hand half of the truss ; then the mo- ment of the stress in Gil will balance the moments of the horizontal re-action at E and the pressure at G, the moment of the increased weight at E balancing the moment of the increased re-action ; thus, or equal to the stress in /A". [ 52 ORDINARY IRON HIGIIWAV-HRI IK;ES. At first thought, it might appear tliat the two stresses found for GH should be added together to obtain the total stress ; but such is not the case, for the wind pressures cannot pass by both the vertical sway bracing and the upper lateral bracnig : so the greater stress must be taken. In all practical cases, the greater stress will be found by considering GH as belongmg to the upper lateral system. The bending moment on the post is and, if m be the distance between centres of gravity of post chamiels, the stress on one channel produced by the bending ^- III The released weight V, on the windward post, passes down the leeward post, producing a stress equal to y on each channel, makinf^ the total wind stress on one channel According to the method given in Chapter IV., if twice this stress or 2C+ F, exceed the live-load stress on the post, mul tiplied by seven and a half {jV), and divided by the intensity ot working tensile stress for lower chords, the post must be pro- portioned for dead-load and wind stresses, instead of dead-load and live-load stresses. All these formulas, except that for the stress in GH, may be made applicable to the portal bracing by putting for d the length of the batter brace, for / the perpendicular distance between centre lines of upper and lower portal struts, for /" the press- ure on one-half of the batter brace, and for P one-fourth of the sum of all the pressures concentrated at windward and leeward panel points of the top chord. If Pi be the pressure at the leeward hip, then the stress on the upper portal strut will be Ldvcn bv the formula C='^(r+P')-^" + ^'-P'' OKDIXARV INOA lllCllWAY-nRlDCES. 53 he stress on The stresses on all vibration rods must he increased for initial tension, or the rods must be proportioned by using Table IX. ; and the stress on each portal strut is to be increased by the sum of the components of the initial tensions in all the rods meeting at one of its ends, taken in the direction of its length. When there is no vertical sway bracing, stiffness is obtained by the use of knee braces, or brackets {AB, CD, Fig. 2), making angles of forty-five degrees with the vertical. Let the notation be as shown in the figure; F being, as before, the release of weight at /-: P is the sum of the pressures at H and G. Taking the centre of moments at E gives b' Vb = Pd and V = Again : taking the centre of moments at A gives the value of the bending-momcnt J/ on the strut at that point ; thus, M= V{b -S)- hPd= ^'Ub - 2S). G k-S-- TV I- I I I I I —b Fig.2 •»-.iP jr««.ip Let // equal the distance between the cen tres of gravity of the two channels of which j the upper lateral strut is comi)osed, then the bcnding-stress will be ^ M P/ '^--k^.bl^'-^^^' The intensity of the working bending-stress being six tons, the number of square inches to be added to the area of each channel, in order to resist bending, will be A C Pi ,, A= -= ,,{b- 2S). 6 1 2b/i ^ ' The stress in AB is found by taking the centre of moments at G, and making the moment of its stress R equal to the moment of the horizontal re-action at E ; thus, and RS\l\ = \Pd, ^ = -^\h = 0-707 ^. • 54 OA'JJLV.lA'y /A'O.V lHullWAV-BRUhiES. As before, to make these formulas applicalile to a portal, make d equal to the length of the batter brace, and P equal to one-half the sum of the pressures concentrated at all the upper panel points of the bridge. To find the effect of the wind on posts and batter braces, use the formula previously found, substituting in it .S' for /. Finally, the stress in an end lower lateral strut, at the free end of the span, may be obtained by the formula C„ = 2« •IV + /cos 6 + '-^ . w' - \ (^- - vy where ;/ is the number of panels in the bridge, tc the sum of the windward and leeward panel wind loads for the lower system, re-' the same for the upper system, / the initial tension in the end lower lateral rod, $ the angle between this rod and the strut, fCthc total weight of the unloaded bridge, and /'the release of weight at a windward shoe. Owing to the fact that the joists of the end panel rest on the masonry, this formula will give a result slightly on the side of safety. One or two applications of this formula will convince the most sceptical, that the general idea that any section is strong enough for a strut between pedestals is a fallacy. Too great a reliance has hitherto been placed upon the friction of the shoe, the released weight there not having been considered ; and the pressure which comes from the upper panel points seems to have been neglected. ORDhXARV IROiX HIGHIVAV-URIDGES. 55 CHAPTER VII. REMARKS CONCERNING MAIN MEMBERS. Top chords should nearly always be built of two channels, will) a plate on top, and latticing or lacing below. It is never good practice to use a single I-beam for top chord or batter brace, because of the great variation in stiffness in its two ])rincipal rectangular jilanes and the difficulty in making neat details for the connections. When the s|)an iDecomcs so short that it appears to be economical to use such a section, it is short enough to employ plate girders which are far superior, both as regartls strength and stiffness, to a bridge with I-beam chords. The same objection applies to an I-beam post, a favorite design of inferior bridge companies. If one were to take the trouble, in passing over a few bridges where they are used, to cast his eye along the posts, he would generally see that they are bent to one side or the other, or to both ; the latter being the case when there are employed what are termed out West "(}iasticutus rods," or horizontal rods five-eighths or three- quarters of an inch in diameter, passing from the middle of one post to the middle of the ne.\t in the same truss. Such rods are a noticeable feature in arch bridges, a class of structure that ought to be universally condemned. The principal objections to these bridges are their lack of rigidity, and their inability to resist wind pressure, because of the absence of efficient lateral bracing. But another grave fault is, that, being as a rule built by companies of the low(}st order, they are weak in section and detail, and the workmanship is poor. They are, without doubt, the cheapest kind of iron bridge that can be manufactured : hence their general adoption throughout the West, where short- sighted economy in building is the order of the day. 5<5 OKDIA'ARV ll<iK\ IllullU AV-liRlih.F.S. The I-hcani is mort- (iftcn found in u,ij)er laU'nil struts, wf^oiL' its use is fjuitc asobjcctioiiahlc, ICvcn if strong enough, whirh it .sekloni is, il i- by no means tlie hes* section for that place, owing to the ditVuuUy in connecting to the t i]) cho Wli re it rests on the cliord plate, and is riveted thereto, the lateral rods being attached to the chord pins, there is a great leverage affcrded to the wind stresses to distort tl\e chord ; and, where connected to the [liii by a jaw, the detail I; as to be either very clumsy or very weak. Anothei objection to I-beams tor lat( ral struts is the little room which there is in the flanges lur innuh- ing rivet holes. Hut the chief one is the small resistance tliat they oft\ I to the iieiiding effect of the wind pressure when there is no vertical sway bracing. \Vh..t lias been said of I-beams in lateral struts can be said with nui.eli more effect concerning I-beams in i)ort:d braces, for great stiffness and strength are there necessary in order to carry the wind pressure upon the upper half of the bridge to the foundations. The proper function oi an I-beam is to resist deflection in the plane of its web: ct)nset|uently it should be used as a floor beam, in which place its depth should seldom be less than ten inches, never less than nine inches. When one is debating about using such small floor beams, he should ligure them for a eon- centratetl wheel load, as well as for a uniformly distributed load. About the only places where a small I-beam can be legiti- mately employed are between the i edestals, as a lateral strut at the fi.xed end of a span, or at the free end if the bridge be narrow and the span very short, and in vertical sway bracing as an intermediate strut. For upper lateral struts, iron gas-pipe was formerly often em- ployed, and is so yet to a certain extent. Regarded as a section, nothing could be better fir more economical ; but the connec- tions made with il are very weak. Then, again, there is the objection that it is a closed column, and consequently inacces- sible to painting. Notwithstanding the fact that two of the leading bridge companies of the I'nited States employ almost exclusively closed columns, such columns are not. by engineers in general, conceded to be so good as open ones, which are always accessible to the paiiU-brush. Sonic other common forms of upper lateral struts are the fol- lowing: two tee-irons trussed, the upper restin- on tiie ehorcis an<l riveted thereto, the low.r ahuttin- a-ainst the same and att.KiK-d by bent phites ; two Uiannels trussed and attachc'd to thr .hords m tlie same manner; a eomi)ination of a channel and a plate, with trussing between ; and two tee-irons laced or latticed, with a jaw plate at each end wider than their flan-es screwed up to the chords by nuts on the ends of the chord ptns' ('win- to their lack of both strength and rigidity, all these are |M.wr contrivances, two channels laced or latticed bcin"- the best lorm of strut that can be designed for the upper lateral system As stated in the "General Specifications," in no highway bridge should the channels in chords, posts, or batter braces be less than live inches in depth, nor in any other part of the sti urture less than four inches. One does hear occasionally of such a thing as a three-inch channel top chord with tuo-inch I Mils, for a sixty ur seventy foot span. JJut, fortunately for the public .safety, such structures are few and far between The author once heard the senior representative of one of the most llnunsh.ng highway-bridge companies in America contend that iwo thice-mch channels trussed make a very good centre post lor short through-spans, -strong enough, because the area called for by the stress is less than three square inches He must either have forgotten, or been ignorant of, the f ict that stillness IS as important a factor in a bridge as simple strength in reality, strength is dependent upon stiffness; for where vibrat on can occur, the stresses are increased, not only in the members where stiffness is wanting, but in adjoining members of the structure. Light sections for compression members arc more economical than heavy ones, and it is generally preferable to use them nut, It the situation be one where the members will be exposed to excessive moisture, the webs should be thickened 1 he top plate for chords and batter braces should generallv I'c from one-quarter to three-eighths of an inch thiJk. Any thing below the inferior limit would be liable to distortion when roughly handled, and to ru.st through too readily; and any thino- above the superior limit would usually be inconsistent with the best distribution of area in the section. 58 (>A'/>/.v.iA-y /A'o.y ///(/////'./ J -/m'/m;a\v. It used to 1)0 customary, and tho practice is still followed to some extent, to make the top plate of varying thickness, or to vary the number of plates, increasin;,^ from the ends of the truss to the centre, makini; the ehanncls of the same dimensions throughout. lUit this method is not advisal)le ; for the proper plAce for the larger part of the material in a chord like the one under discussion is in the channels, and not in the plate. Simi- larly, in any channel, the proper i)lace for the larger part of the material is in the flanges, and not in the web; the reason being, in both cases, that the moments of inertia of the section in respect to vertical and hoiizontal neutral a.xes are increased Iv, removing a portion of the area away from these a.xes, and the strength of a strut increases with the moments of inertiii of its section. Star iron should never be employed in an iron bridge, and there is never any necessity for using tee-iron. Two of the latter sections, latticed by a triple or quadruple intersection ot thin, narrow bars, are sometimes ado])ted for a portal brace ; but it is evident how weak such a strut must be, and it is in the very place where a strong one is most needed. Four angles with the legs turned in, and set at the corners of a .square, laced on the four faces thus formed, make an economi- cal strut, as far as the section is concerned ; but it is probable that the e.xtra weight of detail and the increased cost of shoii- work will make it more expensive than another strut of larger section. Two channels latticed or laced arc the best form of portal strut. Large, heavy cast-iron [jortals made in one or two pieces look very well, and might be made strong enough, but are not so neat and graceful as some other kinds of bracing, besides adding unnecessary dead load to the structure. Cast- iron is not to be depended upon, and should not be used in any part of an iron bridge to resist stress. Channels in posts usually have their webs parallel to the direc- tion of the plane of the truss, with their flanges turned outward : sometimes they are turned inward ; and, where the floor beams are riveted to the posts, the webs are, or should be, placed at right angles to the plane of the truss, the flanges turning out- ward. 0A'/)/.\:tA' y /A'OA' maun '.-/ j ■-uridgi-is. <;cv Theoretically it is more economical, as far as the area <.f the >,eiti()n is concerned, to tuin the flanges in, for the moment of inertia is greater; but, on the other hand, the diiriculty en- countered in riveting in a confined space more than equalizes tile advantage just mentioned. Another advantage which can be claimed for channels turned in, \\/.., avoiding cutting them off before reaching the upper rhord pin, is partially counterbalanced by the increased size of pill, due to the larger leverage thus given to the stresses in the diagonals. Notwithstanding the difficulty in riveting, it is often hiuiid necessary, in swing bridges, to turn in the flanges of the post channels in order to form a good connection with the chan- iiel bottom chords : otherwise, the channels of the bottom chords may be turned in, and the post channels be allowed to bestride tlicm. The objection to cutting away the flanges of channels at the feet of posts has been shown by some experiments made by the Chicago and Alton Railroad Company, as given in a paper i\a(l before the Western Society of luigiiieers by Air. \\. J. Ward, who shows that this cutting-away reduces the strength of the strut about ten per cent. Main diagonals, as will be demonstrated in Chapter X., should have the proi)()rlion of width to depth of about one to four; and the chord bars, the proportion of from one to four to one to seven, according to the number of them in the panel. It is preferable, for ajipearances, to make the counters of square or round instead of flat bars, because of the unsightly change that there would be in the diameter of the flat bars at the upset ends. It is immaterial, except for the effect upon the pins, whether the hip verticals be flat, scpiare, or round ; but the preference is usually given to square iron. I5uilt floor beams in ordinary bridges should be formed of solid plates and angles, and not made trussed ; because, even if the latter method permit of a saving of material, it is more conducive to vibration. Where the panels are long and the roadway is very wide, it would be permissible to use trussed !)L'ams, provided that they be made \ery rigid in their details, and not too slight in their .sections. i;; ! CO C'A'/V .y.i/n' iNox ]iic,iiw.\y-Bi^ii)C,Es. CHAPTER VIII. rUOrORTIONING OF MAIN MKMBKRS OK TRUSSES. LATERAI SYSTEMS, AND SWAY ISKACIXo. HwixG found all the stresses in the main members of the truss and in those of the lateral systems and sway bracmg, and havino- written them alon-side the respective members m the dia-n-mns, the next step is to calculate the sections requn-cd. The dia-rams for the lateral systems and sway bracmg may be rouohly\u-awn in pencil ; for they need not be preserved, as the size's of the members are to be written on the truss dia-ram. For the tension members of the trusses, the sections required can be found by dividing the stresses on the diagram by the proper intensities of working-stress, as given on p. 12; remem- bering- that the intensities for main diagonals are to be inter- polated. When f.u.ncl. the reciuired areas for the sections should be written on the diagram, after the stresses, preuxing them with the letters S. R. (section required), as shown on riue V Then, by using Carnegie's " Pocket-Companu).. pp. 94-105, or some eciuivalent tables, ^an be found the sizes necessary to give at hast the section required, taking care that the sections be in good proi«)rtion. The stresses in the counters are to be increased for initial .crsion by the amounts given on p. 10; or, what is the same tliin.^ the size required can be found from Table IX. by look- ing- '";iown the column headed " Working-Stress = 4 tons per .c,uaie inch," if the bridge belong to Class A, or down the one headed " Working-Stress = 5 tons per square inch, if it belon.i; to Class W or Class C", until a stress is reached which is ec|ual to or greater than one-half or the whole of the .stress on the diuo-ram, according to whctlier doul)le or single counters :)C Oh'D/.y.iRv /A'o.y }ii<.;iiivAY-nRii)(.]Es. 6 1 ES, LATER A I cniplincd ; tlicn, by following;- the horizonla! line which con- tains tliis stress, cither to right or left, will be found the ^ize of the counters or counter required. As previously mentioned, the sections required for, and the sizes of, the hip verticals, can be found without calculation from OIK- of Tallies VI., VII., or VHI. Should the joists and floor- ing,' be of oak instead of pine, the section required for, and the <ize of, hi]) verticals, can still be found from the table by sup- posing an increase of one foot in the panel length. The sizes of the lateral and vibration rods can be found from Table IX. by looking in the column headed "Working-Stress = 7-5 toii^ P^'f square inch," in the same manner as e.xplainetl for counters. If the panel length correspond with the one given in Table IV., or if it do not differ greatly therefrom, there need be no calculations made for stresses in the lateral .systems and sway bracing ; for the dimensions of all the struts and rods for these .systems are given in Table XXV. In that table the (iimcnsions in the column marked " Pan. i " arc the sections rcsi)ectively of the upper portal struts, the portal vibration rods df any), the lower portal struts (if any), and the end lower lat- eral rods. Those in the other columns are the sections resiK'ctively of the upper lateral struts, the upper lateral rods, the post vibration rods (if any), the intermediate struts (if anv), and the lower lateral rods. The portal struts are thus assumed to belong to the first panel ; the first upper lateral strut, with its sway bracing, to the second panel, etc. ; so that, when the bridge has an odd number of ijanels, there is no lateral strut or vertical sway l)racing given for the middle panel. The fort\- toot, fifty-foot, and si.\ty-foot span.^, being pony trusses, have only lower lateral rods. Sloans above one hundred and fift)' feet in length have \ertical sway bracing. If the counter stresses be large, it is preferable to use double counters : sometimes both single and double counters are cm- plt.yed in the same truss. Where there is an odd number of ]xuiels, the centre tliagonals should be made double and adju.sta- hle. The number of main diagonals per panel is generally two ; init, if the sections become so great as to necessitate excessively large chord pins, it is better to employ f.iur ; placing two inside, 02 OKD/X.UiV INOX HIGHWAY-BRIDGES. and two outside, of the top chord and posts. The widths of the main diagonals should, for the sake of appearance, increase from the centre of the bridge to the ends. For the same rea- son, it is well to have all the chord bars of the same, or nearly the same, depth ; the correct area of section being obtained for each panel by varying the thickness and the number per panel. In large bridges it is permissible to reduce the depth of the choid bars towards the ends of the span in order to economize on the pins. It is also permissible, when there are several chord bars in the same panel, to employ depths varying by a quarter of an inch, provided that the bars of smaller depth be placed on the inside. As stated in the " General Specifications," where chord bars are trussed to resist the buckling effect of the wind pressure, the intensities of working-stress for the trussed bars on the net section should be reduced to four tons for bridges of Class A, and to five tons for those of Classes B and C. "Chord packing" is a term applied to the arrangement of the chord bars, diagonals, posts, and beam hangers upon the bottom chord pins. It is a matter of great importance, but is very often neglected. The three princijial considerations to be kept in mind while arranging the packing are, that the bending- moments on the pins are to be made as small as possible, that the packing is to be made as close as circums;ances will permit, and that there be sufficient clearance to avoid all chance of finding the space between the post channels too narrow when the bridge is being erected. The width of the packing is dependent, not only upon the number and thickness of the bars, but also upon the width of the top chord plate. The latter is often, in its turn, dependent u]X)n the chord packing. Th<' usual arrangement is to pack the main diagonals, coun- ters, and beam hangers inside of the posts, and the chord bars outside ; bringing the latter, however, within the batter braces at the shoes, unless the end panel contain four bars per truss, when two should go outside, and two inside. It is not abso- lutely necessary that the chord bars \m\\ in the exact line of the trusses ; an inch or two of deflection in twenty feet being ORDINARY IROX lilGHW AY-BRIDGES. 0?> scarcely noticeable, and making no appreciable difference in the length of the bar : nevertheless, it is better to make the bars as nearly as possible parallel to the planes of the trusses. The main diagonals should be placed next to the post, then the beam hangers, and inside of all, the counters with a filler iK'tvveen them long enough to permit of the screwing-up of the turn buckles, or sleeve nuts. The arrangement of the chord bars will be treated in Chan- ter X. ^ * The sections of the top chords and batter braces are to con- sist of two channels, with a plate on top, and latticing or lacing below. The same depth of channel, and the same width and thickness of plate, are to be employed from one end of the chord t.) the other; the difference in area being obtained by thicken- in- the webs of the channels. On this account, there is often an excess of section in the end panels of the top chord, and, in long bridges, even in the next panels. It is customary and better, but not necessary, to make the depth of the channels in the batter braces the same as that of the channels in the chord. Tlie top plate for the batter brace should be of the same size as that for the chord. The width of the toji plate is dependent upon the depth of the channels ; as the transverse distance between the centre lines of the rivets which attach the channels to the plate should be never less, and not (unless there be good reason) much greater, than the depth of the channels. The least dimensions for such |)lates for different channels are given on p. 15, The chord channels are sometimes spread apart in pony trusses, so as to mcrease the lateral stiffness; and in any bridge it may be necessary to spread them a little to admit of a certain manner of packing below : but, the more narrow the chord plate, the more economy of material will there usually be. To proportion the top cliord or batter brace for a given stress, .issume the deplh of the channels, and divide the length of the' piiiel or batter brace by it, both dimensions being expressed in the same unit. Referring to Table X. or XI., according to the class of bridge to be designed, look down the column marked "Kutioof L to A" until the ratio ju.st found is reached: the 64 ONJ)L\AKy JA'iKV J/lu/IUW ) -/.'A7/n;/'-.V, n umber to the ri<rht, in the first of the three columns, is the s are intensity of working-stress to be used. The three column for the three cases, — both ends fixed, one end fixed and one end hinged, and both ends hinged, marked LiE, L^iO, and (•• respectively. The tables were calculated by the formula of C. Shaler Smith, CM. ; to whom the author is indebted for its use, and for other valuable information in connection with bridge work. Then, to find the area of the top chord or batter brace, divide the stress given on the diagram by the intensity of working-stress taken from the table ; from the quotient subtract the area of the top plate, and divide the remainder by two : the final quotient will be the area of each channel. This calculation should be made with both the stress in the panel nearest the middle of the span and that in the end one, or, in long spans, that in the one next to the end. If, then, with the depth of channel assumed, it be found that there is, in the taljle of channel sections employed, a light channel that will not be much too heavy for the end. and a table for the middle of the chord, all right : ther trial must be made, with a channel of a dif- leavier one sui if not. ano fcrent depth. The greater the depth of channel, the less the ratio of length of strut to diameter, and consequently the greater the intensity sectional area required : : )f workinu-stress, and th( less generally speakin; use the lightest and deepest channel;-: possible, saving in section be small, when it will be the it is well to unless the more econonucal for other reasons, to use the next smaller depth. These rea- sons will be given in Chapter XV. The dimensions of the channels an d pi ate should be written on the cHagram of stresses as shown on Plate V. The sizes of the post channels are to be found in a similar manner to the one just described, with these two exceptions, — that the column for two hinged ends i to he used, and that there is no plate. .Some engineers prefer fixing the uj)])er ends of the i)osts bv attaching them, through the medium of pkites. to the chord, thus saving a little in the section ; but, as will be seen farther on, there is no true economy in so doing. In high double-intersection bridges, where the diagonals are OKD/A.INV /A'OX IIIC.n\VAV-I^R,nGKS. 65. halved and connected by pins passin-^ through the middle of- he post channels, as shown in Fi.-. ,5. Plato [I., the post may be proportioned for half-length witl, both ends hinged; but in this case the counters must extend to the ends of the span although there be no stress in some of them, for the purpose of preventing the posts from moving laterally at the middle " The upper lateral struts and portal struts are to be propor- t.oned by using Table XI. for both ends fixed, and adiing, f necessary, to the section thus found, enough area to resist the bending as determined in Chapter VI The ultimate strength of the intermediate struts, which are Ibcams can generally be found from experiments made by the manuaicturers ; a factor of safety of four being sufficient In default of such experiments, the approximate workino-.stresses ^:^^^^^^^ foi-Lbeams used as pillars may be ta^:; f::m iablc XL., which has been compiled from an old edition of Carnegie s "Pocket-Companion." When the I-beam .strut suppo,sed o bend ,n a vertical plane, its length should be taken c<,u to the istance between the points of attachment of th -a ets but when ,t ,s assumed to bend in a horizontal plane, .ts cngth mu.st be taken equal to the distance between opposite posts of the trusses. i^pposut J^rackets should extend inward and downward, from about l<n,r feet m narro^v bridge s, to about six feet in wid; ones it s|.,ybrac,ng given in labie XXV was proportioned for brack- a of hese dimension,s. Brackets beneath intermediate struts n^onb^rvetostiH^^^ Ti- intermediate lou. r lateral struts being of wood, it will n.H be necessary to calculate their section.s, which p actical ;;;;-c..uo. ' SI, t of two channels laced or latticed, and ■ ttached to the '"' ;'7' P.ns by J,,.. The si.e for the channels is to e - lut utl.er end is really fixed or hinged, but I^cause the ■^tungth of a strut .0 attached is intermediate between that of 66 ORl)/XARy JA'-'-y JiIOJIUA)-!lJ</D'^ES. one witii fixed ends and that of one with hinged ends. It is not positively necessary to use a lateral strut at the fixed end of a span ; but it is much better to do so, especially in long spans, not only to distribute the horizontal re-actions, but also to keep the chords in line, for there is necessarily a little play in the anchor bolt holes. It is not unusual to make the struts between pedestals of the same dimensions at l)oth ends of the span, although the one at the fixed end need not be so strong as the one at the free end. Appendix I., the substance of which appeared as an editorial in the " American Engineer" of July 20, 1883, shows the neces- sity for stiffening, at least the end panels of many bottom chords. This can be accomplished in several ways; one by inserting a strut between the inner chord bars ; another by using channel bars, laced or latticed, instead of eye bars, in which case the net section of the zvcbs alone should be relied on to resist tension ; and another by trussing the inner chord bars. The second of these methods is the most satisfactory, but at the same time the most expensive. When stiffening the end panel, it is well, though not perhaps essential, to stiffen also the second panel, where the stress is the same as in the one at the end. Such a practice is certainly conducive to the prevention of vibration of light bridges under rapidly moving loads. Hip'^vcrticals in three or four panel pony trusses are to be made to resist the compression which might be produced m them by rA-er-screwing the turn buckles of the counters. The section to be employed is cither that of two channels laced or latticed, or two flat bars trussed : in the latter case, as iire- viously stated in the "General Specifications," the intensities of working tensile stress on the net section are to be three tons for bridges of Class A, and four tons for bridges of Classes 15 and C. If two channels be used, the net area of the webs alone is to be relied on to resist tension. ORDINARY IRON UHJUlVAY-BRIDuES. 6; CHAPTER IX. PROPORTIONING OF FLOOR SYSTEM. The wooden portions of the floor system are the joists, floor- ing, hand railing, hub planks, and guard rails, or felly planks. Of these, only the joists require calculation for strength Pine flooring is generally three inches thick, and oak flooring two and a half inches. The hand railing, when of wood, should consist of 4" X 6" X 4' posts, not more than ten feet apart 2" X 6" rails, and 2" X 12" hub plank, all of pine, and built as shown m Plate II., Fig. 13, and as specified on p. 23. The guard rails should be of 6" X 6" pine, connected as speci- fied in the same place. To proportion the joists, first assume their number per panel and their dimensions, in order to determine the total weio-ht of lumber per panel ; to this add the total maximum panc5 live load, or the product of the panel length by the clear roadway by the live load per square foot, given on p. 5, the sum being expres.sed in tons; then, referring to Table XIII. or Table XIV., find, with the given panel length and the assumed depth ol joists, the safe load for a joist one inch wide, and dh-ide this number into the total load just found : the quotient will be the total width of joists per panel, when laid side by side. Divide this total width by the assumed width of one joist : the quotient \vill be the number of joists per panel. If it agree approxi- mately with the number assumed, and if the distance between centres of joists, when in place, will be between eighteen and tucnty-four inches, all right ; if not, another trial must be mr.de, with a different depth of joist, and a new assumed panel wei-^ht ;'l lumlKM-. It may be well, in any case, to try two depths" of joists, m order to see which is the more economical. The 68 oj^n/.y.iKV fKOx inc.invAv-nRinr.Es. minimum size of pine joists slioulil be 3" X 10": the maximum size tliat it is advisable to figure on is 4" X 14". because deeper joists cannot always be readily purchased. It is to be remem- bered that pine lumber can be found in the market in only certain sizes, usually even inches in depth, and ahvays even feet in len-th ; i.e., timbers 3" X 8", 3" X 10", or 3" X 12" are readily procured, while timbers 3" X 9" ^"- 3" X n" are not; also, if one require joists eiKhteen feet six inches long, it will be neces- sary for him to buy lengths of twenty feet, and cut off a foot and a half. Timbers over eighteen feet in length cost more per thousand than those of that and shorter lengths. Tables XV., XVI., XVII., and XVIII. give not only the sizes of joists, and number per panel, but also the total number of feet, board measure, of pine and oak per panel, including, when- ever there is any, waste material. The total load for a floor beam consists of the live load, the weight of lumber which it supports, and the weight of the beam itsctf. The latter must of course be assumed : this can always be done with sufficient exactness to determine the floor-beam load. The latter is assumed to be uniformly distributed be- tween centres of bearings. In calculating the dimensions of a floor beam to sustain a given load, the section of the web is to be assumed ; and the beam is to be proportioned accortling to the formula given on p. 19, and to the principles there enunciated. It may be neces- sary to make two or three designs, in order to determine the most economic depth ; but it will be often found that a variation of several inches in the depth will not affect the weight per foot. The lower lateral strut, which is to be well bolted to the floor beam, will add consi.lerably to the strength and stiffness of the latter. The joists .should be dapped on to the strut at then- bearings, so as to offer a resistance to the lateral deflection of both strut and beam. The lower flange plate, if there be one, need not extend over more than the middle half of the length of the beam. The rivets attaching the plate to the lower flange angles should be staggered, and .should be spaced ah«»«!t four inches apart ; ami (>h'/)/X.l/n- /A'OX niGIIU-AY-liRii)GES. 69 the areas lost from the plate and angles by these rivet holes should be deducted when figuring the net section. In heavy beams, several plates arc often used to vary the section gradually from the centre of the beam to the ends ; but if one share Weyrauch's views upon rivet stresses, as expressed in his "Structures of Iron and Steel," he will avoid any such practice. Many bridge companies reduce the depth of built beams at the ends, in order to save a little weight of iron. This method may be advantageous to the company which pays for finished britlges by the pound ; but it is seldom so to the manufacturer, for the triangular pieces cut from the web are often wasted : be- sides, the e.xtru work in cutting the web, bending the angles, and making square rests for the beam-hanger nuts on the inclined flanges, more than counterbalances any saving of material. For a bridge with sidewalks, reducing the depth of the floor beams at the ends adds to the appearance of the structure, and need not interfere with the bearing of the hanger nuts. Tables XIX., XX., and XXI. give the sizes of floor beams for all cases ordinarily met with. To illustrate the method of proportioning an ordinary floor beam, let us take the case of a beam for a twenty-foot panel, fourteen feet clear roadway, and fifteen feet between centres of trusses, the bridge belonging to Class A. The live load on the beam will be 14 X 20 X i§^^ = 14 tons. The weight of , he lumber, from Table XV., is 2085 X 2.5 2000 = 2.606 tons. Let us assume the weight per foot of the beam to be fifty-five pounds, the total weight of same will then be 2000 = 0.44 ton. The total load on the beam is, therefore, 14.000 + -.606 + 0.440 = I 7.046 tons. ■JO O/WIXA/^ V /A'OX II H IIIW.W --nRllh .KS. The most economic depth for the beam can be found by trial, or by consulting Table XIX., which gives J" X 27" for the section of the web. ■ 1 u Let us assume these dimensions, and take the eflcctive deith D equal to 26"; then substituting in the formula given on p. ig, omitting A\ and remembering that 7' = 4 tons for bridges of this class, gives the half of which is 1.28 d", corresponding to a wei-ht per foot of 4.27 pounds, because a bar of wrought-iron one inch square and three feet long weighs just ten pounds. Referring to Car- negie's " Pocket-Companion," p. 68, we find that a 2.^' X 3" 44* angle will be required. Let us see if a 2"X3" 5* '-mj^'*-^ ^^;'ll dol^or the bottom flange. Assuming that the rivets are |", and the holes \};\ in diameter, the area lost by a rivet hole will be 2 X *■'-" X 11" = 0.430", which, added to 2.56, gives 2.99 c", corresponding' to two angles, each weighing five pounds per foot The assumed angles will therefore be exactly what are required. For stiffeners, let us use 2"X2" 3-1* -ingl^'S- I'our of them at each end of the beam will be needed to take up the compression produced by the stress in the beam hangers, leaving a space between the inner angles equal to about fourteen feet. The ratio of thickness of web 10 depth of same is -^^^ — \q^ Referring to p. 19, we find, by interpolating, that the distance between "stiffeners should be 1.65 times the depth, or about 44.1". The number of spaces between stiffeners in the four- teen feet will be -^^^i^ = 4, requiring six stiffeners, three on each side of the web. The filling plates will have to be _5_" X 2" X 22.1". ^^The method' of finding the number and distribution of the rivets in the flanges will be treated in Chapter XIII.: for the present, it will be sufiiciently accurate to assume that the average spacing is two inches and a half. tVv7V.\./A'J- JA\).\ ///(/// If. I i-ZlAV/JuJ'S. 71 uctivc ck'i th ven on p. 19, r bridges of icrs, three on 1 have to he Wo arc now ready to pass to the hill of iron for the hcani, the list of details for which is ^iveii on p. 30. nil. I, or ii<()\.« Wcl) I i" 27" 16' 3O0# r|)per flan • . . 2 2i"X3" 4.4#L 16' 141 " Lower Han^c . . . 2 2"X3" S*L 16' iro" Still' ning angles. . 14 2"X2" 3.i*L 26i" f/. " Filling plates . . . ' 1 6 " ID 2" 22i" 5S-' Rivet heads . . . 220 pairs (h) o.i6# 35" Tofal weight of beam . 847* Dividin-,- 847 by 16 gives 53 pounds as the weight per foot of the tlixir beam. Referring to Table XIX.. wc find that the beam there given agrees with the one just designed in e\ery respect, except that the weight is a pound and a half per foot greater. This is owing to the fact that the weights in the tables of floor beams were made large enough lo cover a slight variat ion in the d esignnig. There is no need for proportioning rolled beams, be cause m Carnegie's " I'ocket-Companion," pp. 33-44, are given the work- ms. I'll ,^-loads for all the I )eams rolled at the Union Iron Mills. ese loads are directly applicable to bridges of Classes B and multiply the calculated load upon C. For bridges of Class A, the required beam by six (6), and divide by five (5), the n searcl in the "Companion " for a beam to sustain th e resulting lf)ad. Plate girders for short spans are to l)e designed according to exactly the same principles as those laid down for the designing of floor beams. The details, t there should be two inclined stiff 00, the beam, one on each side of the web, their low over the edge of the bed plate nearest to the centre of th are the same, except that ening angles at each end of er ends resting e s IS shown 111 ate pan, Th 17- e distance apart of plate girders should not exceed four- * Tlie metliod for preparing this table K explaineil in Chapter XIV. Xf'^ ..^. ^ n-. ^.J^ ^ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 Hfi I.I 1.25 2.8 1^ •is loK UUI- |||| 2.? 1.8 1.4 ill 1.6 p% (? .% 7i 7: /^ Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y, 14580 (716) 872-4503 IN- ORDINARY IRON II IG I nv AY-BRIDGES. liiii teen (14) feet, on account of the difificulty in obtaining joists lar<;c enough to support the concentrated wagon-loads. Trussed beams are sometimes made with one trussing-post, and sometimes with two. To determine the relative length of the part between the posts in the latter case, — Let /j = length of an end division, /j = length of the central division, and /= 2 /j-f- A = length of beam between centres of supports. The whole beam is now divided into three beams, two of which may be considered fixed at one end, and supported at the other, and the third fixed at both ends. If the moments of the loads do not balance each other over the posts, the rigidity of the connection there may be considered sufficient to insure fixed- ness. The greatest moment for a beam fixed at one end, supported at the other, and subjected to a uniform load of w tons per lineal foot, is \T.i'l{' at the fixed end. The greatest moment for a beam fixed at both ends is ■^u>l.£ at either end. Remembering the assumption of the fixedness of the beam over the posts, it is evident, that, in order to make the moments over these points a minimum, the two values found should be made equal to each other, so that or and Again : therefore and 11 _ 3/2 2 — '2 1 ' /, = 1.224/j. /= 2/, -f A= 3.224/1: /, = 0.31/, = /(l - 2 X 0.31) =0.38/, ussing-post, ORDINARY IRON HIGHWAY-BRIDGES. 73 ,)r the length of the central portion should be about four-tenths of that of the beam between .suj)porls. To proportion the upper flange of a trussed beam having two trussing-posts, such as shown in Plate II., Fig. 16, — Let d = depth of beam proper, D - depth between centre line of beam proper and centre line of bottom cnord of trussing, 7i< = uniform load per foot on beam, /■= },7c{/^ + I,) = load concentrated over one post, and let /, /i, and 4 have the same values as before. The area of the compression flange of the beam necessary to resist bendmg only is given by the formula where C is the intensity of working-stress upon the flange to be taken from the "General Specifications," p. 13, and A' is the area of the web. The stress in either chord of the truss is D' Let /f equal the area of one flange of the beam, supposing that the loads P were really concentrated over the posts, instead of bemg distributed, then and A' + 2^" = area of ideal beam, C\A'+2A") = F=^^^; D where C is the intensity of working resistance to compression. * For proof of tins formul.-,, see .Apper.dix U, which gives the demonstration fo r a similar ili }i\ \f 74 OKDIN/IRV IRON HIGHWAY-BRIDGES. It should be about three (3) tons for bridges of Class A, and four (4) tons for those of Classes B and C. The total area of the lower flange of the beam should therefore be If the beam be a rolled one, as it nearly always is, there is no need of figuring upon the size of the upper flange ; while, if it were a built beam, it might be as well, for practical reasons, to make the flanges of the same size, although theoretically a slight reduction in the area of the upper one would be per- missible. For a beam with a single trussing post, the bending-moment over the post is and the area of flange necessary to resist bending is, as before. A = _ lii/i^ St/C 1//' P, in this case, is equal to zc/^ ; making the re-action at each end of the beam, under the supposition of concentrated loading, The direct compression on the upper chord of the trussed beam is, therefore, r-^^=C'{A'+2A"): and the total area of the flange is ^'L,c"fl + ,c,o-K. 'lii OIWINARY IIWNHIGHWA Y-B RIDGES. 75 ing-moment russed beam The author does not claim that these formulas are exact ; but practically they will prove to be a great deal more useful than others theoretically more correct, but also much more complex. At the end of Chapter XIII., there is given a complete design for a trussed floor beam with two posts. The reason why it is not inserted here i.s, that it is necessary to understand the contents of Chapters X.-XIII. inclusive, in order to properly proportion the details. The weight supported by the four hangers that usually sus tain a beam is that of a panel live load upon both trusses, that of the lumber in one panel, and that of the beam itself. The total load divided by eight times the intensity of working-stress will give the area of the section of a hanger. Square sections lie more closely to the pins than round ones, and take up less room in the packing ; but they must always be upset, which, in short hangers, makes them more expensive than round ones. Single beam hangers are allowable in skew bridges, where, indeed, their use is often unavoidable, or in narrow bridges with short panels, where there is not much weight to be sup- ported. Tables XXII., XXIII., and XXIV. give the sizes of beam hangers for nearly all bridges without sidewalks. The most simple manner of finding the size of single beam hangers for any roadway and panel length is to look in'the table of hip verticals of the same class for the section required, and multiply it by one-half of the ratio of working-stresses for hip verticals and beam hangers: the result will be the area in square inches of the section of the hanger. If the floor and joists be of oak, the tables of floor beams and beam hangers can still be employed by supposing an increase of one foot in the panel length. !: f 76 0/WIA'ARV IROiV HIGHWAY-r>Rllh.l-:s. CHAPTER X. THEORY OF PIN PROPORTIONING. if 8 The subject of "bridge pins" is one deserving of more con- sideration than has been accorded it by engineers, and authors of technical works. Until 1873, when Mr. Charles Bender, C.E., presented his paper on " Proportions of Pins used in Bridges " to the Amei'ican Society of Civil luigineers, very little was known concerning it ; the usual custom among engineers when propor- tioning pins having been to allow one square inch of pin area for every eight or ten thousand pounds of shear in the section most subject to shearing-stress. As ]\Ir. Bender states gener- ally, and as will be shown farther on to be true for iron bridges, it is not the shear, but the bending-moment, which causes the greatest tendency to rupture ; so that in any iron structure it will be sufficient, in finding the sizes of pins, to calculate the greatest moment induced in them by the various members coupled thereon, and to proportion accordingly, due regard being paid to the stresses in the eye-bar heads. Before making any investigations, it will be well to review and summarize the most important results of the investigations of others in this subject. The principal conclusions arrived at by Mr. Bender are, that, for a well-fitting pin of large diameter, a pressure on the bearing- surface of six tons per square inch is not too large ; that for simplicity it is well to assume that this pressure is uniformly distributed over the diameter of the pin ; that wrought-iron, after millions of impacts, may break on the side where the stress is tensile, but never on the side where it is compressive, the ultimate resistance to crushing being about thirty tons per square inch ; that the shearing-stress at the centre of a pin is ORD/X.i/n- //WX IIICllWA y-URIDCES. / / one and thrcc-cij^hths times the average shear on the whole section ; that in iron and steel the ratio between the greatest allowable tensile and the -reatest allowable shearing-stresses should be as 5 to 4, which would make the uniformly dfstributed shear 2.91 tons per square inch, to correspond with a tensile stress of 5 tons per square inch ; and that, owing to various con- siderations, iron in ]Mns may be strained much more than similar iron in tension members. Mr. K Baker, C.K., in " Beams, Columns, and Arches," treats of pins merely incidentally. He finds, that, for iron in solid circular beams, the average value of <^ is 11/ where / is the ultimate resistance per square inch to rupture by tension, and c/. the difference between the apparent ultimate resistance per square inch to rupture by bending and /, according to the equa- tion /''=/+ qi, /'"being the apparent ultimate resistance per .square inch of the extreme fibre which first gives way ; and, that for steel, the value of <^ varies between 1.7/ and 1.9/ Professor Burr devotes five pages of his work on " Stresses in ]5ri(lge and Roof Trusses " to the subject of pins, and illustrates the particular case of a suspension-bridge cable pin, and a gen- cral case for ordinary truss-bridge pins. Professor Du Bois, in "Strains in Framed Structures," also gives a mathematical discussion of how to find the maximum bcndingmoment. Table XII. gives the working bending-moments on all the non and steel pins, and the working-shear on all the steel pins, which will ever be required for highway-bridges. Having cal- culated the bending-moment, the requisite diameter for the pin can he found by looking down the column for the class of bridge considered, until a bending-moment at least equal to the one found is reached. The diameter will be found at either end of the horizontal row thus located. The use of the columns for shear will be made apparent presently. The upper and lower horizontal lines in the tables of bearino-s (lables XXVT. and XXVII.) give the diameters of the pins; the extreme vertical lines, the necessarv widths of bearing-sur- tacT at each end of the pins, including both channel and re- t'lilorcing plates ; and the other vertical lines, the permissible 11'^ 78 ORDINARY IRON IIIGHVVAY-BRIDGES. pressure, on the bearings. The method of using these tables is the following. The pressure .vhich the pin is to carry is to be taken from the diagram of stresses. A trial diameter is then assumed. The vertical column in either Table XXVI. or Table XXVn., headed by this diameter, is to be followed down, until a number nearest the pressure to be carried is found. At either end of the horizontal row thus located will be found the proper width of bearing. Knowing the width of bearing, diameter and pressure, the moment to which the pin is subjected may be at once calculated. Turn, then, to Table XII , and see if this moment agree with the working-moment corresponding to the trial diameter. If it does, all right : if not, another trial is to be made, with a new assumed diameter. After a little experience, the first trial will be sufficient. A consideration of other de- tails, such as widths and depths of eye bars, etc., will frequently aid very much in these trials. To find the least value of the ratio of the diameter of pin to depth of eye bar in an 'ron bridge, by considering the tension in the bar, and the pressure between the pin and bar, — Let w — width of bar, fl'j = depth of bar, d — diameter of pin, C = intensity of working compressive stress, T = intensity of working tensile stress ; then and wd^T = tension in bar, wdC = compression on pin and eye. These, of course, are equal ; and, as C = 6tons when T: tons, there results the equation, d=y, = 0.833//,, .1! i 3! which shows that the diameter of the pin should never be less than eighty-three per cent of the depth of the bar. It is possi- ble, though, that good iron of twenty-five tons tensile strength will resist more than thirty tons per square inch in comprcs- ORDINARY IRON HIGmVAY-liRlDGES. 79 sion : consequently d may be taken at o.M^ as a matter of con- venience. To find the proportion between width and depth of bars for the smallest allowable pin in an iron bridge, — Let the notation be as before, and first let us suppose that there be but one pair of bars acting at each end of the pin, and that the total tension be a fixed quantity. The stress in one bar is iiY/,7', and its moment is wV,7: This must be equal to the resisting-moment of the pin, which is given by the well-known equation d Here R — \T, / = \-,:r\ and D = r = -, substituting which gives Equating the two values of the moments gives w'd,T = -^nrd\ or 64 d. Now, to make the diameter of the pin as small as possible, the moment of the stress must be made as small as possi- ble ; and, as the stress is constant, the lever-arm w must be made as small as possible. But the product of rv and d^ is a constant : so when zv is smallest, d^ must be greatest. But the greatest value of d^ is {d ; substituting which gives 2 3"' 64 and 64 125 «'i' = o.754«',«, or about one-fourth of the depth of the bars. If there be two pairs of similar bars acting at each end of the pin, instead of one pair, the equation of moments will be 2W%T = -^\nTd», 8o o/c/)/.v.i/n- /A'o.v nir.iiwA Y-HRiihiEs. or w = As before, to make d a minimum, re must be made a minimum, or ,/, a maximum : therefore d = \il^, which, substituted, gives 7t' = 0.194^/p or about one-fifth of the depth of the l)ars. For three pairs of simihir bars at each end of the pin, the equation of moments will be substituting in which \d^ for r/ gives 7.' = o.i5(y„ or about one-sixth of the depth of the bars. Finally, if there be four pairs of similar bars at each end of the pin, the equation of moments will be which gives 6,w"d^T = i\TTd\ a' = o.i37./i, or about one-seventh of the depth of the bars. To find the greatest working shearing-stress (supposed to be uniformly distributed) in terms of the working resistance to tension, — Let 5 = actual varying resistance to shearing, considered uniforml}' distributed. The greatest value of .V will correspond to a value of w equal to 0.274^/,; for suppose the moment to remain at its maximum value, and the dimensions of the bar to vary (consequently the stress therein also), the tension in the bar will be greatest for the value of ti' corresponding with the greatest value of d^ : therefore the shear will also be great- est for that value. Equating the tension to the shear gives : i! ^ minimum, ach end of Substituting yiov ,/,, and o.274^«,/) for w, gives 81 and 0-274 (5'/) ^7' = ^^= 0545 7',- l"l" 'f=S tons, .S"='>7->i; folic IJ,.f ^u V.I..0 for .V is, acconli,,':, .;.,,'" ';:;r'"L^""™'"'= ;'-• ■' -.V":;; i-" ^e p™,,..,, „,..,„;„;,?,:';, . ,hi:;":;:i l""li".^'. .t w,ll 1,0 str„„K o,„„,g|, ,„ resist shear ami n" f^ ■I-. I"f...c .1.0 pin co.„„ shear, it >v.„„„ eiU.er brei^^ bl b ' 11.^ "r en,sh„,K, "r the eye of the Ixir w.nil.l „ivc wiv A si, ^M .,u-es.,,ation f„r steel bridges, where 7' = i 3/ , „, C- 'r .....I A' (.he intensity „f working bentii„,.s,re;, = S^T, e,' ./=o.S7]4,/„ t,. = o.i.s,f;,/ and .V-soj- tn,,s 1 ^ . "'">■ "' »-^'^'n„,s.ress'w„en tb-.^ntstr^.e: ^ ,:';,?' l.-lin«-hn,it, and the ratio ;; for ,ha, e„„,h,i„n of stress is a. ..s i.uninunn, an<l eonsetpiently the area of the bar, the tension .heren,, an, the shear „n the ,,in, at their maxin a I . h .reae., allowable shear is, aecor.lin, ,0 llentl " X - X 7' ">, on a steel pn, n, opposite direetions. or a sin.^ie steel bar a.:uns a steel bearing, the pin in certain eases wi 1 e ,h, I :::::u:::Ltr::?is:-' "" •"-'"- ■-- - '- ^■'"' channels can be found after uli.v-i, h '-"-cwccn post tars in the bridge ^^'i:^^:^:^ ^^^^Vl^' '"^ - -npletl on the same pin pnll i„ ,he sante direct! nunes 1^* 82 ()AW>/.\.l/n /A'<>.\ ///</////./ J -A'AV/^i/A'.V. as to reduce the hen(lin<;momcnt.s ; and that the dia-jjonal ties be placed close to the posts, and the beam han^^ers close to the ties. ICspecial care is needed at the panel point where the number of chord bars is different in the consecutive panels. It is possible to arranj^e the bars there, so that there wilt be an extremely large moment produced, or so that it will be smaller than at any other panel point of the bottom chonl. The ne<;lect of any of these precautions will cause an undue bending-moment on the pin. The arrangement completed, the next questions to be decided are, first, under what condition of loading will each pin take its greatest bending moment, and, second, at what point on the pin will this be found. In large bridges, and in many well- proportioned small ones, the bottom chord pins are subjected to their greatest bending-moments when the bridge is fully loaded. Under this condition, the stresses in the chord bars can be taken from the diagram of stres.ses; but those in the main diagonals must be calculated for the load covering the whole bridge, and their horizontal and vertical components be ascertained. After having hail some practice, one will very often be able by simple inspection to decide at what place the greatest moment of flexure will exist ; but, if not, it will be necessary to calculate the values of both horizontal and vertical momenls at different i)oints, and find where their combined result is a maximum. As Professor Burr shows, the actual moment is represented by the diagonal of a rectangle whose sides repre- sent the vertical and horizontal moments. It is usually more convenient to square the component moments, aild the results, and extract the square root of the sum, than to make out a diagram. The moments of the stresses can be easily recorded by draw- ing two curved lines, as shown in the accompanying diagram, representing the directions in which tlu' stresses tend to bend the pin, and writing each moment as calculated under one or other of them, according to whether it would |)rotluce ])ositive or negative rotation. The difference between the sums of each column will give the actual : 1: !■' o/w/x.i/n- /A'o.y ///<;// ir.i r-/,>A7/jf;/;',s-. 83 led bv dr:uv- horizonal or vertical moment, as the case may be. The ondi- ii..n that a load covering the whole i)rid-e may not produce the -reatest moment in the bottom ehord pins is either when there is a sm-le counter coupled at the centre of the pin, or a main (liaj;onal coupled at a distance from the member that takes up its stress. As a rule, single counters and single beam hangers are to be avoided, on account of the unnecessarily large bend- in-moments they produce. The size of pin for the hip joint depends greatly upon the arrangement of the bars which it couples. In a double-intersection bridge, where there are two hip verticals, two long diagonals, and two short ones, the best arningement is to put one pair of diagonals on the outside of the chord, and the other pair inside, close to the bearing; the verticals coming next, and being kept apart by a filler. Some- times it is not advi.sable to couple outside of the chord, in which case the moment would become so great, that it would necessi- tate the employment of a pin whose diameter would make the heads of the eye bars too large for the space allotted them. In such a case, a steel pin can be used to advantage. IIinr--ed ends at the hip joints require large pins, for the entire stresses in both chords and batter braces come upon them with great leverage, due to the necessarily large bearing-surface. Such a connection is not advantageous : it is better to allow the channels to abut. Such hinged ends are a great convenience in erection, but usually necessitate an increase in the sizes of the batter braces and the top chords at the end panels. A detail to obviate this necessity will be given in Chapter XIII. It is not neces.sary to consider the bending-effect of the stresses in the lateral rods upon the chord pins, for the wmd and the live load are not supposed to act simultaneously. Lateral rods should always be so connected to the chord pins, that the effect of the stress in the outer one will be to diminish the horizontal component of the moment on the pin ; i.e., if the tendency of the chord and web stresses is to bend the pin con- vex to the middle of the bridge, the outer lateral rod should IK.int towards the middle ; but, if it be to bend the pin concave to the middle of the bridge, the outer lateral rod should point towards the nearest end of the span. ^1; 84 ORDINARY IRON HIGHWAY-liRinCES. The ends of pins have to be reduced in diameter, so that the nuts and pin pilots may be screwed thereon. Care must there- fore be taken in proporiioning small pins to see that sufficient area be left under the root of the thread to resist the tension on that section caused by the greatest transverse components of the stresses in the lateral rods. The principal objection to the use of large pins is not always the undue weight of the pins themselves, but the increased size of the chord and tie-bar heads, and the room that they take up. On the other hand, it is not always desirable to use the smallest possible pin, as the width of the bearing is an inverse function of the diameter of the pin : so if, owing to the neces- •'ty of a large number of rivets, the re-enforcing plates be long, . micht be economical to increase the diameter so as to reduce .le width. Thickening the heads of eye bars has an injurious effect on the pins, although a beneficial one upon the heads, for the lever arms of the stresses are thereby increased. Bridges with weak pins will not necessarily fail by the rup- ture of the pins. The reason for this is thus stated by Professor Rurr: "The distortion of the pin beyond the elastic limit will relieve the outside eye bars of a large portion (in some cases, perhaps all) of the stress in them. This result will produce a redistribution of stress in the eye bars, by which some will be understrained, and the others correspondingly overstrained. Thus, although the pin may not wholly fail, the safety of the joint will be sacrificed by the overstrained metal in the eye bars." ORDINARY JROA' HIGnWAy-BRWuES. Ill so that the must there- it sufficient the tension components )hjection to itrht of the I and tie-bar to use the s an inverse I the neces- .tes be long, as to reduce an injurious le heads, for by the rup- by Professor ic limit will some cases, ,vill produce :h some will )verstrained. afety of the in the eye 85 CHAPTER XI. PRACTICAL METHOD OF PIN PROPORTIONING. The ordinary method of pin proportioning is to figure the diameters of a few principal pins, and to make the others of the same sizes. Thus, by inspection, can be found which pin near the middle of the bottom chord is subjected to the great- est bending-moment. If there be an even number of panels in the span, it will be the middle pin ; but, if there be an odd number, it may be the first or second pin from the middle, according to the number and arrangement of the chord bars. The vertical component of the bending-moment on any one of these pins is so small in comparison with the horizontal com- ponent, that it may be neglected. For bridges with an even number of panels, — Let T = tension in middle panels of lower chord, and u> = the average thickness of chord bars in these panels ; then, appro.ximately, — = bending-moment on middle pin. This formula may be applied, but perhaps with less .ccuracy, to a bridge having an odd number of panels ; and, if the chord be properly packed, the error will be upon the side of safety. With the exception of the chord pins at the shoes and at "the first panel points from the ends of the span, all the lower chord pms may have a diameter corresponding to this ma.vimum bend- mg-moment. 