aU ! enti \ ant if A ta ae gat i LC i. fits att i URE Areca ei the ue Heine i : Peretti it ie tak Ly sy aaa ita it a ee ate tik iby nye sh A, f EC igael eee ae a a ae shee quae tid itn ft esi Ti fa ne Higie ae rage ry re iy Hee itt at Heth height eet orip gt iy Bat ie fa ean ie Ly ee ee ony a ata sag ate a i i f a tHe it ri, 4 malta Hi He Diets i 1! i tf a ante hntieE i 3 +! 2 ee a ao ioe i. sat EN Hue Te a ie i : t i a hal bea re ah cae ae Base ah ne Be Arh sthit i Bh fa a a a a ah ie es ipigtet : Hes ce nt ae petite Ht it mente: pau Ate i ee are A oe a Hee: a ve ua kets iM ee et oe si) fi a eit itt Hehe ¥ fh Aes i at ie ret UNIVERSITY OF ILLINOIS LIBRARY Book G2AS.% IN Ba Digitized by the Internet Archive in 2021 with funding from University of Illinois Uroana-Champaign Alternates https://archive.org/details/analysisofstress0Ou nse > INTERNATIONAL LIBRARY OF TECHNOLOGY A SERIES OF TEXTBOOKS FOR PERSONS ENGAGED IN THE ENGINEERING PROFESSIONS AND ‘TRADES OR FOR THOSE WHO _ DESIRE INFORMATION CONCERNING THEM. FULLY ILLUSTRATED AND CONTAINING NUMEROUS PRACTICAL EXAMPLES AND THEIR SOLUTIONS ANALYSIS OF STRESSES PROPORTIONING THE MATERIAL Gi romob CONSTRUCTION 2s DETAILS, BILLS, AND ESTIMATES STREETS AND HIGHWAYS PAVING SCRANTON : INTERNATIONAL TEXTBOOK COMPANY 35 iv PREFACE knowledge of the subjects treated in the shortest time and in the most direct manner possible. | In meeting these requirements, we have produced a set of books that in many respects, and particularly in the general plan followed, are absolutely unique. In the majority of subjects treated the knowledge of mathematics required is limited to the simplest principles of arithmetic and mensu- ration, and in no case is any greater knowledge of mathe- matics needed than the simplest elementary principles of algebra, geometry, and trigonometry, with a_ thorough, practical acquaintance with the use of the logarithmic table. To effect this result, derivations of rules and formulas are omitted, but thorough and complete instructions are given regarding how, when, and under what circumstances any particular rule, formula, or process should be applied; and whenever possible one or more examples, such as would be likely to arise in actual practice—together with their solu- tions—are given to illustrate and explain its application. In preparing these textbooks, it has been our constant endeavor to view the matter from the student’s standpoint, and to try and anticipate everything that would cause him trouble. The utmost pains have been taken to avoid. and correct any and all ambiguous expressions—both those due to faulty rhetoric and those due to insufficiency of statement or explanation. As the best way to make a statement, explanation, or description clear, is to give a picture or a diagram in connection with it, illustrations have been used almost without limit. The illustrations have in all cases been adapted to the requirements of the text, and projec- tions and sections or outline, partially shaded, or full-shaded perspectives, have been used, according to which will best produce the desired results. Half-tones have been used rather sparingly, except in those cases where the general effect is desired rather than the actual details. It is obvious that books prepared along the lines men- tioned must not only be clear and concise beyond anything heretofore attempted, but they must also possess unequaled value for reference purposes. They not only give the PREFACE V maximum of information in a minimum space, but this infor- mation is so ingeniously arranged and correlated, and the indexes are so full and complete, that it can at’ once be made available to the reader. The numerous examples and explanatory remarks, together with the absence of long demonstrations and abstruse mathematical calculations, are of great assistance in helping one to select the proper for- mula, method, or process and in teaching him how and non Lt shod be used. This volume treats on the subjects of bridge eae streets and highways, and paving. The subject of bridge design is introduced by two papers on Analysis of Stresses, which virtually form a continuation of the paper on Graphical Statics included in another volume. - - 895 Specifications - - - . - - oe eh Mi Camber - - - - . - - - 903 Exact Length of Diagonal Members - - - 905 Positions of Pins in Chords and End Posts - - 908 General Dimensions of Upper Chord and End Post - - . - - - - - 2 Poot) Clearance - - - - - - - =. OLE Size of Pins - - - - - - - a es a Proportioning Pin Plates” - - - - - 914 Moments on Pins - - - - - - - “925 Constructive Details of the End Post - - - 94] Details of the Upper Chord - - - - - 948. Constructive Details of the Intermediate Post - 951 Constructive Details of the Portal Bracing - - 958 Constructive Details of the Lateral Struts and Knee Braces’ - - - . - - ry aon Constructive Details of the Floorbeam - - 966 Eyebar Heads_~ - - - - - - = 2D Constructive Details of the Lower Chord Mem- bers - - - - - - - - sp ia DETAILS OF CoNSTRUCTION—Continued Constructive Details of the Tension Web bers - - Constructive Details of the Lateral Rods Constructive Details of the Beam Hanger DETAILS, BILLS, AND ESTIMATES Shoes, Rollers, and Bedplates CONTENTS Chord Pins, Pin Nuts, Cotter Pins, and Washers. - Shop Lists. - Iron Order - Lumber Bill- Shipping Bills The Erection Diagram The Approximate, or Preliminary, Estimates The Close Estimate Metal Joists and Stringers - Positions and Connections of Floorbeams Name Plates and Railings Paint and Painting Imperfect Design and Inconsistent Requirements STREETS AND HIGHWAYS Country Roads and Highways Construction of Roads - Maintenance of tlighways City Streets and Avenues PAVING Resistance to Traction Traction Power of Horses General Considerations Relating to Pavements - Paving Materials - Stone Pavements - Wood Pavements - Asphaltum and Coal-Tar Pavements Brick Pavements -~ Curbing and Footways —~ 1X Page 986 992 998 1005 1017 1027 1054 1044 1048 1053 1054 1060 1062 1066 1071 1075 1082 995 1031 1037 1040 1101 1108 Litt 1129 1141 1147 1154 1170 1172 PSN AIVGIS OF SERESSES. THE TRUSS. 1267. A truss is a simple framed structure composed of straight members so connected as to act as one rigid body. While the truss as a whole resists the effect of the external forces acting upon it in much the same manner as shear and bending moment are resisted by a solid beam, each individual member of the truss is subjected only to direct tensile or compressive stress in the direction of its length. In order that this may be the case, the external forces must be applied at the joints of the truss, through which they act upon the structure as a whole. 1268. The simplest possible truss is a triangle, and any truss is merely an assemblage of connected triangles. _As the triangle is a rigid figure whose form can not change so long as the length of each of its sides remains the same, it is the primary and essential element of the truss. A short definition of a truss was given in Art. 1120. 1269. The external forces are the loads, including the weight of the structure itself, and the supporting forces, or reactions, all of which tend to distort the structure or change its form. 1270. In bridge engineering any framed structure so designed that the reactions from the superimposed static loads are vertical is considered to be a truss. This dis- tinguishes the truss bridge from the arch and the suspension bridge, in which the reactions are not vertical. 1271. A symmetrical truss is a truss having both ends alike; if it could be folded at the center upon itself in For notice of copyright, see page immediately following the title page. 686 ANALYSIS OF STRESSES. such manner that the two ends would come together, all corresponding members in the two halves of the truss would coincide. Nearly all trusses are symmetrical. 1272. A simple truss is a truss szmply supported; that is, a truss whose ezds simply rest on the points of sup- port without being rigidly fixed to them. It is similar toa simple beam, and is distinguished from a continuous truss or a cantilever truss by the same characteristics that distinguish a simple beam from a continuous or a cantilever beam. (See Arts. 1222 to 1226.) 1273. The theoretical span of a simple truss is the distance between the centers of its supports. The truss is divided into a certain number of parts or sections, usually of equal length, called panels. The panel lengths are the horizontal distances between the joints of the loaded chord. A truss that is divided into five panels is called a five-panel truss; a truss divided into six panels is called a Six-panel truss, etc. Likewise, a bridge whose trusses are each divided into six panels is called a six-panel bridge. | The stresses in simple, symmetrical trusses only will be analyzed in the following pages. THE MEMBERS OF A TRUSS. 1274. The names applied to the various members of a simple truss are given in Mechanical Drawing, Art. 54, in connection with and preceding Plate, Highway Bridge: Details I, to which reference may be made for the name of any member. When mentioned without reference to their positions in the truss, those members which resist compressive stresses are called struts, or compression members, and those which resist tensile stresses are called ties, or tension members. Each individual member, however, is usually designated with reference to its position in the structure. ANALYSIS OF STRESSES. 687 When the diagonal members of a truss are compression members, they are called braces; the counters are called counterbraces. Inclined end posts are often called batter braces. 1275. A compression member can resist a certain amount of tension also; but a member designed to resist tension only is not usually capable of resisting compression. When it is desired that a tension member shall resist a small amount of compression also, the form of the member must usually be changed. 1276. When the loads upon a simple truss are down- wards, as is usually the case, the upper chord is always in compression, and the lower chord always in tension, In the web system the struts and ties alternate. 1277. The extremities of each member are connected as nearly as possible on a line passing through the center of gravity of its section; the stress in a member is considered to act in a direct line between the centers of its connections, and, therefore, the member itself must be straight. For all purposes relating to the investigation of the stresses in the members of a truss, each member may be represented simply by a straight line indicating the line of action of its stress. CLASSIFICATION OF BRIDGES. 1278. 4ridges are classified according to the positions wn which their roadways are supported. Deck bridges are those that support their roadways or loads at or near the levelof the upper chord. In this class of bridge all portions of the structure are entirely below the roadway, and are not visible from above it. Deck bridges require considerable space below the roadway, and, therefore, the locations to which they are adapted are not very common. 1279. Through bridges are those that support their roadways at or near the level of the lower chords; the loads 688 ANALYSIS OF STRESSES. pass between the trusses, or through the bridge. Bridges of this class are very common. If, in addition to the roadway, they also carry separate footways, the latter are usually supported outside of the trusses. 1. High-truss bridges are those bridges of this class in which the trusses are of sufficient height to require a sys- tem of overhead lateral bracing to be placed between the upper chords above the roadway. ‘This class of trusses is not well adapted to spans of less than 80 feet. 2. Low-truss bridges are those in which the trusses are not of sufficient height to require a system of lateral bracing above the roadway ;. such trusses are also designated as pony trusses. This class of bridges is adapted to short spans only. 1280. Half-deck bridges support their roadways at some required elevation de¢ween the upper and lower chords. ‘They are not very common. 1281. A general classification of truss bridges may also be made according to the manner in which the members are connected. Pin-connected bridges are those in which the several members of the truss that meet at each joint are connected, and transmit their stresses, by means of an accurately turned pin, somewhat resembling a large bolt, which is made to fit very closely into holes drilled through the ends of the members. This affords a simple and convenient means for connecting the members. As the connection acts, to some extent, like a large hinge, it allows each member to readily adjust itself in the line of its stress without developing bending stresses. In this type of truss, each member can be practically finished at the shop; and, in erecting the bridge at its site, the members are assembled and connected, and the structure completed in the shortest possible time and with the minimum amount of field labor. Owing largely to this fact, the pin-connected type of bridge has become very popular in America. ANALYSIS OF STRESSES. 689 1282. Riveted girders is the name commonly applied to those bridges in which all connections are riveted; certain forms of such bridges are also designated as riveted trusses and latticed girders. This type of structure is, by some engineers, very highly commended for spans of about 150 feet or less. For spans lessthan 100 feet, they undoubtedly possess some advantages over pin-connected bridges; but whether this be true for spans greater than 100 feet may be seriously questioned. It must, however, be conceded that the tendency of the best modern practice is towards such details as will connect the truss as a rigid whole. 1283. Under the preceding head may also be classified the type of structures known as plate girders, which are, within the limits of their availability, the best metal bridges known.. But they are not trusses—rather a distinct class of girders. 1284. Trusses may be further classified according tothe form of their design; that is, according to the arrangement of the members and the form of the truss asa whole. But such classification will not be further noticed at present. Several forms of trusses will be discussed in their proper place. The truss represented in Mechanical Drawing Plate, Title: Highway Bridge: General Drawing, is of a design which, for bridges of ordinary span, is very common and popular in America. It is a pin-connected, high-truss, through bridge, of the type commonly known as the Pratt truss; though it is also known as a single-intersection and single- quadrangular truss. Substantially this form of truss was patented in 1844 by Thomas W. and Caleb Pratt as a combination wood and iron bridge. It is the favorite style of truss now used for moderate spans, and is usually con- structed entirely of metal. As a metal structure it pos- sesses advantages over all other forms of trusses. As this truss affords a simple and very practical example, all im- portant phases of its design will be noticed in their proper connection. 690 ANALYSIS OF STRESSES. LOADS. 1285. Under ordinary conditions, a bridge must be de- signed to carry or resist three different characters of external forces or loads. I. The live load on a bridge is the load it must carry, exclusive of its own weight. Usually the live load moves over the bridge, and for thisreason it isalso called moving load. For highway bridges, the live load is assumed at a specified amount per square foot of roadway or a specified amount per lineal foot of structure. -This load is assumed to be uniformly distributed over the roadway, and is known as a uniform load. For bridges so located as to be sub- jected to the passage of heavy loads concentrated upon wheels, the uniform load is augmented by certain assump- tions of concentrated loads or wheel loads. For rail- road bridges the live load usually consists of a system of concentrated wheel loads, or of certain assumed uniform loads that will give an approximately equivalent effect. The amount of live load which a bridge is designed to carry is often called its capacity. Il. The dead load on a structure is the weight of the structure itself. The terms bridge weight, fixed load, and static load are also sometimes used in the same sense. The latter term is not so strictly applicable, as the live load also is treated as a static load. The dead load is generally considered as a uniform load; it is assumed at a uniform amount per lineal foot of structure. III. The wind load is the load due to the force of the wind against the side of the structure. It must be resisted by the lateral systems. The wind load is usually assumed sufficiently large to also include and provide for the effect of such lateral vibrations in the trusses as are likely to be caused by the passage of heavy or rapidly moving loads across the structure. When specified, the amount of wind load per lineal foot assumed for each (loaded and unloaded) chord is usually stated. “ANALYSIS OF STRESSES. - 691 PANEL CONCENTRATIONS. 1286. The amount of load which is transferred to and supported at each joint of the loaded chord is called a panel concentration. In the case of a uniform load, each panel concentration is equal to one-half of the load supported by one truss upon the two panels adjacent to the _ joint, and is called a panel load. 1287. The live load per square foot multiplied by the clear width of roadway gives the live load per lineal foot. This is the roadway load. When the bridge carries side- walks, the sidewalk load per lineal foot, found by multiplying the sidewalk load per square foot by the combined clear width of both sidewalks, must be added to the roadway load. 1288. One-half the live or dead load per lineal foot multiplied by the panel length gives the panel live load or panel dead load, as the case may be. That is, this gives the amount of live or dead load to be carried by each joint of the loaded chord in one truss, it is the panel load to be used in finding the stresses. 1289. The wind load per lineal foot, assumed or com- puted, for either chord, multiplied by the panel length, gives the panel wind load for that chord. EXAMPLE.—A bridge 99 feet long is designed to sustain 100 pounds per square foot upon a roadway 16 feet wide, clear width. The trusses are divided into 6 panels. What is the live load per lineal foot, and the panel live load ? SoLuTIon.—The live load per lineal foot equals 100 « 16 = 1,600 Ib. The panel length equals 0 = 16.5 ft- ‘Therefore, the panel- live load 6 1,600 « 16.5 2 equals — = 13,200 Ib. EXAMPLES FOR PRACTICE. 1. In the preceding example, if the wind load assumed for the lower chord is 300 pounds per lineal foot, and that assumed for the upper chord is 150 pounds per lineal foot, what is the panel wind load (a\ for the lower chord, and (4) for the upper chord ? (a) 4,950 Ib. Ans. 4 () 2,475 Ib. 692 ANALYSIS OF STRESSES. 2. An eight-panel bridge of 120 feet span carries a roadway 18 feet wide in the clear. The live load assumed for the trusses is 96 pounds per square foot of roadway. What is (a) the live load per lineal foot, and (6) the panel live load ? Ae 1 (Dak, boon los " € (6) 12,960 Ib. 3. If for the bridge of the preceding example the wind load per lineal foot is assumed at 3800 pounds for the lower chord and 150 pounds for the upper chord, what is the panel wind load (a) for the lower chord, and (4) for the upper chord ? Are (a) 4,500 Ib. * € (6) 2,250 Ib. 4. Suppose for the same bridge the dead load were assumed to be 760 pounds per lineal foot, what would the panel dead load be ? Ans. 5,700 Ib. STRESSES FROM VARYING LOAD. 1290. In taking up this subject, a comparison of the stresses in the members of a simple truss under different conditions of load will first be made. In solving Question 568, the student drew the stress diagram, and determined the stresses for a truss of three b ¢ cee a 4} aay: pe ze ty A R, 7 e Scale 122400 lbs. FIG. 267. panels, carrying two loads, W, and W,, equal to 4,200 pounds each. In Fig. 267 is represented the same truss loaded with W, only, the load JV, having been removed: For this condition of load, the left reaction Rk, = 4,200 x 12 24 1 1,400 pounds and &, = 4,200 x 36 = 2,800 pounds. ANALYSIS OF STRESSES. 693 At the left of the trussis shown the stress diagram. The line a6 f ais the load line, or polygon, of the external horeeseia, Wand) A, laid of in order.’ For joint 7, the polygon a 6 ¢ a is completed; and the polygon a cda is drawn for joint 2. For joint 8, arrow-heads are marked on dcandc 0 in reversed positions and directions; but it is found impossible to return the pencil from @ to the starting point d by a line parallel to G 4, the only remaining mem- ber which connects at joint 3. Therefore, another member must be introduced into the truss, connecting at joint 3, in such manner that the polygon for this joint can be com- pleted by lines drawn parallel to the additional member and to Gib. Ae member 1G, connécting joints 3 and 4, as indicated by a dotted line, is found to fulfil this con- dition; and the polygondc 6 g d may be completed for joint 8 by drawing the lines 0 gand gd parallel to b Gand G D respectively. For joint 4, the polygon is ad gea, and egbfeisthe polygon for joint 8. A check upon the cor- rectness of the work is obtained in this polygon, as 6 / represents the load BF, or W,, The polygon for joint 6 is a e fa, in which fa represents R,. The two arrow-heads on each line indicate in each case the sense of the force with reference to the joint for which each arrow-head was used. Measuring with the scale used in laying off the load line, and designating compression by the + and tension by the — sign, the lines of the stress diagram are found to rep- resent the following values: ac=+ 2,780 b c= — 2,400 c d= — 1,400 b g = — 4,800 dg=+2,780 Jf e= — 4,800 £e= — 4,200 ad= -+ 2,400 ea=-+ 5,560 1291. A comparison of the above stresses with those obtained for the corresponding members (notation slightly changed) in the solution of Question 568, is instructive. The very prominent and noticeable difference between 694 ' ANALYSIS OF STRESSES. : the two cases is that, while, with the two equal loads upon the truss, no diagonal member is required in the center panel, when one of the loads is removed, the diagonal mem- ber is required. It is evident that if the truss were loaded with W, only, instead of W,, the diagonal 3-4 would be in tension, instead of in compression. As in most types of structures, such diagonals are usually designed to resist ten- sion only or compression only, it would be the general prac- tice to put two diagonals in this panel, one connecting joints 3 and 4, and one connecting joints 2 and 35. When a truss ts partly loaded in a certain manner, mem- bers are required which do not act when the truss ts fully loaded. But it is also noticed that, when the truss carried’ two loads, the stresses in the chords and end posts were greater than when it carried one load. ‘These facts illustrate the following general principles: The maximum stresses in the chords occur when the whole truss 1s loaded; but the maximum stresses in the other members occur when the truss 1s only partly loaded. What the condition of loading should be in the latter. case will be explained further on. THE MAXIMUM LIVE CHORD STRESSES. 1292. A live load will now be assumed for the bridge represented in Mechanical Drawing Plate, Title: Highway Bridge: General Drawing, and the maximum stress in each member due to the assumed load will be obtained by draw- ing the necessary stress diagrams. As has been stated, the theoretical length of the span ofa bridge is the length from center to center of end pins, 1.-e., the pins in the shoe joints. Inthe present case, the distance between the cen- ters of the pins in joints a and a’ is 90 feet; it is divided into five equai panels of 18 feet each. The clear width of roadway, that is, the clear width between trusses, is 18 feet, and the height of the trusses, between centers of chord pins, is 18 feet. The general dimensions of a bridge, such as have just ANALYSIS OF STRESSES. 695 been given, together with the loads and such other infor- mation as may be necessary to make a proper design of the same, are called the data for the bridge. The live load will be assumed to be 100 pounds per square foot. s Lnelive load per lineal foot is, therefore; LOO x 18 = 1,800 pounds. (Art. 1287.) This load is assumed to be applied upon any or all portions of the floor, in such man- “ner as to cause the maximum stresses in the several mem- bers. By means of stringers the load upon the floor is transferred to the floor beams or cross girders, which are placed across and beneath the roadway at the lower chord joints 0, c, c’, and J’. The stringers and floor beams act independently of the truss proper, serving simply to con- centrate the floor load upon the lower chord joints. The amount of lve load supported by one floor beam equals the load per lineal foot multiplied by the panel FeroenOres), 500% 18-52, 400) pounds... One-half ‘this amount, or 16,200 pounds, constitutes the panel load for one truss. (Art. 1288.) When the general dimensions of the truss are given, having ascertained the amount of live load that should be assumed for it, and the points at which the panel loads are concentrated, we have all the data re- quired for determining the stresses due to live load. The stresses are found for one truss, those for the other truss being usually identical. If the trusses have not the same form, the stresses must be found for each separately. As previously stated, the greatest stresses are developed in the chords and end posts when the bridge is fully loaded. This condition of load will first be considered, the values of the reactions will be computed, and the stress diagram drawn to find the live load stresses in the chords and end posts. 1293. That portion of the load upon each end panel which ts carried directly by the abutment does not affect the truss. With the bridge fully loaded as above, one-half of each -end panel load is carried by the corresponding abutment. 696 ANALYSIS OF STRESSES. Therefore, ina truss having panels of equal length, fully loaded with a uniform load, the reactions affecting the truss have the following values: W (x — 1) 2 isi = se == ’ (89.) in which W represents the panel load, and z the number of panels. Scale 1-24000 Lbs. 6 11 FIG. 268. In the present case, therefore, A, = A= o= xX 16,200 = 32,400 pounds. In Fig. 268 is represented a diagram of the ANALYSIS OF STRESSES. 697 truss, together with a stress diagram for this condition of ioagdee Here i") etc.) represent ‘the, pariel loads, -or 16,200 pounds each. Bow’s system of notation is used, but numerals are used , instead of letters, because it is desired to use letters to designate the joints. .Each member of the truss will be designated by the letters of the two joints at which it con- nects, as members a 4 (not member 1-7); but the stress for a will be designated as 1-7, referring to the line of the stress diagram. In drawing the stress diagram, it will be found that the condition of equilibrium can be fulfilled for all joints with- out requiring stress in any of the members represented by dotted lines. When the truss is fully loaded with a uniform oceabereuisenostress anathe members. Cc). C.c’, Ce’, and 'G' ¢. The load line 2-6 is laid off by taking the external forces in order, beginning with X#, and passing to the right across the truss, or, in other words, beginning with #,, and taking the forces in order, passing to the left around the truss, as though they were forces acting upon a single point. By acting through the medium of the truss the forces bear the same general relation fo each other as though acting upon the same point. On the load line, therefore, 1-2 is laid off upwards equal to &, = 82,400 pounds, then 2-3, 3-4, 4-5, and 5-6, each equal to a panel load = 16,200 pounds, are laid off downwards, and finally 6-7, equal to X, = 32,400 pounds, is laid off upwards to the starting point. Commencing with #,, the polygon /-2-7-1 is completed for joint a, 7-2-5-8-7 for joint 6, and 1-7-8-9-1 for joint B. For joint c, retrace 9-8 and 8-3 (that is, mark reversed arrow-heads, and consider them drawn from 9 to 8 and from 8 to 8 respectively. [See Art. 1148]); pass downward on the load line the amount 3-4, equal to IV; a line returning from 4 to the starting point 9 will represent the equilibrant of the forces 9-8, 8-3, and 3-4, that is, will represent the. remaining force which acts upon this joint. As the closing line 4-9 is a horizontal line, it 1s evident that it must > 698 ANALYSIS OF STRESSES. represent the stress in a horizontal member, which must necessarily be the member ¢ c’, this being the only remaining horizontal member which connects at this joint. As 4-9, or the stress in cc’, fulfils the condition of equilibrium for this joint, the members Cc and C’c, represented by dotted lines, do not act with this condition of load. For joint c’, retrace 9-4 (that is, mark a reversed arrow-head, and con- sider it as drawn from 9 to 4); pass downwards on the load line the amount 4-5; it will be found that from 4 the pencil can be returned to the starting point 9 by the lines 5-10 and 10-9, drawn parallel toc’ d' and c' J’, respectively. The conditions at this joint are the same as at joint ¢, except that the positions of the forces are reversed; the condition of equilibrium is fulfilled without requiring the members Cc'-and C’c''to act: Ihe polygons for joints L' b' and a’ are substantially the same as for joints & 6 and a, respectively, and will be readily understood without special explanation. From an inspection of the stress diagram it is evident that the members represented by the dotted lines would not be required to act when the truss is fully loaded with a uniform load. For, in drawing the force polygon for joint c, the point 4 falls at the point 1, showing that the entire vertical force of the left reaction #,, repre- sented by 1-2, is entirely absorbed by the loads IW, and W,, represented by 2-3 and 3-4. Likewise, the right reaction R, (= 6-1) is absorbed by W, (= 4-5), and W,(= 6-6), and between joints ¢ and c’ no vertical forces are acting. To express this in the usual language, there zs no shear in the panelcc'. The effect is the same as though W, and W, were supported by &,, and W, and W, were supported by X&,,. By measuring the lines of the stress diagram, and using the conventional signs for tension and compression, the following values of the stresses are obtained : Stress ina B = 1-7 =-+ 45,820 lb. Stress in'a’ B' = 1-11 = + 45,820 lb. stressin £4’ = 1-9 =-+ 48,600'lb, Stressini gb “= 2-7 = —32.4004D: Stress in dc = 8-8 = — 32,400 lb, ANALYSIS OF STRESSES. 699 Stress incc’ = 4-9 = — 48,600 lb. Stress inc’ 6’ = 6-10 = — 32,400 Ib. Stress in &'a’ = 6-11 = — 382,400 Ib. Stressin Be = 8-9 = — 22,910 lb. Stress in B’c’ = 9-10 = — 22,910 lb. Diteesitiwae a veo) = 62 00Nb, Stress in Bd’ = 10-11 = — 16,200 lb. NoTe.—The above stresses are given to the nearest ten pounds. In order that the student may better judge of the accuracy of his work, the stresses will be so given in what follows. But in actual practice it is never necessary to obtain the stress in any member of a bridge or similar structure closer than to the nearest hundred pounds. It is noticed that the line 7-9 represents compression, while tie line 4-9 represents tensiom. © As these lines coincide, .the student must be careful to distinguish the proper character of stress foreach. The above stresses are the maximum live load stresses in the chords and end posts. As the office of the hip verticals £ 6 and 4’ v' is simply to suspend the panel loads at 6 and 0' from the joints 4 and 4’, respect- ively, it is evident that the greatest stress which can come upon either of these members is the panel load which it supports. Therefore, the above stresses for Bdand B' 0’ are also Maximum. THE MAXIMUM LIVE LOAD WEB STRESSES. 1294. Thestressesas found above for the web members He and J’ c’, however, are not. maximum. The maximum stresses in these and the remaining web members will occur under different conditions of load. Since the two ends of the truss are alike and are acted upon in the same manner by external forces of the respect- ive magnitudes, the stresses in the two halves of the truss are identical, and it is necessary to construct the stress dla- gram for those members only whose stresses are caused by one reaction. in the present case, the upper half of the stress diagram is the only portion necessary to be drawn. Although the complete stress diagram is sometimes drawn for the purpose I. Il,.—6 700 ANALYSIS OF STRESSES. of checking the work, it is customary to obtain only those stresses due to the left reaction. This practice will gener- ally be followed hereafter in obtaining the live load stresses; the stress diagram will usually be drawn for those stresses only which are produced by the left reaction and the cor- responding loads. When stress in any member is men- tioned, it will be understood to mean stress caused by the left reaction; the stress in the corresponding member in the opposite half of the truss, caused by the right reaction, will be of the same character and magnitude. The maximum stresses in the web members will now be found. 1295. ln a Pratt truss, the maximum stress will occur in the diagonal web member in any panel when all joints at the right of the panel are fully loaded and the joints at the left of it are not loaded. This condition will also give the maximum stress (of opposite character) in the vertical member which meets the diagonal in the unloaded chord. This rule, of course, does not apply to the hip vertical, whose maximum live load stress zs always equal to one panel load. The maximum stress in the tie 4c will occur when the joints c, c’, and 0’ are loaded, and joint @ is not loaded. In 54+ 36418 6 this condition FR, = 16,200 x 90 LO oO aes nia 19,440 pounds. In Fig. 269 is represented a diagram of the truss and that portion of the stress diagram necessary to determine the stress in Ac. Those diagonal web members which transfer their load to the right reaction are omitted from the diagram of the truss. The load line 1-2 is laid off to scale equal to Rk, and the polygon J1-2-7-1 is completed for joint a. For joint J, the line 7-2 is first retraced; as there is no load at J, or, in other words, as the load at 0 is zero, the portion of the load line 2-3, which represents this load, has no magni- tude. In the stress diagram, therefore, the points 3 and 2 will coincide; the line 3-8 will coincide with the line 7-2: ) and as the terminus of the last line of the polygon must ANALYSIS OF STRESSES. 701 close upon the starting point, it is evident that no stress can Bemobeainedsforsthe inember) bo ~For joint 6) retrace 1-7 (that is, mark a reversed arrow-head, and consider it as drawn from i to 7), and, as there is no stress in & @, the pencil is returned to the starting point 7 by lines 7-9 and 9-1, drawn parallel, respectively, to B c and C B. (These lines, of course, are actually drawn from 7 and J, respect- a FIG. 269. ively, their intersection locating the point 9.) In other words, 1-7-8-9-1is the polygon for joint 4. The line 8-9 repre- Ssehits tue Maximum stress in bc. As this feiure-is not a complete stress diagram, the arrow-heads marked upon the lines but incompletely represent the characters of the stresses. However, if the arrow-heads have been marked in accordance with the instructions given in preceding articles, the single arrow-head marked upon a line will indi- cate the character of the stress. By measuring 8-9 with the same scale used to lay off 1-2, and noticing the direction of the arrow-head marked upon it, it is found to represent a tensile stress of 27,490 pounds. In Fig. 270 is represented the truss with joints c’ and 0’ loaded, and the joints 6 and ¢ unloaded; also the stress dia- gram for this condition, giving the maximum stresses in Crceand Gc. 702 ANALYSIS OF STRESSES. As no external forces act upon the truss between A, and W,, the entire external space between) these forces is dis- tinguished by the same numeral. Likewise, as no force is acting in the member P 8, the entire space between the members 4a and # ¢ is designated by the same numeral. 18 + 36 90 For this condition of load, A,= 16,200 xX —~——= 9,720 Scale 1210000 lbs. 1 9 11 Fic. 27 pounds; it is represented by the line 1-2, and the polygon 1-2-7-1 1s completed for joint a. As there is no stress in B 6, 1-7-9-1 is the force polygon for joint 4; 9-7-2-10-9 is the polygon for joint c; and 1-9-10-11-1 the polygon for joint C. The stress in Cc is represented by 9-10 = + 9,720 pounds, and: thatin C ¢c’ 1s represented ‘by 20-17 ==43;750" pounds: both stresses are maximum. In Fig. 271, the truss is represented with only joint J’ loaded. This condition gives the maximum positive shear in the panel c’ 0’; that is, it gives the maximum stress that could-be produced by the left reaction in a counter having the position C'd'. This stress is found in order to determine whether a counter is required in this panel. 18 16,200 _ F his load, A, = or this load, 7oo== 16,2 200 X a5 = 5 3,240 pounds. ANALYSIS OF STRESSES. 703 Commencing with 7-2, laid off equal to &,, the polygon ee-7-1 15 completed for joint a. ‘For joint 4, 7-7-9-1 is the polygon; 9-7-2-10-9 is the polygon for joint c; -G-10-11-1, for joint C;. 21-10-2-72-1/, for joint ¢; and i-fi-i2-Je-]; the .polygon for joint’ Cc’. The line 12-173 = — 4,580 pounds represents the maximum stress that could be caused in a member C’JO’' by the left reaction. The 9 11 13 —_ Scale 1£=5000Lbs. ite, Carat. stress in C’c’ from this condition can not be as great as tratround10r Gy in’ the-diagram.of Fio..270* and as Cc" bears the same relation to the right reaction as Cc does to the left, it will have the same maximum stress. But, as previously stated, when the two ends of the truss are alike, only those stresses caused by the left reaction are obtained; as the maximum stress in C’'c' is caused by the right reaction, it is not obtained. The maximum live load stresses have now all been found The maximum live load web stresses are: Stress in B c = — 27,490 lb. C ¢ seb 9:720.Ib: Gree eb Ost: C’.o' = —- 4,580 Ib, 704 ANALYSIS OF STRESSES. It is evident that Figs. 269, 270, and 271 could have been combined in one figure. How to do this will be explained later. 1296. It will be noticed that in the stress diagram of Pig: 271, 21212 = 9-10, J-2 =e | InCemin Athiszeonaicren of load there are no external forces (loads) applied between a and 0’, the vertical shear in all panels between these points is uniform, equal to &,, and positive. The student will notice particularly the fact that the shear in all panels at the left of 6’ equals &,. The same would be true with any number of loads at the right of any given point, provided there were no loads at the left, 1. e., between the given point and &,. This shear is positive; that is, if at any point the truss be conceived to be cut by a vertical plane, the direction of the force on the left of the plane will be upwards, and of that on the right will be downwards. ‘This will be referred to again. THE DEAD LOAD. 1297. In order to satisfactorily decide the amount of dead load to be assumed for a structure, a certain amount of previous experience is very essential, if not really indis- pensable. As the stresses must be determined, the material proportioned, and an estimate of the weight of the structure be made before the amount of dead load is known, it is evi- dent that the assumption of the dead load must be based largely on judgment and past experience. It is very desir- able that the assumed dead load may represent, as nearly as possible, the actual weight of the structure. If it isassumed too light, the structure will not be strong enough; if too heavy, material will be wasted. . In either case, if the error is considerable, it will be necessary to correct the dead load and repeat the operations. It is a not uncommon practice among bridge engineers to consider 400 pounds per lineal foot as the minimum allow- able dead load for bridges; and for very light structures of short span, in which the estimated dead load is very light, ANALYSIS OF STRESSES. 705 to never use less than this amount. This practice will here be followed. 1298. Owing to the various forms of floor, differing requirements of specifications, and varying conditions affect- ing the dead load, no general and satisfactory formula has yet been obtained for it. Indeed, it is extremely doubtful whether the many and varying conditions upon which the amount of dead load depends can be so formulated as to give satisfactory results. It is desirable, however, that the student be guided by a general formula in assuming the dead loads. The following empirical formulas, although but roughly approximate, are useful as guides in assuming the dead loads of ordinary truss bridges. For a capacity of 100 pounds per square foot, Dime Sata bb = eh er ead Ht ae (90.) For a capacity of 80 pn i square foot, w= s+ 5b4o oem ets (91.) In both formulas, zw is ay dead load per lineal foot exclu- sive of the floor and joists, s is a quantity which will here be taken equal to the amount of live load per square foot, 6 is the clear width of roadway, and /is the length of span. In formula 90,5 = 100; informula91,s5= 80. For any other live load capacity s’, find w by formula 90, remembering Hiner OUecallsthe required, déad load w.., phen, | Soak [1 ple EE ] (100—s’). (92.) These formulas have been derived from actual practice; when the results obtained by them are added to the esti- mated weight of floor, the resulting dead loads will ap- proximate reasonably near to the actual loads for highway bridges of ordinary dimension and the usual type of con- Pp LUGuiOname itereas some experiences tne formulas can ‘be adapted to special forms of construction by medifying the values of s. 706 ANALYSIS OF STRESSES. The student must bear in mind that these formulas are given for convenience and the purposes of instruction only ; thev are not to be relied pon in) practice furthersthane to afford reasonable checks. 1299. Having ascertained the kind of floor to be used, the weight of floor and joists must be separately calculated and added to the results obtained from the preceding for- mulas. For ordinary plank floors, supported on timber joists, the student may obtain the weight from the following table, which has been calculated for the three varieties of timber most commonly used: TABLE 29. Weight, in Pounds per Lineal Foot, of Timber Bridge Floor, Consisting of 8" Floor Plank, two 4" x 6" Wheel Guards, and the Required Stringers. Yellow Pine. White Oak. White Pine. Length r : en of Panel) POF Io rece | Seal aratey 1 ano in Feet. |» ad. Additional met Additional ween Additional way. | Width, | ay, | Width. a Width, Add Add Add 12 peas 36.4 .1262.0 felis LO. 22.5 13 245 20) «B64 8276.01 AO. Ge lola yas meee 14 258.8 Bowe 292.8 43 .2 l6i235 23.8 15 274.5 40.8 292.8 43.2 TOts3 Pan ie e! 16 2742 5) ) 4025 PB09S6u sd S06) 117 Teg hae L750 894051 4 A0VS 180908: OA e Ge Dee ee 18 290.3 42.8 309.6 45.6 LSdici WeeG ma 19 290.3 42.8 329.2 48.4 20 290.3 42. 348 .8 j1.2 22 327.0} 48.0 By substituting the proper value in formula 9O, the weight per lineal foot of the structure under consideration, ANALYSIS OF STRESSES. 707 (18 —6)90 , 90? exclusive of floor, is 100+ 5 x 18 + a Gia c oO Bd2 pounds. The floor will be assumed to consist of long leaf yellow pine. From Table 29, this is found to weigh, for 18 feet panel length, 290.3+ 3 x 42.8 = 418.7 pounds per lineal foot. The total weight per lineal foot of the structure will, therefore, be 352+ 418.7 = 770.7 pounds. The dead load will be taken at 770 pounds per lineal foot. As this load is considered to be uniformly distributed over the entire 8 structure, the panel dead load will be eee el = 6,930 7 pounds. THE DEAD LOAD STRESSES. 1300. The dead load is considered to be concentrated at the jointsof the truss. A common practice is to assume each panel dead load to be divided between the upper and lower chord joints of each panel. In an ordinary through bridge with plank floor, it is approximately correct to con- sider two-thirds of each panel load to be concentrated at the lower, and one-third at the upper chord joint. The same results are arrived at in a somewhat simpler manner by the following Rule.—Odtain the dead load stresses by considering the entire dead load to be concentrated at the lower chord joints, denoting compression by the + sign, and tenston by the — sign , correct the stress thus obtained for each vertical mem- ber, by adding to tt algebraically a compressive stress cqual to one-third of the panel load. This practice will here be followed; it has the advantage of giving a stress diagram similar in every respect to that for the live load chord stresses, as the conditions assumed in each case are the same. For, as the weight of the structure is always present in the structure, it is evident that, in obtaining the dead load stresses, the truss must be considered to be always fully loaded with its dead load. Therefore, the stress obtained for any member from the stress diagram for 708 ANALYSIS OF STRESSES. the dead load may be checked by multiplying the corre. sponding stress, obtained from the stress diagram for the full ave load, by the dead load per lineal foot, and dividing the product by the live load per lineal foot. Or, by reversing the process, the live load stresses for the chords and end posts may be obtained from the corresponding dead load stresses. Note.—As a low-truss bridge carries no horizontal bracing between the upper chords, the error due to assuming the entire dead load to be concentrated at the joint of the lower chord is very small, and may be entirely neglected. Therefore, for low-truss bridges the entire dead load will be assumed to be carrted at the joints of the lower chord, and the dead load stresses in the vertical members will not be corrected for the error due to thts assumption. 1301... By formula 89, the dead load reaction R, = 6,930 X (5 — 1) = 13,860 pounds. In Fig. 272 is represented Scale 1=10000 lbs. FIG. 272. a diagram of the truss and that portion of the stress diagram for the dead load which refers to the left reaction: it is in every respect similar to the upper half of the stress diagram ANALYSIS OF STRESSES. 709 in Fig 268. It will require no special explanation; the lines are drawn in the same order as in Fig. 268. The fol- lowing stresses are obtained: Stress ina 5 = 1-7 = + 19,600 Ib. stress in B A’= 1-9 = + 20,790 lb. MIUresceitla.d pes 2 ayee to BGO) ID. Stress in’ 2 ¢ = 3-5 = — 13,860 Ib. DLressilie are 214-9 =.= 207790: Ib. Wiressan ee —7-6.=— — -67930 Ib: miresaan 0 a = 5-9) ===" 9. 800:1b, SUE Tha 8 UA aime Le eee 0,000 Ib. The above stresses may be obtained or checked from those determined by the stress diagram of Fig. 268, by mul- Hang ; 770 attr: tiplying the latter stresses by the quantity aca which is the ratio of the dead load to the live load per foot of length. The stress for 6 6 is found to equal one panel load, or — 6,939 Ib.; to this is to be added algebraically a com- pressive stress equal to one-third panel load, or + 2,310 Ib. Therefore, the correct dead load stress in & 6 is — 6,930 + 2,310 = — 4,620 lb. One-third panel load is also to be added to the stress obtained for Cc; as the stress diagram gave no stress for this member, the correct dead load stress may be taken at one-third panel load, or + 2,310 Ib. COUNTER STRESSES. 1302. The effect’ of the dead load reaction has been entirely taken up by the loads at dandc, as explained for the full live load (Art. 1293), and there is no dead load shear in the center panelcc’. It was also explained that, with a full uniform load, the effect of the shear is the same as though all panel loads at the right of the center were sup- ported by the right reaction. As the dead load is a uniform load; it is evident that in the panel c’ 6’ there exists at all times a negative shear equal to the panel dead load at c’, or 6,930 pounds, which is being transferred to the right Peactionwes DhiS:)issoreater thanethe (positive, shear sof 710 ANALYSIS OF STRESSES. 3,240 pounds produced in the same panel by a panel live load at 6’. (Art. 1295.) It is thus found that no resultant positive shear can occur in this panel, and, therefore, no counter C’ 0' is required to resist it. The following principles are important: (a) The maximum live load positive shear in any panel of a truss 1s equal to the left reaction when all the joints at the right of the panel are loaded and all joints at the left of it are unloaded. (6) The dead load negative shear in any panel at the right of the center 1s equal to the amount of dead load between the panel and the center of the span (including a half-panel load at the center tf the truss has an even number of panels). (c) No counter ts required in any panel beyond the center of the truss in which the dead load negative shear exceeds the maximum live load positive shear; but in cach panel beyond the center in which the live load positive shear can exceed the dead load negative shear, a counter ts required. The latter principle may be better understood from the following considerations: If S is the dead load shear in any panel at the right of the center (negative with respect to the left reaction), and FR, is the maximum live load positive shear in the same (sce (a) above), then the resultant shear in the panel will be the algebraic sum of these two shears, or R,+S, the value of S being negative. If this sum is negative, that is, if AK, is numerically less than S, the re- sultant shear will be of the same character as S, and the stress induced by it in any member will be of the same kind as that induced by-the dead load. In this case, then, the diagonal member in the panel is designed to withstand either compression or tension alone, according as it may be a brace or a tie. But if A, is numerically greater than S, then the resultant shear &, + S will be positive, that is, of a character the same as X, and opposite to S. In this case, Consequently, the member must be designed to with- stand stresses of both kinds (one induced by S when the truss is unloaded or fully loaded, and one of opposite kind ANALYSIS OF STRESSES. ALY induced by the resultant of R,+S when the truss is partly loaded), or else a new member (counter) must be introduced to withstand the resultant shear A,+ S from a partial load. The student should clearly understand the principles stated above. The subject of counter stresses, though ‘simple, is usually found rather troublesome until it is thoroughly comprehended. For clearness the principle will be repeated. (2) A counter stress will obtain and a counter will be re- guired in any panel at the right of the center of a truss when, with no live loads at the left of the panel, the left reaction, due to live loads at the right, 1s greater than the amount of dead load between the panel in question and the center of the truss (including a half-panel dead load at the center tf the truss contains an even number of panels). WIND STRESSES. 1303. Bridge specifications differ somewhat in regard to the amount of wind load necessary to be provided for, the most common requirements varying from 100 to 150 pounds per lineal foot for the unloaded chord, and from 250 to 300 pounds per lineal foot for the loaded chord. Although a total wind load of 450 pounds per lineal foot is rather large for a highway bridge in the ordinary location, it will here be used. Throughout the following articles, and in the questions referring to them, a lateral wind force of 150 pounds per lineal foot will be assumed for the unloaded chord, and 300 pounds per lineal foot for the loaded chord. Of the latter, 150 pounds is to be treated as live load, and 150 pounds as dead load. The wind load upon the unloaded chord will be treated as dead load. 1304. Dead Wind Stresses in Lower Lateral System.—In the example, then, the total panel load of wind load for the lower chord is 300 x 18 =5,400 pounds (Art. 1289); but of this, one-half, or 2,700 pounds, is to be 712 ANALYSIS OF STRESSES. treated as live load, and the same amount is to be treated as f d5—1._. dead load. For the wind dead load &, = Pays 1D... Chen, . tae i. 3) 750 aslowiouiatd melt upwards, and 2’-3' = 11,250 lb., 3’-4’ = 9,000-lb., 4'-5’ = 6,750 ‘Ib., 6-6° = 4,500 1b., and 6-7 = "9 250 Ibaare iad off downwards in order to the starting point 7’ or a. Also, from I’ lay off upwards upon the load line, or, as in the figure, from a point horizontally opposite 7’, lay off upwards upon a vertical line 4,-5,, 5,-6,, and 6,-1,, equal, respect- ively, to 2,888 Ib., 5,775 lb., and 5,775 lb., the amounts of dead load at d, e, and Ff, respectively, that are supported by the vzgh¢ reaction. The right reaction due to “ve load is entirely neglected. Upon the load line, Z'-2’ represents the left reaction ANALYSIS OF STRESSES. 739 due to live load with the truss fully loaded, which condi- tion gives the maximum stress in the member a &. Pro- ject the point 2’ upon a 4, produced if necessary, by the horizontal line 5’ 2’; then, a 4’ will represent the stress in ab. The maximum stress in 4c obtains with the load at 0d removed, all other joints being loaded. For this condition _ 1'-3' represents the reaction, and by projecting the point 5’ upon / ¢ (also produced, if necessary) by the horizontal line J’ 3’, the line 4’ c will represent the stress in Bc. The maximum stresses in C ¢ and Cd obtain with the load at c also removed, all joints at the right remaining loaded. The reaction for this condition is represented by /’-J’, and by drawing through 4’ the horizontal line c’ 4’, the line C’ ¢ will represent the stress in Cc¢ andc'd will represent the stress in C d. The maximum stressesin Ddiand De obtain with all loads at the left of the panel @ e (numeral 5) removed, all joints at the right of it remaining loaded. For this condition i'-5’ represents the reaction, and by drawing through 34’ the horizontal line d' 5’, the lines D' d and @’ e will represent what would be the stresses in ) d@ and D ¢, respectively, if no negative dead load shear existed in the panel d ¢. The negative shear in this panel is repre- sented by 4,-5, and by drawing through 4, the horizontal line 2,,-5,, the lines D’ d, and d’ ¢’,, will represent the result- ant live load stresses in Dd and De, respectively. With the load at e also removed, all joints at the right remaining loaded, i’'-6' represents the reaction. This condition will give the maximum stress for the member & /, if any stress can be found for that member; by drawing through 6’ a horizontal line 6’ ¢’, the line ¢’ f will represent what would be the live load stress in # /, if no negative shear existed in the panele f. But an amount of negative dead load shear represented by 4,-6, is always present in this panel; a horizontal line 6, 7, drawn through 6, will le above the line ¢’ 6’, showing that the ‘negative dead load shear more than counteracts the positive live load shear in this panel. Therefore, no stress can be obtained for a tie in the posi- boveee 7) Lhe maximum stresssin thes vertical member vt 740 ANALYSIS OF STRESSES. - ¢ is produced by the right reaction, and is the same as has been found for Ce. It will be noticed that the dead load numeral 6, is situ- ated above the live load numeral 6’, and that wo stress is pro duccd by positive shear in the panel e f under which the corresponding numeral 6 is situated; also, that the dead- load numeral 4, is situated dc/ow the live load numeral 4’, and that stress 7s produced by positive shear in the panel @e under which the corresponding numeral 4 is situated. This will always be the case, and it will always correctly indicate whether counter stress will be found in any panel of a truss having parallel chords. 1328. The method of laying off the load line and determining in what panel the counter stress ceases may be described in a general manner as follows: (a) The left reaction due to the live load ts laid off upwards upon a vertical line erected at the left support ,; thts consti- tutes the load line, the right reaction due to the live load being entirely neglected. Irom the top of the load line the respective portions of the live panel loads which are supported by the left reaction are laid off in order downwards, taking the loads from the left to the right across the truss, the last load will just reach to the bottom of the load line. From this point, or from a point on a vertical line horizontally opposite to it, the dead loads, sup- ported by the right reaction, are laid off upwards, Be op at the center of the truss and passing in order towards the right until the numeral used to designate the dead load shall fall at a point upon the load line above the corresponding numeral employed to designate a live load. When this occurs, no positive live load shear will be found an that panel of the truss under which the corresponding numeral ts situated, nor in any panel to the right of it. But positive live load shear and counter stress will be found in each panel whose numeralused to designate the live load ts situated ata point on the load line above the corresponding numeral used to designate the dead load. ANALYSIS OF STRESSES. 741 1329. In determining the web stresses, proceed as follows: (b) From the point upon the load line indicating the upper limit of the reaction for cach condition of load, a horizontal line 1s drawn intersecting those web members which obtain their maximum stress with that condition. Tf the members areat the right of the center of the truss, a horizontal line ts also drawn tointersect them from the corresponding. dead load numeral, On a line representing a member of the truss for which the maximum stress obtains in any of the several conditions, the portion below the horizontal line drawn from the lve load numeral to intersect it (and above the line drawn from the corresponding dead load numeral, if the member ts not at the left of the center) will represent the stress in the member. EXAMPLES FOR PRACTICE. 1. By the method just explained, find the maximum live load web stress for the truss shown in Fig. 285, using the data given. Ans. For a & + 47,730 Ib. For C d— 19,090 lb. For 2 c — 81,820 lb. For 2) d+ 3,860 lb. For C ¢+ 13,500 Ib. For D e — -5,460 lb. 2. By the same method obtain the maximum live load web stresses for the five panel truss of the previous articles. THE HOWE TRUSS. 1330. The earliest form of simple truss of any consid- erable length of span that was built for bridge purposes in America is shown in Fig. 286. It was devised by William a = as ——/. ~ wt a ee, saeaese Roscnaeuseaneh ae rpstseeeeeseseeeees - nee . one 4 FIG. 286. Howe, in 1840, and is known as the Howe truss. It isa very excellent form of truss, and is still much used in this country in localities where timber is cheap. For trusses 742 ANALYSIS OF STRESSES. constructed entirely of metal, however, it is not as economi- cal as the Pratt truss. In the Howe truss all vertical members (except end posts) are tension members, and all diagonal members in the web system are compression members. As originally constructed, the Howe truss had short panels with two diagonal braces in each panel, and vertical end posts; the floor was supported directly upon the lower chord, which, therefore, acted as a beam as well as a tension member. All parts of the truss were constructed of wood except the intermediate vertical members, which were iron rods. It is evident that the members represented in the figure by dotted lines can carry no stress; they serve no other purpose than to stiffen the truss. 1331. In modern examples of the Howe truss, those members which do not bear stress are omitted, and the lower chord is usually constructed of metal. Such a truss for a through bridge is represented in Fig. 287. For the sake of FIG. 287. comparison, the same data are assumed for this truss that were assumed for the Pratt truss, treated in the preceding pages; namely, length of span, 90 ft.; panel length, 18 ft. ; height of truss, 18 ft.; clear roadway, 18 ft.; live load, 1,800 Ib., and dead load, 770 lb. per lineal foot. The Howe truss, of Fig. 287, is very similar to the Pratt truss, shown in the previous figures; the essential difference is that in the former all vertical members are ties and all diagonal members are struts, while in the latter the oppo- site is the case. It will be noticed that in the Howe truss the hip vertical is not merely an independent suspender, as" ANALYSIS OF STRESSES. 743 in the Pratt truss, but is an important part of the entire web system; the amount of shear resisted by it is the same as that resisted by the end brace. The method of constructing the stress diagram is substan- tially the same for both trusses, and after what has been ex- plained concerning the Pratt truss, no difficulty will be en- countered in obtaining the stresses for the members of the Howe truss. It must be noticed that, as in this truss the duties of diagonal and vertical members are the reverse of what they are in the Pratt truss, the maximum stress in any vertical web member of a Howe truss, and in the diagonal meeting tt at the upper chord, occur when the joint at the foot of the vertical member and all the joints at the right are loaded, the others being unloaded. (In the solution of Question 595, the student has drawn the stress diagram for a four-panel Howe truss carrying a full uniform load.) EXAMPLES FOR PRACTICE. 1. Construct the stress diagram obtaining the dead load stress in each member in the left half of the truss shown in Fig. 287, using the data given above and correcting the stress in each vertical member. Ans. For a & + 19,600 lb. For ¢ c’ — 20,790 Ib. For & C.+ 18,860 Ib. For 2 6 — 11,550 Ib. For CC" + 20,790 lb. For 6 C+ 9,800 lb. For a &— 13,860 lb. For C c— 4,620 lb. For 6 ¢c— 20,790 lb. 2. Compute the live load stresses in the chords and end posts from the corresponding stresses obtained in the solution of the preceding example. Ans. For a £& + 45,820 lb. For a 6 — 82,400 lb. For B C + 82,400 lb. For J c — 48,600 lb. For CC’ + 48,600 lb. For cc’ — 48,600 lb. 3. Construct the diagrams for the maximum live load web stresses. Ans. For B 6 — 82,400 lb. For 6 C + 27,490 1b. For Cc — 19,440 lb. For ¢ C' + 138,750 lb. 4. Solve the above example by means of the moment and shear diagrams. 744 ANALYSIS OF STRESSES. THE WARREN GIRDER. 1332. The form of truss shown in Fig. 288 is known asa Warren girder. Constructed as a riveted girder, it is a very excellent truss for spans of moderate length. The distinguishing feature of this truss is that all web members are inclined at a uniform angle and no counter members are used, the counter stresses being reversed stresses in the main web members near the center. 19 | al D 3 ERS : : / a \ \ / \ / \ / \ v4 \ \ re i, / < oe MV ae Ria ees] 8 FIG, 288. Although not giving the best possible proportions for a truss of this type, for the sake of comparison, the same data will again be assumed for the truss of Fig. 288 that were assumed for the trusses of the preceding articles, namely: length of span, 90 ft.; panel length; 18:ft.; cheight ontruse. 18 ft.; clear width of roadway, 18 ft.; live load, 1,800 Ib., and dead load, 770 lb. per lineal foot. As it isa through bridge, the joints of the lower chord carry the load; the ANALYSIS OF STRESSES. 745 joints of the upper chord are situated midway, horizontally, between the joints of the lower chord. The stress diagrams are constructed according to the general principles used and explained in preceding articles. The student may also refer to Art. 1148, where a Warren girder was given as an example. 1333. The assumption that one-third the dead load is carried at the upper chord joints is for through bridges ap- proximately correct. If, in the construction of the stress diagram, it be assumed that each entire panel of dead load is carried at a lower chord joint, then the one-third of each panel load belonging to the upper chord is carried in equal parts by the two adjacent upper chord joints. Therefore, the amount of error in this assumption relating to each of the two web members which meet at each lower chord joint is $ X¥ 4=4 panel load. As the stress in each web member bears the same relation to the corresponding vertical shear that the length of the member bears to the vertical height of the truss, the stress in each web member could be readily corrected in much the same manner as explained for the vertical members in a Pratt truss. The error of the assump- tion also slightly affects the chord stresses, however, and these could not be so readily corrected. But the error is very small, and is usually entirely neglected. 1334. The correct dead load stresses may be obtained by constructing a stress diagram for one-half the truss, as shown in Fig. 288. This stress diagram is drawn for those stresses which relate to the left reaction, the right reaction, together with all loads and stresses relating to it, being en- tirely neglected. Only one-half of the one-third panel dead load at Y belongs to this stress diagram, as only that por- tion of this load is supported by the left reaction. This diagram will be readily understood without further explanation. In determining the maximum live load web stresses due to the left reaction, a maximum compression will be obtained for Dc anda maximum tension for Yc’. It is evident that 746 ANALYSIS. OF STRESSES. under corresponding conditions the right reaction will pro-- duce .cxactly the reverseof this, i) ¢, @tensionvin. 27 eanG compression in J) c’. Therefore, both maximum stresses must be written for each of these members which are thus found to undergo reversals of stress under varying conditions of load. EXAMPLES FOR PRACTICE. 1. Construct the stress diagram for the dead load stresses in the members in the left half of the truss shown in Fig. 288, using the data given above and assuming the entire dead load to be concentrated at the joints of the lower chord. Ans. For a £& + 15,490 Ib. For ¢c c’' — 20,790 Ib. For B C+ 18,860 Ib. For 2 6— 15,500 1b. For C D + 20,790 Ib. For 6 C+ 17,750 Ib. For a &6— 6,980 lb. For). Ge c= Fiat. For 6 c— 17,8380 Ib. For c D— 0,000 Ib. 2. Compute the live load stresses in the chords and end posts from the corresponding dead load stresses. Ans. For a B + 86,220 Ib. For B C+ 32,400 lb. For 4 c — 40,500 Ib. For C D + 48,600 Ib. For cc’ — 48,600 lb. 3. Construct the stress diagrams obtaining the maximum live-load For a 6 — 16,200 lb. web stresses, Be Mes ( + 10,870 Ib. Ans. For B&B 6 — 36,220 Ib. For ¢ D) — 10,870 Ib. For 6 C + 21,780 lb. nines 10,870 lb. For C ¢— 21,730 lb. / + 10,870 Ib. 4. Construct a stress diagram similar to that of Fig. 288, obtaining the correct dead load stresses, assuming two-thirds the dead load to be carried at the joints of the lower chord, and one-third to be concen- trated at the joints of the upper chord. Ans. For a & + 15,500. Ib. For & C + 13,280 |b. For C D + 20,210 lb. For a &— 6,930 lb. For 6 ¢c— 17,880 lb. For c c' — 20,790 Ib. For 2 6 — 14,200 lb. For 6 C+ 9,040 lb. For C c— 6,460 lb. For ¢ D+ 1,290 lb. Nore.—Compare the results obtained in the solution of Example 4 with those obtained in the solution of Example 1. GENERAL REMARKS. 1335. In order to obtain reliable and accurate results in the graphical analysis of stresses, it 1s necessary that the diagram of the truss should be accurately drawn to as large a scale as convenient, and that the lines of the stress ANALYSIS=OR STRESSES. 747 diagram should be drawn truly parallel to the corresponding members of the truss. Decimal scales should be used for stress diagrams; they should be large enough to be easily read to the nearest hundred pounds, except in cases where the use of so large a scale causes the stress diagram to be inconveniently large. Scales of 10, 20, 30, 40, 50, and 60 _ parts to the inch are the scales commonly used. The best scales for graphical work are the ordinary paper (pasteboard) scales, which can be obtained 18 inches long; these scales also possess the advantage of being cheap. Besides the necessary scales, a complete outfit for graphical work consists of an ordinary drawing board, a T square, a pair of rather large 45° and 60° triangles, a rolling parallel rule, a hard pencil, a rubber, and a fine flat file to sharpen pencil. The parallel rule, though very convenient, is not indispensable. ‘The paper commonly used is the ordinary cheap detail paper. | It is an absolute waste of time to attempt to obtain the stresses in a bridge or similar structure more accurately than to the nearest hundred pounds. The student should guard against acquiring the habit of attempting to be unnecessarily exact. In this work, accu- racy, using the term in a large sense, is absolutely indis- pensable, but painful and unnecessary exactness should be avoided. Results containing no error greater than one per cent. will be considered correct. After the student becomes thoroughly familiar with the methods of determining stresses which have been explained in the preceding pages, he will be able to shorten the process considerably in nearly every case. T. I1,—9 AE MIENY.SIS OF, STRESSES. (CONTINUED.) TRUSSES WITH INCLINED CHORDS. 1336. All the stress diagrams in the preceding articles refer to trusses having horizontal chords. But such trusses do not afford the greatest degree of economy for long spans. An inclination of 45 degrees, or midway between horizon- tal and vertical, is the most economical for the inclined web members of a truss carrying vertical loads. While this statement applies to all the inclined web members, it, of course, applies to a greater degree to those members which bear greatest stress. Considerations of economy also re- quire the height of a truss at the center to bear a certain ratio to the length of span; this ratio varies with different conditions, but is usually between one-fifth and one-eighth. In trusses of considerable length of span this center height becomes so great that the diagonal members can not be given economical inclinations without making the panels longer than is permissible for wood stringers or desirable for the lateral systems. In such cases, therefore, special ex- pedients are resorted to in order to obtain, as nearly as pos- sible, economical inclinations for the diagonal members, especially for those near the ends of the truss, in which the stresses are very great. 1337. In bridges of long span, some degree of economy of material may be obtained by properly inclining one of the chords. A somewhat greater economy is usually obtained by ‘‘curving” the chord, 1. e., by making the inclination of the chord between joints near the ends of the truss greater than between those near the middle, giving an outline for the chord to some extent approximating a curve. The For notice of copyright, see page immediately following the title page. 750 ANALYSIS OF STRESSES. chord remains straight between joints. When in different portions of the chord the degree of inclination is thus varied, it is called a curved chord. When the degree of inclina- tion of the chord is constant from the center to either end, it is called an inclined chord. Curved chords give not only better economy of material, but also a more graceful outline to the truss than can be obtained by chords having the same inclination throughout. In through bridges it is almost invariably the upper chord that is inclined or curved, although the end panels of the lower chord are sometimes inclined. Ina curved or inclined chord the middle portion is usually horizontal; if the truss has an odd number of panels, the chord is always horizontal in the center panel. The method of constructing the stress diagram for a bridge having curved or inclined chords is substantially the same as for a bridge having parallel chords, though the form of the diagram is somewhat different. An example of a through bridge having a curved upper chord will now be given. Notre.—All stress diagrams noticed in the following pages refer to through bridges, which are the bridges most commonly met with. When the principles are thoroughly understood with reference to through bridges, no difficulty will be experienced in applying them to deck bridges. CURVED CHORDS. 1338. In Fig. 289 is represented a truss of 8 equal panels, having a span of 140 feet. The general design of the truss involves the principle of the Pratt truss; that is, in the web system the vertical members are compression members, and the diagonal members are tensionmembers. It differs from the ordinary Pratt trussinthat the vertical mem- bers are of different lengths, thus varying the height of the truss, as shown in the figure. The clear width of the road- way supported by the two trusses is 16 feet. The live load is assumed as 100 pounds per square foot of roadway. 1339. The Dead Load Stresses.—By formula 90, Art. 1298, the dead load per lineal foot, exclusive of the ANALYSIS OF STRESSES.- 751 (16 —6)x 140 , 140° 8 T 300 — 420 lb. Assuming the floor to be white oak, from Table 29, Art. 1299, the weight per lineal foot of floor for panel lengths of 18 feet is found to be 309.6 + 2 x 45.6 = 400.8 Ib. _ The total dead load per lineal foot of structure is 420 + 400.8 = 820.8 Ib., say 820 lb. As the length of each panel floor, is found to be 100+ 5 x 16+ es 820. ii is se =—wiitepettes-toespane)| dead load is u ee ieloe lb., or say 7,200 lb. For this load, by formula 89, Art. 20 — Mee ae epee 5,200 Th In Fig. 289 is also shown a complete stress diagram for the dead load. By the aid of the notation it will be easily understood. The character of each stress will be readily distinguished. It will be noticed that the stresses in the web members are small, especially the stresses in the verti- cal posts. This is due to the fact that in each panel where the chord is inclined, the vertical component of the chord Stress takes up the greater portion of the shear; thus the vertical component of 1-172, the stress in / C, is nearly equal to 1-4, or the shear in the panel c d, which is carried by the members C DandC d to the point C, and 12-13, the amount of shear in this panel remaining to be carried by the post Cc, is very small. It is especially noticeable that the vertical component of 7-74, the stress in C J, is greater than 7-5, or the shear in the panel d ¢; and, therefore, 14-15, the stress in Dd, is tension instead of compression. It is evident that the stress in DY d will also be tension when the truss is fa//y loaded with the live load, as the conditions are then the same as are assumed for:the dead load. From the upper half of the stress diagram the following dead load stresses are obtained for the members in the left half of the truss: Stress.in @ O=— 2-10 = — 24,500 Ib. Sireccu age G = fen [ewe 4 OU) LD, Stressun @ (2 6-15.17 34.360 41b. W52 ANALYSIS OF STRESSES. Stress ind e= 5-15 = — 39,380 lb. Stressina B= /-10 = - 35,150 Ib. Stress in B C= 1-12 = + 35,250 lb. ; ok 2 In ay Sars RA gn aT PY LS LTT) Lot ee ae CA caer Cc C0 es Cae aa Cees Ce es CO ee ap 2 10 3 11 Seale 1=145001bs. , 13 : 19 ey, ‘ 20 8 22 - 23 FIG. 289. Stress in C D= 1-14 =-+ 39,6380 Ib. Stress in DE = 1-16 = + 42,000 lb. Stress 1n. BO 10-11 = a 200 Ip, ANALYSIS OF STRESSES. 753 Stress in B ¢ = 11-12 = — 14,150 Ib. Stress Ceo ieee — 7 2, 000 Jb: Stress itt Ca = 15-14 =" 8, 050; Ib: Stress it ae 1-1 900 Ib. Stress in D e= 15-16 = — 4,450 Ib. SiLrese ine = 10517 = 0,000 Ib. The above stresses for the vertical members are each to be corrected by adding algebraically one-third the panel load considered as a compressive stress, according to the rule given in Art. 1300. In the present case, the correc- tion to be added is ae 2, 4000lb. -peretore.. the cor- rected stresses in the vertical members are as follows: Stress in B 6 = — 7,200 + 2,400 = — 4,800 lb. Stress in Cc = + 2,950 -+ 2,400 = + 5,350 Ib. Stress in Dd= — 900+ 2,400 = + 1,500 lb. Ditess ie 000 + 2,400 = + 2,400 lb. 1340. The Live Load Stresses.—In that caséy7 — gee ze ab =" and formula 105 becomes an 2 _ We Ww eed RE i (106.) Norre.—By comparing formula 105 with formula 94, Art. 1316, it will be noticed that a single load concentrated at the center of the span will produce just double the bending moment at the center of the span that is produced at that point by the same amount of !oad uniformly distributed upon the same span. 1372. If twoor more concentrated loads are situated in any position upon a stringer, the bending moment at each point along the stringer can readily be obtained by drawing the moment diagram. By constructing the shear diagram also, the point of maximum bending moment will be located by the point where the shear line crosses the shear axis. Or the bending moment at any point may be computed by simply finding the resultant moment of the forces acting on either side of that point. The maximum bending moment in a simple beam, produced by any system of quiescent loads, occurs at a point where the sum of the loads at the left (including, tf necessary, a portion of the load directly at the point) equals the left reaction, or in other words, where the shear ts Zero. > 1373. But the system of wheel loads under ordinary conditions of traffic, as an electric railway car, a road roller or heavily loaded truck, comes upon one end of the stringer, and, proceeding along its entire length, passes off at the opposite end, producing bending moments of varying in- tensity, which at some point during the passage of the loads become maximum. To find where this maximum bending moment occurs, and the position of the system of loads pro- ducing it, the two following principles must be observed: ANALYSIS OF STRESSES. 803 L, The maximum bending moment will occur under a load. IT. The center of the span will be midway between the point of maximum bending moment and the center of gravity of the system of loads. If all the loads belonging to the system are not upon the span at the same time, the center of gravity of those loads which are upon the span must be taken. When the posi- tion of the loads producing the maximum bending moment is found, the bending moment can be obtained either by calculation or by drawing the moment diagram. In the case of two unequal loads upon a stringer (or any other simple beam), the maximum bending moment will occur under the heavier load. Let &, be the reaction on the same side as that on which the heavier load rests, lV, the weight of this load, WV, the weight of the smaller load, a the distance between the loads, and / the length of the stringer (or beam). Thus the distance + from X&, to W, is given by the formula eee l a Phage W (107.) (1477) If W, = W,, then ee In the latter case it will be noticed that the postition of the loads ts independent of those loads, that is, whatever the loads may be, if they are equal, the fosztzon for maximum bending moment is always the same, so long as the length of the beam and the distance between the loads remain unchanged. EXAMPLE.—It is assumed that the floor system of the bridge truss, shown in Figs. 297 and 298, carries an electric railway track, and that stringers are so arranged that each track rail is supported directly on top of a stringer. The car and its entire load, assumed to weigh 16 tons, is supported upon four wheels, each of which is assumed to carry one-fourth of the load, or 8,000 pounds’ the two wheels upon either track are 7.5 feet apart, center to center. What is the position S04 ANALYSIS OF STRESSES. of the wheels upon the stringer which will produce the maximum bending moment ? SoLuTION,—The span of the stringer is equal to the panel length of the truss, or 16.5 feet. Ss s Here, 7= 16.5, a=.5, Ss = and W, —= W, = 8,000 S S lb. Then, formula 108 Lee / i?) ; 3 | 15 — gives a ee 6.575 ft) ‘Distance at W, from center = 7.5 — 6.375 = 1.875, which ; u 7.5 1S ape ye OTF oOnec- FIG. 302. half the distance be- tween WW, and the center of gravity of the system, as stated in II. See Fig. 302. 1374. With three loads upon the span, if the loads are equal, or if the center load is the greatest, the maxi- mum bending moment will occur under the center load. If the two outer loads are equal and are at equal dis- tances from the center load, the maximum bending moment will occur when the center load is at the center of the span. As the number of loads increases, the problem becomes more complicated, especially if the magnitudes of the loads vary.. It may always be solved, however, by applying the above conditions to the several wheels, the maximum _bend- ing moment being usually found under one of the heavier loads near the center of the system. In case of a stringer or floor beam of uniform cross section it is necessary to obtain only the one absolutely maximum moment; in such a case little, if any, difficulty will be experienced. It must be noticed that formula 107 (and the same applies to 108) gives the position for maximum bending moment when the two loads are actually upon the span, but, when a is greater than & it may happen that this bending / / moment is less than ri , or the center bending moment ANALYSIS OF STRESSES. 805 with only W, upon the span. Insuch a case, both moments 1 should be calculated to see which is the real maximum. Furthermore, the value of + given by formula 107 may be so great as to make it impossible for JV, to be upon the span when IV, is at the distance + from &,. This happens 1 an W,). In this case, whenever @ is greater than iC ae Ane eer We 1° the center bending moment v6 is to be taken as the maximum. EXAMPLES FOR PRACTICE. 1. With the loads of the above example in the positions shown in Fig. 3802, what is the value of A, ? Ans. 6,182 Ib. 2. What is the maximum bending moment produced by the same? Ans. 39,410 ft.-Ib. 3. With the loads in the same position, find the bending moment under the right wheel /1,. Ans. 25,773 ft.-lb. 4. Assuming the span of the stringer to be 20 feet, what is the position of the same loads producing maximum bending moment ? Ans. With either load 8.125 feet from the corresponding end of the stringer. | 5. What is the maximum bending moment for the conditions of the preceding example ? Ans. 52,813 ft.-lb. 6. Assuming the span of a stringer to be 18 feet, the two loads upon it to be 9,000 and 6,000 pounds, respectively, and the distance between the loads to be 11 feet, find the position at which the maxi- mum bending moment will occur, both wheels being upon the span. Ans. Under the heavier load at a distance of 6.8 feet from the nearer end, or 2.2 feet from the center of the span. 7. For the conditions of the preceding example, what is the maxi- mum bending moment ? Ans. 38,533 ft.-lb. 8. With the same span and loads as in the two preceding examples, and with the heavier load at the center of the span, what is the maximum or center bending moment ? Ans. 40,500 ft.-lb. 9. With the same loads, but with a span 24 feet in length, what is the bending moment with the heavier load at the center of the span ? Ans. 57,000 ft.-Ib. 10. With the same span and loads as the preceding example, what is the maximum bending moment ? Ans. 60,025 ft.-lb. 806 ANALYSIS OF STRESSES. CONCLUDING REMARKS, 1375. There are several forms of bridge trusses which have not been noticed in the preceding pages. The forms of trusses for which the stress diagrams have been explained are those modern forms of simple trusses most commonly constructed in this country at the present time; they are thought to be representative and typical of approved modern practice. Other methods are employed for obtaining the stresses in framed structures; the method which has been explained and generally followed in the preceding pages is believed to be the most systematic, flexible, and accurate, as well as the most clear and popular graphical method. ‘The principles on which the method is founded are general, and the student will have no difficulty in applying them to any ordinary truss. The examples that have been explained have been given solely for the purpose of illustrating the application of gen- eral principles and the methods to be employed. ‘The design of a bridge must, of course, depend largely upon the phys- ical conditions peculiar to the location and other special cir- cumstances; so that, in order to obtain the highest possible degree of economy and efficiency in each case, it is usually necessary to treat each design separately and independently, especially if the bridge be one of considerable length of span. In doing this the designer must rely upon his knowl- edge of the underlying principles,and upon his own judgment and experience. PROPORTIONING THE MATERIAL. THE MATERIALS USED FOR SUPER- STRUCTURES OF BRIDGES. 1376. The materials commonly used in the construc- tion of the superstructures of bridges are structural steel, wrought iron, and wood. Owing to the increasing scarcity of suitable timber and to the cheapness of iron and steel, together with the fact that metal bridges are more durable than those constructed of wood, the latter material is now little used for bridge trusses. In this country bridges were never constructed entirely of cast iron, although at one time this material was used to a considerable extent for compression members. On account of the unreliable character of this metal, however, it is no longer employed for the superstructure of fixed bridges, ex- cept for such purposes as bed-plates and small and unim- portant details. 1377. A few years ago wrought iron had become the material used exclusively for the main parts of metal bridges; but, although it is still used to some extent, it is being largely superseded by structural steels, which are somewhat stronger and better materials than wrought iron, and cost about the same. The name structural steels is applied to these materials in order to distinguish them from other kinds of steel, such as cutlery steel and tool steel, which are very different. The use of structural steels is becoming more and more general, and the time is probably not far distant when wrought iron will no longer be used for For notice of copyright, see page immediately following the title page. 808 PROPORTIONING® TE Beara PEs structural purposes. Thisis due to two reasons: First, the manufacture of steel is being constantly perfected and cheap- ened. Second, less attention is being given to the manu- facture of wrought iron, and on thisaccount it is not possible to obtain as good qualities of this material as formerly. Structural steels are without doubt the best of known materials for bridges. 1378. When steel was first used for this purpose its properties were not thoroughly understood, and it was not as judiciously used as at present. The mistake of using grades of steel containing too high percentages of carbon was quite commonly made. Steel high in carbon possesses high ultimate strength and elastic hmit, but is hard and brittle, and not uniform; it does not weld readily, and is very liable to injury in forging or punching. In the earlier use of structural steels, the impression that all steel pos- sessed these unreliable properties became common; the brittleness of steel was also believed to be to some extent due to the fact that it is not fibrous. All this gave rise to considerable prejudice against the use of steel for structural purposes, and by many engineers it was considered inferior to wrought iron. But from further experience in the use of steel and more accurate knowledge concerning its properties, it is known that steel low in carbon and reasonably free from certain injurious elements, noticeably sulphur and phosphorus, can be produced that is exceedingly tough and ductile, and in most respects superior to wrought iron. It has also been satisfactorily ascertained that the fiber existing in wrought iron is simply a circumstance of its manufacture rather than any inherent property of the material itself; that it does not make the iron materially stronger in the direction of the fiber, but merely weaker in a direction across the fiber. Steel, having no fiber, is of nearly uniform strength in all directions. Knowledge of these facts has largely removed the objections to the use of steel, and to-day this material is very extensively employed. PROPORTIONING THE MATERIAL. 809 Structural steels are produced by both the Bessemer and the Open Hearth processes. The latter process is generally preferred, as it is believed to give better results. QUALITY OF THE MATERIALS. 1379. Wrought Iron.—Specifications for the quality of the wrought iron used in bridges commonly require an elastic limit of not less than 26,000 pounds per square inch for all grades, and an ultimate tensile strength varying from 50,000 pounds per square inch, for bars of not more than 44 square inches of sectional area, down to 48,000 pounds per square inch, for bars of 84 square inches of sectional area, or for larger bars, for shaped iron, and for plates from 8 to 24 inches in width; and for wider plates, 46,000 pounds per square inch. 1380. They also require that the specimen pieces tested shall before rupture elongate, in a length of 8 inches, 18 per cent., if from bars of not more than 44 square inches sec- tion; 15 per cent., if from larger bars, shaped iron, or plates less than 24 inches wide; 10 per cent., if from plates more than 24 inches and less than 36 inches wide; and8 per cent., if from plates more than 36 inches wide. 1381. It is usually required that the tensile strength, limit of elasticity, and ductility shall be determined from a standard test piece of as near $ square inch sectional area as possible. The elongation shall be measured on an original length of 8 inches. 1382. The following cold bending tests are also required: All iron for tension members and specimens from shaped iron must bend cold, without cracking, through 90° toa curve whose diameter is not more than twice the thickness of the piece. Samples from plate iron must bend cold, without cracking, through 90° to a curve whose diameter is not more than three times the thickness of the piece. Rivet iron must bend cold through 180° to a curve whose diameter is equal to the thickness of the rod tested, without sign of fracture 810 PROPORTIONING THE MATERIAL. on the convex side. When nicked and bent cold, all iron must show a fracture mostly fibrous. 1383. Alliron must be tough, ductile, fibrous, and of uniform quality. Finished bars must be thoroughly welded during rolling, and must be straight, smooth, and free from injurious seams, blisters, buckles, cracks, or imperfect edges. 1384. Although the conditions of some specifications are rather more rigid, the above conditions represent a good quality of iron and contain no excessive requirements. It will be noticed that the elastig limit specified is slightly more than one-half the ultimate strength. This is commonly found to be the case for wrought iron. 1385. In some specifications the ultimate tensile strength per square inch required for bar iron is written 7,000 x area of original bar circumference of original bar 52,000 — (all in inches). 1386. The modulus, or coefficient, of elasticity of a good quality of double refined bar iron, as determined from tests made on finished eye-bars, is from 25,000,000 to 27,000,000 pounds per square inch. It often falls much below these amounts, and often runs as high as 32,000,000; it is usually taken at 27,000,000. 1387. Steel.—As commonly manufactured, there are three grades of structural steel, namely, soft steel, called also mild steel; medium steel, and high steel, called also hard steel. The following requirements are from the ‘Specifications for Constructional Steel,” published by the Carnegie Steel Company, Limited. They plainly indicate the quality of each grade of steel ascommonly specified, and the properties specified for each grade may be considered as fairly representative of that grade: 1388. ‘Soft Steel.—Specimens from finished material for tests shall have an ultimate strength of from 54,000 to 62,000 pounds per square inch; an elastic limit of one-half the ultimate strength; a minimum elongation of 26 per cent. PROPORTIONING THE MATERIAL. 811 in 8 inches, and a minimum reduction of area at fracture of 50 per cent. This grade of steel to bend cold 180° flat on itself, without sign of fracture on the outside of the bent portion. 1389. ‘‘ Medium Steel.—Specimens from finished ma- terial for tests shall have an ultimate strength of from 60,000 to 68,000 pounds per square inch; an elastic limit of one-half the ultimate strength; a minimum elongation of 20 per cent. in 8 inches, anda minimum reduction of area at fracture of 40 per cent. This grade of steel to bend cold 180° toa diameter equal to the thickness of the -piece tested, without crack or flaw on the outside of the bent portion. 1390. ‘‘ High Steel.—Specimens from finished material for test shall have an ultimate strength of from 66,000 to 74,000 pounds per square inch; an elastic limit of one-half the ultimate strength; a minimum elongation of 18 per cent. in 8inches; a minimum reduction of area at fracture of 35 per cent. This grade of steel to bend cold 180° to a diameter equal to three times the thickness of the test piece, without crack or flaw on the outside of the bent portion.” 1391. It will be noticed that no definite line of dis- tinction exists between the three grades, but that the dif- ferent grades blend into each other. Many specifications now allow a variation of 10,000 pounds per square inch in the ultimate strength of each grade. 1392. It will also be noticed that for each grade of steel the percentage of elongation specified is practically one-half the specified percentage of reduction of area at fracture, and that the elastic limit specified is one-half the ultimate strength. This requirement for the elastic limit is easily fulfilled. Recent investigations have shown that structural steel having an elastic limit considerably greater than one- half its ultimate strength can readily be obtained. 1393. The modulus, or coefficient, of elasticity of structural steel does not differ greatly from that of wrought I. LI.—18 812 PROPORTIONING THE MATERIAL. iron; 29,000,000 pounds per square inch is probably a fair average value of this modulus for both soft and medium steel, though it is sometimes taken at 28,000,000 pounds per square inch. 1394. On account of its extreme toughness and ductil- ity, soft steel is especially suitable for rivets, and is largely used for this purpose, although it is also very suitable for the riveted members of bridges for which it is now much used. Medium steel is the material now most commonly used in the construction of the main members of bridges. High steel is somewhat brittle, and is not very extensively used in bridge construction. Intermediate and extreme grades of steel are sometimes specified, as medium soft, medium hard, very soft, or very hard. THE USE OF WROUGHT IRON. FACTORS OF SAFETY AND UNIT STRESSES. 1395. The nature and use of the factor of safety have been explained in Arts. 1214 to 1216. At one time it was not an uncommon practice to construct bridges with certain factors of safety, based upon the ultimate strength of the material; it was customary to use a factor of safety of 4 for highway bridges and 5 for railroad bridges. This practice is still followed to a limited extent, but the more modern and now quite general practice is to use certain al- lowed stresses, called working stresses or unit stresses, whose values vary according to circumstances. The unit stresses allowed for members which receive their maximum stresses often or suddenly, such as web members, and especially counters, are less than those allowed for members which receive their maximum stresses seldom or gradually, such as chords. PROPORTIONING THE MATERIAL. 813 SPECIFICATIONS AND HAND-BOOKS. 1396. In designing a bridge, the values given to the unit stresses are usually in accordance with certain specifi- cations which are accepted as representing reliable engin- eering practice. Several such specifications for highway bridges have been published by prominent American bridge engineers, notably G. Bouscaren, Theodore Cooper, Edwin Thacher, and J. A. L. Waddell. The bridge specifications most widely known, and which have obtained most popular recognition in this country, are those of Mr. Theodore Cooper, a prominent bridge engineer of New York City. These specifications may be said to have become a standard for American bridge practice. 