I N S T R U C T I ONS O N MODERN AMERICAN RIDGE BUILDIN( WITH PRACTICAL APPLICATIONS AND EXAM3PLES, ESTIMATES OF QUANTITIES, AND VALUABLE T'ABLES. j1tuttrateO ht fou lntes ant 30 ictrt $tgsres. By G. B. N. TOWER, CIVIL AND MECHANIC AL ENGINEEI, Formerly Chief E.nginee~r U. S. Nnazy, anid late Cl andler Instructor in Civil Liv Sc cikalike;ger l- L i vztd/! -allegwe. BOSTON: A. \V!-zAUM & COM'PANY, 135 WASHINGTON STREET. I874. Entered according to act of Congress, in the year 1874, by A. WILLIAMS & CO., in the office of the Librarian of Congress, at Washington, D. C. PREF ACE. This little treatise was written for the purpose of supplying a want felt by the author while giving instruction upon the subject. It was intended for an aid to the young Engineer, and is not to be considered as a complete substitute for the more elaborate works on the subject. The first portion of this work mentions the various strains to which beams are subjected, and gives the formulae used in determining the amount of those strains, together with a few examples to illustrate their application, and also the method of calculating a simple truss. The second portion names and explains the various members of a Bridge Truss, and, by means of examples, shows the method of calculating the strains upon the various timbers, bolts, etc., as well as their proper dimensions; and gives, in addition, several useful tables. The explanatory plates, which are referred to freely throughout the work, are believed to be amply sufficient for the purpose intended. So much has been written on this subject that it is next to impossible to be wholly original, and no claim of that nature is preferred. It is simply an arrangement of ideas, gleaned from the various works of standard authorities, and modified by the author's practice, embodied in book form. PREFACE. To give a correct list of all the books consulted would be simply impossible; — but it is well to state that the Hand-book of Railroad Construction, by Prof. G. L. Vose, under whom the author served as an Engineer, has been used as authority in many cases where there has been a difference of opinions among other authors. Some parts have been quoted entirely; but due credit has been given, it is believed, wherever such is the case. It is not claimed that this little work covers the whole ground, but it is intended to describe, and explain thoroughly, three or four of the more prominent styles of Truss, leaving the other forms of Wooden Bridges to a subsequent volume. Abutments and Piers, as well as Box and Arch Culverts, belonging more properly to masonry, will be treated of hereafter under that head. Iron Bridges form a distinct class, and may be mentioned separately at some future period. If this small volume should lead the student of Engineering to examine carefully the best Bridges of modern practice, and study the larger scientific works on this art, the author will feel satisfied that his efforts have not been entirely in vain. Cambridge, Febriuary 23, I874. T 0 W Ei R' Sg Modern Amrerican Bridge Building. BRIDGE BUILDING. The simplest bridge that can be built, is a single beam, or stick of timber, spanning the opening between the abutmentsbut this is only of very limited application-(only for spans of 20 feet and less) owing to the rapid increase in sectional dimensions which is required as the span becomes greater. Next comes the single beam supported by an inclined piece from each abutment meeting each other at the middle point of the under side of the beam-or, another arrangement, of two braces footing securely on the beam and meeting at a point above the middle point of the beam, which is suspended from the apex of the triangle formed by them, by means of an iron rod-These arrangements may be used up to 50 feet. For any span beyond 50 feet, modifications of this arrangement are used which will be described hereafter. Now let us investigate shortly the different strains that the various parts of a bridge have to bear-and the strength of the materials used. The theory of strains in bridge trusses is merely that of the Composition and Resolution of Forces. The various strains, to which the materials of, a bridge are subjected-are compression, extension and detrusion. Wood and Iron are the materials more generally employed in bridge construction-and in this pamphlet we shall take the following as the working strength of the materials-per square inch of section. Tension. Compression. Detrution. Wood,................2000..........1000..........150 Wro't Iron,.......... 15000......... 11000 Cast Iron, 4500.........25000 Tension. If a weight of 2000 lbs. were hung to the lowest end of a vertical beam, so that the line of action of the weight and axis of the beam formed one and the same straight line-the tension on the beani would be 2000 lbs. But, if the beam were inclined, and the force acted in a vertical direction, II. then the strain would be increased in the ratio of the increase of the diagonal of inclination over the vertical; —suppose the beamn is 20 ft. long and inclined at anl angle of 450-and let 2000 lbs., as before, be suspended from its lower end. Now the diagonal being 20,-the vertical will be 14.014 ft.-and the strain will be found as followsc14.014: 20::2000: 2854-lbs. The greater the angle of inclination from the horizontal, the less the strain from a given load —and when the beam is vertical the weight causes the least strain. Compression. If we load a vertical post with a weight of 2000 lbs.,the strain of compression exerted upon the post will be 2000 lbs. Now, if we incline the post-the strain willbe increased, as we have shown above under the head of tension, and in like manner, dependent upon the inclination. But when wood, iron, or any other material is used for a pillar or strut, it has not only to resist a crushing force, but also a force tending to bend or bulge it laterally. A post of circular section with a length of 7 or 8 diameters will not bulge with any force applied longitudinally, but will split. But if the length exceeds this limit-it will be destroyed by an action similar to that of a transverse strain. A cast iron column of thirty diameters in length, is frac_ tured by bending; when the length is less than this ratio-by bending and splitting off of wedge shaped pieces. But by casting the columln hollow, and swelling it in the middle, its strength is greatly increased. Barlow's fortnula for finding the weight that call be sustainled by any beam, acting as a pillar or strut, before bending, is: bWL2 ce bdaX 80E 80E bc, hence L2 now, having the weight given, and assuming the dimensions of the cross-sectien-we shall have FIWL2 and b- WL2 -/80Eb an b OEl in the above formnula, W weight in pounds. III. L length in feet. E a constant. b breadth in inches. dcl depth in inches. Transverse Strains. The strain caused by any weight, applied transversely, to a beam supported at both ends, is directly as the breadth, and square of the depth, and inversely as the length. It causes the beam to be depressed towards the middle of its length, forming a curve, concave to the horizontal and below it. In assuming this form-l;the fibres of the upper part of the beam are compressed, and those of the lower part are extended-consequently there must be some line situated between the upper and lower surfaces of - tho beam where the fibers are subjected to neither of these two forces, this line is called the ne2itdal axis. These two strains of compression and extension must be equal in amount-and upon the relative strength of the material to resist these strains, as well as it form and position, the situation of this axis depends. If wood resists a compression of 1000 lbs. per square inch of section, and a tension of 2000 lbs. the axis will be twice as far from the top as froin the bottom in a rectangular beam. The following table by Mr. G. L. Vose gives, with sufficient accuracy for practice, the relative resisting powers of wood, wrought, and cast iron, with the correspondling positions of the axis. Material. Resistance to Resistance to Rati Dist. of axis from top Extension. Compression. in frac's of tle depth. Wrought Iron, 90........66........ or 0.58. Cast Iron, 20. 111 1 * or 0.15 Cast Iron,....20....... Il....... 21~-Q.......r, or 0.i5. Wood,.....2...1 06 Wood,.......2......... I........ 2 ~,-. or 0.66. Thus we see that the resistance of a beam to a cross strain, as well as to tension and compression, is affected by the incompressibility and inextensibility of the material. The formuila for the dimensions of any beam to support a strain transversely is S 4bd2 1 S = the ultimate strength in lbs. b = the breadth in inches. cl - the depth in inches. 1 the length in inches. lDetrusion. Detrusion is the crushing against some fixed point, such as obtains where a brace abuts against a chord, or where a bridge rests on a bolster; and the shearing of pins, bolts and rivets, also comes under this head. General Abstract. The resistance to the above mentioned strains varies as the the area of the cross section; so that by doubling the area we double the strength. Any material will bear a much greater strain for a short time than for a long one. The working strength of materials, or the weight which does not injure them enough. to render them unsafe, is a mooted point,and varies, according to the authority, from 1-3 to 1-10 of the ultimate strength. The ratio of the ultimate strength to the working strength is called the factor of safety. The following is a table of ultimate and working strengths of materials, and factors of safety: Weight Ult. Ult. Working Strengths. Factor Safety. in lbs. Materials. Ext. Comp. Exten. Comp. Tension Comp. 30 Wood. 14,000 7,000 2,000 1,000 7 7 480 Wrou't Iron. 60,000 64,000 15,000 12.000 4 5.33 450 Cast Iron. 18,000 100,000 4,500 25,v00 4 4 Lateral Adhesion. Lateral adhesion is the resistance offered by the fibres to sliding past each other in the direction of the grain, as when a brace is notched into a chord. or tie beam, at its foot, it is prevented by the lateral adhesior ofthe fibres from crowding off the piece,to the depth of the notch. against which it toes. Barlow's experiments give the latera adhesion of fir as 600 lbs. per square inch, and the factor o: safety employed varies in practice from 4 to 6, giving a work ing strength of from 150 to 100 lbs. per square inch. Y. TABLE OF COMPRESSIVE RESISTANCE OF TIMBER. Length given Safety Weig't Length given Safety Wt. Length in Safety Wt. in Diameters. in Pounds. in Diameters. in Pounds. Diameters. in Pounds. 6 1000 24 440 42 203 8 960 26 394 44 185 10 910 28 358 46 169 12 860 30 328 48 155 14 810 32 299 50 143 16 760 34 276 52 132 18 710 36 258 54 122 20 660 38 239 56 114 22 I 570 40 224 58 106 60 99 In tensional strains, the length of the beam does not affect the strength; but in the beams submitted to compression, the length is a most important element, and in the table given above, the safety strains to which beams may be subjected, without crushing or bendincg, has been given for lengths, varying from 6 to 60 diameters. PRACTICAL RULES. TPensicon-al.train. Let T ~ whole tensional strain. 6 S = strength per square inch. " a - sectional area in inches. Then we have T - Sa. Now to find the necessary sectional area for resisting any strain, we have the following general form-ula: T or, by substituting the working strengths for the various mateT rials in the formula, we have for wood, 2000 T Wrought Iron, a 1 500 T Cast Iron,a - 4500 But, in practice, cast iron is seldom used except to resist compression. yVI astrains of (em tY pression. Allowing the same letters to denote the same things as above, we have for T Woodl, 1000 T Wrought Iroll, 12000 T CaIst I1OI19 a 25000 As this pamphlet has to do with woooclen bridges only, nothing will be said of the proper relative dimensions of castiron columns to sustain the strains to which they may be subjectecd, but a table of the strength of columnis will be found further on. Trransverse ~t-ains. Let W- breaking weight in lbs. s s — constant in table. " b - breadth in inches. d —- depth in inches. L - length in inches. Then, for the power of a beam to resist a transverse strailr, we shall have, W -- 4sbdc2 L This fornula h as been derived froin experiments made by the most reliable authorities. The constant, 1250, adopted for wood in the following formula, is an average constant, derived from the table, of those woods more commonly used. Now to reduce the formula to the most convenient shape for use, we substitute the value of s, and we have ~W 4X1250 bd 2 W- 500Obd2 L But, to reduce thfe load to the proper working strain, we must divide this equivalent by 4, the factor of safety, and we shall have VII. W - 5000bd2 4L Let us apply the formulaCase I. Given a span of 14 feet, a breadth of 8 inches, a depth of 14 inches. Required the safe load. 5000 bc12 The formula W — 4L becomes, by substitution, W - 5000X8X196 11,666 lbs. 4X168' Case II. Given the safety load 18000 lbs. the breadth 9 inches. the length 14 feet. Required the depth. From the above formula we have WX4L V-5000b substituting 1i800OX168X4- 167.2 = 5000x9 \ - 16, inches ne Case III. Given the safety load 22.400 lbs. the depth 18 inches. the length 14 feet. Required the breadth. Deriving b from the foregoing, we have, b — WX4L 5000 X d2 substituting b- 22400X4X168 _ 9.3 inches nearly. 5000 X 324 For a cast iron beam or girder-Mr. Hodgkinson from numerous carefully conducted experiments that, ranging the material in the form of an inverted T —thus, ing a small top flange as well as the.larger bottom one, sistance was increased, per unit of section, over that of a rectangular beam, in the ratio of 40 to 23. VIII. In this beam the areas of the top and bottom flanges are inversely proportional to the power of the iron to resist compression and extension. Mr. Hodgkinson's formula foi. the dimensiens of his girder, is W. 26ad L The factor of safety betng 6 for cast iron beams —the formula for the working load will be, 26ad 6L and, to find area of lower flange, we shall have 6WL a26d The general proportions of his girders ars as follows: Length, 16 Height, 1 Area Top Flange, 1.0 Area Bottom Flange, 6.1 In the above formula for cast iron beams, W = weight in tons. a-= area in sqnare inches of bottom flange. d - depth in inches. h — = length in inches. The web uniting the two flanges must be made solid-as any opening, by causing irregularity in cooling, would seriously affect the strength of the beam. Example.