86 ORDINARY IRON HIGHWAY-BRIDGES. To find the size of the lower chord pin at the first panel point, use the formula, H = Trt) for the horizontal component of the moment, and the formula for the vertical component ; t being the intensity of working- stress for the hip verticals, A their area (S. R.), to be taken from one of Tables VI., VII., and VIII, <•/ the diameter or thick- ness of a hip vertical, and d' that of a beam hanger. The moment given by the formula applied to Table XII. will determine the diameter required. This diameter is to be used also for the pin at the shoe. To find the size of a hip pin, lay off the stresses in one hip vertical and one end main diagonal to any convenient scale, and find the value of their resultant by the parallelogram of forces. This resultant will determine the thickness of the bearing, a trial diameter being first assumed. It is possible that this bear- ing will have to be increased, so that there will be enough iron to transfer the stresses from the batter brace, hip verticals, and diagonals to the chord, as will be explained in Chapter XIII. An appro.ximate test of the sufficiency of the bearing in this respect may be obtained as follows : — Let A — the area of the section of the end panel of the top chord, t/ = depth of cliord channels, / = thickness of web of an entl cliord channel ; then the bearing should not be less than that given by the formula 2(1 Ne.xt find the distance / between the centre of the bearing of ORDIXARY IROX HIGHWAY- lU^IDGES. «7 he formula the chord and that of the diagonal, also the distance /' between tiie former and that of the hip vertical, the latter being on the inside. Calling the stress in the hip vertical F, and that in the diagonal 5, the vertical moment will be /'/', and the inclined one .S7. Next lay out these components to any convenient scale in their proper directions, and find their resultant by the paral- lelogram of moments. This resultant will determine the diame- ter of the pin. If the diameter found agrees with the one assumed, or if it iloes not agree, provided that the bearing was not determined by the trial diameter, all right; but if the bearing were so determined, and the two diameters do not agree, another trial must be made. Where there are more than two main diagonals coupleil at the hip, as is the case in double-intersection and in very heavy single-intersection bridges, one pair is coupled on the outside oi the bearing, and the other on the inside ; so that theoretically the greatest bending-moment is equal to the .stress in the outer l)ar multiplied by the cHstahce between the centre of the bar and the centre of the bearing. Ihit practically the moment may be greater, for the distribution of stresses among the diago- nals may not l)e as assumed : so it is well to determine The moment by imagining the outer bar not to e.xist, and proceeding as explained above for the case of only two main diagonals al the hip, excepting, of course, that the thickness of the bearing must be ascertained by finding the resultant of the stres.ses in the two diagonals and the hip vertical. To calculate the size of an intermediate upper chord pin, the wi.Uhs of chord and post bearings are to be determined as shown m Chai)ler XIII. The former is given approximately by the last formula, where A is the section of the panel of the chord on the side of the pin towards the miiklle of the bridge, ami t the thicl<ness of the corresponding channel. The other is given I'V the formula where A, is the area of the section of the post, and h the depth of one of its channels. 88 o/w/y.'iA'y /Rox higiiwa y-bridges. Next resolve one-half of the diaj^^onal stress vertically and horizontally into /' and /'' respectively. Let / represent the distance between the centre of the diaijonal and that of the ex- tension plate, and /' the distance between the former and that of the chord-bearing ; then V = PI, II = P'l', and M - V'//' + V\ If the bridge be a small one, it will be necessary to calculate only the size of the pin at the top of the first vertical post from the end of the bridge, and to make all the intermediate top chord pins of th e same size. But, if the bridge be a large one, it will be better to calculate the diameter of the pin on the post midway between the end vertical post and the middle of tlie span, and to make all the pins between these places of this diameter, and all the others of the same diameter as that at the eml of the first vertical p'>st. After the diameters of the top chord pins are determinetl, the post and chord bearings should be tested by applying one of Tables XXVI. and XXVII., al- though in most cases they will be found ample. In double-intersection bridges, where the diagonals are halved, and coupled on pins passing through the middle of the pysts, the size of any one of these pins may be found from the moment M = — , I • Ifi n where 5 is the stress on the diagonals as given on the diagram of stresses, and w the width of one of the main diagonals. In all pin proportioning it must be kept in mind that the diameter of the pin is never to be less than eight-tenths of the depth of the deepest bar coujiled thereon. The author wisiies to call attention to the superiority (in his opinion) of the simple method given in this chapter for propor- tioning lower chord pins by formula over the apparently more accurate one given in the la?>l chapter. OKDIiXARY //WA' HIGIIU'A V-HIUDGES. 89 In this method, when the proper proportion of width to dei^th ol bars is adhered to, the diameter of the pins will be ahnost e.^ht-lenths of the depth of the bars, and will be great enou-h to res.st the bending- moments ])roduced by any legitima^'te metliod of packmg. Moreover, after the diameters of the pins have been determined, the ehord ean be packed, if it be advisa- ble, so as to reduce the bending-moments. This supcrabun- <lance of strength in the pins is obtained at the expense of a slight increase in the weight of iron ; and the increased sizes ut heads for diagonals can do no harm, because they do not enter any limited space, as do the heads at their other ends J5ut if, by a skilful arrangement of the packing, vvc can so reduce the bending-moments on the pins, that the diameters ma)- be made small, and the proportion of width to depth of bars larger than that found in the last chapter, the pins may not be as strong as wc imagine them; for we cannot be sure that al the bars are going to pull as we have assumed that they w. . It may be that one of the outer bars is a trifle long, and will not pull at all until the others are well stretched : what then, becomes of our calculated bending-moments ? Any one of them may be so greatly exceeded, that the pin will be strained beyond the elastic limit, and will bend percepti- bly, so changing the distribution of stress in the panel that one or more of the bars also may be strained beyond the clastic limit. i^ut if the pin be large enough, or more than large enou-h .t cannot bend perceptibly : consequently the distdbution"of stress will be much more uniform, even if the bars be of shVhtlv unequal lengths. ^ ^ 90 OJW/.WlAy JROA- UIGIIWAY-BRIDGES, ■ I J,. CHAPTER XII. RIVETING. The subject of riveting is one, which, like that of pin propor- tioninf^ has never received its dr.e amount of attention from bridge designers. Many structures otherwise very strong arc extremely weak in detail, owing to the insufficient numlu'r of rivets employed in the connections and to their improper arrangement. The principal rules for riveting have been given in Chapter II., pp. 17, iS. Rivets should be proportioned for bending and for bearing pressure ; i.e., for any given connection, the number of rivets necessary to resist properly each of these stresses should be determined, and the greater number chosen. Tables XXXVI. and XXXVU. give the working bending, moments and permissible bearing-pressures for bridges of Class A and for those of Classes B and C. For the lateral systems kA both classes. Table XXXVII. is to be used. In these tables the first and second horizontal lines of vulgar fractions and decimals give the widths of bearings ; and the other horizontal lines in the portions pertaining to bearing give the working bearing-stresses for rivets of different diameters. The rest ot the tables needs no explanation. The sizes of rivets ordinarily employed for highway-bridges are from five-eighths to three-cjuarters of an inch ; though half- inch rivets are used for very light channels, and seven-eighths inch rivets for very heavy ones. The weight of a pair of rivet heads for any diameter can be found in Table XXIX. It is well to memorize the.se weights. Where two plates are riveted together, the rivets, driven when hot, contract, or tend to contract, in length when cooled. pin propor- L'lition from ir improper ORDIXARV IRON HIGHWAY. nRiPGES. g, thus drawing the plates together, and produeing a friction which It IS necessary to overcome before shear can come ui^on the rivets. Whether this friction will continue indefinitely is doubt- ful, for rivets occasionally become loosened when the structure IS subjected to oft-repeated loads : so it is not legitimate to depend upon the friction in order to reduce the number of rivets. I'erhaps it is on account of this factor that rivets are seldom, if ever, proportioned to resist the bending-moments that come upon them, notwithstanding the fact that it is this last consideration, which, in most cases, should determine the number of rivets to be employed. Again : if the friction were to be depended upon, it would be only right to allow for the initial tension on the rivets, which tension is sometimes great enough to force off the heads _ It will probably have been noticed by the reader, that' shear- mg-stress upon rivets has been omitted altogether from con- sideration. The author would hesitate before making the broad assertion that rivets cannot shear, although it is probable that bending is the stress which ruptures rivets that are generally considered sheared. This much, though, he will statl- as the result of both theoretical investigation and many practical cases ot designing, that, xvhen rivets arc proportioned foy bcndiug aud bearing, they ,vill have more than snfficient strenq-th to resist shear Sharp edges on rivet holes will certainly cut the rivets, but this IS not shear proper ; and it may be possible that there is a cer- tain kind of fi.vedness about a well-driven rivet which will make the bending-moment less than its calculated value Should the reader wish to verify the statement concernino- bending and shearing stresses, he can do so by using an intei" sity of shearing-stress of three tons for bridges of Class A, and one of three tons and three-quarters for those of Classes B and C 1 he theoretical proof is identical with the one for pins given in Chapter X. "Countersinking" is a term used to denote the sinkino- of nvet heads mto the plate so as to make them flush with its surface. The least allowable depth for the countersinkino- is a quarter of an inch, and the least thicknes.s of plate used for this purpose should be three-eighths „f an inch : fur rivets e.xceedin^^ 92 OKDLXANV /AV.V IIIGUVVAY-HRIDCES. three-quarters of an inch in diameter, these dimensions should be increased by an eighth of an inch. Rivets may be counter- sunk at one or both ends. Making parallel rows of rivets staggered avoids unnecessary weakening of the parts riveted together. There has been much discussion as to whether punched or drilled holes are preferable ; the general conclusion being, that drilled holes weaken the plates less, and when slightly counter- sunk, so as to avoid sharp edges, do not increase the shear upon the rivets, but that punched holes arc so much more economi- cal as regards shop-work, that, when properly made, they are preferable to drilled ones. The improvements made of late years in riveting-machines have increased the efficiency of work with punched rivet holes. Should, for any reason, it ever be necessary, in bridge design- ing, to put a rivet through a plate whose thickness is greater than the diameter of the rivet, the rivet hole should be drilled. Machine riveting is preferable to hand riveting, but there are cases when the latter has to be employed. Field riveting is nearly always inferior to shop riveting. When a stress is transmitted from one plate, through one or more plates, to another plate, the number of rivets must be increased. The rule given by Weyrauch is, that, "for every single shear connection, the indirect force transferrence requires for m intermediate plates ;;/ -f i times as many rivets as for direct transferrence." Keeping this in view, the designer will avoid using more than one flange plate in floor beams, or more than one plate for covering the channels of the top chord. ORD/xXARy //WA- HlGimAV-URWUES. 93 miecessary CHAPTER XIII. PROPOKTIONING OF OTHER DETAILS. The sizes of stay plates used at the ends of systems of lat- ticin- or double-riveted lacing are given in Tabic XXXII , and the sizes of those used at the ends of systems of single riveted lacing, in Table XXXIII. The headings of these tables fully explain their use. Stay plates are to be employed at the middle of posts {vide Plate II., Fig. 15) when the diagonals are halved, and connected by pins passing through the posts ; their sizes being taken from the before-mentioned tables. Stay plates, if they can be so called, are also to be used on the lower portal struts, for the purpose of attaching the knee braces. Pin bearings are .sometimes figured, counting in both re-en- forcing plates and web; but the latter is often omitted. This would be necessary when the holes in the web are bored inde- pendently of those in the re-enforcing plates, for then it is very inij'iobable that the different holes will coincide; but, when the re-enforcing plates are riveted to the web before boring, such a precaution is not only unnecessary, but is a waste of material Py consulting Table XXVIII. can be found at a glance, accurately enough for all practical purposes, the thickness of web of any Union Iron-Mills channel bar, when the wei-ht is given, or vice versa. '^ Where re-enforcing plates act also as splice plates, there should be one on each side of the web in order to insure a crood substantial joint ; although the practice in the building of small bridges IS to omit the outer plate when the pin bearing does not demand its use. The length of a simple re enforcing plate depends upon the ill m 94 ORDINARY IRON IJIGHWAY-BRIDGES. miinbcr of rivets roquircd, and is thus determined, l-'ind, by dividing tlic stress given on the chagram of stresses between the various thicknesses of iron which constitute the bearings, the amount of stress which the plate considered is to carry. It is well, though, to make a liberal allowance, say twenty per cent, ^or the possibility that the stress may not be divided propor- tionately to the thicknes.ses. Ne.xt multiply the stress so ob- tained by the perpendicular ilistance between the central plane of the re-enforcing plate and that of the plate or web reen- forccd : the product will be the moment of the stress upon the re-enforcing plate Divide this moment by the working bend- ing-moment, taken from Table XXXVI. or XXXVII., for a rivet of the diameter to be employed for the connection : the quotient will be the number of rivets required to resist bend- inc:. Next find, from one of the same tables, the working bear- ing-strcss for one of the rivets upon a plate of the thickness of the re-enforced plate or web, and divide it into the stress which the lallcr carries : the quotient will be the number of rivets requiretl to afford sufficient bearing. The greater of the two numbers thus obtained is the one to be employed. Ne.xt make to scale a drawing of the re-enforcing plate, laying out the rivets, if it be possible, symmetrically, and thus deter- mine the length of the re-enforcing plate. In case of a re- cnforced pin hole, if the diameter of the hole exceed one-half the width of the plate, it will be necessary to jiut more rivets in front of the pin hole than behind it ; the ratio of the num- ber in front to the whole number being equal to that of the diameter of the hole to the width of the plate. The method of proportioning splice plates or connecting plates is somewhat similar. For instance, let us take the jilates at a joint in the top chord ; which joint, for reasons to be stated in Chapter XVIII., is always to be placed a few inches to that side of the pin hole farthest from the middle of the span. The stress on the portions of the plates to this side of the joint is that due to the stress in the panel where the joint occurs ; while that on the other portion of the plates is due to the stress in the next panel towards the middle of the span. The number of rivets on each side of the joint will be dependent upon the ORDIA'ARV IROX niCHlVAV-HRlDGES. .trcsscs carried by the channel bars of the two adj 95 'I'll le simplest way to (ind the stress ply its area by the intensity of working-st acent panels, on any channel is to miilti- from either Table X. or XI. Th equally, or otherwise, between the outer and splice the abuttinj,^ channel sary to resist bendiu';- and be ress, which was fouml is stress is then to be divided inner plates which s ; and the number of rivets iieces- uinj;- are to be ascertained in tl manner explained for re-enforcinj; j)lates. To determine the length of a cover plate, find in th manner the number of rivets ///.„/ each su/c of the joint, which -111 take up the stress carried by the chord i)late, and le e same the cover plate with th by plate, and lay out c rivet si)acing to scale. The stress car- ried by the chord plate is equal to its .sectional area multiplied by the intensity previously found for the channels. At the hip joint it is obviou.s, that, where the chord and batter brace are hni-ed upon the pin, the resultant of the thrust in the battrr brace and the pulls in the diagonals and ^•(| iial the thrust u poll the chord, and that the be figured for this thrust; but, where tl section of the splice plates mu.st answer two ...,..,_ hrst, their area (neglecting, on account of its bein- "be citect of the cover plate) must b verticals must aring must be icy are not hinged, the requirements : nt, the 10 sufficient to transfer t the chord a stress equal to that in the first panel ; and o that the pin bearing be sufficient { se cond. sioiiy in the diagonals aiu length of the cover i)late at the h or the resultant of the t en- It carries no stress, simply ad verticals meeting at the hip. The ip cannot be calculated ; for md keeping the rain therefrom Iding to the rigidity of the joint, It the posts be figured f( ate of the chord )r one fixed end, th nocting plate for the post ; and can be extended downward to act e inner splice as a con- ciiuugh rivets used ail th in this case there must be Ml respect to bearing and bending to transfei i)lat e compression in the post to the chord by th c, under th e coniiectiiiL'- e su llO 11 pposition that the ends of the post channel,^ tnlich llDo ot touch the flanges of the chord channels If so much the better; but it would not be safe slmuk II their doing so. The thick they do to count be such that it would not bend bet ickness of the connecting-p]at( ween the end of th( w. 96 f'/.7'/.\'./A')' /h'o.y ii!i:iiw.\y-nRiiH;i:s. post and tlic pill IkiIc wlu-n the post would be on the point of riiptiiic by compression. Where the ends of the posts ;ire fi^^ured iiin;j;cd, which is a decidedly better construction, the cxtennion plates pass inside the splice plates of the chord, and are attacheil to the pins. As before, there must be enough rivets to transfer the stress in the posts to the plate. The thickness of the re-enforcing plates at the lower end of a post is determined ' y the bearing recpiired, and their length in the manner already described, It is l)etter to place these plates on the inside of the posts ; then, if the llaiiges of the channels be i)artially cut away, an extra plate (at least three-eighths of an inch tiiick) can be placed on the outside of each channel. The reason for cutting away the bottoms of the post channels is merely to [jack the cliord more closely, and thus reduce the bending-moments on the pins. lUit, if the method of pin pro- portioning given in Chapter XI. be adopted, the necessity for cutting away the channels, to any extent, vanishes ; for at the middle of the span the web stresses are so small, tliat their moments are neglected, and the pins at the feet of the other posts have an excess of strength. In high double intersection truss bridges with long panels, the diagonals become so long, that it is convenient to halve them, and connect the halves by pins. It is then advisable to let these pins pass through the webs of the ]i()st channels where the diagonals cross, for the latter then tend to stiflen the pcjsts. If intermediate struts also be used at the middle of the trusses, the posts can be figured for half length, with both ends hinged. On account of the stretch of the main diagonal, there would be a tendency to deflect the post. If the diagonals were forty-two feet long, the stretch of the upper half of them would be about one-eighth of an inch ; so that, to avoid this objection, it will be necessary to elongate the pin hole that amount on the lower side, in the direction of the main diagonal. The pin V I'-s should, of course, be well re-enforced in order to compen- sate for the material cut from the channels. The stretch of the counters being less than that of the main diagonals, and the posts crossed by the heavy ones generally having an excess of strength, it is <iOi uccessary to elongate the pin holes in the direction of tl.e 1 ;. 'th 'if the counters. ('/^•n/x.i/n- ,A'ox iin:nuAv_,a„nr.i-:s. In nearly all iron l)ri<l-,>s (Ir. hatti-r I •nils fixed at the pedestals ( 97 i.e., tliev are ri nraees are made with "e plates), although hinj,^,.^ p^dc-stal tlie aJvanta^^' j^ained by tliel fftrndy distributed pi r use is the certa (idly attached to thi '110 not unknown essu re on the rollers, and the disad inty of a uni- a Kroat nierease in the section of the batter 1 I he shoe plate can be attached I'.v bent plates on the inside, the iif channels, with vanta;:c >races. t«) the batter-brace channels outside, or both, or by pieces oiic flange removed, placed on tli C' inside, and :haii- I . ami U,,„,„ , .|,,ir nances t„ ,1,. ,h„c. „la, "'it^' IV. The lower end of the b tiiMied up horizontally, an plate, as shown on :itter-brace plate should be Tl ie area of iveted to the shoe plat a section of the connecting channel '"a.le by a plane perpendicular to the d hraee should be ecpial to the area of >r greater if the shoe \\"i'lcl afford ; and there should b or plate irection of the batter one batter-brace channel, an this pin require greater bearin- th stress from the batter-bracc channel to th '^ enough rivets to transfer thi >i" I>late. Should the b shoe plates, as they ought to do, th iccessary; but such a 1> :itter-brace channels bcai 10 connecting channel against the ere will be more rivets th Details of sh •earing should not b an oes are shown on i'lates II., HJ., ly e counted upon. The rules for proportionmg shoe ,!;i\eii on p. 1 6. very good connection for the h rollc and V'l. r, and bed plates, c iro I'lates III. and IV. Th I'lider one passing entirely below th P joint is the one shown on Miner si^lice plate has five sides, the :Ue is cut to fit closely to the wei)s of 10 joint ; and the outer splice hnice channels, bei the chord and batt DC thi? Is and the rivet heads th ' ■^•'■' "" ^"'- euuKi anti batter- ng made as wide as the flanges of the chan- s detail is, that it re lerem will permit The objection uiother good detail for tl ■quires a good deal of field to rivet inc. ''late II. Ifereth "f the chord, and us joint is that shown in F 'g- 14. wh plates riveted to th those on ere are two connecting-plates on the outside t^vo on the mside of the batter brace, through se on the chord abut against ieh the pin passes. Tl U) -_ outside of the batter-brace channels"; and the batter brace abut against plates riveted to the 'A7V.\'./A') /AV'.\- l/liliniW ! -llh'/PilF.S. itisu le of t!u> chord cliaiincls, all ahuUin^ surface hcini planed to fit exactly; so that, when the in is driven into place, tlie th t will be as ri-id as if it were nveled whole joui <letail demands neat worknuuis Of course this hip, and is consequently some- what expensive counlerbalances but the satisfactory result attained more than the extra cost of the shop-work, and there i^ no neee ssity for figuring on a hiiiLrei i ^-xuX at the hip when Mdpoi :hord. lionuu •ooil me •hor the batter brace and the end panel of the top thod of attaching the upper lateral struts to the which is illustrated on Plates II., IV, the foUowini hortis IS ine iomuwhil;, uim.. .-- ...-■•- nd VI. Let the web of the upper channel lie upon the cover plate of the chord, extendi n thereto ami let the uiK ler f; beiiv' turned downwan faces (. if the lower Ham length of the lowei c pie of inches shorter than the clear roac ccni The coiuieclion is mai to its outer edge, and be riveted ice of the lower channel, its ilanges lie in the same horizontal plane as the :s of the toji chord channels. The f the lateral strut should be a way of the bridge. \annel o tter the head being rive Ic by a plate in the form ol the le led to the lower Ilanges of the inner cluatl Is, and the stem pass channels, lower channe be riveted. The thic of an inch, and the \\'< iiu between the tlanges ( if the 1 of the lateral strut, tt) the we ) o f which it is to kness of the T-plate shoultl be five-ei-hths ntrant angles siu )UU1 be rouiulec oil with a radius ol an inch am half or two inches The wiillh ot the stem s louk 1h' matle is ureat as the elis lance betwt'eii the f the lateral >lrut will permit, ami Lli flanges o equal to the width o It of the head f the tlanges of the chord channels Tl le num her of rivets tor either stem or he: tl must be calcu 1 ilcd for bending and bearing resistances corresponding to the ..•reatest stress that couul ever come upon the channel, which stress is to be calculated by multiplying the area of the channel by the intensity found in Table XI. 'a ..ood connection lor the iiUermediale slruts to the posts is by'means of two l.enl plates at each end ol the strut (vur ITites IV. an ; \-l.). One le.' of each plate is riveted to the web of the inner ch.nme! of the post, and the other to the web nt the I-beam, which i> placed horizontally The vibration rods ORniXANY tRox jinnin-Av-nRiiKiF.s. gg arc attached by holts that pass thro„,-h the two connecting- plates and the wel) of the I-heanv The connection at th^^ upper cm\s of the vibration rod may be similar, if tlie width nl the T connectmg-plate be great enough to permit of the jiassage of a bolt. At tlie intermediate strut connection, there should be cnou"-h nvels used ,n respect to ben.ling and bearing to transfer the calculated stress upon the strut to the connecting-plates If there be but one portal strut at each end of the span it may be connected to the batter brace by two large bolts passi'n. through a jaw plate, as shown in Mg. , ,, Plate II. These bolts ■nay have square heads placed so near the sides of the jaw that t ey cannot turn, the nut having to be screwed upon the ins.de ' ho atter brace. But. if there be two portal struts at each --' "f the .span, the channels are to be turned around ninety <legrees. an<I brought nearer together; so that it will be better n use exter.or bent plates attached to the flanges of the chan- U.s shown on Hates IV. and VI.. in addition to a single lai-e bolt through the jaw. Concerning the best method of connecting the lower lateral nnls. there ,s much chversity of opinion ; although, in ninetynine cases out o a hundred, they are attached to the floor iLml wh.ch are thus made to act as struts for the wind pressure' -Some brulge designers put bent eyes on the lateral ods, and ■un .jsu^^ ^ ohjec lonable, for two reasons : First, the laterals take hold .he weakest part of the beam ; and second, beu.g attach.U^ - ;'^ --/'-" the pins, they permit of too much vibration, •^nothe.cle tad ,s o rivet two 4 by 6 inch angles to the web, and ;-;:;;^ P- through the six-inch legs : this is a little better dm In.' the .same objections apply here. Another is to let the 10 Is pass U..ough the webs, and through rods and plates bent t ;;;': -nc .ace ,s perpendicular to the direction of the lateral rod a- her face parallel to it. and the ot-ier two end faces nr 1 el ';• the web of the beam, to which they are riveted. The^ :'''l- 'ons apply to this, together with two which are sti nTre "■1-tant vz.. that, as at each connection there are to such "'-- -^'"- lateral rods from adjacent panels cri:: h II! Ki B'ii 1- ;' illirw lOO O/wrXARV IROX UICIIWA Y-P.RI nc.F.s. other the lon-itiulinal components of the stresses m tlie latter produce a moment tending to revolve the beam about the upper ed-e of the web. Then, again, the bent plates must be made solieavy that they would withstand, before bucklmg, the ulti- mate pull of the lateral rods ; and it is very seldom that such a detail is made strong enough to stand the ultimate pull of an inch and a half round rod. Another way is to rivet a plate across the top of the beam, and two bent plates or large angles opposite each other, just below the top flange, dropping i)ins through the jaws thus formed. This is the best arrangement yet employed. But in the author's opinion all these details are defective, for the reason that the lateral rods all take hold of the floor beams, which are simply suspended from the i^ns that are several inches above them ; so that, unless the hangers be screwed up very ti-htly, any wind stress in the lateral rod will cause a rockino°at the point of suspension, and, even if the hangers be screwJcl up tightly, the tcmhncy to rock still exists. Ihe only correct place to attach the lateral rods is to the chord pins, ami their stresses should not he transmitted through the floor beams.^ Then come the questions, MIow shall they be transferred? and " How shall the rods be arranged so as to clear the joists . The detail about to be described will answer these questions. Upon the floor beam place a stick of square timber (about ei-ht inches for ordinary highway-bridges), and let the ends fit into wrought-iron jaws, which screw up against the chord pins ; then fasten the timber every few feet on alternate sides of the web by half-inch bolts, to the flanges of the beam, and rest the joists on the timber. The laterals can either be attached by bent eyes to the chord pins (which would be preferable if then- diameters do not exceed an inch and three-fourths), or by ordi- nary eyes to vertical pins passing through the wrought-iro.i jaws In this way the timber not only acts as a lower lateral strut, but serves to give additional stiffness to the floor beam; although the section of the latter should not be diminished on that account. Now, what objections can be raised to this method ,' Some may say that it is a clumsy contrivance, but that is a matter of taste. Others may suggest thai it reduces an no,, '^''^'f>/.yANV //WN H/GI/ll'AV-B/UDGES. loi structure to a combination bridge. Not at all, - no more tlian the emi^loyment of wood for the floor and joists; because, at the same time when the latter are renewed, the wooden struts can be replaced. There is a slight objection for short throu-^h- sixms y,z., that it reduces the headway; but it would not greatly increase the expense to add eight inches to the depth ot the trusses. ^ Another method of avoiding the difficulty is to rivet the floor beams to the posts. But will not this be equally objectionable } Certainly such a connection is better for the beams, as it par- tial y fixes their ends ; but what about the deflecting effects of u-md stresses and passing loads upon the posts.' The trans verse components of the lateral rod stresses act with o-r^at leverage, tor the beams are always attached above the boUom chords ; and the weight of a heavy wagon coming suddenly upon the beam must certainly cause the posts to vibrate trans- versely to the planes of the trusses, but to what extent, and with what injurious effect upon the posts, it is at present im possible to say. I.:ven if there be but little known concern- j"g this attachment, it is certain that a floor beam should never be riveted to only one of the channels of each post. Such an arrangement would produce indirect stresses of a destructive character: consequently the posts should be turned one-quarter way round in order to let the beam pass between them •• l.H.r beams in deck bridges may either rest upon the chords, I'o uing trom the chord pins, or be riveted to the posts In neither case should they be used as lateral struts when the lateral rods are attached to the chord pins, because of the lever- age^that would be afforded to the lateral stresses to produce It is not customary to calculate the thicknesses of beam- '•n.^ci plates, for they are usually made from three-fourths of ■nchtoanmch thick for ordinary highwavbridges ; but n|u cerain assumptions their thicknesses can' be calculated. tHc load on a plate be consi.lered uniformly distributed over ^' l-t.on between the beam-hanger holes, and if the flange of ;;l;;;'nn>c supposed to take up no bending-stress, the plate '"■'> '>^ -nsidered as a beam supported at the ends, and uni- lo: ORD/XARV IRO.V HIGHIV AY-BRIDGES. ii iMi lflW»s formly loaded. For instance, take the case of a twenty-foot panel and an eighteen-foot clear roadway, the re-action at each end of the beam is about nine tons. Suppose the centres of beam-hanger holes to be situated on the corners of a four-inch square, and the plate to be seven inches square, then the bend- ing-moment is i)/ = J ?F/ = ^~ X 9 X 4 = 4-5 inch tons. T? J The resisting moment is — ,-, where R = 5 tons, / = moment '^, (i of inertia = -^JhP = {..(P, and ^, = "■ Equating the moments, substituting, and solving, gives <'/ = about seven-eighths of an inch, a result agreeing with good practice. It is almost need- less to say that this method is very approximate ; for the plate is greatly stiffened by the rigidity of the flange of the beam, while, on the other hand, no reduction has been made for the beam-hanger holes. Lacing, or, as it is often improperly termed, single latticing, is about the most common detail for keeping pairs of channel bars in line : nevertheless, it must be inferior to latticing, especially when the lattice bars are riveted together at their intersection. By inspecting Tables XXXII. and XXXIII. it will be seen that a system of lacing-bars with one rivet at each end of a bar requires much larger stay plates at the ends than does a corresponding system of latticing or double-riveted lacing. The actual sizes of lattice or lacing bars for any strut can be determined only by experiment : it is thought that those given in Tables XXX. anci XXXI. are so strong, that the struts on which they are employed would break in the channels rather than in the bars, and yet not so heavy as to cause much un- necessary use of material. It will be seen also in these tables, that the requisite dimensions of latticing and lacing bars depend not only upon the sizes of the channels which they connect, but also upon the distance apart of these channels : this is due to the fact that the bars are subject to compression as well as to tension. The lengths and weights of latticing and lacing OKI)/A-AKy /A'C.\- JIlCHWAV-liRlDGES. 103 I moments, bars can be found from Table XXIX. It must not be forgotten that these lengths are to be used for cstiinalcs only; as they were obtained from a diagram, and not checked by calculation. The smallest trussing-bars used should be no less than a quarter of an inch by three inches, and the bend for attach- ment should be no less than three inches long, so as to permit of the use of two staggered rivets. The heavier the trussed bars, and the greater the distance between them, the greater should be the section' of the trussing-bars. At the encts of a s\ stem of trussing, the bars should be turned and attached, as shown on Plate II., Fig. 8, and on Plate VT. The lightest bracket used should be no weaker than a 2.1" X 2]" 4.9* angle iron, which section is to be employed only to attach intermediate struts to posts. Where there is no vertical sway bracing, the stresses on the brackets are to be calculated as shown in Chapter VI., and the sections are to be proi)ortioned by using the following table of approximate intensities of workiuir-stress. trut can be I.KXCril (1F STRUT, ]N I'KET. Intkn^.itiks of Wdkking-Stre 4 6 8 aj" X 2i" L. 3'0 2.0 3" X 3" L. o - jr X u" L. 4.0 3-5 3-0 The number of rivets that connect the bracket to the lateral strut and jjost must be sufficient to transfer all the stress in the bracket to each of these members. To prevent the pedestal at the free end of a span from slip- ping in the direction of the length of the rollers, the latter can be notched about a quarter of an inch in depth, for a length of about two inches at the middle, and the shoe plate andVoller plate be planed down so as to leave projections which will exactly fill the notches. This detail is illustrated in Plate VI. For short spans, a sliding-joint such as shown on Plate III. is to be used. 104 OKi)!.\\un- /Kox iin.nwAY-nRiiHiEs. When it becomes neeessary to anchor down the expandinj; end of a bridge, it should be done in such a manner that the shoe could not rise more than an eighth of an inch : thus the projection on the luuler side of the shoe plate will be prevented from being lifted out of the notches on the rollers. l?ed plates and roller jjlates should be anchored to the abut- ments by rods with nuts. When the abutments are of stone, a jrood method of attachment is to drill holes therein just below the anchor bolt holes in the bed plates, enlarging them, if prac- ticable, at the bottom. Split the ends of the anchor bolts several inches, insert small iron wedges in the splits, drive the bolts into place, so that the wedges force the split ends apart, thus partially filling the enlarged bottoms of the holes, and pour in molten sulphur. In figuring lengths of fillers for pins, a clearance of from a quarter to half an inch should be made, so as to allow for varia- tion in thickness of eye-bar heads, re-enforcing plates, etc. : such an allowance will sa\-e a good deal of trouble in erection. When the end lower lateral strut is of such dimensions that it will not fit, without being turned from the vertical between the ttanges of the batter-brace channels, filling-rings can be used between the batter-brace webs and the ends of the strut. Such rings will be necessary, if there be four chord bars in the end panel, and the outer ones be not let into the channel flanges far enough to lie against the webs. In making turn hurkles. n little expense can be saved by hav- ing only one adjusting-end ; the other having a hole, through which passes one end of the rod, which is enlarged into a heail. One advantage of this style is, that the turn buckle can never be lost from the rod. Such a turn buckle should always be used on portal vibration rnds, for a reason that will be given in Chapter XX. Jaws are not a very desirable detail, although so convenient that they are often employed. In the first place they have not a pleasing effect to the eye; and in the second, on account of the bent plates, are iiaole m ou wcakci lium rnight be esti- mated. If the flaii.i;es of the channels be cut away, as is some- times unavoidable, the jiiw plate, from the cut flanges to the iM O/W/A'.l/CV JA^OX HlGHH-AV-HRinGES. ,05 bend, should be able to resist more compression than the rest o the s ru . Such a detail occurs often on the ends of the struts wh.ch keep the pedestals apart. It is generally diffleult to make a satisfactory design for this member, as it interferes .'^V";?'l' rJ^''^'^ ''^^' '°"^''" '^^^•■'-^^ ^y^^*^"^ P'-eviously (lescrd)ed, all the difficulty vanishes Concerning the proportioning of eye-bar heads, there is a variety of both op.n.on and practice. Many specifications call nr a see .on a the eye ec,ual to one and a half times that of he bar for welded bars, or one and a third times the same fo ammered eyes, no,: taking into account the effect which the Ifcrent rat.os of chameter of pin to width of bar have upon t e s reng h the eye. Specifications for the better class ' -t radroad and highway bridges have of late made this d..s .nctu.n but there seems to be some uncertainty as to wha .s the e.xac effect of each ratio upon the strength. On p. 20 i given a table for sizes of chord heads, prepared from actua experiments by C. Shaler Smith. C.E.. who is considered th X.St Amencan authority upon all matters connected with he des.gnmg of bndge superstructures. The subject of chord- head proporfoning is further treated in Chapter XVIII ]>cnt eyes do not make a very good detail, but are 'such a conven.ence that they are often used by good desLniers If he .ameters of the rods do not e.xceecl o^ne inch a hre 1-nths, here ks no objection to using such eyes. The prin pal l;-t to be ra.sed against them is because o^ the eccentri:^^ ^^ iK.y g,ve upon the pin nut. This objection n.ay be n,o.ed by usmg e.ther extra large nuts, or the detail shou". in :;;■'■ '^'''^' ;r' ^".""-^-" "^ ^'l^tes H. and IV.. in which bcKt eyes pull aga.nst a piece of channel riveted to the M ut A stdl greater miprovement is shown on Plate VI. in ;vh.ch a p.ece of bent plate is substituted for the channel • t'h orm. s o more rivets in the connection, and avoids the pc'^^ h.h.M.t^ha^^.g to .nsert a filling-phue between the channjl and In connection with this detail, on Plate VI. is another and a athe, peculiar one. The plate, which was originally in the ""•'" ^'f the letter T, i.s bent .so that the stem n^a^Tbe r veted to io6 oh'p/.y.u^y i/^'o.\ iih'.iiivA v-nRiiHuis. the strut c'lianiu-ls, and the lu-ad may afford a lu-arinj; for the vihration-iixl pin. '\'\\\^ i-oniici-tion is to hi- used whc-n llic hit- oral strut chaiuu' Is aiv so small that ihoiv is no room for a pin to pass thront;)! tho coniu tin- lowi'i' I itinj;- T-plalo uliirh attache's th hanm-l. W'lu'ii, in-causc of th^-ir lar^o (lianK't(.T, tlu loWi,'!' ati'iai roils i. annol ho attached lo the chord pins, 1 )nt must he connected hy vertical pins passin;^,- throu^ii the lateral strut jaws, they must he made lo pull on the midille point of •h of the latter pins hy usini; a ilouhle eye on one of the rods, huLie enough to admit the eye of the eai \\r h a space hetween otiier roil Phis is to avoid al tendency to rotate the lateral strut ahout its a\i«;. The rods can he retained in place hy tillers ahove ani hel o\v, )Ui;h >f the moment of the lon-;itudinal com With this detail. thtMc is a tendency to hreak the jaw tlin the pni holes, hecausc ponen 1 I of the Literal rod stress: the jaw plate must therefore ■)e ma( le wide enoui;h to properly resist this moment Th easies I way lo proportion the plate is to assume its dimensions and to find its resistance lo hendinu', neglect ini; the area lost hy the pin holes (which area is close lo the neutral surface), anil makini; up for the omission hy providin-- a little extra resist, mce. To illustrate the ir.c Ihod, let us lake a two-inch lateral ro makimj,' an an liusses, aiu ole of forty-live de.t;rees with the planes of the 1 lei the distance hel ween centres of pin l)earinj;s Ik- si \ inches. The s tress on such a rod is 3.14 X 7.5 tons, auu t he l)eiHlini;-momenl on thi pin IS X • SS X ,> .ss.s mc h tons, correspomlini; {vide Tahle XII.) lo a ilia me ter o if th ree inches and a fourth. Th e distance from the axis of the pin to the centr e I >f tin iaw hearmi;- wil he .ihout _|. j"_|- i"-|- ;^" - 5". The lon^t;iludinal component oi tin stress on the lateral rod is ^3 the momen 55 X 0.7 = 16.5 Ion s. inakiiu t on the jaw ahoul 3 X 16.5 = S2.5 inch Ions. The thickness of the jaw plate should he %\ and let us assume llio Aviillh to he 7 known formula, The resislinii-moment is given hy th e well- J/ = /?/ (>A'/)/x.i/n' /h'ox j"c,nu'A v-nRiDcr.s. 107 WlUTC A" = 1 1.25 t„ns, / = /,/;,/3 = ji, X V- X (;)•■', and d,=l Siil)slitutiii<^, f^ivc's M: 11.25 X tV^X V X 49 X 7 X 2 1 15 incli tons, nearly. jaw thn'UL;li ^uilinal com st tlKTcton.' nu-nt. llu' (liinciisions, U' area lost ral siiriacx'), little c.Nlra Tlic (lilfi-iviirc bctvvcfii 115 and 82.5, or 32.5 inch tons, is ,t;rcatcr than the rcsistin<;-monicnt of the material lo.st by the pin hole: so the dimensions assumed are ample. U-nuts are objectionable in every case; for, if th stronir en ey are made oii-h to resist without bucklin<; the ultimate i)nll of nice. the rods, they will have ;i very clumsy appear lion of a cast-iron washer will relieve the bendinj; of the U, but not tiie appearance: besides, it is better not to introd iron into a wrou,!;ht-iron structure. he inser- uce cast- It IS now m o filer to take up the omitted portions of Chap- ter IX. iMi-st, to find the number and distribution of the rivets in the ilan-es of the beam there designed, let us divide the fifteen feet between centres of supports, as shown in the accompanying diagram, and calculate the stresses at the points of division. a'6" >< a'o" ) < a'o" >< i'o"> < i'o"> < I'a" 2'f>'' The ro-action at each end is about 8.5 tons, and the uniformly distributed load about 0.0044 ton per lineal inch. The moment at the first point of division from the support is 8.5 X 30 - 0.0944 X 30 X 15 = 212.5 inch tons. At the ne.\t point of division the moment is ^^•5 X 54 - 0.0944 X 54 X 27= 3 21. 3 inch tons, and at the ne.xt j)oint it is cS.5 X 7S - 0.0944 X 7.S X 39 -- 3 75.,S inch tons. loS 0A'/)/A:1 A' 1 • /A'lKV II lull 1 1 \1 i -BAJlKiKS. From the last equation of Appendix II. we have for the value of the flange stress at any section, M S = In this case Dividing each of the moments by 36.7 gives, for the horizontal stresses at the three points of division, respectively 5.8 tons. 8.74 tons, and 10.24 tons. Therefore, between the centre of the support and first point of division, there must be enough rivets to take up a horizontal stress of 5.8 tons; between the first and second points, enough for a horizontal stress of 8.74 — 5.8 = 2.94 tons; and between the second and third points, enough for a horizontal stress of 10.24 — 8.74= 1.5 tons. The vertical pressure upon the rivets of the upper flange is about 12 X 0.0944 = 1. 133 tons per lineal foot, making the total vertical stresses for the three divisions respectively 2.83 tons, 2.27 tons, and 2.27 tons. Combining these by the ixirallelogram of forces with the horizontal stresses last found, gives the total stresses for each division 6.45 tons, 3.71 tons, and 2.72 tons respectively. From Table XXXVI. we find the resisting bending-moment of a five-eighth inch rivet to be 0.18 inch ton, and the working bearing-pressure on a quarter-inch plate, 0.938 ton. Let us first consider the stress of 6.45 tons. It is equally divided between the two angles, making the stress on each 3.22 tons. The lever arm of this last stress is .](] + /l;) = aV' ^"'^ the moment ^.i X 3.22 =0.906 inch-ton, dividing which by 0.18 gives five as the number of rivets required to resist bencUng. Dividing 6.45 by 0.938 gives seven as the number required for bearing. If there be but seven rivets in two feet and a half, the spacing will be five inches, which would be practically too great. It is better to space the rivets two and a half inches near the ends of the beam ; and, if it be thought advisable, the distance may be increased to foiu" or even five inches near tlie middle. ORDINARY IRON HIGHWAY- BRIDGES. 109 iMoni the above, wo may conclude that calculating riv?! .spacin.^; for flanges of floor beams is, as a rule, too much refme- iiunt lor highway-bridge designing. If the depth of the beam W reduced near the ends, or if, by reason of lack of headway biMU-ath the 1 be used, it might be well to -fu tl iridge, shallow beariis Next let us make th irough the above investi-at ion. le design for a trussed floor beam, takin; a twenty-foot panel and a tweiUy-funr foot roadway of a brid'^i ;jives the weight of ai belonging to Class A. Table XIX ordi IK'I- nary built beam for these dimen lineal foot : so let sions as ninety-four pounds us assume the weight of the trussed 1 )eam to be eighty pounds per foot, also the length of beam between centres of supports to be twenty-five feet. The live load will he 24 X 20 X 100 2000 Table XV. gives 3339 as the number of feet of pine lumber per panel, the weight of which is = 24 tons. 3339 X 5 2 X 2000 and the weight of the beam itself is 26 X 80 = 4.174 tons; 2000 = 1.04 tons; makmg the total load equal to 29.214. or 1.1686 tons per lineal f<)t)t. Let us use two jwsts. The central panel should be ten feet long, and each of the others seven and a half feet. Let us assume the beam to be a 10" 30# I, and the depth of the truss five and a half feet centre to centre. Then in the formula 3 4> we will have iv = 1.1686, I, = 10, </ = -f„ nearly, C= 5, P = .]X 1. 1686 X 17.5 = 10.225, /, = 7.5, r"^3, D=s.S, and A' ;d)out 8x032 = 2.56. Substituting these values gives A + A" = 3 21 as the area of one flange. The total area of the section would then be 2 X 321 + 2.56 = 8.98 square inches, which cor- responds altpost exactly with the area of a thirty pound I-beam. h 11 I • ' ( I pit ifliiri no OA'/>/X^IUy /A'(>.\ JlhiJ/UA \-JiRiniJKS. Tho (k'si^n for llu- post agrees with that shown in Fipj. i6, riale II., with tlie exception that the end (Uagonals are not adjustable. The stress on a post is /' = 10.225 tons ; that on the bottom cliord is that on the end diaj^onals is />^i:cO— 10.225 X 1-69= 1 7.28 tons; that on the counters is j'\,/'sLr «' = 0.3 X 10.225 '^ 2.16 = 6.625 tons. The Mitensity for the tension menilK-rs should be four tons, making- the sections required for tlie chord bars and main dtogonals respectively 3.48 and 4.32 square inches. Referrin<; to Carnegie's " rocket-Companion," p. 94, we find that two §" X 2\" bars will do for the former, and two \" X 2^" bars for the latter. From Table IX. we find that two one and a quarter inch rods will be re(|uired for the counters. To the stress on a post must be added the vertical component of the initial tension on the counters, which is about 2 X 1.5 X 0.46 = 1.38 tons; making the total stress 1 1.605. Before ajiplying Table XL., we must multiply this stress by about 1.5, the ratio of the factors of safety for wind bracing and floor-beam struts; making the total stress 17.407 tons. Using the column for one fi.\ed and one hinged eiul, we find that a 6" 15* I-beam will be reciuired. To find the thickness of the pin plate at the end of the beam, let us assume it at five-eighths of an inch ; then the lever arm of the diagonal stress will be .1(5 + 5) = •] inch, and the moment. 17 28 3 X -^" — = 6.48 inch tons. 2 Consulting Table XII., we find that the necessary diameter of pin is two inches and an eighth. Referring to Table XXVI., and looking down the column for a two and an eighth inch pin, we find that the necessary bearing will be, for 8.64 tons, eleven- sixteenths of an inch. It will be more economical to increase the diameter of the pin to two inches and three-eighths than the thickness of the plate to eleven-sixteenths. OKD/XANV /ROX HIGHWAY-BRIDGES. \\\ rhths than Next let us find the number of rivets necessary to attach the plate to the I beam. The horizontal and vertical components of the end diagonal stress are respectively 17 28 X 0.8 = 13.82 tons and 17 28 X 0.6= 10.37 tons. The first of these stresses pioduces bending; and the second, direct tension on the rivets, The moment of the first stress is about 13..S2 X J(!i + i') = 9.5 inch tons, uhirh. divided l)y 0.493, tlie resistiuf^-moment for a seven-ei;;i,ths iiuii rivet, ioiind in Table XXXVI., gives twenty as the nmnber oi rivets to resist bending. To resist tension the number re- quired will be 5 X 0.6 ~ *^' making twenty-four rivets in all for the connection. Seven- eighths inch rivets are rather large for the flanges of a ten-inch beam, as there is not room for full heads : nevertheless, it is better to use them, on account of the increased bending resist- ance.. Using twelve rivets on a side, and spacing them two inches and a half a])art, will make the length of the plate about thirty-two inches. It is evident that there is no need of figuring for bearing in this connection. .\e.\t let us proportion the connecting-plate over a post, assuming the thickness to be three-eighths of an inch, and using live-eighths inch rivets. The moment on the rivets will be 1 1 .605 X ,\ ( 3 + ;. ) = 5 .oS iii,:h tons, which, divided by o. i.S (the resisting-moment of a five-eighths inch rivet), gives twenty-eight as the number of rivets required, or fourteen for each lug. Using staggered rivets spaced two inchrs apart will make the depth of each lug about fifteen inches. The number of rivets necessary for attaching the plate to the beam is partly dependent on the counter stress, and partly upon the length of plate which we consider requisite for fi.xing the cn.l of the post. About eighteen inches ought to suffice for »M{ 112 ORDIXARY IROX HICHWAV-BRIDGES. this purpose. The horizontal component of the counter stress, including initial tension, is 9.625 X 0.89 = 8.566 tons, and its moment on the rivets is S 566 X \{% + f ) = 4.82 inch tons, which, divided by 0.31 1 (the resisting-momcnt for a three- fourths inch rivet), gives sixteen as the number of rivets rec|uire(l. Making them staggered, and spacing them two and a c|uarter inches apart, would make the length of plate just twenty inches. Let us assume the sections of the re-enforcing plates at the feet of the posts to be j," X 5"; then the lever arm for the cho'-d stress will be ^(^ -|- -J) = ^ inch, and that for the vertical com- l)onent of the end diagonal stress o(| + .} + V) = {o ; making the horizontal and vertical component moments on the pin respectively, .23 inch tons 13.044 and 10.225 1(1 4.79 inch tons. The resultant moment is V'(5.23)'+ (4.79)-= 7.09 inch tons. It is evident, that, to obtain the lever arms used, the chord bars must be packed on the outside and the end diagonals, between the chord bars and the post. The diameter of pin correspond- ing to 7.09 inch tons is 2^'; but a 2]" pin is tlie smallest that can be used with a 2^" bar. The post l)earing is am|)le, anil needs no testing. If we divide the bearing-stress equally between the post and the re-enforcing plates, there will come upon each of the latter a stress of 2.9 ; making a moment upon the rivets equal to \ X 2.9 = 1.45 inch tons, which, divided by o. 18, gives eight as the num- ber of five-eighths inch rivets recjuired for each plate. Adding two for safety, s])acing the rivets two inches apart, and allowing room for the eye-bar heads, will make the length of each re- enforcing plate about si.xtcen inches. ORDLVARY IROX nrGIIlVAV-nRIDGES. ,,3 The moment on a counter pin is 4.S1 x i{ij -f U) ^ 3 ni inch t..ns corresponding to a if" pin. % examining Table XX\T ■t u-.ll be seen that a 2I" pin will be required to give sufficient bcnnng .r Ke,errn,g now to the list of details for a trussed beam, oivcn on p. 30, so as to omit nothmg, we can make out the bill of iron as follows : — Uj)l'L'r chord beam l.oucr clioid bars . . I'^nd diagonals . . . Counters Posts Connecting.plates . . Ke-enforcing plates . i'in jilates Stit'teners Tins I'ins Fins Fillers ....".' Rivet heads , . . Total weight of beam 4 2 4 2 4 10" r' I" 6" 3'/ I" -5 2-t" @ 3o#I -4 2i" O '5*1 14" S" 15" 7 3#L O O Q 2# 26' 780* ■3' 150" ■3' 379" IS' 245 " 5-3' 159" 3' 105 " 16" 44'- 32" 167 '■ 8" 30' 10" 25- 10" 20'- 13" 29'- each 8" about 50- 2, 191* 1 hc'^ we>gln of a plain beam for the same place would be -0 X 94 - 3,444, showing a saving of 253 pounds by using a mssed beam At f^ve cents a pound, this would amount to sM-.Os; which IS considerably more than the cost of th- field nvct.ng, and extra trouble in putting such a beam in place A -nnlar investigation for a trussed beam with one post will show "''^t he weight of such a beam will exceed that of a corre- sponding pkun one: so there would be no economy in such a ilcsign for this case. 1(1 >: III! i! t 114 OKD/XAN 1 ■ IKOX men 1 1 '. / ) -/iA'/DUhS. CHAPTER XIV. BILLS OF MATERIALS, AND ESTIMATE OF COST. In making out bills of materials, the list of members given in Chapter III. will prove of great assistance. By its use, one can avoid an underci-,timatc due to an omission of any of the parts of the structure. A good way to make out a bill of material is to prepare si.\ vertical columns, in the first of which write the name of the member ; in the second, the number of pieces ; in the third and fourth, the dimensions determining their sec- tion ; in the fifth, their length ; and in the sixth, the woiglit of all the pieces, or, if of wood, the number of feet, board meas- ure, that they contain. The following examples will serve to explain the methotl : — DILL OF WROL'OIIT-IKOX. Chord channels . . . 12 7" 10,1* [ 2,772# Batter-brace channels . 8 8" i2i#[ 33''/' 3.375 " Plate I X" 4 12" 262' 2,620 " Post channels .... 8 5" c>k# c 22^ 1.144- Lateral struts .... 4 4" r* c <5' 360 •• Lateral struts .... 4 5" 6.^# [ •5' 300 •• Main {liai;onals. . . . 8 r 'T 34' 1.020" Counters 8 3" 4 3" 35' 5-5" Etc "" • " 2.77-# 3-375 '• 2,620 " 1.144 •• 360 •• 390" 1.020 •■ 5-5" ORDINARY iRox j//i;//ir.n--nA'/jH,j.:s. BILL OK LUMBKK. IIS Joists Flooring . . , liand-rail caps . Handrail posts. IJiil) ])lanks . . 1\11\- planks . . Lateral struts . 55 110 20 30 4" 14" 3" 12" 2" 6" 4" 6" 2" 12" 6" 6" 8" 8" '4' 22' 4' no' 112' •4' Total number of feet, hoard measure 5/>47 4,620 440 240 440 672 224 r 2,283 It IS to be noticed that it is often convenient, as in the case of the "Plate" in the "Bill of VVroi.ght-Iron," or that of the "IIuI, planks" in the "Bill of Lumber." to combine several lcnt;ths in one. To the length of each chord bar. main diagonal, and hip ver- tical IS to be added three feet to allow for the weight of the licads ; and to that of each adjustable rod about five feet for the heads, upset ends, and .sleeve nuts or turn buckles Should greater accuracy be required for the weight of an adjustable rod. It will be necessary to ascertain what length will be needed at each end for the heads, and how much for the upset ends ;'nd adjusting-nuts by the followin<' T.AHLI- OF EQUIVALENT LEXGTMS OF RODS FOR UPSET ENDS, NUT.S, .SLEEVE NUTS, AND TURN BUCKLES. h'' -1" I 1 ' ->r ■iV —ill ^" -2h" i" -4" I 6 " -2^ I upset end and i nut I upset end and i nut I ujxset i:\u\ and i nut 1 U])set end and i nut 2 u|)set ends and r sleeve nut 2 upset ends and 1 turn buckle •i feet of rod 'i feet of rod 'f feet of rod 'iV feet of rod 1 •3 feet of rod 3 feet of rod I hcse equivalent lengths do not include the lengths of the I'Psct ends themselves : they represent simply the e.vtra lengths t" be added to the bar to equalize the weight of the nuts, slocve nuts or turn buckles, and the e.xtra iron for enlarging the ends, which arc six or ' " ■ -I ' 'I ('i';lit mcl loui ill ii6 ORD/XARV IROX lIIGIIWAV-BRnyCES. It is not necessary in a preliminary estimate to find the exact quantities of materials, so approximations to actual dimensions can be made. This will be fully illustrated in Chapter XVI. Before considering a bill of material as finished, it is well to look it over to sec that no mistake has been made in the number of the pieces. It is not an uncommon error to put down only half the correct number. As soon as the bills of iron and lumber are made out and checked, the dead load per foot should be calculated, to see if it agree with the one assumed within the limit specified on p. 6. Estimates of cost should be liberal ; for, as a rule, the actual profits on bridges fall short of the amounts estimated. They can be made very readily by using a blank similar to the fol- lowing : — Estimate on Brittgc across Lotiith spoilt ft. Ilcli^ht, ft. Clear Roadwayy ft. .Static Load per lineal ft., lbs. Afoiuiii^ Load per lineal ft., Ids. A'o. Panels. Loigth Panels. ft. : I Cts. @ % © @ loads (o II 'roiis^ht-iron. lbs. Casl-iron, lbs. Lumber, ft. Piles, ft. Hauling, Freight Framing Falsework Erection Spikes J'aintiri; Blacksinitliing Coal Freight on tools Travelling expenses .... Men^s time travelling . . . Bidding expenses Teaming during construction Incidentals Total cost of bridge . . . Cost per lineal foot . . . ORDIXARV IROX HfGHVVAY-nRinarCS. 117 On fair country road.s, a load for a team of horses may be taken to be a ton and a half of iron, a thousand feet of pine lumber, or si.\ hundred feet of oak lumber. The designing of falsework will be treated in Chapter XX. Its cost will include that of the piles in place, if any be required! and that of the lumber, to which should be added about three dollars ])er thou.sand for framing and raising, and a dollar or more per thousand for taking down. Falsework timber can generally be sold for something when the bridge is completed : so a reduction may be made in its cost when the estimate is to be a close one. The cost of erection can be found approximately for ordinary conditions from Table XXXVIII., by multiplying the number of days' labor there given by the average rate of wages for ordi- nary bridge hands. It must not be forgotten that there is a great variation in the cost of erection ; for it depends upon the locality, weather, skill of laborers, efficiency of foreman, etc. Those who feel inclined to question the correctness of this table should make some allowance for the difficulty which the author has experienced in getting any data whatsoever upon the subject. Few bridge engineers care to part with the knowledge which has cost them both time and money \\^ regard to cost of painting, the same difficulty has been encountered : so, for lack of more accurate data, the followino- table will have to suffice. It has been prepared from a few figures of co^,t of painting, obtained at a time when wages were a dollar and a half a day. SrAN 12' roadw.iy. 16' ro.idw.iy 20' roadway. 50' S6.0O ?7 00 8(9.00 100' 22.00 25.00 2S.OO 150' - 45.00 51.00 200' -50' 300' - So.oo 125.00 90.00 140.00 1 70.00 24' roadway $11.00 31 00 57.00 lOO.CO 155.00 1 90.00 IV'lore making an estimate on a bridge, one should endeavor to ohtam as many as possible of the followin<^ i ^i' B V'. t- lit Il8 Oh'n/\AA'\' /AOx ///<;// 11. n-/,'A7/)(;/-:s. DATA I'OK OESIGNMNG IRON IIK.IIWAV liKIOGE SUPERSTRUCTURES, AND I-.sri MATING THEIR COST. Class of bridge required. Length of span or spans. Width of clear roadway. Headway required in clear above floor. Live load, if different from the ordinary. Wind pressure per square foot, if different from the ordinary. Any extraordinary load, such as paved flooring, heavy falls of snow, etc. The velocity of passing loads. Distance of bridge site from nearest railway-station or sea- port. Quality and condition of the roads between these places. Nature of bed of river, and velocity of stream. Height of lower chord above bed of river. Cross section of stream at crossing, showing borings, if any have been made Angle which the direction of bridge makes with axes of piers or abutments. Nature of the country at the site. Any special difficulty that may be anticipated for the raising. Kind of falsework it would be advisable to use. Cost of piles at various places in the neighborhood, if any be required. Cost of transport of same to site. Cost of timber per thousand for falsework. Probable value of falsework timber after bridge is finished. Cost of withdrawing piles, if necessary. Number of lineal feet of piles recjuired. Number of feet of lumber for falsework. Cost of spikes, bolts, and nails for falsework. Cost of driving piles. Cost of transporting pile-driver to and from site. Common laborer's wages. Skilled laborer's wages. Foreman's wages. Wages for team and teamster. ONn/X.lKV IKOX HIGHWAV-nRlDGES. RUCTURES, 119 Cost of siipcrintcrclcncu by cnt^incer or engineers. Number of days' teaming on work. Date when bridge must be finished. I'robable length of time it will take to raise and complete )ri(lge. Chances of fair or foul weather during this time. Chances of having falsework carried away by a sudden rise or in icc-gorge. Chances of a scarcity of laborers. Chances of sickness among laborers. Expenses attendant on same. Cost of tents or other housing for laborers, if any. Cost of iron at mill or foundry. Cost of transport of same to nearest railway-station or sea- port. Cost of lumber per thousand at mill or market. Cost of transport of same to nearest railway-station or sea- port. I'robable expenses for blacksmithing and coal. Cost of tools, if it be necessary to buy .special ones. Wear and tear of plant, and loss of tools. Loss of bolts and timber. Actual cost of raising similar structures under similar circum- stances. Trax-elling expenses of employees to and from site, lidding expenses, if any. Office expenses in preparing plans, etc.* Advisable allowance for contingencies. » Tlus is „su.,lly not considered, as it is a constant e.xpense, and comes out of t!,e aiini.al gross i]rolUs ot the company. 