1397. The stresses for the various members of the bridge shown in detail in Mechanical Drawing Plates, Titles: Highway Bridge: Details I, II, III, I1V, and High- way Bridge: General Drawing, were obtained in Arts. 1292 and following, and are shown written along the sev- eral members upon the stress sheet in Fig. 283. The student should, for his own convenience, make a copy of this stress sheet upon a sheet of paper, cap size, desig- nating the joints by the system of notation shown in Fig. 76 of Mechanical Drawing. This need not be a neat copy, but simply a working copy, and is as well made in pencil. The material for this bridge will now be proportioned of wrought iron, according to Cooper’s ‘* General Specifications for Highway Bridges,” the necessary portions of which will be quoted in Art. 1399. Note.—As a copy of these specifications may be obtained for twenty-five cents, the student will find it to his advantage to provide himself with one. In bridge designing, one of the valuable hand-books of structural shapes published by several of the large iron and steel manufacturing companies will be found of material assistance. Sucha book gives the sizes, weights, sectional areas, and various properties of the structural shapes manu- factured by the company by which it is published, besides 814 PROPORTIONING THE MATERIAL. convenient tables and other valuable information. In prac- tice, a structural hand-book is found indispensable. These hand-books may be obtained from the various iron and steel manufacturers at a small cost. UNIT STRESSES ALLOWED FOR TENSION MEMBERS. 1398. The stresses are found in the various members of a bridge simply for the purpose of ascertaining the amount of strength required for each member, which is given such size and form as to best resist its stress. The material for tension members is more easily propor- tioned than for those which bear compressive stress; there- fore, in the example chosen, the tension members will be first considered. 1399. The tensile stresses for wrought tron, in pounds per square inch of sectional area, allowed by Cooper’s Gen- eral Specifications for Highway bridges, are as follows: Pounds per Square Inch. (z)'-*2OnJateral: bractnee te pie ee 15,000 (2) ‘On solid rolled beams, used as cross floor béams and stringers s:7 ot sleds eee eae ee ee 12,000 (c) ‘‘On bottom flange of riveted cross-girders, net SECHION. (4 us los she aetna ale eet ere ae eee 12,000 (Zz) ‘‘On bottom flange of riveted floor stringers, inet iSectiOn sai es cancete ee et tee eee ee 12,000 (c) ‘fOn floor beam hangers, and other similar members liable to sudden loading (bar iron WiLD:fOreed CNS aig tws ae tn, eee teem 9,000 (7) ‘*On floor beam hangers, and other similar members liable to sudden loading (plates or sha pes) Set SEClion i cer Mae see. open ene eee 7,000 For For Live Loads. Dead Loads. (g) ‘‘Bottom chords, main diag- onals, counters, and long verti- cals’(forvetleye-bars)i 4% sas 10,000 20,000 PROPORTIONING THE MATERIAL. 815 For For Live Loads. Dead Loads. (Z) ‘‘Bottom chords and flanges, main diagonals, counters and long verticals (plates or shapes), PeieseourOunen. Sarssei pies nee 8 9,250 18,500” The following clauses from the specifications also have direct reference to the tension members. As is not uncom- mon, the word s¢razz is used in these specifications in the sense of sfress. (z) ‘‘ The areas obtained by dividing the live load strains by the live load unit strains will be added to the areas ob- tained by dividing the dead load strains by the dead load unit strains, to determine the required sectional area of any member.” (7) ‘Single angles subject to direct tension must be con- nected by both legs, or the section of one leg only will be considered as effective.” (k) Net Section.—‘‘In members subject to tensile strains, full allowance shall be made for reduction of section by rivet holes, screw threads, etc. ‘*In deducting the rivet holes to obtain net sections in tension members, the diameter of the rivet hole will be assumed as } inch larger than the undriven rivets.” (7) Effect of Wind on Chords and End FPosts.—‘‘'The strains in the chords and end posts from the assumed wind forces need not be considered, except as follows: ‘‘ist. When the wind strains per square inch on any member exceed one-quarter of the maximum strains per square inch due to the dead and live loads upon the same member. The section shall then be increased until the total strain per square inch shall not exceed by more than one- quarter the maximum fixed for dead and live loads only. ‘¢2d. When the wind strain alone, or in combination with a possible temperature strain, can neutralize or reverse the tension in any part of the lower chord, from dead load only.” 816 PROPORTIONING THE MATERIAL. (7) Lateral Rods.—‘‘In no case shall any lateral or diagonal rod have a less area than ? of a square inch.” Each of the above items, quoted from the specifications, is here designated by a letter for convenience of reference. It will be noticed that in items (a) to (/), inclusive, the unit stresses are for the combined live and dead load stresses, while in items (g) and (/) the stresses per square inch allowed for the dead load are just double those allowed for the live load. As the trusses for the example are pin-con- nected, the tension members will be of bar iron. The _ tension members of this structure will be proportioned by items (@), (c), (¢), and (¢). 1400. If F is the total live load stress in pounds; P,is the total dead load stress in pounds; S, is the live load unit stress in pounds per square inch; S,is the dead load unit stress in pounds per square inch, and A is the total area of the cross-section in square inches; then, item (7) above may be concisely expressed by the formula | ene eagle A= (109.) Since, according to items (g) and (Z), the allowed dead load unit stress is double the allowed live load unit stress, we have S, =4S,, and formula 109 may be written MeN dee bade terme ie) Aas TiS oe Te (1092.) For clearness, the operations indicated by formula 109 will here be followed. The operations indicated by formula 1092 are, however, slightly shorter, and the student may employ them if he chooses. 1401. Members of a pin-connected bridge, which are designed to resist tensile stresses only, are commonly made of flat, square, or round bars, and are usually placed in PROPORTIONING THE MATERIAL. 817 pairs. Main tie bars and lower chord bars are usually flat bars in pairs; hip vertical bars are usually flat or square bars, but are sometimes round bars. In order that they may be easily fitted with turnbuckles, counters are usually made of square or round bars (preferably square), and are in pairs or single, while lateral rods are usually single round rods. In trusses having riveted connections, the tension mem- bers, as well‘as the compression members, are formed of plates or shape iron, or of the two combined. PROPORTIONING THE MATERIAL FOR TEN- SION MEMBERS. 1402. According to item (z) of Art. 1399, the sec- tional area for the main tie, required by item () (see Fig. 283), 1S an - oD = 3.24 sq. in. The section is made up of two bars 2” x 48”= 3.25 sq. in. As the material composing the required section is determined for each member, the student should note it upon his copy of the stress sheet; it should be marked along the member in the vzght half of the diagram of the truss. According to the same items of the Specifications, the sectional area 16,200 | 4,600 10,000 20,000 sq. in. It is made up of two bars, each 1 inch square, making a total area of 2 sq. in. required for the hip vertical 40 is Salen 1403. The sectional area required for the counter Cc’ 13,750 is —”—— 10,000 members in the center panel should each be made up of two bars, rather than one bar. As item (7) specifies that no diagonal rod shall have a less area than # square inch, which is practically to the effect that no diagonal rod shall pewlessmithaned inch ¢squatre A=" 706° sq... inv)/for™ 2) ‘inch round (=.785 sq. in.), the section of the counter Cc’ is = 1.38 sq. in. It is desirable that the diagonal 818 PROPORTIONING THE MATERIAL. made up of two bars ¢ inch square=1.53 sq. in. The sectional area required by the live and dead load stresses in 32,400 , 138,900 _ the panel ad or dc of the lower chord is 10,000 + 20,000 = 3.94 sq. in. 1404. In highway bridges the lower chords are often proportioned with reference to the live and dead load stresses only; if this were done in the present case, the section could be made up of two bars 24" x 413" = 4.06 sq. in. Likewise, for the center panel cc’ of the lower chord, the sectional area required by the live and dead load stresses is 48,600 | 20,800 10,000 * 20,000 other stresses, the section could be made up of two bars A" 3) — §8sq) in= Bat ithewetlect-got ptinewwindestie-ce> upon the chords and posts should always be considered, especially in the case of a short and light structure. In order to comply with the requirements of item (/), it will be found necessary to considerably modify the section of the panels @6 and dc of the lower chord. But this will be taken up further along, after the design of the compres- sion members has been considered. = 5.90 sq: in. Without reference to any 1405. The sectional area required for the diagonal rod in 14,900 15,000 .99 sq. in. The section is made up by a round rod 14" in diameter = (14)’ X .7854 = .99 sq. in. The area of section for the diagonal in the second panel of the lower lateral 8, 200 15,000 In compliance with item (7z), a round rod 1” in diameter = #9 sq. in, is,,used ‘for this mémpbers =/The area of seetion for the diagonal rod in the middle panel of the lower lateral 2, 200 15,000 A round rod 1” in diameter is used for this member also. For the diagonal rod in the end panel of the upper lateral the end panel of the lower lateral system, item (a), is system, as required by the stress, is =O. so alias system, as required by the stress, is ==. bo 5c Salis PROPORTIONING THE MATERIAL. 819 3,700 15,000 ~~ sq. in. No stress was obtained for either diagonal in the center panel ‘of the upper lateral system. In compliance with item 7, each diagonal rod in the upper lateral system will be a round rod 1” in diameter. system, the section required by the stress is 25 Nore.—Having obtained the sectional area required for a tension member, the dimensions of the bars giving the required area are quickly determined from a table of areas; such tables are given in structural hand-books. 1406. It will be noticed that, in proportioning the material for the tension members, the amount of stress and the allowed unit stress are the only quantities considered. Bars for tension members should be of sizes commonly rolled and suitable for the practical requirements of the shop work; otherwise (with one exception, which will be _ hereafter noticed), the form of a tension member is unimportant. COMPRESSION MEMBERS. RADII OF GYRA- TION. 1407. The form of a member which resists compres- Sive stress bears a very important relation to its strength. Failure of a strut or column is not usually the result of direct crushing, but of bending or buckling. The capacity of a column to resist compression depends upon its length and form, as well as upon the area of its section. Various forms used for compression members are shown in Fig. 303. Of these,-forms 4, 4, C, DY, and = are used for top chords and end posts; forms /, G, 7, 7, X, and Z are used for inter- mediate posts; although forms / and // are also sometimes used for top chords and end posts; forms J7, V, O, and P are sometimes used for lateral struts. Forms G and /are © seldom used on account of the difficulty of riveting; as one head of each rivet is within the assembled piece, it is not easily accessible for machine riveting, Form £ is used for very heavy chord and end post sections. Forms A, s, C, D, and & are very economical. 820 PROPORTIONING THE MATERIAL. 1408. In Arts. 1240, and following, the nature and derivation of the moment of inertia and the radius of gyration were explained. In the accepted formulas for FIG. 303. determining the required area for a strut of given external dimensions, the least radius of gyration of the section is the only variable quantity, when the length of the strut and the PROPORTIONING THE MATERIAL. 821 character of its end connections (i. e., whether flat-ended or pin-ended) are constant. The radii of gyration of the various structural shapes commonly rolled may be found in any of the manufacturers’ hand-books previously mentioned, and, although the bridge designer is constantly making use of the radius of gyration, he seldom finds it necessary to compute it. The exact formulas for determining the radii of gyration of the sections shown in Fig. 303 are often of a complicated char- acter. The following are approximate formulas, which may be used where great accuracy is not required, and also for finding trial values; 7 is the least radius of gyra- tion, and W the depth of the section, as shown in the figure. For torms'A 74, C.D and £, eS r=—W. (110.) For forms /, G, H/, and /, ne - W. (1111.) For form K, " 5 Ay: W. (11 2.) For form ZL, 24. _ #= Wz Toma ae WV. (113.) For form J/ (equal legs), Sle. Yr For form JV (equal legs), pa - W. (118.) 822 PROPORTIONING THE MATERIAL. For form O (longer legs back to back), 1 32 Tn ana CL) For form P, ? =e terion abe bets These formulas are very convenient to use, and obviate the constant reference to structural hand-books. Although in reality they are only approximate formulas, yet the val- ues for the radius of gyration given by most of them are believed to be sufficiently close to the correct values for many practical purposes. The results obtained by formulas 110, 111, 112, 114, and 115 are quite reasonably accurate; those given by 113, 116, and 117 are some- what less accurate, while results obtained by 118 are but liberal approximations. On account of their convenience, some engineers use values for the radius of gyration obtained by such formulas in preference to the exact values. It is, however, better to take the correct values given in the hand-books. FORMULAS FOR COMPRESSION. 1409. Formula 76, of Art. 1256, is Sn vt AlN 1+< 7] af ( gl in which Wis the load upon the column, 5S, is the ultimate strength of the material in pounds per square inch, A is the sectional area of the column in square inches, / is a factor of safety, 7 is the length of the column in inches, / is the least moment of inertia of the cross-section, and g is a constant. Wi PROPORTIONING THE MATERIAL. 823 As/=A/7?’ (Art. 1241) this formula may be written, ayo Aer | ee) 1 Se) me, 1 2 fi+mm) s0+s Omitting the factor safety f and dividing by the area A, the formula for the wltzmate strength per square inch of 4 column becomes ie = = 1 (119.) which corresponds to the form in which this formula for columns is commonly written. In this form it is known as Rankine’s modification of Gordon’s formula, or simply as Rankine’s formula. In Bridge Engineering the following forms of Rankine’s formula are generally used: (1 20.) (121.) (1:22,) For two For pin and For two square bearings : square bearings : pin bearings. 40,000 40,000 40,000 7? Pas Pek, 1 + 1+ 1 + 36,000 7° 24,000 7” 18,000 7? in which 7 is the length of the column and 7 is the least radius of gyration, both in inches. These formulas have been extensively used for the ulti- mate strength of wrought-iron columns or struts, the results given being usually divided by a factor of safety of either 4 or 5 for a unit stress or safe working stress per square inch. They are of the kind known as curve formulas, because, as they contain the squares of / and 7, if the results are plotted for various consecutive values of those quantities, a curve will be obtained. Of recent years, however, some simpler formulas, known as straight-line formulas, have come into quite general use. They are so called because, as they contain only the first powers of /and7, 824 PROPORTIONING THE MATERIAL. the results of any one formula, if plotted, will form a straight line. 1410. For wrought tron the compresstve stresses per square inch of section, allowed by Cooper’s General Specifica- tions for Highway Bridges, are gtven by the following straight-line formulas : (x) Chord Segments. For live load strains: P= 10,000 — 405, (123.) For dead load strains: P= 20,000 — 80-. (124.) (0) All Posts. For live load strains: P=8,750 — 505, (125.) For dead load strains: Py 500 2— 1005, (1 26.) For wind strains: P= 13,000 — 5, (127.) (p) Lateral Struts. For assumed initial strain: P= 11,000 — 604, (128.) In all of which P is the allowed compression per square inch of cross-section, / is the length of the compression member in inches, and 7 is the least radius of gyration in inches. As before noticed, the word s¢razz is used in the sense of stress. PROPORTIONING THE MATERIAL. 825 1411. In using compression formulas, and in all com- putations relating to the proportioning of the material for the members of a bridge, the length of any member taken is always its theoretical length, 1. e., its length center to center of connections. The value of / is given to the nearest inch. 1412. The following clauses of the Specifications also refer to the compression members: (7) ‘‘ No compression member, however, proportioned by the above formula, shall have a length exceeding 45 times its least width. For ratios greater than 45 the constants in the above formula will be reduced proportionately.” (7) ‘‘The lateral struts shall be proportioned by the above formula to resist only the resultant due toan assumed initial strain of 10,000 pounds per square inch upon all rods attaching to them, assumed to be produced by adjusting the bridge or towers.”’ (s) ‘‘ Members subjected to alternate strains of tension and compression shall be proportioned to resist each kind of strain. Both of the strains shall, however, be considered as increased by an amount equal to ,§, of the least of the two strains, for determining the sectional areas by the above allowed unit strains.”’ (¢) ‘* The unsupported width of a plate subjected to com- pression shall not exceed thirty times its thickness, except cover plates of top chords and end posts, which will be limited to forty times their thickness.” (7) ‘* No iron shall be used less than 4 inch thick, except for lining or filling vacant spaces.” (v) ‘‘ ln compresston chord sections, the material must mostly be concentrated at the sides, in the angles, and verti- cal webs. Not more than one plate, and this not exceeding 8 inch fn thickness, shall be used as a cover plate, except when necessary to resist bending strains.” 826 PROPORTIONING THE MATERIAL. DIMENSIONS OF COMPRESSION MEMBERS. 1413. By reference to the formulas given in the pre. ceding articles, it will in each case be noticed that the greater the radius of gyration of the section the greater will be the unit stress, and hence the less will be the area required to resist the given stress. In determining the dimensions of a compression member by any such formulas, therefore, the natural course would be to select a size and form of section giving the radius of gyration as large as possible, which would also require the width and depth of the member to be as great as possible. If this idea were carried to extremes it would result in large members of very thin metal, and there is evidently a limit beyond which the metal would be too thin to be of value asa strut. To obviate this it is the practice to limit the ratio between the minimum thickness of the material and the dimensions of the piece. Thus, item (¢), Art. 1412, limits the ratio between the thickness and width of any plate in a member subjected to compression. In accordance with this specification, the thickness of the side plates in forms /7 and JB, Fig. 304, must not be less than one-thirtieth the distance between the two lines of rivets connecting them to the angles, while in form B of that figure the thickness of the cover plate must not be less than one-fortieth the distance between the two .lines of rivets connecting it to the angles. PROPORTIONING THE MATERIAL. 827 1414. In order that the radius of gyration obtained according to the formula given in Art. 1408, for either section shown in Fig. 304 (i. e., the radius of gyration about the axis x x), shall be the /east radius of gyration of the section; the clear distance between the side plates (or channels, if channels are used) must not be less than that given by the following formulas. The formulas apply also to those similar forms of sections shown at A and F, Fig. 303, in which channels are used. If W represents the width of the member, as shown in Figs. 303 and 304, and c repre- sents the clear distance between side plates or backs of channels, then, For post sections, forms / and //, Fig. 303: sa W, (129.) For chord sections, forms A, 2, C, and D: 7 e c= W. (130.) For a section of the form shown at L, Fig. 303, the radius of gyration given by formula 113, Art. 1408, will be the least radius of gyration of the section when the two pairs of angles which are connected by the lattice bars are separated by a reasonable distance. This distance varies from zero in angles having both legs of nearly equal length (as 3” K 24”) to about 1?” in angles having the longer leg double the length of the shorter leg (as 7” x 34”). Prac- tical considerations generally require them to be separated more than this. Each pair of angles is usually separated $” by the lattice bars. Hence, for W add 4" to the dimen- sion given by the two angles. For a section of the form QO, Fig. 303, formulas 116 and 117 must both be applied; the smaller value of 7 given by these formulas must be used. For form /, the dimension ’ must be large enough so that the radius of gyration obtained (in terms of IW) by formula 118 will be the /eas¢t radius of gyration of the T. II.—1} 828 PROPORTIONING THE MATERIAL. section. It is impossible to give a general rule for the comparative dimensions necessary to satisfy this condition; but the radius of gyration given by formula 118 will usually be the least radius of gyration of the section when the value of V is equal to or greater than that given by the formula 8 Yi 10 W. (131.) In order to be on the safe side, the value of V should always be taken somewhat greater than given by the above formula. Forms //, O, and P are not very satisfactory forms of sections to use for compression members, and should not be used except for lateral struts, and not for this purpose when better forms can be as expediently used. It is generally much more satisfactory and economical to use symmetrical sections, 1. e., those in which the centers of gravity are at the centers of the sections. THE WEIGHT OF WROUGHT IRON. 1415. Before proceeding further it will be well to notice how the weight of a piece of wrought iron may be estimated. By reference to Table 19, Art. 1184, it will be found that the average weight per cubic foot of wrought iron is 480 pounds. For rolled sections of large dimensions the average weight per cubic foot is slightly less than this amount, but 480 pounds per cubic foot is the weight invariably used in estimating wrought iron for bridge pur- poses. A bar of iron 1 foot long and 1 inch square weighs, 480 therefore, “7 = 34 Ib. = a Ib.- If the bar is one yardilane : ; : 10 ; its weight is 3 x > or just 10 pounds. Therefore, given the sectional area of a wrought-iron bar of any form, its weight per foot can readily be found by the following formula, in which A is the sectional area of Bi cst ine ag ot PROPORTIONING THE MATERIAL. 829 the bar in square inches, and w is its weight in pounds per foot of length: ee aA. (132.) If w, the weight per lineal foot of a wrought iron bar of any form, is known, its sectional area may be found by the formula A= Re w. (133) 1416. Wrought-iron structural shapes are rolled in various sizes, and each size may have any weight between certain maximum and minimum limits, according to the practical limits for rolling and the allowed minimum thick- ness of the metal. The variation in weight for each size is, for most shapes, effected by simply changing the distance between the rolls. In specifying any structural shape other than a plate, or a round, square, or flat bar, for which the exact dimensions can be readily stated, it is necessary to specify both the size and the weight. If the weight of a shape is not stated, the lightest weight rolled of the specified size is always under- stood. For some shapes the thickness of metal is some- times specified instead of the weight, though not commonly. Thus, a 4” x 3” angle bar having 2” thickness of metal is usually specified as a 4" 3” L@ 8.41b., but it may be speci- fied as a 4” x 3” x 2” L. The weight and the thickness of metal are never doth specified, as the one determines the other. 1417. The maximum and minimum weights of the various sizes of wrought-iron channels, as commonly rolled, are given in the following table. All mills, however, do not roll channels as light as the minimum weights here given, nor do the maximum weights here given correspond to the maximum weights as rolled by all mills. The weights in the table, however, represent closely the least and greatest weight of each size as rolled by any mill. Each size can usually be rolled of any weight between the limits given: 830 PROPORTIONING THE MATERIAL. TABLE 30. MAXIMUM AND MINIMUM WEIGHTS OF WROUGHT IRON CHANNELS. Size of Channel Minimum Weight, Maximum Weight, in Inches. Pounds per Foot. | Pounds per Foot. 5) 5.0 6.0 + 0.0 10.5 3) 5.7 14.0 6 rao 19.4 c 7 8.9 24.3 8 10.0 28.0 9 122 30.0 10 16.0 od. 12 20.0 93.9 13 29.9 60.3 15 02.0 69.0 1418. The maximum and minimum weights of the most common sizes of wrought-iron angles are given in the following tables. Each size can be rolled of any weight between the limits given: TABLE 31. MAXIMUM AND MINIMUM WEIGHTS OF WROUGHT-IRON ANGLES WITH EQUAL LEGS. Secret Minimum Minimum Maximum ; Thickness of | Weight, Pounds} Weight, Pounds pe Nae Metal in Inches. per Foot. per Foot. NED 7 2.4 4.8 24+ X AL he 2.6 6.0 DEUS Od _ 3.0 8.0 23 x 23 e 4.4 8.8 3x3 1 4.8 11.4 34 x 34 Jy 6.8 14.0 4x4 te 8.0 Los0 ox 5 2 12.0 32.8 Ga 0:04 x 544 < 1059 Xe see a (8.54 x 54+ 16.9 x 50.94); and that required by the 8-inch channels = = (9 x 54+14 x 50.94). The ratio of the former to the- latter is 8.54 x 54+ 16.9 x 50.94 1,322 _ | 1, 9 541A 50, O49 ee 0 eee By using 7-inch channels, therefore, 10 per cent. more of iron is required than by using 8-inch channels. ‘The latter will be used. 1423. For the top chord the section will be made up of two 8-inch channels, each weighing 10 pounds per foot, and a 12” x 4” cover plate, giving a total area of section of 9 square inches. For the end posts the section will be made up of a 12” x 3" cover plate and two 8-inch channels, each weighing 16 pounds per foot, giving a total sectional area of 4.5+ 16 xX 33, X 2=14.1 sq. in. Channels weigh- ing 15.82 pounds per foot would give sufficient section, but the 16-pound channels can usually be more readily obtained, and the difference between the two weights is not material. 1424. The zutermediate posts will be made of four angles connected in the form shown at Z, Fig. 303. By reference to Fig. 3 of Mechanical Drawing Plate, Title: PROPORTIONING THE MATERIAL. 837 Highway Bridge: Details I, it will be seen that the con- nected legs of the angles are separated } inch by the lattice bars. Therefore, if 34” x 2” angles are used, the width W of the section equals 33” + 4” + 34” = 74", and by formula 113, Art. 1408, the least radius of gyration of the Se ODIs 7 le ee 7. he Jeneth of the post is faetter 216 22/- by sformula, 125, Art.. 1410, the allowed live load unit stress is 8,750 — 50 x ad a= 2.750 1b. the dead load unit stress is 2,750 x 2= 5,500 Ib. There- fore, the section required for the intermediate post is 9,700 . 2,300 2-750 | 5,500 By formula 132, Art. 1415, the weight per foot of each one of the four angles necessary to make this section would be ae M a = 3.29 lb. But by reference to Table 32, = 0.00, 5. 101, of Art. 1418, it is seen that the lightest weight of 34” x 2” angles is 4 pounds per foot, and also that the thickness of metal for this weight is 4? inch, or slightly less than 4 inch. According to item (v7) of Art. 1412, the metal in a member must not be less than 4} inch thick. For } inch Q 1/7 _ thickness of metal the weight per foot of a 34 2” angle, ; 10 as computed, is (3.5+2)x4i-x com 4.6 lb. The actual weight, however, is 4.4 pounds per foot. The sectional area given by four 34” « 2” angles weighing 4.4 pounds to the foot is 4.4 x #3, Xk 4= 5.28 sq. in., which is somewhat in excess of the area required. By using 3” x 2” angles the radius of gyration would be .24 X 6.5 = 1.56 inches. The allowed live load unit stress 216 1.56 unit stress would be 1,830 x 2= 3,660 lb. The sectional area required for this size of angle would, therefore, be 9,700 . 2,300 1,830 ' 3,660 of the four 33” x 2” x i” angles. Four 3}’ xX 2” angles would be 8,750 — 50 x =,1,830 lb., and the dead load = 5.93 sq. in., which is more than the section 838 PROPORTIONING THE MATERIAL. could have been used, however, with slightly better economy. The 34” x 2” size of angles was used on account of showing the connections rather more plainly. 1425. The zntermediate lateral struts are proportioned according to items (/) and (7) of Arts. 1410 and 1412. By reference to item (7) it will be noticed that the lateral struts are not proportioned according to the stresses ob- tained for them, but are proportioned ‘‘to resist only the 1 Scale of forces 128000 lbs. 4 2 ‘* as 3 FIG. 305. resultant due to an assumed initial strain of 10,000 pounds per square inch upon all rods attaching to them.” For any strut, the resultant due to the assumed initial strain, or stress, may readily be found by simply drawing a force polygon for the joint at either end of the strut. The con- struction for finding the resultant of the assumed initial stress upon the rods attaching to the strut C C, is shown in Fig. 305. In the diagram of the upper lateral system, the strut C C, and the rods attaching to it are shown by full lines, while all other portions of the diagram are represented PROPORTIONING THE MATERIAL. 839 by dotted lines. Bow’s notation is used with reference to the strut and the attaching rods. The rods are round and 1 inch in diameter. (See Art. 1405.) The section of a round rod 1 inch in diameter is .785 sq. in., and, therefore, the amcunt of the initial strain assumed for each rod is 10,000 x .785 = 7,850 lb. This strain (stress) is evidently tension. Now, considering the forces acting upon joint C, the line 1-2 is drawn -parallel, and to any convenient scale is-made equal to the action of the assumed tension in C C,= 7,850 Ib.; 2-3 is drawn equal and parallel to the tension in CB, =7,850 lb. Then, as 1-2 and 2-3 are equal, 3-1 will be parallel to and represent the compressive stress in C C,, due to the initial stresses in C 4, and C C,; it scales 11,400 pounds. If the sectional area of C C, were less than that of C Z,, the line 7-2 would be shorter than the line 2-3, and a line drawn from 3 to 1 would not be parallel to C C,. In order that the closing line 3-1 may be parallel to C C,, in such a case, it will be necessary to introduce in the force polygon a line representing the difference between the longitudinal com- ‘ponents of the stresses in CC, and C B,, which is taken by the chord CC’. The resultant of the initial stresses in the rods C, / and C, C’ simply resists the resultant of those in C Band C C,, the chords not being required to act. By drawing the force polygon 3-4-1-3 for joint C,, the same amount of stress, 11,400 lb., is obtained for C C, as before, while the positions and directions of the arrow-heads in the two polygons indicate that the resultant stress in C C, is compression. 1426. The amount of the resultant stress in a strut can also be obtained by applying the following general Rule.—Divide the length of the strut by the length of the rod, and multiply the quotient by the assumed stress in the rod. The result will be the stress in the strut due to the in- atial stress in that one rod. The sum of the results thus obtained for all rods attaching to one end of the strut will be the total resultant for the strut. 840 PROPORTIONING THE MATERIAL. The lengths used should be the lengths between the points where the center lines of the lateral struts intersect the center lines of the chords. The resultant R of the assumed stress upon each rod, as given by the above rule, may be expressed by the equation Sats / ? Le AO (136.) in which S, is the assumed initial stress, 7. is the length of the rod on which the stress is assumed, and /, is the length of the strut for which the resultant is obtained. Thus, in the present case, the theoretical length of the strut CC, is 19 ft., and that of the rod CB, is 18? +19? = 26.17 ft. The amount of initial stress assumed for the rod is 7,850 lb.’ Hence, the resultant stress in therstrute 450 = 4,00. 40)... 11). Hence, the weight per foot required for each angle is ese a =".75 lb. Table 32, Art. 1418, gives 10,8 Ib. 842 PROPORTIONING THE MATERIAL. as the minimum weight per foot of 5” x 4” angles, giving for two angles a sectional area of 10.8 X 2 X 33; = 6.48 sq. in. Although the sectional area given by the minimum weight of two angles of this size is found to be considerably in excess of the area required for them, it has also been found to be less than the area required for angles of smaller size. Therefore, each intermediate lateral strut will be made up of two 5” x 4” angles, each weighing 10.8 pounds per foot. 1428. The Portal Bracing.—The design of the portal bracing is largely a matter of judgment; the investi- gation of the stresses which has been made will, however, be found a very helpful guide. In proportioning the material for this member the methods of engineers differ. The method here explained and followed will give very reliable results when a straight-line compression formula is used. It does not apply so well to curve formulas, but may be used without material error. Substantially the same results are obtained by other methods. The stresses at intervals of one foot along each flange of the portal are shown in Fig. 278, to which the student is referred. The stress at each point along the upper flange is somewhat greater than the corresponding stress in the horizontal portion of the lower flange. On account of the inclinations of the brackets the stresses as found along those members are greater than in the corresponding portions of the upper flange. But, as the horizontal portion of the lower flange extends to and connects with each end post, it probably relieves the stresses in the flanges of the brackets to a very considerable extent. To what extent it does so, it is, of course, impossible to say, but the actual conditions will undoubtedly be fully provided for if the upper flange be proportioned to resist its stresses as found, and the lower flange be given the same section as the upper flange. By reference to the figure it will be noticed that, where the depth of the portal is uniform, the stresses at the various points along the upper flange vary by a practically constant difference. Now, neglecting the fact that the stresses in PROPORTIONING THE MATERIAL. 843 the upper flange decrease at the left of c, by reason of the increased depth of the portal, and assuming that the stress atthe left-of 2 is uniform and equal to the stress at c = + 23,520 pounds, that portion of the upper flange which is in compression may be considered to be divided into a series of (seven) elementary struts of varying lengths. Designa- ting each elementary strut by the letter at its right extremity, the length of each elementary strut and the amount of stress borne by it are as follows: Strut c: Stress = + 23,520 —19,820=+ 3,700lb. Length = 3.5 ft. Strut d: Stress = + 19,820 — 16,180 = + 3,6901b. Length = 4.5 ft. Strut ¢: Stress = + 16,130 — 12,480 =+ 3,700lb. Length = 5.5 ft. Strut 7: Stress = + 12,480— 8,740=+ 3,6901b. Length = 6.5 ft. Strut g@: Stress=+ 8,740— 5,050=-+ 3,6901b. Length = 7.5 ft. Strut 4: Stress=-+ 5,050— 1,350=+4 3,7001lb. Length = 8.5 ft. Strut z: Stress=-+ 1,350 = + 1,350lb. Length = 9.5 ft. 23,520 The increment of the flange stress, or difference between the stresses at two adjacent points on the flange, is actually about 3,695 lb. The increment, or amount of stress borne by each elementary strut, as obtained above is, in each case, either 3,700 or 3,690 lb. This slight irregularity is due simply to the fact that each stress is written to the nearest ten pounds. As the amount of stress is the same upon each elementary strut (except strut z), therefore, in order to resist the same amount of total stress, the total area of section required for the seven elementary struts will be the same as the sectional area required for a single equivalent strut of the average length, assuming the radius of gyration to be the same. This will be the case when a straight-line compression formula is used, but it will be only approximate for a curve formula. The slight error due to the fact that the stress upon strut z is less than upon each of the other struts may be neglected; this small error in the length of the equivalent strut will be on the side of safety; that is, the equivalent strut will be slightly too long. The average length of the seven elementary struts is T. I1,—19 844 PROPORTIONING THE MATERIAL. sca a = 6.5 ft. = 78 in, = 7 "THE struts ssupponeued. one direction by the lattice bars, and, therefore, its radius of gyration in that direction (about an axis perpendicular to the plane of the lattice bars) need not be considered. The two flanges of the portal, connected by the lattice bars, form a section similar to that shown at ZL, Fig. 303, and its least radius of gyration is found by formula 113, Art. 1408. Using 33” x 24” angles, with the shorter legs back to back, separated 4” by the lattice bars, the dimen- sion W will equal 3§ + 4-+ 34 = 74 in., and the least radius of gyration will be ae x 7 Ds=1lv8 me Hence, the allewea 100 unit stress is 11,000 — 60 x = = 8,400 lb., and the sectional area required is a =(2.80vsqiin. tin! Tabless2sercrt 1418, the minimum weight per foot of a 34” x 24” angle is given at 4.8 lb. For the upper flange two of these angles will be used, giving a sectional area of 4.8 x 2 x i == BeOO sq. in. The lower flange and the flange of the bracket will be made the same. 1429. It will be noticed that in proportioning the material for the flanges, two stresses only have been used; namely, the greatest stress, which, with a straight bracket, asin the figure, occurs at a point opposite to where the bracket connects to the horizontal flange, and the least stress, which may be considered to occur at the center. For appearance, the portal brackets of a bridge are often curved and otherwise ornamented. In case of a curved bracket, the greatest stress in the upper flange will occur vertically opposite that point where a line drawn through the center of the upper flange becomes tangent to the curve of the bracket. 1430. Let us now determine whether the area of the section as obtained above is sufficient to resist the greatest PROPORTIONING THE MATERIAL. 845 tensile stress in compliance with item (/£), Art. 1399. By reference to Mechanical Drawing Plate, Title: Highway Bridge: Details II, it is found that 8” rivets are used. Ateach point where lattice bars connect, one rivet passes through each angle, and, therefore, according to item (4), two rivet holes 2” + 4” = 2?” in diameter must be deducted from the section. Table 32, Art. 1418, gives.} inch as the thickness of metal for the minimum weight (4.8 pounds per foot) of 34” x 24” angles. Hence, the section to be deducted for the two rivet holes is ? X + XK 2=.3875 sq. in., and the net section remaining is 2.88 — .388 = 2.50 sq. ienebyeitemy (2), OL Art. 1399, the tensile “stress ; per square inch allowed for lateral bracing is 15,000. There- fore, the net section remaining after deducting the rivet holes will bear an amount of stress equal to 2.5 x 15,000 = 37,500 lb., or more than the greatest tensile stress occur- ring in either flange of the portal. It is thus found that the section given by two 33” x 24” angles, each weighing 4.8 pounds per foot, fulfils the necessary conditions for either compression or tension in the flange of the portal. It is to be observed that, in proportioning the material for the flanges of the portal, the condition required by item (s), of Art. 1412, has not been fulfilled. Any por- tion of either flange of the portal is subject to alternate stresses of tension and compression, and, therefore, accord- ing to item (s), each stress should be increased by an amount equal to ;8, of the smaller stress. This condition, however, may be neglected, as is often done. 1431. The size of the lattice bars remains to be con- sidered. It is not customary to proportion the lattice bars according to the stresses; indeed, it is very seldom that the stresses are found for the lattice bars. Relying upon their judgment and experience, bridge engineers are usually able to decide upon proper dimensions for lattice bars without finding the stresses. In the present case, however, attention will be given to the stresses in proportioning the lattice bars. By the 846 PROPORTIONING THE MATERIAL. method explained in connection with Fig. 280, of Art. 1314, stress was found in a lattice bar on the assumption that the web stress due to the increment of the flange stress is borne entirely by the tensile lattice bar connecting at the given point on the flange. This assumption was made for convenience in finding the stress; the total amount of stress in the bars connecting at one point is the same, whether it be borne entirely by one bar or divided between the two bars, and it can always be correctly found in this manner, so long as both bars have the same inclination. In proportioning the material, how- ever, it is reasonable to assume that the total web stress due to the increment in the flange stress at any one point is re- sisted in equal parts by the two lattice bars connecting at the point, one bar being in tension and one bar in compres- sion. The strength of the lattice bars will be investigated on this assumption. ‘The increments in the flange stress, and hence the stresses in the lattice bars, are uniform where the depth of the portal is uniform. Where the depth of the portal increases, the stresses generally decrease, and may be neglected. 1432. Where the portal is of uniform depth, the web stress due to the increment of the chord stress at any point was found to be 5,230 lb. This total stress is assumed to be equally divided between the two lattice bars connecting at the point, tension in one bar and compression in the other. The tension bar will first be considered; its stress is ae = 2,620 lb. The size of the lattice bars will be taken at 2” x £”; it is to be determined whether the sectional area given by this size of bar will be sufficient to resist the stress. The sectional area of a lattice bar of this size is2 x += .5 sq. in., while the area to be deducted for the rivet hole is $X4=.19 sq. in., leaving for tension a net sectional area of .5 — .19=.31 sq. in. By item (2); Art) 1399) the amount of tensile stress which can be borne by this PROPORTIONING THE MATERIAL. 847 section is 15,000 x .31 = 4,650 lb., which is greater than the amount of tension (2,620 lb.) that it is required to bear. 1433. The compression bar will now be considered; its stress is 2,620 lb., the same as the tension bar. By refer- ence to Table of Moments of Inertia, it is found that+the value of the moment of inertia / of a rectangular section is given by the formula b a* j= qt (137.) in which @ is the width of the section, or dimension parallel to the axis, and dis the depth, or dimension perpendicular to the axis. By reference, also, to formula 72, of Art. 1241, it is found that for any section the moment of in- ertia /= A 7’, in which A is the area of the section and 7 is the radius of gyration. By equating these two values of / for a rectangular section, we get ba? Ar =AagCe (138.) But the area Ad = 0d; by dividing both terms of equation 138 by the area, we have for the square of the radius of gyration no on se (139.) ~ e By extracting the square root, a ; r= 3-764 — -289 a. (140.) In applying this formula, @ must always be the dimension perpendicular to the axis. If the strut is unsupported in either direction, as in the present case, the /eas¢ radius of gyration of the section must be obtained; in order to obtain the /east radius of gyration of a rectangular section, the least dimension must be taken for the value of d. In the present case, for the least radius of gyration, 848 PROPORTIONING THE MATERTAL, a= 4} and “7 = 289. % 2.25 = "0723 ine pec hecomt yr. 1a lattice bar is supported by its connection with each tension lattice bar, and, as each compression bar is riveted at its supports, each separate strut length of the bar partakes somewhat of the nature of a strut having fixed ends; there- fore, the clear distance between its connections may be taken as the column length of the compression bar. This dis- tance is about 6.36 inches. By formula 128, otf Art. 1410, the allowed ‘unit stress is 11,000 — 60 x ae = dat ete bes . 2,620 and the sectional area required for the bar is BOQ = 46 Sq: in., ora little: less than the aréa-olja 2 SOO Ib: PROPORTIONING THE MATERIAL. 853 Of these stresses it will be noticed that the dead load stress is always present in the chord; the other stresses are occa- sionally present or may be wholly absent. The compressive stress upon this panel of the chord pro- duced by the wind is equal to 15,300 pounds, and as this is greater than the dead load stress upon the same (13,900 pounds), compression will actually obtain, and, according to the second condition of item (/), (Art. 1399), this stress must be considered. A portion of this compressive stress equal to the dead load tensile stress, simply neutralizes the effect of the latter stress, so that the resultant, or net com- pressive stress, upon this panel of the chord is + 15,300 — 13,900 =+ 1,400 lb. By item (s), of Art. 1412, the mem- ber must be proportioned to resist each kind of stress, but each stress must be considered to be increased by eight- tenths of thesmallerstress. Inthiscase, 8, x 1,400 = 1,100 lb. which added to + 1,400 and — 5,100 gives + 2,500, and — 6,200, respectively, for the wind compressive and tensile stress. As 6,200 is less than oe vont aes the sectional area of the member need not be increased. The section will be made up of four 3” x 24” angles riveted in the form shown at Z, Fig. 303. 1439. By reference to the details of the connections shown in Mechanical Drawing Plate, Title: Highway Bridge: Details III, Fig. 1, it will be found that the section cut out by two rivet holes must be deducted from the section given by each angle. It will be noticed that the lines of rivets in the two legs of each angle are staggered; that is, the rivet spacing is so arranged that two rivets do not come opposite each other in the same angle. When this is done it is not uncommon to deduct but one rivet hole from each angle or piece, assuming that as the section of the same is reduced by but one rivet hole at any normal cross-section its strength is reduced only by the sameamount. But, unless the rivet spa- cing is exceedingly liberal, the section will be weakened by more than this amount, and it is a much better practice to S54 PROPORTIONING THE MATERIAL. deduct one rivet hole for each line of rivets through each piece. This practice will here be followed, and two rivet holes will be deducted from each angle. 1440. When a portion of the sectional area of a tension member is cut away by rivet holes, the remaining portion of the uninjured metal in the section, which is available to re- sist tensile stress, is called the net area or net section. The entire section, with no deduction of area for rivets, is called the gross area or gross section. As the rivet holes are thoroughly filled in driving the rivets, the gross area of a member is counted to resist compression, while the net area only is counted for tension. 1441. According to Table 32, Art. 1418, the mini- mum weight per foot of a 3” x 24" angle is 4.4 lb., and the thickness of metal for this weight is + inch. Assuming the metal in the angles used to be of this thickness, the sec- tional area to be deducted for eight rivet holes (two in each angle) is 2" «45-8175 /$q. 1n., = (See item (4 )eor rune 1399.) This area must be added to the area required by the stresses to give the gross area required for the section. Therefore, 3.94 1.5 =5.44 sq. in. is the gross sectional area required, making the weight per foot of each angle a x ae 4.5 lb. This weight is very little in-excess*of minimum weight of 3” x 24” angles (4.4 pounds), and, hence, the thickness of metal for this weight of 3” x 24” angle is so very slightly more than } inch that the area deducted for the rivet holes will be considered correct. If the weights per foot obtained for the angles were such that the thick- ness of metal would be materially more than the thickness assumed in deducting the rivet holes, it would be necessary to correct the areas deducted to correspond with the greater thickness, and this would again somewhat increase the weights of the angles. The amount of compressive stress to be resisted by the section is 1,400 + 1,100 = 2,500 lb. The dimension W of the section is 3+4+3= 63 in., and by formula 113, PROPORTIONING THE MATERIAL. 855 SY, Art. L408, the least radius of gyration of the section is ~ x Qeeenoein, AS? = [Role ehh in, by taking the unit stress for the wind load midway between the live and dead load unit stresses, it will equal 15,000 — 60 x 216 1.56 = 6,690 ib. The compressive stress upon this member 2,500 6,690 9 is thus found to require a sectional area of =e sq. in.; it is abundantly provided for. The specifications give no compression formula for wind stresses upon the chords, but in item (0) the compression formula for the allowed wind stress upon the posts gives a value substantially midway between the value given by the formula for the allowed live load stresses and the value given by the formula for the allowed dead load stresses. Hence, a formula may be used giving a corresponding value for the allowed wind stress upon the chord. 1442. fanel bc.—By combining the stress /7 with the wind stresses given by the stress sheet for the panel 0c of the lower chord, it is found that the various stresses which can come upon this member are as follows : Live load — 32,400 Ib. Dead load — 13,900 Ib. — 10,200 — 5,100 = — 15,300 Ib : c ] i ’ b] 1 b . Wind load 4 | 15.300 + 5,100 = +! 20,400 Ib. The net or resultant compressive wind stress in this panel of the chord is + 20,400 — 13,900 = + 6,500 Ib. As this is less than the tensile stress, both the tensile and compressive stresses must be increased by eight-tenths of this amount, or 48, X 6,500 = 5,200 1b. This makes the tensile wind stress W = — 15,300 — 5,200 = — 20,5001b. Asthisis numerically D+L 3,90 32,49 , greater than ee ae as capt 11,575, the sectional area must be recalculated by formula 141. The sectional area (A) required by the dead and live load stresses was 856 PROPORTIONING THE MATERIAL. found to equal 3.94 sq. in. (Art. 1403.) Therefore, the corrected area (formula 141) is | 20,500 > 9 © ? Sea rar Pr tare (1 Y 73,900 + 32,400 ) = 4.55 sq. in. The section will consist of four 34” x 2” angles riveted to- gether in the form shown at JZ, Fig. 303, or in the same general formas the member ad. As the required section is greater, the thickness of the metal will be somewhat greater than in the member ad. A thickness of 2” = .37’ will be tried. As the rivets are 2” in diameter, the area to be deducted for eight rivet holes (see item (/) of Art. 1399) is ? xX 2 X 8 = 2.25 sq. in., and the total gross area required is 4.55 + 2.25=6.8 sq. in. For this amount of sectional area made up of angles of this size, the thickness of metal is, quite closely, ie Sie 2) near enough to the thickness assumed (.37 in.) to consider the area deducted for the rivet holes to be correct. The weight per foot of each angle necessary to give this amount of section is ee x = mar iparevas The amount of compression which the section is to be proportioned to resist is 6,500 + 5,200 = 11,700 lb. The dimension W is equal to 3}4+4+34=7 in., and by for- mula 113, Art. 1408, the least radius of gyration of the = -_b2 10,, Whichas 6 section is = x 7=1.68in. Using the same compressive formula as for a0, the allowed unit stress is 15,000 — 60 x 216 : i e = /,290 lb. The sectional area requiredspyetucmcae 11,700 >" — 1.6 sq. in. F290 1.6 sq. in., which is less than the area given by the section. pressive wind stress is, therefore 1443. Center Panel c c'.—By combining the wind stress HT with the wind stresses given on the stress sheet for the PROPORTIONING THE MATERIAL. 857 center panel of the lower chord, the various stresses for that panel are found to be as follows: Live load — 48,600 Ib. Dead load — 20,800 lb. _ é — = — 20,400 : Meri fe ade y, 100 0,400 Ib ( +. 15,300 + 5,100 = + 20,400 Ib. The compressive wind stress is less than the dead load tensile stress. Hence, it can not neutralize the latter or produce a resultant compressive stress, and, according to the second condition of item (7), it need not be considered. But the tensile wind stress (W = 20,400, disregarding the sign) is greater than one-quarter of the combined live and | Dae .F20,8004-48;600 ae 4 = 4 —_=] 1,350), and, according to Art. 1435, the section must be recalcu- lated by formula 141. In Art. 1404, the sectional area A was found to equal 5.9 sq. in. Hence, the corrected ce iad ) ae th Si. 10; 20,800 + 48,600 dead load tensile stress ( Atos, St 5.9 (1+ 1444. As this member is not required to resist com- pressive stress, its section could be made up simply by two 44” x 11” bars, giving a sectional area of 6.19 square inches. But it is desired to illustrate another expedient often em- ployed when a tension member is required to resist a small amount of compressive stress also, namely, that of staying or latticing the chord bars together by bent lattice bars. The chord bars as thus latticed are shown in Mechanical Drawing Plate, Title: Highway Bridge: Details III, Fig. 3, from which the manner of latticing the bars will be readily understood. In order to avoid cutting out too much of the section of the chord bar, small size rivets are gener- ally used to rivet the lattice bars. In order to avoid injury to the metal in the chord bars, the rivet holes are drilled in them. When the rivet holes are drilled, it is necessary to deduct only the actual size of the rivet hole, which is drilled one-sixteenth of an inch larger in diameter than the undriven rivet. Inthe present case the rivets will be i in diameter, 858 PROPORTIONING THE MATERIAL. and the rivet hole in the bars will be drilled =,” in diameter. The thickness ¢ of the bars may be found by applying the following formula: Ss n(w— day’ Cizisse Be ray Dee fe nH in which S is the sectional area, z is the number of bars used, z is the width of one bar, and @ is the diameter of the rivet hole, or the sum of the diameters, if more than one rivet hole is to be deducted. If the value of ¢ is known, and the value of any other one quantity is unknown, that value may be readily found by substituting the known values in the equation. In the present case, if two bars 44” in width are used, by formula 143, the thickness required for each bar will be ¢ = ——_>—__ em —=:/8 In. *) The thickness 2 xX (4.5 — .56) used will be the nearest even sixteenth of an inch greater than this amount, or 43 of an inch; two bars 44” x 13" will be used. By substituting these dimensions in the first form given for formula 143, we have 2 = solving this equation it is found that the actual net sectional area S given by two bars of these dimensions is 6.4 sq. in. (4.5 —.56). By 1445. If a member of this form is required to resist compression also, the radius of gyration is found by formula 140, Art. 1433, d being always the width of one bar. This value will always be the /eas¢ radius of gyration of the section when y, the perpendiculars between the centers of the two bars, is greater than .4 d. The value of y is usually so much greater than .4 ad, how- ever, that it isseldom necessary to apply the preceding rule. As stated above, this member is not required to resist com- pression, and could as well be composed of two ordinary chord bars of such size as would give the required section, without being latticed; they are proportioned with lattice bars simply as an illustration. Lower chord members de- signed to resist compression as well as tension are often called stiffened lower chords. PROPORTIONING THE MATERIAL. 859 EXAMPLES FOR PRACTICE. 1. What is the least radius of gyration of the lower chord member cer Ans. 1.3 in. 2. What would be (a) the live load unit stress, and (4) the dead load unit stress allowed upon this member in compression ? (a) 3,350 Ib. Ans. } (2) 6,700 Ib. PROPORTIONING THE MATERIAL FOR FLOOR- ae BEAMS. 1446. The tensile unit stress allowed in proportioning the material for the bottom flanges of riveted floor-beams or cross girders is given in item (c), of Art. 1399. The bot- tom flanges of simple beams are in tension, while in canti- lever beams the upper flanges are the tension flanges. Item (c) applies to the ¢exszon flange. In almost all beams the tension flange is the bottom flange. The tension flange of a riveted beam must be proportioned in compliance with item (4), Art. 1399. To items (c) and (£), Art. 1399, and (wz), Art. 1412, the following must be added; those that have reference to plate girders being applicable to riveted floor-beams also: (w) ‘‘In beams and plate girders the compression flanges shall be made of same gvoss section as the tension flanges.”’ (x) ‘‘ Plate girders shall be proportioned upon the sup- position that the bending or chord strains are resisted entirely by the upper and lower flanges, and that the shear- ing or web strains are resisted entirely by the web-plate; no part of the web-plate shall be estimated as flange area. ‘‘The distance between centers of gravity of the flange areas will be considered as the effective depth of all girders.”’ (v) ‘‘The iron in the web-plates shall not be subjected to a shearing strain greater than 5,000 pounds per square inch, but no web-plates shall be less than three-eighths of _an inch in thickness.” (z) ‘‘ The webs of plate girders must be stiffened at inter- vals, about the depth of the girders, wherever the shearing T. JI,.—16 860 PROPOR TIONING "TPHECMAPERTIATL, strain per square inch exceeds the strain allowed by the following formula: 15,000 PR eRE: 1 3 900 where // = ratio of depth of web to its thickness.”’ Allowed shearing strain = (144.) 1447. By reference to the stress sheet, the maximum flange (designated in item (+) as ‘‘ bending or chord strain ”’) in the floor-beam of the example is found to be 53,700 Ib., requiring a net sectional area, item (c), Art. 1399, of 53,700 : 12,000 angles to be 2 of an inch in thickness, the amount of sec- tional area to be deducted from the gross section for two rivet holes (one in each angle) is 2x #x* 2=.56 sq. in. Therefore, the gross sectional area of the bottom flange must be equal to 4.48+ .56 = 5.04 sq. in., making the = 4.48 sq. in. Assuming the metal in the flange ' weight of each angle equal to os Se : = 6.4. 1b. / \iatwe 4" x 3" angles are used, the thickness of metal will be very closely ae ae (4+ 3) x 2 inch (.388) that the sectional area deducted for the rivet holes may be considered correct. The bottom or tension flange of the floor-beam will consist of two 4” x 3” angles, each weighing 8.4 pounds per foot; and in compliance with item (w), Art. 1446, the top or compression flange will be the same. =.36 in., which is so near to 2 of an 1448. The latter portion of item (7) specifies that no web-plate shall be less than three-eighths of an inch in thick- ness. If found to fulfil all other requirements, a web-plate 2 of an inch in thickness will be used. According to Art. 1321, the maximum vertical shear in each end of the floor-beam = #, = 20,600 pounds. Accord- ing to item (7) of Art. 1446, this shear must be resisted entirely by the web-plate, while in compliance with item (7) the iron in the web-plate must not be-subjected to a shearing PROPORTIONING THE MATERIAL. 861 stress greater than 5,000 pounds per square inch. The maximum shearing stress is a vertical stress of 20,600 pounds, and the sectional area given by a vertical section of the web-plate, after deducting the holes for the two lines of rivets connecting the flanges, is 22.5 x 2= 8.44 sq. in. The maximum shearing stress to which the metal in the 20,600 8.44 is well within the limit of 5,000 pounds per square inch fixed by item (v). A web-plate 2 of an inch in thickness will, therefore, be amply sufficient to resist the shear. According to item (z) the web of the floor-beam must be stiffened if the shearing stress per squate inch exceeds the stress allowed by formula 144, Art. 1446. In the pres- ent case, /7, the ratio of the depth of web to its thickness, web-plate is subjected is = 2,440 lb. per sq. in., which is equal to a es 64) cand /7* = 64. 644.096... There- fore, the allowed shearing stress per square inch is equal to 15,000 iba 3,000 the web-plate is subjected has been found to be equal to 2,440 pounds per square inch, which is well within the lhmit of 6,340 pounds per square inch fixed by the same formula. It is thus found that a web-plate 2 of an inch in thickness will fulfil all requirements of the specifications without stiffeners being used. But it is desired to illustrate the use of stiffeners, and, therefore, though not required on this beam, they will be used. lo mle «lt iby thi” emqet © Ge4 G FC St,~ ‘4 at ey + 1 ae bad eres heh VWOK Be # ff . Egat \ NP, ie Q Mwed AT. fant | ns ute Aw Xoo. \ Byrne fon. Betis. ‘4 hayes didn Sn Rae nS reed by Acie Coke Say cx 7 ; _ ol ws ae - i + -~ ee SHIPPING BILL. eee a cia ea) Sc rere gh ene ME een ae COMETACESING oe aoe $ oe Siete eet, OC. toc, St DeO Wee gee tga eae eee ae sonzeccnanoenam Roadway............ feet, clear width. PE ie Oe. S70 RM Oe ac im ME EL eel os ane eS tnvenneseneeence Sidewalks... feet, clear width. ‘VEL ERR» P08 2. SED nrne eee aarene ace nr o P ne Wes = | No. and Shippin No. Re- N f aoe pping Mark. Oe nee ees Material in Member. ae Length. Weight. ) : { 2-R| ( 1-Plate 12” « 34" | 2-228 O5.- 6,565. Canter Ge fae fo Ane Boats 1 2-L | ( 2-8” Chans. @ 16 lb. : . § 2-R| ( 1-Plate 12" x Y" 1-225" | 17° 8%" C. tok. eG 4 |Top Chords 1 2-L | ] 2-8” Chans. @ 11 |b. me | ( 18’ 03" C, oe s z \7-Plate 12" x 2 eee) | 18-896 Beto se Bey nerds ) 2-8” Chans. @ 11 Ib. | : : Aerts Posts 4-31%4" X 2" L’s @ 4.4 lb. Latticed 1-225" Py lg Ce to de, BB, 2 cer ad eae 4-314" KX 2%" L’s @ 4.8 lb. Latticed 20) SO ag Eee a 2 |Lateral Struts 2-5" x 4” L’s @ 10.8 lb. 20! Qe ¥ E. to’ E. eB 4 |Knee Braces 2-3' X 24%" L’s @ 4.4 lb. Aaa. beto DB: aa {1-Piate-G So ye 1D 104621; to-k. aay t |Shoe Strut (23/4 een Me io | oe ae aaa) > = 1-Plate 24" X 36" me a2 : FB 4 |Floor-Beams 4-4" X 3" L’s @ 8.4 lb. | = Sas - vine ae 8 |Beam Hangers 14%" X1\%", 1%" S. Ends with Check Nuts T-255 2 eee B. to E. iT f 8 |Hanger Pls. 6exX 3" 2-2" o 434° ©. to C. Ro) 4 |Separators Bt ee 2-2". |. @ 4%" C. to C. ab 4 |Lower Chords 4-3" x 214" L's @ 4.6 Ib. Latticed 2-255" 17 1133" C. to C. Be Fs 4 |Lower Chords 4-3%" x 2" L’s @ 5.8 lb. Latticed 2-255" 17 1133" C. to C. Roe 2 |Lower Chd. Bars 2 Bars 4%" X 18" Latticed 2-255 17 1133 C. to C. Pe 8 /Tie Bars 2 ae | 2-253. 25' Sie. Cato B=o 8 |Hip Vert. Rods Teer” 2-253" 18 253" B. to B. ee 8 |Counters hh" xX 7", 13%" S. Ends 1-128 20! 3'5 Batock:. eg 8 |Counters Va are re Ends, 934" Turnbuckle 1-233" Ea B. to E. a b, 4 !Lateral Rods (ee Cas Oe faa Yar ain ota | 1-158" 19 84" B. to E, ab, 4 |Lateral Rods 1%" QO, 1%’ S..Ends, ro’ Turnbuckle | 1-133 5.0 S Bint is OEE 6 |Lateral Rods On 2134" 8. Ends T-153" 19° 7%" B. to E. tee 6 |Lateral Rods rt "O, 1%'S. Ends, 93" Turnbuckle _I-1 33 5 0 - B.to E. BC, | 4 |Lateral Rods tO; Stee ends St. Nuts] 25’ 105" E. to E. Cs 2 |Lateral Rods Im, 13% 5. nde Si Nuts 26° 214" E. to E. a 4 |Chord Pins 234" 0, 115%" Grip R. Nuts | 1 238" E, to E. B, b, ¢ 12 Chord Pins 237° ©9037" Grip R. Nuts Pe be Om” E. to E. C 4 (Chord Pins 1X" Ox 9% Grip R. Nuts o 11%" E to E. Li 20 |Lateral Pins 134.4), 294 - Grip, OCdtters Os» Eto E. & 4 |Pin Washers For 1 oe Pin o 64" E. to E. LB 4 |Pin Washers For 23/" Pin o 2" E. to E. b 8 |Pin Washers For 234" Pin Crete: E. to E. b 8 |Pin Washers For 23/". Pin | ie ee K.. t07R:, Ginae femiang 7% 3 1A” ee ee L's /§ 2-253" | gae\ ne hOrualoes Drie “17%34' <. BB" * 13 swith Latecon, jo T-1t3" | wie Stand, 7°. x. 972 2 se L's | § 2-253" | ae {Roller Shoes UPL. 22714 See eeaohoe St. & Lat: con. |] 1-142 2 /|Nests Rollers Di, 174 x 14" | 2 |Bed-Plates Si wees ae TA ; | 2-— 1 bent Aen, Pis. er ee ae x 33% 1-176" | 12 |Anchor Bolts Ee O X to’ with Wedges 20 |Field Kivets 78" Cy 234" Wika oF | 20 |Field Rivets ree OF See U: a | Peso. [Field Rivets %" OX 2%’ U..4B3 50 |Field Rivets 5" Cox 176! U3 150 |Field Rivets 8" OX 1% Lear: : 32. »\Bolts 4% O X_I0 Te & 270 Spikes 6" Steel Wire 7 Nails 4%" Steel Wire Paint : F 160 |Erection Bolts %” O X2 & LE 40 |Erection Bolts 4%" O X1%" U. H. Pilot Nuts For 23¢" Pin Pilot Nuts For 134" Pin PROPORTIONING THE MATERIAL. 867 material. The material for each respective member is shown written along the member in the vzg/¢ half of the diagram of the truss and along each web member in the diagram of the lateral systems. It will be noticed that in this stress sheet the stresses are omitted from all members of the lateral systems except the diagonal members. ‘The effects of the lateral wind stresses upon the chords of the lateral systems are considered in connection with the live and dead load stresses in the chords of the truss; they are, therefore, sometimes written with the live and dead load stresses, but are much more commonly omitted. As the lateral struts are proportioned by the resultant of the initial stresses assumed upon the attaching rods, the wind stresses in those members need not be con- sidered, and are usually omitted from the stress sheet. The complete data for the bridge are written below the diagrams, asin the former stress sheet, with additional in- formation designating the kind of material used and the specifications by which the material is proportioned; also, the kind and dimensions of the material for the floor. Some- times, also, the location of the bridge and the name of the designer or builder are placed in the lower right-hand corner of the sheet. The stress sheet as thus completed is intended to convey all necessary information with reference to the general design of the superstructure of the bridge ; it may be taken as a basis for receiving or submitting proposals or making the contract for the construction of the same. Toa bridge engineer it gives nearly all the information relating to the superstructure that is necessary for making an estimate of the cost. It does not, however, give any information in regard to the details and connections, other than to desig- nate the specifications by which they are to be proportioned, which is sufficient for the purposes of an estimate. Some- times the stress sheet does not designate any general speci- fications, but is attached to, or accompanied by, a set of specifications drawn especially to suit the requirements of the structure for which the design is made. 868 PROPORTIONING THE MATERIAL. 1453. In making the complete stress sheet the student should follow the general arrangement shown in Fig. 306. The stress sheet should always show a side elevation of the truss anda half plan of each lateralsystem. Sometimes, for important structures, larger, stress sheets are made, upon which are also drawn end views, showing the portal bracing, and intermediate lateral sections, showing the intermediate sway bracing, floor-beams, and connections. In completing this stress sheet, write correctly, to one decimal place, the weight per foot of each rolled shape used, and write the sectional area of each entire section, using two decimal places, except in case of riveted tension members, for which write the zet sectional area, following it by thewet terse: so: The weights per foot of plates and of round, square, or flat rectangular bars are not usually written. When the different portions of a built member are connected by means of lattice bars, the word ‘‘latticed”’ should be written beneath the member. _ The thickness of the floor plank, the material of which it is composed, the number of lines, dimensions, and material of the joists, and the material and dimenSions of the wheel guard should be given on the stress sheet, and also all other important conditions or lata relating to the design. THE USE OF STEEL. 1454. The members of a bridge are proportioned in steel in the same general manner as when proportioned in wrought iron. The unit stresses and compression formu- las are somewhat different, but, otherwise, the process is. substantially the.same. The observations concerning the forms of tension members (Arts. 1399 to 1401), and the formulas for the relative dimensions of compression members and for the radii of eyration ofthe *direroat forms of sections (Arts. 1407, 1408, 1413, 1414, 1419, and following) apply to steel as well as to iron. Soft steel (Art. 1388) is probably the best and most | PROPORTIONING THE MATERIAL. 869 thoroughly reliable material for bridges. But medium steel is somewhat stronger than soft steel, and, being allowed higher unit stresses, is, therefore, more economi- cal. As medium steel is also quite reliable, it is the material commonly used for bridges at the present time. Specifications for the use of soft steel and medium steel “vary even more than those for iron. The use of high steel in bridges is not usually either specified or allowed. A few of the common and prominent features of the specifications for the use of structural steel will now be noticed. COOPER’S SPECIFICATIONS. 1455. In Cooper’s General Specifications for Highway Bridges, the use of soft steel and medium steel is based upon the practice specified for wrought iron. The speci- fications referring to the use of steel are brief, and are here quoted in full. They are as follows: ‘“Medium steel may be used for tension members, plate - girders, rolled beams, and top chord sections with an allow- ance of 20 per cent. increase above allowed working strains on wrought iron; and for all posts by use of the following formulas, in place of those given for wrought iron: P= 10,000 — 70 for live load strains. (146.) P= 20,000 — 140 4 for dead load strains. (147.) P= 16,000 — 103 for wind load strains. (148.) ‘*Provided, that, in addition to the previous details of construction (1. e., those given for wrought iron), all sheared edges of plates and angles be planed off to a depth of one- quarter of an inch. All punched holes be reamed to a diameter of inch larger, so as to remove all the sheared surface of the metal.”’ 870 PROPORTIONING THE MATERIAL. 1456. ‘‘No sharp or unfilleted re-entrant corners to be allowed.”’ 1457. ‘‘All rivets to be of steel.” 1458. ‘‘Any piece which has been partially heated or bent cold be afterwards fully annealed.” 1459. ‘‘Soft steel may be used under the same con- ditions as wrought iron for all rzveted work. ‘¢Provided, that any rivet hole punched, as in ordinary practice, will stand drifting to a diameter 25 per cent. greater than the original hole without cracking, either in the periphery of the hole or on the external edges of the piece, whether they be sheared or rolled.” 1460. It will be noticed that while by the above speci- fications. medium steel in tension members and in com- pression chord members is allowed unit stresses 20 per cent. greater than those allowed wrought iron, in posts it is quite otherwise. For short struts the unit stresses allowed - by the compression formulas for steel posts are greater than those allowed by the compression formulas for iron posts, while for long struts the formulas give less unit stresses for steel than for iron. The live and dead load unit stresses allowed by the post formulas for steel are greater than those allowed for iron when the strut length is less than 624 times its radius of gyration, but they are less than those allowed for iron when the strut length exceeds 624 radii. For the value given by the iron formula 8,750 — 04 becomes equal to the value given by the steel formula 10,000 — 0-4, when the quotient equals 62.5; and the V4 former value exceeds the latter when exceeds this amount. Many engineers consider this specification for medium steel to be unnecessarily severe. Most specifications allow greater unit stresses for soft steel than for wrought iron. PROPORTIONING THE MATERIAL. 871 EXAMPLES FOR PRACTICE. See stress sheet, Fig. 306. 1. If medium steel is used, what is the sectional area required fo1 the main tie bar Bc? Ans. 2.7 sq. in. 2. What size of bars will give the required area for this member ? 3. What is the sectional area required for the counter Cc’, if com- posed of medium steel ? Ans. 1.15 sq. in. 4. Of what should this member consist in order to have the required area ?_ 5. Using 8-inch channels of medium steel, what is (a) the live load unit stress and (4) the dead load unit stress allowed for the upper chord ? Ans. } (a) 8,760 lb. (6) 17,520 1b. 6. What is the sectional area required for the upper chord ? Ans. 6.74 sq. in. 7. What is (a) the live load unit stress and (4) the dead load unit stress allowed for the end post, using the same size of steel channels ? Ans, § (@) 8,815 Ib. ( (4) 6,630 Ib. 8. What is the sectional area required for the end post ? Ans. 16.78 sq. in. 9. What is (a) the live load unit stress and (4) the dead load unit stress allowed for the intermediate post, using 34" « 2" angles of medium steel ? rer § (a) 1,600 Ib. l (4) 8,200 Ib. 10. What sectional area is required for the intermediate post ? Ans. 6.78 sq. in. REMARKS. 1461. A comparison of the preceding results with the corresponding results as previously obtained for iron sec- tions will be found instructive. It will be noticed that the sectional areas obtained above for the tension member and for the upper chord are less than obtained for the corre- sponding members when proportioned in iron, while those obtained for the posts are greater than for the iron posts. This feature of these specifications is by many engineers considered to be inconsistent and objectionable. 1462. In designing bridges, according to Cooper’s specifications for medium steel, it is always advantageous to make the heights of truss somewhat lower than would 872 PROPORTIONING TAT Nira aa, ordinarily be used in designing by most other specifications. This statement applies to iron as well as to steel, though in a less degree. When designing a bridge having parallel chords, according to Cooper’s specifications for medium steel, a height of truss equal to about one-seventh the span will usually afford good economy. In the example for which the material has been propor- tioned in iron, if the height of truss had been taken as low as the required head-room would permit, say 15 ft., the sections of the top chord and end post would have been more nearly uniform. The sections required for the chords would be increased by reason of the increased chord stresses, while the sections of the posts would be diminished by reason of the diminished strut length. The dead load stresses in the lower chord would be increased, while the wind stresses would be somewhat diminished. THE FATIGUE OF METALS. 1463. What is ordinarily called the w/tzmate strength of a material is the greatest stress to which it can be subjected by a force applied gradually and for a moderate length of time ; it occurs at or just before rupture. Experiments, however, have shown that when forces below the ultimate strength are constantly or repeatedly apphed, they may finally pro- duce rupture; their effect) seems) to be to exhaust: the material, or to ¢zre zt out, so to speak; whence the name fatigue of metals is applied to this phenomenon. Later experiments have shown that the true cause of the phenom- enon lies in the imperfections and lack of homogeneity of the material. 1464. The following law was discovered by A. Woehler, after a series of experiments, and is known as Woehler’s law: Rupture may be caused not only by a force exceeding the ultimate strength, but by the repeated or prolonged action of forces below the ultimate strength. When these forces are alternately applied, the unit stress that finally causes rupture PROPORTIONING THE MATERIAL. 873 depends upon the range of stress, that ts, upon the difference between the alternately applied forces. As this difference tn- creases, thenumber of applications necessary to produce rupture becomes Less. Thus, wrought iron was found to fail after 800 applications of a tensile force of 52,000 pounds per square inch; also, after 409,000 applications of a tensile force of 39,600 pounds per square inch. With forces alternating between 22,000 and 48,400 pounds per square inch, the number of applications required for rupture was nearly 2,400,000; whereas, with a range between 26,400 and 48,400 pounds per square inch, 4,000,000 applications were made wrethout producing rupture. In the two cases last mentioned, although the higher limit of stress was the same (48,400), the effects were different, owing to the difference in the range, 48,400 — 26,400 being less than 48,400 — 22,000. In some cases rupture (by bend- ing) has been produced by the repeated application of a load of only two-fifths the breaking load calculated from the ul- timate strength; a bar that could stand a gradually applied load of 26,000 pounds broke under a load of 10,480 pounds after 5,200 applications. 1465. The preceding facts are of great importance in the design of such structures as bridges which are subjected to varying stresses, whether of the same or of opposite kinds; and it will be readily seen that the resistance of a member can not be accurately determined from considerations of ultimate strength only, but the phenomenon of fatigue must be taken into account. When a member is subjected alternately to stresses of the same kind (all tension or all compression), the allowed or working unit stress ? (pounds per square inch) 1s commonly taken as given by the following formula: Weal (1 ao When the alternating stresses are of different kinds, ) (150.) (149.) minimum. Stress maximum stress J maximum stress of smaller kind 2X maximum stress of greater kind paa(1— 874 PROPORTIONING PRE SMA eet. In both of these formulas @ is a constant depending on the material and on the kind of stress. The value of ais not necessarily the same for the two cases considered. Other and more accurate formulas have been constructed, but those here given are the ones required by some of the most modern specifications. 1466. Of specifications founded on the theory of the fatigue of metals, those of Mr. Edwin Thacher for highway bridges may be mentioned. In them formula 149 is used for tension members, with the following values for a: Values of a. Member. Wrought Soft Medium Iron. Steel. Steel. Chords, ties, counters, long sus- PENCers 5 iid ena: aed eee 9,400 10,800 | 11,700 Platéssandshapese. a eee 8,500 9,700 | 10,500 For members in which tension and compression alternate, formula 150 is used, with 9,400 for wrought iron, a 2 91 0 ROUstorisoltetvedh, 11,700 for medium steel. Other members are proportioned by ordinary formulas, which, although giving somewhat different values from those we have used, involve no new principles. EXAMPLE.—What are, according to Thacher’s specifications, the unit stress allowed for hip vertical # d (Fig. 306), and the required area (a) when the member is to be of wrought iron, and (4) when the member is to be of medium steel ? SOLUTION.—Since the hip vertical is a long suspender, formula 149 must be used, with the values of @ given above for tension members. By reference to Fig. 306, it is found that the minimum stress to which the member is subjected is 4,600 pounds (when the truss is unloaded), while the maximum stress = 16,200 + 4,600 = 20,800 Ib. (when the truss is loaded). These values in formula 149 give, calling the required PROPORTIONING THE MATERIAL. 875 area A, and remembering that required area = total stress + allowed unit stress : (a) P= 9,400(1 + eae = 11,480 Ib. = ae = 1.81) s8q.)in. (3) P =11,700 (1 + a a00) = 14,290 Ib. = we = 1.46 sq. in. SOME ITEMS FROM THACHER’S AND LEWIS’S SPECIFICATIONS. 1467. The requirements of the many specifications in existence are very different; but, if the student has mas- tered the general principles on which they are founded, and the general methods by which they are applied, he will ex- perience no difficulty in adapting his knowledge to the different requirements; the question is simply one of substituting different values for the constant quantities contained in a few general formulas. Some items not before mentioned are of importance, and they are here quoted from the specifications of E. Thacher, and those of F. H. Lewis. 1468. From Thacher’s Specifications for High- way Bridgés.—‘‘ Clearance. All through bridges shall have aclear height of not less than 14 feet.”’ 1469. ‘‘The width from c toc of trusses shall not be less than one-twentieth of the span from ¢ to ¢ of pins.”’ NotTe.—c stands for center. 1470. ‘‘ Flanges.—The compressed flanges (of girders) will be stayed transversely when their length is more than thirty times their width.” 1471. ‘‘ Weds.—One-sixth of the web will be considered as available area in each flange, except at web splices, where the full section will be provided by extending the flange ZL. lI,—17 876 PROPORTIONING THE MATERIAL. plates, or by the addition of separate cover plates. All joints will be spliced by a plate on each side of web.” 1472. ‘‘ Stiffencrs.—All web-plates shall be stiffened at the inner edges of end bearing, and at all points of local concentrated loadings. Intermediate stiffeners will be used if the shearing stress per square inch exceeds 12,000 + Le ; (1 + 3 aa) in which @=clear distance between flange angles or stiffening angles and ¢= thickness of web, both i ING ie sna 1473. Timber.—For beams, allowed fiber stress for yellow pine and white oak, 1,200 pounds per square inch; for white pine or hemlock, 900 pounds per square inch. 1474. For timber struts, the allowed unit stress shall be determined by the following formulas: Yellow Pine. White Pine. HSE ON CS. c.f cet er eae ees 1,075 — 112% 675 — Ver a a dB Nas gs b One fatand one pinienc a. 1,075 — 125, O75 — 100 — € (g Pin .endsie ss sles oes 1,075 — 138 675 — Oe e, \ = leneth ofanembelevayecs In which ; ; ; adie ( a= least dimension of member 7x zuches. 1475. The following are the allowed unit stresses for shearing and bending: Yellow Pine. White Pine. Shearing—Sliding on grain... 130 100 Bearing — Direction of grain.. 1,200 900 Perpendicular to AIT ate ogee ee 300 200 PROPORTIONING THE MATERIAL. 877 1476. From Lewis’s Specifications for Railroad Bridges.—‘“‘ Superstructure.—For spans of 16 feet or less, rolled beams will be used, and from 16 to 100 feet, riveted plate girders. _ All spans over 100 feet will be pin-connected LEUSSES, 1477. Material Used.—lit is required: ‘‘1, That all eye-bars and pins shall be of medium steel. ‘¢2. That all web-plates shall be of steel. ‘¢3. That loop rods and all other devices which are welded shall be of wrought iron. ‘‘These requirements are common to all bridges, whether built of wrought iron, soft steel, or medium steel. The other parts of bridges, however, may be built of such grades of material as the contractor may elect, provided only that each member and each set of members performing similar functions must be of the same grade of material throughout.”’ 1478. ‘Dead Load.—The dead load shall consist of the entire structure. The load of the structure when complete shall not exceed the dead load used in calculating the stresses.”’ 1479. ‘In through bridges, two-thirds (%) of the dead load shall be assumed as concentrated at the joints of the bot- tom chord, and one-third (4) at the joints of the upper chord.” 1480. ‘‘In deck bridges, two-thirds (%) of the dead load shall be assumed as concentrated at the joints of the upper chord, and one-third (4) at the joints of the bottom chord.” 1481. ‘Plate girders shall be proportioned upon the supposition that the bending or chord strains are resisted entirely by the upper and lower flanges, and that the shear- ing or web strains are resisted entirely by the web-plate.”’ 1482. ‘Stiff suspenders must be able to carry a com- pressive strength equal to six-tenths (,°,) the maximum tensile stress.” 1483. ‘‘Stiffened chords will be proportioned to take ry. compression equal to 60—, in which 7 is the maximum ten- Wh b] sion in pounds in the chord, and Z is the span in feet.” 878 PROPORTIONING THE MATERIAL. 1484. ‘‘Coeffictents of friction will be used as follows ; ‘“Wrourht ron oresteel Ontitsel ivan. tire 15 ’ Wrought iron-on steel cn castrirony vas. es 20 ‘COMirourht-ironior steel onvmasonry: enter 25 “Masontyeoneitsell. 7.00. neh oes 200% COMPARATIVE WEIGHT AND SPECIFIC GRAV- ITY OF WROUGHT IRON AND STEEL. 1485. The specific gravity, and, therefore, the weight of both wrought iron and steel, vary according to the purity of the metal, and also according to the density imparted to it by the process of rolling. As a rule, soft steel possesses somewhat higher specific gravity than high steel, while both are denser than iron. The following tables give fair average values of the spectfic gravity and weight of wrought tron and these two grades of steel; TABLE 34. ORDINARY SMALL ROLLED BARS. Weight per Weight per Material. pone Cubic Foot, Cubic Inch, lp Pounds. Pounds. SOLE soLee lemmas 7.86 |; 490.1 2836 Poh Steele meee, 7.83 488.2 2825 Wrougnte lone: scr 7.70 480.1 ie TABLE 35. LARGE ROLLED SECTIONS. : ; Weight per Weight per Material. eee Cubic Foot, Cubic: Inch, y Pounds. Pounds. SO fan leelin hoes er 7.84 489.0 .2830 Mighes teels yi. 7.80 486.6 .2816 Wirouchtelron, ea 7.67 478.3 2768 PROPORTIONING THE MATERIAL. 879 1486. As statedin Art. 1415, it is customary to esti- mate the weight of rolled iron at 480 pounds per cubic -foot, which is believed to be practically correct for the average material. No allowance is made for the slight decrease in the weight of large sections. Medium steel, having properties about midway between those of soft steel and high steel, will average about 2 per cent. heavier than iron. It is customary to estimate all grades of structural steel 2 per cent. heavier than iron. Upon this basis the following values are obtained for steel: By adding 2 per cent. to the value of w in formula 132, Art. 1415, the following value of JV, the weight per lineal foot of a bar of steel, is obtained: Wa A %1.02=34A. (151.) Similarly, A= us (L352) In both of the above formulas, 4 is the sectional area of a steel bar of any shape having a uniform cross-section, i. e., the sectional area of any rolled steel bar. EXAMPLE.—A bar of steel has a sectional area of .4418 of a square inch; what is its weight per foot ? SoLuTION.—By applying formula 151, the weight per foot is found to be .4418 k 3.4= 1.502 lb. Ans. NoTEe.—Some engineers prefer to estimate the weight of steel in the same manner as wrought iron and increase the result by 2 per cent. Thus, in the above example, the weight per foot of the bar, if of wrought iron, would be .4418 x = 1.473 1b., which, when increased by 2 per cent. equals 1.473 « 1.02 = 1.502 Ib., as above. EXAMPLE.—What is the sectional area given by two 6-inch channels, each weighing 8 lb. per foot, and a 10” « }" cover plate ? SoLuTIon.—The area given by the cover plate is 10” x #” = 2.50 sq. 8X2 3.4 Therefore, the total area given by the section equals 2.50 + 4.71 = 7.21 Sq.1ns) ANS. in. The area given by the two channels equals =q 4:71 sq. ih. 880 PROPORTIONING THE MATERIAL. 1487. The weight per foot of a round bar of steel may readily be obtained by applying the following convenient Rule.—Square the diameter of the bar, expressed in quarter aches, and divide by 6. This may also be expressed by the following formula: jigs - (153.) in which lV is the weight per foot of bar in pounds, and d is the diameter of the bar zz guarter inches. EXAMPLE.—What is the weight per foot of a round bar of steel 8 inch in diameter ? SoLuTION.—Expressing the diameter of the bar in quarter inches 9 0 and applying formula 153, the weight per foot is aS ia 1.50 lb. Ans. 6 ECCENTRICITY. POSITION OF PINS. BENDING STRESSES DUE TO WEIGHT OF MEMBER. 1488. The bending moment upon a member under direct compressive stress, due to the weight of the member itself, should always be taken into consideration in fixing the positions of the pins. Some specifications also require the unit stress allowed upon the member to be reduced by the amount of stress per square inch required to resist this bending moment; or, what amounts to the same thing, re- quire the sectional area to be correspondingly increased. Many engineers, however, consider this latter to be an un- necessary degree of refinement for highway bridges. But it is very essential that the pins be placed as nearly as practicable in their proper positions. 1489. Cooper's specifications contain the following: ‘Tf the fiber strain resulting from the weight only of any membereexceeds ten per cent, of thes allowed junit strain on -stichy=member, “such” excess "musts be, consideredmam proportioning the areas.” 1490. Zhe following are from Thacher’s specifications: ‘‘For top chords, the stresses per square inch due to PROPORTIONING THE MATERIAL. 881 weight of member will be deducted from the above unit stresses, the reduction for chords flat at one end being one-half, and for chords flat at both ends one-third the amount for members with pin ends. ‘‘Unsymmetrical sections, composed of two rolled or riveted channels and one plate, shall in chords be so pro- portioned that the centers of pins shall be in the same line and in the centers of gravity of sections. In web members eccentricity .may be made sufficient to counteract the bending stress due to weight of member under maximum load.” 1491. The following are from Lewts’s spectfications: ‘““The effect of the weights of horizontal or inclined members in reducing their strength as columns must be provided for. It will also be considered in fixing the positions of pin centers. ‘‘ All eccentricity of stress shall be avoided. Pin centers will be tin the center of gravity of the members, less the eccentricity required to provide for their own weight; and in continuous chords, pin centers must be in the same plane.”’ In these last specifications the conditions are very clearly stated, and the provisions there indicated will be quite fully noticed. Bending stresses in tension members, pro- duced by their own weight, are not usually provided for, as their only effect is to slightly increase the stress in the lower portion of the member. Furthermore, as the member deflects under its own weight, the bending stress becomes somewhat relieved by the deflection. But with a com- pression member the case is quite different. The bending moment produces eccentricity of stress; the effect of the bending stress combined with the direct stress is practically the same as that of an eccentric load upon a column, 1.e., it diminishes the efficiency of the member asa column. And this weakened condition is further augmented by the deflec- tion of the member due to its own weight. It is thus evident that the bending stress upon a compression member, due to 882 PROPORTIONING THE MATERIAL. its own weight, materially impairs its strength and should be provided for. 1492. The position of the center of gravity of a member is found by a process very similar to that explained in Art. 1373 for finding the center of gravity of a system of wheel loads. The position of a horizontal line passing through the center of gravity of a section may be readily found by applying the following Rule.—Wultiply the area (or weight) of each separate piece composing the section by the distance of its center of gravity from some given or assumed horizontal line, and divide the sum of the products by the sum of the arcas (or weights). The quotient will be the distance of the center of gravity of the entire section from the assumed line. Note.—The assumed horizontal line. from which distances are measured may be avy horizontal line, but should be preferably so situated that the center of gravity of each piece composing the section should be on the same side of the line. Thus, it is convenient to assume the line to pass through the center of the cover-plate, the top of the cover-plate, or the lower edge of the channels. All distances must be from the same line. EXAMPLE.—For the section of the upper chord given in Fig. 306 (see also Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. 1), find the distance of the center of gravity of the section below the tops of the channels. FIG. 307. SoLuTIoN.—The form of the section is shown in Fig. 307; the effective section is composed of two 8-inch channels weighing 10 pounds per foot and a 12” x 4” cover-plate. The sectional area of each channel is 19x ~,=3 sq. in., and that of the cover-plate is 12”x3?"=3 PROPORTIONING THE MATERIAL. 883 sq. in. If all distances be taken from a horizontal line through the center of the cover-plate, as xy in the figure, the distance of the center of gravity of the section from that line may be found by the following computation: Area Distance. Sc. CURT DIALE cain Ge sx tale tote 3.00 « 0.000 = 0.00 db vorgelarsfet ett Roper La Ae ene ee 6.00 * 4.125 = 24.75 9.00 24.75 24.75 Te Hence, Ga 5 2.75 in. is the distance of the center of gravity of the section below the horizontal line xy through center of cover-plate. As this line is 4+ inch above the tops of the channels, the center ot gravity of the section is 2.75 — 0.125 = 2.625 in. below the tops of the channeis. Ans. In sections similar to the above, the distance from the center of gravity of the section to the center of the chan- nels or vertical plates is called the eccentricity of the section. Thus, the eccentricity of the above section is = — 2.625 = 1.375 inches. Tf a pin-connected member were subjected to direct longt- tudinal stress (tension or compression) only, the pins should pass exactly through its center of gravity. But, as a horizontal or inclined member is always sub- jected to a bending stress due to its own weight, this con- dition never fully obtains. As noticed above, it is seldom necessary to provide for the bending stress in a tension member, due to its own weight, and, consequently, the centers of the pins are usually located at the center of gravity of the member. But in a compression member the effect of the bending stress should be considered in fixing the positions of the pins. 1493. Bending Moment on a Member Due to Its Own Weight.—Fig. 308 represents the entire upper chord, of which a section is shown in Fig. 307. The chord is shown in Mechanical Drawing Plates, Titles: High- way Bridge: Details I, and Highway Bridge: General Drawing. It will be noticed that in supporting its own 884 PROPORTIONING THE MATERIAL. weight the chord acts as a beam continuous over two sup- ports. For compressive stresses some specifications consider each end panel of the upper chord as having one flat and one pin end, and all intermediate panels as having flat ends. For direct bending, the end panels are considered as beams having one end fixed and the other simply supported; and all intermediate panels as beams fixed at both ends. Fic. 308. In a uniformly loaded beam having one or both ends fixed, the greatest bending moment occurs at the fixed end. Formulas for the maximum bending moments in such beams are given in the Table of Bending Moments. As, however, the compression members of bridges resist principally direct compressive stress as columns, and as columns do not com- monly fail at the ends, but near the center, the bending moments at the ends may beneglected. It will, therefore, be necessary to consider only the maximum values of those bending moments which occur along the central portion of the member. . Neglecting, then, the bending moments at the ends, the greatest bending moment 47, which can occur along the central portion of a uniformly loaded beam fixed at both ends will occur at the center; its amount is given by the formula (154.) 1494. The greatest bending moment J7, which can occur along the central portion of a uniformly loaded beam fixed at one end and simply supported at the other will occur at a distance of 2 /, from the free end; its amount is given by the formula 9m ll, Ae neoshe iss) PROPORTIONING THE MATERIAL. 