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Ill II II A It 
 
 OF THE 
 
 of 
 
 Name of Book and Volume, 
 

AN 
 
 ELEMENTARY 
 
 AND 
 
 PRACTICAL TREATISE 
 
 ON 
 
 BRIDGE BUILDING, 
 
 AK 
 
 4 
 
 ENLARGED AND IMPROVED EDITION 
 
 OF THE AUTHOR S ORIGINAL WORK, 
 
 S. WHIPPLE, C.E. 
 
 ALBANY, N. Y., 
 IHYENTOR OF THE WHIPPLE BRIDGES, M*. 
 
 SECOND EDITION, REVISED AND ENLARGED. 
 
 NEW YORK: 
 
 1). VAN NOSTRAND, PUBLISHER, 
 
 23 Murray St., and 27 Warren St. 
 
 18T3. 
 

 
 Entered according to Act of Congress, in the year 1873, bj 
 
 S. WHIPPLE, 
 In the Office of the Librarian of Congress, at Washington. 
 
INTRODUCTION. 
 
 It is about thirty years since the An thor s attention 
 was especially directed to the subject of BRIDGE 
 CONSTRUCTOR; and, Lis Original Essays published 
 in 1847, are believed to have aided considerably 
 toward establishing the foundation upon which a 
 knowledge of the principles involved, and the con 
 ditions required in the proper construction of TRUSS 
 BRIDGES, has been built up, and carried to a high 
 state of advancement. 
 
 However that may be, the flattering terms in 
 which his former labors in the premises have often 
 been referred to, as well as the frequent applications 
 for copies of his former publication, since the 
 supply became exhausted, have prompted the 
 issue of the present volume. 
 
 This work inculcates the same development of 
 GENERAL PRINCIPLES, and treats of essentially the 
 same General Plans, Combinations, and proportions 
 for bridge work, as were discussed and recom 
 mended in its humble predecessor; with such 
 
iv INTRODUCTION. 
 
 additions and improvements as subsequent experi 
 ence and observation have enabled the Author to 
 introduce. 
 
 The design has been to develop from Funda 
 mental Principles, a system easy of comprehension, 
 and such as to enable the attentive reader and 
 student to judge understandingly for himself, as 
 to the relative merits of different plans and combi 
 nations, and to adopt for use, such as may be most 
 suitable for the cases he may have to deal with. 
 
 It is hoped the work may prove an appropriate 
 Text Book upon the subject treated of, for the 
 Engineering Student, and a useful manual for the 
 Practicing Engineer, and Bridge Builder. But as 
 to this, the decision must be left to those into whose 
 hands it may fall; and to that arbitrement, with 
 out further remark or explanation, it is respect 
 fully submitted. 
 
CONTENTS. 
 
 Page. 
 
 Preliminary remarks, &c. --..-- 1 
 
 Two Panel Trusses ....... 9 
 
 Three Panel Trusses - 16 
 
 Five Panel Trusses - ... 20 
 
 Seven Panel Trusses. The Arch Truss - - 31 
 
 Trapezoid Trusses with Verticals .... 4G 
 
 Trapezoid Trusses without Verticals .... 54 
 
 Decussation of forces, &c. ..... 64 
 
 The Warren Uirder 69 
 
 The Finck Truss - .... 73 
 
 Characteristics of the Arch 74 
 
 Weight of Structure - 77 
 
 Double Cancelated Trusses with Verticals 80 
 
 Double Cancelated Trusses without Verticals fcG 
 
 Decussation in Trusses with Verticals - - 92 
 
 Deck Bridges - 97 
 
 Katio of length to depth of Truss - ... 100 
 
 Inclination of Diagonals - - - - - 104 
 
 Width of Panel ... .... 109 
 
 Arch Bridges - 112 
 
 Construction of equilibrated Arches - - - - 114 
 
 Webbed Arches - - - 117 
 
 Ordinates of equilibrated curves determined by calculation 119 
 
 Action of the web in webbed Arches - - 125 
 
 Effects of heat upon Arches without Chords - - - 126 
 
 Bridge Materials, Wood and Iron compared - - 132 
 
 IRON BRIDGES. Strength of Iron - - 142 
 
 Experiments on Cast Iron, &c. .... 146 
 
 Safe practical strain of Iron ..... 151 
 Note giving examples of stress of Wrought Iron in several 
 
 structures in use - - 153 to 155 
 Table of Negative Strength of Iron in pieces of various 
 
 lengths and sections 159 
 
vi CONTESTS. 
 
 Pa<jc. 
 
 TRANSVERSE strength of Iron . 161 to 171 
 
 ARCH TRUSS BRIDGES 17_> 
 
 Iron Beams for Bridges 182 
 
 Modes of Insertion of Iron Beams .... 184 
 
 The Link Chord - - - - 188 
 
 The Eve-bar Chord ]^2 
 
 Size of connecting Pins - - - - 193 
 
 Riveted Plate Chord - 19(j 
 
 Trapezoidal Truss Bridges, details ... 200 
 
 Double Cancelated Bridges, details .... 205 
 
 Wrought Iron thrust members .... 214 
 
 Double Chord, a suggestion ..... 224 
 
 Rivet-work Bridges 227 
 
 Sway-bracing ...... 236 
 
 Comparison of Bridge Plans 241 
 
 Bullman Truss - 241 
 
 Finck Truss - - 244 
 
 Post Truss 246 
 
 W hippie Trapezoid - 251 
 
 The Isometric (without verticals) ..... 253 
 
 The Arch Truss 256 
 
 Synopsis of results of analyses 257 
 
 (General Remarks - 258 
 
 COUNTER BRACING, value of 263 
 
 WOODEN BRIDGES Strength of timber - - 274 
 
 Table of Negative resistance of timber - ... 276 
 
 Transverse strength of Wood 277 
 
 Resistance to cleavage 278 
 
 Connections of Tension pieces ..... 279 
 
 Connecting pins of Wood and Iron .... 281 
 
 Splicing . 285 
 
 Construction of Wooden Trusses 288 
 
 Two panel Wooden Truss Bridge .... 288 
 
 Three panel Wooden Truss Bridge .... 294 
 
 Four and Six panel Wooden Truss Bridge - - 296 
 
 The Howe Bridge 302 
 
 Wooden Trapezoid without verticals ... 30$ 
 
 MODULUS of strength of Trusses .... 314 
 
BRIDGE BUILDING. 
 
 PRELIMINARIES. 
 
 I. A bridge is a structure for sustaining the weight 
 of carriages, animals, &c., during their transit over a 
 stream, gulf or valley. 
 
 Bridges are constructed of various plans and dimen 
 sions, according to the circumstances and objects re 
 quiring their erection ; and it is the purpose of this 
 work, after a few remarks upon the general nature and 
 principles of bridges, to attempt some analyses and 
 comparisons of the respective qualities and merits of 
 various general plans, with a view of deducing practi 
 cal results, as to a judicious and economical choice and 
 application of materials in the construction of these 
 useful and important structures. 
 
 II. The force of gravity, on which the weight of 
 bodies depends, acts in vertical lines, and consequently, 
 a heavy body can only be prevented from falling to the 
 earth, by a force equal and opposite to that with which 
 gravity impels the body downward. This resisting 
 force must not only act vertically upward, but the line 
 of its action must pass through the centre of gravity of 
 the body it sustains. All the forces in the world, act 
 ing parallel with, or perpendicular to, the vertical pass 
 ing through its centre of gravity, could not prevent a 
 
 1 
 
2 BRIDGE BUILDING. 
 
 musket ball (concentrated to the point of its centre of 
 gravity) from falling to the centre of the earth, unless 
 it were a horizontal force capable of giving the ball a 
 projection, such that the centrifugal tendency should 
 equal or exceed gravity a kind of force which could 
 never be made available toward preventing people from 
 falling into the water in crossing rivers ; consequently, 
 having no application in bridge building. 
 
 In fact, nothing but a continuous series of unyielding 
 material particles, extending from an elevated body 
 downward to the earth, can hold or sustain that body 
 above the earth, by vertical and horizontal action 
 alone, either separately, or in combination. 
 
 * 
 
 III. Suppose a body, no matter how great or small, 
 placed above the earth, with a deep void, or an inac 
 cessible space benea th it. Attach as many cords to it 
 as you please, strain them much or little only hori 
 zontally the body will fall, nevertheless. Thrust any 
 number of rods, with whatever force you may, hori 
 zontally against it; still the body will fall. This is 
 obvious from the fact that horizontal forces, acting at 
 right angles with the direction of the force of gravity, 
 have no more tendency to prevent, than to promote 
 the fall of the body. 
 
 Moreover, the space beneath being inaccessible, 
 there is no foundation, or foot hold, upon which to 
 rest a post or stud that may directly resist the action 
 of gravity, while the lines of all other vertical forces or 
 resistances, pass by the body without touching it. 
 
 In the case here supposed, the body can only be pre 
 vented from falling by oblique forces; that is, by forces 
 whose lines of action are neither exactly horizontal, 
 nor exactly perpendicular. Attach two cords to the 
 
PRELIMINARIES. 3 
 
 body, draw upon them obliquely upward and outward, 
 in opposite directions, or from opposite sides of the 
 void, with a certain stress, and the body will be sus 
 tained in its position. Apply two rods to it obliquely 
 upward, of a proper degree of stiffness, in the same 
 vertical plane, and on opposite sides of the perpendicu 
 lar, a certain thrust exerted upon those rods, will pre 
 vent the descent of the body. 
 
 IV. Sere, then, we have the elementary idea the 
 grand fundamental principle in bridge building. What 
 ever be the form of structure adopted, the elementary 
 object to be accomplished is, to sustain a given weight 
 in a given position, by a system of oblique forces, whose 
 resultant shall pass through the centre of gravity of the 
 body in a vertically upward direction, in circumstances 
 where the weight can not be conveniently met by a sim 
 ple force, in the same line with, and opposite to, that 
 of gravity. 
 
 For a more clear illustration of this elementary idea, 
 let us suppose a a , Fig. 1, to represent the banks of a 
 river, or the abutments of a bridge ; and gg r , the line 
 of transit for carriages, &c. ; and, let us further suppose 
 a load of a certain weight, w, to have arrived at a point 
 centrally between a a r . The simplest method of sus 
 taining the weight is, perhaps, either to erect two ob 
 lique braces aw. . a w, or suspend two oblique chains 
 or ties pw, p w, from fixed supporting points a a , orpp f . 
 
 It is not necessary that the weight be at the angular 
 point w, of the braces or chains, but it may be sustained 
 by simple suspension at w f below, or simple, support at 
 w" above, and such obliquity may be given to the braces 
 or chains as maybe most economical ; a consideration 
 which will be taken into account hereafter. 
 
4 BRIDGE BUILDING. 
 
 V. Thus we see how a weight may be sustained cen 
 trally between the banks of a river, or the extremities 
 of a bridge. But the structure must not only provide 
 for the support of weight at this point, but also at every 
 other point between a a , orgy ; and it is obvious that 
 the same plan and arrangement will apply as well at 
 any other point as at the centre, with only the variation 
 of making the braces or chains of unequal length. 
 
 This, however, would require as many pairs of braces 
 or chains as there were points between g g f , a thing, 
 of course, impracticable, since the oblique members 
 would interfere with one another, and be confounded 
 into a solid mass. We therefore resort to the transverse 
 strength and stiffness of beams, phenomena with 
 which all have more or less acquaintance, and without 
 digressing in this place to investigate their principles 
 and causes, it will be assumed as a fact sustained by all 
 experience, that, for sustaining weight between two 
 supporting points upon nearly the same level, a simple 
 beam affords the most convenient and economical 
 means, until those points exceed a certain distance 
 asunder, which distance will vary with circumstances ; 
 
PRELIMINARIES. 5 
 
 but in bridge building, will seldom be less than 10 to 
 14 feet, where timber beams are employed. Hence, 
 for bridges of a length of 12 to 14 feet, usually, nothing 
 better can be employed than a structure supported by 
 longitudinal beams, with their ends resting upon abut 
 ments or supports upon the sides of the stream. 
 
 Of course, no reference is here had to stone or brick 
 arches. For, though these are advantageously used 
 for short spans, and in deep valleys, where the ex 
 pense of constructing high abutments for supporting a 
 lighter superstructure, would exceed or approximate to 
 that of constructing the arch, it is the purpose of this 
 work to speak only of those lighter structures, com 
 posed mostly of wood and iron, and supported by abut 
 ments and piers of stone, or by piles, or frames of wood. 
 
 Having then adopted the use of beams for supporting 
 weight upon short spaces, it is only necessary upon 
 longer stretches, to provide support for a point once 
 in 10 or 14 feet, by braces, &c., from the extremities; 
 and for intermediate points, to depend on beams or 
 joists extending from one to another of the principal 
 points provided for as above.* 
 
 VI. For a span of 20 or 30 feet, it would seem that 
 no better plan could be devised, than to support a 
 transverse beam midway between abutments, by two 
 pairs of braces or suspension chains, proceeding from 
 points at or over the abutments, one pair upon each 
 side of the road- way ; this transverse beam affording 
 support for longitudinal beams or joists extending 
 
 * It is susceptible of easy demonstration that the power of beams to 
 sustain weight by lateral stiffness, forms no exception to the principle 
 that oblique forces alone can sustain heavy bodies over inaccessible 
 epaces. But this matter is deferred for the present. 
 
6 BRIDGE BUILDING. 
 
 therefrom to the abutments. When suspension chains 
 are used, it may properly be called a suspension bridge. 
 If braces be employed, it is usually termed a truss-bridge. 
 
 HORIZONTAL ACTION OF OBLIQUE MEMBERS. 
 
 VII. Before advancing further, it will be proper to 
 refer to an important principle or fact which has not 
 yet been taken into account, though a fact by no means 
 of secondary interest. 
 
 The sustaining of weight by oblique forces, gives rise 
 to horizontal forces, for which it is necessary to provide 
 counteraction and support, as well as for the weight of 
 the structure and its load. The two equal and equally 
 inclined braces, ac and 6c, Fig. 
 2, in supporting the weight w 
 at c, act in the directions of 
 their respective lengths, each 
 with a certain force, which is 
 -. -- equivalent to the combined 
 
 ^ action of a vertical and a hori 
 zontal force, [Elementary Mechanics Statics^] which 
 may be called the vertical and horizontal constituents 
 of the oblique force. These two constituent forces 
 bear certain determinate relations to one another, 
 and to the oblique force, depending upon the angle 
 at which the oblique is inclined. 
 
 Now, we know that the vertical constituent alone 
 contributes to the sustaining of the weight, and conse 
 quently, must be just equal to the weight sustained, in 
 this case equal to -J?.#. We know moreover, from the 
 principles of statics, that three forces in equilibrio, 
 must have their lines of action in the same plane, and 
 
PRELIMINARIES. 7 
 
 meeting at one point ; and must be respectively pro 
 portional to the sides of a triangle formed by lines 
 drawn parallel with the directions of the three forces; 
 and that each of the three forces is equal and opposite 
 to the resultant of the combined action of the other 
 two. We have, then, at c, the weight J w, the oblique 
 force in the line ac, and a third force, equal and oppo 
 site to the horizontal constituent of the oblique force 
 in the line ac. Then, letting fall the vertical dc 9 and 
 drawing the horizontal ad, the sides of the triangle acd, 
 are respectively parallel with the three forces in equili- 
 brio at the point c. Hence, representing the vertical 
 cd 9 by v, the horizontal ad, by h 9 and the oblique by o ; 
 and calling the horizontal force x, and the oblique 
 force, y 9 we have the following proportions : 
 
 (1). Jw : x : : v : A, whence, x = J w 
 (2). JMJ : y : : v : o, whence, y = %w 
 
 But \w equals the weight sustained by the oblique 
 ac. Therefore, from the two equations above deduced, 
 we may enunciate the following important rule : 
 
 The horizontal thrust of an oblique brace, equals the 
 weight sustained, multiplied by the horizontal and 
 divided by the vertical reach of the brace ; and the 
 direct thrust (in the direction of its length), equals the 
 weight sustained multiplied by the length, and divided 
 by the vertical reach of the brace. 
 
 VIII. Now, it is obvious that the brace exerts the 
 same action, both vertically and horizontally, at the 
 lower, as at the upper end, though in the opposite 
 directions; the brace being simply a medium for trans 
 mitting the action of weight from the upper to the 
 
8 BRIDGE BUILDING. 
 
 lower end of the brace. Hence, the weight sustained 
 by the brace ac, exerts the same vertical pressure at 
 the point a, as it would do if resting at that point, 
 while the brace requires a horizontal resistance to pre 
 vent its sliding to the left, as would be the case if its 
 foot simply rested upon a smooth level surface. This 
 horizontal resistance may be provided by abutments 
 of such form, weight, and anchorage in the earth, as to 
 enable them to resist horizontally as well as vertically, 
 or by a horizontal tie, in the line a6, connecting the 
 feet of opposite braces. 
 
 These two methods are both feasible to a certain ex 
 tent, and in certain cases ; and, both involve expense. 
 Under particular circumstances, it may be a question 
 whether the former should not be resorted to, wholly 
 or partially. But for general practice, in the construc 
 tion of bridges for heavy burthens, such as rail road 
 bridges, and especially iron truss bridges, where expan 
 sion and contraction of materials produce considerable 
 changes, it is undoubtedly best to provide means for 
 withstanding the horizontal action of obliques, within 
 the superstructure itself; and this principle will be ad 
 hered to in the discussions following. 
 
 The preceding remarks and illustrations as to the ac 
 tion of braces, or thrust obliques, obviously apply in 
 like manner to obliques acting by tension, with only 
 the distinction, that in the latter case, the weight is 
 applied at the lower, and its action transmitted to the 
 tipper end of the oblique, and the horizontal action (at 
 the remote end), is inward, and toward the vertical 
 through the weight, instead of outward ; and conse 
 quently, must be counteracted by outward thrust, as 
 by a rigid body between the points p p , Fig. 1, or by 
 heavy towers, and anchorage capable of withstanding 
 
Two PANEL TRUSSES. 9 
 
 the inward tendency. Hence, in applying the rule be 
 fore given, to tension obliques, and their vertical and 
 horizontal constituents, the word pull should be sub 
 stituted for the word thrust, wherever the latter occurs 
 in said rule. 
 
 TWO PANEL TRUSSES. 
 
 IX. There are three forms of truss adaptable to 
 bridges with a single central beam or cross bearer 
 
 (which may be called two 
 panel trusses), the general 
 JT characteristics of which, 
 
 are respectively repre-- 
 sented by Figures 3, 4 and 
 5. Fig. 3 represents a 
 pair of rafter braces, with 
 
 feet connected by a horizontal tie, and with a vertical 
 tie by which the beam is suspended at or near the 
 horizontal tie, or the chord, as usually designated. 
 
 For convenience of comparison, let bd = v 9 =l,= ver 
 tical reach of oblique members in each figure. Also, 
 let each chord equal 4i?, = 4, and the half chord = 2 = 
 h = horizontal reach of obliques in Figs. 3 and 4. Then 
 ad, Fig. 3, equals \/h*+v* = \/5, and if the truss be 
 loaded with a weight w, at the point 6, bd will have a 
 tension equal to w, and abc, [see rule at end of Sec. 
 VII], a tension equal to J?0, ( = weight sustained by ad), 
 multiplied by the horizontal, and divided by the ver 
 tical reach of ad ; that is, equal to \ w^, = JM? $, = w; 
 while ad suffers compression from end to end, equal to 
 w. But ad=N/5 and i?-l. Whence ia = 
 
12 BRIDGE BUILDINQ. 
 
 making for the four pieces, 2n for tension, and 2M for 
 compression. 
 
 The tie or chord In, suffers tension equal to the hori 
 zontal constituent of the thrust of ql, manifestly equal 
 to the weight sustained by ql, or equal to J w. There 
 fore, the length being equal to 4, the material required 
 in its construction, equals 2M. The remaining mem 
 ber pq (= 2) sustains compression equal to the com 
 bined horizontal constituents of the tension of mq, and 
 the compression of ql, each of said constituents equal 
 to %w, making compression of pq, equal to w, and length 
 being 2, material = 2M 
 
 We have therefore, for this plan of truss, 4M, for 
 thrust material, and 4M for tension material, which is 
 J less than in case of Figs. 3 and 4. Consequently, 
 this plan is decidedly more economical than either of 
 the others, unless the compression material acts with 
 better advantage in the latter than the former ; that 
 is, unless the thrust members in 3 and 4, have a greater 
 power of resistance to the square inch of cross-section, 
 than those in Fig. 5. 
 
 XIIT. As to this, both theory and experiment prove, 
 as will be shown in a subsequent part of this work, 
 that the long thrust members in bridge trusses, are 
 liable to be broken by deflection, rather than by a 
 crushing of the material ; that in pieces with similar 
 cross-sections, with the same ratio of length to diameter, 
 the power of resistance to the square inch is the same. 
 That, since the cross-section is as the square of the di 
 ameter, and the diameters (in similar pieces), as the 
 lengths, the absolute powers of resistance (being as the 
 cross sections), arenas the squares of the lengths. 
 
 v 
 
Two PANEL TRUSSES. 13 
 
 Hence, if the corapressive forces acting upon two 
 pieces of different lengths, be to one another as the 
 squares of the lengths of pieces respectively, and the 
 diameters be as the lengths, the forces are as the cross- 
 sections, and proportional to the power of resistance in 
 each case, and the material in the two pieces, acts with 
 equal advantage, as far as regards cross-section, so that 
 the products of stress into length of pieces, are the true 
 exponents of amount of material required in the two 
 pieces respectively. It follows, that, if on dividing the 
 forces acting upon the pieces in question respectively, 
 by the squares of the lengths, the quotient be the same 
 in both cases, the two pieces have the same power of 
 resistance to the square inch, and in general, the greater 
 the value of such quotient, the greater the power per 
 inch, and the greater the economy, though not neces 
 sarily in the same precise ratio. 
 
 XIV. Applying this rule to thrust members in plan 
 Fig. 3, being the braces, the compressive force equals 
 Jitf\/5, and square of length = 5. Hence the quotient 
 ^w 5/5 = 0.2236^. 
 
 The piece Id Fig. 4, has length = 4 and compression= 
 w, whence, force divided by square of length gives ^w 
 = 0.0625w. This shows the material to be capable of 
 sustaining much more to the square inch in the former, 
 than in the latter case, though it does not give the 
 true ratio. On the other hand, ek and gi, with length 
 1, and stress = J?0, give quotient = %w = 0.5w. 
 Hence, with similar cross-sections, these parts have 
 greater power to the inch than either of the former, but 
 not enough to balance the inferiority of / , as compared 
 with ad and do, in Fig. 3. 
 
12 BRIDGE BUILDING. 
 
 making for the four pieces, 2M for tension, and 2M for 
 compression. 
 
 The tie or chord In, suffers tension equal to the hori 
 zontal constituent of the thrust of ql, manifestly equal 
 to the weight sustained by ql, or equal to J w. There 
 fore, the length being equal to 4, the material required 
 in its construction, equals 2M. The remaining mem 
 ber pq (= 2) sustains compression equal to the com 
 bined horizontal constituents of the tension of mq, and 
 the compression of ql, each of said constituents equal 
 to %w, making compression of pq, equal to w, and length 
 being 2, material = 2M 
 
 We have therefore, for this plan of truss, 4n, for 
 thrust material, and 4M for tension material, which is 
 J less than in case of Figs. 3 and 4. Consequently, 
 this plan is decidedly more economical than either of 
 the others, unless the compression material acts with 
 better advantage in the latter than the former ; that 
 is, unless the thrust members in 3 and 4, have a greater 
 power of resistance to the square inch of cross-section, 
 than those in Fig. 5. 
 
 XIIT. As to this, both theory and experiment prove, 
 as will be shown in a subsequent part of this work, 
 that the long thrust members in bridge trusses, are 
 liable to be broken by deflection, rather than by a 
 crushing of the material ; that in pieces with similar 
 cross-sections, with the same ratio of length to diameter, 
 the power of resistance to the square inch is the same. 
 That, since the cross-section is as the square of the di 
 ameter, and the diameters (in similar pieces), as the 
 lengths, the absolute powers of resistance (being as the 
 cross sections), are.as the squares of the lengths. 
 
 s WW-dU- 
 
Two PANEL TRUSSES. 13 
 
 Hence, if the compressive forces acting upon two 
 pieces of different lengths, be to one another as the 
 squares of the lengths of pieces respectively, and the 
 diameters be as the lengths, the forces are as the cross- 
 sections, and proportional to the power of resistance in 
 each case, and the material in the two pieces, acts with 
 equal advantage, as far as regards cross-section, so that 
 the products of stress into length of pieces, are the true 
 exponents of amount of material required in the two 
 pieces respectively. It follows, that, if on dividing the 
 forces acting upon the pieces in question respectively, 
 by the squares of the lengths, the quotient be the same 
 in both cases, the two pieces have the same power of 
 resistance to the square inch, and in general, the greater 
 the value of such quotient, the greater the power per 
 inch, and the greater the economy, though not neces 
 sarily in the same precise ratio. 
 
 XIV. Applying this rule to thrust members in plan 
 Fig. 3, being the braces, the compressive force equals 
 Jitf\/5, and square of length = 5. Hence the quotient 
 j\w 5/5 = 0.2236^. 
 
 The piece Id Fig. 4, has length =4 and compression = 
 w, whence, force divided by square of length gives ^w 
 = 0.0625w. This shows the material to be capable of 
 sustaining much more to the square inch in the former, 
 than in the latter case, though it does not give the 
 true ratio. On the other hand, ek and gi, with length 
 *= 1, and stress = J?#, give quotient = \w = 0.5w. 
 Hence, with similar cross-sections, these parts have 
 greater power to the inch than either of the former, but 
 not enough to balance the inferiority of /, as compared 
 with ad and dc, in Fig. 3. 
 
14 BRIDGE BUILDING. 
 
 "With regard to truss Fig. 5, ql and pn, suffer each 
 compression equal to Jz0%/2, with square of length = 2, 
 giving quotient = Ji#\/2, = 0.371w, while pq, has com 
 pression = 10, and square of length = 4, arid quotient 
 = J|0 = 0.25z0. Hence it appears that this plan not 
 only possesses a decided advantage in the less amount 
 of action* upon materials, but also, a considerable ad 
 vantage as to ability of compression, or thrust members, 
 to withstand the forces to which they are exposed. 
 
 XV. Still another modification for a truss to support 
 a single beam, is formed by reversing Fig. 3, thus con 
 verting tension members into thrust members, and vice 
 Versa; the oblique members falling below, instead of 
 rising above the grade, or road-way of the bridge. In 
 this case, the long horizontal thrust member c, is di 
 vided and supported in the centre, and its economy of 
 action becomes the same as that of pq, in Fig. 5 ; and 
 the truss gives the same exponents for both thrust and 
 tension material as when in the position of Fig. 3. 
 This arrangement affords no side protection, and is 
 not always admissible, on account of interference with 
 the necessary open space beneath. 
 
 DEDUCTIONS. 
 
 XVI. We seem to learn from what precedes, that : 
 
 (1). Since all heavy bodies not in motion toward, or 
 
 not approaching the centre of the earth (or receding 
 
 from it under the influence of previous impulse), exert 
 
 a pressure equal to their respective weights [vm], 
 
 * By the expression, amount of action, is meant, the sum of products 
 of stresses into lengths of parts, or members. 
 
Two PANEL TRUSSES. 15 
 
 either directly or indirectly upon the earth; and, since, 
 a body crossing abridge, having (as bridges are always 
 supposed to have), avoid space underneath, preventing 
 a direct pressure, it follows, that every such body exerts 
 an indirect pressure at some point or points at greater 
 or less horizontal distance from the body. 
 
 (2). That the pressure of a body at a point or points 
 not directly below it, can only take place through one 
 gr more intermediate bodies, or members, capable of 
 exerting (by tension or thrust), one or more oblique 
 forces upon the first named body, and it is the office 
 of a bridge to furnish the medium of such horizontal 
 transfer of pressure [iv], 
 
 (3. That a single oblique force can not alone prevent 
 a heavy body from falling toward the earth (since two 
 forces can only be in equilibrio when acting oppositely 
 in the same line), and that each oblique force is equal 
 to the combined action of a vertical and a horizontal 
 constituent, of which the first alone is equal to the 
 weight sustained and transferred by the oblique 
 member, while the horizontal constituent, acting at 
 both extremities of the oblique medium, must be coun 
 teracted by means outside of the oblique and the weight 
 sustained by it ; which means are usually to be sup 
 plied by other members of the structure [vni]. 
 
 (4). The direct force exerted by an oblique member 
 (in the direction of its length), is equal to the weight 
 sustained, multiplied by the length, and divided by 
 the vertical reach of the oblique, while the horizonta. 
 constituent equals the weight sustained multiplied by 
 the horizontal, and divided by the vertical reach of 
 the oblique [vn]. 
 
 (5). The amount of material required in a tension 
 member, is as the stress multiplied by the length ot 
 
i6 BRIDGE BUILDING. 
 
 the member [ix] (disregarding extras in connections) 
 and the same is true of thrust members of similar 
 formed cross-sections, sustaining stress proportional to 
 the square of the length of pieces respectively. 
 
 (6). The respective stresses of two thrust members, 
 divided by the squares of respective lengths, give quo 
 tients indicative of, though not proportional to, the re 
 lative efficiency of material in the two members, the 
 greater quotient showing the greater efficiency, or 
 greater power of resistance to the square inch of cross- 
 section [xni]. 
 
 With these rules or principles in view, we may pro 
 ceed advantageously with general analyses and com 
 parisons of different plans, or systems of bridge trussing, 
 adapted to different lengths of span. 
 
 THREE PAKEL TRUSSES. 
 
 XVII. In structures exceeding 25 or 30 feet in length, 
 the length of joists from the centre to the ends, would 
 require cross-sections so great, to give them the requi 
 site stiffness, that their weight and cost would become 
 objectionable. It becomes expedient, then, in such 
 cases, to provide support for more than one principal 
 point, or transverse beam, or bearer. A superstruct 
 ure from 30 to 40 feet long, may be constructed with 
 two cross beams, supported by two trusses with two 
 pairs of braces each, with the feet connected by a hori 
 zontal tie or chord, as seen in Fig. 6. 
 
 The cross beams, may be at b b f , or suspended at c 
 and d, at equal horizontal distances from a a f , and from 
 one another; which latter position they will be re- 
 
THREE PANEL TRUSSES. 
 
 17 
 
 garded as occupying in this instance. Or, the figure 
 may be inverted, thus reversing the action of the several 
 thrust and tension members. 
 
 XVIII. Another, and a more common form of truss 
 for two beams, is shown in Fig. 7. These may be 
 called three panel trusses. 
 
 PIG. 6. 
 
 Pig. 7. 
 
 To compare these two trusses, suppose the two to 
 have the same length and depth, and to be loaded with 
 uniform weights, w, at the two points c and d in each. 
 Then, since we know from the principle of the lever, that 
 each weight produces upon each abutment, a pressure 
 inversely as its horizontal distance from them respec 
 tively, and that the pressure upon the two abutments 
 is equal to the weight producing it, it follows that 6, 
 Fig. 6, sustains f w, and compression = J &o. Hence 
 
 making ab = D,... bc v, and ac = h, ... f^w, becomes 
 J w, and multiplying this stress by length, = D, and 
 
18 BRIDGE BUILDING. 
 
 changingz#toM*,wehaveforniateria]ina6,... M. But 
 D *=/t + v>, whence ^M - J ( 7 | + *) M = (|-f |)M. 
 
 Again, ab r sustains Jw, with length = \/4lt 2 ~+u*, and 
 by multiplying and changing as in case of 6, \ve obtain 
 material in ab 1 , = (-^- 4- ~) M, which added to amount 
 for ab, gives (-^ -f i j M for- the two braces, and 
 (ii + 2v)M for the four. 
 
 The horizontal thrust of ab = f?r while that of ab 
 
 = i lt - 2 ^ = f wi Hence the horizontal thrust of ab and 
 d D 
 
 a6 w = tension of a , and material for chord aa , 
 equals 3 x | M M. Tension of ic and 6W, each, 
 
 equals w, and material for the two = 2 v M, which 
 added to amount in aa f , makes the whole tension 
 material equal to( -f2i ) M, being the same co-efficient 
 of M as was obtained for compression. 
 
 In truss Fig. 7, ... ab and a b (= D = v/A 2 -f v*), evi 
 dently sustain each a weight equal to ?^,-and a stress = 
 ^A 2 -|- r 2 w. Whence, material = (- + v) M for each, 
 
 V 
 
 and ( 2 - -f 2r) M for both, while 66 , equal to A, sustains 
 compression equal to the horizontal thrust of a6, equal 
 to Wj and requires material equal to M, making, with 
 amount in braces ab o b , ( 4- 2r) M. 
 
 Now we have just seen that the horizontal thrust of 
 a6, equal to the tension of chord aa , equals w, and the 
 
 * When is used in the co-efficient of M, then M represents the pr<* 
 duct of the stress, in terms of w, by length according to any assumed 
 unit, which may be equal to v or not. 
 
THREE PANEL TRUSSES. 19 
 
 length being 3A, the material consequently equals 
 M, to which add 2rM for verticals, and we have 
 
 V 
 
 (JE*! + 2 V)M. = whole amount of tension material in 
 truss 7, which is less by n M, than in the case of truss 
 Fig. 6. 
 
 XIX. "With regard to thrust material, it is clear that 
 while in truss 6, the weight on either pair of braces, is 
 transferred in due proportion to both abutments, inde 
 pendently of the other braces, whether one or both pair 
 be loaded ; on the contrary, truss 7, when c only is 
 loaded, must transfer $w to a , which can only be done 
 through a!b , the only oblique member acting at the point 
 a . Moreover, the weight must be communicated to a b , 
 at the point 6 , through the thrust of bd, and the tension 
 ofdb , assuming bd and cb to be thrust members. Now, 
 as either c, or d, is liable to be loaded with weight equal 
 to w, while the other is unloaded, it follows that both 
 bd and cb are liable to sustain weight equal to $w, and 
 require thrust material equal to j( -f v) M for each, 
 
 A or ( 2 n h * -f ^-)M for the two. The whole amount of 
 
 x do o 
 
 thrust material for truss 7, then, equals( -f 2 T)M, 
 (the amount found above) + (?~ -f }t?)]C, equal to 
 (W + 2 v) M, against ( -f SI?)M for truss 6; the 
 difference being pffl jry M. If this be a positive 
 
 quantity, the balance is in favor of truss 7, and if nega 
 tive, in favor of tress 6, as regards amount of action 
 
 on thrust material; while, if i^- : \ v = zero, the 
 amount of thrust action is the same in both trusses. 
 
20 BRIDGE BUILDING. 
 
 Either of these suppositions may be true, according to 
 the relative values of A and v. If h = tV2, 
 
 If h, be greater than iV2 J- - fv is 
 
 positive, and if A be less than v\/2, the value is nega 
 tive. But the amount is trifling in any probable rela 
 tion of A and i , and may be disregarded in this general 
 comparison. 
 
 Calling then, the amount of action upon thrust mate 
 rial in the two plans equal, there is a probable advan 
 tage in favor of truss 7, as to efficiency of thrust 
 material, while the latter truss, shows a positive advan 
 tage over truss 6 in amount of tension material, equal 
 to ( + 2i?) f-^- 2 + 2i?) M = * M. This is equal to 
 
 x 1) x -0 V 
 
 4M, when h = 2v 2 ; which is in tolerable proportion 
 for the trusses under discussion, and, substituting these 
 values of h and v in the expressions of tension material 
 in the trusses respectively, we have (16 -f 2)M for truss 
 6, and (12 -f 2)M for truss 7, being about 28J per cent 
 more for 6 than for 7. 
 
 The same difference would appear with Fig. 6 in 
 verted, the thrust and tension action being the same 
 in amount of each, only sustained by different mem 
 bers, thrust members in one case becoming tension 
 members in the other. 
 
 FIVE PAKEL TRUSSES. 
 
 XX. Truss Fig. 7, may be increased in length and 
 number of panels, by introducing additional panels 
 between the end triangular panels, and the rectangular 
 centre one either of an oblique form, as in Fig. 8, which 
 represents an arch-truss, or of a rectangular form as in 
 
FIVE PANEL- TRUSSES. 
 
 21 
 
 Fig. 10. The truss on the plan of Fig. 6, may be 
 lengthened by introducing additional pairs of inde 
 pendent braces, as seen in Fig. 9. 
 
 For the analysis of these trusses, using the same no 
 tation as before, as far as applicable, that is, making 
 v = verticals ck, in 8 and 10, and equal to nn , pm f , etc., 
 in Fig. 9 ; h = ab, width of panel in each figure, = J 
 whole chord ; w~ uniform weights at the four bearing 
 points in each, and M = weight of material required to 
 sustain a stress equal to w, with length equal to 1 ; 
 then, making Ib = v in truss 8, it is obvious that the 
 two abutments at a and /together sustain 4iv, with the 
 common centre of gravity of all the weights midway 
 between abutments, whence each abutment sustains 
 2w, equal to weight sustained by al. The compression 
 of al therefore equals %w. But al = </h 2 + %v \ 
 which substituted in last preceding expression, gives 
 | v /i 2 4- J v z Wj= compression of al. Whence, multiply- 
 
 V 
 
 ing by length, \/A 2 -f jy 2 , and changing w to M, we 
 have ( H-lJv) M = material for al. 
 
 The horizontal thrust of al, [xvi (4)] equals 
 
 2 10 = w, = tension of chord af. 
 
 |D v 
 
 The oblique member Ik, sustains weight=w (through 
 the vertical cA-* and has a vertical reach = Jv, 
 
22 BRIDGE BUILDING. 
 
 whence it suffers compression equal to^j w, =*^iw, = 
 3 ^A 2 4- jv 2 w, and requires material equal to ( + 
 
 9 
 
 ! I )M, while its horizontal thrust equals --w, *l*t0,i 
 compression of ki, by which it is contracted. The ma- 
 
 O7 9 
 
 terial required for ki, therefore, = M. Material lor ig 
 
 and gf, is the same as above found for al and Ik, and, 
 doubling those quantities, and adding amount just 
 found for ki, we obtain( . -f 3|v) M, -= material in 
 the whole arch. 
 
 The tension of the chord af (Fig. 8), has been seen 
 to be equal to 3 w y whence, multiplying by the length, 
 
 5h, and changing w to M, we have !5?M,*= material for 
 chord. 
 
 The 4 verticals sustain each, weight = w, and the 
 aggregate length being 3Ji>,... material = 3 JVM. This, 
 added to amount in chord, gives ( 4- 3Jv)M, ten 
 sion material required to support a full uniform load, 
 as above assumed. But since any number of the points 
 t), c, dj e, are liable to be loaded while the others are 
 unloaded, it is obvious that in such case, the arch will 
 not be in equilibria, the loaded points tending to be 
 depressed, while the unloaded, tend to be thrust up 
 ward. Hence the arch requires the action of the ob 
 liques, or diagonals, in the three quadrangular panels, to 
 counteract such tendency ; and, as will appear further 
 on, these members will require material equal to about 
 one-third of the amount required in the chord, thus in 
 creasing the amount of tension material for the truss to 
 
FIVE PANEL TRUSSES. 23 
 
 XXI. In truss Fig. 9, each brace obviously sustains 
 a portion, x, of the weight w, which is to ?.0, as the 
 horizontal reach of its antagonist, as to horizontal 
 action, or its fellow and assistant vertically, is to the 
 whole length of chord ; that is, the weight x, bearing 
 at m, through mn f , is to w, as ns to ms ; or, x : w : : 4 : 5. 
 Hence x = $w. This, multiplied by the horizontal 
 reach, equal to A, and divided by v, gives the horizontal 
 
 thrust of the brace, equal to %-w. 
 
 FIG 9. 
 71 
 
 n 
 
 In like manner, mm f sustains a weight x , which is to 
 w, asps to ms, i. e., x : w : : 3 : 5, whence x 1 = |M>, and 
 the horizontal thrust = -| 2 w =* ->; and in general, 
 
 the horizontal thrust of a brace in this kind of truss, 
 equals w, multiplied by the product of the number of 
 sections of chord at the right and the left of the point of 
 application (of the weight), and divided by the whole 
 number of chord-sections, and, by the vertical reach (v) 
 of the brace. 
 
 But the horizontal thrust of mn equals that of n s, = 
 that of mt ,and the horizontal thrust of mm , equals that 
 of m s that of mu, whence, horizontal thrust of the 
 4 braces bearing at m, equals twice that of mn and 
 
 mm together, = 2(4^ + 1-)^ = ^w = 4*w. This 
 
 /O / \ O m O n / .R j. m 
 
24 BRIDGE BUILDING. 
 
 being equal to the tension of the chord, multiplying 
 by length 5A, and changing w to M, gives material for 
 chord = V Adding to this, 4fM, for 4 verticals 
 with stress = w, and length = v, each, makes whole 
 amount of tension material equal to ( +4vJM, being 
 very nearly the same as for truss, Fig. 8. 
 
 XXII. As for braces in truss 9, we have already 
 seen that each brace sustains weight equal to w, multi- 
 tiplied by the number of panels crossed by its fellow, 
 and divided by the number of panels in the whole 
 truss. Hence mn f sustains |i#, with length equal to 
 
 \/A 2 -fy 2 . Therefore, stress = f \/ A 2 +v 2 iv, which mul- 
 
 c 
 tiplied by length, and w changed to M, gives material 
 
 for mn = j(-+0) M = (4 + -$-)M. mm sustains 
 
 f ?0 with length = V4/i 2 + v 2 , whence material = 
 I (4^1+0 } Mj =(^. 9 -f.^L) M . mu sustains M? with length 
 
 -%/9/iHv 2 , and material equals (^+~-)M, while mt, 
 
 sustains Jw, with length = \/16A 2 +y 2 requiring 
 material = (^ + |-)M. Then, adding and doubling 
 
 these amounts, we obtain( +40)lf, against ( 2 -j- 
 
 3Ju)M, for truss 8 ; a difference of about 30.6 per cent 
 when h = v, and about 32.6 per cent when h =* 2v. 
 
 Thus, truss Fig. 8 has over 30 per cent advantage 
 over truss Fig. 9, in the economy of amount of action 
 upon thrust material, with the advantage as to efficiency 
 of action of this material, undoubtedly, also on the side 
 of truss 8. Tension material is nearly the same in 
 both. 
 
FIVE PANEL TRUSSES. 
 
 25 
 
 XXIII. If truss Fig. 9 be inverted, dropping the ob 
 lique members below the road-way of the bridge, thus 
 reversing the action of thrust and tension members, the 
 thrust material would act with nearly equal advantage 
 in both plans, and with about the same amount of 
 action. But the 30 per cent advantage as to amount 
 of action upon tension material, would still be in favor 
 truss 8. Besides, it is only in exceptional cases that 
 this arrangement can be adopted, on account of interfer 
 ence with the necessary space below the bridge. 
 
 XXIV. In truss Fig. 10, suppose the points 6, c, d, e, 
 to be loaded successively from left to right, with uni 
 form weights equal to w each, and suppose the truss to 
 be without weight, as we have hitherto done. When b 
 alone is loaded, \w must bear at /, [xvm] which may 
 be effected, either by tension of bl, thrust of Ic, tension 
 of ck, thrust of kd, &c., by tension vertical and thrust 
 diagonal alternately, till it reaches /; acting in its 
 course upon 4 verticals, and 4 obliques, with a weight 
 upon each, equal to ^w. Or, the weight maybe trans 
 ferred by tension of bk, ci and dg, and thrust of kc, id 
 and gf. These alternatives are subject to the control 
 of the builder, and he will form and connect the parts 
 accordingly. Let it be assumed that the truss has ten 
 sion diagonals, and thrust uprights at c and d, while M 
 
26 BRIDGE BUILDING. 
 
 and eg are necessarily tension members in all cases, in 
 practice. 
 
 Again a weight, w, at c, must cause pressure equal 
 to f w at/, through tension of ci and dg, and thrust of id 
 and gf. This, with the ^w, from the weight at b, makes 
 $w, acting on ci. But the weight at c, causes pressure 
 equal to f?0 at a, necessarily through tension of cl; 
 and since c and bk are antagonistic, the action upon 
 one tending to produce relaxation of the other, it fol 
 lows that only one can act at the same time, unless 
 unduly strained in the adjustment of the truss. Hence, 
 the ^w, which acts upon bk, when b alone is loaded, is 
 overbalanced by the f w, tending to act upon cl, on 
 account of the load at c ; and the result is, that bk is 
 relaxed, the whole weight at b, is necessarily sustained 
 by bl and la, and the {10, which must by a statical 
 necessity, bear at/, in consequence of the loads at b 
 and c, is all made up from the weight at c, leaving only 
 f (jo of this weight to bear at a, through cl. Now, since 
 it is obvious that all load at c, d, or e, must contribute 
 to the pressure at , which can only occur through 
 action upon c?, it follows that bk can only sustain the 
 whole weight of \w, when the point b alone is loaded ; 
 and consequently, that ^w is the greatest weight that 
 bk can ever be subjected to. 
 
 Then, applying another weight, w, at d, it must add 
 f 10 to the pressure at/, through tension of dg and thrust 
 of gf; which last amount, added to f 10, communicated 
 to dg through ci and id, makes f w, as the weight sus 
 tained by dg. But the weight at d, also causes pres 
 sure at a, equal to 10, which can only be done through 
 action, or tendency to action upon dk, and since dk and 
 ci are antagonists, only one can act at once, and that, 
 only with a force equal to the excess of tendency to 
 
FIVE PANEL TRUSSES. 27 
 
 action of the one, over that of the other. Now we 
 have seen that weights at b and c, tend to throw \w 
 upon ci, while the weight at d, tends to throw f ?0 upon 
 dk. Hence, in these circumstances, ci only sustains 
 JMJ, which is transferred to dg through thrust of id, 
 while dk is relaxed, and the whole weight at d, is sus 
 tained by dg; making, with the \w from ci, just above 
 mentioned, $w, equal to the pressure due upon the 
 abutment at/, on account of weights at b, c and d. 
 
 Lastly, a weight, w, at e, tends to give pressure equal 
 to \w at/, through eg Sindgf, and a pressure equal to 
 w at a, through ei, dk, etc. This latter tendency has 
 the effect to diminish by ^w, the tendency of previously 
 imposed weights, to throw f 10 upon dg, reducing it to 
 f 10, and to neutralize the balance of w acting upon 
 ci, after the imposition of the weight at d, leaving c\ 
 and dk both inactive, while eg sustains the whole weight 
 applied at c, equal to w. 
 
 Now, as we have seen, any weight at d or e, tends to 
 throw action upon dk, thereby diminishing action upon 
 ci, and since weight at b and c, both contribute to the 
 stress of ci, it follows that the maximum action upon 
 ci, occurs when b and c are loaded, and d and e, unloaded. 
 
 For similar reasons, the maximum action upon dg, oc 
 curs when e alone is unloaded. 
 
 The maximum weight sustained by Ib, and eg, is the 
 weight applied directly at each of the points b and e, 
 equal to w, and the maximum weights sustained by ei, 
 dk, and cl, are the same as those sustained by bk, ci and 
 dg, each respectively, as just above determined ; while 
 al and gf, both receiving action from weight on any 
 part of the trass, obviously sustain their maximum 
 weight, equal to Zw, under the full load of the truss. 
 
28 BRIDGE BUILDING. 
 
 The section ab, of the lower chord, suffers a stress 
 equal to the horizontal thrust of al, which of course, 
 is greatest vtkenal sustains the greatest weight. This 
 has just been seen to be equal to 2w, and occurs under 
 a full load of the truss. Hence the greatest stress upon 
 
 ab equals 2w , and is communicated without change 
 
 to be, bk being inactive when the truss is fully loaded. 
 The section cd, suffers stress equal to the combined 
 horizontal action of al and Ic, which must be greatest 
 when this combined action is greatest. That is also 
 under the full load of the truss. For, though Ic sus 
 tains J?0 more weight when b is unloaded, the same 
 cause relieves al of the amount of %w. Consequently, 
 the weight borne by the two, is Ji0 less in this case, 
 than when the truss is fully loaded. The greatest com 
 bined weights, then sustained by al and Ic 9 being equal 
 to 3w, the greatest stress of cd equals 3w . This is 
 
 also the greatest compression suffered by the upper 
 chord Ig, since the latter is also equal to the combined 
 horizontal thrust and pull of al and Ic. The stress of 
 this chord is the same throughout, because the obliques 
 meeting at k and i, are inactive when the truss is 
 loaded throughout. 
 
 The maximum compression upon ck and id, equals 
 the greatest weight sustained by d and die, already found 
 to be equal to f w. 
 
 XXV. Having thus ascertained the greatest weights 
 sustained by the several oblique members, and the 
 greatest stresses of the horizontals and verticals, we 
 may deduce the required amount of material, or, per 
 haps more properly, the amount of action upon the ma 
 terial required for the truss, as compared with like 
 
FIVE PANEL TRUSSES. 29 
 
 amount of action in trusses 8 and 9, thus : Max. 
 weight on end braces, 2w x length v/ A 2 -f- v* - stress = 
 
 Hence, action upon material for the , A75 
 tvvo= ................................... (+ 
 
 Max. weight on 2 verticals = f 10 x 
 
 length of the two (=* 20), gives ...... I 
 
 Max. stress of upper chord = 810- 
 
 X length ( = 3A), gives amount ^ 
 
 of action = .............................. ^ 9 
 
 Making total amount of action on 
 
 thrust material = ..................... -5- s l v M 
 
 Aggregate max. weight on 6 tension 
 diagonals = 2 w=4w. This by the 
 length ( = v/A 2 -f y 2 ), gives stress 
 = 4 w \/h? + g a ; whence amount 
 
 of action on material, equals ...... t"f~ "^ 4v / M - 
 
 2 tension verticals sustain each, lw, 
 
 with length = u, giving amount of 
 
 action for the two = ................. 2v M. 
 
 Stress of middle section, lower chord 
 
 = 3w-, X length ( = A), gives 
 
 Q ^ w 
 
 action .................................... d 
 
 4 remaining sections, with stress = 
 
 2u?4 X length ( = 4A), give .......... 8 7 ^M. 
 
 Making whole amount of action on , ^ 
 tension material = . > u ~*~ 
 
so 
 
 BRIDGE BUILDING. 
 
 SYNOPTICAL STATEMENT IN REGARD TO TRUSSES (Figs. 
 8, 9 and 10. 
 
 
 
 
 
 
 B 
 
 
 
 to 
 
 
 fc 
 
 
 
 H 
 M 
 M 
 
 AMOUNT OF ACTION UPON MATERIALS 
 
 
 B 
 
 
 ^0 
 
 H 
 
 "*~ 
 
 
 
 
 Tension. 
 
 Compression. 
 
 TfcoT 
 
 Q 
 
 XX 
 
 ( 207* _L4i t ,) M 
 
 ( w? + 3^ r ) M 
 
 /35^ a , rr v \ M 
 
 9 
 
 XXI 
 XXII 
 
 , 20 A + 1,) M 
 
 ( 207, , 4 ) M 
 
 (J^l + 8v ) ii 
 
 ^ v 
 
 \ -x i/ y AI 
 
 10 
 
 
 ( ~{~ Qv ) M 
 
 V v 
 
 / 28/ a i 1 1 j \ _. 
 
 
 V I/ 
 
 Making A = y * 1, the above table will be as 
 follows : 
 
 8 24JM 18JM 42fM 
 
 9 24M 24M 48M 
 
 10 2lM 18JM 39JM 
 
 XXVI. This shows very nearly the relative amount 
 of tension material required in the several plans; 
 while, as previously stated, the amount of compression 
 material is not so nearly indicated by the figures and 
 expressions giving the amount of action (sum of stresses 
 into lengths of pieces), as in case of tension members. 
 The compression material in No. 8 (the arch truss), is 
 undoubtedly more efficient in action than in either of the 
 others, while that in No. 9, is unquestionably the least 
 so. In fact, this truss will be hardly considered as 
 possessing advantages of any kind, sufficient to induce 
 
THE ARCH TRUSS. 31 
 
 its adoption ; and it will not be considered in the dis 
 cussions and comparisons in regard to trusses of greater 
 span, to which we may now proceed. 
 
 TRUSSES WITH SEVEN PANELS. 
 THE ARCH TRUSS. 
 
 XXTII. In Fig. 11, let md - i>, and h- ab =-. If 
 each of the points 6, c, d, etc., be loaded with a weight 
 equal to w, then, in order that the arch may be in equi- 
 librio under the effects of these weights, without any 
 action of the diagonals, it is necessary that each section 
 of the arch have the same horizontal thrust, since, if 
 one section have a greater horizontal thrust than the 
 one opposed to it at either end, the diagonals alone can 
 sustain the surplus. And, that the sections may have 
 the same horizontal thrust each must have a vertical 
 reach (the horizontal reach being the same for all), 
 proportional to;the weight (W) sustained by each. For 
 illustration, horizontal thrust being equal to W , in 
 order that this expression may represent a constant 
 quantity, h remaining constant, v must be as W. 
 
 Now, ml being horizontal, can sustain none of the 
 weight acting at the point w, through the vertical md; 
 hence mn must sustain a weight equal to w. This is 
 transferred to no [vm], and in addition to the weight 
 at c, makes 2w sustained by no. The latter weight is 
 in turn transferred to <xz, and, in addition to the weight 
 at 6, makes 8w, to be sustained by ao. The vertical 
 reaches, therefore, beginning with ao t should be as 3, 
 2 and 1 ; whence, ob should equal Jy, and no should 
 equal ft . 
 
32 BRIDGE BUILDING. 
 
 The thrust of ao, then, equals 3i0-2, = 610-??., 
 6w \/^!V ; whence, amount of action 
 
 on material* = .............................. (?. -f IJvJxM. 
 