120 ORDLVAKV IKO.y H hi U WAY-BRIDGES. CHAPTER XV. ECONOMY. The first point to be considered, when dccidinj:^ upon the style of" bridge for a certain stream crossing, is the ninnber ol spans. It is, in reality, a consideration of economy wliich determines this ; for the best bridge to l)uild, provided that the water-way be not too much contracted, is the one for whicli the sum of the cost of superstructure and the cost of founda- tions is a minimum. If the water-way be too much interrupted, the design would not be an economical one, even if its first cost were the least, because of the risk of washout to which the bridge would always be subject. In most cases, there is not much choice concerning the num- ber of spans, local considerations often determining it ; but there is occasionally a choice between two or even three numbers. The only way, then, to decide is to make a rough estimate of the cost of the superstructure and the foundations for each number; then, if the choice fall about equally between two numbers, it is better nearly always to adopt the longer spans, because the actual expense for the foundations usually exceeds the amount of the preliminary estimate. Another preliminary point to be settled is whether it would be most economical to build an iron, a combination, or a wooileii bridge. Although this work treats of iron bridges only, still this is a point which ought to be considered. The following mathematical treatment of the problem was given by the late Ashbel Welsh, C.lv, past president of the American Society of Civil Engineers : — rv.v>A\-./ -J- /Rox iiiGnWAv-nR/ncEs 121 1" MM' llIK (CMPAKA-nvK r.CONOMV OF TWO HRIDOKS OF niF- I KKF.NT COST AND I.UKAMIMTV, THAT Wir.L A.NSWKK TMKSAME I'lKPOSK KOUALLV WELL WHILE TllEV LAST ' Lot The the cost and assumed real value of one of them T the time it will last, a the compound interest on one dollar 'for that tune, at whatever rate money is worth to the party paying- for the hndge, and /. the loss on the bridoe at the end of the lime T, or the amount which it would take to make it as -ood as new. Let A' be the real value of the other bridge, C its cost, / lis duration, n' the compound interest on one dollar for that lime, and /.' the loss on the bridge at the end of the time V or the amount required to make it as good as new. And let Tbc I he real value of the bridge that would last forever if all cir- cumstances should remain constant. ' Xow. supposing that the money required for building had been borrowed for an indefinite time, the actual expense at the end of the time T to the party paying for the bridge which would last forever would be aV; and the actual expense at the ciul of the same time for the first bridge, after making it as ^ood as new. would be aC ^ L. These two quantities are equal : therefore the hitherto unknown value of V\^ C4- Z a S.mlIal■l>^ at the end of the time T\ the expense for the bridge which xvould last forever would be a'V; and that for the second bridge, after making it as good as new, if the cost luul been the real value R, would be a' R + L' . As before, these iwo values are equal; and therefore, T' V=R^^j. a I'iquating the two values of V gives and R=C +~-^. a a' 1,1-! 12: ORDI C \RV IROX IIICIIW \IY -H RIDGES. Now, if the value thus found for R be greater than the cost C\ the second l)ridi;e is more economical than the fust ; while, if it be less, the first bridge will be the more economical.' The next economic consideration is that of depth of truss. Upon this subject much has been written, and many investiga- tions have been made; the general conclusion being, that the depth should be from one-seventh to one tenth of the span : some ICnglish writers say from one tenth to one-fourteenth of the span ; while only one, as far as the author knows, — Benja- min r.aker, C.l':., in his treatise on "Beams, Columns, and Arches," — makes it from one fifth to one-seventh of the si)an. Such investigations being purely mathematical, and involving the use of the differential calculus, are of little practical value, as they cannot take into account the numerous variables that ought to be considered. Not only do the stresses in a truss vary with the depth, but also the intensities of working-stress in the compression members. These, again, vary with the number of panels ; and this variation is according to a law or laws altogether too complicated to be handled by the calculus. Again : the intensity of working-stress varies, or should vary, according to the position and importance of the member. In view of the complexity of the question, and wishing to determine the most economic depths for Pratt and Whipple trusses, the author, about a year ago, undertook to solve the problem in a practical manner by assuming the most common clear roadway (sixteen feet), and figuring out a number of dia grams of stresses, and bills of materials. At first he considered that It would be necessary to calculate the total actual cost for every case, but upon further investigation found that il would be sufificient to figure out the sections and weights per lineal foot of the different members of one truss, multiply these by their respective lengths, and sum up the products, neglect- ing all consideration of details, because the differences in the weights of the latter balance each other. Thus, if the depth of a truss be increased by one foot, there would be a little increase in the weights of the lattice bars and rivets and a decrease in , that of the pins anil eye-bar heads. These may be taken as balancing each other, without making any appreciable error. rMvv.\- //>•)■ //cnx nir.mr.w-nRiin-.F.s. ,23 TiK- im.sl economic Icn-tli of pand was at tlic same tinic .nvcst,K.itc-cl, and was determined, witl,ni,t preparing; complete hills of materials, by co.isiderin^^ only those portions of the structure wiiich are affected by the variation in the number of panels. Economy in pony trusses is an element which ou^ht seldom t(. influence the design, for a good bridge of this kind will .re„. erally reqiure more iron than the ordinary calculations demand instead of trying to avoid a little expense, regard should be paid to obtaui.ng a good distribution of plenty of material in Older to partly compensate for the lack of rigidity which' is characteristic of the pony truss. In very wide pony-truss hrulgcs, especially when the length of span approaches its superior economic limit, it might be well to make a few calcula- tions concerning the economic depth; but the number of panels shou d be regulated by the slope of the batter braces, which should never be less than two and a quarter horizontal to one \crtical. The superior economic limit of the pony truss is not a fi.xcd quantity, but decrea.ses as the width of the bridge and the load mcrease, and as the intensities of working stresses diminish l;..r example, comparing a pony tru.ss and a thn.ugh brid-e of sixty.five feet span in four panels, sixteen feet clear roadway, designed according to Class C, there is found a difference of three hundred pounds of iron in favor of the pony truss ; while w'th the same span, for a twenty-foot clear roadway, and bridge designed according to Class A, there is a difference of eleven nindred and fifty pounds of iron in favor of the through brid-e I'..r a clear roadway of twelve feet, the superior economic limit of the pony truss would reach as high as seventy-five feet ; and. m- very wide bridges, the inferior economic limit of the throuoh bn'lge would reach as low as fifty-five feet : but, on account^of > ■guilty, the superior limit of the former may be placed at sixty- ^ve teet ; and, on account of appearance, the inferior limit of the latter at the same length. After making out diagrams of stresses, and bills of materials '"'•"ver one hundred spans, the author came to the followin-^ conclusions : — =" i I 124 (>A'/>/.\.!/:)' j/:(i.\ I Hi, 1 1 WW v-i',RiiH,i:s, n\ I till ^' That if ttu' economic depth he calcuhitod for any span, where the panel length is twenty feet, or the nearest leni^th helovv twenty foet, and if the economic depth for the same span, l)ut with one panel less, be calculated, the latter will exceed the former by one or two feet. That, in places where lumber is expensive, it will not be well to make panels over twenty feet lonj^, or, in places where it is cheap, to make them over twenty-four feet lonj;, because tim- bers exceeding tiie latter lenj;th are not easily procured. Then, too. iji designin<; iron brid<,'es, which are supposed to last indeli- nitelv, it must be remembered, that, as time j^^oes on, loni;- timbers will become more and more expensive, and less easily procurable, even in timber districts ; so that panels exceeding- twenty feet in length should be employed very cautiously. For appearance, through spans of one hundred feet and under should have five panels. The principal objections to the use of the double intersection for short spans are, that, as the rods are long and slender, they will vibrate more than the shorter and larger ones of the single intersection. Any flaw in a small rod will have a proportion- ately greater injurious effect than the same sized flaw in a larger rod. Long and slender rods are difficult to transport, and arc liable to become twisted and bent ; though this objection can be partially removed by halving them, and, as the posts are light, they will spring more under the shock of rapidly moving loads. As the width of roadway and the live load increase, and as the intensities of working-stresses diminish, the inferior limit of the double intersection may be lowered. The table on p. 8 {rives the limits which the author would recommend. The common idea among highway-bridge builders, that a double-intersection bridge should, for economy's sake, have more panels than a single-intersection bridge of the same span and loading, is incorrect. The economic depth for a double-intersection truss is about three feet greater than that for a single-intersection truss of the same span, and number of panels. Tables IV. and V. give the principal results of the before- oA'/'/.v.iAT /AiKv ///(/// ir. I r-/!Av/)(:/-:s\ I2« nu'.itioncd iiuvsti-ati<.ns. The first is the ..nc- to he (M-(lin:.nly iise.l : the .see<-ii<I may he em|)I()ye(l for districts where the tiiii- her is hirj^e and plentiful. There seems to he an iinf..unded prejudice in the minds of cnimiy commissioners and hrid-e sui)ervisors a-ainst Ion- pan- els. Practically they make a hetter brid-c than do short panels ; for tlie members are fewer and lar-er, and therefore less affected' by Haws, besides less subject to vibration, and less hable to maccuracy of construction. The floor beams and joists bein- lar-er. there is less probability of often receivin- their ma.xinum" workin-.loads. The only real objection to Ion- panels is the extra cost of the joist timbers when they arc to be replaced. In addition to what precedes, the following general economic considerations should always receive attention. Field riveting should be avoided as much as possible, and designs should be made so that all the parts will come to-ether readily during erection. '' Kivets should be spaced with regularity, .so as to facilitate tile i)unching of the holes by riveting machines. it is generally better, in through 'bridges, to pack all but the end chord bars outside of the posts, and reduce the width of top chord plate to a minimum. It is not always better to employ the apparently most economi- cal depth of channels. For instanc . if there be a choice of using ten or twelve inch channels for the top chords and batter braces, and if the S(rf/(»/s alone would indicate a saving of sav three hundred pounds of iron by the use of the twelve-inch channels, the others would be more economical ; for the twelve- inch channels require larger stay plates, lattice bars, and re-enf„rcing plates, besides a wider top chord plate, which would increase the weights of the cover plates, chord pins, post lat- ticing, post stay plates, shoe plates, etc., and even add a little to the lengths of the floor beams. the beforc- 1^ ' ilH^i 126 ORDLXARY IROX HIGHWAY-BRIDGES. w , 1r* CHAPTER XVI. COMPLETE DESIGN FOR A BRIDGE. Let the bridge to be designed have a span of one hundred and sixty feet, and a clear roadway of fourteen feet with no sidewalks, and let it belong to Class A. Referring to the table on p. 8, we see that the trusses should be of single intersec- tion. On p. 5 we find that the live load should be eighty pounds per square foot of floor, which corresponds to eleven hundred and twenty pounds per lineal foot of bridge. Table I. gives the dead load as seven hundred and forty-two pounds per lineal foot, say seven hundred and forty pounds. Table IV. gives eight for the number of panels, and twenty- four feet for the economic depth. The diagonal upon 20 and 24 is 31.24, which divided by 24 gives 1.3 for the secant ; and 20 divided by 24 gives 0.833 for the tangent. The panel live load, ic, is equal to 1 1 20 X 20 . ^ 1 y^ = C.6 tons. 2000 The panel dead load, \\\, is equal to 740 X 20 2000 = 3.7 tons. Let us assume that about a third of this is concentrated at the upper panel point, making W = 1.2 tons. The sum of the live and dead panel loads, or W", is 5.6 4- 3.7 = 9.3 tons. 2ntratcd at OlWrNARY IRON HIGHIVAV-BRIDGES. 127 One-eighth of zc is 0.7 ton, which multiplied by i x dves 0.91 ton. ^ '^ ^ The panel dead load multiplied by the secant is 3.7 X 1.3 = 4.81 tons. //'" multiplied by the tangent is 9-2> X 0.833 = 7-747 tons. The following table of data can now be written : — 'to « = 8 /= 20 «'= 24 diag. = 31.24 sec = 1.3 tan 6 = 0.833 71' = 5.6 ^^.= 3-7 ilV,= 1.85 ir = 1.2 iw = 0.7 iw sec (9 = 0.91 ^j sec 6 = 4.81 ^IV^ sec (9 = 2.405 IV" tan ^ = 7.747 ^ IF" tan 6= 3.873 Next let us draw the skeleton diagram shown on Plate V and number the panel points, commencing with zero at the right! liaiul end. ^ First let us find the stresses in the diagonals, using Table XLI 1 he stress in the counter at the point 2 is -Pc sec e - |/F, sec ^ = 3 X 0.91 - 3 X 2.405, a negative quantity, which shows that there is no stress on this member. Let us mark it zero on the diagram. The stress in the couiter at the point 3 is f«. sec 6 - A ^// sec 6 = 6 x 0.91 - 2.405 = 3.055. Fct us mark this and all succeeding stresses on the diagram 1 he stress m the main diagonal at the point 4 is V^^ sec e + ^ IV, sec ^ = ,0 X 0.91 + 2.405 = 1 1.505. That in the ne.\t main diagonal is V^ sec 6 + UV, sec fl = .5 x 0.91 + 3 X 2.405 = 20.865. 128 ORD/X.IR]- /A'OX IinUlU'A Y-BRIDuES. That in the ciul main cliaironal is 2i7i' sec + •!//', sec U !i X 0.91 4- 5 X 2.405 = 31.135. That in the hatter hrace is 28 7i' sec ti -\- \ /Fj sec ^ = 28 x 0.91 + 7 X 2.405 — 42.315. That in the middle post is I,,, _ iJFi + W = 6 X 0.7 - 1.85 + 1.2 = 3.55- That in the next post is JLQ w + \ \]\ + /r = 10 X 0.7 + 1.85 + 1.2 = 10. oc That in the next is ^§w + •;! \V, 4- W = 15 X 0.7 + 3 X 1.85 + 1.2 = 17.25. The stress in the top ehord at the panel next to the centre is 1 IW" y^^\- {Y + 2 + 3) W"-^ = SIF" tan 6 = 61.976. a II That in the next panel is (8 - i) IF" tan 6 = ji IV" tan 6 = 58.103. That in the next is (72 - Is) ^^"' tan e = 6/F" tan 6 = 46.482. That in the lower chord at the panel next to the centre is the same numerically as that in the top ehord at the second panel from the centre ; viz., — 7UF" tan ^= 58.103. Similarly, that in the next panel of the lower chord is 6 TF" tan 6-- 46.482. That in the remaining: panels is (6 - 2?,) ;F" tan ^ 3.I IV" tan 6 = 27.114. 0/^J)/X.lRV //Uh\ HIGHll-AV-BRinC.ES. 129 A check by moments about the hip gives the stress in the lower chord at the end panel 3.] //'" tan ^. which shows that the chord stresses are all right. Next let us determine if any stiffening be required in the end panels. An examination of Table XXV. sh<.ws that the diameter of the end lower lateral rod is one and eleven-sixteenths inches Consulting Table IX., we find that the greatest working-stress that can ever come upon such a rod, including the initial ten- ,sion, is I4.399 + 2.375 = 16.774 teas. The cosine of the angle which the rod makes with the planes of the trusses is about 0.8 : therefore the component of its stress \\\ the direction of the chord is 16.774 X o.S = 13.419. Referring to Appendix I., we see that it will be necessary to assume values for A,h, and r, in order to find the reduced dead load n ., trom previous experience these values may be taken as follows : A, = 10, // = 9, and . = 1, making "^■2 — 370 — = 190 pounds. The reduced panel dead load will therefore be 190 X 20 2000 = 1.9 tons, and the stress on the end panel of the windward lower chord when the structure is subjected to a wind pressure of thirty I'ounds per square foot of surface, will be 3hlV, tan O = lxi.ox 0.833 = 5.54 tons, showing that stiffening is decidedly needed. This result could lavc been predicted with certainty from what was stated in <■ h;i[)ter IV. concerning Table I. Xcxt let us find the sections required for the tension mem- iHTS. 1 30 OKDI.XA A' J ■ /A'( '-\' 11 hill W A J - BRIPGES. Dividing the stress in the counter at the point 3 by 2 gives 1.528; then, looking down the cohinin marked "Intensity of Working-stress = 4 tons," we find the nearest number to be the one corresponding to a diameter of seven-eighths of an inch : so wc will use two seven-eighth inch rods for this place. In reality there is no counter needed in the third panel ; but it will be as well to use a single three-quarter inch rod there to aid in adjusting the trusses, and to take up the shock of passing loads. The intensities of working-stress for the main diagonal are 4i^, 4|, and 5 tons. Dividing these into the respective stresses, we find the sections required as marked on the diagram. As the lower chords at the first and second panels are to be stiffened, the intensity of working-stress for the inner bars at these places will be 4 tons : the intensity for the rest of the chords will be 5 tons. Dividing these intensities into the stresses will give the sections required, which are marked on the diagram. The section for the first and second panels was obtained by supposing that there are four bars of equal size used there ; so that the average intensity is 4.] tons. These two trussed bars of the end panel will not be strong enough to resist the difference between the C()ni|)ressive stress of 13.42 tons and the tensile stress of 5 54 tons or 7.88 tons: so we will have to use an I-beam between them, the trussing-bars being attached to tiie web. This is a more economical arrange- ment than two channels laced or latticed. Let us try a 4" I. Consulting Table XL., we see that for two round ends the strength of a 4" 10* I is 5 tons, because it is held by the truss- ing from lateral deflection. Sul)tracting this from 7.88 leaves 2.88 tons to be resisted by the two bars, or 0.88 ton per square inch, which {vide Table XI.) is by no means excessive. The stress in the top chord is probably so great that the minimum width of top plate will determme the packing u, the bottom chord ; so that the next step will be the i)roiK)rti(iii ing of the top chord. Let us take first the stress, 58.103, and try nine-inch chan- nels, which will give 26\ as the ratio of length to least diameter Referring to Table X. f(u- both ends fixed, we find 3 226 for 26,] diameters, so may use 3.222, which, divided into 58.103, gives ORDINARY IROX HIGJlirA V-nRlDGES. ,3, .8,03 square inches. From p. ,5 we find that the minimum .si.e of top plate for nine-inch channels is A"x iii" 00^ sponchn, to an area of 3.59 square inches, ''suhtracti^rt s from IS 03, and dividing the remainder by 2, gives 7 -.. sauare .nche.s for the area of one channel. whLh' corrc^s 01;,' to wc.g t per foot of 24.07 pounds.* Referring to CanJ^'s "locket-Compan.on." p. 65. we find that ninlinch chapel vary in weight from eighteen to thirty pounds per foot ; so t e n.ncnch channels required will be procurable This cakula -;-; .s not final, for it is not improbable that ten-inc^cl atn Is" will he found more economical. ^'idunus The best way to settle the point is to ascertain the average weight per foot of chord for both cases. Dividing then TT^. and 61 976 by 3.2^^ subtnrMn<r , ,r. ( u ^' ' ^^ " ,■ , • ^\ ^ ^ ." ^"'^^'^^ctuig 3.59 from each quotient, mul- t.l) y,ng the remainders by 10. and dividing by 6. ^ives 18 o7 and 36.08 as the weights of the channel bars for' h ? cond and ourth panels ; which weights are both procurable. Thc^av ra"e of the three sections will therefore be iy.2s square inches co^r responchng to a weight per foot of 57-43 pounds. ' It we employ ten-inch channels, the ratio of len-th to least d-anicter will be 24. tor which Table X. g.ves 3 360 as the !n t.ns,ty of working-stress. Dividing this 7nto eacf ^f ^^^^ .-.se.s gives 18 40. ,7.35. and ,3.80 as the sections required Ihc muumum s.ze of top plate (see p. .5) is A"x r'l" cor ro-sponchng to an area of 3 9. square inches. Subtracting tht from ,3.80. and mulfplynig the remainder by ^ "ves 16.8 I-nuls per foot as the weight of the channels 'n U e^ 1 p nd '1- top chore, but the lightest ten inch channel proc , "^1 -■ Carnegie, p. 64) weighs seventeen and a half pound per f'-t: therefore the area of the section will have to be 4^4 ■Mliiare mehes. 4-4i TlK' a^•erage of the three sections will be ,6.69 square inches dllwt:" "f '^ ' "^'^'^ '' ''■'' ^"""^'^ i-^ "-'' foot ^ 'l.ilucnce between 57 43 and 55.63 is 1.8. which, multiplied by Th: 8.103. iiivcs il 111 III ^ftjp ffi^M IH 1 i K: 9 m V' If n2 OA'/)/x.un- iROx i//(;nir.\y-i!R/in;Es. IIIIP^'^ 240, the total length in feet of the two top ehorils, gives 433 pounds as the apparent saving of iron in the chords hy usin;; ten-inch channels: to this must he added the saving in the batter braces, which could be calculated in the same way. It is, however, unnecessary to make this calculation ; for we can see, that, all things considered, it is better to adopt the ten-inch channels. The sections and weights of the top chord panels are now to be entered on the diagram. It is about time to look to the bottom chord packing, and see if there be sufficient room inside the posts for the diagonals and beam hangiM-s; but we must f^rst proportion the diagonals as marked on the diagram by means of the table on pp. 94, 95, of Carnegie's " Pocket-Companion," and the hangers by referring to Table XXII , which shows that I" square bars will be required, square bars being adopted because there will be very little room to spare inside the posts. Referring to Table XXVIII.. we find the width of flange for a 10" 24.15* channel to be 2.63 inches. Doubling this, and subtracting the product from the width of plate, leaves 7 24 inches for the width between channels. The thickness of the inner splice plate will be about seven-si.xtcenths of an inch; doubling which, adding an eighth of an inch for play, and subtracting the sum from 7.24, will leave 6.24 as the distance between inner faces of post channels The thickness of each inner re-enforcing plate at the foot of a post cannot exceed half an inch, which would leave 5.24 inches for packing the diagonals and hangers. For the second and fourth panel points this will be sufficient ; but at the third there would he room enough to let the counters in, and not enough to permit of turning up the sleeve nuts. We can either substitute a single counter, or widen the chord plate. The former will be prefera- ble, as the counter stresses do not affect the sizes of the bottom chord pins, and the central pin of the upper chord should have an excess of strength in any case. From Table IX. we find that the size of the counter required will be i^ig" square. Ne.xt let us proportion the batter brace. The ratio of length to least diameter is about 37.], for which Table X. gives 2.639 (>A'/)/A:IA'}' /A'O.V IlICIlWAY-liRIDGES. m s are now to unter required as the intensity of workings stress, which divided into 42.315 oives 16.03 as the section required. Sul)tracting 3,91, and mul- tiplying the remainder by Y- gives 20.2 pounds per foot as the weight of each channel of the batter brace. Next let us proportion the posts. We see immediately, from the small stress in the centre post, that its section will be the smallest ever used, viz., that of 5" ;# channels [vide p. 8): so there is no need of calculating the section required. Let us assume six-inch channels for the next post : the number of diameters will then be forty-eight, and the intensity for two hinged ends 1.335. which, divided into 10.05, g'ves 7.53 square inches, corresponding to two 12 55-pound channels. These are not so economical as seven-inch channels : so we will try the latter. The ratio is 41 J, and the corresponding intensity 1.656, wiiich divided into 10.05 gives 607 .square inches, correspond- ing to channels weighing 10.12 pounds per foot. The smallest procurable seven-inch channels weigh 10.5 pounds per foot, which size we will therefore adopt. I. "t us assume nine-inch channels for the next post, making tlie ratio 32, and the intensity 2.193, which divided into 17.25 gives 7.86 square inches, corresponding to channels each weigh- ing 13. 1 pounds per foot. As the lightest nine-inch channels weigh 14,5 pounds per foot, it will be necessary to employ these, unless eight-inch channels be more economical Let us try. The ratio is now iC\ and the intensity r.937; making the area 8.91, and the weight of one channel 14.S5 pounds per foot, On account of the smaller sizes of lattice bars and stay plates, tlie eight-inch channels will prove more economical, in spite of their larger section : so we will adopt them. Xext let us proportion the bottom chord, recollecting, that, in the two end panels, an allowance must be made for one rivet hole in each inner bar, the rivets being half an inch in diameter. It is to be noticed that the proportion of width to depth of chord-bars in the centre panels is about one to five, because there are four bars in a panel, and that the depth of the end I'anel bars approaches the limit for stiffened bars, I'rom Table VL we find the size of the hip verticals to be KJ square. 134 OA'D/.y.lNV /A'O.V 1 1 ICllWAV-n RIDGES. \f Next let us determine the sizes of the pins. If we tai<e the average thiekness of one chord bar at the centre of the span to be \\", we make a little allowance for accidental thickenini; of the heads. Substituting in the formula given on p. 85, viz., M= -, 2 we find the moment to be 23.56 inch tons, and, referring to Table XII., determine the size of the pin to be 3^". The least allowable diameter of pin for a 3J" bar is 3.75 X 0.8 =. 3": so we will use 3|" pins for the five middle panel points of the bottom chords. The chord bars of the end panels being neces- sarily out of proportion, we have to use at the pedestals and first panel points pins 2|" in diameter, the smallest that can be used with bars 3|" deep. It may be well to check the size of these pins. The horizontal component of the moment I ''T I on the pin at the first panel point is - X -^^- ^d.'i mch tons, nearly. The stress in one hip vertical is equal to one-half of the section required, as given in Table VI., multiplied by the inten- sity of working-stress for hip verticals, or .] X 2. 14 X 4 = 4.2S tons. This may be assumed without appreciable error as the load on a hanger. The sum of the thicknesses of a hip vertical and a hanger is almost 2 inches, making the lever arm 1 inch, and the moment, about 4.3 inch tons. The total moment is, therefore, y'iG.S)- -j- (4!^ = 8 inch tons, which corresponds to a 2|" pin ; so that the diameter previously determined is ample. Next let us find the size of the hip pin. From the lormula on p. 86, and Table XXVIII., we find that the appro.ximato thickness of the bearing is about M-4 2 X 10 + 0.3 = 1.02 , say I The lever arm for the diagonal stress will be 1^'", say i", and, for the hip-vertical stress, ^" + ^(i" + i Vfi ") — ^^^""t 2", and the corresponding moments respectively, 15.6 and 2 X 4.28 = 8.6 inch-tons. Laying out these moments in their respective direc- tions, we find the resultant moment to be about 22.7 inch tons. ON/)/X.lA'y /KOX llICllUWY-liianGES. 135 which crresponcls to a diameter of 3]". The resultant of the stress on one end diagonal and one hip vcrtieal, found by dia- gram, IS about 19 tons. Looking in Table XXVI., vvc find that a ])earuig of \" is sufficient. Next let us find Jie size of the next chord pin from the hip iM-om the formula on p. %G, and Table XXVIII., we find that the appro imate thickness of the chord bearing is '17-25 r^io + °-4S = 1-3 1 inches, and that of the post bearing (p. 87), 8.91 — g- = 1.11 inches. Allowing a little for play, the lever arms for the vertical and iiun/ontal components of the stress on a diagonal are respec- tively 1 and 2|": the components found by diagram are about •S tons and 6.7 tons respectively, making the moments 8 inch tons and .5.1 inch tons, the resultant of which is 17. i ^nch tons corresponding to a diameter of 2^. This is large enough fo,^ a three-inch bar. There is no need of testing for bearin- A snn.Iar nivestigation for the ne.xt panel point shows that a 2]" pin will be recpured, which size will also be used for the central pin By referring to Table XXV., we can write upon the diagram the sizes of all the lateral and vibrati.^i rods and the sections "I the upper lateral, portal, and intermediate struts It will b- sufficient to write the sizes of post vibration rods and interme- diate struts on one post only, as they are of the same dimen- sions throughout the bridge. i'lom ]). 54 we take the formula ) tn find the stress on the end lower lateral strut between expand- ""■• Medestals. Here in n = S ^= 2.375 (seep. 10) cos 6 = 0,57 _ 7;5 X 3 X 20 2000 2000 59-2 7c' = i-5_^ >50J<^o ^ 2000 = 2.25 0-7S I m I ^/) ORn/X.lA']- Jh'OX IIHUIWAV-nRIDGES. and r(i7V/r Appendix I) = one-half the lenj^th of span multi- pHed by the release of pressure per lineal foot on the windward truss, or 80 X 30 X lo X 9 ^ — = 7.2 tons. 15 X 2000 ' Substituting these values gives C„ = 9.2 tons. Assuming four- inch channels, the ratio of length to least diameter will be 43, for which, with one fixed and one hinged end, Table XI. gives an intensity of 2.245 : therefore the section required is 4. 1 square inches, corresponding to two 6.83* channels. It will be more convenient for riveting to use 5" ;# channels. At the fixed end of the span a 5" 10* I will answer for a strut between pedestals. We are now ready to proceed with the "Bill of Iron," in making which, close approximations of lengths are allowable. Let us prepare the blank form recommended in Chapter XIV., then turn to the list of members given in Chapter HI., and fill out the form, proportioning as we go any details whose sizes have not been previously determined. The filling-out of the part denominated "Alain Portions" is a very simple matter, and needs but little explanation. It is to be noticed that the lengths of the chord bars and main diagonals have been in- creased by three feel to allow for the weights of the heads, and those of all adjustable rods by five feet to allow Un- the weight of the eyes, upset ends, and adjusting-nuts. The intermediate and portal struts are placed seven feet below the level oj the upper chord i)ins, so as to allow a clear headway of fifteen feet. The size of the floor beam is taken from Table XIX. The grouping of members having some similar dimensions is to be observed. It involves considerable economy of labor, if one has to estimate on many bridges. In filling out the last vertical column, the tables on pp. 8S-93 and 104-109 of Carnegie's " Pocket-Companion " will be found very useful. Let us employ latticing for the top chords, batter braces, posts, and portal .struts, and single-riveted lacing for the latenil struts. '/>'/V.\./AT /A'(;.\- lHuUWAV-liRIlKIE \17 kofcirin- to Tables XXXII. and XXXIII. uf stay plates for the top chords and hatter b iV' X 8", since d = 0.75/?/ that for the middle posts, i" X 5^", r/ being equal to i.i^D; we find the size races to be ha t for the next larger ])osts, J" X 6J", d being equal to D; that for the larirest posts, /fi" X 6J", ^/ being equal to 0.88Z), that for the portal struts, }" X 4f , ^/ being equal to i.i8Z>, tliat for the upper lateral strut; ^" X 8", since ^/ exceeds 2D! that for the end lower lateral strut. ;nu i" X 9", ./ :)cm g equal to about i.5Z>. It at the hip joint we make the thickness of each inner and nutcr connectin-plate I", the cross section of the plates thn.u-h the pin hole by a plane ])erpendicular to the len-^th of the batter brace will be -reater than either that of the Trntter )racc or that of the end panel of the top chord : moreover, the bcarmg will be slightly in excess of that needed to resist the stresses in an end diagonal and a hip vertical, so we may conclude that these thicknesses will suffice. Without committing any grave error, we may assume that the total stress m the end jx.nel of the chord is equally divided between the four connecting-plates, making that on each plate about 1 1.6 tons. The thickness of the web of a 10" .7.5* channel is 03" ^sce lable XXVIII.) : therefore the lever arm for the stress in I 'I H 1- lllll ll! .fif. lit!' I ;vS ch'n/x.ih'V /h'lKX II hill WW v-iiRiih;i:s. a cnnnoctin^'-phitc is il(o.3 -}- o.3;5) =0.338 im-Ii, making the niotncnt 1 1/) X 0.33S = 3.93 incli tons, whifh divick-d by 0.31 1, the rosistin^'-ni(iiiu-nt fur a '■'(' rivet, as ^ivcu in 'I'ablc XXXV'I,. ni\cs thirteen as tlic number of rivets rec|iiire(l to resist l)en(l- ill^^ I'"roni the same table we fmd by interpolation about \.},() tons as the bearin^^-resistance for a |" rivet on a 0.3" plate. The stress tran.sferred to the channel is 2 X 1 1'') = -l-~ tons, which divitled by 1.36 <;ives seventeen as the number ol rivets recpiired for bearing;. It will be convenient to u.^e sixteen rivets, in four rows of four in a row. We can do so Ic^ntimately, as the calculation calling for seventeen is merely approximate. It is evident, without calculation, that sixteen rivets will be enough for the connecting plates on the batter-brace side ot the pin hole, for the stress is less and the thickness of web sliglitly greater. To make the outer plate fit between the flange rivet heads, we cannot have it much more than seven inches wide, unless the said rivet heads be countersunk. Next let us lay out the hip to scale, as in the accompanying figure, spacing the rivet holes according to the rules given in Chapter II., and allowing three inches of length extra for thr part which connects with the batter brace, so as to i)r()vide for the i)ortal-strut connection. This api)roximation is accurate enough for a bill of iron. The circles arc those for the pin ami the limiting distance for non-countersunk rivets. The rivet spacing is three inches along the hori/jMital lines. To calculate the weight of an inner f !' '">- ^ plate, we may divide it into two jiarts '^i by the line ///) in the figure, llic :hJ area of the lower part is ecpial to the length of CD multiplied by the ^r perpendicular distance between AH and Gil, anil that of the upper part by one-half the product of AB and EF. These dimensions are recorded approximately in the "Bill of Iron." The length of the outer connecting-plate is, of course, measured along its centre line. ou/>/.v.iA'y iRox mGiiivAv-nRin^jEs, ,39 n^c-arca of a section of the four conncctinj^-platos at the rst .n ermechate ,anel point of the top ehoni 'sho.id .,.. tlua ea of a sect.on of the two chord channels of the third I'l'icl, or 13.34 square inches. Let us use two i" X 10" =7,5 , and two ^" x 7" = 6.12 j ~ '•'•^^ square inches. The stress carried by the channels of the third panel is ecmal o^ hur area nudt.plied by the intensity of wori<in,.stressI or ,v.,4X3.3^>9^44y4 tons; which may be divided equally between the four plates, making the stress on each plate cihout .... t.>n. Table XXVIIi. ,ives the thickness of .ll^ of a l^' -..-3* channel as 0.45 inch, which will make the lever arm - the stress on the outer plate i(o.45 + 0.43) = 0.44 inch, .1 the moment 11.2X0.44 = 4.93 inch tons, which divided a..' «.'^'^''^ "^^^^ ^^ the number of rivets rec,uire<l to IiKiinnt; ujjon bearmg. be'takJn ar'''"" ''''' "^ '^' ^"'"' '^" ''''''' "" '^' '^^^""^''^ "^^X '0-5 X 3.369 = 35-37 tons, or ai)()ut 8.8 tons per plate. Thc^levx-r arm is .J(o 3 + 0.43) = 0.36 inch, makin. the mo- • H nt .S.8 X 0.36 = 3. 17 .nch tons, which divided by 0,3,1 -nves e^ven as the number of nvets to resist bendin,. Dividin;,7.6 b> i.36 gives thirteen as the number of rivets to resist bearim^ • or convenience we can call it twelve, as the stress is not quite M. g,eat as we as.sumed it. It is to be observed that at the h , e sun>ose that all the chord stre.s is carried by the conn ^ ' ".^-plates. whde at the ne.xt panel point we assume that the jnnncc >ng.plates carry only the portion of the stress trans- over Plate ' rr^'^' ""' r'"""'^" '""^ transmitted by the over plate. The reas(,n for this is, that the cover plate at tbc .p. ben.g bent, cannot be relied upon to carrv stress. At the next panel point the stress on one plate'is 14.49 X 3.;,6(; — I 2.2 tons. 8 i i 11'' Vl%:^ te 140 Oh'n/XANV /A'O.y inuini-AV-BRIDGES. The sections of the plates will have to be two T^' X I o — S.75 j _ j^ gg gquare inches. two-rV'X 7" = 6.13) The thickness of the web is found to be 0.5": therefore the lever arm is |(o.5 +0.43) =0.46 inch; and the moment, 12.2 X 0.46 =5.61 inch tons, which divided by 0.31 1 gives eighteen as the number of rivets for bending. To find the lengths of the connecting- plates we must make, as before, a drawing to scale, as in the accompanying diagram. We thus determine the length of plates for the first intermediate connection to be thirty inches. The length of the plates at the next panel point will be greater by the space required for si.x rivets, or thirty-four inches and a half, and that at the middle panel point greater by the space required for eight rivets, or thirty-si.x inches. Continuing down the " List of Members," we come to the re-enforcing plates on bottom chord struts. Let us make them J>J' X 3" in section. It is not worth while to calculate the num- ber of rivets required to connect them to the web of the I-beam ; because four five-eighths inch rivets will give an excess of strength, making the length about ten inches. Next come the shoe connecting-plates. Let us em])loy the connection illustrated in Plate VI. From Table XXVI. we find the thick- ness of bearing for a 2§" pin and a stress of 13.6 tons to be I" \ subtracting from which 0.38", the thickness of web of batter- brace channels, leaves l" for the thickness of the re-enforcing plate. Assuming the greatest width of plate in a direction perpendicular to the length of the batter brace to be sixteen inches, gives the sectional area of the connecting-plate equal to sixteen square inches, or that of the batter brace : so, pro- vided we have such a width, the half-inch plate will answer the purpose. The .stress carried by the batter-brace channels is 12.12 X 2.639 = 32 tons, nearly, or i6 tons on one channel. The iever arm of this stress is .](,] + «) = -Jg", anc. the moment, T X 16 = 7 inch tons, which divided by 0.493, the resisting- ORDIXARY IRON HIGHWAY-BRIDGES, 141 nioiiK-nt of a seven-eighths inch rivet, gives fifteen as the num- ])cr of rivets required to resist bending. It is better to use seven-eighths inch rivets here, on aceount of their large bcnd- ing-resistance. Tliere is no need of calculatinjr for bearin-- 'lo deternunc the dimensions of the connecting-plate, we will jH-oceed as follows ; t'he distance between the channels at the shoe being 12.5" — 2 X 2.51" = 7.5". In the accompanying diagram let us lay out a centre line AB, and the two parallel lines CD and EF each at the distance 3 1' from AB. h'rom any point A lay niT the lines ACG and AEH, makin"; angles with AB equal to the inclination (if the batter brace to the horizontal, join CE. Draw the lines /A' and EM parallel to CG and EII, and ten inches a therefrom : draw also the centre lines XO and PQ. To allow sufficient clear- ance for the chord heads, the pin holes sliould be five inches and a half above the top of the shoe plate. By crowd- ing the rivets as near as possible to the flanges of the channels, \ve are able to use four rows. Laying out the circles for the pm holes, and limiting distance for rivet centres, we determine the height of the box plate to be about 14". If the vertical sides KD and iMF be adopted, the shoe plate will be 28" long, which is probably too much. To ascertain, let us find the number, size, and arrangement of the rollers. The total pressure on one shoe is , , i860 i X 160 X = 37.2 tons. 2000 ^' Let us assume the dimensions of a roller to be 2" ■^) by 12". Turning to Table XXXIV., we find the permissible pressure on such a roller to be 424 tons, which divided into 37.2 gives nine rollers. Spacing them 3" centre to centre, and allowing a projection of i.]'at each end, would make the shoe plate 29" long. A plate 12]" X 2i)' is not a very good shape. Let us try rollers 2]'V by 15", the permissible pressure for one of which is I Mill 118 ^ B i-U p 'I Im ii? * ' li 142 OA'nLV.lA'V INOX HiaHWAV-BRIDGKS. 5.63 tons ; making the necessary number (37.2 -^ 5.63) seven. Spacing them 3|", and allowing the same projection as before, will make the shoe plate 15]" X 25", a better shape. Allowing the shoe plate to project 3" beyond the front end of the channels will make the length of the connecting-plate 22", which distance is laid off from C to R. The perpendicular distance of A' from AG exceeds 16": so a plate of the shape CGKRSMHEC, before bending, will fulfil all the require- ments. To find its weight let it be divided into a rec- tangle, two triangles, and two parallelograms, as indicated in the "Bill of Iron." The next details on the " List of Members " are the re-enfor- cing plates at feet of posts. From Table XXVI., we find that a 2)\" pin requires, for a stress of 8.6 tons, a bearing of less than half an inch, but, in order to compensate for a slight trimming of the flanges of the channels, there must be a plate on the inside, and another on the outside, of each channel ; and the least thickness for one of these plates is three-eighths of an inch. We will not trim the five-inch channels, so will not have to use an outer re-enforcing plate : this is because there would be no room for a 3,|" pin through such a plate. The requisite length for these plates cannot be exactly determined ; for it is impos- sible to say how much of the bearing-stress is taken up by the web, and how much by each plate. Let us assume that the inner plate of the largest post channel takes up half the stress on the channel, or 4.3 tons. Table XXVIII. gives the thickness of the web as 0.35 inch. Using |" rivets, and figuring S for bending and bearing, we find the number of j rivets required to be nine. Laying out to scale I the foot of the post, as in the accompanying dia- ^ gram, and allowing five inches and a half between the centre of the pin hole and the foot of the channel, we find that the required length of plate is sixteen inches. In the same way, the lengths of the re-enforcing plates at the feet of the other posts might be calculated : but it is hardly worth while ; for, if we make them all of the same length, they will be sufficiently strong without causing much waste of material. ^ 1 ORDLXARY IRON HIGHWAV-nRIDGES. 143 After entering these dimensions on the "Bill of Iron '• we refer agam to the "List of Members." and, after omi'tting rc-cnforc.ng plates at middle of posts, eome to the connecting p a es for lateral struts to top chords. The thickness of these plates should be |". and the average width of the leo-s .1" The area of a 4 6* channel is 1.8 scp.are inches, and the'in'tensity of wo,-k.„g-stress for forty-two diameters with both ends fixed is by lable XI.. 2.74 tons ; making the greatest stress that could over come upon the channel r.8 X 2.74 = 4.93 tons. The lever a™ of th^stress_,s,i(| + |) = ^^ inch, making the moment ]6 X 4-9o - 2.16 mch tons, which divided by 0.380 the resist ,ng-moment for a r rivet, as given in Table XXXVII gives MX as the number of rivets required for attachment '[o the atcral strut channel. Although the leverage is a little greater tor the attachment to the chord-channel flanges, still six rivets uil; suffice, on account of the liberal estimate for stress, and us.ng r,vet tables which have a surplus of strength for lateral system connections. The length of each leg of the T will be about eighteen mches, for various circumstances will necessitate wide rivet spacing in this detail. The stress and leverage being the same in the two attach- ments. It IS evident that six rivets will be required at each ^d the upper channel of the lateral strut for connection to chord Ihere will be just room for this number; putting two through he channe flanges, and four through the plate between t channels. Were these not strong enough, wc could use seven-eighths inch rivets. The ne.\t item upon the "List" is con- necting-plates for portal struts to batter l>'aces. These should have a greater strength than ordinary calculations would "Kl'cate, in order to provide against the niekmg effect of the wind. If we use a jaw plate, as in the s of the accompanying diagrams, and two bent plates, as lo second to attach to the flanges of the strut channels ' " ^;f ''" "^^"- '^'■^^^' ''' P--^>- ^^ainst all con- -'/'■ CD, and /./.. It may be well to test the num- 144 O/^P/X.IKV /A'OX UlCHWAV-BRinCES. J) AW i|il bci- of rivets for the jaw i^late, because it has to act as a re-enforcinj; plate also. I'irst we must determine the size of the pin which attaches the vibration rods. The diameter ot each rod beinp; i|", the greatest working-stress thereon is 7.5 X 0.994 = 7.5 tons, nearly. The lever arm is A(J -f | -f ^) = J". making the moment |x 7-5 =6.56 inch tons. Consulting Table XII., we find i '{' ^^ the diameter required. Table XXVII. shows that there is more than sufficient bearing. Assuming five tons. upon the rc-enforcing plate, we find the number of eleven- sixteenths-inch rivets required to resist bending to be 5 x.^^}±J 0.299 = 6, so that the dimensions in the drawing are sufificient. Let us assume the dimensions for portal connecting-plates to brackets and name plates as |" X S" X 18". The section of a connecting-plate for an intermediate strut should be |" X 3" ; and we will use three rivets for the connec- tion to the pos.c, and four for that to the strut : it would be useless to figure upon these numbers, as the stress is so small. Owing to the peculiarity of the vibration-rod connection, each plate will have to be about two feet long, as can be seen on Plate VI. Omitting side-brace connection, the next item is the end lower lateral strut connection to pedestal, which is by means of a jaw plate |" X 5"- The stress on the strut was found to be 9.75 tons, making 4.88 tons on each channel. The number of three-fourths inch rivets required will therefore be 0.389 There is no need of figuring for bearing. This would make the total length of jaw jilate about three feet, as noted on the "Bill." For the strut at the fixed end, a plate .]" X 5" X 2' will answer the purpose. The next item is the hip cover plate, which we will make of the same s action as the chord plate, and eighteen inches long. ORDINARY IROX IfrGHlVA V-BRIDGES. 1.' 2' will answer 1-or the intermediate joints we must calculate the lenoths of the cm'er plate thus : the stress on the top plate is 3 91 X 3.369- 13 tons nearly; making the moment on the rivets 13 X I'^g =4-o6 mch tons, which divided hy 0.311 gives fourteen as the number of three- fourths inch rivets required to resist bend- ing. For bearing, the number required will be less. The arrangement of the rivets de- termining the size of the plate is shown to scale in the accompanying drawing. Next come the filling- plates. Let us average those for the top chord at J." thick. For the thickness of the filling-plates over end floor beams we "u.st subtract from the distance between centre of pin 'hole and foot of post the half-depth of the chord heads in the end l)aneLs, thus, 1^— 1 _- 1 — 17'--* X X xj . X X X X X ^ X X X X X X X X X y X X X X y k X X ^ si z 5r-^(3l X i! -h20)"= If. The width will be equal to the diameter of the pin, and the length equal to that of the pin between shoulders Next come the extension plates. Let us make them in two th.cknes.ses, the shorter piece extending down to the stay- plates. 1- or the largest post, the total thickness will have to be ' ;^' . or 1 1" ; making that of each plate -^-9,", Neglecting the effect of the stress on the outer plate, the moment ,.. , , <"! the rivets will be 8.6 X .' (O. :!5 + o. s6) = 3 gr fl inch ton.s, which divided by 0.31 1 makes the num- ^' her of three-c|uarter inch rivets to be employed f ei|iKil to thirteen. For reasons advanced in Chap- \ tcr XII., we must count in only one half of those ^ nvets wh.cli pass through the double portion of the plate and the web. Laying off the end of the post to scale, as in the accompanying dia- .i^ram, we determine the lengths of the plates to be twelve and twenty-four inches lespectively The nv.ts above the line AB are to be countersunk: their use 's sm.ply to make the two plates act as one. We mLdit i i lil ;■ IIim' iiii»i 146 ORD/.yAh')- //cox ///(/////'./ )'-/.' AVM/Y-'.S-. calculate the required lengths for the extension plates of the other posts, but it woukl be unnecessary labor ; for if, in the posts with the seven-inch channels, we use two rows of three-quarter inch rivets, instead of three, and in the posts with the five-inch channels two rows of five-eighths inch rivets, making the plates of the same length, we will provide suflficient strength with very little waste of material. The next on the list are the shoe plates, the area for which we have determined to be I5J"X25": their thickness (see p. 16) should be I". To determine the size of the roller plate, we will adopt 3" X 3" 5-9* angles to enclose the rollers, and allow for a motion of two inches, which would make the area 2i|"X33": the thickness should U: I". The area of the plate in square inches multiplied by two hundred pounds makes about seventy-one tons, which is nearly double the greatest pressure on the shoe ; showing that the dimeiv-.ons decided upon are large enough. The area of the shoe plate multiplied by two hundred pounds per square inch is equal to 38.75 tons; and, as the greatest pressure on the shoe has been calculated to be 37.2 tons, it is evident that we may use the shoe plate as a bed plate by properly anchoring it to the masonry. Next come the beam-hanger plates. It will not be neces- sary to calculate their thickness, as the method was fully illustrated by an example in Chapter XIII.; and experience would suggest a thickness of I'^rom Carnegie's " Pocket- Companion," p. 126, we find that ^"square bars upset to i^"; and from p. 131 of the same book we see that the longest diam cter for the corresponding nut is 2.89", say 3"; so that, allowing 1" for clearance, the distance between centres of beam hanger holes will be /', and the width of plate for full bearing 7". We can average the lengths of the plates at 8". The weight of a name plate need not exceed forty pounds. Next come the latticing and lacing bars. Referring to Tables XXX. and XXXI., we find for the top chords and batter braces, where ^/= o 75 D, tlie bars sliould be iV' X ^l" '> ORDIXARY IKON niUHU:iV-i;RHKiES. 14; U)X the middle posts, where d= \.^D, they should be f X i|"j for the next larger post, where ./=Z>, i"x i|"; for the largest posts, where ^/= o.88Z», 1" X ij"j for the portal struts, where,/=i.,8Z), i"x i^i for the upper lateral struts, where./>2Z», 1" X 2j-"; aiul for the end lower lateral struts, wherert'= 1.5Z;, 1" X 2^". The distance between centre lines of rivets in the chord and batter-brace channel flan-es is about ten inches; the space per panel ni chord over which the latticing extends is about eighteen feet ; the corresponding distance in the batter brace IS twenty-seven feet : so, if we space the rivet holes for the latticnig as nearly as possible ten inches apart, there will be twice twenty-two lattice bars recp.ired for each chord panel -i one truss, and twice thirty-two bars for each batter brace, makin- seven hiuidred and eighty-four bars in all. Their ^^^v^\^, from Table XXIX., is found to be 1. 18' + o -'i ;' = i.;i95', say 1.4'. We can average the lengths of the lattice bars for the posts thus : assuming a stretch of nine inches, a spread of eight nuhcs and a half, and .J" as the width of a bar, gives the total length ..034 + 0.18=1.214. say M' . The average length of space on the posts occupied by the latticing is about twenty cct s,x mches ; making the number of bars per post four times twenty-seven. The spread, or distance between centre lines of rivets in channel Hanges of portal struts, is about six inches and a half, 1 ( 1 fc r 4 !! \': ■llUlii!' 148 ORIUXARV IROX HIGHWAY-BRIDGES. and the latticing; extends over about ten feet on the averai^e, after deducting for various plates ; which would make the num- ber of lattice bars per strut about four times nineteen. The length will be about 0.768' + 0.145' = 0.92' nearly. The spread for the lateral strut rivet centres is eleven inches and a half; and, as lacing-bars are used, the stretch must be about si.\ inches and three-quarters in order that the angle between the bars may be sixty degrees. This distance is most readily determined by diagram. The length of a bar is, then, 1. 1 13' + o. 197' = 1.31'- The extent of the lacing is about eleven feet, making the number of bars per strut twice nineteen. For the lacing-bars of the lower lateral strut, the spread of the rivets is about nine inches and a half, and the corres])ond ing stretch about six inches. The length of the lacing is about eleven feet, and the number of lacing-bars twice twenty-two. The length of each bar is 0.936 '-f o. 197' = 1. 1 33'. s^V 1 1'. Next mi the "List" comes the chord trussing, of which we will assume the section to be |" X 3". I^Y ^ I'O".'^!"' approxima- tion, we can find the average length for one panel of one truss to be about thirty-three feet. The lengths of the pins are cal- culated so as to include the weights of the nuts by adding, in most cases, an inch and a half for each nut. The diameter of the intermediate vibration-rod pins is assumed to be i^". The lengths of the bolts include an allowance for heads and nuts. To find if there be any anchorage required at the rollci- end of the bridge, we must compare the overturning and re- sisting moments, or, what is the same thing, the release of pressure on the shoe and the weight thereon when the bridge is empty and there is no wind. In finding the stress on the end lateral strut, we determined the release of pressure to be 7.2 tons, and one-fourth the weight of the empty bridge to be 14.8 tons. The latter being more than twice as great as the former, no extra anchorage will be required at the expan- sion pedestals. As there is vertical sway bracing, the brackets may be light, Let us make them of 2.]" X 2.]" 4.9* angle-iron, and let them of which \vc OA'J)/XAA' J ' I/W.V HIGHU V/ J -BRIDGES. 149 extend vertically and horizontally four feet. Allowin- six inches at each end for attachment would make the total length of a bracket about 6.7 feet. An allowance of ioo# for ornamental work will be sufficient The equivalent len-th of a beam hanger can be thus approxi- mately calculated : twice the distance from the centre of the pm to the top of floor beam equals 11"; twice the diameter of |.in equals about 6"; twice the depth of floor beam equals 54"- twice the length of hanger below the floor beam equals 6"' allowance for two upset ends and nuts equals y^'-, total lcn..th e(|uals 1 10" = say 9'. '^ Let us average the diameters of the fillers at 31", and their weight at io# per foot. The average length of filler is not far lioni 3 . Special fillers will be required at the free end of the span, so as to keep the lateral strut clear of the batter-brace channels, also similar fillers at each end of the span to lie between the outer chord bars and the channels. Let us assume that the channel flanges are notched out to a depth of one inch • then the thickness of the last-mentioned fillers will be i J" and that of the others say |". Let the external diameter be '7" and the internal diameter 2|": the weight per lineal foot will then be (see Carnegie, pp. 105-107) 128.3 - 148 = 113 5 Turn buckles and sleeve nuts have already been included, and there are no connecting chord heads. Next come the jaws for lower lateral struts. From the cen- tre of the lower chord pin to the top of the floor beam being 5.]", the depth <if the wooden strut will have to be 9"; but the jaws need not be more than 7" deep, as shown on the accom panying diagram. The width of the strut need not exceed 7" >'"■■ that of the jaw plate 6". The thickness of the latter sh.uild be \ . The greatest stress upon any lateral strut, found by resolving the stress upon the r,V' lateral rod, is about 7 tons, which stress has to be resisted by the rivets connecting the inner and outer jaw plates. The number of rivets required is 7 X .i __ 0.3X9"-'^' ''''^'^"'1 ^^'''1 make the total length of the two jaw -j^ lyv r^ i^ ISO ORDINARY IROX HIGllWAV-nRinC.ES. I';? plates about 5'. A piece of 6" S.5* chaniK/ will be stron;^' enough for the bent eye bearing. It is not worth while to cal- culate the number of rivet« for the combined upper lateral strut jaw and vibration rod liearins; plate : so we will average the dimensions as in the " V>\\\ ot Iron." Next on the " List " comes the angle iron around the edges of the roller plates, which we will assume to be 3" X 3". weigh- ing 5.9^* per foot. The length on one side is if, and at the end say 4|" on each side of the anchor bolt b'^'l'. ; making seven feet in all for each plate. Next come the pieces of channels, which we will assume to be of the sizes marked on the " Bill," and ne.xt the rivet heads, for which wc will make a separate bill, then enter the total weight with the other items. Considerable approximation is used in ascertaining the numbers ; and the fioorbeam rivets are omitted, for their weights are included in the weight of the beams. The total length of top plate for chords and batter braces is about 370' : let us average the rivet spacing therein at iV\ making the total number 2 X 37° X 12 X ? = 2537. We may say that there is one rivet for each latticing or lacing bar for attachment to channels, and one to every two lattice bars for attaching latticing to latticing. Half-inch rivets will be used for the latter purpose, so as not to weaken the bars unnecessarily. Let us assume that half the stay plates are attached by three-fourths inch, and half by five-eighths inch, rivets, and that there are six or eight rivets per plate. Let us average the number at each joint of the chord at sixty-four, and at each pedestal, not including those through the shoe plate, at thirty-two ; and let us assume eighteen rivets at the foot of each post, six per bracket, and fourteen per jaw. The following will then be the approximate ORDIA'AIiV IRON H/GHH'A V-BRIDGES, '51 BILL OK RI\ l/r HEADS. CONNECTIONS. 2,198 (</ o.oS#= 176* 2,080 @ O.I 6" = 333" 5.715 @o.25"= 1,429" 216 @ 0.40"= 86" Diameters. riatt. to chords and batter braces Latticing and lacing to channels . , Latticing and lacing to tiiannels . , Latticing and lacing to channels . . Latticing and lacing to channels . . Latticing and lacing to channels . . Latticing and lacing to channels . . Latticing to latticing Stay plates to channels Connecting-plates to channels . . . Ke-enforcing plates to channels . . Oinnecting-plates to channels . . Cimnecting-plates to channels . . , Connecting-plates to channels and I Cover plates to chord plates . . . Kxtension plates to posts .... Connecting-plates to shoe plates . . Trussing to bars Liackets jaws Angle iron to roller plates . . . . 304 190 44 1,084 432 648 96 480 440 180 96 60 84 140 2,198 2,080 r 2,537 784 330 S96 244 80 368 280 196 5715 128 32 56 :i6 Total weight of heads :.o24#, say 2,ooo# after deducting for coun- tersunk heads. Ihc number of spikes requifed will be ten per plank of fioor (each piank being 9" wide), six per post of Imnd railing, ten per l)anel for felly plank to flooring, two per joist, and two per jaw • •" ;i!l, 2,rn2. The spikes shoidd be /;," square by 7" Ion-' 152 O/^niXARV /A'OA' llli.llWAV-liRinCES. Consulting Carnegie's "Pocket-Companion," p. \2<.), we find tliat there are 662 spikes to a keg of 150*; so that we requiri.' four kegs, or to *. With the exception of the bolt.s attaching the lateral struts to the floor beams and jaws, each wood bolt must have two wash- ers ; making in all 385, say 400. Each washer weighs about a pound. The weights of most of the nuts have already been included : let us add fifty pounds for lock \nd pilot nuts. The total amount of lumber may be estimated in three ways : first, as in the "Bill of Lumber;" .second, by consulting Table XV., which gives 2,085 as the amount per panel, multiplying this by 8, and adding 515, the numbi.'r of fet't in the lateral struts ; and, third, by consulting Table I., which gives 269 as the weight of lumber per lineal foot, and multiplying this by 160 X/o- The first two methods are accurate; the last, approximate. BILL OK IKON. Top chord channels . . . To[) chord ciiaiincls . , . Top chord channels ... IJattcr-bracc channels . . . Po>t channcl^s Post channels Tost channels Upper lateral strut channels I'.nd lower lateral strut channel; I'ortal strut channels . . . Chord plate ISatter-brace plate .... Intermediate struts, . . . I.nd lower lateral strut . . Ilottom chord struts . . . Main diagonals Main diagonals Main diagonals Counters Counters Hip verticals ...... S 8 S 8 4 8 8 10 10 ' 10" 10" 10" 5" I 8" 4" 5" 4" A" 4' 5" 4" i" 3« I -II 24-15* 17-5* 20. 2# 7# io.s# I4.85# 6# 7# i2.r' I2i" 8#I io#I io#I 23" 3" 3^' O D D 34'25 10,221 S.I"' So.V^ 900 4,Sjo 57(i l.)0 820 6,307 759 OUD/X.IKV /A'OX ///GI/H'A Y-niUDGES. ^11 !<), we find vvc rciiviiiL' al struts to two vvash- ^hs about a II inchulcd : three ways : Itint; Table niulti])lyiii,L; the hiteral ives 2^)9 as ing this by ; the last, io,2::i 5.'/' 56,V^ f 900 t ii/i J f)86 •5' •5' 4,Sjo 4' 576 140 ■5' S20 25' 6,307 •25' 75V / Si;, I |i|)ci lak'ial rolls , . . U|)|)fr lateral rods , . . l'|i|)t.r I.Utral rods . . , l.invcr lateral rods . . , I Kttir lateral rods . . . rinvtr lateral rods . , , I.owir lateral rods , . . \ il>r;iiii)ii rods at portals \ ilu.iiion rods at jjosts . 1 hold bars I liMid hars ' lii'id bars I liord bars . . , , , lliior beams Tiiial weight of main portions Si.iy plates (HI chords and bat- li T braces Slay plates on posts . , . . Stay plates on i)osts . . . , Stay plates on posts . . . . Slay ])lates on u])per lat. struts . Slay plates on lower lat. struts . Slav plates on portal struts . . l'iinnectiiig-i)lates hip inside . I ■' iiinecting-plates hip inside . I'MiiRctiny-plates hip outside . • uniiccliiin-plates int. insidu . CiiiuH-clinj^-plates int. inside . CimiRcling-plates int. inside . CniiiicclinfT-plates int. outside . CdniR'ctiiin-plales int. outside . ('omR'ciiiii;-plates int. outside . < 'tiiuiccting-plates, b. ch. struts . • '"imecting-plates at shoes . . Kcenforcing plates, ft. of posts inside Ki enforcing plates, ft. of posts inside Ke-eiil'orcing plates, ft. of posts inside Ke-enfnrcing plates, ft. of posts "iilsidc Ke-cniurcing plates, ft. of posts mitsiile . . 4 x\" 4 li" 4 \l" 4 Mr 4 i.'ff" 4 li" 4 I" S li" 10 \" s ■\" 8 \i" 16 \" r- \" y- s 16 16 20 4 1 6 8 S S 8 S 4 8 8 4 16 4 S 8 27" A" \" i" /'„" i" \" 1" -1 H '■)" i" 3" 1 ti iJ." 11! w O o o © © 33" si" 3i" Jl" 54i* h. b. i" V r' S" si" 6J" 6J" 8" 9" ■aV 9" 4" -." / 10" 10" 10" 7" 7" 7" 3" 7J" 0" 10" 8" 7" S" 6" S" 29.5' 21' 19' -^3' 16' I2i" loi" II" II" •3i" It" 8" 3'" 36" 35" 30" 34 J" 36" 30" 34i" 30" 10" 22" 7" i8i" 16" 16" 16" 16" 16" 3.4SS 557 3S0 10,459 6,104 5;.')r3 27S 32 76 99 150 28 353 204 250 335 '75 204 235 123 42 367 380 '54 ONP/XARV IROX J in; /III' A V~/lN/nGKS. ConnL'ctinn-platcs, hUcial slnit to clunds <.'onin.'Ltiiig-|)l;itcs, portal strut to batter braces (,'oniicttiiii;-plates, portal strut to i)alti'r braces fonncctiii.n-platcs, portal strut to bracUcts (,'onii(.Htin,L;-|)latcs, portal strut to name plate ConiRLliii.u-plates, int. strut to posts C'oiinectiiiij;-plates, ciul lower lateral strut Coiinecling-plates, euil lower lateral strut Cover plates at lii]is .... Cover plates at int. joints . . l'"illin,i;-iilates at hips .... FiUiug-lilales at int. joints . . Filling-i)lates over lieanis . . I"..\tension plates l'..\tension plates K.xtension plates I'^xtension plates Extension jilates I'',xlensinn ])lates Shoe jilales kulkr jilates He.ini-lianger plates . . . . Name plates Lattice bars on chord and bat- ter braces I, .mice bars on posts . . . . Lattice bars on posts . . . . Lattice bars on posts . . . . Lattice bars on portal struts . Laciug-bars on upper lateral struts Lacing-bars on lower lateral strut Chord trussing Tins, top chord I 'ins, top chord I'ins, top chord i'ins, bottom chortl Tins, bottom chord 8 i6 4 4 10 8 1 6 4 cS 8 8 8 4 4 4 'J M 7S4 432 4.3- 216 304 lyo 44 S 4 4 6 10 8 3" Ml 4 \" rn A" Vr," T-r," ' 4 '.' // ll! •I // ti; 1" @ 1 li 34 3i 2j" 4" 8" 8" 8" 5" 1 2 .'," 10" 10" -,:■" 8" 8" 7" 7" 5" 5" I si" 2ii" 7" 40# If' ,6" 3" o 3' 3' 8.i" 18" 18" 18" 17" iCj" 12" 12" 12" 24" 12" 34" J 2" 24" -5" 3f 8" each 1.4' li' ■r 'i' 0.92' il' 3.3' 16" 1 8" 18" 22" I 20" 'S» f)0 150 f\5 3.1 7« 1S5 ?,i 61 360 245 s.s 377 345 191 So :.57- 844 7SS 3f>S ■tP S,S 147 120 507 241 ORD/X.IRV IRON HIGI/IVA Y-nRIiniF.S. 155 3' '5» 3' 120 8i" "3 18" [ 60 18" 2> '50 1.4' >r f'3 7^ 61 245 NS 377 34 ■- 191 So -.57- 844 78S 3f'5 HI SS 6(0 147 I3'3 120 507 241 Tins, ])ortal vibration .... Tins, |)o:it vibration .... Molts, name |)lates liiilts, vibration rods .... Holts, anchor Hulls, portal struts to i)atter-br. Hulls, hand-rail Holts, lower lat. strut to beams Holts, lower lat. strut to jaws . iiolts, folly plank to floor . . Holts, felly plank to hand-rail posts Hrackets ' 'rnaniental work 8 10 4 10 8 8 68 49 28 66 34 14 il" J?" 1 @ @ II" @ i" I'll l" ill 4 ill 2i"X2j" © \* 5# 8# © © © © © 4.9#L 12" 8" each each 3' each 12" 14" 12" 15" 18" 6.7' 74 61 4 50 98 64 100 5S 41 121 75 460 100 ^'43 232 12 6 100 97 700 •75 -^3 60 2,000 (JOO 400 Heain hangers l'7vpansioii rollers Holler flames, sides .... Roller frames, rods .... Hilkrs 2S >4 4 6 40 8 •4 10 2 14 111 2\" 1 '/ 4 I // @ 7"0 7"0 \ii i ill 6" D 2" io# JK-r ft. 1 13.5* per ft. 113.5* per ft. 6" 14" S.'