-Required the dimensions of a Hodgkinson girder-for a span of 60 feet-with a load of 10 tons in the centre. a- 6X10X60X12 _ 37 inches nearly. 60 X 12 26X 16 and the area of the top flange will be, 37-.= 6.16 inches — 6 so that our dimensions will be as follows: Length, 30 feet.' Depth, 45 inches. Area Top Flange, 6.16 inches. Area Bottom Flange, 37 inches. 1.1-R, 1-1-1~-, I 0 -- I The thickness of web is usually a little greater at the bottom than at the top, and varies from y to'., of the depth of the girder. The bottom rib is usually made from six to eight tinles as wide as it is thick, and the top rib from three to six times as wide as thick, so that, in the example above given, we could have as dimcnsious for the parts Top Flange, 41X 11 inches nearly. Bottom Flange, 6 X2b inchlesnearly. Web, 1 inches thick. The simplest bridge, consisting of a single stick, to span openings of 20 feet and under, is calculated according to the formula d — 4WL v-6000 b.Eacnmple. —The depth of a beam, of 12 feet span and 12 feet wide, to support a load of 22400 lbs. will be.WL _ _.._00. 12. 1 1- 4WL 4X 22400x = 12/X12 _>I04=15 in. nearly. 5000 500 500X 12 - The following Table was calclatod by the above rule —and the dimensions altered according to the actual practice of thle writer. Span. Breadth. Depth. 4 10 12 6 10 12 8 12 12 10 12 13 12 12 15 16 12 18 18 12 20 20 12 22 These dimensions will give ample strength and stiffness. Fig. 1, Plate I. gives an illustration of this kind of bridcge-in which a, a, are the bolsters or wall plates, shown in section, to which the bridge beams are notched and bolted. Fig. 1, A, Plate I, shows the method of diagonally brtacing these beams by planks, dimenlsions of which in- general use are 6 to 8 by 2 to 3 inches. The track should rest on ties, about 6 inches by 8 or 10 inches-the same bolt confining the ends of the ties and dciag2 onal braces when practicable. These ties should be notched on the string pieces 2 or 3 inches —without cutting the stringers Bel.w is'a table giving general dimensions, in inches, of the several parts of a bridge of this description. Span. Bolsters. Stringers. Ties. Braces. Diameter of Bolts. 4 12x12 10x12 6x8 2x8 1 inch. 10 12x12 12x13 6x8 2x8 1 " 16 14x14 12x18 6x8 2x8 1 " 20 14x14 12x22 6x8 2x8 1 Each bolt must have a washer under the head, and also under the nut. For a span of from 15 to 30 feet, we call use the combinaTtion shown in Pla-te II, Fig. 3. The piece A F must have the same dimensions aions a simple string piece of a length A Bso that it may not yield between B and either of the points A or D. The two braces DF and EF must be stiff enough to support the load coming upon them. Suppose the weight on a pair of drivers of a Locomotive tz be 10 tons, then each side must bear 5 tons, andl eachb brace 2 tons - 2 X 2240 —5600 lbs Now, to allow for sudden or extra strains, call 8000 lbs. the strain to be supported by each brace, anl, accordingly, 8 square inches of sectional area would be sufficient for compression only; but, as the bralce is inclined, the strain is increased. Let the vertical distance f rom A to D be 10 ft., a nid, calling the span 30 ft.-A B will be 15 ft. —from whence D F must be 18 ft., then we shall havre the proportion 10: 18::8000: 14400 lbs. which would( require an arzea of about 15 sqcuare inches of section to resist compression, or a piece 3x5 inches. Now, as this stick is rnore than 6 or 8 diameters in length, it will yield by bending-f-and consequently its area must be increased. The load, which a piece of wood acting as a post or strut will safely sustain. is found by the form.ula already given. __ 2240bd3 L2 Now substituting 3 for b, and 5 for d, we haveW 2240X3X125 840000 2592 lbs. 324 324 which is not enough. Using 6 for b and 8 for d, we have W_-2240X6X512 _ 21288 lbs. 824 which is something larger than is actually required, but it is no harm to have an excess of strength. Now in many cases this a.rrangemlent would be objectionable, as not affording sufficient head room on account of the braces —tand we can:as well use the orm of structure givren il PI. I. Fig. 3, since it is evidently immaterial whether the point B be supported on F or suspended from it, provided we can prevent motion inl the feet of the braces, which is done by notching them into the stringer at that point. This of course creates ta tensional strain along the stringer, which is foundl as follows:-iRepresenting the;appliod weight by F B, P1. II, Fig. 2, draw B D parallel to F. C, also D H parallel to A C —D H is the tension. This is the graphical construction, and is near enough for practice. Geometrically we have the two similar triangles A F B and 1) F H, whence AF: D F::AB: DH DFxAB and D I DF- X This style of structure may be used up to 50 feet, but it is not employed for spans exceeding 30 feet in length. It is very customary to nmake the braces in pairs so as to use smaller scant. ling, and gain in lateral stiffness-tthe two pieces forming one brace by being properly blocked and bolted together. Below is given a table of dimensions for the various parts of this style of structure: Span. Rise.'Bolster. Stringer. Braces. Rod.. No. Size. 15 6 12x12 12x12 2-5x6 120 7 14x14 12x13 2-5x8 1 25 8 14x14 12x15 2-6x8 1 30 10 14x14 12x18 2-6x9 1g Single Beams under each. rail firmly braced laterally, and trus~ sed by an iron rod, (or preferably by two iron rods,) and a post on the under side of the beam. The deflection of. the rod is usually taken at - of the span. P1. II., Fig. 1, represents this. style of trussing a beam —which is generally used for spans of from 15 to 30 ft. Below is a. table of dimensions for this truss with single and double rods; if double rods are used only half the given section will be necessary for each one of the pair. Span. Rise. Stringer. Post. Rod. Rods. Feet; In Feet. (single,) (double.) 15) 1- 1 2.,. 61xS;., (dlialn. or 1 dCliaml. 