 Thrust of on, = 2i<; = 6^-^-, = 
 _ f 
 
 6w? %/4!i*!, and material = ........ . ...... (?^ + t?}xM. 
 
 i) v 
 
 Thrust of wm =u;S = 610^ = 
 _ i 
 
 6u? ^^^!, and material == ...... ,..( + IV}XM. 
 
 V ^ V b 
 
 Thrust of ml (= horizontal thrust 
 of nm), =- ^-4-= 6^|, and material = .............. 6-XM. 
 
 Adding these amounts, and repeating the first three, 
 we have (i^L -f 4fv)xM, equal to amount of action 
 upon the arch when fully loaded. 
 
 / y 
 
 The stress of the chord obviously equals the horizon 
 tal thrust of ao. equal to 3^. = 6w ; and is the same 
 
 1 t 
 
 throughout, when the truss is fully loaded throughout. 
 Hence, for the whole chord, we have, stress = 6w 
 multiplied by length (= 7A), and w changed to M, 
 = 42 XM, representing the material required for the 
 chord. 
 
 The above are assumed, for the present, to be the 
 greatest stresses that any part of the chord or arch can 
 
 * By amount of action upon material, is meant the stress of a member 
 multiplied by its length. 
 
SEVEN PANEL TRUSSES. 33 
 
 be subjected to, in any condition of the lond ; ?0, being 
 the maximum weight for any one of the sustaining 
 points, b, e, d, &c. This is a point we shall be better 
 enabled to verify after considering the 
 
 STRESSES OF VERTICALS AND DIAGONALS. 
 
 XXVIII. As the diagonals do not act under a full 
 load of the truss, the verticals must each sustain a ten 
 sion equal to 10, when the weights are applied at the 
 chord ; and, the diagonals acting by tension, serve, 
 when in action, to diminish the tension of verticals, or 
 to subject them to compression, but can never increase 
 their action of tension. Hence, the maximum tension; 
 stress of each vertical equals w. 
 
 In order to bring the diagonals into action, the truss 
 must obviously be unequally loaded ; and, to determine 
 the maximum stresses of the several diagonals respec 
 tively, we may begin by removing the Weight at# ; (see 
 Fig. 11 A), and, to facilitate the process, let 10" represent 
 ic divided by the number of panels in the truss (= 7 in 
 this case), i. e., ID" = }w. Then, the full load of the 
 truss bearing with a weight of 810, =21i0", at i, ... with 
 load removed from g, the bearing at z, equals 2J.10" 
 6*0", = ~L5w" ; and produces a thrust upon ij equal to 
 / ^!i!i. Then, taking^ by any convenient scale, 
 
 on ij produced, to represent the thrust of ij (reduced to 
 w n with a numerical coefficient, according to the pro 
 portions of the truss), and drawing qr parallel with fj, 
 and meeting jk produced in r, it is obvious that the 
 three forces acting alj, namely, the thrust of ij and J/c, 
 and the tension of fj, will be represented respectively 
 by the sides of the triangle jqr y parallel respectively 
 with the directions of those forces; and may be mea- 
 5 
 
34 
 
 BRIDGE BUILDING. 
 
 sured by scale and di 
 viders, or calculated tri- 
 gonometrically. 
 
 Now, it will be seen 
 taatthegreaterthe pres 
 sure at i, the greater 
 the thrust of ij, repre 
 sented by j<?, and conse 
 quently, the greater the 
 line qr, representing the 
 tension of fj. But the 
 pressure at i, is mani 
 festly the greatest pos 
 sible in the case here 
 supposed, except when 
 the weight at g is wholly 
 or partially restored, in 
 which case the tension 
 of fj would be wholly 
 or partially relieved. 
 Hence, it follows that 
 the maximum stress of 
 jO i occurs when all the 
 supporting points ex 
 cept #, have their full 
 load, and the point g is 
 without load. 
 
 Taking, then, fs 
 qr, and drawing si par 
 allel with #/, st will re 
 present the horizontal, 
 and// , the vertical effect 
 (equal to 3wr") of the 
 action of fj ; the former 
 
SEVEN PANEL TRUSSES. 35 
 
 effect being, in addition to the tension of / 1, resisted 
 by the tension of ef, while the latter is counteracted 
 by the weight at /, and the tension of fk is thereby 
 diminished, but not exhausted*. But if the weights 
 were applied at the arch instead of the chord, then /&, 
 in this condition, would suffer compression represented 
 
 by/<- 
 
 XXIX. If the points g and/ be unloaded, the pres 
 sure at i is reduced to lOw", and the thrust of ij = Ww" 
 v/^-H^ Then, taking jq by the scale, to represent 
 
 this quantity, and drawing q r parallel withjf), # r/ 
 compared with the same scale, will give the stress of 
 fj; from which, as in the preceding case, we. obtain. 
 ft ( = 2*0"t), to represent the vertical effect of the ac 
 tion of fj ; and, there being no weight at /, this force 
 
 * Since the vertical reach of jk is that of ij, and their vertical ac 
 tions (horizontal thrust, and horizontal reach being the same), as their 
 respective vertical reaches,^ must react downward at,;, with of the 
 lifting force exerted by ij. Then, if a weight be suspended at g, by 
 the vertical jg, equal to of the weight bearing at i, the forces acting 
 at j, through ij, jk, and jg, are in equilibrio. But if the weight at g 
 be less than ^ of the pressure at i, the tendency of the pointj is upward, 
 and exerts a lifting force upon fj,. But the action of fj, brings into 
 play horizontal reaction injk, equal to that of fj, which gives jk a de 
 pressing action at j, equal to f o! the lift ot jy. This depressing power 
 of jk, depends on forces acting directly or indirectly at k, and which 
 go to make up part of the pressure at i. Hence, jk supports at the 
 upper end, at k, first, f of the weight bearing at i, in virtue of the 
 horizontal thrust received through ij, and second, f of the other 
 (when there is no weight at g), in virtue of the horizontal thrust com 
 municated through^) . Now, g being alone unloaded, the bearing at 
 i is I5w", of which, K\w H is received through jk, in virtue of horizontal 
 thrust counteracted by ij. and \ of the other 5w", in virtue of horizontal 
 thrust counteracted by fj, in cons -quence of the latter sustaining fof 
 said 5w". Hence, fj sustains T \ or |, while jk sustains |f, or | of all 
 the weight bearing at i, when g alone is unloaded ; and 3w", therefore, 
 is the maximum weight sustained byfj. 
 
 f Since jq represents the action of ij, due to a pressure of 15?" at i, 
 and jq , tlie action of ij, due to a pressure of Ww", it follows that jq 
 = iU<7 ; whence q r obviously equals qr, and/s =-&/* Consequently, 
 ft = ){/. But ft represents the lift of fj, = 3*0", whence ft repre 
 sents 2w". 
 
36 BRIDGE BUILDING. 
 
 is expended in causing compression upon fk ; and is 
 the measure of the greatest compression that member 
 can receive through fj. But fk is also liable to com 
 pression, or a tendency thereto, from the tension offl 
 when / and g, are loaded, or g alone, and the other 
 parts unloaded. This, however, in the former case, 
 will never equal the weight at /", and in the latter, the 
 compression will not exceed that just found, resulting 
 from action of fj ; as will be better understood here 
 after. 
 
 Now, asjr represents the thrust ofj&, if we take kv, 
 on jk produced, equal tojr f , raise the vertical vx 
 ft , and join kx 9 the line kx represents the resultant of 
 the forces kv and ft (representing thrust of jk and/A:) ; 
 and xy, drawn parallel with ke, represents the tension 
 of ke ;* This is the maximum stress of the diagonal ke. 
 
 XXX. For, when the left half of the truss has more 
 load than the left hand abutment is required by the 
 statical law to sustain, it is clear that a part of the 
 weight on the left, is transferred from left to right past 
 the centre through dl; that being the only member 
 capable of effecting the transfer. It is also clear, that 
 such transferred weight, together with the weight at e, 
 if any, is sustained by Ik and ek, and causes pressure 
 at i, equal to the weight sustained by Ik and ek. Also, 
 that this pressure at i 9 causes a horizontal thrust in ij, 
 which is all transferred to Ik (except when kg is in ac 
 tion), and gives a lifting power to Ik, equal to J of that 
 exerted by ij (the vertical reach of the former being J 
 that of the latter), that is, equal to J of the weight 
 
 * The sides of the triangle kxy, being parallel with the directions 
 of the thrust of Ik, the tension of ek, and the resultant kx, of the 
 thrust ofjk and fk, which 4 forces are in equilibrio at the point k. 
 
SEVEN PANEL TRUSSES. 37 
 
 transferred by Ik and ek together. But the lifting 
 power of Ik is further increased by J of the weight sus 
 tained byjf) , which increases the horizontal thrust of 
 Ik, the same as a like amount sustained by ij ; also, by 
 J the weight sustained by ek ; this member having 5 
 times the vertical reach of Ik. Now, as each one of 
 these items results from the weight transferred through 
 Ik and ek, and is greater or less in proportion as the 
 last named weight is greater or less (/and g being un 
 loaded), since all the conditions are the same, except 
 as to amount of weight, it must follow that the greatest 
 stress of ek, is when/ and g are unloaded, and all the 
 other points b, c, &c., are fully loaded unless it be 
 when / and g, or one of them, be wholly or partially 
 loaded. But any weight at/, increases the thrust and 
 lifting power of Ik, through increased action of ij and 
 fj both, while it diminishes the amount sustained by 
 ek and Ik, whence the action of ek, is diminished, inas- 
 Vnuch as it transfers to k, a less proportion of a less 
 weight. 
 
 Again, weight applied &t g, while/ is unloaded, re 
 lieves the tension of fj, and diminishes its lifting power 
 represented by/C and vx, and if of sufficient amount, 
 relaxes fj, and brings tension upon gk; so that, when 
 the weight at g equals w, or 7w", Ik has a lifting power 
 = J pressure at i, less what is due to the horizontal pull 
 of gk, plus, amount due to horizontal pull of ek; while 
 the weight bearing at k, equals 9w" (being weight at 
 e (= 1w") -f 2i0" through dl). Now if ek lifts as much 
 as kg, Ik must have as great a horizontal thrust as ij, 
 and be capable of lifting J 16w" (= weight bearing at 
 i) 9 =5ji0" ; which taken from 9w" bearing at k, leaves 
 3fz0" sustained by ek. Then it remains to be seen 
 
88 BRIDGE BUILDING. 
 
 whether gk sustains more than 3w/ , so as to reduce 
 the horizontal thrust of Ik below that of ij. 
 
 "With the truss fully loaded except at the point/, ij 
 sustains verticalljjlGi^, whence^, having the same hori 
 zontal thrust exerts a depressive force=f 16w",=10f w", 
 atj, leaving a balance of 5Ji#", exerted by ij toward 
 lifting the 7w" at g. Hence, only If w" remains as the 
 weight sustained by gk. Therefore, the horizontal pull 
 of e/c, is not less than that of^A;, the horizontal thrust 
 of Ik, is not less than that of ij , and its lifting power, 
 not less than 5 \w", and ek does not lift more than 3f w"y 
 nor as much as when/ and g are without load, as de 
 termined by the process above explained. 
 
 XXXI. To determine the greatest stress to which 
 dl is liable, let the weights at e,/and g be removed. 
 Then the pressure at z, due to the weights at 6, c and 
 d, equals 6w", that is, Iw" for weight at 6, 2w" for that 
 at Cj and 3w" for that at d. We therefore takejg" on 
 ij produced, to represent the thrust of ?J, produced by 
 610"- draw q"r" parallel with fj, and from q"r" find /I" 
 (of course less than// ), and having taken kv on jk 
 produced, equal to jr", raise the perpendicular vV = 
 ft", and draw x y parallel with ek. Then, x y repre 
 sents the tension of ek, from which we find ea", repre 
 senting the vertical thrust of el at its maximum. Also 
 ky f represents the thrust of kl\ and, having taken Id 
 on kl produced, equal to ky , raise the vertical d e , equal 
 to ea" from e , draw e f, parallel with dl, and meeting 
 Im (produced, if necessary), in/, and e f represents the 
 tension of dL 
 
 We have a short way of verifying the correctness or 
 otherwise of the last result, since we know that, in the 
 state of the load here assumed, 6w", is transferred from 
 
SEVEN PANEL TRUSSES. 39 
 
 the left to the right of the centre, necessarily through 
 the tension of de, the only member capable of perform 
 ing that office. Hence the tension of dl in this case, 
 can be neither more nor less than what is due to a lift 
 ing power equal to 6w". Then, taking dc on dm, to 
 represent 610", and drawing the horizontal c b , we have 
 do to represent the tension of dl, and, if e f=*db f , the 
 result is probably correct. We know, moreover, that 
 6*0" is the greatest weight ever transferred past the 
 centre of the trass, the left hand side having the great 
 est possible load, and the right hand side, the least 
 possible. Therefore, di represents the maximum 
 stress for dl, which is equal to w"^ tl * + v * 
 
 V 
 
 XXXII. If the points 6 and c alone be loaded, we 
 know that 8tf/ is transferred through dl, and there 
 being no weight at d 9 this lifting force of dl, must be 
 sustained by the thrust of dm. Having then, found If 
 representing thrust of ml, by a process similar to that 
 by which we obtained // in the preceding case, that is, 
 commencing with jq" f , representing the thrust of ij 
 under a weight equal to 3*0", we take mg = If* on lin 
 produced, raise the vertical g i equal to a line repre 
 senting 3w", and draw i i parallel with cm, when we 
 have i f to represent the tension of cm. 
 
 XXXIII. Or, we may take ok on ao produced, to re 
 present the thrust of ao, due to the vertical pressure 
 (= Ht0") at a, resulting from the weights at 6 and c, 
 draw the vertical k l , representing lw", = weight at 6, 
 and cutting on produced in m f , and I m represents the 
 lifting force exerted by bn ; as is made obvious by 
 forming the parallelogram I n , upon the diagonal om . 
 
 * g f i andy shown in Diagram B, to avoid complication 
 
40 BRIDGE BUILDING. 
 
 Take bo = I m , and draw the horizontal o //, then bp 
 represents the tension of bn, and ow 7 , the thrust of on. 
 Take na r = om , on on produced, draw a b / = bp , paral 
 lel with bn, and, from b n let fall b t c t representing the 
 weight ( =7 w") at c, and the part below nm, represents 
 the lift of cm, whence we derive the tension of cm. 
 The result should he the same as that obtained by the 
 former operation. 
 
 XXXIV. If the point b only, be loaded, we may 
 take ok" to represents the thrust of ao resulting from a 
 pressure of 6?0" at a, let fall k"l" cutting on in m", to 
 represent the Iw" at 6, and m"l" represents the vertical 
 lift of bn. Make bo" = m"i", and draw the horizontal 
 o 77 /) 77 , and we have bp" representing the tension of bn. 
 This is the maximum stress of 6?z, since 6/?, can only 
 sustain the weight at b, less the excess of lifting power 
 of ao over the depressing power of on, both having the 
 same horizontal thrust; which excess is represented 
 by k m and k"m", and is least when the weight bearing 
 at a is least. But the bearing at a (and the lift of ao), 
 can never be less than f of the weight at b, and k"m" 
 etc., can never represent less than f weight at 6, or J 
 of the lift of ao; whence m"l" etc., can never represent 
 more than f weight at b ; consequently bn can never 
 sustain a weight greater than 5w" which is the amount 
 represented by m"V when b is fully loaded, and the re 
 mainder of the truss without load. 
 
 XXXV. With regard to cm, no simple and conclu 
 sive reason presents itself, why the result above ob 
 tained for the stress of that member when b and c alone 
 are loaded, is the actual maximum. But, as the 
 assumed condition is precisely analogous, as far as the 
 
SEVEN PANEL TRUSSES. 41 
 
 case permits, to the conditions under which all the 
 other diagonals have been shown to suffer their maxi 
 mum stresses, it is reasonable to conclude from analogy, 
 and the general nature of the case, that w r e have ob 
 tained the true maximum stress for cm. Should there 
 be doubt whether some supposable distribution of load 
 upon the truss, would not produce greater stress than 
 that above shown for the member in question, it is 
 presumed that such doubt would readily be set aside 
 by an analysis similar to what has already been gone 
 through with. 
 
 UPRIGHTS, OR VERTICAL MEMBERS. 
 
 XXXVI. It has already been seen [xxvm], that the 
 maximum tension of verticals equal w, throughout. 
 We have also seen [xxxiv], that the lift of bn, is always 
 less than the weight at b ; consequently ob is never ex 
 posed to compression, unless the load be applied at the 
 arch, which will seldom be found advisable. 
 
 When cm exerts its maximum lift, the point c is 
 loaded, and the lifting force of cm is all expended upon 
 the weight at c. But when the point b alone is loaded, 
 cm exerts a lift, which is the measure of the maximum 
 compression of en, resulting from tension of cm, since 
 any weight at the right hand of c, would bring more 
 or less downward action at the point m, thereby reliev 
 ing some of the tension of cm, and consequently, 
 diminishing its compressive action upon bn. The com 
 pression exerted upon en by the tension of cm, is found 
 to be about equal to 2w", and very nearly the same as 
 that exerted by^) , and represented on the diagram by 
 ft [xxix], 2w", then, may be regarded as the maximum 
 compression of en. 
 6 
 
42 BRIDGE BUILDING. 
 
 The vertical dm, can never suffer compression to ex 
 ceed 3 w", = greatest weight sustained by dl when d is 
 without load ; and if d be loaded, so as to add to the 
 lift of dl, any weight at d, relieves dm of 4 pounds of 
 compression, to every three pounds added to the lift 
 of dl, so that lw" at d, while it increases the lift of dl 
 from Sw " to 6w", changes the action of dm, from com 
 pression of 3w", to tension of ~Lw". 
 
 XXXVII. Having determined the maximum weights 
 sustained by the several diagonals and verticals, we 
 proceed to ascertain their respective stresses, and re 
 quired amounts of material ; as depending upon the 
 length of each member, multiplied by its maximum 
 stress. 
 
 The greatest weight sustained byjf) , as measured on 
 the diagram, and verified by calculation, is equal to 
 810", or f w ; and the length being equal to \X/i 2 -f-ji; 2 , the 
 stress equals f x/A J -Hp 3 w, and the required material 
 
 V 
 
 equals (- + 2 3 g V)M. The 4 diagonals gk, ek, bn and nd, 
 sustain, each, a maximum weight of 5w", [xxxiv], with 
 
 length = v /r+le^ Hence, stress equ als |%/AM- lf- a w, 
 
 10 
 
 and, material for each, = (^+ \\ f V)M. 
 
 The four remaining diagonals sustain each a maxi 
 mum weight of 6w", = f w, with length = >//^ _j_ v * 9 
 giving stress equal to j y/A a + <& w, whence material 
 
 10 
 
 equals (5^! -f $v) M. Then, multiplying the last two 
 coefficients of M by four, and the preceding one by two 
 for the number of pieces in each class ; adding the 
 products, and annexing the common factor M, we 
 
SEVEN PANEL TRUSSES. 43 
 
 obtain for the ten diagonals, an amount of material 
 equal to (7.14^+5.6260)M. 
 
 The aggregate length of verticals, equals 4-| y, and 
 their greatest tension stress equals w. Hence, 4.666#,M 
 represents the amount of tension material they re 
 quire. 
 
 The two longest verticals sustain a maximum com 
 pression of 3tf?" [xxxvi], or %w, with length =- v. 
 Hence material = 0.857vM. The two next in length 
 
 O 
 
 sustain compression = |tt;, with aggregate length = li?, 
 and require compression material = 0.476t>M, mak 
 ing the whole amount of required material, as repre 
 sented by the amount of action by compression on 
 verticals= 1.333M. 
 
 We have, then, material for the whole truss, as re 
 presented by the amount of action, as follows : 
 
 Under Compression. 
 Arch, [xxvn] 
 Verticals, 
 
 Total, ............................................. (42- + 6u)M 
 
 Under Tension. 
 Chord, [xxvn] ........................... (42^ .............. M) 
 
 Diagonals, ......................... . ....... (7.14^ -f 5.626v)M 
 
 Verticals, ................................... _ 4.666?;M 
 
 Total, ..................... ................ 49.14| -f 10.292^M 
 
 Making h = v 1, these amounts become : 
 Under Compression, 48M. Under Tension, 59.432M.* 
 
 * The difference between this result, and that given in the synopsis 
 on page 20 of my original work, arises from the fact that one was 
 based on a circular arch, and the stresses takuu from the diagram, and 
 
44 BRIDGE BUILDING. 
 
 XXXTII. The preceding results are based on the 
 assumption [xxvn] that the maximum tension of the 
 chord, and the maximum horizontal thrust of the arch 
 in all parts, are equal to the horizontal thrust of the 
 end sections of the arch when the truss is fully and 
 uniformly loaded. Although this may seem self- 
 evident, it may not be amiss to make particular men 
 tion of some of the conditions affecting the case, which 
 may lead to a better understanding of the subject, if it 
 fails to amount to an absolute demonstration. 
 
 The arch and chord obviously act and react upon one 
 another horizontally from end to end, and, as weight 
 removed from any part of the length, diminishes the 
 amount of bearing at both ends, which bearing go 
 verns the stress at the ends, it follows that the ends, at 
 least, of both arch and chord, have their greatest stresses 
 under a full load of the truss. 
 
 It is obvious, also, that no part of arch or chord can 
 have greater stress than the ends, unless it be commu 
 nicated by the tension of diagonals. When the acting 
 diagonals all incline one way, their united horizontal 
 action only equals the difference between the horizon 
 tal thrust of the two end sections of the arch, and the 
 action of chord and arch can no where be greater than 
 at the end from which the acting diagonals incline. 
 
 When acting diagonals incline inward from the ends, 
 the intermediate portions of chord and arch are under 
 less stress than the end portions, and consequently, 
 less than they sustain under a full load of the truss. 
 But when acting diagonals incline outward, toward the 
 
 the other, on a parabolic arch, and stresses mostly calculated numeri 
 cally ; and, from the further fact that in one case, the weight was as 
 sumed to be applied at the arch, and in the other, at the chord ; the 
 former producing more compression, and the latter, more tension upon 
 the uprights. 
 
SEVEN PANEL TRUSSES. 45 
 
 ends of the truss, the intermediate portions of arch and 
 chord are under horizontal stress greater than that of 
 the end portions, by an amount equal to the aggregate 
 horizontal action of all the acting diagonals inclining 
 toward the respective ends. 
 
 Now, as no more than two diagonals inclining toward 
 the end bearing the greatest weight, can be in action 
 at the same time, in a seven panel truss, the question re 
 solves itself into whether two diagonals acting in one 
 direction, can ever exert force enough to over balance 
 the loss of action of the end section, resulting from di 
 minished bearing at the abutment, consequent upon 
 the removal of load, on which removal, the action of 
 diagonals depends ? 
 
 As to that question, the removal of weight from the 
 central portion of the truss, must bring into action in 
 wardly inclined diagonals, while removing weight from 
 one end only, can bring into action no diagonals in 
 clined toward the full loaded end, whence the weight 
 bearing at that end indicates the greatest stress of any 
 part of chord and arch which, of course, is less than 
 under the full load of the truss. 
 
 There remains then, only the case of removal of load 
 from both ends of the truss, which can produce any 
 considerable action upon diagonals inclined outward, 
 so as to give greater stress to the middle, than the end 
 portions of the arch and chord. If the weights at 6 
 and g be removed, the pressure at each abutment is 
 diminished by J of the maximum, or, by 7i0"; and jf;, 
 sustaining only Bw ff at the maximum, and having the 
 same inclination as ij 9 its horizontal action could only 
 balance the effect of %w" removed from ij ; while ek, 
 even if it sustained its greatest weight of 5?0", as it 
 evidently does not, in this case, would only exert the 
 
46 BRIDGE BUILDING. 
 
 same horizontal action as ij would do under 8*0". 
 Hence these two diagonals, under their maximum 
 stresses, which neither suffers, in the present case, 
 would only compensate f of the loss on stress, of arch 
 and chord, due to removal of weight from the truss. 
 
 It may, therefore, he regarded as a matter of extreme 
 probability, if not a rigidly demonstrated fact, that the 
 arch and chord of an arch truss, undergo their maxi 
 mum stress in all parts, under the full uniform load of 
 the truss. 
 
 It is hoped and believed that the foregoing illustra 
 tious of the manner of determining the strains of. the 
 several parts and members of an arch truss of seven 
 panels, will be sufficient to enable the same to be done 
 in the case of trusses of any desired number of panels. 
 
 THE TRAPEZOIDAL TRUSS. 
 
 So designated from the figure of its outline. 
 
 XXXIX. This truss may be constructed with dia 
 gonals and verticals, as in Fig. 12, or without verticals, 
 except at b and #, as seen in Fig. 13. To explain the 
 operation of these trusses, and determine the maximum, 
 stresses of their various parts, we may use the same no 
 tation, generally, as heretofore ; that is, let h represent 
 the horizontal, and v, the vertical reach of the diagonal 
 or oblique members, and D, the length of diagonals. 
 Also, let w represent the greatest movable load for a 
 panel length, supposed to be concentrated at the nodes 
 6, <?, d etc., of the lower chord ; and, let w" be equal 
 to w, divided by the number of panels in the truss (7, 
 in this case), i.e., let w = lw". 
 
 Then, supposing the diagonals (Fig. 12), not includ 
 ing the king braces, ao and ij at the ends ; the verticals 
 
TRAPEZOIDAL TRUSS. 
 
 47 
 
 ob andjgr, and the lower chord, to act by tension ; and 
 the upper chord, or boom, the king braces, and the 
 four intermediate verticals, to act by thrust, or com 
 pression if a weight (w) be applied at 6, it will ob 
 viously cause a downward action equal to w" at i 9 and 
 one equal to 6w" at a. 
 
 FIG. 12. 
 1 23 
 
 ra 
 
 4 
 10 
 I 
 
 5 
 
 15 
 k 
 
 6 
 
 21 
 
 j 
 
 a b c d e f g i 
 
 Now, from what has already been seen, in the discus 
 sion in relation to Fig. 10, the weight acting at i, can 
 only do so by acting successively, or simultaneously, 
 upon 6tt, and each diagonal parallel with bn on the right, 
 by tension, and upon each compression upright and 
 the king brace ?) , by thrust ; causing upon each of 
 these 10 members, a stress equal to w" upon verticals, 
 and equal to w" upon obliques ; D representing the 
 length of obliques, or diagonals. 
 
 A weight (w) at c, in like manner, causes a pressure 
 of 2w" at i, through cm, and other diagonals inclining 
 to the right, on the right hand of c. Also, a pressure 
 of 610" at a. But co being the only member that can 
 transfer weight from c to the left, and, co and bn be 
 ing antagonistic stress upon the one tending to relax 
 the other, the result must be, that both can not act at 
 the same time, from the effects of weight at b and c, 
 and only that one can act, to which the greater weight 
 is applied ; and that, only with the excess of weight 
 acting upon it, over what is acting, or tending to act 
 upon the other. Now, as the load at c, tends to throw 
 
48 BRIDGE BUILDING. 
 
 a weight of 5w" upon co, while the load at b tends to 
 throw It0" on bn, the former tendency must prepon 
 derate c.o must sustain 4*0", while bti is relaxed, and 
 the whole weight at 6, is sustained by the tension of oh. 
 In reality then, cm sustains f of the weight at c, and 
 none of that at b. 
 
 Still, the result is the same, as to pressure at a and 
 i, the former point supporting lw" ,= the whole of the 
 load at 6, plus 4?0" of that at <. , making 11 10", = pres 
 sure due at a, from the weights at 6 and e, while the 
 point i supports oio", all out of the weight ate. Thus, 
 cm, dl etc., sustain the same proportion of the aggre 
 gate weights at 6 and c, as if each weight acted sepa 
 rately, and independently of the other. 
 
 Again, applying a weight (w\ at rf, 8i0" tends to bear 
 at i, and 4?0" at a, through dn and co. But as we have 
 3*0" tending to act on CM, as already seen, this is neu 
 tralized by the tendency to action upon rfw, and only a 
 surplus of 1*0", really acts upon dn in this case, while 
 the 610", = pressure due at , from the weights at 6, c 
 and </, is all made up out of the single weight at d, 
 and the whole of the weights at 6 and c, together with 
 IMJ" from that at </, comes to bear at , giving a pressure 
 of 15?r", at that point ; still the same as if each weight 
 acted independently of the others. And, in general, 
 each diagonal, at all times, sustains the preponderance 
 of weight tending to act upon it, over that which tends 
 to act at the same time upon its antagonist. Hence 
 the greatest weight sustained by any diagonal, is when 
 all the weight tending to act upon it, is upon the truss, 
 and none of the weight tending to produce action upon 
 its antagonist, or counter. 
 
 Thus, when 6 alone is loaded, \ic" is sustained by bn, 
 but when any point on the right of 6 is loaded, there is 
 
TRAPEZOIDAL TRUSS. 49 
 
 tendency to action by co, and the action of bn is de 
 stroyed or diminished. Therefore \w" is the maximum 
 weight sustained by bn. When b and c alone are 
 loaded with the weight (w) at each, cm sustains 810", 
 as already seen, with no tendency to action in dn. 
 But if <-/, or any point on the right of c, be loaded, there 
 is tendency to action in dn^ which must diminish or 
 destroy the action of cm. Hence, cm sustain* its max 
 imum weight (= 3tf/ ), when the points 6 and c alone 
 are under their full load. And, it must be obvious 
 that the maximum weight is sustained by each d&gonai 
 inclining to the right, when the point at its lower end, 
 and all the nodes at the left are fully loaded, and all 
 those at the right are without load. Hence we esta 
 blish the following easy and expeditious practical method 
 of determining the maximum weights and stresses- 
 upon this class of members, in trusses with any number 
 of panels. 
 
 XL. Having made a rough diagram of the truss, as 
 Fig. 12, for instance, place over the nodes o, n, ra, &c., 
 the numbers 1, 2, 3, &c., high enough to admit of a sec 
 ond series under the first, formed by repeating the 1 
 under itself, adding the 1 and 2 together and placing the 
 sum (3), under the 2 in the upper series.. Then add 1, 
 2 and 3, and place the sum (6) under 3, and so on, plac 
 ing under each figure of the upper series, the sum of 
 that figure, and all those at the left, in said upper series. 
 
 Then, it will be seen that each figure in the upper 
 line, prefixed to w", shows the pressure caused at the 
 right hand abutment, by the weight (w) directly under 
 the figure, e. g., the upper figure 3 over d, indicates 
 that %w" is the bearing at i, produced by the weight 
 (w) at d, and so of the other figures in the upper line. 
 7 
 
60 BRIDGE BUILDING. 
 
 In the mean time, the figures in the lower line, show 
 the accumulation of the effects of the different weights 
 
 O 
 
 upon successive diagonals from left to right. Thus, 
 the figure 6 over the point d, shows that dl sustains 
 6w", = pressure due at z, from weights (w) at b, c and 
 d, when those points only are loaded ; in which case, 
 dl sustains its maximum weight, as before seen. 
 
 In like manner, the figures 10 & 15 over eand /, indi 
 cate that 10w" and 15w", are respectively the maxi 
 mum weights sustained by ek and fg, while 2lw" ( = 
 3w), equals the maximum weight sustained by ?J, (by 
 compression, of course), when the whole truss is loaded. 
 
 XLI. Having thus ascertained the greatest weights the 
 several oblique members are liable to sustain (those 
 inclining to the left being obviously exposed to the 
 same stresses as those inclining to the right), we find 
 their maximum stresses by rule 4, [xvi]; i. e., multiply 
 the weight by the length, and divide by the vertical 
 reach of the member. Thus, the maximum compres 
 sion of ?J, equals 3w-, = SM; \//< + r, and the repre- 
 
 v 
 
 eentative of. required material, is ( -f- 3f) M. 
 
 The maximum stress of ek equals 10^"- = 
 Ifw v^ + ^ and its representative for material is 
 
 V 
 
 (1 3^! 4. l|f)jf. Or, the lengths and inclinations being 
 the same, we may take the aggregate maximum weights 
 sustained by tension diagonals, reduced to terms of ?/;, 
 multiply by the square of the common length, divide 
 by v, and change w to M. The ten tension diagonals 
 sustain maximum weights equal to w" multiplied by 
 twice the sum of all the figures in the lower line over 
 
TRAPEZOIDAL TRUSS. 51 
 
 the diagram, except the last, making 70w",=10i0, and 
 require material = (lO- + lOi?) M. 
 
 The tension verticals 06 and jg, sustain the weights (w) 
 acting at b aud# when the truss is fully loaded, which is 
 their maximum stress, and they require material for 
 the two, = 2nn. 
 
 The thrust uprights el and //:, receive and sustain 
 the maximum sustained by dl and ek respectively, 
 which are the measures of their respective stresses of 
 compression, being w" for el, and 10w" for /fc, and 
 the same for dm and eft, making an aggregate weight 
 of 4$w, whence, their representative for material is 
 
 XLII. With regard to stress of the lower chord, the 
 tension of ac equals the horizontal thrust of o, and of 
 course is greatest when ao sustains the greatest weight ; 
 which is manifestly under the full load of the truss. The 
 tension of cd equals the horizontal thrust of ao (through 
 flc), and the horizontal pull of oc ; and must be greatest 
 when the combined action of ao and oc is greatest. Now, 
 although the weight borne by oc is greater by w" when 
 the point b is unloaded, than under the full load, on 
 the other hand, the weight on ao is less by 6w", so that 
 the combined action of the two members, must be 
 greatest when the truss is fully loaded; since no other 
 change can increase the action of either. 
 
 Again, de sustains the horizontal action of ao, oc and 
 nd, when the truss is under a full load ; dl and em being 
 inactive in that case, since the tendency to action is the 
 same in each, whence neither can act. Therefore nd 
 sustains simply the weight (w) at d\ oc sustains the 
 two weights at c and a 1 , = 2t0, while ao sustains the 
 same, with the addition of the weight at 6, making 6w 
 
52 BRIDGE BUILDING. 
 
 sustained by the three members contributing to the 
 tension of de. Now while the maximum weights sus 
 tained by oc and nd, exceed by only 4w/ what they 
 sustain under a full load, neither can be brought under 
 its maximum stress, without removal of load from 6 
 in one case, and from both b and c in the other, thereby 
 diminishing the weight on ao, by 6w" in one case, and 
 by llw" in the other. Hence the stress of de is greatest 
 under a full load of the truss, and as already seen, 
 equals the horizontal action of weight equal to 6w upon 
 oblique members of vertical reach equal to v, and hori 
 zontal reach equal to h. The maximum stress of de, 
 then, equals 6t0-, and that of cd equals the same, less 
 the horizontal pull of dn, due to the weight (20) at d, 
 and is therefore equal to 5tt*-. 
 
 "We have for the lower chord, then, one section, de 
 (with length equal to h), exposed to stress = Qw 
 
 Two sections, cd and cf, with stress = 610 ^ 
 
 Four do., ac and^, = 810- ; 
 
 whence, adding, multiplying by h, and changing w to 
 M, we have to represent required material, 28 M. 
 
 XLIII. It is scarcely necessary to state that the ob 
 lique members ao, and oc, exert at o in the direction 
 from o to n, the same force that they exert in the oppo 
 site direction upon cd. In fact, the thrust of on, and 
 the tension of cd, simply act and react upon one ano 
 ther through the media of ao, oc and ac, whence the 
 compression of on, must be just equal to the tension of 
 cd; and furthermore, the thrust of nm is the indirect 
 counteraction of the tension of de; and, as the two 
 forces are in opposite and parallel directions, they must 
 be equal, being in equilibrio. Also, mlk must sustain 
 
TRAPEZOIDAL TRUSS. 53 
 
 the same compression as ww, throughout, since the 
 diagonals meeting the chord at m and /, are inactive 
 under the fall load of the truss. Of course, kj is liable 
 to the same maximum action as on. 
 
 From what precedes, it cannot fail to be obvious 
 that the maximum action of all parts of the upper chord 
 occurs at the same time with that of the lower chord, 
 namely, under the full load of the truss. We have 
 then, two sections liable to a compression of 5^., and 
 
 three, liable to 6w-; whence the representative of 
 
 required material, is 28 M. We may now sum up 
 the material for the truss, required to support the as 
 sumed movable load through all the changes liable to 
 take place, as follows : 
 
 Material under Compression. 
 Chord, (28^ XM 
 
 King Braces, [XLI] 
 
 Posts, [XLI] 
 
 Total, (34- + 10|v)M 
 
 Under Tension. 
 Chord,[xLii] (28-*- x M 
 
 Diagonals, [XLI] (10 
 
 Verticals, [XLI] 2m 
 
 Total, , (38 + 12i?)M 
 
 Making h v = 1, we have : 
 
 Compression material, 
 
 Tension material, = 50M 
 
 For Arch Truss, Comp. Mat., [xxvn] = 48M 
 
 " " Tension do., = 59n 
 
54 BRIDGE BUILDING. 
 
 XLIY. A trapezoidal truss without verticals (ex 
 cept at one panel width from the ends), is represented 
 in Fig. 13. The members ob and oc, as alsoj*/ and fj, 
 are supposed to be so formed and connected as to act 
 by tension only, and the other diagonals, so as to be 
 capable of acting either by thrust or tension. 
 
 FIG. 13. 
 
 If a weight (?(?), be applied at 6, it will cause a bear 
 ing of \w" at i, and w" at a, the same as in the case 
 of Fig. 12. Now, this weight at 6, might (if bn were 
 removed, and oc were capable of withstanding com 
 pression), be suspended entirely by 06, and supported 
 by ao and oc, in proportion to the bearing produced 
 by it at a and i respectively. But as bn is able to act 
 by tension, and oc unable to act by thrust, the 6w" 
 bearing at a, acts through bo and oa, while the IM/ 
 bearing at i, must first act by tension upon bn ; secondly, 
 by thrust upon nd, since that is the only member meet 
 ing bn at 7?, capable of sustaining weight. Hence, the 
 action of the weight is transferred to d, and through 
 dl to I, thence to/, and so on through fj, andjV, to the 
 abutment at ; acting alternately by tension and 
 thrust, upon six oblique members, producing the 
 same amount of action (= w"-\ upon each. 
 
TRAPEZOIDAL TRUSS. 55 
 
 Another weight (w) at c, must cause pressure at z, 
 equal to 2w" , and at a, equal to 5w". The action there 
 fore, must be divided between cm and oc, in the pro 
 portion of 2 to 5, producing alternately tension and 
 thrust, through the points w, e, k, gj to i ; on the right, 
 and through co and oa, to a, on the left. 
 
 Thus far, the weights have acted upon independent 
 systems of oblique members (except as to king braces), 
 neither weight acting upon any member acted on by 
 the other. But when a weight (w) is imposed at d, it 
 must act upon the same members acted on by the 
 weight at b. The 3w" to be transferred to z, must act 
 by tension upon dl, in concert with the 1/0" of the 
 weight at 6. But the pressure at a, must be increased 
 by 4w/ , which can be transferred from </, only through 
 tension of dn, and dn being previously occupied in 
 carrying \w" from 6, by compression, it follows, since 
 the same member can not be under compression and 
 extension at the same time, that the greater force must 
 preponderate, dn being brought under tension clue to 
 the difference of 4 10" tending to act by tension, and 
 lw" 9 tending to act by thrust, the action of dn, being 
 changed from thrust under Iz0", to tension under 3w". 
 All the weight at 6, then, is sustained by 60, together 
 with Zw" from weight at d, making lOw", which, with 
 bw" from weight at c, makes 15w" = pressure due at , 
 from weights at 6, c and d. 
 
 In the mean time, the weight at d, having obstructed 
 the passage of \w" from b to the right hand abutment, 
 has been obliged to make compensation, by sending 
 4w" of its own gravitating force, nstead of 3w" owed 
 by it to the bearing at i. 
 
 Similar changes of action take place when another 
 weight (w) is applied at e ; which tends to throw 3w" 
 
66 BRIDGE BUILDING. 
 
 by tension upon em, while the weight ate tends to throw 
 2i0" upon it by thrust, as seen above. The result is, 
 that em sustains \w" by tension, and cm, \w" by thrust, 
 while co sustains the whole weight at c, in addition to 
 lw" from e. 
 
 Again, a weight (iv) at /, tends to throw 2w" upon 
 fl, to act by tension ; but as// is already occupied by 
 4w" acting by thrust, / is obliged to depend entirely 
 upon//; at the same time turning back 2w", and re 
 ducing the weight previously on If, by that amount, or, 
 to 2w>". 
 
 In like manner, a weight applied at g, finds gk sus 
 taining Qw" by thrust, whereby it is prevented from 
 pending \w ff (due from it at a), to the left, through 
 tension afgk. Hence, the whole weight at ^ris sustained 
 by jg, and the weight acting on kg is reduced to 610". 
 
 XLV. Thus we see that each diagonal (except oc and 
 fj, excluded by hypothesis), is liable to compression 
 from weights at certain points, and tension from 
 weights at other points ; and, it is manifest that the 
 greater stress of either kind, on each diagonal, is when 
 all the weights are on the truss, which tend to produce 
 upon it one kind of stress, and none of those which 
 tend to produce the opposite stress. 
 
 Hence, if we place the numbers 1, 2, 3, &c., over the 
 diagram, as in case of Fig. 12. [xxxix], it is clear that 
 only alternate weights act upon the same system of 
 diagonals; that only weights under the odd numbers 
 1, 3 and 5 act upon diagonals meeting the lower chord 
 at points under those numbers; and so of the weights 
 under the even numbers 2, 4 and 6. We therefore 
 form a second series of figures under the first, by placing 
 under each odd number, the sum of that number and 
 
TRAPEZOID WITHOUT VERTICALS. 57 
 
 all the preceding odd numbers, and under eacli even 
 number, the sum of that and all preceding even num 
 bers. Then, the number in the second line, is the co 
 efficient ofw f/ , to express the maximum weight acting 
 by tension upon the diagonal inclining to the right, 
 from the point under that number, and by thrust, upon 
 the diagonal meeting the former at the upper chord. 
 
 For instance, the figure 4 in the second line, over d, 
 shows that dl and If, sustains 4i0", the former by ten- 
 gion, and the latter by thrust. This is the weight 
 which must bear at z, in consequence of the weights 
 at 6 and d, the only weights that can produce those 
 specific actions upon those members. On the contrary, 
 this action upon dl and If, is only liable to diminution 
 from weight at /, which tends to throw 2w" upon the 
 left abutment through tension of ft and thrust of dl 9 
 and consequently diminishes the action upon those 
 members, due to weights at b and d. Therefore, 4w" 
 is the greatest weight sustained by dl and If, and 2?0", 
 the weight sustained by them when the points b, d, and 
 /are loaded, whether the other nodes are loaded or 
 not. There is, however, an alternative in this case, 
 which will be noticed hereafter. 
 
 The figure 1 over 6, indicates that bn sustains \w" 
 by tension, and nd the same by thrust, which action is 
 reversed by weights at d and /, which tend to throw 
 6*0" upon these members, namely, 4*0", from d, and 
 2w" from/. Hence, bn is liable to \w" by tension, and 
 610" by thrust, the latter, when d and / are loaded, 
 and b unloaded ; and to 5w f/ (acting by thrust), when 
 all the three points are loaded. 
 
 Then, if we form a third series of numbers under 
 the second, by reversing the order of the second, the 
 one series shows the tension, and the other the thrust 
 8 
 
58 
 
 BRIDGE BUILDING. 
 
 to which a member is liable. But as thrust action is 
 not received by any diagonal directly from the weight 
 producing it, but from a tension diagonal meeting it at 
 the upper chord, we do not learn the thrust of a dia 
 gonal from the figure over it, at either end, but from 
 the figure over the foot of the diagonal by which the 
 compression is communicated. 
 
 Having arranged the diagram as above explained, 
 we form from it a table of greatest weights sustained by 
 the several diagonals, and stresses produced thereby, 
 both of tension and thrust, remembering that tension 
 weights are shown by one series of figures and thrust 
 weights, by the reversed series. 
 
 Diagonals. 
 
 Compression. 
 
 Weights. Stresses. 
 
 Tension. 
 
 Weights. Stresses. 
 
 Under full load. 
 
 Weights. 
 THK. TEN. 
 
 bn and kg, 
 
 Qw" 
 
 j) 
 
 ow/ ~~ 
 
 7) 
 
 Iw" Iw"- 
 
 V 
 
 SM;" 
 
 cm and If, 
 dl and me, 
 
 4 a 
 
 2 " 
 
 4u>"? 
 
 V 
 
 T} 
 7) 
 
 2" 2>"? 
 
 fl 
 
 T-V 
 
 4 " 4w/ - 
 
 
 
 2u?" 
 
 ek and dn, 
 
 1 
 
 y\ 
 
 
 
 6 " 6w"- 
 
 5 " 
 
 fj and co, 
 
 
 
 
 9 " 9w"? 
 
 
 
 9 
 
 13 
 
 22 
 
 Adding and doubling the several weights, we deduce 
 the representatives of material. 
 Under Compression, (3|- -f 3f.r)M 
 
 Under Tension, (6f-** + 6fr)M 
 
 The 2 verticals sustain each I2w", giving 3|i?M 
 
 The king braces ao and ij, sustairl 3w? each, 
 
 requiring material for the two = (6 4- 6i jM 
 
 XLYL The stress of chords is, as in case of Fig. 12, 
 due to action of obliques, and may be fairly assumed 
 
TRAPEZOID WITHOUT VERTICALS. 59 
 
 to be greatest under a full uniform load of the truss. 
 The brace ao has a horizontal thrust = 21V -, = ten 
 sion of ab. The thrust of bn (under the full load), adds 
 bw"- at 6, making 26^"- = tension of be. This is in- 
 
 V V 
 
 creased by 9i0" for tension of oc, and by Zw"~ for 
 thrust of cm, making S7w" for tension ofcd; and, add 
 ing 5w" for tension of dn, and subtracting 2w" for 
 tension of dl in the opposite direction, we have 40z0 
 = tension of de. 
 
 We have then, 1 section sustaining 40M?"-=40w"- 
 2 " " 37 " 74 " 
 
 2 " " 26 " 52 " 
 
 2 " " 21 " 42 " 
 
 Making a total stress=208i0" =29f 10 actingupon sec 
 tions of a common length equal to A, and therefore, 
 requiring material represented by 29f M. 
 
 Upon the upper chord, we have the horizontal action 
 ij andjgf, producing compression equal to 30z0"^ upon 
 
 jk. Add for horizontal action of ek and kg, IQw" 
 making 40w"- =stress of kl. Again, add 4w" for 
 
 horizontal action of If and Id, and we have 44i0 7/ - = 
 J 
 
 thrust of Im. 
 
 Thus, we have for the whofe upper chord, 184v;"^ 
 = aggregate stress upon sections of the common length 
 equal to h. Hence, representative- for material = 
 
60 
 
 BRIDGE BUILDING. 
 
 Aggregate for whole Truss. 
 
 Material under Compression. 
 Chord, (2 
 
 Diagonals, ... (3?- + 3f I?)M 
 End braces,... (6--+6y)M 
 
 Total, 
 
 Under Tension. 
 
 Chord 
 
 Diagonals,... (6f^ + 6?0)ai 
 Verticals, ..... 
 
 Total, 
 
 (36 7 |-f 94My 
 
 Making A = v = 1, Comp. 45.714M. Ten. = 45.714M. 
 
 Grand total, 91.428M. 
 
 "We have here a little over 3 per cent less actiow upon 
 material, than in case of truss Fig. 12, with verticals. 
 The difference is a little less than was shown in my 
 original analysis, that heing based on trusses loaded 
 at the upper, and this, at the lower chord ; the former 
 giving a trifle more action for the truss with verticals, 
 and a trifle less for the other. 
 
 Moreover, the difference was made to show greater 
 still, by assuming that deductions might be made on 
 account of certain diagonals being liable to two kinds 
 of action. For instance, it was supposed that a mem 
 ber formed to sustain a considerable tension stress, 
 might also sustain a small compressive force without 
 additional material (not at the same time, of course), 
 which is undoubtedly the case, on certain occasions ; 
 especially in the use of wooden trusses. This would 
 give still greater apparent advantage to truss 13, with 
 regard to economy of material. 
 
 XL VII. There is, however, another view as to the 
 action of load upon truss Fig. 13, which may modify 
 the results above shown to a small extent. 
 
TRAPEZOID WITHOUT VERTICALS. Gl 
 
 If we strike out the diagonals cm and me, and also 
 dl and (/", all the determinate forces necessary to sustain 
 uniform weights at the nodes of the lower chord, 
 would be exerted by remaining members, although we 
 have assigned to those members, each, the sustaining 
 of weight equal to 2w" under the full load, and twice 
 that weight under certain conditions of partial load ; 
 and it is quite certain that they are necessary to the 
 stability of the truss when partially loaded. But with 
 both halves loaded uniformly, the weight upon each 
 half could be transferred to the nearest abutment, pro 
 ducing equal thrust in both directions upon the central 
 portion of the^ upper, and equal tension in opposite di 
 rections upon the lower chord ; whereas, with one-half 
 loaded, there is no means by which the pressure due 
 at the farther abutment could be transferred past the 
 centre, without oblique members in the centre panel. 
 Still, which mode of action takes place under the uni 
 form load, when the diagonals are in place, is a matter 
 involved in a degree of uncertainty. If the centre dia 
 gonals do not act, under the uniform load, then ek and 
 fj must sustain each 7w", instead of 6z0" for the former, 
 and 9w" for the latter, as above estimated. Also, kg 
 would sustain lw" by thrust, and different results 
 would be produced as to stresses of various parts of 
 upper and lower chords. 
 
 The maximum stress for ek andefo, and for nb kg, would 
 be 7*0"^ instead of 610 -, as found above, and would 
 
 V V 
 
 occur under the full, instead of the partial load. The 
 tension of gj arid 06, also, would be increased to 14w/ . 
 The weight sustained by fj, would be only Iw" under 
 the full load, though liable to the same maximum 
 weight of W, under a partial load. 
 
62 BRIDGE BUILDING. 
 
 For the lower chord, we should have the same co 
 efficient, (21) ofw"- to express the tension of ab and ig, 
 28 for be, 35 (a decrease), for cd, and 42 for de. 
 
 For upper chord, the co-efficients of w"- would be 
 28 for on and kj, and 42 for the three middle sections; 
 no action being imparted by diagonals at m and I. 
 
 XLVIII. This uncertainty of action has no place in 
 trusses of an even number of panels, as in such cases, 
 no transfer of the action of weight can be supposed to 
 take place past the centre, under a uniform load, with 
 out involving the absurdity of supposing the same 
 member to carry weight by tension aiid compression 
 at the same time; except, however, that in case of 
 diagonals crossing two panels, or having a horizontal 
 reach equal to twice the space between nodes of the 
 chords, there will be diagonals filling the same condi 
 tion of crossing in the centre of the truss, both vertically 
 and longitudinally, as in Fig. 13. 
 
 We may obviate mostly, any mischief liable to result 
 in cases of the kind under consideration, by estimating 
 the stresses upon the several parts under both hypo 
 theses, and taking for each member the highest estimate, 
 which will mostly meet all contingencies. Estimating 
 action upon truss 13 in this manner, we obtain the 
 following representative expressions for material : 
 
 Compression. 
 
 Chord, 26^- XM 
 
 Diagonals, (4-- -f 4vM 
 
 End braces,.... 6 
 
 v 
 
 i\h 
 
 Total, (86^- + 10w)M 
 
 Tension. 
 
 Chord, SO^X M 
 
 Diagonals,... (6= 
 Verticals, 4i/M 
 
 Total, (37 10|v)M 
 
TRAPEZOIDAL TRUSS. DECUSSATION. 63 
 
 Making h = v = 1. These expressions give, Compres 
 sion material = 46.855M + Tension do, 47.714M = total 
 94,57iM. 
 
 This shows an aggregate amount of compression and 
 tension action, identical with that of truss Fig. 12, 
 [XLIII.] 
 
 DECUSSATION AND NON-DECUSSATION. 
 
 XLIX. The elasticity of materials affords a means 
 of answering the question as to decussation of forces 
 through diagonals crossing in the centre of the truss, 
 vertically and longitudinally (as in Fig. 13), in specific 
 cases. But the results will vary in trusses of different 
 numbers of panels, and different inclinations of diago 
 nals. 
 
 Suppose the truss Fig. 13 to be so proportioned that 
 the maximum stresses of the several parts and members, 
 will produce change of length equal to E, multiplied 
 by the lengths of parts respectively ; the vertical ob, 
 = i , being the unit of length. Then, the truss being 
 uniformly and fully loaded, and the chords being under 
 their maximum stress, the upper chord is contracted, 
 and the lower one extended at a uniform degree ; and, 
 if the diagonals be unchanged in length, their vertical 
 and horizontal reaches have not been changed by the 
 change in length of chords. Hence, the distance be 
 tween chords is not altered by change in their length. 
 But the diagonals being under stress, by which some 
 are extended and others contracted, according to the 
 stress they are under, as compared with their maximum 
 stresses respectively, the nodes of the chords are al 
 lowed to settle to positions below what they are brought 
 to by the mere change in lengths of chords. 
 
64 BRIDGE BUILDING. 
 
 Hence, the panels are (generally) thrown into more 
 or less obliquity of form, in consequence of inequality 
 in length of diagonals in the same panel. But the 
 centre panel can not assume obliquity, because any 
 tendency of forces to change the length of one dia 
 gonal, is attended by a like tendency of equal forces to 
 produce exactly the same change in the other ; so that 
 the vertical reaches of both must suffer the same change, 
 if any, and both must be under tension or compression, 
 according as the acting forces tend to bring the chords 
 at the centre, nigher together or farther apart. 
 