885 1495. Ina uniformly loaded beam simply supported at both ends, the maximum bending moment J7 occurs at the center; its amount is given by the formula wll Ni Oo La 8 (156.) In all of the above formulas w is the load, or weight of member per unit of length, /, is the length of the beam or member, from center to center of supports or connections, and /, is the horizontal projection of Z,, which is usually simply the panel length. The unit of length must be the same for Z,as for w. It will be found most convenient to take w as the weight per foot of member and J/, as the length of member in feet. In order that the bending mo- ment shall be ininch-pounds, /, should be expressed in inches. 1496. If the member is horizontal, then the distance /, will equal the distance /,. Calling 7, = 7/7, =/, formula1 56 becomes ai 7 Ma, (157.) which is the same as formula 7 of the Table of Bending Moments. 1497. In applying any one of these formulas to obtain the bending moment in a built member, due to its own weight, the weight per foot, as estimated from the effective section, should be increased about 15 per cent. to provide for the weight of lattice bars, rivet heads, etc. EXAMPLE.—What is the bending moment in inch-pounds upon the end panel of the top chord designated in Fig. 306 and shown in Fig. 308 ? SoLuTION.—The sectional area of the chord has been found to be 9 square inches; hence, the weight per foot of the effective section is 9 x= 30 lb., and the total weight per foot about 30+ .15 x 30 = 34.5 lb. As this panel of the chord may be considered as a beam fixed at one end only, the bending moment is found by applying formula 155. In this case, w= 34.5, 7, =18, and 7, = 18 x 12; there- fore, the bending moment ox 54-01 x 1S OS 18 12 AL, = —. 138 = 9,431 in.-lb. Ans. 886 PROPORTIONING THE MATERIAL. This bending moment is positive, and tends to produce compression in the upper portion of the chord and tension in the lower portion. It does not actually produce tension in any portion of the chord, because the direct compression in the chord, being much greater than the bending stress, entirely overcomes the tension, sq that the effect of the bending stress is really to increase the compression in the upper portion of the chord and diminish it in the lower portion. 1498. The position of the pins may be so fixed that when the maximum direct compressive stress comes upon the chord, through the pins, it will produce an amount of bending moment equal to that produced by the weight of the member, but in the opposite direction (negative). This may be more clearly understood by reference to Fig. 309, which is a somewhat distorted representation, in Weight of Member a Center of Gravity ae Applied Force _\€;_ Applied ee Force Fic. 309. outline, of the end-panel member of a top chord, indicating in a general way the relative positions of the forces. The two opposite bending moments will then balance each other, and the resultant stress will be direct compres- sion uniformly distributed over the section. Inthe ordinary form of upper chord and end-post sections, this condition will be effected when the position of the pins is fixed at a distance e, perpendicularly below the center of gravity of the section given by the formula ee ae, SA in which ¢, is the distance in inches below the center of gravity of the section at which pins should be fixed, J/ is a (158.) PROPORTIONING THE MATERIAL. 887 the bending moment in inch-pounds due to the weight of the member, and S, is the total maximum direct compressive stress upon the member in pounds. 1499. In fixing the positions of the pins in compression members in which the center of gravity of the section lies above the center, the total eccentricity, as previously obtained, must be reduced by the amount ¢,, which may be considered as negative eccentricity. The eccen- tricity, as thus reduced, is often called the final, or net eccentricity. EXAMPLE.—At what distance below the center of gravity should the positions of the pins be fixed in the end panel of the upper chord, Figs. 306 and 308, in order that the stress be evenly distributed over the section ? SOLUTION.—The bending moment due to the weight of the member has been found to be 9,431 inch-pounds = JZ. By reference to Fig. 306, the total amount of direct compressive stress upon the member is known to be 48,600 + 20,800 = 69,400 lb. = S.. Therefore, by applying formula 158, é, or the distance below the center of gravity of the 9, 4¢ section at which the pins should be placed, is found to be Lach tee 69,400 186 in. Ans. EXAMPLE.—What is the net eccentricity of this section ? SOLUTION.—The total eccentricity of the section has been found to be 1.875 inches. ‘The eccentricity in the opposite direction due to the weight of the member, or the negative eccentricity, has been found to be .136 inch. Therefore, the net eccentricity is 1.3875 —.136= 1.24in. Ans. 1500. Increase of Section to Provide for Bend- ing Stress.—If in the above example the position of the pins be fixed at 1.24 inches, or practically 14 inches, above the center of the channels, the stress will presumably be dis- tributed uniformly over the section. But in proportioning ' the material for this member, provision was made only for the direct compressive stress, while it has been shown that the member must also resist a bending stress due to its own weight. Therefore, the sectional area of the member should be increased an amount corresponding to the amount of this bending stress. As previously stated, this, by many 888 PROPORTIONING THE MATERIAL. engineers, is considered an unnecessary degree of refine- ment in designing the members of highway bridges; but as some specifications require provision to be made for this condition, a method of determining the required increase of section will be explained. The method given below, though not in strict accord with some elaborate formulas which have been deduced for this purpose, is believed to give results sufficiently accurate for all practical purposes, and has the advantage of being very simple and easily applied. Formulas 72, Art, L241 ,and73, Art. Leas; civerie following values for the resisting moment, which must be equal to the bending moment: (159.) in which, as relating to the present case, J7 is the bending moment in inch-pounds, S may be the fiber stress per square inch or the assumed unit stress, A is the required or the assumed sectional area in square inches, 7 is the radius of gyration of the section in inches, and ¢ is the distance in inches from the neutral axis to the most remote fiber. In order to express the sectzonal arca required to resist the bending moment, formula 159 may be given the form Mc Am won (160.) By taking S to represent the allowed unit stress, and bearing in mind that the formula is applied after the general dimensions of the section are determined, it will be noticed that the values of all the quantities in the second term of formula 160 are known, and the value of A can be found by simply substituting these values. But some specifications require the fiber stress, produced by the bending moment, to be deducted from the allowed unit stress. To meet this requirement, a formula express- ing the amount of fiber stress per square inch may be derived from formula 159, as follows: Mc Pe ed Se (161.) PROPORTIONING THE MATERIAL. 889 As the bending stress due to the weight of the member is always very small as compared with the direct compres- sive stress upon the member, the value of A as determined from the latter will be sufficiently accurate to use in formula 161. As previously stated, the bending moment tends to in- crease the compression in the uwffer portion of the section; hence, the stress in the extreme upper fiber becomes the critical stress, and, in applying the above formulas, the value taken forc should be the distance from the neutral axis to this fiber, or, in other words, the distance from the center of gravity of the section to the upper side of the cover-plate. EXAMPLE.—Referring to the examples previously given in this article, what is the sectional area required to provide for the bending stress upon the end panel of the upper chord, Figs. 306 and 308 ? SoLuTION. —The bending moment due to the weight of the member has been found to be 9,481 in.-lb. = JZ. ‘The distance from the center of gravity of the section to the top of the channels has been found to be 2.625 inches; hence, the distance from the center of gravity to the top of the cover plate is 2.625+ .25=2.875 in. =c. The bending quently, for the value of S in formula 160, the dead load unit stress should be used. By reference to Art. 1422, the dead load unit stress used for this section is known to be 14,600 lb. = S, and the radius of gyration of the section is 3.2in.=7. Therefore, by applying formula 160, the sectional area required to resist the bending moment due to 9,431 « 2.875 the weight of the member is found to be 14,600 << 3.23 eee Eo 7? att Ans. EXAMPLE.—For the same, what is the amount of stress per square inch of section produced by the bending moment, assuming the stress to be uniformly distributed over the entire section ? SoLuTION.—The same values are substituted in formula 161 that were substituted in formula 160 in the preceding example, except that the area of the section, as obtained for the direct compressive stresses, is used instead of the unit stress. The area of the section is 9 square inches, and the stress per square inch required to resist the bending moment is found to be 9,431 x 2.875 9% 3.2? = 2941b. Ans. 890 PROPORTIONING DHE MATERIAL: 1501. In determining the final area of the section, the area required for the bending stress, as obtained by formula 160, may be added to the area required for the direct compressive stress; or, what amounts to the same thing, the stress per square inch required to resist the bend- ing moment, as determined by formula 161, may be deducted from the unit stress. The members of the bridge shown in Mechanical Drawing Plates, Titles: Highway Bridge: Details") IT sole Vein Highway Bridge: General Drawing, were proportioned according to Cooper’s specifications, which do not require that the bending stress upon a member due to its own weight shall be considered in proportioning the areas, unless it ‘‘ exceeds ten per cent. of the allowed unit strains on such member.” As the bending stress per square inch (294 lb.), determined above, does not exceed ten per cent. of the allowed dead load unit stress (.10 x 14,600 = 1,460 Ib.) it need not be considered in proportioning the area of the section. EXAMPLES FOR PRACTICE. 1. In the end post shown in Mechanical Drawing Plate, Title: Highway Bridge: Details I, what is the distance of the center of grav- ity of the section above the lower edge of the channels? Ans. 5.84 in. 2. What is the total eccentricity of this section ? Ans. 1.84 in. 3. What is the bending moment upon this member due to its own weight, adding 15 per cent. for weight of details? Ans. 37,170 in.-lb. 4. What is the ‘‘negative eccentricity,” or distance below the center of gravity, at which the pins should be fixed in order to coun- teract this bending moment ? Ans. .57 in. 5. What is the net eccentricity of the section ? PS sid ae 6. What is the sectional area required to resist the bending stress in the end post due to its own weight ? Ans. 1.39 sq. in: 7. What is the fiber stress per square inch due to the same, if considered to be uniformly distributed over the entire section ? Ans. 781 1b. 8. According to Cooper’s specifications, is it necessary to consider this fiber stress in proportioning the area of the section ? PROPORTIONING THE MATERIAL. 891 GENERAL REMARKS. 1502. The metal for the individual members of any truss bridge is proportioned in substantially the same man- ner as explained in the preceding articles for the example chosen to illustrate the process. Different specifications have somewhat different requirements, but the general methods of proportioning the material are much the same ‘for all. When the operations explained in the foregoing pages are thoroughly understood, no difficulty will be ex- perienced in proportioning the material for a metal bridge according to any specifications. 1503. The relative dimensions of the usual forms of chord sections are determined by formula 135, Art. 1420. Post sections composed of two channels latticed, or of plates and angles latticed in the same general form, should comply with formula 129, Art. L414. All mod- ern compression formulas for wrought iron or steel columns make use of the radius of gyration; and for the forms of section shown in Fig. 303, this quantity is determined ap- proximately, but near enough for most practical purposes, by formulas 110 to 118, Art. 1408. 1504. A tension member having a sectional area of more than about 3 square inches should consist of flat bars, which should always be placed in pairs. A wrought-iron tension member having a sectional area of less than about 2 square inches may consist of square or round bars, preferably the former. They should always be in pairs except when but one bar is used. A single bar used as a tension truss member should generally be a square bar. Round bars are commonly used for lateral rods. The thickness of flat bars used for tension members should always be between the limits of 4 and 4 of thetr width, and preferably between 4 and 1 of their width. The widths of flat bars should be multiples of a half inch; multiples of a quarter inch may be used, but are not desira- ble. The diameters of round bars and the sides of square I. II,—18 892 PROPORTIONING THE MATERIAL. bars should generally be multiples of $ of an inch, though dimensions of sixteenths of an inch may be used. 1505. In the selection of the material for metal bridges the following important considerations should be kept in mind: High steel ts not a suttable material to be used in bridges. Soft steel and medium steel are both superior to wrought tron for bridge purposes. For the riveted members of short span bridges, soft steel ts the best matertal. For all members of long span bridges, medium steel ts preferable, because it produces less dead load than soft steel or tron. lor forged eye-bars, medium steel ts the best matertal. Eye-bars forged of medium steel should afterwards be annealed. Medium steel ts the best material for pins. As steel 1s of nearly uniform strength tn all directions, it as the best matertal to be used for web-plates. All portions of the same built member should be of the same material, | Steel of a thickness greater than #, of an inch ts consider- ably injured by punching ; and, therefore, the use of greater thicknesses for riveted members should be avoided so far as possible. When greater thicknesses are used, the rivet holes should usually be punched Lof an inch smaller than required, and then reamed to the required diameter. Steel of a thick- ness greater than % of an inch should never be used without reaming. This refers to both soft and medium steel, but especially to the latter. 1506. In proportioning the material for the members of a bridge, as well as in the calculations of stresses, unneces- sary exactness is to be avoided, as involving unnecessary waste of time. For the sake of explicitness, many of the computations in this Course have been made unnecessarily exact. PROPORTIONING THE MATERIAL. 893 In general, it may be stated that unit stresses should be obtained correctly to the nearest ten pounds. Areas of sections should be computed and expressed to the nearest hundredths of a square inch, and the weights per foot of channels, angles, or other shape iron to the nearest tenths of a pound. 1507. The student will find it to his advantage to closely observe and study the design of such metal bridges as may be situated in his vicinity, or as may come under his observation; he will thereby obtain many practical and valuable ideas of design, as well as a general knowledge of the usual practice. In doing this, however, he must bear in mind that the ordinary highway bridge does not always represent the best engineering practice, although it usually embodies principles of economical design. Railroad bridges, though possibly of less bold and eco- nomical design, will be found generally to represent better and safer engineering practice than highway bridges. Although the amount and distribution of the applied loads are different in the two classes of bridges, the frzuczples to be applied are the same for both. DETAILS OF CONSTRUCTION. GENERAL REQUIREMENTS. 1508. Thus far in the study of Bridge Engineering, attention has been given solely to the general design. The designing of the details will now be considered. In America, metal bridges are manufactured at shops having special machinery and facilities for the purpose. Each individual member of a metal bridge, and some- times the entire bridge, if a small one, is manufactured complete at the shop. The various members of the struc- ture, as thus manufactured, are shipped to the bridge site, where they are placed in position and properly connected. 1509. Before a bridge is manufactured, the practical constructive details of each member and its connections must be designed, and drawings must be made showing all such details. These drawings are known as detail draw- ings. When the bridge is designed by a consulting bridge engineer, complete detail drawings are usually made before the contract is let. But quite commonly, however, the drawings of the details are left to be made by the contract- ing company after the letting of the contract, the condi- tions for the details being usually covered by specifications. The latter practice is generally the more economical, as it allows the contracting company to use their customary details and such as are best suited to their equipment. But in every such case the drawings for the details should be submitted to, examined, and approved by the consulting engineer before any actual work on the structure is begun. 1510: The drawings of the practical constructive details, from which the different portions of a bridge are For notice of copyright, see page immediately following the title page, 896 DETAILS OF CONSTRUCTION: manufactured in the shop, are called shop, or working drawings. Each member of the bridge is manufactured strictly according to the shop drawings; the workmen are not allowed to vary from the drawings in any respect. Therefore, the shop drawings must not only represent good, practical, and workmanlike details and connections, but they must also be explicit in every particular, and absolutely accurate. Upon the shop drawings all distances and dimensions are plainly marked in figures, and, although the drawings are usually made to scale and the scale is marked upon them, dimensions are never taken by scale from the drawings. The dimensions as marked in figures govern in all cases. Dimensions less than two feet are marked in inches and halves, quarters, eighths, sixteenths, thirty-seconds, and sixty-fourths of an inch, although the last two fractions are seldom used. Decimal fractions are never used in shop drawings. Dimensions greater than two feet are marked in feet and inches, using fractions of inches where necessary. Any inaccuracy in the shop drawings will almost certainly result in a misfit between some parts of the structure. If discovered in the shop, the error can usually be corrected without very great expense or delay, but if not discovered until during the process of erection, the error will usually cause a large amount cf both delay and expense. Hence, the necessity of absolute accuracy in shop drawings can not be too strongly emphasized. This statement is made espe- cially pertinent by the fact that shop drawings are often required to be made hurriedly, so that the liability to error is great. The shop drawings of the highway bridge of 90 feet span, the design of which has been chosen to illustrate the prin- ciples given in the preceding articles, are shown in Mechan- ical Drawing Plates, Titles: Highway Bridge: Details I, II, III, IV, and Highway Bridge: General Drawing. The manner in which the dimensions of the same are deter- mined will now be studied. DETAILS’ OF CONSTRUCTION. 897 SPECIFICATIONS. 1511. As the structure referred to above has, with slight variation, been designed according to Cooper’s Gen- eral Specifications for Highway Bridges, such portions of these specifications as relate to the proportioning of the details are quoted below: (a,) Shearing and Bearing on Rivets.—‘‘ The rivets and bolts connecting the parts of any member must be so spaced that the shearing strain per square inch shall not exceed 9,000 pounds, or ¢ of the allowed strain per square inch upon that member; nor the pressure upon the bearing surface per square inch of the projected semi-intrados (diameter Xx thickness of piece) of the rivet or bolt hole exceed 15,000 pounds, or one and a half times the allowed strain per square inch upon that member. In the case of field rivet- ing, the above limits of shearing strain and pressure shall be reduced one-third part. Rivets must not be used in direct tension.” (0,) Shearing, Bearing, and bending on Pins.—‘‘ Pins shall be so proportioned that the shearing strain shall not exceed 9,000 pounds per square inch; nor the crushing strain upon the projected area of the semi-intrados of any member [other than forged eye-bars, see item (/,)] connected to the pin be greater per square inch than 15,000 pounds, or one and a half times the allowed strain per square inch; nor the bending strain exceed 18,000 pounds per square inch when the centers of bearings of the strained members are taken as the points of application of the strains.” (c,) Strength and Character of Detatls.—‘‘ All the con- nections and details of the several parts of the structures shall be of such strength that, upon testing, ruptures shall occur in the body of the members rather than in any of their details or connections. ‘* Preference will be had for such details as shall be most accessible for inspection, cleaning, and painting; no closed sections will be allowed.” 898 DETAILS OF CONSTRUCTION: (d,) ‘‘ The pitch of rivets* in all classes of work shall never exceed 6 inches, or sixteen times the thinnest outside plate, nor be less than three diameters of the rivet.” ‘* The pitch of rivets at the ends of compression members shall not exceed four diameters of the rivets for a length equal to twice the width of the member.” ‘‘The rivets used shall generally be 8, #, and ¢ inch CiamMevery me (¢,) ‘‘The distance between edge of any piece and the center of a rivet hole must never be less than 14 inches, except for bars less than 24 inches wide; when practicable it shall be at least two diameters of the rivet.” (7:)- “Wherever possible;-allwrivetemmine: pe tac driven. No hand-driven rivets exceeding {-inch diameter will be allowed. Field riveting must be reduced to a mini- mum or entirely avoided where possible.”’ (g¢,) Joints and Splices.—‘‘ All joints in riveted-tension members must be fully and symmetrically spliced.” ‘‘In compression members, abutting joints with planed faces must be sufficiently spliced to maintain the parts accu- rately in contact against all tendencies to displacement.”’ ‘“The ends of all square-ended members shall be planed smooth, and exactly square to the center line of strain.” ‘‘In compression members, abutting joints with untooled faces must be fully spliced, as no reliance will be placed on such abutting joints. The abutting ends must, however, be dressed straight and true, so there will be no open joints.” ‘“The sections of compression chords shall be connected at the abutting ends by splices sufficient to hold them truly in position.” (Z,) ‘‘Web plates of all girders must be arranged so as not to project beyond the faces of the flange angles, nor on the top to be more than ;, inch below the face of these angles, at any point.” * By the pitch of rivets is understood the distance from center to center of rivets in a line of rivets. In a long line of rivets the pitch is usually uniform. DETATES Ol CONSERUGLION. 899 (z,) ‘‘In lattice girders, the web members must be double, and connect symmetrically to the web of the flanges.” (7,) ‘‘ The heads of eye-bars shall be so proportioned and made that the bars will preferably break in the body of the original bar rather than at any part of the head or neck. The form of the head and the mode of manufacture shall be subject to the approval of the engineer. The heads must be formed either by the process of upsetting and forging or by the process of upsetting, piling, and forging.”’ (4,) ‘‘ Zhe lower chord shall be packed as narrow as possible. ‘““ The pins shall be turned straight and smooth, and shall fit the pin holes within ;4, of an inch for pins less than 44 inches in diameter ; for pins of a larger diameter the clearance may be 3/5 inch.” (1) ‘‘ The diameter of the pin shall not be less than two- thirds the largest dimension of any tension member attached to it. The several members attaching to the pin shall be so packed as to produce the least bending moment upon the pin, and all vacant spaces must be filled with wrought-iron filling rings.” (7,) Upset Ends.—‘ All rods and hangers with screw ends shall be upset at the ends, so that the diameter at the bottom of the threads shall be ;4 inch larger than any part of the body of the bar. ‘‘ All threads must be of the United States standard, except at the ends of the pins.” (z,) ‘‘floor-beam hangers shall be so placed that they ‘can be readily examined at all times. When fitted with screw ends they shall be provided with check nuts. Pref erence will be given to hangers without screw ends. ‘¢ When bent loops are used, they must fit perfectly around the pin throughout its semi-circumference.”’ (0,) Batten Plates and Lattice Bars.—‘‘ The open sides of all compression members shall be stayed by batten plates at 900. DETAILS OF CONSTRUCTION. the ends and diagonal lattice work at intermediate points. The batten plates must be placed as near the ends as prac- ticable, and shall have a length of 14 times the width of the member. The size and spacing of the lattice bars shall be duly proportioned to the size of the member. They must not be less than 14 XS GH LOL, scene dae 5 to 6 inch channels. 13.2 NL CDAT ORS pee ee ees 7 to 8 inch channels. 2. ein Ch tOrwe eee eee 9 to.12 inch channels. 2b CCE ATICH LOle spencers 13 to 16 inch channels. a ap as ember el abs 8) phere Joa Way 17 to 20 inch channels. pee eee os Nal elas Heh Poppi Gneke 6 yar. 21 and upwards. ‘¢ They shall be inclined at an angle of not less than 60° to the axis of the*member. ‘The pitch of the latticing must not exceed the width of the channel plus nine inches.” (~,) Reinforcing Plates.—‘‘ Where necessary, pin holes shall be reinforced by plates, so the allowed pressure on the pins shall not be exceeded. These reinforcing plates must contain enough rivets to transfer their proportion of the bearing pressure, and at least one plate on each side shall extend” not, less than six inches; beyond the edceromenrc batten plate.” (7,) forked tEnds.—‘‘ Where the ends of compression members are forked to connect to the pins, the aggregate compressive strength of these forked ends must equal the compressive strength of the body of the members ; in order to insure this result the aggregate sectional area of the forked ends, at any point between the inside edge of the pin hole, and six inches beyond the edge of the batten plate, shall be about double that of the body of the member.” (7,) ‘‘ Lhe attachment of the lateral system to the chords shall be thoroughly efficient. If connected to suspended floor-beams, the latter shall be stayed against all motion.” (s,) Portal Bracing and Transverse Diagonal Bracing.— ‘All through bridges with top lateral bracing shall have DETAILS OF CONSTRUCTION. 901 wrought-iron latticed portals, of approved design, at each end of the span, connected rigidly to the end posts. They shall be as deep as the specified head-room will allow. Knee braces shall also be placed at each intermediate panel point, and connected to the vertical posts and top lateral struts, for trusses 20 feet and less in depth. ‘“When the height of the trusses exceeds 20 feet, an ap- proved system of overhead diagonal bracings shall be at- tached to each post at an elevation sufficient to give the required head-room, and to the top lateral struts.” (¢,) Expansion Rollers.—‘* All bridges over 75 feet span shall have at one end nests of turned friction rollers, formed of wrought iron or steel, running between planed surfaces. The rollers shall not be less than 2 inches diameter, and shall be so proportioned that the pressure per lineal inch of rollers shall not exceed the product of the square root of the diameter of the roller in inches multiplied by 500 pounds (500 /d@). ‘‘ Bridges less than 75 feet span shall be secured at one end to the masonry, and the other end shall be free to move upon planed surfaces.”’ (w,) Anchors.—‘* While the roller ends of all trusses must be free to move longitudinally under changes of tempera- ture, they shall be anchored against lifting or moving sideways. ‘* Variations in temperature, to the extent of 150 degrees (Fahrenheit) shall be provided for.”’ (v,) Led-Plates.—‘ All the bed-plates and bearings under fixed and movable ends must be fox-bolted to the masonry; for trusses, these bolts must not be less than 14 inches diam- eter; for plate and other girders, not lessthan ¢ inch diam- eter. The contractor must furnish all bolts, drill all holes, and set bolts to place with sulphur. ‘* All bed-plates must be of such dimensions that the greatest pressure upon the masonry shall not exceed 250 Ib. per square inch.” 902 DETAILS OF CONSTRUCTION, (w,) ‘All bolts must be of neat lengths, and shall have a washer under the heads, and nuts where in contact with wood.”’ (x,) Camber.—‘ All bridges with parallel chords shall be givena camber by making the panel lengths of the top chord longer than those of the bottom chord, in the proportion of 73; of an inch to every 10 feet.” 1512. In connection with the above items quoted from the specifications, the following important conditions will also be noticed: I. In chatn-riveting, the distance between the center lines of adjacent rows should preferably not be less than three diameters of the rivet, and in no case less than two and one-half diameters. Il. In zigzag, or staggered, riveting, the distance between the center lines of adjacent rows should preferably not be less than two and one-half diameters, and never less than two diameters. Ill. The distance from the center of the rivet hole to the edge of the plate (which should generally not be less than I+ anches) should in no case be less than one and one-half times the diameter of the hole for steel, nor less than one and five- erghths times the diameter of the hole for tron. Tf less than this, allowance must be made for the reduced strength of the joint. LV. The distance from the center of a rivet hole to the end of a wrought-iron plate (which should generally not be less than 14 inches) should in no case be less than one-half the diameter of the hole plus the thickness of the plate plus one-half anch. V. The grip of arivet, 2. ¢., tts length between heads when driven, should never exceed four times its diameter. VI. Countersunk rivets should not be used in plates of less thickness than one-half the diameter of the rivet. VIT. The heads of steel eye-bars should not be made thicker than the body of the bar. DETAILS OF CONSTRUCTION. 903 1513. It will be expedient to explain here the respect- ive conditions distinguished by the terms szxgle shear and double shear, as applied to rivets. See Mechanical Drawing Plate, Title: Riveted Joints. It will be noticed that if the joint shown in Fig. 2, 3, or 4 should fail by shearing of the rivets, it would be necessary that each rivet should be sheared off but once; i. e., ‘cut once in two.” A rivet in this condition is said to be in singleshear. But in the joint shown in Fig. 5d or 6, it will be noticed that if the joint fails purely by shearing of the rivets, each rivet which fails must be sheared off twice; it must be sheared off between each two adjacent plates. The same would be true of the rivets in the joints shown in Figs. 7 and 8 when completed, and of those in the joint shown in Fig. 9. Rivets in such condition are said to be in double shear. It is evident that a rivet can not be in double shear unless it passes through more than two thicknesses of metal. Rule.—Rivets in double shear are allowed double the amount of shearing stress allowed upon the same size of rivets in single shear. CAMBER. 1514. As actually constructed, the so-called horizontal chords of bridges are not made perfectly straight from end to end, but are curved slightly upwards, in order that when the truss is heavily loaded the chord will not be deflected below a horizontal line connecting its ends, which would give it the unpleasing appearance of sagging. This slight curve or crown given to the chords is called camber. In making the working drawings for a bridge, the first things to be determined are the amount of camber and the exact lengths of the members. , The camber of a truss is shown in an exaggerated manner in Fig. 310. It will be noticed that each panel of the lower chord is the chord of the arc of a circle, and that each panel of the upper chord is the chord of the arc of a somewhat larger circle having the same center. It is from this fact that the upper and lower longitudinal members of a truss 904 DETAILS OF CONSTRUCTION. derive the name of chords: It will also be noticed that the vertical members are not truly vertical, but coincide with radii of the circle. FIG. 310. 1515. What is spoken of as the amount of camber is the elevation of the center of the chord above its ends, i..e., the middle ordinate of the total arc, or the versed sine of the angle of one-half the arc. The amount of camber given to a bridge truss is usually from 1 to 2 inches for each 100 feet length of span; that is, from 7545 to z+, of the span, although it may be more or less than these limits. 1516. Inthrough bridges the camber is always obtained by increasing the length of the upper chord, the length of the lower chord remaining unaltered. The span length is practically unaffected by the camber; the slight curvature affects the length of the chord to such:a very small extent that it may be wholly neglected. In changing the form of the truss, the values of the stresses are also changed, but this change is very small and is entirely neglected. The amount z, which the length of each panel of the up- per chord is to be increased in order to give the required DETAILS OF CONSTRUCTION. 905 amount of camber, is given approximately, but sufficiently close for all practical purposes, by the formula ~=8er t= —_, NS (162.) in which ¢ is the amount of camber in inches, / is the height of truss in feet, s is the length of span in feet, and z is the number of panels in the truss. The value obtained for z is fi MIO ES 55 hc The definite amount of increase to be given to the upper chord, however, is commonly specified. In such cases the amount of camber may be obtained by substituting the value of zin formula 162, and solving for c. 1517. According to item (7,) of Art. L511, the panel lengths of the top chord must be increased ,°, of an inch for each ten feet of length. In complying with this specifica- tion, some latitude must be taken in nearly every case, in order to avoid unusual and inconvenient fractions. For in- stance, in the truss of the example the panel length is 18 feet, and if the upper chord be increased 53, of an inch for each ; 3 18; 27 10 feet, the increase in each panel would be 18. 10> BO of an inch, which would be an inconvenient fraction to use. Increasing the panel length of the upper chord by 2 of an inch will be sufficiently close to the requirement of the specifications. EXACT LENGTH OF DIAGONAL MEMBERS. 1518. By increasing the panel length of the upper chord, the lengths of all diagonal members also are increased ; this is shown in asomewhat exaggerated manner in Fig. 311. It will be noticed that the horizontal projection of each diag- onal member is increased by one-half the panel increase of the upper chord. Hence, the length d from center to center of the diagonal is given by the formula piae Vrs (+4). (163.) 906 DETAILS OF, CONSTRUCAION: in which / is the height of the truss, f is the panel length, and zis the increase in a panel length of the upper chord, all in feet or all in inches. In applying the preceding formula, the operations may be somewhat facilitated by the use of logarithms, and still more by the use of a good table of squares. _Buchanan’s tables, giving the squares in feet for every foot, inch, and sixteenth Lefober Sn eee ryt eee ge FIG. 311. of an inch between one-sixteenth of an inch and fifty feet, are especially adapted to finding the lengths of truss diag- onals. In applying the formula without the aid of tables, it is usually expeditious to reduce all values to inches, or, in some cases, to convenient fractions of an inch. EXAMPLE.—In the truss shown in Mechanical Drawing Plates, Titles: Highway Bridge: Details I, H, III, IV, and Highway Bridge: General Drawing, the height of truss and panel length are each 18 feet, while the length of each panel of the upper chord is increased 2 of an inch for camber. What is the length of the diagonal, center to center ? a wise in. «Che panel length is the same. The panel increase 7 in the upper chord is : 3,459 - 16 ; Formula 163 gives the center to center length of the diagonal = 3,456? 8,459? 4,889.64 in. — 25’ 5 Te ag tee ie SoLuTion.—The height of truss is 18 ft. = 216 in. = : z ‘ : Zz g of an inch, and 5 = 7 in.; hence, the expression +> = ~ a " , very Closely. Ans. 9 2 DETAILS OF CONSTRUCTION. ~ 907 1519. The length of the diagonal, from center to cen- ter of fzus, will be taken at 25’ 542”, but in giving the length from center to center of pzz holes, allowance must be made for the clearance of pins. “ (See item (#,) of -Art. 1511.) For this purpose the clearance of each pin may be taken at sz of an inch. If the actual clearance is ;4 of an inch the error will not be of consequence. It is evident that when a member is under stress, the center of neither pin upon which it connects will coincide with the center of the pin hole, but one side of the pin will be in contact with the pin hole, while the op- posite side will be sepa- rated the full amount of the clearance. ‘This is clearly shown in Fig. pie. lf the clearance is zis of an inch, the center Sf the pin will be at a —— > distance of 4X ay = 7, of an inch from the cen- ter of the pin hole. Ir FIG. 312. connected upon a ot ae each end, this tends to make a com- pression member ,*; = 3'y of an inch too short, and a tension member the same mrtitat too long. Rule.—lor all members connecting upon a pin at each end, the distance between centers of pin holes should be made 35 of an inch longer in a compression member, and in a tension member 5 of an inch shortcr, than tts calculated length. In pin-connected structures this applies to all diagonal and lower chord members, but not to upper chord members or vertical posts unless pin-connected at both ends. In the preceding example, therefore, the length of the end post, center to’center of pin holes, is 25’ 542” + 1,” = 25’ 58’: and the length of the ties, center to center of pin holes, is 25' 543" — Ay" = 25' 5,". Thelengthofa res chord mem- ber, center to’center of pin holes, is 18’ 0’ — +,” = 17' 1144". T. U1,—19 905 DETAILS OF CONSTRUCTION. COMPRESSION MEMBERS. POSITIONS OF PINS IN CHORDS AND END POSTS. , 1520. The next step in designing the details will be to fix the positions of the pins in the upper chord and end posts. As explained in Arts. 1498 and 1499, the eccen- tricity of the pins—that is, the distance of the centers of the pins from the centers of the channels—in a chord member or end post should be the same as the net eccentricity of the member. But it is evident that the pins should have the same relative positions throughout the chord and end posts. In the solutions explained in Art. 1499, the net eccentric- ity of the end panel of the upper chord was found to be 1.24 inches; hence, the proper positions of the pins in this mem- ber would be at that distance above the centers of the channels. But in solving Example 5 of Art. 1501, the net eccentricity of the end post was found to be .77 of an inch, at which distance above the centers of the channels are the _proper positions of the pins in the end posts. 1521. ln order to develop the full strength of a com- pression member, tt must be so connected that its resultant maximum stress will be distributed uniformly over its section. In properly designed bridges, therefore, the net eccen- tricity should be made the same throughout the entire upper chord and end posts. Had the chords and end posts of the example been properly designed, the weights of the channels in the upper chord would have been increased until the net eccentricity of this member became the same as in the end post. This would increase the sectional area of a member already having an excess of section, to which considerations of economy would offer some objection. The net eccentricity of the end post could have been made the same as the net eccentricity of the end panel of the upper chord without loss of economy, but the net eccentricity of the chord is too great to allow practical and consistent details. DETAILS OF CONSTRUCTION. 909 In making general designs of highway bridges, it is frequently the case that the time available is not sufficient for determining sections having exactly the same net eccen- tricity. Consequently, conditions of eccentricity are often but loosely considered, and in many cases wholly neglected. In other cases, where time is limited, the designer depends upon his judgment to select sections having nearly the same eccentricity. If he is an experienced designer, he may be able to obtain reasonably approximate results; to do this is, at least, better practice than to neglect the eccentricity entirely. In the example, the top chord and end post sections have been proportioned to illustrate a case of this kind. 1522. The designer of details is seldom the maker of the general design. The detailer must take the general design as it comes to him (in which, it is safe to say, the conditions of ideal perfection are seldom realized), and must from it evolve the best, and, at the same time, the most economical, structure possible. He must meet as best he can the conditions as he finds them. In a case similar to the example, having found that the net eccentricities of the chord and end post are not the same, the best thing to do is to make the eccentricity of the pins in those members a reasonable average between the net eccentricity of the end posts and the connecting or end _panels of the upper chord, and agreeing rather more nearly with the eccentricity of the end post. In the example, the net eccentricity of the end posts has been found to be .77 in., and the eccentricity of the end panels of the upper chord 1.24 inches. Hence, in this case, the pins in the top chord jeep eey a ») i and end post are given an eccentricity of 1 inch. An eccentricity of 13 of an inch would, perhaps, have been as good or even better. The positions of the pins, with reference to eccentricity, in the intermediate panels of the chord are not of great importance, unless the chord stresses are transmitted 910 DETAILS OF CONSTRUCTION. through the pins, which is not usually the case. The pins are always given the same eccentricity throughout the upper chord. GENERAL DIMENSIONS OF THE UPPER CHORD AND END POST. 1523. Sections of the channels used in the chords and end posts are shown in Fig. 79 of Mechanical Drawing. As there shown, the width of the flange in the 10-pound chan- nel (top chord) is 2;4 inches, while the width of the flange in the 16-pound channel (end post) is 2% inches. The latter channel has the wider flange, and as in the built member the flanges of the channels must not project beyond the edges of the cover-plate, the width of this flange will determine the distance between the channels of the end post, back to back. As two channels attach to the cover- plate, the distance back to back of the channels must not exceed 12 — 2 X 2,5, = 7#inches. Inmost cases it is best to allow each edge of the cover-plate to project about 54 of an inch beyond the flanges of the channels; but in the present case, as the channels of the end post, being much heavier than those of the upper chord, have flanges considerably wider than the channels of the upper chord, the flanges of the former channels are placed flush with the edges of the cover-plate. Hence, in the end-post the distance between channels, back to back, is made 72 inches. By. ‘reference’'to Pig. “17 -of “Mechanical” Drawing Viate, Title: Highway Bridge: Details I, it is noticed that on the end post the reinforcing pin plates for the hip joint & are placed inside the channels, and, in order to grasp the pin, extend beyond the channels of thesupper’ chord: in owe: that there shall be ;, of an inch clearance upon each side between these pin plates of the end post and the channels of the upper chord; the distance between the ‘latter, back to back, must be 7%-+ 2x ~,= 74 inches. As the pin plates must clear countersunk rivets, it would have been as well or better to have given 4 of an inch clearance on each side, but it would have produced greater bending DETAILS OF CONSTRUCTION. $11 moment upon the pin. The width, out to out, of the flanges of the channels in the upper chord must not be greater Hianeerne swidtieofithe cover- plated -¢. 1 2cinches, “The width, out to out, of the flanges of the channels is found to be 74+ 2 X 2, = 11% inches, which is less than the width of the cover-plate. Sections of the top chord and end post are shown in Figs. 1 and 2 of the Mechanical . Drawing plate referred to above. ‘ CLEARANCE. 1524. It is very important that members which are to be connected in the field should have sufficient clearance, so that no difficulty will be experienced in making the con- nections. In this the designer must be governed largely by his judgment and the conditions of each individual case, but the following general rules indicate good practice, and will serve as a useful general guide: I. In arranging the several members upon a pin, pg of an wnch clearance should always be allowed between the connect- ing parts of adjacent members, tf eye-bar heads, forged loops, or perfectly smooth plates of a single thickness. IT, If the connecting portion of etther member consists of several thicknesses of perfectly smooth plates, from +5 to +5 of an inch additional clearance should be allowed for each additional plate. Ill. If there are countersunk rivets in the connecting por- tion of either member, not less than} of an inch clearance should be allowed, the countersunk heads being also chipped. IV. If there are countersunk rivets in the connecting por- tions of both members, the countersunk heads being chipped, not less than =, of an inch clearance should be allowed. V. Lf the connecting portion of either member contains rivets with flattened heads or full heads, 4 of an inch clear- ance above the head should be allowed. VI. If the heads of countersunk rivets are not chipped, they should be considered as flattened to 4 of an inch, in estt- mating the clearance. 912 DETAILS OF CONSTRUCTION. The clearance allowed between the connecting parts of members should always be ample; it should in no case be so scant as to cause squeezing or as to permit the possibility of the members not coming properly together. The pre- ceding rules apply to each clearance between the adjacent sides of members. SIZES OF PINS. 1525. The stresses in the different members connect- ing upon a pin produce bending moment in the pin, the amount of which may be determined either by computation or by constructing the moment diagrams. According to itém ‘(b-) of Art TS 01. in “determining, toces leno a moment jwwpon a pin the centers of the. bearings 01, 116 members under stress must be taken as the points of appli- cation of the forces. ‘The positions of the centers of the several bearings upon a pin depend to some extent upon their thickness, which in turn depends largely upon the size of the pin; for the required thickness of each bearing can not be determined until the size of the pin is known: ‘The con- ditions of bearing and bending being thus interdependent, it becomes necessary to assume certain dimensions and make trial calculations. It will be most expedient to assume a size for the pin. 1526. Although the actual requirements are usually different for each pin, it is customary, in order to afford uniformity in the shop work, to make the pins of uniform diameter throughout the lower chord, including the shoe pin. It is evident, therefore, that the diameter of each pin in the chord must be equal to the diameter of the largest pin required inthe same. If the truss has an even number of panels, the largest pin required will almost invariably be the pin at the middle joint of the lower chord. If the truss has an odd number of panels, the largest pin will probably be required at the first or second joint from the center of the lower chord. After some experience, this can usually be determined by inspection. DETAILS OF CONSTRUCTION. 913 When practical, the diameter of the hip pin is also made the same as the diameters of the lower chord pins. Item (/,) of Art. 1511 affords material guidance in as- suming the sizes of the pins in the lower chord. This item requires that, in the lower chord, ‘‘the diameter of the pin shall not be less than two-thirds the largest dimension of any tension member attached to it.” In the example, the member c c’ of the lower chord bears the greatest stress; it would be the largest member in the chord, were the chord composed entirely of chord bars, and it may, therefore, be considered as the largest tension member attaching to jointc. As actually designed, the width or largest dimension of the chord bar in this member is 44 inches, but of this width ;% of an inch is cut out by rivet holes and is not effective section. The width of the effective section is 44 — ;®% = 31% inches, or near enough for present purposes, 4 inches; this may be considered the largest dimen- sion of the chord bar. According to the requirements of the specifications, therefore, the diameter of the pin must not be less than ¢ X 4 = 2.67 inches = 2114 inches, nearly. 1527. Ina truss having an even number of panels, the maximum bending moment J7 upon the pinat the center joint of the lower chord is given approximately, but quite closely, by the formula St Cs 9” (164.) in which S is the total live and dead load tensile stress in the adjacent panel of the chord and ¢ the average thickness of the heads of the chord bars connecting upon the pin plus {1 of an inch. This formula is necessarily applied before the dimen- sions of the chord bar heads have been determined, but if from the general conditions it is thought that it will be desirable to make the heads somewhat thicker than the body of the bar, allowance should be made for this fact in applying the formula. The formula may also be applied at the first or second lower chord joint from the center in a truss having an odd number 914 DETAILS OF CONSTRUCTION. of panels, but the results are not so reliable. In such cases, S should represent the stresses in the adjacent panel towards the center of the truss. Having obtained the maximum bending moment, the size of the pin giving an equal resisting moment may be obtained from Table 40, Art. 1546, which will be further noticed in that article. 1528. The total stressin the panel ce ofithe example (see stress sheet) is 48,600 + 20,800 = 69,400 pounds = S. The thickness of the head of each chord bar in the same panel is £ of an inch, and, consequently, the value of ¢ is $+ 4=+5 inch. Hence, by formula 164, the maximum bending moment upon the pin in the joint ¢ of the lower 69,400 x 18 2 Item (0,) of Art, L511 requires that the bending sstress upon a pin shall not exceed 18,000 pounds per square inch. From Table 40, it isfound that, with a fiber stress of 18,000 pounds per square inch, a bending moment of 32,500 inch- pounds will slightly exceed the resisting moment given by a 28" pin. As the bending moment obtained above is only approxi- mate, it will be well in choosing the diameter of the pin to select a diameter somewhat greater than the diameter thus obtained. Therefore, the diameters of all pins in the lower chord will be assumed to be 2% inches. With reference to the actual bending moment upon it, this diameter will now be investigated for the pin of the shoe joint. chord is, approximately, = 32,530 inch-pounds. PROPORTIONING PIN PLATES. 1529. Shearing Upon Pin.—By the first condition of item (J,) of Art. 1511, the shearing stress per square inch upon the pin must not exceed 9,000 pounds. The total stress upon the end post is 45,800 + 19,600 = 65,400 pounds, one-half of which, or 32,700 pounds, is transmitted to the pin through each channel. Hence, the sectionalarea of the pin, DETAILS OF CONSTRUCTION. 915 32,700 9,000 inches. The sectional area given by a pin or round bar 2? inches. in diameter is .7854 x 2.75" = 5.94 square inches. The shearing stress is found to be abundantly resisted by this size of pin. as required toresist the shear, is = oabe Square 1530. Bearing Upon Pin and Thickness of Pin Plates.—The same item of the specifications requires that the crushing stress (bearing stress) per square inch upon the projected area of the semi-intrados (i. e., the diameter of the pin multiplied by the total thickness of metal bearing upon it, or, in other words, by so much of its length as is covered by the surface of the metal in the member bearing upon it) must not exceed 15,000 pounds, or one and one-half times the stress per square inch allowed upon the member. At 15,000 pounds per square inch, the allowed bearing upon one lineal inch of the pin is 15,000 X 22 = 41,250 pounds, requiring for the total thickness of metal bear- 45,800 +- 19,600 41,250 ing upon the pin = 1.59 inches, or a little less than 12 inches. In finding the value of the allowed bearing stress by ta- king one and one-half times the allowed stress per square inch, the reduction of the unit stress for length of column (i. e., the negative quantity in the compression formula) is ; MS of course, neglected. Neglecting the quantity — 50 — in the compression formula, the live load unit stress allowed upon the end post is 8,750 pounds, and the dead load unit stress is 17,500 pounds [Art. 1410 (0)]. Hence, the bear- ing stresses allowed upon the pin are, for live load stress, 8,750 x 14 = 13,125 pounds per square inch, and for dead load stress, 17,500 x 14 = 26,250 pounds per square inch. The bearing stresses allowed upon one lineal inch of the pin are, therefore, 13,125 x 22 = 36,090 pounds for live load stress, and 26,250 * 2% = 72,190 pounds for dead load stress. The required total thickness of metal bearing upon the pin 916 DETALLS. OF CONSTRUCDION. 45,800 19,600 730, 000 ne, 190 1,%, inches. Hence, it is found that the thickness of bearing required by the allowed bearing stress of 15,000 pounds per square inch asethe. greater. -/Dherefore, thesrequircamie a: thickness of bearing is 12 inches. It will be well to notice that, as the ratio between the live and dead load stresses is the same throughout the chord and end post, and as the unit stresses allowed upon the end post are less than those allowed upon the chord, it follows that the thickness of bearing required by the allowed bear- ing stress of 15,000 pounds per square inch will be greater than that required by one and one-half times the allowed stress, if applied to any portion of the chord or end post in this bridge; hence, the latter condition may be neglected and a bearing stress of 15,000 pounds per square inch used. This refers to the bearing stress either upon a rivet or upon a pin. is, then = 1.54 inches, or a little less than 1531. When, as in the majority of cases, the allowed dead load unit stress is twice the allowed live load unit stress, the preceding operations are very much shortened by the following formulas: Let d = diameter of pin; az — allowed live load unit stress; 2 uw = allowed dead load unit stress; L = total live load stress upon the member; L) = total dead load stress upon the member. Then, at 15,000 pounds per square inch, the allowed bear- ing stress per lineal inch of pin = 15,000 d@, and the required thickness ¢,, of metal is given by the formula L+D iz —_ 15,000 a” (1 65.) The values of 15,000 d@ are given in Table 40, Art. 1546. At 14 (= 3), the allowed unit stress for live load, the allowed bearing per lineal inch of pin = 3 x u x d, and the required DETAILS OF CONSTRUCTION. Oy seca hae ou > Saw Similarly, the D — BCE KB thickness for live load, ¢,= required thickness for dead load stress is 7, = fer Therefore, the total thickness 7 in this case is 2L+ D bee Ter ts re ag (166.) In order to know what thickness should be provided for, we must compare ¢,, with 7, and take the larger. But, for this purpose, it is not necessary to compute both values; a general formula may be derived for the difference 7,,— 7. When this difference is positive, 7,, is greater than 7, and the value of 7,,, calculated by formula 165, should be used; when the difference is negative, the value of 7, calculated by formula 166, should be used. The formula for the dif- ference is found by subtracting formula 166 from formula 165, which gives, after factoring, (7% — 5,000) D — (10,000 — w) LZ t.— —_ ees 15,000 du But, since the denominator does not alter the sign of the fraction, we may neglect it and write Siemon (tw re) sign of [(wu — 5,000) Y — (10,000 — w) L]. (167.) Therefore, formula 165 should be used when the second member of this equation is positive, and formula 166 when negative. Furthermore, by a simple process of factoring we may arrive at some very convenient formulas for the various cases likely to occur. Thus, in the preceding ex- ample, and zz all those of the same kind, we have u = 8,750. and formula 167 becomes sign of (t,,— T) = sign of (8,750 D — 1,250 L) = sign of [1,250 (3 D— L) = sign of (3 D—L)], whence the following 918 DETAILS OF CONSTRUCTION. Rule.—for the bearing thickness of all posts [see Art. 1410 (0)], use formula 165, tf three times the dead load stress excecds the live load stress. In the opposite case use formula 166. 1532. For chord) seginents” [see Art TL Oat): wz — 10,000, and formula 167 gives sign of (¢,,— 1) = sign of 5,000 D, which 1s always positive. Hence, Rule.—Vor the bearing thickness of all chords in compres- ston, use formula 165. For other members to which the same rule applies, see Art. 1399 (gz). In all cases, formula 167 may be used to determine what thickness (whether ¢,, or 7) should be provided for; but it must be borne in mind that the preceding rules apply only to members proportioned by Cooper's specifications or by others containing the same requirements. 1533. Referring to the section of the end post shown in Fig. 1 of Mechanical Drawing Plate, Title: Highway Bridge: Details I, it is found that the thickness of metal in the web of each channel of the end post is 2 of an inch. Hence, the thickness of bearing given by the two channels is 2X #= # of an inch, leaving 13 — ?= { of an inch thick- ness of bearing to be given by the two reinforcing pin plates; in other words, the two pin plates (one on each channel) are each required to be $ X $= +; of an inch in thickness. It is evident that this thickness, obtained for the pin plates, will apply not only to the shoe connection of the end post, but to the hip connection also, provided the same size pin is used. 1534. Shearing Upon Rivets in Pin Plates.— If the stress is assumed to be distributed uniformly over the bearing surface, the amount of live load stress taken by each q's X 45,800 pin plate is equal to = 12,330 pounds, and the “iat ale & 19,600 amount of dead load stress is 4 iE = 5,280 pounds, 8 DETAILS OF CONSTRUCTION. ony or a total of 12,330 + 5,280 = 17,610 pounds. This amount of stress must be transferred from the channel to the pin plate by the rivets. According to item (@,) of Art. 1511, the shearing stress per square inch upon rivets must not exceed 9,000 pounds, or three-fourths of the allowed stress upon the member. The rivets used will be 2 of an inch in diameter, giving for each rivet a sectional area of (8)? x .7854 = .3068 of a square inch. An allowed shearing stress of 9,000 pounds per square inch will give 9,000 x .38068 = 2,760 pounds as the amount of shearing stress that may be allowed upon each rivet. Hence, the number of rivets required by this con- dition is eat = 6.4, or, as the result can not be fractional, 7 rivets. Three-fourths of the live load unit stress allowed upon the end post is # X 8,750 = 6,560 pounds, and three-fourths of the dead load stress is # X 17,500 = 13,130 pounds. The amount of live load shearing stress allowed upon a rivet is 6,560 X .38068 = 2,010 pounds, and the amount of dead load stress is 13,130 & .8068 =4,030 pounds. Hence, the number 12,530 of rivets required by the live load stress is 2010 = 6.1, and . 280 the number required by the dead load stress is - z 030 wl BA ) or, a total of 6.1+1.38= 7.4, or, as the result can not be fractional, 8 rivets. It may be noticed that, as applied to any portion of the end post of this bridge, the more severe requirement for shear is that the shearing stress per square inch shall not exceed three-fourths of the allowed stress upon the member. 1535. When the allowed dead load unit stress is twice the allowed live load unit stress, we may use the following formulas, in which 7 is the total bearing thickness (13” in the moneding example), ¢= thickness of pin plate (,{," in the example), 4 = area of rivet, and w, D, and Z have aa same values asin Art. 1531. 920 DETAILS OF CONSTRUCTION. Taking allowed shearing unit stress at 9,000 pounds, the required number of rivets is eet ee te) > 90004 I (168.) Taking allowed shearing unit stress at three-quarters unit stress allowed for members, the number of rivets is 27(2L4 D) is eh la lay By subtracting 169 from 168 it is found that Sign of (n, —N)= sign of [(u — 6,000) D — (12,000 — wz) L] (170.) If this sign is p/us, use formula 1683 if mznus, use 169. Thus, in the preceding example, where uw = 8,750, (2 — 6,000) D — (12,000 — wu) L= 2,750 D— 3,250 L= 250 (11 D—13 L) = 250 (11 x 19,600 — 13 x 45,000), which, being negative (this is seen at a glance without performing the operations) shows that /V is greater than z,, and that, therefore, formula 169 should be used for the number of TIVELS. Ve (169.) 1536. Bearing Upon Rivets in Pin Plates.—The number of rivets required in the pin plate, when considered with reference to their capacity to resist bearing stress, will now be noticed. The thinnest plate through which the rivet passes is the web of the channel, which is practically 2 of an inch in thickness. As noticed above, the more severe re- quirement for bearing is that the allowed bearing stress shall not exceed 15,000 pounds per square inch. At 15,000 pounds per square inch, the bearing stress re- sisted by a 3” rivet through 2 of an inch thickness of plate, is X 2X 15,000 = 3,520 pounds. The number of rivets 17,610 _ 35520) ae 5 rivets. Hence, at the unit stresses allowed for shearing and bearing, it is found that 8 rivets in each pin plate will required in each pin plate to resist the bearing is DETAILS OF CONSTRUCTION: 921 fulfil all conditions for resisting the maximum stress 1n both shearing and bearing. The number of rivets required in each pin plate, as well as the thickness of the pin plate, isthe same for the hip con- nection of the end post as for the shoe connection. Eight rivets are used in each pin plate at the hip connection of the end post, but at the shoe connection, as six of the rivets are countersunk and four of them also flattened, ten rivets are used. In order to beon the safe side it is well to use one or two more rivets than the calculations require, especially if a number of the rivets are countersunk. 1537. Tables of Shearing and Bearing Values for Rivets.—Operations similar to those explained above, for finding the number of rivets required in a pin plate and for like purposes, may be considerably facilitated by the use of the following tables of the shearing and bearing values of rivets. As allowed by many specifications, the unit value for bearing is double that allowed for shearing, and the tables are arranged accordingly. The values allowed by Cooper’s Highway Specifications, however, correspond with Table 37 for bearing and Table 38 for shearing. Other unit values are used for both shearing and bearing, and other tables will be found in various structural hand-books, but the values given in these tables are those commonly used. According to the common practice, the values given in Table 36 are used for wrought iron in railroad bridges; those given in Tables 37 and 38 are used for wrought iron in highway bridges and for medium steel in railroad bridges; while the values given in Table 39 are used for medium steel in highway bridges. Nore.—In each table all bearing values above or to the right of the upper zigzag lines are greater than double shear. Between upper and lower zigzag lines bearing values are less than double shear and greater than single shear. Below and to the left of lower zigzag lines bearing values are less than single shear. All values in pounds. Shearing valuesat 12,000 pounds per square inch, and bearing values at 24,000 pounds per square inch may be obtained by doubling the values given in ‘lable 36. DETAILS OF CONSTRUCTION. 922 "9e WIAVLE | oooet | o9oFt | ogter | o6ret | o¢err OTgOT | ose6 | orrs | oes | o9¢9 | og9e | 0697 | OGLE || OSLTT | O68e || FEsL’ | TI OSPVTIT | OL9OT | O86 0806 | 0068 | O8Sh | 09G9 | OFLE | 0cbF | OOTF | O8SE || 0c06 OTcP 6109" i OVF8 | OcLL | O8OL | OS&9 | OF9G | OG6F | OGGP | OGSE | OTS || O&99 OTEE STVV e O098S | O86S | 069F | OOTY | OGSE | O&6G | OFES || 0097 0086 8906" $ { | OSLE | O86& | OT8e | OVES | OSST |} OF6G OLFT 6961" $ OTTS | OOLT | OFFE || O99T 0&8 POTT” $ eer ee eth ae | hl Pel Ae Ot See RE Ee eS ea eens a orenbs : ‘your oienbs Ul JOATY VATA ‘youl etenbg sod “q{ 000‘ET 38 ‘SOUT UI 9}¥[q JO SOSSOURIIYL JUIIIYIG 10jJ son[vA Sulsresg Iod ‘qt 00g‘), 72 jo voiy jO 19}9 son[VA 1e9ys “meid ‘LE WIAVL OOOGT | OSSTT | OOSOT | OLLE | 0006 | O&s8 | OOSL | OSL9 | 0009 | OSes | OOST | OGLE | OOOE || OZF6 OTLY Ssh" I 0616 | O&G8 | O8sL | OBsL | 09¢9 | O16 | O8GS | O6SP | OF6E | O86& | O0&9G |) OEl OL9E 6109" i OGL9 | 0619 | OS9G | O9TS | OOLF | OFGE | O8EE | OT86 | OSce || OO0ES 0C9G STPV" = 0697 | OGGF | OGLE | O8GE | OT8S | OPES | OBST || O89E OF8T 8908" t O00 | O0&9G | OLSG | OS8T | OOT 0986 OSTT 6961" s osot | ort | ogtt | over | 099 || Fort: | 8 Maa | ele hte SE | RR Ay ae eesti | Sie ees aoc pete ae ee eienbs : ‘yout a1enbs Ul JOATY qOATH ‘youl eienbg sod ‘q] 000'SI 3¥ ‘soyouy] UI 9}¥I[q JO SASSOUHIYL, JUSIBYIG JOJ san[eA Sursrvsg zed ‘q{ 000‘9 32 jo eoly JO 19} son[vA ie9qsg -ureld 923 DETAILS OF CONSTRUCTION. Q00TS | O696T O8EST | O9OLT | OSLET | OFFFI ogTet | OTST oocot | 0616 | 8st ‘coco | ocee | osrot | oces || Frese | T OSO9T | O€6FT | OSLEL ogge1 | OSFIT OFEOT 0616 | OFO8 | 0689 | OFLE | O6CF || O&DGT | OTES STOO" i OI8STE | O&80T | OF86 | 0988 O8s8b | 0689 | OL6E | Oc6F | OF6E || O866 OFOF SIFT e 0068 | O8EL | O99 | OLS | OG6F | OOTF | OSE || OFFD O0GGE 8908" $ ocee | Oech | OF6S | O8se | OES || OTF | O908 || E96T' | F Of6G O9FS | OLBT OGEG O9TT FOLL’ ti 9 eit ome Ps) ee ges ae eae aS ae Bee e ee : aivnbs : ‘yout sienbs Ur JATY JIATA ‘youl sienbsg sod ‘q{ 000'TS 3@ ‘SoyoU] UT 91¥[ gq JO SassoUYIY YL JUIIIYIG, 10j son[vA Surivsed sod qt] 00c‘0L 32 jo vay JO 1939 son[vA Ivsysg “Creid P ‘6e WTIAVL QO08T | O889T OSLET ogg | oocet | oseet OSELT | OSLOL | 0006 | O88L | OSL | OG9¢ | OOS || OFIFT LOL PS8L° i OSLET | OO8ST | OTSTE | OG80T | OF86 | 0988 | O88L | 0689 | OL6S | OG6F | OFGE || OS8OT | OTFE 6109" i OSTOT | O866 | OFFS |O6CL | OSLO | OL6E | O90 | OGeF | O88 || Of6L O86& Str’ t OGOL | O8E9 | OG9E | OCbF | OGEF | OGSE | OT8s || Oeeg 09LG 8906" $ | OOCF | OF6E | OSE | OT8S | O€ss || OSCE OLLT 6961" $ ‘ogee | orte | oer || ost | 066 || orn: | # bre RS Gini AAs a Aon oe a OA a ee a Peed eine re a dc arenbs et ‘youl o1enbs Ul JOATY sae ite ‘youl otenbg iad ‘q] 0no'st 3% ‘seyouy ul 9}¥[q JO SassoUuyAoIY,L, JUSIOYIG Ioj son[vA Sulivseg tod ‘q] 000‘6 38 Jo voly JO 19}9 son[eA ivsys ~ureld ‘Se WIAVL II,—20 i$ 924 DETAILS OF CONSTRUGCEION 1538. Dimensions of Pin Plates and Arrange- ment of Rivets.—By reference to the sections of the chan- nels shown in Mechanical Drawing, Fig. 79, it will be noticed that the width of the widest plate that can be used upon the outside of the web of the channel of the end post (16 pounds), without rounding the edges to fit between the flanges of the channel, can not be greater than 8 — 2 (2+ +3) = 6¢ inches. Fitting the edges would involve additional and expensive shop work, and, therefore, should not be required when not absolutely necessary. Hence, pin plates 6 inches in width will be used upon the end post. The length of the pin plate will depend upon the number of rivets used and the arrange- ment of the rivet spacing. By item (¢,) of Art. 1511 the distance between the cen- ter cf -a rivet hole and the outer edge of the plate must not be less than 1} inches. If the outer lines of rivets in the pin plates be each located 14 inches from the outer edge of the plate, the distance between these two lines of rivets will be 6 — 2 X 14 = 34 inches; and if a row of rivets be placed midway between the two outer rows, the distance between two adjacent rows will be +x 34=1% inches. This is between two and one-half and three diameters of the rivets, and hence is a less distance between the rows of rivets than is desirable for chain riveting, but isa sufficient distance between the rows if the rivets are staggered. (Art. 1512, items II and III.) The rivets will be staggered, and their pitch will be made equal to twice the distance between the adjacent rows, or 34 inches. The distance from the center of any rivet hole to either the end. of the pin plate or the edge of the pin hole should not be less than 1} inches. The arrangement of the rivets in the pin plate to meet the required condition is clearly shown in Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. 1. It will be noticed that with the rivets arranged as there shown, the shortest distance between the centers of any two rivets is the diag- onal distance between the centers of the rivets in two adja- cent rows; this distance is very nearly 24 inches, or four diameters. The arrangement of the rivet spacing in the DETAILS OF CONSTRUCTION. 925 pin plate should usually be deferred until the size of the pin is definitely determined, and should always be worked out fully in pencil. Any change in the diameter of the pin would affect the required thickness of the material bearing upon it; it would, consequently, affect not only the thick- ness of the pin plate, but also the number of rivets in the same. MOMENTS ON PINS. 1539. Positions of Bearings Upon the Pin.— ‘The thickness of material necessary to give the proper bear- ing upon the pin, as required for the standards of the shoe and for the member in the end panel of the lower chord, will now be determined, in order to find the bending moment upon the pin. This is necessary because, according to item (6,) of the specifications (Art. 1511), the centers of the bearings of the members must be taken as the points of application of the stresses in determining the bending moment. The bearings of the shoe standards must be sufficient to resist the total vertical pressure upon them, which will be equal to the reaction due to the total wind pressure against the portal plus that due to the full live and dead loads. By reference to Fig. 277 (6) of Art. 1309, it will be noticed that the total wind pressure against the portal is equal to 2,700 + 1,350 + 1,350 = 5,400 pounds. Hence, the vertical reaction at the foot of the leeward end post, due to this wind pressure against the portal, is equal to 5,400 x 4% = 5,116, or, near enough, 5,120 pounds. By reference to Arts. 1293 and 1301, it is found that the reaction due to a full live load is 32,400 pounds, and the reaction due to the dead load is 13,900 pounds. It has been found (Art. 1530) that for a bearing pressure of 15,000 pounds per square inch the bearing value per lineal inch of a 22” pin is 41,250 pounds. Hence, the total thickness of bearing required in the standards of the shoe will be 32,400 + 13,900 + 5,120 41,250 of + x 14}=3 inch for each standard. = 1.25 inches, which is a thickness > 926 DETAILS OF: CONSTRUCTION: 1540. The live and dead load stresses in the end panel a 6 of the lower chord are found to be the same as the live and dead load reactions. (This will always be the case for a full uniform load when the panel length and the height of truss at the hip vertical are equal.) Hence, for present purposes, the thickness of bearing of the lower chord upon the shoe pin may be considered the same as that taken for the shoe standards. The shoe joint may be arranged with the standards of the shoe between the channels of the end post and the lower chord members outside of the channels, but it is a better arrangement to pack the lower chord between the channels, with the shoe standards connecting outside of the end post. As the stress in the end post is resisted by both the stress in the lower chord and by the reaction, applied through the | shoe, the bearing of the. end post upon the pin should be between the bearing of the chord and the bearing of the shoe, as shown in Mechanical Drawing Plate, Title: High- way Bridge: Details IV. The distance between the channels of the end post, back to back, being 72% inches (Art. 1523), the distance from outside to outside of the pin plates at the shoe joint is 72 + 2 (8-+ 7) = 9 inches. Rivets should not be flattened to less than + of an inch in height, and are always likely to be about one-sixteenth of an inch higher than marked. The shoe should have a clearance of not less than $ of.an inch on each side of the end post. Hence, the distance between the standards of the shoe is made equal to9+2(4+ + 4) = 94 inches. The distance from center to center of the pin bearings of the shoe standards is, therefore, 9§ + 8—104-inches. See Figs. 5 and 9 of Mechanical Drawing Plate, Title: Highway Bridges Detarlesii lL: 1541. Asthe dimensions of the connecting details of the lower chord member a 6 have not yet been determined, the actual distance between the centers of their bearings, and, therefore, their actual positions with reference to the DETAIGS OF CONSTRUCTION. 927 other bearings, are not known. Other conditions (to be hereafter noticed) may require the thickness of metal in the chord bearing upon the pin to be greater than required by the allowed bearing stress. In such cases it is good practice to assume the positions of the bearings to be the same as determined by the required thickness of bearing, with liberal allowance for clearance. Assuming the clearance on each side between the chord and end post to be }of an inch, the width from outside to outside of the chord connection will be 72 —2 x 4=“7tinches. If each bearing of the chord be assumed to be 2 of an inch in thickness, the same as the shoe standards, the distance between the centers of the chord bearings may be taken at 74 —%=64 inches. The distance between the centers of the bearings of the end post is known to be 73+ 2-+ 5; = 8,3, inches. 1542. Bending Moment Upon the Pin.—The relative positions of the points of application of the forces acting upon the pin (which are the stresses in the connect- ing members transferred by the pin) have now been determined, and the maximum bending moment upon the _pin may be readily obtained. It isconvenient to resolve all forces acting upon the pin into their horizontal and verti- cal components, to determine the bending moments at vari- ous points in both the horizontal and vertical plane, and then find the resultants of the bending moments in the two perpendicular planes at corresponding points. The greatest of these resultants will be the maximum bending moment upon the pin. The forces acting upon the shoe joint, together with the force polygon for the same, are shown in Fig. 313. For each member the live and dead load stresses are combined; the wind stresses are neglected. A mere inspection of the force polygon clearly shows that 2-/, the vertical component of 3-7, the stress in the end post, is equaland opposed to the reaction 1-2; also, that 3-2, the horizontal component of 3-7, the stress in the end post, is equal and opposed to 2-3, the stress in the lower chord. Without performing any operation, 928 DETAILS OF CONSTROUGTION, it is thus known that the horizontal component of the live and dead load stresses in the end post is equal to 46,500 pounds, or the sum of the live and dead load stresses in the lower chord member with which it connects, and that the vertical component of the live and dead load stresses in the end post, which is equal to the reaction, is also equal to the same amount. The vertical forces acting upon the pin, and the horizontal forces acting upon the same, may each be considered independently of the other, giving very simple mm ty Seale of forces 1'-20000Ibs Z| Fic. 313. problems. The resultant of the two results may then be obtained, 1543. In determining the actual bending moment upon a lower chord pin, the effect of the wind stress, though very often neglected, should be considered and provided for ina manner consistent with the method by which its effect upon the chord members connecting upon the pin was esti- mated in proportioning the material for those members. In other words, the bending moment upon the pin should be determined with regard to the effective sections of the mem- bers connecting upon it; a pin having an equal resisting moment would then be as strong as the connecting mein- bers. If the designer has not before him the data used in DETAILS OF CONSTRUCTION. 929 determining the increase of area to provide for the wind load, he may proceed as follows: From the stress sheet he may take the dead and live load stresses (1) and L), divide them by the dead and live load unit stresses, respectively, as given by the specifications, and add the quotients. The result will be the area necessary for live and dead load stresses only. Call this area A. If the area given on the stress sheet is equal to A, this will show that no provision was made for wind stress, and the latter may be neglected in proportioning the pin. But, if the area A, given on the stress sheet is different from A, the amount WV of wind stress that must be provided for in dimensioning the pin is found by this simple proportion: L+D:A::L+D4+4W:A4,; whence, W=(L+D) (5 = 1). In the present case, the live and dead load unit stresses allowed are 10,000 and 20,000 pounds per square inch, re- spectively. From the stress sheet, the live and dead load stresses upon the lower chord member a @ are 32,400 and 13,900 pounds, respectively, or a total of 32.400 + 13,900 = 46,300 pounds. The sectional area required by the live and dead load stresses is tbe -- ica ala = 3.94 square inches. 10,000 20,000 As this is the area given on the stress sheet, no provision need be made for wind stress. At the shoe joint, the additional amount of stress assumed to provide for wind stress, when 4, is greater than A, may be considered to be resisted by the reaction, through the medium of the shoe. At each intermediate joint of the lower chord, if the lateral rods connect upon the floor-beams, and the latter connect upon the pins by means of hangers, this additional stress, assumed to provide for the effect of wind stress, may be considered to come upon the pin through the beam hanger and upon the chord through the pin. In other words, as the wind stresses are resisted by the lateral system, the additional stresses assumed to provide for the 930 DETAILS OF CONSTRUCTION. effects of the wind stresses upon the lower chord may be con- sidered to come upon the chord through the piece by which the diagonals of the lower lateral system attach to the chord. This practice is not in all cases thoroughly consistent with accuracy, but the small error will probably be upon the side of safety. It is necessary to make some assumption by which the forces considered to act upon the pin will be in equilibrium. 1544. The distance, as determined above, between the centers of the bearings of each member connecting upon the shoe pin, together with the stress upon the same, is givenin tabular form below. Stresses which act upwards or to the right upon the pin are designated by the + sign, and those which act downwards or to the left are designated by the — sign. Distance Horizontal Member: Between Vertical Stress, ce Bearings, Pounds. Dodade Inches. ese Shoe, 104 + 46,300 0,000 End post, 833. — 46,300 — 46,300 Lower chord, 64 0,000 + 46,300 It will be noticed that in each column the sum of the stresses designated by the + sign equals the sum of the stresses designated by the — sign. The stress in each member is delivered upon the pin through two bearings, one-half of each stress through each ss bearing. The maximum bending | moment on the pin might be found by the force and moment diagrams; | 8 but in a simple case like this it is 3 ie easier to find it by direct calcula- 3) is ~| tion. Fig. 314 shows one end of | ry §| the pin with the forces acting upon ! | Q! 5 3 38 Ze it.. /Dhe- distances, Detweengetwo | = "| consecutive bearing points is easily a determined from the distances tab- ! Pastas & ulated above. Thus, distance from Fic. 314. & shoe bearing to center (middle) of DETAILS OF CONSTRUCTION. 931 pin = 10} + 2 = 52’; distance from end post bearing to cen- ter of pin = 83, + 2 —4.9,". Therefore, distance between shoe bearing and end post bearing = 54 — ts = 42. The moment of the vertical forces = 23,150 X 3 = 26,770 inch- pounds. The moment of the horizontal forces = 23,150 xX 24% = 19,530 inch-pounds. _ The resultant bending moment upon the pin is found by constructing a force polygon in the form of a right-angled triangle whose base and altitude represent, respectively, the horizontal and vertical bending moments as obtained. ‘The hypotenuse of the tri- angle will represent the resultant bend- ing moment upon the pin. This is clearly shown in Fig. 315. Or the resultant moment may be computed from the hori- zontal and vertical moments in the same Fic. 815. manner that the length of the hypotenuse is calculated in a right-angled triangle. It is equal to 4/26,770* + 19,530" = 33,100 inch-pounds, nearly. 1545. The Resisting Moments of Pins.—Having ascertained the maximum bending moment upon a pin, it is necessary to determine next the size of the pin required to resist the moment. The pin acts simply as a solid beam having a circular cross-section. The allowed bending stress, or stress per square inch upon the extreme fiber of pins (S, of formula 73, Art. 1243), commonly called the extreme fiber stress, is usually taken at 15,000 and 18,000 pounds for wrought iron, and at 20,000, 22,500, and 25,000 pounds for steel, according to the nature of the structure and the requirements of different specifications. For each material the lower unit values are used for railroad, and the higher unit values for highway bridges. Formula 73 is 7 M=—, Cc in which J7 is the moment of resistance (which must be 932 DETAILS OF CONSTRUCTION. equal to the bending moment), S is taken to represent the allowed stress in the outermost fiber (1. e., the extreme fiber stress), ¢ 1s the distance from the neutral axis to the outer- most fiber, and / is the moment of inertia of the cross-section of the pin. From the ninth item of Table of Moments of Inertia, it is 3.1416 a* _ 64 ~ -049 d*, and«c=4¢d¢ being the diameter of-the section, By substituting these values of / and c in the preceding formula, we get .049 S d* M = — id known that for a solid circular section / = — 098 Sda°. (171.) daairy lez ee} The values of J7 and d@ given by these formulas are suf- ficiently exact forall practical purposes. It is, however, much more expedient to obtain the values of J7 from a table prepared by formula 171. 1546. Table 40 gives the values of the resisting mo- ments of pins for each eighth of an inch from 1 to 5§ inches diameter, for fiber stresses of 15,000, 18,000, 20,000, 22,500, and 25,000 pounds. For convenience, the bearing values for 1 anch. thickness ‘of “plate.(—‘dianieter sof spingcslen allowed bearing stress per sq. in.) are also given for bearing stresses of 12,000, 15,000, and 18,000 pounds per square inch. For the resisting moments of pins having diameters ex- pressed in odd sixteenths of an inch, it will be sufficiently correct to use a value 50 pounds less than a mean between the next lower and next higher values. Thus, with a fiber stress of 15,000 pounds per square inch, the resisting moment 19,700 + 23,000 of a 2,'," pin may be taken at 5 — 50 = 21,300 inch-pounds. For intermediate bearing values, a mean between the next lower and next higher values may be taken. DETAILS OF CONSTRUCTION. TABLE 40. BEARING VALUES AND RESISTING MOMENTS OF PINS. Diameter of Pin in Inches. Bearing Values, in Pounds, for One Inch 933 Moments, in Inch-Pounds, for Extreme ge Thickness of Plate. Fiber Stresses of a an ae : ’ 15,00 18,0 5300 8,000 9, 95° 2594 ae Seg Ib. pee Ib. wee lb per i. per Ib. per tb. per 1b. er its er “|Square|Square| Square | Square | Square | Square | Square | Square Inenh va Ine he _ Inch. _ Inch, Inch. Inch. Inch. | Inch. 0. 785| I2,00C} I5,000| 18,000} 1,470} 1,770] 1,960} 2,2I0} 2,450 0.994} 13,500} 16,900] 20,300) 2,100] 2,520] 2,800] . 3,140} 3,500 I.227| 15,000] 18,800] 22,500} 2,880} 3,450) 3,830] 4,310} 4,790 1.485| 16,50C} 20,600] 24,800] 3,830} 4,590] 5,100] 5,740} 6,380 1.767| 18,000] 22,500} 27,000] 4,970] 5,960} 6,630! 7,460} 8,280 2.074| 19,500] 24,400} 29,300] 6,320} 7,580) 8,430) 9,480] 10,500 2.405| 21,000] 26,300] 31,500} 7,890} 9,470] 10,500] 11,800) 13,200 2.761| 22,500] 28,100} 33,800} 9,710] 11,600] 12,g00| 14,600] 16,200 3.142] 24,000] 30,000} 36,000] 11,800} 14,100] 15,700} 17,700] I9,600 3.547| 25,500] 31,900} 38,300] 14,100] 17,000] 18,800] 21,200} 23,600 3.976] 27,000] 33,800] 40,500} 16,800] 20,100] 22,400] 25,200] 28,000 4.430| 28,500] 35,600) 42,800] 19,700} 23,700} 26,300] 29,600} 32,900 4-909} 30,000} 37,500] 45,000} 23,000] 27,C00o| 30,700] 34,500) 38,400 5.412| 31,500] 39,400} 47,300} 26,600) 32,000} 35,500) 40,000) 44,400 5.940) 33,000} 41,300} 49,500) 30,600} 36,800) 40,800) 45,900, 51,000 6.492) 34,500) 43,100) 51,800} 35,000) 42,000) 46,700) 52,500) 58,300 7.069} 36,000) 45,000} 54,000] 39,800) 47,700} 53,000} 59,600} 66,300 7.670) 37,500} 46,900) 56,300! 44,900} 53,900) 59,900) 67,400) 74,g00 8.296} 39,000} 48,800} 58,500} 50,600) 60,700) 67,400) 75,800) 84,300 8.946] 40,500} 50,600] 60,800) 56,600) 67,g00) 75,500) 84,900) 94,400 94 9 ] 9 9 g.621| 42,000) 52,500] 63,000] 63,100) 75,800) 84,200) g4,700| 105,200 10. 321| 43,500] 54,400} 65,300) 70,100, 84,200) 93,500] 105,200) 116,900 I1.045) 45,000] 56,300) 67,500] 77,700) 93,200} 103,500) 116,500] 129,400 II. 793] 46,5ccC| 58,100} 69,800) 85,700] 102, 80c} 114,200} 128, 500; 142,800 12.566} 48,00C| 60,000} 72,000} 94,200] 113, 10C | 125,700] 141,400] 157, 100 13.364] 49,500] 61,900) 74,300} 103,400) 124,000} 137,800) 155,000) 172,300 14.186) 51,000] 63,800) 76,500] 113,000) 135, 700] 150,700) 169,600) 188,400 15.033] 52,50C| 65,600) 78,800} 123,300} 148,000] 164, 400] 185,000} 205,500 15.904} 54,00C|] 67,500) 81,0CO} 134,200) 161,000] 178,g00} 201, 300} 223, 700 16.800] 55,500] 69,400) 83,300] 145, 700) 174,800} 194,300} 218, 500) 242,800 17.721] 57,000] 71,300) 85,50C} 157,800) 189,400] 210, 400} 236, 700| 263,000 18.665] 58,50C| 73,100) 87,800] 170,600) 204, 700} 227, 500] 255,g00| 284,400 19.635} 60,00C}.75,000} 9g0,00C) 184, 100} 220, g0C} 245,400] 276, 100) 306, 800 20.629] 61,500] 76,g00} 92,300} 198, 200} 237,900} 204, 300| 297, 300} 330,400 21.648] 63,000] 78,800} 94,500) 213,100] 255,700) 284, 100) 319,600) 355,200 22.691| 64,500] 80,600} 96,800} 228, 700) 274,400} 304,900} 343,000) 381, 100 23.758) 66,000} 82,500] 99,000} 245,000} 294,000] 326, 700] 367,500} 408, 300 24.850] 67,500] 84,400} LOL, 300} 262, 100} 314, 500} 349, 500} 393, 100) 436, 800 25.967| 69,000] 86, 300} 103, 500} 280,000] 335,900] 373,300) 41g,g00, 466,600 27.109] 70, 50C| 88, 100} 105, 800| 298,600} 358, 300} 398, 200] 4.47, 900| 497, 700 934 DETAILS OF CONSTRUCTION. In the present structure, according to item (0,) of the specifications (Art. 1511), the bending stress must not exceed 18,000 pounds per square inch. By reference to Table 40, Art. 1546, it is found that with an extreme fiber stress of 18,000 pounds per square inch, a pin 2% inches in diameter has a resisting moment of 36,800 inch-pounds. Hence, this diameter of pin will resist the bending moment upon the shoe pin, which has been found to be 33,100 inch- pounds. It may be noticed that, at 18,000 pounds per square inch, the resisting moment given bya2}{ 4" pin is practically 32,000 + 36,800 ee have been sufficient to resist the bending moment. 50 = 34,350 inch-pounds, which would PIN PLATES FOR THE HIP JOINT OF THE CHORD. 1547. Thickness of Bearings for Chord.—The total maximum stress upon the upper chord is 48,600 + 20,800 = 69,400 pounds. From Table 40 it is found that, at 15,000 pounds per square inch, the bearing value for one inch thickness of metal upon a 2?” pin is 41,300 pounds. The total thickness of bearing surface upon the pin re- 69,400 41,300 inches, or, practically, 144 inches. By reference to Fig. 79 of Mechanical Drawing, it is found that the thickness of web in the upper chord channel (10 lb. per ft.) is 34 of an inch, or a total thickness of 51, of an inch for both channels; leaving 141 — 54 = 14 inches thickness of bearing to be given by the two pin plates, or 2 of an inch each. quired for the stress in the upper chord is =="10.68 1548. Pin Plates.—It is desirable that the pin plates should extend beyond and around the pin, Hence, as the pin plates at the upper end of the end post are on the inside of the channels, the pin plates of the chord must be upon the outside. The width from outside to outside of the webs of the channels of the chord is 74 + 2 X 35 = 743 inches, DETAILS OF CONSTRUCTION. 935 while the corresponding width from outside to outside of the webs of the channels of the end post is 72+2x2= 8} inches. This will not allow the pin plates directly on the outside of the webs of the channels of the chord to extend beyond the pin, outside of the webs of the channels of the end post. It will, therefore, be necessary to make the pin plates on the chord double, extending only the outer plates beyond and around the pin. Two pin plates, each ;'; of an inch thick, instead of one plate 2 of an inch thick, will be placed upon the outside of the web of each channel of each chord, and the outer plate only will extend beyond and around the pin. As determined above, the total thickness of bearing required for the chord is 1.68 inches, and the thickness given by the pin plates is 1.25 inches. Hence, the amount of live load stress to be transferred to the pin plates by the rivets is 48,600 x be = 36,160 pounds, and the amount of dead load stress to be transferred by the same is 20,800 X 1.25 | L687 15,480 pounds, or a total of 36,160 + 15,480 = 51,640 pounds. 1549. Rivets Required by Shearing Stress. — Neglecting the reduction for column length, the live and dead load unit stresses allowed upon the upper chord: are 10,000 and 20,000 pounds, respectively. Three-quarters of the live load unit stress (see item (@,) of Art. 1511) is 7,500 pounds, and from Table 37, Art. 1537, the value of a §" rivet in single shear at 7,500 pounds per square inch is 2,800 pounds, while for dead load stress it will be double this amount, or 4,600 pounds. Hence, the number of rivets area : eso, 1G required in the pin plates by this condition is aes } DUL 8 ‘ 15,480 0 = 19.1, or, as the result can not be fractional, 20 4,600 rivets. At 9,000 pounds per square inch, the value of a 8” rivet in single shear is 2,760 pounds (Table 38, Art. 1537), and 936 DETAILS OF)CONSTRUCTION, the total number of rivets required in the pin plates by this 36,160 + 15,480 _ CRON AN in | 1550. Rivets Required by Bearing Stress. —The thinnest plate through which the rivets pass is the web of the channel, which is slightly less than }” in thickness. At 15,000 pounds per square inch, the bearing value of a 8” rivet in }” thickness of plate is 2,340 pounds. (Table 37, Art. 1537.) Using this value, the total number of 36,160 + 15,480 2,340 rivets. The bearing is found to be the critical condition. The required number of rivets as found is for the pin plates upon both channels; the number required in the pin G)s z =, 11 rivets: As the pin plates on each channel are double and the separate plates are of equal thickness, one-half of this number of rivets will be required for each plate. All the rivets neces- sarily pass through the inner plate, but only half of them, or 6 rivets, are required in the outer plate. The arrangement of the rivets in the pin plates of the chord is very similar to the arrangement in the pin plates of the end post, and will require no special explanation. These pin plates will be noticed again. condition is 18.7%, or, practically, 19 rivets. =) Tivets “required gins the. pln ep ateese plates attaching to each channel is MOMENTS ON HIP PIN. 1551. Positions and Intensities of Bearings Upon Pin.—The thickness of the bearing upon the hip pin for each channel of the upper chord, including the pin plates upon it, being assumed equal to ++ 5, + 4% = # inch, the distance from center to center of the two bearings of the upper chord upon the hip pin is equal to 74+ $= 82 inches. At the hip joint, the distance between the inner surfaces of the pin plates of the end post is 72 — 2 x +, = 6} inches, and the distance from center to center of the two bearing sur- faces of the end post upon the hip pin is 644+ 7,+2=7 inches. The main tie bars and hip vertical rods are both DETAILS OF CONSTRUCTION. 937 packed inside, or between the bearings of the end post. As the main tie bars bear greater stress than the hip vertical rods, the former are packed adjacent to the end post bear- ings. The thickness of the tie bar is 1% of an inch, but on account of the pin being situated so near to the tops of the channel, thus limiting the diameter of the head of the tie bar, it is very probable that it will be found necessary to thicken the heads of the tie bars, in order to give sufficient metal back of the pin hole. Hence, in obtaining the bend- ing moment, it will be well to consider the tie bar heads to be £ of an inch thick. Allowing }” clearance on each side, the distance between the outer sides of the heads of the tie bars is 64 —2 x ¢=6} inches, and the distance from center to center of this bearing surface is 64—$=52 inches. The clear dis- tance between the inner surfaces of the tie-bar heads is 64—2 xX $= 44 inches. A clearance of one-sixtecenth of an inch ts all that ts neces- sary to allow between two eve-bar heads, or between an eye- bar head and a welded loop. (See Art, 1524, 1.) Hence, the distance from outside to outside of the loops of the hip vertical rods will be 44 — 2 x 44 = 42 inches, and, as the hip vertical rods are 1 inch square, the distance from center to center of the same is 42 — 1 = 32 inches. The stress in the upper chord is horizontal, and equal to 69,400 pounds. The stress upon the hip vertical is vertical, and equal to 20,800 pounds. The stress in the end post has a horizontal and a vertical component, each of which has been found to be equal to 46,300 pounds. (Art. 1542.) It is evident that the greatest bending moment upon the pin will occur with the truss fully loaded, as this condition will give the maximum stress to every member connecting upon the pin except the main tie 4¢. The stress upon the main tie with the truss fully loaded, not being the maximum stress upon that member, is not shown upon the stress sheet. But it is evident that, in order that the forces acting upon 938 DETAILS OF CONSTRUCTION. the hip joint shall be in equilibrium, the horizontal compo- nents of the stresses of the main tie and end post must be equal to the horizontal stress in the upper chord, as no other stress having a horizontal component. acts upon this joint. Hence, the horizontal component of the stress in the main tie is equal to 69,400 — 46,300 = 23,100 pounds. Similarly, its vertical component must be equal to the vertical com- ponent of the stress in the end post minus the stress in the hip vertical and the one-third panel dead load (2,300 pounds) assumed to be supported directly at the hip joint, or 46,300 — (20,800 + 2,300) = 23,200 pounds. As the vertical and hori- zontal projections of the tie (height of truss and panel length) are equal, the vertical and horizontal components of its stress are found to be practically equal; they are really exactly equal. The one-third panel load of dead load (2,300 pounds) assumed to be applied directly at the hip joint may be con- sidered to come upon the pin through the bearings of the upper chord. The distance between the centers of the two bearings of each member connecting upon the pin, together with the horizontal and vertical stress upon the same, as determined above, is given in tabular form below. Those stresses which act upwards, or to the left, upon the pin are designated by the + sign, and those stresses which act downwards, or to the right, are designated by the — sign, Distance : Beveeen Horizontal : Member. Rieecs Vertical Stress, Bearings, Pp rs Pounds. Inches. Fea Upper chord, 88 + 69,400 — 2,300 End post, (ous — 46,300 + 46,300 Main tie, 5# — 23,100 — 23,200 Hip vertical, 3g 0,000 — 20,800 . In each column the sum of the stresses designated by the + sign equals the sum of the stresses designated by the — sign. DETAILS OF CONSTROCTION. 