# .S.5# 9' •5" 22" 17" -,// I ' " 5' 12" 7 6" i'llleis 1-illeis j.iw plates jaw plates Angle iron on roller i)lates . . I'ines of channels ! Hivel heads Spikes • • • Washers • • • • . * Nuts • • . . . • ■ ■ ■ 1 'I'olal weit'ht of details . . 19,850 57.9' 3 Weight of main portions . . • • Total weight of iron . . . 77.763 1 i I nil. I, OF LUMIU-.R. |oi>ts flooring (e(iuivalent) .... 80 4" ,4" 20' 7.4'''7 160 I ^" 14' 6,720 1 l.iiul rail .... -•" (•)" i l.iiul-rail |)()sts j- 20' 040 34 4" 6" 4' Hull planks 16 2" tj" 20' 640 Iilly planks ' Ucral struts 10 7 6" 7" 6" 9" 20' 14' 960 5'S 'I'olal nnnii)er of feet, board nieasMri' 17,214 156 OI^D/NAKV JROX lllLJllWA V-H RIDGES. Tabic I. gives the weight of iron per lineal foot of bridge as 479 pounds, which multiplied by i6o gives 76,640: adding 600 pounds for the spikes, makes the total weight of iron 77,240 pounds. This indicates an error in the table of only seven- tenths of one per cent, — a very satisfactory result. If we deduct the weight of the end lower lateral struts, roll- ers, roller plates, anchor bolts, etc., which really do not come upon the bridge, in all about 1,400 pounds, the dead load per lineal foot will be "^W^'^ + 269 = 746; which agrees within six pounds with that assumed. It may appear to the reader who has carefully followed out all the calculations in this chapter, that the designing of iron bridges, and estimating weights thereof, involve a great deal of work, and demand considerable time : but such is not necessarily the case ; for an expert could have made this design in from two to three hours, because his experience would have told him the sizes of many of the details and the number of rivets to empiov. In this chapter everything has been figured out carefully enough for making \v'orking-di-awings, instead of merely an estimate of weight ; foi the author considers that it is better to teach the beginner oxact methods in the first place, and leave him to vlevciop ipproximate ones as his practical experience increases. A u!-cful deduction which can be made from the " 15111 of Iron " in this chapter is the proportion which the weight of the rivet lieads bears to the weight of the rest of the iron, excluding that of the floor beanis, spikes, and washers. In this case the ratio is about ^^^^(^ = 2.92 per cent. The average for a number of estimates made by the author is 2.85 per cent, the greatest being 3, and the lfia»t 2.4 per cent. The knowledge of this fact will save consideiable time for any one who has many esti- n^a^es of weight to make. The author at «;n(; time, when in haste, used to figure out the total weight of , jn portions, and divide by a certain quantity less than unity, in order to determine tiie total weight of iron, but has now abandon*.'! the methotl as giving too loo.sc an ap|/roximation, finding that the correct divisor varies considera- bly with the leiigtli <A hj)an and the class o' bridge. Tables 1., II., and III. give the weights of iron for all cases far more accurately Ubim will *ny such apinuxiniation. of brid<ie as ORDINARY IRON HIGHWAY-BRIDGES. 157 CHAPTER XVII. BRIDGE LETTIXGS. The ordinary modus operandi of bridge Icttings is by no means the most perfect that could be devised. A couple of months before the letting, advertisements are inserted in some of the local newspapers, stating that on a cer tain day at noon, in the county town, at the court-house, there will be let the contract for building a bridge, or several bridges, in the county. The length of span and clear roadway are nearly ahvays given; and sometimes this is all, for the commissioners, as a general rule, do not know whether they want an iron or a combination bridge. Sometimes, even, they accept a wooden oiif after advertising for an iron bridge. Occasionally a very fan- list of data is advertised, but such is not the rule. In addi- tion to the local advertisements, circulars are often sent to the various bridge companies, requesting them to send representa- tives to attend the letting. Little do the commissioners think, that in the end the county has to pay the travelling e.\i)enses of each representative who attends, as well as for his time. Instead, they .say, "The more, the merrier," and congratulate themselves when they have a good attendance, thinking, that, the nu):e representatives, the greater the competition. It may Ix' ,su in certain cases ; but ultimately some one has to pay each traveller's expenses, and who but the counties is there to do it > It is true that mailed bids are received : but they are very sel- dom accepted, even if the figures l)e the lowest ; for the commis- sioners are generally unable to resist the combined eloquence ••f half a dozen bridge-men. It would be much better for all parties concerned if bids were all sent by mail, and if the awards were made by a competiMit engineer. It would permit i , .A 'iM'an, I 1 r ! I , ii IWi 158 ORDINARY IRON HIGHWAY-BRIDGES. of the reduction of the staff of each bridge company, the less- ening of cost to the counties, and, what is more important, the building of better structures. When, by means of much com- petition, the contract price for a bridge is reduced to cost, or even below it, what does the successful (?) competitor generally do ? Lose money ? Not at all if he can help it : that is not his way of doing business. He puts up a cheap bridge, cutting down weight on the details, and shaving as much as he dare on the sections. The author does not wish it to be understood that such is the method of the better class of bridge companies. They generally know better than to let their travelling men take contracts for nothing ; and when they do get bitten, as they all do occasionally, they put up the bridge at a loss, and take it out of the next county where they obtain a contract. When remonstrated with for collecting a large crowd to attend the letting of a little bridge, county commissioners have been known to respond, " You see, we don't know exactly what kind of a bridge would be best for the place, nor what style of bridge the money at our disposal will pay for ; and when we get a lot of you bridge-men here, who know all about it, we are able to find out exactly what we need." Travelling bridge-men who know all about it ! Bridge companies are not willing to send their engineers travelling about the country to attend county bridge lettings. They cannot afford to pay for this purpose salaries of two or three thousand dollars per annum, when men can be obtained to do the work for one-third of that amount. When an engineer is found at a bridge letting, it is generally because he has tired himself out at office-work, and needs a little change. It is surprising how little the average travelling bridge-man really knows abo'it bridges, and how incapable he is of giving advice of any value to a commissioner. What he does know is how much bridges will probably cost, and this knowledge lie obtains from the company's engineer. Mis forte is to do tlic heavy talking, in which it is by no means necessary for him to stick to the truth. On the day of the letting, four or five honest farmers (they LUC honest usually, though there have been and are exceptions) ORDINARY IRON HIGHWAY-BRIDGES. 159 mc u'ct to determine upon who shall have the bridge. In some cases, after the bids are opened, the contract is immediately let without discussion, to the lowest bidder. At other lettings' each company's representative is allowed to hold forth, in turn' before the assembly, and show in what way his bridge' is supe- rior to the rest. Some of the arguments advanced are really amusino- One will say "Mine is the best bridge, for it has the most^ron in the chords " (Ignoring the fact that his bridge has a less depth of truss than any of the others). Another says, " My bridge is the best, because it has the most panels ; and it is an acknowl- edged fact, that, the greater the number of panels, the stron-er the bridge." Another will point to the size of his floor beams forgetting that his bridge has one less panel than have any of the others. With such nonsense are the minds of the poor commissioners crammed, until they do not know the difference between a cumter and a batter brace (in fact, it is more than probable that they never did know) ; and the result is, either that the letting is broken up, or that the contract is let to the one who has done the most talking, and has impressed the most lalsehoocis upon the understandings of the honest farmers. Sometimes the commissioners conclude to have the letting done in style, so engage the services of an engineer. Their accjuamtance with the members of the engineering profession being rather limited, they employ to decide for them the county surv eyor, whose technical knowledge is confined to the use of the compass and transit, and whose mathematical education never went much farther than arithmetic. Or perhaps taey will find some one much looked up to in the county as an engineer, who iias been plucked at some technical school, and returned home t«> enjoy the honors of having been a college-man. As Professor Vose, not long ago. stated in a very able article luihlishcd in the "Journal of the Association of Engineerin<. Societies •• and "Van Nostrand's Mag.^irH.." in -r.ier to insure the l)u,l,i,ng of none but good bridges, there miust be a State ■nspector, whose duty it would be to pass iii<lgment on the Pl.nis <.f all bridges, before p.Tn,itting them to be erected in '-K' State. Such an inspedor should be, not an ordinary en-i- i6o (V^nrxANv //c(hv iiighway-bridges. neer, but an expert in bridge designing. He should receive a handsome salary, and be allowed enough assistance to enable him to do his work in a satisfactory and efficient manner. His ter.ure of office should be for life, or for a long term of years, and should be beyond the reach of politics and politicians. As long as his work be done efficiently, his position should be assured to him ; for a man of the requisite experience and ability would not be willing to accept the position under other condi- tions. The letting of bridge contracts to the lowest bidder is the worst method that could be adopted, even when plans and specifications are on file ; for the work generally goes to the most unscrupulous bidder, who will secure his margin of profit by diminishing the weight of the details. This weight should be about twenty-five per cent of the total weight of iron-work in the bridge, and it is quite possible to reduce it to one-half of this amount. If ignorant commissioners must have a rule for letting, it would be better to award the contract to the highest bidder. But the proper way would be to engage the services of a man who knows something about bridge construction, and have him figure out the probable cost of the bridge, allowing a fair margin for profit. A margin of from fifteen to twenty per cent is not excessive, even upon a liberal estimate of cost ; for such a margin by no means represents the contractor's actual profits. From it must be subtracted, not only a portion of the annual office expenses, including salaries of clerks, draughtsmen, and engineers, but also the bidding expenses of several lettings where the contractor has been unsuccessful. Then, too, there is the risk of bad weather, high water, rise in ])rice of iron, delay in shop, etc., any one of which is liable to absorb the whole calculated profit, to say nothing of the liability of losing the bridge by a freshet during erection. When the appropriation is small, it is much better to build a good combination bridge than a poor iron one, because the wood-work of the former can be replaced when it wears out ; while the iron, if properly cared for, is as good as new. Hut a used-up iron bridge is worth little more than the cost of taking; OA'DJXA/n- /A'O.V JIIGIIWAY-BIUDGES. .Cn il^^'l-^vn, and transporting- it to where it can be sold for old TiK. method of having plans and specifications on file for cv.ry competitor to bid upon is not a good one. In the firs 1 ace. .t necessitates the sending of engineers to the letting, or at Ic St ose who are capable of figuring out the weight of a bndge, thus greatly increasing the bidding-expense • then i the p ans are at all defective in design, a fi;;t.cL om^ -nvdhng to b.d upon them. It is much better to let elc company bid upon its own designs V^ most city bridges and for very large county bridges, it is - h a bridge company's trouble to prepare special dL n^s • '-t.lor ordinary county lettings. standard drawings will ansvt .' ^ciy purpose when accompanied by a diagram of stresses and special specifications. If the letting is to be done by an e.vd ncer. a plate of details similar to Plate III. or Plate IV. will Se uf cient but the ordinary county commissioner does not u der <:r ih s"f '""""^- ^^^"^^ ^^ ^- -hat the bridge ^^'11 ook like. Such a picture as the one given on Plate I would be very taking with county comnussio^ers. but thJ e s ..rea dea of labor involved in making such a drawing. As .general rule, a sheet showing side and end elevati.ms an a plan of either the whole or one-half of the bridge, will b 's uot when supplemented by a sheet of details It IS nut unusual for a fancy drawing to take a contract when thcic are much better and even cheaper structures in com,;:;;: ^ JhyHagram of stresses should be filled out as shown on Specifications should be quite e.vplicit without bein<^ Ion- o, -" -ing to a reader of o,-dinary intelligence. The uTh -u 1 recommend the following or some similar form of J 6: OND/XAKY /A'OA' HIC.UWA V-ltRlDuES. SMITH & WILLIAMS, BRIDGE ENGINEERS AND BUILDERS, PITTSBURGH, PENN. SI'FXIFICATIONS FOR BUILDING A WROUGHT-IRON HIGHWAY-BRIDGE. ri Length of Span. — To be feet inches between centres t end pins bearings. Clear Roadway. — To be feet nclies between innermost portions of trusses. Live Load. — To be pounds per lineal foot of bridge. Dead Load. — To be pounds per lineal foot of bridge. Depth of Truss. — To be feet inches between centre lines of chords. Clear Headway. — To be feet lowest part of overhead bracing. inches between floor am Upper Chords and Batter Braces. — To consist of two inch ch;in- uels, with a plate inch by inches above, and lattice bars inch by inches, riveted together at tiieir mid- flle points, below. Splicing of Joints in Upper Chords. — Sliall be madr l)y a jjlate on e:i( li side, as shown in the accompanying draw int,^ Tiiesc plates shall lie of such thickness as to atford sufficient iiearing for tlic pins, and tluir combined sectional area siiall not be less than that of the ciiannels which they connect. Xo splice plate to be less than three-eighths i J) of an inch in thickness. These connections shall be designed •■■"' the supiiosition tliat the entire stress is carried by the jjlate rivets, no reliance being placed on abutting ends of channels. Cover Plates for Choi Js. — Shall be inch by inches ! inches, and sliall contain a^ many rivets on each side of ■'- joint as will suffice t" carry tiie i;reatesL stress tha: cm ever cnnic upon tile chord plates. iiii'!i r s ami JHWAY-BRIDGE. between centres tween innermost between centre ctween floor anil ( >a-/j/a:ia- i - /A'OA- iiuiiiu -,/ J '-nA'/ih;Ks. 163 i'ticI) by Stay Plates for Chords and Batter Braces. — Shall be inches. Posts. - Shall consist of two ciiannels, of sizes as marked on the accompanv- ing diagram of stresses. The latticing for same shall vary from ;"*:'' ''^: , ,■, 7'^*^^ J-^ ^^^^ ^y inches; the'bar; bemg riveted together where they cross each other. The posts are to be attached at their ends to the chord pins, an<l are proportioned for both ends hmj,a.d. At the upper ends the connections are to be made by extension plates, each of which is to have a sectional area between the pin hole and stay plate equal to twice that of the channel to which It isattached. The entire stress in the posts is to be considered as c.-irried by the extension plates and their rivets, no reliance being |.laced on abutting ends of channels. Upper Lateral Struts. - Shall consist of two channels, ''''?"' of sizes , , latticed, given on the diagram of stresses, rigidly attached to the chord. lacing ^ '''■■ lattice '''^'■'' f""" ^'T"*-' •'^liall vary in section from ^^: ,; /"'^•'^^ '° i"^l> by inches; and the .stay plates, from inch by inches by '"'^''^^ '« inch by inches by .. inches s. inch Portal Bracing (at each end of the o laced one i span). — Shall consist of , struts , , , two "•'"'^=>» each composed of two inch channels, as marked on the diagram of stresses, ,^^^.^^^, „y „ars i„ch by inches in .section, with stay plates inch by inches b>' inches; also lour adjustable rods, each inches m diameter. The struts are to be rigid.- atached to the batter i)races. Vertical Sway Bracing(between posts). - Shall consist of two vibration rods, ^■^'-■'' '"ch in diameter, and an intermetliate strut of inch I-beam, weighing pounds per foot, rigidlv attached to t..e posts at a distance of feet inches below the level ot the upper chord pins. End Lower Lateral Struts. - Shall consist of Intermediate Lower Lateral Struts. -Shall consist of inch l,v inch pine timber, lying upon the Moor beams, and well bolted thereto, and attached by vsrought iron jaws to the chord pins. • I ir,4 oN/u.y.ih'v /A'ox iiminvA v-i'>Riin;i-:s. Side Bracing. — Sliall (onsist of indi liy inch pound angle iron, well rivitcd to the t(>|) iliord and to tlii' lluor lu-ams. whicli ari' prolonged feet inches at eaeli end be- yond tiie trusses for this purpose, as shown on the aecomimnying drawing. Bottom Chords. — .Shall consist of eye bars, as marked on the di.igrani of .stresses, tliose in the two panels next to each end of the span being trussed. Main Diagonals. — Shall consist of eye bars of the sections marked on the diagram of stresses. Counters. — .Sh.dl consist of adjustable rods with loop eyes, the sections being as irarked on the diagram of stresses. Upper Lateral Rods. — Shall be from inch to inches round iron, attached by bent eyes to the chord pins. Lower Lateral Rods. — Shall be from inch to inches round iron, attached eithcf to the chord pins by bent eyes, or to special pins passing tiuougli the lateral strut jaws i)y loop eyes. Floor Beams. Shall be rolled iiuilt licanis inches dee]), weighing pounils per lineal toot; web inch by inches; ujiper llanges. two inch by inch pound angles; lower llanges, two inch by inch pound anulcs. Stillencrs to be of inch by inch . pound angles, jier beam, niaele tiush with the vertical legs of the Hange angles by liHing-i)lates. Beam Hangers. — Are to be of four I'ountl upset inch iron. sciuar." not upset: there are to be ^^.^^ of them to cacli beam. Beam-Hanger Plates.— Are to be inch by inches by. men Shoe and Roller Plates. — Are to be inches thick. Pins. — Are to be of the sizes marked on tlie diagram of stresses. They shall be turned so as to tit the pui holes within one-liftieth (jl,,) of an inch. Pin Bearings. — .All jjin bearings ;ue to be properly re-entorced. ; niaikfd on tlic ."s, tlie sections ORDIXARV IROX IIIGHIVA V-IIIUDGES. 1^5 Brackets. - A straight bracket of i,„h by inch pound an :le iron is to l,e used to connect each post to tl,e overhead strut. Ihoseforthf portals are to he ot inch l.v '"L-h pound rivets at cacli lik ui.i,'lc iron The) be connected by Chord Heads. - .Shall be of standard shapes, and so strong that the bar will l.icak in the body rather than in the neighborhood of the eye. Upset Rods.- Ail adjustable rods, unless otherwise specified. ,o have heir ends . Hiarged for the screw threads; so that the dian.eter at the h 'll' .; of .T l"T' ff 1" ""•^--^'-■"'" ^'«^ ^'f -' -ch greater tl an that .,f the body of the bar, scjuare or Hat bars being figured as if of ecjuivarnt round section. Riveting -Riveting shall in every respect be in accordance with standard authonties; and all riveted connections shall be designed for he nvets to resist the greatest shearing, bearing, and bending stresses Expansion. _ .Shall be provided for by . Anchorage. -At one end of ^^^^ .sp,n, the superstructure is to be an- chored to the foundations by bolts, each inches '" •"'^""^'^'•' =^"'' ^' l^^^t feet inches long! Ca.be. Shall be at least finches when the bridge is empty, and '" '^-'^^ "iches when fully loaded. '"°"' ^""'Tiir ^'''" ™""" "^ '""' "^ '"'^'^ by i'Hh ,,^^,^ joists, dai)ped and spiked on the lateral struts; and the lloor plank shall be of_ i„ch pine or oak plank laid diago- nally or square across the bridge, as may be preferred, and well spiS" 1" •''^; J"'-^'-^- ^ f^'lly plank of inch by . ,„ ch nine Hand Railing. — To consist of ^ .0^. "'>.^; IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I u IM 2.5 2.2 ^ IAS IlilM 1.8 1.25 1.4 1.6 ♦ 6" »k V] <^ /^ /. >!^ ^^^ # Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 i !l 1 66 OIWfNARV IROA- HIGHWAY-BRIDGES. Details of Construction. — All details of construction to lie i)ropcily pro portioned with clue regard to the various direct and indirect stresses that may come upon them. All joints to he machine dressed and to fit perfectly. Riveting in the field to be performed in a skilful man- ner, using the button set. There shall be no loose rivets in the bridge. Quality of Materials. — Iron for tension members to have an ultimate strength of pounds per square inch, and an elastic limit of pounds per square inch. Iron for compression members to have the usual correspondence of strength. All timber to be sound and of good quality. Workmanship. — All workmanship to be first class in every respect, and to be performed to the satisfaction of the engineer or commissioner in charge. ., 1 88 (Signed) SMITH & WILLIAMS. With the diagrams of stresses, plans, and specifications, there should be handed in, or sent to the commissioner, a proposal in the following or some similar form : — To the County Commissioners of County, State of Gentlemen, — We the undersigned hereby agree to build, and put in con- dition for travel, the superstructure of an iron highway-bridge of spans, across ' i" "i<= bounty of , State of .according to accompanying plans and specifications, for the sum of dollars cents ($ ). SMITH & WILLIAMS, , 1 88. After the contract has been awarded, the successful com- petitor and the commissioners must sign it, and a bond must generally be given by the company as a guaranty that they will complete the work according to the specifications. It is well for the representative of each company to be provided with ORDLYARV /A'ChV HIGHHA V-IUUDGES. l)lank forms for contract and bond. The author would mend the following for this purpose : — 167 recom- :T BRIDGE CONTRACT. & WILLIAMS. \ & WILLIAMS. This Agreement, made and entered into this nt lifiilijL' hii th day :t;:::Z--^^:--^^^ Count}- of c» » r •' , State of parties of the second part, Witncsseth That the said narties of thp five . 1 of a bridge across > in said county, -'':;,:;*Y,',i;: :''""'' """ '--- - ';-„f *--- '■■■■ l»i<k. a, a. ' , °. " ,"' '""■'.'""'■' •i''!"""' '!"■ '"alcrial tor safd of ItndL^c CO A.[). iSS I'll: Mi' l68 ORDIXARY IROX HIGHWAY-BRIDGES. part contract, and agree to pay to tlie said parties of the first part tlie sum of dollars, payable as follows : /// witness whereof the said parties do hereunto affix their seals and signatures the day and year above written. L^I^AL.] [seal.] [seal.] [seal.] BOND FOR BRIDGE CONTRACT. Know all men by these presents, That we. Smith & Williams of Pitts- burgh, I'enn., as principals, and as sureties, are held and firmly bound to the in the State of in the penal sum of dollars, for the payment of which, well and truly to be made, we bind our- selves, our heirs, executors, administrators, and assigns, jointly and severally, firmly by these presents. Dated at in the County of and State of this day of , i88 The condition of this obligation is such, that if the said Smith ilv: Williams construct bridge in the aforesaid county, according to llie plans, specifications, and contract hereto attached tlien this obligation to be void and of no effect, or otherwise to remain in full force and virtue in law. Principals. Sureties. ix their seals and ViLLIAMS of Pitts- ORDINA R Y IROX HlGmVA Y-liRlDCl-S. 1 69 The previous remarks concerning methods of bridge lettin-s w.ll probably not be altogether approved of by contractor! Mr A. I. Boiler, C.K., in his treatise on "Iron Highway- Bridges, writes, '< It will be noticed in the last clause of the lorin for 'Invitation.' bidders are requested to be present at the opening of the bids, and hearing them read. This is simple just.ce. And when one considers the time required to make plans and estmiates, even for a small piece of work, to say noticing of the expenditure of money incident thereto with l-robable travelling-expenses in addition, no fair-minded man can object to rendering at least what satisfaction may be derived tn.m the public opening of tenders. Bids secretly opened always lead, whether justly or unjustly, to the suspicion of unfair practices, an imputation that can be readily removed by inc method of publicity suggested, a method which can be ()I)jected to by no one. unless those whose mode of doin- busi- ness seeks darkness rather than light." This is a clear and well-stated argument, and it is difficult to propose a method that will overcome every objection advanced. ii„vvever there are some points in it that will bear criticising. iM.r a bridge worth, say, twenty thousand dollars, all that Mr. Bo ler says is certainly correct. But is it so for a small c.nmty bridge ? The majority o. county bridges do not exceed unc hundred feet in length, and they are very often let sino-ly How long wdl it take, in a well-regulated office, to preplire plans and estimates for an ordinary one hundred-foot county hndge. Usually about thirty minutes; at any rate, no more tnan two or three hours. The work consists in taking out of their proper places a blue print of the diagram of stresses a sheet of details, a general plan, and blank forms of specification and pn.po.sal, then filling out the two latter, and enclosin- all '" an envelope for the post. The making out of the estimate ot cost should not take five minutes when the amounts of iron a"'l lumber, and a complete list of data, are at hand If the span be of unusual length, as sometimes happens when re- ])lacing an old structure, it may be necessary to make out a new diagram of stresses, but not to prepare a bill of material • t"i- every bridge company should have tables of weights of iron' I 170 OJaJJ.XAKV /A'OX JlIGIIWAY-IiRIDGES. and amounts of lumber, for all ordinary cases. The actual cost to the contractor, of an ordinary county bridge of one hundred feet span and sixteen feet clear roadway, can be seeii from the following estimate : — Wrouiilit-iron, 27,900 lbs. at 5c 5l>39S 00 Lumlier, io,8<So ft. at #18 per M '95 84 Haulinj.j, 20 loads, at $1.50 30 00 Framing 7 00 Falsework 25 00 Erection 1 50 00 Paintinij; 25 00 Blacksmi thing 5 00 Coal 2 00 Frcii^ht on tools 15 00 Travellin<:;-expcnscs 30 00 Men's time travelling 20 00 Bidding-ex])enses 40 00 Teaming during construction lo 00 Incidentals 50 00 Total cost of bridge f 1,999 ■'^4 Cost per lineal foot, say 20 00 Adding twenty per cent for profit would make the bridge cost the county $2,400. Now, suppose there are ten other bidders present, each of whose expense for time and travelling is forty dollars ; then there will be an additional four hundred dollars to be added to the cost of this or some other bridge, for, as before stated, some one must pay it. Kleven is by no means an unusual number of bidders for a small span : there are often as many as fifteen or sixteen. The estimate for forty dollars for time and travelling-expenses is not excessive, as the author, who has attended a number of lettings, can testify. These four hundred dollars are worth saving, if it can be done legitimately. As for bids secretly opened always leading to the suspicion of unfair practices, it is indeed true ; and there is no way of avoiding the difificulty, except by having them opened by a com- mittee of public men who are above suspicion. These could bo 'J£S. ORDINARY [RON HIGmVAY-IiRlDGES. I/I . The actual bridge of one y, can be seen • ?i,39S oo • 95 84 30 00 7 00 25 00 150 00 25 00 5 00 2 00 15 00 30 00 20 00 40 00 10 00 50 00 i?i,999 '"^4 20 00 ake the bridge are ten otlicr and travelling 1 four hundred t other bridge, leven is by no ill span : there elling-expenses d a number df g, if it can be government employees, and residents of the capital of the State, to which bids for all county bridges should be sent. Ihe duty of the committee would be merely the opening of the bids, and the recording of the amounts. The inspector of bridges, who should also reside in the capital, should then examine the bids, and report to the county commissioners, which, in his opinion,' is the best bridge for the money (i.e., which he would advise tlnm to accept), and which bridges arc up to the specifications, and which not, leaving the final decision to the commissioners. A summary of his report should be advertised in certain of the engineering.papers, say the two which have the greatest circulation, so as to let the public see that there has been fair play, and to clear the inspector of any imputation of unfair prac- tice. The advertising of the report, including the price for each bridge and the estimated weight of iron in same, would serve to prevent any connivance between contractors and commis- sioners ; because any decided departure from the recommenda- tion of the inspector would immediately awaken suspicion. No bids without an estimated weight of iron should be received ; and, should the inspector doubt the genuineness of the estimate, he could easily check it. Then, too, the bridge should be weighed at the railway sta- tion nearest the site ; and, if the weight be found wanting more than a certain per cent of the estimated amount, the contractor .should be fined. \\\ this way the only possibility of fraud would be an agree- ment between a certain bridge company and all the mem"bers of the committee for the latter to insert the contract price in their hid .so as to make it just a little lower than that of any other competitor. Considering that the committee would be composed of a number of the most prominent state officials, the I)robability of such a fraud ever occurring reduces to zero. i • the suspicion e is no way of lened by a com- These could be \72 ORDIA'ARY ]R0,\ IHCllU-AV-nKIDCES CHAPTER XVIII. WORKING-DRAWINGS. I III The first points to be determined before commencing a work- ing-drawing are the scale and the size of the paper. The least scale which it is convenient to use is one inch to the foot, and the greatest scale for a whole drawing should seldom exceed an inch and a half to the foot. If a smaller scale than one inch be used, difficulty will be experienced in writing the rivet spacin"- between the rivet holes. The width of the i)apcr should be from three and a half to four and a half, or ever five feet : and, as for the length, it is better to use roll-paper, and not to cut it until the limits of the drawing be determined ; for it is a great convenience to be able to make ajl the working-drawings for a bridge upon a single sheet The following is a draughtsman's equipment for making working-drawings in a methodical and expeditious manner : a table from four to five feet wide, from six to eight feet long, and about three feet high ; a pair of steps each three or four inches rise, and three feet long ; a bevelled steel straight-edge, at least three feet long ; a beam compass with tangent screw attach- ment ; a couple of small triangles (rubber ones are the best); some four-H and six-H pencils ; a little tracing-paper ; a finely divided duodecimal boxwood scale (the subdivisions being quar- ters, eighths, and sixteenths); a good box of instruments, includ- ing a protractor and a pair of hairspring dividers ; and the usual outfit of rubbers, tiles, pens, etc., that one finds in draughts- men's ofifices. T-squares, large triangles, and parallel rulers should never be used in making a working-drawing. The first can never be depended upon, because of the impossibility of having both board and T-square always perfectly true ; no ORDLVARV f/w.V HIGHWAV-BRIDGES. xy^^ wooden ruler can be relied on not to warp ; and parallel rulers are a delusion. I'or a few inches it is permissible to turn rioht angles with truin-les, but for Ion- distances the beam compass should be used ; and parallel lines can be most accurately drawn by erect- in- a perpendicular near each end of the original line, and laying oif on them equal distances. When distances are a little too great for the triangles, and too small for the beam compass the large ordmary compasses can be used ; but it will be founcl that they are seldom required. The four-II pencils are to be iise.l for writing dimensions, etc., and the si.x-H ones for draw- ing I'lies. The draughtsman should always have at least one ot the latter sharpened to a chisel edge for ruling, and another to a point for sketching. He will find it to be greatly to his advantage to keep his pencils always well sharpened, for an error ot the width of a pencil-line will often cause a great deal of inconvenience. A piece of emery paper or a fine file will be ound useful for sharpening pencils. The tracing-paper will be convenient in transferring drawings of similar chord heads etc. : Its function is merely the .saving of a little time It is generally better to have both a long and a short scale The long one may be divided into feet only, the inches and frac- tions of inches being taken from a diagonal or other small scale If the draughtsman be not provided with a suitable scale he can easily prepare a very fair one for himself on a strip ot the roll of paper upon which the drawing is to be made. The method of projecting one view of a piece from another now will not do for working-drawings. owing to the liabilitv of the triangles to slip. All measurements should be transferred by the dividers ; and, if there be any probabilitv of the points of the dividers having been moved, the distance between them ■should be tested by laying it off once more upon the original length. There should be no more than a single transferrence of any one distance, for errors often increase, instead of bal- ancing. The general arrangement of a working-drawing consists merely in laying out a plan and elevation of one-half of the span, leaving at least a foot of space at each end, and six or a KH na fin 174 ORD/XAKV IROX HIGHWAY-BRIDGES. 1 i I J'i itiii I ■ . , Hi eight inches above the elevation and below the plan, if there be room to spare, with the same distance, or a little more, between. As it is immaterial if different portions of the drawing cross each other, provided that such intersection cause no conflictini,^ of the measurements, the various members may be shown in several \iews alongside of their respective positions in plan and elevation. Thus the top chord may be represented in an under and an upper view above the elevation of the truss, and the batter brace may be shown in a similar manner above and to one side of the elevation. Projections of the posts on planes transverse to the bridge may be drawn alongside and a little below the elevation of these members, the amount of lowering beini;- sufficient to bring the ends of the strut clear of the chords. Attached to the projections of the posts can be shown the inter- mediate struts and vibration rods, with their connections ; antl shortened views of the chord bars and diagonals can be placed alongside their elevations in order to represent the heads clear of all other members. Passing to the plan, on one side is drawn the packed lower chord, and attached thereto the lower lateral rods and struts in half-length ; while alongside the latter can be represented an elevation of the same with the floor beams beneath, and an end view of the beams near by. At the other side of the plan, can be shown half-lengths of the upper lateral rods and struts in two views, and a projection of the portal bracing on the plane of the batter braces, and on planes at right angles thereto. Each detail can be delineated to any required extent in the neighborhood of its position in plan, elevation, or both. If necessary, the panel points on one side of the plan may be brought opposite the middle of the panels on the other side, in order to avoid too much intersection. This arrangement, although a good one, is by no means the only one, and in some cases might not be the best. P'or instance, in skew bridges it would be well to show the whole of the lower lateral system in the plan, and the whole of the upper lateral system above the elevation, in connection with the uppermost view of the top chord, which should be the plan from above. Then, again, if the bridge be a large one, the height may be so OIWIXARV IKOX HlGHWAY-iiRllH-.ES. •75 great that it will be impossible to show the plan below the eleva- tion ; in which case it will be necessary either to make separate fh-.uings for the plan and elevation, or to place one alongside of the other on the same sheet. In making tracings of the work- ing-drawing, the tracing-cloth can be shifted about so as to group similar parts and so as to avoid too much intersection of (liHerent portions. i'rovided that any piece be .symmetrical about a plane cuttino- It ill the middle of its length and at right angles thereto, it uiH i)c sufhcient to show only one-half of the piece ; and the meas- urement may be referred to the end of the member, to the central plane, or to both. Where the same detail is used in more places than one, it is not necessary to shc-A- it more than once provided that it be exactly the same in every respect. As an illustration of how to make a working-drawincr take the case of the bridge treated in the last chapter, and .Assume tliat the paper and table are each four and a half feet wide Lsing the scale of an inch to the foot, the depth of the eleva- tion will be two feet, and the width of the plan one foot four mehes Allowing six inches above the elevation, and as much inore between elevation and plan, will bring the lower side of tne plan within two inches of the <t^Vr^c of the paper: this arrangement will do very well. The first step is to draw a line with the steel straight-edge, as nearly as possible, without takin- t'- im.cli trouble, parallel to the length of the paper, and at a distance of two feet si.x inches below the upper edge This line should be very fine and perfectly straight. It can be made so by prolonging it half the length of the straight-edge at a time, and afterwards testing it in several places. On this line take a ix.int a foot or more from the left-hand end of the paper as the centre of the end lower chord pin. Lay off along this hiu' with the greatest possible accuracy the panel length, until the centre of the bridge be reached: in this case twenty feet must be laid off four times. At the panel points erect short !H rpendiculars with the triangles, and on the perpendicular at the centre lay off the camber, which in this case is three inches l-'^'c 1). 9). Had the bridge contained an odd number of panels 't would have been necessary to draw the middle panel, and (II f I ■ 176 oRp/xA/n- ih'ox iin-.nwA v-nRiDCEs. lay (iff tilt' caniluT of tlirce intlics at each (MkI of this panel. Thon, assumiiiL; iIk- ciirvc of the chord to he a parabohi, th ■ fall from the centre to any panel point is e(|ual to the camber at the centre niulti])lie(l hy the s(|iiare of the ratio of the distance of the panel point considereil from the middle of the span to the half-lenji;th of span. Thus in the case considered, the falls at the first, second, ainl third panel points will be respectively 3(|)''^, 3(1)''^, and 3(|)''^, or \X\ i|", and ,''y", makin<;- the hei^dits of these points above the horizontal line respectively 3" — '•J^", 3" — i|", and 3" — ■,■*,", or 'A"' -i '• '''^'' -lu "' \^''i'<-'li distances are to be laiil out upon the perpendiculars so as to locate the centri's of the lower chord pins. The lenj;th of the panels as thus determined differ from those of their horizontal projections by an inappreciable (piantity. If there be any len^^thening of the chord, it may j^o against the play of the i)ins in the eyes. Ne.\t join the consecutive pin centres, producing them each way a little more than a jianel length, so as to facilitate the erection of perpendiculars thereto. Then at each of the differ- ent centres erect a perpendicular to each centre line meetinj^ there, and bisect the angle between the perpendiculars : the line of bisection will be the centre line of the post. Great care must be exercised in turning these right angles with the beam compasses, two points on each of the perpendiculars being found, so that if these two points and the centre be iu e.\;Kt line, the perpendicular may be relied on as correct. On eaih of these centre lines lay off the depth of the truss, and complete the skeleton diagram. A partial check on the accuracy of the construction may be had by measuring the panel length of the top chord, which should agree with the length calculated as follows. Let / = the increase in tiie ])ancl lengUi of the top chord above that of the bottom chord, c = the cainher at the centre of the span, s = length of span, ^/ = depth of truss, and « = number of panels. OA'D/A'.i/^ y f/wx maim -../ j ■-nmnai.s. , ^y Then, according to the method ^ivc. in Trautwino's « Pocket- ]^ook/> =-ri. vvhere ./ and . may he measured in ^cct. and c andM. inchc. The panel length of the top chord will then Tl,r- {' '' " '''' '^'■•"^■' '^"^^^'^ "f ^he bottom chord Ih.s s not a certain proof of the accuracy of the vvo,V T vo consecut.vc post centre hnes might he ec uaily n i td Z l>c.r correct positions, and on the same side though is u .c sLnvn ,n the next panel. A certain check mus' be obt ujuai to each othei. and agree with tluit found by the formula ^=v/'^^-f(/4-^y, wlitTc /; is the length rcoiihcd l-r <loi,bIc-intcTsc.cti„n hridKcs, the Icgth of the long clh™ . s can be fot,„„ by the nu-thod given in^Ap,.™, .f " ^ u„ h of the .hagonal as „,an„fact„red sb.m ,1 be one si tv latnl length by about a thirty-second of an inch tcNsnin member show the hcnrl^ ult). h • ■• ^.'"^ ^'^ •-^^^'' ^^^^^^ ^n the length from c'entre to centre, as shown on "iHdRier be more convenient, draw out the heads fnllM wi: '," "" '"^ "'""• ' '"■•' -■ b- '"one titho c,,:, , • . inoMded that both p„,s and heads diminish to..ether ' "■ hammered heads the method of eons.rne.ion is «ry sim- Ifililt I' 178 ORDhXAKy /A'OA ///u Jill' A V-nK/DGES. pic. It consists in describing, as in Fig. i of the accompanying diagrams, a circle of radius C/i, equal to that of the pin hole, and a portion of ai.other circle with a radius CB, equal to that of the pin hole plus the product of one- half the depth of the bar HK by the ratio given in the table on p. 20 ; then drawing the lines DE and FG parallel tc the sides of the bar, and at a distance therefrom equal to CB; and with C as a centre and a radius CD, equal to t>vice CB, describing an arc to intersect /;/:' and FG in the points D and F; finally, with D and /^as centres, and radii equal to CB, describing the arcs HL and KM, tansrent to the sides of the bar at //and K, and to the outer circle at L and J/. For welded heads the construction is as shown in Mg. 2, where the pin hole and bar are laid out as before. The dis- tance AB is equal to one-half of UK multiplied by the ratio given in the table on p. 20 ; and the distance SO is equal to UK, or the diameter of the pin hole, whichever be the greater. The cen- tres P and R of the arcs OBL and O'I'M respectively are found by trial ; then DE and FG are drawn parallel to tlie sides of the bar at distances therefrom D// and FK, equal to one and seven- tenths times I'B or KB: and with B and A' as centres, and radii equal to two and seven-tenths times BB or A'/", or, what is the same thing, e(|ual to D// plus J'B, arcs are descrihed cutting /:>/•: in D, and FG in F; finally, with D and /•" as cen- tres, and with radii equal to DN, arcs are drawn tangent to the side, of the bar at // ami A', and to the arcs OFL and O'J'J/dt L and J/ respectively. These constructions, with slight modifications, are taken from Trautwine's " Packet-Book." Next show the iiosts and the attached sway bracing in two projections with all tiieir details. There should be allowed a clearance of about an eighth of an inch for the ends of the posts inside of the chord. The positions for the stay plates should s, are taken from OKDIXAR ] • IROX J I hi nil -A J -HRHH; Es. , -jc, be as close to the pin as possible, allowing a little elcarance for the diagonals The proper positions can be ascertained from the general elevation. The lattice bars should be close to the stay plates : it will not be necessary to show more than a few of them on each strut, the positions of the others beino- indi- cated hy their centre lines, as shown on Plate VI This plate contams a portion of a vorking-drawing for a model of t^he bridge treated in the previous chapter. The small scale of thrce-c|uarte.-s of an inch to the foot was chosen so as not to make the model too large ; and the whole working-drawino- is not gnen, because of the necessarily limited size of the pla^e * I ho principal portions are represented ; so that one can, by studying the plate closely, learn all that it is necessary to know ni order to make working-drawings ; and students are recom- mended to give this matter special attention. Xext show in two projections the top chord and batter brace u-.th all their details, and give several views of each connect- .ng-p ate and other detail in the neighborhood of its position on t e e evat.on. The joints in the channels and plate of the top chord should be located three or four inches to that side of each panel point which is farthest from the centre of the brid-^e - tlKit t e pin holes shall be bored through a single piece, ami thrnugh the thicker of the two abutting pieces At the hip I'Hnt It IS of course unavoidable .o bore the pin hole through the abutting end.s of the chord and batter-brace channel;. .\cx pass to the plan, where the first thing to do is to draw parallel to the original horizontal line of the elevation traces of t.u. central vertical planes of the trusses and of the central piano n the bridge, locating the panel points verv carefully, and as nearly as possible vertically, below their corresponding posi- ■;'"^"" tl^e elevation. Then arrange the chord packTni on <'nc sKle of the plan so as to make the bending-moments on the Pms as small as possible without luu-ing anv of the chord bars i"i I at too great an angle with the plane of the truss a any of the panels have trussed bars, the trussing should he here shown, and the spacing of the rivet holes for same in Tliu scale lia^ been fuitlicr raluc.vl by the oiii'Taver fit^SI'l liiiii 1 80 ORDIXARY IROX HIGinVAY-BRIDGES, the chord bars should be represented close to the plan of the trussed bars. Near the packing should be drawn separate views of the lower chord pins ; giving their number, cHanieter, lengths between shoulders, diameters and lengths of reduced ends, and the total lengths, also the sizes of the nuts. At the right-hand end of the plan, show the lower latercl struts, and complete drawings for the floor system, including beams, beam hangers, beam-hanger plates, bolts, joists, etc. Generally the floor beams will be all alike : so it will be suffi- cient to represent half a beam. It may even do to show only half of a lateral strut, although there are always several differ- ent lengths of them in a bridge, provided that there be written sufficient directions to enable the carpenters to frame all the struts without possibility of error. In writing dimensions, etc., upon a working-drawing, it is immaterial from which direction the writing be read ; that is, it may be read sidewise, upside down, or in any direction most convenient to the draughtsman. In making tracings, this matter can be rectified if it be thought advisable. Full directions for the manufacturer should be writ- ten on the drawing. On the rest of the plan, show the uj^pcr lateral struts with their details ; all the lateral rods with their turn buckles or sleeve nuts, and their eyes in two views ; the end lower lateral strut with its details, and its connection to the pedestal ; the whole of the portal bracing with its connections ; the ornamental work ; and the name plates. Finally, take the list of members, and go carefully over the drawing with it ; seeing not only that each piece is represented, but that there are sufficient measurements given to have it manufactured. The following additional directions and hints may be found useful. Refer each group (if rivets to some local Hue, which is itself referred to the end of the piece, or some other promiiunt part. .Show a section of each member, and write the dinien- sions of all channels, angles, Lbeams, etc., near the secti.ui. Write along each piece its extreme length or lengths, its len-th from centre to centre of eyes, and of what it is composed. The ends of the two pieces of an adjustable rod should l)e separated by at least three or four inches in the turn buckle or sleeve nut. ORDLXARV IRON HIGHWAY-BRIDGES. I8l Mark what rivets are countersunk, and at which end. If the scale of the drawing be large enough, the countersinking can Ik thus represented: draw full parallel lines across the rivet for countersinking on the upper side, dotted parallel lines for Ciumtersinking on the lower side, and two sets of parallel lines crossing each other at right angles for countersinking on both sides. Be careful to always note how many rights and how many lefts of each piece will be recjuired, when there arc both riL;hts and lefts. Do not forget to write conspicuously the scale or scales of the drawing. Lay out all bevelled edges on an enlarged scale, say from half to full size, and mark their dimensions along the edges, referring all measurements to a transverse line through some well-defined point, as the centre of the pin hole. The'se measurements should be checked by calculation. The slight bevels at the joints of the top chord should be treated with^as much accuracy as the bevels at the hip joints ; but, as the bevel is very slight, it will be legitimate to put it all on one of the abutting ends, making the other a square cut. The centre lines for lacing-bars on the under side of a strut should be dotted. In laying out a long row of rivets — for in- stance, lattice rivets, or those for the top plate of a chord or batter brace — calculate the distance of some of the intermediate rivet holes from one end of the strut. Lay out these holes, then interpolate the others ; because, if the spacing be laid out con- tinuously from one end with dividers, any error in the span of the dividers will be multiplied by the number of times the dis- tance is laid off. After laying out a complete system of rivets for any member, check by seeing that the sum of the distances between rivet holes plus the distance of each end rivet from the end of the nuinher is equal to the total length of the member. ]\Iake duplicates of as many ])arls of the bridge as possible, even at the expense of a small amount of iron, not only to save time in draughting, but also in the shop, and to facilitate the work in erection. Arrange to have as few loose pieces for shipment as possible, and mark on the drawing of each connecting-piece to what it is 1 82 ORDINARY IROX IIICIIW AY-BRIDGES. to be attached, or if it 'va to be left loose. Thus the hip con- necting-plates should be attachetl to either the chords or batter braces, sometimes to both ; those of the top chord, to that por- tion through which the pin hole is bored ; those for the upper lateral struts should be left loose. If there be any reason to fear rough handling of the iron in transit, it may be necessary to send some of the connecting-plates separately ; but the more loose pieces, the more field riveting, and the more field riveting, the greater the erecting expenses, and the longer the time and the greater the risk in raising the bridge. Rivet spacing should be as regular as circumstances will per- mit ; and all changes in spacing should be made suddenly, instead of gradually, so as to facilitate the punching of the holes by machine. All measurements should be in feet, inches, and the following vulgar fractions of inches ; viz., halves, quarters, eighths, six- teenths, thirty-seconds, and sixty-fourths. Workmen do not seem to understand decimals : so it is better not to use them. Avoid also the use of the development method, as it is beyond the comprehension of ordinary workmen. The length of all main members should be measured on the drawing, then checked by calculation. When nuts are placed in a confined position, — for instance, pin nuts in jaws, — care should be taken that there be ample room for them to turn in ; as it is very awkward, and sometimes impossible, to screw up a nut which is stationary, by turning the pin. Nuts in confined positions may be turned by hammer- ing them eccentrically. Be careful to design no connection in such a manner that there will be rivets that cannot be driven without incon- venience. This remark is especially applicable to field riveting. It must be borne in mind, that, no matter how carefully the bill of iron was prepared, there will be many minor changes found necessary in making the working-drawings ; but, as a rule, such changes cannot materially affect the total weight of iron in the bridge. ORDINARY IRON HIGHWAY-BRIDGES. I .S3 CHAPTER XIX. ORDER BILLS AND SHIPl•L^fG BILLS. asured on the When there is neces.sity for haste in building a bridge, as there generally is in America, time can be saved by sending a partial order bill to the manufacturers before starting to make the working-drawings, or after they drc partially pencilled. Such preliminary order bills should include only those por- tions which are termed in this treatise "Main Members," and those details of the sizes of which the designer is certain ; for instance, stay plates, pins, brackets, and the plates and angles for built beams. The length of the main members in the bill should be three- quarters of an inch greater than will actually be required, in order to allow for the dressing of rough ends ; and, should there be any doubt in the designer's mind concerning the e.x-act length of any piece, he should make the ordered length great enough to cover any variation which there may be in the design. Of course, where there are bevelled ends on a piece, the extreme length plus the allowance for waste must be given. Where a number of small pieces are to be cut from one large piece, an extra allowance of length must be made to provide for the waste in cutting, say from an ei-hth to a quarter of ;in nich for each short length. After finishing the pencilling for a working-drawing, the remainder of tlie preliminary order bill may be made out and sent. It should be divided into the fol- lowing groups, containing the measurements indicated : — nmnncls No. Depth Weight per fuMt length Kinishfil li;m;ih f I I r i ' 184 ORDINARY IROX HICIIWAY-BRIDGES. Ansles No. 'I'liickncss I IjCS-s \ \Vcinlit in;r fool Length 1' iniahed Icnj;! I-hc,ims ' No. Depth I Weight per foot Length - Finished length Plate. No. Thickness Widih Length i Finished Icni^th Eye bars No. ' Thickness Depth Depths of lie.ids Length centre to centre of eyes Extren;e Icntilh Adjustable rods with plain eyes Diameter. Short I'iece. Long Piece. No. : Rod Upset Ciame- j Length of I end ' tcr pf j loop I 1 eye I.ength, Diame- cenlrc of ter of eye loeiid eye Length of loop Ix'ngth, centre nf eye to end Adjustable rods j with bent eyes No. DiAMETKK. Short Piece. Long Piece. Rod Upset end Diameter of eye length, centre of liend to end Diameter I.eiigth, centre of eye of bend to end Pins ! 1 1 No. ] Diameter. Length between shoulders Extreme length Body Reduced ends Rollers ' No. I.ength between shoulders Kxtremc length Any details which will not go into one of these groups will be made of material that the- manufacturer keeps in stock ; for instance, fillers, washers, nuts, turn buckles, sleeve nuts, orna- h KiiiihheJ length Finished length Vini.shuti Icngtit ExtrcTiiL' Ic-iiutli I.ONC, PuiCE. Length of Length, ORDINARY IRON HIGHU 'A J '-n RIDGES. , 85 mental work, na.ne plates, bolts, and iron hand railing It won d not be a bad idea for bridge companies to keep blank .snn.lar to the foregoing, for preliminary order bills 1 ins should be ordered an eighth of an inch greater in diame ten than requ.red in the bridge, so that they\.ay be t n^^^^^ clown and shoe plates and roller plates, one-sixteen h of an inch thicker, to allow for planin- ^" ^IXrr"^' """"'•'^"' ^""™"--'>'' "^ '^-^ ^-^' fro- No. pieces Thickness Width Length Kind of wood ] I.ONG I'lIXE. A ter the working-drawing is finished, there should be pre- pa.cd to accompany it a final order bill, in which are to be grouped all similar pieces, and all their details wh cl are attached to them in the shop. The following groupin" vv 11 cover any case of an ordinary iron highway-bridge dlw" according to the method of this treatise:— ^lesigned lers Extreme length TOP CHORD SECTIONS. ^Iiannels. ''"IM'lates Lnver |il,iles . ^lay plates Lattice bars . I 'iriiic. ting-plates No. No. No. No. No. No. Depth Width Width Width Width Width Weight per foot Thickness | Thickness i Thickness Thickness I ! Thickness I Finished length Finished length Finished length Finished length Length centre to centre of end rivet holes Finished length BATTER KR.'VCES. I'.xtreme length Channels . 'l'»P plates Cover-plates (hip) ^lay plates Lattice bars . Cnniierting-plates •''liuc plates No. Depth Weight per foot No. Width Thickness No. Wi.lth Thickness No. Width Thickness No. Width Thickness No. Wi.lth Thickness No. Width Thickness Finished length Finished length Finished length Finished length Length centre tp centre of end rivet holes. Finished length Finished length 1 86 ORDINARY IRON HIGHWAY-BRIDGES. CHANNEL BOTTOM CHORDS. Channels No. Depth Weight per foot Finished length Stay plates .... I,acing-bars .... No. Width Thickness Finished length No. Width Thickness Finished length Ke-enforcing plates No. Width Thickness Finished length Connecting chord heads . No. Depth Thickness Length centre of eye lo end, and extreme length POSTS. Channels 1 No. Depth Weight per foot Finished length Stay plates .... 1 No. Width Thickness Finished length Lattice bars .... ] No. Width Thickness Finished length 1 No. Width Thickness Finished length Re-enforcing plates . 1 No. Width Thickness Finished length Channels . Stay plates Lacing-bars Jaw plates UPPER LATERAL STRUTS. No. No. No. No. Depth Width Width Width Weight per foot Thickness Thickness Thickness Finished length Finished length Finished length Finished length END LOWER LATERAL STRUTS. Channels . . . . • I-beams Angle irons .... Stay plates .... Lacing-bars .... Jaw plates No. No. No. No. No. No. Depth Depth Legs Width Width Width Weight per foot Weight per foot Weight per foot Thickness Thickness Thickness Finished length Finished length Finished length Finished length Finished length Finished Icngdi PORTAL STRUTS. Channels No. Depth Weight per foot Finished length Stay plates .... No. No. Width Width Thickness Thickness Finished length Finished length law plates .... No. Width Thickness Finished length Connecting- plate to batter- hrace No. Width Thickness l.ength of each leg Connecting-plate for brackets to channels .... No. W: 'ih Thickness Finished length Connecting- plate for name plates to channels No. Width Thickness Finished length ^GES. Finished length Kiiiisheil lenylh Finished length Finished length th centre of eye Id eml, and extreme length C'h;ninels, I'l.it bars . O/iDLYAJn' I/W.V HIGHlVAY-niUDGES. ■STIFFKNKI) mr VERTICALS. Si;iy plates . . I.,irnij,'-l)ars . Kctiiforcing plates. 'Inissing. 187 No. Depth No. Width No. Width No. Width No. Width No. Width Weight |)er foot 'I'hickness Thickness Thickness Thickness Thickness Finished length Length centre to centre (if eyes, and extreme leti^th Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Finished length Length of etch leg Finished length Finished length INTER.MEDIATE .STRUTS. I-hiMins , t L' liiig-plales . No. Depth No. Width Weight per fnot Thickness Finished length I.engihofeach leg MAIN DIAGONALS AND PLAIN CHORD BAR.S. Nil- Bepth Thickness Depth of heads Thickness 1 Di.atneter of ' Length centre to F.x.n of heads eyes centre of eyes length HIP VERTICALS AND COUXTER.S. No. Sectio Diameter of en- Lengths of loop larged end eyes Lengths centre of eyes to ends, or centre of eye to centre of eye LATERAL AND VIBRATION RODS. No. ' Diam, ' Diameter of U-iigth centre of eye enlarged end to hend or ioop Ungth centre of bend or | Length centre of bend or ••■ye to end of short piece | eye to end of long piece STRUT.S OF TRUS.SED CHORD BARS. No. of Sectii Sizes of heads Section of Ungth of Ungth of strn, cen- | Extre.ne length '"■ssmg I trnssing ' tre to centre of eye of stmt SIDE nRACING. ^''i. .Scctit •Size of connecting-plate Extreme length of brace IRON HAND RAILING. No. of posts I Si.es of posts No. of panels I SiVeofp.anel panel Total length of railing 1 88 Plates Angles ORDINARY IROX HIGHWAY-BRIDGES. nUILT FLOOR BEAMS. No. No. Wi.lth l-etjs Thickness Weight per foot Finished length Finished lenglh 1 III', ! lilies Angles No. No. TRUSSED FLOOR ItKAMS. I-lie.inis . Angles . I'hles . No. 1 No. 1 No. 1 tepth I.e«s Width Weight per f.ioi Finished length Weight per fmit | Finished length Thickness | Finished length ROLLER AND BED PLATES. No. No. Width Legs Finished Thickness Weight per f(X)t NAME PLATES. OTHKK SEPARATE PLATES. Width Di.imcter Thickness PIXS AND THEIR NIT'--. Size of nuts Finished length Finished length No. Dntc. Finished length length under head, or extreme leii;;tli No. Diameter .Angles . Channels . Tee-iron . No. No. No. BOLTS AND THEIR NUTS. Size of nuts length under head, or extreme length BRACKETS. Legs Depth I-egs Weight per font Weight per foot Weight per foot ORNAMENTAL WORK. No. of pieces Description Extreme length Kxtreme length I'.xtrcme length 1 Finished length Kinislied length ORDINARY IRON NIGI/IVA V-BRIDGES. HF.AM IIANOKKS AM) TIIKIR NUTS. 189 N.i. Section I Diameter of I Diameter Siie of nuts anil upset end of eye lockiiuis No. of nuts and lock-nuts Length of one Itg Finished length Finished length Finished length Finished length Finished length KnllclS . ( rii^s-rttcls >i.k-ii,irs . No. SKTS ()[• KOLJ.KUS. No. No. No. Diameter Iliametcr Thickness Length hc-iwecn shoulders Length hclwecn shoulders Width FILLKRS rOK PINS. FAternal diameter Internal diameter TURN nUCKLF.S A\n SI.KKVK NUTS, No. Tap« Kxtreme length F.xtrenie length Kxtreme length Length : F'inished length I'Lilcs . (Ilannels, No. No. JAWS. Width Depth Thickness Weiglit per foot Extreme length lixtrenie length head, or extreme len;;lli r head, or extreme length Extreme length Extreme length r.xtreine length No. Diameter WASIIKRS. Diameter Diameter of bolts SEPARATE RIVETS. length under he.ad] Kind of head Position in bridge j Parts connected PIN PILOTS. External diameter Internal diameter Some companies send also a complete bill of rivets to be used in the shop ; but this is scarcely necessary, as it is more properly the place of the manufacturer to prepare such a bill. 190 ONn/XAKV INOX HIGIin'AV-liKIlH'.ES. The following form will be needed for the purpose : — RIVKTS. MemlMir No, ni.inicter (.oiiKlli between IkmcIs 1 Kiiiil of heads I'arls tonnectcil An allowance of three per cent should be made for waste in shop rivi *s, and from ten to twelve per cent in field rivets. If the hip verticals he Hat bars, they are to be transferred to the group of "Main Diagonals, etc." The posts, chord bars, and diagonals of trussed beams, are included under the general heads of " Posts," etc. The corresponding form of " Shipping Bill " is as follows : — *>! STRUTS. Menilier No. 1 Len>;th ccnlrc to end, ()r extreme len^jth M.irk BARS. Member No. Section Diameter of eyes Size,s of heads Length centre to centre of eyes ; .Mark Rons. Member No, i Diameter Diameter of eyes Diameter of 1 Threads \ l^"gth cemre of eye upset ends : R. or L. , '" ^■"''- '"■ ^'=""-'= "^ eye lo centre of eye Mark No. SIDE BRACING. No. 1 .Section K,\treme length Mark IRON HAND-RAILING. No. of posts No. of panels Mark, ii'aiy FLOOR-BEAMS. Extreme length Mark I I'jrts conncctcil \(.