20- - 12x14 7x8 2', 25 3{ 12x16 8x8 24 " 2 " 30 3' 13x18 9x9 3 " 2 It is as well to tenon the post into the beamn, and also strap it firmly with iron plates-and the end should be shod with iron to form a saddle for the rods to bear upon. Now if we should make a bridge, on the plan of Fig. 3, PI. I., 75 or 100 feet, or perhaps more, in length, the braces A F and F C, would not only be very long but very large, and heavy, and one chief requisite in a good bridge is, to have all the beams so proportioned that they will resist all the strains acting upon them, without being unnecessarily large. It now becomes necessary to have a different arrangement of the parts of the truss in order to obtain increased length of span. Suppose we have a span of 40 feet, as represented in Fig 2, P1. I. Now instead of running the braces from A C until they meet in a point, as before we stop them (at a,; and c, an l place the straining beam, a c, between thenl to prevent; those points from approaching, suspend the points B and D from them, and start the braces B b and D b —and, if the truss were longer, would continue on in the same manner as far as needful. To prevent the, truss from altering its form, as shown by the dotted lines AL-b C', and A E C, by any passing load, wc insert the counter braces marked R. The braces, A a and C c, must support all of thi, weight of the bridge and its load within the parallelogram B a c - and the next set of braces, B b and D b, sustain that part of the'load which comes over the centre of the bridge. Consequently the braces must increase in size from the centre towards the abut. ments. The rods resist the same pressure in amount as their braces-but being vertical, do not need the increase, given to the braces on account of their inclination —but increase simply with the strain upon them, from the centre to the ends of the truss. There are many forms of small bridges differing from those enumerated, in various minor details, but sufficient has been said to give the reader. a fair idea of the strains upon the differentjparts, ancd how to arrange and proportion the materials to resist them. PRACTICAL RIULES AND EXAMPLES IN WOODEN BRIDGE BUIJLDING. In any case that may arise, we imust determine approximately the gross weight of the bridge and its load-as a basis, atnd then wve can proceed,as follows-in case of a Howe, Pratt, or Arch Brace Tru lS. T'o tind the 1)im. ensions of the Lower Chord. The tension at the centrle of the Lower Chord is found by dividitgq the prodclt of the iweight qf the whole bridge and load by the span, by eight times the height-or letting T - tension in lbs., VW weight of bridge aand loa'd in lbs., S=span in feet, and h- rise or heiglht-we have T-WX In this 8hi case we have taken the rise at I- of the span, which is evidently the best ratio between those dinlensions, as it equalizes the vertical and horizontal forces. As to the proportions of the bays or panels, (or that portion'of the truss bonlded by two adjacent verticals, as struts or ties, and the chords,) the ratio of the rise, (or the vertical distance between the centre lines of the two chords,) and the length on the chord should be such, that the diagonal truss members may make an aingle of about 500 with the chords; as the size of the timbers is increasedl by decrea.sing the angle, and, if the' angle is increased, there are mlore timrbers required. Mr. G. L. Vose, in his admirable work on R. R. Con struction, observes very truly that "' The braces, at the end of a long span, may be nearer the vertical than those near the centre, as they have more work to do. If the end panel be made twice as high as long, and the centre panel square, the intermediates varying as their distance from the end,.a good architectural effect is produced." Now it is necessary for us to have some data from which to determine the approximate weight- of the bridge, and also its load. These can be found by comparing weights of bridges in common use, as obtained from reports. In a small bridge of short span, the weight of the structure itself may be entirely neglected, because of the very small proportion the strains caused by it bear to those due to the load; —but, in long spans, the weight becomes a very important element in the calculations for strength and safety-inasmuch as it may exceed the weight of the load. In all Bridges of 120 ft. span, about X of a ton, per foot run, will be the weight of each truss for a single track, including floor timbers-transverse bracing, &c. If the bridge were loaded with Locomotives only, the greatest load would be, on the whole bridge-160 tons =-1.33 tons per ft. run of the bridge, or.666 tons per ft. run of each truss. Now if we make the rise of the bridge 15 ft., and divide the span into 12 panels of 10,ft. each, we shall have for total weight of bridge and load 240 tons, or for a single truss 10 tons to each panel. TLower Chords. Noow to find the tension on WXS theo Lower Chords, T - WXh- and supplying values, we have 8h T 240x120 = 240 tons, or 537600 lbs., for the two Lower 8X15 Chords, and I of this, or 268800 lbs. for one chord. The Tensional Strength of timber for safety may be taken at 2000 lbs. per square inch of section, and lhence the area of timber required to sustain the abive st;rain \ill be 268800 134.4 sq. inches. 2000 But this chord has a;lso to sustain the transverse strains arising from the weights passing over it, and, as in the case of a Locomotive, the weight of 20 tons on 2 pair of drivers, (or 10 tons for one truss,)nlay be concentrated on the middle point of a panel-the chord must be so proportioned as to safely bear, as a horizontal beam, this weight, Suppose we take three sticks XV. of 8"x12", to form the chord (the greater dimension being the depth,) we shall have 3x8"s12-"=388 square inches area of section, and allowing for splicing 72 square inches, " foot blocks, 24 " " " "L bolts, 24 " " " "' vwashers, 8 "' we shall have after deducting allowances (288-128) 160 square inches area, giving an excess over 134.4, the area demanded, sufficient to cover allowances for any accidental strain. Upper Chords. The upper chords are compressed as forcibly as the lower ones suffer tension-owing to the action and reaction of the diagonals. In this case the compression is 268800 lbs., and as 1 square inch of section will safe. lybear 1000 lbs., we have for the area required, 268800 268.8 I000 square inches, —three pieces 8"xll" will give 264 square inches, and this area will require no reduction, as the whole chord presses together when properly framned and is not weakened by splicing. So far, the calculations made would apply to either of the three Bridges mentioned, as well as to a Warren Truss. But now, to obtain -the dimensions of the web members, so called, of the Truss, it is necessary to decide upon the specific variety. The form of Bridge in more general use in the United States is called the Howe Truss, from its inventor, and in spans of 150 feet, and under, is very reliable; for spans exceeding 150 ft. it should be strengthened either by Arch Braces or by the addition of Arches, as the heavy strains from the weight oif bridge and load bearing on the feet of the braces neat the abut. ments, tend to cripple and distort the truss by sagging, although the Baltimore Bridge Co. have' built a Wooden Howe Bridge of two Trusses of 300 ft. span, 30 ft. rise, and 26 ft. wide, without any arch, but it has a wrought iron lower chord, and is only proportioned for a moving load of 1000 lbs. per ft. run. [Vide Vose on R. R. construction.] Ia order to ensure uniformity in strength: in the chordsbut one joint should be allowed in a panel —and that should come at the centre of the panel length-but in long spans this cannot always be done, WVeb Memnbers. We will now proceed to cal culate the web members of a Howe Truss of the foregoing diL mensions, when subjected to the strains above mentioned. lBraces. The end braces must evidently support the whole weight of the bridge and load, which for one end of one truss will be 134400 lbs., and as these braces are in pairs, — 67200 lbs. will be the strain vertically on the stick-but as this stick is a diagonal-whose \vertical is 15 ft., and