939 1552. Bending Moments Upon Pin.—The force dia- gram and equilibrium polygon for the horizontal forces acting upon the pin are shown at (a) in Fig. 316, and at (0) in the same figure are shown the force diagram and equilib- rium polygon for the vertical forces. For the horizontal forces the pole distance is 40,000 pounds. The maximum intercept, uniform from ¢ d, is, to scale, .74 of an inch. Hence, the maximum horizontal bending moment is 40,000 x .74 = 29,600 inch-pounds. For the vertical forces the pole distance is 30,000 pounds, and the maximum intercept, uniform from @ tog, is, toscale, 1.04inches. Hence, the maximum vertical bending moment is 30,000 * 1.04 = 31,200 inch-pounds. The resultant maximum bending moment is equal to VW 29,6007 + 31,2007 = 43,000 inch-pounds. 1553. Resisting Moment of Pin.—For a bending stress of 18,000 pounds per square inch, as allowed for wrought iron by item (0,) of the specifications (Art. 1511), this amount of bending moment would require a pin 3 inches indiameter. But on account of the pin being located so near the top of the channels, it would be very undesirable to use a pin having a diameter greater than 2? inches. Hence, as all the conditions except the bending moment are satisfied with a 2?” pin, it will be better, instead of using a larger size of pin, to use a 23” pin of medium steel. Cooper’s specifications do not directly state the intensity of bending stressallowed upon pins of medium steel. But, as they allow upon medium steel in the main members of a bridge unit stresses 20 per cent. greater than those allowed upon wrought iron, we may assume the same ratio of increase in the bending stresses to be allowed upon the pins. At 18,000 pounds per square inch, the resisting moment of a 2?” pin is 36,800 pounds. (See Table 40, Art. 1546.) An increase of 20 per cent. would give a resisting moment of 1.20 K 36,800 = 44,200 inch-pounds, which ts sufficient to resist the bending moment of 43,000 pounds, as obtained above. T. [1.—21 DETAILS OF CONSTRUCTION. 940 Tiorizontal Forces _ a i a i ig a a a a ee Re Ce ee ee ae a eee ee ee ee eee ee To ' ” 4 Scale of distance 2 mw (D) Scale of forces 1 S S Ss = s bs Sy DETAILS OF CONSTRUCTION. 941 It will be noticed that for this size of pin a bending stress of 22,500 pounds per square inch, which is sometimes used for pins of medium steel, will give a resisting moment of 45,900 inch-pounds. CONSTRUCTIVE DETAILS OF THE END POST. 1554. The dimensions of the connecting details of the end posts having been determined, the constructive details and rivet spacing for that member, with the exception of the connections for the portal bracing, may now be determined and laid out. These should be drawn out entirely in pencil, as it may afterwards become necessary to modify certain dimensions slightly, in order to provide for the conditions of connecting members. The details of the end posts are shown in Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. -1. 1555. The Top View; Positions of Rivet Lines. —The first step with reference to the rivet spacing is to fix the positions of the two lines of rivets connect- ing the cover-plate to the channels. The dis- - tance between these two lines of rivets is governed by the distance a, Fig. 317, from the center of the rivet hole through the flange of the channel to the back of the same, together with the distance, back to back, between the two channels. As the widths of the flanges of the same size channels vary considerably, not only as rolled in different mills, but also as rolled in different weights in the same mill, it is impossible to fix a general standard for the distance from the back of the channel to the rivet holes through _ the flange. The following formula, however, = F!6 31% gives values for this spacing which are sufficiently close for practice: a ice 8 4 a3 (1 73.) in which ais the distance from the back of the channel to 942 DETAILS OF CONSTRUCTION. the center of the rivet hole for the minimum weight of channel, and d isthe depth of the channel, both in inches. peerio ole For channels heavier than the minimum weight, but of the same form, except with thicker web (i. e., in which the weight is increased by simply spreading the rolls), the space a should be increased by the amount a, as derived by the following formula: ge (174) in which zw, is the zzcrease in pounds of the weight per foot above the minimum weight, and d is the depth of channel, as above. The value given to the space a, Fig. 317, should contain no fraction smaller than one-sixteenth of an inch. , 1556. It may here be noticed, incidentally, that from formula 174 may be obtained the thickness of the web or the width of the flange of a channel of any weight, when the thickness of web or the width of flange in the minimum weight of the same size and form of channelis known. In this formula, a, equals the increase in the thickness of web, or width of flange, for cach pound per foot increase in weight. This formula gives accurate results for wrought iron only. The values of the spacing given by formula 173 will, in many cases, vary slightly from the standards adopted by various manufacturers. Each large manufacturer of struc- tural material usually has his own standard spacing, suited to the widths of the flanges in the channels manufactured by him. | Perhaps the most notable exception to the correct appli- cation of formula 173 occurs in the case of light 8” channels. As rolled by some mills, the lighter weights of this size of channels (10 pounds per foot) have flanges no wider than the ordinary widths of flanges in 7” channels. The spacing for the flanges of these lighter weights of 8” channels will here be obtained by applying formula 173 the same as for 9’ channels. When the weight of the channel does not greatly DETAIES OF. CONST RUGRION;: 943 exceed the minimum weight, formula 174 need not be applied. Thus, in the example, for the 8” channels of the upper chord, the space a should equal } x 7++4= 14 inches. Hence, as the distance between the channels, back to back, is 7$inches (Art. 1523), the perpendicular distance between the rows of rivets connecting the cover-plate to the channels in the upper chord is 74+ 2 X 14=9#% inches. This dis- tance should usually be made the same on the chord and end post. The distance, back to back, between the channels of the end post is 72 inches. Hence, the distance a, from the center of the rivet hole through the flange to the back of the 9% — 7% channel, will be made equal to ea; = 1, inches. _ This spacing is shown on the top view of the end post, Mechani- cal Drawing Plate, Title: Highway Bridge: Details I, Fig. 1. If the channels of the end post were of lighter weight, having narrower flanges, the distance between the backs of the channels, and also between the rivet lines, would be somewhat greater. The positions of the rivet dines being thus fixed, the spacing of the rivets is readily laid out. 1557. Spacing of Rivets in Cover-Plate.—By item (d,) of the specifications the pitch of the rivets must not exceed 6 inches, or sixteen times the thickness of the thinnest outside plate. The cover-plate in the end post is 8 of an inch thick; hence, the pitch of the rivets connecting it to the channels must not exceed 16 X 2=6 inches. The maximum pitch of the rivets in the cover-plate has been made 5 inches, though, in compliance with the specifications, it could have been 6 inches. Near the ends of the member the pitch of the rivets should always be materially dimin- ished; and, so far as possible, the rivet spacing should be the same at both ends of the member; that is, the rivet spacing on the two halves of the member should be sym- metrical with reference to the center (between pin holes) of the member. This facilitates the laying out of the werk in 944 DETAILS OR CONSTRUCTION, the shop. The sum of the rivet spaces between the centers of the pin holes should be exactly equal to the length of the member between those points. ‘Thus, in the end post of the example, the sum of the rivet spaces between centers of pin holes is as follows: 53 spaces at Sie TO CNes ean 2 spaces at 4-9. inches =. 0’ 93” 4 spaces at AY itiches ela 2 spaces at Sa ACheS— et) ci 2 spaces 3 and 14+ inches= 0’ 4?’ 2 spaces 24 and2 inches= 0’ 4}” Distance center to center of pins = 25’ 58” At the lower end of the end post, the rivet spacing between the center of the pin hole and the end of the mem- ber should exactly correspond with the length between those two points. At the top of the end post, the rivet spacing must correspond with the holes left vacant for connecting the hip cover-plate, which in this case serves also as a connection for the portal bracing. The bevel for the hip joint should be carefully determined by laying out in pencil, to a large scale, the general dimen- sions of a side elevation of a hip joint somewhat similar to the side elevation shown in Mechanical Drawing Plate Title: Highway Bridge: Details IV, Fig. 13; and the exact bevel should be shown on the side elevation by the base and altitude of a right-angled triangle, one of which dimensions should be 12 inches for convenience in laying out in the shop. The exact length of both cover-plate and channels should be given. 1558. The Bottom View; Batten Plates.—For the details of the bottom view, the positions of the batten plates (sometimes also called tie plates and stay plates) are first approximately determined. Theyshould be as near to the ends of the member as possible, but should give ample clearance for the members connecting upon the pins. The position of the lower batten plate, giving sufficient clearance DETAILS OF CONSTRUCTION. 945 for the lower chord member, may be found by drawing accurately in pencil a side elevation of the shoe joint simi- lar to that shown in Fig. 17 of the plate just referred to, but omitting unnecessary portions. From thisdrawing may also be determined the general dimensions of the standards of the shoe; also, how much, if any, of the lower corners of the channels of the end post it will be necessary to cut off, and how far back from the end it will be necessary to cut away a portion of the lower flanges of the channel, in order that the end post will fit into the shoe with sufficient clear- ance, as shown on the side elevation and bottom view in Fig. 1, same title as above, I. The position of the upper batten plate on the end post, giving sufficient clearance for the hip vertical rods, may be found by drawing the hip vertical rods in their proper posi- tion in the side elevation of the hip joint drawn to determine the bevel. From this drawing may also be obtained the position of the batten plate on the upper chord, giving sufficient clearance for the main tie bars. 1559. Inarranging the approximate position of each batten plate, a clearance of about one inch should be given to the member connecting upon the pin. According toitem (0,) of the specifications, each batten plate must have a length equal to 14 times the width of the member, or, in the present case, 14 x 12=18 inches. The thickness of the batten plates should be not less than ;4, of the distance o between the rivet lines in the parts which the batten plates Ky ie , Pie Colnect, or, in the present. case, i .195 of an inch. a © The thickness of the batten plates, however, may generally be the same as the thickness specified for the lattice bars on the same member, or, in this case, + of an inch. According to the first condition of item (d@,) of the specifications, the pitch of the rivets in the batten plates of the example must not exceed 16 X }=4 inches. By placing each of the outer rivets in the batten plate at a distance of 14 inches from the corresponding end of the plate, there will remain 946 DETAILS OF CONSTRUCTION. 18 — 2 x 14 = 15} inches’ between these rivets, which may 15.5 ee distance between the rivet lines on the lower side of the end post is the same as the corresponding distance on the upper side, or 9# inches. be divided into four spaces of = 3f inches each. The 1560. _ It will be well to notice also that item (d,) of the specifications requires that ‘‘the pitch of rivets at the ends of the compression members shall not exceed four diameters of the rivet for a. length equal to twice the. width ofthe member.” As the batten plate usually comes within this length, the pitch of rivets in it should be considered to be governed by this condition, although this was not done in the example. In any case, however, the following is a safe Rule.—J/n chords and end posts, make the pitch of rivets wn the batten plates as nearly as practical the same as in that portion of the cover-plate directly opposite. This pitch, how- ever, must in no case excecd sixteen times the thickness of the batten plate. 1561. The Lattice Bars.—The portions of the bot- tom flanges of the channels of the end post situated between the batten plates are to be stayed by diagonal bars, called lattice bars.’ When the diagonal stays or braces of this system do not intersect each other at any point between their ends, as is the case on the chord and end post of the example, the system is sometimes called lacing, and the bars are called lacing bars, those bars only which cross each other being called lattice bars. In this Course, how- ever, the distinction will not be made, but all such systems of stays or bracings will be designated as lattice, and the bars as lattice bars. 1562. Lattice bars connected by one rivet at each end, as in the present case, should have a width of about three times the diameter of the rivet used, or, in our example, about 3X 3=1f inches. Item (0,) of the specifications (Art. 1511) requires the size of lattice bars used to connect DETAILS OF CONSTRUCTION. 947 the flanges of 8” channels to be 12” x }’.. The same item specifies that the lattice bars shall be inclined at an angle of not less than 60 degrees with the axis (center line) of the member. ‘The distance between the batten plates may be divided into any number of equal spaces that will give the required pitch. In order that the pitch of the lattice bars may not contain an inconvenient fraction, the spacing may be started from the inner rivets of the batten plates, as shown in Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. 1, or it may begin at points on the channels about 24 inches from those rivets, a distance just sufficient for the lattice bar to clear the batten plate. It is better practice to have the lattice bars connect upon the inner rivets of the batten plates. The positions of the bat- ten plates may be slightly changed to suit the spacing of the lattice bars. It must be remembered that the rivets attach- ing the lattice bars to one channel are midway between those attaching them to the opposite channel, requiring half spaces at the ends, which may both come upon the same channel and count as a whole space, or one may come upon each channel and thus count as a half space. 1563. The exact length / of the lattice bars, from cen- ter to center of rivet holes, should always be given; it may be found by the following formula: f= v (2) + w?, (175.) in which 7 is the pitch of the lattice, 1. e., the distance be- tween two adjacent rivets connecting the lattice bars in the same rivet line, and w is the perpendicular distance between the two rivet lines. If the lattice bars are inclined at an angle of exactly 60 degrees, pa) eee. (177. ©) Thus, in the end post of the example, if the inclination of the lattice bars is 60 degrees, the pitch of the lattice is equal to the length of the bars = 1.1547 x 9.75 = 11.2583 inches, 948 DETAILS OF CONSTRUCTION: or, practically, 114 inches. It is found that by taking ad- 114 pi is made, to count upon each channel at the opposite ends of the latticed length of the member, the bottom plates can readily be so arranged that a pitch of 114 inches can be used. vantage of the half space of = 52 inches, one of which 1564. The distance of the outer rivet in each batten plate from the center of the pin hole should be given. These two distances, together with the rivet spacing on the batten plates and the spacing for the lattice bars, when added together, must give the exact length of the member from center to center of pin holes. On the end post of the example these distances are as follows: 1 space at 12%inches= 1’ 02’ 4 spaces at 38finches= 1’ 3}’ 22 spaces at 114 inches = 20’ 74" dspace. at Seunches =. o. 4 spaces at 3finches= 1’ 33’ lspace at 8%inches= 0’ 83’ Distance center to center of pins = 25’ 53” DETAILS OF THE UPPER CHORD. 1565. The arrangement of the constructive details of the upper chord is so very similar to that for the end post as to require very little special explanation. The thickness of bearing and number of rivets required, determining the sizes of the pin plates upon the chord at the hip, were found in connection with the details of the hip joint. In the cover plate, the pitch of rivets must not exceed 16 x 4 = 4 inches. In the greater portion of the length of the member the pitch of the rivets is 4 inches, but it is reduced towards the ends of the member. Near each end of the panel the rivet spacing is necessarily accommodated to the details of the connecting members. Between the centers of the pin holes the sum of the rivet spaces exactly equals the panel length. On top of the cover plates is riveted the bent plate for DETAILS OF CONSTRUCTION. 949 connecting the portal bracing and also the short pieces of augles forming the lateral connections. The intermediate lateral strut also connects on top of the chord at C, vacant holes for this connection being shown in the cover-plate and cover splice plate. 1566. The lateral connections are placed as near to the portal and intermediate struts as practicable, but allowing sufficient clearance. The angles at which the lateral con- nections or lateral hitches are placed upon the chord are determined by the positions of the points at which the cen- ter lines of the lateral rods intersect the center line of the chord. Each point of intersection is also the center, in each direction, between the rivets connecting the short pieces of angles forming the lateral connections, or, in other words, the center of the lateral hitch. Theoretically, these points, where the center lines of the lateral rods intersect the center line of the chord, should be at the intersections of the center lines of the lateral struts with the center line of the chord. It is impossible, however, to locate the lateral hitches at these intersections, but they should be located as near to them as possible. At the hip joint, the distance from the center of the pin to the center of the lateral hitch is 14,3, inches, and at the intermediate joint C, the distance between the center of the pin and the lateral hitch of the end panel is 8,3, inches. Hence, as the panel length of the chord is 18’ 02", the longitudinal projection of the lateral rods in the panel 2 C, from center to center of connections, i. e., the distance be- tween the centers of the two lateral hitches, is 18’ 02” — (14,3," + 8,3,") = 16’ 2" =194 inches. The lateral projection of the lateral rods, center to center of connections, 1. e., the distance from center to center of chords, is 18 + 1 = 19 feet = 228 inches. In determining the base and altitude of the right-angled triangles which show the angles of the lateral hitches, if the smaller dimension be made 12 inches, by calling the greater dimension x, we have the proportion 194 ; 228 :: 12: 4, whence x = 14.103, or slightly more than 950 DETAILS OF CONSTRUCTION. 14.3, inches. For the convenience of the workmen, one of these dimensions should always be 12 inches. 1567. Splice Plates and Intermediate Joint.— The channels and cover-plate of the upper chord are spliced as near the joint at C as is practicable for the details of the connecting members. The ends of the channels and cover- plates are to be planed to give true abutting surfaces. Ac- cording to item (g,) of the specifications, the joint must be spliced sufficiently to maintain these parts accurately in con- tact. A splice plate is placed on top of the cover-plate and on the outside of the web of each channel. Sometimes, in large chords, small angle bar splices are also placed on the lower sides of the lower flanges of the channels, but it was not done in this case. The splice plates on the outsides of the webs of the channels serve also as reinforcing plates for the pin bearings, as do also the plates for the post connec- tion on the insides of the channels, really giving con- siderably more than the required amount of bearing for the pin. As the splice plates for the channels and cover-plate of the chord do not bear stress, but simply serve to hold the parts in position, no rule can be given for calculating the number of rivets required. ‘The designer must be guided by his judgment and by such conditions as may arise in each individual case, always endeavoring to make a neat and substantial joint. Sufficient clearance should always be given between the heads of rivets passing through the web of the channel and the heads of rivets passing through the flanges of the same. The bending moment upon the pin at this joint is pro- duced wholly by the stress upon the counter rods ; it occurs in the plane of these rods, and is found by a single moment diagram. It will not be necessary to explain the process in detail. 1568. Batten Plates and Lattice Bars.—The size of the batten plates, as well as the size of the lattice bars, is’ the same on the chord as on the end post. The position of DETAILS OF CONSTRUCTION. 951 the batten plate near the hip joint must be such as to give sufficient clearance for the main tie bars, which is deter- mined by a drawing of the side elevation of the hip joint, as previously stated. The batten plate in the end panel near the intermediate joint C is not required to clear any diagonal member, but it should be as near the splice as practicable. It is found that by carefully arranging the positions of the batten plates, the pitch and, consequently, the length of the lattice bars on the chord can be made the same as on the end post. The pitch of the lattice bars throughout the chord and end posts should be made the same where practicable. The rivet spacing on the bottom of the chord between centers of the pin holes should add up exactly equal to the panel length. All rivet spacing in the center panel of the chord is made as nearly the same as that of the end panels as the condi- tions will permit. ‘The position of the batten plate, giving sufficient clearance for the counter rods, is determined by drawing a side elevation of the intermediate joint similar to that shown in Mechanical Drawing Plate, Title: Highway Bridge: Details IV, Fig. 14. As this panel of the chord is made perfectly symmetrical with reference to the center of the panel, only one end need be shown. CONSTRUCTIVE DETAILS OF THE INTERME- DIATE POST. 1569. The Top Connection.—The angles of which the intermediate post is composed connect on the inside of plates that are for that purpose riveted on the inside of the channels of the upper chord. The live and dead load stresses upon the intermediate post are, respectively, 9,700 and 2,300 pounds. Neglecting the reduction for column length, the live and dead load unit stresses allowed upon the post are 8,750 and 17,500 pounds per square inch, respect- ively. Allowed shearing stresses upon a 3” rivet, at three- quarters the unit stresses allowed upon the member = 8,750 X # X.38068 = 2,010 pounds for live load stress, and 952 DETAILS OF CONSTRUCTION. 17,500 x 2 x .3068 = 4,030 pounds for dead load stress. Hence, the total number of rivets required by this condi- tion for connecting the angles of the intermediate post to the plates riveted upon the inside of the channels of the 9,700 , 2,300 2.010 ' 4,030 At 9,000 pounds per square inch, the value of a 8" rivet in single shear, as givene by Table 38, Art. 1537, 1s 2,760 pounds. Hence, the number of rivets required for 9,700 + 2,300 2, 760 =). 4, OT, practically tanl vers chord is the same purpose by this condition is = 4.3, or, practically, 5 rivets. The thickness of metal in the angles of the interme- diate post is + of an inch. At 15,000 pounds per square inch, Table 87; rt. 537, ives the pearing ear of a 8” rivet through 1” thickness of metal at - 2,340 pounds.. Hence, the number “of rivets required bymtmis 9,700 + 2,300 2, 340 = D.ds-Olg plactin condition for bearing stress is cally, 6 rivets. At one and one-half times the unit stresses allowed upon the post, the bearing value for live load stress of a 2” rivet through }” thickness of plate is 8,750 x 3 x § x $= 2,050 pounds, and for dead load stress, 2,050 x 2 = 4,100 pounds. Hence, the number of rivets required by this condition is 9,700 _ 2,300 2.050 aE 4,100 Therefore, it is found that (5.4) 6 rivets, if machine driven, will meet all the requirements. But the rivets connecting the angles of the intermediate post to the plates riveted upon the inside of the channels of the chord are necessarily field driven. According to the latter portion of item (a@,) of the speci- fications, the specified limits of shearing and bearing stress must, for field riveting, be reduced one-third part; or, what amounts to the same thing, the number of rivets, as required by the limits specified for shearing and bearing, must, for field rivets, be increased one-half. Consequently, the number ='§.9, Or, practically 6:t1vets: DETAILS OF CONSTRUCTION. 953 of field rivets required in the present case is 14 x 5.4 = 8.1, or, practically, 8 rivets. 1570. The preceding computations may be a little shortened by means of the following formulas, in which d= diameter of rivet, = thickness of plate, and Z, D, u, and A have the same meanings as in formulas 166 and 168. Number of rivets required by shearing stress at 9,000 per square inch, L+D N,, — 9,000 A” C77.) Number required for bearing stress, at 15,000 per square inch, L+D zz... = =. 5s 15 000a2 (178.) Number required for shearing, at # unit stress on member, yas) gee, i: Number required for bearing, at 3 . 224 D_ 222+ D) ena? 8x Bala The values of 9,000 A are given by Table 38, Art. 1537, and those of 15,000 @ ¢ by Table 37, same article. Instead of computing all the values, we proceed as fol- lows: Since z, and z,, have the same numerator, that will be greater which has the smaller denominator; but, as 9,000 A and 15,000 d¢ have the common factor 3,000, we only have to compare 3 A andid/?. In the present case, 34 = 3 X .38068 = .9204, and.56 d#=5x 8X +=28xX4= “7+. It is not necessary to continue the latter operation, as it is seen at once that the result will be smaller than 3 A. Therefore, 7,, 1s greater than z,,and formula 178 should be used (15,000 d@ ¢ = 2,340, as given by Table 37). The result is 5.1, as found before. In a similar manner, to find whether 179 or 180 should be used, we compare 3 Au with 6d¢ uw, or, since 3 u is il (179.) unit stress on member, (180.) 954 DETAILS OF CONSTRUCTION. common, we compare A and 2d¢. Now, A =.3068, and Qeat=2xsx P= B= .31+, whichis greater thang Therefore, z, is greater than z,, and formula 179 should be used. This gives 1 2 (19,400 + 2,300) _ 2,170 *— “3 3008x8150 BC Dna OTe — 5.4, as found before. In all computations where the same rules are used, it is convenient to construct a general formula, as this saves time and often suggests very short methods for finding the required results. The preceding formulas are derived by very simple arithmetical reasoning, and it would be a good exercise for the student to try to derive them himself. 1571. The width of the post, perpendicular to lattice bars, is 34 -+4-+ 34 = 74 inches. Plates 74” x 7" are used for the connection. As the distance from back to back of the channels in the upper chord is 74 inches, the clear width between these connecting plates is 74 — 2 x 4% = 64 inches. The post is given no clearance between these plates, but its width, parallel to lattice bars, is made the same as the clear distance between the plates, 1.-e., 6 inches. As the upper ends of the angles of the post extend but } of an inch above the lower edges of the channels of the chord, the post can probably be placed in position without clearance, but it would usually be better to give a clearance of ;', of an inch on each side, making the width of the post, in this case, 62 inches. 1572. Spacing for Rivet Lines in Angles.—The lattice bars will be 4 of an inch thick, and, in order that two bars can connect upon each rivet between the angles, the latter must be }-++4=4 inch apart. Batten plates 1” thick are used at the ends, requiring also filler plates #” thick between the angles, except at the two rivets where the lattice bars connect upon the batten plates. As was stated in Mechanical Drawing, Art. 56, the posi- tion of the rivet line in an angle bar is always fixed by the DETAILS OF CONSTRUCTION. 955 distance from the back or corner of the angle. For this distance the values given by the following formula agree with most of the adopted standards: t pe 5 + ¢, CES 1:) in which @ is the distance from the back or corner of the angle to the center of the rivet hole, d is the nominal length of the leg (see Fig. 318), ~-a — ; and ¢ is a constant, having the following values: = For values of d of 14" or less, ¢ = A 6 . For values of d of from 2” to 23?”,c=}’. For values of d of from 3” to 5’, c= }’. For values of @ above 5", hoe FIG. 818. These values of c, when substituted in formula 181, will give the values of a that agree with what is probably the most common practice. But, as in the case of channels, the practice is not uniform, though it is more nearly so. For instance, it is not uncommon to give ¢ a value of 4 of an inch for values of @ of from 14 to 24 inches, inclu- sive. In the intermediate post, the connected leg of the angle is 2 inches wide =d. Hence, by formula 181, the distance from the back of the angle to the rivet line is } + 4 =1{ inches. This fixes the distance between rivet lines at 6 —2 x 141 = 48 inches. 1573. The Bottom Connections.—The rivets con- necting the pin plates at the lower end of the post with the free legs of the angles are staggered with those connecting the angles with the batten plates. As the stress upon the post requires the same number of rivets to connect it at the bottom as at the top, it is evident that more rivets are used to connect the pin plates at the lower end of the post than are required by the stresses. The pin plates should be thick enough to give the required IT. [1,—22 956 DETAILS OF CONSTRUCTION. bearing upon the lower chord pin. Applying rule given in Art: 1531, we ‘see that! 3.x 2;90081S* Jess thane o0m Therefore, the required thickness is given by formula 166, as follows: _ 2X 9,700 + 2,300 ; oe TS Te WE Ee eo} 5 LO iC RUE IB FROM eT eae This would require each pin plate to be only 3;", but such thickness would be too small for strut resistance. 1574. Forked Ends of Compression Members.— Item (¢,) of the specifications (Art. 1511) requires that ‘Where the ends of compression members are forked to con- nect to the pins, the aggregate compressive strength of these forked ends must equal the compressive strength of the body of the members.” The pin plates form the forked ends of the post. In order that the angles forming the post may clear the ends of all other members connecting upon the pin, the pin plates must project beyond the ends of the angles a distance depending - upon the dimensions of the other connecting members. The aggregate sectional area of the pin plates should not be less than that of the angles forming the post. These angles weigh 4.4 pounds per foot, giving an aggregate sectional area of. 4.4 4 43, = 5.28 square inches. The post: is 4 inches wide, and pin plates of the same width and 2 of an inch thick will give an aggregate sectional area of 74 x 2X 2= 5.63 square inches. 1575. The strut resistance of these pin plates will now be investigated. The length of the strut formed by a pin plate may be taken as the distance between its bearing upon the pin and the first rivet connecting it to the angles, if the batten plate supports or stays the angles at or very near their ends. It will be on the side of safety, in such a case, to take the distance between the center of the pin hole and the center of the first rivet as the strut length of the pin plates. In the present case, the distance is 6 inches. DETAILSVORFCONSTRUGTION: 957 According to formula 140, Art. 1433, the least radius of gyration of each pin plate is equal to .289 x 2 =.1084 of an inch. Hence, the live load unit stress, as allowed by formula 125, Art. 1410, is 8,750 —50 x =" = 5,980 pounds. The dead load unit stress is 5,980 x 2 = 11,960 pounds. The area necessary to resist the stresses upon the post is, there- fore, eee + Be aie 5,980 —§ 11,960 the sectional area given by the two pin plates is 5.63 square inches. It is, therefore, found that the strut resistance of these pin plates is ample, when computed upon the same basis as the resistance of the post as a whole. Considered as struts, the two pin plates will bear 5.63 x 5,980 = 33,670 pounds of live load stress. The rivets con- necting the pin plates to the angles of the post should have nearly the same resistance as the pin plates considered as struts. At 9,000 pounds per square inch, the value of a 3” rivet in single shear is 2,760 pounds. (Table 38, Art. 1537.) The metal in the angles forming the post is + of an inch thick. At 15,000 pounds per square inch, the bearing value of a 3” rivet through 4+ of an inch thickness of metal is 2,340 pounds. (Table 37.) The latter is the critical condi- tion. Hence, in order that the rivets connecting the pin plates to the angles shall have the same resistance as the pin plates considered as struts, the number of rivets required for this purpose is saree = 14.4 rivets. Twelve rivets are used for this connection, which is nearly twice the number required by the live and dead load stresses in the post, as found for the connection of the top of the post. The pin plates at the bottom of the intermediate post do not strictly comply with ail requirements as indicated in item (¢,) of the specifications, but they may be considered practically to fulfil the really important requirement of that item; namely, that the aggregate compressive strength of the forked end shall equal the compressive strength of the body of the member. = 1.81 squareinches. As found above, 958 DETAILS OF CONSTRUCTION. CONSTRUCTIVE DETAILS OF THE PORTAL BRACING. 1576. Conditions Governing the Arrangement of Lattice Bars.—The portal is shown in Mechanical Drawing Plate; Titler Hiohway “Bridge: Details Tl Big aan The design of the details of this member consists principally in determining the proper arrangement and dimensions of its connections, and also the arrangement of the lattice bars, and their connections with the flange angles. These are for the most part questions of judgment rather than of calcula- tion. Certain conditions, however, which are susceptible of calculation, must be fulfilled. The conditions governing the arrangement of the-lattice bars will first be noticed. The lattice bars must be connected to and support the flange angles at such frequent intervals that the strut resistance of the flange in the plane of the lattice bars will be at least as great as its resistance in a plane perpendicular to the lat- tice bars, as determined in proportioning the material for the flanges. In order that this may be the case, the distance /, between the rivets connecting the lattice bars to the flanges, in inches, must never be greater than given by the formula Lies a) (182.) in which / is the length of the portal flange (usually taken center to center of chords), 7 is the radius of gyration of same about an axis parallel to plane of the lattice bars, and vy, is the radius of gyration of the same about an axis per- pendicular to plane of the lattice bars, all in inches. The value of 7 is given in formula 113, Art. 1408. Fic. 319. For two angles with the shorter legs connected back to back, but separated by lattice bars (see Fig. 319), the value of the radius of gyration about an axis parallel to longer flanges of angles, i. e., the value of 7,, is given by the formula 28 r= 100 V. (1 83.) DETAILS OF CONSTRUCTION. God! For any ordinary section, the value of 7,, as given by for- mula 183, will never be less than one-fourth the value of 7, as given by formula 113, and it will seldom have a value so relatively small. Hence, the greatest allowed length of /, as limited by this condition, may be found by substituting 47 for 7, in formula 182, as follows: We a anus: DN erp ae (184.) In the present case, the value of 7 is sea Yel, o1nChes. and the value of 7, is a x2. 0 = Or ale inches we. vyaiie of 7 is 19 feet = 228 inches. Hence, the value of /, must not we Soap exceed ts * 228 = 88% inches. As determined by formula | 228 184, the value of 7 must not exceec eo 7 inches, which is less than the value just obtained, and very mate- rially on the side of safety. In compliance with other conditions, however, the pitch of the rivets connecting the lattice bars to the flange angles can never be made as great as either of the preceding values of 7; it is commonly made about 12 inches. Hence, with flanges composed of angles connected by lattice bars, this condition is never liable to be violated, and may be neglected. But there also exists a much more severe condition. 1577. The pitch of the riv- ets along each lattice bar, that is, those connecting the bar with the lattice bars which cross it at right angles, or nearly so, and to the flange angles, must not exceed a certain multiple of the thickness of the bar. This is a much more critical condition than the preceding. Inorder that a lattice bar shall have a reasona- ble amount of resistance as a 960 DETAILS OF CONSTRUCTION. strut, its length between connections should not exceed about 125 times its least radius of gyration. Formula 140, Art. 1433, gives the value of the least radius of gyration of a rectangular bar = .289 ¢, ¢ being the thickness; 125 times this = 36 ¢. Hence, the pitch S of the rivets con- necting the bars (see Fig. 320) should not exceed the value given by the formula Sache (185.) In the example, the lattice bars are + of an inch in thick. ness; consequently, the value of S should not exceed 36 x 4=9inches. If the lattice bars are placed at an angle of 45 degrees with the axis of the member, 1. e., at right angles to each other, the maximum value of / is given by the simple formula Veh (BGT seta 807) = Oe Le (186.) In the example, ¢ = 4, and the value that 7, must not ex- ceed ol & b= 1, ouinches! )Dhis ispthen, the eoverom condition. 1578. In general, if @ and dare the sides, and / the hypotenuse of a right-angled triangle, it is well known that iat SE WV GA 8. If a = d, which is always the case when one of the acute angles = 45°, we have, h=Vei+ai= Va = 2 xX a =1.4142a. (187.) Conversely, if 4 is known, the value of a is h We TE BY or OTL. (188.) 1579. The Practical Arrangement of the Lattice Bars.—In the example the clear width of the roadway is 18 feet: = 216 inches. At each «side.(end) omthesponraieia lattice bars are attached to a somewhat larger vertical bar. By trial it is found that by allowing on each side 144 inches DETAILS OF CONSTRUCTION. 961 between the outer line of rivets attaching the lattice bars and the inner edge of the upper chord, the space remaining between the two outer lines of rivets attaching the lattice bars (= 216 — 2.x 144 = 2128”) may be divided into 18 212.625 ; spaces of — ee 11.8125, or 1142 inches each. The vertical pitch of the lattice bars is made the same as the horizontal pitch, or 114% inches. The legs of the flange angles to which the lattice bars attach are 24” long, and by formula 181, Art. 1572, the distance from the back of 21 the angles to the rivet line is 3 ++34=12 inches. Hence, the depth of the portal, from out to out of flange angles, is 2x 1143+ 2x18 = 268 inches. The space, or pitch, S, along the lattice bars, as given by formula 188, is .7071 x 11.8125 = 8.3526, or 8223 inches. A single space is usually expressed to the nearest sixteenth of an inch; but,. in case the same space is several times repeated, the error thus accumulating may become considerable; hence, in thespresent, case, the (pitch of the rivets in the lattice bars is expressed to the nearest sixty-fourth of an inch. The latticing of the brackets is simply a continuation of the latticing of the main or horizontal portion of the portal. 1580. The Portal Connections.—The upper flange of the portal is to be riveted to the bent plate shown on top of the chord in Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. 2. It is also to be connected to the chord and end post by means of the hip cover-plate, which is shown attached to the flange. The details of these con- nections are somewhat complicated, but the dimensions of the connecting pieces may be determined by accurately drawing them in position. The number of rivets required to connect the upper flange may readily be determined from the stress. The plates used for the connection are 4” thick. By reference to Table 37, Art. 1537, it is found that, at 5” 15,000 pounds per square inch, the bearing value of a 3 962 DETAILS OF CONSTRUCTION. rivet through a }” plate is 2,340 pounds, while Table 38 of the same article gives the value of a 2” rivet in single shear, at 9,000 pounds per square inch, to be 2,760 pounds. Hence, . the bearing is the critical condition. . The external forces acting upon the portal are shown in Fig. 278, Art. 1311. By taking moments about the point where the flange of the bracket connects to the end post, the stress at the point where the upper flange connects to the end post isfound to be 2,700 K 21 + 4,050 x 5 5 ber of rivets required for the connection of the upper flange 15,390 2340 are: to be field driven, eight rivets fare, used = threeusnan rivets connect the flange to the hip cover-plate, and five field rivets connect it to the bent plate on top of the chord, counting as 3-++ 4% X 5= 6.3 rivets. The lower horizontal flange of the portal and the lattice bars of the bracket attach by means of a 5” x }" plate to an angle bar shown riveted on the web of the end-post channel, while the flange angles of the bracket are to be riveted directly to the web of the channel. It will be noticed that the 5” x 4” connecting plate has }” clearance from the web of the channel. It would be impossible to determine accurately the number of rivets required for this connec- tion, but by comparison with the number of rivets required for the upper flange, it is seen that a sufficient number is used. It is necessary to cut away portions of the connect- ing legs of the angles of the bracket flange, in order to con- nect between the flanges of the channels of the end post. All dimensions of the connecting parts, as well as the holes and rivet spacing, must be accurately and plainly shown and marked. The dimensions of the connecting parts may be determined and the rivet holes located by carefully drawing them in place to a sufficiently large scale. This need be only a pencil sketch, but it must be accurate. It is always well to check the results by calcula- tions. = 15,390 pounds. Hence, the num- of the portal is =, O.TIVELSyal 2iSuiLy Go On LNcoe crits DETAILS OP CONSTRUCTION: 963 CONSTRUCTIVE DETAILS OF THE LATERAL STRUTS AND KNEE BRACES. 1581. The Lateral Strut.—The details of this mem- ber are shown in Mechanical Drawing Plate, Title: Highway Bridge: Details II, Fig. 2; they are exceedingly simple. The strut is to be connected to each chord by means of rivets, for which vacant holes-are shown through the horizontal legs of the angles. The number of rivets for this purpose may be calculated from the initial stress assumed upon the strut. The thickness of metal in the angles of the strut is 2 of an inch, while in the chord the rivets pass through both the cover-plate and the cover splice plate, or 4 inch thickness of metal. At 15,000 pounds per square inch, the bearing value of a 2” rivet through 2 of an inch thickness of metal is found to be 3,520 pounds (Table 37, Art. 1537), while at 9,000 pounds per square inch the value of a 2” rivet in single shear is 2,760 pounds. (Table 58.) The latter is the critical condition. In Art. 1425, the resultant stress assumed upon the lateral strut was found to be 11,400 pounds. Hence, the number of rivets required to connect the end of yt Wee Sere) : : the lateral strut is 9 760° = 4.1 rivets. As these rivets are A,tV0 field driven, there will be required 14 x 4.1=6.2; 6 are used. At each end of the strut the two middle holes connect at the center of the cover-plate of the chord, while two holes connect at each line of rivets connecting the cover-plate to 93 . the channels; hence, these holes are spaced = = 4 inches apart. The distance from the two middle holes at one end of the strut to the corresponding holes at the opposite end is 19 feet, or the same as the distance from center to center of chords. The longer or 5” legs of the angles are riveted together, back to back. By formula 181, Art. 1572, the rivet line is fixed at $+ += 22 inches from the corners of the angles. The pitch of the rivets connecting the two angles together will not, within any reasonable limits, be so great as to weaken the member as a strut; hence, within 964 DETAILS OF CONSTRUCTION. such limits, these rivets may be given any convenient pitch. A good rule for such cases is as follows: Rule.—/n angles connected closely together, back to back, make the pitch of the rivets, based upon the thickness of the angles, double that allowed by item (d,) of the spectfications (Art US 1): Thus, inthe example, the pitch of the rivets connecting the vertical Jegs of the angles composing the lateral strut is 16 X 2 X 2 = 12 inches. 1582. The Knee Brace.— The form of the section of the knee brace, Fig. 3 of plate referred to in the preceding article, is similar to that of the lateral strut. The brace is usually inclined at an angle of 45 degrees. The horizontal and vertical projections of the inclined portion of the brace are usually made about 3 feet. In the present case, each is made 3’ 02”, or 36.375 inches; hence, by formula 187, the length from bend to bend is 1.4142 x 36.375 = 51.4415, or, very closely, 4’ 3”. The lower end of the brace attaches to the angles of the intermediate post. As the post is 6f inches wide, from out to out of angles, and the inner rivet holes through the end of the brace to connect it with the lateral strut are 1%,” from the bend, it follows that ox the lateral strut the distance from the middle pair of rivet. holes at the end of the strut (at center of chord) to the nearest pair of holes connecting . 64 : ; the knee brace is oF + 362+ 1% = 412 inches. Deducting one space of 4 inches at the end of the strut, we get 412 — 4q = 364”, or 3' 04”, as marked upon the strut. The posi- tions of the holes in the angles of the intermediate post for the connection of the knee brace are determined in a similar manner. The 3” legs of the angles are riveted together, back to back. The distance from the backs of the angles to the rivet line, as fixed by formula 181, is 3+4=1inches. Ac- cording to the rule given above, the pitch of the rivets is DETAILS OF CONSTRUCTION. 965 made double that allowed by item (d,) of the specifications. The vacant holes in the knee brace are placed rather nearer to the outer edges of the angles than is usual, better to accommodate the holes in the angles of the post and strut. 1583. The Shoe Strut.—This member, which is shown in Mechanical Drawing Plate, Title: Highway Bridge: Details III, Fig. 4, is a lateral strut, and will next be noticed. It can not be completely detailed until the di- mensions of the shoe are determined, but as the details for this member are so simple as to require very little special explanation, they will here be briefly noticed. The angles are riveted together with the shorter legs back to back, and the plate between them. ‘The spacing of the rivets is determined according to the rule given above for the lateral strut, which it resembles in form. The distance from the corners of the angles to the rivet line, as fixed by formula 181, is = + 4 = 12 inches. From Art. 1434, it is known that the shoe strut is pro- portioned to resist a resultant stress of 7,260 pounds. At 9,000 pounds per square inch the value of a 2” rivet in single shear is 2,760 pounds (Table 38, Art. 1537), while at 15,000 pounds per square inch the bearing value of a 2” rivet through a 1” plate is 2,340 pounds (Table 37). Hence, the latter is found to be the critical condition, and the number of rivets required for connecting the end of the shoe strut, if machine driven, is 7,260 2, 340 used. When the dimensions of the shoe have been determined, the position of the lateral pin in the shoe and the length of the shoe strut may be found by drawing a plan of the shoe and its lateral connections, similar to that shown in Mechan- ical Drawing Plate, Title: Highway Bridge: Details III, Fig. 17. The lateral strut must be short enough to clear the loop of the lateral rod. weil, OF, ib neld driven. J+ 5.) = 4.7 rivets; 4 are 966 DETAILS’ OP CONSTRUCTION: CONSTRUCTIVE DETAILS OF THE FLOOR- BEAM. 1584. Positions of Rivet Lines.—In detailing the floor-beam, Mechanical Drawing Plate, Title: Highway Bridge;, Details, 11; Figo. 4, it;will beawell first) tomieeene positions of the rivet lines for the rivets connecting the flange angles to the web-plate, and then determine the required spacing of the rivets along the same. The depth of the web- plate is 24 inches, but (see Art. 1319) the depth of a floor- beam, out to out of flange angles, may be made from } to 4 of an inch deeper thana web plate. Inthe present case the depth of the beam, out to out of flange angles, is made 4” deeper than the web-plate, or 244 inches. The flange angles are’4” 3" angles with the 3 levs conmectedstag tomy er As fixed by formula 181, the rivet lines are 3+ 14= 1?inches from the backs of the free legs of the angles, making the dis- tance betwen the rivet lines of the upper and lower flanges 244 — 2 x 12 = 21 inches. 1585. Bending Moments and Increments of Flange Stress.—The bending stress in the floor-beam is zero at the supports and increases to maximum at the center of the beam, while the shear is maximum at the supports and diminishes to zero at the center. This is true of any simple beam supporting a uniform load, and it is true of a simple beam supporting any load or system of loads, with the exception that the maximum bending stress and zero shear may occur at some point other than the center of the beam. The stress, which at the point of support is wholly a shear- ing stress, gradually changes towards the center of the beam, till at the point of maximum bending moment it becomes wholly a bending stress. The change, however, is not uni- form, but more rapid near the supports. Under the assump- tion that the bending stress is borne entirely by the flanges, and the shearing stress is borne wholly by the web-plate, it is evident that between any two points the rivets connecting the flange angles to the web-plate must be of sufficient strength to transfer to the web-plate the difference between DETAILS OF CONSTRUCTION. 967 the bending stresses at those two points. When the load rests upon the upper flange, the rivets connecting it to the web-plate must also be of sufficient strength to transmit the pressure of the load to the web as shear, although this is done largely by the stiffeners, when the latter are used. The bending moment J/, at any point along the loaded portion of the beam is given by formula 98, Art. 1318. By applying this formula at the center of the beam and at certain intervals (say at each foot) along its length towards the end, and dividing each result by the effective depth of the beam, the several quotients will be the flange stresses at the respective points along the half length of the beam. The stress increment, or difference between the flange stresses at any two consecutive points, must be taken by the rivets connecting the angles to the web-plate in that portion of the beam included between the two points. 1586. The Pitch of Rivets in the Flange.—lf the stress increment be divided by the critical resisting value of one rivet, the quotient will be the number of rivets required between the two points. Although this method is quite commonly employed, the same result may be more easily obtained by the following method: Assuming the shear to be resisted entirely by the web- plate, and the bending stress to be resisted wholly by the flange angles, the pitch fof the rivets connecting the flange angles to the web-plate is given by the following formula: rh in which 7 is the least, or critical, value of one rivet, / is the distance between the rivet linesin the two flanges, and Sis the vertical shear in the beam at the point under consider- ation. The rivets connecting the flange angles to the web-plate are in double shear. From Table 38, Art. 1537, it is found that at 9,000 pounds per square inch, the shearing value of 968 DETAILS OF CONSTRUCTION. a 8-inch rivet in double shear is 5,520 pounds. At 15,000 pounds per square inch, the bearing value of a g-inch rivet through 2 of an inch thickness of plate, as given by Table 37, is 3,520 pounds. The bearing is thus found to be the critical condition, and 3,520 pounds is the value to be given to 7 in the preceding formula. As stated above, the distance % between the rivet lines in the upper and lower flanges is 21 inches. S varies in intensity at different points along the beam, being, as previously stated, maximum at the supports and ZerO;at the Coenen As stated in Art. 1227, The vertical shear equals the reaction of the left-hand sup- port minus all the loads (or all that portion of the uniform load) on the beam to the left of the point considered. Formula 189 will be applied to the floor-beam at the sup- port and at consecutive points one foot apart along the length of the beam. From Art. 1316, the total amount of load upon the beam is 41,200 pounds. But the designer of details must obtain his information, from the stress sheet. According to the latter, the maximum flange stress is 53,700 pounds. ° The depth of the web-plate is 24 inches, and, consequently, the effective depth of the beam is 24.5 — 1.5 = 23 inches. Hence, by applying formula 97, Art. 1318, and dividing by d, the effective depth of the, beam. swe @haveswsas.700) ae ae HONE ia ue from a 8X 23 j which W= 41,170, or, practically, 41,200 pounds. As this is a uniform load, the reaction of each support is 41,200 2 = 20,600 pounds, and the load upon each lineal foot of the beam is 4] ; a = 2,289, or, practically, 2,290 pounds. No load is carried upon the half foot of beam adjacent to each support. The computations for determining the required pitch of the rivets at consecutive points one foot apart along the DETAILS OF CONSTRUCTION. 969 beam are tabulated below. The results in column (ce) will be referred to further along: (2) (2) (¢) (¢) (2) Required Distance of | Amount of Shear at Pitch for Final Point from | Load at Left Point, Rivets, Piteh, Support. of Point. S=20,600—(2) p= a a’ b,, a' cy, etc. Feet. Pounds. Pounds. Inches. Inches. O 0,000 20, 600 go00 a.09 1 1,140 19,460 3.80 Bey 2 3,430 17,170 4.31 4.20 o 5, 720 14, 880 4.97 4.81 4 8,010 12,590 5.87 5.61 i) 10,300 10,500 Tako 6.72 6 12,590 8,010 i 14,880 5, 720 8 17,170 3,430 9 19,460 1,140 As the pitch of the rivets must not exceed 6 inches, the computations are completed only to a point 5 feet from the support, where the computed pitch becomes 7.18 inches. It will be sufficiently accurate to apply each computed pitch to that portion of the beam extending 6 inches in each direction from the point considered. | 1587. Effect of Vertical Load; Final Pitch.— As the beam is loaded along its upper flange, the rivets in this flange must, as previously stated, bear also the pressure due to the load upon the beam, exclusive of the weight of the beam itself. From Art. 1315, it may be found that the estimated load supported by the floor-beam, exclusive of its 1 1 39,9 own weight, is 32,400 + 7,540 = 39,940 pounds, or or os 185 pounds per lineal zzch of the loaded portion. But it 1s usually necessary for the designer of details to get all his 970 DETAILS OF CONSTRUCTION. information from the stress sheet. As previously deter- mined, the total estimated load upon the loaded portion of the beam is 2,290 pounds per lineal foot. From this is to be deducted the weight per foot of the beam itself. The weight per foot of flanges is 4 x 8.4 = 33.6 pounds, and the weight per foot of the web is 24 x @ x 42= 30 pounds, making 33.6 + 30 = 63.6 for flanges and web. If 10 per cent. be added for weight of details, it will make a total of 63.6 X 1.10 = 70 pounds (nearly) per foot. Hence, the load per foot upon the upper flange of the beam is 2,290 — 70 = 2,220 pounds, making the load upon each lineal inch of the 2, 220 12 This load produces vertical pressure or stress upon the rivets connecting the upper flange angles to the web-plate at all points aiong the loaded portion of the beam, while the increments of the flange stress act upon the same rivets as horizontal stresses. The stresses borne by the rivets are the resultants of these vertical and horizontal stresses. The pitch, as given in column (d@) of the preceding table, pro- vides for the horizontal stresses only, and must be reduced so as to provide for the vertical stresses also. The pitch thus reduced may be called the final pitch, and can be determined graphically more easily than by calculation. 1588. _ If zis the vertical load upon each lineal zuch of flange equal to = 185 pounds, as found before. FIG. 321. the loaded flange, and f and 7 represent the same values as DETAILS OF CONSTRUCTION. 971 in formula 189, the graphical construction giving the final pitch is as follows: Construct a right-angled trian- ze SS ! . 3 ok ; 6 x 33 21" ——» $22 sie, ee ab, fig. 321, sate base a ror S35 aais by any convente , Seonor: SRO se 3 Vy ANY ventent scale made © ' —* fea equal to the quantity ~ , considered ! i 1 1 as inches, and whose Lae abis 3 by the same scale made equal to the pitch p in inches, as obtained by | formula189. froma’ layoffa'l’ on the hypotenuse equal toab=f, and bya vertical line, as b' b., pro- | ant EX6 4 erat ‘8459 ‘'e* an 10 v7] Sek ject a' b' upon the base of the trt- “ ane angle. The projected line a' b, thus —F ? F obtained will be the pitch neces- ain sary to resist the resultant of the 13 g .; horizontal and vertical stresses. E : All the necessary eonstructions for the various points along a beam are readily combined in one figure. In Fig. 321 are combined the con- structions for determining the final pitch in the six items (except the first) of the calculations tabulated above. The triangles have a com- | 1,91 { “Lg er ee aa i i 1 | oie aioe ' —< — o39*0F—— sae oe eee CP iae r mon base, which is equal to a 3,520 185 of the several triangles are equal to the pitch required by the re- —19inches. The altitudes —,059 —+— eI | ’ | aa ’ { i — i] —PiG——a | S spective stress increments, as given | | | in column (d) of the table in Art. Wanita hean tha 1586 (except first item). The FIG, 822. final pitches, i. e., the results a’ 0, a’ c,,etc., are given in column (2) of the same table. As there is no vertical load upon the upper flange at the T. II,—23 972 DETAILS OF CONSTRUCTION. support, the pitch at that point is given the same in column (¢) as in column (d@). For that point, the pitch as given in column (2) is the final pitch. The rivet spacing along the flange, giving the pitch of rivets as required and used, is clearly shown in Fig. 322. Near the end of the beam the pitch is made somewhat less than the required pitch, on account of the connections for the lateral rods. The rivet spacing in the lower flange should usually be made the same as in the upper flange. 1589. Stiffeners.—In each stiffener the pitch of the rivets should not exceed that required in the adjacent por- tion of the flange. For practical considerations, however, it is desirable that when possible the pitch of rivets should be uniform in all stiffeners on the same beam. Single stiffeners are sometimes used on the floor-beams of highway bridges, being placed alternately on either side of the beam. The practice, however, is not to be commended. If the beam is supported upon its bottom flange, as in the present case, it should have two pairs of stiffeners at the end, in order to transmit properly the shear upon the bearing. In case of heavy beams and plate girders, that por- tion of the web above the bearings should be also reinforced by additional plates. Were this necessary in the example it could readily be accomplished by using a vd” < 2" X 184” plate on each side of the web-plate, extending as a filler plate under the two end stiffeners. As stated in Art. 1448, stiffeners are not neces- sary in this case, but are used simply as an illustration. They should always be used at the ends of floor-beams. stiffeners are sometimes used without | fillers, in which case the stiffener angles Fic. 323, must be offset or crimped to fit over the DETAILS OF CONSTRUCTION. 973 legs of the flange angles, as in the end view of the beam shown in Fig. 323. It is not economy to do this, however, except in heavy beams. In light beams the cost of offset- ting the angles will usually be greater than the cost of the material for fillers. 1590. Positions of Beam Hangers.—The positions of the holes for the beam hangers through the horizontal legs of the flange angles are fixed longitudinally of the beam by the length of the beam from center to center of chords. Their distance apart across the flange, as well.as the diam- eters of the holes, are determined by the dimensions of the hanger [ Mechanical Drawing Plate, Title: Highway Bridge: Details IV, Fig. 7]. The end of the beam must project a sufficient distance beyond the hanger holes to afford a bear- ing for the end of the intermediate post, this being necessary to hold the beam securely in position. 1591. The Connections for Lateral Rods.—The details of the plate and angle lugs for lateral connections are largely matters of arrangement, but sufficient bearing for the lateral pins must be provided. As the four floor-beams are made alike, the bearings for the lateral pins must be sufficient to resist the greatest stress upon any lateral rod attaching to the beam. The rod in the end panel of the lower lateral system is 1{ inches in diameter, and bears a stress of 14,900 pounds. In order to admit this size of rod the clear distance between the angle lug and horizontal leg of the angle of the top flange should not be less than lt inches. As the rivets attaching the plate for the lateral connection to the flange angles must be countersunk on the under side, requiring ample clearance, the top of the angle lug is placed at the center of the flange rivets, giving a clearance between the bearings for the lateral pin of 13—%=18inches. The holes for the lateral pins are so near to the edges of the flange angles that the resistance of the latter should not be counted. Hence, neglecting the bearing of the flange angle, the distance between the centers of the bearings for the lateral pins is 13+ $= 24 inches. 974. DETAILS OF CONSTRUCTION: By applying formula 106, Art. 1371, the bending moment 14,900 x 24 4 From Table 40, Art. 1546, it is found that, with a fiber stress of 18,000 pounds per square inch, a pin 1? inches in diameter will give the required resisting moment. From the same table it is found that, at 15,000 pounds per square inch, the bearing value of a 1?” pin through 1 inch thick- ness of metal is 26,300 pounds. Hence, the total thickness 14,900 _ 26,300 inch. Two bearings, each 75 of an inch thick, giving a total bearing of 2 xX = #% (.63) of an inch, will give the required bearing surface. As, however, the vertical leg of the angle lug is subjected to a certain amount of bend- ing stress, the metal in the angle is given a thickness of 2 of an inch; the plate on top of the flange is given the same thickness. At 9,000 pounds per square inch, the shearing value of a 5” rivet is 2,760 pounds (Table 38, Art. 1537), which is less than its bearing value througha 2 inch plate at 15,000 pounds per square inch ( = 3,520 Ib., Table 37). Consequently, as the pin plate is subjected to one-half the stress upon the lateral rod, the number of rivets required to connect the plate to 14,900 2, 760 Four rivets are used. upon the pin is found to be = 7,920 inch-pounds. of bearing required for the lateral pin is OO Olean the flange is 4X — in, (5. OTs. DLACLICALLY) = oe TI VeLas 1592. Asit is not permissible to use rivets in tension, the angle lugs are attached by means of bolts. The sec- tional area of the 13” lateral rod is .99 of a square inch, and it will be practically correct to make the aggregate sectional area of the two bolts somewhat more than one-half of this amount. After deducting the section cut away by the threads, the sectional area given by two #" bolts is about .6 of a square inch. | The lateral connections on the floor-beam should be placed as near to the beam hangers as other necessary conditions DETAILS OF CONSTRUCTION. 975 will permit. After the dimensions and positions of the lower chord connections are determined, the position of the lateral connections on the floor-beam may be fixed by drawing plans of the lower chord joints similar to those shown in Figs. 15 and 16 of the plate just referred to. TENSION MEMBERS. EYE-BAR HEADS. 1593. General Requirements and Manufacture. —In pin-connected trusses the main tension members are usually composed of eye-bars. The relative dimensions of eye-bar heads will now be considered. Item (/7,) of the specifications requires that ‘‘ The heads of eye-bars shall be so proportioned and made that the bars will preferably break in the body of the original bar, rather than at any part of the head or neck.”’ The heads of wrought-iron eye-bars are commonly formed by piling the proper amount of scrap iron, carefully selected and suitably arranged, upon the end of the bar, and then, after heating to the required temperature, forging the head into the desired shape ina die under a steam hammer or hydraulic pressure. Other similar processes are occasionally employed. If the welding is perfect, the head becomes thoroughly identified with the bar; but this is seldom the case. Nevertheless, wrought-iron eye-bars have been very commonly produced by the process indicated above which, when tested to destruction, would break in the body of the bar, rather than in the head or neck. Eye-bars are now quite generally made of medium steel, a material which has been found excellent for this purpose. Steel eye-bars are usually formed by first upsetting the bar sufficiently to form the head, then forging the latter into the required form in a die under steam or hydraulic pres- sure. The bars thus obtained are very satisfactory. Steel eye-bars have, however, been successfully made by piling carefully selected scrap and forging, in much the same 976 DETAILS OF CONSTRUCTION. manner as for wrought-iron eye-bars; but great care is required in the arrangement of the scrap and in the forging, and a suitable quality of steel is required for both the bar and the scrap. Whatever the process of manufacture, the bars must be subsequently reheated and annealed before boring the pin holes; this should never be omitted. 1594. Dimensions of Wrought-Iron Eye-Bar Heads.—The relative dimensions of eye-bar heads to fulfil the conditions of item (7,), quoted above, are determined by experiment. A form of head which has been very exten- sively used for wrought-iron eye-bars is shown in Fig, 324. i) ‘ Ce a ee (a eee Q ee 2 FIG, 324. If the thickness of the head is the same as that of the original bar, the dimensions of the head may be expressed in terms of w, the width of the original bar. The dimen- sions a and a’ (see Fig. 324) are each given by the formula a=a= hw. (190.) CA=CA' = radius of pinchole=9) 4 - D ande a e straight lines parallel to the center line of the bar. DB D' is a semicircle of radius d D=7--a, with the position of the center A so taken on the center line of the bar that the dimension @ will have the value given by the formula b= $w. (191.) DETAILS OF CONSTRUCTION. vets This makes CA =r—(A D—d)=r—(r+iw—tw) =, w. &:-F and &’ Ff’ are circular arcs having their Sentenovatiwivc and -Tadite ee ane deat edusie tO: As J). a i= AC. The arcs &.G andl :G ‘should have equal radi O F and O’ F', which should be of sufficient length to gradually connect the head with the main body of the bar; the radius O /of the neck is often made approximately equal to one and one-half times the radius A’ /. If the heads are made thicker than the body of the bar, the letters a, a’, b, and w inthe two preceding formulas must be considered to represent sectional areas instead of dimensions, the sectional areas to be taken on the respective lines as shown in Fig. 324. 1595. At the present time, however, eye-bar heads are generally made circular, as shown in Fig. 325. The center ECOL OU Ole IS AL | ect penes the center of the i head. The dimen- sions for this form of head being simpler, the dies are less ex- pensive than for the \ | form of head shown \ D | \ | ins Pig. 324. * Ac- \ cording to the most \ approved practice, \Y the net sectional area FIG. 325. A through the pin hole (i. e., area d =areas a+a= t(D—d), ¢ being the thickness) should not be materially less than given by the following formulas, in which B represents the sectional area of the body of the bar: When the diameter d of the pin hole does not exceed } of the wath w of the bar: Fi iemoied PLIEY OF (192.) When the diameter d of the pin hole materially exceeds the width w of the bar: ives ees, (193.) 978 DETAILS OP- CONSTRUCTION: If the thickness of the head is the same as the thickness of the bar, a+ a' = D —d may be substituted for A, and w for 4. For wrought-iron eye-bars with circular heads, as used in highway bridges, the net sectional area A across the head is often made equal to one and one-half times the sectional area of the bar. This practice has, in most cases, been found to give satisfactory results. 1596. Dimensions of Steel Eye-Bar Heads.—Steel eye-bar heads, when properly made and annealed, possess somewhat greater relative efficiency than those of wrought iron, and, consequently, do not require so large a percentage of additional material. The heads are generally made cir- cular in form, as in Fig. 325, and the thickness of the head is always made the same as that of the original bar. (See Art. 1512, VII.) If, for steel eye-bars, the et dtmension across the head be represented by A, =a-+ a= D—d, then this net dimension, as compared with the width w of the bar, is given by the following formulas: When the diameter dof the pin hole does not exceed % of the wath w of the bar: A=1.33w. (194.) When the diameter ad of the pin hole exceeds the width w of the bar: A= 14, (195.) 1597. The diameters Y of eye-bar heads are usually expressed nominally in multiples of a half inch; but, as actually manufactured, heads whose diameters are multiples of an inch are quite commonly made ¢ of an inch less than their nominal diameters, in order to admit of being packed inside of channels of the same nominal size. 1598. On account of the practical conditions of manu- facture and of the liability of thin eye-bar heads to buckle behind the pin hole when under strain, the thickness of the head should not be less than given by the following formula: D+w+s tremens cat ¢ (196.) DETAILS OF CONSTRUCTION. 979 For highway bridges the minimum limit of thickness allowed for eye-bar heads should never be less than 2 of an inch. For railroad bridges the minimum limit is 2 of an inch, and this limit might properly be applied to all bridges. CONSTRUCTIVE DETAILS OF THE LOWER CHORD MEMBERS. 1599. The End Panella b; Bearing on Shoe Pin. —The details of the member in the end panel of the lower chord are shown in Mechanical Drawing Plate, Title: High- way Bridge: Details III, Fig. 1. The end a of this member connects upon the shoe pin by means of pin plates riveted to the angles composing the member. These pin plates must be thick enough to afford sufficient bearing upon the pin, and, as they practically fulfil the office of eye-bar heads, they must also provide sufficient metal, at the section through the pin hole and beyond the pin, to comply with the conditions of formulas 190 and 191. According to item (0,) of the specifications, as this mem- ber is not composed of forged eye-bars, its bearing stress upon the pin must not exceed 15,000 pounds per square inch, or one and one-half times the unit stress allowed upon it. As one and one-half times the allowed unit stresses would be 14 x 10,000 = 15,000 pounds, and 14 x 20,000 = 30,000 pounds per square inch for live and dead load stresses, respectively, it is readily seen that an allowed bearing stress of 15,000 pounds per square inch for all stresses is the more severe requirement. The stress sheet shows the live and dead load stresses for this member to be 32,400 pounds and 13,900 pounds, respectively. At 15,000 pounds per square inch, Table 40, Art. 1546, gives 41,300 pounds as the bear- ing value of a 24-inch pin through 1 inch thickness of plate. Hence, the total thickness of bearing for the pin plates 46, 300 41,300 or about 1} inches. Two pin plates, each $ of an inch thick, would give ample bearing surface upon the pin. But required by the stresses upon the member is Salolale 980 -DETAILS OF CONSTRUCTION. at the shoe joint, other considerations will require a greater thickness for the pin plates upon the chord. 1600. Section of Pin Plate Across the Pin Hole. _—From the stress sheet it is found that the net sectional area given by the four angles composing this member is 4.02 square inches. By applying formula 190, at the sec- tion on the lines a and a’ (Fig. 324) through the pin hole, and using areas instead of dzmenszons for the values of w and a, the net sectional area required at the pin hole is found to be 2 X 4 < 4.02 = 5.36 Square inches: Hence, as therpin plate is made 64 inches wide, the total thickness of metal required for the pin plates by this condition is NTH we mE 1.43 inches, which is practically ¢ of an inch for each plate. But this will probably be found not to be the critical condition. 1601. Critical Section of Pin Plate.—As the space between the shoe pin and the cover-plate of the end post is limited, it will be necessary to either cut away the cover- plate sufficiently to allow the pin plates to project through it, or to plane off the corner of each pin plate sufficiently to clear the cover-plate. As the former would have a rather unworkmanlike appearance, the latter expedient will be em- ployed. It will be necessary to cut away a large piece of the metal of the pin plate; consequently, the amount of metal remaining between the pin and the edge of the plate thus formed, 1.-¢.4 onpthé line*asar 1 326, will probably be found to be the critical condition in com- plying with the requirements, aoc and no advantage will be ob- tained by making the pin plate wider than the member itself, or 3-+4-+3 = 6} inches. From Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. 1, it is known that the distance between the center of the pin and the lower side of the cover-plate of DETAILS OF CONSTRUCTION. 981 the end post is 3 inches. Consequently, by allowing |, of an inch as the smallest permissible clearance, the net width ¢ (see Fig. 326) of that portion of the pin plate between the edge of the pin hole and the lower side of the cover-plate of the end post can not be more than d—% X 23 —7,=— 1%, =1.56 inches. As given by formula 190, the sectional area required in the vertical section above or below the pin hole, i. e., the section on the line a or a’, Fig. 326, is 2 x 4.02 = 2.68 square inches, while the sec- tional area required on the horizontal section behind the pin, 1. e:, on the line 6, is | X 4.02 = 3.52 square inches. (Formula 191.) 1602. In the case of a pin plate having the corner cut away, as shown in Fig. 326, in order that the section on the line c, making an angle of 45 degrees with the center line of the member, shall give practically the same resistance as the sections on the lines a and 4, as derived by formulas 190 and 191, respectively, the sectional area on the line ¢ must have the value given by the formula C= £6 w, (197.) in which w represents the sectional area of the member. In the example, therefore, the sectional area required on the linec is 38 X 4.02 = 3.14 square inches. Hence, the total thickness of the pin plates required by this condition is me = 2.01 inches. This is, therefore, the governing condition. Two pin plates each 1 inch in thick- ness might have been used; instead, however, four pin plates each $ inch thick (two double plates) are used. As each pin plate is of uniform thickness, the dimensions 6 andc will be proportional to the area of the sections on those lines. The dimensions c and both areas being known, we have the proportion 3.14: 3.52 :: 1.56: 4, from which ee 3.52 X 1.56 3.14 from the center of the pin to the end of the pin plate is 1.75 + 1.388 = 3.13 inches, or say 34 inches. = 175 inches. Hence, the required distance 982 DETAILS OF CONSTRUCTION. 1603. Rivets for Connecting Pin Plates.—The number of rivets required to connect the pin plate to the angles composing the main portion of the member is deter- mined by the most severe condition of the requirements for the shearing and bearing. The unit stresses allowed upon the member are 10,000 and 20,000 pounds for live and dead load stresses, respectively. As all the determinant conditions (the values of A, d, and ¢) are the same as in Art. 1570, formulas 178 and 179 should be used, and the results compared. As d= 2’, and ¢7=4"sTable 37; Art. D537, vives 15000775. sae Formula 178 gives eg a 32,400 + 13,900 18 2,340 2(2 X 32,400 + 13,900) a 3X .38068 K-10;000 ny maa fl 8 rep Formula 179 gives 2, = The required, number of rivets 1s;.theretore, L0so tide is, 20. Twenty rivets are used to connect the angles composing the member to the pin plates at each end. Sixteen rivets (four in each angle) connect the free vertical legs of the four angles directly to the pin plates, and four rivets (two in each pair of angles) connect the horizontal legs of the angles to four short pieces of angles attaching to the pin~ plates. It will be noticed that each of the four rivets last mentioned has a double bearing value and is also in doubie shear, which gives practically a total value of 24 rivets in the connection of the pin plates, thus making ample allow- ance for countersunk rivets. The details of this connection, though fulfilling all requirements, could be somewhat improved. 1604. Pin Plates at Joint b.—For connecting the pin plates at the opposite end 0 of the member, the number of rivets required is the same. It was found above that two pin plates each 2 of an inch thick, or a total thickness of 14 inches, will give sufficient bearing for this member upon a 2¢-inch pin. With a total thickness of 14 inches, the DETAILS OF CONSTRUCTION. 983 required width of the pin plates, as given by applying 2X xX 4.02 formula 190, Art. 1594, is get 5 = 7.04 inches. Two pin plates 7” x 8” will be used. As determined by formula 191, the pin plates must project beyond the 9 edge of the pin a distance of Oe = 212 inches (very closely), or a distance of 212-+ 12 = 4,3, inches beyond the center of the pin. It will be well to make this dimension practically 44 inches; for convenience in shortening the distance between pin centers », of an inch, in compliance with the rule given in Art. 1519, this dimension is in- creased to 4,°, inches at one end. 1605. Metal Behind Pin; Another Condition. — Pin plates for tension members should not only comply with the conditions required by formulas 190 and 191 for eye- bar heads, but, besides, the dimension 0, Fig. 326, should never be less than given by the following formulas: For wrought tron: 9dt b= oT (198.) For medium steel: at og alban re b= Tr (199.) In both of these formulas d@ is the diameter of the pin hole, 7 is the thickness of pin plate required by the bearing stress, and 7 is the actual thickness of the pin plate. It was found above that the total thickness ¢ for the pin plates at each end of this member, as required by the bear- ing stress, is 1.12 inches. At the end a of the member, the total thickness 7 is 2 inches. Hence, at this end of the member the dimension @, or clear distance from the edge of the pin hole to the end of the member, must not be less than cos aes PAG ss 1.73 inches; or, to express it other- wise, the distance from the center of the pin hole to the end 984 DETAILS OF CONSTRUCTION. of the pin plate, as required by this condition, must not be less than 1.73 + sls == 3.11 inches. At.the end/Oof the memper Ky 6 the dimension @ should not be less than Mees eS Ree iy if inches, making the distance from the center of the pin hole to the end of the pin plate, as required by this condition, equal to 2.77 + 1.88 =4.15inches. As the distance adopted is greater than this, it is found that the condition required by formula 198 has been complhed with. It will not be necessary to take special notice of the arrangement of the lattice bars for this member; it involves no unusual or difficult conditions, and will be readily under- stood without explanation. 1606. The Second Panel b c.—The dimensions of the pin plates for the member in the second panel 6c of the lower chord, Mechanical Drawing Plate, Title: Highway Bridge: Details III, Fig. 2, are determined in substantially the same manner as explained above for the lower chord member a 4; it will be unnecessary to explain the process in detail. It will be noticed that the connections of the pin plates on this member are more simple than upon the mem- ber:a 6, Fig. 1 of the same” plate.) simplicity ot detauerd always desirable and should be obtained whenever possible. The manner of connecting the pin plates shown in Fig. 2 (same plate) is far preferable to that shown in Fig. 1. In order that the relative widths of the members would be such as to connect properly upon the pins, the arrangements of the pin plates as shown for the joint a of the member a 0 became necessary. It will be noticed that in the preceding computations the dimensions of the pin plates have been proportioned accord- ing to the requirements for elongated eye-bar heads. This method, although not very generally employed, is given here as a safe and reliable practice for the pin plates of tension truss members. 1607. Stiffened Eye-Bars; Panel c c’.—The mem- ber in the middle panel of the lower chord is shown in Fig, 3 DETAILS OF CONSTRUCTION. 985 of the plate just referred to. It is composed of eye-bars of the usual form, except that, in order to illustrate another form of stiffened chord, the bars are shown connected by bent lattice bars. The heads are of the form shown in Fig. 325, and, as the diameter of the pin does not exceed three- quarters of the width of the bar, the diameters of the heads are determined by formula 192. By reference to items (o,) and (4) of the specifications, it is found that for forged eye-bars no definite limit is placed upon the intensity of bearing stress, other conditions being usually such that the permissible intensity of bearing stress will not be likely to be exceeded. In the present case, however, the thickness of the eye-bar heads has been increased to $ of an inch, in order that the bearing stress shall not exceed 15,000 pounds per square inch. According to the stress sheet the net sec- tional area of the member is 6.40 square inches. Hence, by formula 192, the net sectional area of the head across the pin hole, 1. e., on the lines a and a’, Fig. 325, must be for 1.6 X 6.40 5) a thickness of { of an inch, the diameter / required for each ) each of the two bars = 5.12 squareinches. With ae ibe fie head is i A + 2.75 = 8.60inches. Heads nominally 9 inches in diameter, but having an actual diameter of 8£ inches, are used. When the eye-bars are not connected by lattice bars, it is necessary to designate only the size of the bar, the diameter and thickness of each head, the size of each pin, the distance from center to center of pin holes, and the number of bars required. In many bridge offices the practice is to simply make a list of the eye-bars required for each structure, giv- ing the above items; in such cases the eye-bars are not shown on drawings, except when required to be latticed. In some bridge works it is the practice to state the diam- eter of the pzzs to be used, as is shown in Mechanical Draw- ing Plates, Titles: Highway Bridge: Details I to IV, while in other shops it is the practice to state the exact diameters required for the pzx holes. 986 DETAILS OF CONSTRUCTION. It is never necessary to give the radius for the necks of eye-bars. As they are always tension members, the distance from center to center of pin holes must be shortened 34 of an inch, in compliance with the rule given in Art. 1519. The’ latticinge “of chord. bars™ is mérely a “matters: arrangement, needing no special explanation. CONSTRUCTIVE DETAILS OF THE TENSION WEB MEMBERS OF THE TRUSS. 1608. The Main Tie Bars B c.—The dimensions of the main tie bar are shown in Mechanical Drawing Plate, Title: Highway Bridge: 2Details IV ig 1 See ee ome joint, the distance between the center of the pin and the cover-plate of the chord, or of the end post, is 3 inches. Hence, it is evident that the radius of the eye-bar head connecting upon this pin must be slightly less than this. The nominal diameter of the head will be 6 inches; the actual diameter, 5£ inches. The diameter of the pin hole will be somewhat in excess of the width of the bar, but not greatly so; consequently, the net sectional area A across the head may be taken at a mean between the values given by formulas 192 and 193, that is,as equal to a-tis The sectional area of one' bar is 2X 142=1.63 square inches, and, as the diameter of the head is fixed at 5f£ (= 5.875) inches, the thickness of the head must be eae ae = «885, or, practically, ~ of an inch. Heads 5g’ x ¥ will be used. As in the present case it is essential that the diameter of the head should under no condition exceed 54 inches, the exact diameter of the head is marked, instead of its nominal diameter. As the pins at each end of the bar are of the same size, both heads will be made alike. The length of the tie bar, from center to center of pin holes, is 25’ 5". (Art. 1519.) 1609. The Hip Vertical B b.—A hip vertical rod is shown in Fig. 3 of the plate just mentioned; it is 1 inch DETAILS OF CONSTRUCTION, 987 square. Each hip vertical member consists of two rods like this. Hip vertical members sometimes consist of ordinary eye-bars, however. In the present case the loop, by which each end of the rod connects upon the pin, is formed by bending the end of the rod into the desired form and weld- ing it back upon the bar, making the rod as nearly of the desired length as possible. The length of such bars is always given between the inner edges of the extremities of the two loops, as shown; it is commonly called the length back to back, and is designated on drawings by the letters Bto B or 6 to 6. Rule.—T7he length back to back of a tension rod having loop ends ts the length from center to center of pins plus one: half the diameter of cach pin, minus 5 of an inch tf the rod 7s not adjustable. Thus, in the present case, the length J fo 6 is equal to , Qe" = Qe" , 93/ 18’ 0" + a ay ay gg = 18 223". The exact length d/o 6 is finally obtained in reaming the inner sides of the loops to fit the pins. Rule.—7he inside length of a bent loop ts always made equal to 24 diameters of the pin upon which it connects ,; or, in other words, the distance from the center of the pin to the inner angle of the weld 1s made equal to 2 diameters of the pin. In the present case, the length of each loop is 24 x 2% = 6£ inches. 1610. The Counter Tie -C c’.—Counter ties usually consist of square or round bars, though frequently of flat bars. The counter shown in Fig. 2 (title as above, IV) isa square bar and connects upon the pins by means of bent loops in substantially the same manner as the hip vertical. The form and relative dimensions of the loop are also the same as described for the hip vertical. The two ends of the rod connect upon different sizes of pins, and the dimensions of each loop depend upon the size of the pin upon which it connects; the loop upon the lower end c’ of the rod, connect- T. I1.—2?4 988 DETAILS OF CONSTRUCTION. ing upon the 2%” pin, is flattened to ? of an inch in thickness in order to pack upon the pin within the required space. Counters are made adjustable, usually by means of turn- buckles, as shown. Sometimes, however, only one of the diagonals in the center panel of a truss is made adjustable. This counter tie will be further noticed in the following articles. UPSET SCREW ENDS. 1611. The end of rods upon which threads are formed are enlarged by upsetting, so that after the threads are cut the remaining portion of the end will be as strong as the unaltered portion of the rod. As the process of upsetting somewhat reduces the strength of the metal, bars in which the diameter at the root of the thread is the same as that of the bar itself, invariably break in the screw end, when tested to destruction, without developing the full strength of the bar. It, therefore, becomes necessary to make up for this loss of strength by upsetting the ends sufficiently so that the sectional area at the root of the thread will be somewhat in excess of the sectional area of the bar. According to item (#,) of the specifications (Art. 1511), ‘fall rods and hangers with screw ends shall be upset at the ends, so that the diameter at the bottom of the threads shall be ;/; inch larger than any part of the body of the bar.” According to Thacher’s specifications, ‘‘the area at root of thread in the upset ends of rods shall be greater than the area of the rod at least 17 per cent.” According to Lewis’s specifications, ‘‘the area at base of thread and at all parts of upset ends will be 15 per cent. in CxcessOl tic areatol tnesvainn The common practice, which varies slightly in different shops, gives an excess of effective sectional area of the screw end over the area of the bar of from about 17 to 50 per cent., the diameter of the upset end always being a multiple of 2 of an inch. The following table, which gives the standard proportions for upset screw ends as used by the Keystone Bridge Com- DE TATE St ORSGO Moi D.C id ON: 989 pany, is fairly representative of the best practice for upset ends: TABLE 41. UPSET SCREW ENDS FOR ROUND AND SQUARE BARS. Diam. of Kound or Side of Square Original Bar. I 178 174 138 1 14 134 1% ae 236 234 236 24 Round Bars. Square Bars. oJ os eis eh, oJ s ao ts, o2 [Eg | Se faa] 28 [53] 38 |e 3 85 |$4e) 58 |Aun) $5 |Se8) b5 [Fae rte eevee dere eis SS nS Ste ary Cfo pS O. © aa BSc! 6g lad 0 fia Le Sun) tad 7 tS Se a ete ae Mey ae OR ES A ee eg Bees eee PAIRS | 4 ble og P v7 a |A oe p D eG |A P Inches. | Inches. Per cent.|| Inches. | Inches. Percent. 34, txt lets 54 34 .62; | a0 21 a ey a) 37 I .84 | 8 41 I .84 8 25 1% .94 7 23 1% | 1.07 7 48 13g | 1.16 6 38 1348 | 1.16] 6 as 5a} 1.28.4 6 29 Etech Lees |, 20 30 14% | 1.39 | 5% 20 1544 | 1.39 | 5% 23 Eves etO2it ck a1 14> \eheao-) 5 18 2 I.91 4% 22 2 1.71 | 4% 30 2% | 1.84| 4% 18 24%) 1.84 4% 28 23% | 2.09 4% 30 24 11.96| 4% 26 2% | 2.18 | 4 21 23g | 2.09 | 4% 24 258} 2.30 | 4 18 2% | 2.18 | 4 18 27% | 2.55 |} 4 28 298 | 2.30 4 7 i. S203 32 20 Ds Ae pee 28 3% | 2.75 | 3% 18 4 2.63 | 3% 23 338 | 3.00 | 3% 26 peea275 Pogiai| 22 Brees STO)| aah | ax The diameter of the round bar or side of the square bar being known, the corresponding diameter of the upset end may be obtained from the table. sometimes required on flat bars. Upset screw ends are In such a case it is neces- sary to find first the side of a square bar having the same 990 DETAILS4OF CONSTRUCTION: sectional area as the flat bar, and then to find from the table the diameter of the upset end as required for the square bar. The length of the upset end may be determined by formula 200, which is given in connection with the dimensions of turnbuckles. TURNBUCKLES. 1612. Having obtained the required diameter of the upset screw end, the dimensions of the turnbuckles are next to be determined. The threaded ends of the two portions of the rod screw into the ends of the turnbuckle, or, in other words, the turnbuckle screws upon the ends of the rods by means of a right-handed screw at one end and a left-handed screw at the other end, so that by turning it inone direction both ends are screwed up, while by turning it in the opposite direction both ends are unscrewed. As the finished turn- buckles commonly used are to be obtained in the market in sizes suitable for the different diameters of thread ends, the various dimensions of turnbuckles are not commonly given on the drawings, it being usually sufficient to designate the dimensions of the thread ends and state the sizes of turn- buckles to be used. But, in order that the proportions of this detail may be clearly understood, the relative dimen- sions of a common form of turnbuckle will be given. The forms and dimensions of turnbuckles vary somewhat as manufactured by different firms, but the form shown in Fig. f } \ | \ 1 ! 1 I ee 327 may be considered as fairly representative. The letters by which the various dimensions are designated are shown in DETAILS OF CONSTRUCTION. 991 the figure. / is the length of the upset end, of which d is the diameter; 7z is the assumed distance between the two ends when the turnbuckle is screwed up in position upon them. All other dimensions relate to the turnbuckle. The several dimensions for this form of turnbuckle, and also the length of the upset ends, may be expressed in terms of das follows: E=2d+14". (200.) J=2d+1". (201.) ex=dt+h" (202.) Date dpa. (203.) sad+H". (204.) r=S 44. (208.) ae 1! Wi a -1 esi (206.) oe eal, f. (207.) Fo alle &. (208.) m= 4, (209.) The value of /, formula 200, is usually made a multiple of 4 inch, although there is no objection to giving this dimen- sion the exact value derived from the formula, which will always be a multiple of + inch. This dimension is commonly given values varying from 2¢d+ 2” to 2d+ 1’; a value of 2 a+ 1%” isto be preferred. The minimum value which may be given to # is 4inches. Formula 200 and the preceding remarks apply not only to turnbuckles, but to all ordinary upset screw ends. In the expression for the value of w, formula 206, when d— 1} guts SP AP the fraction 5 + becomes negative it is simply givena value of zero. The distance 7 between the ends of the screws is variously taken as 3, 4, and even 5d inches; 4 inchesis a good value. A value of 3 inches is, however, not uncommonly assumed. 992 DETAILS OF CONST RUGHIGR: It may be noticed that values of A and m, as given by formulas 200 and 209, will give practically the same relative positions and conditions of the screw endsas a value of 22+ 2” for #, used with a value of 3inchesfor 7. Slight variations in these dimensions are not of consequence, and any consistent rule will be found satisfactory. 