 Now, the forces produced by the load being all con 
 centrated at the points o and j (Fig. 13), the point d is 
 depressed with respect to 0, by the extension of ob and 
 ?i6?, and by the compression of bn. Hence, assuming 
 decussation to have place, giving tension to the diagonals 
 dl and me, equal to what is due to a weight of 1w", ob is 
 under maximum tension and gives depression equal to E, 
 to the point 6, bn and nd are under maximum stress, 
 and give depression, each equal to f E XD 2 * = 
 (1.666/i 2 4- 1.666) E, for the two (D representing length 
 of diagonals, =v/F+I). Then, adding IE for effect 
 of ob, we obtain (1.666A 2 + 2.666) E, = depression of 
 point d. 
 
 The point m is depressed by extension of oc under a 
 maximum stress, giving an amount equal to D 2 E = 
 (A 2 -f 1)E. Also, by compression of cm under one-half 
 maximum stress, to the extent of (JA 2 -f J)E. Hence, 
 depression of point m = (1 J/i 2 + 1 J) E. 
 
 This shows the point d to be depressed more than 
 w, by (1.666 A 2 4- 2.666) E (1.5/t 2 + 1.5)E -(0.166A 2 + 
 
 *Let the diagonals bd and Bd, of two rectangular panels ac and Ac, 
 Fig. 14 (c and d, being fixed points), be exposed to tension in propor 
 tion to their respective cross-sections, receiving each thereby, extension 
 
TRAPEZOIDAL TRUSS. DECUSSATION. 
 
 65 
 
 1.166) E, and the spaces md and le to be increased to 
 that extent; of course producing tension upon c/land me. 
 
 Now, by hypothesis, these diagonals are under the 
 weight of 2w" y giving half maximum stress, and requir 
 ing an increase of vertical reach, equal to (%h 2 -f J) E. 
 If then, we give such a value to A, as will make the 
 last co-efficient of E equal to the one above, it will 
 show that the chords have receded just enough to give 
 the assumed tension to dl and me, and the decussation 
 is a demonstrated fact. To find the value of A, pro- 
 ducingthis result, make,.5A 2 -f .5 = .166A 2 + l,166,and 
 we deduce ,333A 2 =* .666 ; whence h = v"2. 
 
 But this requires too great an inclination of diagonals, 
 and a less value of A, gives a space from d to m too 
 great for the supposed tension of dl and me. Making 
 h = 1 = v, we have increase of distance from d to m 
 1.333E, requiring a weight of 2.666*0", to stretch dl 
 down to the point d. But as no weight or stress can 
 be added to the 2io" assigned to dl and me, without af- 
 
 equal to b e and B E, respectively. This will cause the points b and 
 B to drop to b and B , in ab and AB produced. Join b e and BE. 
 
 Then, the infinitesimal triangles bb e and 
 BB E, right-angled at e and E, are essentially ^ I( 3- 14. 
 
 similar, respectively to the triangles db a 
 dBA. Hence, the following relations : 
 
 (1). bb : b e : : bd : ab, and 
 
 (2). BB : B E : : Bd : ab. 
 whence, bb X ab = b e X bd, and 
 
 From these two equations we derive . 
 
 (3). bb X ab : BB X ab : : b e X bd : 
 B E X Bd. 
 
 But, by the law of elasticity 
 
 (4). b e : B E : : bd : Bd ; whence, 
 
 (5). b e X bd : B E X Bd : : bd 2 : Bd 2 . 
 
 Hence dividing the first ratio of proportion (3) by ab, and substitu 
 ting for the last ratio of (3), its equivalent found in (5), we have 
 
 (). bb : BB : : bd* : Bd 2 . 
 
 Hence the depression due to the extension of a diagonal retainincr 
 the same vertical reach, is as the stress (per square inch), sustained*, 
 multiplied by the square of the length of diagonal. 
 
 9 
 
66 BRIDGE BUILDING. 
 
 fecting all the 5 members contributing to the depression 
 of the points d and m, and in all cases, so as to dimin 
 ish the elongation of distance between d and m, it is 
 reasonable to conclude that by assigning some J, or 
 thereabouts, of the extra weight of .666?0" required on 
 dl alone, it would, by affecting the whole 5 members, 
 be sufficient to correct the error. Let us, then, assume 
 that dl and me sustain 2.15i0", instead of 2*0" as by pre 
 vious supposition. This change requires reduction of 
 weight upon dn, nb and bo, from 5*0" to 4.85*0" for the 
 two former, and from 12*0" to 11.85*#" for bo. Also 
 an increase of weight on we and co, to 2.1 Sic" on me, 
 
 and to 9.15i0" on co. Then bo sustains of the 
 maximum, and gives depression -~-E = .9875E 
 
 bn and nd, sustaining -~ of the maximum, give de 
 pression for the two, equal to 3.233E, making 4.2205E 
 = whole depression of point d. 
 With regard to the point m, we have the maximum 
 
 2 15 
 stress on oc, giving depression equal to 2E, and V- O f 
 
 the maximum on me, giving depression = 1.0T5E, 
 making a total of 3.075E for the point m. Hence, the 
 elongation of the space dm, equals (4.2205 3.075) E, 
 = 1.145E, whereas 2.15*0" upon dl, increases its vertical 
 reach by only 1.075E. This shows that dl sustains still 
 a little more than 2.1 5*0". On the other hand if we 
 assume a weight of 2.2*0" on dl, we obtain the opposite 
 result, showing that dl sustains less than 2.2*0", and 
 hence the actual amount must be between 2.15*0" and 
 
 We conclude then, that dl and me are mot inactive 
 under the full load of the truss, but on the contrary, 
 they sustain, in this case, even more than the decussa- 
 tion theory assigns to them. We learn, moreover, that 
 
TRAPEZOIDAL TRUSS. DECUSSATION. 67 
 
 the question is affected by the horizontal reach of the 
 diagonal, or the value of h. And, since in this case, 
 the point d being depressed by action upon 3 members, 
 and the point m by action upon only 2, we have an elon 
 gation of space between dandm requiring more than the 
 theoretical stress upon centre diagonals, it is natural to 
 conclude, that, in case of a greater number of panels, 
 nine, for instance, where 4 members contribute to the 
 depression of the upper, and only three to that of the lower 
 chord at the centre, the increase of distance between 
 chords, would be less than that required to give the theo 
 retical stress upon diagonals in the centre panel ; and, 
 such is found to be the case. In a nine panel truss on the 
 plan of Fig. 13, the increase of distance between chords, 
 due to the stresses assigned by the decussation theory, is 
 only about one-third of what would be required to 
 give the centre diagonals the stress assigned them. 
 Hence in this case there is less decussation than the 
 theory requires ; and, one or two trials, by ^assigning 
 different weights as sustained by centre diagonals, in 
 the manner pointed out above, would enable a near 
 approxination to the actual amount of decussation to 
 be arrived at, in the case of the nine panel truss, or 
 any other. 
 
 Let us take one more view of this matter, by assum 
 ing no action by centre diagonals, under the full load. 
 Then cm (Fig. 13), is also out of action, and oc alone, 
 under J maximum stress, contributes to the depression 
 of point m, giving depression equal to 2x^E, = 1.55E, 
 (assuming h = v). 
 
 The point d is depressed by the maximum change of 
 two obliques, and one vertical, giving depression = 5E. 
 Therefore the distance md, is increased by (5 1.55) E, 
 =* 3.45E. Hence dl and me must be elongated by 1.725 
 
68 BRIDGE BUILDING. 
 
 times the amount due to the maximum stress, in order 
 to escape action. Suppose the member to be of wrought 
 iron, proportioned to a maximum stress of 10,000ft) to 
 the square inch. Then, the extension due to 17250ft) 
 to the inch, is about seVVoVVo x l en gth "* .00069 X 
 length, and if length 15 feet, tne extension is equal 
 to .00069x15, = .01035 ft. or, say J inch. 
 
 Hence, in a 7 panel truss, as represented in Fig. 13, 
 with h = v 9 if the diagonals in the middle panel be 
 slack, by J inch in 15 feet of length, no decussation 
 will take place, and the centre diagonals will be inactive, 
 under the full load of the truss. If those members have 
 less than that degree of slackness, they will be in action 
 in such circumstances. 
 
 It would be a very badly adjusted piece of work in 
 which such a degree of slackness should occur, and we 
 may fairly conclude, that the centre diagonals, in this 
 class of trusses, are never entirely inactive. 
 
 But the quantity E, is so very small, with any kind 
 of material, and with any co-efficient that may affect 
 it, in practice, that a slight inaccuracy of adjust 
 ment, may so change the practical form the theoretical 
 results deduced by calculation, as to decussation, as to 
 render the latter of no great practical reliability. 
 Hence, after all, perhaps the most unexceptionable 
 course, in this regard is, to follow the rule given before 
 [XLVIII], of estimating stresses on both hypotheses, 
 and taking the highest estimate for each part. 
 
 Now, perhaps, this subject has been discussed at 
 greater length than its practical importance demanded, 
 considering the small percentage of error liable to oc 
 cur in any case ; but with regard to this, as well as to 
 other matters, it is well to know, what may be known 
 
TRAPEZOIDAL TRUSS. WARREN GIRDER. 69 
 
 without inconvenient or unreasonable effort at investi 
 gation. 
 
 THE WARREN GIRDER. 
 
 L. There is another form of truss operating upon 
 the same principle as truss Fig. 13, in which one set 
 of oblique members is left out, so that only one diago 
 nal remains to each panel. The diagonals meet and 
 connect with one another and with the chords, forming 
 alternate nodes at the upper and lower chords. This 
 truss, represented in Fig. 15, requires an even number 
 of panels that the two half-trusses may be symmetrical. 
 
 This is an extension of truss Fig. 5, with tension 
 verticals for suspending floor beams from the upper 
 nodes, when the travel-way is along the lower chord, 
 and thrust verticals ascending from the lower nodes, 
 in the case of what are technically called deck-bridges.* 
 
 We compute the stresses of the members of this 
 truss, by placing the figures 1, 2, 3, etc., over the 
 diagram as in preceding cases, #nd from a second line 
 or series of figures, by adding all those in the first 
 series, as in case of truss Fig. 12, because each weight 
 tends to act upon every diagonal. Each figure in the 
 second line, fs the co-efficient of w" in the expression 
 of the greatest weight transferred to the right hand 
 abutment, through the diagonal crossing the panel 
 next on the right hand of the figure ; and the action is 
 tension or thrust, according as the diagonal ascends or 
 descends toward the right. Thus, the Fig. 6 over o, 
 indicates that 6w" is the greatest weight acting by thrust 
 upon oe, while 10 over the point e, indicates 10w as the 
 maximum weight acting by tension upon em. These 
 
 *The author built several small bridges upon this plan, to carry a 
 rail road track over common highways, in 1849 or 1850, believed to 
 have been the first application of this form of truss. 
 
70 
 
 BRIDGE BUILDING. 
 
 figures only indicate weight transferred from left to 
 right, and it is evident that the same weights in a re 
 versed order, are transferred from right to left, through 
 the same diagonals. Hence, a third series of figures 
 under the second, composed of the same figures in a 
 reversed o*rder, shows the weights carried by the seve 
 ral diagonals from right to left. The figures in the 
 third line, show the weights acting on diagonals next 
 on the left of respective figures. It will be seen also, 
 that the figures under odd numbers of the upper line, 
 
 FIG. 15. 
 
 c d e f g i j 
 
 indicate weights acting by thrust, and those under even 
 numbers, by tension. The figures 6 and 15 over o, in 
 dicate 6w" acting on oe, and 15?fl", on oc, both by 
 thrust. Again 3 and 21 under 2, indicate 3w" acting 
 on co, and 2lw" upon cq, both by tension? The figure 
 28 at the right and left, under 1 and 7, indicate 2Sw" 
 acting by thrust upon aq and jk. 
 
 Now if we add all the figures in the second and third 
 lines standing under odd numbers of the upper line, 
 we obtain the co-efficient of w" for the aggregate maxi 
 mum weights acting by thrust upon oblique members, 
 while the sum of all the figures in like manner, under 
 even numbers, forms the co-efficient of w" for the ag 
 gregate maximum weights acting by tension upon ob 
 liques. The former gives 100w",=12.5w for compres 
 sion, and the latter, 68u?",=8.5i0, for tension. Hence, 
 
TRAPEZOIDAL TRUSS. WARREN GIRDER. 71 
 
 making A=r=l, we have as expressions for amount of 
 thrust and tension action upon material in oblique mem 
 bers, 25M for thrust and 17M for tension. 
 
 One half of the lower chord obviously sustains a 
 stress of 28 w", equal to horizontal thrust of the end 
 braces, and the other half, 60w",= horizontal action of 
 aq, qc and co (under full uniform load), at one end, and 
 of corresponding diagonals at the other end, giving re 
 quired material for chord equal to 44M. 
 
 The compression of the upper chord, equals the hori 
 zontal thrust and pull of aq and qe,= 48w", for f of its 
 length, with the addition of ~L2w" for horizontal thrust 
 of co, and 4w" for pull of oe, making Qw" for the two 
 middle panels. Hence expression for material is 40M. 
 The verticals obviously require tension material equal 
 to 4M, and the aggregate for the truss, is, 
 
 For Compression. For Tension. 
 
 Chord, 40M Chord, 44M 
 
 Obliques, 25M Diagonals, 17tf 
 
 Verticals, 4M 
 
 Total, 65M Total, 65M 
 
 A corresponding truss with 2 diagonals in each 
 panel, on the plan of Fig. 13, shows the same expres 
 sions for materials, or amount of action of both kinds, 
 item for item, and any advantage possessed by either 
 plan, must depend essentially upon the more advan 
 tageous action of compression material. 
 
 Truss Fig. 15, has fewer intermediate thrust diagonals, 
 and greater concentration of weight upon them ; which 
 is favorable; while in the other, the diagonals crossing 
 one another, are enabled to afford mutual support 
 laterally, in certain modes of construction. 
 
72 BRIDGE BUILDING. 
 
 The upper chord in Fig. 15, acts at a decided disad 
 vantage, in having no vertical support for a length of 
 2 panel widths, unless it be especially provided at ad 
 ditional expense. As a deck bridge, with struts, or 
 posts atp, n, I, and lateral tying and bracing, the truss 
 may answer an excellent purpose. But even in that 
 case, it can scarcely be considered as preferable to the 
 truss with a double system of diagonals. 
 
 The Ohio river bridge at Louisville, Ky., has its long 
 spans (about 400 ft), constructed upon the plan of Fig. 
 15, and no plan which we have considered, shows a 
 less amount of action upon material. These are believed 
 to be the longest spans of Truss Bridging in the country. 
 
 An eight-panel truss upon the plan of Fig. 12, gives 
 the following expressions for amount of material. 
 
 Compression. Tension. 
 
 Chord, 43M Chord, 4lM 
 
 Ends, .14M Diagonals, 28M 
 
 Verticals, TM Verticals, 2M 
 
 64M 7lM 
 
 This indicates a difference of nearly 4 per cent, as 
 to amount of action upon material, in favor of the truss 
 without vertical members, generally speaking; i. e. in 
 which there is no regular transfer of action from one to 
 another, between diagonal and vertical members, as in 
 truss Fig. 12. 
 
 This advantage is made still larger in certain modes 
 of construction, by the circumstance that the same 
 members, in trusses 13 and 15, may sometimes act by 
 tension and thrust, on diiferent occasions, without any 
 more material than would be required to act in one 
 direction only. 
 
FINCK TRUSS. 73 
 
 LI. It may be proper in this place, to refer to still 
 another form of trussing, which has enjoyed a degree 
 of popular favor, and which differs somewhat from 
 any we have hitherto considered. The plan is seen in 
 outline, in Fig. 16. Each weight is sustained primarily 
 by a pair of equally inclined tension members, and 
 thereby transferred either to the king posts standing 
 upon the abutments, or, to posts sustained by other 
 pairs of equally inclined suspension rods of greater 
 horizontal reach; which in turn, transfer a part to 
 king posts, and another part to a post sustained by 
 obliques of still greater reach, until finally, the whole 
 remaining weight is brought to bear upon the abut 
 ments by a single pair of obliques, reaching from the 
 centre to each abutment. 
 
 FIG. 16. 
 THE FINCK TRUSS. 
 
 In Fig. 16, are represented three different lengths of 
 obliques, in number, inversely as the respective hori 
 zontal reaches. The first set contains 8 pieces reaching 
 horizontally across one panel, and sustaining each \w. 
 The next longer set, of four pieces, reach across two 
 panels, and sustain eachlw;; one-half applied directly, 
 and the other, through posts and short diagonals. The 
 third and longest set, contains but two pieces, reach 
 across four panels, and sustain together w\ of which Iw 
 is applied directly, Iw through two short diagonals? 
 and 2w through two intermediates. 
 
 Now, as each set sustains the same aggregate 
 weight, namely 4w 9 the material in each set, will 
 10 
 
74 BRIDGE BUILDING. 
 
 be represented by this weight multiplied by the 
 square of the lengths respectively, and divided by v : 
 and, making k = v = 1, the squares of respective 
 lengths are 2, 5 and 17, which added together and mul 
 tiplied by 4w?, and w changed to M, gives 96M=amount 
 of material in tension obliques, the only tension mem 
 bers in the truss. 
 
 The upper chord sustains compression equal to the 
 horizontal pull of one oblique member of each class, 
 obviously equal to lOJw, with length = 8. Hence, re 
 quired material equals 84M. End posts sustain to 
 gether, *7w, centre post 810, and the two at the quarters, 
 one w each, in all 12ic, and the representative for mate 
 rial is 12M ; whence the total for thrust material is 96M, 
 making a grand total of thrust and tension material= 
 192M. 
 
 The 8 panels trapezoid with verticals, requires,... 135M 
 Do " " without verticals, 130M 
 
 This comparison exhibits an amount of action in 
 case of the first (Fig. 16), which, considering that it 
 possesses no apparent advantage as to the efficient 
 working of compression material, would seem to ex 
 clude it, practically, from the list of available plans of 
 construction. 
 
 DISTINCTIVE CHARACTERISTICS OF THE ARCH. 
 
 LIT. We have seen that all heavy bodies near the 
 earth s surface (except when falling by gravity or 
 ascending by previous impulse), exert a pressure upon 
 the earth equal to their respective weights. We have 
 also seen that the object of a bridge, in general, is, to 
 sustain bodies over void spaces, by transferring the 
 pressure exerted by them upon the earth, from the 
 
THE ARCH TRUSS. 75 
 
 points immediately beneath them, to points at greater 
 or less horizontal distances therefrom. 
 
 We have, moreover, seen that this horizontal trans 
 fer of pressure can only be effected by oblique forces 
 (neither exactly horizontal nor exactly vertical), and 
 have discussed and compared, in a general way, various 
 combinations of members, capable of effecting this 
 horizontal transfer of pressure. 
 
 But, without going into unnecessary recapitulation, 
 we find two or three styles of trussing, possessing more 
 or less distinctive features, which promise decidedly 
 more economical and satisfactory results than any 
 others ; and, to make the properties and principles of 
 action of the best and most promising plans as tho 
 roughly understood as may be within the proposed limits 
 of this work, will form a prominent object in the discus 
 sions of succeeding pages. 
 
 The distinctive feature of the arch, as a sustaining 
 structure, consists in the fact that all the oblique action 
 required to sustain a uniformly distributed load, is ex 
 erted by a single member of constantly varying ob 
 liquity from centre to ends ; each section sustaining 
 all the weight between itself and the centre, or crown 
 of the arch, and none of the weight from the section 
 to the end ; so that the weight sustained at any point, 
 is as the horizontal distance of that point from the 
 centre. Consequently (the arch being supposed in 
 equilibrio under a uniform horizontal load), the hori 
 zontal thrust at all points must be the same, and the 
 inclination of the tangent at any point should be such 
 that the square of the sine, divided by the cosine of in 
 clination (from the vertical), may give a constant quo 
 tient. For, regarding each indefinitely short section 
 of the arch as a brace coinciding with the tangent at 
 
76 BRIDGE BUILDING. 
 
 / 
 the point of contact, its horizontal thrust equals the 
 
 weight sustained, multiplied by the horizontal, and di 
 vided by the vertical reach of the brace. But the 
 horizontal and vertical reaches are respectively as the 
 sine and cosine of the angle made by the tangent with 
 the vertical ; that is, as ab and bd, Fig. 17, while the 
 
 weight is also as the sine 6, 
 FIG. 17. of the angle adb. Hence, the 
 
 weight by the horizontal 
 reach, is as ab 2 , or as the square 
 of the sine of adb ; and the 
 constant horizontal thrust of 
 \ the arch at all points, is as 
 
 afc a a& 2 
 
 M* r > ^ 
 Now this condition is answered by the parabola, in 
 
 which bc = cd = -J bd, and |~ = J constant C, whence 
 ab 2 = cb x constant 2(7, which is the equation of the 
 parabola. 
 
 This quality of the arch truss, allowing nearly all of 
 the compressive action to be concentrated upon almost 
 the least possible length, and consequently, enabling 
 the thrust material to work at better advantage than 
 in plans where this action is more distributed, and acts 
 upon a greater number and length of thrust members, 
 enables it to maintain a more successful competition 
 with other plans than we might be led to expect, in 
 view of the greater amount of action upon materials 
 in the arch truss, than what is shown in trusses with 
 parallel chords. Hence, we should not too hastily 
 come to a conclusion unfavorable to the arch truss, on 
 account of the apparent disadvantage it labors under, 
 as to amount of action upon material. These apparent 
 disadvantages are frequently overbalanced by advan- 
 
WEIGHT OF STRUCTURE. 77 
 
 tages of a practical character, which can not readily be 
 reduced to measurement and calculation. 
 
 The preceding general comparisons are tobe regarded 
 only as approximations, and should not be taken as 
 conclusive evidence of the superiority or otherwise, of 
 any plan, except in case of very considerable difference 
 in amount of action, with little or no probable advan 
 tage in regard to efficient action of material. 
 
 EFFECTS OF WEIGHT OF STRUCTURE. 
 
 LIII. In preceding analyses, and estimates of 
 stresses upon the various members in bridge trusses, 
 regard has only been had to the effects of movable load, 
 which may be placed upon, or removed from the struct 
 ure, producing more or less varying strains upon its 
 several parts. 
 
 But the materials composing the structure, evidently 
 act in a similar manner with the movable load, in pro 
 ducing stress upon its members ; the only difference 
 being, that the weight of structure is constant, always 
 exerting or tending to exert the same influence upon 
 the members, instead of a varying action, such as that 
 produced by the movable load. In order, therefore, to 
 know the absolute stress to which any member is liable, 
 and thereby to be able to give it the required strength 
 and proportions, we have to add the stresses due to 
 constant and occasional loads together. 
 
 The weight of structure evidently acts upon the 
 truss in the same manner as if it were concentrated at 
 the nodes along the upper and lower chords, and of 
 the arch, in case of the arch truss. And, since much 
 the larger proportion of it acts at the points where the 
 
78 BRIDGE BUILDING. 
 
 movable load is applied, if we regard the whole as 
 acting at those points, the results obtained as to stresses 
 produced by it, will be sufficiently accurate for ordi 
 nary practice. Still, more closely approximating results 
 may be obtained by assigning to both upper and lower 
 nodes, their appropriate shares cf weight sustained, as 
 may easily be done when deemed expedient. 
 
 If we divide the whole weight of superstructure sup 
 ported by a single truss, by the number of panels, the 
 quotient, which we may represent by w/, will show the 
 weight to be assumed for each supporting point, on 
 account of structure ; and the stresses produced by such 
 weights, added to the maximum stresses of the several 
 members, due to the movable load, will represent the 
 true absolute stresses the respective members are liable 
 to bear. 
 
 Now, as far as relates to parts suffering their maxi 
 mum stresses under the full load, such as chords, 
 arches, king braces, and verticals in the arch truss, as 
 to their tension strain, we have only to substitute TV, 
 (=w;-f w f ), in place of w, in expressions obtained for 
 stresses due to movable load. In other cases, w and 
 w r will have each its peculiar and appropriate co-effi 
 cient. 
 
 The diagonals of the arch truss, are obviously not 
 affected by weight of structure, as they are not so 
 under full and uniform movable load. Moreover, the 
 weight of structure acts in constant opposition to the 
 compressive action of movable load upon verticals. 
 Hence, in truss Fig. 11, where we find the varying 
 movable load gives a maximum compression upon the 
 longest, equal to %w", and upon the next shorter, equal 
 to 2w/ , the weight of structure diminishes those quan 
 tities to 3w" w , and typ" w f respectively. Or, if we 
 
WEIGHT OF STRUCTURE. 
 
 79 
 
 would be more exact, we may add in both cases, the 
 weight of a segment of the arch, which has no tendency 
 to produce tension upon the verticals ; or we may sub 
 tract only f or of w ; thus, 3w/ fz//, and 2?tf" fw , 
 may be taken to represent the compressive action upon 
 the verticals in Fig. 11. 
 
 LIY. In the case of truss Fig. 12, the only diagonals 
 acting under uniform load, are oc 9 fj, nd and ek\ the 
 two latter sustaining, of weight of structure, Ii0 , and 
 the two former, 2i0 . And, the maximum movable 
 weight borne by those members, being [XL] IQw" and 
 15i0", the absolute maximum will be 10z0"+z0 for nd 
 and ek, and I5w"+2w f for oc andjf) . 
 
 Now, if we place the figure 1 under d and e, (Fig. 12 
 A), and the figure 2 under c and/, and so on, in case of 
 a greater number of panels, to the foot of the last diagonal 
 each way, inclining outward from the lower nodes, these 
 figures are obviously, the co-efficients of w to express 
 the weights contributed by the material of the stru - 
 ture, to the stresses of diagonals extending upward and 
 outward from the points to which the figures respect 
 ively refer. 
 
 FIG. 12 A. 
 
 1 2 
 
 1 3 
 
 o n 
 
 8 
 6 
 
 ra 
 
 4 
 
 10 
 
 I 
 
 5 
 15 
 
 k 
 
 6 
 21 
 
 j 
 
 f 
 
 Again, we have seen [XL], that a certain condition 
 of the movable load, tends to throw \w" upon bn, and 
 another condition of such load, tends to throw &w" upon 
 
80 BRIDGE BUILDING. 
 
 cm. But, since, as we now see, the weight of structure 
 tends to throw a constant weight of 2w up6n oc, which 
 is antagonistic to bn, the actual maximum weight upon 
 6n, is lw" 2w/, which will always be a negative quan 
 tity, in practice ; whence bn must always be inactive, 
 and may be dispensed with. 
 
 The maximum weight upon cm, as modified by 
 weight of structure, is in like manner reduced to 3w" 
 w f , which will in practice, be either negative, or of 
 quite small amount. Hence, we have the following 
 rule : For the absolute maximum stresses of diagonals 
 (in case of parallel-chord trusses with verticals), we 
 add the effects of weight of structure to the maximum 
 effects due to variable load, where both fall upon the 
 same, and subtract the former, in cases where the two 
 forces fall upon counter, or antagonistic diagonals. 
 
 In case of parallel-chord trusses without verticals, we 
 add the effects of constant and variable load upon each 
 diagonal, when alike, i. e., when both tensile or both 
 compressive, and subtract the former when the effects 
 are alike. 
 
 DOUBLE CANCELLATED TRUSSES. 
 
 LY. The use of chords in a truss being to sustain 
 the horizontal action (whether of thrust or tension) of 
 the oblique members, it follows that the aggregate 
 stress of chords, is equal to the aggregate horizontal 
 action of all the diagonals acting in either direction e 
 And, the horizontal action being obviously as the 
 number and horizontal reach directly, and as the ver 
 tical reach inversely ; also, the length of truss being as 
 
DOUBLE CANCELATED TRUSSES. 81 
 
 the number and horizontal reach of diagonals, while 
 the vertical reach is as the depth of truss, it follows 
 that the stress of chords is directly as the length and 
 inversely as the depth of truss, other conditions being 
 the same. 
 
 Hence, if the depth of truss be so reduced as to make 
 the ratio of length to depth indefinitely large, the stress 
 and required material of chords, become indefinitely 
 large. On the contrary, if the depth be indefinitely 
 great, al!hough the stress of chords be ever so small 
 the length and required material for diagonals and ver 
 ticals must be indefinitely large. It is manifest, then,, 
 that between these two extremes there is a practical, 
 optimum, a certain ratio of length to depth of truss y 
 which , though it may vary somew r hat with circum 
 stances, will give the best possible results as to economy 
 of material in the trass. This matter will be taken 
 into consideration hereafter, and is referred to here, 
 to show the expediency of generally increasing the 
 depth, with increase of lengths in the truss. 
 
 Now, in trusses of considerable length, and, conse 
 quently, depth, it becomes expedient, in order to avoid 
 too great a width of panel (horizontally), or an inclina 
 tion of diagonals too steep for economy of material in 
 those members, to extend them horizontally across two 
 or more panels, or spaces between consecutive nodes 
 of the chords. In such cases, the truss may be called 
 double or treble cancelated, according as the diagonals 
 cross two or three panels. i 
 
 LVL To estimate the stresses of the members of 
 double cancelated trusses with vertical members, a 
 slight modification of the process already described, 
 [XL, &c.], is required, as follows : 
 11 
 
82 BRIDGE BUILDING. 
 
 Having placed the numbers 1, 2, 3, &c., over the 
 nodes of the upper chord, as seen in Fig. 18, place 
 under each odd number, the sum of all the odd num 
 bers iu the first series, up to and including the one 
 under which the sum is placed ; and the same with 
 respect to the even numbers. Then, the second series 
 of figures may be used in precisely the same manner 
 as that explained with reference to Fig. 12, to deter 
 mine the weight sustained by, and the maximum stress 
 produced upon, each diagonal and vertical, by equal 
 weights upon all or any of the nodes of either chord. 
 
 For example; supposing the truss to have tension 
 diagonals and thrust verticals; take the diagonal hav- 
 its lower end under 5 (upper series), and its upper end 
 under 7. This diagonal may be represented by 5/7, 
 while 5\7 may indicate its antagonist, and so of other 
 diagonals. Then, as we see 9 (the sum of 1 + 3 + 5), in 
 the second series, over the lower end of 5/7, and, as the 
 diagram represents a truss of 16 panels, we know that 
 the diagonal in question is liable to a maximum 
 weight of T V#, = 9w". This amount is to be dimin 
 ished, of course, by the weight due from weight of 
 structure to the counter diagonal. 
 
 Again, the diagonal 9/11 sustains as amaximnm from 
 variable load, 25w"; which will require to be increased 
 on account of weight of structure, since the latter, in 
 this case, acts upon the main, and not upon the counter 
 diagonal, as in case of 5/7. 
 
 Now, to obtain the effects of weight of structure and 
 uniform load, the truss having even panels, we place J 
 under the centre node of the lower chord, because 
 half of the weight w , which is supposed to be concen 
 trated at that point, tends to act on each of the dia 
 gonals rising from that point. 
 
DOUBLE CANCELATED TRUSSES. 
 
 83 
 
 oo 
 
 At the next node from the 
 centre, each way, the figure 1 
 is set, because, of the weights 
 (M/), concentrated at those points, 
 each bears upon its nearest abut 
 ment (the truss being uniformly 
 loaded), through the diagonals 
 running upward and outward 
 from those points. If this be 
 not so, each must transmit a part 
 of its amount past the centre, 
 through the antagonistic dia 
 gonals 7/9 and 7\9, which is 
 contrary to statical law. 
 
 Then we put 1J, 2J, 3J, etc., 
 under alternate nodes from the 
 centre, and 1, 2, 8, etc., under 
 alternates beginning at the first 
 on each side of the centre ; as 
 shown in diagram Fig. 18. 
 
 These figures form the co 
 efficients of w , to indicate the 
 weights acting, or tending to 
 act, upon the diagonals running 
 upward and outward from these 
 numbers respectively, arising 
 from weight of structure, and 
 also, the co-efficients for (iv+w f ), 
 to express the load tending to 
 act on diagonals, arising from 
 both superstructure and mova 
 ble weight, when the truss is 
 fully loaded. For illustration ; 
 
34 BRIDGE BUILDIXG. 
 
 the diagonal 5/7 we have seen to be liable to a 
 maximum stress of w" from variable load, and, as we 
 have the figure 1 at the foot of 5\7, it shows that 
 the weight due to the latter on account of structure 
 is IM? , which must be subtracted from w" to obtain 
 the actual maximum to which 5/7 is liable ; which 
 is Qu)". w . 
 
 If w be equal to or greater than 9w", then 5/7 ia 
 subject to no action, and may be dispensed with. As 
 to the advantage of introducing counter diagonals, 
 merely for the purpose of stiffening the truss, the results 
 of my investigations will be given in a subsequent part 
 of this work. 
 
 The maximum weight sustained by any thrust up 
 right, is manifestly equal to the greatest weight borne 
 by either diagonal connected with it at the upper end, 
 since any weight borne by 3/5, for instance, being 
 transferred to the antagonist of 5\7, thereby dimin 
 ishes by a like amount, the maximum action of the 
 latter. Whence the upright at 5, can receive no more 
 load from the two diagonals, than the maximum load of 
 one, and this relation holds in general. 
 
 The reason of adding alternate figures to form the 
 second series over the diagram, will be obvious, when 
 it is observed that there are two independent systems 
 of uprights and diagonals ; one of which includes the 
 uprights under even numbers in the upper series, and 
 the diagonals connecting therewith, and the other, the 
 remaining uprights and diagonals. Now weight applied 
 at the nodes of either of these systems, can only act upon 
 members of that same system ; that is, weight applied 
 at nodes indicated by even numbers in the upper series 
 can only act upon the first above named system of up 
 rights and diagonals, and vice versa. 
 
DOUBLE CANCELATED TRUSSES. 85 
 
 The main end braces are acted upon by both sys 
 tems; so that to obtain the weight sustained by them, 
 we must add the numbers 56 and 64 (and correspond 
 ing numbers in other cases), making in this case 12(W 
 equal to 7Jw. 
 
 The uprights under 1 and 15, sustain each a tension 
 equal to w, for variable load, and to w+w , for weight 
 of variable load and superstructure together ; which 
 obviously gives their greatest strain. 
 
 Having thus determined the greatest weights to which 
 the several verticals and diagonal members are liable, 
 we proceed as in former cases, to multiply those 
 weights by lengths of diagonals, and divide the pro 
 ducts by lengths of verticals, to obtain the stresses of 
 diagonals ; remembering to take into account the dif 
 ference in length between those having a horizontal 
 reach of only one panel, at and near the ends of the 
 truss, and those that reach across two panels. 
 
 The mode of estimating the stresses upon the differ 
 ent portions of the chords, depending upon the hori 
 zontal action of diagonals, has been sufficiently ex 
 plained. It is only necessary to observe that the end 
 braces produce compression upon the upper, and ten 
 sion upon the lower chord, through their whole lengths, 
 equal to (io+w \ multiplied by the number of nodes 
 of the lower chord, and that product multiplied by - . 
 and that each pair of intermediate diagonals analo 
 gously situated with respect to the ends of the truss, 
 whether acting by thrust or tension, produce tension 
 and thrust in like manner, upon the portions of the 
 lower and upper chords, between their points of con 
 nection with the chords. Thus is generated a progres 
 sive and determinate increase of action upon succeeding 
 
86 BRIDGE BUILDING. 
 
 portions of the chords from the ends to. the centre of 
 the truss. 
 
 In the case of a deck bridge, the weights sustained 
 by thrust uprights, are respectively indicated by the 
 figures over the diagram on the right hand half of the 
 truss, prefixed to w", for movable load, and the figures 
 under the diagram prefixed to w , for weight of struc 
 ture, being the same weight which gives the maximum 
 stress to the diagonal running upward and outward 
 from the foot of the upright. Tension verticals at the 
 ends sustain no weight. 
 
 TRUSSES WITHOUT VERTICALS. 
 
 It will be seen upon a general view of the action of 
 the different parts of a truss with parallel chords, that 
 the diagonals (and verticals when used), form media 
 through which weight acting upon the truss, is reflected 
 back and forth between the upper and lower chords, 
 until it comes finally to bear upon the abutment. 
 
 A weight applied at one of the nodes of the lower 
 chord, of course, cannot be sustained by the tension 
 of that chord, which acts only in horizontal directions ; 
 but is suspended by a tension piece, whether oblique 
 or vertical, from a node in the upper chord. But the 
 upper chord acting also horizontally, cannot sustain the 
 weight. Consequently, a thrust member, either oblique 
 or vertical, must meet the force at that point, to prevent 
 the weight from pulling down the upper chord, and 
 destroying the structure. 
 
 Hence, we see, that in all the cases we have consid 
 ered, of trusses with parallel chords, the weight, whe 
 ther applied at the upper or lower chord, acts alter- 
 
TRUSSES WITHOUT VERTICALS. 87 
 
 nately upon thrust and tension pieces, extending 
 directly or obliquely from chord to chord. 
 
 With reference to Fig. 18, we have regarded the 
 weight as transferred from tension diagonals to thrust 
 verticals, and the contrary. But if we conceive the 
 verticals to be removed, except the endmost, we have 
 only to insert a thrust brace from the abutment to the 
 second node (or the first from the angle), of the upper 
 chord, and to so form and connect the other diagonals 
 as to enable them to act by either tension of thrust, 
 and we have a truss capable of sustaining weights applied 
 at all, or any of the nodes of the upper and lower 
 chords, in the same manner as the truss with verticals, 
 represented in Fig. 18. In this condition, the truss 
 will act upon the principles discussed with reference to 
 Fig. 18. For this modification of the truss, see Fig. 19. 
 
 To estimate the strains upon the several parts of 
 such a truss, due to weights w, w, etc., at the nodes of 
 the lower chord ; we may place the figures 1, 2, 3, etc., 
 over the nodes of the upper chord, as was done in the 
 case of Fig. 18. But, instead of adding alternate fig 
 ures to form the second series, to be used as co-eili- 
 cients of w" , for expressing the weights sustained by 
 diagonals, we add every fourth figure; because it is 
 only the weights at every fourth node, that act upon 
 the same set of diagonals. 
 
 For instance ; the weights at 1, 5, 9 and 13, act upon 
 their peculiar set of 8 pieces (excluding the end braces, 
 but including the tension vertical at 1), and none of the 
 weights at the other nodes have any action upon those 
 pieces ; as is made obvious by an inspection of Fig. 19. 
 
 Again, the weight at 2, 6, 10 and 14, have their pe 
 culiar and independent set ; and so of those at 3, 7, 11 
 and 15, and those at 4, 8 and 12. Therefore, in form- 
 
88 
 
 BRIDGE BUILDING. 
 
 00 00 
 
 11 1 I 
 
 C510O 
 
 *> o - 
 
 ing our second series of num 
 bers, we place under each figure 
 of the first series, the sum of 
 that figure, added to every 4th 
 figure preceding; that is, under 
 12, place the sum of 12, 8 and 4 
 = 24. % Under 5, the sum of 5-f 
 1 =6. The four first figures, 
 having no 4th preceding figures, 
 are simply transferred, without 
 addition or alteration. 
 
 These numbers in the second 
 series, are the co-efficients of w" 
 (w divided by the number of 
 panels in the truss, being 16 in 
 this case), to express the greatest 
 weights acting by tension on 
 each diagonal having its lower 
 
 o o 
 
 end under the number used, and 
 the upper end under a higher 
 number. Also the weight act 
 ing by thrust upon the diagonal 
 meeting the former at the upper 
 chord. The last, or highest 
 number, determines the weight 
 sustained by the tension vertical 
 under the number, the vertical 
 being a member of one of the 
 four sets ot alternate thrust and 
 tension pieces connecting the 
 two chords. 
 
 A third series of figures 
 formed by reversing the order 
 of the second placing the low- 
 
TRUSSES WITHOUT VERTICALS. 89 
 
 est number of the third under the highest of the se 
 cond series, and vice versa, prefixed as before to w" , 
 will show the weights sustained by thrust and tension 
 of diagonals in the reversed order; i. e., whereas one 
 series shows the amount of tension a particular diago 
 nal is liable to, the reversed series shows the thrust 
 the same piece must exert in a different condition of 
 the load. 
 
 Thus we ascertain, as in the case of truss Fig. 13 
 [XLV], that nearly all of the diagonals are exposed to two 
 kinds of action, thrust and tension ; and it is only the 
 preponderance of the larger over the smaller of these 
 forces, which has place when the truss is fully loaded, 
 and it is only this preponderance which is to be used 
 as co-efficient to (w + w 1 ) in estimating the stresses upon 
 the different portions of the chords, and as co-efficient 
 to ?/; , in modifying the effects of the variable load upon 
 diagonals, as aftected by weight of structure. But it is 
 to be remembered that the numbers over the diagram 
 are to be divided by the number of panels, before being 
 used before w and w , in the expression of stresses of 
 members. Thus, we have, as the effect of variable 
 load upon the diagonal 2/4 ..., 2w" (=^w), as the 
 
 1 Q 
 
 greatest weight acting by tension, and ~^w 9 the great 
 est acting by thrust. Hence the weight upon this 
 
 -| Q f) 
 
 piece, due to weight of structure, is (-- -~-)w f 9 w 9 and it 
 produces thrust or compression, because the thrust 
 tendency is the greater. This weight (w }, added to 
 - 8 w, the greatest effect of variable load shows the maxi 
 mum weight which can act by thrust upon that diago- 
 
 "1 ft 
 
 nal, to be -^w+w . We have, also, for the greatest 
 weight acting by tension as modified by weight of struc- 
 
 12 
 
90 BRIDGE BUILDING. 
 
 ture, pit 1 iv j which is a negative quantity when w is 
 less than 8w , as will usually be the case in practice ; 
 consequently that diagonal can seldom or never be ex 
 posed to the force of tension. 
 
 Again .(w+w )-, (h and v representing horizontal 
 and vertical reaches of the diagonal, as in previous 
 discussions), is the amount contributed toward the 
 maximum tension of the lower chord by the diagonal 
 in question, not affecting, of course, that portion of 
 the chord outside of the connection therewith, or a 
 like portion at the opposite end. 
 
 LYIII. It is to be remembered that the tension or 
 thrust of a diagonal, is always equal to the weight sus 
 tained, multiplied by the length, and divided by the 
 vertical reach of the diagonal. 
 
 The method here under discussion for estimating 
 stresses, seems to need no further illustration. But 
 the question as to decussation, affects the case of Fig. 
 19, as well as that of Fig. 13. The two sets of dia 
 gonals which meet the upper and lower chords in the 
 centre, have symmetrical halves on each side of the 
 centre, and no action can pass the centre upon either, 
 when they are uniformly loaded ; whereas, the two seta 
 to which 7/9 and 7\9 belong, have the half of one 
 on either side of the centre, a counter part to the half 
 of the other set on the opposite side ; and the diagonals 
 7/9 and 7\9, will act or not, according as their op 
 posite points of connection with upper and lower chords, 
 are carried farther apart, or the contrary. JSTow, as 
 the points 9 and 7, upper chord, are depressed by the 
 change in one vertical and 3 diagonals, while the op 
 posite points at the lower chord are depressed by the 
 
TRUSSES WITHOUT VERTICALS. 91 
 
 change in 3 diagonals only, we might naturally expect 
 to find greater depression iu the upper than the lower 
 points; though this does not follow as a matter of .ne 
 cessity, since the less number of members, by being 
 more nearly under a maximum stress, might give 
 greater depression than the greater number, under less 
 stress, as compared with their maximum. Now, the 
 vertical at 1, being under maximum weight, gives de 
 pression = E ; (adopting the notation used with refer 
 ence to Fig. 13 [XLIX.]). The two diagonals 1/3 and 
 3\5 being under f J maximum, give depression equal 
 toff x4E(making/i=*;=l), = 3.81E; while the diagonal 
 5/7, under T 4 ^ maximum, gives depression = 0.4 x2E, 
 = 0.8E, making a total depression of point 7, upper 
 chord, = 5.6 IE. Again, the diagonal 1\3, under maxi 
 mum stress, gives depression = 2E, while 3/5 and 
 5\7, under j f rnaxm u m stress, give depression = -J X 
 4E, = 3.2E, making a total for the point 7, lower chord, 
 equal to 5.2E, which is less by 0.41E, than the depression 
 of the opposite point in the upper chord, whereas it 
 should be greater by 0.8E, in order to give to 7\9 and 
 7/9, the tension assigned to them by the decussation 
 theory. 
 
 But we must not conclude from this fact, that there 
 is no decussation in this case. For, if we assume that 
 7\9 is inactive under the full load, it follows that 5/7 
 is also inactive, and that l/3-|-3\5 sustain only Jf 
 maximum stress, producing f }E, = 3.05 E, which added 
 to IE for the vertical at 1, makes 4.05 E, = depression at 
 point 7, upper chord ; while the 3 diagonals contribut 
 ing to depression of the opposite point in lower chord, 
 are under maximum stress, producing depression = 6 E. 
 Hence, we see, that upon this hypothesis, the distance 
 between these two points, measuring the vertical reach 
 
92 BRIDGE BUILDING. 
 
 of the diagonal, is increased by (6 4.05)E = 1.95E. 
 This can not be, without producing tension upon dia 
 gonals 7\9 and 7/9. Since then these members can 
 not be entirely without action, and as previously shown, 
 they can not have as much action as the decussation 
 theory assigns to them, it follows, in this case, that they 
 must act, but with less intensity than the theory as 
 signs them. 
 
 In this case, as well as in that of Fig. 13, the result 
 would be changed somewhat, by taking into the cal 
 culation the weight of structure, which would change 
 to a small extent, the relation between the maximum 
 stresses of diagonals, and the stresses they sustain un 
 der a full load. .For the stress due to weight of struct 
 ure, is constant, and that due to variable load, is greater, 
 upon most of the diagonals, under certain conditions 
 of a partial, than under a full load. Hence, while 
 5\7 sustains (under full load), only { maximum upon 
 that part of the material provided for variable load, it 
 sustains a full maximum upon the part provided to 
 sustain weight of structure. It is easy enough to take 
 these things all into account, in estimating the amount 
 of decussation in special cases. Still, it is doubtful 
 whether any better practical rule can be adopted, than 
 the one previously given, [XLVIII] ; namely, to estimate 
 stresses upon both hypotheses, and take the highest 
 estimate for each part. 
 
 DECUSSATION IN TRUSSES WITH VERTICALS. 
 LIX. In trusses of this class with odd panels, and 
 diagonals crossing two panels, as in Fig. 20, it will be 
 seen, on subjecting them to analysis, such as was ex 
 plained with reference to Fig. 18 [xvi], that, while in 
 trusses of even panels, the figures in the second line 
 
DECUSSATION, ETC. 
 
 93 
 
 over the diagram, indicate the maximum stresses of 
 diagonals, and those under the diagram, the stresses 
 under uniform load (which are generally less than the 
 maximum under partial loads), in case of the truss with 
 odd panels, the bottom figures show, for certain dia 
 gonals, greater stresses for the full, than the upper 
 figures give as the maximum for partial loads. Thus, 
 in Fig. 20, the number 16 over m, indicates 16*0" 
 (=ijj 6 z0), as the maximum weight for #, while the fig 
 ure 2 under the point z, indicates that il sustains 2i0 ( = 
 18i0"), under the full load. It should be remarked here, 
 that the figure 1 under the first two nodes on either side 
 of the centre, and the figure 2 under the next, are thus 
 
 2 2 
 
 FIG. 20. 
 
 45678 
 6 9 12 16 20 
 
 q p 
 
 XKXxx 
 xxRx 
 
 abcdefgijk 
 211112 
 
 placed upon the assumption that all the weight on 
 either side of the centre, is made to act on its nearest 
 abutment. This would necessarily be so, if en andfq 
 were removed or relaxed. But, with those members 
 in place, and properly adjusted, there may be a decus- 
 sation of forces through them, whereby a portion of 
 the weights at e and/, may be made to bear upon the 
 more remote abutments. Now, as the maximum on 
 en is 6w" and that of its antagonist only 4w", the latter 
 is not sufficient to neutralize the former entirely, but 
 leaves a balance of 2w ff which may be transmitted 
 through en to gl, as an offset for a like amount trans- 
 
94 BRIDGE BUILDING. 
 
 mitted through/^ to ds. If this be so, then fm and er 
 do not sustain the full weight of liv, but only W 9 
 which, being transmitted to U 9 makes, with the weight 
 w (=9w;"), applied directly at i, 16w", as indicated by 
 the figures over the diagram, instead of 2w (= ISic"), 
 as the figure 2 under the point i would indicate. 
 
 Now, whether the two diagonals en and/<?, being ap 
 parently, in a state of partial antagonism, do in whole 
 or in part neutralize the tendency of each other to 
 transmit weight past the centre each way under a uni 
 form load of the truss, is not quite obvious, and it may 
 be proper to estimate stresses under both hypotheses, 
 and take the highest estimate for each part of the 
 truss. 
 
 It will be seen that it and cs are the only diagonals 
 in Fig. 20, which show greater stress with a full than 
 a partial load, upon the non-decussation hypothesis. 
 But all the diagonals undergo different stresses, with 
 the uniform load, as viewed under the different theo- 
 riSs, and consequently, their effects upon the chords 
 are different. The end brace as, sustains 4 (w+w ) = 
 4W substituting W for w-rw f ), under either theory, 
 and the tension of ac equals 4w (making A = #6, and 
 v = bs). cs sustains 2~VV, or y TV", whence cd sustains 
 either 6W^ or 5JW*. Again, ds sustains W, or IfW, 
 the former without, and the latter with decussation. 
 This diagonal having a horizontal reach of 2A, adds 
 2W- or 2JW- to tension of chord, making 8W*, or 
 
 8f W , as the tension of de. For er, we have W with 
 out decussation, making a tension of 10W- for ef; 
 while with decussation, er sustains J W, from which we 
 subtract f W", for opposite action of en, leaving |W 
 
DECUSSATION, ETC. 95 
 
 giving horizontal pull =1J W to be added to S 
 
 making 9jW- = tension of ef. 
 
 Upon the non-decussation hypothesis, 5 r and m l> of 
 the upper chord sustain thrust equal to 8W^, and the 
 
 remainder of the chord, 10W-. By the other hypothe 
 sis, sr and ml sustain 8f W -, rq and nm sustain 9J 
 W *, and the other 3 sections, lOf W^ 
 
 LX. "We may derive some more light upon this sub 
 ject, by considering the conditions resulting from the 
 elasticity of materials. Supposing the upper and lower 
 chords to be so proportioned as to be uniformly con 
 tracted or extended under a uniform load of the truss, 
 this does % not require or imply any appreciable differ 
 ence in lengths of diagonals. But the stress upon 
 chords being produced by the action of diagonals, the 
 latter, when, as here supposed, acting by tension, neces 
 sarily undergo extension, by which means, the panels 
 (except the centre one), are changed from their original 
 form of rectangles, to that of oblique trapezoids. For 
 instance, the figure gj.ln becomes longer diagonally 
 from g to , than from n toj, whence the point g falls 
 lower than it would do, if the diagonal suffered no 
 change. 
 
 Suppose then the truss to be fully loaded, and the 
 diagonals il, gl and/m, to be each exposed to the same 
 stress to the square inch of cross-section. In that case, 
 il and gl suffer extension proportionally to their respec 
 tive lengths, thereby causing depression of the points 
 i and g respectively as the squares of those lengths. 
 [See note in section XLIX.] Hence, the point g is de- 
 
96 BRIDGE BUILDING. 
 
 pressed more than the point j, by the extension of dia 
 gonals, by as much as the square of gl exceeds the 
 square of il, or as 8 to 5 ; assuming diagonals to incline 
 at 45. The panel gm, must therefore be oblique, and 
 the distance gm, greater than ni. Again, the point/ 
 suffering the same depression from the extension of/w, 
 as the pointy suffers from that of^, and a still further 
 depression from the compression of mi, and the exten 
 sion of il, it fo.llows that the panel fn must also be ob 
 lique, and the distance /ft, greater than the distance og. 
 
 Now, the obliquity of both of the panels gm and//i, 
 manifestly contributes to the excess of distance fm, 
 over 01. On the contrary, the centre panel eo has no 
 obliquity due to extension of diagonals, or compression 
 of uprights; since there is no cause for obliquity in 
 one direction, more than the other. It seems to follow 
 that en, crossing one oblique panel, must undergo ex 
 tension; but not so much as //n, which crosses two. 
 
 Now, ///i and en being equal in length, the weight 
 sustained by each, is manifestly as the cross-section 
 and extension combined ; and as the former,///?., should 
 be the larger in the ratio of 9 to 6, or as their maxi 
 mum stresses ; if we allow their extensions to be as 
 2 to 1, the greater for/w, the relative weights sustained 
 would be as 18 to 6, or as 6 to 2. Our decussation 
 theory gave their relative stresses as Iw" to 2w /f . This 
 is not a wide discrepancy, seeing that the above com 
 putation is based in part upon a mere approximate 
 data. -w 
 
 We may conclude then, that in cases like the one 
 under consideration, decussation does actually take 
 place. Still it obviously depends upon conditions which 
 are not of the most determinate character. For, if en 
 and/?, be relaxed or removed, under a full load of the 
 
DECK BRIDGES. 97 
 
 truss, dccussation can not take place, for the same ob 
 liquity of the two panels next to the centre one, which 
 produces the tendency toward tension of en and/*?, O11 
 the contrary, tends to relax do and gp, through which 
 latter alone decussation could take place, in the absence 
 of the former. 
 
 On the other hand, if en audfq be sufficiently strong, 
 they may be strained to such a pitch as to bear all the 
 weights ate and/, andleave/m and er entirely inactive. 
 Hence, there is an uncertainty as to the action of these 
 diagonals, which may be best obviated by estimating 
 stresses upon both theories, and taking the highest es 
 timates ; as recommended with reference to trusses 
 without verticals, and as previously suggested with 
 reference to the case in hand. 
 
 In view of preceding facts and principles, it may be 
 advisable to avoid the odd panel in trusses with verti 
 cals, when practicable without incurring more import 
 ant disadvantages in other respects. 
 
 DECK BRIDGES. 
 
 LXL Are those having the movable load applied at 
 the nodes of the upper, instead of the lower chord, as 
 generally assumed in preceding analyses. 
 