horizontal 10 ft., we shall have fIo its length 18 ft. in round numbers, whence the strain along the diagonal will be found from the proportion 15: 18::67.200: 80640 lbs., whence we have an area of 80 inches required for compression, or a stick of 8"xl1". Now, to ascertain if this is stiff enongh for flexure, we will substitute these vralues in the equation W 24 and we have LJz 2240X8x1000 W-,2 0241 0 or reducinig, W-55308 lbs. Now, these proportions will give ample strengtlh for both flexure and compression, for if we block the two sticks composing the end brace togethpl, and firmly connect them by bolts, we shall have a built beam of 24"' x 10"-whence W - 2240X24X1000_ 165925 lbs., 324 and as 134400 lbs. wras all that the conditions demand, we really have ani excess of strength. The next set of braces supports the weight of the rectangle included between the upper ends of the braces and the two clhords, and the dimensions of the sticks are calculated in the same manner. We find, as we approach the centre of the bridge, that the strains on the braces become less, and consequently their scantling should be reduced, but in ordinary practice this is seldom done. REods. The next thing is to ascertain the dimensions of the various tie rods. It is evident that the same weight comes upon the first set of rods, as on the first set of braceswhich will give for the rods at one end of one truss, 134400 lbs.; and as there are two of these rods, each will sustain a strain of 67200 lbs.-and, at 15.000 lbs. per square inch, will have an area of 4.48 sq. inches, and, by Vose's Tables, must have a diatimeter of2j. inches. The sizes of the rods in each set will decrease towards the centre of the bridge ras the weight becomes less. — r r~~~-~~'Y -Y~~~ YI-~V-V V* VI11 IV-~~U~~3U ~~~N V1I~- IIzt ...................................................................................................................................................................... ------------------------------.......... - - - ------------------ ---------- -- -----.... ----------------------------......................... -------------------------................. -............................................... Couinterbraces. Now, as to the necessity of Counterbracing, there are various opinions. The object of it is to stiffen the truss and check vibrations. If a load be placed over any panel point, it causes that portion of the truss to sink, and produces anl elevation of the corresponding panel point at the other end of the truss-thus producing a distortion, which change of form is resisted by proper counter braces. The strain to which this timber is subjected is caused by the moving load on one panel only-and requires only scantling of the size of the middle braces. These counterbraces should not be pinned or bolted to the braces where the cross-as their action is thereby entirely altered-butt it is well to so confine them as to prevent vertical or lateral motion. Shoes. Formerly it was the custom to foot the braces and counters on hard wood blocks on one side of the chord, the vertical rods passing through and screwing against a block on the other side-thus the whole strain tended to crush the chord across its fibres. This is now remedied by the use of cast iron blocks, bearing on one side of the chord, but having tubes extending through to the other side, where the washer plate for the bolts fits firmly on their ends, forming a complete protection, as all the crushing strain is received on the block its elf. WVidth. It now becomes necessary to deter mine upon the width between the two trusses. For a single track bridge for a railroad, 14 ft. is the usual width adopted, and for a highway bridge, from 12 to 16 ft. When a double track is requtred, three trusses are -usually employed, with a width for each roadway of 14 ft. for railroads. 3Bolsters. Large timbers 12 x 12, or thereabouts, are ]aid on the bridge seats of the abutments to support the ends of the trusses, one of these should be directly under each of the extreme panel points. A panel point is the intersection of the centre line of a brace produced, with the centre line of a chord. The rise of a truss is the vertical distance between the centre lines of the upper and lower chords. Camber. Were a bridge to be framed with its chords perfectly horizontal, it would be found to fall below the 3 XVlTI. horizontal line on being placed in its proper position, owing to the closing up of the joints in the upper parts of the structure, and opening of joints in the lower parts, as well as to the compression of the parts. To obviate this defect, it is usual to curve the chords slightly in a vertical direction, by elongating the upper chord, so that the bays or panels are no longer rectangular, but of a trapezoidal form-and, as a consequence, the inclined web members are slightly lengthened, and the verticals become radii of the curve. The amount of deviation from a horizontal line is called the Camber. A table of Cambers for different spans will be found further on, as also a table of multipliers, by which to multiply the camber in order to find the elongation of the upper chord. Part of the Camber table is taken from Trautwine's Edgineer's Pocket-Bood, (which should be the inseparable companion of every engineer,) and part was calculated for this pamphlet, according to Trautwine's rules. The table of multipliers is Trautwine's.?Diagonal Bracing. In order to stiffen a bridge, it shouldl have the two Trusses braced together at the Lower Chords always, at the Upper Chords when practicableand in case of a deck bridge, where the roadway is supported on the upper cherds, it is af well to have rods for vertical diagonal bracas, their planes being perpendicular to the axis of the bridge. The more usual form is similar to the web members of the Howe Truss-the rods from i" to 1" in diameter, and the braces of 6" x7" scantling, footed on wooden blocks, usually. It is more usual to have the tie rods of the horizontal diagonal bracing, and the braces themselves,'meet in a point about midway of a Truss panel on the centre line, nearly, of the chord. This will generally give a half panel of diagonal bracing near each end of the truss-and it is very usual to have the diagonals foot at their intersection there against alcross timber interposed between the trusses, while the tie rod prevents any spreading. FVloor Timbers. The general dimensions of the transverse floor beams, when about 3 feet apart, from centre te centre, are 8" x 14", the largest dimension being the depth. The stringers should be notched to the floorbeams about 1" or 2", and should be about 10" or 12" x 14". The cross ties should be 18" to 24" apart, from centre to centre, and be 32" x 6"' XIX.' Large, heavy bridges require no fastening to connect them with their seats, but light bridges should be fastened, as the spring on the sudden removal of a load, (as when thn last car of a train has passed,) may move it from its proper position. Splices. As the upper and lower chords have to be made in several lengths, securely fastened to each other, and, in order to weaken the built beam as little as