1613. The Counter Tie Continued.—Turnbuckles upon counters are usually placed at a distance of about five feet from the lower end. Asdeterminedin Art. 1519, the length of the tension diagonal, center to center of pz holcs, is 25’ 54%"; hence (see Art. 1609), the length of the counter . 12” + 23” from back to back of loops will be 25’ 5%” + a 25' 7132", Asan error of less than ?, of an inch is of no consequence in an adjustable member, the allowance of =, of an inch for clearance of pin holes may be wholly neg- lected. If the portion of the counter below the turnbuckle is made 38’ 0” long, back to end, then, with a distance of 3 inches between the ends, the length of that portion of the bar above the turnbuckle will be 25’ 7413” — 5’ 3” = 20’ 413”, end to back, or, with an allowance of 4 inches between the screw ends, the length of the larger portion of the bar will be 20’ 312” from back to end. CONSTRUCTIVE DETAILS OF THE LATERAL RODS. DIMENSIONS OF NUTS. 1614. The Lower Lateral Rods; Intermediate Panels.—The rods in the three intermediate panels of the lower lateral system will be first considered. The dimen- sions for each of these rods are shown in Mechanical Draw- ing Plate; Title:, Highway .Bridgéey (Details -iVe" Piowen: By reference to the detailed drawing of the floor-beam (same title, II), it will be found that the distance between the cen- ters of the lateral pin holes at opposite ends of the floor- beam is 19’0”—2 x 82", or 2 x (8' 94") = 17’ 64”= 2104 inches. This distance is the lateral projection, or reach of the lateral rods, in each of these three panels. In the same panels the DETAILS OF CONSTRUCTION. 993 longitudinal projection, or reach of each lateral rod, is equal to the panel length minus the distance between the centers of the two lateral pin holes in the same end of the beam, or 18’ 0°— 0' 53" = 17' 62” = 2104 inches. Hence, the length of the lateral rod, from center to center of pin holes, is equal to 7210.5* + 210.25* = 297.515", or 24’ 933”. As the rod is adjustable, it will be sufficiently accurate to call this length 24) 94", It will be, noticed that the lateral projection of the rod (2104 inches) and its longitudinal projection (2104 inches) happen to have very nearly the same values; the length from center to center may therefore be determined with sufficient accuracy for an adjustable rod by applying formula 184, Art. 1576, using a mean between the two projections. 210.5 + 210.25 ‘) A The mean of the two projections is = 2100 io inches, from which formula 184 gives 1.4142 x 210.375 = 297.512 inches, or, practically, 24’ 94”, as the length from center to center of pins. As proportioned in Art. 1591, all lateral pins are 14 inches in diameter. The length of this lateral rod from back to back of loops is, therefore, 24’ 9$” + i ik ie 24’ 114”. If 3 inches be allowed between the screw ends, the length of the longer piece of the rod will be 24’ 114” — 5' 3" = 19’ 84” from back to end; or, if 4 inches be allowed between the screw ends, the length of the longer piece will be 19’ 74” from back to end. ‘The lengths of the loops are found in the manner explained for the hip verticals, and the diameter and length of the upset ends are obtained as explained in the preceding articles. 1615. The Lower Lateral Rods; End Panels. —The dimensions for each lower lateral rod in the end panels are shown in Mechanical Drawing Plate, Title: Highway Bridge: Details IV, Fig. 5. One end of this lateral rod connects upon the lateral pin in the shoe, and, therefore, its length can not be determined until the position of the lateral 994 DETAILS OF CONSTRUCTION. pin in the shoe has been fixed. However, as it is desirable to notice here the length of this lateral rod, it will be as- sumed that the lateral pin holes in the shoes have been pre- — viously located as shown in Figs. 5 and 9 of Plate III, same title. By reference to those figures, it is found that the center of each lateral pin is laterally opposite the center of the shoe pin and ata distance of 10,3, inches from the center of the chord:. From Fig..4:of «Plate Il) title:as above-m is found that the lateral projection of this rod is 19’ 0” — 103,” — 82” = 17' 57,” = 209+, inches, and that its longitu- dinal projection is 18’ 0” —24”=17' 94” = 2134 inches. Hence, the*length of the rod’from centerto center or pin holes is equal to 4/209.063? + 213.1257 = 298.546 inches = 24' 1025", or, near enough for an adjustable rod, 24’ 104”. The length of rod from back to back of loops is 24’ 10$” + a eor a 25' 04”. If the shorter piece is5')0" from Dack to end, and the distance between the screw ends assumed to be 3 inches, the length of “the longer piece -willae 25' OL" — 5' 3” = 19' 9}” from end to back; but if 4 inches be allowed between the screw ends, the length of the longer piece will be 19’ 81” from back to end. ‘The relative dimen- sions of the loops, screw ends, and turnbuckles have been fully explained. 1616. Dimensions of Nuts.—As nuts are used upon the ends of the upper lateral rods, before calculating the lengths of the rods it will be expedient to notice briefly the relative dimensions of nuts. The standard screw threads recommended by the Franklin Institute have been quite generally adopted throughout the United States. When this thread is used, the diameter d, of: the bolt at root of thread, or the approximate diameter of rough hole in nut before cutting the thread, is given by the formula ad,=a—1.3 7, (210.) in which @ is the original diameter of the bolt and fis the pitch of the thread. (The pitch of the thread is equal to one divided by the number of threads per inch.) DETAILS OF CONSTRUCTION. 995 The standard proportions for finished nuts recommended by the Franklin Institute are as follows: Thickness ¢ of nut: t=d— +’. (211.) Short diameter S of square or hexagonal nut: S=iid+ +,’. (21 2.) Diagonal Z, of square nut: f= 1.414 'S. (213.) Long diameter Z, of hexagonal nut: 7A aa ET Bey (214.) In all these formulas d is the diameter of the bolt. In rough nuts, the dimensions ¢ and S are each + of an inch greater than in finished nuts. These proportions for nuts have not been very generally adopted, on account of the uncommon sizes of bar (not usually rolled by the mills) required to make the nut. Con- sequently, other standards are used for the dimensions of nuts. In bridge construction the standard commonly used for nuts is what is known as the manufacturers’ stand- ard. Table 42 gives sizes and weights of hexagon nuts by this standard. 1617. The Upper Lateral Rods; Center Panel. —Referring to Mechanical Drawing Plate, Title: Highway Bridge: Details I, Fig. 2, it will be noticed that, in the cen- ter panel of the upper chord, the center of the lateral hitch (with reference to the rivet holes) is at the center of the chord, laterally, and at a distance of 8,%, inches from the center of the pin. Hence, the lateral projection of the lateral rod, between centers of the lateral hitches, is equal to the width of the bridge from center to center of chords, or 19 feet = 228 inches. The longitudinal projection be- tween the same points, or the distance between the two lateral hitches on the same chord member, is equal to 18’ 08” — 2 x 8,3,” =16’ 8” = 200 inches, and the length of the diagonal between the same points is 4/228?+ 200° = 996 DETAILS OF CONSTRUCTION. TABLE 42. SIZES AND WEIGHTS OF HEXAGON NUTS. MANUFACTURERS STANDARD. Size of of ay a Thickness| Short Long ee Boit. rigies of Nut. |Diameter.|Diameter.| Nits Inches. Inches. Inches. Inches. Inches. Pounds. i aif 4 i 1.01 7.1 4 zi } 1 1.15 9.8 5 _ B 14 1.30 14.7 5 ay, 5 14 1.44 19.1 5 5 3 14 1.44 22.9 3 at 3 12 1.59 27.2 3 at 1 i 1.73 39 é 25 ue 18 1.88 44, i 25 1 13 1.88 50. 1 us 1 13 2.02 54 1 4 14 19 2.02 64 14 15 iB! 2 2.31 96 4 ee 18 Q1 2.60 134 12 15 14 24 2.89 180 14 1,5; 12 22 3.18 235 12 155 12 3 3.46 300 3 1) 15 34 3.05 370 14 yt 2 34 4.04 460 143 2 34 4.04 450 QL 2 QL 38 4.33 560 Q4 24 Q4 At 4.91 810 Qa pe Qa 44 5.20 980 3 Qi4 3 43 5.48 | 1150 DiPTAIES. OF CONSTR UG DION: JOT 303.289 inches = 25’ 3.%”, or, near enough for an adjustable TOU. 20 fot. From Fig. 4 of the same plate the distance from the center (between rivet holes) of the lateral hitch and the outside of the 34-inch leg of the 34” x 5” angle is 2 inches, and, con- sequently, the length of the lateral rod from outside to out- side of the angles of the hitch is 25’ 31” +2 x 28” = 25’ 84”. From Table 41, Art. LG11, the diameter of the upset end, for a round rod 1 inch in diameter, is 12 inches, and from Table 42, Art..1616, it is known that, for a bolt, or the screw end of a rod, having a diameter of 12 inches, the thickness of the nut is 14 inches. With regard to the amount which the screw end of the rod should project be- yond the nut, no definite rulecan be given. Some engineers consider a projection of one inch at each end to be ample, but for small rods the projection given by the following rule is very commendable: Rule.—Wake the projecting end of the rod equal to the thickness of the nut. This rule is here followed. Hence, the total length of the lateral rod in the center panel is 25’ 84” +. 4 x 14” = 26' 24", as marked in Plate IV, title as above, Fig. 4. 1618. The Upper Lateral Rods; End Panels.— By referring again to Plate III, title as above, Fig. 2, it is found that, in the end panels, the lateral projection of the lateral rod, between centers of the lateral hitches, is the same as in the center panel, or 19 feet = 228 inches, and that its longitudinal projection, between the same points, is equal to 18’ 08” — (144,"+ 83,")= 16’ 2"=—194 inches. Hence, the diagonal distance between the centers of the lateral hitches is equal to 4/228°-+ 194’ = 299.366 inches = 24' 112”, nearly, and the total length of each lateral rod in the end panel of the upper lateral system is 24’ 113’+ 2x (28"+ 14’+ 14”) = 25’ 108”, as marked upon the drawing. The length of the thread ends will be the same as given in connection with the dimensions of turnbuckles. A length of 44 inches, as given by formula 200, would be sufficient for each threaded end. 998 DETAILS OF CONSTRUCTION: CONSTRUCTIVE DETAILS OF THE BEAM HANGER. 1619. The Hanger Rods.—The beam hanger is shown in Plate, Title: Highway Bridge: Details IV, Fig. ”. Onaccount of its form, this member isalso called a stir- rup. The sizeof the beam hanger is sometimes determined in making the general design, but it is often left to be pro- portioned as a detail. The total load upon each floor-beam is 41,200 pounds (Art. 1586) ; hence, the load upon the 41,200 2 ent case, the hangers are composed of bar iron with forged (upset screw) ends, and the unit stress allowed upon them is 9,000 pounds per square inch. [See Art. 1399 (e).] The sectional area required for each hanger is, therefore, 20,600 9,000 Referring to Fig. 7 of the same plate it will be noticed that the section is given by two bars, or, rather, by the two parts or branches of the same bar, one of which, when in position, will be on each side of the beam. Consequently, the sectional area of the bar forming the beam hanger must ©) not be less than — hanger at each end is = 20,600 pounds. In the pres- = 2.29 square inches. 2 bent slightly from a vertical position, in that portion of the hanger above the top of the floor-beam, its sectional area should be somewhat more thanthis. A bar 14 inches square will give a sectional area of 1.27 square inches. This is the size of rod most commonly used for beam hangers in high- way bridges, and would ordinarily be considered sufficient for the present case. As, however, the bar is weakened by bending, a bar 14 inches square has been used. =1.15 isduare- inches) ee As thee pane 1620. From Table 41, Art. 1611, it is found that the diameter of the upset screw end required upon a bar 14 inches squareislfinches. These hangers fit upon 2?” pins. Hence, in order that the screw ends of the hanger may pass over and easily clear the pin, the distance between the centers of DETAILS OF CONSTRUCTION. 999 the two screw ends of the hanger should be about one-eighth of an inch more than the diameter of the pin plus the nomi- nal diameter of one screw end, or 22+ 14-4 1 = 43 inches, as marked in the figure. This determines the distance apart of the two branches of the hanger, which should be parallel from the bottom of the hanger to the top of the floor-beam. ‘The clear distance between the square bars in the parallel portion of the hanger is 43 — 11 = 34 inches, as marked. 1621. The length of the hanger should be such that it may be screwed up so that it will hold the beam firmly against the pin plates of the intermediate post. Fig. 3 of Plate, Title: Highway Bridge: Details I, shows that the pin plates of the intermediate post extend 4% inches below the center of the pin ; whence it follows that the distance from the upper part of the parallel portion of the hanger (at the top of the floor-beam) to the inner side of the bend should be equal to this projecting length of the pin plates plus one-half the diameter of the pin, or 42+ 13 = 64 inches, as marked. This distance should always be determined and marked to the zuzner side of the bend, wot to the center of the pin. On actual shop drawings, the radius of the bend should not be marked, but the diameter of the pin should be given. The top of each upset should be about $ or ? of an inch above the bottom of the beam ; in the present case it is made 4 inch above the bottom of the beam. The amount which each end of the hanger extends below the bottom of the beam is determined by the thickness of the nuts and of the hanger plate, together with the amount which each thread end should project beyond the nut. 1622. The Hanger Nuts.—Each end of the hanger should always be provided with two nuts, the principal, or standard, nut and a small nut called a check nut. The check nut should always be placed adove the standard nut. Hexagon nuts are generally used for hangers. ‘The size of the principal nut is obtained from the standard sizes given 1000 DETAILS OF CONST RUC Eas in Table 42, Art. 1616, by reference to which the thickness of the nut for 1f inches diameter of bolt or thread end is found tobe2inches. The thickness of the check nut is usually # of an inch. Each end of the hanger should project not less than 1 inch beyond the nut. In the present case the hanger plate is of an inch thick. The length of the thread end will be as follows: Above bottom of beam, 4” Through hanger plate, # Through check nut, 3B" Through standard nut, 2” Projection, ike Total ap The length from the end of the hanger to the inside of bend will, therefore, be 5” + 24” + 62” = 2’ 114’, as marked. It is not necessary to give the exact dimensions of nuts on working drawings. The practice in different shops varies somewhat, but in most cases it is sufficient to mark the drawing thus: 1k” Thread Ends. Standard Nuts. 3" Check Nuts. Sometimes special forms of locknuts are used for hangers, in which case the kind of nut required should be stated on the drawings. 1623. Hanger Plates.—The width of the hanger plate should be somewhat greater than the long diameter of the nuts used. Single hanger plates are generally made 5, 54, or 6 inches in width. In determining the thickness of a hanger plate, the latter may be treated as a beam simply supported at the ends and carrying a uniform load. By considering the resistance of the flange angles of the beam, as supported by the stiffeners, and the support given to the hanger plate by the nuts, it will be seen that this assumption is well upon the side of safety, DETAILS OF CONSTRUCTION. 1001 Under this assumption, the bending moment is J7 = — ES Oa 94, Art. 1316), and the moment of resistance, = — (formula Z3, Art. 1243). For a rectangular sec- 3 ba tion, /= ——, andc=4d (Table of Moments of Inertia). 128 Hence, for this form of section, Sf — §s qs b d* a Sod? or > | Sod? R= : (215.) in which S is the fiber stress (= S,, when X is the ultimate ‘resisting moment), 4 is the breadth, and d@ the depth of section. ‘This formula expresses the moment of resistance of any rectangular section. As the moment of resistance must equal the bending moment, J7 = X, or, in this case, Ao = 2 oe , from which See a3Wi LSS (216.) In our example, WV = 20,600 pounds, / = 4? inches, 4 will be taken equal to 6 inches, and S (= S,) may be taken at 18,000 pounds, the same as for pins. Therefore, the thickness of the hanger plate should be, ‘3 X 20,600 x 43 ax 18,000 x 6 Obs aly 1e d=V A plate ¢ of an inch thick has been used. By noticing the manner in which the lower flange of the floor-beam is sup- ported by the stiffeners near the beam hanger (Plate, Title: Highway Bridge: Details II, Fig. 4), it will be seen that, as a considerable portion of the load upon the beam is delivered directly upon the hanger nuts, the hanger plate is relieved of much of its stress as a beam; hence, in this case, a thickness of ? of an inch is probably ample. If the flanges of the beam are not supported by stiffeners reasonably near to the position of the hanger, the hanger 1002 DETAILS OF CONSTRUCTION. plate should be considered as a beam carrying a single load concentrated at the center, in which case the quantity under the radical sign will be just twice as great as in formula 216. But, in such a case, the thickness, cr theguanc- angles to some extent helps to make up the thickness re- quired for the hanger plate. The thickness, as obtained by formula 216, will generally be somewhat greater than the values commonly used. CONCLUDING REMARKS. 1624. All calculations necessary for proportioning, according to the specifications used, the constructive details of the members of the bridge shown in the five plates of Mechanical Drawing, to which we have referred, have now been explained. Various small details, however, such as pins, shoes, rollers, bed-plates, etc., still remain to bé noticed. These, as well as certain features relating to the main members, will be considered in subsequent articles. Conditions and requirements for the details varying from those here noticed are commonly met with, and are required by other specifications. It should also be noticed that, besides the connecting details explained in preceding pages, many other forms of connections are often used. This statement applies especially to the connections for the lat- eral rods and struts, the portal bracing, and the floor-beam. It is not within the limits of this Course to compare and discuss the various forms of practical details. A really com- prehensive knowledge of these can only be acquired by practical experience. The details that have been explained are not in all cases the best possible for the purposes intended; but it has been the aim to illustrate thoroughly the application of the underlying principles governing the proportioning of details, rather than to discuss the various forms of the latter. The principles explained in the preceding pages apply to the calculations and design of details in general; and if the student has thoroughly mastered them, he will experience no serious difficulty in proportioning the details and con- DETAILS OF CONSTRUCTION. 1003 nections for the members of a bridge according to any specifications, and in conformity with the requirements of approved practice. It is absolutely impossible to formulate any system of rules that will apply to all cases and conditions. The prac- tical designer is constantly meeting new conditions, and in many things he must be guided by his judgment and experience. T. I[,—2é DETAILS, BILLS, AND ESTIMATES. SHOES, ROLLERS, AND BED-PLATES. 1625. Shoes.—For the structure shown in Mechanical Drawing Plates, Titles: Highway Bridge: Details I, II, III, IV, and Highway Bridge: General Drawing, the shoes are shown in Figs. 5 and 9 of Plate, Title: Highway Bridge: Details III. Ina shoe, the upright plates which support the pin are called standards or ribs. In the present case, the thickness of each of the two standards is 2 of an inch, and the clear distance between them is 9f inches. (Arts. 1539 and 1540.) The lower or horizontal plate forming the bottom of the shoe is called the shoe plate or sole plate. Before deter- mining the required thickness of this plate, it is necessary to ascertain its required length and breadth. In the present case, the width from out to out of stand- ards is 9 +2 2=114 inches. In order that it may be connected to the standards by 3” x 3” angles, the shoe plate must, as a rule, extend somewhat more than 3 inches beyond each standard, which gives 114+ 2 x 3= 17} inches for the least permissible width of the plate. The width will be made 174 inches. ‘The length of the shoe plate in the roller shoe depends upon the number of rollers required. Conse- quently, before proceeding with the dimensions of the shoe, it will be expedient to notice the dimensions of the rollers. 1626. Roltllers.—The rollers are shown in Fig. 7 of the last plate referred to. As may be seen in the figure, they are secured together by two bars, called side bars. The, turned ends of the rollers are made to run in holes drilled in For notice of copyright, see page immediately following the title page. 1006 DETAILS, BILLS, AND ESTIMATES. the side bars much the same as the ends of pulleys or shaft- ing run in journals. The ends of the side bars are generally connected by round bars, the ends of which are riveted down upon the side bars, attaching them to each other. Such an assemblage of rollers is called a nest of rollers. 1627. The design of the rollers is governed by item (¢,) of the specifications (Art. L511). According to this specification, the diameter @ of the roller shall not be less than 2 inches, and the pressure per lineal inch of the roller shall not exceed 500 4/d. | If the diameter of the rollers be assumed to be 2 inches, the pressure per lineal inch must not exceed 500 V2 = 107 pounds. The vertical pressure upon the shoe is equal to the reaction from live and dead load (46,300 pounds) plus the pressure at the foot of the leeward end post, due to the -wind force against the upper chord, which is equal to - oO bax 2 y A x i ='5,100 pounds.2 Ehes total vertical load that can come upon a shoe is, therefore, 46,300 + 5,100 = 51,400 pounds, requiring the aggregate length of the rollers available for bearing to be ee The constructive details generally require the length of the rollers to be about 1 inch shorter than the width of the shoe plate, or, in the present case, 174 — 1=164 inches long, approximately. Fig. 7 of Plate, Title: Highway Bridge: Details III, shows that the actual length of the roller, from shoulder to shoulder, is 162inches. It will also be noticed that grooves are turned in the centers of the rollers, in order that they may pass over small bars riveted on the bottom of the shoe plate and top of the bed-plate (Figs. 5 and 8, same plate). The office of these bars is to act as a track or guide, over which the grooves in the rollers may run, holding the rollers and also the shoe truly in position. In some cases these bars on the shoe plates and bed-plate are solid ribs formed by planing down the bearing portions a PO. ANCES: DETAILS, BILLS, AND ESTIMATES. 1007 of the plates: In the present case the bars riveted to the shoe plate and bed-plate are 14 inches wide, and the grooves 1g inches wide. As the grooves are made to clear the bars, the rollers have no bearing in this portion of the length, and, therefore, the effective or bearing length of each roller must be considered to be shortened 12 inches by this detail, ma- king the length of each roller, effective in bearing, equal to 163 —1#=15 inches. The number of rollers required ‘is, "9 (A therefore; equal to ea = 4.8, or, practically, 5 rollers. Not less than ¢ of an inch clearance must be allowed between each two adjacent rollers, and a clearance of 4 of | an inch may be used when obtainable. In the present case, if + of an inch clearance is used, the distance from out to out of the rollers will be 5 x 2+ 4x 4+=11 inches. 1628. Coefficient of Expansion.— According: to | item (w,) of the specifications (Art. 1511), ‘‘ variations in temperature, to the extent of 150 degrees (Fahrenheit) must be provided for.” For a variation in temperature of 150 degrees (Fahren- heit), the amount of expansion or contraction of wrought iron is given approximately by the formula l —— 1,000’ (217.) in which e is the total amount of expansion, and / the length, in inches, of the piece of iron (the span of the bridge, in this case) considered. This is usually expressed as a coefficient, and is called the coefficient of expansion. Thus, for a variation of 150 degrees, the coefficient of expansion for wrought iron is .001. For structural steels it is substantially the same. In the example, then, the amount of expansion (or con- traction) to be provided for at the roller shoe is equal to 90 x 12 ie 1,000 to the width out to out of rollers, it is found that the = 1.08, or, nearly, Idinches. By adding this amount DETAILS, BILLS AND? EST IMAGE 1008 yz” 17: 2 Scale of forces 1’=20000 lb. Scale of distances 3’=1 ft. FIG. 328, DITATLUS, “BLEWUS = A0N STM APES: 1009 required length of the shoe plate is 11 + 14 = 122 inches. As but a small portion of the width of each roller bears upon the plate, the distance out to out of the dcarings of the roller will be somewhat less than 11 inches, and a length of 12 inches could have been used for the shoe plate. A length, however, of 13 inches is used. 1629. Bending Moment on Shoe Plate.—It will be sufficiently correct to consider the pressure upon the bottom of the shoe to be uniformly distributed over its bottom surface. This will be practically correct for the anchored shoe, and for the roller shoe the error will be slight. The load upon the shoe is delivered upon the shoe plate through the standards. If, for convenience, we imagine the shoe to be inverted, we shall have, in the case of a shoe with two standards, a uniformly loaded beam resting upon two supports and overhanging each support. As previously determined, the maximum total load upon a shoe is 51,400 pounds. The load upon each standard or, considering the standards as supports, the reaction of each . 51,400 SUpPOrt1§ — 9 the standards, from center to center, is 9£ + 2 = 10$ inches. In Fig. 328 the shoe is. shown inverted, acting as a uniformly loaded beam upon two supports, extending beyond each support. The uniform load upon the beam is represented as divided into sections, and the weight of each section is considered to be applied at its center of gravity. Each section is 1 inch long, except the two end sections, which are each 14 inches long. Consequently, the weight upon each intermediate section is equal to ee = A;d9 6; Ol, practically, 2,940 pounds, and the weight upon each end section is 14 X 2,937 = 38,671, or, practically, 3,670 pounds, as indicated in the figure. (See also Art. 1171, Rule.) The same figure shows the force diagram and moment diagram for this beam. In the force diagram, the pole dis- tance is made equal to 30,000 pounds. It will be noticed = 25,700 pounds. The distance between 1010 DETAILS, BILLS, AND ESTIMATES. that the bending moment in this beam is negative at the supports and positive in the middle portion. (It is evident that such a beam could project far enough beyond the sup- ports so that the bending moment at the center also would be negative. ) Either the positive or the negative bending moment may be the maximum bending moment, and, consequently, the maximum intercept of each character must be measured. The maximum negative intercept occurs at either support and measures —.60 of an inch, nearly; hence, the maxi- mum negative bending moment will be — .60 x 30,000 = — 18,000 inch-pounds. The maximum positive intercept occurs at the center f, and measures.76 of an inch. ‘This shows that the absolutely maximum bending moment occurs at this point. Its value is .76 X 30,000 = 22,800 inch-pounds. On account of the uniform load being assumed to be con- centrated at the centers of the various sections, this bending moment is slightly in excess of the true one, but it is sufficiently correct for all practical purposes. 1630. The exact bending moment upon a shoe of this form may be easily calculated. If a beam is uniformly loaded over its entire length 0, Fig. 329, and the amount 7p. EERE LAB ra te ee es | 8 Ba eae FIG. 329. which it projects beyond one support is equal to the amount J’ which it projects beyond the opposite support, the bending moment J7/ at the center will be given by the formula W b Ws in which IW is the total load upon the beam, and s and 6 have the values indicated in the figure. This bending moment will be positive or negative, according as the result is positive or negative. DETAILS, BILLS, AND ESTIMATES. 1011 This formula assumes a uniform load over the entire breadth 4 of the shoe. When the rollers are grooved in the center, as in Plate, Title: Highway Bridge: Details III, Fig. 7, they will support no load upon the groove, and the bending moment at the center of the shoe, as given by formula 218, will be a little too large when positive, and too small when negative. It would be.possible to state a formula for such cases, but the bending moment for each particular case can be readily computed by applying the principles of moments. The negative bending moment — J/ at either support will be given by the formula W p° 2b? in which f may represent either / or f’ of Fig. 329, for this formula applies whether / and 7’ be equal or unequal. In our case the bending moment at the center of the shoe 17.5 : 51,400 is, by formula 218, ar ae (10.5 a ~ ey) ee (219.) ) = 22,488 inch- pounds. The bending moment at either support is (for- 51,400 3.5° mula 219) —~ a = — 17,990 inch-pounds. 1631. Thickness of Shoe Plate.—We have seen (Art. 1623) that the moment of resistance of a beam of nelipie et gh rectangular section is X= go whence, 6A (7 een SF" (220.) In the present case the length of the shoe plate, corre- sponding to the total width of the beam, is 13 inches. But, as shown in Fig. 5 of the plate just referred to, the section at the center of the shoe plate of the expansion shoe (the position of maximum bending moment) is reduced by three rivet holes. By considering the diameter of each rivet hole to be 4 of an inch greater than the diameter of the undriven rivet, 1012 DETAILS, BIULS, ANDEESTIMAr ir: the width to be deducted for the three rivet holes is 3 xX 3 = 21 inches, making the net length of the shoe plate, acting as the effective width of the »beam, equal to 13 — 21=10% inches= 6. As the load is somewhat dis- tributed, and the shoe plate materially supported and strengthened by the horizontal legs of the angles forming the standards, the value of S may be taken at 18,000 pounds, the same as for pins. By substituting the values of Rk, S, and din formula 220, we get, for the thickness of 6 & 22,800 the shoe plate, d= 18,000 x 10.75 = .84, or, nearly, £ of an inch. There are no rivet holes to be deducted from the section at the center of the shoe plate of the anchored shoe, and, consequently, the value of 6 for this shoe is 13 inches, and aay ane =),76. 01, practicalhyije-2Ot .Aneancil wees thickness of ~ of an inch, however, is used for the shoe plates of both the roller and the anchored shoes. It is to be noticed that, for the roller shoe, the rollers and bed-plate may be considered to act somewhat as beams, thus assisting the shoe plate sufficiently to make up for the section cut out by the rivet holes. This being the case, a thickness of 3” would probably be sufficient for the shoe plates of both anchored and roller shoes. The standards or ribs of the shoe must be given such form as will clear the upper flanges of the channels of the end post. For bridges of moderate span the form of the stand- ards is commonly made symmetrical with reference to a vertical line through the center of the pin hole. In many shoes the horizontal legs of the angles forming the stand- ards are turned outwards, and the smaller angles (in the present case, 3” x 3” xX 2" angles), connecting the vertical legs of the larger angles to the shoe plate, are omitted. Sometimes, also, each standard consists simply of a vertical! plate, connected to the shoe plate by a single angle. The standards shown in Plate, Title: Highway Bridge; Details III, Figs. 5 and 9, are very substantial. The two shoes DETAILS, BILLS, AND ESTIMATES. 1013 there shown are alike, with the exception of the small guide bar on the bottom and the connection for the shoe strut on the roller shoe, and the holes for anchor bolts in the anchor shoe. 1632. Another Form of Shoe. Although the form of shoe shown in the plate just referred to is commonly used for bridges of moderate span, other forms are often used, }, of an inch for each chord bar, and plus + ofan inch for cach riveted member ; but the total amount added should never be less than the constant c. For the value of the constant c, the practice varies. The value of this constant, as determined by any oneof the three methods indicated below, will be found satisfactory. (1) for all chord pins : aie a (221.) (2) For chord pins having diameters Less than 8 inches : c= }’. (222.) From 8 to 6 inches : rae A (223.) Greater than 6 inches: c = 3". (224.) (3) Lor chord pins of any diameter D: pols W ai 4”, (225.) In using the last formula, the value of c may be taken to the nearest sixteenth of an inch. In practice, however, when the grip of the pin, as esti- mated by any one of the preceding formulas in connection with either of the above rules, contains a fraction smaller 6 DE PATS, BIPUSe AND: ESTIMATES, 1019 than one-eighth of an inch, the fraction should be called one-eighth. The amount added to the net width of the member or members, to obtain the grip of the pin, is to insure the fin- ished portion of the pin passing entirely through the mem- ber, making allowance for probable variations in width. Ti GE: general form isshown in Fig. 334. It isunnecessary to give here the exact dimensions of this nut, which vary somewhat irregularly in the different sizes, but for convenience the following approximate dimensions may be given with refer- ence to J, the diameter of the finished pin. See the figure. Diameter d, of rough hole for screw: 3 ‘do D— =f. (228,) Diameter R of recess: RD nen 20%) Short diameter S of nut: Steins af (230.) Long diameter L of nut: Bab ee: (231.) Length t of thread: 3 ity. Depth r of recess: 12 meagre Total thickness T of nut: 9) Me heap In applying formulas 226 to 234, inclusive, the diam- eter DY of the pin should contain no fraction smaller than 4+ inch; if the actual diameter of the pin contains a smaller fraction, the full quarter inch next above should be used. Values from these formulas will be obtained to the nearest sixteenth of an inch, except formulas 226 and 228, for * This is correct for 7 threads to the inch, and may be considered near enough for 8 and 6 threads to the inch, which are the sizes of threads commonly used for pin nuts. DETAILS, BILLS, AND ESTIMATES. 1025 which the values will be obtained to the nearest eighth of an inch. It will be noticed that the length of the thread, as given by formula 232, will be in all cases 4 inch less than the length of the screw end of the pin, as given by formula 2273 which may be expressed in the form a es ots It is not necessary to give the dimensions of pin nuts on shop drawings (or shop lists); it is usually sufficient to give the required dimensions of the pins and state the kind of nut required. _ 1641. Cotter Pins.—Pins of the form shown in Plate, Title: Highway Bridge: Details IV, Fig. 12, are: called cotter pins. They are often used for lateral pins and for certain other purposes, but are not commonly used when the diameter of the pin is greater than about 3 inches. In general form, a cotter pin is somewhat similartoa bolt. It usually has a round (cylindrical) head, and at its opposite end, instead of having threads cut, it has a hole drilled to receive a small split pin formed by bending a piece of half round iron, so the flat sides will be in contact. The split pin so formed is sometimes called a key, but it is more commonly known as a cotter. The end of a cotter pin is tapered slightly in order that it may be more easily inserted into the pin hole. | | | FIG. 335. A cotter pin is shown in Fig. 335. The relative dimensions 1024 DETAILS, BILLS, AND ESTIMATES. of cotter pins given by the following formulas will be in accordance with good practice, each result being taken to nearest sixteenth of aninch. See the figure. Thickness T of head: Diet, Diameter H of head: he Be PAE If (236.) Length C of cotter: Gee ee a (237.) Diameter or width c of cotter: Caan Lie (238.) Diameter h of cotter hole: 1, =e = 16 : CRED Diameter d of end: d= D, 240.) Length e of end: 3 1 ” Fae Dore (241.) Length t of taper: Poe (2 Total length L of pin: d beret 6 PSY (243.) In these formulas / is the diameter of the finished pin. 1642. The grip of a cotter pin is determined substan- tially the same as for a chord pin, but formula 222 should generally be used for the value of the constant. DETAILS, BILLS AND ESTIMATES: 1025 The grip of acotter pin should always be given from the under side of the head to the tnner (or nearest) edge of the cotter hole, as shown at G in Fig. 335. The preceding formulas represent practical and economi- cal dimensions for cotter pins, but as the diameter and grip are the only really important dimensions of a cotter pin, slight variations in other dimensions are not of conse- quence. EXAMPLE.—For a cotter pin having a diameter of 1% inches, and a net grip of 24 inches, what are the remaining dimensions, as given by the preceding formulas ? tte Bee SoLUTION.—Thickness of head, 7 = me a z= 3 Diameter of head, ffm A$ Ae 2 == OH. Length of cotter, C=14x1#+ 4=24". Diameter of cotter, Gs) <1. Diameter of cotter hole, Z= §++74,—,%". Diameter of end, @=°4xX%18=17". Length of end, eé= #X1#+ =f’. Length of taper, f= +X 4=7%". Length of grip, G=24+ += 23". Total length of pin, L=2¢+ 84+4=4". 1643. Pin Washers.—In Plate, Title: Highway Bridge: Details III, Figs. 10 to 13, are shown small rings of sizes to fit loosely upon the pins. They are used to fill the vacant places between the various members connecting upon certain pins, and serve to hold the members in their proper positions. These rings are known variously as pin washers, packing rings, and filler rings. They are, as a rule, formed by bending strips of metal into circular form so that the inside diameters will be about 4 of an inch greater than the diameter of the pins. The metal used is from 5%; to $ inch thick. In determining the lengths of pin washers, sufficient clearance must be given, making ample allowance for vari- ations in the thickness of the members. If this is not done, and the pin washers do not fit readily into place, they are very liable to be omitted in the process of erecting the bridge. In determining the lengths of the pin washers. 1026 DETAILS, BILLS, AND ESTIMATES. practically the same allowances are made as in rule II, Art. 1637, for determining the grip of the pin. EXAMPLE.—What should be the length of the pin washer for the hip joint of the bridge shown or the Mechanical Drawing plates? SoLuTION.—The distance between the inner surfaces of the pin : vi ; plates on the end post at the hip joint is 72 —2 x 16 64inches. See Plate, Title: Highway Bridge: DetailsI, Fig.1. By allowing 4 of an inch on each side for the riveted member and ;% of an inch for each forged bar, the length of the pin washer will be 64— 2x vie 4x : ~~ 4x a2 inches. Ans. See Plate, Title: Highway Bridge: Details III, Fig. 10. 1644. The Shop Drawings.—The details of the members and their various connections, as shown in Plates, Titles:»: Highway Bridge: Details lee isi eco er ies with the calculations necessary for proportioning the same, have now all been explained. In the order of procedure for the construction of the bridge, the shop drawings may be considered to be completed, It will be well, however, to notice that, in many cases, sizes and dimensions which, in the plates referred to, are shown marked as dimensions, are usually simply stated in actual working drawings. ‘The sizes of all plates, bars, and shape iron should be distinctly stated upon the drawings, and such dimensions as will be clearly understood from such statement may be omitted. Thus, for the main tie bar, Plate, title as above, IV, Fig. 1, the marked dimensions 2”, 18", 5£", 6", and {” would usually be omitted in the draw- ng, but under the drawing would be written: 13 ue Main Tre Bar, 2" x —",; Heads, 5%" x 3 16 , 8 required. This statement gives all necessary information concern- ing the main tie bar, except the sizes of the pin holes and the length from center to center of the same. Shop drawings, and, indeed, nearly all bridge drawings DETAILS, BILLS, AND ESTIMATES. 1027 are made upon tracing muslin, in order that they may be blue-printed. The drawing is usually made in pencil on detail paper, then traced and finished in ink on the tracing muslin. As many blue-prints should be taken as are necessary for the office and the different shops. BILLS. SHOP LISTS. 1645. What is stated above concerning the main tie bar is true also of many other members; in fact, it is true of nearly, if not quite, all forged members. Therefore, instead of showing such members upon the shop drawings, it is the practice in most bridge offices to state the necessary dimensions upon certain blank forms or sheets, thus con- veying the same information with much less labor. Such sheets are commonly known as shop lists. The fol- lowing will serve to illustrate the general forms of shop lists. Two somewhat different forms are given for eye- bars. It will be noticed that lists (4) to (£), as filled out, give all necessary information concerning the forged members shown in Plate, Title: Highway Bridge: Details IV, Figs. 1 to 6. In these lists are given in each case, not only the dimensions of the finished bar, but in the column headed Ordered Length is also given the length of the rolled bar necessary to give the required finished dimen- sions. This feature of the shop lists will be more fully explained in the following articles. For the student’s convenience, the figure to which each item refers is designated in the left-hand column. Lists (A) and (4) are simply two differ- ent forms which serve the same purpose. It will be noticed that, in stating the lengths back to end in list (D), 4 inches are allowed for the distance between the two screw ends, according to the practice indicated in DETAILS, BILLS, AND ESTIMATES. 1028 (1 314) 46 8% ‘O| 9 | FS | PES SS |S | ag | et Xo) 8 Ig ‘y}sueT ; : "s1eg ‘portnboy | pe19p10O fT i it L l 4 Hf jo 9ZIG | JoqUINN IPN T ‘ON W9YS ‘UOLT JYSNOLA “[ello}eI{ “Sav ad-dAA “LSIT 2A9AOA (PV) 1029 DETAILS, BILLS, AND ESTIMATES. (¢ ‘3Iyq) v8F 0% 'O v9 see 88S (81 vER 19 | LX al | a8 97 0} UIedYy ‘yy Sus] ‘doo7T jo} ‘utg jo ‘yoegq 0} yorg ‘ulg Jo | ‘doo’y jo ‘leg ‘pormbay pelapio y4sue’T | 1oyoweiq y4sue'y Jojowriq | yysuoyT joozig | 19quinn Se “ON J0YS “0 06 weds G&L ‘ON doyg ‘8L¢ ‘ON pRIyUOD ‘UOAT JUSNOLAL “[elI9IeI *SdOOT GAGTAM HLIM SAVA “LSIT 29NO0Oa (9) (T “S1q) the oe Orders | = eS ‘eg Ce # | Xie | aH xe 8 Ig "SOYyOuUyt 1994 ‘soyouy ‘J99 47 ee ree HE OTIOUT &. Saad alte ar eee et SOIL ‘soyouy ‘soyou. | mba ‘yySue'q ‘pray jo} ‘utq jo bid ells Skid fe hs ‘ulg Jo | ‘pray jo | ‘eg jo acre “YIP po1epiQ ez1q | Joyomvicy | 79349) OF F079) | s93;0uIeIC QZIS 9ZIS yysua’7T ‘T “ON 3999S “0406 uedg “GEL CON doys "8LG “ON JORIJUOD) ‘UOLT JYUSNOLAA “[elI9JeIW “SUV A-AAA “LSIT F9AOd (7) DETAILS, BILES* AND ais iI Masi 1030 "HOI? ,F 07 w9z PLT x £6 j ate 9 NS at¥ ie 40 iG cat ag Eine Meee Ha, 0G AS at vel Flea itl ueV MeO 9 be OMe? sty $1 0. ta a OI “ / 7] “ ; “J [A 7] ks 7) | ‘ cs rd x ka 8 aLl (OG O wtV wth W198 /OL vel “ve £6 { ut io se at vel 40 iS axe ah * pore i at as it¥ el et$ 0G itl ad ; ‘yosd Sloeg Rep eelecla| ‘yosdq jo | yosdg jo} jo pug 0} ‘UI jo ‘doo’T jo Poles pe1spi9o yysue7yT | 10j0wWeIq | doo7y jo yoeq} s9jyowIeIq | Y}Sua'T yysuo’y yysuayT ‘§ “ON W9YS ",0 06 weds G64 “ON doys ‘U0LT JYUSNOAA{ “[ellojeI “SATHOAANAAL GNV SdOOT GAGCTAM HLIM SUVva (7) ‘Ieq jo eal> ‘poimboay JoquinN (9 “31q) Oe ‘29 (¢ 317) ‘9D ‘9D (% “814q) ae! wae ‘YIP ‘849 ON JRIZUOD “LSII a7VAOA (Z) BARS WITH UPSET SCREW ENDS. Material, Wrought [ron. Shop No. 735. FORGE LIST. DETAILS, BILLS, AND ESTIMATES. 1031 Sheet No. os Spaeuc sia: cc . Diameter ‘it = Diameter | Length : Contract No. 2 Number Size of Ordered Bar. Upset. 2 | End to cn of Upset. Length. Nuts. ss Mark. Stand. ; 26' 5! 26’ 12” 12” 1’ 4 4 4 5 ia (-) 1 ” 4 2 BC. CaGe (Fig. . 1" 4 Stand. ain ie ies ee i ee oi Art. 1612. The lengths of upset ends given in lists (D) and (£) are also in ac- cordance with the practice there indicated. For the details of pin-con- nected members, the practice in some bridge offices is to indicate the size of each pin hole by stating the size of the pin, allowance for the clear- ance of the pin hole being made in the shop. In other bridge offices the practice is to state the exact diameter actually required for each pin ole. Each practice has its advantages. Either system will obtain the required results if con- sistently followed, but the latter practice is to be pre- ferred. On the Mechanical Drawing plates and in the shop lists given above, the former practice has been fol- lowed, except in list (4), in which the diameter of the pin hole is stated. In lists (/’) and (G) is given all necessary information concerning the pins shown in Plate, Title: Highway Bridge: Details IV, Figs.9 to 12. In list (7) the lengths of all screw ends are given according to formula 227. In list (G), all dimensions of DETAILS, BILLS, AND ESTIMATES. 1032 itv | | 90 ate 8 yal bie ts ‘99% CARE 0 ‘IDA ae yysuoy “an “Ie fof Se Fok dneat "SIOYSEM '¢ “ON W2US “SNId GUOHDSD eS RO ee yy rd OOM ae ac PAG OD Menge ‘yysueyT «=|‘weiq ‘pslapio bi 8 8 8 v atl wth u16 wil atl A siz ¥ me wt if v@0 a! L ne ¥ 8 a Ke wth uS Ll ul mo (TL “S1q) 5 uo] 9) (Or “31q) CL | 1993S “W| 2 ‘9 °g (6 S14) Fr |S W| 2 ‘pa -1inb “9A | -peisoqeyy ‘yIe] 13q -uIn N “OLG "ON, 3981}UO07) “\LSIT ANIBHOVA 1033 DETAILS, BILLS, AND ESTIMATES. OT ; I “1 uol] ( SIO - ( aoyouy S ue ane ue (9 ‘S17 ) Z (ST “BI 188 /OT ‘O req U7 2 i aV ay 8 yUL As Wee ie Pax al OG uolyT I) ‘yysueT «| werd) ‘pe , eS, 2 oan ae? & 2 P a YN Ee eae Nad ie ge “Ie ‘pa1apioO | a "9L4G ‘ON JORIJUOD ‘9 ON P2US "Nid AWALLOS “LSIT ANIHOVA 1034. DETAILS, BILLS, AND ESTIMATES. the cotter pin are according to the formulas given in Art. 1641. For the details of pins, the correct diameters of the finished pins are always stated. The forms of shop lists, as used in the different bridge offices, of course vary somewhat, but the forms given serve to illustrate the general system. The blank forms for shop lists are generally printed upon tracing muslin or upona thin bond paper which will blue-print. IRON ORDER. 1646. General Method of Procedure.—After the shop drawings are completed, the next step in the process of the construction is to make out the iron order. The com- panies who manufacture bridges do not usually roll the iron themselves. A few of the larger bridge companies own both rolling mills and construction shops, but even in such cases the management of each is generally separate and distinct from the other. The greater portion of the material for each bridge is ordered from the rolling mill in the exact lengths required, making due allowances for the requirements of manufacture. There is, practically, no waste in such ordered material, beyond that necessary to finish it properly. 1647. Certain common sizes of channels, angles, plates, and bars are carried in stock by most bridge works. Stock iron is ordered in lengths of 30 feet. For iron rolled in lengths greater than 30 feet the prices per pound are some- what higher. This fact should be borne in mind in making the design for a metal structure; the lengths used should generally not be greater than 30 feet. A list of the material carried in stock, called the stock list, should always be kept in the office, and the material checked off as used. From the shop drawings, a list of the material required to make the -various members of the structure is made out. In this list, the material is taken in substantially the same order as it appears upon the shop drawings. This list is known as an order list. DETAILS, BILLS, AND ESTIMATES. 1038 The order list is then carefully scrutinized and compared with the stock list, and such sizes as are carried in stock are marked to be taken from stock. When this is done, a second list is made, in which the remaining pieces, not car- ried in stock, are grouped and classified, the various pieces of each size and shape being assembled together. In this classification, the channels are usually written first, followed by the angles or other shape iron, then by the plates, flat bars, square bars, and round bars, respectively. In this list, also, the lengths of short pieces of plates or bars of the same size, such as pin plates, batten plates, etc., are usually added together, and the aggregate length given in one or more pieces. In such case, the length of each piece thus formed must not be more than 30 feet. This classified list of the material to be ordered is called the iron order. It is made out by the engineering department of the bridge works, and then transmitted to the business department, by whom the actual order is placed with the rolling mill. 1648. Ordered Lengths of Material.—In making out the order list for the material for a bridge, certain rules must be observed with reference to the ordered lengths of the material. Pieces of plates, bars, angles, or other shapes, which are not required to be finished to exact lengths, or to be upset, welded, or forged, are ordered in neat lengths, that is, in the lengths actually shown on the drawings, without any allowance for extra length. When a number of short pieces of the same size are required, however, a single plate, hav- ing a length equal to the aggregate length of all such plates, is usually ordered. When short pieces of plates are to be cut diagonally, or on a bevel, they are usually ordered in such rectangular lengths as will best cut to the required dimensions. 1649. If one or both ends of a rolled or built member are to be planed, in ordering the material a certain amount must be added to its finished length, to provide for the material taken offin planing. This amount varies somewhat LT. ll.—2&7 1036 DETAILS, BILLS, AND ESTIMATES. with the form of the planer used; but with the machines commonly used in bridge shops, the amount to be added for each finished end should generally be as follows: Tf the greatest dimension (width) of the member does not exceed 6 inches, add } of an inch. Tf the greatest width of the member exceeds 6 inches, add lg of an inch for each additional 6 inches width, or fraction thereof. This may also be expressed by the following formula: 1 b 4 TR Re (244.) in which a is the length to be added for each finished end, 6 is the width of the member in inches, and ¢ is a constant which, for most planers, may be taken at ;, of aninch. In ioe. eee this formula, any fraction in the value of the expression r; should be considered as unity. 1650. In ordering the material for eye-bars, upon which the heads are to be formed by piling and forging, the length of bar required beyond the center of the pin hole is given for one head by the formula vee wv a=5—-(F+e) (248) in which a is the additional length of bar beyond the center of the pin hole, // is the diameter of the head, wis the width of the bar, and c is a constant, which may usually be taken equal to # of an inch. This formula applies generally to wrought-iron eye-bars. The additional length a of the bar beyond the center of the pin hole, required to form one eye-bar_head by upsetting and forging, is given by the formula a=3(H—w)+te, (246.) in which /7 is the diameter of the head, w is the width of the bar, andc is a constant, which must be obtained from the practice of each shop, but may usually be taken equal to DETAILS, BILLS, AND ESTIMATES. 1037 ay 3— +e This formula applies to steel eye-bars as generally manufactured. The additional length @ beyond the center of the pin, necessary to form one welded loop upon the end of a round or square bar, is given by the formula a=3.57 D+ 4.57 d+, (247.) in which / is the diameter of the pin, @ is the diameter of the round, or the side of the square bar, and ¢ is aconstant, which wiil here be taken simply equal to zero. 1651. The additional length ~ necessary to form one upset upon the end of a round bar is given by the formula u= (3 es 1) jas Sp (248.) in which PD is the diameter and £ the length of the upset end, d@ is the diameter of the original bar, and ¢ isa constant, which may usually be taken at # of an inch. The additional length w necessary to form one upset upon the end of a square bar is given approximately by the formula w= 185. (=; ~121) +e, (249.) in which SS is the side of the square bar, ) and # have the same values as in formula 248, and ¢ is a constant, which may usually be taken as 1 inch. Results obtained by formula 249 are not generally as satisfactory as those obtained by formula 248, It is in all cases roughly approximate to take the length required to make each upset end as equal to the length of the upset. 1652. If ordered cut tothe required length, the ordered length of a chord pin may be the sameas its finished length, as obtained by formula 227 and the preceding rules. This length will be given by the formula TAGE ate (250.) 1038 DETAILS, BILLS, AND ESTIMATES. in which Z is the length, G is the total calculated grip, and Dis the diameter of the pin, while cis a constant, which, for lengths of screw ends as given by formula 227, will be equal to 2 inches. If all pins of the same size are ordered in one piece of a length sufficient to be cut into the required lengths, the value of c will be 4 of an inch greater, as will be hereafter noticed. The ordered diameter of a chord pin greater than 1,5 inches must always be a multiple of 4 of an inch. The ordered diameter will be at the full eighth of an inch greater than the diameter required for the finished pin. (See Art. 1639.) 1653. Rivets are made with one head; the second head is formed in driving. For the proportions of rivet heads given in Mechanical Drawing, the length of the rivet before driving, allowing sufficient additional length for forming the head in driving, should be : For round heads: l=14;G+1¢¢+.6. (251.) For countersunk heads: ad = ligG+s +e, (252.) In both of these formulas, 7is the length from the under side of the head: tothe end of the rivet before driving the diameter, and G is the net grip of the rivet, while cisa constant which may generally be taken at 2 of an inch. These formulas apply to machine-driven rivets in punched (unreamed) holes, and will be found generally satisfactory. As the additional length of rivet required to make the head is affected by the power used in driving and by the size of the die or cup used to form the head, both of which vary in different shops, it will in some cases be found necessary to use a different value for c. For hand-driven rivets, no satisfactory formula can be given. The additional length of rivet necessary to form the head will differ in hand riveting done by different men, DETAILS, BILLS, AND ESTIMATES. 1039 and the proper amount to allow for this purpose can be learned only from experience. Formulas 251 and 252 give fair approximations, and will be adopted here. In stating the lengths of undriven rivets, fractions smaller than eighths of an inch are not commonly used. 1654. If a lattice bar is connected by a single rivet at each end, the total or ordered length Z is given by the formula L=ltwte, (253.) in which / is the length from center to center of rivets, w is the width of the bar, and ¢ is a constant, which has usually different values for different widths of bar, and also in differ- ent shops. It will here be taken as 2of aninch. Liberal allowance should be made in ordering the material for lattice bars, as there is always more or less waste. 1655. In ordering the material for beam hangers, the length U of that portion of the hanger bar above the center of the pin may be found by the formula U=1.57(D+2), (254.) in which J is the diameter of the pin, and d@ is the thickness of the bar. 1656. Allthe preceding formulas, except formula 254, contain a constant c, which is in each case a quantity de- pending upon the methods and conditions of the shop work. It is, therefore, evident that this quantity, as used in any one of the formulas, will probably not have the same value when applied to the practice of different shops. The values here given are believed to represent a fair average of good practice. For convenience in using formulas 245 to 252, inclu- sive, the results given by each formula, as applied to the various sizes, should be tabulated. In actual practice it is essential to have the results arranged in convenient tables, so that, for any common size, the required length may be read at once from the tabie. In preparing each table, 1040 . DETAILS, BILLS, AND ESTIMATES. however, the value of the constant c should conform to the practice of the shop for which the tables are to be used. 1657. Order Lists.—Two examples of parts of order lists are given below. List (/7) is the order list for the mate- rial required for the end post, Plate, Title: Highway Bridge: Derails le bao eis The lower end a of the end post is not planed; conse- quently, no allowance of extra length need be made for this end in ordering. The upper end / of the end post is planed ona bevel. In such cases, the amount given by formula 244 is usually added to the length of the cover-plate for finishing the upper end; it is not, however, always added to the length of the channels, although this is done in the present case. Plates with the corners sheared off, as the tongues of the pin plates at the hip joint, are generally listed in rectangu- lar form, without reference to the shearing, which is usually done at the bridge shops. They are almost always ordered as one plate (or more, if necessary) of length equal to the aggregate length of the several plates required of the same size, and are sheared into the required lengths and forms at the bridge shops. For plates sheared to dimensions, the mills charge a higher price than for plates simply cut to ordinary lengths. As rivet iron is always carried in Sage lists of the shop rivets required are not commonly given on the order lists, although it has been done in the present case. When lists of rivets are given, however, all rivets of the same length are generally given in the same item. 1658. List (/) is the order list for the material required to form the members and details shown on Plate, Title: Highway Bridge: Details IV, Figs. 1 to 12. The ordered dimensions are those required to make the finished dimen- sions given on the shop lists in Art. 1645. The ordered dimensions of the material should be given on the shop lists and working drawings, in order that the workmen may be able to select easily the proper material for each member. DETAILS, BILLS, AND ESTIMATES. 1041 The ordered lengths of forged bars are seldom expressed by fractions smaller than eighths of an inch, although six- teenths may sometimes be used. In making out order lists, it is well to use, in each case, the eighth of an inch next above the calculated length. (/7) ORDER LIST. For 4 End Posts. Material, Wrought Tron. W’ cht Length. afark: Number| Name of Size. 1b. . To’al| Ord- R’quir’d Shape. Inches. pen Rt} Ft. In. Wt. |der’d ab 8 |Chans. 8 16 | 25 |1014 O ab 4 |Angles. | 24x 24] 4 3 | 42 O ao 4 |Plates. 2x ¢ 25 | 1013 O ab 8 |Plates. 6 X q5 Leeds O ab 8 |Plates. 6 Xq 1 | 13 O ab 8 |Plates. x ox) ene O ab 180 |Bars. 1¢x 4 1 | 12 S Where Used. Shop. Rivets Cov. Pl. | 512 |O heads.| $x 24 S Bat. Pl. 72 |O heads.| 8 x 2 S Lattice. | 184 |O heads.| #8 x 2} S tee, 32 |O heads.| 2x14 S Pin Pls. 80 |O heads.| #2 xX 2 S lei hema SE 48 |O heads.| $x 18 S Pin Pls. 16 |C.S.hé’ds| 2x 128 S Field. Rivets. Hip Cov.| 16 |O heads.| § xX 28 S Hip Cov. 4 |O heads.| 8x 14 S PortCon.} 32 |O heads.| # xX 1? S PortCon.} 16 |O. heads.| $x 1¢ S 1659. and weights of channels and angles, as well as the sizes of Stock Material and Iron Order.—The sizes 1042 DETAILS, BILLS, AND ESTIMATES. plates and flat bars, most commonly used at bridge works, are generally carried in stock. Round and square bars of one inch dimensions and less, and sometimes the common sizes of much larger bars, are carried in stock. Rivet iron, turnbuckles, standard and recessed nuts, spikes, nails, wood screws, washers, several sizes of bolts, and all small extras of like nature are always carried in stock. small bars, such as the small flat bars used in making the heads for cotter pins or the half round bars used for making the cotters, are carried in stock, and are cut off in small pieces as used. such material’ iss teqiired tobe listed upon the order list only for the purpose of checking off from the stock lst, and, therefore, the lengths need not be given with very great accuracy. But the lengths of the larger pieces of stock material, which are to be forged or cut to certain dimensions, must be given accurately. 1660. In making out the iron order, all short pieces of the same size (width and thickness) are assembled in one or more long pieces of the same aggregate length. Short pieces of plates and angles, for such purposes as pin plates, batten plates, lateral-hitches, etc., are simply sheared off, and require no allowance for cutting. But bars for pins are usually cut by turning off, which requires about 4 of an inch to be allowed foreach cut. (See formula 250.) When the order list has been made out, it is compared with the stock list, and such sizes as are in stock are marked on the order list with a letter S, and are checked off from the stock list. The iron order, or list of required material not carried in stock, is then made out from the order list. This material is checked off from the order list by marking either the letter O or the date on which the iron order is made out opposite each item that is trans- ferred to the iron order. A copy of the iron order, as thus made out, is generally sent directly to the rolling mills by the business department of the bridge'works; if it is a large DETAILS, BILLS, AND ESTIMATES. 1045 (7) ORDER LIST. For forged Members and Pins. Material, Wrought Tron. (Except where otherwise marked.) Contract No. 78. Shop No. 735. Span 90'0". Sheet No. um. . Weight.| Tength, | Mark. Pe Name. pee one tae cs ates Ordered. quired. Foot. | Feet: |Inches. yee 8 | Bars. | 2 x 43 25 | 94 O ee 8 | Bars. tx ¢ 6 | 54 5 Ge" 8 | Bars. ix ¢£ 21 | 64 S Bob 8 | Bars. Leesa 20 | 43 O Beare bars. | 1." O 26 | 72 S ewe embars. || 'L 7 O 26 | 114 S ab.| 4 |Bars. | 14"0 6 | 2% O Wie wbark:. | Lalo 20 | 11 O bc, 6 »Bars.. }el«*’O 6 | 24 S bc, G j.Bars. jb.” O 20 | 92 S figy:| 8 |\Bars. | 14x 14 6 | 114 O iefeie a, Velates: |B. x 2 OQ: 8 O 14 bic hars. f S* —— 84 S a 4. | Bars. 24" O 1 | 24 Sst’l O Bape bor Bars. 24" O 1*|-0r St’l O c 4 (Bars. |\1t" 0 0 |113 O ats.) 20.) Bars. 1h O 0} 4 O Lats.| 20 | Bars. ax 35 Chae Gas S) Lats.| 20 |40’s 3" 0 | 64 S Nuts| 16 | Stand. |For1{"0 5 Nuts| 32 |Ret. (|For2 ’O S Nuts} 8 |Rec. |For1}’oO S Gc’ 8 | Tbkls. |For 12’0 0 | 9% S mo. | A | Tbkls. |For 1}O 0 | 10 S bec 6 | Tbkls. |For 120 0 | 92 S 1044 DETAILS, BILLS, AND ESTIMATES. order, several copies are usually made, by blue-printing or otherwise, which are sent to various rolling mills, request- ing them to quote prices on the order. List (A’) is the iron order for the material ordered from order lists (/7) and (/). K) IRON ORDER. Contract No. 578. Shop No. 735. Span 90’ 0". Sheet No. 7. Weight. Length. Mark. pare Name. Material. Bas ers RaaRat ee ab 8 |Chans. |W. Iron| 8 16 | 25)1044 ab 4 |Angles.|W. Iron} 24x 24) 4 3| 43 ab 4 |Plates. |W. Iron|12 x # 25 | 1042 ab l. \Plates: )We droniig= x! 12} 0 ab 1 |Plates. |W. Iron} 6 x 7 Loves leg 1 .)\Plates. -|We Iron) (§ =e 6] 0 Be}\ 8 |Bars. |W. Iron) 2 x 43 25 | 94 i. 8 (|Bars. |W. Iron; 14x 14 6|}114 Bob 8 iBars. (}Wolron) a x4 20 | 43 ab, 4 |Bars. |W. Iron} 14” 0 6 | 22 ab, 4 (Bars. |W. Iron} 14” 0 20 | 11 G 1 |Bars. |W. Iron| 1f£’ 0 10 | 114 a 1 |Bars. |M. Steel] 22’ 0 17 | 34 LUMBER BILL. 1661. General Observations Concerning Tim- ber.—Of the bills of material required in the construction of a bridge, the last bill to be made out is the bill of the lumber. The kind of lumber and the essential dimensions of the same to be used for the various purposes are given on the stress sheet, from which information the lumber bill is made out. | As kept in stock by dealers, the lengths of pine lumber DETAILS, BILLS, AND ESTIMATES. 1045 are commonly multiples of two feet, but oak lumber can usually be obtained in lengths of odd feet also. When lum- ber is ordered in lengths of odd feet and can not be fur- nished as ordered, it is furnished in the next longer lengths of even feet. Lengths not greater than 20 feet are easily obtainable, but greater lengths are difficult to obtain, and are expensive. Therefore, the panel lengths of bridges in which timber joists or stringers are to be used should, if possible, not exceed 20 feet. As commonly sawed, timber is nearly always a few inches longer than its nominal length. Consequently, if the panel lengths of a bridge are in even feet, the joists for the bridge, if ordered of a nominal length the same as the length of panel, will be long enough to give full bearings upon the floor-beams. It is necessary for the joists in the end panels of a bridge to reach to the extreme end of the bridge, or somewhat beyond the extremities of the shoes; this requires the joists in the end panels to be about a foot longer than those in the intermediate panels. This will be readily understood by reference to Plate, Title: Highway Bridge: General Drawing, Fig. 1. 1662. Relative Heights and Arrangement of Joists.—Timbers of the same nominal width always vary slightly in their actual widths. Consequently, in order that joists may have a uniform height over bearings, they should be sized down to uniform widths at the ends. The uniform width to which the joists in a bridge are to be sized is usually + inch less than their nominal width. That portion of a bridge abutment upon which the shoes and bed-plates rest is called the bridge seat, and that portion which extends above the bridge seat for the purpose of a retaining wall is called the back wall. By reference to the partial elevation and top view of the abutment shown in-Higs. 1 and 2 of the plate just referred to, it will be noticed that a step in the masonry, six inches above the bridge seat, projects out seven inches from the back wall. This is to support the ends of the joists at the expansion 1046 DETAILS, BILLS, AND ESTIMATES. end of the bridge, which is necessary in this case, in order that the joists may clear the lateral rod. At the expansion shoe, the top of the lateral rodis$ +2+4+24+ 2-4 14 = 5} inches above the bridge seat. (See Plate, Title: Highway Bridge: Details III, Figs. 5, 7, 8.) The top of the roadway floor plank will be 11$-+4 3 = 14} inches above this step, or just even with the top of the back wall. At the expansion end of the bridge, the center of the shoe pin will be $+ 2+ $+ 5 = 82 inches above the bridge seat (see same Plate and Figs.), or 83 — 6 = 28 inches above the masonry step that is to support the joists. At the inter- mediate panel points, or joints, of the lower chord, the tops of the floor-beams will be 42 inches below the centers of the lower chord pins, or 4% — 22 = 22 inches lower, with respect to the lower chord pins, than the top of the masonry step that is to support the ends of the joists at the expansion end of the bridge. Consequently, in order that the joists shall all have the same elevation, with reference to the lower chord pins, it will be necessary to place a bearing plank or riser piece, about 22 inches thick, upon the top of each floor- beam, for the joists to rest upon. Each bearing plank will be a 10” & 24” oak plank placed lengthwise upon the top of the floor-beam, as shown in Plate, Title: Highway Bridge: General Drawing, Fig. 2. These planks should be secured to the flange of the floor- beam, either by bolts passing through the flange angles or by steel nails clinched under them. As the bolt holes would cut out a portion of the flange section, the latter ex- pedient will here be employed. Such bearing planks are not very commonly used; the joists being generally placed directly upon the flange of the floor-beam. Itis not really essential for all portions of the floor to have the same eleva- tion with reference to the lower chord pins, and, there- fore, such bearing planks may be omitted without any real detriment to the structure. At the expansion end of the bridge, it will be necessary for a notch to be cut in the lower edge of each joist, in order that it may clear the shoe strut. Although this is not a DETAILS, BILLS, AND ESTIMATES. 1047 really commendable thing to do, the notch is so near to the end of the joists, that it will probably not weaken them. This could be avoided only by raising the joists 314 inches higher. 1663. The Bill of Lumber.—For this bridge, the bill of lumber will be as follows (see stress sheet): BILL OF LUMBER. |S ifs mp ha ea aie | a RR c cn wae saat Gontrade Noe. ero atah tn eee feet Roadway............. feet, clear width, Poauekilenoths .2 * PCCU ee aa. Sidewalks............. feet, clear width. Num- ber of Name. Size. Length. NOE Material. idcee Feet, B. M. 30 Joists oe Oe a MO 1,890 |Yellow Pine 20 Joists 34°12" | 19’ 0’ 1,330 |Yellow Pine Plank 3” Thick 18’ 0” 4,968 |Yellow Pine 12 |W. Guards} 4’x 6’ 16’ 0" 384 |Yellow Pine Total Yellow Pine 8,572 4 | Bear. Plk.| 24’ 10’ 18’ 0" 150 | White Oak It will be noticed that in the items for the joists, wheel- guards, and bearing planks, all dimensions are given, while for the floor planks only the length and thickness are stated. The floor planks may be of any width not less than 7 nor more than 10 inches (they are usually of different widths), but their aggregate width must be equal to the extreme length of the bridge, which will be about 92 feet. This will be the case if they give the required number of feet board measure. The wheel-guard timbers may be in any lengths, uniform or varying, but their aggregate length must be sufficient to extend the entire length of the bridge, upon each side of the roadway, with six inches lap at the joints. As lumber is sold by the thousand feet (or hundred feet), 1048- DETAILS, BILLS, AND ESUIMATES: board measure, the number of feet board measure in each item should be calculated and written opposite the item in the column headed Number of Feet, b. M. A foot in board measure is one foot square and 1 inch thick. SHIPPING BILLS. 1664. Nature of a Shipping Bill.— When the shop drawings, shop lists, order lists, iron order, and lumber bill have been made for a bridge, the next office work in hand is to make outa detailed list of all members, pieces, and materials that are to be shipped to the bridge site and used in erecting and completing the bridge. Such a list is called a shipping bill. All things listed upon the shipping bill are weighed out from the shop and shipped to the bridge site. The shipping bill gives a list and partial description of all finished members, parts of members, and connecting pieces shown on the working drawings and described in the shop lists, and is made principally from these. A brief descrip- tion of each member is given, witha few essential dimensions, in order that each member may be readily identified and roughly checked. The shipping bill includes also items of material not shown on the drawings nor given in the shop lists, such as the field rivets, bolts with nuts and washers, spikes, nails, lag screws, paint, etc., required to complete the structure, as well as the erection bolts, pilot nuts, and other things required in its erection. It will be well to notice here the requirements for some of these items of material. 1665. Field Riwvets.—The diameters, lengths, and number of field rivets required may be obtained from the shop drawings; they will correspond to the vacant holes shown on the drawings. The number of rivets actually re- quired of each size must be increased from ten to fifteen per cent. to provide for waste. The percentage of waste depends to some extent upon conditions at the bridge site, difficulty of erection, etc., and can be estimated only by a very liberal DETAILS, BILLS, AND ESTIMATES. 1049 “approximation. ‘Twelve per cent. is, perhaps, a good aver- age allowance for this purpose; it is a convenient practice to make the total number of rivets required of each size equal to the multiple of ten nearest to, but generally above, the estimated number with the percentage added. 1666. Bolts and Washers.—Ordinary bolts will be required to bolt the wheel-guards to the floor planks. Bolts # of an inch in diameter should be used for this purpose ; each bolt should have two washers. These bolts should, under ordinary conditions, be spaced about 6 feet apart along each wheel-guard. Hence, the number z of bolts required for the wheel-guards in one roadway will be given by the formula L n= 3 - 2, (255.) in which Z is the extreme length of span in feet, which may commonly be assumed to be 2 feet longer than the length from center to center of end pins. Any fraction in the : elas 2 expression -~ may be neglected. In order to afford ample drainage for the roadway, the wheel-guards are elevated from 1 to 2 inches above the floor planks, by means of shims, which consist of pieces of plank about a foot long, placed under the wheel-guard of each bolt. The wheel-guard is laid flat, i. e., with its broadest dimension horizontal. The bolt passes through the wheel- guard, shim, and floor plank. Hence, the length / of the bolt, under nead, will be given by the formula =Et+e, (256.) in which g is the grip of the bolt, equal to the aggregate thickness of the wheel-guard, floor plank, and shim, and ¢ is a constant which, for bolts not more than } of an inch in diameter, may be taken equal to 1 inch. EXAMPLE.—(a) What number and (4) what length of bolts will be required for the wheel-guards of the bridge shown on the Mechanical _ Drawing plates, it being assumed that the wheel-guard is to be blocked up by 2-inch shims ? 1050 DETAILS, BILLS, AND EsTIMATES: SoLuTION.—(a) By formula 255, the required number of bolts is 92 3 + 2 = 32 bolts. Ans. (2) The thicknesses of the wheel-guard, shim, and floor plank are 4, 2, and 3 inches, respectively. Hence, the length under head of each bolt will be 4+2+383-+1=10inches. Ans. 1667. Spikesand Nails.—Each roadway plank should be spiked to each joist upon which it rests by two spikes. As the widths of the planks should average about 9 inches, the total number of spikes z required for this purpose will be given by the formula ee 3 ] in which Z is the extreme length of the span, and /V is the number of lines of joists. Some specifications require the spikes used in spiking the roadway planks to the joists to be ;-inch wrought spikes 7? inches long. But it is doubtful whether such large spikes are really required or even advantageous. Common 60-penny nails (1. e., cut spikes, 6 inches long) are frequently used. Steel-wire spikes (round) are very satisfactory for this purpose. Nails and spikes are always sold and shipped by the pound or keg. The number of spikes required for the floor planks may be found by applying formula 257, and the number of pounds (or kegs) necessary, in order to give the required number of spikes, may be obtained from Table 43. An allowance of about 10 per cent. should be made for waste. (257.) EXAMPLE.—If steel-wire spikes 6 inches long are used for the floor planks of the bridge shown on the Mechanical Drawing plates, (a) how many spikes, and (4) how many pounds of spikes will be required ? SOLUTION.—(a) As given by formula 257, the number of spikes to 8x 92 x 10 — —— = 2,458. If 10 per cent. be added for waste, the number of spikes required will be 2,458 + 245 = 2,700. Ans. (6) By reference to Table 48, it is found that, for steel-wire spikes 6 inches long, there are 10 spikes to the pound. Hence, the number of pounds 2,700 ’ is Or ie = 270 lb. Ans. be used is required is 1051 OgI yn £0z% on SSS > obz < gSz a go Se W aa) ze Z } "ey 9)y:! r ij 1 y etesh") “ha 55 *er ginlti-1 1» ened Yee a ‘gt opel"t-1 41) aod Se a "sx of i} f 1! \" ; : Bs 4 ee oo VY = —_ | ssi = 00000 rete bHoadl nooo tl etlotl aoitesta aip¥ sold ey, jot: wy th by me aca y ee \ 8 A * ery Th a i eae “— a. be es ed eo g nS al ES A Ss a8 = a <. cae RRS Center Line. 23’ Pin. ” 23” Pin. Pr Cate 23" Pin. P.W.ig— 9F" Grip. L.C.7%2"P.P. D.C. 7'xF P.P. 54” (oe erate: = : IP.dg xe P. PE lid "Dp re ” 150 Pa lagi wo [imi | MT. 242 13 Se Ld. abt = wy H. Vid xi po a Hi Fila q a C.F. xg i gr. 4j x1; Bers i 12" wt fT, V.1 y he - Pott bee . MDL 2552" sachet $d " LOU EPP. Contract No. 578. aE Des 8 Oi RRB os Height of Truss Clear Roadway.... 6 SPQ e) & st PW. L.0.7x2'P.P. 1.0.72" PP. 8”CSeparator. On Hanger. FIG. 336. Erection Diagram. Location, Jones’ Crossing, Sycamore County, Pa. et), JEhe st BLOF SANK... 5 lore 38" Vellow Pine. = 18 feet. fotsts, 10 lines, 84" x 12" Spee Pine. = 18 feet. Wheel-Guard, 2 lines 4" Yellow Pine. DETAILS, BILLS, AND ESTIMATES. 1055 made by an experienced bridge engineer, a preliminary estimate will often approximate quite near to the actual weight of the structure. If the detail drawings of the structure have been made previous to the making of the estimate, the latter will, of course, be much closer. The preliminary estimate usually gives the same informa- tion that is given upon the stress sheet, together with an approximate detailed estimate of the weight of the material. In fact, in many cases, after the stresses have been deter- mined, they are copied upon the estimate sheet, the material is proportioned and also written upon it, and the estimate is made before making the stress sheet. The stress sheet is then made from the estimate sheet, to be submitted with the proposal or to form a part of the contract; the esti- mate sheet is filed for office reference. 1674. In making the preliminary estimate, the weight per foot of each member is estimated according to the material shown on the stress (or estimate) sheet, and this weight multiplied by the length of the member, in feet, for the total weight of the member. The length of each mem- ber, always expressed in feet and decimals of a foot, is taken from, center to center of the intersecting members. An additional amount is commonly added to the center-to-center length of each member, to allow for the weight of certain details. This is the common method of providing for the weight of, eye-bar heads, loops, upset screw ends, and turn- buckles, in estimating the weight of forged tension members. For riveted members, the additional weight of the details is approximately estimated. Some engineers, however, add certain percentages of the estimated weight of the main members, to provide for the weight of all details. 1675. Assumed Lengths and Equivalents.—lIt is not possible to give a system of rules for approximate esti- mates that will be found satisfactory in all cases. The estimator must necessarily be guided by his judgment and experience. The following general rules are, perhaps, as nearly satisfactory for ready approximations as any that can 1056 DETAILS, BILLS, AND ESTIMATES. be proposed. These rules give a length for each member, the weight of which, estimated according to the material of its regular section as shown on the stress sheet, is assumed to be approximately equivalent to the weight of the member, including certain details: . The length L of certain members hereafter designated, which is to be used in estimating their weight, may be taken as given by the formula Lata G, (259.) in which 7 is the length of the member from center to center of the connecting members, and ¢ is a constant which, for the various members, may generally have the following average values: Te. sor each 7end- post] 2.2 ee c= 14 feet 2, For each end panel of top chordie. Ca le ereet 3. For each intermediate panel of topchord..c= 4 foot A. For each intermediate post)... .e ee Gai) We reCEG 5. For each riveted tension membetey eee Ce eee 6. For eachtlateral strut... eee eee Comat) ame oe > For each forged eyé-bat ... see eee 6 = ostiies the width of the bar. 8. Foreach adjustable bar having two screw ends with nuts... . 2.53). eee G == eect 9. For each bar having two loop ends...... 0 Lees. 10. For each adjustable bar having two loop ends ‘and'a turnbuckle. )ae see C=) De eeL In each of the first three items, the weight of the addi- tional length ¢ will be approximately equal to the weight of the pzx plates, while in the fourth and fifth items, it will be approximately equal to the weight of the pin plates and other connecting plates. In the sixth item, the weight of the additional length ¢ will be approximately equal to the con- nections for the lateral strut. In each of the remaining items, the weight of the additional length c will be approxi- mately equal to the weight of all details of the members; that is, to the amount which the weight of the finished _ tes ee ee DETAILS, BILLS, AND ESTIMATES. 1057 member exceeds the weight of the plain bar having a length /. It must be remembered that these values of c, though fair average values, are but roughly approximate and may be modified according to the conditions of each special case. 1676. Latticing.—For each single system of latticing in which the lattice bars make an angle of about 60 degrees with the axis of the member, the aggregate length of the lattice bars will be approximately equal to twice the center-to-center length of the member. For each single system of latticing in which the lattice bars make an angle of about 45 degrees with the axis of the membez, the aggregate length of the lattice bars will be approximately equa? to 1.4 times the center-to-center length of the member. These lengths are independent of the wzdth of the mem- ber. If a double system of latticing is used, or if the mem- ber is latticed on both sides with a single system, the aggregate length of lattice, as obtained by the above rules, should be doubled. 1677. The lengths of the batten plates are governed by the requirements of the specifications. If Cooper’s specifi- cations are used, the length of each batten plate will be one and one-half times the width of the member, or the aggregate length of the batten plate upon each end post or chord member, having a cover-plate, will be three times the width of the cover-plate. 1678. Each knee brace may be assumed to be 5 feet long. 1679. The weight of each lateral hitch composed of short pieces of angles, similar to that shown in Plate, Title: Highway Bridge: Details I, Fig. 4, may be taken equal to the weight of 24 feet of the lateral rod connecting upon it. 1680. Jf the diameters of the chord pins have not been determined, in making the estimate, the diameter of all lower chord pins and of the hip pin may be assumed equal to about 1058 DETAILS, BILLS, AND ESTIMATES. three-quarters the width of the widest eye-bar in the lower chord; the diameter of the remaining pins in the upper chord may be assumed to be two-thirds as great as or equal to one-half the width of the widest chord bar. 1681. The lengths of all chord pins may be assumed equal to 14 times the width of the cover-plate on the upper chord or end post, making no allowance for the reduced diameters of the screw ends. The weight of the pins thus estimated may be considered to include the weight of the nuts and washers. 1682. J/fa portal ts latticed with ordinary 2” x }" bars, the weight of the /a/ticing (including weight of rivet heads), in pounds per lineal foot of portal, may be taken equal to five times the depth of the portal in feet. The aggregate weight of both portal brackets and the portal connections for each portal may be taken equal to the total weight of 8 feet in length of the portal proper; conse- quently, the length of portal having parallel flanges may be assumed to be equal to the clear width of roadway plus 8 feet. 1683. The weight of all rivet heads in each line of rivets in a member may be assumed as follows: For 4-inch rivets, +4 pound per lineal foot of member. For 3-inch rivets, ? pound per lineal foot of member. For #-inch rivets, 8, pound per lineal foot of member. For §-inch rivets, 14 pounds per lineal foot of member. Ot b With this assumption, the two lines of rivets connecting a system of latticing may generally be considered as a single line of rivets. 1684. Ji estimating the weight of the floor-beams in a bridge having a single roadway and no sidewalks, the length of flanges, web-plate, and rivet lines in the flanges may be assumed to be equal to 1} times the clear width of roadway plus the width of both chords. This will provide for the approximate weight of the stiffeners, fillers, and other details. awe ee J 2g r f A Aye Y : v7 4 i. Feelgeaet os ai Myon Yo oye] 7 ay tt. EY de baot oe ap, : ;. tee — ‘X's 19 ee: ™ ie £ —. Ye E 3 I Pid: Bi) r Oye r ein palsies] ‘et .alT mops ‘abwoll Jovint ’ 44-2 ye =F Mx © Eee on he ee 3 at (tebe! | he ex, bao yo é 0 Ges re wae : ‘ ‘) |) oe P ms "yi Par yo [4s “! one mT, al Fiend trie ‘zbsolt javia a 183 n4li- ig! WY , 1 7Teu vse ex 3. aif Hehe © ebooll Joulyh | ae ek mat ye oH iso [ ante "rf nel nx’ a want gnol ft xo gaeriosi Ar XQ '6 a “oak evar act Jte aad bedo | caconate bapa’) ri moO 1 Abad ' ra i a shad - pte thot <7 i ar D. m.. ta xy Sab toot cnr. . Bd "px 2 ‘i) o Oy win » e mS Ped ld ate & * Nr ~~ ‘ps , I ds a3 mx" Ae ‘4 | fetal in spate of gate C. to Ce ee | Eeaehtor Pruss£Clto Ci eae ft Live | Sammie ten nasa nen ee we enna sce eecenanesecesenssa. Oar lb. per lin. ft., trusses Len th ae : . > ; age ee ee ee BP ‘ Emenee 2 eee ft. eo a Load SE TREE oo ID=peéer Jin: ft, trusses, ether Roadway eee eclear width Panel Live Load, one truss, Bee ea) ee i on nena Sidewalks erees Pemciear width Panel Dead Toe ON Geitige® suey awe es. tae eth: aterial, gee der 2 Length of Digeonal iS Maren eee Dea oe eas a Se rcCallOie tars, ce eee S Member. Stress. ipti ‘ale i i Description of Material. Area Given. SUN ARS oe : Weight, End Post Pees ter) i2i x 34" ab + 19,600 is Chans. @ 16 |b. 4s ee 54 2,538 attice, 13/" x yi" Batten Piet no? x yu’ x 18" ae vee ae ane : 56" Rivet Heads ye I : Top Chord iat Tesb 32 oe fi . Be a aS BRP + 20, 800 ea Chauns. @ to lb. § ae ae 57 ai 2° attice: Bars; 1 3/"x 14" : Batten. Pis.. abe wi 18” a wee ae ah 5g" Rivet Heads 67 162 108 ; Int. Post + 9,700 | 4-314" & 2" L’s @ 4.4 Ib. 5.28 17.6 4o 70 Ce + 2,300 | | Lattice, 13/" x Y" -44 1.46 72 aes Batten Pls. Se oe I. 75 5.83 oats 20 56" Rivet Heads 67 30. 24 Low. Chd — 32,400) | 4-3" KX 24%" L’s @ 4. 6 1b. N.S. Sos 18.4 46 846 ab — 13,900 | | Lattice Bars, ry x Yr" 44 1.46 2 105 Batten: Pls.; 6! Kaye 1.5 5. 3 15 55" Re ey Heads | .67 36 24 - — 32,400 } | 4-34 “L's @ 5.8 1b. N.S. saay | 23:2 46 1,067 — 13,900 § roe” ee ly Ay 4A 1.46 72 “Tos Batten Pls., 6" oe ae 1.5 | 5. B 15 cates et Heads .67 56 22 ' == A600 11) Beabbars 412" < 18", N.S. = 6, 150 (Pe eee 20. a¢ — 20,800 § Lattice ioe 13" x y" of oie ee a : ee 5%" Rivet Heads 67 18 12 H. Vert. — 16,200 } B Bob — 4,600 § 2-Bars, 1° X 1" 2.0 6.67 41 293 Ties ee Du] SOO) ” it Be ti, ess pele sey Sots 3.25 10.83 53-7 582 Cc — 13,750 |2-Bars, 7%" X 7%" 1.53 5.1 62 316 Pins 8-3" OC x 15” long (steel) 24.00 ine) 240 -2" OG X 15” long 10.45 2.5 6 6-Lateral Hitches for 1" QO 2.61 13 39 Total Weight of one Truss, 10,014 ‘Total Weight of two Trusses, 20,028 ee OE — 3,700 |4-Rods, 1" QO 79 2.61 112.8 204 E& eRods,.2” 'O -79 2.61 56.4 147 ab, —14,900 | 4-Rods, 1%"O 99 3-31 126.8 420 bc, — 8,200 |4-Rods, 1° QO 279 2.6% 126.8 331 OG, — 2,200 |2-Rods, 1" O 79 2:61 63.4 165 BB; 4= 314" X24" L’s @ 4.8 lb "6 IQ.2 } Latticed 2 feet deep 10. Ph ee mate CE 2-5" 4" L’s @ 10.8 lb. 6.48 21.6 4o 864 KB a es 24" oe @ 4.4 lb. 8.8 20 17 aa P16 xX ' J a | 1 2-434" X 24! Vie @ 4.8 Ib: 4.38 | 14.6 20 292 4-Fl. Bms. | — 53,700 Web Pl., 24" K 3%" X 20-0" 9.0 30. 92 2,760 4-4" X 3" L’s @ 8.4 lb., 26-0" 33.6 92 3,091 5%" Rivet Heads 133 g2 | 127 8—-Hangers + Ges 1.56 ata 96 a : Sioce Eilers, and Bed PI. | 310 Bolts, Spikes, and Nails 32 Total Weight of Metal, | 31,842 DETAILS, BILLS, AND ESTIMATES. 1059 1685. ln estimating the weight of the forged beaim hangers, the length of the rod forming each hanger may be assumed to be equal to twice the nominal depth of the floor- beam plus 8 feet. This will include the approximate weight of upset ends, nuts, and hanger plate. 1686. Lhe total weight W of the shoes, bed-plates, rollers, and anchor bolts for one span may be roughly approximated by the formula PaO (260.) in which S is the span, 4 is the clear width of the roadway, and cis a variable coefficient which may be taken equal to a8 with a minimum value of $. 1687. Zhe total weight of bolts, spikes, and natls re- quired for the roadway floor may also be roughly estimated by formula 260 by giving ¢ a value of .2. In estimating the weights of structures, the tables of the weights per foot of the various sizes of round, square, and rectangular sections, given in structural hand-books, will be found very convenient, if not indispensable. The sectional areas of most of the members are given on both the stress sheet and the estimate sheet, and, for such members, the weights per foot may be most quickly obtained from the sectional areas. This can not be done, however, in the case of riveted tension members for which the net section only is given. 1688. The Estimate of Weight.—The approximate estimate of the weight of the metal in the bridge is given on the accompanying sheet. This estimate is made wholly from the informaticn given upon the stress sheet shown in Fig. 306, Art. 1452. In this estimate, the weights per foot of rectangular bars, and of those members for which the gross sectional areas are given, are obtained from the areas. The weights of round bars are obtained by formula 153, Art. 1487. This formula applies to steel, and, therefore, the results must be reduced 2 per cent. for iron. The lengths 1060 DETAILS, BILLS; AND ESTIMATES. of all members, as used in this estimate, are the lengths ob- tained by the preceding formulas for assumed equivalents. 1689. Accuracy of the Dead Load.—When the estimate of the weight of the metal in the structure has been made, the designer can readily ascertain whether the proper amount of dead load was assumed for the structure in cal- culating the stresses. In the present~case, the total esti- mated weight of the metal work is 31,842, or, practically, 31,800 pounds. Hence, the weight of the metal work fer lineal foot of the bridge is aha = 354 pounds. As estimated by formula 9O, Art. 1298, the weight per lineal foot of the structure, exclusive of the floor, was found to be 352 pounds. ‘This is only 2 pounds per lineal foot in excess of the weight as estimated, and the assumed dead load may, therefore, be considered correct. It will be well to notice, however, that had the unneces- sary latticing been omitted from the center panel of the lower chord, and the remaining panels of the lower chord been formed of eye-bars latticed similar to the center panel, instead of being made up with angles, the weight of the structure would have been somewhat less. THE CLOSE ESTIMATE. 1690. In some cases the detail drawings for a bridge are made before the contract is let for its construction. If the structure is designed by a consulting engineer, complete drawings are usually made showing all details clearly. In such cases it is possible to make a very close preliminary estimate of the weight of the structure by calculating the weight of each separate piece and estimating the weight of the rivet heads. The weights per hundred of the rivet heads, as ordinarily formed upon rivets of the four sizes most commonly used, are as follows: DETAILS, BILLS, AND ESTIMATES. 1061 in. 2.2 7a Pepreeelerray TIUCISS 6oc.. 0.0. es ellie a ats TTL oe Weight tn pounds per 100 heads. .5.% 10.9 thes 2 Countersunk and flattened heads are commonly counted the same as full heads, though countersunk heads should really not be counted. The length of a lattice bar having two semicircular ends, each connected by a single rivet, may be taken equal to the length from center to center of rivets plus the width of the bar. Where the length of a piece is expressed in feet and inches, in estimating the weight it will be found convenient to reduce the inches to decimals of a foot. Results are always taken to the nearest pounds; fractions of pounds are not used in the results or total weights. 1691. Asan example of a portion of a close estimate, the weight of the end post, estimated from the shop draw- ing, Fig. 1 of Plate Title: Highway Bridge: Details I, is given below: Weight Total No. Material. Size. Length. per Hat Weleht 1 Cover Plate, 12” x 3" 25' 108" 15.0 388 2 8” Channels, @ 16lb. 25’ 103’ 32.0 828 1 24” 24” Angle, @ 4b. 3’ 4B” 4.0 14 2 Pin Plates, 6" x +5" Ll’ 24" 7.5 21 2 Pin Plates, 6" x 7a" EDO a iad 7.5 20 2 Batten Plates, 12’x }" ise Aig 20.0 30 45 Lattice Bars, 13”x +" 1 Fees Fe 1.46 (el 560 Rivet Heads, For 2” Rivets 10.9 61 ERE ke ae Ee ee eee 1,433 In the approximate estimate given in Art. 1688, the aggregate weight of two end posts was found to be 2,538 +- 2, 849 PA PAE 8 Is, or — = 1,425 pounds for 149 + 60-+ 10 ,849 pounds, o1 9 p each end post. This differs by only 8 pounds from the above close estimate. Where ends are beveled, or corners are cut off, it is, in 1062 DETAILS, BILLS, AND ESTIMATES. most cases, customary to estimate them as though full and square, making no deduction for the metal cut away. ‘This is because the material cut away is simply wasted and must be paid for the same as any other portion of the bill of material. For the same reason, no deduction is made for pin holes and vacant rivet holes. Indeed, for the same general reason, it is customary in some bridge offices to estimate the weight of the vzve/s required, instead of the rivet heads, as it is desired to arrive at the weight of material required to manufacture the structure, rather than the weight of the finished structure. In other bridge offices, however, it is customary to estimate the weight of the finished* members. — The: latter] practices ie= newmlost common, and, with the exceptions noticed above, is followed here. In this connection, it will be well to remark that, in roll- ing the material, the rolling mills usually demand to be allowed a variation in weight of 24 per cent. from the specified weight. It is thus evident that it is useless to attempt to be exceedingly exact in making estimates of weight. Beyond a reasonable degree of accuracy, any effort in the direction of exact estimates is time wasted. METAL JOISTS AND STRINGERS. 1692. Description.—Thus far in the study of bridge designing, wood joists are the only ones that have been noticed. Metal joists, however, are often used for bridges, especially in cities and where the traffic is heavy. They are generally solid rolled beams having a cross-section of a form somewhat similar to the letter I; such beams are known as I-beams (sometimes written eye-beams). I-beam joists usually rest upon the upper flanges of the floor- beams, though they are sometimes supported upon angle lugs riveted to the web of the floor-beam; they are riveted to the flanges, or to the lugs, as the case may be. The floor is laid directly upon the I-beams; if a plank floor, it is DETAILS, BILLS, AND ESTIMATES: 1063 usually fastened by steel-wire spikes driven each side of the joists and clinched under the flanges. 1693. Strength of I-Beams.—The various proper- ties of I-beams of the different sizes rolled, together with convenient tables of the safe uniform loads for the same, will be found in any structural hand-book. From the tables of safe loads, the size of I-beams required for any ordinary load and span (panel length) can be selected at once, without calculation. For concéitrated or unusual loading, it is necessary to find the bending moment upon the I-beam. The student has learned how to find the bending moment upon a sim- ple beam under any system of loads. Having obtained the bending moment, in inch pounds, it is only necessary to select, from a table of the properties of I-beams, the size of beam which will give a resisting moment equal to the bend- ing moment found. The moment of resistance 7 of a solid beam is (formula 23, Art. 1243) e 7 & i In the case of steel or wrought-iron I-beams having equal flanges, c is equal to one-half the depth of the beam. As the moment of resistance X must in all cases be equal to the bending moment ./, the value of the latter quantity, in inch- pounds, should be used for X. By dividing the moment of resistance, as expressed by the above formula, by S, the numerical values of the resulting quotient may be readily tabulated for different sizes of I-beams. The quotient which will be designated here by Q, has been called the section modulus. This appears to be an appropriate name, and will here be used. The value of QO may be readily obtained by dividing both terms of the preceding equation by S, as follows : Q===+. (261.) 