 It will readily be seen, on a brief contemplation of 
 Figures 12 and 13, for instance, that weights applied 
 at the upper chord, act directly upon compression 
 members, either erect or oblique, as the case may be ; 
 and are thence transferred to tension members at the 
 lower chord ; according to the general principle, that 
 weight applied at the upper end of a member, always 
 acts by compression, and that which is applied at the 
 lower end, by tension. 
 13 
 
98 BRIDGE BUILDING. 
 
 In the case of truss Fig. 12, the action of tension di 
 agonals is precisely the same, whether the weight be 
 applied at the upper or lower chord. But the compres 
 sion verticals, in the deck bridge, sustain as their maxi 
 mum, the weights indicated by the figures immediately 
 above them respectively, from the centre toward the 
 right hand ; and these weights, of course, are equal to 
 those acting upon the diagonals respectively meeting 
 the verticals at the lower chord; and consequently, 
 greater than when the weight is applied at the lower 
 chord. For illustration, in Fig. 12, as the truss of a 
 deck bridge, the vertical fk sustains 15w;", the same as 
 jjf, whereas, in the case of a " Through bridge" (with 
 load applied at the lower chord), fk sustains only IQiv" 
 communicated to it through ek. 
 
 In the deck bridge also, the tension verticals bo and 
 jg are essentially inactive, merely sustaining a small 
 portion of the lower chord. The chords suffers the 
 same stress in both through, and deck bridges. 
 
 LXII. Load applied at the upper chord of truss Fig. 
 13, acts by thrust directly upon the diagonals meeting 
 at the upper chord, and the maximum weight (from 
 movable load), sustained by diagonals meeting at one 
 of the upper nodes, are indicated by the two figures 
 immediately over the node ; the larger figure referring 
 to the diagonal running toward the nearer abutment ; 
 e. g., the numbers 4 and 6 over the point m, signify 
 ftw" = greatest weight borne by me, and 4w" the 
 greatest borne by me. 
 
 It is obvious also, that the maximum thrust of any 
 diagonal, equals the maximum tension of the diagonal 
 meeting the former at the lower chord ; that is, maxi 
 mum thrust of me, is equal to 6w" , = maximum ten- 
 
DECK BRIDGES. 99 
 
 sion of co. The maximum thrust of bn being equal to 
 9i0"--, the maximum tension of bo, equals w" . Tins is an 
 extra weight thrown upon the point o, in consequence of 
 the vertical bo, being turned out of its regular direction 
 of a diagonal in the position of bp* in order to throw 
 its load upon oa, whereby op and pa are rendered un 
 necessary. The weight borne by oa, therefore, instead 
 of being 12^;", as indicated by the figure 12 at o, is 
 
 The figure 1 over o, denotes the tendency of \w" to 
 act upon oc, by thrust, by which tendency the tension 
 of oc, under a full load of the truss, is reduced 
 to 5tf". 
 
 LXIII. If Fig. 12 be assumed to represent a truss 
 with tension verticals and thrust diagonals, the figures 
 over the upper nodes, prefixed to w n indicate the 
 weights tending to act by compression upon the dia 
 gonals descending toward the right from the nodes 
 respectively ; which weight is transferred to the verti 
 cal meeting the diagonal at the lower chord. This 
 constitutes the maximum load of the vertical, in case 
 of a deck bridge. Otherwise, the maximum stress of 
 verticals is shown by the figures immediately over 
 
 FIG. 13A. 
 
 v o n m I k j 
 
 a b c d e f // i 
 
 * The point p, not seen in Fig. 13, is assumed to be at the intersec 
 tion of a vertical line through the point a, with the upper chord- 
 produced. The arrangement above alluded to, gives the truss a reclan- 
 gular, instead of a trapezoidal form of outline, which involves no more 
 action upon material, though it increases the number of members in 
 the truss. [See Fig. 13A.] 
 
100 JLJRIDGE BLILDING. 
 
 
 them, prefixed to 10", provided, that in this case, the 
 
 maximum stress of a vertical can never be less than w. 
 = the weight applied immediately at its lower end. 
 
 RATIO OF LENGTH TO DEPTH OF TRUSS. 
 
 LXIV. Having explained and illustrated, it is hoped 
 intelligibly, methods by which may be computed the 
 stresses of the various parts composing most of the 
 combinations of members capable of being used in 
 bridge trusses, with a view to giving to each part its 
 due proportions, it may be proper to give attention to 
 the general proportions of trusses, and such other con 
 siderations as may affect the efiicient, and economical 
 application of materials in bridge construction. 
 
 The ratio of length to depth of truss is susceptible 
 very great range, and it is obvious that some certain 
 medium, in this respect, will generally give more ad 
 vantageous results, than any considerable deviation 
 toward either extreme. For, it will be observed, that 
 in the expressions we have derived for the amount of 
 action open chords, - appears as a factor ; v represent 
 ing the depth of truss, between centres of chords. 
 Hence, the smaller the value of v, the greater the 
 stresses of chords, so that when v=0, these stresses 
 become infinite, and the chords require an infinite 
 amount of material ; in other words, the case is im 
 possible. On the other hand, if v be infinitely great, 
 though the stress of chords be reduced to nothing, the 
 verticals and diagonals being infinitely long, and sus 
 taining a definite weight, also require an infinite 
 amount of material. 
 
 Now, between these two impracticable extremes 
 where shall we look for the most advantageous ratio ! 
 
LENGTH TO DEPTH OP TRUSS. 101 
 
 It can not be the arithmetical mean, for there is no 
 such mean between v = 0, and v infinity. Un 
 doubtedly, we shall be unable to do more than answer 
 this question approximately; and that, only with refer 
 ence to specific cases; for the ratio suitable for one 
 length of span, and in one set of circumstances, will 
 often be found quite unsuitable under different circum 
 stances. 
 
 WQ have seen that the material required in chords, 
 is in general, inversely as the depth of truss, or as -. 
 Also, that the material for verticals and diagonals, in 
 creases with increase in the value of v ; though not h 
 a determinate ratio. But assuming the latter classes 
 of members, including the main end braces of the Trape 
 zoidal truss, to increase in the ratio at which v in 
 creases, while the chords diminish at the same rate, 
 we might reasonably assume, that the minimum amount 
 of action upon materials would occur when the amount 
 of action upon chords were* just equal to that upon all 
 other parts of the truss. 
 
 By recurrence to the analysis of truss Fig. 12, 
 [XLIII], we find amount of action upon chords, re 
 presented by 56-M, and that upon all other parts, by 
 
 22.570) M. Here, h is equal to J part of the 
 length of truss, while v is variable ; and, by making 
 these two co-efficients of M equal, and deducing thence 
 the value of v, we have the depth of a 7 panel truss in 
 which the amount of action upon chords, equals that 
 of all other parts. Thus, putting 56- = 16-- 4- 22.57i , 
 
 substracting 16-, and multiplying by v, we have 40A 2 = 
 22.57^ ; whence v = </(^L], =1.34A nearly. This 
 gives length to depth of truss, as 5.2 to 1. 
 
102 BRIDGE BUILDING. 
 
 Again, referring to analysis of truss Fig. 10, we find 
 action upon chords represented by 20--M, and action 
 
 upon other parts, by ( 8- -f 11.2y) M. To make 
 these quantities equal, requires that?; = 1.03A, and that 
 the length of truss be equal to ^ times its depth, or 
 nearly 5 to 1. 
 
 From this last case, we may infer as a probability > 
 that a ratio of length to depth as 5 to 1, is the most 
 economical for a truss of 5 panels, other things the 
 same. We know, moreover* that by making v = J^ in 
 the same truss, we double the amount of action upon 
 chords making it equal to the aggregate upon all 
 parts with the ratio of 5 to 1, while the action, and 
 consequently, the material of the other parts is probably 
 seduced one-half. Hence, a ratio of length to depth 
 as 10 to 1, probably increases the aggregate amount of 
 action by some 25 per cent, over what takes place with 
 a ratio of 5 to 1. We may therefore unhesitatingly 
 conclude, that whether the ratio of 5 to 1 be too small 
 or not, the ratio of 10 to 1 is much too large. 
 
 Referring again to the 7 panel truss, it appears above, 
 that a ratio of 5.2 to 1 indicates the same amount of 
 action upon chords, as on all other parts. But we can 
 not with certainty infer that the absolute amount of action 
 upon the truss, is less with v=1.34/*, than with v=h ; 
 in which case length is to depth a,s 7 to 1. In fact, if 
 we estimate the absolute amount of action, assuming 
 these two values off successively, we shall find no es 
 sential difference in the results. Hence, if other con 
 ditions were the same in both cases, it would follow 
 that the ratios of 5.2 to 1 and 7 to 1 were equally 
 favorable to economy, and that there is a better ratio 
 still, between the two ; probably, about 6 to 1. 
 
LENGTH TO DEPTH OF TRUSS. 103 
 
 But the conditions arc not the same in the two cases, 
 aside from the different values of v. For, while with 
 v=/i, the diagonals incline at 45, in the other case, 
 their inclination from the vertical is considerably less, 
 being only about 37. This, we shall see hereafter, is 
 a less favorable inclination for diagonals acting by ten 
 sion, than 45; and, since the ratio of 5.2 to 1 shows 
 an equality as to economy, with the ratio of 7 to 1, 
 with the more favorable conditions on the side of the 
 latter, it would seem at least, highly probable that the 
 ratio of 5.2 to 1 is the more near approximation to the 
 desired optimum. 
 
 No\v, after much thought and investigation, with 
 some considerable experience in planning and con 
 structing truss bridges, I can give no better pra ticai 
 rule as to the proper depth of a truss of a given length, 
 than to adopt that ratio between 7 to 1 and 5 to 1, 
 which will best accommodate the desired length of 
 
 O 
 
 panel (or value of A), and afford the best, and most 
 economical inclination of diagonals; matters to which 
 attention will shortly be directed. 
 
 It is not supposed, however, that these limits of 
 ratio will not frequently be exceeded, particularly in 
 the adoption of a greater ratio than 7 to 1. In case 
 of the very long spans dared and achieved in this age 
 of rail roads and locomotion, engineers may recoil from 
 the towering altitudes of 50 or 60 feet depth of truss 
 which some of the long spans now occasionally con 
 structed would require, perhaps more in deference to" 
 European precedent, and from an instinct of conserva 
 tism, than from regard to economy, and a true appre 
 ciation of the real merits of the question. But for 
 important bridges for heavy burthens, a ratio greatei 
 
104 , BRIDGE BUILDING. 
 
 than 8 to 1 can not be regarded as commendable, ex 
 cept in rare and peculiar circumstances. 
 
 INCLINATION OF DIAGONALS. 
 
 LXV. We have seen the absolute importance of ob 
 lique members in bridge trusses, and we have also 
 seen the excellence, in point of theoretical economy, 
 of the trapezoidal truss, with parallel chords con 
 nected by diagonal members, with or without verticals. 
 Now, since there is an endless variety in the positions 
 which a diagonal member may assume, it becomes an 
 important question, what degree of inclination these 
 members should have, to give the most economical and 
 satisfactory results. 
 
 The inclination may be increased till it reaches a 
 horizontal position, or diminished till it becomes a ver 
 tical ; when, in either case, the member ceases to be a 
 diagonal, and becomes incapable of performing the 
 office of effecting a horizontal transfer of vertical pres 
 sure. 
 
 The greatest efficiency of material used in diagonals, 
 is manifestly, when the weight sustained by a given 
 quantity of material, multiplied by the horizontal 
 reach, gives the largest product ; and, w r hen the mem 
 ber acts by tension, the weight capable of being sus 
 tained by a given amount of material, is as the cross- 
 section directly, and as the rate of strain inversely. 
 But the rate of strain, or stress produced by a given 
 weight, is as the weight multiplied by the length of 
 diagonal (D), and divided by the vertical (y), or as 
 
 while the cross-section is inversely as D, or as 
 Hence, the weight is as - -s- D , = V 3 . 
 
INCLINATION OF DIAGONALS. 105 
 
 Now, representing the horizontal reach by h, the 
 efficiency of the material must be as -| equal to 
 
 ~5"X- Then, making v, constant, and dividing by v, 
 
 the expression becomes, - a ~, still being proportional 
 to the efficiency of material. Consequently, that value 
 of h, which gives the largest value to the expression 
 w iH indicate the inclination at which the diago 
 
 nal will act with the greatest efficiency. 
 
 This value of A, is found by differentiating the func 
 tion -rrr a (h being the variable), and putting the dif 
 ferential equal to : by which process we obtain : 
 
 <* (?*) = ( -^5r^= whenee ca " celil s the 
 
 denominator, v 2 d h + h 2 dh = 2/i 2 d/>, and h 2 dh = v 2 dh* 
 Then, dividing by dA, and extracting the square root, 
 we have h=u ; thus showing that an inclination of 
 45 is the most advantageous for tension diagonals as 
 far as relates to those members alone. 
 
 THRUST DIAGONALS. 
 
 LXYI. The efficiency of material in a thrust brace, 
 is directly as the useful effect produced by the member, 
 and inversely as the amount of material required in it. 
 
 Now, the useful effect, as in the previous case, is 
 as the weight sustained and the horizontal reach, while 
 the amount of material, depends not only upon the 
 stress and length, but also upon the ratio of length to 
 diameter, which affects the power of resistance. 
 
 Theoretically, the power of resistance is as the cube 
 of the diameter (d), divided by the square of the length 
 (=i; 2 xA 2 ), a rule which is not sustained by experience, 
 
 * d(Roman), before a variable, or the function of a variable, denotes 
 the differential of such variable or function. 
 
 14 
 
106 BRIDGE BUILDING. 
 
 except in case of long slim pieces which break by 
 lateral deflection, under a comparatively small com- 
 pressive force. We will, however, use the rule for the 
 present occasion. 
 
 The efficiency of the material then, will be as the 
 power of resistance and the horizontal reach directly, 
 and as the stress produced by a given weight, in 
 versely ; which stress is as^li^L. "Whence we have 
 
 V 
 
 _^_^_v/^+P ( ^ ) proportional to the efficiency 
 
 of material in a thrust brace. Making 6^=1, the last ex 
 pression becomes A , and the value of A which gives 
 
 the greatest value to this function, will indicate the 
 inclination at which a thrust brace will act with the 
 greatest efficiency, as it regards the brace alone. 
 Differentiating, and putting the result equal to 0, we 
 have : 
 
 d ( h } = dh l pa + h * ] *-* h (g +^ * X2ftdA_ Q whence 
 
 V+^)r (tfH-/**) 1 
 
 multiplying by the denominator (i^+A 2 ) 8 , we obtain 
 dh (v z +h 2 )* = A (v 2 + A 2 )J X 2MA, and, dividing by 
 x/(v 2 + A 2 )dA, we have v 2 + h 2 = f Ax2A = 3A 2 whence, v 2 = 
 3A2_/j2 ^ ^h^ and by evolution, v = A>/2, and h =-^ 
 = 0.7072y. 
 
 If we deduce the value of the expression *. | ? 
 (which is equal to the horizontal reach divided by the 
 cube of the length of brace), putting hv and A=Jy 
 successively, we find the degree of efficiency less than 
 the maximum, as above determined, by about 9 per 
 cent in the former, and 8 per cent in the latter case ; 
 showing that considerable deviations may be made in 
 the inclinations of thrust braces without much detri 
 ment to efficiency of material in braces, when required 
 
INCLINATION OF DIAGONALS. 
 
 107 
 
 by other considerations ; which will often be the case, 
 as will be seen hereafter. 
 
 EFFECTS OF INCLINATION OF DIAGONALS UPON STRESS OF 
 CHORDS AND VERTICALS. 
 
 LXVII. The comparative effects of different posi- 
 sitions of diagonals upon the chords, may be illustrated 
 with reference to Fig. 21. It is manifest that a given 
 weight w on the centre of this truss, will produce a 
 vertical pressure equal to %w at each of the points 
 a and 6, and that each oblique member between a and iv, 
 will sustain a weight equal to Jw; and will exert each 
 a horizontal action upon the upper and lower chords, 
 equal to JM/. Hence, the stress of chords in the centre, 
 
 will equal %w xn, in which n represents the number 
 of oblique members between a and w, or between 
 
 ac 
 
 a and c. But n equals ^whence \w l n = ^w- 
 
 a * 9 z V 
 
 The term h having been eliminated from the last ex 
 pression, it shows that the inclination of diagonals has 
 no effect upon the stress of chords in the centre, pro 
 duced by weight in the centre of the truss ; and by 
 similar reasoning it is shown that the same is true in re 
 lation to other parts of the chords, or to weight at any 
 other points in the length of the truss ; the only differ 
 ence being that the shorter the panels, or the smaller 
 
108 BRIDGE BUILDING. 
 
 the value of A, the shorter the intervals at which the 
 increments in the stress of chords are added, and the 
 less the magnitude of such increments, in the same 
 proportion. Hence, in general, there is no difference 
 in the stresses of chords, whether the diagonals have 
 one inclination or another. 
 
 With regard to the effect upon verticals, that part 
 of their stress which they receive through diagonals, 
 is equal to the weight sustained by those diagonals, 
 and is the same for a given weight, whatever be their 
 inclination. On the vertical we, the pressure is re 
 ceived directly from the weight. But on the next ad 
 jacent vertical, on either side, one-half of the same 
 pressure is received through to the intervening diago 
 nal, and transmitted to the next, and so on to the end. 
 
 Consequently the aggregate action of verticals, pro 
 duced by the weight w, is equal to w -f \wn, taking n 
 for the number of verticals receiving their stress 
 through the medium of diagonals, and which is equal 
 to the whole number less 3, when the number is odd, 
 and the verticals act by thrust, as assumed in the case 
 of Fig. 21. If the weight be applied at the lower 
 chord, the whole action of verticals is communicated 
 through diagonals, the latter acting by tension. 
 
 Hence the aggregate action of verticals increases and 
 diminishes with their number, and economy as regards 
 those members, would require the diagonals to incline 
 at a greater angle with the vertical than that which 
 is most favorable as to the diagonals themselves. 
 
 We have seen, however [LXVI] that by placing the 
 diagonals at 45 when they act by thrust, we lose about 
 9 per cent in economy of those members, and we now 
 learn that such an arrangement increases the economy 
 in verticals to a considerable extent by diminishing 
 
WIDTH OF PANEL. 109 
 
 their number ; the actual amount depending somewhat 
 upon the number, and not deducible by a general rule. 
 
 We shall not, however, err greatly in assuming, that 
 with an inclination of 45, for thrust diagonals in con 
 junction with tension verticals, the loss upon the 
 former is quite made up by saving in the latter, and 
 that a less inclination in this case, should be regarded 
 as very questionable practice. 
 
 In case of tension diagonals and vertical struts, a 
 saving in material may undoubtedly be made by mak 
 ing the horizontal greater than the vertical reach of 
 the diagonal, whenever such a course is found consist 
 ent with a proper regard to just proportions of the 
 truss in other respects ; such as width of panel, depth 
 of truss, etc. 
 
 THE WIDTH OP PANEL. 
 
 LXVIII. Which we have represented in our formu 
 lae by A, has only been hitherto considered as to its 
 relations to v, representing the depth of truss. 
 
 With regard to the best absolute value of A, .the ques 
 tion is affected by the relative expense of floor joists, 
 and the extra amount of material and labor in forming 
 connections at the nodes of the chords ; as well as, in 
 some cases, the lengths of sections in the upper chord. 
 The latter requires support laterally and vertically at 
 intervals of moderate length, depending upon the ab 
 solute stress, which, other things the same, governs the 
 cross-section. 
 
 The upper chord usually, of whatever material, has 
 a cross-section so large as to exclude all danger of 
 breaking by lateral deflection, in sections of 10 to 14 
 feet ; and, as there will seldom be occasion for exceed 
 ing these lengths in cancelated trusses, the increased 
 
110 BRIDGE BUILDING. 
 
 expense of joists for wide panels, and the expense of 
 extra connections in narrow ones, are the principal 
 considerations affecting the absolute value of A, as an 
 element of economy. 
 
 The transverse beams, supposed to be located at the 
 nodes between adjacent panels, may, of course, be pro 
 portioned to the width of panel, so as to require essen 
 tially the same material in all cases. But the joists, or 
 track stringers of rail road bridges, the depth being 
 proportional to the length between supports, have a 
 supporting power as their cross sections; and since the 
 load, at a given weight to the lineal foot, is directly as 
 the length, it follows, that to support the same load per 
 foot, as bridge joists are required to do, the cross-sec 
 tion should b as the length. The expense of joists 
 and stringers, therefore, is directly as the width of 
 panel.* 
 
 On the contrary, the expense of connections 
 will be as the number of panels, nearly, and conse 
 quently, inversely as their width, or inversely as the 
 
 *The thickness of joist most economical for a short reach would be 
 liable to buckle with greater length and depth. Hence joists require 
 increase of thickness with increase of length and depth. The thick 
 ness should be as the depth, and the cross-section, as the square of the 
 depth (d). 
 
 Upon this basis, the required material for joists, increases at a greater 
 ratio than the increase in width of panels. The supporting power of a 
 joist or beam of a given form of section, or a given ratio of depth to 
 thickness, is as the cube of the depth directly, and the length (I) in 
 versely ; or, as -y. If there be two joists of depths respectively as d and x, 
 and lengths as I and nl, their supporting powers P, P 7 , for load simi 
 larly applied, will be as-j- to ~. But the power should be as the load ; 
 in other words, as the length of joists. Hence we have the proportion, 
 -.- : . : : I : nl, whence, nd* and x = dn$ . Now n is as the length 
 
 of joists, and the depth, therefore, is as the f power of the length, and 
 the cross-section, and consequently the required material, .as the ^ 
 power of the length. Hence, if m represent the material for joists 
 with panels of a given width, the material for panels twice as wide, 
 will be represented by m X x j /2*=m^ r 16 = m2.52. But this is rather 
 anticipating the subject of lateral, or transverse strength of beams. 
 
WIDTH OF PANEL. Ill 
 
 length of joists. Hence, if we could find the point 
 where the cost of connections (consisting of extra 
 material in the lappings of parts, connecting pins, 
 screws and nuts, and enlarged sections at the ends of 
 members, together with the extra labor in forming the 
 connections), becomes equal to the whole cost of ma 
 terial in joists or stringers ; that would seem to indi 
 cate the proper width of panel, or value of A, as far as 
 depends upon these elements. 
 
 But aside from the fact that our data upon this 
 question are so few and so imperfect, that it would be 
 mere charlatanism to attempt to reduce the matter to 
 a mathematical formula, the occasions would be so 
 rare which would admit of the application of such 
 formula, without incurring disadvantages in other re 
 spects, such as improper inclination of diagonals, un 
 suitable ratio of length to depth of truss, &c., that no 
 attempt will be here made to give any thing more 
 definite upon thfl point, than to refer to the best pre 
 cedents and practice of the times; which seem to con 
 fine the range of width of panel mostly within the 
 limits of 8 and 15 feet. 
 
 Within these limits, and seldom reaching either ex 
 treme, plans may be adapted to any of the ordinary 
 lengths of span, by adopting the single or double can- 
 celated trusses, Figs. 12 and 13, or 18 and 19, or the 
 arch truss Fig. 11, (which unquestionably contain the 
 essential principles and combinations of the best trusses 
 in use), according to length of span, the purposes of 
 the bridges respectively, or the taste and judgment of 
 engineers and builders. 
 
112 BRIDGE BUILDING. 
 
 ARCH BRIDGES. 
 
 LXIX. An arch bridge may be distinguished from 
 an Arch Truss Bridge, by the fact that in the former, the 
 bridge and its load are sustained by one or more arches 
 without chords ; and, consequently, requiring external 
 means to withstand the horizontal thrust or action of 
 the arches at either end ; which means are afforded by 
 heavy abutments and piers, in case of erect arches, and 
 by towers and anchorage in the earth, in case of in 
 verted, or suspension arches. 
 
 It is not the purpose of this work to treat elaborately 
 of either of these forms of bridging, as the author s 
 experience and investigations have been mostly con 
 fined to truss bridge construction. But as some of the 
 largest bridge enterprises and achievements of the age 
 are designed upon the principles hiMje referred to, a 
 brief notice of the subject, and some of the conditions 
 affecting the use of these classes of bridges, may be 
 regarded as desirable in a work of this kind. 
 
 Suspension, or inverted arch bridges of very great 
 spans, have long been in use, both in this and foreign 
 countries ; and the capabilities of that system have been 
 pretty thoroughly tested experimentally and practically. 
 
 But bridges supported by erect metallic arches, have 
 hitherto been confined to structures of moderate span. 
 Within a few years, however, the magnificent enter 
 prise of spanning the Mississippi at St. Louis by three 
 noble stretches of about 500 feet each, supported each 
 by four arched ribs of cast steel, has been undertaken 
 and is understood to be in rapid process of execution. 
 The interest naturally felt in the progress and final 
 result of this grand enterprise, by students and practi- 
 
ARCH BRIDGES. 
 
 113 
 
 tioners in the engineering profession, will perhaps aid 
 in rendering the following brief, and somewhat super 
 ficial discussion acceptable. 
 
 LXX. An erect arch subjected to the action of 
 weight, or vertical pressure, is in a condition of unsta 
 ble equilibrium ; and can only stand while the weight 
 is so distributed that all the forces acting at each point 
 of its length, are in equilibrio. To illustrate this, we 
 may assume the arch to be composed of short straight 
 segments meeting and forming certain angles with 
 one another, and the weights applied at the angular 
 points. 
 
 A weight at <?, Fig. 22, for instance, acts vertically, 
 and, if dc be produced till it meet the vertical drawn 
 
 FIG. 22. 
 
 L 
 
 through b in w, then the triangle bcm has its sides 
 respectively parallel with the directions of three forces 
 acting at the point <?; namely, the weight at the point 
 c, the thrust of the segment 6c, and that of dc. Hence, 
 if these three forces be to one another as the sides of 
 said triangle, that is, if the weight (w) : thrust of be : 
 thrust of dc : : bm : be : cm, then they are in equilibrio. 
 If w be greater than is indicated by this proportion, 
 the point c will be depressed, bed approaching nearer 
 and nearer to a straight line, and becoming less and 
 15 
 
114 BRIDGE BUILDING. 
 
 less able to support the weight, and a collapse must 
 result. 
 
 If w be less than the above proportion indicates, it 
 will be unable to withstand the upward tendency of 
 the point c, due to the thrust of be and dc (or, to the 
 preponderance of the vertical thrust of 6c, over that of 
 dc), the point c will rise, the upward tendency becom 
 ing greater and greater, and the result will be a col 
 lapse, as before. The same reasoning, and the same 
 inference, apply to any other angular point, as at c. 
 It is, therefore, only in theory that such a thing as an 
 equilibrated erect arch, can exist. The arch is here 
 considered as a geometrical line without breadth or 
 thickness. 
 
 It is this property of instability, in the Erect Arch, 
 that the diagonals in the Arch Truss, [Figs. 5 and 11] 
 are designed to obviate, and to enable the arch to re 
 tain its form and stability under a variable load. 
 
 LXXI. Still, in theory, an arch maybe in equilibrio 
 with any given distribution of load, whenever the points 
 a, 6, c, etc., are so situated that the sides of the trian 
 gle bcm, for instance, formed by a vertical with lines 
 respectively coinciding or parallel with the two seg 
 ments meeting at c, are proportional to the 3 forces 
 acting at c, as above stated, and so at the other angu 
 lar points of the figure. 
 
 To construct an equilibrated arch adapted to a given 
 distribution of load, consisting of determinate weights 
 at given horizontal intervals between the extremities 
 of the arch, we may proceed as follows : 
 
 Draw a horizontal line representing the chord ak, 
 
 and upon the vertical Cft, erected from its centre, take 
 
 . Cf equal to the required versed sine, or depth of the 
 
I 
 
 ARCH BRIDGES. 115 
 
 arch at the centre. Also, take//=Qr, and erect verti 
 cals upon the chord, at all the points at which the load 
 is applied, and join a and t. 
 
 Then, if the load be uniformly distributed (horizon 
 tally) upon the arch, we have seen, [LII], the arch 
 should be a parabola, to which of course, at is tangent 
 at the extremity, a. But, regarding ab as tangent to 
 the curve at r, half way between a and b (horizontally), 
 we seek the abscissa /$, which is to Cf: : rs 2 : aC 2 . 
 Then, taking the distance of/w=/s, au is tangent to the 
 curve at r, and coincides with the first segment (ab) of 
 the arch. (These segments are supposed to be so 
 short, that the tangent and curve may be regarded as 
 essentially coinciding, for the length of a single segment) . 
 
 Now, the thrust of ab, is to the whole weight bear 
 ing at a, as ru to us ; and, erecting the vertical al, such 
 that al : ab: : weight at b : thrust of a, and drawing 
 the straight line Ibc, cutting the second vertical in c, we 
 have be for the second segment of the arch, being in 
 the line of 6, which represents the resultant of the two 
 forces acting at b ; namely the weight at b, and the 
 thrust of ab. 
 
 In like manner, take 6m, representing the weight at 
 c, and the straight line mcd, meeting the third vertical 
 in dj gives cd as the third segment of the arch. 
 
 Kepeat the same operation for each of the succeed 
 ing segments de, ef, &c., till the arch is completed, and 
 it is obvious that the forces acting at each of the several 
 angular points 6, c, d, &c., are in equilibrio ; and that 
 the arch throughout is, theoretically, in a state of 
 equilibrium. 
 
 We may vary this process so as to secure greater 
 accuracy of construction, in the following manner : 
 
116 BRIDGE BUILDING. 
 
 Producing Ibc till it meets Ct in y, we see that abl and 
 ubv are similar triangles, and al : uv : : horizontal dis 
 tance of I : horizontal distance of v, from the point 
 b. Hence, we may take the point v instead of the point 
 I, by which to establish the position of the line be, and 
 thereby secure greater relative accuracy of measure 
 ment. 
 
 So may we also take m , or IV instead of bm, to de 
 termine the line cd. By this means we multiply the 
 small spaces al, bm, &c., and diminish the amount of 
 error in measurement, and if the angular points, or 
 nodes be at uniform horizontal distances, the process is 
 very simple. 
 
 LXXII. We have assumed, in describing the arch 
 a, 6, c, <Y, &c., a uniform distribution of load, horizon 
 tally. But the general process is obviously the same 
 for an unequal distribution, after locating the first seg 
 ment ob ; which we may do by first ascertaining the 
 amount of bearing at <2, due to the load of the arch. 
 This will be to the whole load, as the distance of the 
 centre of gravity of load from &, horizontally, to the 
 whole chord ak. For instance, if the centre of gravity 
 be halfway between C and A , one quarter of the load 
 bears at a. The weight bearing at #, whatever it be, 
 may be represented by A; and supposing it to exert 
 the same horizontal thrust at a as half the load (W), 
 would do when uniformly distributed, we take u in 
 ft, so that J W : A : : uC: u C* Then au f gives the 
 direction of & , and we proceed in the same manner 
 
 * We may assume any amount of horizontal thrust, and the greater 
 the assumed thrust, with a given load, the less will be the depth of 
 the arch, and vice versa. It is proposed here to construct an equili 
 brated arch a , b, c , dj&c,, of about the same rise at the crown, as the 
 jiormal curve, a, b c, d, &c., has. 
 
ARCH BRIDGES. 117 
 
 as before using the weights given for the several nodes 
 of the arch, to determine the points c , d f , &c. These 
 being connected by straight lines, we have an equili 
 brated arch adapted to the given distribution of load. 
 
 LXXIII. But of course, this arch will not stand 
 under any other disposition of the load. To obviate 
 this difficulty, and to construct an arch which will 
 stand under a variable load, without the chord am? 
 counter-bracing of the arch truss, the device has been 
 adopted, of constructing the arch of such vertical width 
 that all the equilibrated arches or curves, required by 
 all possible distributions of load; may be embraced 
 within the width of the arched rib. Then, if there be 
 sufficient material to oppose and withstand tjie forces 
 liable to act in the lines of said several equilibrated 
 curves, complete vertical stability must result. 
 
 The proper width, or depth of the arched rib, will 
 depend upon the length and versed sine of the arch, 
 as well as the amount and distribution of load ; and 
 the material will act most efficiently, when mostly dis 
 posed in the outer and inner edges, or members of the 
 rib, and connected, either by a full, or an open web, to 
 distribute the action between the outer and inner mem 
 bers, according as the resultant line of action approaches 
 the one or the other of those members. 
 
 The normal form of" the arch should be such as to 
 be in equilibrio under a uniform load,* and hence it 
 will be parabolic, as to the movable load, and the 
 weight of road-way, and catenarian, as to the weight 
 
 * The method above explained, for describing an equilibrated arch, 
 is applicable to all cases where the load, both constant and variable 
 acting on the several parts of the arch, is known, whether it be the 
 normal curve, adapted to a full load, or a distorted curve, suited to an 
 irregular distribution of load. 
 
118 BRIDGE BUILDING. 
 
 of arches (as far as they are uniform in section), and 
 should approach the one or the other form, according 
 to the weight of arches, as compared with the other 
 weight to be supported thereby. 
 
 The distance between outer and inner members, or 
 the width of web, reckoned from centre to centre of 
 those members, should be such that no condition of 
 unequal and partial load, could throw greater action 
 at any point of either member, than the extreme uni 
 form load would throw upon both. 
 
 Let us suppose that the curve a, 5, <?, d, etc., be cen 
 trally between the two members and that dd f , and hh f 
 be the greatest vertical departures, in ward and outward, 
 of any equilibrated curve, from the normal curve a, 6, 
 c, etc. 
 
 Let us further suppose that the thrust of the arch 
 at the points d and A, be } as great under the load act 
 ing in the curve of greatest departure from the normal 
 as the extreme uniform load produces at those points. 
 Then, if the outer and inner members of the rib, be 
 placed at a distance of six times the greatest departure 
 of the distorted from the primary, or central curve, 
 one member will be twice as far from the line of action 
 (at the point of greatest departure), as the other, and 
 the latter will sustain two-thirds of the action, equal 
 to one-half the action of the full load, and the same aa 
 in the latter case. 
 
 If the width of web be less than six times the great 
 est aberration of the distorted curve, the action, under 
 the suppositions above, will be greater upon one mem 
 ber than that due to a full uniform load ; a condition 
 altogether to be avoided. 
 
 A few trials at constructing curves adapted to as 
 sumed possible distributions of load, may determine 
 
ARCH BRIDGES. 119 
 
 satisfactorily what condition gives the curve of great 
 est distortion and the greatest departure from the nor 
 mal ; and the amount of action under that condition, 
 can be readily calculated with sufficient nearness, 
 whence the proper width of web may be deduced. 
 
 LXXIV. The points of the equilibrated curve may 
 be located by calculation, and perhaps with as much 
 ease, and greater accuracy than by construction. 
 
 Suppose Fig. 22 to have a vertical depth, Cf, equal 
 to one of ten equal sections of the chord ak. Having 
 found the length of/tf, in the manner already explained 
 [LXXI], it is known that for a uniform loud at each 
 angle, the vertical reaches of the several segments, 
 begining at the centre, are as the odd numbers, 1, 3, 5, 
 7 and 9 ; and, if we conceive Cf to be divided into 25 
 equal parts (25 being* the sum of these numbers), each 
 of these parts will be equal to 0.04G/, or .04^; and this 
 factor, multiplied by the numbers 1, 3, 5, &c., give the 
 vertical reaches of the respective straight segments, 
 which vertical reaches being substracted successively 
 from v, and successive remainders, show the several 
 verticals to be as follows: At the centre,/, vertical = 
 Cf=v. At e, vertical v .04y = .96y. At d, verti 
 cal = (.96 .12)i? = .84y; at c, vertical = (.84 .2)y = 
 .64*?, and at 6, vertical = (.64 .28)u, = .36v. This es 
 tablishes the normal curve for uniform load. 
 
 Now, supposing the weight of structure to be equal 
 to Iw at each of the angles of the arch, and also, that 
 a movable load of a like weight, w, be acting at each 
 of the five points/, g, h, i,j ; the permanent weight of 
 structure gives a bearing of 4.5w; at a, and the movable 
 weights at /, #, A, &c., give respectively .5w, Aw, .3w, 
 
120 BRIDGE BUILDING. 
 
 .2i#, and ,1?0, together, equal to 1.5w ; making the 
 whole bearing at , equal to 6w;, which is th less than 
 if the same weight were distributed uniformly. 
 
 Then taking Cu f f Cu, and drawing the line au r , 
 (not shown in the diagram), we have the inclination of 
 ab f , the first segment of the required curve, which gives 
 the same horizontal thrust at <z, as the normal curve 
 would exert under the same load uniformly distributed. 
 We find/^ (=/s), by the proportion. 
 
 Cfifs:: 6V (= 6?) : sr 2 (= 4^?~ : : 25*; 2 : 20.25-i; 2 : : v 
 : .81v; and, reducing I.Slv (=Cu), by one-seventh, we 
 obtain GV = 1.5514v. This length is to aC : : A (=610), 
 : horizontal thrust of ab ; that is (making ^=1), 1.5514 
 
 : 5 : : Gw : , 8 ?! , = 19.33i0, = horizontal thrust ab. 
 
 I.ool4 
 
 K ow, if this thrust be represented by J-a(7, = r=l, 
 then w will be represented by a space equal to Trqo> = 
 
 .05173, which is equal to the vertical departure (D), of 
 b c from ab uf. Knowing the value of this departure 
 which, of course, is directly as v, and inversely as a (7), 
 we can locate the points e , d! , e f and/ 7 , by their verti 
 cal distances from au , as follows : The vertical at 6 , is 
 evidently equal to Jxl.5514, = .31026; consequently, 
 the vertical ate = 2x. 31026 .05173 = .56879. Ver 
 tical at d = 3x. 31026 3X.05173 = .77559. Vertical 
 e = 4x. 31026 6X.05173 = .93068, and the vertical at 
 /*, equals 5X.31026 10x.05173 = 1.034, showing that 
 the new curve crosses the normal, between e and/, and 
 / is above/, but not shown. 
 
 Then, if each of the segments 6V, c f d f , &c., be pro 
 duced to meet the indefinite vertical drawn through a, 
 they will evidently cut that line at intervals of D, 2D, 
 3D and 4D together, equal to 10 D, = .5173. Then, 
 
ARCH BRIDGES. 121 
 
 the weight at/ being 1 equal to 2i0, it follows that f g f 
 makes twice the deflection from e f that the latter 
 makes from d e\ that is, equal to 2D in the horizontal 
 distance of It 1 , or 1, or 10D (== .5173), in the distance 
 a (7, or 5. Hence, fg produced, cuts the vertical at , 
 twice as high as e f cuts it, or, at a point 1.0346 above 
 a; being just as high as the point/ ; except a small 
 difference resulting probably from omitted fractions. 
 This shows that f g 1 is horizontal, and tangent to the 
 curve at its vertex. 
 
 It follows that all the weight at/, and at the left of 
 that point, is brought to bear at , and all that at y , 
 and on the ri^ht thereof, bears at k. This affords a 
 
 O * 
 
 check upon our work thus far, as we already knew 
 that the bearing at a was equal to Qw, and we now see 
 that this is made up of ~Lw at each of the four points 
 /, c , d , e , and 2w at / . If/ ^ were not horizontal 
 the arch could not be in equilibrio under the assumed 
 condition of load. 
 
 Now, as we manifestly have for the 4 remaining 
 segments, a vertical reach for each, as the weights 
 they respectively sustain; i. e., equal respectively to 
 2D,4D,6D,and8D; making 20D (=00; altogether, we 
 have only to subtract these quantities successively from 
 Cf (=1.0346), to obtain the lengths of verticals at /* , 
 i y , / ; as follows : 
 
 1.0346 2 x .05173 = .93114 = vert, at li 
 .93114^-4 x. 05173 = .72422= " " i f 
 .72422 6 x. 05173 = .41384= " "/ 
 .41384 8 X .05173 = " " k 
 
 The differences between these lengths of verticals, 
 and those of the normal curve at the same points, show 
 
 16 
 
122 BRIDGE BUILDING. 
 
 the aberrations vertically, of the distorted, from the nor 
 mal curve, as below. 
 
 Nor. Dist. Below. Above. 
 
 &6 -.86 .81026.04974 " 
 
 CC =.64 .56879=.07121 " 
 
 cM =.84 .77559=. 06441 
 
 eef = .96 .93068=.02952 " 
 
 Dist. Nor. 
 
 ff =1.034 1.00= .034 
 
 #/ =1.034 .96= .07446 
 
 hh = .93114-.84= .09114 
 
 = ,72422 .64= .08422 
 
 j/ = .41384 .36= .05384 
 
 LXXV. From this exhibit, we perceive that the great 
 est vertical aberration externally for the condition of load 
 here assumed, is at M , and equals .091?;, and the great 
 est internally, at cc (or a little to the right of these 
 points in both cases), equal to .071v, traversing a zone 
 equal in width to .162y. nearly J of the versed sine of 
 the normal curve. 
 
 Now, we have seen that the horizontal thrust of the 
 arch for a gross load of 14w, equals 19.23w, with the 
 assumed proportion of versed sine to span, as 1 to 10, 
 . whether upon the normal or the distorted curve ; and, 
 the thrust being evidently as the gross load, other 
 things the same, it follows that, with the full gross 
 load of 18w, or 2w at each angle, the thrust would be 
 to 19.33w? as 9 to 7. Hence the load, as above assumed, 
 produces J, or 77^ per cent of the maximum thrust 
 under the full uniform load. 
 
 The uniform load being supposed to act equally upon 
 the outer and inner members of the rib, the action of 
 50 per cent is due to each; and, in order that neither 
 
ARCH BRIDGES. 123 
 
 member, at tbe nearest approach to the equilibrated 
 curve, may be subjected to greater stress than under 
 the greatest uniform load, the web. should be so wide 
 that (assuming the outward and inward aberrations to 
 be each equal to the mean of .081v, and putting x = 
 width of web), x: Jo:+.081v : : 77.7 : 50. Whence 50z 
 =38.88z+77.7x.081w; and z=.557tf. 
 But this value of a: being equal to the distance verti 
 cally across the web between c and d, or between h and 
 f, is greater than the distance square across, about in the 
 ratio of distance from a to/, to the line aG, in this case 
 as-v/26 : 5. The actual width of web, therefore, is only 
 .545^, still considerably more than half the versed sine 
 Of. 
 
 The condition of load here supposed, may or may 
 not be the one requiring the greatest distortion of the 
 equilibrated curve. The case has been assumed to 
 illustrate this discussion, as it seemed likely to be near 
 the condition requiring the greatest width of web ; 
 and I leave this part of the subject, without attempt 
 ing a more general and determinate solution of the 
 question. 
 
 LXXVI. The movable load has been taken as only 
 equal to the weight of superstructure, upon the suppo 
 sition that this style of bridging would seldom be 
 adopted, except for very considerable lengths of span, 
 where the weight of superstructure is relatively greater 
 than in case of short spans. 
 
 This double arch, as here under consideration, con 
 sisting of an outer and an inner curved member, con 
 nected by a web, in order to act most efficiently should 
 be so adjusted that the outer and inner members may 
 be subjected to equal action under a full maximum, 
 
124 BRIDGE BUILDING. 
 
 uniform load. Hence, the normal and equilibrated 
 curves, representing the line of the resultant of forecs 
 acting upon the arch, have been assumed as terminat 
 ing at each end, at points centrally between the ex 
 tremities of the outer and inner curved members. 
 
 It might seem possible that the distorted curve 
 adapted to the above assumed condition of load, might 
 so fall as to recross the normal between the points tff 
 greatest departure and the ends, and thus diminish the 
 extent of aberration, and the necessary width of web. 
 If the curve a, 6 , <? , etc., be turned upon its centre, by 
 raising the end at a, by f rc/s of the greatest departure, 
 that is, by -f x.081v,=.054?;, the aberration half way 
 between a and/, where it is at or near its maximum 
 point, would be reduced by .027?;, and become .054y 
 just the same as at the end. The other end would drop 
 to the same extent, and would reduce the outward 
 aberration in the same degree. This, of course, would 
 be the least possible extent of aberration ; and if we 
 could rely upon the resultant stress following this curve 
 in such a position, it would enable us to diminish the 
 width of web to .364y. 
 
 But there seems to be no obvious reason why we 
 should assume the equilibrated curve to take the posi 
 tion just described, rather than one with the left end 
 below a, and the other above &, thus increasing instead 
 of diminishing the aberration. Hence, in the case of 
 an arch ribbed bridge, liable to a movable load equal to 
 the weight of structure, foot for foot, upon the whole or 
 any part of its length, if the web of the ribs be less 
 than 36-100th, of the versed sine (Cf Fig 22), certainly, 
 and if less than 54-100ths probably, the material in the 
 principal members is liable to greater strain in some 
 parts, under a partial, than under the extreme load ; 
 
ARCH BRIDGES. 125 
 
 which would be decidedly an unfavorable condition, 
 with regard to economy. 
 
 LXXVII. The operation of the web in distributing 
 the action upon the outer and inner curved members 
 of the rib, and transferring it from one to the other, 
 may be understood by the diagram Fig. 23, exhibiting 
 said curved members, connected by a web consisting 
 of a simple system of diagonals, capable of acting by 
 thrust or tension as may be required. 
 
 The normal curve is represented parallel with, and 
 midway between the curved members ; and the equili- 
 
 FIG. 23 
 
 brated curve is represented as crossing the normal 
 near/, meeting it again at a and A:, at the ends; and 
 having its greatest aberrations at c and A. It is mani 
 fest that the action of the outer member at ?, is to that 
 of the inner one atj, asJA to ih (inversely as their dis 
 tances from the distorted curve), and that the action 
 upon the outer diminishes, while that of the inner one 
 increases each way from i andj, until the action upon 
 the two becomes equal at the meeting of the curves at 
 k, and at the crossing point near/. Hence the dia 
 gonals leaning toward the point i must act by thrust, 
 while those leaning fromj, act by tension. On the 
 contrary at d, where the greatest compression is upon 
 the inner member, and diminishes each way, the dia 
 gonals leaning from c, act by thrust, while those lean- 
 
126 BRIDGE BUILDING. 
 
 ing toward c, act by tension. The tension diagonals 
 are represented by single, and the thrust diagonals, by 
 double lines. 
 
 But the action changes more or less with every 
 change in the position of the load, and if the load were 
 reversed upon the two halves of the arch, each dia 
 gonal here represented as acting by thrust, would then 
 act by tension, and vice versa. 
 
 Now, assuming that dc = Jce, and that the action 
 upon the inner member at this point equals twice that 
 of the outer one, it follows, since the action should be 
 come equal upon the two at , that of the whole 
 thrust of the rib must be transferred from the inner to 
 the outer member between c and a, by the thrust and 
 pull of diagonals, exerted in the direction of the normal 
 curve ; the action accumulating and increasing upon 
 successive diagonals each way from c, and in like 
 manner from k. 
 
 The action of diagonals is still further affected by the 
 transfer of the action of load, from the outer to the inner 
 member ; the load being first applied directly to the outer 
 curved member. Hence it becomes a somewhat com 
 plicated problem to determine the maximum action 
 of diagonals ; especially as the complication becomes 
 increased by taking into account the 
 
 
 EFFECTS OF TEMPERATURE. 
 
 LXXVIIT. The expansion and contraction of metallic 
 arches without chords, the ends remaining fixed as to 
 position and distance asunder, must obviously cause 
 the intermediate portions to rise and fall with -the 
 increase and decrease of temperature. 
 
 The outer and inner members, if parallel, being 
 similar concentric arcs, will rise and fall, by the same 
 
EFFECTS OF TEMPERATURE. 127 
 
 changes of temperature, proportionally to their respec 
 tive radii ;* the outer one undergoing the greater ver 
 tical change, whence, it must follow that in warm 
 weather the outer, and in cold weather the inner 
 member sustains the greater relative compression , a 
 result for which there appears to be no obvious remedy, 
 except by balancing the end bearings upon pivots at a 
 and k ; which would allow the two curved members to 
 adjust themselves to an equal action upon the two. 
 Or, if the curves be formed upon the same radius, and 
 of equal length, they would rise and fall alike, and the 
 distance across the web vertically, would be the same 
 at all parts of the arch. 
 
 In this case, as in all others, of the arched rib, the 
 depression of the arch, whether from reduction of tem 
 perature, or the action of load, would be attended by 
 increased thrust action, or diminished tension action 
 upon diagonals less inclined from the vertical position, 
 and the reverse of action, upon those more inclined. 
 
 The absolute rise or fall of an arch, resulting from 
 a given change of temperature, may, without essential 
 error, be regarded as proportional to the change in the 
 length of a circular arch of the same span and depth 
 (from chord to vertex), within the limits of change 
 produced by temperature ; and, may be found by the 
 following process : 
 
 Divide the square of the half chord by the depth of 
 arch (i?), add the divisor to the quotient, and half the 
 sum equals the radius. Divide the half-chord by the 
 radius, to get the natural sine of half the arc ; find 
 in the table of giatural sines, the angle corresponding 
 
 * The curves not being supposed to be circular arcs, it is not strictly 
 correct to speak of their radii, but the meaning will be comprehended. 
 
128 BRIDGE BUILDING. 
 
 with the sine thus found, and double that angle, for 
 the number of degrees in the arc. Multiply the num 
 ber of degrees (reducing minutes and seconds to the 
 decimal of a degree), by .01745329 (= length of a de 
 gree, radius being equal to 1), for the length of the arc. 
 
 Then, in the same manner, find the length of an arc 
 upon the same chord, and with a depth (v r ) one or two 
 per cent greater or less than v ; and, the difference in 
 length of arcs thus found, is to the difference between 
 v and v , as the change in length of arch due to the 
 given change of temperature, to the rise or fall of the 
 arch, resulting from such change. 
 
 By applying this rule to a specific case, we can the 
 better appreciate the importance of the effects of change 
 of temperature upon this species of arched ribs. If we 
 assume an arch of 500 feet chord and 50 feet depth, =r, 
 we find the length of arc to be 513.25 //. The length of 
 an arc of the same span, and a depth (v f ) = 51 /., is 
 513.715//., the difference being 0.465/if. The expan 
 sion of steel for a change of 110 Fahrenheit, is 
 .0007271 x length (513.25), = .37318. We have, there 
 fore, .465 : 1ft. : : .37318 : .8025ft. = rise or fall of the 
 arch in the centre, resulting from a change of 110. 
 
 Regarding this rise in the centre as the abscissa of 
 a parabola, and the half chord as the corresponding 
 ordinate, the rise at any other point of the curve is 
 equal to the difference between .8025, and the abscissa 
 answering to the ordinate of the given point 
 
 Suppose the point be 10 feet from the end, and the 
 ordinate, of course, 240/2., we have, 250 2 : 240 2 : : .8025 
 : .7395 = abscissa for the given point , whence, the 
 rise at that point, equals .8025 .7395 = .063/if. 
 
EFFECTS OF TEMPERATURE. 
 
 129 
 
 Fio. 24. 
 
 Let Fig. 24 represent the end portion of the arch, abe 
 the upper, and gc the lower member, ag and be the 
 
 width of web, =12 . 6, with a 
 horizontal reach of 10 , equals 
 10.75 . Then, bg being re 
 garded as a rectangle, the 
 diagonal ac= 16.1ft and the 
 temperature being raisedllO , 
 the points b and c rise to 6 and 
 c , 66 being equal to the ver 
 tical rise multiplied by the 
 cosine of the angle abd, i. e., 
 equal to .062 X cosine abd. 
 This angle is a little over 22, and its cosine about .93 
 whence bb **. 058ft, =<?c . Joining a with c , and draw 
 ing c f at right angles with ac, and ac r (as these lines 
 are essentially parallel), we have c/,=cc x sin. acb=cc 
 x =. 038ft, = the contraction required to take place 
 in the length of the diagonal ac, to accommodate a 
 shange of 110 in temperature. 
 
 In the mean time the point e rises to e , the distance 
 ee being equal to .1147, so that c e f is extended about 
 the same as ac is contracted ; a change equal to what 
 would be produced by a force of 70,000 Bbs to the square 
 inch of cross section. 
 
 If the normal length of the diagonals be adjusted for 
 a medium temperature, the change would be half the 
 above amount each way, or equal to that produced by 
 35,000 ft)s to the inch. 
 
 Succeeding diagonals toward the centre would be 
 affected in a similar manner, though in a less degree ; 
 and the consequence must be an accumulation of thrust 
 or compression upon the inner member toward the 
 centre, and the outer one toward the ends, upon a rise 
 17 
 
130 BRIDGE BUILDING. 
 
 of temperature, and the reverse on a fall below the 
 normal point. 
 
 THE WIDTH OF WEB. 
 
 LXXXIX. For an arch of 500 ft. chord, and 50 foot 
 depth. We have seen that, with a load as assumed 
 [LXXIV], with reference to Fig. 22, the aggregate aber 
 ration outward and inward, traverses a zone of .162i ? , 
 equal in this case, to .162 x 50 = 8.1 ft. If the web, 
 therefore, be 8.1 feet wide between centres of curved 
 members, the equilibrated curve will reach the centre 
 of said members at the points ot greatest aberration, 
 both ways, and the whole thrust at these points, will fall 
 upon a single member, producing as we have already 
 seen, 77 fa per cent of the amount of thrust due to a 
 maximum uniform load ; being over 55 per cent more 
 stress under a partial than under a full load. 
 
 Again, suppose the web to be 12 feet wide. The 
 distorted curve would approach within two feet of the 
 outer and inner curved members, throwing upon one 
 member at one point, and upon the opposite member 
 at another point, almost 30 per cent more action than 
 what is produced by the full maximum load. It was 
 shown moreover [LXXV] that nothing short of .545r= 
 .545x50=27.25 feet width of web, could be relied on to 
 give as small a stress upon the curved members in this 
 particular case of a partial, as that produced by a full 
 maximum load. 
 