\e for waste in field rivets. )e transferred to osts, chord bars, nder the genera! is as follows : — ; lo centre of eyes j Mark ( ih centre of eye rrti, or centre of lo centre of eye ORDINARY IRON HIGHWA Y~BRIDGES. ROI,I.KK AND men I'l ATES. 191 No. Toniiion (fixed or free cnfl) M.irk, if any I NAME PI.ATKS. c No. Dtite OTHER SEPARATE PLATES. Position M:irk PINS AND THEIR NUT.S. Nil. ■ Uiamcter Length between shoirlclers F.xtreme length dimensions of end* Mark nOLTS AND THEIR NUTS. I'iameter ni.-,meter of upset ends , Length inrdcr head, or extreme length : URACKETS. Position Kxtreme length Mark : ORNAMENTAL WORK. No. of pieces Description Mark BEAM HANGERS AND THEIR NUTS. ^''). Diameter of eye No. of nuts and lock-nuts Mark ROLLERS. No. of sets 1 1 ,1 < 1! '.\i ' i' , ' i 1 1 ii i \ " fiji 192 ORDIXA R J • IROX lUClIW '.1 1 -BRIDGES. FIl.I.KKS rOR IMXP. No. External ilhuiictcr I Inlcrnal ilianicler I^iiRth Mark TURN l!L'CKI.i:S AND SI.KKVl-: NUl'S. No. Taps JAWS. No. INisilion Mark WASIIKRS. No. 1 >ianiLtcr niamclcr of bolt SI".r.\R.\TK RIVr.TS. No. I Diameter I I.eiiRlh umler head Kind of head i Position in liiidge | Parts conneuted PIN IMI.OTS. No. j l-'..\lernal di.unelcr Intern, d diameter .Mark Tlie followinj,^ is the system of maikini;- iron before shipment which the author would recommend. It should be thoroughly comprehended by the manufacturer, the foreman i.i chari^e of ert'ction, and the time-keeper or clerk, if there be either em- ploved on the work. Where the work is very extensive, the time-keeper generally checks the material as it arrives on the ,i;round. l'"irst, if there be more than one span, each piece of each span should be marked with a daub of color peculiar to that span : thus the first span may be white, the second yellow, the third bl-'c, etc. ; care being taken to choose such colors as will be readily distinguished upon the iron-work. The colors may be marked in the last column of each divisimi 'JOES. OJWlXAA^y /A'OX Uniinr AY-BRIDGES. I/Onslh Mark Mark meter of bolt ridge i Parts connecttd Mark l)cforc .shipment lid be thoroui;hly lan i.i charge of re be either eiii- -kecper generally 1. ch piece of each peculiar to that jcond yellow, the ich colors as will n of each division 1 t I ' I ,94 ORDLWIKV IRON HIGHIVAV-RRIDGES. Chord bars to be marked i A, i B, i C, 2 A, 2 B, 2 C, -tc. ; the numbers corresponding to those on the diagram, and the letters denoting the position in the panel, A being for those on the exterior side of the truss, B for those next to the outside, etc.- Side braces to be numbered to correspond to the panel points to which they belong, and to be marked R. or L. Iron hand railing rccjuires no marks except E on the end posts and panels, if these be different in any respect from the others. Floor beams to be numbered to correspond to the panel ]-)C)ints. Roller and bed plates to be marked R. or L., if there be any difference. Name plates require no marks. Separate plates to be numbered so as to correspond to the panel points to which they belong, and to be marked R. or I... if necessary. Lower chord pins to be marked L. o, L. i, L. 2, etc. ; the numbers corresponding to those of the panel points. Upper chord pins to be marked U. i, U. 2, U. 3, etc.; the numbers corresponding to those of the panel points. Portal diagonal pins to be marked P. Vibration-rod pins to be marked V. Pins at middle of posts to be marked I\I. i, M. 2, M. 3, etc.; the numbers corresponding to those of the posts. Lower lateral-rod pins not to be marked, for they should be shipped attached to the jaws. Bolts need no mark, but should be boxed before shipment. Brackets to be marked P. or L (portal or intermediate), also R. or L. Ornamental work to be marked R. or L. Beam hangers to be numbered so as to correspond to the panel points to which they belong. Rollers need no marks. , • , , Fillers to be marked the same as the pins to which they '^Tur^'n buckles and sleeve nuts, being attached to the rods before shipment, require no marks. )ond to the panel L., if there be any OliD/A'ARV //W.y niGHlVA J --BRIDC.ES. , 95 Jaws to be numbered to correspond to the panel points Vashers need no marks : they should be boxed, or strung on bolls, betore shipment. Rivets need no marks, but should be boxed r.lot nuts need no marks, as there are so few of them required In addmo,. to these marks, there should be others for those nK;.nbcrs wh.ch are to be riveted together in the field, and ulmh are assembled in the shop when the rivet holes pre- v.ously punched are reamed. These marks should be punched ■nto the n.)n with a steel point, and should consist of one, two three or four dots upon each of the pieces so assembl d, in Oder that no piece during erection will be put into the wrmig correspond to the i fr^ w %\ ^ ' i j ,- 1 ■ 1 > 196 ORDhX^lRV IRON HIGHWAY-BRIDGES. In il ■' ' ■ ; 11 ■ 1 . 1 J CHAPTER XX. ERECTION AND MAINTENANCE. The number of men required to erect an iron highway-brid<];e will vary from half a dozen to sixty, or even more, according to the length of span, width of roadway, location, and the time to be occupied in erection. For any one bridge, there is a certain number of men which will be more economical than any other number ; and it is only experience which will enable one to tell beforehand what this number is. " If there are too few hands, the work will lag, and difficulty will be experienced in handling heavy pieces : on the other hand, if there are too many men, the travelling expenses, and the time spent in travelling by the extra men, will be wasted, and the total amount of effective work tlone by each man per day will be less. If, for any reason, there be need for haste, it will be economical to have a large force of men, notwithstanding the last-mentioned consideration. For raising ordinary county bridges, the author would recommend the following numbers of men in a gang : io\- pony truss-bridges, six men ; for through-spans not exceeding eighty feet, seven men ; from eighty to one hundred feet, ei-ht men ; from one hundred to one hundred and twenty-five feet, nine or ten men ; from one hundred and twenty-five to one hundred and fifty feet, eleven or twelve men ; from one hundred and fifty to one hundred and seventy-five feet, thirteen or four- teen men ; from one hundred and seventy-five to two hundred feet, fifteen or sixteen men; from two hundred to two hun- dred and fifty feet, from sixteen to twenty-four men ; and, from two hundred and fifty to three hundred feet, from twenty-four ORDINARY IRON HIGHWAY-BRIDGES. 197 to thirty-six men. The long spans require a proportionately greater number of men, on account of the heavy sections For the same reason, the numbers given should be increased, if the bridge be wider than the ordinary size. For city bridges, which arc proportioned for heavy loads and for smaller intensities of working-stresses, the numbers should be increased from ten to twenty per cent. When great haste is necessary, the numbers .should ])e doubled. The most economical number of men will depend, too, upon their skill ; for green hands work at a great disadvantage in brulge-raising. They do not know how to use their stren-th and require the foreman to stand over them to show them how to <!.. their work ; besides, they are often so light-headed as to be unable to work aloft. Sailors make excellent bridge-men on account of both their agility and their training, which has taii-ht them to do in a few minutes many a difificult little piece of work that ordinary hands would puzzle over for hours It IS necessary to have a few experienced men in every o-an- • the more of them, the better, provided that their travelliito^ expenses, and wages when travelling, do not render their employment too expensive. The cost of raising a bridge depends more upon the foreman than upon the men. The best men will fail to do their full quota of work if the foreman be not energetic. Nor does it suKice to have simply a good worker for a foreman : he must know iiow to keep the gang busy, or they will stand by and look on, while he does all the work. He should also have their K<HH u-,11, or the progress of the work will be unsatisfactory I he outfit for a gang to raise ordinary county bridges should be as follows : — ■ forge, 2 pairs of tongs, 2 button setts for each size of rivets 5 ^In't-l'ins of each necessary size, 2 handle cold chisels, i aiullc drift p.n, 12 cape chisels, 6 plain chisels, 3 wrenches for \ nut.s, 3 wrenches for |" nuts, 2 riveting-hammers, i lio-ht ^loc Rc, r heavy sledge, 4 hand lines |" diameter, 4 guy lines > diameter by 130' long, 2 fall lines l" diameter by no'lon-^ 6 to lorope sling.s, 2 sets 8" blocks. 2 snatch blocks, 5 steel I 198 ORDINARY IRON HIGHWAY-BRIDGES. crowbars, 3 cross-cut saws, 2 augers i" diameter, 2 augers I" diameter, 4 augers f" diameter, 3 axes, 2 adzes, 8 timber trucks, 4 monkey wrenches, 4 chains, 2 crabs, 2 holding-on bars, 3 jack screws, several large wrenches for pins, and, if neces- sary, a pile-driver with its appurtenances. The ordinary weight of a pile-driver hammer varies from sixteen hundred to two thousand pounds ; and the height of the driver is about thirty feet. The cost for such an apparatus complete is about two hundred or two hundred and twenty-five dollars. If the gang be a large one, or if the span exceed one hundred and fifty feet in length, the numbers of some of the tools on the list will h.;ve to be increased ; for instance, those of the bars, ropes, and timber trucks. Bridge carpenters generally carry tools of their own : so, if there be much timber work in connection with the bridge, it will be sufficient to employ more carpenters, and not to pur- chase a larger outfit of carpenters' tools. In getting ready to 'erect a bridge, the first step is to prepare the ground in the neighborhood of the site, so that there will be room to store the material and for the men to work. When the iron is received at the site, it should be checked, and niiy pieces from which the marks have been obliterated should he re-marked. The iron should be piled systematically, similar parts being grouped ; and no iron should be allowed to lie uix n the ground. It should be piled so that there will be no trouhic in getting at any piece which may be required ; and the parts to be used first should be placed nearest the bridge site. The piers and abutments will be supposed to be erected, as this work does not aim to treat of foundations. The next step is to put the falsework in place. If the bed of the stream be dry, or nearly so, the bottom hard, the distance from the bed to the lower chord less than eighteen feet ; and if there be no danger of a sudden rise of water with a swift cur- rent, the floor and joists can be used for falsework. If the distance from the bed of the stream to the bottom chord be greater than eighteen feet, and the other conditions be the same, timber bents on mud-sills will be required. The size of a mud-sill should vary from 6" by 6" to 1 2" by 1 2", accord to be erectc(l, as ORDINAR V IROX HIGH II VI V-BRHJGES. 1 99 in- to the hardness of the ffround, the weight upon the sill, and the height of the falsework. It is not necessary that the tim- bers be square. For ground not especially hard, wide timbers lai.l on their flats are preferable, because they distribute the ])ri'ssure better. If there be but one tier per bent, two posts will be enough, when the width of roadway does not exceed si.xteen feet. Tiicsc- posts should batter about one inch to the foot, and should be cn\ereil by a cap about 6" by 6" or 8" by 8", long enough to i^-o- jcet two feet beyond each truss. The upper ends of the po^ts should lie directly under the trus'ses, and the caps should be (hift-bolted thereto, i; the roadway exceed sixteen feet, there should be an intermediate vertical post. The bent should be braced by diagonal flat timbers, say from 2" by 6" to 3" b)- 8", according to their length, running in opposite directions, one on each side of the bent, and bolted or spiked to the posts and cap. If there be two tiers in a bent, the inclined posts should batter two inches to the foot (or three inches if there be dan-er "I High wind), and there should be a vertical post under eJch miss. liach tier should be bracerl with diagonal timbers, as before. The greater the danger of high wind, the more effec- tively should each bent be braced. Alternate consecutive bents should also be braced diagonally on their outer faces, and all consecutive bents should be connected by longitudinal horizon- tal planks well spiked to the caps. These planks will be useful, in fact often necessary, for the workmen in passing from bent to bent. If there be more than two tiers per bent, the batter "1 the inclined po.sts should be three inches to the foot. A ,^o;k1 jieight for each tier is sixteen feet. Where the bottom is soft, or where the water is deep and I'lpid, piles will be required to rest the bents upon. There should be from two to five piles per bent, according to the width of the latter; a pile being placed below each vertical and inclined post. These piles should be braced in the direction of the stream by flat timbers bolted thereto. Any bracing that mav he given them transversely to the stream shoukf^be at such a distance above high-water level as to cause no obstruc- tion to boats, trees, ice, or other floating objects. Ji 200 Oh'D/A'ARV /RO\ llhillWAV-niilDGES, If the bottom be bare rock, incaiKible of holdini; piles, the nnid-sills must again be resortcil to. Tliey should be weighted so that they may be sunk into place, then drift-bolted to tiie roi k. This can be done without the aid of a diver. Of course the sills must be firnily attached to the lower tier before being put do Wl). I'he lops of all piles should be cut oif to an exact level, sn that, when the bents arc- erected, the ui)per surfaces of llu' upper caps will lie in the same hori/ontal plane. On these caps should be placed timber-beams stretching from one bent to the ne.xt, and lying immediately under the trussis: joists will answer the purpose. It is generally customary to place the bents under the ])anel points ; but the author |)refers to jiut them two feet to one side, so that the floor beams may ho swung into place without taking down the falsework. This method may, and probably will, recpiire an extra bent at one end of the span; so, if the bents be expensive, it is better to put one under each panel point, and remove the ui)i)er tiers before swimm- ing the floor-beams. The level of the top of the longitudinal beams should be at least six indies below the feet of the posts, so as to permit of the use of camber blocks, like those shown on Plate VII. The angle which the contiguous faces make with the horizontal (less, of course, than the angle of friction ol the wood) enables the untler block to be easily knocked out when the span is to be swung. The timbers for the caps and posts of the falsework are gen- erally square, and the sizes for the latter are to be ft)und from Table XXXIX., after the stresses in them have been ascer- tained as foil ows Let \]\ = weight i)er foot of the iron-work of the l)ridge, W., = average wci,L;lu per foot in lieiglit of one bent of falsework and the tiniliers whose weij;lit it s\ii)i)orts, p =: wind pressure i)er sijuare loot, A = area per lineal fool which the two trusses ])resenl to tlio wind (it is generally a!)0ut five or six scjuare feel), A! — the average area subject to wind pressure per foot in height on one bent, ami its share of longitudinal bracing, /= i)anel length, OA'D/NAJiV IRON niGHWAY-lUUiHil'US. IS strctcliin<r fro 201 :mtl then .•„ c.,, c„ etc. = horizontal distance l)otu-ecn centre h'nes of inch-ned posts niuasured along the caps, rt'= dejUh of truss, ./,. ./,, d„ etc. = heights of the different tiers commencing at the top A = vertical distance between centre of chonl and upper cap of bent, 6 = the angle wliieh the inclined posts make with the ver- tical ; pA/= i)rossnre on trusses at each panel point, />/t'l/^ = i)ressiire on U])per tier, />A',/, == |)ressure on second tier from top, /.'/V3 = pressure on third tier from top, aii.l the stresses /'„ F,^, /r, etc., in the inclined posts of the hrst, second, and third tiers respectively, will be Lnven bv the equations, ^ L-.-'- + . sec 6, /; = c»v:c. + &c. hcse formulas are obtained under the supposition that the ■nclincd posts are not aided by the vertical ones, which suppo- ■sition IS necessary in order to avoid anibi-uity : it would be correct, were the falsework on the verge of overturning If the tunber be green, the error thus made upon the side of safety .spdvantageous ; but, if the timber be dry and of good quality, ,t IS permissible to make a slight reduction in the size K.vcn by Table XXXIX. In applying the table, find the size of 202 oRD/A'AJiy /A'OA' n/ami'Ay-jiR/ih,/:s. '. its scjiiarc timber rec|iiirc(l for a stress I\ and lenj^th ^/, sec 0, that for a stress l'\ ami length d^ sec ^, etc., then take the greatest of these sizes. The vertical posts should be .strong enough to withstand a working-stress given by the equation, where // is the number of the tier considered, and S the stress in the corresponding vertical post. One dimension of the vertical posts should be the same as the side of the square which is the .section of the inclined posts; so that the diagonal braces may be flush with the entire faces of the bents, and be bolted to the verticals without the inter- vention of filling-pieces. These equations seem very long, and no doubt many practical bridge foremen would look upon them with disdain : neverthe- less, if the falsework is to be designed by any other method than that of guessing, this is the way in which it should he done. The more elevated the bridge, the more important does it be ome to properly proi)ortion the falsework. The values of ]Vi and A' will have to be assumed, or roughly calculated, before applying the equations. The other quantities are, or shoiikl be, known. The value of /> may be taken from ten to fifteen pounds per square foot, unless the situation be mure than ordi- narily exposed, when it may be taken at twenty pounds. Bridge companies can afford to risk the chance of a hurricane striking the bridge before it is swung. The sections of the caps are generally made the same as those of the inclined posts. The caps should be dapped to receive both upper and lower ends of vertical and inclined posts. The vertical posts should be drift-bolted through the caps, the bolt being long enough to project five or si.x inches into each post ; and the inclined posts should be held in place by wooden splice pieces, one on each side of the bent, project- ing above and below the cap, and fastened at each end by a bolt passing through the two splice pieces and the post. This attachment may be used for the vertical posts instead of the OKJ)/\.tA'y /KOX HIGIlWAY-Iil^lDaES. 203 h to withstand a and .S' the stress drift bolts, if it bo preferred. For additional security against slippin-, a third bolt may be put throu-h the splice pieces and the cap; or cleats may be nailed to the latter above and below at the toe of each inclineil post. All bolt holes in timber should be accurately located and bored before the falsework is erected. On this account the bents should be all built after one pattern, so that the parts may be interchangeable. If the bents be of different hei-hts the variation may be effected in the lowest tiers. Holt.s* arc' always preferable to spikes for connecting timbers, especially when the falsework has to be taken down, and re-erected for another span. Care should be taken to avoid any unnecessary injury to the timber, in order that it may not be sold at too tjreat a loss after the work is finished. There should be at least two plank walks on top of the lower falsework, exterior to the trusses, and a runway midway between, formed of several joists set on edge for the purpose of brin-in- out the material thereon upon timber trucks. '' '"^ The posts of the upi)er falsework should rest on the caps of the lower falsework, a few inches inside of the trusses, unless the i)ents are placed beneath the panel points, in which case they should be placed two feet to one side : they should be attached to the caps by splice timbers and cleats. The hei-ht of the upper falsework should be such that the upper surfac'of the caj) wdl be at least si.x inches below the under sides of the upiK-r chord .sections, so as to pennit of the use of camber i)l(ieks between. The author would suggest that the end bents of upper false- work be made three or four feet higher than the others, and the use of four posts instead of two (one on the inside, and one on tlie outside, of each truss), in order to aid in raising and holdino- ui place the heavy batter braces. After the latter are put in position, a horizontal timber may be firmly bolted to the bent at the level of the other bent caps, for the temporary floorin- to '■^'st upon. Stout beams stretching from bent to bent wil? be icciu.red as fulcra for the levers by which the chord sections a>e handled. The ui.per falsework should be braced by diao-o- iKil timbers, both longitudinally and transversely. The sizes'of J 204 ()A'/)/A.iA'i- /A'ox ///(,// ii'.i r-/.7v'//n;/;.v. the posts should tjencrally be about 6" by 6" : when the trusses are hij;h and the chord sections heavy, it might be well to increase the size to 7" by 7". The caps of the upper falsework should be deeper than their breadth ; because they have to act as beams, and may be subjected to considerable shock when the chord sections are being put in place. The method of bracing shown on Plate VII. is specially advantageous in this respect. In both upper and lower falsework, the diagonal bracing in planes parallel to the axis of the bridge should, for economy's sake, be placed between alternate pairs of bents ; tiiat is, every other space between bents should be braced. The end spaces shoulil, however, be braced in any case. Plate \T1. gives an illustration of how the working-drawings for falsework should be made. For economy of space, the scale has been taken at an eighth of an inch to the foot ; but it should, if intended for an actual case of framing, be four times as great. A drawing of this kind should be accompanied by bills of lumber and iron, prepared in a similar manner to that given in Chapter XIV. for the span. Measurements of distances between bolt holes should be both calculated and scaled. Those on Plate VII. were simply scaled, as the plate is intended for illustration only. The foreman of the work should be provided with a blue print of the working-drawings for the bridge, unless the type of structure be one with which he is perfectly familiar. He must also be provided with a " Raising Bill," which should consist of a skeleton diagram of one truss, with the following information written thereon : — Size of each truss strut, and tie, and mark for same, also number of pieces of same in a panel of one truss. Diameters and lengths S. to S. of truss pins, with their marks. Diameters, lengths, and marks of fillers for same. Sizes and marks of all separate plates belonging to the trusses, each in its proper position. ■ »' .if sr O/W/A'.l/n- /A\hV niC.HUWV-lih'llH-.ES. 205 to the trusses, each A (liafjram for the lower lateral system, giving the following information : — Sizes and marks of rods. riisitions of same, showing which eyes arc to go next the trusses. Sections, len},'ths, and marks of lateral struts. Diameters and lengths of lateral pins, if any. Diameters and lengths of fillers for same. Si/.es and marks ol jaws, if there be any difference between them. A diagram for the upper lateral system and portal bracing, giving the following information : — Sizes and marks of rods. Positions of same, showing which eyes are to go next the trusses. .Sections and marks of lateral and portal struts. Diameters and icngtlis of jjortal pins. Diameters and lengths of fillers for same. 1 )iameter and length under head of portal strut attaching bolts. lie should also be provided with a plan of the bottom chord packing (the transverse dimensions being exaggerated, so that the .size of each piece may be written thereon), a bill of bolts, giving the number and position of each kind, and a clear state- ment of the system of marking the iron. liefore starting to erect the bridge, the foreman should study carefully all the plans, so that he will have a clear picture of the bridge in his mind's eye, and will not have to be continually referring to the drawings during the erection. On a work (If any magnitude, there should be kept on hand a few standard nuts of each size ordinarily used, so that the loss of a nut 01 two will cause no delay : for the same reason there should be a tew extra bolts of each size. The material, as a general rule, is all piled on one side of the >trcam : the raising should therefore be commenced at the other side, so that the passage of the material will not interfere with the work. If there be no objection, the far end of the bridge should be the fixed one, so as to start from something pernia- nent ; but this is not absolutely necessary. To illustrate the method of raising, take, for example, the 2o6 ORDINARY IRON HIGHWAV-nRIDGES. iiHIl' M bridge treated in Chapter XVI., and assume that the founda- tions, with their anchor liolts and falsework, are in place. The first thing to be done is to lay out the centre line of the bridge upon the falsework caps, marking it with a small-headed tack on each cap, then the centre lines for the trusses in the same way. This can be done either with a transit, or with a carpen- ter's chalk-line ; care being taken to make the transverse measurements to the outer lines exactly perpendicular to th«; central line. A test of the accuracy of the perpendiculars can be made by the three, four, and five method, using a tape-line. Next, mark the exact positions of the panel points upon the longitudinal beams under the trusses, and place the camber blocks, levelling over them so as to make the lines joining the central points of their upper surfaces parallel to the curve of the chords. It is better to have the blocks a trifle high, say, an eighth of an inch near the centre, and a sixteenth of an inch near the ends. Four small nails will hold each pair of camber blocks from slipping during the work, and they can be left so as to bo easily extracted before swinging the bridge. Next transfer the centre lines of the trusses to the tops of the camber blocks, and mark accurately the first panel points from the fixed end, then, starting there, pack the chord bars of both chords. It might be convenient to have a few hard-wood pins to fit the holes pretty tightly, so as to aid in getting the bars properly placed longitudinally. After the chord packing has made some progress, run out the two batter braces, and hoist them into place by means of pulleys attached to the cap of the first bent of falsework, which bent should have been previously guyed and braced so that it canmit possibly be disturbed by the effect of the pulleys. As soon a.s each batter brace is raised, and the anchor bolts pass through the holes in the shoe plate, the nuts should be tightly screwed down in order to aid in holding the batter brace in position. It will not do, however, to rely solely on these, for the threads of the end bolts might be stripped : consequently a hard-wood supporting block must be strongly bolted to the two adjoining posts of the bent of the upper falsework. This block igress, run out the ORDINARY IRON HIGHWAV-niUDGES. 207 Should have a bevelled ed-e, the angle of bevel bein- equal to the slope of the batter brace, so that the iron-work will not rest on a sharp edge of wood. If the lattice bars interfere with the hcaruig, as they arc liable to do, rough notches can be cut in a ninuite on the bevelled face so as to bring the bearing upon the channels. Meanwhile the end lower lateral strut, the portal struts, and the portal and end lower lateral rods, having been run out, the thiee struts are to be put into place ; the upper ones being re- tained there by their connecting bolts, and the lower one by the end pins, which should also pass through the chord bars, fillers, and end lateral rods. Such small portions of the structure as pins, fillers, and beam hangers, should not be brought out upon the falsework until required for use, for fear of their being lost overboard. Nothing more will be said about running out these and other sniall por tions. but it will be assumed that they will be at hand when wanted. It should be an understood thing between the fore- man and the men, that any one who drops any portion of the hridge into the water forfeits a certain amount of his wages .Such an arrangement will make green hands a little more care- ful than they are apt to be generally. As the portal rods are adjusted by turn buckles with sino-le tap ends, they may be omitted until after the portal struts are riveted to the batter-braces, because the riveters can then work to better advantage. They can be left upon the abutment until ret|iiired. •Next run out, and hoist upon the falsework, by means of pulleys attached thereto and timbers used as levers, the end .sections of the top chords, working them into place by the lovers, and attaching them temporarily at the hips by bolts, puttnig in at the same time the end diagonals, but omitting the liip verticals and fillers, so that room may be left for the hold- m,-;-on bars. The other ends of the chord sections rest on the (.amber blocks. Next run out, and hoi.st into place, the first vertical posts, Ivttmg the upper ends lie in the open ends of the chord sec- tions. ?o.s ORf^X.lR]- /NO.\ lin'.inVAY-BlUDGES. m Now start the rivet i;ani;- at work on tlie portal, and let them follow up the work as it progresses, not leavinij the portal until they have made the hip attachment, connected the portal struts, and put the brackets and ornamental work in place. Next briny; out the second sections of the top chords and the second set of diagonals. Raise the chord sections into place, as before, with pulleys and beam levers, holding them there until temporary bolts are put into a few holes through the con- necting-plates, filling-plates, and channel webs, and until the pins are run through the posts, diagonals, and fillers. The latter, in this case, will not interfere with the riveting. Ne.xt run out and put into place, as before, the second pair of posts ; then bring on the third sections of the chords, the third set of main diagonals, and the first set of counters, putting all three into place as before, and so on until the end of the bridge is reached. Meanwhile the wooden lower lateral struts should have been framed, and the jaws attached to their end's. Just before the riveters complete the riveting of the jiortal, the first upper lateral and intermediate struts should be run out, and bolted into place ; but the upper lateral and vibration rods should be omitted, as they would be in the way of the riveters, and can be readily inserted afterwards. About the time that one-half the span is erected, commence running out the lower lateral struts and rods, putting them into place, inserting the hip verticals and fillers, and coupling the lower chords into their final position, leaving the beam hangers lying horizontally, so that, when the longiludinal supporting- timbers are removed, they will drop into their proper places. A little before the riveters reach the end of the span, the upper lateral and vibration rods slK)uld be put into place, and screwed up about the right amount. When the end of the bridge is reached by the riveters, and as soon as they have ri\eted the hip connection, and attache,', the main diagonals and hip verticals, the last couplings of the bottom chords can be made at the pedestals. The shoes rest upon the rollers, which should have been put in exactly transverse to the direction of the bridge, and blocked so that they cannot move. ORDIAARV IROX niGini-AV-BRIDGES. 209 The last connection for each truss can easily be made by raising the h.p either with levers or by jack-screws, and either pressing against the shoe with jack-screws abutting against <,cks chained to the roller plate, or by attaching a ptir of blocKS to the pedestal and first panel-point lower chord pin After the final coupling has been made, and the riveting is fin.shec knock out the upper chord camber blocks, so as to bring a the weight of the upper part <,f the bridge upon the posts ; then take down the upper falsework Next knock out the camber blocks of the lower chords, lovvcr- .n,^^them together gradually so as to bring no shock upon the X.xt run out the first floor beam to the end of the bridge, and rcn.ne the runway of the second panel, in order that the beam nuiy be dropped between the lateral struts and lateral rods, and swung into place, lowering it beneath the ends of the han-^ers then raising it up. inserting the filling-plates, putting on%he anger plates, and screwing up the nuts. lu this way attach 11 t c loor beams, seeing that the hanger nuts are screwed up rnily but not to such an extent as to endanger stripping thL 'vads. 1 hen bolt all the wooden lateral struts to the iTeams Iinuigh the holes previously bored, which holes should be at Ic:.st a quarter of an inch greater than the diameter of the X.xt screw up every adjustable rod to the proper tension, u uh can be ascertained by the sound they make when tappec "illi a hammer. a^^'- Xcxt uash off any mud or other impurity that there maybe ho in.n-woik. and give it two good coats of paint wherLer he —sh will reach. The best kinds of paint to use are lead -n s, when they can be obtained unadulterated; but they are """ -^o'l. Iron oxide is a good paint, but requires more fre- H^'-'t a-newal. The color should be such as to readily show any M." of r..t : various shades of gray are efficient in L respect •""1 'He at the same time pleasing to the eye IlKrc remains nothing now to be done except to put on the i-^S floor, hand railing, and felly plank, a matter'so simple 210 ORDINARY IRON IIIGIllVA V-BRIDGES. that it is unnecessary to describe it here ; the only point worthy of attention being, that the joists should be dapped one inch on to the lateral struts, and that they should go on so hard that it will be necessary to drive them into place. This can bo accomplished by cutting each dap a sixteenth of an inch short, and bevelling the end of one dap slightly, in order to give the joists a start when they are being driven down. When they come to their bearings, they should be spiked to the lateral struts by a five-inch spike at each end, driven obliquely. In regard to the flooring, Mr. James Owen, C.E., in a paper read before the American Society of Civil Engineers, specifies as follows : " Lay no plank wider than nine inches. This pre- vents wide joints in shrinkage. Bore all holes for the spikes to prevent splitting, and put no spike nearer than four inches to the end of the planking.'^ In long bridges of several spans, it may be economical to dis- pense with the upper falsework by using a travelling derrick, running upon wooden stringers, for the purpose of handling the heavy ''sections. Under these circumstances, the whole of the portal might be connected while lying upon the falsework, then hoisted into place in one piece, and supported there In- shore timbers from the first bent of falsework. The brid-c should be completed as the traveller retreats : otherwise there will be difificulty in carrying the members past the traveller. The material should be brought on cars within reach of the derrick. , r , , , The last thing to be done is to take down the falsework, ami draw the piles f"om the bed of the stream. The latter is easily accomplished by a crab on the bridge ; the rope being attached to the head of the pile, which is vibrated transversely ni all directions while being lifted by the tension of the rope. There is no reason why a well-designed iron highway-brul-e, when properly cared f.-r, should n<.t last forever. Under loads which are light and slowly moving, compared to those of rail- road-bridges, the iron cannot possibly wear out ; and, when properly protected from the weather, it cannot rust. Of course the wooden parts of the structure must be replaced from time to time as they wear out or decay. ORDINAR V IRON HIGH W A V-B RIDGES. 2 \ r When knots begin to project above the surface of the floor they should be adzed off, both for the comfort of those drivin-' over the bridge, and to prevent vibration. After half an inch has been worn off one side of the planks, they should be turned over; and when another half-inch has been worn off, or before bcTqlced '"''"'^ ''''''' ''^"' °^ ''''^"''' ^^ ''"'">'' *^">' should It would be well for county commissioners to buy all the liunbcr needed for renewal a year before required for use so that It may be well seasoned. Iron bridges should be thoroughly inspected for rust spots at least once a year; and. if any be found, the bridge should be rcpauuccl One or two spots in places where something might have rubbed off the paint may be touched up with a brush ; but generally speakmg, when rust spots begin to appear, it show that two good coats of paint are required Immediately I he adjustable members should be tested occasionally by tappu^g wth a hammer. This duty should not be intrusted to an .gnorant workman, who will turn away on the nuts until he s ears the thread or breaks the rod. . Whenever, in driving over a bruise, any of th. iron-work rattles, it shows that something is ou ;f fj-tmcnt. Generally speaking, a well-proportioned H budge wdl not get out of adjustment unless some one rit" ff ""'' " '"^" '"^''^^^- ^^'^h combination bndge. It ,s a different matter, for the shrinkage of the wood may loosjn the counters. 11! 'm - ■' < • APPENDIX L A NEGLECTED CONSIDERATION IN HIGHWAY-BRIDGE DESIGNING. Sim: ciFicATioNs for highway-bridges generally call for strength to resist a wind pressure of at least thirty pounds per square foot of exposed surface ; but there are many such structures in the United States whose trusses would not, unaid-^d, withstand this pressure. Granting that the lateral rods are large enough, that the upper lateral and portal struts have sufficient strength to resist both direct thrust and bending, and even that the lower lateral rod connection is all that could be desired, still the bridge may be far from fulfilling the requirements, as the following investigation will show : — Let and then / = the assumed pressure per square foot, A = the area in square feet per lineal foot of the vertical pro- jection of that i)art of the structure lying below a hori- zontal i)lane, whicli passes midway between the chords of a through Pratt-truss bridge (the windward truss and hand-rail are not supposed to slielter the leeward ones) ; /// = IV = wind load per lineal foot for the lower lateral system when the bridge is empty. Let ^1 = the total area of bridge per lineal foot exposed to the wind pressure, // = the vertical distance of the centre of pressure above the level of the bed-plate, / = the panel length, "5 Ik 2l6 i\ • I I ■ '4 II 1 ■'"i \ > ' \ : 1 f I: and APrKXDIX I. b = clear width between trusses, c z= width of one truss, (/ = depth of trusses, lV^ = dead load per lineal foot for one truss, ly^ _ reduced dead load per lineal foot for the windward truss ; then the overturning moment of the wind per lineal foot is /J,//, and it has the same effect as that of a couple of lever-arm /; + ,-, and force, b-\-c' that is, the weight per foot on the leeward truss is increased, and that on the windward truss is decreased, by this amount, which gives the equation, n = number of panels in the bridge, n = number of any panel, counting from the nearest end of the span ; Let and then and IV/ = panel wind load, IV.,/ — reduced panel dead load. The compression on the windward bottom chord of the «/* panel will be ^{n-n^lV-^, if we consider that the inclination of a lateral rod to a line per- pendicular to the planes of the trusses is tan - 1 ^. The tension in the same panel, due to the reduced dead load alone, is except in the case of the first panel, to find the stress for which //j must be made equal to two. APPENDIX /. the windward truss ; m the nearest end of m chord of the nC" ral rod to a line pcr- in ~ ^ T- The tension load alone, is : the stress for which 217 Now, if this tension be less than the compression just found tlic chord at the panel considered, if not a compression member' or If It be not externally aided, will buckle ; for flat bars cannot ho .died upon, when acting separately, to resist compression Ihe following inequality should, therefore, hold true : — {n, - !)(« _ n, + I) J^-'> „.(« _ n,)^^^. H) inspecting the chord stresses in a few Pratt truss through i.ndges. It can be readily seen, that, if this inequality hold true for the second panel, it will hold true for all the others The three following cases are fair samples of bridges with wiiKh the author has met in his practice. The wind pressure assumed is thirty pounds per square foot. ('^ A 140' span of 12' clear roadway is 23' deep, consists of seven panels, weighs 460 pounds per lineal foot, presents to the wind about SIX square feet of surface below the middle horizontal plane for every lineal foot, and about eight and a half square feet above and below. The centre of pressure is about 8 feet alx.ve the shoe plate, and the width of the truss is i foot These data give W^ = 73, and, for the second panel, W„ and («i-0(«-«, + i)7=xg. W «i(« - «i)-, = 150. (2) A 150 span of 14' clear roadway is 24' deep, consists of cigh panels, weighs 540 pounds per lineal foot, presents to the wuK about six and a half square feet of surface per lineal foot lor the lower lateral system, and about nine square feet above and below. The centre of pressure is about 8| feet above the shoe plate, and the width of the truss is about i foot 1 hese data give \\\ =117, and, for the second panel, and '^ n^\n — «i)-j = 167.1. ft i8 APPENDIX /. (x\ A 1 20' span of 16' clear roadway is 22' deep, consists of six panels, weighs 530 pounds per lineal foot, and presents the same surface per lineal foot as in the last case. The centre u pressure is about 7-1 feet above the shoe plate, and the width of the truss is I foot. These data give W^ = 146, and, for the second panel, («, - i)(« and VV tiiin - tii)-j = 97-5- In all these cases ^ («, - i)(« - «j + ^)-f < «i(« - «i)t' How is it, then, that more bridges do not fail by the bucklins of the bottom chord under wind pressure ? For two reasons. First, the probability of a bridge ever being subjected to a pressure of thirty pounds per square foot over its whole length is very small ; and, second, that in a well-built bridge, where the joists arc dapped to the floor beams, the joists would take up the compression that would tend to buckle any panel of the chord except the first. , . , , i In view of the fact of the small chance that a bridge has ol ever being subjected to the assumed pressure, it would be legiti- mate to trust somewhat to the stiffness of the joists in cases where ^ ry («, - i)(« - «, 4- i) ^/' < «i(« - «i)T' and not to make the chords stiffened throughout, except in short 'Ti^, as the joists cannot stiffen the end panels, the chords in these panels should be proportioned to resist the compression due to the difference between the longitudinal component of tht greatest stress in the end lateral rod, including the initial ten- sion, and the reduced dead-load stress, whenever the former .s in excess of the latter. It is often well, for the sake of hot rigidity and appearance, to stiffen the chords in the second panels when those in the first panels are stiffened. APPENDIX I/. 219 APPENDIX II. hout, except in short and DEMONSTRATION OF FORMULA FOR FLOOR BEAMS. Let the notation be the same as given on p. 19, viz. : — A ^ = area of bottom flange in square inches, A' — area of web in stiiiare inches, A" = area lost by a rivet hole in square inches, ly = the uniformly distributed load in tons, Z = length of beam in feet between centres of supports, /? - depth in feet between centres of gravity of flanges,' T = intensity of working tensile stress in tons. The moment at the centre of the beam is ^^. Let us take the centre of moments at the middle of the web, which will correspond w.th the neutral surface, if we assume, which is nearly true, that the upper and lower flanges are of the same area, and are subjected to numerically equal stresses The moment of the load is resisted by the sum of che moments ' of the flange stresses and those of the web stresses. The sum of the moments of the flange stresses is 2{A-A")Tx~={A-A")TD. ^ J^hej-esisting-moment of the web stresses is found as fol- The resisting-intensity of stress on the fibre most remote rom the neutral surface may be taken equal to T; then that for any fibre ^^ the distance .r will be, by the common theory of flexure, -^f. The stress on an elementary area at this :'A ] 1 gives, for the total resisting-moment of the web, D '^7>-=f[(?y- (-?)']= Equating-moments gives APPENDIX II. distance will then be ~bdx, where b and D' are respectively the width and depth of the web. The moment of this stress is ^-I^.bdx, integrating which between the limits ^ D , ly ;c = H and ^2 2 bTiy = \ATiy. = (^A- A")TD ^\A'Tiy. If we put D for U , we will commit a small error on the side of safety ; then will and therefore ^^ = TD{A - A" + \A'), A-^L iA' + A" Q. E. D. If M be the moment at any section of the beam, and R the intensity of stress on the fibre most remote from the neutral surface at the same section when the beam is fully loaded, we can write the equation M=ARD^-\A'RD, where A is the area of the top flange, and V is, as before assumed, equal to D; from which we have M D{ATwy M S=RA = 4-0 where .S is the stress on the upper flange at the section consid- ered. This last formula is useful in determining the rivet spacing in the flanges of built floor beams and plate girders. APPENDIX HI. 221 y are respectively it of this stress is ts APPENDIX III. ;rror on the side of ; beam, and R the e from the neutral is fully loaded, we id V is, as before ; the section consid- ermining the rivet nd plate girders. METHOD OF FINDING THE LENGTH OF THE LONG DIAGONALS IN A DOUBLE-INTERSECTION BRIDGE. Let then and or /= panel length of bottom chord = GD or DB in the accom- panying diagram, c = half increase of panel length in top chord, d = depth of truss between centres of chords = AB, a = angle between radial line at panel point and perpendicular to lower chord ; • -1 ^ « = sm — , a DE:c::l:d, DE = i BG^.G£=.s/^^=2^^''^. .(LJ". When the camber is small, BG can be taken equal to 2GD In triangle A£G, AB and BG are known, also angle ABG = 90° + 2«. if 222 APPENDIX ITL AB + BG:AB-BG\: tan \ [i8o° - (90' + 2a)] : im\\_BAG-BGA'\; BAG-BGA = 2tan-i [^Irli^'^Gs"-")} Again : {BAG - BGA) -[■{BAG + BGA) = 2BAG = {BAG - BGA) H- (90° - 2a), which gives BAG; also BGA = 180° - {BAG + 90° + 2«) = 90° - (BAG + 2a) : finally, AG= AB cos BAG + BG cos BGA = length of diagonal required. t w \ \_BAG - BGA\ ; (45-.)} ), which gives BAG; - i^BAG-\-z(t)\ of diagonal required. ( i !:'■ 13' J ADDENDA. In an otherwise very favorable review of this treatise by The America.. Engineer," there was pointed out a serious halvSr "'"'^ attachment of a floor beam by Jour In the words of the review, "the inner loop will take neirlv ■not quite all the load at the panel point, when the bridg t ..^t adjusted; and this not only becomes constrained iLf f int: hr"'""^ f '""'^ ^^"^'^^ '''^''■* The numbe; 1 ^ ? r "^ ''■' ^°"^^^"t'y w^'-king loose, presum- ably by stretching, m railroad-bridges in which this detail is used, demonstrates its unsatisfactory character " The author has long recognized the inequality of distribu- >on of floor-beam load between the inner and outer hangers but considered that the low intensity of working-stress on these members would compensate for the objectionable in- "luality. Such has been also, in all probability, the opinion of most American engineers ; for beams, when not riveted to the posts, are nearly always suspended by four hangers. The fact the inner hangers working loose can have been only lately -vered It shows, however, that this detail needs improve' nt, uKl as hc> aim of this treatise is to design structures J^^^^^^^o^tjh^^ of so doing is to use single beam • Main diai;()nal. 221; 226 ADDENDA. hangers ; but this method will not always work, owing to the <acat bending-movements which they produce upon the puis. For instance, take the case of a 20' panel of a Class A bridge having a 24' clear roadway, and two 6' sidewalks. The weight supported by each single hanger would be about 23 tons, and the distance between centres of main diagonals would not be far from ten inches. These data give a vertical bending- moment upon the pin equal to 57-5 inch-tons, which aloue would call for an iron pin 4!" in diameter ; but, when combined with the horizontal moment, it would require a much larger pin than a practical designer would care to employ. The double hangers in such a case are a necessity, but the connection must be such as to distribute the load eqttally iq^on them. Such a distribution can be assured by using the follow- ing detail : — ,.111 On the under side of the beam at each end is attached by four rivets a plate about five-eighths of an inch thick, six inches Ion- and as wide as, or a little wider than, the beam flange, Th£ plate is placed symmetrically to the plane of the truss; and the middle of the under side is grooved so as to receive one-sixth of the surface of a pin about two inches in diameter, which rests in a similar groove on the top of the beam-hanger plate The lateral dimensions of this plate will be slightly greater than usual, but the thickness need not exceed three- quarters of an inch. To prevent the plate from rupture by bending, there are attached to the under side by countersunk rivets two angle irons, or plates bent into the form of angle irons, the vertical legs being connected by countersunk rivets, which in the neighborhood of the pin pass as nearly as may be through the neutral surface of the T beam, and elsewhere near the lower edges of the angles. As the axis of the pin is parallel to the length of the bndgc the vertical legs must be transverse thereto. This detail will be readily understood by referring to Plate VIII. _ To illustrate how to find the sizes of the stiffening plates, number of rivets required, etc.. let us design a beam-han^er plate, when the total weight upon the four hangers is ict. tons The centres of the beam-hanger holes may be assumed i, 5 ADDENDA. 227 to be situated on the corners of a six-inch square. This would make the bending-moment on the plate thirty inch-tons, which would be resisted by the T-shaped section of the two bent pates combined with the uncut portion of the beam-hanger P ate below the pin. Assuming the latter thickness i", and the plate stiffeners to be of 6" X 6" X i" angle iron, would make the T about 12" X 6f' X i", the centre of gravity of wh.ch ,s about 5' above the bottom. The moment of inertia IS, tlierefore, i', X 12 X (i.o)'^-h 12 X (i.o)^-hTV X r X (5.5)3 + 5-5 X (2.25)^ = 54-1-. The resisting moment is given by the equation M = d, so taking 7? = 4 tons. J/=1J<_14^ 43-2. As the bending-moment was thirty inch-tons, the sizes assumed are ample. It will be well to use three-quarter-inch countersunk rivets (the largest possible), so as to make the different portions of the T head act together. There is a tendency to bend the plate in a direction at rio-ht angles to the one considered, the moment for which is fifteen inch-f.ns on each side of the pin. This will be resisted by a couple whose forces act as compression on the top plate of ^he T, and tension on the rivets near the bottom of the an-les lakmg the centre of moments at the middle of the top plate and the distance therefrom to the horizontal centre line of the nvetj^ioles as 4! inches, will make the tension on the rivets i,i'? — 3.42 tons. Using an intensity of only two and a half tons, because of the initial tension on the rivets, will make the section required 1.37 square inches: consequently two i" rivets will be sufficient. l! 1 1 J! 11 228 ADDENDA. The difference in the total weight of iron per hneal foot caused by the use of this detail will be from six to ten pound., which weight should be added to those given in Tables I II., Tnd III., under the heading "Floor System/' whenever this style of beam-hanger plate is to be employed It will be noticed in the diagram on Plate V II., that the floor-beam stiffeners at the support are placed close together so as to take up the vertical reaction of the hangers transferred by the auxiliary pin. The sectional area of these stiffeners should be about equal to that of the hangers. Plate VIII illustrates a detail by which the foot of a pes may be riveted or bolted to the floor beam, for the purpose of aiding the distribution of lower lateral rod stresses among the chord bars. This is accomplished by means of a jaw plate be- tween the post channels, and by turning up the ends of the exterior re-enforcing plates, so as to permit the passage rivets or bolts. The latter may be considered pre erabc , they need not be screwed up very hard, but should ht with .rcat accuracy in the holes. Their object is to prevent tor- ^ion of the post, but not to aid the beam hangers in resisting ^'^ When this detail is employed, the lower chord pin at the first panel point should pass through holes bored in bent plates, which are to be well riveted to the floor beam. _ It is probable that most bridge designers wdl consider this arran-^ement to possess too much refinement for highway- bridges, preferring to trust to the rigidity of the joists as sug- ^^'¥here'is'no' doubt, though, about its being a detail that could be advantageously employed in railroad-bridges. When ve>rtical sway bracing is used, the detail or t e upper lateral strut connection, shown on Plate VIII., will be oun be an improvement on the one previously described, in that it obviates field riveting. ., 1 „f ti^A It consists in the use of a double ]aw on the end of t lateral strut, and two nuts of different diameters the pin be n aoubly shouldered. The office of the inner and larger to press the end of the strut against the chord ; and that of ■ I I ADDENDA. 229 the outer one, to take up the pull of the bent eyes, the injuri- ous effect of which is mitigated by the inner jaw plate. When no vertical sway bracing is used, the detail described on p. 98 will probably be preferable ; because it involves the spreading apart of the lateral strut channels, and thus furnishes a greater resistance to bending the strut. The use of the im- pr()^•cd detail will not affect the sizes of the lateral strut chan- nels as given in Table XXV. Plate VIII. illustrates also an improved connection for the portal struts, avoiding the necessity for field riveting. The increased depth of the jaw plate at the pin hole is an impor- tant feature, its object being to resist the bending effect of that component of the stress in the portal rods which is parallel to the length of the batter brace. Whenever the portal rods exceed ij"in diameter, this im- proved shape of jaw plate should be employed. n\ n M GLOSSARY OF TERMS. 'It Ml GLOSSARY OF TERMS. Adjustable Member. — A member of a bridge the length of which can be iiK K asrd or iliniinishcd at will. Angle Iron. — Iron rolled into the shape shown in section on Plate II Apex. — The intersection of a brace with a chord or flange; called al.so a paiK'l point. Axis of Symmetry. — A line dividing an area into two parts equal and .similar to each other, and similarly di.sposed to the line. Bar. — A piece of iron flat or square in .section. Batter. — Slope, or inclination, to the vertical; usually measured by the tan^aiit of the angle, or so many inches to the foot. Batter Brace. — The inclined end post of a bridge. (Plate I.) Beam. — A member intended to resist bending. Beam Hanger. — A rod or square bar supporting a floor beam from a clion! pin. (Plate I. and Plate II., Fig. 13.) Beam-hanger Nuts. - Nuts on the ends of beam hangers, serving to press the tl(,or beam against the feet of the posts or against the chord heads (Plate II.. Fig. 13.) Beam-hanger Plate. - A plate placed beneath the end of a floor beam for thu iRaiii-luinger nuts to rest against. (Plate JI., l"ig. 13.) Beam-trussing Posts. — Posts for trussing beams. (Plate II., Fig. 16.) Beam-trussing Rods.— Diagonal rods for trussing beams, (pfate II. Fitr. if).) ' Bearing. — A resting-place, usually for a pin or rivet. Bearing- Pressure. — The pressure on a bearing. Bed Plate. — A plate to distribute pressure upon masonry. (Plate III ) Bending-Moment. _ The moment of a force or forces which bend or tend to bend a piece. Bending-Stress. — The stress produced in a piece by bending. Bent. _ A frame of timber or iron, usually the former, as a bent of false- work. Bent Eye. — An eye on the end of a bar, the plane of which makes an angle with the direction of the length of the bar. Bevel. _ The slope on the end of a piece. 2,n '^i III* m 234 GLOSSA/^V OF TEM.IfS. Bill of Material. — A list of various portions of material giving dimensions and weights, or other quantitative measurements. Block. —A system of one or more pulleys or sheaves, so arran^^d in a frame or shell as to multiply the power of the rope passing around tlieni, or to change its direction. Board Measure. — The measure of timber, the unit being a piece one foot square and one inch thick. Timber is sold at so much per thousand feut board measure, usually written, per M. b. m. Bolt. — An iron rod with a square head at one end, and a thread and nut at the other . Brace. — Generally a strut, but sometimes the term is applied to a tie. Bracket. — A knee or knee brace to connect a post or batter brace to an overhead strut. (I'late I. or Plate II., Fig. i2.) Built-Beam. — A beam made up of plates and angles riveted together. (I'late II., Fig. 13-) Burr. — A rough edge or ridge left l)y a tool in cutting metal. The term is sometimes used for a nut. Button Sett. — A tool for forming the heads of rivets. Camber. — The upward curvature of a truss. It is measured by the heigiit of the middle point of tlie centre line of the lower chord above the line joining the centres of end pins. Camber Blocks. — Blocks of wood used in erection, so placed as to be easily removed (Flate VII.) Cape Chisel. — A tool for cutting iron. It consists of a rounded edge on the end of a sliort rod. The edge is very obtuse, so as not to break easily. Centre of Gravity. — That point of a body about which the weights of pll the different portions I)alance. Channel, or Channel Bar.- Iron rolled into the shape shown in section on I'late 11.. Fig. i. Check Nut, or Lock Nut. — A contrivance to prevent a nut from turning when sul)jected to shock. Chord. — The upper or lower part of a truss, usually horizontal, resisting compression or tension. (I'late 1.) Chord Bar. — A member of the chord which is sul:)jected to tension. (I'late I.) Chord Head. — The enlarged end of a chord bar, through wliich the pin passes. Chord Packing. — The arrangement of the bottom chord of a truss. Clear Headway. — The vertical distance from the upper surface of the floor to the lowest part of the overhead bracing. It is a measure of tlie licigiit of the highest vehicle that could pass through th- bridge. Clear Roadway. — The horizontal distance, measured perpendicularly to the planes of the trusses, between the inner edges of the batter l)races. It is a measure of the width of the widest vehicle that could pass llirougli the bridge. ..ii: GLOSSARY' OF TE/iAfS, 235 aterial giving dimensions i, and a thread and nut at :tion, so placed as to be Cleat — A narrow strip of wood nailed to something for the purpose 01 kwwwr a piece of work in its proper place. Co-efficient of Friction. - A numerical quantity, which, multiplied into the normal pressure, gives the frictional resistance. It is equal to the natural tangent of the angle of repose. Cold Chisel. — A tool for cutting iron. Column.- A pillar or strut; a long member which resists compression Component. -One of the. parts into which a stress may be resolved 'or divided. Compression. -A stress which tends to shorten the member which is siilijccted to It. Concentrated Load. _ A load which is, or may be considered, collected at one or more points. Connecting Chord Heads. -Chord heads used to connect bottom chord channels to pms. (Plate II., Fig. 10.) Connecting-Plate.- A plate!ised for connecting two pieces Contmuous Spans. -Consecutive spans connected over the points of support. Counter. -An adjustable diagonal which is not subjected to stress bv a uniloimly distributed load covering the bridge. (Plate 1 ) Countersunk Rivets.- Rivets, the heads'of which are let into one or both of the plates which they connect, so as to leave a Hush surface or surfaces Couple. — Two equal and parallel forces not acting in the same line. Cover Plate.- A plate used to cover a joint, or to connect two pieces of the top chord plate, (llate 11., Figs. 11 and 12.) Crab. -A slow-motion machine, worked by a crank for the purpose of winding a rope x\\Mm a drum, thereby raising a heavy weight. Dap.— To notch timber onto its bearing. Dead Load. -The weight of all the parts of the bridge itself, and any thing tiiat may remain upon it for any length of time. Deck Bridge.- A JM-idge in which'the passing loads come upon the upper chords or the upper ends of the jiosts. Deflection. -Motion laterally, or at right angles ro the length of the piece it IS also used for the amount of motion, and is generally expressed in inches Depth of Truss. -The vertical distance between the centre lines of upper and lower chords. ' Diagonal. — A member running obliquely across a panel. In this work all the (ha-onals except the batter braces are tension members. Diagram of Stresses. -A skeleton drawing of a truss, upon which are wrm, II the stresses in the different members. (Plate V ) Double Intersection. -The style of truss where the diagonals cross the posts at the middle of their length, as in the bridge shown on Plate 1 Double-riveted Lacing. _ Lacing in which each bar is connected by two "vets at each end, (Plate 11., Fig. 13,) 236 GLOSSARY OF TERMS. I I ■^f \[ Drift Bolt. — A round or square piece of iron, usually from one to three feet long, without head or nut, used to connect timbers. Drift Pin. — A slightly tapering rod of hard steel, used for making rivet holes coincide. Its use is more convenient than advisable. Effective Area. — The gross area of a section, less that lost by rivet or pin holes; the net area. Elastic Limit. — That intensity of stress at which the ratio of stress over strain commences to show a decided change. . For wrought-iron it is from twelve to fifteen tons. Erecting-Bill. — A bill of material for a bridge, so arranged as to facilitate the finding and placing of members during erection. Expansion Joint. — The connection of pedestal to bed-plate, shown on Plate 111. Expansion Rollers. — A set of half a dozen or more turned rods of exactly the same diameter, placed under the shoe plate at one end of a truss to permit of expansion and contraction. (Plate II., Fig. 9.) Extension Plate. — A jjlate riveted to the end of a strut channel, and pro- jecting beyond it, to permit of the passage of a pin. (Plate II., Fig. 12.) Eye. — A hole in the end of a member to permit of the passage of a pin. Eye Bar. —A bar with an eye at each or one end. Factor, or Factor of Safety. —Tlie ratio of ultimate load to greatest allow- able working-load. This term is getting out of favor among engineers, as its use has been somewhat abused. There is no such thing as a factor of safety for a well-proportioned bridge, for each member should have an intensity of workinc-stress proportionate to the character and amount of work which it has to perform. Fall Line. — A rope used in erection for raising and lowering weights. Falsework. — Temporary timber work to support a bridge during erection. Felly Plank. — A guard rail so placed as to catch the felly of a wheel, and thus prevent the vehicle from striking the truss. (Plate II., Fig. 13.) In wide bridges a felly plank is often placed midway between the trusses, to prevent vehicles passing from one side of the bridge to the other. Field Riveting. — Riveting done in the field, or during erection. It is the poorest and most expensive kind of riveting. Fixed End. — An end of a strut so firmly connected as to prevent all motion of the strut in the neighborhood of the end. Filling- Plate. — A plate tlie function of which is to make flush two surfaces (Plate II., Fig. 12.) Filler. — A small ring of iron or piece of ])ipe placed on a pin in order to keep in position the members coupled thereon. Fixed Load. — A load remaining i)ormanently, or for a considerable length of time, upon a structure or portion of h structure. Flange. — The upi)er or lower chord of a beam. It is the principal part for resisting either compression or tension. Flexure. — Bending. GLOSSARY OF TERMS. 