1064. DETAILS, BILLS, AND ESTIMATES: | Radius of Gyration, Neu- tral Axis as before. | Se = = = F&F SS FS FS fF ~ ~ Cave GS IN 203) G5 WP oi ONS eS N 12) .08 .20 .O4 i Io 0.99 0.95 0.91 0.87 On/7 0. 66 0.59 1694. The following table gives various properties of the steel I-beams rolled by the Carnegie Steel Company, Limited : TABLE 44. PROPERTIES OF STEEL I-BEAMS. 32 22 |2 |e. |82 Bo Sohal ee ee ae oa A a ag |d oo - Cus a i) a pepe e 2 SoS Ae eS er hate hoc ee di |B ly #1 Bae Moless lis sess cele neaee gobs | ee) ig se eee ee alee role Us os ee arte el Sa soma e RY. by re el SS is Mier ean on am OC O| 90a se: [ha | OG ei Ope | wl g Og oe teen ree emerge a |eado rea ° by |t.6.8 loo oat eo Mees O_We a] | 8 | Se log \ES eee ea ee ae 2 - 3 a = ae 5) Sr oe Sa Be hohe RI Dia forapibanl febrile: arise ae Q r Y be 24 | 80 | 23.5 |-50}| 6.95 |.0123] 2059.31171.6/ 9.42 | 41.6 20 | 80 | 23.5 |.00| 7.00 |.015 | 1449.2/144- 0l7c85 45. 2O G4 | TS. One oo Bone 1146.0/114.6] 7.80 | 27.3 Ts} 80} 23.5 1.9797 | 6.47 1.020 1a OS OO Asien: sate Von) God iO a Oot 644.0} 85.9] 6.04 | 30.4 15 | 50.14.93 eA SW 5-75 42020 heb eto OlOroO sean CS |oAd ei LecOn 4 Osan oS 424.1] 56.6] 5.94 | 14.0 [2 |°40 ,TIj71%39 | 5. 50)/:025 | 251. eA G led oo wet one L2Q 22 EO aes S eee S 222531 2770) (A Oba alone TO} BIN 0.7.1 +37.) 5-001, 029. hb Okrs| asa. anArOoman TO:4635,7| Fo 5a a ee 4 122-551) 24654. OOl nes O7 | 2r-| Cee ee es Onions O4 ALLOW PTO mss ea 8 | 18) 5.3]-25] 4-25 |-037 | 57-8] 14.4] 3.30 | 4.35 a) Ae CA a ee oe ee 38.0110.86| 2.92 | 3.42 6] 1324 2.3452 2eeeoreOn Gg 23/5 Toca. Venmen2 7 5. | FOR: 23 309a 2 2egeoareanG 12.4) 4.00) 27050-1220 4 TA <2, Tob siemens, Cale yas 5. tie2 ont. OG) hong 3 6) _ 1:0 16¢20)) @-20uo0. 2.0) TET Al Te 2 t MiG eee Cunt The properties of I-beams given in this table are for the DETAILS, BILLS, AND ESTIMATES. 1065 minimum weight to which each pattern can be rolled. It will be noticed that, in several cases, more than one pattern is used for the same depth of beam. From formula 261 it isevident that, having obtained the bending moment J/ in inch-pounds, it is only necessary to divide it by the allowed unit stress, and select from the table a size of I-beam having a value of QG equal to the quotient. M In case the value of aS does not correspond to any value of QO given in the table, but is intermediate between any two values of Q there given for the same depth of beam, the zext lower value of QO should be selected from the table and subtracted from = calling the remainder Q,. This is expressed by the formula eee (262.) BEA! ae a a Then, the additional weight per foot JV, necessary to M ; give the required value of Q (equal to =) will be given by the formula Q, emanate 9.) in which @ is the depth of the beam, and JI’, is the required additional weight per foot above the tabulated weight. That is, W, is the weight per foot necessary to give a section From formula 261, 0+ U,= = If W, be added to the tabular weight per foot for which the value of Q was taken, the sum will be the weight per foot of the I-beam giving’ the required moment of resistance. it will sometimes be found, however, that the weight per foot as thus obtained will be greater than the minimum weight of the next larger size of I-beam. In such cases it will be more economical to use the larger size of the beam, modulus equal to Q.. ~~) 1066 DETAILS, BILLS, AND ESTIMATES. although it will give a value of Q, and, consequently, —_ a moment of resistance somewhat in excess of that re- quired. Table 44 and formula 263 apply to steel I-beams only. For iron I-beams, OQ Veg OR’ (264.) But iron I-beams are little used at present. EXAMPLE.—What will, according to Cooper’s specifications, be the size and weight per foot of an I-beam composed of medium steel, required to resist a bending moment of 32,540 foot-pounds ? SoLuTIoN.—According to item (@) of the specifications (Art. 1399), the unit stress allowed on a solid wrought-iron rolled beam is 12,000 pounds per square inch, and, according to Art. 1455, medium steel may be used for rolled beams with an allowance of 20 per cent. increase above the unit stress allowed on wrought iron. Hence, in the present case, the allowed unit stress will be 12,000 + .20 x 12,000 = 14,400 pounds, requiring a value of Q equal to ee == 26.95. ee By reference to column Q of Table 44, it will be found that the nearest value of Q below this required value is 24.5, which is the section modulus of a 10” I-beam weighing 25 pounds per foot. By formula 262, QO: = 26.95 — 24.5 = 2.45, and by formula 263, W, = tk. = 5 pounds. Hence, a moment of the resistance of 32,340 foot-pounds will be given by a 10” I-beam weighing 25+ 5= 30 pounds per foot. Ans, POSITIONS AND CONNECTIONS OF FLOOR- BEAMS. 1695. Ina through bridge, the floor-beams are some- times supported just below the lower chord, and sometimes just above it. These two positions of floor-beams with ref- erence to the chord are commonly designated as beams below chord and beams above chord, respectively. 1696. Beams Below Chords, Single Forged Hangers.—In the bridge we have been designing, the floor- beams are supported below the chord by a single forged DETAILS, BILLS, AND ESTIMATES. 1067 beam hanger or stirrup at each lower chord joint. This method of supporting floor-beams has been very extensively employed, though it is not now as much used as formerly. One of its disadvantages is that when the diagonal members of the lower lateral system are attached to the floor-beams, which act as lateral struts, effective connections are not afforded between the lateral diagonals and the lower chords, which also act as the chords of the lateral system. This is especially the case when the lateral rods are attached to the webs of the floor-beam, as is sometimes done. 1697. Double Forged Hangers.—In order to de- crease the bending moments upon the pins, two hangers at each support, called double beam hangers, are some- times used. As these can usually be placed adjacent to the ties which support the pin, they will evidently produce less bending moment upon the pin than a single hanger at the center. If floor-beams were absolutely rigid, double beam hangers could be employed to advantage. But the material in floor-beams possesses elasticity, and, as a beam deflects under its load, it throws the greater part of the load upon the inner hanger, and, consequently, upon the inner tie bar. Certain devices may be used to equalize the load upon the hangers, but the cost of such devices will counterbalance the saving effected by the use of double hangers, and it will probably always be found more advantageous to use single hangers. No better connections between the lateral diago- nals and the chords are afforded by double hangers than by single hangers. A disadvantage common to all forged hangers is that, as they have screw ends, the nuts are liable to work loose. This tendency, however, may be somewhat obviated by the use of check nuts, or some one of the various devices known as nut-locks, nearly all of which are more or less effective. The best forms of beam hangers, however, have no screw eas: 1698. Plate Hangers.—An excellent form of beam hanger is composed of one or more plates attached to the end IT. [I.—29 1068 DETAILS, BILLS, AND ESTIMATES. of the floor-beam, as shown in Fig. 337. The plate forming the hanger is riveted to con- necting angles, which also serve as end stiffeners for the floor-beam. The hanger should preferably consist of a single plate. It must be thick enough to give suff- cient bearing upon the pin, and, in compliance with for- mula 196 of Art. 1598, should never be less than 2 of an inch thick. In some cases, in order to avoid an FIG. 337. excessive thickness of plate, it will be found expedient to attach a shorter reinforcing plate to the upper portion of the hangers, as shown. In order to prevent bending moment on the rivets attaching the connecting angles to the web of the floor-beam, and in order better to distribute the stresses upon the latter, the filler plates under the connecting angles should be attached to the web-plate by one or two rows of rivets besides those in the connecting angles. In designing the hanger, it is necessary to provide suffi- cient bearing surface upon the pin, sufficient metal above the pin, and sufficient sectional area on each side of the pin hole to resist the tensile stress in compliance with item (/) of the specifications (Art. 1399); enough rivets must also be used to connect the hanger to the connecting angles and to connect the latter to the web. The student has learned to do this, and it will not be necessary to give an example. The length of the floor-beam, from out to out of connect- ing angles, will be equal to the distance from center to center of chords minus the thickness of one beam hanger. The length of the flange angles and web-plate should be about $ of an inch less than this. The plate hanger is, in some respects, the best beam hanger yet devised. It does not, however, form any better connection between the DETAILS, BILLS, AND ESTIMATES. 1069 lateral diagonals and the chords than the forged hanger, when the lateral diagonals are connected to the floor beam. 1699. Stiff Beam Hangers.—Floor-beams of Pratt trusses are sometimes supported below the chord by rivet- ing them to the angles, channels, or other shapes forming the vertical members, which are extended below the chords for this purpose. This forms an excellent attachment for the floor-beams, and affords efficient connections for the lateral diagonals, but it is not economical, and, for this reason, not much used in highway bridges. The objection noticed with regard to double hangers, namely, that when the beam deflects under its load the inner bearings will take the greater part of the load, to some extent applies to this form of support also. This con- dition is, however, somewhat counteracted by the stiffness of the posts, and may be further obviated by the use of deep (and, consequently, stiff) floor-beams. In designing this form of support, the bearing upon the pins and attachment of pin plates must be sufficient to provide for both the stress upon the post and the load upon the beam. 1700. Beams Above Chords.—In through Pratt truss bridges, the floor-beams are not uncommonly sup- ported above the lower chords. Where the head-room is sufficient to allow it, this is the best position for the floor- beam; it affords excellent connective details and is econom- ical. With this detail, the lateral rods may be attached to the lower flanges of the floor-beams; in which case, stress in the lateral rods will neutralize a small amount of the tension in these flanges. The floor-beams are simply riveted to the vertical mem- bers, the form of the connection depending upon the form of the member. If each of the posts consists of four angles, latticed in the form shown in Plate, Title: Highway Bridge: Details I, Fig. 3, the floor-beam is usually riveted between the angles forming the post, as shown in Fig. 338. In this detail the pin plates must be proportioned to take not only the stress upon the post, but also one-half the total load 1070. DETAILS; BILLS, AND Hs TIMATES: upon the beam. In order that the beam may be placed near the lower ends of the angles forming the post, the metal along the center line of the inner pin plate must be cut away through the upper portion of the plate, in order to straddle the web- plate of the beam. The metal is cut away by punching a row of contiguous holes with a square punch, making a continuous cut for the proper distance down the center of the plate, begin- ning attheupperend. ‘There is some objection to thus cutting a slot down the center of the inner pin plate, but if it is not done it will be necessary to elevate the beam sufficiently to clear the tops of the pin plates, which FIc. 338. would further decrease the head-room and also require a stay plate in the post below the floor-beam. The condition of unequal loading upon the pin plates due to the deflection of the beam, noticed with regard to double hangers and the attachment to the post below the chord, will, to some extent, be present in this detail also, and will have the further disadvantage of producing a bending moment upon the post. To obviate this, floor-beams are sometimes made to connect upon a pin placed in the axis of the post. Various other devices are used to deliver the floor-beam load equally upon the pin plates. But, if the floor-beam is made deep enough to prevent excessive deflec- tion, the simple detail shown in Fig. 338 is believed to be about as efficient as any that can be devised. It is to be noticed that the deflection produced in the post is usually in the plane of its greatest strength, and that, while slight deflection is produced in the post, it is by the beam also supported against further deflection. The detail represented in Fig. 338 is for connecting the floor-beam shown in Plate, Title: Highway Bridge: Details II, Fig. 4, to the post shown in Plate I, same title, Fig. 3. DETAILS, BILLS, AND ESTIMATES. 1071 NAME PLATES AND RAILINGS. 1ZO1. These two features of the design of bridges have thus far been entirely neglected. The design of either the name plates or the railing does not involve any real prin- ciples of engineering, and will, therefore, require but a passing notice. Name Plates.—Upon nearly all metal bridges are at- tached cast-iron name plates giving the name of the com- pany constructing the bridge, with date of construction, and sometimes other data, such as the names of the officials purchasing the bridge, etc. This information is given by raised letters cast upon a plate of suitable size. The names are formed by attaching the letters in the proper positions upon the wooden pattern used in casting the plate. Letters are made especially for this purpose and are usually kept in stock; they can be purchased at almost any hardware store. The name plates are attached by rivets or bolts to conspic- uous portions of the bridge; if a truss bridge, they are usually attached to the portals or to the end posts. It would be well if the guaranteed capacity of the bridge, as well as the name of the builder and date of construction, were required to be shown on the name plate. 1702. Wood Hub Guards.—Railings are used for two general purposes, namely, for closing the openings between the web members of the trusses along the outer edges of the roadway, and for hand railings along the outer edges of the sidewalk. Railings along the outer edges of the roadway, for the purpose of closing the openings between the members of the truss, may serve also to protect the members from the hubs of passing vehicles. In fact, this is commonly understood to be the principal office of these railings, and they are generally known by the name of hub guards. For many county bridges each hub guard consists simply of a line of plank attached to the posts of the truss at the height of an ordinary wagon hub above the roadway floor. This is commonly a 2” X 10” plank, dressed on one side and 1072. DETAILS,:- BILLS; ANDRES Tinie iio painted, and bolted to the posts so that its center will be about 24 feet above the roadway floor. In such cases no attention need be given to the hub guard in making the shop drawings, further than to show bolt holes in the posts at the proper distance above the lower chord pins for attaching the hub guard, and some arrangement for attach- ing it to the hip verticals. If the hip verticals consist simply of round or square bars, this attachment will usually be a U-shaped bolt or a bolt made in the form of a hook, so that it will hook around the hip vertical rod. Wood railings, of the form shown in Fig. 339, are some- times placed along the outer edges of the roadway. Many eve” of the highway bridges in the aa central, western, and southern RQ | portions of the United States | have short trestle approaches, and in such cases this railing extends along the outer edges SSS SS 3 Zs | ; Ni « of the roadway across the entire Bx : aS . bridge and approach. These railings are not attached to the trusses, but the posts are halved "6 upon and bolted to the outer UD, «6 lines of roadway joists, as 256%12" Weeliliiil A ec Wate ated c= apy iNT es shown. The construction will ——S |i 2 . = Sil = be readily understood from the S yh, uy a U purnayy |} : a | figure. Although commonly S Eh, constructed as here shown, SSS SL «Cheeses railings are sometimes made lighter, the posts being 4" x 4", the upper railing pieces FIG, 339. 2” x 4", and the lower railing pieces 2” x 8”. Although this may be called a hand rail, it is here noticed under the head of wooden hub guards. 1703. Iron Hub Guards.—On some county bridges, and on most city bridges, iron hub guards are used. In some cases, each hub guard consists simply of two lines of DETAILS, BILLS, AND ESTIMATES. 1073 gas pipe, about 2 inches in diameter, attached to the posts of the truss. When gas pipe railing is used it is necessary only to designate the required size and lengths of the pipe, with the couplings, and show the arrangement of the fast- enings by which it is attached to the posts. Usually, some kind of standard fastenings are used, which simply require certain holes to be shown in the posts. What is probably the best form of hub guard consists of two angle bars latticed. This railing is usually from a foot to 18 inches in depth; that is, one angle is placed froma foot to 18 inches above the o ticing is used, composed of light lattice bars mak- ing an angle of 45 degrees with the angles. The gen- eral construction of such hub guards, with the. splices and _ fastenings, must be shown on the shop drawings. In Fig. 340 is shown a portion of a latticed hub guard, with tS oad the manner in which it is attached to the intermediate post; it is composed of two of the lightest 3” x 2” angles, double latticed with 1}” x 3” lattice bars. As here shown, it is at- tached to the intermediate post by means of short pieces or clips of the same size of angle. The design of the hub guard is merely a matter of detail; no further explanation will be required. A double system of lat- 1704. Hand Rails.— Many different designs are used for hand rails, all being more or less ornamental. All-hand rails, however, consist essentially of an upper and lower horizontal rail, connected by a webbing of lattice or other light ornamental work. Sometimes a lighter rail is also placed about midway between the upper and lower rails. The lower rail will generally consist of two angles, while if a middle rail is used it will usually be a single angle. 1074" DETAILS, BILLS, AND VES EIN a The upper rail is made in various forms and is often quite ornamental. The top of the upper rail is usually about 3 feet 9 inches above the sidewalk floor, and the lower rail should not be’more than 6 inches above the floor. The openings in the lower part of the lattice work should not be more than 6 inches square. The rails are supported by posts attached to the ends of the floor-beams. They should usually be braced at intervals of about 8 feet. Both rails are connected and supported at each post, but it is quite commonly the case that the lower rail only is braced at intermediate points. It will not be necessary to show here any designs of hand rails, but it will be well to show the manner in which the posts are connected to the ends of the floor-beams, because this connection forms a part of the engineering design of a structure. The posts quite commonly consist of two angles each, but sometimes consist of four angles each, and sometimes of other forms. 1705. Attachment of Hand-Rail Posts.—Posts are sometimes riveted rigidly to the ends of the floor-beams, as: shown vin Hiow3415) 22 his forms an excellent attachment, so far as the attachment itself is concerned, but it is very in- convenient for getting the upper rail in straight line. The attachment not being ad- justable, if the rail is not put in perfect line before the posts Fic. 841. are riveted). Or iit titoneeaies cause it should afterwards get out of line, it would be very difficult, if not impossible, to put the rail in perfect aline- ment. For this reason various adjustable attachments are used, by means of which the rail can be lined up without difficulty. A very common adjustable attachment is shown in Fig. 342. It consists of ashort brace connecting the post with the DETAILS, BILLS, AND ESTIMATES. 1075 projecting end of one of the lower flange angles. The brace passes through a _ hole in the flange angle, and the attachment is made adjustable by means of two nuts upon the brace screwing against the flange. By means of this adjustment the top of the post may be readily thrown in or out and the railing be put substantial- ly in line before the last rivet attaching the post to ' =~ BIGr G83. the floor-beam is driven. But even after the post is riveted, its top can, to some extent, be sprung in or out by this adjust- ment. the members to which they apply. CONCLUDING REMARKS. 1727. The design of a structure should be simple; it should, as far as possible, conform to the requirements of the stresses, and be complete in every detail. Each part and detail of a structure should be strong enough to bear alone the stress for which it is intended. The structure as a whole can not be stronger than its weakest part, and it is useless to make one part relatively stronger than another. Each detail should not only have the required strength, but it should be simple and practical. At each joint where several members connect, the connections should, if possible, be so designed that the axes of all the connecting members shall intersect at a common point. The designing of such - details requires skill, judgment, and experience, as well as careful consideration of all the conditions attending each case. Each detail should be well studied and made assimple and practical as possible, having in mind the economical re- quirements of the shop work and erection. The simplest details are the most difficult to design. Where there are several similar details they should, if pos- sible, be made alike, as the shop work is thereby much facilitated. Familiar details should generally be used. In nearly every bridge office certain standards of construction are adopted. These should be used whenever practical, be- cause the shop men are familiar with them, but a good detail should never be sacrificed for the sake of using a standard. The shop drawings should be so made as to be readily un- derstood by the workmen. All letters, words, and figures written on them should be plain and easily read. In making shop drawings it must be borne in mind that they are for the purpose of conveying exact information to the shop men, 1088 DETAILS, BILLS, AND ESTIMATES. who are not supposed to have, and generally have not, any knowledge concerning the structure other than that obtained from the drawings. The information given on the drawings must, therefore, be complete and explicit. Information once given should generally not be repeated; dimensions or rivet spacing shown on a top or bottom view should not be again shown on the side elevation. Such repetitions not only require unnecessary labor upon the drawings, but tend to confuse the workmen. Where two members are exactly alike except that the positions of cer- tain corresponding dimensions are reversed, as the portal connections on two end posts, it is sufficient to show the di- mensions in one position and mark the members vzg/t and left. It is generally sufficient to show half top and half bot- tom views of chords and end posts; in such cases they are shown together in one half top and half bottom view, both being shown as seen from above. The lower ends of ver- ical and diagonal-members should generally be at the left on the drawing. No computations whatever should be left for the workmen to do; every necessary calculation relating to a structure should be performed in the office. The workmen will do well if they properly carry out the construction according to the drawings. Although the dimensions for any part of a bridge are never taken by scale from the working drawings, the scale, together with the title and date, should, for conve- nience in the office, be given in the lower right-hand corner of each drawing. STREETS AND HIGHWAYS. COUNTRY ROADS AND HIGHWAYS. GENERAL CONDITIONS. 1637. City Streets and Country Roads.—The difference between country roads and city streets is largely a difference of quality and condition; the principles under- lying their proper location, construction, and maintenance are essentially the same for both; but, as the application of those principles is simpler in the case of country roads, the latter will be considered first. 1638. What Constitutes a Good Road.—A good road is easily recognized in driving over it, yet the con- ditions necessary for a road to be a good one are not very generally understood. It will be well here to notice these conditions, in order to determine what things are to be obtained,and then we may consider the problem of how to obtain them. In order that a road may be satisfactory for public travel, it should be dry, solid, of easy grade, and smooth, Other conditions may be, and usually will be, desirable, but these conditions are essential. They are named in the general order of their relative importance. 1639. A Good Road Must Be Dry.—This is very important. A water-soaked road can not be good, and a road that will retain water on its surface will soon become water-soaked. A road composed of light, porous sand _will be firmer and better when moist than when thoroughly dry, but it will not retain water on its surface, and will For notice of copyright, see page immediately following the title page. 996 | STREETS AND HIGHWAYS. not become water-soaked, because the water will rapidly percolate through it. In other words, such a road is self- © draining. For all other kinds of roads, thorough drainage must be provided, so that they will not become water- soaked in any kind of weather. 1640. A Good Road Must Be Solid.—The material of which a roadway is constructed should be such that it can be thoroughly compacted, so as to sustain the travel ona firm, unyielding surface, and without the formation of ruts. The resistance to travel will be small on such a road, while on a soft road, or a road cut up with ruts, the resistance will be great. With almost all materials used in road making, a solid road may be maintained without great difficulty, if the drainage is thorough. 1641. A Good Road Must Have Easy Grades.—A road may be otherwise good, and still be of comparatively little value as a public highway, by reason of its steep grades. Such grades limit not only the loads that can be hauled over the road, but also the speed of travel, without any compensating advantage. A grade that is so steep that a descending vehicle must be held back by brakes or otherwise is too steep, as the energy expended by the brakes or by the holding back of the team is simply wasted. There is a corresponding expenditure of energy in ascending the grade that would not be necessary on an easier grade. In almost every case, excessively steep grades can be avoided by a judicious location of the road. 1642. A Good Road Must Be Smooth. — Roads may be dry and solid, and have easy grades, and still be quite unsatisfactory because of their roughness. The roughness may be due to uneven piaces in the surface, or merely to loose stones lying in the roadway. Whatever the cause, it is a very undesirable condition, which is both annoying and detrimental to travel; although it not uncommonly exists, there 1s no reason for it except negligence. STREETS AND HIGHWAYS. 99 LOCATION OF HIGHWAYS. GENERAL CONSIDERATIONS. 1643. Importance of Proper Location.—A matter of the first importance relating to the subject of highways is that of their location. This involves a consideration of their alinement and their grades. Although these subjects are both of great importance, they are seldom properly considered in determining the locations of roads. The subsequent value of a road, as a public thoroughfare and means for transportation, will depend largely upon the judicious and proper location of it with reference to its alinement and grades. The grades of a road will not only directly limit the speed of travel and the magnitudes of the loads that can be hauled upon it when in a given condition, but, by influencing the conditions relating to drainage, they will, indirectly and to no inconsiderable extent, affect the condition of the roadway also. A road properly constructed and maintained, will be, to a large extent good or bad ac- cording as its grades are favorable or unfavorable. The grades should be the paramount consideration in the loca- tion-of a road, and the alinement should be, so far as pos- “sible, such as to give the most favorable grades and efficient drainage. 1644. Location of the Older Highwayss—Many of the older roads of the country were constructed along former emigrant trails and roads cut through the wilderness ~ from one settlement to another. The construction of these roads followed the general development of the country, and was in no sense systematic. As is to be expected from the circumstances, such roads were not always located in the best possible positions, and, in many cases, the locations were quite unfortunate. While this is to be regretted, yet it is the legitimate result of the conditions attend- ing the settlement and development of our country, and can not now be remedied without relocating the roads, 998 STREETS AND HIGHWAYS. 1645. Common Modern Practice of Road Loca- tion.—In the location and construction of the public high- ways through the country at the present day, however, the conditions are entirely different, and the public have a right to expect that these roads shall be properly located, and con- structed in the best manner possible with the means at hand. But this is rarely ever done. A highway constructed from one place to another through the country is almost always located either upon an approximately straight line, or along the division lines between properties. The matter of grades usually receives very little consideration, except where the slopes become so steep as to be almost, or quite, prohibitory ; the matter of drainage is seldom considered at all. As arule, the men who lay out these highways are not engineers; they neither understand nor appreciate the engineering features involved, and think that all essential conditions are fulfilled if the road is reasonably direct be- tween terminal points, and is located in such a position as to be satisfactory to the property owners along the. route. Whether the route is over hills and through swamps is a matter they usually disregard, and they are satisfied if the road occupies the least valuable land and adheres as closely as possible to property lines. This practice is radically wrong and should be abandoned. The value of country property is affected to no inconsid- erable extent by the condition of the roads leading to the market towns, and it is greatly to the interest of property owners that these roads be constructed and maintained in the best manner consistent with a reasonable expenditure. This end can be attained only by good engineering in the location and construction, and by intelligent supervision in the maintenance. 1646. Highway and Railroad Locations Com- pared.—lIt is quite safe to state that, had the railroads of this country been located in the same manner as the high- ‘ ways, comparatively few would have been built and success- fully operated. The principles underlying the proper o STREETS AND HIGHWAYS. 999 ° location of a highway are much the same as those upon which the location of a railroad is based, and there is no sufficient reason why the location of highways should not also be based upon principles of sound engineering and common sense. In railroad location, the obtaining of favor- able grades and thorough drainage are recognized as among the chief conditions of a good road, and the location and alinement of the road are made largely subservient to these ends. These should be the chief considerations in the loca- tion of highways also, although considerably steeper grades are practicable for highways than for railroads. 1647. Considerations Relating to Alinement and Grades.—In locating a highway through the country, its alinement should be such as to give the best available grades, and afford thorough drainage. If sufficient care and judgment are exercised in the location, excessive grades can usually be avoided. In the majority of cases, it is much easier to go around a hill than to go over it, and a ju- diciously selected route around the hill will not usually be much longer than the route directly over it. For, while the route around the hill will deflect laterally from a straight line, the route over the hill will deflect from it vertically, and the difference in length of the two routes will not gen- erally be very great. When impossible to avoid crossing a hill or ridge of high ground, the crossing should be made by devious courses and easy grades, rather than by a direct course and steep grades. The hauling power of a team is so much greater on easy grades than on steep grades that it more than compensates for the difference in distance. For a given load, the work required to overcome a rise of one foot will be equivalent to that required to haul the same load, on a perfectly level road, a distance of from about " to 22 feet on an earth road, 15 to 30 feet on a gravel road, and 30 to 40 feet on a macadam road,* according to the con- dition of the roadway surface. Moreover, on steep grades, * These may be taken to be about the usual ranges of values, though the actual values may, in some cases, vary above or below these limits. 1000 STREETS AND HIGHWAYS. the roadways are damaged much more by storms than on easy grades. During a single storm, the storm water flow- ing violently down a steep roadway may cut out deep chan- nels and seriously damage it. On the other hand, a perfectly level grade is seldom desirable for a roadway, because, unless the roadway is situated along a side hill, the opportunity for efficient drainage will not be afforded. Where there is no reason for deviating from a direct course, the road should be made~as direct as _ possible between the points which it is to connect. Due regard, however, should always be given to the matters of grade and drainage, which are of much greater importance than direct alinement. In northern climates, roads leading from valleys to higher ground should preferably be located on slopes facing the south or west, where they will be most ° protected from storms and snowdrifts during the winter, and soonest clear of snow in the spring. RECONNAISSANCE AND SURVEYS. | 1648. Examination of Country.—A highway should be located in practically the same manner asa rail- road, although the conditions to be fulfilled are not nearly so rigid. As one of the first steps, the locating engineer should go over the entire route on foot and carefully study all itsfeatures. He should become thoroughly familiar with the country traversed, and his study of the route should be s0 thorough as to practically determine the position of the line. The work will be much facilitated by having a reliable map of the territory traversed. If a good topographical map is available, the approximate position of the line may be determined with reasonable certainty before going into the field. The amount of work necessary to be expended upon a reconnaissance will depend upon the difficulties attending each particular case, but it should always be sufficient to select the best possible route. In some cases, rough measurements should be taken, in order better to determine the practicability of the route and STREETS AND HIGHWAYS. 1001 from which to construct a rough map where none exists. Courses may be measured with a pocket compass, and dis- tances may be estimated by the eye, or by the aid of a pedometer. Differences of elevation may be estimated by means of an aneroid barometer and by a hand level. The Jatter instrument will also be useful in estimating slopes. From such measurements, much valuable information may be obtained. 1649. Selecting the Route.—The terminal points and those points through which the line must necessarily pass must first be determined. Such points will be towns, villages, and other centers of population or com- merce, passes between mountains, and the most favorable points for bridging large streams. These will be fixed points from which the line must not deviate. Between these points, the best possible route should be selected, with reference to easy grades, thorough drainage, and suitable material for the roadbed. The route should be as direct as practicable, and should first be selected without any regard whatever to property lines. After the route has been selected, howev Br Cas eas of land boundaries should receive pineideracon, though, 11 some cases, this may be deferred until after a REED, line has been run. It will usually be found that, in many places, the route of the highway can be so adjusted as to follow the division lines between properties without serious disadvantage. Thisshould be done, where possible, without detriment to the line, as it will usually be much more satis- factory to the property owners, but such adjustment should not be made to the serious injury of the route. It is not essential that the route selected should be even approximately straight. Angles may be made wherever the conditions require them. In this respect, the location of a highway differs materially from the location of a railroad. Angles in a highway should not be made unnecessarily, how- ever, as a reasonably straight roadway presents a much more pleasing appearance than one having many turns and angles, T, IV,—t13 1002 STREETS AND. HIGHWAYS: 1650. Running and Marking the Line.—When the reconnaissance has been made and the general route selected, the line should be run withatransit. If necessary, in order to select the best route, more than’one line should be run, and the most favorable line adopted. The line run should be the center line of the highway. Stakes should be set on this line at the end of each interval of one hundred feet, and numbered consecutively, beginning with zero at the starting point. Each point so marked and numbered is called a station. A transit hub should be driven at each angle in the line, and the exact position of the point should be fixed by a tack driven in the top of the hub; its position along the line should be designated by the number of feet, called the plus, from the preceding station. The position of each point at which an angle occurs in the line finally adopted should be fixed upon the ground by measurements to permanent objects, or to reference stakes set outside of the limits of the roadway to be graded, so that after the construction of the road the exact point can readily be relocated. After the road is constructed, this point should be marked by a long stone, or other enduring monu- ment, set deep into the ground. The position of this monument should be fixed by measuring and recording the courses and distances to two or more witness trees, or other permanent objects. If the line constructed is thus well marked, much annoyance and uncertainty will be avoided with regard to the position of the line in after years. The station and plus at which the surveyed line intersects each section line, land boundary, stream, railroad, or exist- ing highway should be carefully noted. Where the surveyed line crosses each section line, it should be tied by measure- ment to the nearest section or quarter-section corner. The positions of the initial and terminal points of the surveyed line should be fixed by measuring the course and distance to the nearest corner of the Government land survey; when convenient, it will be well to fix each point by measurements to two different corners. STREETS AND HIGHWAYS. 1003 GRADES. 1651. Levels and Grades.—Levels should be taken along the line thus located and marked. In taking the levels, notes should be made of all important topographical features, such as the position and size of watercourses, the timber, the character of the surface, and especially the character of the soil. From the levels taken, a profile of the line should also be made in practically the same manner as in railroad location. The important topographical features of the country should be noted on the profile. By means of the profile thus made, the available grades should be carefully studied, the maximum rate of grade fixed upon, and the grade line established. 1652. The grade line is the line representing the surface of the finished roadway, from which may be deter- mined all elevations along the same. It is usually shown by a red line on the profile. While the route is being located, the profile should be made and the grade line fixed each evening for that portion of the line run during the day. For it will sometimes be found that the line located during the day, or some portion of it, will prove to be so unsatisfactory with regard to the obtainable grades that it will be necessary to relocate it. This condition will be definitely shown by the profile, and if the making of the profile thus progresses daily with the locating of the line, the unsatisfactory portion of the line can be relocated the next day before proceeding. 1653. The rate of grade, or the gradient, is the rate of rise or fall along the grade line. The rate of grade may be expressed as the amount of rise or fall in a unit of horizontal length, in a hundred units of horizontal length, or in any given horizontal distance, as in one mile. It may also be expressed as a vulgar fraction; when so expressed, the amount of rise or fall in any given horizontal distance is written as the numerator, and the horizontal distance in which the rise or fall occurs is written as the denominator, both being in the same unit. When the rate of grade, 1004 STREETS AND HIGHWAYS. expressed as a vulgar fraction, is reduced to the form of a decimal fraction, it will express the amount of rise or fall per horizontal unit, and will correspond to the sine of the slope. (See Art. 1478.) The rate of grade is very commonly expressed by the amount of rise or fall per hundred units; when so expressed, it is called the rate per cent,.. The rate per cent. of a grade is, therefore, the number of units of rise or fall in each hundred units of horizontal distance. In writing the rate of grade, it is customary to indicate a rising grade by a + sign, and a falling grade by a — sign. Thus, a grade rising 2 feet in a horizontal distance of 100 feet would be marked on the profile + 2.00%. The4%sign is not uncommonly omitted. All computations relating to rates of grade may be based upon the following simple RULES: I. Zhe rate per cent. of a grade ts equal to tts total rise or fall in any given horizontal distance divided by the hort- zontal distance and multiplied by 100. It. he total rise or fall of a grade line in any given horizoutrl distance ts cqual to the rate per cent. of grade multiplied by the horizontal distance and divided by 100. Wi. he horizontal distance in which a grade line hav- mga given rate per cent. will rise or fall a certain amount, ws equal to the amount of rise or fall divided by the rate per cent. and multiplied by 100. EXAMPLE 1.—What is the rate per cent. of a gradc that rises 12.24 feet in a horizontal distance of 450 feet ? SOLUTION.—By rule I, the rate per cent. will be cqual to 12.24 x 100 750 = 2.12 per cente Ans. EXAMPLE 2.—What is the total fall in a grade line ina horizontal distance of 648 feet, the rate of grade being — 4.25 per cent.? SoLuTION.—By rule II, the total fall will be equal to — 4.25 x 648 — On 100 = — 27.54 feet. Ans. STREETS AN Dy HIG WAYS. 1005 EXAMPLE 3.—In what horizontal distance will a grade line having a rate of + 2.00 per cent. rise 10.64 feet ? SOLUTION.—By rule III, the horizontal distance will be equal to 10.64 « 100 a, Pp oro “ 500 hee feet. | Ans 1654. Maximum and Minimum Grades.—The steepest grade on a route is commonly spoken of as the maximum grade, and, likewise, the flattest grade on the route, that is, the grade approaching most nearly toa level grade, is commonly called the minimum grade, These respective terms are also applied to those grades that have been decided upon as the steepest and flattest grades fermissible upon the route. The maximum and minimum grades upon the route will generally be the same as the maximum and minimum permissible grades. The grade adopted as the maximum permissible grade is sometimes called the ruling grade. With reference to the maximum and minimum rates of grade, the terms Maximum gradient and minimum gradient are also used. In locating a highway, a certain maximum grade should be fixed upon, and the route should be so located that this maximum grade will not be exceeded. On any portion of the line, however, any grade not exceeding this maximum grade may be used. ‘The easiest grades should be used on those portions of the road where the travel is heaviest, and the steepest grades where there is the least travel. If the road leads to a large city or market town, the grades near the city should be easier than at points more remote, because the traffic near the city will be greater in amount and heavier in character than at remote points. The maximum grade should not be steeper than 9 per cent. for earth roads, 64 per cent. for gravel roads, and 3 per cent. for macadam roads, in any case where possible to keep within those limits, and, preferably, should never be steeper than about 3 to 5 per cent. for any kind of road. In order that efficient drainage may be provided for the road- way, the minimum grade should not, in ordinary cases, be 1006 STREETS AND HIGHWAYS. flatter than 1 per cent., and should never be materially flatter than one-half of 1 per cent., except on first-class pavements. COMPARISON OF ROUTES. 1655. Conditions to be Compared.—Where it has been found necessary to run more than one line in order to select the best route, the profiles of the different lines will afford a fair basis of comparison. The principal conditions to be considered in comparing the routes are as follows: 1. Convenience to Traffic.—The road should, so far as possible, be located in sucha position as to accommodate those who are to travel upon it. The route that will best accomplish this, and, at the same time, afford equal advan- tages with regard to the other essential conditions, will be the best route. 2. Short and Direct Route.—All other conditions being equal, the shortest route will, of course, be the best. 3. Lasy Grades.—The route having the easiest grades will be the best, other conditions being equal. 4. Small Rise and Fall.—The route having the smallest total amount of rise and fall will offer the least fo¢a/ resist- ance to traffic, irrespective of the steepness of its grades. Hence, with all other conditions equal, such a route will be theese, 5. Lhorough Drainage.—The route selected should have such position and such grades as to afford the opportunity for thorough drainage of the roadway. This condition is not usually difficult to obtain, but a route not affording thorough drainage should not be selected. 6. Suitable Material for Roadway.—When there is any difference in the character of the soil along the different routes, the route having the best material should be selected as the best route, provided all other conditions are fulfilled to an equal extent. hy i. Small Cost.—With allof the above conditions equally fulfilled, the route which can be constructed and maintained STREETS AND HIGHWAYS. 1007 at the least cost will be the best route to select. The mat- ter of cost is a very important consideration, and, in many cases, it will be the governing condition as against all other conditions. From the above, it will be noticed that the considerations involved in the comparison of the routes are of two kinds, namely, those relating to the efficient accommodation of the traffic, which is the result produced, and those relating to the cost of producing this result. The first six conditions named above are of the former class; the last condition only is of the latter class. In some cases, however, the last con- dition will outweigh all the others. 1656. Means and Method of Comparison.—A comparison of all except the first of the conditions noticed in the preceding article will be given by the profiles of the routes. The length, grades, rise and fall, character of the soil, and, to some extent, the opportunity for thorough drainage, will be shown for each route by an inspection of its profile while the approximate cost of construction may be easily estimated from the same. 7 In comparing the gradients, the rates of grade should be compared with special reference to the rates of maximum grade on the different routes, as this condition will greatly affect the magnitudes of the loads that can be hauled over the roads. In the comparison of the lengths of the routes, the total ineffective rise and the excessive fall should be included. By ineffective rise, as the term is here used, is meant that rise and fall in the grade line which is zo¢ due to the differ- ence of elevation between the two ends of the route; it is the total number of féet actual vzse in the grade line en- countered in passing from the higher end of the route #o the lower end. By excessive fall, as the term is here used, is meant that fall in the grade line which is in excess of cer- tain rates of grade encountered in passing in the same direction. Should the grade line on any portion of the route, in passing from the higher to the lower end, fai/ L008 STREETS AND HIGHWAYS. more than 9 per cent., 6.5 per-cent., or 3. percent tfor earin, gravel, or macadam roads, respectively, then each foot of fall zx excess of such rates will be considered as excessive fall. These are about the average rates of grade, giving, respectively, what is known as the angle of repose for the three kinds of roadways named; on descending grades steeper than these, a holding-back force must necessarily be applied to the loads. Ineffective rise and excessive fall are both counted in a direction passing from the higher to the lower end of the line.* 1657. Comparison of Lengths.—The length of the route, taken in connection with the ineffective rise and ex- cessive fall, will here be called its resisting length. The resisting lengths of different routes may be compared by referring them to the work required to move a given load over them. If m is the coefficient of friction, the work zw performed in hauling a weight W along a horizontal dis- tancexhisw=Wmh. If, however, in the distance / there occurs a rise (or excessive fall) 7, the work necessary to haul the weight along the inclined path is w=Wmht Wr. In order to reduce this to an equivalent level grade we must give wa form similar-to that of.” €Puv then, r 7 Whereis oa and the value of w' becomes w'’ = Wmh+ 7 = Wim h'= Wm (h-+h'), which shows that the inclined path is equivalent to the corresponding horizontal path increased by the quantity 4%’, or. In general, if 7 is the length of a route, and /, the equivalent length of a route having, with respect to the former, asum of excessive falls and ineffective rises equal to 7, we have Lt Lae (203.) * Given a body resting on an inclined plane, the body will generally slide down the plane. But if the inclination of the plane to the horizon is gradually diminished, a limit will be reached at which the resistance of friction is just enough to prevent sliding. This inclination is called the angle of repose. It is different for different materials. The tangent of the angle of repose zs egual to the coefficient of friction. STREETS AND HIGHWAYS. 1009 , and may have the following* values: : yi where ¢ is equal to — we For earth roads, Co Le For gravel roads, eee: ony For macdadam roads, ¢ = 33. By comparing the resisting lengths obtained by applying formula 203 to the grade lines of the different routes, a reasonably just comparison may be made between the routes with regard to what may be considered as their com- parative resistances to traffic by reason of actual length, ineffective rise, and excessive fall. 1658. Soil, Traffic, Cost.—Some comparison of the character of the soils along the different routes, with ref- erence to their adaptability to the purposes of road build- ing, may be obtained from the notes given on the profile. For each route the opportunity for thorough drainage can be largely judged from the profile, enabling a reasonably just comparison of this condition also to be made. The amount of grading, as estimated for cach line from its pro- file, taken in connection with the amount of bridging and number of culverts required, as shown on the profile, will setve as a basis for estimating the relative cost of the different lines. A comparison of the first condition, convenience to traf- fic, can be made only from an examination of the routes on the ground or from a very complete map. The road should, so far as practicable, be so located as to be the most con- venient for the greatest portion of its traffic. The positicn of a road that will best accommodate its traffic will gener- ally be that in which, all other conditions being equal, the sum of the distances through which each ton of freight is moved and each passenger travels will be a minimum; in other words, it will be that position which will require the * These are about average values and may be used for ordinary roads. The actual values will generally vary from about 7 to 22 for earth roads, 15 to 80 for gravel roads, and 80 to 40 for macadam roads, according to the condition of the roadway surface. (Sec Art. 1647.) 1010 STREETS AND HIGHWAYS. ; 3 : : Ss S 3 | Sl = = Nd 8 2 wR 250 S| Mi mH i nt | iil ial Za — eon a SIE EEE es Fic. 399, STREETS AND HIGHWAYS. 1011 mass of the traffic to be moved the least distance in reach- ing its destination. Some consideration should also be given to the question of whether a road will be pleasant for those who are to travel upon it. In the case of pleasure drives, this should be an important consideration. The basis of comparison with regard to economical loca- tion has been concisely stated by Prof. Spalding in the following language: ‘‘ The most cconomical location is that for which the sum of the annual costs of transportation, the annual costs for maintenance, and the interest on the cost of construction, is a minimum.”’ IX AMPLE OF ROAD LOCATION. 1659. The Conditions Assumed.— Let it be assumed that it is desired to locate and construct a highway between the points A and #4, Fig. 399, which are 6,000 feet, or slightly more than 14 miles, apart, measured in a direct line. The topographical features of the country are quite clearly shown in the figure, the relative elevations being shown by contour lines. It will be assumed that the road is to be constructed to sustain a very heavy traffic between the points A and 4, and that it is not essential for it to pass through any intermediate points, though rather desirable that it should pass through or near the points @ and e in the valley, provided such location will not be disadvantageous in other respects. As the road is one of considerable im- portance, several routes are surveyed, in order to determine the best route. ‘The profiles of the difterent routes are shown below the map in Fig. 399. Only the surface lines are shown in these profiles. In order to avoid confusion in comparing the different profiles, the grade lines have been omitted; they may be considered to have approximately the same positions as the surface lines and to be somewhat more uniform. 1660. The direct route Aadc Vis the shortest as regards hcrizontal distance, being just 6,000 feet long, hori- zontally. But the profile shows that, in passing from the 1012 STREETS AND IIGHWAYS. higher terminus 1 to the lower terminus 4, by this route, a rise of about 43 feet is encountered between a and J, and another rise of about 19 feet occurs betweenc and 4, inaking a total ineffective rise on this route of 43-+19= 62 feet. Between the end A of the line and the first crossing of the stream, which is a distance of 625 feet, the fall is vo X LOO Hesie suming that the road is to be an ordinary earth road, then, as stated in Art. 1649, that portion of the fall in excess of 9 per cent. should be treated as a like amount of rise. A fall of 9 per cent. for a distance of 625 feet would bea total fall of 9 x 6.25 = 56.25 feet, leaving an excess of 75 — 56.25 = 18.75 feet. Alsoin the 400 feet of horizontal dis- tance, situated between points distant 350 and 750 feet, respectively, to the right of J, the fall is about 50 feet, or at a rate of ee ='12:5' ‘per cént. ; which isean /exceseacn 12.5 — 9 = 3.5 per cent:, or.a total excess of 4.00 X 3.5 = 14 feet. By applying formula 203; the length of route /, to be assumed in making the comparison will be equal to 6,000 + 12 x (624+ 18.75 + 14) = 7,137 feet. This route would also involve very steep grades, the maximum in one direction being not less than 12 per cent., and in the opposite direction about 5 per cent. about 75 feet, or at the rate of =f 2 Der_COnte agri se 1661. The route 4 dc J, following the general course of the stream, would usually be the route first tried, especially if the surveys were made from the lower terminus / towards the upper terminus A, as will most commonly be the case. The surface line A de J’ is the profile of this route. It will be seen from this profile that the route is a quite favorable one, having only the very small amount of inef- fective rise that occurs betweenc’ and B. The length of this route is 6,250 feet. In the first 1,000 feet from A, however, this route has a fall of about 85 feet, requiring a grade of 8.5 per cent., which is steeper than is desirable for the character of the traffic that the road is to sustain. . STREETS AND HIGHWAYS. 1013 In the attempt to avoid this steep grade, the lines A 7’ s’d and A 7’ s' e are run as alternative lines for a portion of this route. The profiles of these lines are shown by the surface lines A?7’s’ ad and A?’ s' 2 respectively. The line A 7's’ d increases the length of the route by the amount dd’, or about 70) feet, and the line A 7’ s’ ¢ increases it by the amount ee, or about 600 feet. Hence, the total horizontal length of the line 4 s’d A will be 6,250 + 700 = 6,950 feet, and the total horizontal length of the line 4 s’ e & will be 6,250 + 600 = 6,850 feet. There is no excessive fall in this line, but between the points c’ and & there is about 8 feet of ineffec- tive rise, giving a theoretical increase of 8 x 12 = 96 feet in the length of the line. For the purposes of comparison, therefore, the value /, for the line A s’d B is 6,950 + 96 = 7,046 feet, and for the line 4 s’e B it is 6,850 + 96 = 6,946 feet. For both these lines, the maximum grade is 5 per cent.; it occurs between 7’ and s’. 1662. The route A fkmoB is surveyed at a higher elevation along the opposite side of the valley. This line is 'amodification of the direct line Ad dc 4 ; it is quite crooked, however, and its length, horizontally, is about 7,060 feet. For this route, the surface line A #2 4" is the profile. Its maximum grade, which is between z and /, is 5 per cent. Between the point f and the terminus /, there is about 12 feet of ineffective rise, making the value of Z, for this route equal to 7,060 + 12 x 12 = 7,204 feet. 1663. The Route of Easiest Grade.-—As the traffic upon the road is to be of a very heavy character, making easy grades a very important consideration, still another line is surveyed, for the purpose of ascertaining whether a line having very easy grades can be obtained. This line is located very carefully, with the object of obtaining, if pos- sible, a line having no grade steeper than 2.5 per cent. Such a line is obtained; it isthe line 4 s ¢vw 4, having a length of about 7,550: feet. There is no ineffective rise or excessive fall on this line. The surface line A s¢w 4” is the profile of this line. The greater portion of the line approximates a 1014 STREETS AND HIGHWAYS. uniform grade of 2.4 per cent., anda maximum grade of 2.5 per cent. can be easily obtained. 1664. The Tabulated Comparison.—lIn order to afford a ready comparison between the different lines sur- veyed, the values that have been determined are given below in tabularform. For convenience of reference, the different lines are numbered. This tabulation of values, together with the map and profiles of the routes will enable an intelligent selection of the route to be made. From the values of /,, and of the maximum grade, it is seen that routes number 2, number 4, and number 6 are the most favorable ones. Route number 2, or the direct route through the valley, is a thoroughly prac- tical route, provided the maximum grade of 8.5 per cent., extending for a distance of 1,000 feet, is not objectionable. This route gives the smallest value of 7. Route number 4 is a modification of route number 2. It reduces the maxti- mum gerade to 6 per cent), and increases*the lenoth om ihe line nearly 700 feet. Route number 6 follows the brow of the hill on the left side of the valley. This is the longest of the routes surveyed, but it obtains the very easy maximum grade of 2.5 per cent., and, as it has no ineffective rise and Actual Resisting | Maximum Number. Line. Lenvth 7 sic leosth 7a Grade, Feet. Feet. Per‘ Cent 1 A peLb 6,000 mie t 12.0 2 AdeBbB 6,250 6,250 8.5 3 As'dB 6,950 7,046 5.0 4 Arsseels 6,850 6,946 5.0 5 Amob 7,060 7,204 3.0 6 Aswh 7,550 7,550 RAD fall, it gives a value of 7, the same as the actual length of the line. This is much the best route for heavy traffic, and STREETS AND HIGHWAYS. 1015 for a mixed traffic will generally be the most satisfactory. If the character of the traffic is light, so that a grade of 8.5 per cent. is not a serious disadvantage, route number 2, leading directly through the valley, will generally be the most satisfactory. If it is necessary to pass through the points d and ¢, and, at the same time, have no grade steeper than 5 per cent., route number 3 will fulfil the conditions; but, if there is no reason why the road should pass through the point d, route number 4 will be slightly shorter. RELOCATION OF ROADS. 1665. The Present Conditions.—In most parts of this country, so many roads are already located that the necessity for locating new ones does not often arise, and when such necessity does arise, the road is usually a short one and its position is determined mainly by the existing roads and local requirements. The problem that now most frequently occurs in the location of country roads is that of changing the location of short portions of existing roads, in order to obtain better grades, shorter routes, or better ground and drainage. 1666. The Common Defects.—Heavy and unneces- sary grades are the most common defects of ordinary country roads. Such grades are often due to improper loca- tion. Many roads have been located along property lines and on the shortest obtainable routes, without due regard to the question of easy grades, even if the latter were easily obtainable. In such cases, the defect can be remedied by relocating all or a portionof the line. Sometimes, however, the road, as originally located, 1s unnecessarily long and devious, and it becomes necessary to relocate all ora portion of the road, in order to obtain a shorter and more direct route. Again, the character of the ground over which the road passes may be such that to maintain the road in good condition is difficult and expensive, and in some cases impossible. Better ground can generally be obtained by a new location. 1016 STREETS AND HIGHWAYS. 1667. Roads on Section Lines.—Almost all regions of the United States in which the Government lands have been surveyed since 1785 have been surveyed according to the system of rectangular townships and sections. In such portions of the country, it is a very common practice to locate the roads along section or quarter-section lines, and this practice has been the cause of a considerable amount of unfortunate road location. Where land boundaries are formed by section or quarter-section lines, as is commonly the case, the roads should preferably be located along such lines, provided such location is not in other respects disad- vantageous to the roads. Straight lines should not be followed, however, when more advantageous routes can be obtained. 1668. The Example.—In Fig. 399 the straight route Abc B may represent an existing road constructed along a section line. This route proving quite unsatisfactory on account of its steep gradients, a new location is made on the line A gmo 4, having much easier grades. Again, the route Ade may represent an existing road following the general course of the stream through the valley. This road being satisfactory except as regards the 8.5 per cent. grade on that portion adjacent to the upper end A, a sufficient portion of this end of the road is relocated to obtain an easier grade. The location A 7’ s' d will be quite satisfactory for this purpose, except that it will require the abandonment of the entire portion A d of the old line, and the construction of about 3,000 feet of new line. The location A 7’ s’ ad’ will retain all of the old line except the portion A-@”, or about 1.190 feet, and will require the construction of only 2,000 feet of new line. The length of the line will be increased 2,000 — 1,190 = 810 feet, by the relocation) OfSthis portico shown by the profile, the maximum grade on the relocated portion of the line will be about 5 per cent. 1669. Maps and Records.—When the route of a highway has been satisfactorily and finally located, a map of the line should be made for the purpose of record, show- STREETS AND HIGHWAYS. 101% ing accurately all its courses, angles, and distances, the points at which it crosses land boundaries, section lines, streams, railroads, and existing highways, together with the courses and distances to, and the descriptions of, all wit- nesses taken at the angles and at the starting and terminal points of the line. The map should also show the positions of the starting and terminal points, and convenient points along the line, with reference to the nearest corners of the Government land survey. The map may also show a profile of the line, though, for a country road, this is not very essential, as the profile will not be of great value as a matter of record after the road is constructed. As a means of reference in regard to the grades and drainage, however, the profile will be convenient and should generally be shown. All inrormation given on the map proper, that is, all information relating to the alinement and position of the line, should also be given in an accurate written description of the surveyed line. The map and description should be filed with the proper township or county officials for a permanent record. MATTERS FOR PRACTICAL CONSIDERATION. WIDTH AND CROSS-SECTION. 1670. Width of Right of Way.—The entire area of a road included between fence lines is known as the right of way; it is so called because it is the right of way for the road, which must be obtained, by purchase or otherwise, from the owners of the properties over which the road passes. The best width for the right of way of a road isa matter that must be determined by judgment and accord- ing to the requirements of each particular case. The widths of country roads vary greatly. A width of 4 rods, or 66 feet, is common for important roads in some parts of the country. In other parts of the country, very narrow roads are often met with, some being little more than nar- row lanes, probably not more than a rod in width. Roads 3 rods, or 494 feet in width, are quite common. T. IV.—t4 1018 STREETS AND HIGHWAYS. A width of 66 feet was probably first adopted largely for convenience of measurement and computation, it being the length of a surveyor’schain. It has proved to be a good practical width, however, and is not only used for many country roads but for city streets also. It is wide enough to accommodate all possible requirements, and is about as narrow, as is generally desirable for northern climates, for the snowdrifts caused by the fence lines often extend across and block the roadway in narrower roads. Rights of way narrower than 66 feet are, however, very common. 1671. Width of Roadway.—The width of the graded driveway should be from 12 to 30 feet, according to the re- quirements of the travel. A width of 12 feet is ample for two teams to pass and is sufficient for cross roads and unim- portant roads in the country. A driveway 16 feet in width will often be sufficient for country highways that are main arteries of travel. The conditions requiring a width of 30 feet for a roadway in the country are exceptional, and the conditions requiring greater widths are very rare. The width of the roadway should, in all cases, be limited to the requirements of the travel. It has been found that a width of roadway just sufficient to accommodate the travel is more enduring than a greater width. Any additional width beyond that necessary to accommodate the travel is almost always a disadvantage, for it lessens the possibility of effective drainage and otherwise impairs the condition of the roadway. 1672. Cross-Section of Roadway.—Water is the chief enemy of good roads. In order that the water shall run off from the surface of the roadway, instead of soak- ing into it, the roadway should be crowned, that is, it should be made higher in the center than at the sides. The surface line should be given the form, in cross-section, of either the arc of a circle, or of two straight lines slop- ing downwards and outwards, with their two inner ends joined by the arc of a circle about five feet in length. The amount of crown, that is, the height of the center STREETS AND HIGHWAYS. 1019 of the roadway above its edges, should be sufficient to effectively drain off the water from the roadway, but should not be great enough to cause inconvenience to the travel; it will generally be about one-fortieth of the width for ordinary earth roads,\about. one-sixtieth of the width for good macadam roads, and about one-eightieth of the width for well-paved streets. These ratios should be varied according to the character and condition of the roadway; a well-made roadway will require less crown than an in- ferior one. The reason for this will be readily understood when it is considered that the crown of the roadway is for the sole purpose of throwing off the water into the gutters or side drains. DRAINAGE AND WATERWAYS. 1673. Drainage.—All matters relating to the loca- tion and construction of a highway should conform to, and be directed towards, a condition of thorough drainage. The alinement should be such as to give proper grades, and the grades should, in turn, be such as to give effectual drainage. For thorough drainage is the condition most essential to a good road. A vast amount of water falls upon a mile of roadway during a year. If the roadway is to remain in good condition, it is imperatively necessary that escape be provided for this water in some other man- ner than by soaking into the roadway or into the ground at the sides of the roadway. Ground saturated with water can form neither a good roadway nor a good foundation for a roadway. On the other hand, some materials which when water soaked are thoroughly unreliable will, when effectually drained, become reasonably satisfactory for the purposes of a roadway. For instance, a roadbed of either clay or quick- sand wouid, if completely water soaked, be almost, if not quite, impassable. Buta mixture of clay and quicksand, if kept thoroughly drained, would make a: reasonably good road. The water should be promptly removed by means of sur- face ditches along or near the edges of the roadway. As 1020 STREETS AND HIGHWAYS. some of the water will always soak into the ground, even with the most perfect system of surface drainage, drains should also be placed beneath the roadway to effectually remove the water from the subsoil. Such drains will here- be called subsoil drains. Where the ground is naturally dry, or where the earth foundation of the roadway is com- posed of a material not rendered soft and yielding by water, the subsoil drains may be omitted and the drainage effected entirely by the side ditches. 1674. Arrangement of Drains.—Fig. 400 repre- sents the cross-section of a roadway; it is not drawn to scale, and is intended merely to show the general arrange- ment of the drainage system. The material of which this Fic. 400. roadway is composed is not indicated, as the principles of drainage will apply much the same for any material. By reason of the crown given to the roadway 7, the greater portion of the storm water will be thrown off into the side ditches @ and a’, along which it will flow to some outlet into a natural drainage channel. In the figure, the outlet to the side ditches is shown at o; the ditches discharge a this point by means of the cross drain 6, which may reprc- sent any drain leading from the side ditches to the outlet. The arrangement of the outlet drain here shown is not necessarily the best for this purpose; it is simply an arrange- ment suited to the conditions shown. The side ditches may often discharge directly into a stream or a larger ditch crossing the roadway. The subsoil drains d@ and ad’ are placed beneath the road- way for the purpose of rendering the drainage complete and effectual by removing the water from the subsoil, That STREETS AND HIGHWAYS. 1021 portion of the cross-section drained by the subsoil drains is shown by lighter shading than the undrained portion below. The drain d@ is represented as an ordinary small tile drain, and the drain @'is represented asa common stonedrain. In an actual case, both drains would generally be of the same kind; the two kinds are here shown merely for illustration. Stone drains are formed by simply filling a narrow trench with stones, the larger stones being placed at the bottom and the smaller ones towards the top. The trenches in which tile drains are laid are often filled with gravel and small ‘stones for a considerable distance above the drains. The subsoil drains shown in Fig. 400 discharge by means of the cross drain ¢ leading to the outlet o’. This cross drain need not be as large as the cross drain 6 which con- veys the storm water from the side ditches. The arrange- ment for conveying the water from the side ditches and subsoil drains to the channels of natural drainage should, of course, be varied to suit the requirements of each particular case. When cross drains are employed, they will not usually be in the same vertical cross-section, as shown here for convenience. 1675. Single Subsoil Drains.—It is cheaper to use a single drain, placing it under the center, than to use two Fic. 401, drains under the edges of the roadway. Single drains are the more commonly used. The cross-section of an ordinary earth road having shallow side ditches and a single subsoil drain is shown in Fig. 401. The drain here shown is made of flat stones laid up in box form, and covered with a layer of small stones. Where flat stones are abundant, this is a 1022 STREETS AND HIGHWAYS. cheap form of drain. The layer of small stones is often omitted. Tile drains and ordinary stone drains are also used; tile drains are best for the purpose. Good drainage may generally be obtained by single sub- soil drains, but any examination or repairs of such drains will necessitate the disturbance of the roadway, which is un- desirable. By placing the subsoil drains under the outer edges of the roadway, they can be inspected and repaired whenever necessary, without disturbing the central and most important portion of the roadway. ‘Two drains under the outer edges will also give more efficient drainage than a single drain. 1676. Dimensions, Depth, and Alinement of Drains.—The diameters of the tiles used for subsoil drains should be between 3 and 5inches. Subsoil drains should be placed at sufficient depth below the surface to escape the destructive action of frost. The depth necessary to escape frost will vary in different localities; a depth of 34 feet may be taken as a safe average. The side ditches should be given such depth as to prompt- ly and effectually remove the surface water. Where subsoil drains are not used, the side ditches should have sufficient depths to drain the subsoil also. The best depth will, in any case, depend upon the nature of the soil, the natural drain- age, and the position of the outlet. The slopes of the sides of the ditches should not be steeper than 1 vertical to 1 hor- izontal, and, in very unstable soils, not steeper than 1 ver- tical to 14 horizontal. The side ditches and subsoil drains should be constructed upon either straight lines or uniform curves, and to uniform grades. This is very important in order to develop any- thing like the full carrying capacity of the drains and ditches, for the flow of the water is greatly retarded by crooks and irregularities in the channel. The tile drains, especially, are very liable to become choked by the deposits of solid matter caused by the retardation of the current, due to irregularities of grade and alinement, although, for- STREETS AND HIGHWAYS. 1023 tunately, subsoil drains carry comparatively little solid matter in suspension. 1677. Necessity for Waterways.—Ditches and drains are provided along and beneath a roadway for the purpose of draining it. In order to convey the drainage water from the ditches on the upper side of the roadway to a suitable outlet, it is generally necessary to provide means for it to cross the roadway. Provision must also be made for the drainage waters from adjacent lands to cross the roadway. «This drainage water may flow in natural chan- nels, as in the case of brooks and rivers, or in artificial channels, as in the case of ditches and drains. Wherever a stream of water crosses the road, an opening through or be- neath the roadway must be made for it, whatever may be the size of the stream or the kind of channel. 1678. Required Size of Waterways.—The re- quired size of the waterways is the first thing to be deter- mined in deciding upon the character of the opening. The waterway provided must be large enough to pass the maxi- mum flow of water that is likely to be given by the stream, while considerations of economy require that it shall not be larger than this. Hence, the size of waterway required by the maximum flow of the stream is what it is necessary to determine as nearly as possible. The maximum flow of a stream will depend upon a num- ber of conditions, the most prominent of which are the maximum rate of rainfall; the size, shape, character of sur- face, and slope of the area drained; and the length, position, character, and slope of the channel. Most of these con- ditions are of difficult accurate determination, and can not be expressed by exact mathematical formulas. It will be noticed, however, that the conditions are analogous to those for determining the required size of a storm-water sewer, as studied in the section on Drainage. The maximum storm effluent from the area drained by the stream may be found by the method there given, and the required size of the opening may be found by treating it as a pipe flowing full 1024. STREETS AND HIGHWAYS. if it is a closed culvert, or as an open channel if it is anopen culvert or bridge. It is generally advisable, however, to measure the flow of the stream at high water, if opportunity is afforded for doing so. An idea of what size of opening may be required for the maximum flow can generally be acquired more accurate- ly by this than by any other method. In many cases, some person living in-the vicinity will be able to point out the highest point reached by the water, from which information the size required for the waterway can be easily determined. 1679. Formula for Waterway.—When not prac- ticable to measure the flow of the stream at high water, the - required capacity of the waterway may be estimated with sufficient accuracy by applying the following formula : We EAE, (204.) in which a is the required area of the opening in square feet, A is the drainage area in acres, and ¢ isa coefficient depend- ing upon the nature of the country and of the channel of the stream. The following values are used forc: For comparatively level areas, c = 1.0. For compact, hilly ground, ae ee For abrupt, rocky slopes, eget AAUP For conditions intermediate between those described, in- termediate values of ¢ may be used. The value of c should be somewhat higher for an approxi- mately square area than for a long, narrow valley, and higher for soil of an impervious nature than for porous soil. If the course of the stream is reasonably straight, or if it has con-’ siderable fall and rapid current, the value of c should be greater thanif the stream has a winding and tortuous course, or very little fall and a sluggish current. If judgment and care are exercised in the use of the coefficient, reasonably good results may be obtained with this formula, and it has the advantage of great simplicity. It will be well to notice that a more rational expression for the required area of the waterway would appear to in- STREETS AND HIGHWAYS. 1025 volve the fourth root of the third power of A, similar to the Buerkli formula for storm-water effluent. (See formula 118, Art. 1451.) Such a formula for waterways has been proposed. As, however, the accuracy of this formula, and of any similar formula that can be proposed, will depend very largely upon the use of a suitable value for the co- efficient, and as a considerable margin of safety must be allowed in the area of a waterway, as determined by any formula, it is believed that the one stated above will be found about as satisfactory as any. EXAMPLE.—What size of waterway is required for a stream draining 400 acres of hilly ground, the soil being of a quite compact nature ? SOLUTION.—For such a drainage area, the value of c will be 1.6; hence, by applying formula 204, the required area of the waterway is found to be 1.6 4/400 = 32 square feet. A waterway 4x8 feet will give the required area. MATTERS RELATING TO THE CONSTRUCTION OF HIGHWAYS. ROADS AND MATERIALS. 1680. Materials Available for Country Roads.— The roads which can be constructed from the materials and with the means ordinarily available in the country may be classified as broken stone roads, gravel roads, and earth roads. More costly roads are not at present neces- sary in the country, and could not be constructed with the means available. Indeed, in many places, lack of means prevents the construction of any but the last-named class of roads. BROKEN STONE ROADS. 1681. Of What They Consist.—A broken stone road consists essentially of a layer, or wearing surface, composed of fragments of broken rock, spread upon a foundation pre- pared toreceive it, the whole being consolidated to a firm, uniform surface by rolling or by the traffic passing over it. The fragments of broken rock so used are sometimes called road-metal. Roads constructed of broken stone are classi- fied as macadam roads and telford roads, from the 1026 STREETS AND HIGHWAYS. names of their originators. The appearance of the comple- ted roadway is practically the same in both systems, the distinguishing features being in the foundations. Macadam’s system consists essentiaily in spreading and compacting one or more uniform layers of suitable rock broken into cubes of nearly uniform size directly upon an earth foundation which has been previously formed to the proper grade and cross-section and thoroughly compacted by rolling. A cross-section of a macadam road is shown in Fig. 402. Telford’s system is much the same as Macadam’s PITH TTI VAT OE iauisanssistartebatrepaeee Soo a (ibeanawsee, ILD 4 wamraasern’ ay Ue WW MSS L\\ FIG. 402. except that the layer of broken stone forming the wearing surface is spread upon a paved foundation. This paved foundation is formed by blocks of stone from 3 to 8 inches in depth, set close together upon their broadest edges. The _ cross-section of a tel- } ford roadway is shown | in Fig. 403. The blocks ‘ .4 of stone are set upon the SS earth foundation and their sizes graduated according to their position, as shown in the figure. Macadam’s system is the more popular in this country. When properly constructed, it has been found to makea satisfactory roadway, and is considerably cheaper than Telford’s system. The expense of the latter system is too great for it to be available for ordinary country roads. All broken stone roads referred to in this course will be understood to be macadam roads. For those important suburban roads on which the travel is ofa character not requiring a more substantial pavement, and for those country roads on which the travel is of sufficient importance to warrant the outlay, broken stone may be very advantageously used as a road material. It is doubtful, however, whether this material will ever be very generally ISHN STREETS AND HIGHWAYS. 1027 used for country roads, asthe expense of construction and maintenance would, in many cases, be greater than the im- portance of the road would warrant. The cost of construct- ing macadam roads will generally be from about two to five thousand dollars per mile, a cost which, for most country roads, is prohibitory. 1682. Quality of the Broken Stone.—A _ good quality of stone should be selected for road material. The stone should be hard, tough, and elastic, and should have good binding properties. It should offer ahigh degree of resist- ance to abrasion, but need not necessarily be of high crush- ing strength. The stone should also be of such quality as not to soften or deteriorate under the action of the atmos- phere. ‘Toughness and resistance to abrasion are two very essential qualities. The varieties of rock most suitable for road-metal are ¢ra/, syentte, granite, chert, limestone, mica-schist, and quarts. These are named in the order of theirrelative values. Sand- stone, clayey slate, and rock of indurated clayey material are not suitable for road-metal. Sandstone is not suitable because it, has practically no binding properties; the frag- ments do not bind together to forma solid mass, but remain simply an accumulation of separate fragments, which soon become ground and crushed into sand by the traffic. Clayey stones have poor binding qualities, and, when saturated with water, become very soft and easily crush into mud. 1683. Size of Broken Stone.—Before being spread upon the roadway, the stone should be broken into small fragments. The proper size for these will depend, to some extent, upon the nature of the material. The harder and tougher the material, the smaller the fragments should gen- erally be. A common rule requires that the stone shall be broken small enough to pass through a 24-inch ring. It is also a not uncommon practice to use somewhat larger pieces in the bottom courses of the roadway than at the top, the stones at the bottom being from 2 to 3 inches in greatest dimension and those at the surface not more than 2 inches. 1028 STREETS: AN DeHIGAW yo. This is probably a good practice, though it may be doubt- ful whether it is sufficiently advantageous to warrant the additional expense of separating the sizes. Opinions differ as to the best practice. Some advocate the use of stone of uniform size, while others believe that the best results are obtained by using sizes varying from a maximum of about 2 inches down toa minimum ‘of about 2? of an inch. The | fact is, probably, that stone of uniform size will wear more evenly, while variable sizes and the presence of smaller ae, fragments facilitate the binding together of the mass. GRAVEL ROADS. 1684. Where Adaptable.—Where gravel of suitable quality can be obtained in the vicinity, it will generally be the best available material for an ordinary country road. This will be especially the case for roads on which the char- acter of the trafficis hght. Where suitable gravel is obtain- able, the cost of a well-constructed gravel roadway will generally be not more than from one-quarter to one-half that of an equally well constructed macadam roadway. In order to be maintained in equally good condition, however, the gravel roadway will require more attention: and more frequent repairs than the macadam roadway. But it should be understood that, for ordinary travel of a rather light character, it is quite possible to maintain a properly con- structed gravel road in a condition equal to that of a macadam road. The cost of such maintenance, however, would probably be about one and one-half times that of the macadam road. | The subject of gravel roads, and of gravel as a road material, is of great importance in this country, and is deserving of closer attention than it has received. Although gravel is a popular material for road making in the country, because it is well known to be the best natural material available, yet its possibilities as a road material are not well understood. For light travel, a gravel road, properly con- structed and maintained, with thorough drainage, may be an ideal road. STREETS AND HIGHWAYS. 1029 1685. Quality of the Gravel.—Gravel consists of | small fragments of stone, broken from the original bed-rock and more or less rounded by the action of water and ice, the pebbles thus formed generally representing the most en- during portions of the original rock. The varieties of gravel are many and diverse, and the quality varies exceedingly, according to the nature of the original rock, the action of the water, and the extent that the material is affected by decay. On this account it is difficult to make any very definite statements concerning the different varieties of gravel. ; Among the best gravels for road purposes in this country are those known in New England as blue gravels. They consist of fragments of undecayed rock of a trappean nature, and occur in considerable quantities in the northeastern portion of Massachusetts. Gravel composed mainly of white quartz pebbles is of very little value as a road material. These pebbles are very smooth and possess scarcely any binding power; where they constitute more than half the mass, the gravel is usually worthless as a covering material for roads, unless mixed with some binding material. Be- tween these two extremes, that is, between the undecayed trap pebbles, which are the best, and the white quartz pebbles, which have the least value, are the pebbles of syenite, granite, chert, limestone, and mica-schist, occurring > in great variety and widely differing quality, but all pos- sessing more or less value as road material. Much the same qualities are desirable for gravel as a road material as those that have been noticed for broken stone. The gravel for road material should be sharp and com- paratively clean; it should be screened before being spread upon the roadway, in order to separate from it the excess- ively large pebbles and also the injuriously fine and loamy material. If found mingled with a large proportion of clay, it will be worth while to wash it. Gravel for road material should not contain more than one-fourth part sand or clay, and not more than one-half of its pebbles should be com- posed of white quartz. Gravel composed of stones of 1030 STREETS AND HIGHWAYS. angular form, such as is taken from pits, is much better for road purposes than that composed of round or oval pebbles, such as is commonly found in the beds of streams. Where the gravel is composed largely of white quartz, round smooth pebbles, or any material having small cement- ing capacity, a binding material should be added. Probably the best available material for this purpose is the ordinary red or brown iron ore found in nearly ail parts of the country. It is very common in swamps, and is valuable for this purpose even when very impure. Where this ore is not available, a small admixture of clay will serve as a fairly good substitute. EARTH ROADS. 1686. The Conditions.—In many cases, gravel for road material is not obtainable, and the cost of broken stone is so great that the importance of the road will not warrant its.use. In stich cases, the road must be sngde ofssiien material as is available, and this material should be so used as to give the best possible results. Where the travel is not of too heavy a character, a quite satisfactory road can be maintained with ordinary earth material, provided the drainage is thorough. It is well to notice that comparatively few of the earth roads throughout the country are as good as they could easily be made to be. By reason, largely,of improper location, insufficient drainage, and neglect, the average country road is in a condition far from satisfactory during a large portion of each year. By changing the location, where necessary, and by thorough drainage and prompt and systematic re- pairs, the condition of country roads may be greatly im- proved without much additional expenditure. 1687. Materials of Earth Roads.—A thoroughly drained clay road may be quite satisfactory for ordinary travel; even a road constructed of quicksand, if very thor- oughly drained, may sustain light travel fairly well. For such roads, however, thorough drainage of both the surface and subsoil is absolutely essential, and the fact can not be STREETS AND HIGHWAYS. 1031 too strongly emphasized. Clay roads will not generally become so dusty in dry weather as to be unpleasant for travel; but, if not thoroughly drained, they may become nearly or quite impassable in wet weather. Quicksand, when thoroughly saturated with water, will not only be im- passable, but also dangerous. Clean, silicious sand is, of itself, a very poor road material. It has scarcely any binding power and will not pack so as to give a firm, unyielding surface. The value of such sand may be much increased by mixing with it a certain propor- tion of clay as a binding material. A mixture of sand and clay in proper proportions makes a good road material, and the addition of clay to a sand road, or the addition of sand to a clay road, will generally much improve either. The material known as hardpan, which is a general mixture of clay and gravel, is an excellent material for roads. When it contains too large a proportion of clay, clean gravel or sand should be added. Loam, containing a large proportion of decomposed vege- table matter, is about the least valuable of the materials employed for road-making purposes. Loam is composed chiefly of silicious sand, clay, carbonate of lime, and vegetable mold, orhumus. The character of loam varies greatly, ac- cording to the proportions of its different ingredients; its value as a road material will be about in proportion to its freedom from decomposing vegetable matter. ROAD CONSTRUCTION, BROKEN STONE AND GRAVEL ROADS; DRAINAGE AND FOUNDATION. 1688. Drainage System. — The system of drains should generally be constructed first. Where cuttings occur, however, such cuttings as are necessary to form the road- way must be made before the drains are constructed. The ditches and drains should be laid out with care. The arrangement of the drainage system has been noticed quite fully in Art. 1674. The best positions for the side ditches 1032 STREETS AND HIGHWAYS: and subsoil drains will depend principally upon the charac- ter of the soil and the covering material used for the road- way, and also, to some extent, upon the topography of the country. Systematic subsoil drainage will generally be necessary in localities where there is a lack of natural drain- age. . In some cases, however, the subsoil may be quite effectually drained by deep side ditches placed a few feet outside of the outer edges of the roadway. 