 This would be an inconvenient, and an expensive 
 width of web, and probably a less width would be pre 
 ferable, even with a greater occasional stress upon the 
 curved members which might be enlarged in section 
 in parts liable to the greater stress. But I shall not 
 undertake at this time, to determine the exact optimum. 
 
BRIDGE MATERIALS. 131 
 
 Finally, considering the difficulty of securing the 
 most efficient thrust action of the curved members of 
 the arch, the serious disturbances as to the action of 
 the diagonals composing the web system, occasioned 
 by changes of the temperature, together with the extra 
 weight and strength of piers and abutments to with 
 stand the horizontal thrust of the arches, it seems rea 
 sonable to conclude that the erect metallic arch bridge 
 will only be adopted under rare and peculiar circum 
 stances ; and that in such cases, the plans should be 
 subjected to especial examination and investigation. 
 
 Truss bridges possess the advantage of having all 
 the forces in operation, except the vertical action of 
 weight, and the opposite resistance of the end supports 
 resisted by means of members contained within the 
 structures themselves, and composed of materials of so 
 nearly uniform expansibility by heat, that no important 
 disturbance in the relations of the different members, 
 can be produced by changes of temperature. Plans, 
 also, may be so arranged as to secure a near approxi 
 mation to uniform maximum stress upon all the parts ; 
 at least, to a much greater degree than seems practica 
 ble in the case of the arch without chords. 
 
132 BRIDGE BUILDING. 
 
 BRIDGE MATERIALS. 
 
 LXXX. Having discussed the general principles 
 and relative characters and merits of different plans 
 and forms of bridge trusses, and their proper propor 
 tions, particular and general, the question as to the 
 best materials for the purposes of bridge construction 
 may properly be considered. 
 
 We have seen that the materials of a bridge truss 
 are principally subjected to two kinds of action, that 
 of tension, and that of compression. Lateral, or trans 
 verse action should be avoided in the principal parts 
 and members of the truss. 
 
 It is obvious then, that those materials best calcu 
 lated to resist these kinds of force respectively, should, 
 when practicable without sacrifice of economy, be em 
 ployed in the situations where those forces are respect 
 ively exerted. For instance, when the diagonals act 
 by tension, the upper chord (or the arch, in case of 
 the arch truss), and the verticals, should be composed 
 of the material best adapted to the sustaining of a com- 
 pressive force, while the lower chord and the diagonals, 
 should be of the.best material for sustaining tension. 
 
 "Wood and iron are the only materials that have been 
 employed in the construction of bridge superstructures 
 to an extent worthy of notice ; and it seems reasonable to 
 conclude that on these we must place our dependence. 
 
 Cast iron resists a greater compressive force than 
 any other substance whose cost will admit of its being 
 used as a building material. Steel has a greater power 
 of resistance, but its cost precludes its employment as 
 
BRIDGE MATERIALS. 133 
 
 a material for building purposes.* Wrought iron re 
 sists compression nearly equally with cast iron. But 
 its cost is twice as great, which gives the cast iron a 
 decided advantage. 
 
 On the other hand, wrought iron resists a tensile force 
 nearly four times as well as cast iron, and 12 or 15 
 times as well as wood, bulk for bulk. 
 
 Not only are these the strongest materials, but they 
 are also the most durable. In fact, with proper pre 
 cautions, they may be regarded as almost imperishable. 
 
 It would seem then, that wrought iron for tension, 
 and cast iron for compression, were the best materials 
 that could be employed in building bridges. But 
 wood, though greatly inferior in strength and dura 
 bility, is much cheaper and lighter, so that, making up 
 with quantity for want of strength, and by frequent re 
 newals, its want of durability, it has hitherto been 
 almost universally used in this country for bridge 
 building; and, in the scarcity of mezns, and the un 
 settled state of things in anew country, where improve 
 ments are necessarily, to a great extent, of a temporary 
 character, this is undoubtedly the most economical 
 material for the purpose. 
 
 But it is believed that the state of things has now 
 assumed that degree of settled permanency in many 
 parts of this country, and available means have accu 
 mulated to that extent which renders it consistent with 
 true economy to give a character of greater permanence 
 to our improvements ; and, in the erection of import 
 ant works, to have more reference to durability, even 
 at the cost of a greater present outlay. In this view 
 
 * This remark, made originally some twenty-five years ago, may re 
 quire some modification at the present time, when steel is being em 
 ployed extensively for rail way track, and in some important arch and 
 suspension bridges ; but not in truss bridges, to the writer s knowledge. 
 
134 BRIDGE BUILDING. 
 
 of the subject, it seems highly probable that one of the 
 channels in which this tendency of things will develop 
 itself, will be in the extensive employment of iron in 
 the construction of important bridges. With this im 
 pression, I proceed to some general comparisons as to 
 the relative cost and economy of wood and iron as 
 materials for bridges. 
 
 LXXXI. The power of cast iron to resist compres 
 sion, equals some twenty times that of wood ; conse 
 quently, it will only require one twentieth as much of 
 the former to withstand a given force, provided it can 
 be put into a form in which its liability to flexure, and 
 yielding laterally, is not greater than that of wood. 
 This may be accomplished in part, by giving the iron 
 a hollow form, so as to make the diameter of the pieces 
 approximate to an equality with twenty times the same 
 amount of wood, which must generally be used in a 
 simple rectangular, or cylindrical form of section. 
 
 Assuming, then, that a cubic foot of cast iron will 
 do the same work as 15 cubic feet of wood (after mak 
 ing allowance for the necessarily smaller diameter of 
 the iron), we can institute a comparison which would 
 seem, upon the surface, to show the relative economy 
 of the two materials. 
 
 A cubic foot of cast iron, manufactured for the work 
 will cost about $13.00. 15 cubic feet of wood in abridge 
 will cost, say $6.00. Whence it appears that the cast 
 iron is more than twice as expensive, in the first outlay, 
 for sustaining a compressive force, as wood. 
 
 Again a cubic foot of wrought iron in the work, say 
 450 ft> at 7 Jets. =$34.00. 
 
 Wood is about ^ as strong as iron. But about one- 
 half of its fibres must be separated in order that the 
 
BRIDGE MATERIALS. 135 
 
 other half may be so connected in the structure, as to 
 be available to their full strength, acting by tension. 
 Hence, it will take some 30 feet to equal one of iron ; 
 for which it will cost, say $12; showing a difference of 
 a little less than three to one ; making the average for 
 both kinds of iron, reckoning equal quantities of each, 
 about 2.6 to 1. 
 
 To offset against this, we have the superior durability 
 of the iron, which, as before observed, may be regarded 
 as imperishable ; whereas, wood requires frequent re 
 newals, at a cost each time, equal to the iirst outlay. 
 Now, the first cost of the iron is sufficient to provide 
 for the first cost of the wood, and nearly two renewals. 
 Besides this, money, though an inanimate substance, 
 is, nevertheless, in these usurious times, made t<> 1 e 
 exceedingly prolific ; insomuch, that with good man 
 agement, it is found to double itself once in ten or 
 twelve years, according to the hardness of face in the 
 lender, or of fortune in the borrower. 
 
 Assuming 5 per cent per annum as the net income 
 of money invested, the term of time in which the 1 ffc 
 dollars saved in the wooden structure, will require to 
 produce,one dollar for renewal, will show the time that 
 wood ought to last, to be equal with iron in economy, 
 
 One dollar and sixty cents at compound interest will 
 yield, at 5 per cent, one dollar in a little less than ten 
 years. Therefore, if an imperishable iron structure 
 cost 2.6 times as much as one of wood, and the latter 
 last but ten years, and money will net 5 per cent, com 
 pound interest, the two materials are nearly upon a par 
 as to economy. 
 
 Experience has shown that wooden bridges, unpro 
 tected by roofing and siding, seldom last with safety 
 over eight years, or thereabouts ; and, the more there 
 
136 BRIDGE BUILDING. 
 
 be expended to increase the durability, the less surplus 
 capital will be left to be invested toward renewals. 
 
 LXXXII. But the above comparison is too super 
 ficial and general to be entitled to a great deal of con 
 fidence, except, perhaps, as it regards the sustaining 
 of a given weight by a simple post, or suspending it by 
 a bar or rod of iron or wood. In the complicated as 
 semblage of pieces forming the superstructure of a 
 bridge, there are numerous other facts and considera 
 tions which materially vary the results. First, there 
 is a difficulty in connecting pieces of timber in such a 
 manner that every part may be proportioned to the 
 strength required of it, to the same extent as can be 
 done with iron. Second, it is frequently necessary to 
 use considerable quantities of iron in bolts and fastenings 
 for putting together a structure of wood requiring great 
 stability. Third, wood soon loses a portion of its 
 strength by partial decay, and consequently, requires 
 additional strength in the beginning, that it may be 
 safe for a time after decay has commenced. 
 
 Hence, but little can be predicated upon the simple 
 general comparison of wood and iron as to strength 
 and cost, relative to the comparative economy of the 
 two materials for bridge building. 
 
 It is only by comparing the results of actual experi 
 ence, or, where this has not been had, by comparing 
 the results of detailed estimates, upon well matured 
 plans, founded on well established principles, that a 
 satisfactory conclusion can be arrived at. 
 
 With regard to wooden bridges, much experience has 
 been had, and the reasonable presumption is, that a good 
 degree of economy has been attained in their construc 
 tion. But the idea of building iron bridges in this 
 
BRIDGE MATERIALS. 137 
 
 country, is of recent date, and but little has been experi 
 mentally proved in relation, to their cost and qualities. 
 
 LXXXIII. This much, however, my own experience 
 has demonstrated. Having received Letters Patent for 
 an " Iron Truss Bridge," upon the arch truss plan, and 
 constructed two bridges thereon, over the Enlarged 
 Erie Canal (of 72 and 80 feet spans), one of which has 
 been in use for six years, it may be regarded as a de 
 monstrated fact, that bridges may be sustained by 
 iron trusses. It has also been shown that the cost of 
 the above class of bridges, is only about 25 per cent 
 more than the same class of bridges of wood, as hereto 
 fore built, under the most favorable circumstances, upon 
 the Erie Canal. That the iron portion, constituting 
 some three-fourths of the whole, as regards expense, 
 in the iron bridge, gives fair promise of enduring for 
 ages, while the wooden structure can only be relied on 
 to last eight or ten years. 
 
 Upon these facts, experimentally established, I found 
 the following comparison : 
 
 A common road bridge of 72/. span (the usual 
 length for the enlarged Erie Canal), will cost, with 
 iron trusses : 
 
 For 7,000 ibs. of cast iron at Sets., $210. 
 
 " 6,000 " " wrought iron, manufactured 
 
 for the work, at 7cts., 420. 
 
 " Timber, labor and painting, 230. 
 
 " Superintendence and profit, 80. 
 
 "Whole first cost, $940. 
 
 $175 will renew the perishable part once in 
 9 years, to produce which, at 5 per cent 
 compound interest will require capital of, 320. 
 
 Total for a perpetual maintenance, $1,260. 
 18 
 
138 BRIDGE BUILDING. 
 
 "With wooden trusses, fastened with iron 
 
 for timber, labor, paint and profit, $550 
 " 2,000 Sbs. of iron fastenings, 150. 
 
 Whole first cost, 700. 
 
 (Some have cost 1000, or 12,000, and taken 
 
 3 to 4 thousand pounds of iron) 
 
 To renew $550 worth of perishable material 
 
 once in 9 years, will require, at 5 per 
 
 cent, compound interest, 1,000. 
 
 Total for perpetual maintenance, 1,700. 
 
 The reason of the apparent difference between this 
 result, and that arrived at from the general comparison 
 of the cost, &c., of wood and iron, is, that the bridges 
 here referred to, have been constructed with a very 
 large amount of iron fastenings, and with large quanti 
 ties of casing and painting for protection and appear 
 ance. Were the comparison confined strictly to the 
 expense of timber work, in the sustaining parts of the 
 trusses, the result would be found not to differ so es 
 sentially from that of the general comparison. 
 
 The above estimate of 700, for the first cost of a 
 72 foot wooden bridge, though considerably below the 
 average cost of canal bridges of that description, is 
 nevertheless believed to be greatly above the minimum 
 for which bridges may be built, dispensing with the 
 parts which are not essential to strength. 
 
 It is probable that bridges may be built for 500, as 
 about the minimum, of equal strength and convenience, 
 and nearly the same durability, as those hitherto built 
 upon the Erie Canal Enlargement at a cost of from 
 800 to 1,000 dollars. Upon this supposition, which 
 may be regarded as an extreme case in favor of wood, 
 the comparison will stand thus : 
 
BRIDGE MATERIALS. 139 
 
 First cost of wooden, structure, $500 
 
 Capital invested at 5 per cent to produce $500 
 
 once in 9 years for renewal, 909 
 
 Total for perpetual maintenance, $1409 
 
 The same for iron structure, as above, 1260 
 
 Balance in favor of the iron bridge, $149 
 
 Finally, since theoretical calculation and general 
 comparison show a probable advantage, for a long term 
 of time, and experience, as far as it has gone, shows a 
 decided advantage in favor of iron, it would seem very 
 unwise to discard the latter, without at least a fair 
 trial of its merits. If in the first essays at iron bridge 
 building, the iron bridge has competed so successfully 
 with wooden bridges, improved by the experience of 
 ages, may not the most satisfactory results be antici 
 pated from an equal degree of experience in the con 
 struction and use of iron bridges ? 
 
 LXXXIV. Presuming the affirmative to be the 
 only rational answer to the above question, I have ar 
 ranged the details of plans for carrying into practice 
 the preceding principles and suggestions in the con 
 struction of rail road bridges of iron. 
 
 I have also made careful detailed estimates of the 
 expense of bridges of different dimensions and in dif 
 ferent circumstances, some of the more general results 
 of which I will here state. 
 
 In proportioning the parts of a rail road bridge, 1 
 have assumed that it may be exposed to a load of 2,000ft>s. 
 per foot run, for the whole, or any part of its length, in 
 addition to its own weight; and in case of tension, have 
 allowed one square inch cross section of wrought iron 
 for every 10,000 ft>s. of the maximum strain produced 
 
140 BRIDGE BUILDING. 
 
 upon every part by such weights, acting by dead pres 
 sure. In case of thrust, or crushing force, I have al 
 lowed one square inch cross section of cast iron, for 
 every 12,OOOSbs. acting on pieces (mostly in the form oi 
 hollow cylinders), of a length equal to 18 diameters, 
 and a greater amount of material, where the ratio of 
 length to diameter is greater; always having regard 
 to practicability, as well as theoretical proportions, in 
 adjusting the dimensions of the part. 
 
 My estimates, made upon these bases, have fully sa 
 tisfied me that a bridge of 100 feet span, with track 
 upon the top (with wooden cross-beams), will cost about 
 $2,000, or $20 per foot, assuming the present prices 
 of iron (1846), in ordinary circumstances. If the track 
 pass near the bottom of the trusses, the expense will be 
 increased by two or three dollars a foot. 
 
 For a span of 140 feet, by a liberal detailed estimate 
 I make, in round numbers, a cost of 4,000. For 70 
 feet, I estimate a cost of 9 to 10 hundred dollars, ac 
 cording to circumstances. 
 
 Thus it will be seen that actual estimate makes the 
 cost of a single stretch of any length, very nearly as 
 the square of the length, as should be expected from 
 the nature of the case. Hence, knowing the cost of a 
 span of any given length, we readily deduce that of a 
 span of any other length, in similar circumstances, with 
 reliable certainty. 
 
 Now, although my investigations have forced the 
 conviction upon me, that where strong and durable 
 bridges are required, iron should be preferred in their 
 construction, still there is a multitude of cases where 
 wooden structures should be preferred ; especially in 
 sections of country comparatively new, where timber is 
 
PRACTICAL DETAILS. 141 
 
 plenty and capital scarce ; and where improvements 
 must necessarily be of a more temporary character. 
 
 With this view of the subject, I have given consi 
 derable attention to the details of wooden bridges ; and, 
 with a good deal of invest.gation and experiment, have 
 arranged plans which are confidently believed to pos 
 sess important advantages over the plans generally in 
 use. 
 
 The preceding few pages have been transcribed from 
 the author s original and first essay upon bridge build 
 ing; and are introduced here, not on account of any 
 practical value they may possess in the present state of 
 progress in the science of bridge construction. But 
 they may possess some little interest as marking about 
 the starting point of the construction and use of Iron 
 Truss Bridges. 
 
 If the estimates above exhibited, of the cost of iron 
 bridges, appear small and inadequate, under the lights 
 furnished by the experience of a quarter of a century, 
 much allowance may be claimed on account of the 
 change of times and circumstances within the period in 
 question. And, when it is borne in mind that the 
 author actually contracted for, and built iron railroad 
 bridges of 40 and 50 feet span, for $10, and of 146 feet 
 for $30 per foot, the estimates above given may not 
 seem entirely preposterous, although much higher 
 prices are obtained for bridges of like dimensions at 
 the present day. 
 
 PRACTICAL DETAILS. 
 
 LXXXY. In preceding pages I have endeavored to 
 give a short and comprehensive general view of the 
 
142 BRIDGE BUILDING. 
 
 subject, and to ascertain and point out the best general 
 plans and proportions, for the main longitudinal trusses, 
 or side frames of bridges, and the relative stresses ol 
 their several parts. 
 
 The side trusses may be regarded as vastly the most 
 important parts of the structure, and the strength and 
 sufficiency of these being secured, there is much less 
 difficulty in arranging the remaining parts, the forces 
 to which they are exposed being much less than those 
 acting upon the trusses. I propose now to enter more 
 into details, and give such practical explanations and 
 specifications as to the strength of materials, the 
 methods of connecting the several parts or pieces, both 
 in the main trusses, and other parts of the structure, 
 illustrated by the necessary plans and diagrams, as, it 
 is hoped, will enable the young engineer and practi 
 cal builder to proceed with judgment and confidence 
 in this important branch of the profession. 
 
 IRON BRIDGES. 
 STRENGTH OF IRON. 
 
 LXXXVI. Iron has the power of resisting mechani 
 cal forces in several different ways. It may resist forces 
 that tend to stretch it asunder, or forces which tend to 
 compress and crush it; the former producing what is 
 sometimes called a positive, and the latter, a negative 
 strain. It may also be exposed to, and resist forces 
 tending to produce rupture by extending one side of 
 the piece, and compressing the opposite side ; as where 
 a bar of iron supported at the ends, is made to sustain 
 a weight in the middle, which tends to stretch the 
 
IRON BRIDGES. 143 
 
 lower, and compress the upper part. This is called a 
 lateral, or transverse strain. 
 
 Iron may likewise be acted upon by forces tending 
 to force it asunder laterally, in the manner of the ac 
 tion of a pair of shears. This is called a shear strain ; 
 and though less important than either of the preced 
 ing cases, it will frequently have place in bridge work, 
 partially at least, in the action of rivets, and connect 
 ing pins. 
 
 With regard to the simple positive and negative 
 strength of iron it is only necessary for me to state in 
 this place, as the result of a multitude of experiments, 
 that a bar of good wrought iron one inch square, will 
 sustain a positive strain of about 60,0001fos. on the 
 average ; and a negative strain, in pieces not exceeding 
 about twice the least diameter, of 70 or 80 thousand 
 pounds. But in both cases, the metal yields perma 
 nently with much less stress than the amounts here 
 indicated ; and hence, as well as for other considera 
 tions, it can never be safely exposed in practice, to 
 more than a small proportion of these stresses, say 
 from | to J. 
 
 Cast iron resists apositive strain of 15,000 to 30,000fbs. 
 to the square inch, but usually, not over 18,000. But 
 it is seldom relied on to sustain this kind of action es 
 pecially in bridge work, wrought iron being much bet 
 ter adapted to the purpose. On rare occasions, it may 
 perhaps safely be exposed to a strain of 3,000 to4,000ft>s. 
 to the square inch, but should not be used under ten 
 sion strain, when wrought iron can be conveniently 
 substituted. 
 
 Cast iron, however, is capable of resisting a much 
 greater negative strain than wrought iron ; its power 
 of resistance in this respect, being from 80,000 to 
 
144 BRIDGE BUILDING. 
 
 140,000ft>s. ; seldom less than 100.000 to the square 
 inch, in pieces not exceeding in length, twice the least 
 diameter. 
 
 But in pieces of such dimensions as must frequently 
 be employed in bridge work, fracture would take place 
 by lateral deflection, under a much smaller force than 
 what would crush the material. It is therefore neces 
 sary to take into account the length and diameter, as 
 well as the cross-section, in order to determine the 
 amount of compression which a piece of cast iron, or 
 any other material may be relied on to sustain. 
 
 LXXXVII. The cause of lateral deflection resulting 
 from forces applied at the ends, and tending to crush 
 a long piece in the direction of its length, is supposed 
 to be a want of uniformity in the material, and a want 
 of such an adjust of the forces that the line joining the 
 centres of pressure at the two ends, may pass through 
 the centre of resistance in all parts of the piece. 
 
 These elements are liable to considerable variation, 
 and can not be very closely estimated in any case. 
 Therefore the absolute power of resistance for a piece 
 of considerable length, can not be deduced by calcula 
 tion from the simple positive and negative strength of 
 the material, but resort must be had to direct experi 
 ment upon the subject ; and, even wide discrepancies 
 should naturally be expected in the results of experi 
 ment, unless the lengths of pieces experimented upon, 
 be very considerable. 
 
 In respect to pieces, however, having their lengths 
 equal to twenty or more times their diameters, a some, 
 what remarkable degree of uniformity is found in their 
 powers of negative resistance, and the following for 
 mula, deduced theoretically, though not fully sustained 
 
IRON BRIDGES. 145 
 
 by experiment, may be useful in determining approxi 
 mately the relative powers for pieces of similar cross- 
 Bections, but different dimensions. The power of 
 resistance (R), is as the cube of the diameter (d) 9 directly 
 and as the square of the length (I), inversely, that is, 
 R is as -^. 
 
 The reason of this formula may be illustrated with 
 reference to Fig. 25, in which adb represents a post 
 loaded at a, so as to bend it into a curve, of the half 
 of which cd is the versed sine. It is obvious that in 
 this condition, the convex side of the post is exposed 
 to tension (or at least, to less compression YIG. 25. 
 than the other side), and the concave side 
 to compression ; also, that the effect of the 
 load at a, toward breaking the post at d, 
 is as the versed sine cd, which is as the 
 square of ab. But the power of the post 
 to resist rupture transversely, is manifestly ^ 
 as the cross-section of the post (i. e., as .the 
 square of the diameter), multiplied by the 
 diameter. Hence, the power is as the 
 cube of the diameter. Now, the ability of 
 the post to sustain the load at a, is directly 
 as the power to resist rupture, just determined, and 
 inversely as the mechanical advantage with which the 
 load acts, above seen to be as the square of the length 
 of the post. Hence, the formula. 
 
 We shall see as we progress, the relation which this 
 formula seems to bear to the results of experiment. 
 
 The following list of experiments made by the author 
 some 25 years ago, though few in number, and upon 
 a somewhat diminutive scale, nevertheless, may afford 
 some light as to the law governing the resisting power 
 of cast iron in pieces of different lengths, as compared 
 19 
 
146 
 
 BRIDGE BUILDING. 
 
 with their diameters. It may at least enable us the 
 better to appreciate the better lights since shed upon 
 the subject. 
 
 LXXXYIII. EXPERIMENTS UPON THE 
 STRENGTH OP CAST IRON, IN LONG PIECES. 
 
 Ends, flat cones or pyramids. 
 
 NEGATIVE 
 
 JL 
 
 Form 
 
 Inches. 
 
 02 
 
 G 
 
 g 
 
 
 
 
 of 
 
 
 rZ 
 
 .S 
 
 9, 
 
 a 
 
 Remarks. 
 
 c 
 
 section. 
 
 a 
 
 J~ 
 
 ^ 
 
 gj 
 
 5 
 
 
 si 
 
 
 s 
 
 
 ^ 
 
 ^ 
 
 1 
 
 
 1 
 
 Cylinder 
 
 is 
 
 9. 
 
 016 
 
 990 
 
 1002 
 
 Broke T Vn. from centre. 
 
 2 
 
 " 
 
 
 M 
 
 " 
 
 978 
 
 990 
 
 Broke ^ in. from centre. 
 
 8 
 
 Square 
 
 i 
 
 4< 
 
 0.15 
 
 803 
 
 854 
 
 Deflected cornerwise, and flew 
 
 
 
 
 
 
 
 
 out without breaking. 
 
 4 
 
 " 
 
 " 
 
 " 
 
 
 
 914 
 
 938 
 
 Broke in half a minute not 
 
 
 
 
 
 
 
 
 cornerwise, inch from centre. 
 
 5 
 
 Cylinder 
 
 A 
 
 7.1 
 
 0.126 
 
 1417 
 
 1437 
 
 Broke in 3 seconds, ^ in. from 
 
 
 
 
 
 
 
 
 centre. 
 
 6 
 
 M 
 
 
 
 < 
 
 u 
 
 1377 
 
 1397 
 
 Broke || in. from centre. 
 
 
 
 " 
 
 " 
 
 " 
 
 " 
 
 
 
 Piece flattened by flask not 
 
 
 
 
 
 
 
 
 shutting true, and had been 
 
 
 
 
 
 
 
 
 straightened with the hammer 
 
 
 
 
 
 
 
 
 where it broke. 
 
 7 
 
 
 
 < 
 
 4.5 
 
 
 2580 
 
 2580 
 
 Broke in 1 minute into 4 pieces 
 
 
 
 
 
 
 
 
 of nearly equal lengths. 
 
 
 
 
 
 
 
 
 Piece of same as last experiment. 
 
 8 
 
 " 
 
 " 
 
 4.5 
 
 
 3218 
 
 3218 
 
 Broke in \ minute into 3 pieces 
 
 
 
 
 
 
 
 
 in centre, and 1 in. from centre. 
 
 9 
 
 Square 
 
 
 
 4.5 
 
 
 2813 
 
 2838 
 
 Broke in minute, y^ in. from 
 
 
 
 
 
 
 
 
 centre, deflected parallel with 
 
 
 
 
 
 
 
 
 sides. 
 
 From experiments 7 and 8, in the above table, it 
 appears that cast iron will sustain at the extreme, in 
 cylindrical pieces whose lengths equal about 14J dia 
 meters, a negative strain of 41,000 to 51,000fbs to the 
 square inch, say an average of 46,000. Square bars, 
 according to experiment 9, length equal to 18 diame 
 ters (or widths of side), will sustain about 45,000ft>s to 
 the square inch. 
 
IRON BRIDGES. 147 
 
 Now, a hollow cylinder of a thickness not exceeding 
 about Jy of the diameter, according to calculation, has 
 a stiffness transversely, about 50 per cent greater to the 
 square inch than a solid square bar whose side equals 
 in width the diameter of the cylinder. Hence, a hollow 
 cylinder of a length equal to 18 times its diameter, 
 should sustain a negative strain of 67,500 fts. to the 
 square inch. But it should be observed, however, that 
 direct experiments upon the transverse strength of the 
 pieces used in the experiments leading to the results 
 and conclusions above stated, as to negative strength, 
 showed themto possess uncommon strength transversely, 
 even to from 30 to 50 per cent greater than the fair 
 average transverse strength of cast iron ; as will be seen 
 hereafter. It is therefore not considered proper to es 
 timate the strength of hollow cylinders of the propor 
 tions above stated at more than 45,000 or 46,OOOIbs. to 
 the square inch. 
 
 The hollow cylinder is undoubtedly the form best 
 adapted to the sustaining of a negative strain, having 
 equal stiffness in all directions. It is therefore highly 
 desirable that the power of that form of pieces to resist 
 compression, with different lengths, should be ascer 
 tained by a careful and extensive series of experiments. 
 But until that shall have been done, and the results 
 made known, I shall assume the above estimate upon 
 the subject, as probably not very far from the truth ; 
 subject, however, to correction, whenever the facts and 
 evidences shall be obtained, upon which the correction 
 can be founded.* 
 
 In the mean time, since we know* not the exact ratio 
 between the greatest safe practical stress, and the ab- 
 
 * Since the original writing of this paragraph (25 years ago), exten- 
 tensive experiments and investigations have been made, in the direction 
 
148 BRIDGE BUILDING. 
 
 solute strength of iron, and therefore should in practice 
 keep considerably within the limits of probable safety, 
 it becomes a matter of less importance to know the 
 exact absolute strength; though this, of course, is de- 
 sirable. 
 
 LXXXIX. Having decided upon a measure of 
 strength for pieces of a given length, we may properly 
 endeavor to ascertain the rate of variation for different 
 lengths as compared with the diameters. 
 
 It is seen in the table, [LXXXVIII] that two cylindri 
 cal pieces of 9 inches in length, bore the one 990, and 
 the other 9781bs., giving a mean of 984 pounds. 
 
 Now, by the formula -^, the same cylinders reduced 
 to 4.5 inches, should sustain four times as much, or 
 3936ft>s. But, by experiments 7 and 8, we find that 
 they bore only 2,580, and 3,218, a mean of 2,899 
 pounds. Whence it appears that, the diameter being 
 the same, the strength diminishes faster than the length 
 increases, but not so fast as the square of the length 
 increases ; being about half way between the two. In 
 fact, if we examine the results of these experiments 
 throughout, we find that the weights borne by pieces 
 of like cross-sections, whether round or square, were 
 very nearly the arithmetical mean between the results 
 obtained by considering them to be inversely as the 
 simple length, and as the square of the length, succes 
 sively. 
 
 For illustration ; take experiments 1 and 5. If the 
 piece 9 inches long bore 990 ft>s., taking the strength 
 
 here indicated, and ingenious and convenient formulae deduced upon 
 the subject involved, which might perhaps, be profitably substituted 
 for the writer s own crude deductions in this behalf. But, as previously 
 remarked on other occasions, the latter may possess interest as affording 
 a monument upon the line of the march of progress. 
 
IRON BRIDGES. 149 
 
 to be inversely as the length, we have this proportion 
 i : ~ : : 990 : 1,255. Then, taking the strength to be 
 inversely as the square of the length, we have : 1- : ^i_ 
 : : 990 : 1,591. Taking the mean of these results, we 
 find (1,255 + 1,591), + 2 = 1423. This is the weight 
 which, according to the rule, the piece in experiment 
 5 should have borne, and it varies only Gibs, (less than 
 J of one per cent), from what it actually did bear. 
 
 Again, take experiments 1 and 8 ; in which the 
 lengths were as 2 to 1. Supposing the weights to be 
 inversely as the lengths, and as the squares of the 
 lengths successively, and taking the mean of the re- 
 sults,wehave (1,980 + 8,960) -^-2=2,970, which is 248ft>s. 
 less than the weight borne in experiment 8. But it is 
 also 390Sbs. greater than that borne in experiment 7, by 
 a piece of similar form and dimensions, but an inferior 
 specimen. It does not seem, therefore, that the rule 
 is widely at fault. 
 
 The same rule applied to experiments 4 and 9, 
 lengths being also as 2 tol, gives 2,784 Jfos. as the bear 
 ing weight, and 2,814 as breaking weight for No. 9 ; the 
 former varying 71ibs. and the latter 24ft>s. from the 
 weights shown in the table. IsTow, if we observe that 
 the one broke in a quarter of a minute, and the other 
 endured half a minute, it is no extravagance to assume 
 that if No. 9 had been loaded with 24Sbs. less, it would 
 have stood J of a minute longer, giving a result in pre 
 cise accordance with the rule. 
 
 From what precedes, it is believed that the following 
 may be adopted as a safe practical rule for deter 
 mining the power of resistance to compression, for 
 pieces of similar cross-sections, after knowing from 
 experiment, the power of a piece of given dimensions, 
 and similar cross section. 
 
150 BRIDGE BUILDING. 
 
 Rule : Make the power of resistance as ~, and as sue- 
 
 L li 
 
 cessively, and take the mean of the results thus obtained, as 
 the true result ; D representing the diameter (or width of 
 side, in square pieces), and L, the length of the piece. 
 This rule will be probably apply without material 
 error, to pieces of lengths from 15 to 40 times as great 
 as their diameters, and perhaps for greater lengths ; 
 although, in bridge building, greater lengths will sel 
 dom be employed.* But, as the length is reduced to 
 8 or 10 diameters, or less, it is manifest that the power 
 of resistance increases at a less rate than that given in 
 the rule. For, we see by the table of experiments, 
 that a square piece of a length equal to 18 diameters 
 (experiment 9), bore at the rate of 45,0001bs. to the. 
 square inch, which is nearly one-half of the average 
 crushing weight of cast iron, and one-third that of the 
 strongest iron. But according to the rule, a piece of 
 half that length, or equal to 9 diameters, should sustain 
 135,000ibs. which is about the maximum for cast iron ; 
 whereas, experiment shows that the power of resist 
 ance increases with reduction of length, down to about 
 2 diameters. It may, therefore, be recommended to 
 apply the rule above given, to hollow cylindrical, and 
 square pieces above 15, and to solid cylinders, above 
 12 diameters. From those lengths down to 2 diame 
 ters, it cannot lead to material error to estimate an 
 increase of power proportionate to diminution of 
 length, according to the differences between the weights, 
 or resisting powers determined as above, for square 
 pieces and hollow cylinders of 15, and solid cylinders . 
 of 12 diameters in length, and the absolute crushing 
 
 * It is probable that for greater lengths than 40 diameters, the for 
 mula -j alone, would be more nearly sustained than in case of smaller 
 lengths. 
 
IRON BRIDGES. 151 
 
 weight of the iron ; that is, if a square piece whose 
 length equals 15 diameters bear m pounds, and the 
 crushing weight for pieces of 2 diameters be n pounds 
 to obtain the resistance (R), of a piece of (15 a), dia 
 meters in length, take m + ~ (n ?n)=R. 
 
 XC. It has already been remarked that in practice, 
 materials should be exposed to much less strain than 
 their absolute strength is capable of sustaining for a 
 short time. This fact is universally recognized, and 
 the reasons for it, are perhaps, sufficiently obvious ; 
 still it may be proper to mention a few of them in this 
 place. 
 
 First, there is a great want of uniformity in the 
 quality and strength of materials of the same kind, 
 and no degree of precaution can always guard against 
 the employment of those containing defective portions 
 possessing less than the average strength. 
 
 Again, when materials are exposed to a strain, al 
 though it be but a small part of What they can ultimately 
 bear, a change is produced in the arrangement of their 
 particles, from which they are frequently unable fully 
 to recover ; and whence they generally become weak 
 ened, especially if they be repeatedly exposed to such 
 process. Hence, it often happens that a piece is broken 
 with a smaller strain, than it has previously borne 
 without apparent injury. 
 
 Xow, there is no means of estimating exactly the 
 allowance necessary to be made on account either of 
 these facts, as well as, probably, many others. Con 
 sequently, we can not determine with certainty, how 
 much of a given material may be relied on to sustain 
 with safety a given force. We should therefore, incline 
 toward the side of safety, the more strongly, in pro- 
 
152 BRIDGE BUILDING. 
 
 portion as the consequences of a failure would be the 
 more disastrous. The breaking of a bridge is liable, 
 in most cases, to be a serious affair, involving hazard 
 to life and limb, as well as destruction of property. 
 Hence, they should be constructed of such strength 
 asto render failure quite out of the range of probability, 
 if not absolutely impossible. 
 
 XCI. Good wrought iron bars, will not undergo 
 permanent change of form under a tensile strain of less 
 than from 20,000 to 30,000 pounds to the square inch ; 
 and though they will not actually be torn asunder with 
 a stress below 50 or 60 thousand, and often more, to 
 the inch, any elongation would certainly be deleterious 
 to the work containing them, even if not dangerous 
 from liability to fracture. Hence, it is certainly not 
 advisable to expose the material to a stress beyond the 
 lowest limit of complete elasticity. 
 
 In the original predecessor of this work, the tra 
 ditional allowance of 15,000ft>s. to the square inch, was 
 adopted as the tensile stress to which wrought iron 
 might safely be exposed, and beyond which it was 
 deemed improper to rely upon it. No evidences or 
 arguments since that time, have induced a change of 
 opinion in this respect. But in the case of a bridge, 
 there is variety and uncertainty as to the exact amount 
 of load, as well as in relation to the limit of safe strain 
 for the material ; and while it seemed probable that the 
 load of a single track rail road bridge would never ex 
 ceed 2, OOOIbs. to the lineal foot upon any part of its 
 length, still, seeing that rail roads were comparatively 
 a new institution, and iron bridges for rail roads almost 
 unheard of, especially in this country, it was deemed 
 wise, in recommending their introduction, to so adjust 
 
Iiios BRIDGES. 153 
 
 their proportions as to meet almost any possible con 
 tingencies. 
 
 This could be accomplished either by assuming a 
 greater possible load for the bridge, or a lower limit 
 to the stress of materials with the smaller load, with 
 the same ultimate result. And, perhaps the former 
 would have been the more consistent course, as avoid 
 ing the seeming absurdity of the assumption that iron 
 could safely stand a strain of 15,000ft)s. in a common 
 bridge, but only 10,000ft) in a rail road bridge ; and the 
 no less seeming absurdity of assuming that the same 
 material could stand 50 per cent more strain in a bridge 
 composed partly of wood, than in one entirely con 
 structed of iron. Now, instances in great numbers 
 could be pointed out, of rail road bridges of wood and 
 iron, where 2,0001bs. to the lineal foot would produce 
 a stress considerably exceeding 15,000 to the inch upon 
 certain bolts of wrought iron.* 
 
 * The author had occasion several years ago to refer to the following 
 instances in corroboration of the statement above made, in this wise 
 " The best evidence that exists as to the capacity of a material to bear 
 a strain with safety, is derived from experience as to the strain it has 
 been exposed to in works, and conditions similar to those in which it 
 is proposed to employ it, and where it has by long usage, proved itself 
 adequate to the labor required of it. If wrought iron, for example, 
 has been used in railroad bridges for a great number of years, in 
 numerous and repeated instances, where a given load, in addition to 
 the weight of structure, would produce upon it a tension of 15,0001b -i. 
 to the square inch, and has withstood such usage without cases of fail 
 ure not caused by manifest defects in the quality of material, or by 
 casualties which such structures are not expected to be proof against ; 
 it may be fairly assumed to be reasonably safe and reliable in other 
 railroad bridges where; a similar gross load can not produce a greater 
 stress ; and much more so, where a like load can only produce a stress 
 one-half, or two-thirds as great. 
 
 Now, it is provided in the plan herewith presented, that a load of 
 2,00011)8. to the lineal toot upon each pair of rails, on the whole, or 
 any part of the length of the bridge, can not produce upon any part of 
 the wrought iron work in the trusses, a tension exceeding 10,0001bs. 
 to the square inch ; and, to show that such provision is eminently safe 
 and liberal, I proceed to give some examples of what the same mate 
 rial is liable to with the same load in other structures, where long and 
 severe usage has fully proved its sufficiency. 
 
 16 
 
154 
 
 BRIDGE BUILDING. 
 
 A ud yet, it was deemed expedient by the author of 
 this work, in the outset of the introduction of iron rail 
 road bridges, to provide that 2,000ft>s. to the foot upon 
 each pair of tracks, should not give a stress exceeding 
 10,000ft) to the square inch upon any part of the wrought 
 iron work, not from a conviction that the material was 
 unsafe under a stress of 15,000ft)s. but to provide against 
 the possible contingency of its being sometimes exposed 
 to greater stress than that produced by a dead weight 
 of 2,000ib. to the lineal foot. 
 
 XCII. The use of cast iron to sustain a tensile 
 strain, should undoubtedly be avoided, as a general 
 
 To begin with an instance near at hand ; the bridge from the island 
 to the main shore on the Hudson River rail road at East Albany, has, 
 in one of its stretches, trusses 48 feet long, in 8 panels. It is a double 
 track bridge with three trusses, of which the middle one sustains one- 
 half of the two pairs of tracks, and of the loaas passing over them. 
 
 The truss is composed of top and bottom chords, and thrust braces 
 of timber, and vertical suspension bolts of wrought iron, in pairs ; and 
 it is at once obvious that of the weight of the tracks and their loads 
 (or, of the half bearing upon the centre truss), is concentrated on the 
 two pairs of suspension rods located 6 feet from each end. [See diagram.] 
 
 The weight of middle truss, and other parts of the structure sus 
 tained by it, probably exceeds 16,000 Ibs., of which |, or 14,000 Ibs. bear 
 
 FIG. 23 A. 
 
 upon the endmost suspension bolts. Add 2,000 Ibs. per foot for | of one 
 pair of tracks, or rails, and it makes 56,0001bs. upon the suspension bolts 
 in question, with only one track loaded. These bolts are 4 in number, 
 and If" in diameter; and, allowing -fa" to be cut away by screw 
 thread, the aggregate net, available cross section of the four, is equal 
 to 4.43 square inches ; whence the tension, with only one track loaded, 
 is 12,641 Ibs. to the square inch, and 22,120 Ibs. to the inch with both 
 tracks loaded. 
 
 2. The bridge leading into the freight house of the Boston rail road, 
 at East Albany, is a " Howe bridge," and acts upon the same princi 
 ple as the one just spoken of. It is a double track bridge with two 
 trusses, having 8 panels of 10 8", and is a heavy covered bridge. Al 
 lowing 04 tons for weight of superstructure, or 56,000 Ibs. for the por 
 tion sustained by the endmost bolts of each truss, and 2,000 Ibs per 
 foot upon one track, of which $ at least, bears on one truss, giving 
 
IRON BRIDGES. 155 
 
 rule; and, if on certain occasions it should be liable to 
 that kind of action to a small extent, the stress should 
 probably not be allowed to exceed 3,000 to 4, 000 pounds 
 to the square inch. 
 
 When exposed to compression, in pieces of such 
 length as to break by lateral deflection, it is believed 
 it may be safely loaded to one-third of its absolute ca 
 pacity. If a long piece exposed to a negative strain 
 have a defective part, it does not diminish its power 
 of resistance to the same extent as when it acts by ten 
 sion. The power of negative resistance being, in a 
 measure, inversely as the deflection produced by a 
 
 100,000 Ibs. on the end bolts, we have 156,0001bs. sustained by 6 bolts 
 of iy diameter, containing 8.1 square inches, besides screw thread. 
 This" is a strain of 19,259 Ibs. to the square inch with one track, and 
 25,432 Ibs with both tracks loaded with 2,000 Ibs. to the lineal foot. 
 
 3. The East bridge over the creek in the sonth part of Troy, is a 
 double track covered bridge with three trusses, having 8 panels of 
 12 8" each, or 88.60 ft sustained by the endmost suspension bolts. 
 Say, of weight of structure bearing on end bolts of middle truss, 
 86,000 Ibs. and of load upon one track 88,666, making 123,666 Ibs. on 4 
 bolts of \ diameter and two of If" diameter, having a net cross-sec 
 tion of about 7.65 square inches. Hence the stress must be 16,156 Ibs. 
 to the inch, with one track loaded, and 27,750 Ibs., with 2,000 Ibs. to the 
 foot upon each track. 
 
 4. The West bridge over the same stream, a few rods below the last 
 mentioned, has three trusses containing 9 panels of 10 ft. each in. 
 length. It is a high truss bridge with roof and siding. 
 
 For weight of superstructure on endmost bolts of middle truss, say 
 28,000 Ibs. and for load on one track, 84,000, making 112,000 Ibs. on 
 4 bolts of \\" containing a net section ot 5.41 square inches, giving a 
 tension of 20,702 Ibs. to the inch for one track, and 36,229 Ibs. for both 
 tracks loaded with 2,000 Ibs. to the lineal foot. 
 
 5. The bridge across the Erie canal near Canastota, on the N Y. C. 
 B. R., is a double tack bridge with 2 trusses, which have 9 panels of 
 10 feet. If the superstructure be estimated to weigh 40 tons, it gives 
 a little over 35,000 Ibs. on the end bolts of each truss. Add f of 80 
 tons for 2,000 Ibs. per lineal foot upon one track, and it gives 141,666 Ibs. 
 on 4 bolts of \\" diameter, and 5.41 square inches of net cross-section ; 
 equal to 26,173 Ibs. to the inch, with one track, and 36,044 Ibs. with botk 
 tracks loaded." 
 
 All these cases are stated from personal examination by the author, 
 except the last, which was reported to him from authority considered 
 reliable. The cases were not selected, but taken as the most accessible, 
 and convenient for the author s observation. And still, he can not 
 help regarding them as remarkable, and somewhat exceptional cases 
 
156 BRIDGE BUILDING. 
 
 given weight, and the deflection depending on the stiff 
 ness of the piece throughout its whole length, the 
 power is manifestly only diminished as the amount of 
 defect, multiplied by the ratio of length of the defective 
 part, to the whole length ; that is, if the piece be de 
 fective so as to lose one-fourth of its stiffness, for that 
 part of its length to which is due one-tenth part of the 
 deflection, the deflection will only be increased by 
 Jx^ = J0-> au d the power of resistance is diminished 
 in the same ratio ; whereas the power of positive re 
 sistance would be diminished by J. 
 
 The effect of negative strain, moreover, is believed 
 not to be so deleterious to the strength of iron, as that 
 of positive, or tension strain ; though I can refer to no 
 particular facts or evidences in coroboration of the 
 opinion. 
 
 Upon the whole, I am inclined to estimate the power 
 of cast iron to resist compression (as against the tension 
 of wrought iron at 15,0001bs. to the inch), in pieces of 
 lengths equal to 18 diameters, for hollow cylinders, at 
 15,000fts. for solid cylinders, at 8,000, and solid square 
 pieces, at 10,000ibs. to the square inch of cross-section 
 
 There are other forms of section for cast iron mem 
 bers of bridges, which it will frequently be convenient 
 and economical to employ where lateral stiffness, as 
 well as longitudinal resistance is required, among which 
 may be named, the cruciform +, the T, and the H form. 
 
 The former of these, with equal leaves, probably 
 possesses about the same resistance to the square inch, 
 .as a solid square which will just contain the figure. 
 For, though it is not so stiff to resist a simple lateral 
 force diagonally of the including square, as parallel with 
 its sides, and would be broken by tearing asunder the 
 flange, or leaf upon the convex side, still when under 
 
NEGATIVE STRENGTH OF IRON. 157 
 
 longitudinal compression, the tension upon that leaf 
 would be so.mewhat relieved. 
 
 The T and H section will usually be employed where 
 greater stiffness is required in particular directions, and 
 if proportioned with judgment, will usually possess about 
 the same power to the inch, as the including a olid square, 
 or parallelepiped. 
 
 XCIII. Having determined (approximately, at least)^ 
 the safe strain for pieces of a certain length, and the 
 ratio of variation in power, depending upon change of 
 length, we readily deduce the safe strain for pieces 
 of similar action, with any given dimensions. 
 
 The following table, exhibiting the negative power 
 of resistance to the square inch of cross-section, for 
 hollow and solid cast iron cylinders, and solid square 
 pieces (under which class may be included the -f T and 
 H formed sections, under proper conditions), calculated 
 for length of from 2 to 60 diameters, is intended to 
 show the safe practical rate of strain for the material, 
 being about one-third of its absolute strength, in col 
 umns headed J, and one-fourth of the absolute, in those 
 headed J ; the former to be used against wrought iron 
 at 15,000, and the latter, where wrought iron is esti 
 mated to sustain 10,OOOIbs. to the square inch. 
 
 This is the author s original table, slightly modified 5 
 with the addition of two columns showing corresponding 
 weights at J and J of the absolute strength, as calculated 
 by "Gordon s formula," deduced from Hodgkinson s, 
 experiments upon cast iron hollow pillars; which is 
 regarded as the best authority upon the subject at the 
 present day. Also, two corresponding columns for 
 wrought iron hollow pillars, according to the same au 
 thority. 
 
158 BRIDGE BUILDIXQ. 
 
 The Gordon formulae are : 
 
 for cast iron, S = 80,000ft). -r- (1+ .0025^), 
 
 for wrought iron, S = 36,000ibs. -4- (1 -f .00033|). 
 
 S representing absolute strength per square inch 
 of section, , the length, and d, the diameter of column, 
 both referring to the same unit of length. Or making 
 d = 1, we have = I 2 . 
 
 The table of negative resistances, presents a scale of 
 numbers so adjusted as to touch at certain points esta 
 blished by experiment, and running in consistent gra 
 dations from one to another of such points. 
 
 The columns for cast iron hollow cylinders, are the 
 only ones referring to the same class of pieces, and ex. 
 hibiting the difference in results, arising from differ 
 ence in the mode of calculation. The Gordon formula 
 is supposed to give results agreeing with those of ex 
 periment, for lengths included within the range em 
 braced by the experiments from which the formula 
 was deduced. "Within that range, those results may 
 be presumed to be more reliable (being founded on 
 trials of the same kind of pieces as those to which they 
 refer), than those in the author s original table, based 
 upon trials of solid cylinders and parallelepipeds. 
 
 Taking the 4th and 6th columns, it will be seen that 
 the numbers agree at some point between the lengths 
 of 18 and 20 diameters; the numbers above that point, 
 being the larger in column 6, while, below that point, 
 they are larger in column 4, down to about 50 diame 
 ters, where they come together and cross again, and 
 those in 6, are thenceforward the larger. But the 
 differences are small, for the range of lengths princi 
 pally employed in bridge work. 
 
2* 
 
 L 
 
 d 
 
 NEGATIVE STRENGTH OF IRON. 
 
 159 
 
 +1 
 
 - - ^> ^ * . > 5, *s "^ ^ . ^ 
 
 JO C7 O 00 O CO rH OO > O lo" Tji" rjT cc" SO JO CO O?" of O?" O?" 
 
 Hw 
 
 :>< GO, CO O, t-, ^ <N, CO * T Ci 
 
 
 2^ o coS 
 t-coojot-o 
 
 3 co o p co f> o Tt^ 65 S co co, 10 cs^ ^ c:, 10 ?J s? o i- t~ -^ 
 
 CO (?> C? i-i 1-1 O O O O >O O -^ ?> 1-1 O <M C5 1C -f CO O C? {> JO 
 
 co co co co co TO co TO o CQ i.t -f ac o} o c; < - c? co r: o i~ o c 1 ? 
 
 CO^ TH^ Ci t^_ O CC_ i-^ Oi O^ 00^ i-^ OC t-^ CS^ C ^ ^ C^ O C^ OO^ C3 O_ O^ OS 
 cc"i-i 70 o"^C3 o v t- iC~C>iT-r 
 CO CO W GQ Ci O7 O* T-I 1-1 T-I r-i 
 
 O TH 00 TH O O CO JO O O O ITS IO t^ -rH CO ^ t- CO O CO CJ O O 
 CO C? CO^ tt O P -^ i-^ O O O_ i-^ "^f t>, i^ JO ^ t-^ CO, O, O\ l\ CO O 
 
 O^OOOCOpOSOCOCO^O i -H 
 
 so to * <?j T-T cs > o" -^ co" of o" cs" cs 
 
 01 0^ W 05 CQ 
 
 x> co cs J.^ T-H 
 0*0 ^f co co o? 
 
 to 
 
 Hw 
 
 CO 00 < O O * OC O O7 
 
 T-I O t>- CO T-H CO ^ CS CO Lt> f- CO CO 1C IT T" 
 
 t o ^ cc co to --r 90 o o? 10 8>f~ x S 
 o" o" o" o" cs cs" cs oo" co GO" GO t-" >" o so 10" 
 
 . cc 
 
 I c 
 
 IdWC^CiOJCCOOCOCOCO^^iOiOCO 
 
160 BRIDGE BUILDING. 
 
 One obvious reason of the more rapid increase of 
 numbers in the 6th column, for lengths under 15 or 
 16 diameters, is, that in the latter, the crushing weight 
 for the iron is assumed at 100,OOOIbs. to the square 
 inch, whereas, by the Gordon formula it is limited at 
 80,OOOIbs, and that formula can give no result greater 
 than that limit, even when Z=0. Now, if 80,0001bs. 
 was less than the actual crushing load for the kind of 
 iron used in Hodgkinson s experiments (from which 
 the Gordon formula is understood to have been de 
 rived), it must follow that Gordon s formula gives 
 results smaller than the true ones, for short pieces. 
 This is probably the case, and, although Mr. Gordon s 
 formula is very simple and ingenious, sliding smoothly 
 and plausibly from one extreme in length to the other, 
 it unquestionably gives closer approximations to 
 correct results for the ordinary range of lengths, than 
 when applied to the very short pieces. 
 
 The numbers in the table are deduced upon the sup 
 position that the thrust members in a bridge, will not 
 act with less advantage than when bearing upon a pivot 
 at each end of the axis of the pieces respectively ; and 
 it is not deemed proper to assume that, in consequence 
 of having flat end bearings, the piece in any case can 
 sustain a greater stress than is indicated by the num 
 bers in the table. 
 
 It will be observed that, in order to obtain the ab 
 solute strength of a piece, we should multiply its cor 
 responding number in the table, by the denominator 
 of the fraction (J or J) at the head of the column. 
 
LATERAL, OR TRANSVERSE STRENGTH. 161 
 
 . 26. 
 
 LATERAL, OR TRANSVERSE STRENGTH. 
 
 XCIV. The transverse strength of bars or. beams, 
 would seem to be deducible from the positive strength 
 of the material, in the following manner : 
 
 Let ab, Fig. 26, represent a portion of a rectangular 
 beam or bar, projecting from a wall in which it is 
 
 firmly fixed. If a weight be 
 applied at w, the upper part 
 of the beam will be extended, 
 and the lower, compressed ; 
 and, where these portions 
 meet, is what is called the 
 neutral plane. Experiment 
 shows that this plane, in 
 rectangular beams, is central between the upper and 
 lower surfaces ; or at least, very nearly so, for all 
 elastic substances, until they approach rupture. 
 