217 ) arranged as to facilitate to bed-plale, sliown on re turned rods of exactly t one end of a truss to Floor, or Flooring. — That part of the bridge which directly receives the tr;v>rl. (Plate II., Fig. 13.) Floor Beam. — A beam to support a portion of the floor and its load. ll'latu 1. and J'late II., f^ig. 13.) Forge. — An apparatus for heating iron. Framing The carpenter work on timber. Giasticutus Rods. — A term (perhaps unauthorized, but in common use aiiiimg Imdge builders) to denote a small horizontal rod connecting the middle points of two adjacent posts of the same truss, for the professed purpose of lixinu or holding the posts at the middle in order that they may be figured for halt-length. The benefit derived therefrom is more imaginary than real. Girder — Any structure to cross a chasm or opening. The term is gener- ally applied to short structures for places where it is not advisable to use trusses: for instance, a plate girder, or a rolled girder. Guard Rail. — See felly plank. Guys, or Guy Lines. — Lines for bracing the top of a pole, derrick, or any simihir apparatus. Gyration — See radius of gyration. Hammered Head. — A head formed on the end of a bar by hammering. Hand Lines. — Small ro])es used in erection. Hand Rail, or Hand Railing. — An iron or wooden frame placed on or near the outside of a bridge in order to prevent persons or animals from lalliiiu' therefrom. (Plate IV., or Plate II., Fig. 13.) Hand-rail Cap. — The upper longitudinal timber or timbers of a wooden liand-railing. (Plate II., Fig. 13.) Hand-rail Post. — Post for supporting a hand railing. (Plate II., Fig. 13 ; Plate IV.) Headway. — See clear headway. Hinged End. — An end of a strut connected only by a pin. Hip. — The jjlace at which the top chord meets the batter brace. Hip Joint. — The joint of the top chord and batter brace. Hip Vertical. — A rod hung from the pin at the hip for the purpose of ^^ls]n iiding the floor beam. Holding-on Bar. — \ lever to hold against one end of a rivet while the liuh! at the other end is being formed with a button sett. Hub Plank. — A plank to protect the iron-work of the truss from being strink by the hubs of passing wheels. (Plate II., Fig. 13.) I-Beam. — A piece of rolled iron of the section shown ow Plate II., Fig. 2. Initial Tension — The tension caused in any adjustable member by screw- ing; lip the adjusting apparatus. Intensity. — Tiie intensity of a stress is the amount of stress upon a square iiuli (il section. Intermediate Strut.— An overhead strut in high bridges, attached to the posts (it ()p])osite trusses, and lying between the upper lateral strut and llic ilcxir. In deck bridges, if used at all, it would lie between the upper and hnvcr lateral struts. (Plate I.) ittiiii If « 238 GLOSSARY OF TEIUfS. Jaw. — A connection on the end o£ a strut similar to that shown on Plate II., Fig. 13. Joint. — A place where two alnitting or lapping pieces are connected. Joist. — A timlier l)eam that supports part of the Hoor and its load. (Plate I. and Plate II., Fig. 13) Knee, or Knee Brace See bracket. Lacing. — A system of l)ars, not intersecting each other at the middle, used to connect the two channels of a strut in order to make them act as one member. (Plate II., Fig. 12.) Lacing-Bar A bar belonging to a system of lacing. Lateral Rod. — A tension diagonal of a lateral system. (Plate I.) Lateral Strut. — A compression member of a lateral system. (Plate I.) Lateral System. — A system of tension and compression members forming the we!) of a horizontal truss connecting the opposite chords of a bridge. Its puri^oses are to transmit wind pressure to the piers or abutments, and to prevent undue vibration from jjassing loads. Latticing. — A system of bars crossing each other at the middle of their lengths, u.sed to connect tiie two channels of a strut in order to make them act as one member. (Plate II., Fig. 12.) Lattice Bar. — A bar belonging to a system of latticing. Leg. — One of the two portions of an angle iron separated from each other by the bend. Lever Arm. — The perpendicular from the centre of moments to the line of action of a force. The lever arm of a couple is the perpendicular distance between the lines of action of the two equal and parallel forces. Live Load. — The moving or passing load upon a structure. Linville Truss (also called " Double Ouadrangular," " Whipple," and " Double .System Pratt " truss). — A truss with vertical posts and diagonal ties spanning two panels. It is the truss represented on Plate I. Lock Nut. — See check nut. Loop Eye. — .In eye on the end of a rod or square bar, elongated into the form of a loop, as shown on Plate II., Fig. 16. Lower Falsework. — The falsework below the level of the lower chords. Main Diagonal. — A tension member of a truss, sloping uinvard towards the nearer end of the sjian. Main diagonals in iron bridges are not adjust- able. Moment. — The [jroduct of a force by its lever arm. Moment of Inertia. — Represented by the equation, / - Ap'^ = Zr'-dA, where // is the area of the section considered, p the radius of gyration, ■.\w\r the distance of any point from an assumed line lying either in the surtace or outside of it: in other words, the moment of inertia of a surface about any a.xis is the product of the area by the square of the radius of gyration ; or it is the summation of the products of each differential of the area l>y tlie sc^uare of its distance from the axis. If the axis lie in the surface, the moment of inertia is called a surface moment of inertia; while, if the axis tttJili ii GLOSSARY OF TERMS. 239 r to that shown on Plate .re bar, elongated into the be perpendicular to the surface, the moment of inertia is called a polar moment of inertia. Monkey Wrench. — A wrench capable of being adjusted so as to fit nuts of (lilt'erent sizes. Moving Load. — See live load. Mud-Sill. — A timber, usually from 6" by 6" to 12" by 12", at the bottom of a i)C'nt. It is laid horizontally in a trench, and the posts of the bent rest upon it. Name Plate. — A plate of iron placed in a conspicuous position on a l)ii(ls,'e. containing the name of the maker or designer of the structure. Negative Rotation. — Rotation in a direction opposite to that of the hands of a watcli. Net Section. — See effective area. Neutral Surface. — That part of a member subjected to bending, which is iitithLT extended nor compressed. In symmetrical wrought-iron beams, with equal or nearly equal flanges, it is taken to be at the centre line of the web. Nut. — A small piece of iron with a threaded core to fit on the screw end of a bolt, rod, or bar. (Plate II., Fig. 6.) Order Bill. — A form of bill used in ordering material from the manufac- tuiTrs. Ornamental Work. — Fancy work at the portals of a bridge to give it airhilccturnl effect. (I'lates I. and VI.) Overhead Bracing. — The upper lateral or vertical sway bracing in tlir()u;,'h bridges. The term is usually applied to the vertical sway bracing, if tlicre be any ; if not, to the upper lateral bracing. Packing. — See chord packing. Panel. — That portion of a truss between adjacent posts or struts in Pratt tiu.--s bridges; called also a bay. Panel Length. — The distance between two adjacent ])anel points of the .-laiiio ciiord. Panel Point See ape.x. Pedestal. — The foot of a batter brace or end post. (Plate II., Fig. 9.) Permanent Set. — The alteration in length of a piece of material which has liein ^ui>jected to stress, remaining after the stress has been rem ;ved. Pillar. — See column. Pilot Nut, or Pin Pilot. — A nut, one end of which is a truncated cone, used to ])rotect the thread on tlie end of a pin when the latter is being driven into place. (Plate II., Fig. 5.) Pin. — A cylindrical piece of iron used to connect bridge members. (Plate 11 . i'ig, 5.) Pitch. — The distance between centres of consecutive rivets of the same Plane of Symmetry. — A plane tlividing a body into two equal and sym- iiutiiial i)arts similarly disposed in reference to the plane. Plant. — Tools and apparatus useil in construction. ! I i 240 GLOSSARY OF TERMS. H ' f Plate. — A piece of flat iron wider tlian a bar. Tlie common distinction between the two is that a plate is attached to something else, and acts witii it, while a bar is an independent member. Plate Girder. — A beam, built of plates and angles, used to span a small opening, generally less than forty feet. Pony Truss. — A truss so shallow as not to permit the use of overhead bracing. Portal. — The space between the batter braces at one end of a bridge. Sometimes the term is applied to the portal bracing, though incorrectly. Portal Bracing. — Tiie combination of struts and ties in the plane ot tlie batter braces at a portal, which transfers the wind pressure from the upper lateral svstem to the abutment or pier. Portal Strut. — A strut belonging to the portal bracing. (Plate I.) Positive Rotation. — Rotation in the direction of the hands of a watch. Post. — A vertical strut. (Plate I.) Pratt Truss (called also the " Murphy-Whipple," or "Quadrangular" truss;. — A single-intersection truss with vertical struts and diagonal ties. Quadrangular Truss. — See Pratt truss. Radius of Gyration. —The radius of gyration of any surface in reference to an axis is ;he distance from the a.xis to that point of the surface in which, if the whole area were concentrated, the moment of inertia in reference to thu axis would be unchanged. It is therefore equal to the square root of the ratio of the moment of inertia over the area. Ream. — To enlarge a rivet hole. Reamer. — A tool for enlarging rivet holes. Re-enforcing Plate. — A jtlate used for the purpose of providing additional pin l)earing, or strength, to compensate for material cut away. (Plate 11., Figs. 1 1 and 13.) Resolve. — To divide a force into component parts. Rivet. — A short piece of round iron tightly connecting two or more thick- nesses of metal, and having, when in place, a head at each end. Roadway. — The passage-way of a bridge for vehicles ; usually means clear roadway, q. v. Rod. — A piece of round iron. Rolled Beam. — An J-beam. (Plate II., Fig. 2.) Roller. — See expansion roller. Roller Frame.- A light frame of iron for holding the rollers in position. (Plate II.. Fig. 9.) Roller Plate. — The plate upon which the rollers rest, and which itself rcs^ upon the masonry. Rope Sling. — See sling. Run. — A line, or string; as, a run of joists. Set. — The extension or compression of a piece of material under stress. Shear, or Shearing-Stress. — The resistance which a body offers to the ])assage,or to the tendency to passage, of one section along the next consecu- tive section. GLOSSARY O/-- TKKMS. 241 Shipping-Bill. — A list of portions of a bridge, arranged in a manner to f;uilitate counting and chucking when tlie material is received after shipment. Shoe. — Another term for pedestal, q. v. Shoe Plate. — The plate on the under side of the shoe, resting on the rollers, l)ed-i)late, or masonry. Side Bracing.— A bracing for pony trusses to attach the panels of the top chord to the floor beams prolonged, in order to fix the panel points of the top chord. (Plate 111.) Sidewalks.- Roadways at the sides of a bridge for foot-passengers on,y. Single Intersection. — That style of truss in which the diagonals do not ao>s the posts. It is rejjresented in skeleton on Plate V. Skeleton Drawing.— A drawing which shows only the centre lines of in(iii!'(.r.s. such as a diagram of stresses. (Plate \ ) Skew Bridge.- A bridge in which the horizontal lines joining correspond- in- panel points of the opposite trusses are oblique to the planes of the trusses. Sledge A heavy hammer, or mallet. Sleeve Nut. — An elongated nut, the core at one end having a right-hantl ihrLmI, and that at the other a left-hand thread. Its office is to lengthen or sh(irt-n a tension member. (Plate II., Fig. 16.) Sling. — A loop of rope, very useful in erection for making a hasty attac h- nuTit. Slope. — Inclination to a horizontal plane. Snatch Block. — A block with one side capable of being opened for the insertion of the rope. Its office is to change the direction of the rope. Span. — The length of a bridge from centre to centre of entl pins or licarin^s. Spikes. — Large nails for timber work. (Plate 1 1., Fig. 13.) Splay. — To spread at one end the two main portions of a member. Splice. — A joint connected by means of plates. Splice Plate. — .A connecting jjlate at a joint. (Plate II., Fig. 12.) Spread. — The distance ajiart laterally. Staggered Rivets.— Rivets are said to be staggered when each rivet of one row is opposite to the middle of the s])ace between two rivets of the next row. Static Load. — Dead load. q. v. Stay Plate. — A plate always used at the end of a system of lacing or latticing. (Plate II.. Fig. 12.) Stiffening- Angle. — .An angle iron used to stiffen the web of abeam. (Plate 11.. i'iv'. I3'l Stiffener. — A piece of iron used to stiffen the web of a beam : it may be of an^'lc or tee section. (Plate II., Fig. 13.) Strain. — The extension or comjiression of a piece of material which is or lias been under stress. Stress. — The internal resisting force of a piece of material wiiich is .•-trainnl. Strut. — ,\ member which resists compression. ■JAl (//.(AS-.V./AM' ('/■• /rh'MS. Sub-Punching. — Tlic punchinj; of livcl lioks wluil) liavc to hu afterwards vnlaij^ed by roaming. Sway Bracing. — Bracing transverse to tiie i)lanes of tlie trusses, lis ol)ject.s are to resist wind pressure, and to prevent undue vibration fn.in parsing loads, (i'late 1.) Table of Data. — .\ list of the known circumstances that affect the design- iiig of a structure. Tap. — .\ screw for cutting a thread in a nut. Tee or T iron. — A piece of rolled iron of the section shown on I'lule II., l'ig.4. , , Tension. — \ stress tending to elongate a body. ThreaJ. — The spiral part of a screw or nut. Through Bridge. — A bridge with overhead bracing. Tie. — .\ tension iniMnber; generally refers to a main truss. Timber Truck. — A small, strong wooden frame, with an iron roller set entirely below the upper surface. It is used in bridge erection for moviiii; large timbers and heavy weigiits along a runway. Tongs. — Part of a riveting outfit; used for holding and carrying heated rivets. Transverse Component. — \ component in a transverse direction ; geiiLi- ally intended for a component peri)endicular to the jtlanes of the trusses. Truss. — \\\ assemblage of tension and co.npression members so arranged as to transmit loads from intermediate i)oints to the ends. Trussing. — A poor substitute for lacing or latticing. (I'late 11., Tig. S, r-iate VI.) Turn Buckle. — .Similar to a sleeve nut, and for the same purpose. The siilesare open, so that a crowbar maybe inserted for the purpose of screwiin; tip. Turn buckles are used for larger bars or rods than are sleeve nuts. (I'late II., Fig. 1 6.) Ultimate Strength. — The greatest load ;hat a [Hirtion of material can bear. Uniform Load. — .V load so distributed over an entire structure, that eiiual lengths everywhere receive ecpial portions. U-nut. — A piece of iron, in the shape of the letter U, through whidi passes the threaded end of a rod, and which affords a bearing for the nut, with room to screw up the latter. Its use is not permissible in tirst-cla.ss bridge con- struction. Upper Falsework. — The falsework that lies above the level of the l.nver diords. Upset End. — An end of a rod or bar enlarged for the cutting thereon of a screw-thread. Vibration Rod. — A tension member for vertical or i)ortal sway bracing. (I'late 1.) Washer. — A piece of cast or wrought iron to distribute the ])ressure of a I ol; head or nut over tiiiiluT. ' I'lato il.. Fig. 6.) li hiivf to 1)C' aderwanls ;s that aiicct the dcsigii- tion shown on Plate 11., GLOSSAh'\- OF TKAWfs. 243 Web. — The portion of a truss or beam I)etwcen the flanges. Its office is piiiiripally to resist shear. Welded Heads. - Heads first worked into shape, then welded on the l>ars Whipple Truss. — .See Linviile truss. Wind Shakes. — Cracks in timber caused by the wind while the tre e was Working-Drawings. -iJrawings containing all the measurements neces- sary lor construction. Working-Stress. - The stress, usually the greatest stress, to which a i.iece 1.1 nial.rial is or should be subjected. Sometimes incorrectly employed for iiiliiisiiy of working-stress. Wrench. — A tool for screwing up nuts. ling and carryiug healed HHij 1 •'aBBBt i ■i ■ i .i INDEX. •Sa 111 <i INDEX. Allowance for waste, 68, 183, 190. Anchorage, 8, 104, 148. Aiifilf irons, 19, 146. Area opposed to wind pressure, 6, 4S. Jiars, best proportions for, 79, 80, 89. Hatter braces, limiting slope for. 7. Hattcr-brace plates, minimum dimensions of, 14. Pattfr braces, proportioning of, 6j, 132. Hattcr-bracc sections, 1 1, 63. Heam-liangcr plates, ij, loi, 146. •'(.•am lian.ners, 23, 75. licains, wooden, 23, 67 ; Tables xiii., xiv. Bearings, 21, 77, 93; Tables xxvi.-xxviii., xxxvi., xxxvii. Bearing-stress, 13, 76, lit'd plates, 16, 104, 146. lieiuling effect of wind on posts and bat- ter braces, 9, 52. BciuliMg-strcsses, intensities of, 13, 78. Iit;nts, 199, 200, 203. Best iiroportions for bars, 79, 80, 89. Hi'Vfis, iSi. Hills of iron, yi, 113, 114, rsi, 152. ol lumber, 115, 155. of rivets, 151, 190, 192, of bolts, 188, 191, 205. Bills, erecting, 204, 205. order, 183, 185. shipping, 19a Bolts, 23, 24. Bond, 168. Bottom chords, 59,62,66, 215. Braces, side, 7, 164. latter, 7, 9, 14, 6j, 133. Brackets, 22, 53, 103, 148. Uridge lettings, 157. Bridges, classification of, 5. styles of, 7, 38. liuilt Hoor beams, 12, 19, 68, 107; Tables xix.-xxi. Camlier, 9, 175, 176. Camber blocks, 200. Carpenters' tools, 198. Cast-iron, 24. Cast-iron portals, 58. Channel bottom chords, 11, 66. Channels, properties of. Table xxviii. Checking, method of, ri6, iSr, 182, 198. Chord bars, 59, 62, 66, 79. Chord heads, 20, 177. Chord l)acking, 62, 81, 132, 179, 206. Chord jjlatcs, 14, 63, t'hord projiortioning, 64, 129, 130. Chord sections, i r. 59, 62, 63, 66. Classification of bridges, 5. Clear headway, 7. Clear roadway, 6. Closed columns, 56. Columns, formula for, 12. Complete dcsinn for a bridge, 126. Comprossive stresses, 12. Connecting-plates, 15,94-99, 137-144. Connection for lateral systems, 10, 98-100. Continuous spans, 9. Contract, form of, 167. Cost, estimates of, 116. Cost of bidding-expenses, 170. of blacksmithing, 170. of eiecticni, iiy. 247 i! 248 INDEX. Cost of falsewDvk, 117. of franung, 1 17. of hauling, 117. of Uimljcr, 68. of painting, 117. of jiilc-drivcr, 198. Counters, 12, 40, 41. 46, 59- 61, 127. 132- Countersunk rivets, 91. Cover plates, 16, 95, 144' Cutting off flanges of channels, 23, 59,96. Data, table or list of, 3S, 1 18. Dead load, 6, 32, 126, 156. Deck bridges, 46. Demonstration of floor-beam formula, 219. Depths of truss, economic, 3S, 124; Ta- bles iv, V. Design for a bridge, 126. Details, jiroportioning of, 75, 86, 93, 136. Diagonals, length of, 177, 221. Diagrams of stresses, 40, 127 ; Tlate v. Diameters of rivets, 15, 90; Tables .\.\i.\., xxxvi., xxxvii. Dimensions, marking of, iSo, iSi. Distributi(Mi of material in struts, 59. Double-intersection bridges, 7, 44. Draughtsman's equipment, 172. Draughtsmen, hints to, 180. Drawings, working, 172, Economic depths, 38, 124. Economy, 57, 59, 120. Effect of wind pressure on members, 9, 48,99, 215. End lower lateral-strut connection, 104. 144. I'.nd lower lateral struts, 10, 56, 65, 135. I'.nd panels, stilfen-.l, 11,62, 66. 129, 215. Eipiipment, draught.unan'.i, 172. for raising gang, 197. i:,|nivalent length for iU-'ada, nuts, etc., 115. lueeting-bills, 204, 205. I'',recting-gang, 196. Erection, 196. Estimates of cost, 1 16. Iv\pansion, S. l'"..v])ansion joint, 103, 104. l-lxpansion rollers, 21, 103, t4l, 20S. l':xtension i)hites, 16, 96, 145. 19, 68, 107 ; Tables Eyes, 20, 105. ICye-bar heads, 20, 177, 178. Falsework, 198. Falsework pillars, sizes of, Table xxxix. Felly plank, 23, 67. Field riveting, 24, 92, 125. Filling-plates, 145. Fillers, 104. Final order bill, 185. Flanges, 19, 68, 107. Floor beams, built, i: xix.-xxi. details for, 19, 30, 71, no. limiting depth for, 19. riveted to posts, lOl. rolled, 12, 71. trussed, 30, 72, 109. Flooring, 23, 210, 211. Floor system, 67. Foremen, 197, 204. Form of bond, 168. of contract, 167. of projiosal, 166. of specifications, 162. Formula for built beams, 19, 219 for coUinms, 12. fcjr trussed beams, 72. Framing falsework, 117, Z03. Friction, riveted plates, 90. shoe, 8, II. Functions of J-beams, 55, 56. Cas-jiipe i-lruls, 36. Cieneral specilkations, 5. Girders, 18, 19, 71. Cuard rails, 23,24. • Hammers pile-driver, 198. Hand railing, 23, 24, 67. Hangers, I)eain, 12, 22, 75. Heads of eye bars, 20, 177, 17S. Headway, 7. Hints to draughtsmen, 180. Hip connection, .'•;3, 95, 137, 138. Hip verticals, 12, 14. 59- 6' ! Tables vi.- viii. Hub pUuik. 23.67,115. I-beams, 13, 55. 56,71. L\/)i:x. 249 S, 20, 177, 178. liars, sizes of, Table xxxix. 23. C". (, 24, 92, 125. , 145' )ill, 185. 58. 107. built, 12, 19, 68, 107 ; Tables xi. ar, 19, 30, 71, HO. depth for, 19. ;o posts, lOI. 2,7'- 30. 72, 109. , 210, 211. 1, 67. 17, 204. id, 168. act, 167. nsal, 166. ficatidiis, 162. ■ Imilt lieams, 19, 219 nuns, 12. sed beams, 72. scwork, 117, 203. ■etcd plates, 90. I II- if I-beanis, 55, 56. pile-(lii\er, 198. ig, 23, 24, 67. earn, 12, 22, 75. yc b.irs, 20, 177, i~?>- 1 ■ aiiulUsmen, iSo. L-tion, .S3, 95, 137. '3^- lis, 12, 14. 59. 6'i 'I'al'l" ^i'- , 2;,. fl7.l'5• 3, 55. jC'. 71. Im linatioiis of lattice and lacing bars, 15, Iiulirect transferrence of stress by rivets, 92. Inilial tension, 10; 'I'able i.\. lii^lni'tion, 21 1. liitL-nsily of bearing-stress, 13, 76. of bending-stress, 13, 78. of compressive stress, 12. of tensile stress, 11, [2. Iiilermediatc strut connection, 98, 144. Iiitinnediate struts, 51, 56,65; Table x.xv. imn, bills (jf, 71, 113, 114, 151, 152. cast, 24. hand railing, 23, 24. weight of, 33, 155, 156. Jaws, 22, 100, 104, 106, 143, 144, 149. JiMiu, sliding expansion, 103, 104. Joints, top chord, 94, 139, 179, 20S. Joists, 2^, 67, 209; Tables xv.-x^•iii. KiKcs, or knee braces, 22, 53, 103, 148. I ,iliiir in erecting, 117. in framnig, 1 17, 19S. [,.uing-bars, 15, [02, 146, iSi ; Table xxxi. i.aleral-rod connection, 10, 99, 106. Lateral rods, 14, 4S, 6r ; Table xxv. strut connection, 98, 104, 144, [45. struts, 9-1 1, 49, 56, '.',65, 135; Table xxv. svstems, 48, 61. l.atlire bars, 15, 102, 146; Table xxx. I.tngths, limiting, 6, 7. of diagonals, 177, 221. of lattice r.nd lacing bars, 102 ; Table xxix. ol span, 6, 7. lAtlini; bridges, 157. Limiting depths of pony trusses, 7, 123. depths of lloor beams, 19. lengths of span, 6, 7. sizes of sections, 8, 57. slope of batter braces, 7. Limit of clear roadway, 6. Li-t of data, 38, 118. of mend)ers, 28. LiM' loads, 5, Ti^i, 37, 126. Ltiads, deatl, 6, ^2, 126, 156. Toads, live. 5. 32, t,7, 126. snow, 35, 46. for wooden beams. 67 ; Tables xiii., xiv. Lock luits, 22. Loop eves, 20. Lower end of post rc-cnforcing, 95, 142. Lumber, amount per panel, Tables xv.- xviii. bill of, 115, 155. list of members, 28. iNLain diagonals, 59, 177, 221. members, 55, (x). Maintenance of bridges, 211. Marking iron, system of, 192. of dimensions, 180, iSi. Material in struts, distribution of, 59, 64. Materials, bill of, 71, 113, 114, 115, 151, '52, 155. tests of, 25, 26. Measurements, method of recording, 180, 181. Mend)ers, list of, 28. Method of erecting a bridge, 196. of (inding lengths of diagonals, 176, of reccjrcling measurements, 180, 181. Nfcthods of checking, 116, 181, 182, 198. Middle of |)ost connection, 96. Minimum dimensions of chord and batter- brace plates, 14. Xanic i)lates, 24. Xeglccteil consideration in highway- britlgc designing, 215. Xumbc" of men recpiired for erecting bridges, 1 17, Nuts, 22, 115. ( )ak lumber, weight of, 6. use of tables with, 61, 75. Order bill, tinal, 185. prelimin.irv, 183. ( )rnamental work. 141). Outfit for draughtsman, 172. for erecting-gang, 197. Lacking, chord, 62, 81, 132, 179, 206. 250 INDEX. i' |i T';iiiitin!T, 25, 117, 209, 211. raiifl lengtli, most economic, 38, 123, 12S. of toj) chord, exact, 176. rilc-drivcr, 19S. Pilot mits, 84. Tin bearing. 21, 77.93- I'iiie lumlier, 6, 23, 24. Pin holes, 21. I'in pilots, 84. Pins, proportioning of, 76, 85. steel, Si, 83. working bcnding-moments, etc., for, Table xii. Plant, 197. Plate girders, 7, 19, 71. Pony trusses, 7, 123. Portal-strut connection, 99, 143. Portal struts, 52, 54, 61, 65 ; Tabic xxv. Posts, 9, 40, 41, 43, 45' 46- 59. 64. 133' Posts, hand rail, 23, 67. Post sections, II, 58. Practical method of pin projjortioning, 85. Pieliniinary order bill, 183. Proportioning of batter braces, 63, 132. of beam-hanger plates, loi. of beam hangers, 75. of bottom chords, 62, 66, 128. of brackets, 103, 14'^- of built floor beams, 68. of chord bars, 62, 66, 1 28. of counters, 60, 127, 130. of details, 75, 86, 93, 136. of end lower lateral struts, 65, 135. of expan.sinn rollers, 103, 141. of falsework, 19S. of floor system, 67. of hip connection, 95, 135. of intermediate strut counection, 98, 144. of intermediate stmts, 65. of joists, 67, of knee braces or knees, 103, 148. of lateral rods, 14, 61. of lateral-s'.ut connection, 99, 103, 143. 145- of lateral struts, 61, 65. of lateral systems, 60. of lower end of posts, 96, 142. of lower lateral struts, 65, 135. Proportioning of main truss members, 60. of middle of post connection, 96. of pins, 76, 85. of portal-strut connection, 99, 143. of portal struts, 61, 65. of posts, 64, 133. of re-enforcing plates, 93, 96. of rivets, 91. of rolled beams, 71. of rollers, 103, 141; Tables xxxiv., XXXV. of shoes, 97, 140. of side bracing, 7. of sway br.icing, 61. of top-ch<ird coimection, 94, 129. of top chords, 63, 1 28. of trussed beams, 109. of upper end of post connection, 95, MS- of upper lateral-strut connection, gS, 143- of upper lateral struts, 61. of vd)ration-rod connection, 98, 105. of vibration rods, 61. Proportions for bars, best, 79, 80, 89. Proposal, form of, 166. (Quality of workmanship, 25, 166. Ratio of width to depth of bars, 79, 88. Recording of measurements, 180-182. Reduction of ends of pins, 84. Re enforcing plates, 16, 93, 96, 142. Rivet heads, 90, 150; Table xxix. Riveting, field, 24, 92, 125. rules for, 17, 90. Rivets, bending-moments, etc., for. Tables xxxvi., xxxvii. bill of, 151, 11/3, 192. countersunk, 91. diameters of, 15, 90. in llanges of beams, 20, 107. Rivet spacing, 18, 20, 107, 181. Roadway, clear, 6. ki)d>, eipiivalent lengths for upper ends, etc., 1 1 5. Roller plates, 16, 104, 146. Hollers, 21, 103, 141. I Rules for riveting, 17, 90. INDEX. 25' f main truss members, 60. f post connection, g6. 85. rut connection, 99, 143. ruts, 61, 65. ^ 133- ing plates, 93, 96. I. ;anis, 71. 103, 141 ; Tables xxxiv., 7, 140. cing, 7. icing, 61. d connection, 94, 129. (Is, 63, 1 28. beams, 109. ml of i)ost connection, 95, ucral-strut connection, 98, iteral struts, 61. n-ro(l connection, 98, 105. n rods, 61. r bars, best, 79, So, 89. of, 166. kmanship, 25, 166. to depth of bars, 79, 88. neasurements, 180-1S2. nds of pins, 84. lates, 16, 93, 96, 342. D, 1 50 ; Table xxix. 24,92, 125. 17,90. ^■moments, etc., for. Tables cxxvii. I, !</), 192. nk, 91. of, 1 5, 90. of lieams, 20, 107. 18, 20, 107, 181. r, 6. ■nt lengths for upper ends, 5- 1(1, 104, 146. ,3, 141. ting, 17, 90. Scales, 172, 204. Sections, limiting sizes of, 8. Sections of members, 8, 11. Shearing-stress, -^-j, 80, 91. Shipping-bill, 190. Shoe connection, 97, 140. plates, 16, 97, 140, 146. Side bracing, 7. sj/c.-. of floor beams, Tables xix.-xxi. of hip verticals, Tables vi.-viii. of joists. Tables xv.-xviii. of lacing-bars, Table xxxi. of lateral rods. Table xxv. <if lateral struts. Table xxv. of lattice bars. Table xxx. of pillars for falsework. Table xxxix. or pins. Si, 86, 134. of portal rods, Table xxv. of portal struts. Table xxv. of rollers, Tables xxxiv., xxxv. of sections, limiting, 8, 57. of stay plates. Tables .xxxii., .\,\,\iii, of vibration rods. Table xxv. Skclctiui diagram, 40, 44. Skew bridges, 3, 75. Sleeve nuts, i r^. Sliding expansion joint, 103, 104. of pedestal, 8. Snow load, 35, 46. Spacing, rivet, 18, 20, 107, l8l. Specitications, 5, 1G2. general, 5. on tile, 162. Spikes 23, 151, 210. Splice |)lates, 15,94, 139. Star iron, 58. Mav plates, 137; Tables .xxxii., xxxiii. Sleel pins, 81, 83. Suffeiied bottom chords, 11,62,66, 129, -•15. hip verticals, 14. Milfeners, ic), 70. Stresses on batter braces, 9, 41, 45, 52, 54, 12S. on beam hangers, 75. oil bottom chords, 41, 43, 45, 128, 215. on brackets, 53. on built beams, 107. on chords, 41, 43, 45, 12S, 215. Stresses on counters, 40, 45, 127. on double-intersection trusses, 44. on end lower lateral struts, 10, 54, 135. on falsework, 200. on floor beams, 73, 107. on hip verticals, 41. on intermediate struts, 51. on lateral systems, 48. on lower lateral rods, 49. on lower lateral struts, 49. on main diagonals, 40, 45, 125. on pins, 76. on portal rods, 51. on portal struts, 51, 53. on single-intersection trusses, 38. on sway bracing, 61. on top chords, 41, 43, 44, 128. on trussed beams, 109. on trusses, 3S. on upi)er lateral rods, 49, on ujjper lateral struts, 49. on upper lateral systems, 48. on vibration rods, 51. Structure, test of, 26. Styles of bridges, 7. Sway-bracing, 9, 48, 61. System of marking iron, 192. Table of data, 38, 118. Tee-iron, 19, 58. Tensile stresses, intensities of, 11, la. Tension, initial, 10; Table ix. Test of structure, 26. Tests of materials, 25. Thicknesses of webs of channels, Table xxviii. Threads, 14. Timber, 23, 25. Tools used in erection, 197. Tojvchord connection, 94, 129. joints in, 94, 139, 179, 208. panel length of, 176. Top chords, 41, 43, 44, 63, 128. Truss, economic dejjth of, 38, 124. Trussed beams, 30, 72, 109. Trusses, pony, 7, 123. Trussing, 14, 103, 148. Turn buckles, 22, 115. Turning-in of channel llangos, 58. I 252 LXDKX. Units, 2. Upper end of post connection, i6, 95, faiscwoik, 104. lateral rods, 14, 49, 61. lateral-strut connection, 9S, 143. lateral stmts, 9, 11, 49, 61, 65. Upset rods, 14, 115, 165. Vertical sway bracing, 49, 61. Vibration rods, 51, Ci. Washers, 22, 1 1;2. Waste, allowance for, 68, 1S3, 190. Web stiffening;, t9, 70. thickness of. Tabic xxviii. Weights of materials, 6, 6S. of iron, total, in bridges, 35, 155, 156; Tables i.-iii. I of rivet hcatls, 151. 156; Table x.xix. ! Widths of flanges of channels, Table xxviii. Wind pressure, amount of, 6. area opposed to, 6. 48. effects of, 9, ^S, 99, 215. Wooden hand railing, 23. lateral struts, 10, 100, [49. Working bearing-stresses, intensities of, '3- 76. bending-stresses, intensities of, 13,76. compressive stresses, intensities nf 12; Tables x., xi. drawings, 172. loads for wooden beams. Tables .\iii., xiv. shearing-stresses, intensities of, 76. tensile .stresses, intensities of, u. Workmanship, 25. Wrought-iron, weights of, 33, 71, [31, i ;;,-, 156; Tables i.-iii. INDEX TO ADDENDA. f!cam-hangcr plates, 226. Fioor-beam connection to foot of post, 228. Floor-oeam stiffeners, 22S. Foot of post connection to floor beam, 228. Improved beam-hanger plates, 226. Improved portal .strut connection, 229. upper lateral strut connection, 228. Lateral strut connection, 228. Portal strut connection, 229. Proportioning of beam-hanger plates, 226. Stiffeners for iloor beams, 228. 40 50 _6oJ 70 80' 90 100 no 120 130 140 160 170 180 190 200 210 22cF~j 230 _240 2503! '260 __j 270_| 280 Ij 290_J 300 1 1 f channels, Table nt of, 6. 6, 48. 9, 215- 23- 100, r.|9. sscs, intensities of. ntensitics of, '3.76. ses, intensities of, i\. )eanis, 'ral)le> .xiii.. intcnsities of, 76. tensities of, i of. 33. 71. '3' ' ' 5:> A. ■onncction, 229. coiniection, 23,S. 1, 228. 229. langcr plates, 22IJ. IS, 22S. TABLE I OT OF IRi CLASS A, 18' Roadway 6pan„ rERAi. J Floor STEM, 1 System. 40 20 50 20 60 "lO 70 - S7 80 -■;< 90 -4Q .49 no - 55 120 ■5' . 130 - 57 140 '5°Z - 61 160 170 i8o~ 190 200 210 220 230 240 250 260 270 280 290 300 77 S4 86 86 80 ^7 89 /i fl TABLE I. TABLE OF WEIGHTS PER LINEAL FOOT OF IROr GLASS A. Span. 1 i iKl^^aliS. 1- : '43 12 Lateral System. Roadway. 1 14 Roadway. 16' Roadway. 18 Roadway. Klckik System. Limber. 193 194 1S7 '93 200 219 230 24. D. L. 400 j 404 423 469 ' -ST3-I Trusses. I,ati;kal System. 1 LOOK Svste.m. LlMUKR. I). L. . , 'I'mssES. Latkrai. SVSTKM. Floor System. Ll'MUEK. ,D. L. Trusses. '53 192 184 '99 -'4 „ '» -» 1 -,)- 279 Lateral System. 20 20 FiJJOR System. Lumber. 40 26 ' 30 ! '45 20 20 39 41 - ' / 21S 210 "217 407 j '47 20 20 30 54 47 48 54 _ 74 54 242 244 443 4S8 500 526 541 575 636 266 50 16S !54 161 -or 2:0 20 .50 '75 442 ! i 182 68 268 60 44 164 170" 30 52 57 459_ 473 486 ' '74 1^1 8rr^ 200 221 242 266 233 ::42 30 57 53__ 4') 5S_ _ 51 _ -_54 _ 86 257 70 49 45 43 30 44 69 65 266 276 291 "" ?0 ::S 1S2 221 48 45 45 50 46 53 49 53 6f. 40 40 225 241 2(>9 25« 50 1 250 50 ! 26(') 47 1 308 ' 90 29 522 5S2 " 64 ' 100 43 30 39 41 39 "■ 47 61 336 3'4 336 3'4 no 42 33 32 518 '. 240 2fxS 298 i 320 |_354 370 53 48 54 50 286 308 285 308 692 "714 754 779 f'3 120 44 55' ' 2(^) _25,S__ 269 269 2|;S 6.5 644 295 330 48 51 3'7 l346_ ~'374~ 62 64 130 52 49 35 230 57S i 602 42 41 140 34 241 672 703 745 ' 1 354 ! 390^ i 389 4'3 426 461 491^ 489 49 50 Al^ i36 150 — . — 44 55. ■ 69 74 7" 80 Ji _ 286 77 7 -s ""79"* Sr Hi 83 83 ' 84 _ Sli >S() <p 89 1 66 3'4 336 160 43^ 5' 55 53 55 53 55 54 55 -3S8— 2S6 308 811 '822 Z857: 87C> .^.922 i 90,5 _ 04(' 962 1012 '053 1077 -__399_ 440 _470 ^ _509_ S07_ 549 ' 587 621 661 603 739 780 "826" 872 1 64 170 ' ! ;-_374___ 395 424 74 45 43 67 3'4 180 -- — t 72 75 26() 773 1 64 O9 336 3'4 190 — 1 45 25S 796 i 286 308 286 r 308 286 200 : i 7" 79 76 79 78 Si 67 7' 68 72 ."^ 73 1 72__ 71 ^ ■» / - 7' 336 3'4 _336_ 3'4 210 - !i 1 220 n 1 1 514 548 57S 230 , ! 1 240 — - - ■■ — 54 i .'^OvS 5; 3°8 "54 308 336 3P 3.36 250 ,__j — 641 260 i 1 80 2-0 280 336 336 336 290 i i j 300 i TABLE I. :. FOOT OF IRON PRATT TRUSS HIGHWAY -BRIDGES. CLASS A. 18 Roadway. 20 Roadw ay. LlMnER. D. L. 22 Roadway. 24 Roadway. Span. <l)SSES. SVSIKM. 20 20 30 57 ^}_ 4') * 49_ 55* St 57 = -54_ 61 77" -s 79 I St Si ~'^3" «3 " «5 S(p ' SC- SI) 90 S9 Fl.Of)R System. 68 Lumber. D. L. 482 535 545 Trusses. Lateral System. 20 Floor System. Trusses. _'59__ 300 202 203 216 Lateral System. 1 Floor System. Lumber. 1 D. L. : 559 616 Trusses. 168 20^ Lateral System. Floor System. ■ 87'"" 105 1 Lumber. D. L. 153 266 2f)8 -57 161 201 207 72 290 _ 292 528 582 21 23 — 30 63" S9 79 315 2 1 ■_339 . 34' 327 600 ' 664 40 50 60 70 80 go 192 21 81 90 317 22 I'''4_ 86 30 100 82 78 ^ 74 2S0 290 _30'~ 325 628 646 -"683 743 116 304 640 ..2'S 210 223 30 67 63 '.36 696 .■w_ 6y 65 266 276 580 598 626 686 60 92 "89 3'S 663 .^'05 L_339 ^ 113 1 -!';2 ____7'o_ : 739 1 7S4 214 221 S'3 5' 327 681 23-^ 64 61 291 336^ 243 242 274 S3 52 56"' 86 86 " 89 88 35' 733 253 293 33<^ 374 436 55 110 107 ■"376 "" 249 267 SO S3 60 .S9_ 71 74 __364 34-^ 364 " __342__ 404 382 807 834 53 60 58 66 ,._.432 410 S-6 , 911 : 966 ; 1009 100 279 63 3'4 __336__ 3'4 ^13''' ' 70.1 75« 300 -335 __ 372 „ J97 764 S06 i 841 : 8S4 " 3^3 "3 no no j 120 i 130 140 _-'5o__ 160 3'7 62 72 350 391 388 404 ..382 890 432 3t«J_ 64 773 8r4 _75 63 9' 919 IIS i 410 .)'J9 6X 66" 72 __364__ 342 62 69^ 90 90 ' 404 93 1 382 93(> 966 "^''035 436 64 7' "4 4.32 ___"7 410 116 1 432 1028 1067 374 3'4 336 80S "860 40c 41S 457 482 ~ 66 75 876 933 957 —429 __ 457 476 399__ 64 85 88 87 73 3f'4 9> 95 404 502 ^_ ^96 _ 99 98 11.39 422 67 64 69 3'4 ^_«7.-»_ 912 77 74 342 ■ 497 , 524 ^. 93. _ 92 95 93 96 ._95_. 98 96 99 .98 lOI 100 ! /°3^ _ 101 382 1060 1108 1132 1189 546 120 119 410 116S 170 180 190 200 210 220 230 240 250 260 440 336 3"4 364 i 1000 95 ; 404 -_^?8 _,__382 96 , 404 576 621 662 " 662 696 '752' 802 _ 859, .904 959 1002 1062 nil 432 I3l8 470 927 5'9 90 79 : 342 1 77 ; 3f'4 ■ 1023 1076 io6i I "3 5'''4 101 -9? 102 lOI r .'04 ._ 103 '03 106 ^los"" '07 106 122 i 410 (247 5o<) 67 7' 68 72 7.1 0() _72 71 ^ ■> / - 7' _ 336 3'4 _336_ 3"4 336 3.3'' ,53<^ 336 986 968 1029 1051 1 103 "1149 1177 1230 554 555 589 "73 7>S 75- 798 84. _ 892 93'' 88 91 603 -605 _ 644 12! 7_ 432 __ 410 '307 1 291 ',345 1384 507 So 342 _364 342 97 " 96 382 124 549 90 93 94 93 96 95 98 96 _ 77 _ 404 1232 '23 432 5'^7 So_ ii4« 1190^ 1250 1282 "1335^ '.375 •4.32 •472 , 6S9 733 782 821 874" 919 ._973__ 1020 loi 382 1263 '324 1380 1417 __'478 1520 1580 1623 125 124 139 _I26 '30 129 '32 '3' _4'°^ 432 432 02 I 78 3C4 81 1 364 , So 3f'4 83 : 3''4 _.98__._ 102 ^ 404 '453 i5'8 1558 66 f 404 Cm loi 1 404 l-'°5 J '.404 ^^ 103 404 106 404 .._4.32 __ 432 739 1621 270 280 7 So 336 336" 336 1268 1318 1362 Si "84"' 82 3^-4 3''4 3''4 ' 432 4.12 432 1663 ,S26 1727 290 ,S72 104 404 '774 300 -1 -4 11. F IRON ] S B. r' — Jway. P_ . SF .M. Ll'MllBK. I), t 266 47v 1 ilkS SK^ ~257'^' 5 lie 266 55': . =76__ 56*. 2<)l S'lk,'- 1 33<' "5; 1 3'4 66', 1 _'336_.. 7'.'. 1 3'4 7^'( I 336_^. 7()»< 3'4. 78r _ 336„ 81; 3'4 82„ _336_ 86; 3'4 J_87 3,V' 9" 3M 9a 336_ 94 3'4 (/. - }i<> 100) 33'- 1 104! 1 3;" 10- ! ^;" T 1 1 1, ',<> 1 I.) ' 1 iS .;>' u: E II. F IRON ] S B. r' iway. 24' Roadway. Sf Span. 1 1 , <K M, ! Ll!MIIEK. l>. I 1.. Tri.'sses. I.ATHRAI. SVSTKM. ^^:i^. '— ■ 1). 1.. j 266 2(>S 257 266 276 2()I •»7i33 5i;S9 S«io4 '43 ' 184 1S4 '79 1 '94. , 226 21 78 339 ^ 341 567 • 129 1 (152 7C0^ 746 _ 40 ! 50 1 70 1 80 ' 90 22 94 30 67 62 122 3=7_. ..3.W 352 376 SS'23 5fH44 5')l.S7 ! _ 94.. lOI 98 ■" >> - — 33(> 3'4 3.16 0570 66:9, 7 "41 200 297 327 53 60 58 96 101 43.2 410 ^A3^ 861 ()09 100 no i 120 9<) 432 -' — 3'4 330 3U 336 314 33*' 7-'<)5 i 3"S 64 71 103 1 410 105 1 410 <)40 988 r -,,89 1 ""10.S7' 1078 1 122 1144 U_'30 ; 140 : .50 j 160 170 180 i 190 200 76te^ 78^0 8 1 '162 82,S2 SO:25~ 1«7:43 9 "03 397 409 43' 4(>S 492 t— S3?__ : 563 96 99 '■98 104 107 106 .432 410 I.432_ 410 1 432 101 I0<) - — 3M 3' 4 _9?!77 _ 94,28 •/"SI 564 596 641 102 lOI 104 III 410 ! ii8i '233 1261 210 1 220 : 230 no 432 112 1 410 33" 100J05 (>So 102 i '" . . 432 1319 240 -'._ 53<^ 33" 104*52 10" Sj 1; 725 701 105 '03 i "5 1 "3 43- 1 ~ 1 1 10;, 250 260 ,V,<' 1 . 1 ;, 807 10<) ! i.r, ! 4>' 1 .1 V ' 7ro 2 ' ;,;(. "4.<)4 842 .OS i IIS 13- ' I4^'l 280 ' ^\(> I iiSiij i, 891 '07 iiS t;,2 IS43 290 3 vP 122.48 9-'' 10<l iir 13- 1 s'^o ' 300 , 1 — TABLE II. TABLE OF WEIGHTS PER LINEAL FOOT OF IRON I CLASS B. 40 5" 60 ;o 80^ 90 ;ao '.10 :20 :;o ;40 oO :6o :-o :So igo :90 210 230 240 2jO 200 2-0 ;!,-. 250 ICO 197 2l6 48 44 49 30 29 32 239 ! 2->2 3' ! . 1 1 : — TABLE 11. 700T OF IRON PRATT TRUSS HIGHWAY- BRIDGES. CLASS B. IMAGE EVALUATION TEST TARGET (MT-3) // &r #D ^' ///„ 1.0 I.I !lfiM IIIIIM 1^ IM 112.2 S l£ III 2.0 118 1.25 1.4 1.6 ^ 6" ► m ^ 1 //, /y, :^^»>> /^ Photographic Sciences Corporation #4 ^^"'4 V 4^^ A 6^ %*■ '^^ 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 ABI OT ( CLA 18' R(. Spai rKRAL Fi 40 >TEM. SVJL - 20 i" 20 •■ bo JO 70 r 80 57 ' S< 40 ♦y ♦9 120 55 ' 5' no 57 ' 140 ISO 54 ibo J 70 n 7S 190 '9 {I 200 U 220 <3 2,0 <3 240 ^S 250 260 '4 ^6 ^(t 270 280 V 2qo »7 ^00 W J '9 ' . ABI OT ( CLJ^ i8' R(. Spai 24' Roadway. Span. rEKAL iTEM. 40 —^-20 Kl 1 SviUMBER. D. L. Trusses. Lateral SYSTE.M. Sl^^il I^-B-- D. L. 315 536 139 21 71 339 557 40 60 ■ 70^° -80 57 -90 5^ -,oo»9 -..0*9 301 56s 172 22 85 „32S 327 594 50 304 593 172 172 30 no 629 60 _3'S 623 67 86 339 656 70 327 333 357 644 ■83 62 92 351 681 80 665 210 55 89 87" 358 705 90 711 238 272 ^300"^ 53 38s 757 1 100 120 55 - .30^5. .40 57 - .50 5=* 1 " 100 341 357 736 60 92 366 78s 828 no 774 58 90 385 120 130 34 « 801 337 66 94 366 858 -357 832 862 3(>i ._ 64 __ 7' 93 385 899 140 341 374 96 3(^ 901 150 n 357 884 392 96 94 385 961 160 - 'r 'If" 341 904 425 99 97 366 9S2 1 170 II ,90 ^-f- 357 .341 933 958 998 984 442 98 96 385 1016 180 190 i 200 1 210 220 230 ' 240 [ 250 1 260 ' 270 280 290 30ft t 481 lOI 99 102 101 104 99 i 366 1042 '2.0 ^i— 220 ■^ — .. 357 34' 5" 98 385 1088 508 536 577 612 "653-^ 68s lOI 366 1072 .357 1023 1050 i094~ 100 385 tii7 240 J — " 2S0 "* 34' •357 (02 366 385 1 144 102 101 104 1 195 26^ ^6- J80 ^9 "290 *7 w »^ - •9 .357 ... .,357 ^.'■38_ 1162 ios_ '03 385 1242 102 'O5 104 107 106 385 1271 ,357 ,157 .._;357 357 1207 ">235 727 106 385 385 .385' 385 '3'9 J.346 1399 758 804 105 107 1283 .35. 838 106 143' TABLE 111. TABLE OF WEIGHTS PER LINEAL FOOT OF IRO^ CLASS C. 12 Roadway. 14' Roadway. 16' Roadway. 18' Roadway. Span. no,c<:,-c Lateral iRlSSts. SYSTEM. sLr,. Lumber. D. L. Trusses. Lateral System. i D. L. 410 Trusses. Lateral System. Kloor System. LUMBHR. V. L. Trusses. 143 Lateral System. 20 Floor System. 49 Lumber. 266 40 143 20 -5 '93 368 494 i 143 20 1 33 217 143 161 20 40 241 431 50 I'll 20 29 194 161 20 35 208 414 20 45 232 448 167 20 57 72 255 5o 140 30 42 187 389 144 30 47 210 421 148 •58 30 62 45 234 464 490 '58 167 30 57 257 70 I4.S 49 So 149 45 27 193 409 '53 52 37 217 451 54 241 247 249 272 58 54 266 271 24 198 409 158 48 34 222 455 166 50 42 498 S'2 545 _^79_ 194 206 53 90 1J9 43 24 198 418 170 181 45 34 223 465 181 47 42 49 49 52 274 ;oo 169 43 23 217 446 45 32 245 497 '93 47 39 49 301 no 180 48 26 206 455 •97 50 34 232 S08 213 S3 42 257 560 23' 55 ' 52 290 120 198 44 25 217 479 1 219 46 32 245 _53Z-__.. 559 239 268 48 40 272 594 256 St 50 _30'_ 290 130 JI9 52 28 206 500 244 260 285 298 S3 35 232 245 __-32._ 245 54 43 _==57__ 272 257 272 617 284 57 53 140 :-!,2 49 27 217 520 49 34 S«3 289 49 42 647 301 54 51 301 290 -_J°' 150 53 66 36 601 3'6 55 45 668 327 61 54 160 35 639 11' 69 43 710 344 77 52 ro 3'8 74 37 ., 232 656 33' 74 46 44 257 272 703 729 343 78 SS 290 ibo 1 ; 1 3>8 72 75 35 245 665 342 76 35<'> 79 53 56 30 ' 290 :qc j 340 37 232 679 370 80 46 257 748 409 81 81 200 390 386 76 44 272 767 763 54 301 210 ! 79 76 46 257 405 426 83 83 57 290 220 230 1 405 45 272 793 810 55 301 1 433 456 79 46 257 457 483 5'5 538 85 84 86 ^ SO " ^) 87 58 290 240 1 1 78 81 45 272 846 j 878 ^ 897 56 301 250 1 484 46 272 272 59 301 260 1 505 80 45 56 59 _30'_. 301 270 ' 280 1 1 ! 1 574 603 638 668 i 1 1 1 1 1 57 301 301 301 290 90 89 59 57 300 < 1 1 TABLE 111. . FOOT OF IRON PRATT TRUSS HIGHWAY -BRIDGES. CLASS C. i8' Roadway. 20' Roadway. 22' Roadway. 24' Roadway. Span. USSES. Lateral System. 20 Floor System. 49 Lumber. 266 D. L. 465 Trusses. Lateral System. Floor System. Lumber. 290 D. L. — . , 1 Floor System. Lumber. D L. Trusses. Lateral System. Floor System. Lumber. D. L. '43 146 174 168 20 60 503 530 148 21 ! 64 315 536 139 21 71 339 557 40 ib7 20 30 57 255 __4_89_ 21 67 278 178 175 22 74 301 565 .72 22 85 325 594 50 60 iS« 72 257 507 30 83 280 551 30 94 304 593 '72 172 30 110 327 629 ib7 57 58 266 540 172 60 68 290 582 177 63 76 315 623 67 86 339 656 681 70 80 '79_„ 53 54 271 55° 562 599 623 •83 204 56 64 295 591 190 59 75 1 327 644 '83 62 92 351 !94_ 49 _ 52 274 5' 62 308 618 2T3 2:^b S3 73 333 665 210 55 89 87"" 358 70s 1 90 206 49 49 301 225 254 SO 58 329 656 52 70 357 711 238 272 53 385 757 100 23' 55 1 52 290 56 61 1 3'6 682 269 58 73 341 736 60 92 366 785 828 no 256 5' 50 301 653 277 53 59 329 3'6 713 738 294 56 72 357 774 300 58 90 385 120 130 2S4 57 53 290 679 305 60 62 327 63 75 341 801 337 66 94 366 858 301 54 5' 301 290 702 322 59 59 329 764 344 62 74 357 832 862 363 64 93 _J85_ 899 140 150 327 61 54 _„348_ 66 62 _3l6 _ 7l7 380, 69 77 34J 374 71 96 366 901 344 77 52 _JO' 769 337 365 ' 379 85 60 329 806 367 90 75 357 884 392 96 94 385 961 160 343 78 55 290 761 88 63 3'6 827 397 93 92 78 1 341 904 425 99 97 366 082 i 170 3S^> 79 81 S3 S6 301 290 784 808 87 61 329 851 412 77 357 933 442 98 96 .385 ior6 ; 180 3SO 411 90 04 316 876 447 95 80 341 958 481 lOI 99 366 1042 I go 409 81 54 301 840 "830 436 88 62 329 910 475 93 78 81 357 998 5" 99 98 385 1088 200 405 83 83 57 290 432 9' 65 3>6 899 47' 496 533 96 341 984 S08 102 lOI 366 1072 210 220 230 240 250 260 270 426 55 30' 860 455 90 62 329 931 95 80 357 1023 536 577 lOI 100 385 i"7 457 85 58 290 885 489 93 65 3'6 958 9,8 96 83 34' 1050 104 102 366 "44 483 84 86 86 " »<; 87 56 301 919 553 91 63 66 329 329 996 1037 565 81 357 1094 612 653 68s t02 lOI 385 "95 5' 5 59 301 956 976 94 603 630 669 99 9^^ lOI 84 82 _3S7_ 357 _"38_ 1 162 105 '03 104 385 1242 53'^ 56 59 30 « 30 • 577 93 64. 67 329 1059 1 100 102 105 385 1 27 1 574 1019 612 96 329 85 357 1207 123s 727 106 1 385 I3'9 603 57 30' 1044 644 95 1 05 68 66 329 329 tI29 1173" 700 742 100 «03 lOI 83 357 758 105 104 38s 385 385 '346 280 638 90 89 59 57 301 30 ' 1084 (III 682 98 86 357 1283 •35' 804 107 107 '.399 143' 1 ! 2go 668 713 96 329 raoo j 774 j 84 357 838 106 106 30f> \ niBMIMIMIf TABLE IV. ECONOMIC DEPTHS AND PANEL LENGTHS. Span. So' yo'" 100' No. of Depth. Panels. SlNC.l.K NTBRSECTION. Dnimt.E NTEKSKCTION. 5 5 S 6 16. ?' 18' - 20' no' 120' 21' 6 21' 26' .^ '30' .40'" '50' i6o' .70' i8o' .90' 200' 210' 7 22' 7 23' 8 23' 26' 8 9 24' 27' 29' 26' 9 27' 30' _ 32' ' 33' 34' 35' 10 ! 10 i 220' -'30' "240' 250' 260' 270' 280' 290' I II ' 12 36' ^ 12 38' ^39' 13 '3 40' 14 14 'S „ '; '5 41' ■ 42' ; «' - -- 44' 1 . PI m £>i>.''%tiLE£££M» TABLE V. ECONOMIC DEPTHS AND PANEL LENGTHS. Span. .So' 90' 100' No. of Panels. 1 Depth. SlMil.R Intkksh niiN. If).!' IS' DoiiBl.E Intkkski rioN. 5 5 5 20' no' 120' 1 ,?o' 140' ' 5 81' 22' 22' 23' 24' 25' 5 6 6 26' '50' \(yo' i;o' i.so' 190' 200' 2 1 o' 220' 2 ;o' 2.(0' 250' 2(X)' 7 27' 7 S 8 2.S' 27' 30' 2S' 32' 34' 35' 36' 9 10 10 ~ 37' P' 10 1 1 1 1 40' ■ 41' 42' 270' 2.S0' 2()0' JOO' 13 12 '3 13 43' 44' 4.S' 4(/ MHi '% ''^^^S A ■^B c- - n 1 9f ' II * m\ ' -xlpl- -n TABLE < In which tlic wDfkiii^-strcs The uppc ;i()iis ri<iuii"C( Panel '* Length. RoaJ' IC 0.01 i.oo / 2 r' 12 1.09 '-- li 13' l.iS 1 / i 2 \% 14 ! 1.27 „ f 2 4 15 \ i.3(. ' 16' a r \ 1.45 / 2 V «7 '•54 18' 2ir ..64 ; 2 ij' 19' '■7.^ '21" 20' i,S4 21' - '" I.V5 2 lA 2.07 I 23' 34' h'.1 : 'I' 2.29 I I \ TABI 111 whic \\iiikii\i^ The ;iiiii.s tl'i Panel I >3' '4' '5' i5' 17' 18' '9' I ^ 23 \» \ 24 TABLE VI. TABLE OF SIZES OF HIP VERTICALS FOR BRIDGES OF CLASS A, III which thi' hvt,' load i>. owe liiiii(lr(.'(| pdiiiuls ]n-v st\udiv foot of tioor, ami the \\nrkiiij;-.strt'ss on the verticals is lour tmis to liu' s(|iiarc inch. 'i'lic ii|>|»i'r fi,L,Mircs i;ivi- the sizes nf the hi|. vi'ilicals ; the lower ones, the sec- ; idiis mniired. Panel 12' I4' 16' 18' 2o' Length. Roa Iway. Roadway. Roadway. Roadway. ; Roadway. ic •3' '4' ■5' 16' '7' 18' '9' -• I "CI 0..JI a" 2 fn 1.00 □" J i"G 1.09 n" 2 H"a I.lSu" 2 ir'u 1.27 a" 22 23' 24' 2 S'a 1.36 a" 2 ;"a 1.43 a" 2 iru 1.04 a' 2 \Va 2 1" □ r..S4 a' J l"U i -■ 'yn 2.0; CJ" J 2 i.'.'a'^r 2.i.sa" I 2.2() n" I 2 fn i.ooa' "2 fro" l.lfjD" 2 H!"ir 1.26 D" 2 fiT 1.370" 2 i"a 1.48 D' 2'-B''d i.SyO" ^ irn I.2I D* 1.33 a'_ 1.45 u" 2 5" □ i.3sa" 2 !?□ 1.64 a' 2 rn 1.51 n* 2 H" □ 1.69 a' 2 i"D i.SoD" 2 i"a 1.91 a" 2 r'a 2.02 D' 2 ii^B'a 2.14 D' ■nra «.sf» a" 2 n"a i.fxSd" 2 I'D i.Si D» 2 I'D j-gin' 2 ^ya 2.0s a" 2.r7 a" 2 . r D^ 2.29 D" 77i"a" 2.43 D' 2 ir'D 1.77 a'' 2 I" a 1.90 a* 2 ■,>-," n 2.04 D" 2 lya 2.18 a" 2 iji"a 2.32 D" • 3 \ra 1.66 0' 2 i"q 1.S1 D' 2 I" a 1.95 D"^ "2' I, "5" a 2.10 :!" —— -n 22' 24' Panel Roadway. Roadway. Length 2 ir'D 1.67 D' 2 i"a 1.S4 a" 10' 2 I'D 2 I'D U' 1.84 D' 2.03 n" 2 r'a 2.00 a' 2 ■,',''0 2.19 a" 12' 2 ii»»"n 2.16 D" 2 li'a 2.36 D" 13' 2 li'a 2.32 D" 2 ii"o ^ 2-53 D" • 2 ii"a 2.27 d" 7 .l"a 2.40 D" 2 il'a 2-53 □"_! 2 ift'a ! 2.6.S a' I 2 -A" a 2.-,SD" -• '.Va^ 2.73 n" 2 ri"n 2.S7 □" I7i" a"" 3.01 n" : 'i"a I ,i6 a" 2 iiV'o 2.(>i a' 2.760" 2 i}"a 2.92 n" • 2 i^"a 3.00 a" 2 lA'D 3.27 D" 2 1 ■■'. " n 2.71 c" 2 ii"a 2.s6a" 2 lY'D 3■°^ 0" 2 iA"a 3.45 □" 2 .ft' a "2 .ft ''"a" 3-3" n " 2 .J" 7^ 2 iT'n 3-74 o" 2 iV'a I 2.99 P" ; 2 «ft"a 3-1'' O" I 2 .ft"D 1" 3.34 □' I 3' 54 CJ" i "'2 If a I 3v4 G" ' 2 irt"a ' 3.95 □" J 2 T^"a"''' 4.16 a" 3'27 D" 2 .t\,"a 3-4('0" 2 .r'a 2 <i',"a 3.87 a" 7irt"n 409 a" 2 il"u ! 4.3; o" I =3 «7' 18' 19' 20' 21' 22' 2 li'a 4.56 n" 24' TAB In \vh uiukir Ih I Kills r Panel Length ! II 13 14' ■5' 16' 17' i 'f ■9 12' 23' TAB In wli \\(M kir Th h Ills r Panel l.uiiKth I 12 ! '3 I - ; 14' '5' 16' ! '^' J -s' '9' ^3 J '1 TABL lii whict uMi kino-.; The 1 tiiMis rccj- ! Panel Length. 10' I ! «i' 12' I 13' >4' ■^ 1 .6' I ■7' 1 8' 19' 22' ■!3 -4 TABLE VII. TABLE OF SIZES OF HIP VERTICALS FOR BRIDGES OF CLASS B, In which tlio live Io;ul is one huiuhcd pnuiuls per sciuare foot of floor, and the udikin^-stress on the verticals is ti\e tons to the stjuare inch. The upper figures ;4ive the sizes of the hip verticals ; the lower ones, the sec- ' n'lis recpiired. Panel 12' Leng '4 i6' 10 ! II I 12 ^3 'h. Roadway. Roadway. Roadway. I8' 2o' 22' I 24' I Panel Roadway. Roa.lway. Roadway. ' Roadway. I Length. 2 r a 0.72 a" 2 i"a 0.79 a" 2 f''a 0.86 a" 7 i" a" 0.94 a" 2 fa 1. 01 a" 2 fa i.os n" 2 \f,"a t.isa" 2 ir □ 1.30 a" - 5' a" I.^SC" Ti'~a~ 2 f n 2 f n 0.84 a' 0.96 a" 2 fa -' fa o.(;2 a" 1.06 a" 2 fa -^ f,V'n 1.00 n" r.isn" i.os a" ' '2H''"a~\ 1.17 a" i :: H"o • 1.260" ! 1.35 a" - \ro 1.24 a" 2 i"a 1.34 a" 7";" a ■-t-1 g" I r.09n" '■ - ircTT 1.20 D" I I '-.i' g" : 1.41 g" 2 l"a i-s-g" ■: W'a t.02 n" , 2 5" a i.43_g" 2 I'a I.S2 a" ..61a" 1 1.71 a" : r I I. ■'g .•>•> g" 2 {>"a - i.V'g 1.74 g" 2 i"a 1.830" 2 I " a I. Si a" : i"a 1.91 g" 2 I" a 2.01 D" 7 ..'.rg" 2.11 a' 2 j''a 1.54 g" 1. 04 a" 1.7 ya" 2 \"a I. S3 a" 2 I" a r.94 g" - i,'.i"D 2.00 D" - 'rV'g 2.1S a" 2.29 a" 2 H'-a \ r.7jg" I 2 I" a ' ''Ssg" ! I 2 i"o S 1.9CD" ' 2.07 D" I 2 i^,,"n ■ j 2.ic)n" I 2 ii"o r - <rc! ' I 2.4C n" I 2 t^"a i I 2.60 n" ; I.. -2 0" - r^' 2 (" a 1.44 aj'_ - I.; - '•.=i5g" Ijrg" 1.67 a" : i"D i.SoD" 2 i"a 1.93 a" :.05 D" 3.17 g" ^ ■r'g^" .:.J9g" : il"g :.12 n"_ - iu"g -'•57 g" 2 V'a ^•34_g^' 2 rg '•47 g" 2 n"a '•59 a" 2 l-r' a 1.72 g" 2 I'a ..85 a" 2 i" a 1.98 a" 2 i^'a 2.12 D" 2 r,',,"a 2.26 a" 2 .i"g 2.39 □" 2 i\"a 2.53 a" 2 r'g '•45 □" 2 [fa i.()o a" '•74 a" 2 i"a 1.S8 a 10' II' 12' 2 ra 2.02 a" 2 'I'r/'g 2.16 a" 2 ij"n 2.31 a" rrfa 2.46 a" » , '3 14' 15' 16' '7' 2 'I's'g 2.61 a" 18' 2 ii»,"a 2.67 a" 2 If a 2.83 a" 2 !,'.."a 2 If a 3.00 D" 2 -i' n j.sr, n" 2 'I'/D 3-'7n' - 'fa Lj 2.76 a" 2 i|"n 2.<)2 n " 2 if a 3.01)0" 2 i^f a 19 3 2S 0" 2 'A'g 147 D" 'a -'.41 n" 2 'I'/g 2.-4 n" 2 «l"a ?3 C 2 iT'g 3.65 o" 22' 23' 24' I \' lo' II' 12' 13' 14' '5' 16' '7' iS' as' 22' 23' 24' ffc-^i TABLE C In which the I "tress on the riic upper tiiiiis reciuired. Panel 12' Length. Roadw lo' 2 f'l 0.60 Z II' 2 :l"i o.()5 C 12' 2 f, C.71 C 13' , ,i :: •}"[ 14 '5' 16' >?' 18' ■9' o.S;, C 2 I" I 0.S9 C 2 I" I - I I I I 01 c -r'i 1.0; c - 1 1 . 1 ;, C -■ U" i.-'>. C 23 24' - 4" i-ll C I.;; I S M M ii * ^ im r Panel Length. i 1 10' : ii' i 1 ■ 12' '3' >4 '5' i6' 1 18' '9 20' 2!' - ^Itf^^ .*.-« TABLE VIII. TABLE OF SIZES OF HIP VERTICALS FOR BRIDGES OF CLASS C, III uhk-h tlu' live loail is cii;hty pDunds per square foot of floor, and the workinj;- -ircss on the verticals is five tons to the sciuaic inch. The upper figures give the sizes of the hip witieals ; the lower ones, the sec- tions retiuired. Panel Length. [ Roadway. 10' '4 Roadway. '3 '4' '5' ,,r\ 2ro o.<)5 n" 2 f n o.fx3 n" 2 r a 0.6s D" 2 fa 0.690" 0.7 s D" 2 }"n C.71 0' 2 i" a 0.S2 n» 2 J" a c.77 □" 2 fa 0.S9 n" 2 |"n 0.S3 n" 2 f n 0.S9 n* 2 }"n 0.97 D" 2 }"n 1.04 n" 2 fn " 0.98 a" 2 f □ 20 Roadway. 2 f n 1 .CO G " 2 I'D "" 1.10 a" 22' 24' Panel Roadway. Roadway. | Length. 2 fn 1. 12 n" '7' 18' 19 23 24' 2 f a MI n" .11 n 13" □ .19 D" - I" a i i-oi n" j 1.07 n" i 2 fa ' 1.13 D" I - ira 1. 2 1 n" 2 fr'D : 1.2S n" i —r, 1 - 4 n : r.;,6n" i 2 i" □ '•44 a"^ j - Vn -^ ira 1. 18 D" 2 H'a 1.25 a" 2 IT a 1.32 D" -^ V'a 1. 41 a" '^ U "n 1 J7 □" 2 i •a 1 35 a" 2 I" a r-jon" r.jS a" - ir"~a' 1.67 n" 2 r'a 1.4,5 a" 2 i" a ^ 1-5' a" 2 1 .i " n - \ro 1. 7 1 □" 2 1" n 1. 8 1 n" 2 !"□ 1.90 n' 2 i"n 2.00 n" 1.07 D" =^lra~[ 1. 16 a" "2H"a'^: __>;=s_a"_; "2 fa \ '•34 g" j 2 fa ^"' 1.42 D" 2 U"a j 1.22 D" 2 \r a ^■j3 a" 2 i"n 1.43 a" 2 i.rn 1.20 ;" 2 ii'a 1.3, Q' 2 j'T 1.403" 2 j'a 1.50 a" i.io Z" 10' 13' 2 r'a ! 1.54a" ! r^r'^a 1.65 a" 1. 51 a" t 2 H'a 1.70 a" - Kra I 1.(0 a" I ^fr a I 1.70 a" [ 2 I " lJ j I .yo o " \2 i"'n I 1. 91 D" 2 i"a 2.02 a" 2 13 1..S1 3" 2 ra 1.02 a" 2 i,vF 2.03 y ^ 'A' a 2.ir,a" 2.2S 3" 3fr'a 1.76 a" 2 i"n 1.87 a" 2 i"a 1.99 a" 2 'h"a 2.11 a" 16' 2 iiV/'a -_--3p" '2 7j"a" 2.36 a" 2.50 a" j 19' ar aa' 2 'A" a i 2.13 a" _ - 'i's"'J 2.24 n" 2 IJ'D 2..10 a" "2 iyp7 2.~: -J" 2.64 D" T^h"a~ 2.rs G" If ^-M, II 12' «3' 14' '5' 16' 11' 18' 19' 20' 23 Sl»— w™. TABLE C In whicli the stress on the The upper tioiis re(|uire(l. Panel 12' Length. Roadw 2 f 1 10' 0.60 C II' 2 i"i 0.65 C 12' 2 r'l 0.71 c 13' 2ri t.77!: ,^' 2 ft «5' 16' »7' 18' 19' 20' 23 21' o.S;, C ' 2 f~| 0.S9 c " 2 r'l 0.05 c -• I" I I 01 C 3 f 1 1.07 c ■. Iff t - ( ' 1 . 1 ;, c i.-M r - I.i" i.jS z 2 l"\ - v' i-tt c t 1 .4^ ■>-^*tf?%;^;.,<*''Mj&?-- I 10' II' '3 14 '5 U- 17 18' 19 20 23' h ^"'-^^^MiV^iUj/^^ TABLE VIll. TABLE OF SIZES OF HIP VERTICALS FOR BRIDGES OF CLASS C, 111 wliii-li the live load is eighty pounds per square foot of floor, and the workinj;- >tress on the verlieals is the tons to the si|u:irr null. The u\)\)vv tijiurcs give the sizes of the hip \iitieals; the lower ones, the sec- tions reiiuired. Panel la' Length. Roadway. 10' 2 f D 0.6o D" II' 2 fn 0.65 n" 12' 2 f □ C.71 D" '3' 2 fa <-77 □" 14' I 16' Roadway. Roadway. «5' 16' «7' 1 8' 19' 20' 2 fa : 0.S3 a" ' 2 f "ni^ 0.S9 n" 2 fa 0.1)5 a" 2 r'a r 01 a" - _ . 2 fa 2 fa o/k) a" 0.79 n" 2 fa 2 f n 0.7s a" 0.S7 n" 2 :t" a 2 fa 0.S2 a" o.<>5 a" 2 fa 2 fa 0.89 D" i.oj a* 2 ^"0 2 fa 0.97 n" ...in" 2 fa 2 ir'n 1.04 a" 1.19 a" 2 fa 1.07 a" 2 }*"□ 1.16 a' 2 H"n 1.25 a" 23' 21' 2 fa 1.07 a" . 1 » r-i - I ■'^ 1.1;, a" 2 vrn I.-' I n" - \Va i.jS n" 2 r'n I. Via" - i"n i..t.t a" 2 fa I. II a" 1.18 a" 7]ra" 1^25 D" 1.32 a" 2 fa 1.41 □'' "2 r □ 1.50 n" 2 U"a 1.27 a" T 2'"j"a^ ' 1.35 a" 1.43 a" •l"o r.si n" - ir'n i.(.i n" .71 a' 'n I-;; 2 !?,"□ 1.5'^a" 2 ira i.f)7 a" a ir'a 1.7 ^ n" 2 i"n I. Si a" 2 I'a up a* 2 I" a J. 00 n" 2 jf a 1.70 a 2 r'n i..^'o n" -• r'a i.yi a" 2 ra 2.0; a" 2 1,^5" a 2.13 a" 2 \i\-,"n 2 irV.'n 2 I A" a 2.0.5 □" 2.23 a" 2 i,'«'a 2 ira 2.i()n" 2.36 a" 2 ii"a 2 If a 2.2S -" 2.50 a" 2 ifn 2 I h" 2.40 G* 2.64 a" 2 if a 2 iA"n ^ ~ ■, ^f 2.7S r," 2 if a vo.^ n" .... .,.„*.-* v...i. In tlic In the ! f it a Ji, 1 TABI In tons of two ti- the initial tension u Intensity OJ Stress = E Q r i.2r)S \r 1.451 i" \ 1 .650 n" i 1..SS5 i" 1 J.140 ■i^" 2.423 "S" 2.726 ' 1 i " 3.057 -1" 3.40S ' xV 3-7S7 4.190 4.f.i7 1 '," ; -k" i 5.o(xS 5-547 ■ 1.1" : 6.04(> 6-573 If 1 7.120 ' ij-r i 7.fK)5 , 1 i '■ ' S.294 ' iir' ! «.9»7 j" ' 9.568 -'^" 10.239 A" ' 1 o.( );;S - 1 •' 11.057 1 H" ^ 1 12.404 ! -'ft" , i '3-'7S --r' 1 '3-')70 ,7 » -Vfi ' l-~'t,i A" 1 vl>-," ■■•"*«•#<.■ ■ TABLE IX. TABLE OF GREATEST WORKING STRESSES, ]n tons of two thousand (2,000) pounds, on adjustal)le round and square rods, exclusive of the initial tensions ; also the initial tensions. u e Q f 7 " !i""" 'A" ■i" ' iV ti" 1 1" '}.'." 1 i|r' ; If 1 1;' ' - 1 •> > * '' - 1.1 -i" '■ -h" -]'■•< -V Intensity of Working Stress = 4 tons. 1 Intensity of Working Stress =; 5 tons. Intensity c Stress - © )f Working 7.5 tons. 1 Initial T ensions. u it 1 1 Q J" liV" ' "I" i w ; 1" I ifV ,''^"" ■ i" i ';v' " 1 •-, ■,» — ; 'H' 'f 'iii' , 1 ij" " 1 ! 'H" i 2i" 2^" I 2 A" ! 2i" ' 2,\" ' u 01 1. m 3-574 4-'57 4.789 5-4:^i____ (1.230 I 7-0.38' 1 7.904 r 8.830 9-814 10.850 j 11-956 1.3-117 ® —1 I.26S ~ '-45' 1. 6 so 2.140 2-423 " i-5'7 1.710 2.178 ' 2.507 2.815 .3_-76o 4-303 .|.S(K5 6.205 6:931 " 0.500 : 0.025"' 0.63 s 0.794 0-953 1.846 1 1.970 2-257 2-576 2.927 3-308 3620 4.163 2-875 .3-284 __ 3-730 j 0.750 ! 0.875 1 1.000 2-405 2-730 3.0S7 1.111 1.270 4.216 1.125 1.429 2.726 3-476 4-740 1.250 1.588 1.746 3-057 3-»94 5-305 1-375 1.500 1.625 3.40S 3-7«7 4-347 4-636 5.140 5-675 5-908 „iL'5S0__ 7-2.10 7-95' 8.710 7-704 s-523 ~ 9.3«7 10.29S 1.905 2.064 4.82S 4.190 5-341 1.750 2.22*1 4f'i7 S-*^'^!^., 5.o(kS 6.4(0 1 6.240 6.836 1.875 2.000 2 381 2.540 "-253 '4-335 5-547 7.065 7-463 9.508 12.256 15.611 16.947 , 18.342 2.125 2.699 6.04(1 7.706 8. 119 '0.345 ^„.i3^P4___ 15-540 16.726 2.250 2.858 3.016 6-573 8-.376 8.8aS 11.223 2-375 7.120 9-077 y.8io 10.571 9-527 10.276 12..38 19-794 2.500 2-625 3-3,i4 3.493 7-(m 13-092 21 .305 22.874 8.294 8-9' 7 ' 9-5('''^ 10.239 11.056 14.085 17-959 _i'>237 20. 5(1 J 23-3-1') 24.811J 2(1.321 20.476 _ ;j.Si ; 2.750 3.000 'i-36i__. 12.190 1 11.867 1 vl iS 24.503 2(1.190 3.651 3.810 12.708 13-580 14..,83 1 '5.4'7 16.380 '7-.?75 18.400 '9.457 1CI.|I)0 17.300 18.450 i<).f)40 ~ 20867 _22.23S___ 23.440 24.780 i -'ii.i;o 13-047 27.935 29-7,39 31.003 ' 3.3.524 3-125 3-250 .3-.375 3-500 3-969 4.128 4.2S(, 4445 4.604 __ 4-763_ 4.921 5.C80 ! io.<)3S 1 1 -657 12.404 '3-936 14.854 .5,807 1 13.17s i I6.7S8 1 35-504 3625 3-750 __3:S75 4.000 1 3.()70 1 v'.;(. 17.801 _j8rs4T:: 37-541 3<).(i40 41 r'ls I 4" 1 ' L t 2 2 2 2 ^ INIANNEL STRUTS. Ratio, /, to D. IHii S)® Ratio. A K. /'. 64 64i " 65 66 ^■'.. 10 loi 1 rr"~ 1 ni 4.20! i.4t9 4-I4! 1-377 4.1 M i-3S6 4^oS: 1.335 4-05,: i-.VS 4.02^ 1.296 3.99.; 1 .276_ 3.96; 1.256 3.901 1.219 3.S7: 1.200 3.841 1. 182' 3.Sii 1.165 _3-7'^' '-M-S 1.569 '•553 '•53« '•523 12 id '5 ■5i i6 17 1-508 66.i 67 67.1 68 68i '■493 1.479 1.464 1.450 '•435 6.ji 70 1.421 : '-407 '■393 70J 71 '•379 1.366 I7J ! _,V75> '•"30 ■'■"-' _L-1' -3 „ 3(19; 1.097 3.61 >; i.aSi 3-63: J .064 3.60; 1.04S 7..L. 72 ' 7-^ 73 ' 1 73.' i 74 '•353 IS "' i iM-i 20 1.340 1 1-3-7 i-3'4 1.301 ! I.2S8 .-ol x"' i-o.v'. :\': '•-"n ::i 21.1 21\ ,1-5 1. i-oi.S y\\.. 1.003 3 |Si o.<)SS ;,.',;' o.>);( I 75r "7C> 7'V, , 1.2(13 i"'-\si : 1.23S 1.220 j -xi 3.-IJ' 0..)()0 7'^ J I.2r4 1.202 ! -M 3.31K 0..)', i 7S i.itii -'■t' .l-viC O.')J0 - ^ , 1.171) ^5 3.311 o.i)07 3.2S: 0..S94 3.2^; o.S.sf "'1 s<-> 1 . 1( i.S 1 1 V I.I |(. 27 1 1 - 1 5.2 2( O.SuS 319} 0.856^ 3.r-( o.S(.| S.i Si Si 1.124^ 1 1 , 1 1 1 tj ® i ® I 1. 130 I.! 16 1. 102 I .aS8 '•075_ 1 .0(32 '•04 9 1.024 I.OII O.IY)') o.(j87 0-975 0.96;, 0.951 0.939 0.()2S 0.1)17 O.(i0li o .S>)5 Jo.SSs 0.S7.1 o.si).) 0.S54 o.S.14 o.S-vt 0S24 o.S 1 4 0.S05 o.7')5 0.780 0.-77 o.7(i.S <\"5>.) 0.750 0.741 0.832 0S20 0.809 0.797 0.786 _°-Z75. 0.765 0-754 _^-Z44 0-734 0.724 0-7 '4 0.704 0.f)<)| o.'iS5 r.676^ 0.067 1.658 0.649 0.640 0.032 0,02 I 0.01 (} 0.60S 0.600 0.592 ■ 0.5S4 0-57*^ 0.569 0.5<i2 0-555 0.54S o. 5 ) I 05.il 0.527 0.^20 I ^Ha , '^■-J^:'~ '/»«»i«»**««i«***" INTENSITIE Ratio, A to D. Uti 1 !%• O d 10 1 1 4.205 4- 140 3.900 i 10^ 4±75 4-103 3-'M7 ~\\ i 4-145 ; 4.066 3-')04 Mi ' 4.IM i 4.029 3.S(,2 i:: 1 ^__'»:°L^5 ' 3-993^ 3„Sm I2i ' 4-05;, i 3-95^' .5-775 '.) i_i:°f3_^ 1 3-9 '9 3-73- '■3L..: 3-993 3.8S2 3.aS,S i '"* ,Vr/'2 ,?S45 3-<'45 '-(i ; ,v93- ' 3-«07 1 3.()0i '5 i 3.901 3-770 ,._3-557 '5i : 3-.S72 3-732 3-5'4 ■ K) ;vS4> 3-<''')5 ' 3-470 I'.i ;,.Sir ._ 3/'57 - 3-4 -'4 i 1- 3-7.SI 3.620 I _3-5'\3 .1:^^^ 3-75' .V34> 1^ .vr-i 3-54''> 3--')5 ISJ .•,.(.92 _3.5aS ' _3-252 ly 3.6()2 J-471 ^ 3.209 '"J. I 3.632 3-434 3.1(1(1 , '° 1 3.()Q2 3-397 _.v'-'3 20) J "3-573~" .3-360 1 3.0.S0 1 .1-51? 3-323 3.03S 2^\ ,v^l 1 3.2S6 _ 2.91)0 '', i _J4«5^J .3-250 "j-9S3 32i ; 3.456 ' .V2I4 2.912 1 -:? . 1 3-4-"' 3- '78 2..S7. -r?i ,i-,)'): 314- 2.,S30 :^4 __ 3-.i''9 3. 1 G() 1 _2.7.;o ' 2-»rj 3-340 i 3.070 : 2.750 -^S 3-i'i 3■<^^^ 2.710 -5!. _3.^x^ ; 2-<)')<) 2.670 , ^6 j; J-- 54 ! 2.964 1 2.6 ;o :f,i • V-'jd 2.')2f) 2.:^n\ J" 3i,),s . 2.S.,5 -■^i'l -Ti ii 3-f70 ^ 2..S(iO .•515 TABLE X. INTENSITIES OF WORKING-STRESS FOR CHANNEL STRUTS. CLASS A. [0 I I 11.^ 12 I I ill I > Id K.i IS |S) I') :i -' ' i 2 "* 22\' dd..« ii»3> #(§ 1 .(.JO 5 .1.140 ,v90O ■t-'7=; 4.103 J-947 .(.i.i; .|.o66 3-904 1 , .(.III .1.029 3.862 1 4.0S5 3-'W.5 ;,.Si9 Ratio. ..- — z to /;. i aa -(■o,s;, -♦-023 3-993 .V9.P C3® OdD 1 Ratio, I to I). HIS 2.826 2-477 46 2.241 2.792 2.441 47 47i ^ 2.219 -^759 2.404 2.368^ •■332 2.297 2.198 2.725 2.176 2.692 2.659 48 48.J 2.15s 2. '34 2.627 2.262 2.227 ~ -A'93_ 2.160 2.127 2.094 2.061 49 2. 113 -•595 __19i_ 5° sol 2.092 --53' 2.072 2.051 2.500 5' 2.031 2.46(j 2.43S 52 52^ 2.011 1.991 2.408 2.030 '-97 1 -^378 1.999 53 1.952 2.34S 1.968 -1-S37Z 1.908 1.849 1.820 S3k ••933 2.318 54 1.914 2.289 S4i 1.895 ..S76 1.839 2.260 55 2.203 5Si 56 ' -147 J.I19 '•793 1.765 •-73S S6i 57. S7i 1.8 21 1.S03 2.0()2 -•.06; -' ■039 o'3 1.0S7 1.1X12 M2 I ss- 1.8(13 8;u 1,81; t.710 1 .684 17.58;' J -^31 1.607 '•5«3 '-55« 1S09 1 .486 1.46,1 1-112 5« i.7r)8 _ SS-1 59 _, "S9i 60 '-751 '•734 1.717 1.700 f)0i 1.683 6, 1.666 1 6..^ i.'>49 : 62 ^'3 I -"32 1.616 1.600 1.584 ,1 \ -s„ INTfiANNEL STRUTS. Katio, /. I.) D. Gill 10 4-367 '0^ 4-343 II 4-3 '9 ^^\ 4.294 \z 4.270 I2i_ 4.245 ' .1 .\.220 \ INTENSITIES Ratio, /. I.) D. 10 IfiiO "* ®© 4-/'7 4.299 l-'43 11 4-343 4-3 '9__ 4.26S __4.ro5 _ 4-237^ 4.067 Hi 4-94 4.20f) 4-029_ 1 1 4.270 4-'75 3-992 .2i l4;245_ 4.142 3-950 '3 4.220 4.1 10 3-9 '4 '.3i___ ..'♦•.'91_ 4.077 3-875 1 1 l.Kx) l.045_ 3-836 Mi- 4.144 4.012 3-795 's i 4.1 18 3979 _ 3-755_ 15I 4.o<).S .v<)4^> 3-714 i() 4.o().S 3-913 3-674 ,r,,i_| 4.042 3-879 __3A33 '' __.' 4.015 3-S45 3-5''-' '7) _.!•<)' K) .VSi, 3-55' IS 1 __3-0''t J-777 : 3-j'o_ iSi ' 3-'»>'' ^3-743 3469 !■) .)•')'-' 3-70.S 3.428 n»J VSJSd ,v''>74 3'387_ JO 3.,S(,o 3-<'40 3-346_ -'Oi 3-\V> V(')o6 3305 Jl ;v'So7 3- =171 3.J64 -Mi 3-7.SI 3-537 y--:^ ' ti 3-755 ; .1-502 3''82_ -V', 3-7 ^S 3-4f>S 3- '42 " 1 3-702 .)-433 3.I02_| , 1 ' ',,•17(1 3-.VI.S ;,.o()2 ( -'t ,!■''!') 3-VM 3-o.:3 1 -•■('. ;.!._•;, .;■!-■') J.. ^3 1 -■5 .v3'i'> ,v-'»5 -"»3_i -•-.'. 3-.vO , ;,.2;)i •■'m '■ ^(^■■" II 3-544 ! _3---7 i "2.864 ■' .hi_ : 3-5'Sli 3 I'M 2.S2fi^ "' - -- il . 3"»9i 3.1(0 2.7S8 1 i7K.ii 3-465 3- '27^ 2-750 ! TABLE XL INTENSITIES OF WORKING-STRESS FOR CHANNEL STRUTS. CLASSES B AND C. iuC 2.712 2.674 Katto, /, to Z>. ■a I 1® ®® i.6i6~ '-593 1.570 1.547 '•525 '•503 r.4S2 ' ..40, I 1.440 1.420 1.400 r.3So1 i.36o"'| '•342 i '■323 '•305 1.286 1.268 1.250 . '•'99_ 1.182 j 1.166" Ratio, L to D.\ mm ■ ® 0.976 0.963 0.951 0-939 0.926 ,v»;4 46 _2.-.5S' 2 2.529 2 040 016 992 968 944 921 898 64 644 1.842 1.327 J.O()l 46J 47 47 i 1.826 1.312 .)-02S 2.638 2.602 2.507 I 65 6si 66 1.809 1.792 1.297 1.282 j.()95 2.485 _i^ 2.463 I 2.</)J 48 1.776 1.760 1.267 >.253 2.930 2.529 48i 2.440 I 66i 0.915 0.903 0.S91 0.S79 0.867 2.S97 2.494J 2.459 49 2.418 I 67 67] 68 1.744 i ■■7^8_ , i-7ti 1.238 '•-23 1.209 2.,S6., 49i SO 50^ 2.396 > 2.374 I 875 853 83 > 2.S32 2.424 2.S00 2.390 2-356 2-323 2.289 2.2S7 2.225 2-353 ' 68i 69 I 1.696 '-'95 1.1S2 2.76.^ 5' 2-333 ' 809 >87' 1.681 1.665 1.650 0.856 0.845 0.834 0.824 0.813 -•73S 5>i 52 S2i 2.312 I 69i 70 1.168 2.707 2.292 I 2.272 I 2.251 I 2.231 I 2.21 1 I 766 745. 724 703 '683" 665 648 626" 604 ■•IS4 2.676 70i 1.636 t.140 1.127 2.f.46 S3 71 1.622 1.607 2,015 2-193 2. 161 2.130 2.100 S3^ 7ii 1.115 -.'•'°3 1.090 1.078 0.803 2.585 S4 S4i 72 1.591 0.792 ~ 0.782 0.762 0.752 -■55'^ 2. 191 I 2.I7I I 2.151 I 2.132 1 i 72i 1-577 •-563 '-549 1-534 2.526 S5 ssi 73 2.496 2.069 2.039 73i 74 1.066 1.054 1.042 1.019 1.007 2.467 56 2.439 2.010 564 2.1 13 I 585 566 744 1.521 „''S07_ 1-493 1.479 0.743 2.4 1 2 i.98r| 1.952 1.924 1.896 I.S69 1.842 I.SI5 I.7S9 1 1-763 ••738 1.712 t.6S8 1.664^ r .640 57 57i 2.094 I 75 0-734 2.;,S;; 2.075 ' 547 754 0.725 -•35S 58 1 2.056 j I 1 2.037 I 2.019 • 529 5" 493 475 45S_ 441 424 407 39' 375 .^59 1.149 '•'.?4 1.1 iS ..103 " i,oS8 ^ '-073 1.059 76 , 764 _ ; 77 0.716 2.,\zn S8i 1.466 0.996 0.985 0.974 C.963 __o.953 0-943 0.922 0.707 2.;,oi 59 _.'-t53_ 1.440 1.426 ~J4'3 0.1 «>s 2=73 59i 60 1 6or- 2.000 I 1 .9S2 1 ..964 !"1 1.946 r 1.028 I 1.910 1 1.893 ' 1.876 1 : 774 o.(xS9 :.:\--. ! 78 o.(')S 1 .'..MS 784 79 o.'i-'; -M'l.' 61 62 1.400 O.Ods J.KK) 1-045 '■°3'_, 1.017 i O.OC)0 794 1.388 •-376 0.65- 2.140 : 80 0.649 2.115 62i 63 63i L 8°i St '•363 ••3S> 0.912 0.641 2.0<p 0.902 0.S91 0-633 .•.065 1.859 1 343 si4 1-338 0.624 T> K i T/ ■m V. TABLE OI AND ST STRESS] g (« Q C\.\»* A J S-9 -•i" :•' •i" .S4 <j.i) =r_ "S i' " 1 t ^ '* -^ ! i.v.> » t " '5-.5 ^i"^ _^ '"-s ," i<)'i ir~ i__"-5 .>v'" 1 25-3 ■_.-«••? vi"^ I .?'<' }V 1 35.'. M'' ' .v^..s '*'_ 4^.« ■i" ! 47-1 li" S'-7 ir S<'-5 rr I (.1.7 ■li" 1 07.1 li" ! 72.S ii" 7S.<) li". S.So ^ j 1)3.0 a'" i <)<). 1 - 1 " 1 (W J. ^ - 1 " ^ 1, lll.', -T" I )0.0 « 5'>o TABLE XII. TABLE OF WORKING BENDING MOMENTS FOR IRON AND STEEL PINS. AND OF WORKING SHEARING- STRESSES FOR STEEL PINS. M i ! ft 1 \\" >'v if '*— -•i" ' -•r - n Resisting Moments for Bending. Kl., Resisting Shearing- Stresses. W E 5 lUllV. Su ! .S|l l-,!.. 1 a.i« A. Cl,i»!>f< L.ncr.il H Anil C. { Synlcm. C'Iam a. Cla»iM;» CUu A. CtauMi H and C. 1 3.1 ■I ! ' 2.9 1 1 ! .V .}•; J-o \""" .: " 8.5 II.O , 'i* 2j" " _- 2i" 2?" 3' 3i" 4.0 4.8 1 5.9 40 5.9 III 7.2 ~ 7,, H.S""- " 7.S i)..S II.S 1 ■ ■ .. . «3:3 12.1 15.2 7-1 8.9 10.6 12:6' ' .4.8 " 17.2 19.9 22.9 "It ll-- i3w 17.2 8.4 9.9 10.5 1^3 134 'f""^ _, '54 i i<r 11 i7-« i 19.3 15.8 21.3 -4' >>S 144 18.4 :vo i 18,9 23.6 ^r 1 1.1-3 . 16.6 21.3 JO.Il 20.8 26.1 ?"