possible, it is necessary to adopt some form of splicing whereby the greatast amount of tensional strength may be retained in the chord with the least amount of cutting, and yet have a secure joint. Such a splice is shown in Pi. II, Fig. 4, and below is a table from Vose's Hand-book, giving reliable dimensions. Span. AC BB CD Feet. Feet. Inches. Feet. 50 1.00 1I 1.50 100 1.25 2 2.00 150 1.75 21 2.25 200 2.00 3 2.75 This manner of splicing requires tbe back of the splice block to be let into the chord stick, against which it lies, about -a of an inch. To show how the various Engineers differ, as to their estimates of the sizes of the several parts of bridges, I subjoin two Tables —one by Prof. G. L. Vose, a well known Engineer, and one by Jno. C. Trautwine, an Engineer of note also-and I would premise that a bridge built according to either would be amply strong. TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE. G. L. VOSE. Q w n o a) 50 10 7 2f —8x10 7x 7 5x5 1-1} 2-1 75 12 9 2-8x10 8x 8 5x5 2-11l 2-1 100 15 11 3 8x10 Sx 9 6x6 2-13 2-1 150 20 13 4 8x12 10x10 6x7 3-2 3-1 200 25 15 4-8x16 12x12 7x7 5-2 5-1 TABLE FOR DIMENSIONING A HOWE TRUSS BRIDGE. JNO. C. TRAUTWINE, C. E.; I An Upper A Lower An End ACentre. Counter. End Centre Chord. Chord. Brace. Brace. od. hrd.' _ _ _ Rod Rod. 75 12103 6x9 3 6x2 x8 2 6x6 1 6x6 2 1 25 6 83 4x5 3 4x102 4x6 2 5x5 1 4x5 211 2 % 75 12 10 3 6x9 3 6x11/2 6x8 2 6x6 1 6x6 217 2 1 100 1511 3 6x1013 6x1212 8x9 2 6x8 1 6x8 2 2 321T 11 125 18 12 4 6x104 6x132 8x102 6x9 1 6x9 2/2% 211 150 2113 4 8x104 8x14 3 9x10 3 6x9'2 6x9 3 23 31 1 175 24 1414110x12 4 10x1513 9x11 3 8x8 2 8x8 3 2%/ 3/1~ 200 2715 4112x121412x16 3 9x12 3 8x1 2 8x1013 27 3 13 Both of these tables were calculated for a single Railroad track, and would answer equally well for a double Highway Bridge. In the bridge according to Trautwine's Table, each lower chord is supposed to have a piece of plank, half as thick as one of the chord pieces, and as long as three panels, fi'mly bolted or. each of its sides, in the middle of its length. PRATT'S BRIDGE. This is opposite in arrangement of parts t.o a Howe Bridge, as the diagonals are rods, and sustain tension, and the verticals are posts, and suffer cominpression: Lxamnple. - Span = 100 feet. Rise -- 12 " Panel - 10 " Weight per lineal ft. = 3000 lbs. The tension on the lower, or compression on the upper chord, will be 300000X100 = 333333 lbs. Tihe dimensions of the 96 XXI. chord and splicing would be found in the same manner as for a Howe Truss. Suspension IRods. Fig. 1, P1. III, represents an elevation of a Pratt Bridge. Now, it is evident that the first sets of rods must support the weight of the whole bridge and its load, which we have found to be 300000 lbs. Each truss will have to sustain 150,000 lbs., and each end set of rods 75,000 lbs. Now, if there are two rods in each set,-each rod will have to bear a strain of 37500 lbs., and this will have an in_ crease due to its inclination, so that the strain on it must be found by the following proportion: Height: diagonal:: W W' or 12: 15.8::37500: 49375 lbs. Referring to the Table for bolts, we find that 2'-L gives a strength a little in excess, and will be the proper size. The next set of rods bear the weight of the whole load, less that due to the two end panels, and sq on. Fig. 2, P1. III, shows the manner of applying the rods. The bevel block should be so fitted to the chord that it will not have a crushing action. Cotunteirs. Top and bottom chords are always used in this bridge, and consequentlythe counter rods have only to sustain the movable load on one panel. The weight of the moving load cannot be more than 2000 lbs. per lineal foot which, for a panel of 10 ft., gives 20000 lbs., or 10,000 lbs. fcr each set, and if we have two rods in a set, the strain on each rod will be 5000 lbs., increasing this for inclination, we shall have, 12:15.8::5000: 6585 lbs., requiring a rod of s of an inch diameter. The posts in this bridge correspond to the braces of the Howe Truss, but being vertical, are not so large. Subjoined are two Tables, one by Prof. G. L. Vose, and one by Mr. Trautwine, giving principal dimensions for bridges of different spans of the Pratt type of Truss. XXII TABLE OF DIMENSIONS OF A PRATT TRUSS. PROF. G.. L.OSE. wr, O0 50 10 2-8x10 5 x 5 4x4 2-1 2 —1 1-1 75 12 2 —8x10 6x 6 5x5 2 — 1 2-1 1 —1 100 15 3-8x10 7 x 7 6x6 2 —13 2 —1 2 —1 125 18 3 —8x10 8'x 8 6x6 3 —1 3=1 2 —13 150 21 4-8x12 9x 9 6x6 3 —2 3-1 8 —1 200 24 4-8x16 10x10 6x6 5=-1 5-1 3 —1T TABLE OF DIMENSIONS OF A PRATT'S TRUSS. Main Brace Rods. Posts. iUpper i Lowe r Counter Chord. Chord. Rods. e jcTb. I ~ _ Co. ___!c~.... 4 A | ~ o~ O O. O O. 25 6 831 4x5 3 4x10 2 1 2 1 1 17,W 3 4x5 3 4x4 50 9 913 6x7 3 6x10 2 1 1 1 3 6x6 3 6x5 75 1211013 6x9 3 6x11 1]2 21 1 1j 3 6x7 3 6x5 100 15 11 31 6x10 3 6x12 2 f17{ 2 2j 1 2 3 6x9 3 6x7 125 118112 41 6x10 4 6x13 2 11 2 24 1 2k 4 6x9 4 6x7 150 121 13 4; 8x`10 4 8x14 3 le 3 2 2 1 ]4 8x8 4 8x7 175 24 14 4110x12 410x15 3 14 31 21 2 1 410x1014110x8 200 27 15 4 12x12 412x16 3 14 3 21 11- 412x10 4110x8 This table is partly given in Trautwine's Engineer's Pocket Book, and partly made up front directions therein given, XXIII. TABLE OF DIMENSIONS FOR SMALL SINGLE TRACK PRATT TRUSSES. ri5 - q.4& co -* 0E Fl 30 9xl1 4x9 7x9 1 1. 1: 1 40 10x12 4x10 8X10 1~ 1i 1i 1 50 10x14 5x10 9x10 14 20 13 I 60 12x15 5x12 9x12 1 2 2 1 70 12x17 6x12 11x12 1a 24 2- 1 This bridge possesses an advantage over the Howe Truss for the panel diagonals can be tightened up by screws, so that every part of the truss can be forced to perform its work. Ii Howe's bridge the adjustments must be made by wedging the braces and counters. Below are given the dimensions of a Howe bridge on the Vermont Central R. R., at South Royalton, (single track, deck.) 0l 0: Braces. Rods. 150 0 12 4 —6x13 4 —6x13 2-8x 1x9 3-14" 6x8 7 The bridge over the White River, on the Passumpsic R. R., is a Howe Truss, strengthened by an arch. The verticals are of wood, and the diagonals foot on steps formed by enlarging the ends of the verticals. The counters are in two lengths, and are adjusted by wedges at the points where they intersect the braces. The bridge is in two spans, and has a double track, and consequently three trusses. There are two timber arches to each truss, and the truss is supported on them by connecting them to the verticals by short cross pieces notched into the XXIV. posts, and resting on the upper surface of the arches. It is a very stiff bridge, and similar to the one at Bellows Falls, bdth having their axis oblique to the channel of the stream they cross. The timbers could hardly be procured now, except at great expense. Ca ae y arches and truss, 9x3; stringers x4. span is only 175 feet, the number of Panels being 14, as in the W. R. Bridge-the other dimensions are the same. Below are given the dimensions of a Howe Truss of 108 ft. span, weight to be borne on upper chord.;.c o o,-dQm z; v;;;1 m 4 v ~ 0 0 0 o Ft. Ins. Ins. Ins. Ins. Ins. Ills. Ins. 182 3 14 2 8 — 3x1 2 8-3x1 2, 2-8x10 1-72x1l 2-2 8 9x16 Diagonals xplank iRods used fFloor the pieces must be bolted thoroughly with ] bolts. A form