 The tendency of the weight at w, then, is to produce 
 rotation about the point c (or, the line of intersection 
 of neutral plane and face of wall) and the cohesion of 
 the upper portion cd, and the repulsion of the lower 
 part, cb, tend to resist rotation. Now, to determine 
 the amount of this resistance, which is the measure of 
 transverse strength, we will first consider the upper 
 portion ; and it is obvious that, at every part of the 
 cross-section, the resistance to rotation is as the 
 resistance to extension, multipled by the distance of 
 the part above the- neutral plane. But the resistance 
 to extension, by the law of elasticity, is as the degree, 
 or amount of extension, which is determined by the 
 distance from the neutral plane ; parts at 2 inches from 
 this plane, or the centre of motion, being extended 
 21 
 
162 BRIDGE BUILDING. 
 
 twice as much as those at one inch, and resisting twice 
 as much. 
 
 Then, denoting the distance from this plane by the 
 variable, quantity x, the resistance to extension by any 
 part, equals x multiplied by a certain constant (s), and 
 may be denoted by sx, while the resistance to rotation 
 about c, equals sx 2 . 
 
 Again, representing the horizontal breadth or thick 
 ness of the beam by /, we have t.dx to represent the 
 differential of the section (in its state of increase from 
 c toward d), and s.t.x 2 dx, the differential of resistance. 
 Then, integrating, aud making x = cd A, we have the 
 whole resistance to rotation, of the part above the neu 
 tral plane, equal to J s.t.h 3 = ^t.hxhxs.h. But s.h 
 becomes equal to the positive strength of the material 
 when x=cd = A, and t.h = the area of section above 
 the neutral plane. Therefore the power of this part to 
 resist rotation, is equal to J of the area, multiplied by 
 half the depth of the beam, and by the positive strength 
 of the material; in case the negative strength exceed 
 the positive. 
 
 Now, it is obvious that the part below the neutral 
 plane exerts exactly the same amount of resistance to 
 rotation, as the part above. Therefore the whole power 
 of resistance to rotation about c, in other words, the 
 resistance to rupture, is equal to J of the whole cross- 
 section, multiplied by J the depth of beam, and by the 
 positive, or cohesive strength of the material ; that is 
 equal to J C.t.Dx^D, = C,t.D 2 ; in which expression, 
 D represents the depth ((/6), and (7, frhe cohesive power 
 of the material.* 
 
 * Another mode of illustrating this case, is the following 1 : It being 1 ob 
 vious that the resistance to rotation about c, by each lamina from the neu 
 tral plane outward, is as the extension it undergoes, and the leverage 
 upon which it acts, such resistance must increase outward in u duplicate 
 
LATERAL, OR TRANSVERSE STRENGTH. 163 
 
 If we wish to determine the greatest weight (W), 
 which the beam is capable of bearing when applied at 
 any horizontal distance (L) from c or d, we institute 
 the equation, W.L = J C.t.D 2 ; whence we have : 
 
 6L % 
 
 This formula applies to all projecting rectangular 
 beams, when the force (W), acts parallel with the 
 sides, and L represents the nearest, or perpendicular 
 distance of the fulcrum <?, from the line in which the 
 force has its action : provided, that if the material 
 have greater power to resist tension than compression, 
 C is to be taken as representing the repulsive, instead 
 of the cohesive power. 
 
 XCY. This formula is deduced on the supposition 
 that the material is perfectly elastic, so as to suffer no 
 permanent change of form until the strain produces 
 actual rupture. There are few substances if any, and 
 certainly wood and iron are not such, that fulfill this 
 condition so nearly but that considerable discrepan 
 cies are found between the deductions of theory, and 
 the results of experiment. Indeed in the case of cast 
 
 ratio to the increase of distance from that plane, and decrease in a like 
 ratio, inward. Hence, if we represent the resistance of the outer lamia 
 by the base of a pyramid having its apex at the neutral plane, and its 
 base coinciding with said outer lamina, the resistance of any other 
 lamina will be represented by the section of the pryamid made by 
 snch lamina, or a lamina of the pryamid at the point of intersection, 
 of the same (indefinitely small) thickness as the lamina of the beam 
 in question ; and the sum of resistances of all the laminae of the beam, 
 will be represented by the Bum of laminae of the pyramid ; and will 
 bear the same ratio to what the resistance of all those lamina? of the 
 beam would be, if all were acting at the distance of the outermost 
 lamina, as the solidity of the pyramid bears to a prism of like base 
 aud attitude ; that is, in the ratio of 1 to 3. But the resistance of the 
 outer lamina, equals the absolute strength of material (C), multiplied by 
 half the depth of beam. Hence, the resistance of tlie half beam equals 
 Cxi cross-section X depth of the half beam ; being the same result 
 as above obtained by integration. , 
 
164 BRIDGE BUILDING. 
 
 iron, experiment shows the transverse strength to be 
 fully twice as great as it is made to appear by the above 
 formula. 
 
 If in the expression 5!, we make L=D, it may be 
 reduced to C.t.D\ showing that the power of a pro 
 jecting rectangular beam to sustain weight at a dis 
 tance from the fulcrum equal to the depth of the beam, 
 is only one-sixth as great as the positive (or negative, 
 in case that be the smaller), strength of the material. 
 This is a convenient way of expressing transverse 
 strength, viz : as equal to a force of so many pounds 
 to the square inch of cross-section, the force being un 
 derstood as acting upon a leverage equal to the breadth 
 of the beam in the direction of the acting force. 
 
 If we call 18,000ft>s. to the square inch, the positive 
 strength of cast iron, we may call the transverse 
 strength (according to the above deduction), \ 18,000 
 =3,0001bs. ; meaning that a bar one inch square will 
 sustain upon its projecting end, 3,OOOIbs. at 1 inch 
 from the fulcrum, and proportionally less, as the dis 
 tance is greater. 
 
 ^"ow, experiment shows that it will sustain twice this 
 amount, and frequently more, so that we may in reality, 
 reckon the transverse strength of cast iron at about 
 6,000ft>s. to the square inch. 
 
 I know of nothing to which to attribute this great 
 discrepancy between theory and experiment, except a 
 want of complete elasticity in the material, and per 
 haps, also to the assumption of too low an estimate 
 (18,000) Bbs. for the co-hesive power of cast iron. 
 
 Cast iron, when exposed to a transverse strain, suf 
 fers extension on one side, and compression on the 
 other ; and the power of resistance to both these effects, 
 increases very nearly as the amount of extension or 
 
LATERAL, OR TRANSVERSE STRENGTH. 165 
 
 compression, until a certain point or maximum is 
 reached, and after passing this point, the power dim 
 inishes. Now, it is reasonable to suppose, in fact we 
 can hardly suppose the contrary, that for a certain in 
 terval on each side of the maximum point, the power 
 of resistance remains nearly stationary. But this sta 
 tionary interval is reached on the positive, much sooner 
 than on the negative side, and the inevitable conse 
 quence must be, that the neutral plane is transferred 
 further from the positive side, so as to preserve the 
 equilibrium between the resistance to extension and 
 the resistance to compression. Hence, the amount of 
 resistance on the positive side is increased, both by the 
 increased area of section exposed to tension, and in 
 creased leverage, or distance from the neutral plane. 
 
 Moreover, a greater portion of the fibres (so to speak), 
 of extension, act with their full power; since, while 
 the outside portion is passing through what we have 
 called the stationary interval, successive portions toward 
 the neutral plane, are reaching and approaching that 
 interval. Hence, some considerable proportion of all 
 the fibres of extension, may act with their maximum 
 power ; whereas, if the material were perfectly elastic 
 up to the point of actual rupture, only the outside fibres 
 farthest from the neutral plane, could act with abso 
 lute power, and all other parts, only in the ratio of 
 their respective distances from said plane. To illus 
 trate, suppose the extreme positive side, when ex 
 tended one inch, reach the stationary interval, which 
 is one inch more. It follows that when the outside 
 has passed to the other limit of that interval, one-half 
 of the positive portion of the bar, will be within the 
 the range of that interval, and act with its maximum 
 power, producing one third more resistance to exten- 
 
166 BRIDGE BUILDING. 
 
 sion than the same fibres could afford if the body were 
 perfectly elastic, up to the point of rupture. I know 
 of no more plausible manner of explaining the observed 
 discrepancy between experiment and calculation upon 
 the subject. 
 
 But, having well authenticated direct experimental 
 evidence as to the transverse strength of cast iron, we 
 may safely be guided thereby; and, though it would 
 be a satisfaction to find a complete agreement between 
 the results of direct experiments, and the deductions 
 from those that are indirect, still, where such agree 
 ment is not found, the direct evidence should have the 
 preference. We may, therefore, regard the transverse 
 strength of cast iron in pieces with rectangular sec 
 tions, as equal to 6,OOOIbs. to the square inch, upon a 
 leverage equal to the width of the piece in the direction 
 of the force. 
 
 "Wrought iron has something over three times the 
 positive strength- of cast iron, on the average; and if 
 we consider its transverse strength to be in the same 
 ratio to that of cast iron, its transverse strength would 
 be about 20,000 pounds. That is, the projecting end 
 of a bar of wrought iron one inch square, should sus 
 tain, at one inch from the fulcrum, a weight of 20,000ft>s 
 But it becomes permanently bent with about one-third 
 of that weight, and therefore, in practice it should not 
 be exposed to more than 4,000 to 5,OOOSbs. as we should 
 manifestly keep within the elastic limit, as well in case 
 of a transverse, as a direct tensile strain. It may, 
 therefore, be recommended to estimate the transverse 
 strength of wrought iron at 5,000fts. as against a ten 
 sile strain of 15,OOOJbs. to the inch, upon the same ma 
 terial, and 3,500 to 4,000 transverse, against 10,000, 
 tensile strain. 
 
LATERAL, OR TRANSVERSE STRENGTH. 167 
 
 Cast iron having an average absolute transverse 
 strength of 6,000ft)3. should not in practice, be exposed 
 to over from 1,000 to l,5001bs. to the square inch, ac 
 cording to the circumstances in which it is used. 
 
 XCVI. Representing by A the area by D the depth 
 and by L the length (from fulcrum to weight) of a pro 
 jecting rectangular beam, the safe load, according to 
 
 the above assumptions, equals 5,000 for wrought, 
 
 and 1,500 for cast iron. 
 
 If the beam be supported at the ends and loaded in 
 the middle, using the same symbols, the safe load is 
 four times as much ; that is, 20,000 for wrought, 
 
 LJ 
 
 and 6,000 for cast iron. This follows from the fact 
 that the lifting force at each end, equals only one-half 
 of the load, and acts upon a leverage equal to -JL, hence 
 it takes 4 times the weight to produce the same stress 
 on the beam. 
 
 If the load be equally distributed over the length of 
 the beam, the safe load is twice as much as when it is 
 concentrated at the end of the projecting beam, and in 
 the middle of the beam supported at the ends. For, 
 in the former case, each part of the weight produces 
 stress at the fulcrum in proportion to its distance there 
 from, and the average distance of the whole load, 
 being only half as great, the stress is only half as much 
 as when the whole load is at the end. 
 
 In the latter case, the beam being regarded as fixed 
 in the centre, the lifting force at the end, tends to pro 
 duce a strain in the centre, measured by the force mul 
 tiplied by its distance from the centre, in other words, 
 by the moment of the force with respect to the centre. 
 On the contrary, the load tends to produce a strain in 
 
168 BRIDGE BUILDING. 
 
 the opposite direction, according to the distance of 
 each part of the load from the centre. This, as just 
 seen in the case o the projecting beam, is equal to 
 half of that produced by the lifting force at the end. 
 Hence the effect of the weight neutralizes one-half 
 of tendency of the lifting force at the end, to produce 
 stress in the centre of the beam. 
 
 Upon the same principle is based the following rule 
 for determining the stress at any given-point in the length 
 of a beam, however the load may be distributed. 
 Take the moment with respect to the given point, of 
 all the forces on either side of said point, tending to 
 deflect the beam in one direction, at the given point, 
 and all the forces on the same side, tending to deflect 
 it in the opposite direction, and the difference in the 
 sums of those opposite moments, is the measure of the 
 stress at the point in question. 
 
 As an illustration, if the cross-beam of a rail road 
 bridge support tracks 5 apart, the beam being 15 be 
 tween supports, and a weight W bear equally upon 
 the two tracks, each end support lifts JW, and the 
 moment with respect to the nearest track, is JWx5 = 
 2.5W. There being no force acting in the opposite 
 direction between the end and the weight upon the 
 rail, 2.5W (upon a leverage of 1 foot), is the measure 
 of stress of the beam at the rail. 
 
 If we seek the stress in the middle of the beam 7J 
 from the end, and 2J from the rail, the upward force 
 at the end is JW, the same as before, and the moment 
 jWx7J = 3.75W; while the moment of the weight 
 on the rail, is |Wx2J, = 1.25W. Hence, the stress 
 in the centre = (3.75 1.25)W = 2.5W, the same as at 
 the rail. 
 
LATERAL, OR TRANSVERSE STRENGTH. 169 
 
 Taking the moment of the end lift with respect to 
 the off rail, we have jWxlO, = 5W, while the moment 
 of weight on the near track, with respect to the off 
 track, is J Wx5, = 2JW, acting in the opposite direc 
 tion. Hence, stress at the off track, is equal to (5 2. 5) W 
 = 2JW. 
 
 Again, assuming a point at 2 from the end, the mo 
 ment of the lift at the farther end, is J W X 13 =6.5W. 
 The sum of moments of weights upon the two jails is, 
 J\Vx8-fJWx3 =5.5W in opposition to the effects 
 of the end lift. The stress of the heam, therefore, at 
 the given point, is (6.5 5.5) W, = W ; being the same 
 result as if we had taken the moment at the near end, 
 = JW X 2, = W, with no opposite force on the same 
 side of the given point. 
 
 Hence, we see that the stress is the same at all points 
 between the rails, while it obviously diminishes from 
 the rail to the end, in proportion as the distance of 
 successive points from the end diminishes. Therefore, 
 the beam having a uniform depth, in order that the 
 strain be uniform on all parts, the thickness should 
 taper uniformly from the rail, to an edge at the sup 
 porting points. If the thickness be uniform (the cross- 
 section being rectangular), the depth may diminish as 
 the square root of distance from the support diminishes; 
 that is, may have a parabolic form, This follows from 
 the fact that the stress at different points in the length 
 is as the distance from the support, and the power of 
 resistance, as the area multiplied by the depth, in other 
 words, as the square of the depth, the area being simply 
 as the depth. 
 
 XCVII. Iron beams of a rectangular section will 
 seldom be used in bridge work, the material acting 
 22 
 
170 BRIDGE BUILDING. 
 
 n\ore effectually in a web and flange form, as in the I 
 beam, with about half the material in the flanges. In 
 this kind of beam, the web may be estimated as a rect 
 angular beam say at 5,OOOIbs to the inch (on a lever 
 age equal to the depth of the beam), while the flanges 
 may be estimated at 15,000ft>s upon a leverage of half 
 the depth of beam, less half the thickness of flange, 
 thus : for a beam 12" deep, web \" thick, flanges 2" 
 wide and f" in average thickness on each side of the 
 web, we have 6 square inches of web section at 5,000 = 
 30,0001bs. plus, 6 inches of flange section at 15,000 X 
 leverage of 5,625", equal to 42,187ft>s. on a leverage of 
 the depth of beam, making a total of 72,187ft>. ==6,015ft>s. 
 to the inch upon the whole section. 
 
 Hence, it is deemed safe to estimate the working 
 strength per square inch of wrought iron I beams, in 
 the above proportions of web and flanges, at 6,000 
 Ibs. for projecting ends, and 24,000 -for beams sup 
 ported at the ends, and loaded in the middle ; and 
 double those amounts of distributed load. For instance ; 
 a 12" I beam of 12 square inches in section, and 16 
 long, between bearings, is good for 24,000 X ] =F 
 18,000ft)s. in the middle, 36,000 distributed uniformly, 
 and 26,1801bs. upon two rails 5 feet apart, or 5.5 feet 
 from end supports. 
 
 XCVIII. One of the cases in which wrought iron 
 is frequently exposed to transverse strain, is in the use 
 of cylindrical pins for connecting the other parts of 
 bridge work. In such cases, the forces will act with a 
 certain leverage which can be nearly determined. The 
 power of a round pin to sustain a transverse force act 
 ing on a leverage equal to the diameter, may be as 
 sumed at about T ^ less to the square inch, than that of 
 
LATERAL, OR TRANSVERSE STRENGTH. 171 
 
 a square bar upon a leverage equal to its width of side. 
 Hence, A representing the area of section, D, the diame 
 ter, and L, the length, the safe stress = 4,500 A ~ acting 
 
 on a projecting end, and 18,000- acting in the middle 
 between two outside bearings ; that is, a V pin with 
 centres of outside bearings 6" apart, will bear in the 
 
 middle, 18,000 X = 2,355ft>s. If the pin connect an 
 
 eye V thick, between one of \" thick on each side, the 
 length (L) between centres of outside pieces, will be 
 1"; whence, a V pin will bear 4 times as much as in 
 the preceding case; or 2,355 x 4 = 9,420ft)3. The 
 tensile strength of a 1" round rod, being ll,7751bs. 
 being equal to the cross-section (0.785), X 15,OOOR)s. it 
 $hows that the strength of the rod is greater than that 
 of the pin, in the condition here assumed, in the pro 
 portion of 11,775 to 9,420. Therefore, the stiffness of 
 the pin being as the cube of the diameter, in order to 
 find the diameter (#), of a pin for connecting V bars 
 by eyes and connecting straps, we have this proportion 
 9,420 : 11,775 : : I 3 :x 3 , whence z = 1.077 = to about 
 -1*3 larger than the diameter of the rods to be connected, 
 and in this proportion for any size of round rods con 
 nected by straps and pins or bolts. 
 
 But if the eyes and straps be drilled, so as to fit the 
 pin through the whole thickness, the action approaches 
 the shear strain, and the pin should have about f the 
 area of section of the bars to be connected. The author 
 would recommend, however, for general practice, that 
 connecting pins be considered as acting by transverse 
 stiffness, upon the lever principle, as above discussed. 
 
172 
 
 BRIDGE BUILDING. 
 
ARCH TRUSS BRIDGES. 173 
 
 ARCH TRUSS BRIDGES. 
 
 XCIX. The general form in outline of the Arch 
 Truss, may be seen in Figs. 8 and 11. 
 
 The forms of the different members, and the modes 
 of connecting them to form the complete structure, are 
 many, and a minute description of each possible variety, 
 in this respect, even if such a thing can be regarded as 
 practicable, will not be undertaken on this occasion. 
 
 The arch may be of cast or wrought iron in various 
 forms of section. The following form of cast iron arch 
 has been extensively used in the state of New York, 
 with uniform success and satisfaction. The arch is 
 composed of cast iron sections, equal in number to 
 the number of panels in the truss ; an odd number 
 being deemed preferable. In Fig. 27, o. on m presents 
 a top view of the arch, and D, a top view of the chord, 
 from end to centre; and A and B, enlarged cross-sec 
 tions at p and </, adjacent to the cross-bars to be de 
 scribed below, and which also appear in the figure. 
 Each piece consists of two side portions of an ~~| formed 
 section, connected at the ends, and at 2 or 3 intermedi 
 ate points, by cross-bars of a J formed section for the 
 intermediates, and at the ends, with sections as seen at 
 (7, where a view of the arch connection is shown, as it 
 would appear if cut vertically and longitudinally 
 through the centre, and the near half removed. 
 
 The width of the side plates of arch castings (from 
 the top), should be about ^ of the length of pieces, 
 with an average thickness of from T ^ to J of the width. 
 The top plate, about the same thickness (or a trifle less, 
 to prevent a tendency in the piece to become hollow 
 
174 BRIDGE BUILDING. 
 
 backed in cooling), and a width, a little over one-half 
 that of the side plate. 
 
 The resisting power may be estimated as in the table 
 of negative resistances under the head of square, &c., 
 pieces, calling the width of side plates the diameter, 
 and using the column under J, for trusses supporting 
 12 feet or more width of flooring, and the column 
 headed J, in case of trasses supporting a width of 10 
 feet or less, to each truss. 
 
 The intermediate cross bars should have about the 
 same thickness of plate as the side portions, a depth, 
 about f that of side plates, and top plate not less than 
 f as wide as the top plate of side portions. 
 
 End cross-bars should have a top width of about f 
 the width of side plates, and cross-section sufficient to 
 sustain a whole gross panel load for the truss, by trans 
 verse resistance. If it have a depth equal to J of its 
 length, and a form of section as strong as a rectangular 
 bar, it will safely sustain 1,000 to l,2001bs. to the inch ; 
 and it is recommended to allow one inch of section in 
 each end cross-bar to every l,000ft>s, sustained at the 
 joint. Then, there being two cross bars together, the 
 point will be doubly secure. 
 
 Semicircular notches in the ends of contiguous arch 
 pieces, form a vertical circular hole at the joint, for the 
 passage of the vertical member. 
 
 When the side plates are thin, the thickness should 
 
 be increased for a few inches from the end, to afford a 
 
 FIG 28 suitable bearing surface at the joint; 
 
 r-pirv and the ends of arch pieces should 
 
 I I flllll Hj be fitted (usually by planing), to a 
 
 I y proper bevel to form a fair joint. 
 
 The joints, however, are sometimes 
 
 formed by cutting taper key seats (as seen in Fig. 28), 
 
ARCH TRUSS BRIDGES. 
 
 175 
 
 in one of the contiguous ends, to admit wrought iron 
 wedges about an inch wide, and in sufficient number 
 to give a bearing upon wedges, equal to at least one- 
 half the section of iron in the chord. This method has 
 answered well in a large number of bridges, and is 
 convenient for adjusting the arch in line; but the 
 planed ends form much the more workmanlike joint. 
 
 The centre arch piece has usually a full top plate 
 over the whole width of the piece. 
 
 The endmost section, or foot piece of the arch, con 
 nects with the chord by means of horizontal holes in 
 FlG 29 tf 16 ft et to receive the ends 
 
 of an o^en end iink of the 
 chord, which is secured by 
 screws and nuts as shown 
 in Fig. 29, representing an 
 inside view of the foot of 
 one branch of the arch. 
 
 C. The chord is composed of two long links of round 
 or square iron to each panel, connected by cast iivn 
 
 connecting blocks at 
 points vertically under 
 the arch joints. The 
 form of these blocks is 
 represented in F?g. 30. 
 They diminish in length 
 from the endmost to the 
 centremost, the former 
 being long enough to re 
 ceive the links running parallel from the connection 
 with the arch, and the ne&t block, being shorter by 
 twice the diameter of the link iron ; the ends of links 
 toward the centre of the truss, going next the ends of 
 
 FIG. 30. 
 
176 BRIDGE BUILDING. 
 
 connecting blocks, and outside of the ends pointing 
 toward abutments ; and, the members of each pair of 
 links being parallel with one another. [D, Fig. 27.] 
 
 The connecting block has an oblong section where 
 it receives the links, being rounded on the sides to tit 
 
 the semicircular ends of links. 
 Jbia. 30 A. mi , , , , 
 
 I here should be an accurate 
 
 fit between these parts, to 
 effect which, perhaps, the best 
 plan is to ream the ends of 
 links, and turn the bearings of 
 blocks to a uniform size. For 
 this purpose, the block is cast with extra metal to be 
 turned off at the bearings, and with the portion be 
 tween bearings a little thinner vertically, than the 
 turned portions, as shown in Fig. 30A, in which a is 
 a section and bb are the bearing surfaces. 
 
 The vertical thickness of the block where it receives 
 the links, should be at least 1J times the diameter of 
 the link iron, and the cross-section multiplied by the 
 width of block, and divided by diameter of link iron, 
 should give a quotient about 13 times as great as the 
 cross-section of both sides of the link. 
 
 The middle portion of the block is cast with the 
 proper size and form for the upright and diagonal 
 members to pass through in the required directions, 
 and is provided with suitable facets for the bearings of 
 nuts. The least cross-section through all or any of the 
 holes, should be at least one-quarter greater than the 
 section at the link bearings. In Fig. 30, , b and c re 
 spectively represent a side, end and top view of the 
 cast iron connecting block. 
 
 The oblong section of the connecting block was 
 adapted to obtain greater transverse strength in the 
 
ARCH TRUSS BRIDGES. 177 
 
 direction of the strain. But it has recently occurred 
 to the author, that perhaps, after all, a circular section 
 of block would have the advantage, inasmuch as it 
 would not require so short a bend at the ends of 
 links ; whence they could the better adapt thems Ives 
 to the block, and would not require so great a disturb 
 ance in the condition of fibres or particles of the iron 
 in forming the bends. With a diameter of block equal 
 to 3 times that of the link iron (in case of round iron), 
 it is believed that good iron would suffer the bend 
 without material deterioration, or greater liability to 
 break the ends, than in other parts of the link, espe 
 cially if welded in the straight part. 
 
 The enlarged central portion of the connecting block 
 has upon its upper side, a flat surface rising a little 
 above the links, to afford a beam seat for the cross 
 beams of the bridge to rest upon ; which, in case of 
 wooden beams, should present a bearing surface of 30 
 to 40 square inches. 
 
 CL The upright is made of round wrought iron, 1 j 
 to 2 inches in diameter, for bridges from 60 to 100 feet 
 in length, when designed for common road purposes. 
 The upper end is furnished with a screw nut, and a 
 ring or collar welded on at a sufficient distance below 
 the nut to allow the arch castings, and eyes of dia 
 gonals to come between nut and collar. 
 
 The lower end is turned or swaged down to a dia 
 meter J " or " less than the body of the rod, for a 
 length sufficient to reach through the connecting block, 
 and receive a nut on the end. This is to form a 
 shoulder at the upper side of the block, to act in case 
 of a thrust action of the tfpright. 
 
178 BRIDGE BUILDING. 
 
 The two longest uprights have usually been made 
 double and divergent from the collar downward, the 
 branches being of iron from J" to f " smaller in^ dia 
 meter than the single uprights, and passing through 
 the connecting block near the links, either inside or 
 outside, as deemed most appropriate, with a thin nut 
 above, and a common nut below the block ; also a cast 
 iron washer above the upper nuts, for the beam to rest 
 on, instead of resting upon the central part of the 
 block. The object is to give lateral steadiness to the 
 arch, and diminish its vibration. 
 
 A better effect in the same direction is produced by 
 connecting the upper ends of those uprights across 
 from truss to truss, in case of long bridges. For this 
 purpose, the upright may extend a little above the 
 arch, when necessary to give head-way (or, perhaps 
 better still, the arch itself might rise higher above the 
 chord, thus diminishing the action upon both arch and 
 chord), and a light cast or wrought iron strut intro 
 duced, to counteract the tendency to vibration of the 
 arches, arising from the spring of the beams. As the 
 the two trusses naturally tend to vibrate in opposition 
 to each other, it is suggested whether simple ties of 
 f " iron, would not so break the regularities of the 
 vibrations Cis to prevent their increase to an objection 
 able extent. The rigid strut, however, would be more 
 effective, being capable of acting in both directions ; 
 and, if thrown into the form of a graceful arch, it 
 would be ornamental withal. 
 
 GIL The diagonals are round rods, with an eye at 
 the upper, and a screw and nut at the lower end of 
 each ; the screw portion being about J" larger in dia 
 meter than the plain part of the rod. Tsvo eyes of 
 
ARCH TRUSS BRIDGES. 179 
 
 diagonals go upon each upright (except the endraost) ; 
 that of the rod running downward toward the centre 
 going above the other, the better to prevent interfer 
 ence with the cross-bars of arch pieces, as will be un 
 derstood by reference to C, Fig. 27. 
 
 The eyes He in horizontal positions, the rod in each 
 case being bent to the required pitch to meet the con 
 necting block. The bend should be as near as may be 
 to the eye, without preventing a fair bearing of the eye 
 upon the collar, or the subjacent eye. Care should be 
 taken to have fullness and strength in the neck of the 
 eye, that it may withstand the indirect strain at that 
 point. 
 
 The proper sizes for diagonals and chords should be 
 such, in common road and street bridges, as to afford 
 at least one square inch of cross-section for each 
 15,0001bs. of stress produced by the greatest load to 
 which such bridges are liable, which in the author s 
 opinion, should be estimated at about lOOIbs. to each 
 square foot of bridge flooring, exclusive of weight of 
 structure ; a rule which he originally adopted, and has 
 adhered to in practice with most satisfactory results. 
 Many bridges have been constructed with lighter pro 
 portions than this rule would require, some of which 
 have endured, while others have failed. 
 
 It is true that ordinary road bridges are seldom ex 
 posed to lOOfbs. to the foot of floor surface, but it is 
 nevertheless, deemed expedient to provide for such 
 a contingency. 
 
 The modes of estimating stresses of different parts 
 of the truss, have been fully discussed in preceding 
 pages, [xxvn &c.], and it seems unnecessary in this 
 place, to specify more particularly the dimensions of 
 the several members of the truss. 
 
180 
 
 BRIDGE BUILDIXG. 
 
 FIG. SOB. 
 
 CIII. Another devise for the connections of diagonals 
 at the arch, is to replace the bent .eye of the diagonal 
 
 by a straight end with screw 
 and nut, and to have oblique 
 holes cast in the ends of arch 
 pieces for diagonals to pass 
 through, on each side of the 
 upright. [See Fig. 30B]. 
 The diagonals may be single, 
 or in pairs. The latter plan 
 is preferable, as giving a 
 better balanced action ; es 
 pecially in case of rail road bridges, which are subject 
 to greater action upon diagonals. This plan obviates 
 a degree of lateral strain upon uprights, resulting from 
 the eye connection. In this case, the upright should 
 have a shoulder bearing on the under side of arch 
 
 O 
 
 castings, to sustain the thrust action. 
 
 CIV. It will be seen that these trusses, having a 
 width of base equal to about one-fourth of the height, 
 will support themselves laterally, without any assist 
 ance from one another, or from other parts of the 
 structure, wherefore the flooring, including cross 
 beams, may be entirely of wood, and may be renewed 
 at pleasure, without any disturbance of the iron work ; 
 a property peculiar to this kind of truss. 
 
 The original design, therefore, was to use wooden 
 cross-beams, formed in two pieces, as by slitting an or 
 dinary beam vertically, bolting the parts together, and 
 boring at the ends for the uprights, so that they may be 
 conveniently put in and removed whenever they re 
 quire renewal. Diagonal braces of wood, or what is 
 much better, tie rods of iron with an eye at each end, 
 
ARCH TRUSS BRIDGES. 181 
 
 and a swivel or turn buckle adjustment near one end, 
 a pair between each two consecutive beams, to which 
 they are bolted near the uprights, are required to pre 
 vent a lateral swinging or swaying of the bridge ; 
 whence these members are usually called sway braces, 
 or sway rods. In the end panels the sway rods are 
 attached to the feet of the arch. 
 
 Upon the cross-beams, longitudinal joists are placed 
 to support the floor plank, a thing so simple, and so 
 generally understood as to require no further descrip 
 tion or illustration in this place. More or less casings 
 and finishings of wood work outside of the road way, 
 are usually added, according to circumstances, or the 
 taste of the builder. 
 
 CV. The rise of the arch above the chord, will admit 
 3f a considerable degree of variation. A pitch of 24 
 to 26 degrees for the end arch pieces, it will seldom be 
 advisable to exceed in either direction. That pitch 
 divided by the whole number of joints in the arch (6, 
 for a seven panel truss), gives the angle of deflection 
 at the joint, equal, of course, to twice the angle of bevel 
 for ends of arch pieces. 
 
 This, however, does not produce an arch in equili- 
 brio under a uniform load, which, as we have seen, 
 [xxvn and LII] requires a parabolic curve, while equal 
 deflections produce a curve between the parabola and 
 the circular arc; not departing from the former, how 
 ever, widely enough to be of material moment for or 
 dinary spans. The effect is only the throwing of a 
 trifle more action upon certain diagonals ; for which 
 the convenience of uniform bevels, is, perhaps, an ade 
 quate offset. 
 
182 BRIDGE BUILDING. 
 
 CYLINDRICAL ARCHES. 
 
 CYI. Arch Truss bridges have been constructed 
 with cylindrical arch castings, in connection with up 
 rights, dividing and diverging downward from the 
 arch to the beams, thus serving to give lateral support 
 to the arch, and preserve it in line. 
 
 This form of arch castings was supposed at one time, 
 to possess sufficient advantage over that already before 
 described, and which is commonly known as the In 
 dependent Arch, to warrant its adoption, inasmuch as 
 it is the stronger form to withstand compressive strain. 
 But it is also more expensive in the manufacture, to 
 an extent perhaps sufficient to balance any practicable 
 saving in weight of metal. Hence, the Independent 
 Arch has acquired decidedly the greater popularity, to 
 which its just title can scarcely be questioned. Further 
 detail, therefore, as to the mode of constructing the 
 cylindrical arch bridge will not be here recited. 
 
 IRON BEAMS FOR BRIDGES. 
 
 CVII. It is now over thirty years since the writer s 
 attention was first directed to the subject of Iron Truss 
 Bridges ; a period which may be said to comprise the 
 history of the use of iron as the sole or principal mate 
 rial in the main supporting members of those useful 
 structures. 
 
 At that time, there was one Iron Truss Bridge in use 
 in the state of New York, and only one, to the writer s 
 knowledge, either in this state, or in the world, though 
 the fact may be otherwise. 
 
 That bridge, though possessing merit as the result 
 of a first effort, did not prove a complete success, hav- 
 
ARCH TRUSS BRIDGES. 183 
 
 ing failed, and, being rebuilt, failed a second time, 
 many years ago; so that, at the present time, a certain 
 Iron Truss Bridge built by the author of this work in 
 1841 and 42, upon the Arch Truss plan, essentially as 
 described in the last few preceding pages, is believed to 
 be the oldest Iron Truss bridge in use in this country, 
 if not in the world. 
 
 At that time, it was not thought advisable to attempt 
 more than the construction of Iron Trusses, to be used 
 in connection with wooden, beams, joist, &c. ; which 
 latter portions could be renewed as required, with 
 comparatively little trouble, and at much less cost, 
 than the interest upon the extra expense of iron beams 
 would amount to within the lifetime of wooden beams. 
 But as the public mind seems now to have become 
 convinced, not only of the safety and expediency of 
 the use of iron for the trusses, but also for the beams 
 of bridges, it becomes a question of interest to deter 
 mine the best manner of constructing and inserting 
 such beams. 
 
 CYIII. Four general plans of iron beams have been 
 used successfully ; namely, the cast iron web and 
 flange beam, the wrought iron skeleton, the composite 
 (wrought and cast iron), and the solid wrougth iron 
 rolled web and flange, or I beam. These may all be 
 used with good results, in particular cases, and under 
 modifications adapted to respective circumstances. 
 
 For general use, however, I regard the solid -rolled 
 I beam as entitled to a decided preference ; and, with 
 out discussing relative merits in this place, I propose 
 simply, at this time, to suggest plans for adapting the 
 last named beam to the Whipple Arch Truss, thus 
 making the plan about all that can be hoped to be at- 
 
184 
 
 BRIDGE BUILDING. 
 
 tairied, as a cheap, substantial and durable iron bridge 
 for general use, for spans varying from 40 to, perhaps 
 125 feet. 
 
 For bridges 16 to 18 feet wide in the clear, and 
 panels ten or eleven feet long, a 9 inch beam, weighing 
 30Bbs. to the foot, is in good proportion ; and when 
 side walks are not required, the beams may be cut 
 with square ends, just long enough to go between the 
 uprights of opposite trusses, and provided with a fixture 
 at each end, formed of a plate of iron about f" thick, 
 7" wide, and about 2 long, bent in the form of a jews- 
 harp bow. The loop, or bow (w, Fig. 31), is to encir- 
 
 FIG. 31. 
 
 cle the upright, and the straight sides, to receive the 
 vertical web of the beam between them, and to be 
 fastened thereto, by two bolts and nuts. One of these 
 should be 1J" in diameter, and long enough to receive 
 the eye of a lateral diagonal tie, or sway rod (to prevent 
 swaying or swinging), under both head and nut, and 
 placed about 5|" from end of beam, and 2J" above 
 lower edge of plate. The other bolt may be 1J" or 
 1J", and placed with its centre 1J" from end of beam, 
 arid from upper edge of plate. The thread of the screw 
 
ARCH TRUSS BRIDGES. 
 
 185 
 
 should not run into the plate, even if a washer be re 
 quired in order to fetch the work together. 
 
 A convenient modification of this fixture is to have 
 it made in two pieces with two f" bolts outside of 
 the upright, as seen at c, Fig. 32. This affords a con- 
 
 Fia. 32. 
 
 venient means of attaching a light bracket (6), to sus 
 tain face plank and coping (a), over the chords, such 
 as are commonly used in this kind of bridge. It also 
 enables iron beams to be inserted in bridges originally 
 built with wooden beams. 
 
 The connecting block in this case, should have an 
 elevated ring around the upright, for the eye of the 
 fixture to bear upon, to keep the beam from bearing 
 altogether upon the inside of the upright, and produc 
 ing unequal strain. 
 
 CIX. Another suggestion is, to form a stirrup in the 
 upright just above the connecting block for the beam 
 to pass through and rest in : as seen at 6, Fig. 31. This 
 will admit of projecting beams to support side walks. 
 
 The stirrup may be formed of iron 1" by 2" or 2J", 
 according to the character of bridge. The iron should 
 24 
 
186 BRIDGE BUILDING. 
 
 be upset, so as to give sufficient width and strength at 
 the bottom of the stirrup to allow a 1J" stem to be 
 screwed in, to pass through and support the connecting 
 block. This stem may extend above the bottom of the 
 stirrup, about ", a hole being made in the under side 
 of the beam to receive that projection. The thread of 
 the projecting part of the screw, which enters the beam, 
 should be turned or chipped off. This plan may be 
 used in bridges either with or without side walks. 
 
 Again, the upright may terminate in a flange at the 
 top of the beam, and bolts screwed or cast in the top 
 of the block, or running through the block with head 
 or nut below, one on each side of the beam, and con 
 necting with the flange of the upright, as shown at B, 
 Fig. 32. 
 
 In the case of double uprights, the beam being cut 
 to go between the inner branches, the fixture plates 
 should lap about 20" upon the beam, and extend so as 
 to clasp both branches of the upright. 
 
 CX. To introduce the solid wrought beam in bridges 
 with sidewalks originally constructed for wooden beams, 
 the following plan is suggested. 
 
 Let the beam be cut, say 1" shorter than the space 
 between opposite uprights. Then, take for each end 
 
 FIG. 33. 
 .p 
 
 ! ni> ^ 
 
 of the beam, two plates J" thick and 7J" wide, or, 
 wide enough to fill the space between the flanges of 
 
ARCH TRUSS BRIDGES. 187 
 
 the beam at V from the centre, so that one being 
 placed on each side, they will be kept far enough 
 apart to admit the upright between them. The plates 
 should be long enough to lap 20" upon the beam, and 
 extend to outside of side walk. They may be bolted 
 with two V bolts near the end of the lap, and one near 
 the end of the beam by the upright; as seen under the 
 letter u in Fig. 33. A 1 J" bolt in the centre of depth, 
 and 7 or 8 inches from the upright, will serve both to 
 aid in holding the plates in place, and to connect the 
 sway rods I. These plates should not be cut by bolt 
 or rivet holes in the upper part, except at considerable 
 distance from the upright u. 
 
 Small bolts or rivets, r r, etc., should be inserted at 
 intervals of 9 or 10 inches, near the lower edge, with 
 thimbles to stay the extension plates apart, 
 leaving a space equal to the diameter of the 
 upright. In Fig. 33, s-w is a part of the 
 extension for supporting side walk ; s, a 
 cast iron saddle weighing about 4Sbs. for 
 joist bearings, and c, a cross-section through 
 the splice. 
 
 To afford a proper bearing upon the con 
 necting block, it is proposed to use a 
 wrought iron ring (R. Fig. 34), high 
 ^> x l enough to throw the whole weight upon 
 the extension plates ee, and f" to V in 
 width, except on the side next the beam proper, where 
 it is to be clipped or drawn down to J". This, how 
 ever, is not an essential point. In case of bridges 
 already erected, the ring will have to be left open as 
 at R , and when used, heated and closed around the 
 upright. 
 
188 BRIDGE BUILDING. 
 
 CXI. The Link Chord, composed of a set of links 
 to each panel, connected by pins or connecting blocks 
 (the latter affording also points of attachment for ver 
 ticals, diagonals, &c.), both for Arch and Trapezoidal 
 trusses, was originally adopted by the author, as the 
 readiest means of putting the requisite amount of chord 
 material in a manageable form, both as it regards manu 
 facturing the parts, and erecting the structure. This 
 form renders the whole section available for sustaining 
 tension, avoiding any loss in rivet or bolt holes for 
 forming connections. 
 
 The experience of more than a quarter of a century, 
 during which time many hundreds of bridges with link 
 chords have been constructed, and used in almost all 
 conceivable conditions, (in many cases, undoubtedly, 
 the links having been but imperfectly manufactured 
 and fitted to the connecting blocks), with a degree of 
 success and satisfaction seldom exceeded, may reasona 
 bly be regarded as fairly establishing the efficiency and 
 safety of this mode of construction, when proper care 
 is used in the performance of the work. 
 
 Continued and successful usage in a multitude of 
 instances, is regarded as a better criterion as to the 
 reliability of a plan of construction, than a small num 
 ber of isolated tests, however severe ; and such usage 
 the link chord has been subjected to. 
 
 CXII. The theoretical questions to be considered in 
 this case, would seem to be, as to the possible deteriora 
 tion of the cohesive strength of the iron, produced in 
 forming the bends at the ends of links the indirect, 
 or lateral strain in those parts, resulting from imper 
 fection of the fitting to the connecting block or pin, 
 and, the imperfection of the weldings, both as it re- 
 
ARCH TRUSS BRIDGES. 189 
 
 gards complete cohesion, and the tendency to crystalli 
 zation under the welding heat, not being fully destroyed 
 by subsequent hammering and working. 
 
 The whole process of the manufacture and refinement 
 of iron, is based upon the principle that disconnected 
 pieces of iron brought in contact under intense heat, 
 but without complete fusion, and subjected to violent 
 compression, as by hammering or rolling, will unite, 
 and become a single piece or mass. 
 
 Every bar of refined iron found in the iron market, 
 is composed of half a dozen or more parts, which were 
 once separate and disconnected. Those having been 
 " fagoted," or placed in juxtaposition, and submitted 
 to a welding heat, and passed repeatedly between 
 ponderous rollers, or subjected to the blows of heavy 
 hammers, are united and drawn into bars of required 
 sizes and forms for use. 
 
 These masses, taken from the furnace and suffered 
 to cool without hammering or rolling, would be found 
 more or less crystaline and brittle. But the latter 
 operations prevent such a result, and the iron becomes 
 more or less soft and flexible, even in a cold state. 
 
 Iron which has undergone the uniform process of 
 rolling, is generally of uniform quality and strength 
 throughout the whole piece ; and, as far as it can be 
 used in that state, without re-heating and re-working, 
 it may be regarded as somewhat more reliable than 
 when it has been forged and welded into different and 
 more complex forms. . 
 
 The high temperature required in welding, demands 
 experience and judgment in determining the proper 
 time to " strike," that is, when the metal is hot enough 
 to adhere firmly, but not overheated to burning. 
 Moreover, though the hammering required to bring 
 
190 BRIDGE BUILDING. 
 
 the parts together and reduce them to proper form and 
 size, may prevent crystalization immediately at the 
 welded point, still on either side are portions which 
 may have "been heated so as to change the arrange 
 ment of particles, and not subjected to sufficient ham 
 mering to counteract the deteriorating tendency. 
 Hence, a break is more liable to take place a little on 
 one side, than immediately through the welded part. 
 
 To obviate this liability, the parts to be welded should 
 be enlarged by upsetting several inches from the end, 
 so as to admit of re-drawing under the hammer a little 
 beyond where the intense heat has reached. 
 
 But theory aside for the moment, although the 
 avoidance of welding in work to be exposed to great 
 stress is desirable, it is nevertheless a fact established 
 by large experience, that welded parts will bear as 
 great a strain as takes place in well proportioned 
 bridge work, with as much certainty as ever has been 
 realized in any department of the means of locomotion. 
 
 Danger lurks everywhere at all times. In railroad 
 travel, boilers burst, rails break, wheels and axles 
 break, etc., etc., but the failure of a weld in bridge 
 work is rare indeed, and very few authenticated cases 
 can be referred to. 
 
 I would, however, prefer a weld in the straight part 
 rather than in the end of a link, unless made with an 
 excess of section around the bend. "Whether a bend 
 around a pin of 1J or 2 times the diameter of the link 
 iron is more liable to break than the straight sides of 
 the link, I can refer to no reliable authority to deter 
 mine. The longitudinal strain is no greater in the 
 bended, than in the straight parts, if well fitted to the 
 pin. But of course, it can not be expected to have a 
 fit so close as to ensure a firm pressure quite round the 
 
ARCH TRUSS BRIDGES. 191 
 
 semi-circle. Hence the bearing is mainly on the back 
 Bide of the pin, until by a yielding to compression, and 
 by a slight bending of the link end, a pressure is pro 
 duced all around. 
 
 This slight bending, good iron will undergo without 
 having it? strength impaired, when in its normal con 
 dition. But this condition is disturbed in the process 
 of bending, the outside portion being extended, and 
 the inside compressed, whereby the stiffness of the part 
 is increased. In the outside portion the power of re 
 sisting extension is increased, while that of the inside 
 portion is possibly diminished ; and, whether the 
 aggregate resistance to extension is increased or dimin 
 ished, experiment alone can determine ; and, undoubt 
 edly, the more soft and flexible the iron, the better can 
 it adapt itself to a bearing upon the pin. Hence, it 
 should be allowed to cool gradually from a full red 
 heat, after the shaping is finished. 
 
 Hence, also, the necessity of extra section in welded 
 ends, which, being less flexible, must obtain bearing 
 surface by compression and yielding of contiguous 
 parts, rather than by bending, and consequently, must 
 undergo greater transverse strain in the end of the link. 
 
 CXIII. A link formed of wire J"in diameter, formed 
 to a pin /j" in diameter at one end, and brazed with 
 a long lap at the other, suffered a permanent stretch 
 in the straight part, of one per 0. of its length, with no 
 apparent injury at the ends. Other analogous experi 
 ments have shown similar results, namely, that the 
 straight portions will yield before the bended portions. 
 
 Now the same degree of disturbance in the metal 
 takes place in a small, as in a large rod, bent to a 
 curve whose radius has the same ratio to the diameter 
 
192 BRIDGE BUILDING. 
 
 of the rod. Hence, it is difficult to avoid the conclu 
 sion that rods of soft and flexible iron, such as ought 
 to be used for tension members in bridge work, bent 
 to a proper fit upon connecting pins of diameter about 
 twice that of the rods, and formed into links by weld 
 ing in the straight parts, are quite safe under any stress 
 within the limits adopted in bridge work. 
 
 But it seems to be more convenient to form the weld 
 at one end of the link, if not both, and such has been 
 the usual practice; and, as before remarked, if a sur 
 plus of metal section quite around the bend be secured, 
 and the work well performed, this plan can scarcely be 
 regarded as faulty, especially, in view of the long, 
 varied, and successful usage of such vast numbers of 
 links made in this manner. 
 
 Now, although the link chord is very simple, effi 
 cient, and convenient to make and manage, there are 
 available alternative devices, some of which will be 
 here described. 
 
 THE EYE-BAR CHORD. 
 
 CXIY. This is composed of two or more single rods, 
 of oblong, square, or round section to each panel ; 
 connected by cylindrical pins passing through strong 
 eyes at each end of the chord bars. 
 
 This plan until recently, has involved quite as much 
 welding as the link chord; the eyes having been 
 formed in separate pieces, and welded to the body of 
 the rod. But within a few years a process has been 
 devised by the Phoenix Iron Co., of Pennsylvania, for 
 upsetting and forming eyes upon rolled bars. A mold 
 or die gives the desired form and size to the head, and 
 aside from the fact that a violent disturbance of the 
 normal condition of the iron is produced in the vicinity 
 
ARCH TRUSS BRIDGES. 193 
 
 of the bead, there can be no question as to the excel 
 lence of the work produced ; and it is undoubtedly, 
 perfectly reliable, under any stress to which it is ad 
 missible to expose the material in bridge work. 
 
 Figure SOB represents the joint of an eye-plate chord 
 at Cj adapted to the arch truss. Upright and diagonals 
 have each an eye to receive the connecting pin at the 
 lower end. The upright has a washer above the eye 
 to form a beam seat above the eyes of the chord plates. 
 Perhaps the washer should be in the form of a saddle 
 or stool, with downward projections bearing upon the 
 pin outside of the diagonals ; or, perhaps inside, in 
 case the diagonals be in pairs, as before suggested. 
 [cm.] 
 
 SIZE OF CONNECTING PIN. 
 
 CXV. Considering the average bearing upon the 
 pin, to be at the centre of thickness of the eye, or link 
 end, as the case may be, the thickness of the eye indi 
 cates the leverage upon which opposite links act, when 
 side by side upon either end of the pin. Estimating 
 the strength of the pin, then, at 4,500ft>s. to the square 
 inch of section, with a leverage equal to the diameter 
 of the pin [see xcvm,] we obtain the proper diameter 
 of the pin as follows : 
 
 Let a=area of section in link or chord bar. 
 tf=thickness of eye=leverage of action. 
 2=*=diameter of pin, in inches. 
 
 Then, .7854x 2 =area of pin section ; and this multi 
 3534.30 
 
 plied by 4,500 -|,= .^ e q ual to tbe res i gt j n g p 0wer 
 
 of the pin ; while 15,000a=the power of the link ; and 
 putting these two expressions equal to one another, 
 and deducing the value of #, we have the required 
 diameter of the pin, ^4.244a.* inches, =x. 
 25 
 
194 BRIDGE BUILDING. 
 
 CXYI. If #=4 square inches, and =1.5 inches, 
 then a.t = 6, and x = ^6x4.244 = 2.94 inches. 
 This diameter of pin is required to withstand the action 
 of the chord alone, which is the only stress upon the 
 pin when the chord is at maximum tension. But 
 when the diagonals running in the same direction 
 horizontally, with the inside links, are brought into 
 action, they act in conjunction with the links in pro 
 ducing stress on the pin. 
 
 Now, the greatest stress upon bn, Fig. 11 [see xxxiv] 
 occurs when the point b alone is loaded, and the links 
 ab sustain f of their maximum stress from movable 
 load, and bn. sustains 5w ff , giving a horizontal pull of about 
 6 5u>", the amount varying with depth of truss. Again, 
 besides the 6w" bearing at the point , in virtue of 
 the movable weight (10), at 6, we have 3w due to weight 
 of structure, also bearing at a ; and assuming &w . to 
 be equal to li, or 7w" the whole pressure at a, equals 
 13i0", when the horizontal pull of bn equals 6.5w". 
 
 The tension of ab, in the usual proportion of arch 
 trusses, equals about 2J times the bearing at a, whence 
 the stress of ab with the point b alone under load, 
 equals 13^"x2.25* = 29.25u>". Deducting from this, 
 6.610" for horizontal pull of bn, it leaves 22.75w" = 
 stress of be. Then, assuming the diagonal to act in 
 the centre of the pin, and the length of pin between 
 centres of bearing of outside links to be 27", we find 
 the stress at the centre of the pin, by taking the mo 
 ments with respect to the centre, of the action of the 
 two links at either end of the pin. The difference of 
 these moments, the forces being opposite, is the mo 
 ment of the force producing stress at the centre of the 
 pin; in other words, it is the force acting transversely 
 
ARCH TRUSS BRIDGES. 195 
 
 upon the pin, at a leverage of 1 inch, the inch being 
 our unit of length. 
 
 "We found the pull of ab = 29.25io", or 14.625^" at 
 each end of the pin, which multiplied by distance from 
 centre (13.5") gives a moment = 197.4375*// , while for 
 be, the moment is JX22.75X12" = 136.500" ; and the 
 difference = 60.9375w" = stress in centre of pin, upon 
 a leverage of I". 
 
 Assigning such a value to w" as will give the as 
 sumed stress of 15,0001fes. to the inch upon ab with the 
 truss fully loaded, with a bearing at a, of 2lw" for mova 
 ble, and lw" (= 3*0 ), of weight of structure, we find a 
 stress of 28 x 2 J ( 63)z0" = 8 X 15,0000ft>s. = 120,000ft>s ; 
 whence w" = l,905Ibs. which, being substituted in the 
 above amount of 60.9375*0" gives the stress in pounds 
 at the centre of the pin, on a leverage of 1", equal to 
 116,086Ibs. 
 
 We have seen [xcvin] that the resisting power of 
 a projecting pin equals 4,500, which in this case, equals 
 4,500AD (L being = 1), equal to 4,500 X.7854X 3 . Then, 
 making this expression = 116,088ft>s. we have x = 3.2" ; 
 being 0.26" larger than is required* to withstand the 
 action of chord alone, at its maximum stress, as already 
 shown [cxvi.]. 
 
 By similar process we find very nearly the same re 
 sults with respect to the shorter pins toward the centre 
 of the truss. For, although the maximum action of 
 diagonals takes place under greater stress upon chords, 
 the difference is balanced by diminution in length of 
 pins toward the centre of the truss. 
 
 Should this mode of connection be adopted, the pre 
 ceding illustrations and examples, it is hoped, will 
 enable the proper proportions of connecting pins to be 
 determined for trusses of whatever dimensions. 
 
196 BRIDGE BUILDING. 
 
 A RIVETED PLATE-CHORD. 
 
 CXVII. May be formed of Hat plates as long as may 
 be conveniently managed, connected by splicing plates 
 of a little more than half the thickness of the chord 
 plates, one upon each side, riveted or bolted with such 
 a distribution of rivets, &c., as may not weaken the 
 plates by more than the width of one rivet hole. 
 