^ u , Iff ,vi" 15-3 ^_ '7-S __ 19.9 1 i2.5 1 25-3 19.J 21.8 24-5 28.0 1 22.9 28.7 36.3 34.'J 35.1 3'4 34-2 37-' 40.1 43-2 46.5 34.8 I 29-8 3 '.8 36.0 45.0 27-3 38.1 33-7 i 29.6 3t-6 37-9 40.5 SO.C 1 32-0 1 3r 5V 3i" 1 31" \ 3f"' , 31" i '♦".- ! 41* ' 4i' 4i" 4V 2S.3 i .V <> 354 424 45-3 5<^-'' i 34-5 39-5 474 50.(1 (\\.2 .37- ' ,?r i 35-' 43-8 S2.6 56.2 70.1 7--f' 85.() 39.8 49-9 48.5 53-5 (..(.J 6;. I (kS.5 4».7 53-4 ti" a" 42.8 i _j47il: 45.6 57.0 58.9 70.6 75.4 ')\-: 82.7 10 -,.11 90.4 1 1 .;.o 98.7 >-;v4 48.6 60.7 64.6 S'-7 54.8 58.1 64.6 ;(i.S 70/) 68.6 oi-r 77-1 ' 72.8 <)I.O 7^-7 107.4 1165 134.1 w 61.5 I4.vi> i 65.0 76.9 81.3 )J" iS;.') lo6.() [2G.2 i;-S ' r.S.; 1 S;.6 1 vi ^ 1"^'' 1 r-'-i i 'JO-' ;'■ ji ()2.0 115,0 1.17.2 , IS4.0 r 58.(1 M1.S.1 1 1701 -'13.0 li 75-8 94-8 5" ' 5]" Si" 5i" , sr 1 5f 6' ! it 79-7 99-6 104.6 ;J" 1-1.; i 1;, ;.! II 83-7 >.■■ "1-3 ^V '■•-•s 1429 18.' -':S.7 '' 87 .8 \tyC,.o -1-" 9'-9 ;;o(),(i 96.1 _'_\| 100.4 1 :!.!>i.'i 1! '04-f< ro<i.7 114.9 15.V' 1 6'" |i '5"'" 1 254-4 1 i II .09.3 i ^4 //' = lino 1 lattc > ii FOADS THAT CAN BE iTr.iutwine's formula. /('— ,.„ where //'=1(): Ti.Mm, and in rij;ht or It't't haiiil vertical line for -"r, and a horizontal line through the latter, ir 8' 21" ^ 22" i i -3" 24" ! ().o.44 io.3').S 11.882 1 13.500 : 8' 9' 10' 1 7.14') S.Jii) 1 5.7.S8 ' 6.655 ; 4.7S4 5. 500 9.3S8 . 7.604 1 6.285 10.667 j 8:640 7:141' i 9' LJ0'„ u' II' 1-2' ] { 4.0JO 4.622 342s 3-98S 5.281 4.500 ! 3.880 ' 6.000 '"5,112 12' 13' ! t4' isH '4' 1 2.953 3-396 4.408 ; 15' i6' '7' "1 2-573 2.600 3-3^0 2,971 3.S40 . .3-375 2.9S9 «5' 16' «7' . 2.261 2.003 ; 2.303 2.631 1 8' i 1 i.7'^7 2.054 2.347 2.667 18' 1 >9' ; 1.603 ..S43 2.106 2-393 19' 20' 1.447 1.664 I. (JO I 2.160 20' 2l' i-3>3 1.509 1.724 1.959 1 21' t 22' 1. 196 •-.375 1.57 1 1.7S5 22' 2.V 1 1.094 1 I-2SS >-43!L •-633 - 23' 24' '\ 1.005 i '-'56 1.320 1.500 24' 25' 25' 0.926 1 1.065 1. 217 1.3S2 26' : 0.S56 ! 0.')S5 'j'-S. 1.278 26' 27' h__0:Z?4,_ 0.913 28' J j 0.73'^ _| 0.849 29' 1 1 o.6,SS , 0.791 "•043 0.970 o.()04 1.185 • 27' : 28' 1 29' 1.102 1.027 30' o.'i.t;; 0.7.(0 o.S4i; 0.1)1 <> 30' \' FOR FINDING THE S ■|k tads bciiij;" those which will ]' //'=z]();ul in tuns, // = depth ot bi'ani in T(i find the sate ilistribiited luad fo line for k'n^th of span. The number fo latter, miilliplied bv the witlth of beam ii I ' S" 9" 10" II" I. 8' 0. soo 0.7 r 2 0.977 1.300 I.( 9' 1 10' o.,v)5 0-1-0 i 0.5^3 0.4 5f) 0.772 0,625 1.027 ~O.S32 I.; I.C II' la' 0.2h4 . 0.222 0.1 Si) o-.i;? o-S'7 0.434 0.370 o.CkSS 0.492 0..^ 0-.3I7 ^ 0.270 0.7 13' o.( 14' 1(15 0.2}} 0.319 0.425 0. 15' 0.14.' O.203 0.278 0-370 0.. 16' 17' 0.l2t, I 1 1 0. 1 7<S 0. 1 5S 0.244 0.215 o.3-'5_ 0.2S.S 0.. 0-, 18' >9' 0.01 )l) O.O.SI) o.u6 0-I93 , 0.173 _ 0.257 0.230 0. 0. 20' o.aSo 0.114 0.156 0.20>S 0. 21' 22' 07 ^ O.Ottd 0.10;, 0.01)4 0.142 0. 1 29 0.I.S9 0.172 0. 0. 23' o.o.S() 0.1 iS 0.157 0. 24' 0.079 0,109 0.145 0. 25' 26' 27' 0.100 0.123 0.114 0. ._°-°93. 0. 0. 28' 0.106 0. 29' 30' i 0. ■-O'-JWp:- TABLE Xlll. BINDING THE SAFE UNIFORMLY DISTRIBUTED LOADS THAT CAN BE BORNE BY PINE BEAMS. d^ Is hrin- those which will pnuhice a (Ictlcctinn ol only 4^0 "'' ^'^^^ ^P^"' calculated hy Trautwine's formula, W - |^^.^. where (ins, ^/ = depth (if beam in inches, ami / -:-- len-th of span in feet. Ihe safe distributed load for any span, h.ok m tiie upper horizontal line for depth of beam, and in right or left hand vertical of span. The nuiuber found at tiie iniersection of a vertical line through the former, and a horizontal line through the led bv the width of beam in inches, will ^i\e the load re(|uired. |vSrJ'r'''«(»l jr-. liiK' litti '^*Msii' ..u™^ p LOADS THAT CAN BE c'd by 'l'raut>vinc's forimi!:!, //'. Mo/ .„ whore pth of l)c;im, ;in(l in ri-lit or left li;iinl vertical Iji,^. ic foniier, and a horizontal line through the lalte I ') 20' 21" 22" 23" 16.531 24" - . 1 1 1 IO.S70 .2.5S3 14.467 .8.781; '^ .'- .1 M-SSS 9.()42 '•-43' r 3.062 14.841 9' .'■*- .''- __ 6-957 5-749 «-053 6.655 9.259 10.5S0 "S.744' 12,021 9-935 i:__to' n' 7-652 .-' 4.831 5-592 6.430 7.347 1 8.34S 12' ,.5 .|.ii6 __:v549 4-765 _.J.IO(J 5-479 .. 4-7-4 6.260 ^ 5-.i97 7-"3 6- '33 ' 13' 14' .' ' 3.092 3-5^9 4-"5 4--0J 5-34;, 15' i'' 2.7. s 3.146 3-'"7 4-133 4.691 > 16' i' 2..(07 J.7S(, 3.204 3.061 4.1^1) 17' 1 1 _ -147 -'•4X5 2.S58 3-265 3-7 '0 i 18' 1 r _L9i7 _ 2.231 2.56; 2-<)3" 3330 19' ;' '-739 2.013 : 2.315 J. (.,,5 yOO^ 20' '•577 ! I.S26 1 2,0<>S 2-3W 2.7 2() ai' '-437 ! 1.664 I '-9' 3 2.186 2.4S5 22' ;S i-;,'5 1.522 , '-750 2.000 -'•--■1 23' '■>5 i..'oS i.3i>S , 1.607 '-\r J.0S7 24' /■I 1,113 l.2.S,S , I. ,81 1 .tM(3 1 .gj ^ 25' 1 J 1 .020 i.tyi 1 >-369 ! ••565 i 1.7 7S 26' ,s 0.954 1.105 1.270 1 45' i.'M'» 27' ,ll 0.S.S7 1.027 i.rSi 1-34') 1-533 28' ,'' o.Sj- o,'):;S I.IOI i 1.258 ' 1.429 i ag' .'.) *■ . . > ■ N i ; i.rj'i ' '"> i.r/' 30' i Trvs FOR FINDING THE TIk' loaJs hciiii^ thosr whifli will //'-- load ill tons, r/ = (k'i)th of beam To tind thr safe (listrihutcd load liiK' lor kn;;tli of span. The number latter, multiplied bv the width of beam 1 1 9' lO' n'~i 8" 0.695 _9:SSo_ 0.445 o.3()8 0.309 9" 10" 1 II " 1.809 1.430 "•157 _ 0.957 0.804 0.685 " o.59r" I 0.991 0.783 0.634 .^°-S-4. 0.440 0.375 Q.2S2 O.24S 0.2IC) 0.196 0. 1 76 0. 1 58 0144 0.131 0.120 0.tI0 '•3S9 1 ■■°74_ 0.S70 °-7 19_ 0.604 0.444 0.340 0.301 0.241 0.2 J 7 o.I97_ 0.179 0.164 0.151 0.129 H la' 1 1 ' _ '3' '4' ' 0.263 0.227 - 1 15' o.iijS 16' 0.174 1 17' 0.154 18' ! 0.137 19' 0.123 20' 0. 1 1 1 0.452 0.400 o.3.';7 0.321 0.289 ■ 1 21' 22' 23' 24' 25' 26' 27' 28' 29' 30' O.IOI 0.092 0.262 _o^239_ 0.219 0.201 0.185" 0.171 o.ifo O.I 48 — ^w 'H B H- ^B. '- -"- — 1 -..- •'^ I \ i TABLE XIV. FINDING THE SAFE UNIFORMLY DISTRIBUTED LOADS THAT CAN BE BORNE BY OAK BEAMS. .a.ls iK'in- th.^se whirl! will pnuluc. :, (lcfk'cli,,n of only ,i,t •'» tli'- span, calculated bv Irautwinc's formu'i IT^ '^'^- where ,,,,.,.. ' ' 1 1.5/^' n tons, ^/ = depth ol beam in mcho, and / = length of span in feet. 1.1 the .safe distributed load tor any span, look in the upper horizontal line for depth of beam, ami in ri-ht or left hand vertical ,th ol si.an, Ihc number b.und . the intersection of a vertical line through the f.,rmer, and a horizontal line through the plied by the width of beam in inches, will give the load reciuired. n 9" 10" 1 1" _T.8o9 1.430 1.157 0.9S7 0.804 0.685 ' 0-59''" 0.452 0.400 0-357 0.321 0.289 0.262 0.^39 0.219 0.201 0-185 0.1 f)0 0. 1 4S ,2" 2.34S '3" i 14" 1 ■5" 16" ■7" 18' 19" 20'' 1 21" 22" 23" 24" 1 ^s. 0.99' 0.634 0.440 o-37_.S 0.32;, '•3S9 '•°74^ 0.S70 0.719 0.604 "oTsfr 0.444 0.386 0.340 0.301 0:26s" 0.241 0.1 <)7 o.i7<) 0.164 J=-9^*S_, __3'7-S 2.946 4-5«S 3-623 5-565 4-397 .J-562 2.944 ^ 6.675 S-274 __4-272 3-53' 7.924 9-3 '9 __7-36j^ _5-964_ 4.929 _4:^'4L 3-529 ' IC.S70 ' S.5S8 6.957 5.749 ' 4.S31 4116 _J-_549 3.092 ^2.718 _„-l407~_ __2a47 1.927 '•739 '.577 '•437 _I2.583 9.942 8.053 _L4_467_ 11.431 9.259 J6.53'_^ 13.062 10.580 8.744 7-347 18.783 ! _i4.84i ; 12.021 ! 9.935 ' 8.348 8' 9' >io '-"^SS i 2.359 6.261 _5-o7i^ '4.191 MS j68 1 50;, i.'in i 2.386 2-93S 2.425 2.038 to' J.242 , 1.579 1.972 .'■^57 _ 6-655 7-652 II' 12' joy 1.044 0.889 0.767 0.668 1327 2.474 2.108 2.967 3-522 _-5:.S9i_ 4-765 4.109 6-430 1. 130 ' 1.412 «-737 1.497 2.52S 3.001 5-479 6.260 7-"3 ' 6.133 5-343 \ 4.696 i 4-159 1 13' -!/ C.849 1.217 1.817 '-5S3 _l'39i 1.232 1.099 0.987 2.179 ..899 2-5S7 "=54 3-043 2-651 4-724 5-397 14' 15' 16' 17' 18' 9A 0.282 0.24S 0.2 19_ 0.196 0. 1 76 1.060 _'j.3°4_ 1. 146 1.015 0.906 3-579 3.146 2.786 4.115 .3-617 4.702 74 -_9-5^7,. _^°-74''> 0.932 1.669 T-478 1.318 1. 98 1 2.329 4- '33 .vt 0.520 0.661 0.464 0.589"" 0.4 1() , 0.529 0.376 0.477" _o.34i ! 0.433 0.31 1 1 0.395 0.284 j 0.361 0.261 i 0.332 0.826 0.736 •-755 2.064 3.204 3.661 Si 1-565 1.841 1.65: _2-4«5_ 2.231 2.8 58 3-265 2-93' 2.645 3.710 1 3-330 3.005 2.726 2.4fi5 2.274 ' 2.087 ; 1-92.? ! I-77S 1 '-649 , ' '-5.13 UM29.| '■3,'/> 11. 0.661 0.813 r.183 1.405 1.268 2-565 19' ' 20' 21' 22' 23' 24' 25' i 26' 1 27' r 28' r 29' ti ^ 0..58 1 44 0. 1 3 1 0.t20 O.I 10 0.596 0.541 ^ °-493 " 0.451 0.734 0.665 0.606 _°;S09, 0.470 434 _ 0.403 __o-374 0-349 i 0. ^.-6 0.891 1.068 1.491 2.013 1.826 2-3'5 01 0.808 0.736 0,673 .0:969^ 0S83 0.808 0.742 0.684 1.150 ""1.048" 1.23: 2.098 2-399 '.)-' 1.664 '•9'3 2.186 2.000 — 0-959 0.881 1.12S '•3'5 1.522 '-7 50 0.1 51 0.411 0.617 0.570 _o.527 o.4,S9 1 __o.454 i 0.424 ! c. ;ci'i '■03i 1.208 1.1 13 1 .02() 0.954 O.8S7 0.827"^ 1.398 ..288 1.607 '•837 0.129 0.240 0.306 1 0.3S2 0.222 0..'S2 0.353 o.joii 0.2(12 ; 0327 0. 11)2 O.J).( 1 0.304 0.81 1 0.954 0.750 0.88: 0.696 ; 0.8 i.S 0.647 761 .48. 1.369 1.270 "1.181 1.693 '-565 1-45' 1-349 _'-A58 _ 1.175 0.632 0.586 . °-S45 0.508 0.4- q 1. 191 1. 105 1.027 J_p.95S3 S()5 0.17') o.-'j; c -' 1 • 0..-84 0.603 ; 563 0.700 l.IOl l.02() Pa Let i I I I I 1 1 1 1 I \' \ i OF CLASSES A AND B " ^ , /•'! 12"; ami ^iiard rails, 6"x6 Pa Ler I I I > J 1 Roadway, 24' clear, j '" ' i 1 201 No. of Joists. •3 Size of Joists. ,5" X 10" No. rai! per Hand- Posts panel. Panel Length. !0' 11' 12' I '3' 14' 1 1 15' 16' 17' 18' 19' 20' 21' , ,3/ 24' •y 1382 I4S4 1710 >3 \ 3" X 10" !' >3 3''X'o", 3" X 12" 1 13 '3 — 1782 i y X \2" 205() 2136 •S •3 ' 3" X '2" 1 3">^'4" -tX) ;,oSo 3339 »S 3" >< 14' 16 1 3" X 14* I 4 'S 17 14 4" X 14" 1 "• 1 4 , ' i 4«x 14* 467 -• J 4* X 16" 6 16 1 18 20 4* X 16* 6 j 4' X 16" 4" X If." \ 6 m -. I "K i TABLE OF PINE LUMBE I'loorin- 3" thick; hand-rail \u Panel Length. Roadway, 12' clear. No. of Roadway, Joists. 14' clear. No. of Joists. Road 16' cl 10' II' 12' 691 776 1 8 sr 806 842 '}02 1 944 S 8 i 99 i 10.) '3' i 990 1 1 10 S ' -.\ W lOJd 7 ; ..5^ S '-7' 15' ' 16' 1 rSo '--I •.^'S 9 8 \ '45' <,57f> ,yj 17' 18' ! 19' 1 |00 MP i TV, 8 '5('5 1670 9 Tjc 10 lS,,i 8 I 1950 9 2 '57 20' 21' 1 ') 1 i 2aS5 2177 1 .0 1 S 2.V)2 7 1 J (20 22' 23' 24' 1 S 2.536 9 25«5 10 27S« 3024 12 .15 -S OF PINE LUMBER TABLE XV. REQUIRED PER PANEL IN BRIDGES OF CLASSES A AND B (including waste material). a ainu ti .rin^ 3" thick ; han.i-ail posts. 4"x6"X4'; hand rail. tw.. pi.ccs. 3"x6"; huh rails, y'x.:"; and .au ■A^ydn] rails. 6"x6'' 1 3. of Roadway. if^ts. 14' clear. 1 No. of Joists. Roadway, 16' clear. 1 7 776 8 sr.i 7 902 8 i . 8 S 9 8 1 998 7 I 944 i 1046 7 IIIO' I j;,o " "5^ 1278 s i;,iS '4S<J ;- >37<'' ■ S2S i 9 10 1730 J 1670 .84, ! 1950 2aS5 2177 1 2336 9 10 i 8 9 -'5; 2.(20 j ) ir 1:; i' ■^1 30-4 No. of Roadway, No. of Roadway, No Joists. 18' clear. Joists. 20' clear. II Ro 24 \ > IDGES OF CLASS C 2" ; and ^aiard rails, 6"xC)". Roadway, 24' clear. No. of Joists. Size of Joists. No. Hand- rail Posts per panel. Panel Length. IJOI '3 ,?" ^ 10" r „ 1 3" X 10 10 II i;,S-' •3 '454 'J j 3" X 'o" 13 13 ifiii) '3 ! 3* X '0' ; 1 lyio «3 1 3' X 12* i 3" X >2" 4 ! »4 — 13 «5 jrsS •5 3" X '^" 16 -',5^7 '3 3" X 14* 1 '7 :4f)2 14 3" X 14" '> 4 1 18 20 - 1 3730 15 3' X 14' ^'/■J >3 4' X 14* 3393 >3 ' 4' X If/ 6 21 1 3465 '^ : 4' X 16' 6 ' 22 .V"!.?-' '4 4" X 16" , ' 23 .)I(K3 .6 i 4' X 16' ! ^ I 24 J ^ 1 TABLE OF PINE LUMBER REQU (inclu Floorinj;- 3" thick ; hand-rail posts, 4"x6"X4'; ha Panel Length. Roadway, No. of Roadway, No. of Roadway, No. of Roadwa 12' clear. Joists. , 14' clear. Joists. 1 16' clear. Joists. 18' cleai 10 11' 12' 13' 14' 15' 16' 17' 18' 19' 20' 21' 22' 23' 24' 691 SoO S42 94' ioj6 ijif) I s ^'1 IO.S5 1 7 "133 7 |()fX) 7 2236 S ■ rrC' s 902 8 944 8 ros4 8 ..5.^ 8 1270 8 1360 9 1502 8 1 1544 8 1740 9 I- 1899 2400 2ri7 2502 2672 8 8 8 9 10 86; 998 1046 1 167 1278 1408 1504 1667 f7'S 1924 2II2 2420 24')S 276S 2944 9 10 9 10 9 10 94'' 1094 II4S 12S0 1404 ■; '5t'' jl \(<.\S ■ 1 I iSS() 2178 2325 2663 -7K .)034 33 1 1 TABLE XVI. LUMBER REQUIRED PER PANEL IN BRIDGES OF CLASS C (including waste material). id-rail posts, 4"x6"X4'; hand rail, tw pieces, 2"X6"; hub rails, 2"x i:"; and guard rails, 6"x6". of ts. Roadway, i6' clear. j -, . 86 1 ! 998 No. of Joists. 9 9 9 Roadway, 18' clear. 94C 1094 No. of : Joists. Roadway, 20' clear. No. of Joists. M II II Roadway, 22' clear. 1116 1286 No. of , Joists. 12 1 2 Roadway, j 24' clear. 1:01 13S: '454 No. of Joists. '3 •3 •3 Size of Joists. _„.. _.._.__. ! 3" X 10" No. Hand- rail Posts per panel. 1 1 2 i Panel Length. 10' 10 1031 ro 1190 3" X 10" 3" X •o" i 4 1 : 4 1 11' 1 12' 13' 1046 1148 ID 10 10 1250 •352 it67 9 1280 1404 •393 II •504 1656 1 .822 19S4 12 1 2 1O19 i-S: •3 '3 ; 3" X 10" 4 1278 •530 II .. 12 II 12 i 3" X 12" 4 14' 1408 1504 1667 9 i 10 '^ i 9 1 .0 j 1 '546 164S .8J2 10 1684 '79- 12 14 12 i960 :i:S •3 '5 •3 ' 3" X 12" ! 4 15' 1 1 3" X 12" 4 1 i6' 17' 10 •997 2162 '-r-7 3" X 14" 4 •7'S ; 1886 10 2120 2291 2546 2752 •3 2462 -730 14 1 3" X 14" 4 18' ! ; 1924 2112 2.78 2325 12 2362 •3 II •4 •5 i 3" X 14" 4 19' 20' j 9 10 10 10 2539 2965 3393 •3 1 4" X 14" 4 2420 > 24C)8 276.S -944 10 1 1 ' 2663 2:17 .1034 .vV14 2907 II II 1 ** 3150 , 32.6 35(if' 1 2 12 •3 '5 •3 ; 4" X 16" i 6 21' 22' 1 i 1 . , 1 ' 2967 3300 ' 3465 •3 '4 16 4" X 16" 6 II '3 i 4" X 16" 6 6 1 i 3616 •4 3S88 ! 4" X 16" I \ I I VluvA ! Length. '9' T^ PANRIDGES OF joists and llo'y.i'. i, , ;,.„ „ puard-rail, 6") ^^' ''''''''' ~^'''' '^■■'> ^.11, .V'xr.v The upper fij ^vaste , Pan.-l Ltnglh. Roadway, 12' clear. No. of ). of I Size of No. Hand- „ Joists. lists, ji Joists rail Po?ts Panel I " per panel, length. \ TABLE OF PINE AND O. Joists and floorint;' of oak, and other lumber pine an 1 f;uard-rail, 6"X6''. Tlie upiKT figures in each rectangle are for pin - Panjl Roadway, No. of Roadway, No. of Roadway, N 1 Ltngth. i 12' clear. Joists. 11 14' clear. Joists. 16' clear. Jc 1 1 51 , ; 117 / ' 1 ;<> •1S3 S ! ,56 550 1 200 200 8 200 ' .\>^^ 7 5f'5 G43 f 1 JOO 200 8 1 200 i "' ■>35 7 620 70s ; :jS 22S s, 1 22S '3' 1 61s 7 712 S09 ' :!j.S 2 28 8 22S 'l' -5" 7 7 770 256 «75 ^ , i S 256 '5 730 1 S45 960 , , j;() 1 i 7 25.) 8 256 ' " ^1(1 944 1072 , JS,( 2.S4 8 284 '7 ciJO / ; loll,; 1207 f i8' JS4 284 8 284 i».Si , / 1 "34 1287 1 '9' 3'- 1142 7 1 >3'8 S i i 3'2 "495 •o' 3'- 1-53 7 1 312 1447 8 3'- 1640 , 35'> - r^s" s 356 1-100 / ; "''5 lS;,o 22' 35" 1 fii 3^4 7 35'> 1709 3^4 8 , 1 ^ 35<' , '93'^ , 1 7 ' 8 384 '^J 1 ;S() 1S29 2072 Vi-t 11S4 3«4 1 ^V '"11 1992 9 1 2368 1 TABLE XVII. OF PINE AND OAK LUMBER REQUIRED PER PANEL IN BRIDGES OF CLASSES A AND B. oak, and other lumber pine. Flooring 2.]" thick; hand-rail posts, 4"X6"X4'; hand rail, two pieces, 2"X6"; hub mil, 2"X 12 :ach rectangle are for i)ine, the lower for oiik. The ciuantitics include waste material. oadway, .' clear. 1 No. of Joists. Roadway, 16' clear. No. of Joists. Roadway, i8' clear. No. of Joists. Roadway, , 20' clear. 1 No. of Joists. Roadway, 22' clear. No. of Joists. I "^ Roadway, 24' clear. 1 1 No. of Joists. Size of ' Joists. 1 No. Hand- rail Posts per panel. 2 Panel Length. 1 ;(> 8 156 200 643 200 705 9 'J i 9 ! 9 If- 617 10 156 683 1 200 798 II II '50 750 '5'' Si 7 13 2.!"X8" 2i"Xl0" 10' 200 8 8 200 200 790 228 906 10 10 10 200 875 1 -°° ' 953 13 4 XX' ta' 13' 14' 1 '5' ' 16' 1 ■/ 200 620 200 87.5 228 i '003 32S 10S5 256 1190 256 1328 1 284" ! '494 i :S4 . '^"3_._. i 3'2 i 3'2 t 2027 ' 356 2260 : "356 '" __239L 384 255« • .3«4 2Sd., II 200 960 I 2 1 200 ! '045 13 4 22^ 7'- '-'s"\ 228 1 800 II 22S IIOO I 2 1 2 I "* 228 1197 22S r2.,5 »3 13 2|"Xir' ; 1 4 ; 2JS 770 " 1 960 8 ' =56 i 1072 S '^^ 1207 ^' . "284"" '^ 1287 8 i! 3' = 228 9S0 j~ 256 ~~ '075 1200 '""' Is.i ■'" 1 ',;o 10 10 I i 2J8 1 1190 2^"X 12" 4 1 2's,6 9 1 9 1 II II I 256 1 1305 ! 2S6 i '4.56 !"""2^6 1 'I'O 2^6 1 5.S4 '3 i 13 ' 2.|"XI2" 4 1 i 250 944 10 I "^ 3" X 12" ! .1 1 28., 10(1; 9 9 10 II i 284 1 1637 284 1746 312 2025 I "^ 1 2S4 ' 2S4 1S99 •3 3" X '3" ^ ! ~28r' 1 1 "i.i 2S4 ; 14.10 3'- _ 1672 '833 356 2045 356 i 21(1? .vS4 23 '5 3^4 .'did 10 10 11 II I 2 '■' 3" X '4" j 4 1 18' ;.'- i;i^ 12 i -''2 i 2202 13 3r'xt4" : 4 1 ''' \ 20' 1 21' 22' ! 23' .V- 1 1.1" J 8 31- 1640 "" 356" ! 1830 : 35" i '93''' i 9 10 10 10 10 12 3'2 2220 35'' ; 2475 i 356 i 2O18 1 384 2801 384 ^ 3112 I 2 3' 2 ' 2.113 13 4" X 14" ^ .>.=;|' S 1 — ^ — 9 9 1 9 1 1 II 11 I 2 1 2* 14 20i)O '3 4" X ,5" 6 ■' 35(i 1 2845 3^4 ' 3044 384 33'JO 13 . 4" X 16" 1 i 4" X 16" 6 350 1709 8 •3 ! 6 3^4 1H29 .3''^4 • 99- 8 i 3S4 2072 3^4 2368 9 1 1 '3 15 4" X 16" 6 24' r n \ Panel Length. 10' n' 12' 13' 14' 15' 16' 18' 19' 20' 21' 22' I 23' 24' i ANEL IN BRIDGES loistshand rail, two pieces, 2"xCi"\ luib rail, 2"x i-"; iiul oriKirc atcrial. Panel Length. lo' ii' 12' pof ,ts. 1 • Roadway, 24' clear. No. of Joists. Size of Joists. No. Hand- rail Posts per panel. i 2 Panel Length. 156 200 200 101;, 228 1159 228 '-57 256 1420 2 5(> I. (So 2.S.1 1722 2S4 .1'- 20 so 22(12 .55" 2SlS 35" 2757 3«4 ,i'04 >3 i 2J"X8'' 2 1 " X 9" 2i"X9'' 1 — - - - i 2i"Xll" 2j"X.2'' i 10' I.? 4 11' 12'' 13' 14' 15' 16' 17' 4 1 13' j' ' 14' 15' : ' 13 '3 4 4 4 1 •3 '3 ■3 1 j 16' 1 ! 17 1 I ! 1 » 2j"X 12" 1 3" X '-■' 1 , - . - - i ^ ^ '-^ ;," X 14" 3^X14" ! 3i"=<'4' ' 4" X 14" ;, 4" X 16" 4 4 i '«' i 4 4 1 4 18' 19' 1 20' '3 >3 14 : 19' ao' 2a' 23' 24' 21' ' 5 1 22' i 5 1 . 23 - 1 6 •4 '3 ' 6 ! 6 24' ! 2 4" X !()" : ' 6 If JS TABLE OF PINE AN foists and tloorin^^ of oak, and other lumber iiid jTuard lail, 6"x6". The uiipcr tiguix's in each rectangle are for 1 Panel Length. Roadway, 12' clear. ^ 4j7 ' 200 ,88 1 200 i i S.8 I 228 594 22S 64^ -5" 730 -.56 760 2S4 , 888 1 284 , 950 312 i ' 1060 3'- 1 172 35" I2V) 1 s ' 3^4 1586 _ 384 1616 >4o. of Roadway, [oists. 14' clear. No. of Joists. 8 Roadway 16' clear lo' 11' 12' 13' 14' 15' 16' 17' 18' 19' 20' 21' 22' i 23' 24' 7 7 156 i 4.S3 ,56 550 200 565 200 ()0O 228 688 8 200 643 8 200 r,83 7 8 228 783 "y"\ 228 747 8 228 849 , 1 / 1 7 7 256 ' 845 2 -^0 j 8S0 284 1027 \" ^84 1098 8 8 ! 8 960 -"256 1000 j ^84 " ; I i(>6 2S4 ; 1-46 7 3>2 i 8 1225 3'= i 8 : >353 J 3>2 i390_ 3'2 " 535 7 35" ' 8 ' 1 '!44 356 9 ; 'f^94„_ 1. 384 i 8 '829 ; ^ 35*' ■738 8 7 35" 1907 384 2072 7 3M 8 1S(,., 384 21 12 — TABLE XVIII. JLE OF PINE AND OAK LUMBER REQUIRED PER PANEL IN BRIDGES OF CLASS C. ol oak. and other lumber pine, iqooring 2,1" thick ; hand-rail posts, 4"X6"X4'; hand rail, two pieces. 2"X6"; hub rail, 2"X 12"; in each rectangle are for pine, ihe lower for oak. The cjuantities include waste material. Roadway, 14' clear. No. of Joists. Roadway, 16' clear. No. of Roadway, No. of Joists. 18' clear, i Joists. Roadway, No. of I Roadway, 20' clear. Joists. 22' clear No. of Joists. ' ' .., i- ' c- £ No. Hand- p__.i Roadway, No. of 1 Size of ^^-^ p^^j^ Panel 24' clear. Joists. I Joists. ^^^ ^^^^^j Length. Panel Length. lu I ' I i I J t i"» .i»j M f Panel Ituiltlicim, ().'# |)fr fool Wcl), yx-^o" ir.> fl 1 -.1 " V ^^ - -tt. -. lUiilt-hcmii, ().)J# |)ti foot \\t\,,\"XT,0" .«' i .''■' ! Kiij.lw.iv. li I'li.ir 1..- t.«I I.'" (-■•I ; v>« I. . !.•" (.■•I, Ml l<,' V.«I, ,M I lliillt lit'.iiii, |i« |iii liuit lliiill In.iiii, I Wdi, I'xi.)' Wil.. J"<jj l'|i. ll., .' j"x .'J" \.%» .in«li' \ I'll. rt.. i :' ' I., rt.. 1 -•' X r |« .mull' I- H„ 1 j'X 1 JIJ" l.'«I. Ml !<.' V>«I, Ml ""!' t"!«I I •■,,.•« I,... i;. III! III. nil. r!* I" I '■•■•< Uih. I'X |S' I I'll. -• j"x .•!" V5«.im'.lf I ll , J .'"x ;(• \ «• mull' ly I--*!. ■'! IIiiiIi-Ihmiii. I'll* I'll I. Mil W.I,, i'x |S- I I', ll,, .' .'"x Jj" IS* .iiiuK* I ll , -• •■•' ,r .|« .inuli' !.•■ I-'*!. Ml I'llllt Ih'.IMI, |I« |»I ImmI Uil., l"x i,|' I |., It., -• .•'xjl" vi;«.iiinli I ll, .' : » i" i« .iiiulv I !.•■ (-■•I Ml r.iiilt Ikmih. i-'l* pit l"il W.I., I'x.m" I i- ll, i J'x.'}' ?;«,inKi> I ll . .• .'"x i' .()» ,llllilt• |y■|-•»I. Mr I laiili Ik.1111, 44# |ur I'm..! Will, [-x.-r I p. ll, .• .•'x.-J' 1 ;»,lll^lr I ll . -• j'X )• 4« .lin;k- I," ;r*I, .M |; nil 1.1- nil, i;* I'll ImmI Wil., l"x jj' I |i. ri, J J'x.'i' i.;#4iinlr I . rt., J j"X i'4«,iiikU- I ;' no* I, M. Iiiiili-l'f.iiii, |''1» |iir (,"'! Wtl., ('xji' I p. rt., .• 2"xjj" v.s**"*;!'' I I., rt.. .: -•' ~< '," 1» -I'luli- 1 5* ^'^ !• '' Hiiill-U.iin, !*<« pil (m.,1 W.I,, >'xj(' Ip, A.,1 l'' 4" )■$» .ingk' I , rt , ; j"x r i« .iii»!U' i;' 5o« I. Ml liiliil-lif.llll, \<0 piT ImmI Wil.. \- ' 2S" I p. rt., : j'X •[" y!i» .inKk- I ll,, ■ .''X ;■ .|«.inf;lc k" ;,*I. Mf l;ilill Inaill, V* |»1 fMMl Wtl., y Jl," Tp. rt., J J"x jj" v,S*'i»".l'' I , ll , .' .-'x (• 4# .iiikIi; I ;" 50» I, iir , P.iiilt l.iaiii. V* i'l'i f""' Will, l"x .-s" I p. ll., ; j"x i".l«.iiiKle I ll, -• .'i'x i'.).!*:"!),!!' 1 ;■ ?,-.« I, Ml Pun! Ik-.IMI, 5-'# plT ImmI WM., l"x.>fi" I |,, rt., J i'y \' ,|« -injiii' I, rt , J .'J* ' ;" I 4».in«lt'^ P.inli 1.1 .1111, ;;« pit (mm! \', . I.. J"x :r' 1 ;, ll , .• j'X (' |« .iiml'- I ll., J .•4'xj"4.,|#.iii«l>.- I J" l.'«I. Ml is" V1«I, Ml llllill l,t' nil, |.'|« pir ImmI llllill I'l.llll, ; Will, I'X. -o' ; Wl-ll, J"X;| I p. rt, -• .'"x jj" j,5«,innli. I'p, A.,1 j"» I., rt, -• J*x ," |II,iiikIc l,.rt,.»j"x ij'4J»I. I J 4J» ^, Ml I'llill lit'.lln, ,| I* pil ImmI Will, I'X.i 'iS'SO#l.Mi llllill lit.iiii, A.i Will, I'X.'-, I p. rt,. -• J'X.'J' 4.s«,lll|;lr I'p. rt., J3"' I., rt., -• .-'x \- i«.iihu- I., rt., : j"x '5* so*r '" llllill In'. nil, (S* pii Im..i Will, l"x ..•" |,'50#I,, Iliiill'liiMiii, Will. I'xj Will, l"x ■:• Will. I'X ji rp. rt., .' j'x.'i" vs«,i"hI' I p. rt., ii'' 1. rt.. .' i"x V' («.inKli' I., rt., JJ'X . 5"* I. ■ Itiiili-hiatii, Will, |"X;i lluili 1,1 .nil, ,|i* pn ImmI Will, I'x.v,' Will, |-X;i I P rt., -• j'x.M" v-,«.iH.;li Ip. rt. ja": I., rt, .' j'X ;,• («.ihKl' I I- rt., 2 i|'' !<,' ;m«I, MI . i^iuiiLi.*.. i^!«p.M-. '"'•'?:•"'• W.I,, I'X js- ^'''■' '*: i|-.".---'-«-'!'.v^*'^"«i^' ,'',, :',r, I., rt,. J J'x.)'.t)»,iiiBle^ ^1. II. . Jj It* (o*T, iir I ,. ., , .1 i.i .»« . i f . llllill lii.nu, lluill lii.llll, <0» pir ImmI j Wil., i"<Jli' ill .' Ip, rt,JJ■x.•l',s«.l„^u■| l"'■•;; l,.H,. jj'x,'.,«.i„nk ji-".-'- >« i;" ;o»I. Ml I . ,, , , - . . I'.inlt I't.im. liinli l.r.nn, 5I« I" I .... ,.^ , ...... • I \\ ill, 1 X J, l-p.rt,.Jj'x.," ,«.nu,l.- : ',, ."^^^ I. rt. J Ji'M^l |» .m^;lc J '""••■ -^ '■_ I.'Vf^'"'. I , '""iit'-". \v''h,rx';.r'" ;\vci..rx,. Ip. rt, J J"x ^'4».iiikIc I, rt , J Ji"" r I 1* •mull' llllill Iv.iiii, ^;» p.r f.i.il W,|.. I'x j; I p. rt , J j'X i' 4« .mt'.li' I., fl., 3 Jl'X3•4.4».^nBl'-■ ll>. rt., J j" I., rt., J J"x IliilU-lx.nii, Will, I'X , I- p. rt., J j" l.rt., J i"x r.iiili-lii-.im, Vli* l"-i '""' liiiili l".ii". Will, J-xj;' [Will, I'xj I'p. rt„ J Jj'x f i,.(« .iiii'lr I'prt, J Jl I., rt.. 3 s'Xj' s#.inKli: U rt.. 3 3j' K .,1 Iway. 12 Cliar. llinl|.|i.Miii, >;!» pi I fM.iI HiiillliiMin, \V,|,, l"v..s- jW.l,, I'xi Cp, rt., J j"». Jj" t 5»."'t;l^- ' I' 'I. - -" I., ll . J j'X r s»-i",i;li: '■■ "■ -• -l" liuili liiMiii, ^'>i* pii I'l'il 1 liuiiil'i.iiii, Wll., I'XJ.,' IWlb, I'X: I'p. rt,, J j'X jj" 4.-,» .n.Klc I r|,. rt., J j" 1,. rt„ J j'x.ii' vi«."iKl>-- il-rt.. 33") lillill-I.IMlM. S.S(« p. 1 ImmI Hllill llialll, iwi'li, J-x;,o' W,l., I'X, I I'p.rt, J jr^-r l•l»•'"^■.''■ ' I'- "•- -i jl.. ll., J j.|«xj|" vi«-i"i'li- 1.. rt„ j.i'; I |liillil«,nii,'il(# pii ImmI ' lliilli-licani IwM,, I'/p" \V,I., I'X I'p, rt., J -■';< r <»# aiif,!.- Ip ll,. J i 1.. rt„j Ji'''-.i"''7*-'">'.li' jl., rt, j/; K,M,lway. 14' Clear. Roailw TAbLL XIX. TABLR OF FLOOR BEAMS. CLASH A I J- (■•I, ■■. Kii.iilw .u lb' Ctr.ii Km..,Iwjv, mcii^r, Koj.Ujy. joClt«r, KoaJway, 13' Cliar. | Ko«away, >4' Cltur. iJiig'l, ■■• • •- I ••• ■ I'x >•' "til, I X J"* Will, ^ X |o j Wtl), I X )o Wd., l'*i'»" \Vil.,l"»---- IWvM'x:,' ,":»., , "^'•■kM"' i Wtl.,rx.lo' I., rt.. i .'x ,,' U..nKk- ' I.. «.. » :•>« .' W .»«l» I.. H.. » r X .,' U a„Kk. '■ "• ' '^ ** » »• •""<''• '• " ■ ' -'l ' ■■ I ' "S* -"«"■ 1 '• "- ' »"x .«' 7.^# ..-ml llV|.'«I. "t IS'V>*I. ■• H'.S"«I. "I lliilll Nmiii, |.'l«|ni I liiiilllK.iii,, I »iiir I.Mil lliiill Kmiii, kj* pir I..m1 ""iI'I«.'mi. >.:»]"< f IIuMi.Ih.imi, (.|J» i«r loot Wil., I'xjn- I Wth. fx;,' Wil., |"xj(," \V<I., ("xj./ Wil., I'x^,' I'l'. Il, -• .•"« Jl" V5«>>»kIi' l'l>- ri. J -■•- Ji' 1.5«.iiik1i- . I'l'. II-. J -•">< )' ■(• .i"»',lf ^ ''• " ' ' •*" ^i' + "i* "'»•'' ' !'■ "■• • ■'''*.)' '■• ""W'*^^ l,.rt, jy'x (• l».i"Klf |l..rt.. JJ'x,'.,#anRW l..rii,a jfxy.)|« ; I H • .'x ,1' , -« ,„:,|, I .1, • •'■- i'6.7#»ngl. Illllll In, 1111, n;« p. r f lluill.lR'.lMI, 'i|J» \wt lout Ulltlll' I angl« W.l„rx.., \V.I,,|-x..,' ' ^^''"1 "^f , , )\'I.|'VK Wd,,l'x.,o' I 1. tl . <"x.r ..« iMul, lull •• •!■ n».iiiuU l*^'''"' ^- ** ' H««iik1'^' I I' il. ••-•'xY' S«''"kI'' I |.. 11., 33-x ,''(«.invlf I'll,! ; VxV'. .'*' ; .',1 ;v- , ,■ ,^U_.| '■• "■• ' ^'^^i' '••"•^"^ , ■ ■ "•; >'^ >" ^^ ■•:::'^ ' "•• '£y_r.:*j^^ Illllll Ik'.iiii, is* 1'>i I \\<l., l"xj<" Will, J'x; U l|.. il, .• j'x.'f isW.iiii;!. l|i, 11., J j" ■ ;J" .i.5*>'iml^' I 11,. .■ .•" < l" (» .Ihnlr I.. 11., i J'X )' |» .lliKl'' n" V* I. "1 I V i;o«I. ' 1 Huili Ik-.iiii, (i» pi'i loni Miiililiiaiii, ,:» pii (mil Will, l"«.M' Wil'. I'x.- ,' U I |i II. .' J"x.M" V^*'"!-'.!' I'l'. ll. -• -•■ • 1' («.inKli.' ^ I,. Il . -• .■■ X i' |» .iiikI, , I,. II.. } i\'f 1' I |« .iiitjlf ' n" ?(>• T, "I , , I , , , .._ , . liii i-lii'.iiii, ;;»|"i l'"ii 1.11,11 1.1,1111. isi« |i.T 1-..1 ; Will, 1">.'S' ' ' , -■ , . » 1 I I' Il . .' J • !' 1« .iiikU' Il I p. II.. -■ .• «-• vs».iii>;l. I . . 1 . , . , « I I . - .'! ■ i II* .1 lulc ■~i H' Ko* I. "1 tliilllln.lin. so* I'lf '""' Will, J' ■< jiV Il I p !l.J .-'x.'!' ] s« .ihkIi' 1 , Il . .• .'"x 1" .{« ,iiij;li- IS" sr*!. "I r.iii!i 1.1.1111. SI* I ' ' i""i Muili 111 im "o* iH-r fiiiii Hiiill l>iniii, ssl* pii fm.' , llultl U'.im, 0:« per fmn riilli luam, 6ri« I'lr fiiul ' '' ' ' "' ' "■-•"" Will, I' X JO- Will, |"x p" Uli.ll,. .' jfx ,' v'(*^iiinl' I p. 11., ).fxj*7,j«aiinlf I,, rt., J jJ'xjJ'(,.5«aiiBU I II.. J3»x/7.7#anglc Will. I'x.'S" l[>. Il„ J .•'■xV.i,s«.>"j;li- I,, rt., JJi'X.r .S».ii'Kle Itiiilt'lii'iiiii. ssi* pir ('><>t Well, J'x.n' I'p, rt., -• .•'■> .'i' ,|.5#.inKli' I.. Il , 2 .'"x 1' s* angle lliiillln.im, 5;* 1'^'' '""' Will, l"X;.i' l!p.ll., J :"x:lV( s«anKle I.. II., js'x.d' s..5« angle lliilliliiMin, fi)J» per (mil I'.iiili.licain, 70* per limi Will, I'x p' Will, I'x jo" I'p, ll„ : .•'X I'fHi.niiKlc t p. rt, .' I'x ii'7,;#aiinli' 1.. rt., 1 Jj'xy <i,7(|laiiKlc I.. 11., i i'Xf ».)m angle lluill lii'.im, ifi4 ptr fiiiil I lliiili liiain. fit,>t per (mit r.iilll luam. 75# per fiiut Will, J'xio' , Will, l"x 10' Will, iSj'x vt" llnllllieam, 67)* pi 1 I Well, l"x p' lip, rt., J i"x )• 7. j# angle L. rt. -• i" r :-» M<y\<- 10' II' Illllll 111. nil, 70* pel (mil Well, I'x 10' I'p. rt , i I'x \\" :.:*.innle l„ rt„ I I'x rs.|»aiigle Ilnlll l«ani, 75* |« r (mil Well, ,'„"x,„' I'p.rt,,.' jf X;J''fi,s»,iii^lc I,, rt,. J r'x.f 7,.'# iin^'.lt llnilllieain, 7.S* pir (mil Well, i^'X.id' I'p, rt,, : ^'x )l"(i,4»anKle L. rt., iyx3''7.j#,inHle Hnlll'lieani, S|# per (mil Well, i',,"x i.S" I'p, rt., 2 ^''X •j''4.s«angle | Ip, rt,. } J'X^J' (1,4 angle I p, ll.j ;j''x il")!.;* angle 1 I'p. rt,, .' i'x ij'(i.4« .iiigle I.. rt„ J i'x i|' 5..1«angle ] l„ rt. : fx f 7,j# angle I II. j fx 1' 7.:* an^le ] I.. Il,, j .f xj" 7,j# .lll^le Huilt-lHain, fio# per (mit Well, J'xio" Ip, rt,, .' -•■'X )" 5# angle I«rt, a .j'X )' 5,i)»;mglc lliiilllii.iin, ;iil« |ii 1 (""I liiiili lieani, fi^J* inr (mil Will. I'x 10 Illllll liiain. drj* per (cmt I uiltliiani, 76J# per (mil Well, t'x )o" \\il', r'd'x.-iS' Tp. rt, 2 ;»'x 1' 7,:#anKle I ji rt,. j jj'x .•j'(i,s»angle I., fl., J 3'x 3" 7.7# angle I rt,, 1 j'X j" 7.j# angle Illllll lieani. 70* per (mil Hnilllieani. 78* per diot Wei), J"x p' Will, yx J,' :" :: ' : wiii, i- ><...,■ wu., i"x,o' weh. j-xp- w.i,, ,',,''Xi(. , ''; ' '^^ , . , 'ip, rt, .■-•■-.M' 4,s» angle I'p, rt„ 2 .')'x.,- 5,5* angle ; I'p. (I., j fx ,J' 7,7* ,,ngl. I ;., H„ 2 2-x il* (,,.|» .nigle ' '"l ' "' r * '• ' ^""' I., rt,, 2 2-x ij- 5,j» angle I,, rt., 2 jj-x-l' <^-5« a"Kl«-' ! !-• «■. : ,f>< .i" !<t» •ingle I.. lU 2 j'xj" 7.2# anslc is' so* I, iir Illllll 111, nil, S-'* per I'll. I W. I.. \"-< :('r ,li- Ip, rt . 2 2''x !'4«.ingle 1., Il . -• .'Tx i' II* .ingle I llllill li.-.iiii. S'l* l"f fi»>' W,l.. i'x:;' i I p, ll„ 2 2"^ r .|» .ingle ''' il.. rt., 1 3j'X.)"4.4».1liglc ' lliiilllie.iin. ;,S« per lo"l |:iiilr-lie.nn. ("is* |)er (mil I Well, I'x V Will, I'X 50' I I'.iiill-lii.iiii. Sli« per (■"'1 1 Well, J-X27'' <li- .1 I'p, rt„ 2 2j"x ^" 4,4* angle I'p, rt, 2 21' m' s.;* angle I., rt,, 1 J'Xj" 5* .mgle I'p. rt„2 i"^:\' 4, s« angle I'p. rt., 2 2'x 3I' fi,)* angle I., rt., 2 2'x ;!' s,.i# angle 1., rt„ 2 i'x / 7,2* angle Hnililie.im. i'># per (out liuilt-lieain, f/ij* per (nut Well, r'^.P' ' ^^'''''' rx,3"' I'p. rt., 2 2 ' X )" 5* angle Lp, rt., 2 21'' X j' r..7» .ingle l„ «.. s 3'X j" 5.i>» angle i I,, fl., 3 j'XjJ* 7.7* angle _ _ 1 linill.lie.ini. ii;« per (""I Hiiill-lieani, (*)» jier (not Well, J''*<r'" Will. |"X p' I'p, rt . 2 .rx^" 7.2* .ingle I,. 11., J j"Xj"8.4#aiigle lliilll-lieain. 75* per (mil IIiiilt-lH'ani, .Sl« per (mit Well, I'/X Vt" Well, rj'XlS' I'p.rt,, 2 2f X2i|'(i,.s«angl. I'p. rt.. 2 2"x ,l'ri,4*angle I., rt,. 2 J'X)' 7,2* angle l„ rt,, 2 .fx )" 7,2* angle Ilnlll III ,1111, ,s.'i« p< r Imii Well, ,'',,"xj,S'' I'p. H„ 2 2rX3''fi,7#angle I ■ 11,, 2 r'<.ir77#a"Klc I'liilt-lii ,1111, .S(i* per (mil Well, ,'„"x>S' I'p, rt.. 2 j'x 55" 7,7«.iiigli I.. fl.,^3'XJ"S..(*angle '3 L. rt.,i2j''x2|'6.5# angle I'.ullt.lie.inl, SSl* I'll I'l"' liniltlieani, !.;(* per (i"'l Will, I'v.-'S"' : Well, 1-x,,'' I'p. rt., 2 j'xjJVi s« .niglf ' I', tl, 2 j'x -,'(*. ingle I.. II., 2 2''x i' 's#.iiigle III,-' 'l'- ;" ii:#.ingle i Unlit lieani, s''!« per (nut llnilt'-lie.iiii. i.s» pir (mil Well, l"x i< lliilll-lieain. 70* per fnnl Well. I'X p" rp, II., 2 I'x jl"; 7# angle 1,. rt.. 2 fx i" S.,|» angle Uniltlieam. 764* jwr d Will, fi/X,;" l'p,rt„2 2rx2j'ri,s« '■ III l'p.rt„ 2 2i"x 5' (-.,:« angle I,. rt„ 2 3'X3" 7.2#aii.;i. I I,, fl., 3 3'X3l'' 7.7* angle Ilulltlicam, 82l# per (mil Well, />,'x.,S' llnllllie.ini. 7.S# per I I llnlll-lieani, S(i# per (""l Will. t'',."'<,V'" Well. ,»,,''X3.S' I'll, rt,, 2 2'xj|'(i..|*,ii'. 'i| lp, rt„ 2 3'x !j' 7.7#angk l„ rt„ 2 3'X3' 7,2* ,111.;!' I,, rt,, 2 3'X j' S,.|« .angle Illllll lieani, 75* per (not Well, ,''fl"X vi" Itulll-lieani. 7oi# per t' ■ ' Well. ^,-X;7' l■||, rt„ 2 2-x 5|"l,.,,«.llil I., rt., 2 3'X )' 7.2«.iiH'.K Ilnlll beam, ,S2l# per (i"ii Well, ^/XiS- I'liilllieam, S<)# per fnnt i Well, ,■',., "xj.S' I'p, rt,. 2 3''X3"8,.|« angle l„ rt.. 2 .j"'*.!!' y* '""git' llnilt-lieam, i)I# per (mil Well, r'./x.vS' I'p. rt, 2,V'x ,i"iri»,iii^k 1„ rt,, 2 i"x (" ii.7» ;iiinle IllllltlnMni, I).)* pel l""l Well. ,'..,' X3S'' lp, II., 2 3'X4''i),7«,in(',l. 1„ rt,, 2 3°X3J'' io,.|* aiiiji Hiiilt Kani. .Sf)» per fimt Well. ,VX;S- Ip. 11,. 2 3 ■ X !'' ,S,4« angle I,, rt., 2 3"X3l" y# angle Uniltlieam, 91* per (out Well, i-'.-XiS- VV, I, I " X 2.,' W.li, l" X ,„ ' Well, ,', • X ,4' Well, f,x 3V j ^^ eii, ,-, • X 3h • I'p II • •'X2i'' i,5#,ingle rp,rt..2 J'- ■,l'l..4#aiigle|rp,rt„22f X2i''(..s«angle;rp.rt„22j"X3'(i,7*,i.Kle,l'p,il,.23'X3j''i,«.ingle I rt '• •'X3l' 5,3* angle I.. II. 2 I'x ;' 7 2# angle I I.. rt„ 2 3' X 3- 7,2* angle 1.. rt., 2 3'X3j' 7,7« angle , 1,. rt. 2 3'x 4" i,,;* angle Hullt lieani, i>S» per font W'll'. ,•■„■ X3S" l'li,ll.,2 )''x,-,!'ii-.l» angle I., rt., 2 i"x jj" 1 1,7* angle llnilllieain, ioi# per (out Well, iV.'XjS' I'p, ll . 2 3"X4'' 11,2* aiii;U 1„ rt,, 2 3''X4' 1 2.7* .mgle lliiill-liiMin, S^i* I" I I' Well. I'x, I'.iiill I'l.iiii. '-,' = pii (""I I liiiill lie.iin. 7(il# pii ("I'l I Ilnlll lieain, Ss* 1 ' ""■-•■' W'lli, /i,,,"X3S'' 1 Well, ,'.,'X3S" | Weli. , W'.l., i"> 31 ■ Well. iV,"X,s' ■am, Ss* per l.'.l Hnllllu am, f)4« per f'loi ! Ilnlll liiani, I0|» pel l.i"l - ■"" Well. ,'.,'X3S" W'eli. ,^,.,"X3,S' I'p, rt.. 2 3"x 4' .i.7« angle I I'p. rt.. 2 3l"x |" u-S.nv.le Well 1"^ '" \\ili, 1 > ;i. wen. J-,; A i^ ..ll., f,,, ^.ji . I., -.r- I.. I',, li ■ -r < •(- I -« .nigli II'- Il . - -•'.■ ■ ;■• (■-* ■"'kI^' I I'P- "•• - -i'x 2i''(..5»angle I I'p. rt.. 2 ^'x^' 72* .iii..!. I'p, rt.. 2 3-x 4' .,.7« angle I'p. rt.. 2 3S-X , ' 1 2« .in,le I. ll„ 2"2l"X2|'' SI* ...i^'l"-' ; 1- rt,. 2 3"; .[. 7 7«.'»>!l^' 1 I" II" -■ -i'x.r 7-2# angle j I.. 11., 2 3"X3'' 8.4* angli I. rt„ 2 3'X3i' to.,,* angle I., rt„ 2 3i X4' I3.'*.n'gle I liiiil, 111 „„ <i>l« „. , l""t ' lliiill-lieani, 1 -■= p. r L-.l : H l-eam, 7S# pel (uol ' llnill-lie.ini, SC* per (""i nnlli-lieam, .>S# per foot lluill-lieam. ICX* per ("..1 ' ' Wili.l-. ,-,..'■ W'll, ,V"x,„" iWili, ,"„-X3S' ! Will, ,'■.,• x,S" {Well. ,V''X3S" x ;i'r,..,#aiii'.le; Tp. rt. 2 ,\~'-}\' ; ;3 •'!'.■'• ; lp, rt.. 2 3''X3.rio..|#anjL j Tp. :!.. 2 4j"- .f I2.ii».i W. Il, I"/ p" I' n, ,1 ■ •"' i-|*.ingl.- 1 I'. H. 2 i"- r ;■-!» •"'>;l^ Iprt. 2 2-X3i',V.,#,i,iKle; rp. rt..2 3-X3i- ; ;= ■'i'.> j 1 p.n..2 3-x.!i io.|«:anj,le ; l p. :.. 2 4 "4 .2.i,*.,i.K.e 1, ,|.,V4"'X3'(,.7#.ingle jl.,rt,2 rxr::#..ngl«^ I . rt. 2 i'x 3" 7 -•# ..ngle :l..rt.,2 v'x 3- S..,» ..m;Ie , I.. 11,. 2 3'x 3i- u,7# ..ngle | 1„ rt„ 2 3i '< 4 i.V'.#;.ugle 14 '5' 18' 22' 23 24 K.-ailway. M' Clear, ' Roailwav if.' Cle .r. K.niilwav, i8' Clear Roailway, ao' Clear Koailway. 22' Clear, Koailway. 24' Clear. ,';,'";„, »1. \ •«Si> ■■-^ . m ^^fflj'w % \ i w Pail. 1 Koailway. 12 Clear. ,!■>« I u, yM\ lo' ,;o# I ^o\■ y\*\ l:iiilt hum, iSia |n-r I'.int Wil., l"x t Roailway, 14' Clear. ioJ",iil#I Kuailwa IJ".|J#I,., Ituilt-lic.nti, Will, l"xi, Up. II., I 2" I., n., -• c"x 18' ■9 1::" .l-'*!, iir I ;'.(:# I.' Iluillln'.im, jSJ* per fool lluilllH.iin, Well, J'Xi.S" ; \Vil>, 1' X:, I'p. 11., 2 .:"x:!>' ;,.5* •'"«!'■ ' I'l'- ''•■ - -" I.. 11.. 2 j"xj.i";,.s#.in);le I- ll., -• .-"x ij'.i:#I, or ;i3".So»I' li\iilll>eai\i, viS* l"r f""' i liiiill-'"-!"'. \Vcl>, J'xiS" ' : Well, I'xj Cp. fl, .- j'x.'l' v.S«.iiinle I p. 11., -• i" I., rl,, .• .-"x ;■' |# .mule . I., ll., J 2")< !-•' .|j#i. .11 ij";;"*!.! liuilllu-.iin, .|i* pel f""l I lUiiU-Ueain, Wei., rxh," IWel.. I'x: fp. ll., 2 yx.'i" _^.5#an(;le Tp. ll., J 2" I., tl., -' yx;,'' ,)# allele . 1,. il„ .' :'> i.'".ir#I, ..1 lV'.^o»I. lUiill l.eani, i-'l* per f....t lliiilll.. am, I Wei., !"< -o ' i Web, V'x: |..ll, .- .'"X _-r •,.^«.inule ' Tp, ll., -■ --"x i\' ;.5# ai.};le I'p. ll., -■ :' 1 . ll , 2 '"x -y v>» an.ule I., ll , J :"x ;■' I* ■>"(;>>■■ i l- I'-. •: 2") ir .i.'«I. ..1 ,ii"5o»I, ..r j' 5" .10*1. Piiili-beam. 3Sl« pi 1 l.n.i Huili-he.im, .|:1« p.r f.i.>t liuilllie.ini Uel., fXis" i Wei., }"x JO" IWel., l"x. Ip. ll., • .'"x.-r .v;«anule Tp ll,. • .-"x.'r v^*•l",l;le Tp. ll.. : .' I 1! . ' J X iV \\1t .^ll^;le I., ll, 2 .-'x '/ .(* allele : I., ll., J .' ' ^ 1,- |;3 I, ..1 1^" :;o»I, ..r [15' 50*1. Pmlt-l.eain, vi!* per f""l M.i.ii-I.e.im, .( |* p. 1 f'.'.t liiiill lie.im Well, )"x,S- W.I., I'xji" ,\Vel., 1"X Ip. tl., z j'x 'i' v>«-'"e.l'' l"l'' 'I. - 2"x;i\v.;*.»i'Kl>-' I'P- "•• - - 1,- ll., : 2"x ;' .|«.ii,Mle I., ll., 2 2"x^"4# allele , I., ll.. -• sj" I .'" .(2* I. ..r 1 S" .^o* I, ..I ! I .V 50* X lli.ill-lie.im, V)** per f.".l Huiltl.. am, .(5* pel f.".! liuiU l.eani Wei., l-><'^" ' Well, I'x 3-" W.I., I'x , Tp. ll , .' j"x :Y ;.;» .iiiBle I'l'. ll., 2 -•■x .-r vi* -'"Kle Ip- ll . •! ^ I I., ll., -• i'x j' 4#,lllKk- j I., fl.. 2 I'XJ- .)« ailKle I 1.. tl.. 2 2" "i2'42»I,..r |l.S'.5o#i,..r | l!„i|,.l,..am : P..iili-|.e.im. .|i# pel fo.,i liiuli-I.e.uii, ,|i« I'er I. ...I | ^^.^^^ Wei., r XI,,- Well, r >■-■.' !(■ ,1 , , fp. ll, 2 2"X2r.!.;«.m^;l. fp. II. 2 2-x,r .v;*--"'.''.!'- ,',, ', ,. 1.. ll, 2 -•" X ',■ .|» .uiKle , 1- ll-. -• •:'■'' 1" t* -"'K'e- , ''__'" I ,- , .a T ..r ll" SO* I. "f i> •.. 1 I- 4--* !■ ■" [J ' ■»■' 1 lluill-lieaii i liiiill-ln.im, 42i« per f....l llmlt-lie.ini, 4.* j.er f....l ^^.^^^ ...^ : Wei., i" ' --O- Wei.. I'x 2^ ,. '',, 1 l-p. ll, 2 2-x 2r 15« .ii.Kle ^ l-p. ll , 2_2'x 2i\?.5* »"«le , '^j _ ' ", I., ll, 2 2"x ;,• .t#.mKle I 15" V,»I, ..r I., ll, • I'y- \'' 4#annle I \' V* J, < lUiitl-hean Uiiili-I.e.ini, n« per f""t llmll-l.e ,1111, soJ» per I....1 \^^^^ y^ Wei., r^-i' Web, I'X^f'" I-,, ,1 , l-l.. ll, 2 2-X21- v;«ani.le I'p. ll, 2 2'x 2i" 1^« aM,-le 1. ;;; p. I 1.. ll. ;■ |# aiiKle I.- tl-. -' -' * )" 4* •'iik1>; I., ll, 2 2' iVv-»I. "1 ^,0;,.«I, ..1 'ituili-K-aii llmli-lnam, 4;* per l""l Hmll-li. .1111. ';2» per I....I ^^.^^^ Wei.. T"--' iWel.. rx24' I-,, t'l - fp. ll.,2 2'X2r •,.5»aiH',le l-p. ll. 22" xjj' 4- S#.->iH',le '' ■/, I., tl , 2 I'f-s' 4» allele is" v.#I. ..r - limit l.eaiii, -tC* per fmil Wei., i'x 2i- I., ll.. 2 2''x ',!" .;■•,« -1"; Hiiilt-lieam. i;2l# per (....I lliiill-i.e.ii Wei., l"X2s' Wei.,!"" Tp. II, 2 2''x2r4 >#-iiii'ie rp.ti., 2 . I tl, 2 2-X (M#.">M.l'- ['•■"•-- .1 -i ^ |>"V«I.'" I |l,iiltl.i-.iiii, q;» i'er I....I limit l.eai P„„lll»..m. p-i»pei (....1 ,^^.,,, J.., „,. W.l., r> Wel.,rx-r , ri.. tl, • 2"X2r I sSaiiKle rp 11,2 r,,.il,2 2 «2l ;s«...el. I „,,..x,J',.,«.,„j;le 1.11.2 J I, tl. -■"- !" I#- I'.in.l IS' i'l*!. '•' |l„illl.>-am. SI*).. 1 l-.l I'.uill-lH'il' I'-eil 1" ■ I '* I" ' ' ■ ' Well, i"X 27* \V el.. I": ^^'' ''■*""''' ,. » 1 i-p.ii...'-'-x-l-|-^*'"H'i' I'P "■•J I |, ll,2 2"x:l" !.s« mul.- I 1^1 .-.-x il- s,t« in,.,l. I..ll,22 I., ll, 2 2"x i" 4«anKli 1 Kna.lway. 1 a CI ar K.M lw.iv, 14 CI. .11 Koal TABLE XX, TABLE OF FLOOR BEAMS. CLASS B Roailway. M' CU'ar. Koaitw.iy, lO' Clear. Roailway, i8' Clear. Roailway, 20' Clear. KuaJway, 22' Clear. Roadway, 24' Clear. i,''^"^! ' ^ Length. loj- ill* I |J".|.'#I, i>r l(uill-l)c.ini, 3SJ# per font Wth, J'X iS- I'p. II.,; j"x.vi';,.f;* •'»«'>-■ I.. Il, .' j'> -vl" .'vS* •!"«''■ 1J".(.'#I, nr llnill.|ic.\iM, .|i,J# |ii-r fniii Weh, l"xi,|' ' Ip. 11., : : ' :l",v.S*.>iit;li- I.. 11., J _• X ;" .|#.iMv.le i;'.,:#I,„r Huill.lii.itn, \},\^ per fiiDt Well, \" X .-o" I'p. 11., J :"x jI" v5* •'|'k1<.' I., ll., .! .'" X j" 4# .-iiikIc |J".|:#I. or I 15" 50* I "f lliiilllieain, Vll* I'l' l'"ol ; liuiltlie.lm. 15# per f.i.il Well, J"x |S" ! Will, 1"> .-i" Ip. ll , -• -•">< -'l' v.i*-i"Kl^' I'l'- ll' - -■ < -1" .Vli* '""K'^' 1.. ll,. -• -•" x ,\" |» .ui.nle 1 I., ll., .: -• X ;" .)# angle 1:" .|j»I, ..1 ;i3"5"*I."r lliiill he.iiii, .(i« per f.M>t : lUiilllieain, .|ii# per fciul Wei., yy. M' : Wei., |"x:y' I'p. ll., -• '"x.-r 3. ;« angle l].. ll., : y x:r' j.;* aiigk 1., ll., 1 ::"x ;■' .)# angle . !.. ll., -• : ' ■ i" I* -'"K't' IJ".!-'*!, MI ' 15" 50#I, "r linill beam, i-'lS per foot ' Hnil|.|ieain, .(:S# I'er (o.it Wei., l"X.-o ' I Web, |"x j;" .;lo ' I'p. ll., -■ :!"x zV i.5» angle V\: ll., -• :' x zV 'vSWangli le jl,. ll, .' n'x;- .(». ingle | I., ll, -• ;" x ;' 4#juigle 1 15' 50*1, •■! 1 1 5" 50* !• "I- il ' Unill.heani, .|.'1« pir Inol | ItnillI.e.iMi, |.)« per f.iol ! Weh, J"x:c- i Wei., fx,;" igle fp ll.. -■ j"x.-r ; ;«.inule I'p. ll., -' .• " x : J " j. 5* •''»«1'^ Ir 1. ll. .: j"x ," 1* angle : 1.. ll., J -• ' x t' 4* angle 1^" v.»I, or I r.i' :;o»I, or ,1 l;ii;il-lie.lnl, .(,|« p. r font lUlill lie.iin, ;ii#perfo.il \V,I., i'X.-l" , Wei., i'X.M,' ,glr I'p. ll., J ::'x.'J" v;*.rngle I'p. II.. ^ .' ' x •,' .i# angle I., ll, r 2" X ;,'.(« angle , I., ll., .: jT < ;" |..l* angle I ;" \ot\. Ml ! 15" 50*1, Ml .1 liiiili l>. am, -i^* per I'mmI llnill l.eain, ;i !« pi r ImmI .Well, J-X2:"' Wei., I'x-;- igle I'p. n., : :'x .'!' ,vi* ■'"Kle t'l'. ll . .: '-" < -T \->* ••>"«l'-' I., tl.. 2 3"x ?" !« .ingle , I., ll., -' ;"> ;' 5* •■•"kI'-' l.S' 50* L '"■ j Hiiiliheam, ;-'l# I'cr f.iMi 1 I lUnlt.lie.un, .)(* per lui.l | ... .,, i"x ••!.'' ... 1. 1 ,• ^. . >* I ' ^ 15" 50*1, iir lliiilt.lii'.ini, .i'.# per fmit Wei., l"x j:" I'p. II., J i'^i\' .).5#angl 1.. ll., .' j"x j" |# angle 15" ifM I, (.r r.itill luMin, .(S.l* per I'omI Wei., I x.-.|" ' ., ., , 1.,. , . i I'inll lieani, ?.(# per fmit r.uilM.eain, 5ol# per flint ,,. , ,, , Well, V'XJd' Well, J'X27" ,. , ■ , ,, ^ , ' !'■ II.. 2 .I'X l" .».i# angle L'p.ll.,.yx..4'j.s#..ng|. , „.,...l'x,"5Vangle I.. II., .' 2" X 5"., Wangle \ S ^* h 15" 50* I, or l:nill.l.ea,n, s\\* l>^r f....t ' l''"l'-'«^»n<. 55l# 1'" foot Weli,J"x..,« Weli,i'x../ Iliiill-licain, 5.SJ# per foot Well, }"x 30" Up. fl., :: 2"X25"4,5#aiiglc I.. H., 2 2"X3j" 5.3# angle Huilt-lieam, 62# per foot Well, J' X 30' lp.ll.,.-y'x:i" 5;#.nngle I'p. ll., . ."x -i'+S* angle ' I'- H- = ='X:i" 4.;# angle Vp.ll.,. ^J'x j'5-5#-->ngle 11' I., ll., J J' X 3 " ;|#'.u.gle I I.. II., .' zV X 3" 5# angle_ ' "'• - -i "^ 3° 5# angle 15' 50* T, or I llniUlie.mi, ;ol# ii.'t fuol 1 ''"i"''".'-"". 54j# pcr foot |;,nli.bcain, 57# per foot Well, r'x.O'" iWel,,l-x:!7' \V,h,}'X3o' I'M 11 . ."x-r •c«inele"-'l'''l"""''=l ■'■■'5*^"'^'' I >. ll., 3 =' X .;r 4.^^ .angle 1.'h.!; ; "xr i*;n*o ' i '■■ "'• = =rxyjW^ l . .l..--^'X3i-,3*.angle l:'nil|.l!.nm,"si !# per foot | ""il'-l'^'a"'. 5Si# 1'" foot i;,i,l,.l,ean,, Tx* per foot Wel,,i"xr4''' Wcli,rx=S" U>l,, i-X3o" l-p. 11., 3 3'X:r.,.5#angle^'l''"" - ""''-i -fS* angU I ,. il., : 2-X3' ;# .-.ngle I., tl, 2 2j"X3" ;#angle j '- "" ^ =i">^3'' 5# a»Kle I ll , i^'^i' 5.9# angle I, ll., 2 2}"X2}"6.5#.inglc IJuilt-lK'ain, 63j# per foot Well, }"X30'' Up. tl., 2 2"X3" 6# angle 1.. n., 2 2j"X3"6.7#angle 1 Huilt-licani, ri5# per foot i Web, J'X3o" L'p. ll.. 23' X3»fi.5# angle ! L. fl., 2 3"X3" 7.2#angle 13' lUlillbe.iln, 5:1# pel f.M.I ; lluill.beain, 57* per foot , r.iiilt-lieani, 62# per foot llnill beam. (r\% per foot Web, 1"X25' Well, j"X2i)' W.b, J'xio" Web, i'Xjo" I'p. ll., 2 2"X2J' 4, 5» angle • I'p. ll., ; 2"x :J' 4.5* angl« IV il , 2 2i''X3' 5.5# angle I,, tl, 2 2i"X3' 5« angle ' I., fl., 2 2"X3l' 5.3* angle I ll., 2 2}"X23" 6.5# angle *> I o, J ^ iu L'p. ll,, 2 3"X 3" 7.2# angle I 1.. fl., 2 3'X3J" 7.7#angle I '4 ISuiltbeam, vij* l"^r foot j llnill beam, 59# per foot buill-lieam, (,},\* |icr foot HniH-lieam, 70* per foot Well, i"x:i,' i Web, )-'X;o' Wib, i-X3o'' Web, ("Xjo* , l'p. fl., 2 2'X2l"4.;#anglc!L'p.fl., 2 2r'X2r.t.9#angl. i ]. fl., 2 2'X 3" 1* .angle ^V'^- - .'i'x 34" 7--# angle 1.. II, 2 2j"X3'5#.ingle 1 I,, fl., 2 2-X3i" 5.3* an;, - I il., 2 2j"X3' i'.7# angle j I- fl- 2 3"x 3" S.4# .angle | liuilt-beam, 75* per foot ..en, * 'v ->J ..en, 4 '^ ^ ,. . i., ^ " .>" .»eij, j-j ^3'* l'p. ll, 2 2"X 24' 4.5* angle l'p. fl., 2 2'X3' 5* angle Ip. fl., 2 3"X 3" b.s* angle l'p. fl., 2 2fx 2j"(i.5# .lngle l.. fl., 2 2l'X3' 5# angle 1.. fl., 2 3"X3" 5.9#anglc I fl., 2 3"X3" 7.2# angle I'.uili beam, "# per foot 1 linilt-beani, b2# per foot ' liailt-lieam, 70* per foot Well, I" X 2./' ; Web, J" X 30' Web, J' X 30' llnill-beam, 555* per fooi lluilt-beani, 6o# per foot liuilt-beam, CjJ* per foot Web, \' X 2.S' Web, J" X 30" W >b, \ ' X 30' .. »...,» ... 1 ,, .t __«,..»-*. 1. 1.. .1 . .n ^ ,» ,■ .^^ 1.. lUiilt-lieani, 76J# per foot | Well, IX2.;' i Wei), J X30 "en, t ^3" ^^ il'. T'.!"x 35" j^, l'p. fl„ 2 2rx 2I' 4.<)# angle' l'p. fl., 2 2J-X 3' i;.5# angle l'p. ll, 2 3'X3i" 7.7* angle L'p.fl.,2 2j"x 2:i"6.5*angle I.. fl., 2 2r'x 21" 5.,)* angle I I,, fl., 2 2}'x 2}' (i.5# angle L. I, 2 3"X3'S.4#angle , L. fl., 2 3''X3' 7.2^ .mgle . Uiili.beam, s^* per fool j llnili-bcam, (n,\* per fo, 1 : l;nilt.lie.am, 75* per foot liuillbcam, 78* per foot Web. J"x,o' iWeb, J'Xio" Web, |»j'X34'' | Web, ,■•,'■ x 36' ' .•..".-■■' i-r I Web J X'!,' Wei., J X',o j W el., J X. ;o "en, fj -v j4 | ■■>■■. m ".v hVeb, \-S2i' 1^. • , ,->,,,.^.5#a„(,U l-p.tl,2 2rx:r'4..»#angle l'p, fl.. 2 2"X5"r*an i. i I'p.fl., 2 2;'x 2rf..5# angle : Up. «.. 2 2i"x 2^' ('..sSangle „g|.. l'p, fl.2 2"x.-r3,5«angle , ^^ , ,-x a'" =.,# angle | I., fl., 2 2rx 2^ 5.4* angle |l,. fl., 2 2.4' X 3" f,.7# ..n.. I . ll, 2 3-x 3- 7,.* angle I., fl., 2 3' x 3- 7.2# angle j I,, fl., 2 2"x i" 4#,ingle _ ! ' - - lit ngic 15" i;o# I, or j |.,||||.|„..|,„^ ^,|# |„,|- f,„,| ! II, lilt, beam, (o* pel foot ' llnill-beam, b;* per 1. linill-beam. .p# |ier foot ^^.^^^^ ^.^ . - j ^y^.,^^ j.^ ,,,. ^y^.,,^ l"X3o" ^^'•■''' rx25' |. ,'| , ."y,l'4.5#angleiUp. fl,2 '''x ij' i;.,* angle l'p. ll, 2 2'X 3!- (.,.1* ,1 Up. II, 2 2'x2l 3-5*»"*;l^' , I.. „., , ,»x if' 5.5« angle | I,, fl., 2 f '^ i" .s..;# .mgle . I,, fl., 2 3"X3' 7-»->"- L fl., 2 2"X3' 4»angle -' | IJuilt-beam, 76i# per foot Weh, ft" X 35' Hiiilt-beam, ,Si# per foot Weli,ft'X3,S' Up.fl.,2 2J"'x2f"fi.5#aiigle;Up.rt.,2 2f X2j"fi.5«angle I., tl, 2 fxy 7.2« angle I L. fl., 2 3''X3" 7.2# angle 18' ■ 9 I5'50#l.o, i;„i;i.beain i;;«p.ifoot ' llnilt.be.un, fii i# |.. 1 fool ! llmlllieam, fi7j» p. 1 i. t I llnill-beam, sol* per lo.il „•.,!, i-yvS i Web, ("x ,0' Web, I'Xjo- Web, J'X2(." " ' Web, J'X2l." ,.|, ij^ , ,;v,jv,.5#.,„^ii.lrp,fl„22l''X5' .;.i;#.ingle:i'p.fl„22rx3-::» ngle Up. ri„ 2 2'x 2i' 3,-,* angle ^ ^ __,^ , ^ |^, ^ „ _ , ,.^^j. f,^^ _^,,j,|^, | , „^ _, ^-^ 3!' 7.7s .. I.. 11.2 2" x; 4* angle '^ llnill-beam, 7S# per fool | Ituill-be.am. Si;* per foot Web, ft' X 3(1" ! Web, ft'X3,S- I'p. ll, 2 2'X3l" fi.4# angle , Up. ll, 2 \"-<f 7. 2# angle 1 , fl., 2 ;,"y }," 7.2# angle IS" v.»I.oi ltuilt-b( am, i;2» per fool Well, J'X24' Itnilllieam, v* per foot Web, ("x:,,- Wel.,rx2r U|i.fl.,2 2i'"'2r,|.'(«angle;U|., fl., 2 2"X3'l*,ingle ngle , Uii. fl.. 2 2-x .J 4.S# angle ' '^ - ,^^ „^^ , ,..^_,, (,^,^ ^,„^, Iliiilllieam, fi3l« per foot | llniltbeam. 70* per I'... Web, fxp" j Web, J'xjo' U].. fl., 2 3"X3r7.7«. lluilt-bcam, 711,1* per foot Web, ft'X37'" l'|i. ll, 2 2"X3l'6.4#angle L. fl., 2 i"X3' S,4# angle Uii. fl.. 2 2"x .J'4.S# angle ^ ' ^'^ -■' ,: _ ;^^^|^. ' ^ ^^] ]-,^ ^.. (,,^ ^,„^,^. I ^ „ _ , ^.'^j. s.4#,„v.'- I. fl.. 2 3'X3' 7.2* angl I., ft., 2 2''X3l'' v.«'1"kI<' , - - ! I»am,,2j«,ierf.io, l.nilt-be.im. ,s« pe, foot I llnil, b. .u„. o;# per foot ' Ilnillbeiin, 7.« per f- l^nl,-lie,i,n^ Si* pe, loot Web, l-x._s" Well, i-X3o- W , b, i ' x ,o' Web, ft'X54 Web, rtX3,S llnill beam, S(># per fool Web,ft-X3S" J,, Up.ll, 23" X3i'7.7#. angle I., fl., 2 3"X3",S.4#angle lliiill-be.im, .Si)# per loot ■Web, ,»,"X3S' rV'^^^^'.-WwIeT fl^'^r>>r,.|*angU :;; 2V;U-<M*a,,gle: X^ .■ l'p. fl.! 2 2-x 3r .M*angle Up. ll, 2 3-x 3" S.4* angle :"«'' t.'fl,";^-X3l^.;;!::u ;..' fl !:^i5,^j*3!,;;:4.^, ,.',,.,: 3" X 3- 7.2* V l'l.^rx3^^*ang;, I., fl., 2 3' X 3" 7.2* ..ngle ... tl. 2 3-x 3 r 9* angle , 1, i.-i .*peri ib,i,.-i..,..p...io,., '^.......,.^.. -;--M*.- is'ft"^.r""""" ^!:;:-:p^-'- W.l'.i-^"" . '^•'■•1'^;?". ,._.. ,.. ,'.''';,'.,;:.,.,.,*.. ',-„,;':.rx.r„..*,K . rp,„.,.,l-x 3- n.7# angle l U,.. H,, 2 3-x 3r"» angle I fl.. 2 3'X3l-7.7#angle 1,. fl., 2 j"x 4' .).7# -mgle '" Iw.bl'vo- Web, rX30' Web, l-x,o' Web, ,;, X35 i,-,, ,1 . .-y .1" , -^tt.iiiele l'|. fl, 2 2-x il' .;.•,# .mgle Up. fl.. -• ■l-x ,' (.,7#aiigle Up.fl.,22j X2I (:;» ""^''' I ,1 '. ."x ,[•" ,. ,« angle , 1.. ll. 2 ,'■ x ,- ;..|» .."Kl^' !■■ »■. -' -l" x 31" 7.7* angle j I,, fl., 2 3"x l' 7-2* an; 23 p.mlibeaiii. i;i«|"i loot Iluill beam. 11 ;a per fool '* Well, rx 27- ^^''l Iliiilllieam, (■«)# per foot ' llnill-beam, -S« pel f. W.b, \--x io- , Will, ,■•,,' Uuli-beam, S-s» per b.oi ' llnilibeam, ii4« per fool Web. ft-X!>*- :*]B'::f;:;:£ ;^:ii;-':.:i'sf l^J'^v^Vis^:^' :^v!v;^x:i '-;"n-^i-';,;.::f r';,:';;-i^i^;;:j::S Koa.lwav, 14 I'll .11 Ro.i Iw.iv ,1. Cb- ir. Rna.lwav. 18' Clear. Roa.lwav. W CI. ai Roa.lwav. 22' Clear. Roa.lway, 24' Clear, U.mel l.ellglll. M Panel Length. T^? i i< ^^B?*-* \ Panel I Roadway, 22' Clear. RoaJway. „• Clear. ^^^^^ i I ^^|^*"*Jrgp^?S!jB^*.- J- \ I ) Lr ■•.h KiLulway. w Clear. Roadway, 14' Clear, .■■,(* I "!«I in- v-^i 10" JO* I 10" ,^o# I loi- jij#l I >9 2i »1 i;"4J«I, or IWiill'lH'ani. .?Sj« pel fiiiit k/ '.oa I I Well, J"X iS" l|>. a. 2 :"x-\" !.!;» .in};li' 1.. tl., 2 ;"x jj" ^.5«.■lll^U■ |i;".i:«I. ... : liuill l.l.llll. iSJ* p.'l I.I..1 I' !'J«I Wfll, \"X iS' 1 Tp. II., 2 2'y- -r ;, 5* .iMv.li' I 1,. 11., r j-vjj" .v.';«.iivl' |i;-4^«I. "i lj".io#I i \Vcl>, J'x iS' lip. II., .• j'xrj ";,.!;« .inglc I 11. II.. .• .'"X 5* 4*anylc i I.-". I .•*!,.. I ' IUiill-l>c.nii, 4I# per foot loi" jijal I Well, I'Xi.,' ] I'p. II., 2 .I'x.-r.v.'i*. ingle I., n., J c'x f 4»an^;k• l.•"4J#I, ..t i-'- .i-'aj, ,.r lliiilt 1>c.iin, 3>>5* pi 1 I. ."I r.iiili lie.im, |-'t« ].et (....i Well, J"X i.S- ' Wei.. 1"X -o" I'p. Il , • .;"x .•!" ).^» .innle I'p. ll.. -' -'■x.'J" j..;" ■'"Kie I, ll., -■ 2">i2\" j.5« angle | I., ll., 2 .-'Xj' 4* angle I-" 4-'* !• "f ";" i°*J.- '" lliiill-lK-.im, iSJa p. I (....1 1 lliiili-lieani, 4.'J* |.ei P.,ii Will, l"x iS" ; Well, \'x 20' I p. ll., -• .'"xji" V5# angle ' Iji. ll.. -■ 2~ < 2\" v5*-'ngle !■ ll ■ " -■"■< -T 3-5* •■>"«'"•■ '•■ "■■ - -"" i' -l* '"'y'^' |.-"4J#I. ..1 ; 15" 50* I. "I l:iiili-lie.irii. ;.iS* 1"-' '""' ' l'inl'l"-'>"i. 11* P'''' f""' Wei), J"xiS" Will. J"x:i" 1 p. ll.. : .!"xjj" v5» angle lip. H., 2 2' X 2\' V5* ^ngle 1 , ll , J J"x j" 4# angle j 1.. ll., 2 I'xf .|» angle 12" 4J#I, III : i>' 50#I. iir lluill-lie.lln, Vl!« per fmit i limit tieam, 4^» |ier f.i..I Well, }"x l.S' " : Well. J'Xjj' I p. rt., 2 2'y- -•}■ ;.s# angle fp. i) , .• .-"x .M" ■,.;* .mgli 1 I.. II.. .' 2'x •;■ 4» angle ' I., ll., J j'x ;" |» angle I •' 42# J, 111 15" 50* I. iir Kiiilt-lieani, 4i# per fuol j Ituill-lieam. .{Crit per (....1 Wet., )"X !.)■ i Well, J'x.-;' ' fp. ll., J .:"x.'J" ,i.|;»aiiglei ('p. II., ; :'x .'J' ;,.;» .ingle I , ll,, 2 -'"x f 4# angle ; I., ll., • 2" x ;" 4* angle MJ'4.-#I, ... I5'5'->«L"1 |:iiili licani. .\:\1i |ier fnot j lluilllieani, 47 J# |ier I....1 Well, }'y jo' i Well, J-K-'l' I p. ll., -■ 2'x 2V' !.5» angle I'p. ll.. -■ .'"xji" V5* angle 1 ll. J j'x i' 4#angle ! I., ll. ,-•-•" x ;' 4# angle 'i" .VJ"!. "I i 15' SO* I.'" ilu.ll lieani. 4|» pel (mil , linilllieain, ,1.|* pel I....1 Wei., j",-:.-!" ! Well. J'XJ5' I p, ll,. :: ;" ' -r i,s*an;;le Tp. H.. .! .'"x -J' ; :;» .mgle 1. ll. i' i» .I'lrl l„ ll.. ,1» ,ingle . ;" 5o« I. 1.1 I ;" ;t* I, ..r P.iiilll.ea In* per r...l Hililtlieain, 5oJ# pel (....l Will. \"X22'' ■ Well. J-X.'d- I p ll. -• J-X -J" J na.iilgle t rpll. J J-x .•)' i,5».lllgle I ll ,.•.•■'';" 4# angle I., ll, .■ .•' X j" 4» angle Pan-l LenK'li Roa Iway. I J Clear. Koailway, 14 Clear. Koailwa' iy'4.'#I." Iluill'lu-ain, Well, \"x,i- Ip. ll., : .'": I.. II., -' j'x ij'.i:»I,i, lUiill-lieam, Well, l'Xi> I' p. tl., J 2"> I., ll.. -• -••x IJ"4J#I, n t'.nilt-lieatn, Well, i"xt( Tp. ll, J -•": 1.. ll., .' j"X ij" 4J«I, a I'liilt-lie.nn, Well, 1"X|, I p. ll., -•;": I., ll., J .'"X !i-'"4-#I.e ' lliiill.l.eain. Well, \'X2< Ip.ll., -•-•" . I . II., J 2'y. ' ' ':•" .SO* !• ' Hililllie.tm. Well. \'X2 l-p. II.. .' 2- j I.. II., J J"X I "5" 50* I. f ' Huilt-beani. ' Web, 1 " < -• ' I'p. ll., 2 2' I.. Il„ .' -•"x I s" V^ I, I llnill I., am, Will, yX2 rp. ll,. -.•" I., ll., J J"X 1 1;'' 50# I. I llnill-lieani. Well, j'x - rp.ll..--.-' 1,. ll., ; J"X j 15' 50*1.' ' Iliillllicam, Well, J'x J L'p. II., 2 2" I.. II.. 2 'J'; ' 1 5' 50# I, . Illl.ll-l.e.ini. Wei., i"^- Ip.ll., .-.•■ i I.. 11., 2 4" I'.nilt-lieam. Well. \" • .• rp.ll.jr l„ ll. -• .'"X I lliiiUliram. ' Wil.. 1"X2 r,. ll.,.. -'• I.. (1., .: -•" X I limli III ...n. Wei., \'x: Ip. II,, • -•- I.. (I., - - ■ n.iilt !ie,im. Well, \'X2 l-p II,, .. 2' I„ ll. .• -•"> kiw, TABLE XXI. TABLE OF FLOOR BEAMS. CLASS C. Roiiilway, 14' Clear. Roailway. 16 Clear. Koailway, i8' Clear. Roadway, 20' Clear. Kuailway, «' Clear. Roadway, 24' Clear. Len"*h I 10" ;o# I I 10" iri# J loj" .ill* I I.'".1J#I, (.t I2"4J#I, iir IWiilt-luMin, ii)l# ptr flint I liuilt-lii-.nii, .ni# per font Well, }"xi,S' " i\Vel,. I'X.V I'lK II., .• .•"\.-i," vs* .iiiKle I l'|i. II., 2--"xjJ' j,5#,„,kIc I.. II., - ■'- ' - -" - ' ... - -»--• - '5".So#I. "r '"5"5o*I.i>r 1 1, ■„ . ,^ , , Huil..|Ka,„, .,8J# per fn,„ 1,,„|, wL, ;,# p.r f„„. I ''"'■''"'"'• 5^^* 1- """ '■- Wdi, i"X24" W.I., |-x,(," \,.,^f ,. ^ , .^ .•;■■ .VS# .-."Kle i I'p. II.. = .-x ..J- j,5# angle I'p. 11., 2 2" X 2]' .v.S«.."m1' I'l.. H., .- .-'x .^l' ,.5#.-»nglc I '';, "■; ^.' "^.'^ '/i ..'''''r .-1 ,;..S# .innlc il.. ll..;:2"X.i'4#aimle I.. 11., j ^'x 5' .,# ,,nj;le I il, : ..'x ,' 4» .niKle i'-""--XJt 5-,i» -"'Ble i.''.(2«I, ,ir ij",(:#I, ..1 15"50«I. iir i;v5«I, ... Iliiill-hi.iiii, .(o'a i.ii f.ii.l nuill I..Mni, |-,* per f....t llciilli.eaiii, 49j# per (....I linh liiani. 5)# per fi...t liuilllitani, ;;# per font Well, J'X IS" Weh. \'X2,- I Wei., i'x .'5' Ud., i"x .f," 1 Wel>, i"x -•./' I'p. II., .' J"x.-|, ;.!;« ant;le Ip. ll., I., ll., .• 2'xf I* an "III. I *jp , wel., I X jj- Wlh, JX-f)" j ■•-■■. ( " -J «anj;le Ip. ll., .' yy ,{■■ ;.5«aii«lc ] I'p. ll., 2 .•" X ij' 3.^* ai.cl. I p ll., .. .''X j" .|# angle i l-'i''"-- 2'x 2\' .is# m^W igle^ |l..Jl., J.-"x.iV|«anKle I., ll., .' j'x / 4« an^le 1. ll., J j'x .J' 4.5# angle '■ "•. 2 J'Xjf 5.3* .in«lc i;"4.'«I,..r i5'5o«I,..i i5"5o#I,..r 1 r.iiilt-l.eani, 41 J» per f....l Huilll.e.im, 41* per f..iil ' ll.nll lie.nn, 5oJ# per f....l '''"H I'™". 53* \"--' '""» i li"dl-lH:im. i>i\« per t I Wei., 1"X.-..' Wei., j"Xj(j" Wcl., 1"X2(." ; Wei), V'Xp' ! ,y I'p. ll., J yx .^J' ,,S#.'nj;l.- ^ I ■ "■• - -''^•'" ■'■5* ••>"«'<'• I,. II., ; J"x ," 4# angle ' ' ' ''• - -I'x .V 5* »"«!<-■ Wei., J'xio" I'p. ll., -• ■"Xjl" i.5«ai.Kk I'p, ll, : ^x .-J" V5# .mgle 1 ll., : -•'■ X j" I* angle , ].. ll., .• j " x f 4# angle i:' 4.-«I, i.r 1 1 5' 50* I. or .1 lliiill l.e.iin. 5SI* |.ei li...t r..ull-lie,iMi, |i la per fc.i.l 1 lluill-lie.iin, .|7# pet f.M.I Wei., 1"X |,S-" Wei.. l"Xi.,-" i Web. 1"X.'5' I p. ll, J j"x -J' V5» aiii;!.' I p. ll., J 2" ^ 2]' ;,.5*ani.,le . Up. ll., 2 .-"x j J" 3. 5* angle 1,. II., :; 2' X jj" V5« angle I., ll., -• -■" ^ ;,' ;» .mglc 1 t,. ll., : j'x 3" 4# angle Well, }'x.-4'' L'p. tl., 2 :;"x.'J" 3.5# :int;le I., ll, 2 j"X3"4#aiii;lf j i:" 4J*I. ..r ! t:!" 4J»I, ..I i 1 5" 50* I, ,.i I llniltl.e.m., 3^ J* p.-i l..'.t ' 1 '.11 ill. In am. \\^^ pt r f.ii.t l.nilt-Iii'ani. .(S^ft per f.n.t I W.I., 1 "X i.S" " Wcl., I'^.T," ' Ip. ll., J -•■ x.-r 3 5* aiii'l. Ip. ll., : _■'<.''" •,.5# angle 1 I,, ll., -• J'X.'J'' 3.5«angli ■ 1. ll., .' : ' ^ ; ' i« angle 112" 4;* I, or i^'^o*!. ..r ! 15" 50*1, (.r ' r.nill-l.e.iin. 3i).i* per f....l llnili-lieani, 45* per fni.t , Muilllieani, 50!* per P.i.l Wei., i'x I.S" " Wei., ("x:!- ;Weli, l"x:o' I I p. ll.. -■ .■"x:J-3.|;« angle l'p. ll.. ; .■■"^: 53. 5* angle : l'p. ll., -' i'x .•{" 3..>* -uml' I I . ll. .• -■" X 3" 4# .ingle I 1.. ll, :! 2" X 3- ,# angle I., ll, : -'"x 3" 4* angle 1:" 4.'« I, i.r |l5"50»I,or 15'50#I,or ' lluili-l.e.ini, 4i» per fi.i.t ' lUiill-lieani, 41* per font Kiiiltlieam, 51 J# |)er f.>..t j Wei., J"x K,' Well, 1 ".'.-•.•- 'i Well, J"X-4' jrp. ll, J J'x.-r 3.5* angle l'p. ll, .• j"*:'." 5.i# angle : l'p. ll, 2 ^''xjj" 4.5#angli I., ll, ; ;"X3' 4«angle I ,. ll. : j' < ;' i* angle : I,, ll, 2 ifx 3' 5* angle i-'l-'I.'T i^'SO*I.'.i !>5"50*I."i lliiill he.ini, t.'l» per li...t llnill I.Lani, |-|3 per (-..,1 ; lliiilil.! ..111, ^.-l* pet (....I Wei.. l"x.'o" " Wil., \"y 2]' ' Weh, J"x.-5' . l'p. ll. : j'x.'l" 3.;« .ingie l'p. ll, ■ .' ■ .M " 3.5« angle l'p. ll, -• j"x .ij" 4.,#ang]. I I., ll. 2 2'xy 4# angle I., ll. -■ .'' ■ ;' 1» angle | I,. 11., 3 :\"Xi' 5# angle H'SoWT. nr K"io»I. .11 I I, ., , .4. , . , , , ,^ .. , , - . . liuilt-beam, ^5J# per I1...I I I'.inltl.eam, 4.v(# pet Pi.it lliiilt-lieani, yiS |ier In..! , Y" ' . 1.. ll, = 2" X ," 4# angle ; I ,. ll, .' .-X , 4* a.^gle _^'" --*'*■' 5* ••"t^'- 15" 5o#I, or llnH'tlieani, ,jj# per f..nt ''"iH-'H'^"', 5.|J.« per fn.-t Wei., I'X;!,' W.l.. l"Xj,S- I'p.ll, 2 2-x ," l#.''ngK "I'' "'• - .;"xn"l-5#-'"Kl'.- I., ll, 2 2"X2V 4.S# :mgle ' ■ ''■• - -i"^ 3" 5# •'"kI<-' L'p. ll, 2 j'X^i" 4. 5# angle 1.. ll, 2 2'x ;(' 5.-,# angle liuilt-heani, Co* per font Wei., rx.P" I ,3' Up. 11,2 2" X 3" 5# angle I.. t1.,2 3"X3"5.,j«..ngle I llnill beam, 53!* pet I....1 KiiiU-I.e.im, ;5i# pet l..nl lUnltl.eam. (.:« per f.i..t Web, J"XJ(." W.I.. t"X2,/' . Web, J' X 30'' l'p. ll, 2 2"X2r 4.;#.M.:l 1 |.. 11,2 2-X2J' 4.5* angle j l'p. ll, 2 2i"X3" 5.5#atigle I., ll., 2 2fxf 5# angle I. ll, 2 2l"X3' 5» .ingle I., ll, 2 2i"X2J'' (..j* angle llnill beam, 544* per l....t biiili-beani, ^7* per |....t llnill-beam, (>,]k* per ln,.t Web, J"X27'' Will, J'Xp" Web, J'Xjo" l'p. ll, 2 2"X2j-4.5«ai..:le I p. ll, 2 2" x 2*' 4.5* aiigU 'l'-"- - :"x 3" i*.ingle I., ll, 2 2i"Xf 5# angle I. ll. 2 2'x^y 5.3# angle | '•••'•• - .: J " x .5 ' <'';* •'"KI'; liniltl.eani, 55}* per f....t I'.nilt-beani, ('k)# ]iet f.n.l . limit-beam. '.5* per foot Web, }" x 28" Well, J" x 30" j Web, i ' x 30" l'p. ll, 2 2"X2i'4.5»angl. l'p. II, 2 2'X3" s* angle < I p. ll. 2 3"x 3' ('..5* .mgle I,, ll, 2 iJ'X 3" 5# angle I., fl., 2 3'X3" 5..j# angle : I., ll. 2 3"X3" 7-* "'gle 4le W5-5o«I.nr .5' SO* I."' H.,il,-l.e.„n. .,l*l.erf...., I llnilibeain, .|4# per fnnl ' limit-beam, v.l* per font ,,.^ ; Web. J"x--." Well, rx2V' ■, ;' -l 1- * 1 j ip. 11:2 2-X2r 3.5* angle, up. ll. 2_2~x ■ 4# angle \\ '-^VJ ^'^ ;^.:;;t jl,.ll.. 2 2'X3-.,#angle j I.. II, 2 2V' x 3' 4.4* angle \f-»-'-- X^J 5-.l» .mj-l^ llS"i;o«T. or is' so* I. or 1. 11 ,• . . 1 , ,. , , ,„ . . Mill 1.1 am, ssJ* pel I.II. I 1 limit l.e.im.4^«l"r (n-l limit-beam. 51 i» per I.... 1 1 ■■ v v" Web. J" x.. 2' Web, I" X 20- ;^''';l ""f ip.ii:2 2-x2r,..».o,g., rp.ri.,2 2-x3 ,*.,ng,e ';,":v,;^i^*:f i I.. ,1, 2 2'x ,- ,« anglc_ , I.. II, 2 2\-X i ,.,« angb- ,^"^^l limuf .i!o.% per f,..,t ' ;^:1;'^:': ^ ^' ''' ' ' WebT-.f "" '""' up.V2'2-x2r.vs*.>ngii 'I-''-"- '5*-Ki.' u,:.;i.,2 2rx.r-,...*..ngi. I., ll, 2 2'X3".,#.-ingle Ipil. 1. ll. .'.'■■, a angle 1. ll. 2 2J"X2|" v.(#.ingle gle IS'Sr^I, ..r |l!uilllK-am, -,2'aper b.ni llnill I... im, s.S# per I..1.1 ll,„lt.|ie.,m,47l*lie. l-H |^^.^,^^ j.,,,^^, • ^,^.,,, j-, ,,;. )^'''', '"":',' I- » , il'p ll,2 2-X2) ,.S#.'ngle Up.d.,2 2i-X2l",...#.mgl, lp.ll.22X2i I5».i"gle ,'„ ...,,,.^,, , „ .,,■■, .r = ,a„.,.l,. I., ll, 2 2'x ;• 4# angle , I.. II, ■ .•''X3I' ;-,# angle I.. ,. |» .mgli "5'St>*I."f : limit b. ll", '■-• per (....I llnill l..-.im. («# per font llmll-liea ).»« pec f....t ^^.^^^ _, Web. I'Xj.r T^''^""":-' ,. , , l'p. ll. ■ • na.mgle l'p. 11,2 2'x, i"-v.i#a..r.U i5"so#I,nr ■ l;„ilt br.im, 5s# I'T f""« biillt-beani, 5ol» pel |....t .,'l' Web, J'X2l.'' ;li-' t'pll. 2 2"x :\" PS* angle Well, 1"X2S' l'p. ll. t'.niltbcam, fn \1t per fnot Well, yx ,0' llmil-iie.im. ;;# per |....t Itnilt-I.i .tm, 02# per b.(.t Web, i"X2.)" Web, J''X3o'' l'p. tl, 2 2" X 2i' 4.sa ai.fl l'p. ll, 2 2I" X 3" 5.5* angle I., ll, 2 2"X3}' 5.3# angle 1,. ll, 2 23"X2}"6.5#angle lliiill-beani, yi# |ier (... 1 liniltbeain, 63^* per font Web, I'Xjo" Web, J'X 30" l'p. ll, 2 2J'x 24'4.i)#ange| l.'|..tl., 2 2"X3'(*angle I., ll ■ .. - .- Ilnilt'beani, C.7J* |.er loot Well, }'X3o" Up. ll,2 3"X3"7.2«angle I.. 11., J3"X3i"7.7#aiigle llnilt-lieain, 70* per foot I Web, J' X 30" ; Up. ll, 2 3" X 34" 7.7* angle I 2 2"X3J" 5.3a angle 1.. tl, 2 24" x 3° (.7* angle ; I,, ll, 2 }"'<:," .S.4# angl liiiilt beam. f:2* p. I 1 llnill-beam, (.74# per font Miiilt-beani, 71.4* I'er l....t j Web, i " X 30" Well, \" X 30" , Web, ,55" x 35" ; I'p.ll, 2 2\"x;i' s-S#i"i-l. Up.ll, 2 }'X]' 7.2# angle j Up.ll.,2 2f X 2}" (i.5#angle I,. II, 2 2i'x .!i'0.5# .oi^le : I., tl, 2 j'x jj' 7.7* angle '•■ "■. = 3'x j" ".-'* anglf lluilt-beani, 6il# per f.- 1 ' liuiltbeani, 70# pet foot ' llnill-Iicam, 7S# per font I Web, J- X ,o' , Well, I" X 30" Web, ,>/ X 3(1' ' Up. ll, 2 3"X34' 77* angle I'p-ll. 2 2"X3|" 1,. i* .uigi.- I, ll, 2 X'x f ,s.4# .ingle ; I., ll, 2 i'x X' 7.2* .mgle Up. ll, 2 2"x \' i*aiiL! I., ll, 2 24' X 3" (..7*,m; llnill b. on, (.5* per 1.."! Web, l"x 30" Up. ll, 2 2"X3l '(..4a m. I ■ ll, 23" X 3" 7.2#.nigl. llnill l.i.im, (<.l* p. I !■■ Web, i'Xja' Up. 11,2 24''X3'l..7a,i: I- 11-. -'j'X,3r7-7«-i".-- . I linilt-beani. 75* per font j llnilt-be.in;, Si« per foot | Well, ,\"X34'' I Web, ,';."X3.S' ; Up. H.,2 2fX2J"(..s* angle' Up. ll, 2 2'x 3!' i..4a angle I,, ll, 2 i"x f 7.2# angle j 1.. ll, 2 fxf 7.2» angle I ' llniltbcani, 7(.la pir l....! Ilnilt-beain, .S2l# pe' t,...t ' Web, |>,,,"X3s Web. ,';.,"x3S" I Up.ll.,2 2i'X2(-r..j#.ingle Up. ll. 2 24''X3'(..7#.inglei I,, fl., 2 3"X3' 7.2#angle I., ll. 2 3'x 34' 7.7* angle Unilt Iieam, fiO# per (•■ Web, J"X3o" l.S# angle Up.ll, 2 24" X i" s.5# angle Up. ll. 2 3-X3"7.2#ai , 1., Il.j 2->. i|' ;#angle l." ll. 2 2- x j)' f, .,« angle j l. fl.. 2 3" x 3" ,S..,# .m:;i. I, ll, 22 X3 4» angle ' ^; __j Roadway. 14' Clear. Rna.lway, 1 Clc:ir. R.ia.lway, i8' Clear. Roa.lway, Jo' Cle.o llnill beam. 7.S« per foot ' linili be.im, .Ss# per I....1 Web, ,V."X3(.' Web, ,»,,"X3S" Up. fl., 2 2'x ,1' i..,|a.uigl. l'|.. ll. 2 ;,'x 3' 7..'a .mgle I., ll, 2 3" X 3" 7.2a angle I . ll, 2 3 " X 3" ,S. p-t .iii,;li- Rna.lway. 12' Clear. Rnadwav. 24' Clear. i«' ■5 16' >7' 18' llnill-beam, (xrtt ].ei f..nl llnill-beam, 654* per fnot I Unill-lieain, 7S# per f<.ol | Web, J"X3o' Web, }'X3o' Web, ,s,,"X34' | ,^, Up. ll, 2 2" X 3- 5a .ingle Up.fl.,2 3'X3-|..5«angle li'. ll, 2 jj'x 2j- b.saangle' I., fl., 2 3'X3" 5,>)#angle 1.. fl., 2 3- x 3- 7.2a angle I . ll, 2 3' X 3" 7,2* angle | »3 24 Panel Length » >< X -J OQ < Ji "^ I WH- ' li. ' k J r. -J 00 o PQ < o - A 3 w « M V a b i «« N « w i^ . , . . S a. CI, s . a. s . . 3 '- — 1, , Ui :j j; ^n^ ^^x ^ ^ ] ;^ .^ 0^0 © D l^o- 1 " \«. "E-C'«, W« (^^ (OH* ft ft. t WW t~r* ViW •e It ft (2 jr i, a" . . 3 ^ S. £. 3* ,. §■ ^ 13 '>': \^\Iy. •r^u^v; -> ^ >-L uT-^^. 5 a I © D © a© © D '0 ,© a ) t fc t fe < inw , w^ti H« u^w •^: frs^i . 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Uj X -1 „ y. y. •■ : D fl' ©P© ©P© © n -, Sr ft: -£< Siri. ^ w* Ml* ^,?w^iM.;<-«-4--H'lH-'"l-.'-H' Q :s 3 » □ o a a 3 y»^ TOt^ =; a a 3 a a 3 3 3.^ D ^' ;i. ™ ■ Sh « - 3 « 2-. — S-i ^ 3 a a. 3 ^ D^,^ ^ ^^ ^^x; r;^^ U-i D ^^' n ,: D ^ ft ft Q fc r^H- «H<ft. ««. mH" fc rtH- PSM" fc «H» •.«.*• ft «H- ■* " • .^ r- a a 3" _• _• ^ . ^ ^ X] "^ "^ y. ^^/, :'^>^< -< n . : P a ^ ft^P© ooN- wN-te rtfljl «'^»|" fc r<M : M — -", "* Uj -- /. a !^- n 1^ 3 ;?; ©DO © u y a t a 1 . 3 ' a y, © 10 ^ li ;_) X. ;© n ■ - -^y r a© ;/'. ft ° a (S S ii o V TJ (J (4 M e X u n m ^ u ■n u m o vo Oi V / I / {,. l'\NKl. - 1! M I g g sg n i'pan in No. of Kcct. Panels. liil«. iiMfy u( Wm.i PrL's' lire, 40 40 40 40 40 40 40 33 I : . I ' V M I v II CK ,11 Ho.ulway. T" I. I I'WI r.\si I. ). . ■■« [ r • J" J^'l^C 1 i4'<*[ ' s 4" 6» r ; J 4" (■)« r I 2 5"7«T" i4'<'«l i I ' • 4"^) I'ANKI KL J. I'ANKI I. I'ANKI. I, I'ANKI. 150 2^" 7*1 3 4' ii* C J 4'()#r I 125" 7..s# r 2 4" c# r j 1. >r^" , 'A'- • fr''> : _ 'L'i'r ■' _ij"^ 1 2 5'7rs«[ -'4"''»C 14~I>*[ 2 6'85#[ 14'b»i i ii-/ -L t jiV- ' ■"•' i ! 1!" •■> _i5'ii^ |J0"S5*[; J4""«t I 34"t>»[ j :,36'S.,S#f 24'0*[ i 7 35 I ''■ Ij'-^ "''•J I i'-'J i Ij"^ |_ij"0_i ij">' I II'? I |":;:_ '!_ "I'l _iA'® ^ I 0" (i 5« [' V 4" ()« t" 2 4"(*['i " j6'i).7#f : 4" 6# [ 2' 7 35 I 'fV ■ h'.!*'^ , ill' ■' h'«" p i " :i7'lo.5*C'-'-l'f>-5*C 2 8 35 , •! I 'i''-' i6a . 8 30 30 igo 30 30 JO y\" 14 Cli'ar Ko.iiKv.iy. I'ANKI. 5. I'ANKI 4. H' w r u. }'0 V4"<*£" J'j''* J4"(w»r* 3 4'f>»t J'© I'Q 3 ?• 7» [ 2 4» (*T 1"0 j|35"75»f M'f^T , _.„ _ _iJ'^? H'c 1 2 5" 7..s« r 2 4" c# [ 2 4" <>« [■ ■ • '■ '24'CHiir 2 4" 6#t 4'(i«r I I'tfi'- If--' i « '3_ ,r^.. ij'©'- Ir© - ■•-' 2 4'6»[ -r.'i.*> V.»VjJr^ I'ANKI. V I'KNH I iC Cli .11 K().i..wjy. I'lSKI, 3 I I'ANKI. J I I'ANHI 4, j r\NI,l 5. I'VMI li I'VMI. 24'<^>»li J" © 30 24a 12 i 30 30 250 260 30 2 4' Mf [ I 3 li' ■-■ r '-^ \ 2 4' i* [ 4" •'** I L±H" • ' 'A"'-'^ 'f :-^ 3 4" (* [ 2 4' f* [ . 3 4" 'i* [ I i ii%'© I i.V'>- 34"'* [ 4''.S#T I .'^v-.- iH' ■ -• 4' <* [ ! 270 M-^ 14 290 15 30 J4'(*C ; 4" <* [ - '/' U" '■• 4* .S# I t ■!4","»[ I I 2 4"6#[ U" « .*" '", 4* S# I I'O 2 4'T># [ 4'K*I ■ r» _ ^ 't ■ 3 4' (i« r I 3 4' (* t >iV ' ' i,'/^'^ 1;," , I,!'© 4».S«I 4'',S#I li" ■ I,'.," • , 3 4",'*[ -t';i;#_[ ;;^;[ 4*ti 4'Li I .i'ti _Jtl_ 'J JL 'A'''' .^ 'Kj" I'ANI 1 30 3 4"6« J. ^.^ _^ tr " 2 4" (* [ r ■* 4»^; I,",' * I 3'7""io.5# t li -•1^1''^ i 3>'Ti.5#[i __,r© i 3 4' 6.8# 1 1 3ll'© 3 4'f>#[ , ^■rj' ; 2 4" (...S« £ J 1 l.l»[ li" • 2 4' (>.t* [ 3 4' I* [ 3 4" 7» C 3 4"''»[ = 5"7#[ 2 1 1' •' 3 4'"* t T' ■ .; 5' r* t 3lJ" • 3 4" (* r 3 5'7#l ~H*'^ ir • 3 4"(«[ 1" ',.. 2 4* (..S# tr-' 2 5" r.2# 1}' © .•!(>»[ i 2 4" f* f 11"© I"© I,,'© ! iK© li':- : I,'/ .- .■I i*[ 2 4'(1«[ - (•■: {" © I -*I 4''S#I I. ■ ! l,»,">-> • • ii« r '3 4' (•)« r I r© f»© l4""»[ *:\ 4"*.S#I 3 4' (I* [ 1" ■ a I ,-.s»I .r's«I I ,' ■ j \\' '■• \ I,','-' V ■ -•,.*[ j 2 4' 6* [ 2 4' (* [ ' : ■ ' vv ■■■ ,',";■- !' '^ i u ■ ■' ' : #1 4 f<#I 4 >;»I '. ■ ; I//'" ! uv- ir-' 2., ','•••. 3 4' l..3# [ 3 5' 7..!# [ 3I,V." ^ 3 4''"l#[ li" ■ 3 5'7''*[ 3 4 (1.1* r iir • 3 5" s» C 3 V I';*! fi" .S,3#| 2 1 1" '■ ^ 5'V«1 - 1 1H» [ , ' » I 1 »I I -• I * [ < 4 .^''1 -■ 1 '■- : ir>"" ! uv- ir-' 4'(# [ ! 34"(i«r 3 4'i*r ij' • Il .•4';.*[ 3 .1" (* f 3 4" r* t 4"*S»I 2 4' (# 4''s« t 'J ■ 3 4'';'»[ 4" •'<# I lA'^ 4'(*[ I A" ■ 4'S*I I ,'S«I li;" <r ■■ I i Ij" •■ . -Ml h*l Mr •' .•4 '*[ .•4'»a| 4''>«I 4''.S»I - U ■ 2 4"1*[ iC • i" ■ 4" S# I ii'.r' ■ 3 4" "» [ 4''s»I il" ■ 3 «•'■«{ 4' '•I •■rt" • 3 4"l*[ ij' ■ 2(i''J.S» Ift- • S7" lo.5« -||2 7' io.5« - '■'""' i 3 7" 11. 5» I 'J" ■ lis' 1 3.5* 3 .C 7# [ I 2 iC • [_ ' i''' ' I 3 5":»[ ; 3 il" • I 2 4" li.S» I '1"/ • -• 5- :* [ 4'i»I 1 , ,'„*[ ( ^ ■ 4 -".sal i|'.-." ■ J 4"_i* [ 2 4" (« [ -• I ..*[ 1 ■ (" ■ 4",S#I 'I' ^ I '■* [ 'l'.," ■ 'l'.-." • -• r'"«[ ''I ' .•4"i*t ' -1 ''^t 4''s«I ■r ■ i" © r • 4"S»I U' • 3 4'' ■* t *.".'■ 4^'V#I It' ■ -■!■-[ 3ir • 8 4 ,<;■.?« 3 3" r» [ 3 1,'/ • .• 4" i'.:« 1 1 " ■ 3 5' :» [ 3 .\- 1.10 ,.1" . 3 5" :-■« 2ll' ifYm 2 5- s# [ 4 *»1 Jj'«" ' -^■'7#[ i»" ■ i 3 5'.S.5# ii 3%'7*[ 1;" • -■ '// • 2tf'..;«i ' '/■■!* 3.,''-.,«[ 1=^74* 3 d' r,.j# 3 li' -^ 3 5"7'J* -la 2U' tt»\ 3 ', ■ 3 S" !*» I TABLE XXV. TABLE OF LATERAL SYSTEMS AND SWAY BRACINr, \M I S r\M I !■ I'VM I. 7, i - I' CO *» ■ (' .s# I I A" ■ r ■ ,-s#I 'V ■ 4'(« t r ■•^» I hV ■ r '■*[ r ■ I .^*i r ■ ij' • -•4'i«t i" • 4" ># I ■r ■ ■ 't ,,''s#i 4''-* I li'- I'ANI I, I. j I'ASH. J. r " !,r- . I,'.,' •' ;^'- -•r'i*[ I 1 1" - ir • -■ 4" <* [ 1" • J 4' (,.5« [ tf ■■ :! S" 7.-'» [ ll- ^^ .■..•,s.,»[ '.'/ • il -.''■'" ' — 37" io.5«[ ll__ir • Hi J 7" io.5»[ , ">'/■•■ , 'i" ■ ui^" '■!-5*[ lU r;. .ir i; .i 'v. /. I'ANKl. ,). I'AMI I l'\SII V ' TAMI I', I r\MI 7 I'VNH, S. I'\NM I, fwn I I ' !