of bridge that has been used to some extent on the Baltimore and Ohio Railroad, x1r. Latrobe, is the Arch Brae1x14 Truss. In this form of Truss the braces lare octly 2x, afrom the abutments to the head of each vertical; thnels the load is trans ferred at once to the abutme nts, without passing through a se-. R. Bries of web members. The ounter dbracinsg is are the samected by means of a light lattice,-and is applied to both sides of the chords, and the intersections of the diagonals are f aste ned while the bridge is straine d by a load- thus preventing recoilso that the effect of a moving load is to lighten the strain on the latticeeffect of a moving load is to lighten` the strain on the lazttice — - - - - -------- — m —--------.. a s... 1 l c |lI l | a_ z l I r|1|1B1||-|11 rl l *Ei | XxV. without otherwise affecting the Truss. There are two models of this style of bridge, to my knowledge; one built by Prof. G. L. Vose, on a scale of g an inch to the foot, and representing a span of 150 feet, which supported 2,500 lbs. at the centre, and a movable load of 150 lbs., proving itself to be strong and rigid enough for any thing. The other, on a scale of 1 inch to the foot, and representing a spall of' 76 feet, was built by the Class of'73, of the Thayer Engineering School, under the writer's direction, and though bearing very heavy weights, has never been thoroughly tested —it has, however, been subjected to the sudden shock of 1040 lbs. falling 20 inches, without injury, several times. Subjoined are the dimensions of the models mentioned. DIMENSIONS OF A MODEL OF AN ARCH BRACE TRUSS. G. L. VOSE. Length, 7 feet. Height, 1 foot. Width, 1 foot. Chords, 4 — x 1 inch. Braces 4 — x I " Lattice, ~ x " This represented a span of 150 ft., a rise of 20 feet, and a panel of 15 ft. Weight, per running foot of bridge and load, was taken at 3000 lbs. The method of calculating the dimensions of this truss, from the foregoing data, is as follows. The half number of panels is 5, and the lengths of the corresponding diagonals (neglecting fractions) are /202 x 152 = 25 feet. V202 x 302 - 37 "./204 x 452 - 49 4 " V202 x 602 = 64 " V202 x 752 = 78 " 4 xxVI. he weigt upon each set of braces is that due to ones panel, or 30Q0X1 545000 lbs., half of this, or 22500 lbs., is the weight for one truss only-and, as there is abrace under each of the 4 chord sticks, we divide by 4, and have 5625 lbs. per stick of. the brace; —now, correcting for inclination, we shall have 20.: 25::"5625 -7031 lbs. 20: 37:: 5625' 10406 lbs. 20: 49::5625: 13781 lbs. 20: 64:: 5625:18000 lbs. 10: 78: 5625.: 21937 lbs. The weights found show the compressional strains on the several braces; —and, were the pieces to be proportioned for compression:only, their scantling would be quite small-but on aCcount of their elasticity, they require:larger dimensions. These braces should not be fastened: to;the verticals,-but should be confined both laterally and vertically, where they pass them. The length of beam, for which wee have to guard agains flexure, is the length between verticals in any:panel. In panel No. 1, it'will be 25: feet, " " 2, " " 1:8 "' " " 3, " " 17 " "- " 4,''-: 16 " Now, using the formula 2240 b d d2 we shall have, in round numbers, the following dimensions: For the 1st panel, 25 feet long, 8 x 10 ".2d.' 37 " " 8x10'; 3d " 49 " " 8x10 " 4th' 64 " 8 x 10 cc 5th " 78 " " 8 x 10 For the lattice work, a double course on each side of each truss, in long spans; and a single course, in shorter spans, of 3 x 6, or 2 x 9 plank, bolted at intersections, is sufficient. -XXVII. GENERAL TABLE OF DIMENSIONS FOR ARCH BRACEt TRUSS. G. L VOSE. Span. Rise. Chords. Ties. Braces. Lattice. 50 10 2 —810 1-8x10 2 -6x6 75 12 2-8x10 1 —8x10 2-6x6'2 x 9 100 15 3-8x10 2 —8x10 3-6x6 or 150 20 4 —8 X2 3 —8s10 4 —6x8 3 x 6 200 25 4 —816 3-8xi0 4-6x9 The arch braces must all foot on an iron.thrustblock, of which a view is given in Fig; 4, P1. III; and the centre of pressure of:the braces must be directly over: a, bolster, to prevent. crippling. The several sticks forming a brace must be blockedltoogetherrat intervals, and When they are splice d,- butt joint shoul; be used-aUd it should come i n th;e centre of a panel. tBelOow are given the dimensions, of: the Thayer Engineering oSh'if model. -4 W Q z o P.O Ins. Ins. Ins. Ins. Ins. Ins, 12 8 2-1x4 1-sx5 2- xj.xt; 13 There are several -other forms, of Bridge, the most notable among:which are the:Whipple, McCallurm's, Post's;: Towne's, Haupt's, and Burr's. But enough' has been said to give the: stdent an:-idea of the general arrangement -of the difirent parts'of a Truss, and to' e:nable him t::o::tO determine::the strains.' to whiceh the.various-:members are'subjected. -Nothing will be:said i regard to Woodea Arches,- as our space is -too limited. 3Pile Bridging. A bridge of this deseription is useful in crossing marshes, or in shallow water. Fig., P1.! I1, gives a good example of this kind of bridge, under 20 feet in height. If on a curve, there must be extra bracing on the convex side. XXV. II. Trestle NVoork. This is a cornbination of posts caps, and braces;-and is used for both temporary and permanent works. Plate IV, Figs. 1, 2, 3 and 4, give some of the best varieties in use. Figs. 1 and 2, may be used up to 15 feet in height; Fig. 4, up to 20 feet; and Fig. 3, to 30 ft. The distance apart of the various bents should not exceed 10 or 12 ft., unless braciug is introduced between them, and the bents should always be raised above the ground a few feet on a solid mason_ ry foundation. Want of space forbids any mention of abutnents and piers, which really come more properly under the head of masonry. Iron Bridging is gradually working its way into favor, and Will probably eventually supersede wooden trusses; —but in many cases wood is the only material at hand —and therefore some knowledge of Wooden Bridging is desirable. It is intended to follow this pamphlet with a portfolio of sheets containing working drawings of several kinds of Wooden Bridges, taken from actual measurements of some of the best specimens of the different styles of Truss in use. PRACTICAL NOTES. When putting a truss together in its proper position, on the abutments,' false works' must first be erected to support the parts until they are so joined together as to form a complete self-sustaining truss. The bottom chords are first laid as level as possible on the false works, then the top chords are raised on temporary supports, sustained by those of the lower chord, and arle placed a few inches higher at first than their proper position, in order that the web members may be slipped into place. When this is done the top chords are gradually lowered into place. The screws are then gradually tightened, (beginning at the centre and working:towards both ends,) to bring the surfaces of the joints into proper contact, and by this method, the camber forms itself, and lifts the lower chords clear of the false XXIX. works, leaving the truss resting only upon its proper supports. The subjoined Table will be found useful in estimating the strains on a truss when proportioning a bridge for any moving load. Table of weights per running foot of a bridge, (either of wood or iron,) including weights of floor, lateral bracing, &c., complete, for a single track. 