 The area of rivet section should be at least f to f as 
 great as the net section of the chord plate, on each side 
 of the joint; and, go, Fig. 34J denoting the splicing 
 plate, the distance cd, from the joint to the centre of 
 the first rivet hole, should be at least twice the diame 
 ter of the rivet (depending somewhat upon the size of 
 rivet and thickness of plate, as well as the soundness 
 of grain in the iron). The succeeding rivets, a, ,/, 
 &c., should be placed alternately on opposite sides of 
 the centre, so that the oblique distance ac (== 0), may 
 equal the transverse distance (= T), + the diameter 
 of whole (= II ). Then, representing the longitu 
 dinal distance be, by L, we have T+H = 0, and 
 (T+H) 2 = O 2 , - T 2 +L 2 = T 2 4-2TH-fII 2 ; whence L 
 = \/2T.H + II 2 . 
 
 If the plates be 6" wide, and T = 3J" (which is re 
 garded as in good proportion, the above formula gives 
 L == 2J" very nearly, for a f " hole. Then, 5" being 
 allowed for the space ce, and 2" each for cd and eg, the 
 splice plates would have a length of 20J", and { of the 
 whole section of chord plates would be available for 
 tension; since an oblique section through two holes, 
 would quite equal a direct transverse section through 
 one hole. 
 
 The amount of rivet section above given is estimated 
 upon the assumption that each rivet must be sheared 
 
ARCH TRUSS BRIDGES. 197 
 
 off in two places; and that it will resist, those shear 
 ings, each, with about f of the force required to pull 
 the rivet asunder by direct longitudinal strain. 
 
 It is obvious that the two rivets e and/, Fig. 34 J, sus 
 taining a portion of the stress of the chord plate, relieve 
 in the same degree the stress upon the portion between 
 those rivets and the joint, or end of the plate ; whence 
 it is not necessary to preserve the same section in the 
 portion thus relieved, as in other portions of the plate. 
 Therefore the rivets a and c, nearer to the joint, may 
 be larger than e and/, when the section of plates re 
 quires more rivet section ; provided always, that the 
 least net section of splice plates, have as great an area 
 as the chord plate has through only one of the smallest 
 rivets. For instance, four f" rivets are sufficient for 
 plates 6" x J". But plates 6" xf" require more 
 rivet section say " for e and /, and -|" for a and c ; 
 while, the same for the former and V rivets for the lat 
 ter, give about the required section for plates 6" x f". 
 This leaves in each case, the same proportion of net 
 available section of plates. 
 
 Moreover, if rivets a and c be placed opposite to each 
 other, and /be removed to , the rivets being " and 
 V respectively. Then, the smaller rivets sustaining 
 over J of the stress, while the others sustain less than 
 f, the latter may cut off J of the net section (which is, 
 in this case f" less than the whole width of plate), and 
 still leave enough to sustain more than their own 
 legitimate share of the stress. 
 
 This may be done by one rivet or two, placed op 
 posite c ; and thus the length of splice plates may be 
 shortened to 15 J inches, instead of 20 J, as represented 
 in the diagram. But, as in this case, the long plate 
 has a net width of 5J" and the splice plates, only 4" 
 
193 BRIDGE BUILDING. 
 
 the latter require 31J per C. more thickness than the 
 former, so as to nearly or quite balance the saving in 
 length. 
 
 As to the proportions of parts, in this kind of work, 
 I would suggest that the thickness of plates be from Jth 
 to y^th of their width, and the diameter of rivets, from 
 1 to 1 J times the thickness of plates. If plates be very 
 wide and thin, they may be liable to be strained un 
 evenly, and if very narrow, an unnecessary proportion 
 of section is lost in rivet holes. 
 
 FIG. 34*. 
 
 CXYIIL The end connections of plate chords of this 
 kind, may be effected by riveting on side plates at the 
 ends, as seen at E, Fig. 34J, so as to give a thickness 
 that will allow about J of the width of plate to be cut 
 away by a hole for the connecting pin P, either round 
 or oblong with square ends for adjusting keys or 
 wedges. 
 
 Or, the side plates may be omitted, and two key 
 holes made in the middle of the plate, one for a key 
 having a thickness equal to the diameter of the smaller 
 rivets, and far enough from the end to admit of another 
 hole nigher to the end, with about 2" between the holes. 
 This may, if necessary, have twice the width of the other 
 hole, and should leave at least twice the width of hole, 
 between hole and end. 
 
 The width of the wider hole, -{-twice that of the other, 
 should equal about half the width of the plate ; and 
 the keys should be driven to an equal bearing before 
 the work be subjected to use. 
 
ARCH TRUSS BRIDGES. 199 
 
 The connecting blocks used with this chord, sus 
 taining only the horizontal action of diagonals, may be 
 considerably lighter than those used with the links, 
 especially in arch trusses. In order to transfer the 
 horizontal action of diagonals to the chords, mortises 
 may be made in the plates, as seen at m Fig. 34^, not 
 wider than, the smallest rivets used in splicing, to re 
 ceive tenons of wrought iron cast in the block. 
 
 As to the merits of the riveted plate, as compared 
 with the link chord, it may be assumed that two splices 
 are sufficient for any truss not exceeding 100 long, and 
 that the weight of splicing plates and rivets will equal 
 4 or 5 feet extra length of plates, say 6 per cent upon 
 a chord 80 long. To this we have to add about 14 
 per cent for extra section to compensate for rivet holes, 
 making 20 per cent of iron lost in forming connections. 
 
 Links require about half -as much extra material, to 
 be taken up in bends, lappings, and enlargement of 
 section at the ends; showing about 10 per cent less 
 iron for the link, than for the plate chord. This would 
 amount to about 400ft>s. for two trusses of 80 , with 
 links of 1J" round iron. But this may be nearly or 
 quite balanced by 500 or 600ibs. of castings, which 
 may be saved in weight of connecting blocks. 
 
 The economy of material being so nearly equal in 
 the two chords, their relative merits must depend 
 mostly upon the comparative cost of manufacture, and 
 the relative efficiency of the chords in use. It is deemed 
 far from improbable that the riveted plate chord might 
 be found, on fair and thorough trial, to be worthy of 
 extensive use in arch trusses, in place of the link chord. 
 The fact that in the plate chord, the iron is used in its 
 original condition, as it comes from the rollers, is cer 
 tainly favorable. 
 
200 BRIDGE BUILDING. 
 
 BRIDGES WITH PARALLEL CHORDS. 
 
 CXIX. These may be constructed with or without 
 vertical members, and inform, either rectangular, with 
 vertical end posts, or trapezoidal, having inclined 
 end members, or king braces, as exbibited in Figs. 
 12, 13, 18 and 19. 
 
 TRAPEZOIDAL TRUSS BRIDGE, WITH TENSION DIAGONALS 
 AND COMPRESSION VERTICALS. 
 
 For short spans, less than 70 or 80 feet long, the 
 simple cancel, as in Fig. 12, will generally be used, 
 with trusses too low to admit of connection between 
 upper chords, except in case of deck bridges. 
 
 The same plan of lower chords composed of links 
 and cast iron connecting, blocks, may be used, as 
 already described for the arch truss. The connecting 
 blocks are shorter, and may be cast in connection with 
 the upright, or the latter may be in a separate piece. 
 In the latter case, the block should have a suitable seat 
 to receive the upright, and keep it in place. 
 
 As the upper chord depends upon the stiffness of the 
 beam and upright for lateral support to keep it in line, 
 the upright should be firmly attached to the beam, and 
 at right angles therewith. 
 
 There is no means of estimating exactly the trans 
 verse force which the chord may exert upon the up 
 right. But if the ends of chord segments be properly 
 squared and fitted, the lateral tendency will be quite 
 small. It is recommended, that each upright have a 
 transverse strength sufficient to withstand a force of 
 l,000fts. acting at the upper chord ; that it have a web 
 and flange form of section, with a width of we!) at the 
 
BRIDGES WITH PARALLEL CHORDS. 
 
 201 
 
 FIG. 35. 
 
 connection with the beam, not less than ^ s of the dis 
 tance of upper chord from the beam. 
 
 Fig. 35 will serve to illustrate the modes of connec 
 tion for most of the members of a bridge of the kind 
 under consideration. That 
 part of the upright between a arid 
 6, is contracted in length. Other 
 wise, the parts are represented 
 in nearly correct proportions. 
 At c, is represented the connec 
 tion of the upright with the end 
 of the beam, by means of a 
 double eye and bolt, as shown at 
 h. This receives the web of the 
 beam, to which it is secured by 
 the transverse bolt, which should 
 be long enough to receive the 
 
 eye of a swaj r rod under both head and nut. The stem 
 of this fixture extends through the upright at its widest 
 part (whence it may taper in both directions), and is 
 secured by a nut upon a screw of about 1J" in diame 
 ter. The beam should rest with its lower flange upon 
 a small projection cast upon the upright, and not hang 
 upon the connecting fixture. 
 
 If so preferred, the sway rods may be connected by 
 a screw and nut cast in the end of the connecting 
 block, as seen at d. This plan has been used, but the 
 connection by the bolt at c is deemed preferable. 
 
 The outer and inner flanges of the upright at the 
 top, being increased to nearly an inch in thickness, ac 
 cording to size of bridge, and extending 3 or 4 inches 
 above the web, terminate in semicircular concaves to 
 receive the pin connecting the diagonals with the 
 upper chord. A full view of the flange at the top of 
 26 
 
202 BRIDGE BUILDING. 
 
 the upright, with the pin resting in the concave, is 
 shown at e. 
 
 A heavy cross-bar from flange to flange at a, and 
 light cross-bars at intervals of 16 to 18 inches from a 
 to 6, serve to support the flanges, and stiffen the piece. 
 
 The diagonals are formed with eyes to receive the 
 connecting pin at the upper end, and screws and nuts 
 to connect with the block at the lower chord, in the 
 same manner as in the arch truss. 
 
 The main diagonals, those inclining outward from 
 the centre of the truss, should be in pairs, and in size, 
 proportioned to the stress they are liable to, as deter 
 mined by the process fully described in sections 
 xxxix, &c. 
 
 The links acting in conjunction, horizontally, with 
 the main diagonals, should go on next the end of the 
 connecting block, as that arrangement obviouslypro- 
 duces less stress upon the block. 
 
 The upper chord, usually formed of hollow cylinders, 
 has openings in the underside at the joints, for uprights 
 and diagonals to enter, where they connect by means 
 of the transverse pin already mentioned. The cylin 
 ders should have an extra thickness for 3 or 4 inches 
 from the ends, and a strong collar around the opening, 
 to restore the loss of strength occasioned by the open 
 ing; and the ends should be squared in a lathe, to 
 secure a perfect joint and a straight chord. 
 
 If it be required to give a cambre to the truss, the 
 ends of cylinders should be slighly beveled at the ends, 
 making the under side a trifle shorter. This is easily 
 effected by throwing the end opposite the one being 
 turned, out of centre more or less, according to the 
 cambre required. An 8 panel truss requires an ex- 
 centricity equal to ^ of the requiredr ise in the centre 
 
BRIDGES WITH PARALLEL CHORDS. 203 
 
 of the truss. For any even number of panels, make a 
 series of odd numbers, 1, 3, 5, &c., to a number of terms 
 equal to half the number of panels; add the terms of 
 the series, and divide the required cambre by the sum, 
 and the quotient equals the required excentricity to 
 give the proper bevel. 
 
 For an odd number of panels, take as many even 
 numbers 2, 4, 6, &c., as equal half the greatest even 
 number of panels; add the terms and divide as before 
 for the excentricity. For illustration, for 8 panels, the 
 four odd numbers 1 + 3 + 54-7 = 16, whence the excen 
 tricity should be Jg of the cambre, as above stated. 
 Fora 7 panel truss the three even numbers 2+4+ 6 = 12. 
 Hence the excentricity should be * 2 of the cambre. 
 The reason for this ruje will be obvious without more 
 particular demonstration. 
 
 At the obtuse angles of the truss, a hollow elbow is 
 inserted (#, Fig. 35), reaching about 10 inches each 
 way from the angular point, at the centre of the con 
 necting pin, with an opening in the under side for up 
 right and diagonals to enter, where they are fastened 
 by a pin or bolt, as at the intermediate joints ; the 
 cylinders meeting the elbow, being shortened by as 
 much as the elbow extends from the angle, either way. 
 
 The vertical member connecting with the elbow, is 
 exposed to tension only, sustaining a weight equal to 
 the gross panel load of the truss. It may be composed 
 of two wrought iron suspension rods, united in a single 
 eye at the top, and diverging downward to a connection 
 with the beam and connecting block; or, it may be of 
 cast iron, like the intermediates, with wrought iron eye 
 plates, in place of the cast iron flanges with concaves 
 as seen at e. These should be fastened by efficient 
 means to the cast iron part of the upright; which lat- 
 
204 BRIDGE BUILDING. 
 
 ter should have a cross-section nowhere less than 
 one square inch to each 2,000ft)3. of the gross panel 
 load. A complete wrought iron connection from beam 
 to elbow, however, is to be preferred. 
 
 The thickness of web and flanges of the uprights, 
 should be from f to J inch, and the cross-section of 
 upper chord cylinders should be about 20 per 0. greater 
 than that of the portion of bottom chord forming the 
 opposite side of the oblique parallelogram included be 
 tween consecutive main diagonals and included sections 
 of chords ; as d e k I, Fig. 12. 
 
 The upright should be so formed as to bring the cen 
 tres of upper and lower chords in the same vertical 
 plane. 
 
 Sway rods in this class of bridges, should be about 
 y in diameter; with a turn buckle near one end for ad 
 justment, and an eye at each end, for connection with 
 the bolt at c. The screw working in the turn buckle 
 is cut upon the short piece, which should be J" larger 
 in diameter than the long piece which has no screw 
 upon it. 
 
 The lower chords, king braces, and sway rods of the 
 endmost panels, connect with cast iron foot pieces 
 upon the abutments, as represented 
 in Fig. 36. The portion of lower 
 chord in the end panels, usually 
 consists of single rods, instead of 
 links, with an oblong eye at one 
 end to receive the connecting block, and a screw and 
 nut for connection with the foot piece (Fig. 36), at the 
 other end. 
 
 This plan of construction will generally yield pre 
 cedence to the Arch Truss plan, for short spans, except 
 for deck bridges upon rail roads, in which case the 
 
BRIDGES WITH PARALLEL CHORDS. 205 
 
 structure will be secured laterally, by x ties, or sway 
 rods between beams, and between king braces at the 
 ends ; no X bracing being required between lower 
 chords. 
 
 Low trusses constructed in the manner above de 
 scribed, have been used satisfactorily for supporting 
 the outside of wide side walks ; answering the pur 
 poses of a protection railing at the same time. For 
 this purpose, the uprights are only 5 or 6 feet long, so 
 as to bring the upper chord about 4 feet above the 
 flooring. The first instance of this kind was in the 
 case of the canal bridge on Genesee street in Utica, 
 built 18 or 20 years ago, and repeatedly copied since. 
 
 CXX. Bridges from 80 to 100 feet for common roads 
 may be constructed with single canceled trusses, 13 to 14 
 feet high ; in which case the panels will require to be 
 wide (horizontally) in order to avoid an inclination of 
 diagonals too steep for good economy. 
 
 But for railroad purposes, the trusses require a depth 
 of about 20 feet to afford sufficient head room under 
 the top connections, unless the beams be suspended 
 below the bottom chords. Hence, the 
 
 Double Cancelated Truss 
 
 should be adopted for " through bridges " of spans 
 exceeding 70 or 80 feet. 
 
 Figures 18 and 20 exhibit in outline, the general 
 character of the double cancelated trapezoidal truss 
 bridge ; and, it is only necessary in this place, to de. 
 scribe feasible modes of forming and connecting the 
 various members ; which may be done essentially as 
 described in the preceding section, with such modifi 
 cations as follow. 
 
206 
 
 BRIDGE BUILDING. 
 
 FIG. 37. 
 
 Cast Iron Uprights 
 
 are composed of two or more pieces. When of two 
 pieces, they may be connected by flanges and bolts at 
 the centre, where they should have a diameter of about 
 $ *ij- of the length, and a cross-section determined by 
 the maximum stress, and the power of resistance of 
 the material, as indicated in the table [XGIII.] 
 
 The upright may taper from the centre to either end 
 to a diameter of 5 to 6 inches, internally. The lower 
 
 end is to stand upon 
 a properly formed 
 seat (h Fig. 37), 
 upon the connect 
 ing block of the 
 lower chord, and 
 may have an open 
 ing at the bottom, 
 upon the inner side, 
 where the beam 
 may enter and rest 
 upon a seat (e), inside of the upright, upon the con 
 necting block. The strength destroyed by this cutting 
 the post should be restored by additional metal in a 
 band or collar (c, Fig. 37), around the opening, and, 
 if necessary, by the wing flanges dd, extending 6 or 8 
 inches above the opening. To avoid too much cutting 
 of the post, the flanges of the beams may be reduced 
 to 3 or 3J inches in width. The post and beam seat 
 upon the connecting block may be elevated 3 or 4 
 inches above the links, as may be required, so as to 
 allow sway rods to pass through with simple screws 
 and nuts for adjustment; thus dispensing with turn- 
 buckles. 
 
BRIDGES WITH PARALLEL CHORDS. 207 
 
 Holes should be cast in the central part of the post, 
 for diagonals to pass obliquely through. Or, what is 
 perhaps better, the connecting bolts may be length 
 ened so as to permit the insertion of an open box, or 
 frame, between the flanges, as seen at a, Fig. 37. 
 This intermediate piece should be so constructed as 
 to close the ends of the hollow pieces meeting it, and 
 prevent the water from getting inside. 
 
 The top end of the upright is forked, with concaves 
 for the connecting pin to rest in, as described in the 
 last section, and as seen at a, Fig. 38. The cap piece 
 of the post may be cast separate, or in connection with 
 the upper half of the column. Both plans have been 
 satisfactorily used. All joints, when practicable, 
 should be accurately fitted by turning or planing. 
 
 This plan of a cast iron upright, composed of two 
 principal parts, with or without the centre piece, is 
 perhaps as good as any for general use ; the principal 
 disadvantage being the difficulty of giving a sufficient 
 diameter in the middle for stiffness, without two much 
 reducing the thickness of metal, or increasing the 
 amount of cross-section beyond the proper theoretical 
 proportions. 
 
 To obviate this difficulty, the device adopted in the 
 original model of the Trapezoidal bridge, was that of 
 using truss-rods, or stiffening rods, to secure the post 
 against lateral deflection, after the mannner shown in 
 Fig. 38. 
 
 In the case of using stiffening rods for the uprights, 
 it may be recommended to form each half of the column 
 in two pieces, somewhat in the manner above described 
 for the whole one, without stiffeners; making the 
 piece forming the end portion about Jth shorter 
 
208 
 
 BRIDGE BUILDING. 
 
 than the other, with a strong flange at the larger end, 
 to afford attachments for the stiffening rods. 
 
 Fm. 38. 
 
 In Fig. 38, a c d exhibits the upper half of the up 
 right ; A, the stretcher at d ; /,-, the flange at c (enlarged), 
 and , j, enlarged sections of the two ends forming the 
 joint at c. The piece running toward the centre has no 
 flange at <?, but has :m increase of thickness for a short 
 distance from the joint, as shown atj, and a diameter 
 about I" larger than the abutting piece, which latter 
 has a small burr entering the former J" or J" to keep 
 the ends in place. At tf, each of the pieces meeting 
 at that point, has a bi-furcation, so as to form an open 
 ing for diagonals to pass through, at the same time 
 passing through the stretcher h. 
 
 The lower half of the upright is the same as the 
 upper, except the end, which is squared to fit a flat 
 bearing upon the connecting block. An enlarged ver 
 tical section of the lower end is shown at , Fig. 38. 
 See also Fig. 37, where is shown the arrangement for 
 the beam to enter the opening in the lower part of the 
 upright, as described a few pages back. 
 
 Floor beams of wood or iron may be suspended be 
 low the chords by bolts passing down through the 
 connecting blocks, or, wooden beams may be in two 
 
BRIDGES WITH PARALLEL CHORDS. 209 
 
 parts, resting upon flanges cast upon the upright a^out 
 3" above the lower end ; the beam timbers being hol 
 lowed out upon the insides, so as to embrace the up 
 right, in part, leaving a space of 2 or 3 inches between, 
 and secured in place by bolts and separating blocks. 
 
 The mode of inserting iron beams by means of open 
 ings in the uprights, has already been explained. 
 Lateral x ties, or sway-rods may be inserted by bolting 
 to the beams (Figs. 31 and 33), attaching to the inner 
 end of connecting blocks, as at </, Fig. 35, or by passing 
 through the block between the links and the post and 
 beam seat, in the manner referred to two pages back. 
 
 Diagonal tics of wrought iron, and transverse struts 
 
 O O 
 
 of wrought or cast iron, are also required between the 
 upper chords, to keep them in line. Cast iron cross- 
 struts may have the web and flange form of section, 
 with shallow sockets at the ends, to admit the connect 
 ing bolts at the upper chord to enter, after passing 
 through eyes upon the upper sway-rods and nuts to 
 hold them in place. These sway -rods require turn- 
 buckles for adjustment, when they extend across one 
 panel only. Bat if the bridge be wide between trusses, 
 the rod may extend only from the end of one cross- 
 strut to the centre of the next, where it may pass 
 through the strut, and receive a nut on the end. Thus, 
 four rods meeting at the centre of the strut, each 
 having its appropriate hole to pass through, all as near 
 to one another as practicable, with sufficient space for 
 nuts to turn (see a and e, Fig. 39), it forms a conven 
 ient arrangement for adjusting the rods to a proper 
 tension, at the same time affording lateral steadiness to 
 the cross -strut. 
 
 The end-most struts, however, should have no rods 
 connecting with them in the centre, as they can have 
 
210 
 
 BRIDGE BUILDING. 
 
 no antagonist rods on the opposite sides to prevent the 
 springing of the struts. The end panels should have 
 two. full diagonals with turn-buckles, and two half 
 diagonals connecting with the centre of next strut. 
 
 FIG. 
 
 In Fig. 39, a shows the middle of the cross-strut, 
 with the upper flange removed ; c, a joint of the upper 
 chord, where the connecting bolt passes transversely, 
 receiving eyes of sway-rods, and nut, and entering the 
 end of the strut at d\ the upper part of the strut being 
 removed, down to the socket. The bolt bears upon a 
 slight swell in the bottom of the socket, to ensure a 
 central thrust : (see also, 6, Fig. 38). At e is presented 
 a side view of the centre of the strut, showing the ar 
 rangement of the holes. 
 
 A similar device has been used with good effect for 
 giving lateral support to posts or thrust uprights, of 
 the web and flange form, so proportioned as to have 
 greater stiffness transversely than lengthwise of the 
 truss. 
 
 It has been demonstrated that the weight sustained 
 by these posts, increases toward the ends of the truss, 
 while the tension of counter diagonals runs out to 
 nothing, a little way from the centre of the truss. For 
 instance, 4/6 Fig. 18, sustains w" Ifw , which is a 
 negative quantity whenever w is less than 4w/, that is, 
 
BRIDGES WITH PARALLEL CHORDS. 211 
 
 when the greatest movable load is less than four times 
 the weight of structure, as is usually the case. But 
 instead of dispensing with that member, and other 
 counters on the left, they may be made in two pieces 
 each, off" or " iron, connecting with the upright at 
 the crossing by screws and nuts, in the manner above 
 described ; thus preventing the uprights from deflect 
 ing lengthwise of the truss, where the greatest weights 
 act upon them, and where otherwise, they would re 
 quire to be heavier. 
 
 GENERAL TRANSVERSE SUPPORT. 
 
 CXXI. The system of cross-struts and diagonal ties 
 serves to preserve the upper chords in line, but does 
 not prevent the whole structure from swaying bodily 
 to the right or left ; a result which would be fatal to 
 the structure. 
 
 In the arch truss Fig. 27, the width of base at tlie 
 bearings upon abutments, resulting from the peculiar 
 form of the arch, affords the required stability in this 
 respect. 
 
 In case of the trapezoidal truss, when high, various 
 devices have been resorted to for producing the 
 same results. For deck bridges, cross tying between 
 king braces at the ends, is an easy and efficient means 
 of accomplishing the object. For through bridges, 
 guys from the connecting bolt at the elbow of the ob 
 tuse angle, anchored in the abutment, may be em- 
 ploj^ed. But this requires extra length of abutments 
 and piers, and the effects of change of temperature, 
 are, to tighten and slacken the guys, so as to impair 
 their efficiency. 
 
 To obviate the latter objection, double acting guys 
 (acting by thrust and tension), applied at one side only 
 
212 BRIDGE BUILDING. 
 
 of the bridge, have been employed ; the effect of 
 temperature being only to very slightly sway the 
 bridge laterally, but not so as to be detrimental to sta 
 bility. This also, requires 5 or 6 feet more length of 
 pier, than what is necessary to bear the vertical pres 
 sure. 
 
 Again, the king braces have been made with two 
 branches diverging from the elbow to a base of 2 or 3 
 feet in width, according to height of truss. This plan 
 has been used in a large number of bridges, with sa 
 tisfactory results. But it contracts to a small degree, 
 the available width of bridge ; not, however, so as to 
 produce material inconvenience. 
 
 Another device is, the introduction of two or more 
 long beams, extending 5 or 6 feet outside of the trusses, 
 say at the first thrust uprights from the ends (as over 
 Figs. 3J, 3J, Fig. 18), with guys extending from the 
 connecting bolt at the upper chord, to the ends of said 
 long beams (see g Fig. 38). 
 
 Arches may also be introduced at the ends of the 
 bridge, attached to the king braces, say a quarter of 
 the way down from the top, and with the connectingbolt 
 at the elbow. These may be made with a full, or an 
 open-work web, and flanges of 2J or 2J inch angle 
 iron upon both sides of the web, at the top, and around 
 the arch, and either angle iron or plain flat bars, along 
 the sides next the king braces. 
 
 A web of jV plates placed edge to edge, and bat 
 tened upon both sides with plates of the same about 
 4 /r wide, riveted alternately on each side of the seam, 
 with angle iron, etc., as above, riveted once in 6", forms 
 a stiff and substantial arch for the purpose under con 
 sideration, such as have been used effectively in a 
 bridge of 160ft. span. 
 
BRIDGES WITH PARALLEL CHORDS. 
 
 213 
 
 Moreover, simple arch braces extending from the 
 king brace to a stiff and substantial cross beam from 
 
 elbow to elbow 
 (see Fig. 40), will 
 effect nearly the 
 same result as the 
 arch. In both 
 cases, a considera 
 ble degree of lateral 
 stress is liable to 
 be thrown upon the 
 king braces, which 
 accordingly should 
 be strong, or sup 
 ported by truss 
 rods, and struts 
 opposite the feet of the arch or braces. 
 
 Whether the truss rods be used or not, it is advisa 
 ble that the connection with the king brace be made 
 by means of a bolt running through the whole dia 
 meter of the king brace, with nut or shoulder bearing 
 externally and internally upon both sides, to counteract 
 any tendency to collapse. 
 
 Fig. 40 presents an end view of a bridge, showing 
 arch braces, with truss rods to sustain the thrust of 
 arch braces against king braces. The internal figure 
 gives an enlarged view of the connection at the elbow. 
 A strap a (about }"x5"), bent twice at right angles, 
 is riveted or bolted to the flanges of an I beam 
 (about 9" deep), leaving a space of about 4 inches from 
 the end of the I beam, for eyes of two sway rods and a 
 nut upon the large connecting bolt. This bolt in large 
 bridges being from 3 to 4 inches in diameter through 
 the elbow, is reduced to 2 or 2J inches in the part pro- 
 
214 BRIDGE BUILDING. 
 
 jecting through the strap above mentioned, and the 
 eyes of sway rods. 
 
 The truss rods may not be necessary (with substan 
 tial king braces), for spans not exceeding 150 feet, 
 But they will add to the security, in all cases of rail 
 road bridges having cast iron king braces. These 
 members being over twice the length of the cylinders 
 in the upper chord, are usually cast in two pieces, and 
 connected by bolts and flanges in the middle, where 
 they have a diameter of about 2 ^ of the length of 
 brace, and taper to the size of the upper chord at the 
 ends. 
 
 CXXII. WROUGHT IRON THRUST MEMBERS. 
 
 The trapezoidal bridge, as described in detail in the 
 preceding section, and as originally intended, is a 
 wrought and cast iron bridge. But it will readily be 
 seen that with slight modification of detail, it is easily 
 adapted to the use of wrought iron upper chord, verti 
 cal posts, and main end braces ; which latter, for con 
 venience, have been designated in this work, as king 
 braces. 
 
 All of these members may be in the form of the 
 patent wrought iron column of the Phoenix Iron Co. 
 of Pennsylvania, formed of flanged segments, united 
 by riveting ; or of rectangular wrought iron trunks, as 
 well as various other forms of section. 
 
 For the Phoenix column, a cast iron connecting 
 piece may be inserted at the joints of the upper chord, 
 with ends formed to enter the squared ends of the 
 chord cylinders, and receive them against a shoulder 
 of the connecting piece. This piece may have an 
 opening in the under side to receive the diagonals 
 and uprights, where they are secured by a transverse 
 
WROUGHT IRON THRUST MEMBERS. 
 
 215 
 
 connecting bolt, in the same manner as at the joint of 
 the cast iron chord cylinders, as before described. In. 
 this case the upright may have a cast iron top piece, 
 formed as seen in Figs. 35 and 38 upon the top of cast 
 iron uprights. A separate top piece has sometimes 
 been used with cast iron verticals. 
 
 FIG. 41. 
 
 The connecting piece may also be formed as indi 
 cated in Fig. 41, with a downward branch like pro 
 cess to meet and receive the squared end of the vertical 
 in the same manner as the horizontal part connects 
 with chord cylinders. In this case the connecting 
 piece must have openings as at b b Fig. 41, for the eyes 
 diagonals to enter. 
 
 Fig. 41, shows an inside view of the joint piecej as 
 it would appear if cut vertically and longitudinally, 
 and the near half removed. The horizontal part con 
 sists of a cylindrical shell a little thicker than the 
 wrought iron chord cylinder, with ribs upon the out 
 side corresponding with those of the wrought cylinders, 
 and as shown in end view c. Upon the inside, the 
 ring and flanges a a, project inward, leaving usually a 
 space of about 5 inches (according to dimensions of 
 
216 BRIDGE BUILDING. 
 
 bridge), for eyes of diagonals. These are to ease the 
 lateral strain of the connecting bolt or pin. 
 
 The process meeting the vertical, may be rectangu 
 lar in horizontal section, composed of two parallel flat 
 plates, in form as may suit the taste of the designer, 
 united by two irregular plates formed to the profile of 
 the parallel plates. The openings for diagonals, are, of 
 course, through the irregular plates. These are drawn 
 in at the bottom so as to form a square with the paral 
 lel sides, large enough to cover the flanges of fhe 4 
 segment column selected for the upright. See Fig. 41. 
 
 The inside of the square d, is filled in to form a hol 
 low round, about an inch less in diameter than the 
 hollow of the column, that it may have a ring or collar 
 (represented by the inner white ring around d), project 
 ing about 2 inches beyond the shoulder into the wrought 
 iron column. 
 
 On the top of the joint piece may be an arrangement 
 of oblique holes for the attachment of lateral X ties, 
 and on the inside, facing the opposite truss, an abutting 
 seat for the cross-strut, which may be in the form of a 
 6" I beam, or such other form as may be preferred. 
 
 The foot of the post may stand upon a properly 
 formed seat upon the connecting block of the lower 
 chord, with an opening to receive the beam, in the 
 same manner as described for the cast iron post. See 
 Fig. 37. 
 
 It will be necessary ror diagonals to pass through the 
 centres of uprights, and for that purpose 10 or 12 inches 
 in length, as may be necessary, may be left out of two 
 opposite segments, and the strength thus lost, restored 
 by additional metal, in such form as may be found con 
 venient and efficient. Or, a cast-iron middle piece may 
 be inserted in the upright. 
 
WROUGHT IRON THRUST MEMBERS. 217 
 
 lu the case of an upper chord of rectangular trunks, 
 and uprights of other than a cylindrical form, the joint 
 piece will be correspondingly modified. 
 
 The position of diagonals may be reversed, connect 
 ing by an eye with a wrought cylindrical connecting 
 pin at the lower chord, and by screw and nut with the 
 joint piece of the upper chord. This involves merely 
 a question of practical economy and convenience. 
 
 Sometimes, also, the connection is made by an eye 
 at both ends of the diagonal, depending upon accuracy, 
 as to length, in the manufacture, for the proper ad 
 justment of parts. It is also practicable to provide 
 means of adjustment in the length of vertical members. 
 
 CXXIII. But, to enumerate all the changes, and 
 peculiarities of detail admissible in the construction of 
 the Trapezoidal Truss Bridge, even if practicable, could 
 hardly be regarded as expedient in this place. The 
 essential requisities are, to provide material enough of 
 good quality in all parts, to withstand the forces to which 
 they are respectively liable, with efficient connections 
 of parts, by the most direct and simple means, and with 
 s ich an arrangement and adjustment as may produce 
 the most uniform degree of strain upon all parts of 
 each member. For instance, ecah section of the lower 
 chord is usually composed of several bars, and it is im 
 portant that each should sustain its proportionate share 
 of the stress. 
 
 In the link chord composed of two links to each 
 panel, if the links be properly fitted, the two sides of 
 each must act very nearly alike, while the connecting 
 block acts as a sort of balance beam to equalize the 
 tension of links acting upon its two ends ; and, if the 
 two links of a pair vary slightly in length, the connect- 
 
 28 
 
....... 
 
 ?% 
 
 218 BRIDGE BUILDING. 
 
 ing block still secures equality of stress upon the two. 
 The same is the case with regard to a chord composed 
 of two eye bars instead of links, to each panel. 
 
 But the serious mistake is .sometimes committed, of 
 putting the two links or bars upon the same side of 
 
 those in the succeeding panel, 
 FlG - 42 - as in Fig 42 ; where it is ob- 
 
 F vious that the inside links (a, 
 
 * b y c), are exposed to more ac 
 tion than d, e,f. 
 
 For, if the inside links be 
 8", and the outside ones 4" from centre of pin, since 
 a and b tend to turn the pin in one direction about its 
 centre, and d and e in the opposite direction, the forces 
 being in equilebirio the moments (with respect to the 
 centre), of forces tending in one direction, must be 
 equal to those of forces tending in the opposite direc 
 tion. Hence, representing the stresses of the several 
 links by the letters designating them respectively on 
 the diagram, we have 3 X (a -f b) = 4 x (d -f e), whence, 
 a + b = | (d -f e) ; showing J more stress upon the in 
 side than upon the outside links. 
 
 On the contrary, if the link e, be removed to e upon 
 the inside of a, then d and e act in one direction, and 
 a and b in the otjier; and, assuming as before, the 
 inside links to be 3", and the outside ones 4" from 
 centre of pin, we have 4a -f 36 = 4d + 3e . But a -f d 
 = b + e , and if the force be communicated at the ends, 
 equally upon the two , sides of the chord, giving equal 
 stress upon a and o?, for instance, the tendency is to an 
 even balanced action throughout the length of chord. 
 
 Hence the two links of each panel should always 
 act upon the connecting block or pin, at equal dis 
 tances from centre of pin. 
 
MULTIPLEX CHORDS. 
 
 219 
 
 MULTIPLEX CHORDS. 
 
 CXXIV. In very long or heavy bridges, the required 
 amount of chord section in the middle portion of the 
 truss, is so great, that k is deemed expedient to intro 
 duce more than two links or eye hars to the panel. 
 This is sometimes done by alternating them upon the 
 connecting pin, increasing the number and sizes ac 
 cording to the increase of stress from panel to panel 
 toward the centre. 
 
 This mode of construction, unless the bars be ar 
 ranged and proportioned with almost impracticable 
 care and nicety, is liable to be attended by an accumu 
 lation of lateral strain upon the connecting pin, beyond 
 what it can bear without bending, or springing so much 
 as to materially disturb the equality of stress upon 
 the links, or chord bars. 
 
 FIG. 43. 
 
 To illustrate this subject, let Fig. 43, represent one 
 quarter of the chord of a 16 panel bridge. The line 
 CC may denote the central axis of the chord running 
 through the centres of connecting pins ; D, at a dis 
 tance of, say 8" from C, the line in which the diago 
 nals act upon pins, and the other parallel lines at 
 intervals of 3" from D, and from one another (see Figs. 
 
220 BRIDGE BUILDING. 
 
 on right hand of diagram), the centres of thickness of 
 links, at which points the action of respective links 
 is supposed to be concentrated upon the pins. Also, 
 let a, by c, etc., represent the panels of the chords. 
 
 Now, if 15W, or 15, represent the stress upon the 
 chord in the two first panels, a and 6, that of the suc 
 ceeding panels to the centre, will be as 22, 34, 44, 52, 
 58 and 62 (see lower figures in diagram), and the dia 
 gonals (producing increments of action upon chord), 
 will have a horizontal action represented by 7 in panel 
 b, by 12 in panel c, and so on by 10, 8, 6, 4. These 
 being added successively to 15, produce the numbers 
 just stated for the chord in the several panels. 
 
 The first three panels, a,b and c, require only one link 
 upon each side, as indicated by the oblique black lines. 
 The 4th panel, d, may have 2 links on a side, and the 
 most favorable position for them, as regards action 
 upon connecting pins, will be as shown, diverging 
 from the central axis, so as to bring the end toward 
 the abutment, nearest to the main diagonal connecting 
 with the same pin. 
 
 The first pin, connecting a and 6, having two equal 
 forces acting in opposition, but at different distances 
 from the centre line (7, we take the moments of these 
 forces with respect to that line , which are, for a, 
 15xl4=210,andfor6, 15x11=165. The difference (45) 
 between these moments, equals the moment of the 
 resultant, or the lateral stress of the pin, exerted on a 
 leverage of 1". 
 
 Assuming the value of W, our unit of stress (and 
 always understood as annexed to the figures denoting 
 stress), to represent 5,000ft>s. we have for stress of pin 
 in this case, 45 X 5,000-*-L. The L, being V may be 
 omitted in the expression. 
 
MULTIPLEX CHORDS. 21 
 
 Then,rnakingz=diameterofpin,itsresistingpower= 
 A5.x4,500 (see [xcvm])= .785z 2 x x x 4,500 -r- 1"= 
 3,532. 5r 3 ; and putting this equal to 45x5,000 (the stress 
 above found), we obtain =4" (very n early), = required 
 diameter of pin. 
 
 At the next pin we take the moments of one link 
 15xl4"=210, and one diagonal, 7 x8"=56, making 266 
 in one direction, against that of one link, 22x11"= 
 242. Hence the resultant moment = 24, and 24 X 
 5,000=3,532.5x 3 , gives the required diameter of pin in 
 the centre, ==3J , nearly. But this is the general 
 stress in the portion of pin between diagonals, and 
 may be greater or less than at certain points where 
 forces are applied. For instance, if the aggregate 
 moments of forces in opposite directions be equal, the 
 resultant moment is nothing, and the middle portion 
 of the pin, between diagonals has no stress, and might 
 be cut out and removed, as far as strength of chord is 
 concerned. In the case in hand, the moment of link 
 6, with respect to link c, equals 15"x3= 45=stress of 
 pin at centre of c. Hence the required diameter at 
 this point is found by the equation 45x5,000=3,532.5 
 Xx 3 , whence =4", the same as pin ]STo. 1. 
 
 At the next pin, if we add another link, making 2 
 links sustaining 34W, at an average of 14" from centre, 
 giving a moment of 476, against one link, 22x14, + 
 one diagonal 12x8=404, we obtain a resultant mo 
 ment of 72 ; whence, 72x5,000 = 3,532.5x 3 , and x = 
 4.67 inches, = required central diameter of pin, and as 
 will be readily seen on trial, the greatest required at 
 any point. 
 
 Again, assuming at the 4th pin 2 links and 1 dia 
 gonal against two links, we have for the former, 
 34x17" + 10x8 = 658, and for the latter, 44x14 = 
 
222 BRIDGE BUILDING. 
 
 616, whence the resultant moment is 42. Therefore 
 the equation 42x5,000 = 3,532.5z 3 , gives;r = 3.9 inches, 
 = required diameter in centre, while for the outside 
 link on this pin, the stress, 17, multiplied by 3 shows 
 
 a moment of 51. Hence, x = ^* = 4.16 inches 
 
 O,Oo/a.O 
 
 = required diameter at that point. 
 
 At the 5th pin, there are 3 links, against 2 links and 
 one diagonal, giving moments for the latter, 44x17 + 
 8x8 = 812, and for the former, 52x17 = 884 ; whence 
 the resultant moment = 72, and x = & (? 2x j;-" uo ) = 4.67 
 
 , #,532.5 
 
 inches. 
 
 The moments at pin No. 6, are, for 3 links, 52x20, -f 
 (for diagonal) 6x8 ==1088, in one direction, and for 3 
 links, 58x17 = 986, giving a resultant of 102 ; whence, 
 
 Lastly, adding another link at the 7th pin, the 
 moments are 58x20 -f (for diagonal) 4x8, = 1,192, 
 against 62x20 = 1240, whence the resultant is 48, 
 and* -X^jgp- 4-08. 
 
 In this case the eyes, or link-ends are supposed to be 
 bored in the direction of the pin, a little obliquely to 
 the direction of the link, so as to bear through the 
 whole thickness, as long as the pins remain perfectly 
 straight. But the pins having a degree of elasticity, 
 and considerable length, must yield to the action of 
 links, springing more or less in the direction of the 
 greater sum of moments. It will be seen, moreover, 
 that in each case, the consecutive ends entering the 
 outside link, as 3 and 4, 5 and 6, &c., are always sprung 
 toward one another ; the inevitable result of which 
 must be, a relief or relaxation of the outside link, 
 whence it must sustain a less degree of strain than its 
 fellows located farther from the ends of the pins. 
 
MULTIPLEX CHORDS. 223 
 
 * 
 
 Now, as a 12 foot link, under a stress of 10,000ft>s. to 
 the inch is extended less than f - of a foot, a slight 
 
 1 jUUU 
 
 springing of connecting pins would relax the outside 
 links materially, especially when the pins tend to spring 
 toward one another. 
 
 Again, if the links run parallel with the centre of 
 chord, and at right angles with the connecting pins, 
 as indicated by the double black lines (Fig. 43), the 
 moments of forces upon pin No. 5, for instance, will 
 be for 3 links acting toward .the right hand, 44 x 
 17 -f (for diagonal) 8x8 = 812, against 3 links acting 
 toward the left, with moments equal to 52 x20 = 1,040, 
 
 showing a difference of 228 ; whence=^( 228 * 5>000 ) = 
 
 3,582 5 
 
 6.85 inches -= required diameter of pin at the centre. 
 
 At pin No. 6, are 3 links with a combined moment 
 of 52 x 20, -f (for diagonal), 6x8, = 1076, against 3 
 links with a combined moment of 58 X 17 = 986, show 
 ing a difference of 90 ; consequently, x = ^/( 90 * 5 - OQO ) = 
 
 o,532.5 
 
 5.03 inches = required diameter of pin. 
 
 Such would be the result as to stress and required 
 diameter of pin, provided the pin remain perfectly 
 straight. It is true that the spring of the pin in the 
 direction of the greater moment, or sum of moments, 
 will, in practice, produce an obliquity in its direction 
 through the eyes, which will throw the centres of bear 
 ing upon the pin, nigher to the adjacent sides of the 
 eyes, and thus reduce the difference of opposite mo 
 ments, and consequently, the stress upon the pin. But 
 such relief to the pin must be attended with a disturb 
 ance of the central and uniform strain of the chord 
 bar ; the strain being brought near one side of the bar. 
 Moreover, as this can only result from actual springing 
 of the pin, there must inevitably be a degree of relaxa- 
 
224 BRIDGE BUILDING. 
 
 
 
 tion of the outside link, whenever the pins at its two 
 ends are deflected toward one another. On the con 
 trary, an outside link or bar connecting with two pins 
 springing from one another, is necessarily subjected to 
 greater strain than those nighor the centres of pins, in 
 the same panel. 
 
 In this case, the forces tend to spring the pins toward 
 one another at the ends, whence the outside link" must 
 suffer more or less relaxation. 
 
 It seems unnecessary to carry these examples further. 
 The above results show a decided advantage in the ob 
 lique position of links, diverging toward the centre of 
 the span, so as to have the inside link opposed to the 
 diagonal. 
 
 The arrangement of links, or eye bars, here assumed, 
 and the amount of stress assigned to them, are no ex 
 aggeration upon what has been put in practice. But 
 the preceding calculations must be sufficient to demon 
 strate the exceptionable character of such practice. 
 Two links upon a side (4 to the panel), after two or 
 three panels next the end, so thin as not to occupy 
 an unnecessary length of pin each taking hold of 
 the pin outside of the succeeding one toward the cen 
 tre of the truss, may be admissible. But a greater 
 number, in the opinion of the author, for reasons al 
 ready given, is not to be recommended. 
 
 DOUBLE CHORD. 
 
 CXXV. To obviate the difficulty attending the use 
 of the multiplex chord, consisting of many links in a 
 panel, we may make use of what may be distinguished 
 as a Double Chord. 
 
 We have seen [LVI], that in double cancelated trusses 
 with vertical members, there are two independent sets 
 
DIFFERENT MODES OF CONSTRUCTION. 225 
 
 of diagonals and verticals, which have no interchange 
 of action between one another. Now, each of these 
 sets may have its own lower chord, also acting inde 
 pendently, each of the other, but uniting at the same 
 point at the foot of the king brace, which is common 
 to both sets of web members. 
 
 In such case, the two chords (which we may call sub- 
 q/ior^s), may be one above the other, and composed of 
 links or eye-bars, extending horizontally across two 
 panels ; the links or bars of one sub-chord connecting 
 opposite the centre of those in the other, and the up 
 rights in one set, being as much longer than those in 
 the other, as the distance, vertically, between the up 
 per and lower sub-chords. 
 
 By this means, about one-half of the extra material 
 in chord connections would be saved; and a more uni 
 form stress upon the chord bars secured, than would 
 be practicable, even with 4 links acting upon one con 
 necting pin. 
 
 DETACHED, AND CONCRETE PLANS OF CONSTRUCTION. 
 
 CXXVI. In the plan of Trapezoidal truss had under 
 consideration in the last few preceding sections, the 
 several members are formed in separate pieces, to be 
 erected in place, and connected by screws, bolts, con 
 necting pins, &c., as the parts of wooden bridges and 
 building frames are erected, after being framed and 
 prepared, each for its particular place. 
 
 There is another mode of construction, in which 
 members and parts of members are permanently riveted 
 together in place; or, in case of small bridges, the 
 whole structure is permanently put together at the 
 manufactory, and transported by water or rail to the 
 place of erection and use. The former of these may 
 29 
 
226 BRIDGE BUILDING. 
 
 be called the detached, and the latter, the concrete mode 
 of construction. 
 
 The detached plan is probably the best adapted to 
 wrought and cast iron bridges, and also, at least, equally 
 adapted to bridges entirely, or essentially constructed 
 of wrought iron, when vertical thrust uprights are em 
 ployed. 
 
 But it can hardly be regarded as advisable to con 
 struct iron bridges with independent members, without 
 thrust verticals. For, although as we have seen, [XLVI,] 
 the latter plan shows a trifle less action upon the ma 
 terial than the plan with verticals, the oblique thrust 
 members in the web, are 40 or 50 per cent longer (ac 
 cording to inclination), as well as being in greater 
 number, and sustaining less average action to the piece. 
 
 The 7 panel truss, Fig. 12, has 4 compression verti 
 cals, liable to an average action of 8w" ; while truss 
 Fig. 13, has not less than 6 diagonals, liable to an 
 average compression of -w" \/2 (when the inclination 
 is 45), equal to 5.65i0". In the mean time, these 
 members being- over 40 per cent longer, and sustain 
 ing only about the same aggregate amount of action, 
 can not be so economically proportioned to perform 
 their required labor, when acting independently, as 
 the fewer and shorter uprights. 
 
 Still, the Trapezoid with individual members is 
 practicable, probably with about the same economy of 
 material without verticals as with them ; and, if it be 
 deemed expedient to adopt the former, the modes of 
 forming and connecting the various parts may be so 
 nearly like those already described for the latter, that 
 particular specifications will not be given in this place. 
 
 The essential conditions to be observed, are, besides 
 proportioning the parts to the kind and degree of strain 
 
DIFFERENT PLANS OF CONSTRUCTION. 227 
 
 to which they may be exposed, to see that the forms 
 of diagonals liable to compresaive action, be made 
 capable of withstanding such action, according to the 
 table of negative resistances [xcin] ; and, that those 
 liable to a change of action from tension to compres 
 sion, and the contrary, be formed and connected in such 
 manner as to enable them to act in both directions. 
 
 CXXVII. In the concrete, or rivet work plan of 
 construction, the Trapezoid without verticals may, it 
 is thought, be generally adopted with advantage. 
 Upon this branch of the subject, however, but little of 
 detail will be attempted at this time, the author having 
 had very little direct practical experience in the pre 
 mises. 
 
 The first point to be attended to, of course, as in all 
 cases of bridge construction, is, to arrange the general 
 outline and proportions of the truss ; that is, the num 
 ber of panels, and depth of truss suitable for the par 
 ticular case in hand. This being done, the amount 
 and kind of force, whether thrust or tension, to which 
 each part is liable, should be determined ; for which 
 purpose, the value of w, and of w (the variable and 
 constant panel load for the truss), must be assumed, or 
 estimated according to the best data at command ; 
 when the stresses of the several parts are readily ob 
 tained by process already explained; [XLIV, &c.]. 
 
 We are then prepared to assign the requisite cross- 
 section to each part, and to adopt a suitable form of 
 bar, or combination of bars and plates, for each mem 
 ber. Thrust members will usually (if long), be formed 
 of several parts, mostly flat plates, angle iron, T iron, 
 and channel iron, united by riveting in such form of 
 cross-section as may give the largest diameter practi- 
 
2:23 BRIDGE BUILDING. 
 
 cable without too much attenuation of the thickness 
 of material, a point upon which no certain rules can be 
 given. 
 
 Flat plates, when connected by riveting at the edges, 
 may be of a width of 30 to 40 times the thickness per 
 haps, without liability to " buckle" under reasonable 
 compression. When riveted along the centre, a width 
 of 12 to 20 times the thickness, will be in better pro 
 portion. 
 
 UPPER CHORD. 
 
 CXXYIII. A good upper chord may be made in 
 rectangular, or box form, of flat plates and angle iron ; 
 or, for small bridges, of channel iron, with flanges 
 either inward or outward, upon the two vertical sides, 
 with flat plates upon upper and under sides ; the upper 
 riveted, and the lower one either riveted, or put on 
 with screws, tapped into the lower flanges of the 
 channel bars. 
 
 The upper plate, when flanges turn inward, may 
 project half an inch, or an inch, and the lower one, 
 come even with the sides. The channel bars should 
 meet at the nodes, or connecting points, and a splice 
 plate covering the joint may project below the chord 
 far enough to form a connection with diagonals by 
 riveting. (Fig. 44). 
 
 Diagonals acting by tension only, may be plain flat 
 bars of width from 8 to 10 times the thickness. Those 
 acting by thrust principally, may be of T iron with 
 short diagonal bars riveted to the mid rib, (e Fig. 44), 
 giving a width corresponding with that of the upper 
 chord, or with the space between tension diagonals, 
 so that the latter may be riveted to the cross-plate of 
 the T iron at the crossings, to give lateral support to 
 
RIVET- WORK BRIDGES. 
 
 229 
 
 the thrust members. Angle iron may also be used in 
 stead of T iron, in these members. 
 
 FIG. 44. 
 
 \ 
 
 o 
 
 
 
 
 
 
 1 
 
 c 
 
 o o 
 
 o 
 
 
 1 
 
 O 
 O 
 
 o 
 
 o 
 
 o. 
 
 J 
 
 
 
 "6 o 
 
 O 
 
 3 
 
 Diagonals acting by both thrust and tension, should 
 be formed and connected with reference to the forces 
 they are liable to. 
 
 For small bridges, small plain I bars may be used 
 for thrust diagonals with advantage. 
 
 In all cases of tension, rivets should be so arranged 
 when practicable, as to leave all the section available, 
 except the diameter of a single rivet hole; that is, 
 no section through two or more holes, including the 
 one farthest from the end, should have less area than, 
 a square section through one hole, [cxvii, Fig. 31.] 
 
 In Fig. 44, a, a, &c., represent tension diagonals, of 
 plain flat bars, with cross-section proportioned to the 
 stress in each case; 6,6 thrust diagonals of T iron 
 and short diagonal plates, as seen at e ; c, e, the upper, 
 
230 BRIDGE BUILDING. 
 
 and <f, the lower chord ; the dotted line J, shows the 
 meeting of lower chord plates, about 4 inches toward 
 the abutment from the point of meeting of the several 
 centres of chord and diagonals. The side plates of up 
 per chord may meet at the centre of the node, or con 
 necting point. 
 
 The upper splice plates are of irregular form (or, they 
 may be cut on a regular slant from upper to lower 
 angle), but such as to cut without waste of iron. They 
 may be clipped out upon the under side, as by the 
 curved line, or not, as may be preferred. 
 
 The lower splice plates may be rectangular, and of 
 such length and width as to admit of a sufficient num. 
 ber of rivets, properly arranged, to be equal in strength 
 to the net section of chord plate and diagonals. 
 
 It is scarcely necessary to repeat, that rivet section 
 connecting two thicknesses of plate only, should exceed 
 the net section of plate by as much as the direct tensile 
 strength exceeds the shear-strength of iron. 
 
 LOWER CHORD. 
 
 CXXIX. The following plan of a flat plate bottom 
 chord adapted to a connection of diagonals by connect 
 ing pins, is transcribed from the author s former work ; 
 and, by widening the splice plates, as in Fig. 44, ia 
 equally adapted to the concrete mode of construction ; 
 i. e., by rivet work. 
 