<!■ • r I .•4'<.«[ 20 CI ar koii.ivvay. I'VM r 5, r\sn |, TsM I, 5. I'wfl. (j, i I'ANI.I. ;. I'ANI-I, S. WIT I. I'WI I (* [ |i- uv ■ ji 2 5'7#C j"4" (* [ h".-," ■ -• 5" 7» [ ll 2 4" l,.S» [ -• 5" 7# [ -■ "i" ■ 2 4" (,.5« [ '«■' ■ := 5" 7* [ -• 4" l'.7» [ I J" • ^ i' 7» [ .' 4" I..'* C 1.'" ■ -' I : _ J 5" 7-<* E 'ir ■ IJ • i -• 5- ^i.S* [ -• ?: 7» c ■ ' =(. -• >" 7* C ijl" :o -• 4" <* t 4""S#I ll" • - 4" <•» [' '.C " 4-"s«I ' .' " ' ■ I I* [ I is' ■' 4*.s#I ! • 1 '■#[ I,'.'," ■ I ■»! 4'",S«I I lA" ■ ' -•4""*[ : i4't«C I ':•:,;' I 4",s#i I -•4-'.<M#tl ' ''"^ 4',^#I -•r •■ -'V'7"l*[ - I ■■■ -■ I.- K* X a I J' •' 4^S#J :J:^-L ir • J 4" I* [ H" ■ » ■ i 4" <•» [ ' „ 1" 111 2 4"'>»[ J4'&#[ 4'S#I 'A" ■' 'A ''' i '•' 4".S#I -• 4" I* [ |,V ■ 4 ,s«I 'l' ■ -•4"/*L -•4'(*[ 4' ,S« I i;' ■ '■}■' : 4"'s# I 'iV ■ '^ 4' s# I I J " • = 4'0#[ 4'".S«I 'r'.r ■ -<,'.'*£ 4*fi*i -■ 4' I* t 'i'r- 4*^#I !<■' • t ^ 4* S#I IlJ' •■■ !Y'7*T| 3 4'l*[ la* a _s— J4 ll" -• 5' '^ t <A'® ' 1 ■! ' in j;-"io.5»r ;4"(*r <r ■ i\' ■' .■r-u..-#[ -^5"7«C . 'iv; • Fl 1:1 3 4" (* [ i" • \V ■' 2 4"'*[ 3 4''*[ » ■ 4" s« I I ' ■ - 4 '■« [ I " ■ 4»,S«I h'.-." ■ - 4 '-=[ I 4'^»I 1;" -•.,'..= [ r.i ,' tr ■ H' ■ z 4" '* [ r ■ i 4*1.1 4""s*I 1 ,"''«I 1 , '■ ' ■ 1 ' " ~l ■,■.,*[ ,*s«I 4*S»I li' ■ = 1 -■ I 1* [ ir ■ ,*S3l 'ir • .•4' .,,-,*[ ii; ■ 4* >■# I i|r' • -' 4' I* [ li' •■ 'tr • h' ■ 4's»I ■4'i*[ '\" ■ ,-\« I '1" ■ I -•»'i*t ',^::;' ! 4"'s*I I _uY ■ I kK ;•' 4" s* I ly ■ 2 4'l*[ 4*,S*I 1 1" ■ -• (■' <* t h: ;: - 4' "« [ li. ;, 4'"S«I 1 ,'.. ' ■ I ' sa I -■»■;;■* t .• 4" I* [ 1' I" 4" ■•<« I 2 4'6#[ 4".^#I 1 1" ■ 1" •' i .■'■*! - ■' i ',* t 4*8*1 -• I — J — 5' - ir •' 1 " ■' |..-,Vu.5»[, 2 3'7»[ I 2 4V'»r ..,, p fl' ^i:^«-[ Ts" 7« c ' ... ' 'V^' I A ■ U • ■! 5" 7» C , -• 4' <* [ -''A' •■' I r® = 4" <).5» [ 5' lo# I -5"7-5»C, =4'(*[ IJ' -■■ = 5''7«[ ! 4".S#I I,',- ■ . ij' - -• 5' 7* [ ■! 4' (•■}* [ ir • |^"5'7."^#C 1 4" C* [ tr® _ r ^ ir ^' 1' ■•' J4'7*r ,^.,:„ 2 4' r* [ I" •) _•!' •' -' 4" <* C I 1 ' "O 5 !?* I 2 4"6#[ ■^'■7*C i 4*^1 ' I. ' ■ ll" ' ,,-■5 7.'«L -4 "■!»[ 4'S#I 'A' ■ 2 4" (« [ lA' - 4* s» I 'I' •■ 4" 0..!« [ i 4' <* [ 'rV-' I 'iV ■ 4»Wi 1,'/ •' ■ tr * .■4'(«[ ' >iV. ■ -4''«[ I ' ' ■ -• 4 '-*.C .■4;t*t ll,'"' 4 S»I 1 5 ' • -'■•'.!*[ 1 1 ' ■ 4"'s»I 1 I,'...- ■' ' - •C,,''' c 44,1 1 .• 4' I* [ |,V' ■ ^' 1' I* C I 4*W I 'l' ■ i4'<*-t I 4 .S#I ■■^" ■' • 1" '■^ i 1 4^>«I iiV." ■ • !''« [ ji'-. ■_ J.0 I ,v,- ^' ' It 4*^«I t 1" S» I !l ^'h''-" if 5" 7.3* [ 1 1 I j '-" 2s'!i.4#[ - 5" 7» [ ij'o) *' \ 4'S#I '.'.I- M ■ J 4' i.» [ J 4" 1* [ I,'/' 1", ■ ^I 4'>«I ' 4''^* I lj'0 2 li"0 J' 2 5' 7-4# t 4''.S* I >U"^=^ _ij'--> 2 6'S.5»[ 2S-J#[ 2ii|'e J' a 2 5* 7.4» [ 4" S# I 2(.'X.5#[! 2 5'_7#[ i'^5'7-7»[ 4*S#I < i ij- ■ if •■ _^ j(i"!S.i« [ 2 5'7*[ ' ■ 2 1.1" ? I ■•?.' - ' |2 5'7..,,«[, 4''^«I 2(.'9#[ ! 2 5:7#[ , I It-.! ! ■\ 2 I j" ! '-':' '•■' j ;2 5'7.<#[: 4*'.X»I ; ' itr ■ 'ir ■ '-"'■"•5»[ -5;7»[ ^ 2,r. ll' -\7*[ -t'i^,*! ^ I.' 10* [ J ;' 7» [ I r • - 1,'V ■ tr ■ :--,-s..»[ 4»,s#i ' 2,1,,' • i;' ■ 2 (." io.5» [ 2 .^' 7» [ -'f ■ \l ■ '\r ■ ■ -- 10.5a [ -■ -, ;« [ 'r -1 ! 4':s#i 1 '<■■: ■ - !■'■»[ 'iV.; 2 4'l« [ '■''" ; 4'^s#I 2 4' (■# [ ■ j'^a }"0 I" ■' 4"S*I 'i" ■ 2 4",'..3* [ , 4»,s«I iiV • 2 4" (...(» [ '"■>,'■ ■ 'ir ■ 2 5- 7» [ !■;■ • I'i' ■ i .s»i 'W ■ 25 :-[ '(*[ jl" -J r •' 2 4'f*[ ( ■' 5" )';'* I 2 4''(*f ir •' 4" »# I 2 47'»c 4^ 'A' • 2 4" (« [ 4'il 1 1 " ■ '- 4 ','* [ 4"S«I UV ■ -' 1' '„■* t 'I'i' ;' 4""^#I I 2 4'0#[ j i " 4" ^* I Jl''." ■ 2 4' 6# i 1_^0 4 ■'".".» I i,V," ■ 4*Wl uV ■' _ 2 4' "0* [ f^- 4*S«I ll"i' ■ 24 l>Jr [ a- 4*S«I !',■■■ 2 4^*[ ¥^ ■ 4' (« [ j.' ■ 4"*.-^* I 1 " .' 2 4;(*[ 4" .^* I ■4" 0*1 I' 5-0 4" ,s» I 2 47* [ i» 5'? 4-.S«I 'V ■ 2 4'i-a[ 1'0 }'0 24" f* [ j'0 i." ■' 4-.S«I ■ iv ■ 2 4' !>« [ r,, -•■ 4's»I 4*-I I 1 X" ■ !r4"i>.N»[ ! 1' J 0' «.5» [ 2(.'..o» t I27" co.5»[ !/■ !!»[ 2./.2.5»|:: 2t,-i2.,»£: 2,v' I :,.!«[ iy7.5»Cj 3 1/,,' 3 5'.-<»t 2 'I'l" ■, I 55' ?■=« t i I ll".< • Vs" 7.7« [ ;2 5'-,.t»c I 1; ■ j 2 5' .S.2* [ = 5 ,7;5« C 2~0' S.5« [ 2 if .' ^ 5," V [ I 20' .S.5« [ ! 2,i'-' j 3 5'S#[ _ ■}' ^7 I 2 0" s.5« [ ; 2 5- J;3* [ 2 6" S.7# [ 4" "« [ ,1" ■ 2 4" 1* [ i" ' !■■ 2 4"l«[ 2 4"i*t 2 4 • l« [ 1" . ',•.•,■■ • 2 4" (* [ ■ K I* ^ It' '■ <v ■ 3 4''*C 5";o»I ii'\ • 2 4" (...a [ >.\: ; 5'.o»I 1! ■ 3-4;,..* c Ai ir ■ 2 ,;: -a [ 1 i«r 24 («[ 4 sal >r ' 2 5- 7# [ U' ■ 'U" • -• <■ r« [ 2 1.' ■ ;., ■ ,; M,',s.5*[ 4 •;»! I, -"I" I ,\sal 24 i« [ 2 4 c.a [ ■ r ■ <\y ■ 2 4'.a[ 4'S»I '\V ■ \- ^= I 24 '*[ ■I :^f I ' !'-■ 2 4- l« [ I r., ' 4' .-^a I i',' • 2,'',*[ li' ■ 2 1 ca [ I i ,'s= I 4 sal 1 |V, • 2 !'<*[ 1 2 4 ','■«[ Ml 1 1";. " ■ - 1 »>* [ '7*1 - (■ I* [ ''V ■ l"'-al J"0 i%3 i'Q 1'": ' •■) 4".^* I I i " • -■ '-'„'* t .'"sal _• t <•«[ 1 ■' ■' ^' ■ 1 '■' ■■ . ,'sal M ■ 2 0" O. I it [ 2 I i ■• . 2 6' S.;a [ li' ■ 2 0' .>5» [ 2 iC ■ 2 6',S.5*[ ij'V 1 26' I0# [ 2l-^;a:' I ' ; ' 2 u' 10. 3* [ ;" 10* I 'i.v," ■ 2 5 ■ ;a [ 'iV7 5' '10* I i\" ■ -' 5" 7# [ li' . V ■' 5" loa I _iiV ■ ^"5" ra [ tV ■ ;■ -a [ 'i' ■ i" ■ 5'ical 1 5 "^5" 7a [ >v ■ C 'ioa I 'i\r ■ 2 5' -.la [ 5- i« I '!'■ ^ 25 -,ia[ If.' ' ' =1 5" loa J 2 0'S.;a[ 5'ic^I |2 7'ie.5a[ r^ : 2,\V ■ ' 2 (.->.;-[ I ; ■ ■ :,2; 10.;= I 2 ■|J ' ■ -J I..'. ■ - 1 ■■ i \V ■ TABLE XX TABLE OF LATERAL SYSTEMS AND SWAY BRACINt'i IMNKt. 7. I'ANII I. J 0- »,J» f 2 f io.5» £1 : -" 10. 5» [ r ,>M. 1. _ r .- » 1. If t X" ■-■'' 5 4","*T" a r'i*t _iiv:® 3 4" (•"T ll'/ -^ ■ a r:..ir i: .1'.../. I'.VNH ■,. I'WII ). I'WH V TaNII (■. I I'VNKI ;. V\\i\ 'S I'ANI I I r\M I -■I! CI ar Koauv.\: \'ss\\ ; I IM I |, r\Nl I IvM \'\S\ I I'ANFt N. - 4 -||.:-.o.5»[^.5,;»[ '■=1 ' ^[ -I = 1 il" ■ z 4" 1* [ 'i".-," • -■ li" • ii'V • . 5- ;« [ , -'4"'i'-5»c! li --'•>' li" ■ . ?" 7.^« [ 'I' ■ - 5" 71* [ -i,\" ■, ■5 7*C 11.!' ■ - 5" ■'^» [ ■}'^7n - ;" ^-i* [ - 1 r ■ - 5'; 7* [ 7»[ !,'.'« ^ (." ,s.5i» [ '"> [ J 5" 7# C 4''.S# I 1 ; ' " _ I,'/' • : II* [ 'i'.-," ■ 1 i ' ';> i' ■' * ■ ■, ' ' - •,','*C 4''* I 1 1" ' '-1 ' 4" s» I ilJ' • ; t' 6..|» [ li" • \" ''-I* [ hV ■ 1*S#I >ir • I I'll' '^ : W" ''^ - 57 ;= [ . 1, ,,« [ ^ I."..' ■ -' 5" 7'>« [ I ^, 1 - . - 1 ■ ■ J (j ■<>.:,»[ 2 5"7.;^[ J ()■' io# [ :[ .: . "!..-»[ m" • : 1" (..^» [ I '. " • 1*^*1 MS' ■ 1^' ■ :* N* I •!r • iT ■ 5" .S# [ J * 8# I "2 47*£-; I " oj ! ^4"«»tT .K'^ ! -4"<*C , I r • : .t"".s» I >■'.," ■ - 4" I* [ iiV ■ 4 ■^«I 'F' • -4""»[ I .i " ' I ''■ ./ ,s« I 1.'.-' ■ -■ 4" !•» [ l.i„" ■ J .," !,« [ u; ■ ■'7*1 4As«I i i4" ■ - 4" "* [ 1.1; ■ .,-•>,« I 1 1", J 4" '* [ I I ',; " • i.V ■ ''"'„'* t I.' 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' '•■•■„' ■ J6".S.;#[ :,■ i'*I li" ■ ir • - V « 5" '0*1 ■A"" •' 3 4; ...,#[ \ ' ^ 5"io#I Ij" • iiv," ■ - ■>■' 7» [ 'ft" • .ts' "V 5" io«I i,v." • 3 4";-«C 3" \o* I 'l.i •' 3 4" <; ;» [ 5-^lL'l 2/,o ! •0 •0 i' -■' ■ r SJO i 1* [ ■ 3 ll" io« [ 3 (]■ ,^.;^it |. i 'i'/" 3ir.s.5»[^ 5 io*I 'J • 1 Ij"" ■ r" ■ J' a 1 •! 1 r.-." ■ iir J..' io.-,#[; = ir- jC.",S.-,«[ 1 ■;- lo.ja [ 1 u' .-, -,» [ J 7' ln.5» !_ 5^tl ir ■ : -:;7-r - 5 5-' 1 - 5 ■ 1 .J 'i ~ 5 1 1 I s" 1 /" '■• r ■ lr>« I v ■ io« T ,1" ■ '":* [ ;3 u" io.5# [ '\r ■ 3 7' io.5# [ 3 ij" 3 li' S..(# [ iir • -• 7" io.5# [ Xi 3 7' KVS# [_ 3,|,('© 3 I.' n..,« [ 3 S.i~ I ; 1*1 i|.'' lo*I ■ i.r ■ 3 ll" ,s.^a [ •i" "•' 1 ■', 5' ,ra I 1 : _• ( 1 . . - -- r M" !'■ •' 5' I'o^ I M" - 5 ■ 7* [ 1,'V© ■•.- 10*1 It" • 5 10*1 ll".!" • S lo»I 5 ic* I 1 ; ■' ■ 5' 1',-- I 5-'?:=i '1'.' ■ ',v, 'i:"" '• 3 I i'» [ «" • i.r •■ ^' loS I li' ' i 5"";*i -■4 «*■•!: r - ' i.'i" • I ,' 1 " - i ,70, i 300 1 IMAGE EVALUATION TEST TARGET (MT-3) W. // {./ ^.A^ "% 1.0 I.I ■ 50 M 1.8 1.25 1.4 1.6 -^— 6" — ► Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 .5^"^%* f/. i/. ^ J a SAiw; ItivorkDni Upper horizontal line shows diameter of pin. •'ticaB ( -g : '- 3i' si' 5i' sS" 51" 5r 6" 1 J0.i3 0_ 11.40 I J 2.66 3 .13-92 '4 16.41; 6 17-723 ^20.250 21.52;! i-4-05 "4 1^5-3> -S •6.5SJ6 ,..7.848 ' .55-44 5 !,i7.:07?; ' |lo-5o^. ' il3-03 5' t5-5f^'i5,_. ,8.of) 8 |i0.6jp .3 iV ¥ r - -- 26.20 28.22 30-23 28.88 29-53 31.64 30.94 32-34 32-25 33-00 33-75 34-50 36.66 _35::25 37-45 36.00 J8^5_ 40.50 42.75 I" 34-27 36.28 _35-?'_ 37-13 i 35-86 i 'vV 1 'V 1 ir ! ''rt""' 37-97 38.81 39.66 38-30 39- '9 40.08 40.97 43-'3 ■ 45-28 47-44 41.86 40.31 _ 42j33_ 44-.34 46.36 41.25 43-3 > 45-38 47-44 42.19 44.06 4(1.27 45.00 47-25 _i-»:3?_ 4O.41 48.47 49-50 48.52 49-59 50.67 5';75„ 58.50 63.00 ' ■"67V50" 48.38 49.50 50.63 5'-7S 52.88 52.41 56.44 60.47 64.50 ^•8-53 72.56 53-63 57-75 61 .88 - (j6.oo 70-13 74-25 54.84 59.06 63.28 . <^7-5o_ ■71.72 75-94 56.06 "6038"" 57.28 61.69 6<j.o9 64 .rK) 69.00 73-3' 77.62 _7ojo_ 74.91 79-3' 83-72 ; 88.13 92-53 96.94 72.00 76.50 8 1.00 ""85.50 1 2' i 2^' i 2V' 2i" 76.59 80.63 84.66 88:69 92.72 96.75 1 100.78 104.S1 108.84 78.38 82.50 ~ 86.63' "90-75 _94:88_ <«.oo r io7.:5 111.38 115.50 '23-75 So. 16 '"8I.38 88.59 92.81 97-03 105.47 109.69 Ti3.9i iiS.n 122.34 J 26.^56 81.94 86. 2 5 90.56 _94:87- 99.19 J.°3.- S0__ 107.81 1 12.12 1 16.44 ■:o.7"5;" 125.06 j 90.00 r 94-50 2*" i 2r" i 2r 1 99-^-^ 101.34 J05-73. j 1.0.16 114.56 118.97 123-38 127.78 '_i93:50_ 10^00 11 -'.50 11 -.00 121.50 liOOO 1130.50 i Li5 0o_ J39:5o_ 1 144.00 21" -i — 1 -^ - ♦— 1 1- 4 ;- ' i' 3V 112.88 ii6.yi 129-37 132.19 . .'3i-59. — ^' >^*,! V I TABLE FOR FINDING THE NECESSAKY TABLE XXV WIDTH OF BE Having given the total pressure on said s urface, and the diameter of the pi n. This table is calculated for a working comipressive stress of 6 t Vertical 1 les of inches show width CT.A.SS A. ■i" •r' li" H" 2" 2i" zi" 2|" 2i" 1 2i" 2f 2F f 3*" 3r 3*" i" 31' 3r 34" 4- 50 4.88 5-25 5-63 6.00 6.38 6.75 7-59 8.44 9.28 7-13 7.50 7.88 8.25 8.63 9.00 9-38 9-75 10.13 ).5o 10.88 11.25 11.63 5.06 S.48 5.91 6.33 6.75 7-17 8.02 '8.91 ' S.44 9-37 8.86 "9.84 10.83 9.28 9.71 10.12 10.55 10.97 n.40 :.8i 12.23 12.66 13.08 i" H" S'63 6.oq " 6.57^ 7-03 7-5° 7-97 8.77 10.31 10.78 11.25 11.72 12.19 12.66 13-92' ;-i3 1359 14.06 ^•53 6.19 i 6.70 7.22 7-73 8.25 9.80 10.31 11-34 11.86 12.38 12.89 13-41 :44_ 14.95 15.47 1 5^98 6.75 1 7.31 7.88 8.44 9.00 9-56 10.13 10.69 11.25 II. 81 12.38 12.94 13.50 14.06 14.63 15-19 -75 10.31 16.88 17.44 "7-31 i 7^92" 7.88 1 8.53 S.AA i O.U i 8-53 9.14 9-75 10.36 10.97 11.81 11.58 12.1)1 12.80 13-41 14.02 14.63 15-23 15.84 16.45 .06 17.67 18.28 18.89 9.19 9.84 10.50 II. 16 ~ 11-95 12.47 I3.I.. 13-78 14.44 15.09 15.75 16.41 17.06 17.72 1.38 19.03 19.69 20.34 Q.84 lO-SS 11.25 12.00 12.66 - '3-36 14.25 14.06 14-77 15-47 16.17 16.88 17-58 18.28 18.98 1.69 20.39 21.09 21.80 l" 1 Q.OO 9.75 ' lO.W 11.25 12.75 13-50 14.99 15-75 16.50 17-25 18.00 18.75 19-50 20.25 .00 21.75 22.50 23.25 iX" ! 9.56 i"o.:i6 '■■ " II. 16' "•95 ..■.-•7S__ 13-50 13-55 14-34 15.14 15-93 16.73 17-53 18.33 19.13 19.92 20.72 21.52 •31 23.11 23.91 24.70 "ij" '' 10.13 '°-'5' ' 1T.81 " 12.66 ^ 13-36 " 14-34 15.19 16.03 16.03 16.87 17.72 18.56 19-41 20.25 21.09 21.94 22.78 ; :63. •94 24.47 25.3' 26.16 27.61 TX"" ■ ' io.6q~ 11.58 j 12.47 1425 15-14 16.92 17.81 17.80 18.70 . 19-57 20.48 21.38 22.27 23.16 24.05 J'S-»3_ 26.72 1 11.25 12.19 1 '313 14.06 15.00 15-94 16.88 18.74 19.69 20.63 21.56 22.50 23.44 24.38 25-31 1.25 •56 27.19 28.13 29.06 1 u,S 12.S0 1 n.78 1477 15-75 16.73 17.72 18.70 19.67 20.67 21.66 22.64 23.63 24.61 25-59 26.58 28.55 29.53 __30:52 . if" 12.38 I'i.'' ' '341 14.44 15-47 16.50 17-53 18.56 19.59 20.61 21.66 22.69 23.72 23.72 24.80 24.75 25.88 25.78 26.95 26.81 28.03 27.84 ; .88 29.91 .^J°i94_ _3h97_ 14.02 15.09 16.17 17-35 18.00 ._''1:.3J3_ 19-13 19.41 20.48 21-55 22.64 29.11 J .19 31.27 32-34 33^42 16.88 20.25 21.38 22.48 23-63 24-75 25.88 27.00 28.13 29-25 J°i38 -^ •55L 32-63 3i75 34.88 20.52 21.94 33.16 24.36 25.59 26.81 28.03 29.25 30-47 3'-69_ 32-91 , •13 _ ■75 35^34 36^56 37^78 40.69 23-63 24.94 26.23 27-56 28.88 30.19 31-50 32.81 34-13 35-44 , 37-97 , 38.06 _ 39-38 _ I J" -- - 26.72 28.10 29-53 30-94 32-34 33-75 35.16 _j6i56__ 40.78 42.19 43^59 "" i i 1 29.97 31-50 33-00 34-50 36.00 37-50 _J9-84_ 42.19 . J9-oo^ 40.50 ».0" 1 43^50 45.00 46.51 35-06 36.65 „38/2S„ 41.44 ^43-03 J 1.03 46.22 '48".g4 47.81 50-63 49.42 i 38.81 40.50 43.88 __15:56 ¥21.^ 52^32 21" -i" 44-53 46.32 48.76 4S.09 - .50 51.66 J4^3«„ 53.44 _-5'^-25_ 55^23 1 — - - -- . J?L^3 J __5**::14_ 2|" i _,_._. - — ■I.J 57.09 59.06 61.88 61.04 6395 2j" 2*" -• J i._ 3» "3T' 3i" 3i" "3l" 3i" 31" 4" i — ' — — ! ; 1 ■ i 1 11 ; 1 1 1 1 _„ -^ — . TABLE XXVI. ^ WIDTH OF BEARING-SURFACE AT EACH END OF PINS, g coniipressive stress of 6 tons per a" on the projection of the semi-intrados upon a diametral [ les of inches show widths of bearings. CTASS A. plane. Upper horizontal line shows diameter of pin. i" 31' 31' 34" 4" 4F 4k' 41' 4i' 4f' 4}' 4F 5' 54' Si' 51' 5i' 5l" 5J" 54" 6" ).50 10.88 11.25 11.63 12.00 12.38 12.75 13-13 13-50 13.88 ¥ .81 12.23 12.66 13.08 13-50 13.92 14-34 '477 15-19 15.61 16.03 "i7;8r i" •'3 I3S9 14.06 M-53 15.00 15-47 15.94 16.41 16.88 17-34 18.28 20.63 •44 14-95 15-47 15.98 ^6.50 17.02 17-53 18.05 18.56 19.08 19-59 20.11 W 75 .06" 10.31 16.88 17.44 18.00 18.56 19-13 19.69 20.25 20.80 21.38 21.94 22.50 23.06 23-63 i" 17.67 18.28 18.89 19.50 20.11 20.72 21-33 21.94 22.54 23.16 23.76 24.38 24.98 25-59 26.20 1 4" •38 19.03 19.69 20.34 21.00 21.66 22.31 22.97 23-63 24.27 24.94 25-59 26.25 26.91 27-56 28.22 28.88 29-53 1.69 20.39 21.09 21.80 22.50 23.20 23-91 24.61 25-31 26.01 26.72 27-42 28.13 28.83 29-53 30-23 .30.94 31.64 32-34 l" .00 21.75 22.50 23-25 24.00 2475 25.50 26.25 27.00 2774 28.50 29.25 30.00 3075 31-50 32.25 33.00 3375 34-50 35-25 36.00 ■31 23.11 23-91 24.70 25.50 26.30 27.09 27.89 28.69 29.47 30.28 31.08 31.88 :, ■■'^'■ 33-47 34-27 35-0' 35-86 36.66 37-45 _3?f5_ 40.50 IT^" ■94 24.47 25.83 25-3' 26.16 27.00 27.84 28.69 29-53 30.38 31.21 32.06 32.90 33-75 34-59 35-44 36.28 37-13 37-97 38.81 39-66 26.72 27.61 28.50 29-39 30-28 3'-'7 32.06 32-94 33-84 3473 35-63 36-52 37-41 38-30 39-'9 40.08 40.97 41.86 4275 'A" .25 •S6 .88^ 27.19 28.13 20.06 30.00 30.94 31.88 32-81 i 3375 34.68 35-63 36.56 37-50 38-44 39-38 40.31 41-25 42.19 43-13 44.06 45.00 I}" 'A" •r lA" •i" ir 'f 28.55 29-53 30.52 3'-50 32-48 33-47 34-45 35-44 36.41 37-4' 38-39 3938 40.36 41-34 42.33 43-31 44-30 45-28 46.27 47.25 29.91 30-94 3 '-97 33-00 34-03 35-06 36-09 37- '3 38-15 39- '9 40.22 41.25 42.28 43-31 44.34 45-38 46.41 47-44 48-47 49.50 .10 31-27 32-34 33-42 34-50 36.00 35-58 36.66 3773 38.81 39-88 40.97 42.04 43- '3 44.20 45-28 46.36 47-44 48.52 49-59 50.67 5175 .50 32.63 3375 36.56 34-88 37-t3 38-25 39-38 40.50 41.62 42-75 43-87 45.00 46.13 47-25 48.38 49-50 50-63 5175 52.88 54.00 •'3. 75 :38~ 35-34 38.06 3778 39.00 40.22 41.44 42.66 43.88 45-08 46.31 47-53 51..8 48.75 49-97 51.19 52.41 53-63 54-84 56.06 57-28 58.50 39-38 40.69 42.00 43-31 44-63 45-94 47.25 48.55 49.88 52.50 53-8' 55-13 56.44 5775 59.06 60.38 61.69 63.00 40.78 42.19 43-59 45.00 46.41 47-Si 49.22 50.63 52.02 53-44 54-84 5"6-25 57.66 59.06 60.47 61.88 63-28 _ 64.69 69.00 66.09 67.50 ii" an 43-50 45.00 46.51 48.00 49-50 51.00 52.50 54.00 55-49 57.00 58.49 60.00 61.50 63.00 64.50 66.00 67.50 70.50 72.00 2" 1 2i" i 2i" •63 46.22 47.81 49-42 51.00 52.59 54-19 55-78 57-38 58.96 60.56 62.15 63-75 65-34 66.94 68.53 70.13 71.72 73-31 74.91 79-31 76.50 81.00 •25 4S.94 50-63 52-32 54.00 55-69 57-38 59.06 ] 60.75 62.43 64.13 65.81 67.50 69.19 70.88 72.56 74.25 75-94 77-62 .88 51.66 53-44 55-23 57.00 58.78 60.56 62.34 1 64.13 65.90 67.69 : 6946 7'-25 73.03 74-81 76.59 78.38 80.16 81.94 83.72 85.50 2J" 2t" .i;o 54-3« 56-25 58.14 60.00 61.86 6375 65-63 , 67.50 69-37 72-83 71.25 73-»« 75-00 76.S8 78-75 80.63 82. 50 84-38 86.2 5 88.. 3 90.00 ■',i 57.09 59.06 61.04 63:95^ 63.00 64.97 66.94 68.91 I 70.88 74-81 76.77 78-75 80.72 82.69 84.66 86.63 90-75 83.59 90.56 92.53 94-50 6 1. 88 66.00 68.06 70- > 3 72.19 ! 74.25 76.30 78.38- 80.13 82.50 84.56 86.63 88.69 92.81 94.87 96.94 99;«00' •■4 »._ 69.00 71.16 73-i' 75-47 77-63 79.77 81.94 84.08 86.25 88.41 90.56 92.72 94.88 97-03 99.19 iot.34 -i°57/r lyf<Xl6 fi 14.56 118.97 /ioj-jo lOiS.oo 24" J -— - 74-25 76.50 78-75 8r.oo 83-24 86.71 85.50 89.06 87.74 90.00 92.25 94-50 96.75 99.00 101.25 105.47 103.50 107.81 112.12 82.03 84.38 91.40 95-05 9375 97-50 96.09 98.44 ; 100.78 '03.13 1 IIJ.W 3i" 90.18 92.63 99-94 103.78 102.38 1 104.S1 107.25 109.69 i 11 --00 ' r,i" ■ 98.71 101.25 106.31 108.84 111.38 115.50" 119.63 113.91 I 18. 1-!, I 22.^4 II 6^44 i '2'-5>-' 1: Xi" 107.64 ito.25 i 112.88 1 16.91 ■'_-0.7i_ 125.06 123-38 ' 120 4' 127-78 i 130.50 j '3500 J' 3*" 3i" 1 4' 12375 I26A6 129.37 132.19 1 1 133-69 136.59 139-50 i 1 i i 1 1 144.00 ♦ \ ■ 31" 12.19 "1371 XVII. ' BEARING-SURF •ompressivc stress of 7.} Don a diametral plane. Upper lines of inches show vvidl AND C. I f I 0' TABLE XXV TABLE FOR FINDING THE NECESSARY WIDTH OF BE Hiving given the total pressure on said area, and the diameter of the pin. This table is calculated for a working compre: horizontal line shows diameter of pin. Vertical lines c CLASSES B AND TABLE XXVII. ' WIDTH OF BEARING-SURFACE AT EACH END OF PINS, ted for a workinj; compressive .stress of 7.} tons per n" on the projection of the semi-intrados upon a diametral plane. r of pin. Vertical lines of inches show widths of bearings. CLASSES B AND C. Upper -i" 3" ' -1 3i" 3i" 1 3r 12.66 14-24 3i" .1* 3:1" 7,1" "4-53 16.35 18.16 4" 4J" 4i" 41" 4r 4-3" A\" 4i" 5" A" ¥ H" 4" W V 10.78 1 11.25 12.66 11.72 13.18 : r2.i9 13-7' 13-13 >3-S9 14.06 15.82 15.00 _'S:47_ 17.40 J5:?4 . 17-93 16.41 16.88 18.94 21.09 J7-34 19-S' 21.68 „-3:^5_ 26.02 ^8.18 17.81 20.04 18.28 18.7s 21.09 23-44 25-78 28.13 30-47 32-81 12.13 _ ■4-77_ 16.41 ~i8^r 19.69 21-33 15.29 16.99 18.69 „-°-39__ 22.09 16.88 18.46 20.57 13.48 14.06 14-65 ; '5-23 16.76 1S.28' 19.S0 i5.82_ 17.40 18.98 20.57 17-58 18.75 20.63 >9-34 19.92 20.51 22.27 22.85 14.S2 15-47 16.88 16.11 1 19-34 .9.98 2 1. So 23.61 21.37 21.91 23-9' 25.90 27.89 29.88 31.86 33-87 22.56 24.61 26.66 28.7. 23.20 ' 25-3^1 ' 27-42 29-53 24-49 25.14 27-42 16.17 17-58 . 21.09 22.85 24.61 26.37 28.13 22.50 24.38 23.20 25-14 27.07 26.72 17-52 18.28 "19.69 19.04 1 21.97 28.9s 29.71 18.87 21-33 22.15 22.97 23-79 25-49 27.19 25-43 26.25 30-35 3i-'7 31-99 34.28 36-56 38-85^ 20.21 21.09 22.S5 24.38 25.(JO 27.42 23-73 . 25-3' 26.89 24.6 r 26.25 27.89 27-25 29.06 "30.88~ 28.13 30^00 3f.88 33-75 29.00 >-94~" 32.87 30.76 32-81 .3' -64^ 33-75 32-52 34-69 36.S6 ' 39.02 41-19 33-40 35-63 37-85 3S-'6 I" 21.56 22.50_ 23-9" 25-3' "26.72 28.. 3 29-53 23-44 24.90 26.37 27-83^ 29.30 30.76 _32-23 33-69 _35d'> 38.09 41.02 43-95 46.S8 49.80 37-50 39-84 42.19 22.91 28.89 29.88 34-86 35.86 •A" li" 24.26 28.48 29-53 3'-i7 «32.8i 30-59 _32.29 33-98 31.64 32.70 34.80 35-86 36.91 37-97 40.08 41-13 25.61 28.95 30-47^ 3' -99 3.3-52 _30.o6_ 31.64 33-22 34-80 . 3^-39 . 37-97 33-40 .35-'6_ 36.91 _ 34-5J__ 36-33 38.14 35-63 36-74 37-85 39-84 41.84 38-96 40.0S 42.19 42.30 44-53 " 43-42 44-53 lA" li" lf^T" li" 26.95 37-50 39-38 _j8-_f'7_ 40.61 41.02 43-07 45.12 43-36 45-53 47.70 49.86 52.03 45-70 46.88 49.22 28.30 34-45 35.68 -44-30^ 46.41 48.52 46.76 47-99 29.65 30-94 , 32-34 33-75 36.56 _39^38_ 42.19 45.00 47.8. _36-oj)_ 37-73 37-38 39.08 38.67 39-96 41.25 _J3'L3_ 45.00 48.75 52-50 5'-25 42-54 44-47 43-83 48.98 _ S?-_27__ 52-56 54.84 51-56 31.00 35-04 36- S6 40.43 42.19 .._4i78_ 43-59 47-23 50.86 45-82 47-17 51.21 53-9I 56.25 •A" •i" ,r If" •r 2" "2i" ' 1--.14 39-38 40.78 50.27 54-14 58.01 47-81 51.80 49-22 53-32 50-63 54-84 53-44 ')5-04 39.61 42.66 4i-'3 42.66 44.18 45-70 56-37 57.S9 59-41 60.94 37-73 44-30 45-94 47-58 49.22 55-78 57-42 61.52 59.06 60.70 62.34 63-98 65-63 40-43 45-70 48-75 5' -80 54-84 47.46 50-63 49-22 52.50 50.98 52-73 54-49 59-77 63.28 65.04 66.80 68.56 70-31 79-69 43- '3 54-38 56-25 ..J8:i2_ 61.76 60.00 "^63.75 67-50 71.25 75.00 78.75 61.S8 65-74' 69.61 63-75 65.63 67-50 69-38 71-25 73-'3 53-79 56-95 ^55-78 59:06 57-77 59-77 67-73 71.72 75.70 69-73 71.72 73-71 78.05 75-70 77-70 61.17 63.28 65-39 69.02 73-83 75-94 So. 16 82.27 84-38 2\" 2r 6o.i2_ 62.34 __-^i-S7__ 67-97 66.80 73-4« 77-.?4 77-93 80.16 82.38 "86772 84.61 86.84 89.06 70.31 72.66 79.69 83-67 82.03 86. 1 3 _„90^3„ 94-34 84-38 88.59 92.81 S9.06 93-52 91.41 95-98 93-75 98.44 2i" 2|" 2j" 73-83 76.29 81.21 91-05 95-39 , 82.50 85.08 8S.95 87.66 91.64 97-97 100.56 103-13 _ 97-03 99-73 104.06 108.40 102.42 105.12 107.81 ^-. - — 98-44 101.25 106.8S 109.69 112.50 117.19 3" 3i" 3i" 3i" — — 105.47 i"-.\3 114.26 118.83 115.78 121.86 123.40 126.56 I ■li ,-•"[.(•. '5"[ ' F Thick- 1 ness of j Web in Inches. 0.250 _i'l?7S 0.300 1 _o.3-'5 1 0.350 ' 0.375 1 0.400 L?4-'5 ! |_o.450 1 0.475 0.500 ; 0.525 i 0.550 ! 0.575 0.600 i 0.625 0.650 L2:^7'5 ' 0.700 i "0.725 '0.750 0.775 i_o.8oo p w A F W A oo — 60, ,^54 106 1 «*J f«, 30.00 3072 3 '-72 3--7-' 3.5-72 '^2.7f~ 2-73 2-75 2.7S 2.80 ■"2.S3" 2.«5 2.S.S 2.93 2.95 ^^-'^ 3-00 303 3-05 3.08 __3-'o .l-'5 3-20 354 9.00 9.22 y-52 9.S2 ' 10.12 ro.42 — - I06 \ 40.00 r 4 1.25" 1 42.50 1 43-75 4500 : 46.25 ! 47.50 ._4«75. 5000 ~S'-2S~ 52-50 53-75 55-00 j 56-25 i 57-50 L..,5f<-75 60.00 3-53 3-5f' ,^58 3.61 3X)C 3.68 3-7' 3-73 (XD 35 12.00 ^ 12.3s -2.75 '3-13 '3-5° 13.88 14.63 15.00 "15.38^ 10 3472 .5f>-72 37-72 3«:72 3<>72 40.72 14--72 43-72 44.72 85 6o'~ 35 10 10.72 11.02 II.J2 . 11:62 I 1 .92 12.22 »2.S2 12.82 13-12 3-76 3.78 3-81 •— ' — '575„ r6.i3 1.3-42 16.50 3-83 0.825 _4.S72 _ 46.72 47-72 4S.72 49.72 13-72 14.02 14.32 14.92 16.88 3.86 3.88 3.01 3-').i 0.850 _o^75 0.900 ^0.925 " 0950 -■— 17-25 <7-<>3 18.00 i\ k I » ~rr Thick- I Web in I Inches. 4" [•-■'• W 605 1.S2 0.0:5 0.67 I' 3' 1.92 6.71 2.03 7.00 2.10 os-^ ■1" £■/■■■ 5"[-'- F ly A 2.13 2-23 2-33 F '■75„ '•77 1.80 1.83 " 1.8s 1.87 1.89 IF 7-02 744 7.8s 8.27 A 2.1 1 - ■ F-- 1.62 7.08 .-•4i_! 7-74 1.69 2.24 7-36I 2.49 1.65 1.67 1 1 72 I-74 1.70 8.0S 8.4 1 2.43 2-53 -2.63" ••77 1 8.74 ^ 1 9.00 ^•1°^. — — _- i 1 1 - - — 1 — ^ 1 — j i 1 1 i i — — 1 1 1 — 1 i 1 1 1 i ! i _ 0.050 •f - 5"C ■' 1 5" [ ■ ^'•■ i^ ," [ , ./. (," [ . //. /• IF j1 W A F 1.94 ..96 A F IV 10.46 1096 11.4(5 II 96 12.46 1296 ""1346" A 3 '4 329 3-44 .rs9 374 3-89 4.04 '•"S 7-02. 744 7-8S 3.11 1.69 9.08 273 2.S5 2..;8 3.10 3-23 8. 58 2.57 1.81 1.84 1.86 — 1 77" 1.80 2.24 '2.36" 2.49 172 1.74 «.77 950 9.91 '0-33 •0-7J 11.17 11.58 9.0S 9 5° 2.72 ^.2.8S_ 1.S3 8.27, 2.01 2.04 1.85 1 1,87 1.89 . 3-3S 348 3.60 _ 2J36 _ . /2°9 2.11 j . / ! 1 -^ ! 12.00 12.42 12.83 '3.2 5 .3.68 14.00 1 13.96 14.46 14.96 4.19 tt-34_ 449 479 - 373 3.85 2.14 2.16 3.9« 2.19 2.21 _2l2.3_ 15.46 '4.20 — .-. 1 1 _ 1 , — , 1 L .. .^ - — — . — — . — — - , 1 1 . i . i 1 - — --- '. ..-- 1! 1 M-auM- . FINDING the \vcij;ht per TABLE XXVIII. THE DIMENSIONS OF UNION oot in pounds, A the area of section in square i IRON MILLS' CHANNEL BARS nches, and F the width of flange in inches. , 7" [./.'. S"[.W. S" [ . />'. y" [ • ^-i- 9" [ • /"- 10" [ . A. 10" [ . /.'. ' \ .1 \ /■• ir ^i A IV A /'• t A / ;v A F ly A F IV A / I - .- r- 2.30 2.32 — 12.79 J.84_l 2.02 ]_ _ __ 4.04 204 .j 16.00 4.80 '4.98 " S..8 - 5-40 2.43 2.45 2.52 0.) „4^3 2.30 13.46 "7-50 5-25 2. 68 1 4.40 2-33 i4-«3 4.24 2.10 16.59 14-50 1 4-35 2.50 5-58 16.00 4.80 18.33 S-So 2. j6 01 4.58 14.79 1546 __4:44_ 4.64 '7-25 2-35 i9-Jo _.__S-.8J_ 6.03 2.48 2.50 19.17 5-75 ■^ 4-75 i 2.3S 2. 1 2 17.92 5-38 237 20.10 20.00 6.00 2. -l-i).5 2.40 - 18.59 •9-25 s-ss 2.40 2.42 1 1 20.85 6.26 2-53 2-55 2.58 2.60 2.63 2.65 2.68 20.83 6.25 2 5. 10 2.43 5 78 21.60 6.48 21.67 6.i;o 2. '59. '7 3i_ )2 5.28 2-45 19.92 S-98 2-45 2.47 2.50 _22-35_, 23:10 23.85 24.60 _^S-3S_ 26.10 26.85 671 6-93 7.16 22.50 6-75 2. S-(5 2.48 20.89 6. 1 8 23.33 7.00 2.( 563 5.80 ^i5° . 2-53 .^"55 21.25 21.92 ~22.^ 6.38 24.17 7.25 2.( 6.58 2.52 ... ..„ 7-38 25-00 7-50 2.( 6.78 1 2.55 I 7.61 25-83 7-75 2.( 23.26 6.98 ■^■57 2.60 2:62 " 7-83 8.06 2.70 2-73 26.67 8.00 1 • 23.92 7.18 ... 27-50 8.25 2-; i 2459 7.38 27.60 8. 28 2-75 28.33 8-50 1 ■ ! 25.25 7-58 2.65 28.35 8.51 8.73 8.g6 2.78 2.80 29.17 30.00 8.75 2.- 1 25'92 778 2.67 29.10 29.85 9.00 2.{ 1 26.59 7.98 8.18 2.70 2-83 ! 27.25 i 27.93 2.72 i 1 8.38 -^_._-jZ5___ 1 ~- 1 _ ( 1 1 1 1 " 1 — 1 1 1 , s. A 10' [ . /.'. 10" [ . C. 12" I. A. 12" [./,'. .2"[.C. •5"L '' Thick- ness of Web in Inches. F W A F W A F W A F W A F w A F vv 1 A /'■ 0.250 20.00 20.67 Coo 1 0.275 1 0.300 1 0.325 1 0.31:0 17-50 S-25 2-43 2.56 2.52 '8-33 5-50 2.46 6.20 2.58 20.00 6.00 3-01 22.54 6.76 3-01 19.17 5-75 2.48 21.50 6.45 2.61 i 23.54 706 3-04 i 20.00 6.00 2-5' 22.33 6.70 2.63 1 24.54 736 3.06 -^ 1 0.37s i 0.400 20.83 6.25 _ 2 53 2.56 ^-3-i7__ 6-95 2.66 ! _..=5-54 __26.54_ 27-54 7.66 7.(u) 8.2'^ _309 3" i 21.67 6.i;o 24.00 7.20 2.68 30.00 3072 0425 22,50 6.75 2.58 24.83 7-45 2.71 3-'4 9.00 9.22 2-7' 0.450 i 0.475 1 0.500 |..°_-S25 1 0.550 0-575 0.600 0.625 n-ii 7.00 2.6, 1 25.67 7.70 2-73 2.76 2.73 28.54 8.50 3.16 2-73 1 ■ ■ 24.17 7.25 2.63 1 26.50 7-95 29-54 8.86 319 3'-72 9.52 2-75 1 25.00 7-50 2.66 ! 27.33 8.20 _32-72 33-72 9.82 2.78 40.00 12.00 3-53 2S-«3 7-75 2.68 28. 1 7 : 29.00 8.45 2.8 1 i 1 10.12 2.80 2-83 41.25 12.38 3-56 26.67 S.oo 2.71 8.70 2.S3 2.86 34-72 10.42 42.50 '2-75 '3-'3 3-58 3-6. 3-63 27.50 8.25 2-73 L29-83_ i 30-67 8-95 9.20 35 72 10.72 2.85 43-75 28-.33 8.50 2.76 2.88 2 91 .36-72 M.02 2.88 45.00 '3-50 t -.-?-i7_, 30.00 8.75 2.78 31-50 9-45 37-72 38-72 11.32. 2.90 46-25 13.8S 3.66 0.650 0.675 0.700 !?•_"- 5 0.750 0775 o.Soo 9.00 2.81 l,--2,l 9.70 2.93 i 1 11.62 2-93 47.50 '4-25 14.63 3.68 11^ __2,2,-'^l 9-95 2.96 1 i 39-72 40.72 41.72 42.72 ir.92 2-95 1 48.75 34.00 10.20 2.98 . 12.22 2.98 5000 15.00 '5-38 3-73 _34;83^. 10.45 _3:0L_ 12.52 3-00 3-03 _5i:2S _ 52-50 3-76 3-78 12.82 '5-75 43-7^ 13.12 3-05 3.10 53-75 16.13 3-81 1 44.72 13.42 55-00 56-25 57-50 16.50 3-83 0.825 0.850 0-875 0.900 0.925 0950 4572 '3-72 16.88 3.86 1 I 46.72 14-02 I 3.13 '7-25 3.88 47-72 1 '4-32 1 3- '5 14.62 1 3.18 58-75 '7-63 .3-91. 3-93 i 48-72 1 49-72 1 60.00 18.00 14.92 j 3.20 j ! 1 1 '^4 ^^tim- Ft I'N — .1 -t -5 _■! 5 S 5 y ■/ — t ■' i \ ! _) -_< — -i t — \ ( ( l< I( t 1 I( IC 2C 2C -' J m ?< Width, in inches. Weight per in Dound foot, C End allow- ance for one ; bar. Rivet- Heads. 1 1 ' __ i" h" i!" — _ 4' 5" 6" 6r 7' 7r 8" 8]" ~ </ 9i" lo" ioi" 11" up" 12" " " 1 TKR, IN INCHES. OF TWO HEADS, IN I'Ol'NDS. ™~ i5 '•2S 0.14s 0-153 0.161 i o.oS __. 1.36 1.46 ' ••57 1 Tri 0.12 0.16 0.20 0--5 0.32 0.40 0.47 — . 1-95 —.._ — 0.180 \h I "" ^ 1.67 1 1-78 i 1. 88 2.aS 2.21 2-34 0.1 88 . 2i 2i 23 2i 2J 0.197 ~ 2.97 3- '3 ; 3-29 3-44 0.215 0.223 2.47 2.60 H — ♦ o.2;fi 0.250 I 0.258 ; 266 0.274 ! 0.2S2 ( _t 12.1'' i .3" i •3i" ; ' t' 14^^ ts' : ■ sM ! I()" I o-.^5 -5 2-73 2.86 i ^? 1 .3 5 300 "3-26 3.f« 3 3i 3l 3? 3i 35 3^ 33 1 4i .1-75 ■ 3-9« ; * 1 i 1 1 3y) 4.06 1 0.291 , -4 : 1 4.22 1 4'"J . - 1 4.S5 j 5.00 5.1(1 299 iSi" "20' 1 20^" ! 21" 21 r i J 0.30- : 0'3'5 ' 0.332 1 0.340^ — 1 1 -_ -- -- ! — 1 1 1 0.34S - ! I ! m ii^ TABLE OF LEI Weigl Approximate Lengths, in Feet, betw TABLE XXIX. TABLE OF LENGTHS OF LATTICE OR LACING BARS. Weight per foot of same, and weight of rivet-heads. ximate Lengths, in Feet, between Centres of Rivets. TABLE XXIX TABLE OF LENGTHS OF LATTICE Weight per foot of same, and weight of ■ OR rivct-h LACING ead.s. BARS. Approximate Lengths, in Feet, between Centres of Rivets. 990_ 009 031 11" I Li" 12" 1 2 J" •3" i3V 14" 144" •5" I c'" 16" i6i" 17" • 7-i" 18" i8i" 19" •9i" — - r!o27 1.119 1.^38 1. 157 1. 180 1.204 1.045 1.065 1. 08 1 1. 104 1. 122 i.T7"s^ •-•95 1.21S "..238" - 1. 214 074 t02 r28" 153 1.086 I. no 1.230 1.250 1.269 1 .289 ••307 ••327 '-347 1.548 •-587 '•■45_ 1. 169 i-194_ 1. 219 ••364 ••399 ••135 1. 160 1. 187 1.274 1.309 '•383 1.420 1.440 1.456 '•475, ••495 ••5^7 ••538 1.494 • •S^4 1.226 1.252 1.261 1.284 •-295 1.320 '•332 _i-353_ •-.377 •-367 r.402 1.388 1.426 1.458 '-53^ ••567 1.602 1.625 1.640 1.678 1-739 181 210 .240 .268 .300' ■33^ ■395 .428 I 2 1 3" 1.242 1.246 1.270 Z'^75. 1.306 1.312 ••344 1.414 1-447 1.471 1.494 1.478 1.502 •-553 1.572 1.5S8 1. 610 1.661 1.700 '•774 ••793 ••338' 1.362 1.369 1.404 '-4,57 ..644 1 .6S0 1.720 •-75S 1.S30 1.268 1.298 1.329 1.300 ^■33^ ••395 1.428 ••459 1.485 ■-5'4 1-527 ••559 _'-58i_ 1.610 1.596 1.619 1.644 1.630 1 1.667 1.650 1 1.689 ^ ••704 1.7:5 •-739 1.776 1.814 1.850 '•329 1 .356 1.388 ••357 1.388 1.390 1.422 1.422 '•453 1.518 1.550 '•759 •-795 •-833 1.868 1.450 ' 1-477 1.480 i.546_ r.5'72 '-577 1.679 1.714 •-738 _^749_ ••77' _J:""9_ 1.S07 ~f.829 1.S17 1.851 1.888 _'-357.. _J-390__ J-422 , J -453 1.419 1.448 1.509 1.540 1.567 ._L-.595_ 1.623 1 .650 1.604 1.630 '-657 '•637 1.664 1 .670 '•704 1 .840 _'-'^"7._ ••_9L3_ 1.422 1.450 1.448 1.476 1.506 ••5.16 '•599 1.627 1.652 1.697 • •730 1.762 1.786" 1.811 ••7'i5 1.864 1 .900 1.936 ••477 1.50C •■535 ••565 ••565 ••593 1.689 I.7I4_ 1.742 ••723 ••753 1.SJI 1.852 1.887 r.923 1.956 1.480 1.509 ••5.3<^ 1.567 ••599 1.6S1 ••745 1.776 _J.-^-^-_ i.8t6 1.902 1.928 1.911 ••935 1.944 1.969 1.978 •459 1.485 1.514 1.540^ • •572 ••595 1.627 •-657 1.689 ~f.723" '-753 1.786 _':623_ 1.652 "1.681 1.714 _J-745 1.776 1.811 1.842 _l876_ 1.911 1.944 1.680 1.710 1.771^ 1.S05 •■835 1.863 I.iS(i() i.,S()5 '-'J- 5 2.003 •494 1.518 1.546 1.680 1.710 1.709 1.740 1.769 1.800 1.801 1.83. 1.960 __L994 2.028 .527 ••55° __l--577__ 1.610 1.604 ••637 1.630 1.G64 _i.697_ ••730 1.762 1.740 1.770 i.8?o 1. 861 1.892 1.956 1.988 2.023 2053 :S59_. .596 f'3o .667 l7_°'L •739 V.584 1.742 '•76'; i.Soi 1.800 1.830 1.829 1.859 1.890 1.8 sy 1.889 1.890 1. 92 1 1.951 1 .9M0 2.009 ~IK°37l 2.0(17 1.9S2 2.016 2.042 2.070 2.100 2.046 2.081 1.619 i.650 1.689 1.644 1.670 1.771 1.920 _ 1-950 _ •-977 2.013 2.038 "2.068 2.098 2.1 27 2.156 2.187' 2.219 2.2.^9 2.077_ 2.109 1.679 1.704 1.805 ••835 1.83, 1.863 1. 861 1.892 1.920 1.948 2.102 "2.131 2-133 _J-7i4_ 1.749 • •73« 1.921 1.950 1.9S0 2.013 _L977_ 2.009 2.008 2.037 2.161 1.725 1.77 1 1.807 1.840 1.877 _l-79S_ 1.S29 "T.864~ 1.900 1A93'''^ _'//'9_ 2.005 2.040 2.076 ~^27n4 1. 82 1 1.852 1.887 1.869 1.902 1.895 1.928 1.960 1.994 2.028 2.061 1.925 r.956 1.9S8 2.022 "2^053 " 2.089 2.122 2.TT5'" 2.1S9 2.225 ••95' 1.982 2.016 2.046 2.081 2.115" 2.129 2-159 2.189 '•7 59 1-779 1.8.7 1.S5. 2.038 2.068 2.01 )S 2.156 2.187 2.219 776 .81.) '•795 '•8^,3 '•935 _K969 2.003 -i037__ 2.071 2.106 2.140 2.042 2.070 2.100 2. 1 29 2.186 2.216 2.244 ••923 2.077 2.102 2.131 2.161 2. 192 _J;J59 2.1S9 2.2.M 2.216 2.244 2.273 ;s5o" .886^ ;02S 1.868 1.888 ••9'3 1.947 " 1-983 1.956 1.978 2.109 "2^140 2-^33 2.165 2.244 2.276 _---73._ 2.304 2-303 __l-.?05_^ 1.940 1.926 1.990 2-013 2-3.33 1-959 2.026 2.060 2.04S 2.083' 2.120 2.095 2.129 2.146 2:179 2.214 ^ 2.248 2.172 2.229 ._."--4 . 2-257 2^253 2.2S4 2.280 12.313"^ 2-,M3 2-374 : 18" 2.308 1-337., __ 2.334 2.364 ^^.-■3(>3_. •959^^ 1-977 2.034 2.020 _Ji!S7.„ 2.094 2.206 2.240 2.273 16" -•393_ 2.016 2.099 =••34 2.164 2.200 Mi" 2.264 2.297" 2.288 1 2.319 2.368 ! 2.39() 2.400 2.428 1 -•42 5 _ ol" 2.051 2.070 2- 153 2.178 2-324 2-319 2-455 1 12'," •3" •31'" ■4" 1 - " » r 1 " i6i" .7" 1 '7/' 1 iS.i" 1 19" , '9'/' . 1 Width, in inches. Weight per 1 in pounds Foot, End allow- ance for one bar. Rivet-Heads. iSi" 19" •9i" 20" 20 V' 21" 21.^" 22" 1 DlAME- TKR, IN INCHES. Weight OF TWO IIE.MIS, IN POUNDS. o.oS i8" v ■h" ■ill 4" 4V' 5"' 5i" 6" I-2S 0.145 i •.36 0.153 0.161 '1 It', 0.12 6i" 7" • J 1.46 ••57 •■95 5, 0.16 0.20 0.25 74" 8" 9" n'" 9/ 10" lOi" O.I 80 - ■ ■ 2 ..67 1.78 1. 88 2.08 2.21 0.188 1.678 1739 1.700 ••774_ •793 2i 0.197 IS I a 0.32 0.40 1.720 I7SS 1.830 1.850 1.867 1739 1.776 1.8 1 4 1.886 1.940 .'•^59 ••977 2.016 2.051 2.070 ^2.094 2{ 2? 2h 2.34 2.97 3.'3 0.215 0.223 0.231 •759 ••795 ••'^33 1.868 1.905 11" 2-47 4t 0.47 0.55 •779 1.817 1. 85 1 1.888 1.926 •-959 1.996 _2.o34_ 2.057 Hi" 12" 1.807 1.840 ..877 ••9>3 1.947 1. 983 2.020 2.60 I 1.829 1.864 1.900 r.923 1.936 1.969 2.005 2.040 2.076 2.099 2.120 2.140 2- 134 2. '53 2.17S 2.200 I2L" ,.852 1.887 1.956 1.990 2.026 2.060 13" 2i 273 2.86 3.29 0.250 1.876 1.911 ••935 1.960 ".'988" 1.969 1994 2.022 1.978 2.013 2.048 2.071 2.083 i3->" •4" " ~.4i" 2? 3-44 0.258 1.902 2.003 '2.028 2.037 2.106 1.928 2.061 2.122 2.129 "1.155" 2.164 o7 3-00 .5 (v^ 1 ^ ■,r,r. • .c)S6 2053 2.089 2.189 2.22 s ■5" '5i" 16" "i6.i" 1.982 2.016 2.042 2.046 2.077 2.081 2.US 2.146 '~2Tr72^ 2.179 _ 2-214 2.240 2.248 2-273 3 3i ! 1 3-^3 3.26 3.39 375 3-91 1 0.274 O.2S2 — 2.109 2.140 2.206 2.0 1 J — — 2.038 2.070 2.102 2. 131 2^33 2.165 2.199 2.229 __=fS7_ 2.284 2.204 2.29-: 2.068 2.100 2.161 2.192 2.224 2.253 2.280 2.2S8 2.319' 2.343 2.368 2.396 2-324 2.349 _ 2.374 2.400 72428; 2-445 _-4«2 2.510 2-543 2-570 2. 596 3\ 33 4.06 0.291 2.098 2.129 2.159 2.189 3.221 nV 2.127 2.156 2.187 2.219 2.249 2.313 2-337 2.364 18" 4.22 1 0299 2.156 2.1 86 2.216 _2.244_ 2.273 2^303 2.276 2.30S 2-334 1 84" 3i ' 2.187 2. 216 2.244 2.304 2-333 4-38 ' 4-54 4-69 0.307 2.219 2.244 2.276 2.273 =•304 2.363 2.393 2.423 2.450 2.47S 2.509 2^543 2.425 • 9-^' 20" Vo.i" 21" 21I" " 22" 3? 35 3l 4 1 0.3 '5 0.323 2.249 _-i-333__ 2^3''3 2^393 2^425 2-455 i •91." 2.362 2.392 2.423 2.452 2.4S2 2.392^ 2.422 2.450 2.4-9 2.510 20.i" 2.452 2.470 _-:5°9_ 2.542 2.570 211" 1 2.280 2.308 '2.337 "-•3f'S " 2^334 2.364 2.396 2-3^3 2-343 4.S5 ; 0.332 5.00 : 0.340 2-374 j..\oo 2.428 1 iS" 1 iS.i" i 19" 20" 21" 22" 1 5.16 ' 0.34S J: H ^ TABLE CHA> SPAC /) = (! ;k'cs i>f c tiVL'ii. the ;o!itaitiinj /) 4" 6" 7" 8" 9" 10 ' 12" «5" '1 TABLE XXX. TABLE OF SIZES OF LATTICE BARS FOR CHANNELS OF VARIOUS DEPTHS, AND SPACED AT VARIOUS DISTANCES. /' — (k'ptli of clKinncl, ;ui<l ,/ = distance between inner cs ..f ciiannels. If tlie value of d lie between the values •,rn, the size of lattice bars is to be taken from the column i'ltainin^ the luxt /aixts/ value of (/. /> 4" 5" 6" 7" 8" 9" 10" 12" Sizes of Lattice-Bars. </=zD </ = 1.25/? ' '/ = '-5^ '/ - '^S^^ : "' '■ iD \" ^ 'i" i" X >l" k" X JS" V X 'J" A" x'4" {%" X 2\" 3" X jj" J" X It" \" X U" 1" =< >(■' 1" X Ij" i'4"x 14" X \\ X 1" X ,r' i" X .f X l|" }" X li" V X ,r' i" X .4" j"_^-" I" x_|r ( X 2" X i" A'xir ' A'x 2^" rt"x 2r ^"x:i- ^"x^r'ift"^^ ■J" X zV' i" X 21" A"x"2i" a I t^ !• ^>l' TABLE NEL! AT V I) -( I,m.'s ot », ,ivi'ii, till rniitaiiuii n 4" 5'_ 6"' 7" 8' 9' 10 ■ 12 ' 15'' !•'■ • ''-'"'l-' ■'HI l|l.l,JI|.iJj,i^WBK* TABLE XXXI. TABLE OF SIZES OF LACING-BARS FOR CHAN- NELS OF VARIOUS DEPTHS, AND SPACED AT VARIOUS DISTANCES. n — (lci)tli <»t" i-'haniu'l, and </ = distaiui.' hftwcL'ii iniuT iiaci's (if (.liaiiiicls. If the value of li lie between the values Jveii, the size of UKMiij;-bars is to i)e taken from the eolunii I containing the inxt /ti/xisf value of </. /> ,/ --: /) Sizes ol Latiiifj-Bars. ,/ : \.l-^/) ,/ = I.5/J ./= 1.75/^ 1 4" r X iv' 1" X ,!■' i 1" X ,T" V X -'" 1" X :{■ 5' 6" 7" 8' r X ,t' i' X 3* i" X 3^* xV X :r i« X 2" r X 2i» ^"X2r I'/'x-i' , A"x..i- ^" X 2f ^'xlir A'x.i' ll-/ X -M" rV" X 2f r\"x.f 9" lO' y X -i" ,Y X 2i' .V," X 3" A' X 2f r X 2f" Vxa' r X .•;■• r X 3" 12" 15" '~ r X J" V X ^,r r X ,;r i" X 3i" ;.. V ,- I •^^' C/3 < < H J CQ < K a « t C/3 < < H o J < :r I/. C ■:r. 2 .E « -I ^ i ^ . Si ■- ;^ rs 3 ^ >^ c - j: 75 "J .E i '^ ? rr C r; — ^ — rj V *-- -c .j; C C o ^ \\ T. > ■=. c rt j;C ~ c — ~» X3 II X - C S. u •• <« & >. m W 1/1 u N « t »») ♦'♦Oi -f' ^' n lA T»^ TC'i *^^ ■•#• ' ^^ '/I '» 1 \ "1 ■ "1 «f 1 " * • ' « ,► • « i "I "■' O t>., t-. W5 » On' i i . I I ) I '1 fO "1 '•) f») r^ "f M I j ! I ^ T^ f^i f*) f1 rn r1 '^ r-, .,. .f "T •** • '"¥• "*" 11* ■*» «iw — I i I I , I I ! t! f1 *^ n fO — -r Ssl^ 2 l>.'~!!» "** ''Vi"'V *U •** •**" » » » « » 1 C o : M I >o /I If 'i - tu - O \ E 1 . I) i I t 'K '•} ii W fc cr. H I « - -^ -> :r. o y > tc tr, -^ j:: V "J "1 IxvO U I o « 1 -^ « ta tr ■^•^a"={sl< « "i! r^. O t^ t-^;o ' f^ c- t- ■ ! 1 ! i I "-I ft — ir> t o » J T IT' ? • H"^ "^,< <i -^i ■• i/"j 'O ^'"^ 'C r^ « i 1^ O o tf} t^, CN O - '1 fl^o : ""• ss S; fc t t ■^ -*-t «M . o vo vo >: ~ t » t t . L- L- l^lj. -T LO, u-1 v£ .>2 ^ ^ ■V. c •/: c »- !L- * ' '• "". c o ! w l"(irnui the (Iki Uia. \ D.a. 1^ 'I ■ormii BRIDGES OF CLASS A. l;i^ f roller in inches. The first aiul last vertical liiie; ivc the diam'^'i'-" l»~''nussil)Ie pressures on the rollers. M" ;,.(V5 3.85-5 J. 1595 4-^4'L^ 9.11 i 4- 1.) 4.4 ^^'L >()! !l 4.5>«=' ' 4.v>0- 4.,S4 4'1 6i .Si 5.00OO lo" _9:63 10.13 10.37 lo.fio 10.S3 tt.27 I. 4S I I .1 ic ) I r.c» 12.50 C5' 9-47 <>S4 10.20 10.57 975 10.13 10.50 lO.SS 10.02 10.40 10.67 10.79 11.17 10.28 11.07 11.46 •0.53 10.78 10.94 11.19 M.45 1 \.6() '1.34 11.61 11.87 11.75 12.02 11.02 12.29 Il.2f) 1 > 1 ■» 12.56 11.50 1 1 .92 '^■.y __'--^-... ri.72 12.17 12.40 12.62 •3.07 II.OI 1 2.S6 '3-3- IJ.Ki [2.(1;, 1 ',.10 i,v;i> I2.3S 12.S; ';v.i3 13.S0 !:;._;() ',)07 '3-55 14.04 12.7.) >3-^9 13.78 14.27 13.00 •3-50 I |.0O 14.50 28' o-').i 1.56 1.86 2(» 3.20 378 4^03 4.28 ±JiiL 4.76 5.00 2f JLt" I? 11" Di / TABLE OF PERMISSIBLE PRESSU I'ormula, /- = o.J5V'<7, where /- is the pressure in tons per Hue: tiie diameters, and the upper and lower lines the leii-ih ot roll 3-3» •54 I 3-64 3.'^5 4.68 4.-6 4.S4 4.<)2 3-64 _3^9 3-77 4.1 3-89 4.2 4:°'_ 4.3 -( I 1 4-S 4,24 3-95 i 4-oS J 4.IS _ 4-35 _ 4.46 4.56" 4.66 4.76 4.86 4.96 4.24 1 A^^3 44« __4-5L 4-59 5-oS S-'4_ 5-4L 5-5° 5-30 5-4' J- 5' 5.6. 5-7' 5.S1 5.91 6.00 5'74 5.sr)_ 5-97 6.o8_ 6.19 6.40 6.^0 D;a. 6.ig_ "6.31 643 >55 6.66 "678" 6.S9 K" 6.63 6.76 "6.89 7.26 "7.3'^" 7.5c 6.93 _. "^f) „ 7.07 7.21 7 OS 7.4S 7-5' 7.(y) 7. SI 7.95 7.62 . >S.O(i 7-75 8.23 - .s- 8.00 16' 8.50 S.I S.( H-5 8.7 s.s ().0 t8" TABLE XXXIV. WISSIBLE PRESSURES ON ROLLERS FOR BRIDGES OF CLASS A. . „.cssu,.. in .ons per Im.al inch „f roller, and ,/ ,l,e clian,c.cr „( roller in inches. The «>»' ;'»'' J-'^;"'''^'' '""^ .er lines the len-lh .if rnller,s. The inlern,ecli,ae spaces c.ntain ll.c pemnss.ble pressures on the tollers. I \ lf» TA\, 1 Orniuhi Dia. ii to" -fk 4'i .l--'>- ■l-l- ■4-<"> t. S-oO i., \s...'^ U^ .v.K ; _?•■'', k 5'5^, /t ' _ S'<'i ft; 5- 74 ?-\5 Da in' ta\es of classes b and c. iirniul:i roller in inches. The first and last vertical linos i!K' i.ianj^j^. [HMMiiissihlc [)rcssurcs on the ••oilers. iDia. ID a. rr r.t 26" 27" -1-4- ■I.5V 4-9i -M' i 5-53-, 5-85 I 10" I0.,]4 10.70 11.05 11.7J 12.04 I '-■35 j t2.66 I2.<)() I '.5--5 r I ;,.;•< I I (.0<) Mo l.l.(.J 0.M5 10. V) 10.75 I r . I ;, I I ..\'! ir..S4 l-M'l I .'.5.' I-;. 17 14.07 I4-V' 1 5.^:0 10.;, t 10.72 11.10 1 io.7(. 1 l.lO "•55 ' 11.16 1 1 II.CKJ 1 II >> 1 1 .i>S IJ.41 1 ' 1 -93 iJ.jS 1J.S2 1 12.30 12.75 1 •3-2' ' \:M 1 ■,. 1 ;, 1 -yCtO 1 1 voo IMS i.i'C 1 M'34 '3.^3 113 1 1 iUk 14.1.S 1 1.(k) I I'v-I') 1 I-5I 1 5.0;, 1 '43' 1 1-^4 i;.r 1 14.(..' 15.111 1 5.70 1 14.1)1 1 5.47 1 i().o2 ; 1 1 ; _M i;.-S i(..;,4 1 1 ^ :;o , II 1.07 i().65 1 15.78 1 16.37 ! i^-QS ; ' 1.48 2.40^!; 2:,s7 3-67 I .(.06 ; t4> ' 4.Sj i 5.19 .v55 ' 5.')o 0.24 Dia. 11' I ■>" '» 6.57 6<)0 -•54^ JS' -i' 1 't " -A ,1 3r -.1 ' 3i" D;a. 4 V- TABLE OF PERMISSIBLE PRESSURES I'ormula. / = c).,:;i 25VV, whciv / is the pressure in tons per 1 '■;<• dianietcrs, and the ujiper and lower lines the len-tli of r Da. 10" 1 1 " \2" '3 14" •5" 16" I ~'' l^ . — ■ 1' 3..,s 4.13 4.2« .I.4J 4.56 4.0(:i 1 -'1 !.;,S 4^51_ 4.71 ' 4. so 5. CI 5.i() 4-59 4.7S 4.96 5- '3 5-30 5.47 5-f'3 4.98 5. IS 5-36 S74 5.98 6.20 6.42 6.12 6.51 ■•03__ 7-^7 7v4 7.()7 6. 5-79 6.37 6.61 6.85 _7.07 ^ 7.29_ 7..S0 7- 5-37 5:56^ 5-75 _ 5.92^ 6.09 " 7 S-99 6.19 6.3S 6.s6 / 6.63 6.83 7-03 7 " s s .\.S2 ■•30 5.7.S 6.26 (•••74 7.22 771 S.|.i s „ -•'■94_ 5.06 viS 5'57 5-70 5-93 6.0S 6.22 6.42 6.92 709 7.26 7.60 7-77 7.91 S.io S.29 S.p S.I.I 8.S1 s 6.5S 6.74 _ 9 9 _;.;,o 5-^3 6.36 6.S9 7,42 7-95 S.48 11.01 9 5.41 ;.'); 6.50 7.04 7.58 S.I 2 8.66 i)..'0 1) ;.;:; 1 i.os 6.63 7. IS S.29 S,S4 'i-,W 9' ^cv, (i.:!o 6,76 7-3- 7.S() S.45 9.01 O.vS 10. -74 1 •■■;-' (i.Sc) 7.46 S.04 S.Ol <Mil n.-(> 10 5..S5 '■■43 1 1 " 7.OJ 7.(0 13" S.iS 14" S.77 .5" y-35 l()" 17" 10 n.i. 10" IS TABLE XXXV. :ble pressures on rollers for bridges of classes b and c. the pressure in tons per lineal inch of roller, and d the diameter of roller in inches. The first and la.st vertical lines >\ver lines the len,i;lh of rollers. The intermediate spaces contain the permissible pressures on the rollers. ■ 5" S74 5-98 6. 20 f,.42 16" 6.12 >7" 7.03_ 7'^7 18" .9" 7.57 20" 7.66 '7.97 8.27 ' 8. 56 8.84 9.11 9-.l« 9-f'3 9.88 10.60 10.83^ 11.05 11.27 11.69 21" 22" =3" 24" 25" 26" 27" 28" 29" 30" Dia. i ) 0.89 __7:'7 1AA_ 7.70 8.04 ! S.42 8.80 9.16 9.10 "9.56 9^57 9.96 10.34 10.70 11.05 _":39 11.72 9^95 10.36 10.34 10.76 10,72 II.IO 11.55" 11.48 11.95 12.40 >i" 1 'i" ! 2" ' 2j" i 6.37 6.61 6.85 7.07 __7-29 7.50 S-37 8.68 8.99- 9.28 ■9.S7 lO.tl 8.76 11.16 ) 7.85 8... 3 8.40 8.6 s __'^:'>' ' 9-39 9.62 10.07 "10.28 9:4i_ 9.72 10.02 9.51 9.S4 9.92 10.61 10.75 11.13 II. 16 "•55 11.58 11.98 11.99 ) 12.41 12.82 13.21 13.60 •3^97 ^ 14.33 14.69 _ J 5:03 ._i5i7_. 15.70 12,84 ) 6.63 ' 6.83 7-5' __7:J1_ "•07 S.M 8.0 r 8.St <).0I <>:o 9. vS ' .>.76; 9.94 17" 7.96 ^ ^-'^^ S.44 8.67 8.89 9.12 9-33 9.S4 974 9.94_ io.i4_ io.;,3 10.52 iS" 10.17 10.48 10.78 11.08 n.36 11.49 "■93_ 12.30 12.66 13.00 •.3^34 12.38 12.75 i3-'3 13.48 '3^S3 14.18 13.26 14.06 '-M5~ 14.82 '5- '9 '5'55 1 __15-9_o_i 16.24 ! 10.93 11.21; 1T.56 11.86 12.15 12.44 12.72 12.99 n.84 12.19 12.S5 I3^i7 13.48 ) 7.03 7.22 7.41 7:60" 777 7-95 _ 8.I2 S.29 845 8.61 ' «77^ ,5' _io.3i 10.60 10.87 2\" \ __77i__ ^7:9 L 8.10 12.04 '2-35 12:66 1 2.96 '3-25 13-53 13.81 14^09 '4^35 14.62 2|" 2i" ■ 3" 10.63 10.88" 1 1.13 "•37 11.60 11.83 1 2.06 12.28" ) 11.14 11.40 n.66 11.65 11.92 12.19 I2^4S _'3^67 '3^99 ) 8.2(J 8.48 8.66 " 9.01 _>'9 935 16" ^•5> 14.84 15.16 15^47 i5^78 '3^78 14.07 _'±36_ 14.65^ lli'93_ 15.20 I4^3' 14.62 14.91 11.91 12.15 12.39 1 2.63 12,86 22" to. 50 12.71 13.26 16.02 16.57 16.90 17,22 "7^54 1 3J" 3r " 3i" I 10.70 10.91 II. II 12.96 I3'4S -J 13-52 •3-78 ^•C'3 'S^So 15.78 16.34 16.07 16.65 16.95 16.37 28" 19* 20" 21' 24" 23" 26" -.-" -/ 29" 30" Dia, : 1 J I BL RIV Beari \" ()88* 57S^ 094 (109 867^ 1-5 BLE X RIVET T CLASS Beanng-strcsse ■\" ir — - — (.SS' 0.719' ' c 578" 2.696 1 2.<X)6 I 0<)4 .V-3S_^ r^- .^505 J (lOtJ K74 ; S67 4.044 , < 1 125" !■•. I 156" ; I iSS" in u ',ia .r ] :in' I.-'JO" n 6.750 ' 7 T- S.cKi s,. .fl ( • "• 'T- iMitim M i l il l llil l T""' It. u U a I " i J 1 ■ 1 i " 1" 1 J 1 c ._,J-'. 1 '. ' . « liliMllM.- M'lMKNTS IS I.NCH TUNS j [ 1 ! 0250* V n 32 S It 18 0.344' r 0.375' 0.406" 1.219 1372 1524 1.677 , o.43»' 0.469" 0.381" 3'3'' 0093 0.131 I.So 23<)_ 0.31 1 0305 '.'It ()o; 73(1 o..S,s"5 1 04() °7S0_ o.i;3S I '03L_j 1 ' '25 ! ; 1 219 0.844 0950 '055 ribi 0.938 1.055 1 290 1 524 l(.4l "•75S .875 ' ■•>■;.) 2. no J 032 1 161 1.289" 1 125 1.266 1 406 1547 1688 1 .829" ''969 2.110 27250 2.31)1 - xV J-3'3 . 1.477 1 641 ' 1.805 1.969 1 -''33 1.407 '■S«3 >7S8_ -i:934_ 2.110 1.419 r.266 1 548_ 1677 1.S05 "i-934 2.063 2.102 2 32 1 1.829 1981 2.2S6 T438 2 500 2.742 '•372 2 286 '3'2 . 1 406 1 500 1 ;<M 1 i,\- 1 477 I 582 1687 1 7' 13 I Si,,S , 2.2()7 , 2.401 1 2625 2.461 26.37 2.8.3 27S9 2..>S9 ,vi'M TABLE X: RIVET TA CLASS 1 Bearing-stresses i r W" 0.406" 1. 219 1372" 1 524 1,6-7 " 1 .S29 l.>Si 2.2S(, 243S 2 51)0 2.74.' A" O.43.S'' i.477_ I 641 '•'r>l''JL. 2.297 2625 27S') ii" 0,469* V 0.500* 0.531* 0.563* w r 0.625" w 11" 0.719* J' j-jys' 0.594* 0.656' O.c'kSS* 0.7s i-^S 1.407 ■•5«3 1.75S " '•'AM 2.110 2286 1.500 ' I.6S8 ' I-S751 2.'jf.3 2.350 2.625 .2.S13 3.000 3.1SS" 3 375 •594 - L993_ 2.192 2-39« 2.590 2,789 2.<>S9 1.188 3.586 r.688 1.782 1 .899 2.005 2.no ' 2.227 2.1 10 A-344_ 2.579 2.813 3.047 3.2S1 3S'<> 3-750 3-9X5 1.210 i.:(i6 2.578 2.836 3.0',i4 3.(0) 3.867 ^ 41^5 4,VS3 .(I'll 2.6(j6 2.966 3.235 3-505 _ .3-774 4.044 1 406 2.461 ' 2.708 2.954 "" 3.200 3-445^ 3.692 3-938 4-430 2, Si ' 547 I (vSS 2.321 _y3i_ 2.74^ 2.952 3.164 2.450 2.673 3-37 1 .829 2.895^ .3' 17 3-.340 3-65 1 (/«;) 2.1 10 2.461 2 6.?7 2-813 2..J89 3'6| .1').] 4.JI 2. 2^0 3-,376 3.563 3:5«7__| .V7S6 3.797 ! 4.oaS 4-313 4-5S3 4.S,2 4. so 4.7S i;.o6 \ I) 1 Ts [ vS" :t it '1 3LE x: ilVET TA ASSES B . Bearing-Stresses w i vS" j 0.719" ' 0.7; •',3 J-J70 3-5 »o : I 1 _ ^•707_ •t-o-H _ \ 4-7 '6 4.9: it 5.054 5-2; ;'i 5-,5"J' S.r3; ■1; 5.7 2« 5-9; ■ 1 6.005 6.y. Ik" 1. 1 25" '3i ' III 'Hi i\" .156" ; i.iS.s" I, J 19" i ,.2-0" S.43S 9-4'A? i 1 i ZZI~ I — - — - - - \"~ - ')757 ir.ojo ro.jS4 10. ;.|.S c a Q _r u " \\" i 1 ■; I" w -i!_li'«M !i / I I I TABLE XXXV RIVET TABLE. CLASSES B AND ( Henoing-! MOMENTS i IN IN1.H i TCJNS o.ii; 0.164 r HI I ■' ■A" 0.225 0-^99 0.389 0/3 1 7_ 0.759 0.')20 1 . I 04 1.311 i" i , 0.250" ^Y A" 1 0.313" 0.344" r 1 0.375" Ji" 0.281" 0.406" 1 0.938 i 1.055 ..,72 1.2S9 1.406 1.758 1.929 2.100 2.281^ -•46.M 2-637 2.8 1 3 2.9S9_ 3.164 1-523 1.055 ; i-is? i-3'9 l-45'_ 1. 61 2 ':7i.4_ \ 1. 172 '■3'9 1.465 1. 61 2 1-759 _i.905 2.051 2.98_ 2.491 1.905 1 1.289 1.45' 1.771 i.930_ 2.093 2.256 2.418 2.579 2.740 2.901 2.093 , ' .406 1.583 2.2S1 __'_-?i3_ 1 .640 1.758 1.875 •■7'5 1.S46 1-978 2.1 10 2.474 2.6()() "2.857 3-047 1 .'/)2 2.242 3-23^ J 109 2.374 2.63.S 3-428 Bearing-stresses in tons. 1.64 1 i.S46_ -'.051 -•.2 5f)_ -•.461 .•.S7I"" 3.07 6_ ,v28i_ ,v486_ i w . i" 0.500" 1T» hi 0-531" A" 0-563" 19" 12 r iV H" li" 0.719" J" 0.750" ii" 0.469" 0-594" 0.625" 0.656* 0.68.S" 0.781 1.758 1.978 2.,.j8l 2.418 2.637 2.857 1.87 s 2.110 1.988 2.240 2.491 2.740 2.100 2.222 _ 2-3-44__ 2.637 2.930 3-223 3-516 3.809 4.101 4-395 4.688 4-98V " 5-274 3-077 3-585 _3:692__ _3i999„ 4.306 4.614 4.922 5-230 2.369 2.638 2.902 " 3-I65 ' 3.428 3.691 3:9j6^^ 4.220 4-t84 2.503 2.784 3-063 3-~34' 3.619 3-896 4-'75 _3-_2-'3_ 3-5-16 3,S(j8 _4.i.p 4-5"" _4-834 _5-'5'> 5-4:9 • 2-344 2.579 3-370 3-S16 3-707 3.868 2.8 1 3_ 3-047 2.989 3-238 3.486 3-736 3-985 4-235 4-483 4.044 4-380 4.219 4-395 4-570 4.761 3.070_ 3.296 3-516 3-7.36 3.281 .■3;S16; 3-750 4. aw 4.716 5-054 5-39' 5.728 4.921 5-273 _S-62S__ 5-977 6-328 5-i2( S-4<),1 4-454 4-733 5.01 1 5.86c 6.22f 3-955 4.748 5-538 5.801 6.065 6.59? ^ABLE XXXVII. RIVET TABLE. CLASSES B AND C. Bearing-stresses in tons. Diameters. i w u" : r M" W 0.813" II" 0.844" *" 2 0'/ 0.906" w 0.938" w 1" 1. 000" i^V •1^" ^iV «l" I .1 » '52 •A" 1. 1 88" -^" 1 T 0.68S" 0.719" 0.750" —. : 1 0.781" 0.875" 0.969" 1.031" 1.063" 1.094" r.125" I.I 56" 1. 219" 1.250" , a" " r - J. H" i" If 3-2^3 3-5l6 • J-37„o__ 3-5>6 - 3-707 3.868 ._4-39S_ 5.126 5-493 5.860 6.226 6.592" 4-570 4-95' 5-33' 5-713 6.094 1 i ' 1 4.044 4.219 _4-747^_^ 5.142 _ 5-537^ 5-933 6.329 4-923 6.358 6.812 _4-"P__ 4:38o_ _±570_ 4.921 5-273 _ .S;333 _ 5743 5-948 6.373 6.797 7.222 7.647 6-153 - ^''WJ^ 7.031 7.47' 4-5" . _4-834__ 4716 5-054 6.562 7-031 7.500 i 6.153 6.563 6.973 7-3^3 8.J04 5-' 56 5-391 5.625 7.266 7-735 7.969 8.438 8.966 9-493 -- 5-479 5.728 5-977 6.328 6.475 6.856 _.'^7_25 7.120 7.720 7.969 8.438" S.219 8.702" 8-3.^,6 S.967 8.7 1 7 9.757 i 5.801 t 6.065 7.910 8.174 9.229 10.020 10.28.J 10.5^8 i I \ r\ 'Hi 12 10' ('0' .So' 100' 1 lo'" l-'O' 1-0' I So' lip' RoaJwaj Hi •(O- •So' i ^^^ / bpan I 50' <)0' So' 100' IJO' l-o' i.'Sr' 190' ::.)o' -TO JOO' TABLE XXXVlll. LABOR IN ERECTION. do' 70' So' i;o' 100' I 10'^ I Jo' " I ;o' I ro' ii«i' 1-0' l,V' uyV -M '. ' .'|o' -•V/ W' 104 I I no .•S4 I IS ' I - 170 -0.1 -,V' . vi 5 .v.) -1". 310 5 ^" r ;o I. So -I ; .•50 . » ' 5 .!"> -110 540 650 "10 770 8.50 S»IO IP KV) '0 \<i(') 11)0 200 -v;" 239 J()4 2;S ^ot 1 ' 7 .'■} ' .>5' ' .i~ 'I .i'i5 Jir ■i >■ < 404 ^ 4^^ 5'7 544 "0 f^iOO (ij ', USll 7-- ■fi 7S,S ■^13 S;(, S-i) <)22 040 (jno I if, JIO -'^1 ■115 57' MM < It r-) io.;o r j = I Table! TONS OF ^'"g-strcss, J i„ I-engtl lor Ml/^l JO.OJ A -<)-\: ,,) ->^-A-, I TABLE XXXI) TABLE OF WORKING-STRESSES. IN TONS OF 2000 POL Calculate! by the fumu.Ia/'^ ''''''-^y wla-rc /' is c.|„;.l l„ Hk- w<.il<i„K.stro.ss. J tho area in I -f U.004 D I y;!* 1 i I.lMlgtll 1 1.10 1 .<ir 4 4i .t.,,s 5" 5i" 0" 14.10 7" _I7^42 7i" 21.24 25-3H 8i" 29.90 9" 34.79 9i" 40.05 10" 45.f'<'' : loj" 5i.fi.f II" 57.96 I.J" 64.64 12" v^ 1 ,',.02 '<■}' ..«-53 II. ir 71.6c '•74 4.14 j.iSli 7^95 10.43 '330 |6.5() 20.20 24.34 3S.65 33-4« lS.6i 44- 11 50.02 5<J.27 62.87 (h),S2 ••59 „ 1 j(-. 3'55 3-83 5.07 . 7.45 '1.95 «>8o 9.21 •-••55 n.S4 " iS.fxj 14..SO 19.32 I.S.27^ 33.07 _ 27.44 26.2(> 32.12 3.1.S4 "^ 37^^8 35.79 43.62 41.13 48.42 46.83 54J9 53.90 61.10 59-33 67.97 66.15 o.;(i ' ■ ' • -•'" _. 3.2.1 4'7.5 (>.5i .*<.(.5 1 1.17 14.07 '7^37 21.05 25^'3 29.51) 34.43 3().66 ' 45^2f> 49.59 47.W 57.58 6|.2S 1 1 1 o.;o 0.64 1,1 1 2,01 l.M. 3.01 1 2.S5 4.41 |I3_ li.lO 5.72 .S.14 7.(i() '^^•55 '1-97 •334 ij.i.l 10.51 ' .S-70 1 20.0S 34.03 32.1)1) ! 2.S..]S .IV •' 4.V72 42.22 5S.''<4 54.13 6...45 (0.64 0.-,i) 1.7.1 .v^>7 .SvV^ / •-•* .1.42 M..|.) '4.y3. lS.3() 3I.(>S , 26.04 30^59 35.48 .10.75 46.42 5-'.45 58.S6 1 J 0.;; 0..). p 1 .(ij 2..1.S •,.t<2 5.05 (i.Si S.I II 1 II.3.S 14.21 17.43 31.03 25-01 29^39 3416 .i9.3- 44.87 j 50.80 1 57." 0.51 0.1)2 1.51 -■,V) .v.V.) 4-75 'M3. S.44 i_l0.79 '3^52 16.62 30.11 2.V<>S 2S.25 32..S() 37^9't 43.37 49.19 SS.58 i ; 0.4S 0.S5 I..1I 2.I.S .^I9 4.4S ().0S 7.W 1 10.26 13..S7 I5.S() «).24 22Sy.) 27.14 3'-('7 3''^5') 41.91 47.61 53.70 ' OJ -^.-if _ o.Sc 1 ,;,.' 2.0; j.Ol 4-2,? 5--'-> 7 •5''^ '>74 12.27 \ ' .V ' 5 I.S.tl 22.05 36.07 30.49 1 35^30 40.49 46.08 52.05 1 1 0.42 0.75 1.2-1 li»2 2.,S3 3'W 5'44 7.19 9.27 ll.(K) '4.47 17.(1. 21. 1? 25.06 2')..V' , .Vt'O.) 39. '2 4.|.59 SO-4 5 I ; '. 0.39 0.70 '•'7 I.Sl 2.07 3-78 5.16 (1..S3 «.82 11.15 ; •3^.\? Ki.SS 20.29 24.09 28...7 1 ,i2.8.1 37.79 •y.'4 ! -iS.,SS '3 J?-.37_^ O.fiT) I.IO '•7 1 -■.''.1 3-5« 4 •■*<■) -.4'! S.40 10.(14 ' '3^22 l(..|l> I'M" 33.16 27,22 31.68 • 3''. 52 1 4^.75 47..17 1 ; ', ' o-.H 0.02 I.C4 r .( i2 -■.]'> .i-39 4"t (. iS .S.OI 10.17 12.65 13.11 1 S.49 IS.70 -I t -n 26.26 ■?0. t!6 -■9.47 2S.45 35.28 ,54.0s 32.93 40..W 39.08 37.82 45-.^9 ■ 4.1.47 43.0S 10' ' 0.32 0,59 0.()S '•5.5 2-27 3-22 4..I2 .,ss 7.<->4 9-7 • 14.85 17^95 2':,.2U i(-.l' 0.30 ^-?',5S_ o-T, i|5 -•'.^ ",.0() .1.20 r.iKi 7.29 9.2.) II. ro 14.2.) 17.24 20.()0 24^.?4 1 7 0.21) 0.52 O.S.S '•,57 J.Cl 2.1)1 ;,.9S ^ ,\^ (i.i)(i S..SS 11.11 i.5''7 '"•57 I9..S3 2.V4''> 27^45 31..S4 3f'.59 41.75 I '"!' 0.27 0.50 0..S3 1 .;,(.) I'M -'•77 ;,S, :.IO (.(.; S.50 10.65 13.12 •5^93 1 9.09 22.61 26.50 30.77 35-4 • 40.45 1 iS' 0.20 0.4; 0.-9 1.24 I..S3 . -•''■•__ .v''4 1"''7 (1 ;() S.I 5 10.21 1 2.60 1 5.32 ..S.,!.S 21.S1 25^59 29-75 ,34.28 .59.20 ' J^il 0.25 0-45 0-75 i.iS 1.76 -■•52 .v47 1.1.1. (..10 7.. So i).So 12.11 '474 17.71 21.04 24.72 2.S.76 3,?. '9 37-99 1 M C.23 0.4.1 0.71 1.12 \.(>S 2..|0 .V.?2 |.|(, S.S4 7-J9 9.41 11.64 14.19 17.07 20.29 23.88 27.82 .32.13 36.82 \n\ 0.22 0.41 0.<vS r.o; 1.(0 2.29 ;,.i.S 127 S.()0 7. IS 9-05 11.20 •3'''7 l(..4(. i().i;i) 23.07 26.91 31.12 35-70 0.21 _o^y) 0.65 1.02 ••53 2.19 3-04 1.09 5^3S 6.t/j 8.70 10.78 •3'^7 1 5..SS iS.ijj 22.50 26.04 .50.15 ,54.61 , joV 0.20 0. ■;- 0.(t2 O.yiS i..|(. 2.10 2.91 v<)2 5.1(1 ( ..( .2 S.V' 10. vS I2.(..) 1 5.32 1S.27 21.56 25.21 21J.20 33-57 1 -:i 'Jv).> 0.59 0.> )] 1.40 2.01 2. So >■ . / 4'i> ''■.i7 S.05 10.00 12.24 i4-7'» 1 7. (.5 20.86 24.40 28..30 .32.56 °A~^^ 0.57 0.S9 ■•.U 1.92 2.(l.S ;.l.2 4.7(. "•13 /•75 9.64 il.Si 11...-S 17.0(1 20.18 23.<'3 27.42 3 '-59 ' ■' -' C.^,2 O.-yl O.S( ) 1.29 I.S5 •^•57 .5-47 4-57 5.IJ0 7-47 9.29 1 l..|0 i.'v7') lf..^O ").53 22..SS 26.51) ,30.65 i jJl 0.52 O.Sj 1.24 I.7S 2.47 "v34 4.41 V<H) 7.20 .S.i), 1 I.OI i.v.i.; 1 ;.i)() iS.()o 22. IS 25-7') 29-75 - 1 ! 0.50 0.79 l.lS r.71 2-37 1 f 1 4.24 5'I7 (1.1)4 S.(,5 io.(.;, I2.,S.| 1 5.44 1S.51 21.49 25.02 2S.SS -.U' f! 0.4.S o.7() 1.14 1.04 ^-•-9 v09 4-0.) 5.^0 (1.70 S.V- 10.27 1 2.47 '4^').i '7.7t 1 20.S4 -4 ,57 28.05 ^4' H 0.4() 0.73 _ 1.09 I.5S 2.20 2.99 3^'>.^ 5.10 ().4() S.oS 'i-'i.i 12.06 '4-17 17.19 j 20.21 2.5^55 27.24 1 -5 ■--- - - 0.70 o.()5 1 .05 _ I.OI o.9,S__ o.(»4 0.91 o..S,S 0.S5 I.S2 '•47 ' I.41 ..36 i.,;2 1.27 '•23 1.19 1.15 .2. 1 2 2.05 1.97 i.<p 1.84 ..7.S t.6() 1.6 1 ^ -••^7__ -•/ 7 .MkS 2.5S J. 50 J.42 -•■>.> 2.2() 2.19 VSo '"^•f'5 3^.=;4 3^4- 3.20 .v'O _ 3.0U 2.</) l.'i-- 4-,';'> ^4.21) 4.15 4.02 ;,.S9 (1.25 (>.0.| '" 5.S4 S.(.5 .S-47 5.29 5.12 4^'>7 4. Si 7. Si 7'55 7., 30 7.06 (..S4 6.63 6.42 (..04 i).(.i 9.00 ' •'^•71 S.4.1 S.lS 7.')4 7.(«) 7^t7 11.67 11.51 IO-9.S IO.(.l 10. 21) 10.00 ().(.S <»-.i9 ().I2 1-1.02 i;,.'io '3' '7 12.77 i2.;,i) 1 2.02 1 1.07 "•3.1 1 1.00 i(i.(.6 16.15 1 5.67" 15.20 i 14.7(1 1 '4,53 i 1 5.112 : 1.5.52 ' '.(•'I 19.60 19.02 "lS.47 '7-93 17.41 ll).92 l(..14 15.119 1 vvl --•''*7__ 21.57 20..)5 20. 56 I9.-I) 19.25 '■^•73 iS. 22 2(i..|6 ^sr ! 24.99 1! ^rr' - - — 2 1-,;<:' ■ -'r -t -3-6.5 - ,' — 22.1)9 22.,56 " — , 2 1 .76 21. iS J, -'^, Ml ..5f. J. I 2 2..SI ;,.(.(. 4.()7 5.S(, 7 • 2 .5 S.S3 10.70 '2.-7 1 Ivl2 '773 20 (.2 " . -— - .._ ^ — •■5' 1..16 1.12 2.05 1 .99 ' -93 2.72 -•57 341 4^53 4.40 l-'7 5.6IJ 5^S-' 5^.v 7.04 6.S.1 j i,.(,5 1 S6j ,S.5(, •^■'3 10. 41) 10. 1 1 ').^3 , 12.42 1 12.10 1 11.7.. 1 14.71 _ ' 1.50 ' 3-VI3 17.25 i6.,So i(>.;,(i ! 2O.0S IV-S7 ■ |i).0(l - — - '•37 1.S7 '•77 2.4<) 2.42 -•35 v24 .V'S ^•o() 4.15 _4-03 ;v92 5^2 1 5.117 49.? 6.46 j (1.2S i 6.11 7'')i 7-'") 7.4.S <).57 9.31 9.0(1 11.44 11.14 lo.S-i '3-.S« '.)•-' I i 2.,S8 JS^94 '.S.r5 15.14 I i,S.5S iS.ii 1767 ' - ^ - '•7' _ * 2.2S 2.16 2.10 2..>S 2.S.) 2.Sr 2-7 1 VSi .v70 ,v''0 4'7') 4.1.(1 (•54 |.|2 .S-79 5.64 5^4') 7.29 7.C9 6.1)1 (^■•73 S.S2 S.5.) '^•37 S.I 6 1 0. 5 1 10. .50 1 10.04 1 9- 7 9 1 12.54 12.2,5 1 1 .92 1 1 .65 14-76 j '4-.5y 1 14.04 i,5.(xj 17.22 l(i..So i().40 16.00 ^ I 13i'""i 1 M'' ' " 2.0.1 -'■'17 2.10 'v\- 3^,15 (•,ii .1.19 .v3.^ S.21 6.:(. 6..10 j 7^'»6 I 7-7'' ' 9.55 9.5' 1 ' ' 31 ! 1 1 .07 1 '3^.5'' '3^o5 1 5.02 15.25 1 1-' 1 x-V" . _ -•.VI 2.\U 1-24 ;,.Mi i .1.09 .V'»S 4.97 ! (..24 1 (.oS ] 7-^7 ; 7-.v'^ i).09 .N.S7 . 1 o.So i 10.155 j 12.74 12.41 I 14.S9 'I-.S5 l 5./ 1 - ., voS ;.i)o 4^>i.5 { .v')| i 7.-I S.(j() 1 0. 50 1 12.15 1 14.22 1 V ■ ;.oo .V79 4-~2 y~') 7-o; ■"^•4.^ ■ lO.Od 11. S7 1 ' 3-89 2.93 3^70 1 l.(« 1 .vO.S 1 (,.S7 S..'(. .;.S,5 , 1 1 .60 1 '.5-.t8 i 1 ; - . ___. 2.'.() i ,v'" ! 1 ■;•.•■) 1 (171 (.,;;; S.Od 7.SS \ 9.r«D 9.. 59 i "•.54 1 1.09 '327 '3' 2 1 "W^" - j' ,M 1 l..'S "i ■ - 7 II. tw 7.70 .).iS 1 0.S4 1 2 70 i .V V' < i-i'i 1 .V ' 5 i (..21. 7-5.) S.97 10.(0 i '243 rjA' 1"' 1 ! ' .|.09 .vC.> 1 ().12 ; 7^,V. 1 S.7S 10.57 12. H) ABLE XXXiX. )NS OF 2000 POUNDS, FOR SQUARE WOODEN PILLARS. K-strcss. A ll.c a.va in a imlu's. /. tlu- I.„^th in inches, and JJ the length ni side <.f s.marc in incncs f \ TAE I Len^ I (> s lo I ..' I 1 III IS ^ Bit TABUD AS STRUTS IN LATERAL l\ Length in I .,' loH J s#i. 1 (, s 10 I J M III iS -•■) Ji'i -•S to MDK- WAV*. I 1..' <).-' 7-4 6.0 S-o .».o -•5 2.0 '•7 ••5 '•,1 I.I o.<r o.S o.S 0.7 o.r. KiK.K WAVH IV-' I ',.0 '■^•7 1 1 ; I'.e I! iri. 13.3 I I .() I 1.0 10.5 1 0.0 ''•5 ,s.,s _S.3 "7.7 6.7 (>.0 5.(1 5.0 .SlDR- WAV*. lo.S^ lO.J l).0 7-t S-9 4.S .|.0 2.0 I.S 1.6 1.4 t.2 1.0 o.y 0.8 0.7 0.6 0.6 o.; KlXiR. WAVH. io.8_ lO.f) 10.) lO.J 10.0 7 9.8 s.s Length of Strut in feet. n i) ® ® 10 12 It 5.S .v.> "5.0 4.8 4.3 4.0 .50 1.5 1 ',.0 t-5 ().G 3 3 4 <).o C) 10., 7 1 ' »4 I (6 8.0 ^ r8 7-5 20 7'0 22 6.6 34 6.2 :i 26 12 '5-0 1 32 34 ; 36 3« 1 40 16.5 1. 18.0 12 H)S '3 21.0 't 22. , '5 24.0 16 25-5 t7 27.0 «8 2S.5 JO.O .i9. 20 1 ■ I^HK^HDI^HH TABLE OF APPROXIMATE WOR 1 L ength of S in feet. trut 7" 20# !• 7" l'^# I- f~\ f SlIIK- F.IH.K- SlDK- Ki)(;e- I Si . \^ ■.^ v^ \S \\s. « \v^. » W-. WAYS. w - =^- - ^. _ 1 1 '"" I -''•7 27.0 1 24.2 24.5 M 2 •y '■5 1 JIl.t 26.9 -'-1-0 2.}..( 1 vO -' -\vO . 26.7 22.7 -I'.l (. ■'•'_ ■5^" 23.0 26.S 21.0 24. J 1 s (i.e. I 20.^ 26.2 1S.7 2.|.0 1 10 7*5 5 I.S..' 26.0 16.5 ^,v7 1 12 0.0 ('. '5-7 ^ -5-7 '1 i-t.5 _ 2;,.5 1 1 I '°i_ / _'3-7 _; 25.2 ..^'-•5_ 23.1 1 1 1 1 J.O ,s r2.o 2.1.7 1 1.2 ■> > — |S 1 ',.; t) 10.3 2-1.2 1 ')■: ■>->■* ' J ''>'^ 10 ->o 23-7 ,S.s ^!''i — i * 10.5 1 1 s.o ; 23.0 7- > 1 "■• iS.c 1 J 7.0 --■.1 (..5 'o-i:2 z i'>5 21.0 i 1 1 1 (i.j 21.7 -M.l >• / '^.a 20.2 j.> i<).^ V- 15 16 '■0 20.5 4i 1.S.7 ^, .t.o I s.o ^ * -5'.> 17 (.0 li|.2 .V ^ '7-i . ■,l) 27. c I.S . '-^ IS.I, "v- 170 ;^ .•S.5 10 .V-: I.S.O vO II 1.3 : __ 10 .lO'O 20 .vO '".74 i 27 16.0 TABLE XL. PROXIMATE WORKING LOADS FOR I-BEAMS USED AS STRUTS IN LATERAL SYSTEMS OR SWAY BRACING. 20# I. 7" iS# I- ()■' II* I ; 6" ..; i 5#I 1 1 #i. 5" 'o* I. j! 1" io» I. 4" 8# 1- i 1 Length of Strut in feet. F.DC.K- wws. SlDK- W.WS. 24.2 24.0 22.7 21.0 Kni-.E- . 1 WAYS. ^""347^1 24.4 J 1 24.2 ' SlI.K- j WAYS. i 21.2 20.0 I, So 1 5.S '3-7 "■7 IOC S.7 7 ■ ^ (.., ___S-7 )•-' 3 7 3-? ]■[• ■J "i ■» 1 2.0 KlM.R- U AVS. 21.6 Ji.S J 1 .2 :i J0.7 _ JO. 2 i'i-7 t'l-2 I S.7"" iS.l i-.o II. : i v5 1 i.o || =; 1 (0 130 IJ.3 SmK- W.WS. KiHM.:- VVAYS 18.2 i8.r 18.0 " 17.9 '7-7 '7.5 17.1 SlDl-;. WA\s. 16.0 '37 1 1.7 97 8.0 Kdc.e- WAVS. [6.0 SlllE- ' EUGE- ' WAYS. j WAYS. SlDK- 1 F.IK.E- ' Side- ways. Edge- i WAYS. mm 413 ® ® 9 27.0 18.2 '7-7 .fi.s 1 5.0 '3-- i_ "■s„ 9.2 8.0 6.7" i 5.O. 4.S 4.0 3-5 3> -•7. 2.0 1.7 13.8 ,3.8 'J-5 '.V5 !-•" 1 3--' 11,.: 13.0 10.8 10.8 I 26.9 26.7 LS-9. '57 11. 1 1 9.7 13.0 12.8 10.2 "9.0 10.6 i "10.4 ; 2 " "4 6 „._'-5. 3-0 I 2 26.5" '5-5 14.9 12.6 9.2 '\ 12.7 74 10.2 4.5 3 2(1.2 ^lS.7 "1 24.0 16.5 2;,.7 i 8.1 : .2,4 74 ■ i^o I S'9 1 0.0 9.8 8 6.0 4 2f).0 6.7 12.2 6.0 j 12.2 "5^ 11.6' 4.0 1 1 .0 3- 'O'S.J j.S 10.0 4.8 10 7-5 5 ' ^v" 1 1.2 -3-' 65 54 4.4 ' ^3-6 3-0 14-5 14.0 I.VS '3-0 ^ ._ ■-•5 12.0 II. s i 54 \ - 37. _. 3'0 12.0 ~ri.7" 4.0 .^2 9-3 12 9.0 6 ""' 2^2 ' .6.7 16.2 'S-7_; •5-2 8.8 14 16 18 10.S 7 ~'- ' 2:1.7 ■■ "•3 10.8 10.4 2'S 8.4 12.0 8 9 10 II -4- ().; 32.2 7.5 ! 21.2 1 ■y- ' 20.2 4.S 1.S.7 4.0 iS.o .;.; 17.; 2.0 8.0 I '3-5 -V7 ^^ 2-5 ! 2.2 1 2.0 -•- , 9-5 , '•» 7-5 20 15.0 -3-0 , .4.7__ 14.2 13-7 _ '-_-Z__ I 2.2 2.6 2..5 1 2.0 1.8 1 0.0 9:6 9.2 \S.7" S.I 2.0 : 8.8 j , ..6 7.0 6.6 22 16.5 1 .- S.2 1 ..; .-77- 1-3 7-2 >■' i 6.7 0.1) ' 6.3 0.S j 6.0 0..S ' 5.6 ■7 '0.7; 5-- _ O.h 5.0 ; .4 24 18.0 12 1 1.0 10.4 ')7 y.o 8.2 7-5 1 1.6 '•5 1.2 6.2 26 __'9-.S_ 21.0 '3 ' 1 I I.O 5-8 28 14 '^O ^ ' 1 .6 1.4 1.0 o.y ' 0.9 5-3 30 ^ 22.5 24.0 '5 ''■3 1 7-'5 1 I.I 1 6.8 1 I 6.2 0.8 5.0 1 °7 J.:S„_ 0.6 4-5 0.6 4.2 32 16 34 25-5 17 11.7 ri.2 10.7 10.2 > H)- 36 27.0 18 .]•- '"" 16.0 C.7 '9 ^ : 18.0 ! 3-0 i ^-7 ■ O.f) 38 j 30.0 0.8 1 5. 1 ' 0.5 4.0 40 20 > ' 174 Ml Twp < llol h.'ll.im ( li.ittc I l;i.i Diagonal I'ovl criiin I I'ciSl (DihIs 'RUSSES. tv \' \ \ \^ \ { 4 \ \ \ e \ \ \ \ \ \ : J . J \ \ 8 Panel. Memi' Tuii ri„.r.l IV, " i 8 6 _ri 8 9 Panel. w Multiply by W'. I'.'-iioiii ( ii,,i J.J ji "I 3i Ji " " ; 6 7 9 ') 10 10 10 lO _ — ... . 4 4 4 4 i tan • .Utcr lli.U(.' I 'i.igiiii.ll . 74 1 7i V 3* , V 7 7 <) 9 10 10 r o f .u l'"-l ri'Iiruiiji V -'i I'nst (DiHk r V it i ~~k V ' i -4 s«t ». 1 ¥ ! a I o ! To the .'♦tre** ..n i' -^ ■— - ^ each post mu^^^ be .uiileil JJ", i STRESSES IN SI w = panel live load on one truss, U\ = panel dcail load on one truss, Jf"=upiKM- panel dead load on one truss, = inclination of diagonal to vertical. 1 3 Panel. ■ 4 Panel. i 5 Member. 70 - 1 „ i 7V 2 70 Tup Chord .... I I 2 3 t» i* , . 2 .1 '• .... 3 (t ti 1 1 •i r.'itt.uu Chord ... I i i • I t It It <> 1 1 1 I >i 1 -, 1 , " " • ■ ■ 3 i 1 " " ... 4 It li , . C I'.attcr IW.uf . . . . f I S 'i '^ 1 Diagonal ...... I i 1 i 4. t 1 3 i 4 5 -- 1 6 I'(jst ('I'liriuiglil'.iidKc) 1 i i! .i (. i. 1 " . 3 i t l'.»t (Dcck-Hridnc) . i -»- 1 - ti tt t. 2 i_ _^ .1 t. It , i 1 1 !■ TABLE XLI. STRESSES IN SINGLE-INTERSECTION TRUSSES. I on one truss, d on one truss, cad load on one truss, diaironal to vertical. anel. 4 Panel. \ 5 Panel. 1 6 Panel. 7 Panel. . 7T 8 Panel. i 9 Panel. Multiply by ;F. w ... ^ Wx i 2 w 3 w f^'. IV s 6 u< n\ 7t; 1 , 2 3 4 4 5 6 6 7 9 10 10 4 4 7 ij tanff 3 3 4i 4i 6 :i ; 7i 9 — . , j 6 6 8 s 10 Ti 2 ^4 4 4 10 , I I -> 3 3 74 1 74 i 4 1! - i 4 li - 2 3 3 5 6 3 3 4 5 6 7 9 7 i — ; --^--1 ! 1 i 1! 10 10 4 !: ■ 1 — — I 'J 2 O — I ^ 2i 1 ¥■ 3 ! ¥ 1 3i i ¥ ' _ i ; ¥ « 2 I — 1 ¥ i J I -- --1 ■ k ¥ 4 ^ i^"^ t ! ■ 1 1 » 1 i -^ ¥ 1 ° ' — 1 -'i -2 ■ ^ ¥ _ ^ ___— . ■: T. s-^.; i -i g i, i I ! '.^ 1 'i ¥ 2 4 1 _i t ,1 i T ¥ ¥ ¥ I J -i To the stre** ow 1 — 1 ¥ ¥ 'i -i J^ 2 i I Ibe added W. ^ -i r o ~j - - \ V i II \ 'A i-\ \ i 1 1 1 f \ J /SSES. 13 Panel. w 11 l5 W W v/- 14 Panel. w I 3 I) 1 1.' 13 ; 1 r 13 15 Panel. mJ Mi .8i 23i W 1 i8i 23i w w %' ^4i 24i 6i 6i <'i Mi .Si '>i Mi I SI W w w w ^"5^ Multiply hy t.in a. STRESSES IN D ;i> — panel live luad n\\ oik- truss, //', ~ panel tleail Unvd on one truss, /r'^iijiper panel dead load on one tiuss, u = inclination of short diagonal in \iriu'al, 13 = inclination of Ion;; diaj^niuil to VLilual. MEMBER. Top Choii U It (1 II . . . • 7 — - — — -^ ^- littnin (' hcl.l . . . I II kl . . 2 7 Panel. • 3 ; • 4 "'. 8 PuiKl. Panel. V V V V /r, r4 V s ;| ¥ 11 " . • • s II II . . 6 II II . • 7 r.uui lliacc . Diammal . . I I Ti • 4 ■ 5 J r 3\_ S 7 3i S_ 7 9 ¥ V V if 'V ¥ I Sll 1 -i 6l ] 7 " 8 9 10 "(wt Cl'lin ii>;h liri(U» 1. I 1 ♦ ■ V o I ? '7 i1^ st (1 )ei k lliiilgL) . I . » " . 2 7~ '' " . 3 L 4 J 6 -? i -^ : . "^ 1 i ' ¥ ; ° _ '^^_ i -i 1 1 ■J -5 1 V l_ V TABLE XLII. STRESSES IN DOUBLE-INTERSECTION TRUSSES. truss, ' truss, (Ml (MR- tlllSS, . (lual t(p \riii(.';il, ,oU.il t(l Vl'llUcll. ■J f i 1\ lM;il(«I. < \ ^ DOUBLE INTER WROUGHT IRON HlC -> f i ■ vv ;;? . ;:? ;■ ■iff" ,H- DOUBLE INTERSECTION DUGHT IRON HIGHWAY BRIDGE lMiit(»I. X ^* ♦J f .y ^i^:y^'-':^ ".ell HO' ,11""' "'* .1!'"^ I. I \ ¥<>. h-u, I IM.ilo II i-tn.i „,,,'/,;-.,,. - - ^ ^ ^ ^ 1 i- f HJ u. II I GENERAL DESCRI 5*^ 3 O /"//'^ f.'/,,iiil>il //(ifnlli OiOir/_ 1 .)-. .-..itltiiiU^SiUi GENERAL DESCRIPTIVE PLATE OF DETAILS i\ (i N. I'lalclll, is J £M::\ t- ^ .1^-^l.J \A" K m k ■vn i — Li 1. 1 , DETMLS FOF IRON HIG •? ^ :, J J -> J J J -J v A V J J 2_i— i-i-^- _J_J_J__J,'J! i ,. io O J "q" o o o j\-> J o Q !_ j; o DET/^ILS FOR A PONY TRUSS IRON HIGHWAY BRIDGE. PlaU'IU. ^■r'..-'^—-^- \ O O O y -» . J ■> S~>,O...J: o cTo o J Q o oo o_2_2 -51-^7 11 r \ I DKTAILS fohA SINGLI: LVI WIIH SI 1)1'] -i 4- 9F ^- *-M- !|! j- H ~ ^ :^ -+- :'^ Sf] •Ma SINCJLi: IXTKHSKCTIOX HHIIX;!: nil SIDi: WALKS. I'hiio l\ r 1 m ..^^ > . ,T^ -?:t- - ^ * > » )" ) . Vnr/iitAi / ' ^y K'tf't/ A/nJutt'fftji// Shif/iii/ 7'okiri /hiK/lllill ■/ri/liifi/l/ /ooJ. .:%^ I'Uih'V RIES At 'A ■laGHWAY CU A. Wl 1 I • DIAGRAM OF STRESSES POR A 160' SPAN IRON HIGHW CLA.SS A. ^v ? /O" J IS' JOSOv," Total,>r. U 41 fj' / •%•</,",' 7'/. .? .0/ a^ T()t(,/Srr /7 25 n' ," /f>" ?4/s'r 7hMSpr. U.4!fn ■' .?..0/ ' i» 77./I4.S.H. on:.' ■■ 4 '- J'v 6\)2 ;• 4G4S'!,S.h'. .O.J 4 ••>■' .v-'^' //.;/; 7x./a;'X.h'. //.(>:' /;>//^r/ .Vr. //. /:' '? — — • Z7/Jr>4 ^ — S/xin nrrir It'cfif/iiiiv lit mi l.piKilh Dr/tf/i of Trit.y hire 1.11(1(1 Dcdil 1,(1(1 tl Wind I'lTS-Vd" S/l OF STRESSES AND SECTIONS PliUrV. POR A O' SPAN IRON HIGHWAY BRIDGE. CLASS A. ^^. /jY /4.4!)n' S'er. /S. 40 n" /8.40\\ .kj '. II. a? ■' o.6t } ' 6.W t " //./,'-' ~- — DATA^ , _ SfKIII lOOp hrar lli>ti(h\:iv /-/ - /t/nri l.piKilh ,'vy ■ Drplli i>ffni.« ;v " Li \r 1.011(1 ll?Ofjn/}. DpoiI 1.(1(1(1 i40' ' ■■ Wind I'lrs-siirr Jrr s(//'/ / '■/// l.(fl. Hod. S^KU'Ht^f -^ 'i'^ ■1 O O <> C I ,}unrttfff . 1 .•).>r,j, . I'UiUA'l ,*t XH' Mill lliilr) .■•*■ »f ,J :%■ / -'■■ 4fUl;H^' i fhriiiifpf il'lf f-'itrnntWft ^ Y c" «* e' fif>'htu,f,ln J ' tit* Hill >':vi ■ ■ fO' r.r. limtr SJilf Of Vr^ >?•».; " 4 h'Ui-r: .*V/*«y > /• J'. ■»V ■■i:V^ ' *ll?^ I.,mith-'''l'ilr I'l ■■• '. KsKlUtt r,\- ■ l.f/(.-»H"»' ffXtt'tttl' \' •=.«." ^"; .rfiart/Uf • '>"■■',<.'' ' " ' " '' •.Ji'i !■:■ •s \- r -n m — T ■ 1, ^44</i /■in.,;- f-.' ' plutPttitttri».*iit ' similar yitit.tniimTf V €. lo'. =5 5 '' /. , f //. .> f,if ty ■"• Iff «» "^ tyr irttiatrrinrnff *• Hi'i -ufMf*ni'M'm' S 4 ii» r^i - 7''n o.~oo o n cvo*o~c o o o^ v^V o o oft o *r» o o o o o o o o o o o c* o o cv 1-1 r\ O O O O- O O- O- '>- 0--0 *J^._ -v O O O «5 ^\_o _*> O "o_o j> O _0_0 ^ • o V , tf^» h'ninw like fhi.f. '/ittt rtfjfit.'i ami fwt' */>.*■ fhpfiat ? o t. p^^., :k PORTION OF A WORKING DRAWING FOR A 160 FT. SPAN mON HIGHWAY BRIDGE \ 'H <C^<^ \ X X ■'■*'■'''"' ■ -X . i i ,! n |i ii . ! \nm'nl^rfiiii"f '.i.i.: nJ I imtv Hutnirl ." t(}" y/*/'.' 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JjJ^'T .'/,.' • < • . /.VA" ■ •Wtitn n:/'Min<f' i^' » ' . :.-^' «'• \ n,.,- 1; in./.- .V ■V r ' *»%• t ¥ ■•f ? 1 •r .<■ .« 1(H ^ >^ .-, ^ 3 1 '•V /«>, / '\tMirtHff > O O O O O O- O O- O-O-O-'O -o -o o * • V/* Untnvi like ffti.v /iii) ntjluji atul fm> bp,\ /.•> •.?.' ;.., O »1 o o ^ »..\ V / X X X > -' / - - -t--tti>r^i^:-"l"".'.f'''':'^ J 4 ^x" 1*4* -I "rr' '■'""' ' ft- FiaWVl^ r» O U O i-> O O O- L» O O Q Lf -,^b, <iA . 1 I > XI itM.*''' '/ir^f^ '•»>"" '*"•/<" ■^tfii rtnis*- ' , Jmni ami* hd^fr imiteftim nme \ S CO '"•'""' . V o O O ""vfi'Mfj V o © e ■"' /;• ^»• r>' .' '"> TrutI ' P«i^"i»fl ffOifFSi/T '-t't^ltm/. tron matte /4S.7 r //M.ryVir .-v ■*v<^ ■*->■ • > \ '■ . '/ X X 'l.'f ' 'vW XX ^ » ifiV t o o ;e o o 1 c o ' 4 hllfr.t ! '? Una .4li tiers ^^« funa •r.juii.,. .iy ■ (. r y ?«•,•• .'l' L '.^^ .'-- v-w -^v, -:^X" ,^C < ;^ A X X. X. !" l,r^Hiifi'lia„nrl,ii iii«*''tiili' /f> "'.y fiiiiii^ii t ", t c t-^ 4; '- fffrtHsfof/nnfriy't.-Hfrrs r /ff // .'7 and/ ■W'fS'rfhff i ^- Hirvl .ytnrinu IJf Lrmllh ,;' I'Mi- Hill ^-V- -vi-r f.ilH^jr/Htr.rAii^ ■ IT.' III! lliilffrftH'i'i- Tliirkliff> ■ ?' ' lilt t ' fi.'.f'li-i , -' ■ Stfliinm/l'Afmi'^i _ t'tiimif I's Imir' > ,, ■3 <f> /<•" iflntmiiny f'litff H'trt y/'hj nfffJ'V*"''*/;'" fff" " r Hunts , _i .'^ ~ , ^. ; 'imittildia 4 ; 'fv. • ■ * /.;v , ■ 4 ni IIS ilki' ItttS ,^_.^ ... t , . ll,\SniiiTiil>iirtiill'l''>ll'i" '■'•t'l-iV"! 'Sit , .till fllUf t 'I •^'> Uu^HfruLtn lU- .liiiiiit.-KliuxJ'rtli^m^-.X'^^-^ .' o o '« '^ -^ 'iA .^. T I* o o.. > • o ■■* (-Vt' I" .''■'°. -j,f>frtiii Jutrn' III 11 ^f. i7 >'/\. /"■/ - >< ^ * ■» ; l^~ ■Xi r, ^, \,S . 1*^ puit^fatnrnMh ■ '• >/ I ^ ? 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