1689. Preparing the Foundation. — For gravel and macadam roads, the earth foundation of the roadway, which is sometimes called the roadbed, should be formed to the proper grade and cross-section, and thoroughly com- pacted by rolling, before putting on the covering or surface material. The surface line of this earth foundation, which is called the subgrade, should be, when the foundation is finished, at a distance below the grade line equal to the in- tended thickness of the covering material. The earth foundation should slope from the center each way towards the gutter. , This slope’should: asa rule: beat the sates about 1 in 30; that is, the roadway should be given a crown equal to about one-sixtieth of its width, but this crown should be in the form of two uniform slopes falling outwards and connected at the center by a short curve, rather than wholly in the form of a curve. Where the surface of the completed roadway, for a gravel or macadam road, is not materially higher than the Y Yy 7 V7 7 M0 . Fia. 404. natural surface of the ground, the roadbed is formed by excavating a shallow trench of the proper width to receive the covering material. This is clearly shown in Fig. 404, which is the cross-section of a macadam road for which the drainage is effected wholly by the deep side ditches d@ and a. In some cases, flat stones or planks are set on edge along the STREETS AND HIGHWAYS: 1033 outer edges of the roadway, as at c and c’, forming what is called curbing, but this is not usual for country roads. In the figure s is the subgrade; it is at the surface of the road- way foundation. In preparing the foundation, the excavation should be made to sufficient depth to remove the surface soil and all material containing vegetable mold, roots, and decaying matter of any kind. The excavation should, where practic- able, be carried downwards until a satisfactory material, such as firm gravel, compact sand, or true hardpan is reached. If a consolidated undersoil or hardpan is encountered a short distance below the surface, this should not be broken, even if is somewhat above subgrade, as it will afford a better foundation than can be obtained at greater depth. A clay foundation should be thoroughly underdrained. If the ex- cavation extends below subgrade, it should be brought up to subgrade by filling in suitable material, such as gravel, sand, a mixture of sand and clay, etc. The foundation should then be thoroughly compacted by rolling with a heavy roller. After a thorough rolling, the surface will be more or less uneven. The irregularities in the surface must be removed by cutting down the high places and filling in the hollows, after which the rolling is continued. This process is continued until a firm and even surface is obtained. Upon the foundation thus prepared, the covering material is spread, CONSTRUCTING THE ROADWAY. 1690. Applying the Surface Material; Broken Stone.—lIf the covering material is broken stone, it should be applied in layers not exceeding 5 inches in thickness, and each layer thoroughly rolled. As the rolling continues, the hollows formed should be filled with material of small size, so that the surface will be even. On the last layer, the roll- ing should be continued until the material is so compacted that the rolling produces no perceptible motion. The stones will then be bound together in a compact mass. ‘This bind- ing together of the stones is due chiefly to the fine particles T. IV.—41o 1034 STREETS AND HIGHWAYS. and small fragments of stone which are ground and crushed from the larger pieces by the process of rolling. These fine particles form a mortar or cement, which fills the interstices between the stones near the surface and binds them together. This will be especially the case with limestone. When the binding process is thorough, it forms a continuous crust with a hard, smooth surface, which has the appearance of a solid mass and is almost impervious to water. The com- pacting and binding may be assisted by watering moderately during the process of rolling. Water in large quantities, however, would have the opposite effect. The stone dust, or fine fragments of stone formed by the stone-crusher in the process of crushing, if spread upon the surface of the broken stone covering before or during the process of roll- ing, will aid the binding. The necessary thickness of the covering of broken stone will depend upon the nature of the foundation, the thorough- ness of the drainage, the completeness of the binding, and the character of the traffic to be sustained. Less thickness will be required by light travel than by heavy travel; a covering well bound together need not be as thick as an imperfectly bound covering; a firm, thoroughly drained foundation will not require as thick a covering asa less perfect foundation. The thickness of the covering of broken stone should not be less than 4 inches, and a thickness greater than 12 inches will seldom be required. Macadam considered 10 inches of well-compacted broken stone upon a solid, well- drained earth foundation sufficient for a roadway sustain- ing the heaviest traffic. A thickness of from 8 to 10 inches is sufficient in almost all cases. 1691. Construction of Gravel Roadways.—Gravel roads should be constructed in the same general manner as macadam roads, although they may be constructed on a more liberal basis, and the principles of construction need not be so rigidly adhered to. The conditions relating to the preparation of the foundation, thickness of the covering material, and thorough compacting should be substantially STREETS AND HIGHWAYS. 1039 as described above for broken stone roads, although the gravel covering may, with advantage, be made thicker than is necessary for broken stone, and the question of economy is not generally of so great importance. The addition of gravel to an earth road, under almost any circumstances, can scarcely fail to be an improvement. In certain cases, even a light layer of gravel may prove a great benefit. Where the subsoil is of a porous nature and . well drained, a light layer of gravel, well compacted, will effect a very material improvement. Where the material of the roadbed is clay, however, the thickness of the layer of gravel should be not less than 6 inches, and should pref- erably be more. In general, the thickness of the covering of gravel should be from 4 to 12 inches, and even a greater thickness will almost always be beneficial. It is advanta- geous to thoroughly compact both the earth foundation and the gravel covering by rolling. A smooth, firm surface may thus be produced which will be but little affected by the wheels of vehicles. If the rolling is omitted and the compacting left to vehicles, the gravel covering should be quite sharply crowned, as the tendency of the traffic will be to flatten it. EARTH ROADS. 1692. Construction of Earth Roadways; Drain- age.—In the construction of earth roads, the most essential conditions are ordinarily thorough drainage for both the surface and subsoil, and thorough compacting of the road- way surface. Thisis especially the case with roads of clayey material. Roadways of nearly pure sand, however, are injured rather than benefited by thorough drainage, as the sand is more firm and stable-in a damp condition than when dry. Roadways in light soil of a sandy nature, having a good natural drainage, will seldom require artificial drainage. 1693. Proper Use of Materials.—In the prepara- tion of the roadway, all material containing roots and vegetable matter should be removed; if this necessitates excavating below the intended surface of the finished 1036 STREETS AND HIGHWAYS. roadway, the excavation should be refilled with the best material obtainable. Judgment should be exercised in the selection of this filling material. It should be of such char- acter as to improve the condition of the natural foundation when mingled with it. A judicious mixture of sand and clay will make a better road than either material by itself. When clean, coarse sand or gravel is mixed with just sufficient clay to bind the particles together, a very hard and compact mass is formed . that is nearly impervious to water and but little affected by it. Ifthe natural foundation is loose, porous sand, a layer of clay from 4 to 8 inches thick will make a hard and durable road. ‘The sand will keep the clay thoroughly drained, and the clay, when dry, will form an excellent roadway surface. The addition of a small proportion of clean sand will give the clay a better consistency in wet weather. Where the natural foundation is clay, a layer of sand a few inches deep may often be employed with good results. The sand will afford protection to the underlying clay, and will form a surface which will not become soft and unstable in wet weather. 1694. Forming the Roadway.—The roadway should be given a proper crown. Slopes falling outwards each way from the center, at the rate of about 1 in 20, with the cen- tral ridge rounded off, as shown in Fig. 405, will shed the > Vj Yj y Yj water well and make OC Pel) 2 2008 form of cross. Fic. 405. Section — (formvean a roads. The ditches should be made with sides not steeper than about 45 degrees, or 1 to 1. Certain special machines, commonly called road-machines, are manufactured for for the purpose of grading earth roads. The machine con- sists essentially of a large steel blade so mounted on wheels that it can be adjusted to any desired position with refer- ence to the roadway surface. If used intelligently, road- machines can be employed to advantage in the construction of earth roads and earth foundations of gravel and macadam STREETS AND HIGHWAYS. 1037 roads. The blade of the road-machine makes a clean, uni- form cut, giving the surface the proper shape with compara- tively little labor. The use of the road-machine should be guided by intelligence, however; it can easily be so used as to do more harm than good. After the roadway is graded, it should be thoroughly compacted by rolling with a heavy roller. During the process of rolling, all high places should be cut down and all hollows filled, so that the finished roadway will have a smooth and even, as well as a hard and compact, surface. Thorough rolling is very important. If the earth forming the roadway be left 1n a ioose condition, to be compacted by the wheels of traffic, it will pack unevenly and will be more or_less cut up by ruts, which will hold water and cause the formation of mud-holes. If, however, the surface is thoroughly rolled, it may be made sufficiently firm to sus- tain the ordinary traffic, and if kept free from ruts and thoroughly compacted, may be capable of resisting the penetration of the water, and form a very excellent roadway, requiring only occasional repairs. MAINTENANCE OF HIGHWAYS. 1695. Necessity of Constant Attention and Prompt Repairs.—In order to maintain a road in good condition, it must be given constant care and attention. Repairs should be made, not periodically, but whenever necessary. The ditches and drains should always be kept open and in good working condition, weeds should be cut down, and the surface of the roadway should be kept intact. This may be done by immediately filling any small breaks in the surface, and filling and smoothing over the ruts caused by vehicles and the channels washed out during storms, then ‘¢horoughly compacting by rolling. Such re- pairs should be made promptly and before the damage has become serious. This will not only prevent the road from getting in very bad condition, but will also make the cost of repairs a minimum. 1038 STREETS AND HIGHWAYS. 1696. Repairs for Earth Roads.—A road should -not merely be put in good condition occasionally, but it should be eft in good condition at all times. After long- continued rains or the melting of winter snows in the spring, the surfaces of earth roads will necessarily become somewhat softened and will be more or less cut up by the wheels of vehicles. If the roads are in proper condition. at the begin- ning of such wet periods, however, and the drains are kept well open during its continuance, the injury to the roads and the duration of their bad condition will be a minimum. As soon as possible after an extended wet period, the roads should be put in proper form and thoroughly com- pacted by rolling. This should be done while the ground is still somewhat moist and yielding, as it can then be worked more easily and compacted more closely by rolling than after it becomes thoroughly dry and hard. In making re- pairs to an earth or gravel roadway, the road machine may often be used to good advantage, as it affords a ready means of smoothing up the surface. When ruts begin to form in a clay road, it is sometimes advantageous to run a light smoothing harrow over the roadway and then roll thoroughly. 1697. Repairs for Broken Stone Roads.—Broken stone roads will not require repairing as often as earth and gravel roads, but they should, nevertheless, have constant attention. They should be frequently cleaned of all mud and dust. When repairs to the road surface become neces- sary, the best method of doing it will depend somewhat upon the character of the surface material and the weight of the traffic passing overit.. If the surtacesis oieaecere material, wearing easily, it should be repaired promptly whenever a rut or depression appears. Material of this kind binds readily with new material, and repairs may be made without difficulty. The new material for repairs should be the same as that of the road surface; it may be placed upon the roadway in small amounts and compacted by the traffic. STREETS AND HIGHWAYS. 1039 Where the surface material is hard and durable, it will wear quite evenly and require very little in the way of small repairs. But it will not unite readily with a thin coating of new material, and when repairs become necessary, it will usually be more satisfactory to make more extensive repairs, putting on sufficient new material to form an additional layer. If only a thin layer of new material is added, it will often be.necessary to first break the bond of the old material by picking or otherwise loosening it at the surface, so that it will firmly unite with the new material. 1698. Size of Wheels; Wide Tires.—Closely as- sociated with the subject of road maintenance is that of the size and shape of the wheels on the vehicles that pass over the roads. Small wheels and narrow tires have a much more injurious effect upon the roadway than do large wheels and broad tires. It should also be noticed that vehicles with springs have a less injurious effect upon the roadway than those having no springs. ‘The exact relation between diameter of wheel and resistance of rolling friction is not well defined; but the general fact is known that the greater the diameter of the wheel, the less will be the resist- ance. On this account, and because, also, wheels of large diameter have greater bearing surface upon the roadway than those of small diameter, the larger wheels have the less injurious effect upon the roadway. In this country, how- ever, wheels of small diameter are very little used on vehicles employed for carrying heavy loads, especially in rural districts. Wide tires also have a much less injurious effect upon the roadway than narrow tires. The wide tires distribute the weight over a greater bearing surface, and, the weight being the same, the pressure per square inch upon the surface of the roadway will be less than in the case of the narrow tires. The wide tires do not cut into the roadway and form ruts, as do the narrow tires, but, acting as rollers, tend to com- pact the roadway. Wide tires would probably not have been practicable for the early roads of this country, which 1040 STREETS AND HIGHWAYS. were necessarily very rough, but as the roads become im- proved, the use of wide tires on all heavily loaded vehicles becomes practicable and very desirable. As is to be expected, there is some difference of opinion with regard to how wide the wagon tires should be. The best width of tire will de- pend upon the weight of the load and the character and con- dition of the roadway surface; as these vary greatly, no general rule can be stated for the width of tire that will be entirely satisfactory. Perhaps as near an approach to a satisfactory general rule for the width of tire would: be as follows: Rule.—7he tires of all freight wagons should have a wrath of not less than one inch for each 1,200 pounds of total load upon four wheels, or 300 pounds upon each wheel, with a minimum width of 24 inches. Thus, for a four-wheeled wagon carrying a load of 3 net tons, or 6,000 pounds, the width of tire should not be less 0 than ae = § inches. 1,200 5 inches CITY STREETS AND AVENUES. LOCATION AND ARRANGEMENT. 1699. General Statement of Conditions.—The principles of location, construction, and maintenance, as relating to ordinary country roads, have been studied in the preceding pages. Such applications of the principles involved are quite simple. In cities, however, the condi- tions are more complex, and, on account of the closer limitations and the different interests involved, the problem becomes more complicated. Better roadways are required, because the traffic is of a heavier character and much more dense; and a better class of work is possible, because of the more ample means provided. Consequently, the principles of good construction must be more rigidly adhered to, while, at the same time, their application is generally more difficult. The principles which have been studied in their STREETS AND HIGHWAYS., 1041 application to country roads will now be studied in their application to city streets. 1700. Of What the Location of City Streets Con- sists.—City streets are not located in the same manner as country roads, although the principles governing the loca- tion of country roads should also be considered and, so far as practicable, complied with in determining the positions of city streets. Certain conditions, however, which do not affect the location of country roads exert a great influence in the location of city streets. In locating a road through the country, considerable freedom of choice can usually be exercised; the property interests involved will not generally be such as to prevent the road from being located in nearly, if not quite, the most favorable position with reference to construction and maintenance. In cities, however, it is quite otherwise. Property is very valuable, and, in order to utilize the entire tract to the best advantage and make it to the greatest possible extent available for business and residence purposes, it is necessary that the streets be laid out according to some definite plan or system that will give easy communication between all parts of the city. Consequently, the position of each street must be considered with reference to the positions of other streets. To do this is virtually to plan the town site. Some of the important matters to be considered in laying out town sites will now be noticed. The subject of town sites is also treated in the section on Land Surveying, which the student should reread carefully before proceeding. 1701. Purpose and Best Arrangement of Streets.—The streets of a city are for the purpose of affording direct and easy communication between its dif- ferent parts, and giving convenient access to all places of business and residence. ‘This, being the purpose for which streets are built, is the most important condition to be con- sidered, and should be kept well in view in laying out the streets of a city. The system of streets should be so planned as to give the most direct and easy communication 1042 STREETS AND HIGHWAYS. between all parts of the city, and, at the same time, give the greatest amount of frontage available and desirable for business and residence purposes. This can generally be accomplished by the rectangular system of blocks described in the section on Land Surveying. The natural features of many localities, however, will require more or less deviation from any regular system. The conditions will sometimes be such as to require the introduction of diagonal and curved streets in a more or less irregular manner. BLOCKS AND LOTS. 1702. Form of Blocks.—The rectangular form of blocks can be the most advantageously subdivided into building lots, and the streets so formed are convenient for communication, if occasional diagonal avenues are provided along the lines of most frequent travel extending in such directions. The rectangular form of blocks also permits such a systematic arrangement of names and numbers that, to any one familiar with the system, the locality of a place will be evident from its address. The form of the blocks will necessarily depend largely upon the arrangement of the streets. The introduction of diagonal avenues and curved streets into a rectangular system will give a more or less irregular form to the blocks adjacent to such streets and avenues. Blocks adjoining a river or other body of water, or adjoining a railroad that is not parallel with the streets, will necessarily be more or less irregular also. The form of such irregular blocks will be governed wholly by the arrangement of the streets and such other matters as must necessarily be considered in connection therewith. Where there are no curved or diagonal streets or other features requiring blocks of irregular form, the blocks should be laid out rectangular in form and uniform in size. 1703. Most Advantageous Form of Blocks.— Though the blocks should preferably be rectangular, they should not be square. The form of block that is generally most advantageous is rather more than twice as long as it STREETS AND HIGHWAYS. 1043 is wide. The distance between streets in one direction should only be what is necessary for the proper depths of the lots facing upon the two streets, while in the other direction the streets need only be close enough together to conveniently accommodate the traffic. A quite satisfactory form may be obtained for the blocks by first laying them out in large squares having the length of each side equal to four times the depth of a lot plus the width of one street. An intermediate street can then be laid out in either direction through the middle of each square, thus dividing it into two blocks of a desirable form, as shown in Fig. 406. This arrangement is also convenient for laying out the diagonal avenues, as, when desirable, the intermediate street may be omitted in those squares through which the diagonal avenues extend. Fic. 406. Fic. 407. The intermediate streets may be laid out in different directions through the different squares, when so desired, but it is generally much better to have them all extend in the same direction, so as to be continuous. In order to afford convenient access to the rear of the lots for the delivery of merchandise, etc., an alley may extend lengthwise through the middle of each block, as shown in Fig. 407. Such an alley will be found a great convenience in residence blocks, and scarcely less than a necessity in business blocks. In any case, the value of the alley as a matter of convenience to the occupant of each lot will be much greater than would be the value of one-half the width of the alley added to the depth of the lot. Comparatively 1044 STREETS: AND HIGHWAY=s: little advantage is to be derived, however, from alleys extending across the block. 1704. Size of Blocks.—The size, as well asthe form, of blocks will necessarily depend, to some extent, upon the arrangement of the streets. This will be especially the case with such irregular blocks as are formed by the introduction of diagonal and curved streets. The sizes of such blocks will be governed almost wholly by whatever conditions require them to be of irregular form, and little else can be said with reference to their sizes, except that they should, so far as possible, be given such dimensions as can be advan- tageously divided into desirable lots. In subdividing them into lots, each block should be divided in such manner as may be most advantageous for that particular block, but with some regard also to the manner in which the other blocks are divided. Where the blocks are rectangular, their sizes will depend somewhat upon the size of the tract that is being laid out, for it will evidently be necessary for the sizes of the blocks to be such as to advantageously divide up the entire tract. If the tract to be laid out is an addition to a city, the sizes of the blocks should be governed chiefly by the sizes of the blocks and the positions of the streets in the adjoining por- tion of the city. When not affected by these conditions, the blocks should be uniformly of such size as can be divided into lots of the-desired ‘size,. By reference to Fig? 406-it will be seen that where there are no alleys through the blocks, the width of each block is equal to twice the depth of the lots. Where an alley extends lengthwise through each block, as in Fig. 407, the width of the block will be equal to twice the depth of the lots plus the width of the alley. The length of a block may be approximately equal to, or somewhat greater than, twice its width, as indicated in the preceding article. The length of a block, however, must be so adjusted as to be divided into lots of the desired width, and must often be modified to accommodate other conditions. STREETS AND HIGHWAYS. 1045 1705. Size of Lots.—The sizes of lots vary greatly in different cities and often in the different additions of the same city. The lots are seldom less than 90 or more than 160 feet in depth, however, or less than 25 or more than 75 feet in width. | As arule, the lots are larger in small towns and villages than in large and densely populated cities. In towns situated in agricultural districts, a customary size is 66 feet in width by 132 feet in depth (1. e., 4 by 8 rods). On the mercantile streets of such towns, there are usually three ‘¢doors ” or business places to each lot, making the width of ; 66 Si each business place equal to - = gaitect. «In cities. of. can- siderable size, 40 feet in width by 150 feet in depth is a common size. In large cities, sizes of 25 by 100 feet are common. STREETS AND AVENUES. 1706. System of Streets and Avenues.—lIf the streets extending in one direction are about twice as far apart as those extending in the other direction, i. e., at right angles, and the total volume of travel is approximately the same in both directions, it is evident that the streets that are the further apart should be about twice as wide as those that are nearer together, in order to equally accom- modate the travel that will come upon them. For each one of the streets that are farther apart must accommodate about twice as much travel as each one of those that are nearer together. Accordingly, these thoroughfares which extend in one direction and are at a considerable distance apart are made much wider than those which extend in the other direction and are nearer together. In such cases, the broader thoroughfares extending in one direction are called avenues, and the narrower ones extending in the other direction are called streets. Such a system of streets and avenues is shown in Fig. 408. The streets extend in one direction and the avenues in the other, with an avenue extending diagonally through the 1046 STREETS AND HIGHWAYS: system. The primary system of square blocks is shown by full lines, and the intermediate streets laid out through these blocks are shown by dotted lines. Second street is shown as continuous through all blocks, but Fourth and Sixth streets are not shown continuous through those blocks through which the diagonal avenue passes. For the con- ditions common to most locations, this is probably the best general system that can be devised for laying out streets and avenues. In order to suit the conditions of each special Avenue D. 3rd Street. 6th Street. %th Street. 9th Street. 5th Street. Ist Street. _2nd Street. eS Z] Avenue A. Fic. 408. case, the system should, of course, be more or less modified when necessary. 1707. Complete and Systematic Arrangement of Streets; Growth of Cities.—The arrangement of the streets should, in all cases, be systematic, both with reference to the complete plan and to possible future exten- sions ; it should be such as to provide the most direct com- munication possible between different parts of the city. In order to most conveniently accommodate the travel, each street should, if possible, be continuous throughout the extent of the city. By causing the travel between different parts of the city to take indirect and devious routes, much needless inconvenience and waste of time may result from an unsystematic and non-continuous arrangement of the streets. | STREETS AND HIGHWAYS. 1047 If a city could be laid out complete in the beginning, and the requirements of the travel between different portions could be foreseen, there would be no difficulty in so planning the system of streets as to best accommodate the travel. But this is never the case. The growth of cities is often very irregular, and it is difficult to foretell either its magnitude or its rate. ADDITIONS. 1708. Anticipated and Actual Growth; Addi- tions.—In some cases, where large areas have been laid out in the anticipation of founding large cities, the expectations have not been realized, and only villages or small towns have grown up. In such cases, whatever development occurs will generally consist in the occupation and building up of a portion of the area originally laid out, and will usually conform to the original system. The more common case, however, is of just the opposite nature. in many places, large cities have grown up where only small town sites were originally laid out. In suchcases, as the growth of the city demands it, additional areas, called additions, subdivisions, or extensions, are laid out adjacent to the outer limits of the original plot, and, as these additions become occupied and built up, the city is still further extended by laying out other additions adjacent to the outer limits of the older additions. The area of the city, as thus developed, will consist of a quite irregular patchwork formed by the original plot and the various - additions. 1709. Common Method of Laying Out Addi- tions.—Each tract of land laid out as an addition to a city will generally represent an individual interest. That is, the tract of land, when laid out as an addition, will be owned by an individual or by an association of individuals, called a syndicate. The owner of the tract, becoming convinced that it can be disposed of at a good profit if divided into city lots, will proceed to lay it out asanaddition. The chief aim of the owner will be so to divide up the tract as to obtain 1048 STREETS AND HIGHWAYS. the greatest possible number of salable lots, regardless of all other considerations. Unless the matter of laying out new additions to a city is regulated by municipal legislation, the streets will seldom be continuous and uniform through the different additions, but many streets will have jogs or offsets, others will extend only through one addition, while others will have different widths in the different additions through which they pass. The engineer employed to lay out an addition will often be required to make his work conform to whatever ideas the owner may have formed concerning it, but he should endeavor, so far as possible, to make the system of streets harmonize with the streets of the adjoining additions. Such matters should properly be regulated by municipal legisla- tion, but they. seldom are so regulated. The owner of the tract generally lays out the addition to suit his own interest or convenience, and dedicates the streets to the city; the legislative body of the city then usually goes through the formality of accepting the addition, without much regard to whether it harmonizes with the adjoining additions. 1710. Example of Liberal Plans; City of Wash- ington.—An excellent example of the liberal and system- atic arrangement of the streets in laying out the original plan of acity, and also of the irregular and unsystematic extension of the suburbs is given by the city of Washington. The plan of the city was originated by Major L’Enfant, a young officer of the engineer corps of the French army that aided in this country in the Revolutionary struggle; the plan was approved by President Washington, and the city was laid out in accordance therewith by Andrew Ellicott, about the year 1791. The rectangular form of blocks was adopted, and the streets were laid out on a very liberal and systematic basis. The streets extend north and south, and east and west, crossing each other at right angles. From the capital as a center, the streets extending east and west are named A, B, C streets, etc., in order north and south; while those ex- ~ STREETS AND HIGHWAYS. 1049 tending north and south are named First, Second, Third streets, etc., in order east and west. There is also an elaborate system of diagonal avenues, named after the dif- ferent States, several of which radiate from the Capitol. The generous and extended system of streets and avenues indicates that the city was laid out, either with a view to its becoming a vast metropolis, or with a very accurate con- ception of its future importance and requirements as the UY HS | ET | RO / Sw oe DEP Gas | eee ICME SOO _ EDT aSS22 at) ( JSNOWOOLIUGUU0 ALY ALI oS 1 SENG SRR Ae Oo SCAMS DOAN RD Ac ID ooo OOS S200 bar NO a alls bau Rte AJA CULL” ee ay Fic. 409. Capital City of the country. At all events, the original plan of the city proved adequate for its development during the greater part of a century. In Fig. 409 is shown a portion of the city of Washington, including a part of the original plan, with the adjacent suburban additions, Of the area here shown, the portion that was laid out in the original plan is easily recognized. It consists of a rectangular system of blocks with a quite T. IV.—I6 1050 STREETS AND HIGHWAYS. elaborate system of diagonal avenues, generally having open squares or circles at their intersections. The streets and avenues of this portion are planned according to a quite complete and regular system. On the other hand, the streets of the suburban additions here shown are laid out in a very irregular manner, and are wholly without system or harmony. Many of the streets are short and inconvenient of access, where they could just as well have been continuous and convenient. In some cases, the streets of adjoining additions do not connect with each other. Asa result of this poor arrangement, property in this vicinity must certainly have less value than if the streets were laid out according to a regular and _ har- monious system. All street extensions within the District of Columbia are now, however, required by law to conform to the general plan of the city of Washington; the effect of this is that the regular street lines of the city are gradually being extended into the suburbs, and the suburban additions are gradually being made to harmonize with the systematic plan of ‘the city.. The expense of doing ithis» however mis ai doubtedly great; it could easily have been avoided had the proper legislation been enacted in time. But the legislative bodies did not as clearly foresee the future requirements of the city as did the able engineer who laid out the original plan. GENERAL MATTERS. 1711. Consideration of Topographical Features. —While the arrangement of the streets of a city should be such as to give direct and easy communication between, and convenient access to, all places of business and residence, the arrangement that will best accomplish these ends will always depend more or less upon the natural topographical features of the locality. The matter of grades must be carefully considered—much more carefully even for city streets than for country roads. The more important the thoroughfare, and the greater the volume and heavier the character of the traffic, the more important. becomes the STREETS AND HIGHWAYS. 1051 matter of grades. Steep grades should be avoided wherever possible; the grades onimportant thoroughfares, especially, should never be steep, if it is possible to obtain easy grades. It is much better for an important thoroughfare to be located around a hill than over it. If steep grades are un- avoidable on some streets, the grades should, if possible, be so arranged that the steep grades will occur on comparatively unimportant streets. In hilly localities, therefore, the consideration of easy grades may often require material deviation from the rect- angular system of blocks, although, in some cases, it may be possible to retain the main features of the rectangular system, and so lay out the system of diagonal avenues as to allow the main volume of travel to pass around the hills on easy grades. 1712. Curved Streets.—In order to obtain easy or even tolerable grades, it will sometimes be necessary to in- troduce curved or crooked streets in a more or less irregular manner. Curves may often be advantageously employed on residence streets to effect a reduction of grades or saving of earthwork. In some cases, the esthetic effect may aiso be much enhanced by the use of curved lines for the streets. The direction of the street should never be changed by an abrupt bend, except at the intersection of another street. Where curves and other irregularities in the arrangement of the streets occur, great care should be exercised to avoid the introduction of short streets in an irregular manner. In all cases, the streets should be, so far as possible, con- tinuous, and the arrangement should adhere as closely as possible to some well-defined system. The straight and curved streets should be arranged harmoniously. 1713. Parks.—The fact that growing vegetation is an important factor in purifying the air makes it desirable that parks be laid out at frequent intervals throughout the densely populated portions of a city. It is not necessary for these parks to be large and elaborately laid out, but they should be numerous, to serve as fresh-air spaces in the 1052 STREETS AND HIGHWAYS. crowded portions of a city. The smail triangular pieces cut off by the intersection of diagonal streets, or other irregularly shaped pieces not suitable for buildings, can very advantageously be laid out as small parks. Such parks, though they consist only of grass lawns containing a few trees, will serve to ornament the city and considerably raise the value of adjacent property, and, at thé same time, will tend to keep the air in the vicinity purer than it otherwise would be. At suitable localities throughout the city, entire blocks, and even much larger tracts, should be laid out as parks. Blocks of irregular shape, such as those formed by curved and diagonal streets, should generally be selected. Such blocks will not only be less advantageous for building upon, but will also generally present a better appearance when laid out as parks than will the blocks of rectangular form. Tracts of ground that are too rough and precipitous to be conveniently built upon are quite suitable for parks, and can generally be devoted to such purposes with excellent results. MATTERS RELATING TO PRACTICAL FORM | AND DETAILS. WIDTH OF STREETS. 1714. Importance of Great Widths.—The width of ‘city streets 1s a’ subject that does not receive the.con- sideration it properly deserves. The subject is very im- portant, not only as relating to the convenience of travel, but also as affecting the health and comfort of those whose residences or places of business occupy the streets. For, in closely built-up districts, the width of the streets will practically determine the amount of light and air that can penetrate into the buildings. The width of street here referred to is, of course, the total width between property lines. It is often the case that convenience to travel is the only condition considered in laying outa street, and this is but imperfectly considered; if the street is wide enough to accommodate the travel that is likely to come STREETS AND HIGHWAYS. 1053 upon it, then it is thought to be wide enough forall possible purposes, and no other condition is thought to be of suffi- cient importance to be considered. This, however, is a great mistake, for all conditions affecting the health and comfort of the residents are of great importance and should be carefully considered. 1715. The Usual Widths.—In the different cities of this country, the streets and avenues are laid out in various widths, but generally between the minimum and maximum limits of 50: and 200 feet. Widths of 60, 66, 75, 80, and 90 feet are commonly used for streets, and the widths of avenues are commonly 100, 120, 125, 150, and 160 feet. 1716. Streets Are Commonly Too Narrow.—In nearly all the large cities, the streets, as laid out, are too narrow. They are generally quite overcrowded by the travel. In closely built up districts, they are also usually quite dingy; the adjoining buildings have meager hght and insufficient ventilation, and are often more or less damp. Such conditions are evidently quite unsanitary. They prevail, to a great extent, on streets of large cities that are closely built up with tall buildings. Property adjoining such streets certainly can not be as valuable as though the streets were wide enough to permit air and light to penetrate freely into the buildings. The reason that the streets of large cities are so com- monly narrower than they should be is chiefly because the future of a city can not be foreseen when the streets are laid out. In many cases, what had been laid out for an ordinary town has developed into a great city, requiring many new additions and extensions to be laid out. Each new addition is commonly laid out merely as a residence suburb, and if, as is usually the case, there is no law regulating suburban extensions, the owners of the property, interested only in getting as many salable lots out of it as possible, will gen- erally make the streets as narrow as possible without injur- ing the sale of the lots. As long as the tract so laid out re- mains an uncrowded residence suburb, with residences set 1054 STREETS AND HIGHWAY: well back from the street and having spacious lawns, the narrow streets will be reasonably satisfactory. During the growth of the city, however, the nature of many localities will become materially changed. Districts devoted to trade will be occupied by manufacturing plants, the mercantile interests will encroach upon the inner residence districts, and the sparsely settled suburbs will become closely built up residence districts. The width of street sufficient for the uncrowded suburbs with residences set well back from the street will be quite unsatisfactory for the closely built up district with houses set out to the property line. It would be still less satisfactory if the streets were built up solidly with very tall buildings. 1717. Widthsin the City of Washington.—-In the city of Washington, the streets are generally 70, 80, 90, 100, and 110 feetin width, though one important street is 160 feet wide, and one short, unimportant street is only 40 feet wide. Almost all the avenues are 160 wide, though a few have widths of 130, 120, and 85 feet. The law now requires that, in laying out new streets and avenues, the width shall not be less than 90 feet for streets or 120 feet for avenues, interes mediate streets, called places, may be laid out within blocks with a width of 60 feet, but the distance between full width streets must not be more than 600 feet. This city probably has the best and most liberal system of streets of any Ameri- cancity. The beneficial results of its liberal policy with re- gard to streets are evident in itslarge growth and popularity as a residence city, and the corresponding property values, as well as in the greater comfort of its inhabitants. 1718. Suitable Widths for Streets.—In cities of large size, where the houses are built closely together and extend out to the property line, the residence streets should, if possible, have widths of not less than from 80 to 100 feet, in order to present a good appearance and afford plenty of light and air. For outlying suburbs with ijarge lawns, a width of 60 feet may be satisfactory for the streets, thougha greater width is to be preferred. In large cities, however, STREETS AND HIGHWAYS. 1055 such suburbs are always liable to become densely built up districts, and for such cities a greater width is very much to be preferred. Moreover, a lot 120 feet deep upon a street 80 feet wide will generally be more valuable than a lot 130 feet deep upon a street 60 feet wide. As a rule, important commercial thoroughfares should never be less than 100 feet in width, and, if lable to be occupied by street-railway tracks or bordered by very tall buildings, they should be much wider. In many towns, a width of 4 rods, or 66 feet, is adopted for all but the more important streets, and this is a reasonably satisfactory width for streets that are never liable to become thoroughfares of commerce. ‘That is, it isa fairly good width for the resi- dence streets of towns that are so situated as not to be likely to ever become important commercial centers. For really satisfactory and desirable streets, however, greater width is necessary. THE ROADWAY. WIDTH AND CROSS-SECTION. 1719. Width of Roadway.—What is said above relates to the total width of streets between property lines. This width will not necessarily be wholly occupied by the pavements. Indeed, except in important business thorough- fares, it is seldom that the entire width of a street is occu- pied by the roadway and sidewalks. As the width of these can be easily changed whenever the pavement is renewed, they should always correspond with the immediate require- ments of the traffic passing over them. ‘The width should, of course, always be sufficient to easily accommodate the traffic, but widths materially greater are disadvantageous. The width of the roadway should be such that it will a// be used. The width necessary to accommodate the traffic will, of course, depend upon the volume and character of the latter. A width of 80 feet will usually be sufficient for the roadway of a crowded commercial thoroughfare in a large city, while a width of 60 feet will accommodate the traffic of 1056 STREETS (AND HIGHW ferme. a very important business street. For many -business streets, a width of 50 feet will be ample for the roadway, while for others, a widthof 40 feet will be sufficient. For residence streets, the width of roadway should generally be from 24 to 36 feet, according to the importance of the street and its position with reference to the routes of greatest travel. The widths of the roadways on important residence streets of an American city of about 100,000 inhabitants are being re- duced, as the streets are paved, from 34 to 30 feet; the for- mer width having been found to be greater than is required, considerable saving in the cost of paving and maintenance is effected by reducing the width. When no portion of the roadway is occupied by street-railway tracks, a width of 24 feet will accommodate a very large amount of light driving, and will be sufficient for many residence streets not situated along the main lines of travel. Even less width will some- times be sufficient for roadways in smalltowns and villages. On streets of light traffic, the roadway should be narrowed to the width really required; this will beadvantageous rather than otherwise, as it will often permit the narrow roadway to be improved much more than it would be possible to improve the wider roadway with the funds available. 1720. Cross-Section of Roadway.—lIn its relation to country roads, this subject was noticed in Art. 1672. What is here stated relates more particularly to the cross- section of citystreets. Experience has shown that it is necessary to provide gutters or side ditches along the outer edges of the roadway, in order to carry away the surface- water, and that, in order that the water falling upon the surface of the roadway may be thrown off into the side gut- ters, the center of the roadway must be made higher thanits outer edges. The form of cross-section that will best accommodate these conditions will depend chiefly upon the character of the roadway surface and the nature of the traffic sustained upon it. Before a roadway is paved, its cross-section will havea more or less irregular form and will but roughly approx- STREETS AND HIGHWAYS. 1057 imate any theoretical figure. Unpaved roadways, however, are generally so laid out and graded as to more or less closely approximate some theoretical form of cross-section. When a street is paved, it is givena definite cross-section, the form of which will depend upon the kind of pavement, the grade of the roadway, the nature of the traffic, and the ideas of the engineer in charge of the work. Some kind of gutter is always provided along each outer edge of the roadway, and the roadway between the gutters is elevated by giving ita convex form. The elevation given to a roadway between the gutters iscalled the crown, and a roadway so elevated is said to be crowned. CROWN. 1721. Amount of Crown.—The highest point in the crown of a roadway, that is, the highest point in the surface line of its cross-section, will here be called the summit of the crown. The height of thesummit of the crown above a straight line through the outer edges of a roadway, or bottoms of the gutters, will be designated as the amount of crown, and also asthe height of crown. The amount of crown necessary to efficiently throw off the surface water into the side gutters and, at the same time, cause no incon- venience to the traffic, will depend chiefly upon the character of the roadway surface andits grade. The crown or lateral slope of the roadway should never be so great as to cause inconvenient tipping of vehicles in driving on the side of the roadway, as this would cause the traffic to follow the center of the roadway, with the effect of rapidly wearing away that por- tion and destroying the crown. The more smooth and per- fect the roadway surface, the more easily will the water flow off, and, consequently, the less will it need to be crowned. Well-paved streets will require much less crown than ordinary earth roads. For paved roadways, the crown, or lateral slope, should be less on steep than on flat or level grades. This will make the roadway surface somewhat less slippery and in- convenient for travel on steep grades, while there will gen- erally be no difficulty about the water reaching the gutters 1058 STREETS AND HIGHWAYS. without damage to the roadway, if it is paved. On the other hand, for an earth or gravel roadway that would be liable to become damaged by the water following the road- way and washing out gulleys and channels in flowing down steep inclines, the crown, or lateral slope, of the roadway should be zucreased on steep grades, in order to more quickly throw off the water into the side gutters and, so far as possible, prevent it from flowing down the roadway. In spite of such precaution, however, if the roadway is not con- stantly kept in good repair, water will flow along in the wheel ruts and in the depressions worn by the horses’ feet, and do more or less damage on steep inclines. 1722. Formula for Amount of Crown.—It is im- possible to express the above conditions in exact mathemat- ical formulas. Hence, no really satisfactory formula for the amount of crown can be given. As the amount of crown should generally be proportional to the width of road- way, however, we may write, for a comparatively level grade, the formula 70g —1 C= [7 +2" ao , (205.) in which ¢c is the amount of crown, or height of the center of the roadway above its outer edges; w is the width of the roadway; fis the per cent. of grade, or rise per 100 units (usually feet) of horizontal length, and gq is a coefficient relating to the character and condition of the roadway sur- face. No. exact; values-can be voiven fons tom direc kinds of roadways, however, it may generally have values about as given in the table of Coefficients for Roadway Crowns (Tables and Formulas). For ‘a level grade, 7 =o. andi yew. 1723. Exampie.—(a) A common earth roadway 24 feet wide has a grade of 5 per cent. How much crown should it have ? SOLUTION.—As given in the table referred to in the preceding article, the value of g fora common earth roadway is 7. By apply- STREETS AND HIGHWAYS. 1059 ing formula 205, and using this value of g, the required amount of crown is found to be a4. 24K 5X G—D) _ wor att ae BGs ee of afoot. Ans. EXAMPLE.—(4) A roadway 48 feet wide, paved with asphalt, has a grade of 1.44 per cent. How much crown should it have ? SOLUTION.—By applying formula 205, and using the value of gas given for asphalt in the table, the required amount of crown is found to be 48 48x 1.44 x (5 —1) __ Ties Bae SO La .064 of afoot. Ans. EXAMPLES FOR PRACTICE. 1. A roadway 35 feet wide, paved with wooden block pavement, has a grade of 6 per cent. How much crown should it have ? Ans. 0.50 ft. 2. An ordinary gravel roadway 20 feet wide hasa grade of 4 per cent. How much crown should it have? Ans. 0.44 ft. 3. A roadway 60 feet wide, paved with brick, hasa grade of 2 per cent. How much crown should it have ? Ans. 0.555 ft. 4. A common earth roadway 16 feet wide has a grade of 9 per cent. How much crown should it have ? Ans. 0.535 ft. 5. A broken stone roadway 24 feet wide has a grade of 3 per cent. How much crown should it have ? Ans. 0.415 ft. 6. A roadway 36 feet wide is paved with granite block pavement. If it has a grade of 4 per cent., how much crown should it have ? Ans. 0.36 ft. 1724. Form of Crown.—With reference to the man- ner in which the crown of the roadway is effected, two different forms of cross-section are advocated and used. In one form, the surface line of the cross-section is the arc of acircle or a similarcurve. This form of cross-section is shown in Fig. 410; it will here be designated as a curving crown. As will be noticed in the figure, a considerable portion of the roadway surface adjacent to the center, in this form of cross-section, is nearly level, while near the outer edges the lateral slope of the roadway is quite steep. The tendency of this will be to cause the greater part of the traffic to follow the center of the roadway, producing the greatest wear upon that portion. 1060 STREETS AND HIGHWAYS In the other form of cross-section, the surface line consists of two straight lines having the proper inclination and con- nected by a short curve at the center of the roadway, as Yili NS OOM. UY YUYU&mgygyKxs4j;zjyn Y VI a Fic. 410. shown in Fig. 411. The length of the curve at the center is generally made about five feet, or a little more than the width of anordinary carriage. In this form of cross-section, which will be designated as a sloping crown, the lateral slope of each side of the roadway extends uniformly to the gutter, and the width of the nearly level portion at the center is greatly reduced. This obtains a more efficient drainage, and, at the same time, permits teams to drive near a w. — ay tj (SALTED A Wb lsd fli tiys tig sess 22p99- ia LZ Mis Y/Y Wf Y////7 YH YW . Y/ Fic. 411. the curbing with nearly as much comfort as upon any other portion of the roadway. 1725. Elevations on Cross-Section.—In laying out the cross-section of a roadway, it is necessary to determine the elevations of the surface at different points across the roadway. In nearly all cases, whether the roadways have curving or sloping crowns, the summit of the crown is at the center of the roadway, and the slopes of the sides are symmetrical with reference to the center... uch a, crows will here be called a symmetrical crown. In this and the three following articles, symmetrical crowns only are considered. The grade line of roadway represents the elevation of the summit of the crown. Consequently, for any cross-section having a symmetrical crown, the elevation of the roadway surface at the center is given directly by the grade line, and the eievation of any other point in the surface of the cross- section must be: referred, tothe cievation, of otade mre STREETS AND HIGHWAYS. 1061 elevation of any point in the surface of the cross-section, other than the center or summit, must be determined by its distance below the grade line. Thedistance of any point in the surface of the cross-section below the grade line, or summit of the crown, may be easily determined by means of the rectangular coordinates of the point, taking the origin of the summit of the crown. (See Arts. 1464 to 1472.) 1726. Coordinates to Curving Crown.—For a cross-section having a curved surface line, as shown in Fig. 410, 2 good form is given by a circular curve. The equation of the curve, however, will be more simple for a parabolic than for a circular curve, and as, for so flat an arc, the two curves will be practically identical, the parabolic curve will be used. With this curve, if + and y are, respect- ively, the abscissa and ordinate to any point / in the surface line of the cross-section, with the origin at the center 0, as shown in Fig. 412, the value of y for any corresponding value of 1, or, in other words, the distance of the given point below a horizontal line tangent to the roadway surface at the center, will be given by the formula ett x? S Deraae rr eae (206.) in which ¢ is the amount of crown, and w is the width of roadway, both in feet, as shown in Fig. 412. In this figure, the amount of crown is, for clearness, somewhat exaggerated. 1727. Coordinates to Sloping Crown.—A cross- section having a symmetrical sloping crown is shown in Fig. 413, the amount of crown being somewhat exaggerated. In this figure, as in Fig. 412, cand ware, respectively, the crown and width of the roadway, while x and y are the abscissa and 1062 STREETS AND HIGHWAYS, ordinate, respectively, of any point f inthe surface line of the cross-section, with reference to an origin at the center 0 of the roadway. The two sides of the roadway, or portions tg and ?@ g' of the surface line of the cross-section, have a uniform slope, while the portion ¢ ¢’ or 6 is a short parabolic curve which joins the two slope lines and is tangent to them. oy | ea Rae SES aL oS re te ee ee Le i FIG. 413. The rate s of lateral slope for these uniformly sloping portions of the roadway surface is given approximately by the formula ee 7 Oe ah (207.) The coordinates of any point on the curved portion of the cross-section are given by the formula eh At the tangent point ¢, where the curve portion of the surface line joins the straight slope line, the abscissa + will b ces ib ae have the value —; by substituting this value for x in formula 6)? 208, and reducing, the ordinate becomes b y= —. (209.) The coordinates to any point f along the straight slope line ag will be given by the formula ens (« = ) (210.) This formula may, if desired, be used instead of formula 209; for, at the tangent point 7, the abscissa x will be b 9” will reduce it to the form of formula 209, equal to —, and this value substituted for + in formula 210 STREETS AND HIGHWAYS. 1063 rine EXAMPLE.—(a) If the roadway described in example (a) of Art. 1723 be given the amount of crown as there determined, in the form of a curving crown, what will be the ordinate to a point in the surface line of the cross-section distant 8 feet from the center of the roadway ? SOLUTION.—The width of the roadway, as given in the example referred to, is 24 feet, and the crown is .7125 of a foot; the abscissa +, or distance of the given point from the center of the roadway, is 8 feet. By formula 206, which applies to curving crowns, the value of the 4 .'7125 « 8? 942 ml = .3167 of a foot, very nearly. ordinate y is found to be Ans. EXxAMPLE.—(é) If the roadway described in example (2) of Art. 1723 be given the amount of crown there determined, in the form of a slo- ping crown, what will be the ordinate to a point in the surface line of the cross-section 15 feet from the center of the roadway, assuming the length 6 of the central curve to be 5 feet ? SOLUTION.— The width of the roadway, as given in the example referred to, is 48 feet, and the crown is .364 of a foot; the abscissa +, or distance of the given point from the center of the roadway, is 15 feet and the length 4 of the central curve is 5 feet. By applying formula 207, the rate of slope s in the uniformly sloping portion of the cross- 4X .364 2x 48 —5 By applying formula 210, the value of the ordinate to a point in the roadway surface 15 feet from the center is found to be section is found to be = .016 of a foot per horizontal foot. y = .016 (15 — $) = .22 of a foot. Ans. EXAMPLES FOR PRACTICE. Note.—The following examples relate to those given in Art. 1723. In each case, the width of roadway and amount of crown will be taken as given in the corresponding example of that article. The results will not be carried bevond the fourth decimal place. 1. If the roadway of Example 1 be given a curving crown, what will be the values of the ordinates to the surface line at points in the cross- section, distant, respectively, (a) 2.5 feet, (4) 5 feet, (c) 10 feet, (d) 15 feet, and (¢) 17.5 feet from the center ? (a) .0102 ft. | (6) .0408 ft. Ans. (c) .1683 ft. (d) .3673 ft. (2) .5000 ft. 2. If the roadway of Example 2 be given a sloping crown, with a central curve 8 feet in length, what will be the values of the ordinates to the surface line of the cross-section at points distant (a) 4 feet, 1064 STREETS AND HIGHWAYs: (4) 8 feet, and (c) 10 feet from the center? (@) What will be the rate s of the uniform side slope ? (2) late (6) .38 ft. (c) .44 ft. (2) .055 ft. 3. If the roadway of Example 3 be given a sloping crown, witha central curve 9 feet in length, what will be the ordinates to the surface line of the cross-section at points distant (a) 3 feet, (0) 4.5 feet, (c) 10 feet, (2) 15 feet, (2) 20 feet, and (/) 25 feet from the center? (g) What will be the rate s of the uniform side slope ? (az) .020 ft. (6) .045 ft. (2) Looe Ans. 4 (@) .255 ft. (e) .355 ft. (f) .455 ft. ~ (zg) .020 ft. 4. If the roadway of Example 4 be given a curving crown, what will be the ordinates to the surface line of the cross-section at points distant (a) 4 feet, and (0) 8 feet from the center ? nes ( (a) .1888 ft. ( (0) .585 ft. 5. If the roadway of Example 5 be given a sloping crown, with a central curve 8 feet in length, what will be the ordinates to the surface line of the cross-section at points distant (a) 4 feet, (4) 6 feet, (c) 8 feet, and (@) 10 feet from the center? (é¢) What will be the rate s of the uniform side slope? (a) .088 ft. (0) .166 ft. Ans. { (¢) .249 ft. (@) .382 ft. (e) .0415 ft. 6. If the roadway of Example 6 be given a sloping crown, with a central curve 8 feet in length, what will be the ordinates to the surface line of the cross-section at points distant (a) 4 feet, (4) 8 feet, (c) 12 feet, and (@) 16 feet from the center? (¢) What will be the rate s of the uniform side slope? (a) .045 ft. (6) .135 ft. Ans. (c) .225 ft. (d) .315 ft. (2) .0225 ft. Ans. GUTTERS AND CURBING. 1729. Gutters.—As has been previously stated, some kind of an open channel must be provided along each side of a roadway, to receive the water from the surface of the roadway and convey it toa drainage outlet. Side ditches, STREETS AND HIGHWAYS. 1065 such asare shown in Figs. 400, 401, 404, and 405, would be unsightly, dangerous, and otherwise impracticable for crowded city streets. For the purpose of surface drainage in city streets, therefore, those portions of the roadway adjacent to each outer edge are given such form as to serve as gutters for conveying the water from the surface of the roadway. ‘These gutters are made so shallow as to still be, to some extent, available for driving purposes when not required for drainage purposes. 1730. Forms of Gutters.—Various forms of gutters are used; three different forms are quite common. The YY —Ao-— ® Lie. FIG. 414. form shown in Fig. 414 is the simplest and, all things con- sidered, is probably the most advantageous for well-paved roadways. It is very commonly used with the best pave- ments. Inthis form of gutter, the crown of the roadway is continued regularly to the curb line, the gutter being formed by the angle between the sloping surface of the roadway and the vertical side of the curbing. The full width of the roadway is thus left available and convenient for driving. The form of roadway shown in Fig. 415 is the same as that shown in Fig. 414, except that the bottom g Mlddlllldddidua 7/7 Fic. 415. of the gutter is made level. Little, if any, advantage is gained by this, however, and the form of gutter is not generally as good, nor is it nearly as extensively used, as the form shown in Fig. 414. Where the gutters are paved with cobblestones, the form shown in Fig. 416 is very com- monly employed. When a substantial stone curbing is used, it is doubtful whether any advantage is gained by this form of gutter, while it possesses the disadvantage of T. 1V.—17 L066 STREETS AND HIGHWAYS. narrowing the available driveway w’ and also of making it inconvenient for carriages to drive close to the curbing. For convenience of reference, the forms of gutters shown YY), MEH i 7 Ld a ——_— Fic. 416. in Figs. 414, 415, and 416 will hereafter be designated as forms a, 6, and c, respectively, as marked in the figures. 1731. Width of Gutter and Crown.—lIn Figs. 415 and 416, zw’ is the width of the crowned portion of the road- way, or width between gutters, while g and yg” are the widths of the two gutters. The width of gutters is some- times made equal to the amount of crown, although they are quite commonly made materially wider. It is evident that for gutters of forms 6 and c the crowned width of the roadway w’ will be equal to the total width of the roadway minus the width of the two gutters, or—when the width of gutter is made equal to the crown—minus twice the amount of crown. In applying formula 205 for determining the amount of crown in roadways having gutters of forms 6 andc, the full width of the roadway between curbing may be substituted for w, but in applying formulas 206 or 210 for obtaining the ordinate at the gutter, the abscissa + should, of course, zw’ be taken equal only to one-half the crowed width, or oe 1732. Height of Curbing.—Flat stones or planks are usually set on edge along the borders of the roadway, as shown at e, ein Figs. 414, 415, and 416. These are Fic. 417. called curbs or curbing. In some cases, earth or gravel roadways have gutters paved with cobblestone where no curbs are set. In such cases, a good substitute for curbing STREETS AND HIGHWAYS. 1067 may be formed by the cobblestone pavement, as shown in Fig. 41%. The stones are usually set vertically on edge, but are sometimes set somewhat sloping. The curbing is generally placed at the same height as the center of the street. In other words, the top of the curbing is usually set to the grade line adopted for the Street. FOOTWALKS AND STREET LAWNS. 1733. Sidewalks arc constructed of different ma- terials, such. as gravel, wood, brick, stone, concrete, asphalt, etc., and are generally given such widths and placed at such heights as will best accommodate the conditions of each case. 1734. Widths and Heights of Sidewalks on Business Streets.—On business thoroughfares, the entire space between the curbing and the building line is usually occupied by the sidewalk, which commonly consists of stone or other substantial material. ‘The edge of the sidewalk adjacent to the curbing is always placed at the same elevation as the curbing, 1. e., at grade, but the edge adjacent to the building's is elevated somewhat above this, giving it a slight inclination towards the gutter for the purposes of drainage. 1735. Widths and Heights of Sidewalks on Residence Streets.—On residence streets, the construc- tion of sidewalks does not follow any rigid rule; they are generally given widths of about one-fifth to one-sixth the widths of the roadway, or from about 5 to 10 feet. Dif ferent materials are used in their construction. Wooden sidewalks consist of a wearing surface of planks extending crosswise of the walk and spiked to longitudinal stringers. These walks are generally made of such widths that the planks will cut from the commercial lengths of planks with- out waste. Widths of 4 feet 8 inches (which will cut from a 14-foot plank), 5 feet 4 inches (which will cut from a 16- foot plank), 6 feet, 8 feet, etc., are commonly used for plank sidewalks. When these are replaced by walks of a more substantial nature, the same widths are often retained. 1068 STREETS AND HIGHWAYS. The outer edges of the sidewalks on residence streets are commonly placed about 2 feet from the fence line. The sidewalks of residence streets are generally placed at grade wherever the natural cross-section of the street is sufficiently level for this to be done without inconvenience or disadvantage to the adjoining property. It is decidedly the best practice to put @// sidewalks either at grade or at a certain small fixed distance (3 or 4 inches) above grade; this is especially true of the sidewalks of paved streets. In many cities, however, the elevations of the sidewalks in residence districts are varied materially from the street grades wherever such variation will better accommodate the adjoining property. This is illustrated in Fig. 418, in FR oy DID ph Ages ms “BS ge Vie, 2 egy pe ws é€ y t i] 13 iy ELORFRL SSS v7 FET 7s g| tll CE FIR Le *~ vs) See 1 eee 1 >| i. ! Qi S ie Ay Fic. 418. which, in order to accommodate the elevated position of the adjacent property, the sidewalk on one side of the street is elevated considerably above the surface of the roadway. This practice should be avoided whenever possible, as the resulting appearance of the street is not nearly as good as when both sidewalks are placed at grade. This is a matter that is not usuaily left wholly to the discretion of the munic- ipal engineer, however, but is often regulated by city ordinance, or, possibly, by some provision of the city charter. In such cases, the engineer must be governed by such regu- lations as may exist. 1736. Lateral Slopes of Sidewalks.—For the pur- pose of drainage, sidewalks should have a slight lateral slope STREETS AND HIGHWAYS. 1069 towards the curb. On closely built up business streets, in which the entire width between the curb and the building line is occupied by the sidewalk, this lateral slope of the sidewalk will fix the elevations on the building line. The edge of the sidewalk adjacent to the curb will be placed at the elevation’ of the curb, that is, at the street grade, and the edge of the sidewalk adjacent to the building line willbe higher or above grade an amount equal to the width of the sidewalk in feet multiplied by the lateral slope per foot. In some cities, a lateral slope of .24 per cent., or 1 in 40, is given to the sidewalks; a slope of 2 per cent., or 1 in 50, however, is generally very satisfactory for this purpose and will here be adopted for all problems. All that portion of the street between the curb and the property line* should be given this uniform lateral slope, whether wholly occupied by the sidewalk or not. 1737. Street Lawns.—Those portions of a residence street not occupied by the roadway and sidewalks should be GM ad 1h 4 iii © x S YY Q ter ; I & $ 80° $ 3 > = £ FIG. 419. laid out as lawns, with at least one row of trees on each side of the roadway. In Fig. 419 is shown the cross-section of a residence street 80 feet wide, having a roadway 40 feet in width, and two sidewalks each 8 feet inwidth. A single row * The boundary line of a street, or dividing line between the street and the adjoining property, is known variously as the property line, building line, block line, fence Line, and, some- times, street line, though the latter term is more commonly ap- plied to the center line of the street. ‘Top “Old 1 \ pac a PrN “4 SS STREETS AND HIGHWAYS. 0 qadong wz euyyT ‘Och “VIA ae Dace eee se re . ep r 766 102 ! G6 YY : Yi) 4, J HE, > Yj ED. LES Vj, Yj COG Ye ‘ig YY, UY MELEE SM OWAAY 4 EES j COO $ LESSEE LLESOMEZ, VL PY //Lis Pra ai Yl \) aurqy fizsadodd Z Ce CNW, yar ~~ re we oe vo ‘ede, , “iy ny Ba sd aurT fhysadordss ‘ wr yi a d - Aan wird Bh 1S & 5,25 ., EG a) AF 5 Win “yd Deen S - | eurvT fipvadold STREETS*AND- HIGiWAYS, 1071 of trees is shown on each side of the roadway, between the sidewalk and the curbing. With these widths, however, if the residences are set well back from the property line, another row of trees could be advantageously introduced between the sidewalk and the property line. In cases where the lawns are of large widths, two rows of trees are sometimes set along each side of the roadway be- tween the sidewalk and the curbing, as shown in Fig. 420, which represents the cross-section of an avenue 120 feet wide, having a roadway 50 feet wide and two sidewalks 10 feet wide each. The arrangement there shown is gener- ally well adapted to avenues of this width. Other arrange- ments are, of course, employed. In some cases, the sidewalk is placed nearer the curbing, leaving most of the lawn space between the sidewalk and the property line. This is not as good an arrangement as that shown in Fig. 420, however, because the position of the sidewalk is neither as pleasant for pedestrians nor as conveniently accessible to the resi- dences. Very broad avenues sometimes have two roadways, which are separated bya lawn extending along the center of the avenue and containing one or two rows of trees. Such very broad avenues are called boulewards. The cross- section shown in Fig. 421 is somewhat similar to that of the Western Boulevard, New York City. The importance to a city of clean and well-kept lawns can scarcely be overestimated. They serve not only as a means of ornamentation, but also as a means of purifying the air, and thus have a beneficial effect upon the health of the inhabitants. STREET INTERSECTIONS. DIFFICULTIES ENCOUNTERED. 1738. Different Elevations of Curb Angles.—The proper arrangement of the grades at street intersections is often a quite troublesome matter. Where two streets in- tersect, it is quite desirable that the crown of each street should be continuous to the center of intersection. It would 1072 STREETS AND HIGHWAYS. also appear desirable for the grade of each street to continue uniform to the center of intersection, but this is a matter often involving considerable difficulty. In Fig. 422, 4 Band C Dare the “center lines*of two-streetsuntersectinoweaca other at right’ angles: “Che: points aye.e,-andeerarestne angles of the curbing, and are called curb angles, or curb corners. Instead of being really angles, however, as shown in the figure, they are often the quadrants of small circles. ‘Let it be assumed* that’ the total widths oi@eacn street is 60 feet, and that the width ac and ad of each road- a, lop) f 1 =| | | | ma A Re cana Pa St SS ea eer eee | Fata Peete eee rs aA ae . | D FIG. 422. way is 40 feet; also, that the grades of the street descend at the rate of 2 per cent. for A Band's per cent. tore — ee the directions indicated by the arrows. The grade lines of both streets must, of course, have the same elevation at 9, the intersection of the center lines. As computed by the grade of A 4, the elevation of the curbing would be, at the points a and d, the amount .02 x 20 = 0.40 of a foot above the in- tersection 0, and at the points c and 6 the same amount below it. As computed by the grade of C D, however, the elevation of the curbing at a and ¢ would be .05 x 20= 1.00 of a foot above the intersection 0, and at d and 0 it would be the same amount below it. Consequently, we STREETS AND HIGHWAYS. 1073 obtain the following elevations, with reference to the inter- section o, for the curbing at the points a, c, d, and J, desig- nating elevations above by the + sign and elevations below by the — sign: On Grade of On Grade of Difference Curb-Angle. A B. GJ). in Feet. a +. .40 + 1.00 0.60 C — .40 + 1.00 1.40 a + .40 — 1.00 1.40 b — .40 — 1.00 0.60 In the last column is given the difference between the elevations of each curb angle, as determined from the two different grades. It is evident, however, that each angle of the curbing can have but one elevation; how to harmoni- ously adjust these diverse conditions is a problem that is in some cases quite difficult of solution, and one concerning which quite different views are held. Some of the methods employed wiil now be noticed. METHODS OF ADJUSTMENT. 1739. Method by Adjustment at Curb Angles.— When the grades of the intersecting streets are quite flat, so that the difference in the elevations of the curb angle, as determined from the two grade lines, is quite small, the curbing of each street may be carried at the street grade through the entire block to the property line of the inter- secting street, and the adjustment of the elevations of the curbing be made between the points where the curbings in- tersect the property lines. Thus, on the portion 4 of the street A B, Fig. 422, the curbs may be set to the regular street grade as far as the points c, and J, on the property line of the intersecting street C Y); and on the portion C of the street C ) the curbs may be placed at the regular street grade as far as the points @, and c, on the property line of the street A B. The elevations of the curbing at the points c, and c, being thus fixed at the grades of the respect- ive streets, the elevation of the curb angle may be deter- mined by giving the curb a uniform grade between the 1074 STREETS AND: HIGH Waayis: points c, andc,. More satisfactory results will generally be obtained, however, by making the elevation of the curb angle a mean between its different elevations as gtven by the grade lines of the two streets; the elevation of the curb angle will here be determined in this manner for this method of adjustment. This method of adjustment, however, will not be satisfactory where the grade of either intersecting street is at all steep. . 1740. Method by Independent Curb Grades.—A better method of adjusting the elevations of the curbing, where the grade of each street continues uniform to the center of intersection, is to set the curbs at independent grades through the block from curb angle to curb angle. Having determined the elevations of the curb angles at the two adjacent corners of a block, by calculating for each its elevation according to the grade of each intersecting street, and taking the mean of the results, as in the preceding method, the grade of the curbing is made uniform through the block from curb angle to curb angle, provided there is no change in the rate of the street grade along the block between the curb angles. (If the rate of the street grade changes at one or more points along the block between the curb angles at its adjacent corners, the grade of the curb- ing should be made uniform from the elevation fixed for each curb angle to the elevation of the street grade at the nearest change. In some cases, it may be found advisable to fix the elevations of the curb angles somewhat above or below the mean of the elevations calculated from the two street grades; this will not be done here; however. ~ (ius; referring to Fig. 422, the curbing would be set at a uniform gerade from the curb angle a to the curb angle at the left- hand corner of the same block, corresponding to the curb angle c of the adjacent block, provided there was no change in the street grade between those points. 1741. Method by Level Intersections.—Another method of harmonizing the grades at street intersections is to make the grade of each street level across the intersect- STREETS AND HIGHWAYS. 1075 ing street, either from property line to property line, or from curb line to curb line. The total amount of rise or fall necessary to each street between any two successive intersecting streets will be effected wholly along the block between the property lines of the block, or between the curb lines of the two intersecting streets, as the case may be. If the rise or fall is effected wholly between the property lines of the block, then, at the property line of each inter- secting street, the grade changes to a level grade and con- tinues level across the full width of the street. At the points 0,, 0, 0g, and o,, Fig. 422, where the center line of each street crosses the property lines of the intersecting street, the grade lines have the same elevation as at the center of intersection o. The elevation of the curb will require no special adjustment; at every cross-section of the street it will be the same as that of the street grade directly Opposite. “At the points 2, @,, and ¢., ¢, ¢c;, and-<¢,, etc., the curbs will have the same elevation as the points @,, 0 and as the center of intersection a. The results will generally be more satisfactory if the changes of grade for each street are made at the curb lines of the intersecting street. This will give a slightly greater distance in which to attain the necessary rise and fall be- tween two adjacent streets, and, consequently, a slightly easier grade, and will allow the grade of the curb to con- tinue uniform to the curb angle, giving a somewhat better appearance. Only that portion of the intersection included between the curb lines is made level. This level portion of the intersection will be the rectangle having its four angles at the curb corners a, c, @, and 0, Fig. 422; at these points, the tops of the curbs will have the same elevation as the Genter of intersection... By the method of level intersections, the problem of harmonizing the system of grades is put in the simplest pos- sible aspect. On this account, it is a quite popular method and is much employed. On steep grades, however, it has the disadvantage of giving two abrupt changes in the grade line at every street intersection. Moreover, in ascending Sai Fat <4 8 aie 1076 STREETS AND. HIGHWA Ys: such a grade, the level intersections will have the appear- ance of descending in the opposite direction. ‘This may be to some extent corrected by the following modification of the method. 1742. Modification of the Method of Level In- tersections; Laterally Sloping Roadway.—Where two streets intersect, it is not commonly the case that both streets have steep grades. If theyintersect upon a hillside, it will usually be the case that one street will have the same general direction as the slope and that its grade will be cor- respondingly steep, while the other street will have a direc- tion across the slope or along the side hill, with a compara- tively level grade. It will generally be advantageous tothe residences and lawns along the latter, or side-hill street, as well as to the street intersections, to give the surface of this street a lateral slope in the direction of the general slope of the natural surface. With a sloping crown, this can be done by simply throwing the summit of the crown towards the upper side of the roadway. A somewhat similar effect can of course be accomplished in other ways, but this method will be the only one noticed here. 1743. Eccentric Crowns.—The form of cross-section is shown in Fig. 423; it will here be called an eccentric a a’ x ee y 7 = YY) YY yy Uj ZY Y YY YYW ]/ Yj 7 | // crown. With the crown in this position, if the same uni- form slopes are retained for the sides of the roadway, the top of the curbing a’, on the side nearer the summit of the crown, will be higher than that of the curbing 0’, on the opposite side, by the amount d, as shown in the figure. If the street A 5, Fig. 422, be given a cross-section of the form shown in Fig. 423, the curb angles a and d and the curb angles ¢ and 6 of the former figure will correspond, respectively, to the curbs a’ and 0’ of the latter figure, and FIG. 423. STREETS AND HIGHWAYS. 1077 the street CD, Fig. 422, may have the rate of grade = (ae (Fig. 423) across the street A 2, while in all other respects the intersection may be treated as a level intersection. The changes of grade should preferably be made at the curb. lines. The expedient of modifying the level intersection by giv- ing a lateral slope to the roadway of the street extending along the side hill can often be employed to good advan- tage. No adjustment of the grades of the curbs will be required, except, merely, such adjustment of the eleva- tions of the curbing on the side-hill street as may be neces- sary to give the proper lateral slope to the street. The grade of this side-hill street, to which is given the lateral slope, should be level across the intersection. On the in- tersecting street, that is, on the street extending up and down the hill, the elevation of the curbing will then be the same as that of the street grade in the same cross-section. 1744. Formulas for Eccentric Crowns.—The cross-section of the roadway shown by a somewhat exagger- ated outline in Fig. 424 is the regular form of cross-section Fic. 424. with sloping crown, except that the summit o of the crown, instead of being at the center m of the roadway, is at the distance ¢ from the center and nearer the higher curb a’. This distance ¢ will here be called the eccentricity of the crown. For a cross-section having an eccentric crown, the length of the central curve joining the uniformly sloping portions of the surface line and the rate of slope on the latter should remain the same as though the crown were symmetrical; the rate of slope should be as given by for- mula 207. This being the case, the amount of eccentricity 1078 STREETS AND HIGHWAYS. of the crown necessary to give the desired difference be- tween the elevations of the curbs will be given by the formula a 4 aes .-oe" ee (211.) in which e is the eccentricity of the crown and d is the difference in the elevations of the curbs, both in feet, while s is the rate of slope as obtained by formula 207. The height of both curbs above the gutters or adjacent surface of the roadway should generally be made equal to _the height of crown as given by formula 205, and as sub- stituted in formula 207, to obtain the value of s. If both curbs have this height above the gutter, and the eccentric- ity of the crown be as given by formula 211, then the ele- vation of the summit of the crown will be a mean between the elevations of the two curbs. In other words, the top of . wes : a . the higher curb a’ will be at the distance 5 above the summit of the crown, and that of the lower curb 0’ will be at the same distance below it. Although the rate of slope will re- main unchanged, the amount of crown will really be some- what less in an eccentric than in a symmetrical crown. Formula 211, for the eccentricity of the crown, does not apply correctly when d, the difference between the eleva- tions of the curbs, is greater than the value-of 2. by the formula d, = s (w — b), (212.) in which s is the rate of slope, zv is the width of the road- way, and @ is the width of the curved portion of the crown, as in formula 207 3 d,, 1s the maximum difference between the elevations of the curbs to which formula 211 will correctly apply. as given 1745. Roadway with Uniform Lateral Slope.— When d has a value greater than that of d,,, as determined by applying formula 212, the crown should be omitted, and the roadway surface should be given a uniform slope from curb to curb, as shown in Fig. 425. For a cross-section of STREETS AND HIGHWAYS. 1079 this form, the elevation of the highest point in the surface line of the roadway, or the point a,, Fig. 425, should gen- erally correspond to the elevation of grade. The rate per foot s, of uniform slope across the roadway, or the amount i $$$ FIG. 425. of vertical fall in each horizontal foot, will be given by the formula : | | | | | | | | x WH ULLLLLELY. SJ J, Eee (213.) in which d is the difference in the elevations of the curbs, and w is the width of the roadway, as shown in Fig. 425. The rate of slope s,, as given by this formula, will generally be somewhat less than the rate of slope s, as given by for- mula 207 and used in formula 212. The height of each curb above the adjacent surface of the roadway may be made equal to the amount of theoretical crown c substituted in formula 2Q7 to obtain the value of s. The curbs may have any desired height above the surface of the roadway, how- ever, so long as both curbs have the same height. 1746. Exampeie.—For the roadway of Example (4) of Art. 1728, (2) how much eccentricity must be given to the crown in order to elevate the top of one curb .48 of a foot above the top of the lower curb? (4) If the difference in the elevations of the curbs be .72 of a foot, will the formula for eccentricity apply correctly ? (c) With this difference between the elevations of the curbs, if the surface of the roadway be given a uniform slope from curb to curb, what will be the rate of slope 5; ? SoLUTION.—(a) In the solution of the example referred to, the rate of slope s in the uniformly sloping portion of the cross-section was found to be .016; the difference d in the elevations of the curbs, as stated above, is .48 of a foot. By substituting these values in formula 211, the necessary amount of eccentricity for the crown is found to be equal to . A8 2X .016 (6) The width of the roadway is 48 feet, and the width of the central curved portion is 5 feet (Art. 1728). By substituting in formule = 15 feet. Ans. 1080 STREETS AND HIGHWAYS. 212, we have dm = .016 (48 — 5) = .688 of a foot. The difference of .72 of a foot between the elevations of the curbs is greater than this value of dm; hence, for this difference, the formula for eccentricity will not apply correctly. Ans. (c) By applying formula 213, the rate of uniform slope across the v9 roadway 5s, is found to be Se aaa) Leer yN S17 EXAMPLES FOR PRACTICE. Note.—The following examples relate to those of Art. 1728 in which sloping crowns were assumed. To the roadways of those ex. amples, which are now, for convenience, assumed to have level grades, the formulas for laterally sloping roadways will be applied. 1. For Example 2, the width of roadway is 20 feet and the height of crown is .44 of a foot. (a) What will be the value of @,, for this road- way? (6) If one curb be elevated .55 of a foot above the other, -will the formula for eccentricity of crown apply correctly? (¢) How much eccentricity of crown will be necessary to give this difference in the pert ake bale heights of the curbs? ae § (a) .66 ft. (cy) Oo Fe. 2. The width of roadway and height of crown for Example 3 are 60 feet and .555 of a foot, respectively. (a) What will be the value of @»m for this roadway ? (6) With a difference of one foot between the heights of the curbs, will the formula for eccentricity of crown apply correctly ? (c) How much eccentricity of crown will be necessary to give this difference in the heights of the curbs ? ‘Aine { (2) 1.02 tC “U(c) 2 ft. 3. For Example 5, the width of the roadway is 24 feet and the height of the crown is .415 of a foot. (@) What will be the value of @,, for this roadway? (4) If the top of one curb be placed .75 of a foot above the top of the other curb, will the formula for eccentricity of crown apply correctly ? (c) If the roadway surface be given a uniform slope from curb to curb, what will be the rate of slope ? Ans § (a) .664 ft. U(c) .08125 ft. 4. For Example 6, the width of the roadway is 36 feet and the height of the crown is .386 of a foot. (a) With a difference of .50 of a foot between the elevations of the tops of the curbs, will the formula for eccentricity of crown apply correctly ? (46) How much eccentricity of crown will be necessary to give this difference in the elevations of the curbs ? Ansis (0) Leak tte 1747. Elevations of Block Corners.—The angles of the property line, ge, 2 and we Big 422 ate caue block corners. With reference to the street A £4, the STREETS AND HIGHWAYS. 1081 block corner c’ is opposite the point c, of the curbing where it crosses the property line of the street C ); but with ref- erence to the street C D, the same block corner c’ is opposite the point c, where the curbing crosses the property line of the street A &. In the case of an intersection level between property lines, the curbs will have the same elevation at the points ¢, and c¢,, in which case the elevation of the block corner c’ will be the same as computed by the lateral slope of each sidewalk in the manner noticed in Art. 1736. If the intersection is not level, however, the curbs will not have the same elevation at the points c,and c,. In any case, the elevation of the block corner will be given by the formula BOS, +e,+ Se (zw, + w,). (214.) in which c’ is the elevation of the block corner, c, and c, are the respective elevations of the two curbs at points opposite the block corner (see Fig. 422), w, and w, are the widths in feet between the block corner and the respective curbs (the widths c’c,andc’c,, Fig. 422), and s, is the lateral slope per foot between the curb and the building line, which is here taken at a value of .02 (see Art. 1736). 1748. Exampie.—The curb cc, Fig. 422, is at a distance of 12 feet from the block line a’ c’, and has a grade of 2 per cent., descending from c; the curb ¢c. isat a distance of 10 feet from the block line 0’ c’, and has a grade of 5 per cent., ascending from c. If the curb angle c has an elevation of 102.48, what should be the elevation of the block corner ¢'? SoLuTION.—The elevation of the curb at ¢c, will be 102.48 — .02 x 10 = 102.28, and the elevation of the curb at c, will be 102.48 +.05 & 12 = 103.08. By applying formula 214, the elevation of the block corner 102.28 + 103.08 2 .02 & (12 + 10) SANGO ke A ne: c’ is found to be EXAMPLES FOR PRACTICE. Note.—The following examples refer to Fig. 422. 1. The curb aa, hasa grade of 2 per cent., ascending from a, and the distance aa, is 10 feet; the curb aa, has a grade of 5 per cent., ascending from a, and the distance aa, is 12 feet. If the elevation of io AY ts 1082 STREETS AND HIGHWAYS. the curb angle a is 102.48, what should be the elevation of the block coriera Ans. 103.10. 2. The curb dd, has a grade of 2.10 per cent., ascending from ad, and the distance dd, is 8 feet; the curb dd, has a grade of 4.85 per cent., descending from d@, and the distance @d@, is 12 feet. If the elevation of the curb angle d@ is 102.48, what should be the elevation of the block corner @'? Ans. 102.473. 3. The curbangle 4, which has an elevation of 102.48, is at a distance pret of 11 feet from the property line 64’ c’ and at a distance of 15 feet from the property line 6’d'. The curbs 64, and 6d, have grades of 2.20 and 5.24 per cent., respectively, both descending from 4. What should be the elevation of the block corner 0’? Ans. 102.226. 4. The distance cc, is 15 feet, and the curb has a grade of 6.84 per cent., descending from c; the distance cc, is 12 feet, and the curb has a grade of 1.25 per cent., ascending from c. If the curb angle ¢ has an elevation of 87.42, what should be the elevation of the block corner c’ ? Ans. 87.252. 1749. Drainage at Intersections; Location of Catch-Basins.—In order that vehicles may pass smoothly over street intersections, the crown of each roadway should be continuous across the intersection; the crown of either roadway should not be broken by the gutters of the inters éc time street. It is: ¢vident however, that some provision must be made for the storm water from the gutters on the upper side” Giwemaa crown. Each of the inter- secting streets shown in Fig. 426 is assumed to have a descending grade in the direction indicated by the arrows marked along its center line, and the crown of each street is assumed to be continuous. With such grades, the storm water from the gutter c, can flow around the curb angle c into the gutter c,, as indicated by STREETS AND HIGHWAYS. 1083 the curved arrow, and, likewise, the storm water from the gutter 7, can flow around the curb angle @ and find an out- let in the gutter d,. The storm water from the vicinity of the curb angle J can flow away in either gutter 0, or 6,.. In both of the gutters @, and a,, however, the storm water flows towards the curb angle a, and, as there is no gutter leading away from this curb angle across the crown of either roadway, some provision must be made for the storm water from these gutters. If a storm-water sewer extend along either of the inter- secting streets, the problem of providing for the storm water at the curb angle a may be easily solved by simply putting a catch-basin at the curb angle, as indicated by the dotted circle. The storm water from the gutters a, and a, would be received directly into the catch-basin, from which it would be conveyed into the sewer. Catch-basins would also gen- erally be placed at the curb angles c and d to receive the storm water from the gutters c, and d@,, so that the gutters c, and d, would not be overcrowded. It is evident that a catch-basin would not be required at the curb angle 0. If there be no storm-water sewer along either of the inter- secting streets, so that the storm water must be conveyed wholly by the surface gutters, it will be necessary to provide a conduit leading from the gutter at the curb corner towards which the water from both streets flows, corresponding to the curb angle a, Fig. 422, across and beneath the roadway, discharging into the descending gutter, as the gutter c, or d,, atsome point far enough down to give the required depth below the roadway surface. In some cases, it may be ad- visible to provide such a conduit under each roadway. MATTERS RELATING TO GRADES. ESTABLISHING GRADES. 