30.281 629 80 Q43S 0 bt-4."'rW Tons. lbs. Tons. lbs. Tons. lbs. Tons. lbs. 25.266 596 70.404 905 140.614 1375 200.792 1774 30.281 629 80.434 972 150.643 1440 225.867 1942 40.313 701 90.464 1039 160.673 1507 250.940 2105 50.343 768 100.494 1106 170.703 1575 275 1.013 2269 60.374 838- 120.554 1241 180.733 1642 300 1.087 2435 The weight of a single track railway bridge may be taken as equal to that of a double track highway bridge,-and the trusses that will be large enough for one will be large enough for the other. The greatest load that a highway bridge can be subjected to is 120 lbs. to the square foot of surface. TABLE OF CAMBERS FOR BRIDGE TRUSSES. Span. Cambcr S Span. Camber. Span Camber. Span. Camber. feet. Inche.. Feet. Inches Feet. Inches Feet, Inches.:.O8 76 2.5 17 5.8 2T 9.2 30 1o0 100 3.3 200 6.7 Soo { tQ 50 1.7 120 4.0'225 5 325 10.8 60 2.0 150 5.0 250 8.3 350 11.7 TRAUTWINE'S TABLE FOR FINDING INCREASE IN LENGTH OF UPPER CHORD BEYOND THE LOWER CHORD ON ACCOUNT OF THE CAMBER. u:ltipy;. MuLtiply M; -lti Multiply De t:,of. Cam Depthm:of: Camber Peptl, of C:mber Depth: ofCamber. r[\i~Ss.- by f Truse. b y r'. by: rus s. by 1-4-span'2.00 1-8 span 1.00 1-12span.666 1-16span.500 1-5 " 1.60 1-9 ".888 1-13 ".614 1-17 ".470,1 —:'' 7'" 11 { i;11, 7.'i1-5"::..533. 1-20"..400 TABLE OF AMERICAN WOODS. Weight pr Resistance,:in-bs-;per square Kind. cubic foot in inch. Value of s. pounds. Extension Compression. White Pine. 26 12,000 6000 1229 YellowPine. 31 12,000 6000 1185 Pitch Pine. 46 12,000 6000 1727 Red Pine. 35 12,000 6000 1527 Virginia Pine. 37 12,000 6000 1456 Spruce. 48 12,000 6000 1036 Tamarack. 26 12,000 6000 907 Canada Balsam. 34 12,000 6000 1123 White Oak. 48 15,000 7500 1743 Red Oak. 41 15,000 7600 1687 Birch. 44 15,000 7000 1928 Ash. 38 16,000 8100 1795 Hickory. 51 15,000 7200 2129 El m. 45 16,000 8011 1970 The above table is compiled from a much fuller one in Vose's Treatise on R. R. Construction, TABLE OF BOLTS AND NUTS CALCULATED FOR A WORKING STRAIN OF 15,000 LBS. PER SQUARE INCH OF SECTION. Diameter. Area. Strength in Weight per Tnickn's No. thr's Inches. Sq. inches. Pounds. foot. Square nut. of nut. per inch. 1-2.19635 2940 0.66 1 1-4in 34in 12 5-8.'30680 4602 1.03 1 3-8 3-4 10 3-4.44179 6630 1.49 11-2 7-8 to 7-8.60132 9019 2.03 1 3-4 1 9 1.78540 11775 2.65 2 1 8 1i1-8.99402 14910 3.36 2 11-8 7 1 1-4 1.2272 18405 4.17 2 1-4 1-4 7 1 3-8 1.4849 22260 5.02 2 1-2 13-8 6 1 1-2 1.7671 25505 5.97 2 3-4 1 1-2 6 1 5-8 2.0739 31095 7.01 2 7-8 1 5-8 5 1 3-4 2.4053 36075 8.13 3 1 3-4 5 1 7-8 2.7612 41415 9.33 3 1-4 1 7-8 4 i2 3.1416 47130 10.62 3 1-2 2 4 1-2 2 1-8 3.5166 53190 12.00 3 3-4 2 1-8 4 21-4 3.9761 59640 13.40 4 2 1-4 4 2 3-8 4.4301 66450 15.00 4 1-8 2 3-8 4 2 1-2 4.9087 73620 16.70 4 1-4 2 1-2 3 1-2 2 5-8 5.4119 81178 18.20 4 1-2 2 5-8 3 1-2 2 3-4 5.9396 89094 20.00 4 3-4 2 34 3 1-2 2 7-8 6.4918 97377 21.90 5 2 7-8 3 3 7.0686 106029 23.80 5 1-4 3 3 3 1-4 8.2958 124437 27.90 5 3-4 3 1-4 3 3 1-2 9.6211 144316 32.40 6 3 1-2 2 1-2 TABLE OF SAFE WORKING LOAD IN LBS., FOR HOLLOW CAST-IRON COLUMNS. [ G.I. Vose.] Outside di- Length or height in Feet. Metal Thick ameter ness in inches. 8 I 10 12 15 1 18 20 in inches. _- — o. _ _-__ — __ — 3 16000 14000 13000 11000 9000 7000 6000 3-8 4 30000 29000 26000 24000 22000 18000 16000 1-2 5 50000 37000 45000 42000 39000 37000 31000 5-8 6 59000 57000 55000 52000 49000 44000 41000 3-4 7 101000 99000 96000 92000 88000 81000 76000 13-16 8 131000 129000 12000 12226 000 1100 18000 109000 105000 7-8 9 169000 167000 164000 160000 156000 146000 141000 1 10 210000 200000 200000 200000 190000 180000 180000 1 1-8 11 250000 250000 240000 240000 240000 230000 220000 1 1-4 12 300000 300000 290000 290000 290000 270000 270000 1 1-2 14 450000 430000 410000 380000 370000 350000 330000 1 3-4 16 520000 500000 480000 460000 440000 420000 400000 2 18 650000 630000 610000 590000 560000 520000 470000 2 1-2 20 800000 760000 740000 690009 6500001590000 540000 3.-,.........,-................,-,........... ......................................................................................................................................................... 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A Series of Designs, Plans, anid Specifications, from $200 to $20,000, for Homes for the People; together with Warming, Ventilating, Drainage, Painting, and Landscape Gardening. Cloth...................... 3 50 -THE RUDIMENTS OF ARCHITECTURE AND BUILDING. By J. Bullock. 8vo., Cloth...................................... 3 50 HATPFIELD. THE AMERICAN CARPENTER. By R. G. Hatfield. 7th edition. 8vo., Cloth. —............................................ 3 50 TREDGOLD. THE ELEMENTARY PRINCIPLES OF CARPENTRY. [By Thomas Tredgold, C. E. 5th edition, revised and enlarged. 1 large 4to., ex. Cloth...................... I......................... 12 50 — ELEMENTARY PRINCIPLES OF CARPENTRY. By Thos. Tredgold. Revised from the original edition and partly rewritten by J. T: Hurst. 12mo., Cloth. With plates. London, 1871............... 9 00 NICHOLSON. CARPENTERS' NEW GUIDE. By P. Nicholson. Revised by K. N. Davies, and containing new Designs for Roofs, Domes, etc., by S. Sloan. 4to..................................... $4 50 SILLOWAY. TEXT-BOOK OF MODERN CARPENTRY. By T. W. Silloway. Illustrated. 12mo..................................... 1 50 VODGES. THE ARCHITECT'S AND BUILDER'S POCKET COMPANION AND PRICE-BOOK. By F. WV. Vodges. Cloth, $1 50. Morocco Tuck. 2 00 AVELING. CARPENTRY AND JOINERY. A useful Manual for the many. By S. T. Aveling. With original and practical illustrations. 12mo., Cloth............................................... 1 25 XMONCKTON. THE NATIONAL BUILDER. A complete work on Constructive Carpentery, Stair Building, and Hand Railing, for the use of Architects, Builders, Carpenters, and Stair-Builders. By Jas. H. Monckton. 4to., Cloth. Plates................................ 6 00 WORKS OF REFERENCE. URE. A DICTIONARY OF ARTS, MANUFACTURES AND MINES. By Andrew Ure, M. D. 6th edition. Edited by Robert Hnnt, F.R.S. Greatly enlarged and re-written. 3 vols. 8vo., Cloth. London, 1867. 25 00 WATTS. DICTIONARY OF CHEMISTRY AND THE ALLIED BRANCHES OF OTHER SCIENCES. By Henry Watts, B. A., assisted by eminent scientific and practical Chemists. 6 vols. 8vo., cloth. London, 1866-68........................................................... 62 00 MUSPRATT. CHEMISTRY AS APPLIED AND RELATING TO THE ARTS AND MANUFACTURES. By Sheridan Muspratt. 2 vols. Royal 8vo. H alf Russia. ~.................................................... 30 00 SPON'S DICTIONARY OF CIVIL, MECHANICAL, MILITARY AND NAVAL ENGINEERING. With technical terms in French, German, Italian and Spanish. Edited by Oliver Byrne. Royal 8 vo., Cloth. Illustrated. Vols. I. to VII. ready. Per vol......................... 5 00 TOMILgN SON. ENCYCLOPA2DIA OF USEFUL ARTS, Mechanical and Chemical, Manufactures, Mining and Engineering. By C. Tomlinson. 3 vols. Large 8vo., with fine illustrations. Half Russia. 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