1750. Objects to Be Attained.—lIt is usually quite difficult to properly decide all the various matters that must be considered in fixing the grades for a system of streets, and adjusting them so as to harmonize at intersections, The 1084 STREETS AND HIGHWAY s: three main objects to be attained are: first, the prompt removal of the surface water; second, the easiest gradients, and third, the good appearance of the street. 1751. Removal of Surface Water.—In order that the surface water may be promptly and effectually removed from a roadway, the rate of grade for the street should never be less than one-fourth of one per cent., that is, .25 of a foot per 100 feet; the grade should not be as flat as this except in extreme cases and with first-class pavements, such as brick or asphalt. A minimum grade of one-half of one per cent. is as flat as should generally be used, and a grade as steep as one per cent. 1s very désirable. . Where the oradqe line of a street has the same elevation at the intersecting streets at both ends of a block, instead of making the grade level through the block, it should be elevated in the center of the block sufficiently to cause the water to flow in each direction towards the intersecting streets. If the street is sewered, the grade may be depressed at the center oierne block by locating catch-basins there; it will, however, gen- erally be better tolevate the grade at the centers mae block. 1752. Easiest Obtainable Gradients.—This will be governed largely by the character and slope of the natural surface,.and the nature and extent of the improvements that have been made along the street... Where no improve- ments have been made, quite deep cuts and fills are per- missible in order to obtain favorable grades. But where buildings have been erected and improvements of a per- manent nature have been made along a street before the grade is established, as is frequently the case, due regard must be given to such improvements in fixing the grade. The engineer must simply study the conditions as he finds them, and work out the most favorable grade possible to those conditions. | This will seldom be as satisfactory a grade as could have been established before the improvements had been made, but it should be as free from abrupt changes and approach STREETS AND HIGHWAYS. 1085 as near toa uniform grade between street intersections as possible, thus giving the easiest obtainable gradients. It is important that the grade of a street be established as soon as possible after the street is laid out and before im- provements are made; the improvements should then con- form to the established grade. 1753. Good Appearance of Street.—Although the matter of appearance has been placed last, it is by nomeans the least in importance. The general appearance of a street greatly affects the value of the adjacent property; it is, consequently, of great importance that the grade of a street be such as to give it a good appearance. Where possible, the grade of the street and the curb line should ex- tend unbroken through each block from curb angle to curb angle. When it is necessary to change the grade at some point along the block, the change should be made at a prop- erty line, and should be as small in amount as _ possible. Where the necessary change in the grade is considerable, the total change should be accomplished by means of several small, uniform changes, approximating a vertical curve, rather than by one abrupt change. If residences have been built along the street before the grade is established, as is not infrequently the case, some regard should be had for the appearance of the lawns in fix- ing the grade; the appearance of a@a// the lawns should be considered in the aggregate, however, rather than the appearance of any particular lawn. The appearance of the street intersections must also be considered. In short, the appearance of the entire system of grades, as a whole, must be carefully considered, for it is their effect as a whole, and not the effect of any particular detail, that will be noticed. 1754. General Methods of Procedure.—As stated above, it is usually quite difficult properly to decide all the various matters that must be considered in fixing and harmonizing the grades for a system of streets. There is no established custom among municipal engineers with regard to this, and the practice varies materially. Indeed, STREETS AND HIGHWAYS. 1086 "9391S pUOIS “OUT] YOoT, "J991}JG puoos9G ‘OUI, qindg *J991}G pU0IIG “oUT] 19}Udd) "499139 puoosG =‘oUT] qing "J99IJG puodseg ‘oul] YOoT_ "J9914S ISI «= “OUT] Yoo, "SYICUIOY Og °G—|06 VIL OL° PIT Ae AOOR SLT 0°O eo OES EL Oérey EL Sha a oi 00° S198 "SLL YSA0 LL xX |9§° SOT ‘IOV ‘oper | 9PPID -InS jo JTEY ‘SUOTJEADTY ‘qing 1ySRI OS @ We FEU VEL OF Le eOsG Le X |00°STT| O'STL O50 00791 LSE sit xX |00°STT| O'STT OV LEO SEL 98° PIT] ¢ VIL O'S J9E° SIT] 6°SIT GEOL a OLE xX |9€° SOT) 7'80L "Q08] ‘opuay | 8PPND) -ing jo 91° ‘SUOTIEAITH “AEMPPO OL Re al seo aE OL FIT = 100sc TT 0°0 Aevoeg1y 94° FIT 98° FIT 00°C +198 SIT | 96° OTT xX |98°80T "Q0BJ ‘apeisy | 9PP4D -m¢ JO O}EY ‘SUOT]BAZA ‘qing ¥eT OT tee 0c og + hos 06 + CT ial ST rei ‘U0T}EIS OL JFAULS LS¢/7 WOUA LZAZAILS NIVFW AO AGVAD "auNOOUaA AAdVAD STREETS AND HIGHWAYS. eLOST some engineers prefer not to follow the same rule with regard to any two streets, but in each case to establish such a grade and harmonize it with that of each intersecting street in such manner as the conditions of that particular case may seem to demand. This is probably a better prac- tice than to attempt to follow any rigid rule, for a method that would be satisfactory in one case would be likely to prove unsatisfactory in another. In general, it is a good plan to fix first the grades of the streets extending in one direction, choosing the direction of the more important streets and taking them in the order of their importance; then fit in the grades of the cross streets, taking them also in the order of their importance. In fit- ting in the grades of the latter streets, it will often be found advisabie to modify the grades of the former more or less. If the system of streets is extensive, a contour map will often be of value as an aid in fixing the grades. When the street grades have been finally fixed, the grades of the curbs should be harmonized at the intersections in the man- ner that may be best suited to each case. GRADE RECORD. 1755. Records of Grades.—A complete and system- atic record of all grades should be preserved in a book kept for that purpose, and generally known as a grade record. For each street upon which a grade is established, this record should give the rates of grade along the different portions of the street, with the elevation of each station, or, at least, of each street intersection and point where the grade changes. The information given should fully describe the grade of the roadway and of each curb. This record should be supplemented by a complete and accurate profile of the street. All information should be so well indexed as to be easily and quickly accessible. The book in which the records of the grade are kept should be made especially for that purpose, with pages so ruled as to be convenient for recording the grades. The best form for this record book will depend somewhat upon 1088 STREETS AND HIGHWAYS. the engineer’s ideas and methods in recording the grades. For most cases, the accompanying form of page will be found satisfactory. The notes given are merely for the purpose of illustrating the method of recording the grade. It will be noticed that, in recording the rate of grade, a rising grade is indicated by a-+ sign, and a falling grade is in- dicated by a — sign; a rate of 0.0 is given for a level grade. In order that each station or plus where the grade changes may be easily distinguished, it is designated by a X marked in the column for the rate of grade. CITY BASE AND BENCH MARKS. 1756. The City Base.—All elevations relating to the grades, and to all other matters of municipal improvement, should be referred to, and measured from, the elevation of a point on some permanent object in the municipality, of which the elevation is known from a record, or to which a certain elevation is assigned; the elevation of the point, whether assigned arbitrarily or otherwise determined, is permanently fixed and recorded. The elevation of this point will be its distance above an imaginary horizontal plane adopted as the zero elevation for all levels. This plane of zero elevation is usually called the city datum, city base, or, simply, the base. It is a great advantage for all the levels of a municipality to be referred to the same base. The elevations of any points in the municipality can then be readily compared by simply determining and com- paring their elevations above base. Moreover, if the eleva- tions of certain fixed points of reference are determined and recorded, with regard to the base, the elevations of any points on a grade line, as recorded, can easily be obtained from these and fixed upon the ground. 1757. Bench Marks.—A point whose elevation is determined and recorded for reference is called a bench mark. For the levels of a municipality, it is customary to fix, arbitrarily or by comparison with some object whose elevation is known, the elevation of one point as the princi- pal and governing point of reference; this is called the STREETS AND HIGHWAYS. 1089 primary bench mark. From this, a system of aux- iliary bench marks, or secondary bench marks, should be extended throughout the municipality. The ele- vation of the primary bench mark, when once fixed, remains unchanged as the final point of reference for all levels ; the elevations of all other points, including the system of sec- ondary bench marks, are obtained from, and referred to, the elevation of the primary bench mark. The elevations of the secondary bench marks, however, depending upon the accuracy of the levels by which they are established, are, of course, subject to correction in case any error is dis- covered. In cities near the seashore, the elevation of mean tide is not uncommonly taken as the city base; from this base, the exact elevation of some fixed and permanent point is estab- lished as a primary bench mark. For inland cities, how- ever, the base is commonly taken simply at some multiple of 100 feet below the permanent point chosen for the pri- mary bench mark. MARKING AND PERPETUATING THE STREET LINES AND PROPERTY LINES. NECESSITY FOR MONUMENTS. 1758. The Obliteration of Lines.—In most cities, it is very difficult to accurately locate the positions of the street and property lines. In many cities, there are streets whose lines can not by any possible means be accurately and certainly located in the positions where they were originally established. The stakes and monuments that originally marked the lines, and which have not uncommonly been of a temporary nature, become decayed, removed, and destroyed during the development of the city. As the result of care- lessness and indifference, it is often the case that no effort is made to preserve the markings of the lines, and they become more or less obliterated, and, in some cases, wholly obliterated. It is the experience of all cities that much trouble and annoyance, and often serious litigation, is caused by the obliteration of lines and boundaries. 1090 STREETS AND HIGHWAYS. The destruction of the original markings of the lines would not be a very serious matter if the buildings and fences were built exactly along the property lines so as to accurately mark their positions. This is not always, or even usually, the case, however. It appears to be the natural instinct of property owners to attempt to get possession of as much of the adjacent land as possible; the land properly belong- ing to the street is generally considered as common plunder. The buildings and fences first erected are not uncommonly found to encroach upon the adjacent property; both build- ings and fences very commonly encroach upon the street. The lines of existing fences and buildings can not be de- pended upon as the bases of measurements to establish other lines, except in cases where they are positively known to be COLrec’ ‘ 1759. How to Mark the Lines.—In order that the true positions of the street and property lines may be accu- rately determined at any time, they should be permanently marked by durable monuments set deep into the ground; the positions of the monuments should be determined and fixed by measurements to other permanent objects, and the descriptions and positions of the monuments and the objects to which the measurements are taken, with the measure- ments, should be recorded. The importance of establishing and recording a sufficient number of such monuments to definitely describe and perpetuate the positions of all street and property lines can scarcely be overestimated. Much trouble and annoyance, and more or less expensive litigation, will be saved thereby. | The monuments should be established at all important street intersections. If the street lines or block lines areso marked as to be readily determined, the internal property lines of the block can generally be easily determined from the block lines. To establish monuments that would per- manently define the positions of the street lines would ap- pear to be a simple matter, but it is found to involve very serious difficulties. te STREETS AND HIGHWAYS. 1091 POSITIONS OF MONUMENTS. 1760. Positions Commonly Adopted.—Where to place the monuments for street lines so that they will escape destruction during the progress of municipalimprovements is a question that has never been satisfactorily answered. Three different general positions adopted for the street monuments in different cities, and advocated by different engineers, are: at the intersections of the center lines of the streets, at the block corners, and on arbitrary lines at some certain uniform distance from the block lines. 1761. Monuments on Center Lines.—The most convenient and, in many respects, the most satisfactory position for the monuments is at the intersections of the center lines of the streets. Most engineers favor this posi- tion. Monuments set well into the ground and entirely below the surface along the center lines of the streets will génerally remain convenient and reliable as points of refer- ence until sewers are constructed on the streets. As the sewers are usually located along the centers of the streets, monuments set on the center lines are generally destroyed in the excavation of the sewer trenches. The monuments may also be destroyed by excavations made for other purposes. If not set deep, they may be destroyed by excavations made in constructing street-railway tracks. 1762. Monuments on Block Lines.—Monuments set at the block corners are also convenient for determining the lines. They will be safe from being destroyed by ex- cavations made in the street, but will almost surely be obliterated in the construction of buildings or fences along the block lines. The corner of the building, or the corner post of the fence, will always be said to be placed ‘‘ exactly where the stake was”’; if the width of the street is measured between two such corners, however, it will generally be found to be somewhat narrower than it should be. The corner of a fence or building can not be depended upon to indicate the location of the true corner, unless its position with reference to the true corner is positively known. The 1092 STREETS AND HIGHWAYS. block corners are even less satisfactory positions for the monuments than the intersections of the center lines of the Streets. 1763. Monumentson Offset Lines.—In order that the monuments marking the block lines may not be destroyed in the construction of fences and buildings, they are some- times placed on arbitrary offset lines located in the streets at some convenient and yf) _ uniform distance from V///, the block line. ‘This is _ the WY fy i _ yy V7 illustrated in Fig. 427, none nnanng f nnn pmmennnnnm—nm—- 1 Which are shown the block lines and the offset lines at the intersection | oftwo streets. The full | i lines are the block lines, m and the angles 0 are the i a Ge ee — — +} 0 S| = WY, «Dlock corners; the small YYygg circles m represent the Y _ monuments, and the L dotted lines are merely BIGg ce: the arbitrary offset lines on which the monuments are set. These offset lines are usually at some uniform distance from the block lines, which offset distance must be shown on the records. The minimum offset distance employed for this purpose is usually about 1.5 feet, and the maximum 1s about 4 feet. In other words, the monuments are usually set at some uni- form distance of from 1.5 to 4 feet from the block corners, measured perpendicularly from the block line. On residence streets, such positions are generally quite satisfactory for the monuments. An offset distance of 1.5 or 2 feet will usually bring the monuments between the block line and the sidewalk, while a distance of 3 or 4 feet will generally bring them under the sidewalk; in either of these positions, the monuments are not usually likely to be disturbed, so long as the street remains a residence street. On business streets, SS Q a a en eo a STREETS AND HIGHWAYS. 1093 however, monuments placed in any such positions will generally be destroyed in constructing the buildings. In most business blocks, the basements of the buildings are ex- tended beneath the sidewalks, as vaults for the storage of fuel, etc. In excavating for these vaults, any monuments set in the street near the block line will be certain to be destroyed. Such positions for the monuments are satisfac- tory only on residence streets where no excavations are made beneath the sidewalks. MATERIAL FOR STREET MONUMENTS. 1764. Requirements for a Satisfactory Monu- ment.—There is considerable difference of opinion with regard to what forms the most satisfactory monument for marking street lines. The monument should be easily dis- tinguishable and should be of as permanent a nature as pos- sible. It should be of durable material and should be set deep in the ground in such manner as not to be easily dis- turbed. It is also desirable that it be so arranged that, if the upper portion be disturbed or destroyed, the lower por- tion will still remain to indicate its position. Many differ- ent kinds of monuments are used, from wooden stakes to cut-stone posts. It will be well to notice briefly some of the different materials commonly used for street monuments. 1765. Wooden Stakes.—In the greater portion of the Government land surveys, the corners are marked with wooden stakes. In ordinary land surveys and in the sur- veys of village plots, wooden stakes are also extensively employed to mark the corners. Such stakes will soon decay, and though they form much more durable marks than is generally supposed, they can scarcely be considered to be permanent monuments. If a wooden stake is driven into soil of light character, the form of the stake will remain distinctly discernible as long as the soil remains undisturbed, though the stake itself be wholly decayed. The exact space occupied by the stake will be filled with the dark mold re- sulting from its decay, and this will be easily distinguish- 1094 STREETS AND HIGHWAYS. able in light colored soil of a sandy nature. ‘This fact has been of great value in re-establishing the corners of the Government land surveys. While wooden stakes have well served their purpose in these surveys and are satisfactory for temporarily marking survey lines, they are not suitable for permanently marking street lines in a city. 1766. Iron Stakes.—Corners are often marked by iron stakes. These commonly consist of pieces of gas-pipe or of ordinary round wrought-iron bars about three-quarters of an inch in diameter; they are generally supposed to be more permanent than wooden stakes. They possess one peculiar advantage; when there is no other iron near, the position of an iron stake will be indicated by the movement of the needle of a compass when held near to the ground in the immediate vicinity of the stake, thus enabling the stake to be quickly found. Such iron stakes will rust away ina comparatively few years, however, and they are, therefore, not very satisfactory as monuments for the lines and cor- ners of surveys. Larger stakes would, of course, last longer before rusting out, and it should also be noticed that cast iron will resist rust much better than wrought iron. 1767. Brick Monuments.—For some _ purposes, reasonably satisractory monuments may be made by boring into the ground with an ordinary post auger about four inches in diameter, and placing bricks end upon end in the hole thus formed, then filling around the bricks with pul- verized rock, coal, charcoal, brick, lime, or other indestruct- ible material easily distinguishable from the surrounding soil. One advantage of brick monuments is that the re- moval of the upper bricks will not disturb those below. Such monuments, however, though reasonably satisfactory for the corners of land surveys in the country, are not well adapted to marking the lines of city streets. 1768. Monuments of Pulverized Material.— Similar to the brick monuments are those formed wholly of indestructible pulverized material. They are formed in the same manner as the brick monuments, except that the STREETS AND HIGHWAYS. 1095 bricks are omitted, and are adapted to about the same purposes. 1769. Fireclay Monuments.—Solid cylinders of vitrified fireclay, of suitable length and diameter, make quite satisfactory corner monuments. Such cylinders or corner posts, 4 inches in diameter and 2 feet long, are manu- factured by the Jackson Fireclay Company, of Jackson, Mich., who, so far as we know, are the only manufacturers of such monuments. These monuments can be set in a hole made by a 4-inch post auger; they should be set with their tops nearly a foot below the surface. 1770. Monuments of Cement.—A monument that is probably more satisfactory than any of the preceding can be formed by boring into the ground with a post auger, as for the three preceding kinds of monuments, and filling the hole with mortar composed of one part hydraulic cement to about two parts clean, coarse sand. A cross X can be marked in the top of the monument to indicate the exact position of the corner orline. When the mortar has become set, it will form a very substantial and durable monument. 1771. Stone Monuments.—Probably the best monu- ments for marking the positions of lines and corners are those composed of very large stones. The stone for a street monument should be somewhat of the general form of a pyramid or prism, and not less than about 3 feet in length; it should be set with the larger end downwards. The smaller end of the stone should be so dressed as to forma suitable top for the monument that would be easily recog- nized; the exact position of the corner should be indicated by a X or other suitable mark. It is unnecessary that any other portion of the stone should be dressed, as it will be buried deep in the ground out of sight. Monuments com- posed of large, heavy stones are not easily removed, destroyed, or even disturbed; they are, generally, the most permanent and satisfactory monuments for marking lines and corners. 1096 STREETS AND HIGHWAYS. SETTING, WITNESSING, AND RECORDING MONUMENTS. 1772. Manner of Setting Monuments.—Monu- ments should be set so deep in the ground as not to be easily disturbed. In setting them, the earth should be well packed around them, so that there will be no danger of them set- tlinge out-of position. “1f (set in) the roadway .etnossno.. should be from about six inches to a foot below the surface, according to circumstances. If set in a paved street, an opening to the top of each monument should be left in the pavement; the opening should be covered by a casting similar to the cover of a sewer manhole, though smaller. When monuments are set under the sidewalk, their tops may be just beneath the sidewalk, with an opening through the sidewalk protected by a casting, or the tops of the monuments may be flush with the surface of the sidewalk. When the monuments are set on the block line, or between the biock line and the sidewalk, they may project somewhat above the surface of the ground, if desired. The monu- ments should be set in such manner as to be easily accessible and, at the same time, not easily disturbed. 1773. Witnessing Monuments. — Although the monuments should always be of a permanent nature, they are likely to become destroyed, removed, or disturbed in the improvements attending the development of a municipality. Their positions should therefore be thoroughly fixed and identified by measurements to other permanent objects, so that, if disturbed, they can be replaced in their original positions. Moreover, such measurements enable the monu- ments to be easily found when beneath the surface of the ground, and to be positively identified when found. As the objects to which measurements are taken will also be liable to become destroyed or removed, measurements should be taken to a sufficient number, so that, if some are destroyed, the position of the monument can still be determined from those that remain. If there are not a sufficient number of permanent objects in the vicinity, reference monuments may be set to which measurements can be taken. These should project above the ground, so as to be easily seen. STREETS AND HIGHWAYS. 1097 The practice of identifying the positions of monuments marking the lines and corners of surveys by means of measurements to other permanent objects is called witness- ing the monuments. It is a simple and effective method of identifying the positions of monuments, and is very com- mon among surveyors. The objects to which the measure- ments are taken are called witnesses, witmess trees, witness monuments, etc. 1774. Restoring Monuments. —If a monument that has been well witnessed is destroyed or removed in the construction of improvements, it will generally be possible to replace the monument in its original position after the improvements have been completed. The monument should not be replaced, however, until after the ground has become thoroughly settled; if replaced before, it is liable to settle out of position. It is to be borne in mind that it is not the monument itself, but its posztzon, that is of value. 41775. Records of Monuments.—Accurate records should be kept of the positions of all monuments marking lines and corners. All measurements witnessing the posi- tions of monuments, with descriptions of the monuments and witnesses, should be recorded. Each monument and its position with reference to the street lines should be described, and all witness measurements identifying its position should be given, with descriptions of the witnesses to which the measurements are taken. The records of monuments fixing the positions of street lines, and of the witnesses identifying their positions, should be copied into a book kept for the purpose, and should be so indexed that the record of any desired monument can be easily found. ENCROACHMENT OF LINES; STATUTES OF LIMITATION. 1776. Encroachment of Lines.—In connection with the subject of marking and perpetuating the street and property lines, it will be well to notice the subject of en- croachment, as relating to the acquisition of title by adverse T. IV.—19 1098 STREETS AND HIGHWAYS. possession. This is a matter which must in all cases be settled either by mutual agreement between the parties interested, or by the courts; but it is well for the municipal surveyor to understand his proper position in relation to it. That fences and buildings are not always upon the true property lines, but very commonly encroach upon the street or upon the adjacent private property, is a fact well known to all experienced surveyors. Most surveyors also under- stand that lines of such fences and buildings may, under the usual conditions and after the lapse of sufficient time, become the legal boundaries of the property. 1777. Statutes of Limitation.—In order to placea limit upon the continuance of litigations and disputes over property lines, the laws of the different States decree to the effect that apparent and undisputed possession to any fence or building line for a certain period of time (which period of time varies in different States) will establish such lines as the legal boundaries of the property. Such laws are called statutes of limitation, and the occupancy of property by which title is gained under the statute of limitation is commonly known as adverse possession. 1778. Duties of the Surveyor with Regard to Encroachments.—lIt should be clearly understood by the municipal surveyor that he has nothing whatever to do with the legal boundaries of property established by the statutes of limitation. Such lines do not in any way affect the positions of other lines. They are wot survey lines and can not be taken as the basis of any surveys or measurements relating to the establishment of other property lines, except in cases where subsequent deeds may specially mention them as the basis of the description in a conveyance of property. With this exception, the only lines which the surveyor has to deal with are the true lines of the original survey. These are the only lines for him to run or to survey from. If any particular boundary line or portion of a boundary line becomes legally established in any position other than on the true line of the property as originally laid out, that is a STREETS AND HIGHWAYS. 1099 matter to be determined by the courts; the services of the surveyor are manifestly unnecessary in such a case, as his work would merely show that the line was not in its original position. After the line has been established by the courts, the surveyor may be called upon tc mark and describe its position. Such a line, however, in no way affects the work of the municipal surveyor in determining the positions of other lines; its position may become the legally established boundary for that particular line and property, but it does not affect the.position of any other boundary line. BAR i leN Ge. TRACTION. RESISTANCE TO TRACTION. 1779. Asan introduction to the study of pavements, it is necessary to consider the resistance to traction as weil as the tractive power of horses. The total resistance to traction may be said to be composed of three distinct re- sistances, namely: axle friction, rolling resistance, and grade resistance. For the present purpose, the resistance of the air may be neglected. 1780. Axle friction depends entirely upon the nature and lubrication of the bearing surface of the axle and upon the magnitude of the load, being directly propor- tional to the latter. The effect of this resistance is constant and usually small, and may be neglected. 1781. Rolling resistance relates to the resistance which the roadway surface offers to the wheels of vehicles rolling upon it. It may be subdivided into two classes, -namely: Ist, the resistance due to small obstacles in the roadway or inequalities in the roadway surface; 2d, the re- sistance of a wheel rolling upon a smooth surface, which resistance is called rolling friction. 1782. Resistance Due to an Obstacle.—This is measured by the horizontal force necessary, when applied at the axle, to raise the load upon the wheel to the height of the obstacle. In Fig. 428 the tractive force ¢, and the load qw are both applied upon the axle a. From the theory of moments it is known that, in order that the tractive force ¢~, may be sufficient to balance the wheel, supporting the For notice of copyright, see page immediately following the title page. 1102 PAVING. weight w upon the obstacle 0, the moment of the force ¢, acting upon the lever arm y must be equal to the moment of the force w acting upon the lever arm +, or, to ex- ¢ press it algebraically, 74, y= w +, from which Sarai em ged AOD (215.) a J 7 —0 iG. 428. being the radius of the wheel and o the height of the obstacle. The value of 7,, as given by this formula, measures the resistance of the obstacle, and any tractive force greater than 7, will pull the wheel over the obstacle. For small obstacles, this resistance may be considered to be inversely proportional to the square root of the diameter of the wheel. It should be noticed, how- ever, that the resistance of small obstacles and inequalities in the roadway surface is due largely to the shock produced by them, and is greater at high than at low speeds. 1783. Rolling friction is due chiefly to the com- pressibility of the roadway surface, which permits the wheel to somewhat compress or indent it. It is sometimes called resistance to penetration. When the wheel of a vehicle is drawn upon a roadway sur- face it will indent it and produce in it a wave that is forced along ahead of the zy wheel, as indicated in Fig. 429. The | wheel is thus always climbing a slight FIG. 429. inclination, or, more correctly, and what amounts to about the same thing, is constantly compressing new material. This resistance is less for large than for small wheels, but the ratio by which it varies has never been definitely deter- mined. Some experiments that have been made indicate that the resistance is approximately inversely proportional to the diameter; other experiments indicate that it is ap- proximately inversely proportional to the square root of the diameter; while, from mathematical investigation, it has PAVING. 1103 been concluded that, for wheels rolling upon roadways of homogeneous material, the resistance to traction is inversely proportional to the cube root of the diameter. It is probable that the last conclusion is the most nearly correct. If this is the case, then the resistance of a wheel of a certain diam- eter will be to that of a wheel of one-half the diameter as 1 . V1 WB difference. As the variation in sizes of the wheels on ordinary road vehicles is not very great, this condition may generally be neglected, and for practical purposes the re- sistance may be taken equal to the load multiplied by a co- efficient depending upon the nature and condition of the roadway surface. or as 1: 1.26 (nearly), which is not a very great 1784. Tractive Resistance on Various Surfaces. —Numerous experiments have been made to determine the tractive force necessary to haul a given load upon various roadway surfaces. The results vary through a wide range, as is to be expected when the many different conditions that may affect the results are taken into consideration. The table of Resistance to Traction, given in Tables and For- mulas, is compiled from different sources and is believed fairly to represent the results of the experiments that have been made; it gives the approximate maximum, minimum, and mean tractive forces, in pounds, required to haul a load of one gross ton (2,240 pounds) at an ordinary pace, on level roadway surfaces of the kinds named, and also the mean tractive force in fractional parts of the load. Itisto be understood that these values are but rough approximations. The frictional resistance to traction on a level roadway is given by the general formula i= OW, (216.) in which ¢ is the tractive force necessary to overcome the rolling resistance, zw is the load, and c is the value given in the last column of the table for the various kinds of roadway surfaces. The constant c is called the coefficient of rolling friction. 1104 PAVING. 1785. Grade Resistance.—In ascending inclines a very great part of the tractive force is expended in over- coming the resistance of gravity due to the incline, which is equal to the load multiplied by the total rise and divided by the length of the incline; in other words, it is equal to the load multiplied by the sine of the angle made by the incline with a horizontal line. Fic. 430. Fig. 430 represents a wheel on an inclined plane B C, whose inclination to the horizontal is the angle Ad C B= x. The weight on the axlec is w, represented graphically by the line c 6. According to the principle of the parallelogram of forces (Art. 884), the weight «w may be resolved into the two forcesca = w,andcd=t,, the former perpendicular, thelatter parallel-to B.C. ~ The anegles*2 @Geanda vente each equal to A C 4, on account of having their sides per- pendicular to the sides of A CB. Also, ca=— 67a, as these two lines are opposite sides of the parallelogram ca 0d. The components 7, and w, are easily found by solving the right-angled triangle c 0 d, as follows (see Art. 754): bie 0 OS ee ee (217.) 1) Ui COO Sain = ale sete (218.) The force ¢/, is the resistance due to the inclination of the surface 4 C, and is independent of the friction. In order to PAVUNG 1105 find the resistance due to friction, we apply the following general principle: | . The friction between two surfaces ts directly opposed to the direction of motion, and equals the normal, or perpendicular, pressure between the two surfaces multiplied by the coefficient of friction. (See Art. 1784.) In the present case, the pressure between the two surfaces is w,. Therefore, the frictional resistance offered by the wheel is PE a= 2 7e COs oe (219.) If 7 is the total tractive force necessary to just pull the wheel up the plane, we must have f= te 4 fF w (sitet - ¢.cos-7),* (220.) If we wish to prevent the wheel from rolling down the plane, we reason thus: The direct force pulling the wheel down is 7,; but in this case the frictional resistance ¢, opposes the downward motion; the resultant force 7, acting down the plane, and the one that is necessary to apply in an opposite direction, to keep the wheel from moving down- wards, is, therefore, T,=t,—t, = w (sin r—c cos +). (221.) If we put the total rise Ad =f, the inclined length BC =i, and the horizontal length A C =—J,; the values of Z,, w,, and ¢, become: wp wp {= = md (222.) l; V¥PPt+l,? wl, w L, d, Li = a SX (223.) l; Vp’ +4, P sa aR EL ya AR alld Sa I. (224.) ; ; rT ey p from which corresponding values can be written for 7 and 7\. * The force 7’ is really only sufficient to balance the resistances; in order that there may be motion, the tractive force must exceed 7. But, as any excess of the tractive force over 7, no matter how small, will produce motion, we usually say that 7 is the force necessary to pull the load up the plane. 1106 PAVING. 1786. Approximate Formulas.—Where the incli- nation is small, we may write, approximately, /; = /,, whence Pi ere x lie W == UW) 1 == 6 We compat ce tori 216). The quantity f represents the rate of rise per unit h of (horizontal) length. The rate per 100. or per cent-‘is evidently 100 xX f Calling 7, the rate per unit, and 7,,, the h rate per cent., there results: ee (225) h reno oe (226.) h Pree ates f=r=78 (227.) Therefore, we have the following expressions for the value 8) 8 (3e he os T 100 Lae : 100° i= w (228.) rh Easy pi Bar ota Alison eerie es (; +¢) 13h; (Fs +<). (229.) 1787. Angle of Repose.—In descending a grade, the component ¢, becomes an accelerating force, and it may be necessary to apply a holding-back force 7, (formula 221), in order to keep the vehicle from ‘‘running away.” It is evident, from formula 221, that this will be the case when- ever ¢, is greater than /,, that is, when the component of the weight along the plane is greater than the resistance due to friction. If ¢, is greater than 7,, the force 7, will be nega- tive, which means that the vehicle will have to be pulled down the incline, no holding-back, or brake, force being necessary. It may happen that the resistance of friction is just enough to keep the wheels from rolling down, in: which case’ 7. = 7. and, therefore, from. formulas 2 © ae Sits t; er aCOSete PAVING. 1107 In this case the angle + (Fig. 430) is called the angle of repose; it is the angle just beyond which the resistance of friction is no longer sufficient to keep the body from sliding or rolling. This angle, of course, varies with the nature both of the surface of the incline and of the rolling body. A general expression for it may be found from the preceding equation; for, if we callit x,, we have (see Fig. 430) 2 Sitiat et COS st a= th “he e,’ and the equation referred to becomes l js rs whence (Art. 754), Pine ; batt, (230.) h Therefore, the angle of repose ts the angle whose tangent ts equal to the coefficient of friction. If the coefficient of friction is known, we look in a table of natural tangents for the angle whose tangent is that coefficient, and that will be the required angle of repose. Since hee Riana srees 100 7-., Ly it also follows that the per cent. of grade giving the angle of repose is Zz < To eer Ue (23 15) u 1788. Examp.e (a).—What will be the tractive force required to draw a wheel 5 feet in diameter, supporting a load of 400 pounds, over an obstacle 6 inches (=.5 foot) in height resting upon a level roadway surface ? SoLuTION.—The radius of the wheel will be one-half the diameter, or 2.5 feet. By formula 215, the tractive force 7/, will be equal to 400 x 4/(5 — .5) X.5 35 —.5 = 300 pounds. Ans. EXAMPLE (6).—What will be the total tractive force required to haul a load of 5,000 pounds upon an ordinary macadam roadway having an ascending grade of 4 per cent. ? 1108 PAVING. SoLuTIoN.—As obtained from the table of Resistance to Traction, the value of c for ordinary macadam roadways is 3; =.04. By formula 229, 7=5,000 (45 + .04) = 400 pounds. Ans. EXAMPLE (c).—What will be the rate per cent. of grade giving the angle of repose for an ordinary Belgian-block pavement ? SoLuTION.—From the table, the value of c for an ordinary Belgian- block pavement is 7, = .025. By substituting this value of cin formula 231, we get “100 = 100 x .025 = 2.5 per cent. Ans. EXAMPLES FOR PRACTICE. 1. What will be the total tractive force required to haul a load of 6,400 pounds upon a roadway paved with asphalt and having an as- cending grade of 2%? Ans. 192 lb. 2. What will be the total tractive force required to haul a load of 3 gross tons upon a roadway paved with good granite blocks, and having an ascending grade of 5 per cent.? Ans. 504 Ib. 3. What will be the rate per cent. of grade that will give the angle of repose for a roadway paved with ordinary granite block ? Ans. 4.00%. 4. What will be the total tractive force required to haul a load of 4,800 pounds upon a hard-rolled gravel roadway having a grade of 3 per cent.? Ans. 304 lb. 5. What will be the rate per cent. of grade giving the angle of repose of an asphalt pavement ? Ans. 1.002. 6. What will be the total tractive force required to haul a load of 2 gross tons upon an ordinary earth roadway having a grade of 104 ? Ans. 855 Ib. 7. What will be the tractive force required to draw a wheel 4 feet in diameter, supporting a load of 200 pounds, over an obstacle .4 of a foot in height, resting upon a level roadway surface ? Ans. 150 Ib. THE TRACTIVE POWER OF HORSES. 1789. General Statement.—The loads that a horse can pull upon any given roadway surface will not necessarily be proportional to the resistance to traction offered by the surface, but will depend upon the strength of the animal, its training, its familiarity with the roadway surface, and its ability to obtain a foothold upon it. Owing to the differ- ence in strength, speed, and training, the work that can be performed by different animals varies greatly, and it is pos- PAVING. 1109 sible to make only a roughly approximate statement with regard to the average amount of work that a horse can do. 1790. Average Work of a Horse.—The tractive power of a horse diminishes as the speed increases. Within moderate limits of speed, say from three-fourths of a mile to four miles per hour, the tractive force that can be exerted by a horse is nearly inversely proportional to the speed; the amount of work performed may, therefore, be considered constant. It is considered that a good average horse, weighing 1,200 pounds and traveling at a speed of 2.5 miles per hour, or 220 feet per minute, can exert, on a smooth, level road a pull or tractive force of 100 pounds, which is equivalent to 100 K 220 = 22,000 foot-pounds of work per minute. This represents the work of a rather superior horse, however, and it will probably be more correct to assume that the average horse, working regularly 10 hours a day, can exert a tractive force of 90 pounds when travel- ing on an ordinary level roadway at a speed of 2.5 miles per hour. This is equivalent to 90 * 220 = 19,800, or say 20,000 foot-pounds of work per minute. This value will here be used. Hence, for moderate speeds, the average tractive force that can be exerted by a horse will be given by the formula ) nae ee (232.) in which /’ is the average tractive force in pounds and s’ is the speed in feet per minute. If the tractive force #’ is known, the average speed s’ at which a certain load can be transported may also be com- puted from formula 232. As there are 5,280 feet in a mile and 60 minutes in an hour, speed expressed in miles per hour can be reduced to feet per minute by multiplying by 5,280 and dividing by 60, oP ae PaO, 20U) or by multiplying by the fraction — == 88: 1791. Maximum Work and Tractive Force ofa Horse.—The work done by a horse is greatest when he 1110 PAVING. moves at a speed of about one-eighth the greatest speed with which he can move when drawing no load; this will be called the speed of greatest work. The force exerted at this speed is about 0.45 of the utmost tractive force that the animal can exert at a dead pull. From this it may be seen that a horse can exert for a short time a tractive force of about double that which he can exert continuously, so that much heavier loads can be hauled over steep short grades than over the same grades if long. Hereafter, in problems, the maximum tractive force of a horse at a dead pull will be taken at just double the average tractive force, as given by formula 232. 1792. Examp te (a).—What will be the tractive force that can be exerted by an ordinary horse at a speed of 4 miles per hour ? SoLutTion.—A speed of 4 miles per hour is equal to AIS 352 feet per minute. Hence, by formula 232, the tractive force that 20,000 352 can be exerted by an ordinary horse at such a speed will be 57 pounds (nearly). Ans. EXAMPLE (4).—If, for the conditions described in Example (4) of Art. 1788, the load is drawn by two horses, what will be the average speed ? SoLuTion.—If the total tractive force of 400 pounds is exerted by two horses, then each horse will exert a tractive force of sa = 200 pounds, 2 20,000 300 = 100 feet per minute. Ans. and the average speed will be EXAMPLES FOR PRACTICE. 1. At what average speed will two horses haul the load of Example 1, ACtedi2 O82 Ans. 208.3 ft. per min. 2. What will be the average speed at which two horses can haul the load of Example 2, Art. 1788? Ans. 79.4 ft. per min. 3. How many horses will be required to haul, at a speed of 200 feet per minute, a load of 8,000 pounds upon a roadway paved with good granite block and having a grade of 2.50 per cent. ? Ans. 4 horses. 4. How many horses will be required to haul a load of 8,000 pounds at a speed of 200 feet per minute upon a roadway paved with asphalt and having a grade of 1.50 per cent. ? Ans. 2 horses. PAVING. HERI PAVEMENTS. GENERAL CONSIDERATIONS. 1793. Object of Pavements.—Pavements are con- structed for the purpose of improving the facilities for, and reducing the cost of, transportation, and for increasing the safety, speed, and comfort of travel. The office of a pave- ment is to furnish an impervious covering that will protect the soil of the natural foundation, and distribute the con- centrated weight of the loads more evenly upon it, at the same time affording a smooth, even surface that will offer the least possible resistance to traction, and over which vehicles may pass with ease and safety. 1794. Qualities Essential to Pavements.—A good pavement should be: Ist. Impervious, in order not to retain water or surface liquids, but to facilitate their discharge into the side gutters. 2d. Such as to afford asecure foothold for horses, and not to become polished and slippery from use. 3d. Hard, tough, and durable, so as to resist wear and disintegration. 4th. Adapted to the grades. 5th. Suited to the traffic. 6th. Smooth and even, so as to offer the minimum resist- ance to tracticn. 7th. Comparatively noiseless. 8th. Such as to yield very little dust or mud. 9th. Easily cleaned. 10th. Economical with regard to first cost and main- tenance. It is also desirable that the pavement should be of such material and construction that it can be readily taken up in places and quickly and substantially relaid, in order to give access to water, gas, and sewer pipes. 1795. Of What a Pavement Consists.—A_ pave- ment consists of two more or less distinct parts, namely, 1112 PAVING. Ist, the wearing surface, and 2d, the foundation by which the wearing surface is supported. The wearing surface may be termed the working portion of the pavement; it is that visible part with which those who travel over it are familiar. It receives and sustains the traffic, and is that part of a pavement by which the traffic is directly affected. The first nine items of the pre- ceding article relate directly to the wearing surface, which must be of such material and so constructed that it will not only be best suited to the traffic but also resist its destructive effect in the best possible manner. The wearing surface, however, is properly little more than a surface, and is not of itseli capable of sustaining the traffic and distributing its weight over a sufficient area of the yielding soil beneath it. Hence, it is necessary that the wearing surface should rest upon, and be sustained by, a foundation having sufficient strength to resist deformation and to distribute the concentrated weights of the traffic over a sufficient area of the underlying soil, so that the lat- ter will sustain it without injury. In any pavement the value and condition of the wearing surface,and,consequently, the value of the pavement, will depend largely upon the foundation. 1796. Different kinds of pavements are generally designated by the names of the materials used for their wearing surfaces. Prominent exceptions to this are the macadam and telford broken-stone pavements, which have practically the same wearing surfaces, but differ materially with regard to their foundations. These pavements are named after their inventors. _ There are and have been many varieties of pavements, of which the following are the ones most extensively used: Asphalt pavements. Wood-block pavements. Brick pavements. Cobblestone pavements. Stone-block pavements. Broken-stone pavements. These are named in about the order of their comparative merit, although the comparative merit of different pave- PAVING. 1113 ments will depend greatly upon the character of the traffic to which they are subjected. When properly constructed and each kind of pavement is subjected to the character of traffic to which it is adapted, most of these pavements have proved fairly satisfactory. Each kind named may be taken to represent a class- Under the name of asphalt are included not only all kinds of asphalt pavements, properly so called, but also all pave- ments composed of bituminous products, such as_ the pavement known as vulcanite or coal-tar distillate, etc. Under the name of ‘‘stone-block pavements” are included all pavements composed of stone shaped to any required form, such as the pavements known as granite block, Belgian block, etc. The name ‘‘wood-block pavements” includes all wood pavements, while by ‘‘cobblestone pave- ments’ is meant all pavements composed of natural stone, unshaped and unbroken. CHOICE OF PAVEMENTS. 1797. Factors Involved.—The selection of the pave- ment most suitable to a given roadway will depend greatly upon the local circumstances attending each particular case. The suitability of the pavement should be considered with reference to each of the following conditions: Ist, adapta- bility; 2d, serviceability, including safety; 3d, durability, and 4th, economy. It will be well here to notice each of these conditions separately, although they are more or less dependent upon one another. 1798. Adaptability.—The pavement upon a road- way should be adapted to the class of traffic that will pass over it. The pavement suited to the roadway of a suburban district would not be suited to the roadway of a manufact- uring center, and the pavement suitable for a residence street would not be well adapted to the requirements of a street sustaining very heavy traffic. In general, it may be stated that for important commercial thoroughfares iL ae 1114 PAVING. sustaining heavy and constant traffic, granite-block pavements are suitable; asphalt, brick, and wooden-block pavements are well adapted to the requirements of streets in localities where noise is very undesirable, such as important residence streets and streets devoted to retail trade; while, for pleasure drives and suburban streets having lhght traffic, broken-stone pavements are suitable. 1799. Serviceability.—The serviceability of a pave- ment, or its fitness for use, may be measured by the expense caused to the traffic using it, that is, the fatigue of horses, wear and tear of vehicles, loss of time, etc. It will depend to some extent upon the foothold that it affords to horses. The rougher the surface of the pavement, the more secure will be the foothold afforded, while at the same time the greater will be the resistance to traction. Cobblestone pavement affords an excellent foothold, but offers great resistance to traction and causes much wear and tear of vehicles and fatigue of horses. Asphalt pavement affords a less secure foothold for horses than almost all other kinds of pavements, but it also offers less resistance to traction and causes less wear and tear of vehicles and fatigue of horses. The best measure of these conditions is the expense to the traffic using the pavement. For this purpose, however, no statistics are available. The cost of wear and tear on differ- ent pavements has been roughly estimated to be as given in the following table: TABLE 36. Estimated Cost of Wear and Tear on Different Pavements, in Cents per Mile Traveled. On -cobblestone*pavemente.. 7 es eee a ee 5.0 On Beloian-block- pavement vn she eee 4.0 On*granite-bl6ck pavements 1. a ae eee eee 3.0 Oniwood pavement aren sian ate eee eee 2.5 On first-class broken-stone pavement............... 1.2 On“asphalt*pavement?.a eee eee eke O 1800. Safety.—The consideration of safety is properly included in that of serviceability. The comparison of different pavements with regard to safety is commonly PAVING. 1115 based upon the average distance traveled by a horse before it falls, this distance representing the comparative security of foothold offered by the pavement. The comparative security of foothold afforded to horses by roadway surfaces of different materials, stated in the order of their safety, is as follows: 1..Earth (dry and compact). 2. Gravel. 3. Broken stone. 4, Wood. 5. Sandstone and brick. 6. Asphalt. ”%. Granite block. Statistics also indicate the following conditions with regard to the safety of three very common pavements, namely, asphalt, wood, and granite: Asphalt and wood are most slippery when merely damp, and safest when perfectly dry; they are also safest when clean. Asphalt requires but little moisture to become very slippery; it is in its most slippery condition when the dry weather comes after rain. Wood requires more rain than asphalt before reaching its most slippery condition, but the slippery condition lasts longer. A small quantity of dirt on asphalt makes it very slippery. Asphalt is usually dry and safe in winter during frost, while wood, retaining moisture, is very slippery. Under snow, however, there is very little difference. Slipperiness may be prevented on asphalt by sprinkling it with sand, and on wood by sprinkling it with gravel. More or less dirt and dust will, of course, result from this. The tendency of the sand will be to wear out the asphalt, while the tendency of gravel will be to preserve the wood. Granite is most slippery when dry and _ safest when thoroughly wet; it is also less safe when clean. In damp weather the granite blocks become greasy and slippery. The blocks always become more or less rounded by the traffic, and, in dry weather, if the granite is of a hard, close- grained variety, their surfaces will become polished and very slippery. 1116 : PAVING. 1801. Durability.—The durability of a pavement is that property that relates to the length of time that it is able satisfactorily to sustain the traffic, that is, to the length of time that it remains serviceable. This will not neces- sarily be as long a time as the pavement remains in use nor as long as the actual durability of the materials composing it. The pavement will remain serviceable only as long as its surface remains in proper condition. The best measure of the durability of a pavement is the amount of traffic, estimated as tonnage, that it will sustain before it gets in such bad condition that the current expense to the traffic from using it, in excess of the expense that would be incurred from using a perfect pavement, will be greater than the interest on the cost of renewing it. The durability of a pavement will depend to a great ex- tent upon the condition in which it is maintained, especially with reference to cleanliness. A covering of dirt about an inch in thickness will protect a pavement from abrasion and greatly prolong its life. The covering of dirt, however, is very unsanitary and otherwise objectionable; in wet weather it produces mud, and in dry weather, dust. 1802. Life of Pavements.—The period of durability of a pavement is commonly spoken of as the life of the pavement. The life of different pavements under like con- ditions of traffic and maintenance may be taken as given in the following table: TABLE 37. Comparative Life in Years of Different Pavements. Min. Max. | Mean. Granite 4 aS ee FE ne em on ng rere or a i. 7 se 7 , a Ee i ash? Y fs ~ ¢ } a i - + 1 -- - te mh | ee. » eT, « yi om pe WR eh acintare ged. ee te eel Dale 0% 1 a : sae HIGHWAY BRIDGE: DETAILS-lI. te « a Wrought Irom. oa Gee Some ee feata:l//fe_ | All rivets are § Ye He, |) om Ree on ee a a eee Se ee ee ee a a a ee ee oe ae ee ap ee ee = ors g7, ’ 2. ae’ — =—- —-— 71> ; s LN NA OL oa eee egees Se cirene ee eednes am to eameat et Lo alee ete eee 3 Ss 2s Ca ee ee ee oe Oe ere teitrans Ja 22 -= ---~----=-- -+ st rrr en nn he - - - - - - - Se -- + - - h e p eF (Gte Fe ees ye JOPHIN SII TH, CLASS NP 4529. SF SS ‘J > : 7 : a > ee 7 7 rr] y K Se SF <7, Z ‘L3h)3hgh/24y x 7 . - : A cane a ee Sean é 23x2kl @40lb. Had ——/29, * 3f +5838 +f ae 22,Spaces @ Mg = 20— 24 —_—__——_ 25-53 C.toC. i a, Sa é _FighEind Post.” Twoktght. Twoleft. _ 2-8[?s@/0l. 18-8" * LL.A x xMé Inside. "PLOxRx/2# (in a ety Copyright, 1895, 1897, by THE COLLIERY ENGINEER COMPANY. All rights reserved. pn i) SEY a, NE of } u ia ree @ 2a 2S WER LGhL A) ge elie é < el. 92 Liyaede age. ms F- 15 Sp. @ /14 B Xx Dis: a e oe te =/4—03 ro tate 39 bn epee id Lhe henge a ae oe {EER arora eae Ep SSS = ; oo G + : a eae PL12%$x/8 Lig2 lop Chord. BEx5x ZL 5S" _Iwo of this. 24x2x41L. 4h / ----€ Nig)* be my 2 rs Pe ee Ney a8 2S te j Ss Ly gBRBN UY es FA oct pS a er RA Ns IN ll ol Qa ; = \ NM ea iG = nas 7 ». SF re et 3 4 ab teb Mar = — =F fed enals Caen od hase aie Daneel Telco Canty themed dada watery mois Wan etn b besCus inte Wnaden 5) f \ Se. af Ae - < ke od We = ———— = SS ae ee pe arg oe oes SPN NLRC ST Waa? 0h CSAS GF ic ‘aoe NY eee ee ICES OQ) SAMOS ge 3a? gE teraliT (tc. On lop Chore. Pl.t2xd xis" FG AL ¢ oe lerp2Xx 4x72 \ MES ‘| a ge 26 3X4 x G0" GAB -S ci U ae 3 4 odxel ! t ; 78 LeG3 L oe ae Ost. | £95 Portal Connection. _ four ff ERS. | Or Top Chord. JUNE 25,1893. | i el aul an tw mae ee lagee Lm 6.095 fei XY 0 Bios » mt, , a le Se a +4 “4s ‘ 4s oa ana ~4? ‘ 6 : “ey wiv teehee t) “Seat ys TERR ae bh 2ihgeerecro) XI- GE a” x4 PlateS Materiac: So ee Wrough tl[ron. - SS A La ‘4 ) | ‘y r * ! | i I ih CHD asd - H | TH a by 34 3" i Nae 4 ee a or Beis °° 1% y + 35 we | <3 “ te 3, | 4 ThisHlole in Aron t Angle ody, : “4 k-4$ 48 58 Hd Za 2 Note: Alt rivets are £" HIGHWAY BRIDGE: DETAILS-Il. ee Scale: /$=/ft. /0-O End to Center ——— rie op A POS @ 8 =E-/0§ Do pe é a oe ——— — C1 (1S aff XN ZF AF as SF a F z. a ZF IL 17-108" a Ty AL@4BUB4 ig? 5 Oe Hi Ge tt) ele a Fig l Portat. ‘ Two of thzs. Falla No | yy “ey ” 6 i _LO¢ 5. Hee Brace. _ “ o t Fo ur of tats. iS : ‘ ae ae : ——— 37 Poree = 950.@ /2=9 2 See -——3'- 0s al ee ——_—_——--——-/0'+0" ina to Cente; perc iNew 1 {SS SD fan X 4 Tint. Clit ee ae eS es He yA t x i : ’ Be. 2-5 4 L's @ /0.8 1b. 20-0" Fig2. Lateral Strut. Lwo fthis._ a fas SOON af BS ee let “T™ aie a co a see 2 a a A al GON Eh =m qn pn nan pn nnn nnn as eno vi ee ae af RF “ee yj ee rd ~ WZ Bolts ler lexgxe$h ” a a7] 44 4EX3x# LOZ 9I+/0 End to Center "L @402b. 239" —6- -O— 6-H Plate 24% x19-8" a Ix Leg, A ) Floor Beam. Fourof this. by THE COLLIERY ENGINEER COMPANY. SOKN sSNITHL, CLASS NP ASRS, All rights reserved. 4) ”~ Copyright, 1895, 189 JUNE 25,1893. \ ‘ he ae ' ~~ ES ~~ Saat! eS ha a it velo i - ye uy yon . er i tied ; I HRB fOER oN pene - ies ped ty s . : =f < one ie seis “> oa fain oe ace er Seed oe p ee + Rats. 2%, no Ali oi +e pe ee RE Apel a ares tae . ped and) — ' iP-y : + ; | ‘ : : — oe Ney = yw + aad -_ es O05 — engine, it ¥ Resa Pin, ppptagersat: _ HIGHWAY BRIDGE: DETAILS -II 27 Pin. Da : , is 8 Note: All rivets erag? # urtless otherwise pesciieeds : be Y ( Z ° Ly ae ta PBF = aes © | SN Se = Z I. SSS oes 1 we dty- Cay hs | @ : ba a phat tos oy “ted pte BX2S Vs@4 sib, 16°93" } het. V! Bia Jf “ 4 sf es) le She ear ee 74 / STtgs PLEZXEXIOE é |}———46.Sp. eras! hole “ld a £ Dae SE Coe ue nipsewiae: We etd rea"| re pees palaces 18iPeh = sts fs Rigg TI TD TR AC Hg ADA TO 1 FOr AG OOS SOS a NE 7 yy mis + : =o bor eo PBS eee LN ELGREX/O ee ee ee a J ioe GROG nek ONES et os wy : = 5 ee Sr | ~Ieg poe S6 95 FZ ween ei \F T= Sar ES SAE te: Ease ven : serene : oases : -L pS ge SE PULLEY ONG XSF. saaneel ae A ne yA -3GX2US @ 5.716.725 = Filterexpiet/ Fig! End Panel Lower Chora. Filler 2£4¢45/ * | 3 : es: 2 | ra Four of thts. ; 7Chor here Four of this. ee fug2. Second Panel Lower Chora. 28Pin. Four of This. / a Og Plate 6XZX/6-/ = Ss 2 8-55 ‘Ered to a Ger Ae oem a ; Rivet Holes ariglee js. 4 seri tean Be ce 3bxe8 L’s@4.8 18.16+/08- Konel Dror = Sap Mae rea See ef er 4g LOSD. @og= =/6+3* Uh GE | Wwe I. Nog Jee Lead. SB be Girisd Two Two of this. a Pa te Le ; ee: : : SS 2 re >_"-* Segre SS » : PAAS..k : ~" wk ~~“ a eer 2: < - a. ‘ a i hokes y ah Gm war hy Xow i i: HIGHWAY sis el DETAILS-IV. Scale: a @ 2a) a ae ta =e —) i ia ch it ry \ST “aaa \ Sw] i fee H } | rp v7, fod a nh G a ” Res: eke ee occcumbenmnrnce? cel] pare SUN by ae a AlCl Matertal Wrought Lrore untless otherwzse wspeczfied. _Liy EBA HANGER Ly tORE FCS. | LEG 9PIin, Steel. Lourof this: ot 5 Lig DIGS Tie Beer: ee LQht f CRS. fig Pere. 209 peo orcneal L4G 8 5EPAa7Tator- C Piss a —LOUr Cees as four of thts. a 20- Loa" Wa mon ISPin. 1 Be a a ny Pin. _Fig2 Counter ju wie anaes ; - Nag a pie _hrght of Chis. 23 Pin. os eet sets, gga Le pee i <9}. a 4. Sckae S- B “ : le LEGS. BottomLaterat Rod. e Be E ie. four of this. LQ. cree ” ag” ©, +4 Sanaa 3 1 Sn nage LONER s ee oan to 18-23 , : bs EPR ar te. xe Meo EPire. Pin _Flep Vertical Rod. ze es ; H/ _ ie Rad ie Te mt ee 2 i BS a rs ea | Wa A y va wo af k a Ax 43- ee A 4 Rods 25-105. | a, eS 19-74 i ee Su tineaadahene ey Sota am A GP pks Lames, Lily Lop Lateral Rod. LbG6. BottomL aterat Lod. fee Stet A this. S20. of this. SOPEN SMITH, CLASS NP ASAD Copyright, 1895, 1897, by THE COLLIERY ENGINEER COMPANY. All rights reserved. JUNE 25.1893. COSPON SSW LD FELINE MILOL *PeATOSoI SJYB3II ITV ‘lo Oo}! to) c te) ie) ° oll [e) O}} fo) ° io ral —— ° O Z fe) ° = | = ||| —=— ORS ie 1) Se OF Olm® 5 a F oO = = ——— = as == ORB 0 ofOo 0 NOX ° re ° oll\| ° of \\\ fe) oll] ° oll| ° oll ¥ i] ° Ol} ° ol) ° of ° fo) [e} O jo fe) Co O (e) O io ° jo ra) jo WY III! C4 ogee Oo Ni Ow Oo Hi to | oO T 2 Bea 9 Saar 9) 2 | id \\ MVS eH) | ch oo Cor cm r ————— UOT TIT = AT ce aaa o.9 00000000000 090 : ee SSS —— 0.0 000000 90000000000 0 8-O-o-5 5 { LOO | P l { t {| ‘ANVdUNOD YAANIONY AUAITION AHL Aq ‘L6RT ‘GEST ‘WUsrrAdog €68/ OS AMAL =e oO” Ay. 4 oy SS 4d 5} 9 I Sg ‘w ‘oe nf QS BY ies teas Be i aiceetiaan Sia Bas ea By Fa ek ig) 3S] 38 3 > eg] a} I a sy 1 8 be ae ei rr n Oven ANY PAGES CONTAINING TABLES AND FORMULAS. COEFFICIENTS FOR ROADWAY -CROWNS.* —_—— Value Character of Roadway. of ¢. Common earth roadways...... | zy Ordinary gravel roadways.....| 35 Broken stone roadways....... bale Wooden block pavement...... dy WCopblestone pavement......~. ay Granite block pavement....... | sty Well-laid brick pavement..... isa First-class asphalt pavement..| 7+, * This table gives the value of g in the formula sip p(i0g — 1) eset E 800 in which c is the amount of crown, w is the width of the roadway, and f is the per cent. of grade. INGREDIENTS FOR ASPHALT PAVING MATERIALS. Material. Per Cent. (1) PB UA LUV CECI LGRE Cenc teri ee # a. oo eee ee I Sand. 252 igs ee se ee cone a s) Brokenstone ay est tek ice ee 7 (3) Pértland cement 2 2 ee eee I DANG Jo sess yb ae one lee ee ee ee 24 Gra Velie ois 65h IRR eae cetera coe ee 3 Broken Stones.“ ek eae ee eee 5 TABLES AND FORMULAS. . 3 RESISTANCE TO TRACTION ON DIFFERENT ROADWAY SURFACES. Resistance to Traction. In Pounds per Gross Ton. Character of Roadway Surface. ferrerns of Load Maxi- Mini- | Pa mum. mum. lt Earth (ordinary) Ren te oe 300 125 200 ar Earth (dry and hard)....| 125 iio 100 sis Gravel: (COMMON), © 50. 147 140 143 ar Minvelthard- rolled): 6. .2 pie 75 hy Macadam (ordinary)...... 140 60 go ay Matadam (G00) v.22... 80 4I 60 ar Macadam (best) s?.2..%.". 64 30 50 ar Cobblestoneé*(ordinary)/4) ss. Puan 140 ae Cobblestone (good)....... Pars ve i 75 gly Granite block (ordinary).| .... aPar go se Granite block (good) .... 80 45 $67 }. a. Granite block (best) ..... 40 25 34 ae Belgian block (ordinary)..| .... Fash 56 Jy Belgian block (good) .... 50 26 38 = HATE Oar Rtas, ioe eed 56 32 44 ahs Wooden block (in good OATCL LOTR gens o's ais 40 20 30 alg JRE OTE WS) og eee er 39 15 22 aid INGREDIENTS FOR DISTILLATE PAVEMENTS. Material. Per. Cent. Sa Gps en Te ela ts S cr ety dw 4 Sa 63 to 58 Pore Stone OF LOCK OUSt .6 a ayy is >< 26.10 23 Dtetiliateapavine .cement. <5 ce. cue Tato 15 eee Te COMIC or errs «estes on = it 1, 90 PlOseer mer och sivean af cite oahe Ss 0.15 A Los Ramet PL ISE YL Caentel ea ehat ait aiorsi os pask ee «5 0.10 4 TABLES AND FORMULAS. CRUSHING RESISTANCE OF DIFFERENT PAVING MATERIALS. Resistance in Pounds per Square Inch. Material. Minimum. | Maximum. Average. Graniter anaes Sees 5,300 35,000 £9,000 Trap-1GCkis 2.72. eee 19,700 22,300 21,000 Sandstotes..) ease ee eee 2,200 42,800 10,600 LimeéstGn eosin eeoeeee 3,600 16,900 9,200 Brick, "paving. ..eee ee 7,000 18,000 9,000 Bricks commons) fee I,C0O 12,000 3,400 WiGGd eis: 5s ee 2,900 19,000 7,000 SPECIFIC GRAVITIES AND ABSORBING CA- PACITIES OF PAVING MATERIALS. Material. Specific Gravity. pacaetnaiiman Granite cto wnt, cee 2.60 to 2.72 7 1sto meobG Limestone@... i. ss 2A Ost Or 27 5 5.00 tO .200 DANCStone nes. DRT Cee ais 6.80 to 2410 Bricks payin? en pee 1.90 to 2.70 7.00 tO .140 Brickcommon..ca ee 1.50 tO 2.00 25.00 to 2.000 WOO. cehoe ect om Beas £34 COs se 9.00 ton) #16e ASpnalit eee ees .goto 1.80 | Nearly impervious eo ee eee INDEX LA PAGE Abrasion, Tests for. s ; 1130 Absorbing capacity of paving ma- terials . = - : . 1132 Accuracy of dead toad : 1060 Additions to cities . ‘ 1047 Adjustment of grades at curb angles. ; 2 4 ‘ 1073 Adverse possession . ‘ ; - 1098 Aggregate and matrix . ‘ ae tlao Alinement of roads. ; : - 999 Alternate stresses, Latticing of members subject to 857 ih stresses, Provision for, by Cooper’s specifi- cations r * . 825 Anchor bolts, Position of - . 1016 HS bolts, Size of . ; .» 1016 = bolts, Specifications re- lating to . " + gor 4 bolts, Various forms of 1016 Anchors, Specifications relating to gor Angle of repose ; f 1008, 1106 Angles in tension, Connection of . 815 xe Maximum and minimum weights of : ° 2. .830 Area, Gross and net A . 854 * Increase of, to provide pe bending stress . ; se ORT “ Increase of, to provide for wind stress . A x ae Beye ‘“« “Minimum, of lateralrods . 816 ‘ ~of bridge member, Determi- nation of y 815 * Reduction of, at poe required of steel 811 “Reduction of, by rivet holes 81s Arrangement of floor joists . 862, 1045 oS of rivets . 924, 941, 946 Asphalt . A é ; - 1135 Ee Bermudez . F : Heda “block pavements . Fe eet at gutters A : - SeLLIOX PAGE Asphalt, Lake and live . . <) 2154 = pavement on railways 1162 ne pavements - . 1154 ot: paving cement. 1158 *. Rock ; eer S5, 5rOs as Rock, pavements . an £163 oy Sources of supply of II54 Asphaltic cement ‘ 1140, 1158 Asphaltum (see also Asphalt) 1136 id paint . p : - 1077 on pavements 1154 a Refining of 1157 Attachment of hand-rai! nosts . 1074 Avenues . 5 ‘ : : . T1045 Axle friction . ‘ 1101 B PAGE Back wall of bridge. . . 1045 Balanced section : ‘ pane O42 Baltimore truss, Desarvipton of 778 = truss, Stresses in, graph- ically determined 779 Barbed bolt 2 : A é 1017 Basalt : , : ; mxrrga Base, Bituminous, for asphalt pavements . ° T156 as Ctty = d 1088 Ss Concrete, for pavements . 1143 whe Hydraulic, for asphalt pavements 1156 Batten plates, Design of 945, 950 a plates, length of, Estima- ting the 1057 se plates, Pitch of rivets, in 946 oe plates, Specifications re- lating to . : : 300 Batter braces . é s A - 687 Beam, Bending moment of . 884 nA flanges, Pitch of rivets in 967, 971 ss overhanging both supports, Uniform load of 7 we hangers, Designof . E IOIO 998 Xil INDEX PAGE PAGE Beam hangers, Double . 1067 Bolts, Anchor . ; : : oe LOL de hangers, Ordered length of 1039 ‘SS Trectian. : i 4 - 1052 a hangers, Plate 1067 & SBormsror 1017 hangers, Position of 973 ‘* for wheel guards, Naber ae hangers, Single . 1066 and size of . 1049 se hangers, Specifications re- “ Shearing and bearing lating to 89g stresses allowed on 897 zs hangers, Stiff . ~1069 ‘* Specifications reiating to go2 se hangers, Weight of, used Boulevards ; : at 1071 in estimates . 1059 Braced portal, Stresses in 795 Beams above cherds 1066, 1069 ~=—s Braces of truss . 687 os below chords 1066 Bracing, Specifications yalnteae is goo Bearing stress on pins ae 932 Brackets, Sidewalk . 798 a stress on pins, Determi- Brick pavements 1170 nation of . 915 Sean ii 1137 os stress on rivets . 897, 921 “ " Size of paving 2. eYIGs be stress on rivets, Determi- Bridge, Classification of foaae on. 690 nation of . 920 oe Deck ; , 687 es stress on timber 876 ee floor, Weight of. < 700 Bedplates, Design of IO14 a Half-deck . - - 688 Be Specifications relating ie High-truss . 688 to Fs ‘ : oe POOL ce Low-truss ; : 688 Belgian block 1135 e Pin-connected . : - 688 i. block Pvanicnte 1142 we Riveted : : 689 Bench mark, Primary : 1089 oe seat 1045 Bending moment due to weight of ee Through OST, beam 883 ay Truss, arch, and suave es moment in el Bast ace sion, distinguished 685 to wind pressure 851 Broken-stone roads. 1025, 1033, 1038 ae moment in floorbeam 728 st stone pavements 1146 es moment in floorbeam Burnettizing timber 3 : a LIES with sidewalks 799 be moment in pins 927 = moment on shoe plate 1009 C PAGE Be moment, Position of load Camber . : A = 2 + 903 for maximum 802 ee Effect of, on length of * moment, Stresses due tb 735 diagonals . ps : 905 re stress allowed on pins 897 ‘S Increase of panel (eneen te stress due to weight of to provide for , 4 + NOO4 member . 880 “A Specifications relating to go2, go5 i. LESE ear. - 809 a Usual amount of 904 Bill of iron ; 1034 Camel-back truss . ;. ; 1 775 ‘of lumber . ; 1044, 1053 Cantilever truss 5 x 686 ** Shipping 1048 Capacity of bridge . : Ae telirers: Binder course 1157, 1168 Cast iron, Use of, in bridge wore: 807 Bitumen ; 1136 Cement, Asphaltic . s Ap enh obra ots! Bituminous base foe BETA pave- cS Bituminous PR erie «, £E40 ments 1156 . Distillate paving 1168 Bs cement 1140 Center of gravity found by mo- : limestones 1135 ments : : : - 882 ‘e sandstone . ; 1135 Channels, Distance between, in Block, Belgian . F : LLL chord sections . 827 as corners. 1080 ha Formula for width of Blocks, City 1042, 1044 flange . ‘ 833 ‘* ‘Expansion be , . 1152 * Maximum and mini- “ -Paving (see Paving Blocks) mum weights of 5 EES INDEX PAGE Check-nuts ‘ é : : - 999 Chemical treatment of paving blocks. ; : ‘ : Chord stresses, Formula for, in Howe & Pratt trusses . 762 stresses, Formulas for, in inclined-chord and _ di- vided panel trusses . 768, 781 stresses from wind pres- Sure = 3 4 5 Ole Chords, Curved : : ; ~ 750 a Effect of wind stresses on 850 1152 ch 66 Inclined ae a ; 750, 764 ve Lower, Design of 818, 979 *“* ‘Upper . . 833, 948 if: Widthof . " : a 760 City base . ‘ : : , . 1088 . aatum : ; ‘ é 1088 Clay 5 ; ‘ : ; : - F137 Clearance between eyebars . a OT if General rules relating BO. . ° : Ore a of pinholes. : . 899 Clerk Maxwell method for the graphical-+determination of LVesSeS\ s . . ‘ - °733 Goals tar" ©: } , ; : eee +s: ee >. tar pavements : « 21954,.1167 Coat, Cushion (see Cushion Coat) Cobblestone pavements . II4I Coefficient of elasticity of struc- turalsteel , - A ee eb OL Aex pa hsrons of wrought iron and steel . ; ; 3, LOOT a of friction. : . 1008 As of friction. of wrought iron, steel, and ma- sonry ; : ap. eyo ‘ of rolling friction 1103, 1107 Cold-bending test. : , . 809 Columns, Formulas for unit stress allowed on . ‘ . 824 i Length of : ene 43 Rankine’s formula for resistance of : i > B83 Compression mein bers F Hy ee 3: members, curve and straight line, For- mulas for - 823 eS members, Length of 825 ms members, Propor- tioning of 826, 833 ee members, Symmeét- rical and unsym- metrical , . . 1084 Xill PAGE Compression members, Unit stresses allowed on 824 members, Usual forms of . : . 819 Compressive stresses, Formulas for, based on fa- tigue of metals . 873 cs stresses, Formulas for steel. . 869 * stresses, Formulas for wrought iron 822 Concentrated loads cA . 690 ae wheelloads . ab COG Conerere, * “ : : . A) ails. Connections, Strength of 4 .- 897 Construction of pavements . meet iat " of roads °. 4 <2 Ose Continuous truss, i = < 8eC Cooper's specifications for highway bridges . : : 5 i » 869 Cost of pavements 1118, 1128 Cotter pins ; , ‘ : 1023 Be pins, Dimensions of . . 1024 a pins, Grip of : : . 1024 Counter stresses, When, are in- duced : ; - : , ~ 7oo Counterbraces . : : : - 687 he Design of . 987, 992 “ When, are required 711 Countersunk rivets . Country roads (see also Roads) pe roads, Difference be- tween, and city streets 95 Course, Binder , 1157, 1168 Cover-plates, Maximum width and 1083 thickness of , : # Ges he plates, Pitch ofrivetsin . 41 af plates, Width of . ; ONE Se: Covering capacity of paints . - 1079 Creosoting of timber F : 5 ELSS Crossing stones ; : - . x182 Crown, Curving and sloping . «. 1059 Me Eccentric . ; : S =i1070 . of roads : : A 1018 es of streets. é ; +). 1057 Crushing resistance of paving materials é : . ~ phrgt Curb angles ; : » f « 1675 a COrners. ‘ FS - 1072 Curbing, Construction of 4 . 1172 =) Height of . : : . 1066 Curve formulas for columns , » 023 Curved chords, Graphical deter- mination of stresses yng x : A 50 «© chords when used ... 749 xiv’ INDEX PAGE PAGE Cushion coat for asphalt pave- Design of compression members 826, 833 Tents ee : : 1160 — ,OL Counters: s 4 987, 992 se coat for brick pavements 1171 ‘of diagonal members 986 coat for stone pavements 1143 = of end post . 833, 941 oe coat for wood pavements 1149 os of floorbeams 859, 966 es of intermediate posts 951 D PAGE o of knee braces 964 Data of bridge . : : : “2 O05 Ys oflateralrods . é Qg2 Dead load . ‘ ; : 690, 704 * of lateral struts . 838, 963 ‘* load, Approximate formulas = of lattice bars 845, 958 for calculating 705 si oflower chord . 818, 979 “load, Difference between oh of pin plates 914, 944, 980 assumed and final 1060 Oy of pins . 912, 931, 936 *“ load, Distribution of, be- Me of portal Beaches: 842, 958 tween upper and lower ix of shoe strut 848, 965 chords . 707 ss of tension members 817 ** load of bridge wit th Ss tee - A of tension web members 986 walks 798 ek of ties °. : . 986 ** load stresses 7) of upper chord 833, 948 ** load stresses for, wrodete, ce Practical hints concerning 1087 iron compression mem - Detail drawings, Natureand useof 895 bers (Cooper) . 824 #&Details of floorbeams 966 ** load stresses for ae ne My of specifications, Relating iron tension members to : 897, 902 (Cooper) 814 Diagonal Serpe ies Calculation of ‘* load stresses, Grouioal ae exact length of 905 termination of, in Balti- ru members, Design of 986 more truss . : : 77 S members, Economical in- ‘* load stresses, Graphical de- clination of . 5 749 termination of, in Petit Diagram, Erection 1053 truss : 787 Dimensions of nuts. : Ar falels) ** load stresses, Graphicn es ee of timber floor aeiceae 865 termination of, in truss Distillate pavements 1167 with curved chords 751 mi paving cement 1168 ‘* load stresses, Graphical de- Divided panel . = . " ee 77 termination of, in truss Dolomite . ; “ 1135 with inclined chords . 765 Double beam aeteer 1067 *““ load stresses, Graphical de- oo intersection or aa ah te termination of, in truss quadrangular truss 774 with parallel chords . 707 Drainage of roads IOTQ, 1031 ** load stresses, Graphical de- Drawings, Detail and working 895 termination of, in Whipple oc shop, Data given on 1026 truss E ; A oS Durability of pavements 1116 Deck bridges 687 “bridges, Ticeepntion of dana E PAGE load between chords of 877. Earth roads . 1030, 1035, 1038 ‘* bridges, Minimum stress in Eccentric crowns at street inter- center strut of ome Ow sections : 1076 “bridges, Stresses in 711, 715 Eccentricity, Newatiog ; ; ». O07 Depth of floorbeam Nay 5) wi Neto ‘ : ~ 887 Ee. tess 749, 862, 871, 875 Ht of pin plates . 1084 ‘** of truss used for lateral sys- ss of pins é : - 886 terse. ; 712 4, of section. . a a) ROS Design of batten plates 945, 950 = of stress, Iiffects of . 881 of beam hangers. 3 GOS Economical form and height of 3 of bedplates - - » 1014 bridge truss . A ° ° ° 749 . INDEX XV . PAGE Economy of pavements . ‘ ve TL, Effect of wind on chords and end posts : 815, 850 Effective depth of dcacient S730 Elastic limit of structural steel in general. . 811 = limit required by eieciticn: tions for steel . OLS a limit required by specifica- tions for wrought iron.. 809 Elongation reauired by specifica- tions (steel) ; i 9 Sic required by specifica- © tions (wrought iron) 809 “ec Encroachmert of lines . 3 - 1097 End posts, Correction for wind stress 815, 850 ‘* posts, Design of 833. 941 Erection bolts, Use and dimensions EY a: " . 1052 “ * diagram, Ratitre ted uses CFS ‘ ; eV L053 Error in determining maximum web stresses - . 2 P 793 Estimates of weight of epitartal, Making . ‘ 5 - 1054 Expansion, Coefficient of tor wrought iron and steel . . 1007 *s in bridge work, Peovts ding for : + QOT, 1007 He of paving blocks . pe xa Be rollers, Design of . 1005 Ke rollers, Specifications relating to . ; . ~ OnE External forces intruss . A . 685 Eyebars, Clearance between - 937 ra FHeads of . “ s 899, 975 F PAGE Fatigue of metals, Cause of . . 872 he of metals, Formulas for unit stresses founded on 873 Le of metals, Importance of, in structural work. : 9873 Ss of metals, Requirements Ota : : : ¥ hess “a of metals, Specifications foundedon . F 874 Ah of metals, Woehler’s fae relating to A . . 972 Fiber stress x 5 : - poh: Field rivets : ‘ A F . 1048 Filler rings, Uses of ; : 3. LOze Final pitch of rivets, Determina- tionof . . s . ° Ag Gteye PAGE Fixed load ‘ ; ; - 690 Flange stresses in Haas renin: For- mulafor . 2 ; oe ese. stresses in portal, Deter- mination of 721, 725 Flanges of channels, Width of Ae tier: og Pitch of rivets in 967, 971 Staying of . F : 875 Flat-ended columns, Require- se ae ments. for ‘ - : ‘ . 1086 Floorbedm hangers 998, 1066 “stresses ‘ : - 726 Floorbeams . - 7 . = 720 eg Bending moment at any pointof . - 728 cs Design of 859, 966 “5 Effective and _ total depthof . : 730 # Formula for w Stefi of : “ - 927 ke Maximum dines stressin . z © 73° Maximum shearin ., 731 Position and connec- tionsof . : 1066 Ly Shear at any point of 968 vs Weight of, used in estimates. : - 1058 _ with sidewalk canti- levers : ; - 798 Floor, Details of ; é - 0966 ‘© joists, Arrangement of 862, 1045 y joists, Dimensions of . « 865 ‘* = joists, Metal . 1062, 1064 ‘* joists, Stresses allowed on . - ‘ : «) 863 I WeIritc Or. ° : - 706 Footways, Artificial stone * £176 os Brick : P . 1297 Compressed Eeaeai te 6 2. + Details of ; ~ Shey re Gravel . : a EEOE “ Natural stone - axis *S Sheet asphalt 7 + 1178 e Tar concrete . , < Tico ss Wood - ‘ : - 1180 Forces, External 5 - 685 Forked ends, Specifications get Cins ty A : " . <2) -G00 Foundation for asphalt pave- ments ‘ . 13156, 1164 s for block-asphalt pavements. - 1166 for brick pavements 1170 for coal-tar or distil- late pavements . 1168 Xvi INDEX PAGE . PAGE Foundation for granite- block Graphical determination of pavements Tras stresses in inclined os for wood pavements 1147 chords . : 765 Foundations of roads 1032 -t determination o f Friction, Axle IIOL stresses in lower lat- te Coefficients of, for ateeh eral system . 711, 715 wrought iron, and ma- y determination of Ssoury,) - 878 stresses in Petit truss 787 es Coefficient of rollin 1103 o5 determination of oe General law of ; SeeLTOS stresses in Pratt Rolling. 5 ‘ LeeLIOL truss 694, 707 s¢ determinations ot stresses in Warren G PAGE girder? * .6t jos, pee Girder, Latticed : : ; . 689 Graphite paint . , : ; . 1078 * Plate. - cee OSG Gravel roads 1028, 1034 “plate, Effective Gepen: of . 859 Greenstone ; ‘ : : ek ‘¢ plate. Minimum thickness Grip of cotter pins 1024 of web of . P 3 . 859 ‘* of pins, Determination of 1018 Me plate, Stiffening of . - 850 Gross section . 4 : = Ose ‘© plate, Thacher’s specifica- Gutters . “ : : ° . 1064 tions relating to . . 875 ©) chords. & : - g5t Imperfectdesign . - : - 1082 INDEX PAGE Inclined chord . ‘ aaa tee Inclined chords, Formulas for stressesin . A 763, 781 “ chords, Stresses in truss having 765, 768 be chords, Use of . a TAG Initial stresses in lateral rods, Treatment of 825, 838 Intermediate posts, Design of 833, 841, 951 Intersections, Street 1071 Iron hub guards 2 ; : + 1072 * order : 7 - a eerOys ‘““ order,how made ., « 1035, 1042 ** “oxide paint , - A - 1077 J PAGE Joint filling for pavements 1144, 1151, 1171 Joints, Splicing 5 : - 898, g50 » ») ae5 * of pins . 1037 a of various members, Esti- mating the ‘ ; » 1055 ie Theoretical, of bridge members . : - . 825 Lewis’s specifications . : . 877 Life of pavements : 1116 Light weights . - . : - 1083 Limestone. ; 1134 3: Bituminous 1135 Limitation, Statutes of 1098 Limiting values of pitch of rivets 808, 964 Line of action of stresses in mem- bers. P ; : - 687 Lines, Hacpoanhinesk of. : - 1097 ‘* street, Marking and per- petuating : 1089 Live chord stresses, Maximum . 6094 “load =. ‘ 600 ‘* load stresses a v1 lowe a es Vv Cooper's specifications for wrought-iron members 814, 824 load stresses, Graphical de- termination of, in truss with parallelchords . + Aood load stresses, Graphical de- termination of short method 737 load stresses in Baltimore truss ‘ 782 load stresses in fchetda fad d from dead-load stresses . 753 load stresses in Petit truss . 789 load web stresses, Maximum — 699 load stresses in truss with Ur y Cul Omen crined chords 753, 768 load stresses in Whines truss : . F : « 1776 XVill INDEX PAGE PAGE Load, Concentrated ‘ A A siete) Maximum stresses in chords, Con- Dead ; ; . 690 dition of loading for 694 “ “Bffect of diginbution of, on a stresses in) chords: stresses inmembers . eo 604 Graphical determina- Loads, Moving . c : * — 6go0 tion of . ; : 697 | “PAGS wee : ne. a . * Gor - stresses in deck pridees 715 ‘* Position of, for maximum Es stresses in diagonal and bending moment . - 802 vertical members of ey Unione 3 A - - 690 Pratt.crusse. P 700 + Wheels 4 : : ae. aaletsye: us Wind . ‘ : : - eo Location of city streets . ‘ - 1040 oe: of highways G97, IOI se of highways and rail- roads compared . 7h 008 Lomas recessed nut : : » . 102T Loops of bars and rods 987, 1037 Lots, City : ; 4 1045 Low-truss bridges . 3 “ - 688 Lower lateral system, Graphical determination of stresses in 7Ily 715 Lumber, Bill of 1044, 1053 = Usual sizes carried in stock ; : ° LOnd M PAGE Macadam pavements - . set tAO ts roads A - ; 1025 Maintenance of highways 1037 a of pavements . + L126 Map of highway road 1016 Materials, Absorptive capacity of paving. : : 1132 ue Crushing resistance of paving. 1131 a Ordering 1034 “e Sizes of, carHedin aoe IO4I ‘ used for pavements 1129 es used in bridge con- struction. 2 2 COT ee used in bridge con- struction, Selection of 8o2 Matrix and aggregate II40 Maximum and minimum wolehts of channels . ; %, 1030 O bending moment, Posi tion of loads for - 802 : Error in, from assump- tion of panel concen- trations ‘ : 7S * length of compression members. goes &¢ live-chord strevcee - 604 eo load web stresses . : 699 es shear in floorbeam a e7at stresses in Howe ioaes 742 stresses in web mem- bers, Graphical deter- mination of . : : Joa stresses in web mem- bers, Short method for . A ; ne VEY Medium steel, Properties of, re- quired by specifications 811. 2 steel, Unit stresses al- lowed on d - 869 Members, Convenient and limiting dimensions of . 28 WSOE , Exact length of diago- nal ; Z ; ros pe Line of action of stresses ine cl : - a OOF < Maximum and mini- mum dimensions of . 825 My Stresses in, affected by distribution of load 692, 694 “e Tension and compres- sion “ . 686 oe Theoretical length ef « 825 Metal floor joists. Z . Ic62, 1064 Metals, Fatigue of . ag Es ore Mineral pitch . A : 1136 Minimum area of lateral rk: ES zs diameter of pins 899, 1020 . thickness of web of gir- der 7 : - - 859 Modules section . : si - 1063 Modulus of elasticity . < . 80x Moment diagram, Determination of stresses by : 733 Moments, Principle of, ee ohed KG determination of stresses in braced portal 5 F 4 - 796 Monuments for street lines . « I0Q1 Moving load. : - - «4660 N PAGE Nails, Dimensions and weights of 1050 Name plates. : “ : LOL Negative eccentricity . : - 887 Net eccentricity 4 - ‘ . 8O7 INDEX X1X . PAGE PAGE Net section of bridge members 815,884 Pavements, Safety of . TII4 Wats, Check . 3 : 699 bs Sandstone-block sen ht ‘Dimensions of : - 994, 996 iS Tonnage of traffic ‘* Lomas recessed . s = tO2T over . 1124 See Pilot oe - ; IOIg py Wood . 1147 “ Standard aps: 9099 ~=@ Paving blocks, Asphalt . 1165 cis blocks, Chemical treat- O PAGE ment of ‘ . r1g2 Order list, Making an 1034, 1040 oe blocks, Expansion of. A pee urdered lengths of materia. 1035 = blocks, Granite 1144 “ blocks, Sandstone 1145 d PAGE Y blocks, Wood 1149 Packing rings, Usesof . : + 2025 Petit truss, Description of 786 Paint, Asphaltum ,. A ~ 1077 * truss, Graphical determina- ‘* Graphite : = : - 1078 tion of stresses in 787, 789 “* ion-oxide . : 1077 Pilot nuts : 1019 *“* Red and white-lead : 1076 Pin-connected bridges 688 Painted surface, Amount of . . I080 ** connecied bridges, Use of 877 Painting of bridges 4 * +. 2675 ** -pilot, Use of : 1020 Preparing iron for . - 1081 ‘* plates, Design of 914, 944, 980 Paints, Covering capacity of . - 1079 ‘© plates, Dimensions of 024 Panel F : ; . 686 ‘* plates, Eccentricity of 1084 ‘* concentrations P ‘ s 60% ‘** plates for tension members, ** concentrations, Error arising Metal behind pin in 983 from assumption of . ft sa ““ plates, Strut resistance of 936 eT ided: : ; : Sey i 5 ‘* washers, Description and uses ‘* Increased length of, to pro- ef? ~ é : 1025 vide for camber go4 Pinholes, Clearance of 899 i lesigths: —. : ; ‘ 686 be Reinforcing plates in goo = load. : : . : 691 Pins, Bearing stress allowed on 897, 932 ** load, Determining the 691 *“* Bending moment on 927 Patks:. = ; ‘ 3 s rose ‘* Bending stress allowed on 807 Pavements, Asphalt, for railways 1168 “Clearance of . 899 Bo Asphalt block 1165 * Computation of bending mo- ss Asphaltum . Lrs4 men on : ; * 027 a Belgian-block . 1142 ‘* Correction in size of, to pro- f Brick ; 1170 vide for wind stress . . 929 a Broken-stone . reat ‘* Determining size of gI2, 932 St Choice of . 1113 ‘* Dimensions of, used in esti- ¥: Coal-tar “ 1154, 1167 mates . : , : . 1057 3 Cobblestone L141 ‘“* Graphical determination of ‘ Construction of . 1141 bending moment on 936, 939 Me Cost of A 1118, 1128 ‘* grip of, Determining the 1018 7 Different kinds of 1112 “ “hip, Design of. 936 ts Distillate. 1168 “ Length of 1024, 1037 fs Durability of 1116 ‘“ Maximum bending moment sf Economy of 1117 5 ae , f " 913 = Essential qualities ‘* Minimum diameter of 899, 1020 of Fs " TER LITS “ Position of , , 886 Bs Granite-block 1143 ‘** Position of bearing on 925 as Life of . 1116 “Resisting moments of, how a Macadam 1146 determined . 4 : Se ites “6 Maintenance of . 1120 ‘* Screw ends of . g 1019 = Materials used for . 1129 “« Shearing stress allowed on 807 - Objectiof ‘ ee ey ‘* Table of resisting moments ud Rock-asphalt . « 1163 rae ae . : ° ° sg8s PAGE Pitch, Final or resultant, how de- termined . : = OTE ‘“* of rivetsin batten plates . 946 “of rivets in beam flanges 967, 971 “ of rivets in cover-plates LOA: “ of rivets in portal bracing . 959 “ of rivets, Limiting ‘values Okwe . : : 898, 964 ‘Ss (Minerals? . . A « | t1g6 Plate beam hangers A : . 1067 “ .sirders.. A - : oan 009 ‘© girders, Allowed _ shearing stress in web of . ; 859, 877 “© girders, Assumed distribu- tion of tension and com- pression in . ° «4. 850 “ girders, Effective dentn OL SO ‘* girders, Minimum thickness of webof . . 5 elie ‘* girders, Position of figndes on web ; 4 +P tslstss ‘“ girders, Stiffening of d 7, S59 girders, Thacher’s specifica- tions relating to . : S75 Plates, Design of . ; - 2) O45 i Maximum widthof . Fae ete ie Reenforcing, at pinholes . goo Portal bracing, Designof . at okt vo Designof . A . 842 3 Functions of a. é Ae pas 4 Stresses in braced 4 e7OS “$ Stresses in latticed’ . eo < Weight of, used in esti- mates 3 . ; LOSS Possession, Adverse : : - 1098 Position of loads for maximum bending moment . - 802 ee of pins . ; : . 886 Posts, end, Design of : 833, 941 ‘* intermediate, Design of Aye, Gh: Pratt truss, Condition of loading, for maximum stress . . FOO truss, Description of . . 689 “Sotruss, Hormulas fon chord stressesin . : se truss, Graphical determi. tion of stresses in 3 694, 707 truss with curved orinclined te se “6 chords . $ 5 773 Preparing iron for painting . . 081 Proportioning material for ten- sion members 5 ; : Or? R PAGE Radius of gyration, Approximate formulas for value of . ; ao Beh INDEX PAGE Radius of gyration, Cases in which formulas give least . R27, ‘of gyration in usual com- pression members . : oer Railing for bridges . F 1072 Railroads, Location of, éotapared with location of highways . 5 efets! Railways, Asphalt paving of . 1162 Ramming of brick pavements ee 1170 of stone pavements trad of wood pavements 5 Line Rankine’s formula forcolumns . 823 Reaction in truss, Determining . 6096 Reactions for wind pressure at ec foot of end posts Seip’ Recessed nut . 5 . . ro2L Records of tiehtey: s - : + x0x6 = of street grades - 1087 Red-lead paint . F : ; . 1076 “lead paint, Proportions for mixing . 3 ; ; - 1080 7, lead, Use ota, : ; . 1079 Reenforcing plates at pinholes . goo Relocation of roads . ‘ ° + « LORS Repairs of roads 4 - : ron 7 Repose, Angleof . - . 1008, 1106 Resistance, Grade, in highways 999, 1008 - grade to traction. 1104 ee of paving material to crushing . A 7 drge ds totraction . 5 + ¥ 110% Resisting length of roads : - 1008 ae moment of pins 2 A Nok Resultant pitch of rivets A =) OFT Right of way . 4 2 1017 Rivet holes, Considers’ in de- termining net section se OLS holes, Distance from, to back of angle . . = OSS holes, Distance from, to back of channel . tet OAE holes, Distance from, to edge of piece , - 898, go2 Riveted girders ; A A - 689 oe ee és oo trusses E ‘ ° - 689 Rivets, Arrangement of, in batten plates ‘ c +) 946 it Arrangement ae: in cover- plates < . + 104m e Arrangement He in pin plates 5 i 5 © 924 bearing on, Determining . 920 Bearing stress allowed on ; - 807, 921 Countersunk A : 1083 Dimensions of . : 1038 INDEX XX1 PAGE PAGE Rivets, Ordering . : 909 ce Broken-stone » 1025, 1033, 1038 he Comparison of , . 1006, 1009 es Construction of . , werogt aE Drainage of F 4 . I01Ig sbi Earth . . . 1030, 1035, 1038 ‘s Gravel . F . 1028, 1034 ‘* Location of . : « Q07.-rorT = Maintenance of . é 1037 a Materials for ‘ : » To2s5 Me Objections to steep . - 999 v Qualities of good » 995, 1006 - oe Relocation of * ‘ ErOTS Roadway, Construction of . 1033 ie Cross-section of (high- ways) . - ' - 1018 bs Cross-section of, for streets . 1056 + Width of, for nts orave 1018 ie Width of, for streets 1055 Rock asphalt. & ‘ : ee ei ‘* asphalt pavements 1163 Rods, Sway ‘ ‘ R - - | 795 Rollers, Expansion . : + QO, 1005 Rolling friction ; ITOI Ropes, Strength of, aud Diets sions of . , F Ob Ruling grade of hipiways 1005 Rust, Protection of bridges from . 1075 Ss PAGE Safety of apavement . : IlI4 Sand . s ‘ : : i 2 Cantilever . ‘ : . 686 se Gomtinuous, ~~ : ° - 686 ‘“ Essentialelement of . 3. 685 ** External forces of - = = 0on ‘“* Howe : : . : ee Tae ‘““~Membersof . : : . 686 Se retit - : 5 706 >) -Praté, single- quadeaneitar, single-intersection . - 689 “« Simple . : ‘ : - 686 a opan ot. : P : - 686 ‘** Svmmetrical . : : Se OsS ‘© Whipple. , : : 73 ‘* withinclined chords . * 749 Turnbuckles, Dimensions of . OR oe Position of, on coun- ters : . . go2 U PAGE Uniform load . ‘ ° - 690 Unit stresses allowed for tension members . ‘ A Fad Poh’ ‘* stresses allowed on medium steel . ; ‘ : A tke) “stresses allowed on timber . 876 XXill PAGE Unsymmetrical sections . . - 1084 Upper lateral system, Graphical determination of stresses in s) SAU; Upset ends, Dimensions of . - 989 “* ends, Length of bars hav- ing : : 4 , 1037 “sends, Specifications rela- ting to : : . = Og vi PAGE Varying load, Stresses from . - 602 WwW PAGE Warren girder. “ = 6744 ae girder, Grapiical es 0 mination of stressesin . 745 Washers for boltsin wheel guards 1049 ‘ for pins 1025 Washington, City of, Pennine the 1048 Web members, Design of : Fa telshe. ‘* “members, Economical incli- nation of A ; : 749 ‘“* members, Maximum eereaain LNs : ; ° » 700 “plates, Maximum shearing stress in ; . : 859 ‘* stresses, Error in the eters mination of maximum - 793 ‘* stresses, Short method for determining ‘ : 737 Wedge bolt = ‘ : 1017 Weight, Maximum and minimum, of wrought-iron chan- nelsandangles . 830 of floorbeam 727, 1058 2 of materials used in esti- mates : : 3 - 1058 ie of members, Estimating the . ; ‘ : » 1055 ok of nails and spikes 1051 aS of rolled sections of wrought iron, high, and soft steel : ; . 878 e. of steel : P . 878 Me of timber bridge por «5706 4 of wrought iron : 828, 878 Wheel guards, Details of ‘ - 1049 e loads ; : = A - 690 me loads, Concentrated , 5.) SOx Whippletruss, Assumption regard- ing distribution of stresses in i - 975 y truss, Description of » 973 ia truss, Graphical deter- mination of stresses in 775 White-lead paint. ‘ . - 1076 XXIV PAGE Width, Maximum, of plates in com- pression . : ; » 825 ‘of flange of channel . A tiete! + Soft truss Gwe > < mOrS Wind load, Assumed amount of . 690 ‘* load, Stating the . . « 691 ‘* pressure, Transmitting to and by the portal F a7 tS ‘¢ pressure, Provision for, in chords and end posts 815, 850 ‘* pressure, Provision for, in designing pins . 3 - 929 ‘* pressure, Reactions from, at feet of end posts ; - 720 ** stresses, Graphical deter- mination of, in lower lat- eral system : 5 711, 714 “* stresses, Graphical deter- mination of, in upper lat- eral system : : 717 “ stresses, Transmitted to the anchorage . 5 ° . 715 Weoehler’s law relating to fatigue of metals “ ; - - 872 INDEX PAGE Wood pavements . ° ° . 2147 Pe) paving se. ‘ . ° . 1138 Wooden hub guards ; 4 + 1071 Working drawings . ; : - 896 Mh BELESSESa as . . ot eres oh stresses allowed on me- dium steel members 869, 874 * stresses allowed on wrought-iron compres- sion members 824, 874 os stresses allowed on wrought-iron tension members 5 : 814, 874 Wrought iron, Coefficient of ex- pansion of . ‘ . 1607 id iron, Properties of, re- quired by specifications 809 es iron, Supposed advan- tages of, over steel . 808 os iron, Use of, in bridge work : : : a Oy “ iron, Weight of A . 828 < iron, Weight of rolled sections of . ° - 830 ain | as anid ¥ y mn Dar at wa U mM 112 066968386 a nN