 The plan contemplates each half-chord as composed 
 of two courses of plates (except near the ends), spliced 
 alternately, one at each node so as to " break joints." 
 The two half chords are to be placed at such distance 
 apart as to accommodate the connections with dia 
 gonals, and with uprights, when used in connection 
 with uprights. 
 
RIVET- WORK BRIDGES. 231 
 
 For a 16 panel truss, as arranged in Figures 18 and 
 19. Suppose w = 12m (m representing l,0001bs.) ; w 
 4w, and W = 16w, = w -f w ; diagonals (except the 
 steep ones), inclining 45. 
 
 The end brace, then, sustaining 7JW = 120w, [LVI], 
 produces tension equal to 60/n, upon the first and 
 second section of chord, in Fig. 18, the proportions for 
 which will be here considered. Allowing then, 10m 
 to the square inch, each half chord requires a plate of 
 about 8" by r V, up to the second node from the end. 
 
 This plate may extend say within 8" of the centre 
 of the connecting pin at the 2d node, where it may be 
 connected with a |" plate, by two splice-plates about 
 27" long (see A. Fig. 45), with a net section equal to 
 the y y plate, or, say J" thick. Fig. 45, exhibits a 
 disposition of rivet and pin holes, at A, so arranged as 
 to preserve the full section of plates, less the diameter 
 of a single V rivet hole. 
 
 Or, the splice-plates maybe 1" shorter, and J thicker, 
 and the two rivets next the joint (j), on either side, 
 opposite one another, as at BB, Fig. 45 ; thus giving 
 the same section (of splice-plates), through two opposite 
 rivets in the thicker, as through one rivet in thinner 
 and longer splice plates. In this case, the joint should 
 be 4|" from centre of connecting pin (p), and a little 
 more, when the rivets exceed V in diameter. 
 
 At the third node, an increase of section is required, 
 and a f" plate may be added on the inside, lapping 9 
 or 10 inches back of the pin, with a J" splice plate of 
 the B pattern to balance the extra inch in width re 
 quired for opposite rivet holes, and a 2" pin hole. 
 
 The inside plate continuing past the next, or 4th 
 node, the f" outside plate may be met by, and spliced 
 to a |" plate, in either of the modes indicated by A and 
 
BRIDGE BUILDING. 
 
 B, Fig. 45. On plan B, the outside splice plate should 
 be at least J" thick, and the inside one, T 5 g ". In this, 
 as in other cases where a thinner plate meets a thicker 
 one, the former is to be furred out to the thickness of 
 the latter. 
 
 At the 5th node, the outside plate may continue, 
 while the inside one is succeeded by a f" plate, with a 
 " splice-plate inside, and one of T V thickness upon 
 the outside ; splice-plates in all cases being intended 
 to be upon the outside, and not between the two courses 
 of plates forming the half chord. 
 
 The same general process being continued, each 
 course being spliced at alternate nodes, and breaking 
 joints with one another, we introduce in the outside 
 course, a V plate from the 6th node to the centre 
 of the chord, and a J" plate from the 7th node, past 
 the centre to the 9th node, and so on, with a reversed 
 order of succession to the other end of the chord. 
 
 The two 1" plates in the outside course, should meet 
 at the centre connecting pin, and all other joints should 
 be a few inches from the pin, on the side toward the 
 end of the chord, as in diagram, Fig. 45. 
 
 FIG. 45. 
 
 O I 
 
 Each pair of splice plates should have a minimum 
 net section, together with the net section of the con 
 tinued plate, at least equal to the sections of the con 
 tinued, and the thinner spliced plate, through one of 
 the smaller rivets used in the splice ; and the relative 
 thickness of the two splice plates should, as nearly 
 
RIVET- WORK BRIDGES. 233 
 
 as practicable, be inversely as the respective distances 
 of their centres from the centre of the spliced plate. 
 
 For illustration ; at the 6th node, the continuous 
 plate is |", and the thinner spliced plate J", making in 
 the two, a thickness of 1J", by T 1 for the net width ; 
 giving a section of 10J square inches. This splice re 
 quiring 1J" rivets next the joint, to give the necessary 
 rivet section, the net width of splice plates and con 
 tinuous plate through two opposite \\" rivets, is only 
 5J". Consequently, the aggregate thickness required 
 to give 10J square inches, is about 1.91" ; and, deduct 
 ing 0.625" for the continuous plate, we have 1.285" 
 for thickness of the two splice-plates. 
 
 Then, representing thickness of spliced plate by a 
 (disregarding the furring plate, or including it in the 
 quantity a), that of the continuous plate by 6, that of 
 the two splice-plates by c, and that of the thicker one 
 by x; we form the following equation, as will be ob 
 vious on reference to Fig. 46, which is an edge view 
 of splice at node 6. 
 
 xx J (a+x) = (c x) X (b+ J (a+c x) ; whence, the 
 formula x =* c x (a+2b+c) H- 2 (#+b + c). 
 
 This formula applied to the case represented in Fig. 
 46, gives x = 0.7804", and c x = 0.5046". 
 
 FIG. 40 
 
 , I ! ^ <, ^. , 
 
 The letter a in the diagram shows the splicing of a 
 1" with a " plate, the thickness being equalized by a 
 furring plate. 
 
 Figure 46 gives also, a general idea of the splices pro 
 posed for this kind of chord, in case of the adoption of 
 30 
 
234 BRIDSE BUILDING. 
 
 the short splice plates and opposite rivets, aa seen at 
 BB, Fig. 45. p indicates the connecting pin (which, in 
 the concrete plan of construction should be replaced 
 by two opposite rivets, as seen in Fig. 44), having a 
 cross-section in the parts passing through the chord 
 plates, about equal to that of one of the two main dia 
 gonals connecting with each pin respectively, at the 
 several nodes. 
 
 The body of the pin between chord plates, should 
 have lateral stiffness enough to withstand the stress 
 produced by diagonals horizontally, estimated upon 
 the principles of the lever, which will be greater as the 
 distance of diagonals from chord plates is greater, and 
 the contrary. If the bearing of the upright upon the 
 pin be between the diagonals and the chord plates, as 
 by a bi-furcation like that at the upper chord (see a 
 Fig. 38) the body of the pin will usually require a 
 section about equal to that of the two main diagonals 
 connected with it. But this is no certain rule. 
 
 The ends of the connecting pin should extend through 
 the chord plates so as to receive a thin nut upon each 
 end, and also the eyes of sway rods upon the inside 
 end, in case that mode of connection be adopted for 
 those parts. 
 
 In the case of trusses without verticals constructed 
 in rivet work, the best balanced action will be secured 
 by connecting diagonals between the splice plates, by 
 means of rivets through both, thus bringing each dia 
 gonal bar directly over each half chord, and producing 
 uniform stress, as nearly as is practicable. When dia 
 gonal bars do not fill the space between splice-plates, 
 the deficiency may be made up by furring plates, or 
 thimble rings. 
 
RIVET- WORK BRIDGES. 235 
 
 Tension diagonals will usually require from 25 to 33 
 per cent of extra section to make up the loss in rivet 
 holes. In thrust diagonals, no allowance need gene 
 rally be made for rivet holes, as rivets properly distri 
 buted, will not impair the efficiency of the member in 
 withstanding compression. 
 
 With* regard to the relative merits of this kind of 
 lower chord, k requires, in the proportions above as 
 sumed, namely, 8" width of plates and 1" diameter of 
 the smaller rivets, about 14 per cent of extra section 
 on account of rivet holes, through the whole length. 
 For splice plates and rivets, at least an equal amount 
 should be allowed, making 28 per cent for waste ma 
 terial, over and above the net available length and 
 cross-section. The corresponding waste in the link 
 chord, and in the eye-plate chord [cxiv], can scarcely 
 exceed 10 per cent, when the connections are made 
 with wrought iron pins. 
 
 Hence, the advantage as to economy of material, 
 seems decidedly in favor of the latter plans ; and the 
 cost of manufacture can hardly be estimated in favor 
 of the former. If the riveted chord, then, have any 
 claim to favor and preference, it is mostly owing to 
 the fact, that being manufactured cold, it escapes the 
 deteriorating effects frequently resulting to iron in the 
 process of forging and welding, and the risk of flaws, 
 and imperfect cohesion of the welded surfaces. 
 
 How far this consideration should be regarded as an 
 offset, or an overbalance to 15 or 20 per cent, of ma 
 terial lost in rivet holes and splices, further experience 
 and observation alone can probably determine. 
 
236 BRIDGE BUILDING. 
 
 SWAY BRACING. 
 
 CXXX. The primary and essential purpose of a 
 bridge is, to withstand vertical forces which are certain, 
 and, to a large extent, determinate in amount. ~W"e 
 can estimate nearly the weight of a train of rail road 
 cars, a drove of cattle, or a crowd of people ; and the 
 amount of material required to sustain them. 
 
 But the lateral, ar transverse forces to which a 
 bridge superstructure is liable, are of a casual nature, 
 depending upon conditions of which we have only a 
 vague and general knowledge ; and, can not predeter 
 mine, their effects with any considerable degree of 
 certainty. 
 
 We know full well from experience, that it is always 
 expedient to provide every bridge superstructure with 
 means of support against transverse horizontal forces ; 
 and we introduce certain parts and members for that 
 express purpose. These have been frequently alluded 
 to heretofore in this work, under the designation of 
 sway rods, lateral ties, or lateral braces. But no attempt 
 has ever been made, to the author s knowledge, to 
 point out the proper sizes and proportions of such 
 members, upon any determinate principles or data. 
 
 In this respect, reliance has mostly been placed upon 
 "judgment," and general observation as to precedent 
 and common practice ; as was the case in fact, with 
 regard to bridge construction generally, until within 
 the last twenty-five or thirty years. Within this 
 period, and since the extensive use of iron in bridge 
 construction has been introduced, more attention has 
 been given to scientific principles, in adjusting the pro 
 portions of the several parts and members designed to 
 withstand the effects of vertical pressure. 
 
SWAY BRACING. 237 
 
 The modern bridge builder, if he has been properly 
 educated for his business, having arranged the outline 
 of his truss, makes his computations, and marks upon 
 each line of his diagram, so many thousand pounds of 
 tension upon this, so many tons of compression upon 
 that, and so much shear strain, or lateral strain upon 
 each rivet, connecting pin, or beam, and assigns to 
 each place a member containing such an amount, and 
 such a kind of material, as experience has proved to 
 be sufficient to sustain the given stress with safety. 
 
 Thus far, his course is scientific and sensible. But in 
 arranging his system for securing lateral stability and 
 steadiness, science can lend him but little assistance. 
 
 He knows the wind will blow against the side of his 
 structure ; but whether with a maximum force of one 
 hundred pounds, or as many thousands, he has no 
 means of knowing with any considerable degree of 
 certainty, or probability. 
 
 He knows, furthermore, that every deviation from a 
 straight line by a body passing over and upon a bridge, 
 even to changing the weight of a pedestrian from one 
 foot to the other (unless his steps be directly in front 
 of one another, and this could hardly form an excep 
 tion), is attended by more or less tendency to lateral 
 swaying of the structure. 
 
 Every inequality in the line of a rail road track, 
 laterally or vertically, unless both rails have precisely 
 the same vertical deviation, produces a transverse mo 
 tion in the centre of gravity of the load, and conse 
 quently a, lateral sway in the structure. The passage 
 of a carriage wheel over a stick or a pebble, raising 
 one wheel above the opposite one, changes the centre 
 of gravity of the load to the right or left, and impels 
 the structure in the opposite direction. 
 
288 BRIDGE BUILDING. 
 
 These are some of the external causes generating 
 transverse action, and motion of the structure. But 
 in addition to these, the upper chord itself, acting by 
 thrust, is, at best, in unstable equilibrio, and liable at 
 all times to exert more or less transverse action, and, 
 if not kept in line by an efficient system of transverse 
 bracing or tying, will lose its equilibrium, and be de 
 prived of the power of performing its appropriate 
 functions in the structure. 
 
 Now, these disturbing lateral forces are quite small, 
 compared with the vertical action upon the trusses ; 
 and, the vertical strength of the truss does not neces 
 sarily imply any power of resistance transversely ; the 
 tendency of the lower chord to preserve a straight line, 
 being essentially balanced by that of upper chord or 
 arch to buckle laterally;* provided the chords be so 
 dependent upon one another that both must sway to 
 the right or left at the same time. 
 
 Hence, it is always expedient to provide some es 
 pecial means for counteracting these lateral forces, 
 which is usually done by the introduction of a system 
 of horizontal diagonal ties or braces (small iron rods 
 in iron, and the same, or timber braces, in wooden 
 bridges), below the track or platform, in the horizon 
 tal panels formed by consecutive beams, and the chords 
 of opposite trusses. Also, when trusses are sufficiently 
 high, diagonals and cross-struts are introduced between 
 upper chords, to prevent lateral buckling. 
 
 No attempt will here be made to assign specific 
 stresses as liable to occur in sway rods or braces, 
 based upon calculations from the uncertain and in 
 determinate elements upon which the lateral action upon 
 
 * The only truss known to the author, not liable to this lateral buck 
 ling, is the W hippie Independent arch truss, shown in Fig. 27. 
 
SWAY BRACING. 239 
 
 bridges depends. Bat, judging from experience and 
 observation, it may be recommended that iron sway- 
 rods be made of iron not less than f inch in diameter, 
 for bridges of five panels or under, f inch from six to 
 ten panels, inclusive. For twelve and fourteen panels, 
 f inch for ten middle panels, and { inch for the rest ; 
 and, for sixteen the same as last above, with the ad 
 dition of a pair of 1 inch rods in the end panels. 
 
 These are the least dimensions recommended (in all 
 cases exclusive of screw thread), for ordinary bridges 
 with panels not much exceeding 10 feet. For panels 
 approaching or exceeding 12 feet, J- inch may properly 
 be added to the above specified diameters generally. 
 
 If upper sway rods connect in the middle of cross- 
 struts, with a longitudinal reach across two panels, [see 
 cxx, and Figs. 38 and 39], they may safely be made 
 smaller than when they cross one panel only. 
 
 The action of wind is nearly a uniform pressure from 
 end to end of the structure, and causes mu<jh the same 
 progressive increase of stress upon sway-rods, as the 
 weight of structure and uniform load produces upon 
 diagonals in the trusses a fact which was recognized 
 in assigning larger sway-rods at and near the ends of 
 long bridges. But the casual impulses resulting from 
 unevenuess in track or platform, giving slight lateral 
 movement to passing loads, and acting at single points 
 here and there, this way and that, do not produce an 
 accumulation of effect toward the ends. Hence, as it 
 regards withstanding the latter forces, no variation in 
 sizes of sway-rods is required. 
 
 CXXXI. Sway-rods acting by tension would ob 
 viously draw the opposite chords toward one another, 
 but for the resistance of transverse beams or struts, 
 
240 BRIDGE BUILDING. 
 
 while they also exert a longitudinal action npon the 
 chords, thereby increasing or diminishing the stress 
 npon chords, due to the action of structure and load. 
 Chords, however, are usually proportioned without 
 provision for increase of stress liable to accrue from 
 action of sway-rods; and, from the small sizes of the 
 latter, as compared with the former, and the obliquity 
 of their action, seldom expending more than half their 
 direct stress npon the chords longitudinally, this small 
 action may be neglected, as forming one of the con 
 tingencies for which a large surplus of material is al 
 ways provided in chords, over what is actually required 
 to withstand the effects of any probable vertical action. 
 
 Certain modes of inserting and connecting sway-rods 
 have been previously alluded to, sometimes with the 
 beams by means of eyes and bolts [cviri, Figs. 31 
 and 33], and sometimes more directly with the chords 
 [cxix, Fig. 35, d, and Fig. 39, d. ] 
 
 The best connection is that which gives the nearest 
 approximation to central and uniform action upon all 
 parts of the chord, and also of the beam or strut. The 
 plan described in section cxx, and seen in Fig. 37, when 
 admissible, affords a good connection for bottom sway 
 rods. 
 
 Undoubtedly there may be better devices for the 
 purpose under consideration, as well as for other de 
 tails, than any that have occurred to the author. But 
 such as are herein described have mostly been put in 
 successful practice, and are thought not to be seriously 
 faulty. 
 
COMPARISON or PLANS. 241 
 
 COMPARISON OF DIFFERENT PLANS OF 
 IRON TRUSS BRIDGES. 
 
 CXXXIL It is the purpose of this chapter to can 
 vass the relative merits of most of the several systems 
 of IRON BRIDGE TRUSSING, which have claimed and re 
 ceived more or less of public notice and approval during 
 the last few years ; and of which the distinctive princi 
 ples have already been discussed in preceding pages ; 
 though not in the precise combinations here about to 
 be presented. 
 
 We may take the number, lengths and stresses (the 
 latter governing principally the required cross-sections), 
 of the several long pieces or members of the truss, in 
 the manner employed in the fore part of this work, as 
 affording a near criterion of the comparative cost and 
 economy of the bridges respectively. Then, after re 
 ference to such peculiarities as may seem advantageous 
 or otherwise, leave the reader to his own conclusions 
 in regard to the relative merits. 
 
 TKE BOLLMAN TRUSS, Fia. 47, 
 
 Is founded upon the general principle discussed in 
 sections xxn and xxm, with oblique tension rods, and 
 a thrust upper chord, in place of the thrust braces and 
 tension lower chord as represented in Fig. 9. 
 
 Let Fig. 47, represent a truss 15 high, and 100 long ; 
 or, in the proportion of 1 to 6f . Also, let w represent 
 the maximum variable load for each of the points c, d, 
 e, etc., and w (say,= Jw), the permanent weight of 
 one panel of superstructure, supposed to be constantly 
 bearing at each of said points. Then making "W" = 
 w X w , we have JW = weight sustained by ac. 
 31 
 
242 BRIDGE BUILDING. 
 
 How, we have seen [vn], that the stress upon an 
 oblique in such case, equals the weight sustained, mul 
 tiplied by the length, and divided by the vertical reach 
 of the oblique ; and, assuming that the member requires 
 a cross-section proportional to the stress, it follows that 
 (making ab = 1), the amount of material required in ac, 
 will be as the weight it sustains, multiplied by the 
 square of its length. Hence, the material required in 
 <?, must be as f W X a<: 2 . Then, diminishing be until 
 ac coincides with ab, W X ab 2 becomes "W, which is 
 still proportional to the material required in ac (which 
 has now become = a&, = 1), and, being replaced by M, 
 representing the actual material required to sustain the 
 weight "W", with a length equal to ab (our unit of length), 
 in a vertical position, we have only to substitute M X 
 ac 2 for W x ac 2 r to know the actual material necessary 
 to sustain the weight W (at a given stress per square 
 inch of cross-section), with any length and position, 
 retaining the same vertical reach, equal to unity. 
 
 It must be obvious, therefore, that M, with the co 
 efficient used before W, to express the weights respect 
 ively sustained by the several oblique rods in truss 47, 
 will, when multiplied by the squares of the respective 
 lengths of those obliques, show the amount.of material 
 required in their construction, under the conditions 
 above expressed. 
 
 Let m = JM, and A = be. Then, we manifestly have, 
 for material in the 14 obliques of the truss in question 
 7m (#+!)+ 6m (4A 2 +1) + 5m (9A 2 +1) + 4m (16A 2 +1) + 
 3m (25/t a +l) + 2m (36A 2 +1) + 1m (49A 2 +1) = (336A 2 + 
 28)m, for those meeting at <7, and a like amount for those 
 meeting nil; making a total of (672A 2 -f56)m. But 
 A 2 = 0.694, which substituted in the last expression, 
 gives 522.368m, = 65.296M. 
 
COMPARISON OF PLANS. 243 
 
 FIG. 47. 
 
 BOLLMAN TRUSS. 
 q p o n m I 
 
 The thrust of the chord al, equals the horizonta. 
 action of the 7 obliques connected with cither end. 
 Making then x = JW, and h = 6c, == \bk, it is obvious 
 that each oblique carries weight equal to x x the number 
 of panels not crossed by it, while its horizontal reach 
 equals h x the number of panels it does cross. -Hence, 
 the horizontal action of each oblique, equals hx X the pro- 
 duct of the numbers of panels at the right and loft 
 respectively, of the lower end of the oblique. 
 
 The compressive force acting from end to end, upon 
 al, then, must be equal to Ax (7, -f 2x6, -f 3x5, + 4 2 -f 
 5x3, + 6x2, + 7), = 84Ax, = 10jWx0.833, = 8.75W. 
 
 Multiplying stress by length, and substituting M, we 
 have 8.75 X 6.66M 58 JM = material required in /, at a 
 given stress per square inch of cross-section ; M being the 
 amount required for a unit of length (a6), to sustain 
 the unit of weight (W), at the same rate of stress. 
 
 Add 7M for two end posts, with length equal to 1 
 and bearing weight equal to 7W, and we obtain 65 JM 
 as a total for thrust material in long pieces, not includ 
 ing 7 intermediate uprights, not properly to be class- 
 fied with other parts, as their action is merely incidental, 
 except that of supporting the weight of upper chord. 
 
 The parts above considered, mainly determine the 
 character of the truss as to economy of material. 
 
244 BRIDGE BUILDING. 
 
 Other parts, such as short bolts, nuts, connecting pins, 
 &c., although just as essential, are comparatively, of 
 small amount and cost, except the intermediate up 
 rights, which will be referred to hereafter. 
 
 If the truss be used in a deck bridge, and the end 
 posts be replaced with masonry, the intermediates 
 will sustain the same weight as the ends sustain in a 
 through bridge, thus giving the same representative of 
 material as above found. 
 
 THE FINCK TRUSS, FIG. 48, 
 
 CXXXIII. Possesses several of the characteristics 
 which distinguish the Bollman plan. Both dispense 
 with the bottom chord, which is common to most, if 
 not all other plans of truss, for both iron and wooden 
 bridges. Both also employ a pair of tension obliques 
 acting in horizontal antagonism to each other, at each 
 of the supporting points c, d, e, &c. But while in the 
 one, the members of each pair of obliques are of equal 
 length and tension, in the other, the pairs consist of 
 unequal members (except at the centre), as the dia 
 grams will sufficiently illustrate. 
 
 It will readily be seen that Fig. 48 exhibits three 
 classes of obliques, consisting respectively of 2, 4, and 8 
 members to the class. Supposing a truss of the same di 
 mensions and proportions, and subjected to the same 
 load, as in case of Fig. 47, and using the same notation, 
 as far as applicable; it is manifest that each of the 8 
 short obliques, sustains J~W~. The 4 next longer sus 
 tain upon each, a weight equal to W - one half directly, 
 and the other, through the short obliques and uprights. 
 The two long obliques. sustain 2W each, being the half 
 of 1\V, received directly at/, and 1 and 2 respectively 
 
COMPARISON OF PLANS. 
 
 245 
 
 through the upright, from members of the other classes, 
 meeting at the point p. 
 
 The material required for all the obliques, then, (ab 
 being = 1, and be = A), is 8 X J (A 2 + 1) -f 4 X 1 (4/t 2 -f 
 1) + 2 x 2 (Iti/i 2 -f 1)M, being the number of pieces in, 
 each class multiplied by co-efficients of W in \veight s 
 sustained, and by squares of length respectively, and 
 the sum of products multiplied by M. 
 
 Subsituting in the above expression the value of A 2 , 
 (0.694), and, reducing and adding terms, we derive 
 material in obliques = 70.296 M. 
 
 FIG. 48. 
 
 FINCK TRUSS. 
 
 asrqponml 
 
 k 
 
 The compression upon the chord a I, is equal to the 
 horizontal action of one member of each class of ob 
 liques, communicated at each end ; that is, equal to 
 (i h -f 2/i + 8/i) W, = 10J h W ; and, multiplying by 
 length ( = 6.66), and substituting 0.833 for A, and M 
 for W, we have (10.5 x .833 x 6.66)M = 58.J M, to re 
 present the material required in al ; the same as in 
 case of Fig. 47. 
 
 The uprights of the Finck truss obviously sustain 
 12W, namely, 3| at each end, 3 in the middle, and 1 
 at each of the quarterings, r and n. But, in comparing 
 this with the Boll man truss, it seems fair to offset 6 up 
 rights, not including the end and centre ones, in the 
 Finck, against 7 in the Bollman truss not estimated ; 
 bus leaving 10M for uprights in the former, making 
 
246 BRIDGE BUILDING. 
 
 a total of 68 JM, for compression material, excepting 
 the 6 intermediate uprights, excluded as above. 
 
 Both of the above considered trusses exhibit a beau 
 tiful simplicity, and facility of comprehension in prin 
 ciple, and they will be left for the present, for a 
 discussion of the 
 
 POST TRUSS. 
 
 CXXXIY. This, like the two preceding plans, is 
 designated by the name of its distinguished designer 
 and publisher, S. S. Post, Esqr., of Jersey City. 
 
 Fig. 49 gives a general view of the only specimen 
 of this truss which the author has had an opportunity 
 of examining. It is a sort of compromise between the 
 trusses represented by Figs. 18 and 19, of which the 
 object sought appears to have been, to obtain a nearer 
 approximation to the most economical angle of incli 
 nation for both thrust and tension members (between 
 chord and chord), by inclining the latter at an angle 
 of 45, and the former at a less angle with the vertical. 
 These are both favorable conditions, considered alone 
 and by themselves, as we have already seen [LXV and 
 LXVI] ; and it is proposed to compare the economy of 
 this particular arrangement, with that of a truss having 
 vertical posts, with oblique tension diagonals ; as well 
 as with other plans, preceding and succeeding. 
 
 Assuming the same length and depth of truss, and 
 the same load, both constant aud variable, as in the 
 preceding cases, acting at the points x, y, w, &c., let w 
 represent the greatest variable load for the length of 
 one panel, and w the weight of superstructure bearing 
 upon one truss, for the same length, supposed to be 
 concentrated at the nodes of the lower chord, and as 
 sumed to be equal to %w. Also, let 1 equal the verti 
 
COMPARISON OF PLANS. 247 
 
 cal depth of truss (between centres of chords), and let 
 tension diagonals incline 45, and posts lean 1 horizon 
 tally to 3 vertically ; the space between posts being 
 two-thirds of the depth of truss. 
 
 FIG. 49. 
 
 Mr. PosCs Truss 
 a 5 e d e f g h i Tc I 
 
 n m 
 
 Then, omitting counter ties up to (/", from the left, 
 as neutralized by weight of structure ; we see that the 
 weight at z, being only j as great as at the other nodes, 
 on account of the short space xy, 3w -r- 80 (or 3w", 
 substituting for the occasion, w" for w -f- 80), represents 
 the proportionate part of that weight, tending to ber.r 
 upon the abutment at m ; and this, with VLw" for 
 weight at v, and 20^tf" for weight at u, + "2$iv" lor 
 weight at t, makes 63w" accumulated upon if, when 
 #, v, u and t alone are loaded. 
 
 Now, the action upon this truss is less certain and 
 determinate than where the thrust pieces are vertical, 
 or inclined equally with the tension pieces. But sup 
 posing that the weight of superstructure at s, or at 5 
 and r together, neutralizes, or reflects back a part 
 equal to w , or JSOtt/ , = 27w" nearly, of this 6Zw", we 
 have a balance of36JV, as the maximum weight for if. 
 
 Then, whether this 63w/ r * which must go to the 
 
 *This full amount 63w" is used here; for, although it is assumed 
 that only 5, part of it is transmitted through tf, the balance is restored 
 from weight of structure which otherwise would pass to the abutment 
 aty. 
 
248 BRIDGE BUILDING. 
 
 abutment #t m, in virtue of the loads at x, i?, u and /, 
 is transferred through fs to s^, or through/? to rh ; or 
 whether it is divided equally or unequally between the 
 two, is not quite obvious. But assuming, as what 
 might seem probable, that it is transferred in equal 
 portions to s^and rh, in that case, sg sustains as a maxi 
 mum, 3(3?0" for weight at s, + half of 63w", making 
 say 67?" ; supposing that sg and re sustain none of the 
 weight of structure ; which, though probably not 
 strictly true, will not materially affect the result. 
 
 Again, (we are now considering the nodes at the 
 lower chord as being loaded successively from left to 
 right), the weight at r gives 44 w" to rh, in addition to, 
 say 32w" tending to be transmitted from tf, and w 9 or 
 27w" for structure, making 103*0". 
 
 For maximum weight on iq, there is due to movable 
 weight at q, 5 2>v", + Qlio" from sg, + 27w" on account 
 of weight of structure, making 146*0"; while pk sus 
 tains (60 + 103 + 27)M>", = 190a?", and ol sustains (68 + 
 146+27)w" = 241". The maximum weight upon nl, is 
 made up of that of pk + f (10+10 ) at n, = 270i0". 
 
 Having thus determined the maximum weights 
 which these diagonals are respectively required to sus 
 tain, disregarding some small matters of uncertainty, 
 of little practical importance, we find the sum of these 
 maxima, for the 6 pieces parallel with ue on the right, 
 to be 783*0", = 9.7875*0. Then, multiplying by 2 (the 
 square of the common length, ay being = 1), and sub 
 stituting M for w ( as M was substituted for W in the 
 preceding cases), w r e derive 19.575M = material re 
 quired for the 6 pieces in question. Add to the last 
 amount 3.7M for the steep diagonal nl (being the square 
 of length by weight sustained, and w changed to M ); 
 
COMPARISON OF PLANS. 249 
 
 and we have the whole material for tension obliques 
 in the half truss ; which doubled, exhibits for that class 
 of. members in the whole truss, 46.55M ; omitting 6 
 counter ties, not required to sustain structure or load, 
 and the value of which will be considered (in general) 
 hereafter under the head of counter bracing. 
 
 The short section mn of the lower chord, has no de 
 terminate action. The section no has a tension equal 
 to J of the weight acting on nl and kn, under a full 
 load of the truss, equal to J the weights upon r, p and 
 7?, fur nl, and J of those at r and p for kn ; the whole 
 equal to J x2J (w+w )+% x2 (?(;+</; ), = 2.11 w. 
 
 To this, the diagonal ol adds at o, 2 (w + w r ), and 10 
 adds J(w-fw ), making 5.22z0 tension of op; while 
 a like addition at p, for the action of pk and hp, shows 
 8.332(7 for /N/. Again, ^ adds at q, w+w , equal to 
 1.33u , while rh contributes a like amount at r ; mak 
 ing for qr and rs respectively, a tension of 9.66*0, and 
 ll//;, restoring neglected fractions. 
 
 It is probable that a small decussation of forces 
 through re and sg, under a full load of the truss, would 
 modify these stresses slightly, but not so as to produce 
 a material difference in the final results of the present 
 discussion. 
 
 Summing up the stresses thus determined for differ 
 ent portion of the lower chord, counting like strains 
 upon corresponding sections, and deducing the re 
 quired material (as above done with regard to dia 
 gonals), remembering that the length of sections equals 
 of unit} , we obtain 41. IM = material required in 
 lower chord. This added to 46.55M , the amount above 
 determined for obliques, gives tension material for the 
 whole truss, equals to 87.65M . 
 
250 BRIDGE BUILDING. 
 
 Now, it is manifest that the quantity here represented 
 by M , has the same ratio to that denoted by M in the 
 estimates of material for trusses Fig. 47 and Fig. 48, as 
 the weight w in the former case has to the weight W 
 in the latter. But W was used to express J of the 
 gross load of the truss, while w represents only -fa of 
 the variable, assumed to be equal to j of the gross load. 
 Therefore w : W : : f x^ : \ ; whence, w = 0.6W ; 
 and M = .6M. This equivalent substituted in the ex 
 pression 87.65M , gives 52.59M = tension material for 
 the post truss. 
 
 The maximum weights sustained by the thrust 
 braces, equal respectively those borne by the tension 
 rods communicating such weights, and for the 5 pieces 
 on either side of the centre, the amount is equal to w" 
 X (36 + 67 -f 103 + 146+ 190) = 6.77w, which doubled, 
 gives 13.54w; for the whole of that class of members. 
 This aggregate weight, multiplied by the square of the 
 common length of pieces (1.11), with w changed to M 
 produces 15.02M , = 9.01M. 
 
 The end section (kl) of the upper chord, sustains 
 compression equal to the weight upon ol and J of that 
 upon nl, under a full load of the truss, = 2 (10 -f i# ), 
 + }x2f (w+w f ), = 3.88w. Add 2 (w+w f ) for weight 
 on j9/c, and J of that amount for that on ATI, and it 
 makes a compression of 7.44?# upon ki. 
 
 Again, adding w+w f ( = 1.33itf) for action of qi, and 
 J of the same for that of io, makes 9.22w for compres 
 sion of ih, while a like addition for action of rh and hp, 
 makes 10.99^ = compression of hg and gf. We may 
 call the last stress llw, as some fractions have been 
 neglected. 
 
 The above amounts of stress upon the several sec 
 tions of the half chord, added together and doubled to 
 
COMPARISON OF PLANS. 251 
 
 represent the whole chord, and multiplied by the length 
 of section (f ), produce 56.72w?,= 34.03 W ; whence, 
 material for top chord = 34M ; very nearly. 
 
 The two end posts obviously sustain the gross load 
 of the truss (deducting what comes upon one half of 
 the short spaces mn and xy), which equals 9J (w -f 
 w f ), = 12.66w; and, the length being 1, the material 
 equals 12.66M = 7.6 M. 
 
 Summing up the amounts thus determined, of mate 
 rial for the several classes of thrust pieces, we have : 
 
 For Braces, or inclined posts, 9.01M. 
 
 " Upper Chord, 34.00M. 
 
 " End Posts, 7.60M. 
 
 Total, for Thrust, ; 50.61M. 
 
 " " Tension, 52.58M. 
 
 WHIPPLE S TRAPEZOIDAL TRUSS. 
 
 CXXXV. The distinctive characteristics of this plan 
 are, an Upper Chord made shorter than the Lower, 
 by the width of one panel at each end, giving to the 
 truss a Trapezoidal form dispensing with non- 
 essential members, and proportioning the several parts 
 in strict accordance with the maximum stresses to 
 which they are respectively liable ; principles and de 
 vices first promulgated in the original edition of this 
 work, and applied by its author in the construction of 
 trusses with parallel chords, with or without vertical 
 members. 
 
 Truss Fig. 50 has vertical posts and tension dia 
 gonals; and, using w and w 1 to denote the same quan 
 tities as in the last preceding case, and pursuing the 
 method explained with reference to Fig. 18, [LVI], we 
 have the maximum load for 3/5 equal to 4iv ff JM? 
 
252 
 
 BRIDGE BUILDING. 
 
 (malting w" w divided by the number of panels = 
 O.litf), = Aw 10, since w = %w. For 4/6, we have 
 .610, without increase or diminution on account of 
 structure ; while, for the 3 next diagonals on the right, 
 we have successively,. 9?0 + JM/, 1.2*0 -f w and 1.6i/; + 
 Ijz0 , making altogether 3.7*0 + 3*0 , = 4.7z0 ; showing 
 for the 5 pieces, 5.53w. This being doubled and mul 
 tiplied by square of length (2.775), and w changed to 
 M , gives material for 10 long diagonals = 30.69M 7 . 
 
 The two steep diagonals togther, sustain 4 (w -f 
 w ), = 5Jw, which, multiplied by square of length 
 (1.44), produces material = 7.68M ; while the two ten 
 sion uprights manifestly require 2f M . We have con 
 sequently, material for the system of tension obliques 
 and verticals = 41.03m . 
 
 The end brace obviously sustains 4J (w + w ), and 
 exerts a horizontal stress = 4?0 (two-thirds of the weight 
 borne), upon the two first sections of the lower chord. 
 The steep tension oblique adds of weight borne, mak 
 ing 5.76^ for the next section, while the two succeed 
 ing diagonals toward the centre, adding 1J times the 
 weights borne successively (under a full load of the 
 truss, of course), give 8.42*0 and 10.19*0, for tension of 
 second and first sections from centre, respectively. 
 Then, adding, doubling, and multiplying by length of 
 section, we obtain, material for lower chord = 43.16M . 
 
COMPARISON OF PLANS. 253 
 
 Add to this the amount for diagonal system as above 
 found, and we have the whole amount of tension ma 
 terial for the truss = 84.18M = 50.5M. 
 
 The maximum weights sustained by obliques, and 
 by them transferred to 7 thrust verticals, being in the 
 aggregate = 6.62*0, the length of members being unity, 
 need only the substitution of M , to express the re 
 quired material for said verticals ; which, reduced to 
 terms of M, equals 3.97M. 
 
 The first and second sections of the upper chord, ob 
 viously sustain the same action respectively, as the 
 fourth and fifth of the lower chord while the 4 middle 
 sections of the former, receive the additional action of 
 diagonals 3\5/7 (upper figures), under full load. 
 Hence we cipher up, material for upper chord = 32.6M. 
 
 The end braces, sustaining 9 (iv+ w f ) = 12io, with a 
 length whose square is 1.44, obviously require material 
 = (12xl.44)M = 10.37M. 
 
 The truss, then, requires thrust material, for upper 
 chord, 32. 6M, for end braces, 10.37M, and for up 
 rights, 3.97M ; making a total for the truss, of 46.09M. 
 
 Tension material as above, total 50.50M. 
 
 TRUSS WITHOUT VERTICALS. 
 
 CXXXVI. Assuming a truss (Fig. 51), of same 
 length, depth, and number of panels, and same load, 
 variable and constant, as in the two cases last consi 
 dered, with diagonals crossing one panel only, we have 
 nearly the Isometric Truss,* adopted by Messrs. Steele 
 
 and McDonald. 
 
 Arranging the numbers over the diagram, as in Fig. 
 51, and using the process explained [XLVII, Fig. 19], it 
 
 * In the Isometric, the diagonals incline at 30, while in Fig. 51 they 
 incline nearly o4. 
 
254 
 
 BRIDGE BUILDING. 
 
 will be seen that either end brace, and the obliques 
 parallel therewith, are liable to maximum weights as 
 follows, proceding from end to end. 
 
 FIG. 51. 
 
 End Brace 4.5 (w+ w r ) 
 Oblique^o. 1 .................. 2.100" 
 
 " " 2 .................. 1.533" 
 
 " " 3 ................. . 1.066" 
 
 " " 4 .................. 1.600" 
 
 " 5 ..... . ............. 233" 
 
 " " 6 ., 
 
 Compression. Tension. 
 6.000 w. 
 
 .233?0 
 
 .600 " 
 1.066" 
 1.533 " 
 2.100 " 
 
 2.666" 
 
 Totals 
 
 11.533i0 
 
 Then, doubling for the two sets, multiplying by 
 square of length (1.44), and changing w to M , we have, 
 to represent material.... for compression 33.215M, ten 
 sion 23.616M . 
 
 The end brace, sustaining 4.5 (w -f- w }-, = 6?tf, exerts 
 a tension of 4w upon the end section of the lower 
 chord. The next brace sustains 1 (w -f w f ) = 2*0, 
 making a tension of 5.333z# for the second section. 
 The tension and thrust diagonals meeting the chord 
 
 f The small thrust action which the movable load tends to throw 
 upon 6, 7 and 8, and the small tension upon 1 and 2, are neutralized by 
 weight of structure. 
 
COMPARISON OF PLANS. 255 
 
 at the next node, sustain together (under a full load of 
 the truss). 3 (w -f w = 4*0, adding -f of which, gives 
 Sw =H tension of the 3d section, while 2f?0 borne by 
 the obliques meeting at the next node, makes a tension 
 upon the 4th section equal to 9.777*0 ; and IJw; at the 
 next node (the tension diagonal only, being in action, 
 under a full load), gives for tension of the 5th section, 
 10.066*. 
 
 Adding the stresses of the several sections of the half- 
 chord, doubling, multiplying by the common length 
 (f), and changing w to M shows material for lower 
 chord = 50.37M,. 
 
 The end section of the upper chord sustains thrust 
 equal to f x (weight on end brace, (= 610), -f weight 
 on tension oblique meeting said brace), = f 8.66610 = 
 5.77*0. 
 
 The two obliques meeting at the first node from the 
 end, sustain together 4i0, adding 2. 66610 to the above, 
 and making a compression of 8.44 Iw upon the second 
 section ; while succeeding diagonals make the stresses 
 of the 3d and 4th sections, 10.222*0, and ll.lw; re 
 spectively; whence, by process already employed and 
 described, we derive : 
 
 Material for upper chord 47.392M = 28.435M 
 
 Add for end braces, 17.28 " = 10.368" 
 
 " " other obliques, 15.935" = 9.561" 
 
 Total for compression material, 80.607M = 48.364M 
 
 Tension, chord, 50.37M* 
 
 Obliques, 20.616 
 
 Verticals, 5 
 
 78.986M -47.391M. 
 
 Grand Total, 95.755M. 
 
256 BRIDGE BUILDING. 
 
 THE ARCH TRUSS. 
 
 CXXXVTI. A parabolic Arch Truss of the same 
 length, depth and load as allowed in the five preceding 
 cases, and having 9 panels, will compare, as to repre 
 sentative of amount of material, as follows : 
 
 Let w / represent the variable, and w tn = \w t , the per 
 manent panel-lo*ad. Then, taking the greatest depth 
 of truss (15/.), as the unit of length, as before, the 
 length of chord will be 6.666, and the verticals respect 
 ively 1, 0.9, 0.7, and 0.4. 
 
 The length of panel (ll.lll/.), being divided by 15/. 
 (the unit), gives .74074. Hence, tension of chord = 
 
 4 (w / + w /f ) x 74 t 074 , = 1J x 7.407410,, which, multiplied 
 
 by length of chord (= 6.666), and w n changed to M,, 
 gives representative of material = 9.8765 x 6JM, = 
 65.843M, ; in which M,is the unit of material, proportional 
 to the unit of length (15 ,) X unit of stress, w r 
 
 The maximum tension of diagonals, as determined 
 instrumentally by process explained [xxvn, &c.,] va 
 ries from 1.11 z^, to 1 J^ ; and, taking the highest, mul 
 tiplying by the aggregate length (15.4), and changing 
 w, to M,, we obtain material = 20.52M y . 
 
 The verticals sustain tension, each, = lJw /5 with an 
 aggregate length of 6, giving material = SM, ; making 
 a total of tension material = 94.376M,. 
 
 The horizontal thrust of the arch, must be in all 
 parts the same as the tension of the chord (at the maxi 
 mum under full load), and it is manifest that the ma 
 terial for each segment, must be to that of the middle 
 segment, as the squares of respective lengths to unity ; 
 that is, equal to material in said middle segment, mul 
 tiplied by squares of respective lengths. 
 
COMPARISON OF PLANS. 
 
 257 
 
 But the representative for the middle piece equals Jth 
 that of the lower chord, = 7.31^,. Hence, this amount 
 multiplied by the sum of squares of all the others, +1 
 for the middle segment, found to be 9.058 + 1, = 10.058? 
 gives, to represent material for the whole arch, 73.584M / . 
 
 Then, the vertical members are liable to be exposed 
 to compressive action, represented by the small amount 
 of 2.058M,, which added to the above^ gives a total of 
 compression material, equal to 75. 642 M,. 
 
 Now, the factor M y , here used, is to the factor M 
 used in the preceding cases, manifestly, as fxj, to J, 
 as -Jj : J, whence, 12M / = 8M ; and we reduce the co 
 efficients of M,, by J, and change M, to M, to bring the 
 last results to the same standard measure as in the 
 preceding. 
 
 Effecting these changes, we have, for tension 
 material, Chord 43.895M, -f Diagonals 13.689M + 
 Verticals 5. 333M, equal to a total ol 62.917M. For com 
 pression, Arch, 49.056-r-Verticals, 1.372, = 50.428M. 
 
 SYNOPSIS OF PRECEDING DEDUCTIONS. 
 The following tabulated statement may promote the 
 convenience of comparison : 
 
 Trusses. 
 
 Material required expressed in Ms. 
 
 Designated. 
 
 Tension 
 total. 
 
 Compression. 
 
 Comp. 
 Total. 
 
 Grand 
 Total. 
 
 Chord. 
 
 Ends. 
 
 Posts, &c. 
 
 Bollman, . 
 Finck, 
 
 05.296 
 70.206 
 52.590 
 50.500 
 47.391 
 62.917 
 
 58.333 
 58.333 
 34. 
 32.6 
 28.435 
 {49.056 
 
 7.000 
 7. 
 7.6 
 10.37 
 10.368 
 
 * 
 
 3.000 
 9.01 
 3.97 
 19.561 
 1.372 
 
 65.333 
 68.333 
 50.610 
 46.94 
 48.364 
 50.428 
 
 130.629 
 138.629 
 103.200 
 97.44 
 95.755 
 113.345 
 
 Post, 
 Whipple, . 
 Isometric, . 
 Arch, 
 
 {Arch. 
 
 33 
 
258 BRIDGE BUILDING. 
 
 CXXXVIII. The figures in this table are to be 
 understood in all cases as prefixed to the quantity M, 
 which, as far as relates to tension material, represents 
 a determinate amount of wrought iron ; while, as it re 
 lates to compression material, M represents an amount 
 of cast or wr-.-uy -t iron, varying as the forms and pro 
 portions of parts vary. But, in the present discussion 
 M may be assumed to have a uniform value in ex 
 pressions relating to material under the heading of 
 chords; and of ends, whether oblique or vertical. 
 
 The quantities under the head posts, require in 
 general, probable twice as high a value for M, as tha.t 
 required for the other classes of thrust members, as it 
 regards all but the first named truss, while the first is 
 not represented in that column at all, although the 
 parts there referred to are as indispensiblc, practically, 
 and require nearly as rrmch material as corresponding 
 parts in the other plans. 
 
 With regard to plan No 2 (the Finck), 6 posts ac 
 tually required (two of which, at the quarterings, sus 
 tain determinate weight equal to W each), are also 
 omitted in the table, to place this plan upon an equal 
 footing with the preceding one. 
 
 There is also a consideration with regard to the ef 
 fects of load upon these two trusses, especially the 
 first, which render it partially necessary to use diagonal 
 ties, or " panel rods" in the several panels ; and such 
 have usually been introduced wherever such bridges 
 have been constructed. 
 
 As any one pair of suspension rods in the Boll man 
 truss may be under full load, while the others are 
 without load, the loaded node would, in such case, be 
 depressed, while that on either side would retain nearly 
 its normal position. Thus would result an obliquity 
 
COMPARISON OF PLANS. 259 
 
 in panels adjacent to the loaded point, and consequently, 
 a tendency to kink in the upper chord, by opening 
 the joint above the loaded point upon the under side, 
 and the next joint either way, upon the upper side. 
 Hence the compression of certain chord segments 
 would be thrown upon the extreme upper side at one 
 end, and the lower side at the other end. This would 
 be decidedly an unfavorable condition, which the panel 
 rods are used to obviate by distributing the load of 
 loaded points over adjacent, and more remote parts of 
 the truss. Otherwise, the bridge would act under a 
 passing load, somewhat in the manner of a pontoon 
 bridge. 
 
 By estimating a reasonable amount of material for 
 posts and panel ties, the figures in the table, opposite 
 the first two trusses would be materially increased. 
 
 Hence, it must be obvious that the necessary mate 
 rial for the two above named trusses, is not so fully 
 represented in the table, as in the case of the other 
 four; with regard to which assigning proper values 
 to M in the different columns of the table, and assum 
 ing the members to adhere to one another as firmly as 
 the different portions of each cohere among themselves, 
 a complete truss would be formed in either case (of 
 dimensions as above assumed), sufficient to be used in 
 a bridge required to bear a gross load equal to 4 times 
 the weight of superstructure ; provided the proper 
 ratio of safe variable load to weight of structure be as 
 3 to 1 ; as is nearly the case with regard to a 100 foot 
 bridge.* 
 
 * M, in the preceding table, represents a piece of iron, 15 long sus- 
 ficient to sustain with safety, a weight W, equal to ^ of the gross 
 maximum load f>r one truss of a 100ft. bridge. Allowing l,0091bs. to 
 the linea! foot for movable, and 3331bs. for permanent lo -d, W, repre 
 sents -I X 133,3331bs.= 16,66Glbs. Then, reckoning the safe stress of 
 
260 BRIDGE BUILDING. 
 
 In such case, the results already obtained, would 
 show the relative cost of the several trusses (excepting 
 the first two), with almost absolute exactness. 
 
 But, as the parts of a truss can not be so connected 
 and welded into a single piece, without enlargements 
 at the joinings, by any skill or process now in use, we 
 have to include as an item of cost, in all plans, a con 
 siderable amount of material above and beyond the 
 net lengths and cross-sections, as here before deter 
 mined with regard to the trusses under discussion, re 
 quired for the lapping of parts, screws and nuts, eyes 
 and pins, &c., to form the connections of the different 
 members with one another. 
 
 With regard to the trusses under comparison, no 
 obvious reason presents itself, why any one should re 
 quire a percentage of allowance for connections ma 
 terially greater than another. Leaving out the two 
 first, as perhaps already sufficiently discussed, the 
 others consist of about the same number of necessary 
 members, and with the exception of the arch truss, ad 
 mit of nearly the same forms and connections of parts. 
 The Isometric, or Trapezoid without verticals, presents 
 the fewest lines in the diagram; but some six of those 
 lines represent both tension and thrust members, either 
 separate or combined, which probably complicates the 
 
 iron (thrust or tension), at say 10,0001bs. to the inch of cross-section, 
 it takes If square inches to sustain the weight W ; being about 5lbs. 
 to the foot, or 84flbs. for 15 . This, increased by say, 20 per c. for 
 extra material in connections, gives the practical value of M ; which, 
 multiplied by the co-efficient of M in the table, produces approxi 
 mately, the respective weights of trusses. 
 
 Now, 1 X 84.37 == lOlilbs. which multiplied by 113.345, the co 
 efficient for the Arch truss, gives for the weight of that truss, 11.4761bs. 
 Add for 10 feet width of platform (with wooden beams), say 5,000ft. 
 &. m. of timber and plank, equal to about 20,000 Ibs., and we have 
 31.47Glbs. to represent the permanent load of the truss. But we have 
 assumed a truss proportioned to sustain with safety 133,3331b., which 
 is a little more than 4 times the weight of structure here above esti 
 mated as supported by the truss. 
 
COMPARISON OF PLANS. 261 
 
 details of connection, quite as much as the extra three 
 members in truss No. 4. The Post truss presents the 
 larger number of acting members, even omitting six 
 counter ties seen in the diagram, with apparently no 
 advantage as to modes of connection. Both the Post 
 and the Isometric have 10 members represented in the 
 4th column of the table, whereas the Whipple truss 
 has only 7, and these the shortest of all ; and, as the 
 material in these parts manifestly acts at a disadvan 
 tage, they being comparatively long and slim, and sus 
 taining slight action, any excess in their number, would 
 seem to be unfavorable to economy. 
 
 It is believed, however, that the Post truss would be 
 improved in economy by reducing it to a trapezoidal 
 contour, as, for instance, by removing the parts outside 
 of bx and kn (Fig. 49), and changing the tension pieces 
 av and ol for others connecting 6 with y, and o with k ; 
 thus converting the figure to a trapezoid very similar 
 to that of Fig. 50 ; and, by striking out one panel from 
 the latter, and arranging parts as in Fig. 20, except as 
 to inclination, the relative merits of inclined and ver 
 tical posts, as represented in these two plans may be 
 fairly tested. 
 
 Analysis of trusses modified as just indicated, show 
 tension material slightly in preponderance with the 
 vertical, and thrust material a little the greater with 
 inclined posts ; the average being about one per cent 
 greater in the case of vertical posts. 
 
 This balance, though trifling in amount, is upon tho 
 side where it was to be lookod for, in view of the re 
 sult of investigations had with reference to Figures 12 
 and 13 [xxxix XLVI], as well as the case of the Iso 
 metric. Both the Post truss and the Isometric, as to 
 principle of action, may be classed with Fig. 13, where 
 
262 BRIDGE BUILDING. 
 
 weight is transferred from oblique to oblique, and not 
 from oblique to vertical, and the contrary. The same 
 may be said of truss Fig. 15, sometimes called the 
 Triangular, in which verticals are used merely to trans 
 fer the action of weight from the point of application 
 to the connections of the obliques ; after which, the 
 weight has no action upon verticals. 
 
 Now finally, we see by table of results, that if the 
 Post truss be changed to the trapezoidal form, as above 
 suggested, it will occupy a position, as to amount of 
 material, or more strictly speaking, the amount of ac. 
 tion upon material, between Fig. 50 and Fig. 51 ; which 
 latter differ from one another less than 2 per cent ; a 
 difference, which would undoubtedly be increased 
 somewhat, under different general proportions of trusses. 
 For instance, while Fig. 50, shows an inclination of 
 diagonals used in connection with verticals, probably 
 nearly approaching the optimum, Fig. 51, though su 
 perior to the true Isometric (with angles of 60), in 
 the greater inclination of its obliques, would give still 
 better results with an inclination of about 40. 
 
 CXXXIX. On the whole, we must look to other 
 quarters than the amount of action upon material, for 
 plausible ground upon which to found a decided pre 
 ference for either of the three plans in question. A 
 difference of two or three per C., and even more, may 
 easily result from greater or less facility of constructing 
 and erecting the structure, while a regard for appear 
 ance may also be worthy of consideration. Hence, 
 Engineers and builders will adopt one or another plan, 
 according to individual taste and judgment, and tho 
 one who carries out the principles of either system with 
 
COUNTER BRACING. 263 
 
 the greatest skill, and the best materials and workman 
 ship, will probably produce tbe best bridge. 
 
 Judging from the preceding tabulated statement, 
 the arch truss seems, prima facie, to labor under a 
 somewhat formidable disadvantage in the fact that it 
 shows an amount of action upon material 10 or 15 per 
 cent, greater than the three preceding plans just es 
 pecially referred to. But for the light of experience, 
 we might be led to discard the plan without a trial. 
 
 But, having chanced to be the first plan of iron 
 Truss successfully put in use, and having had its ca 
 pabilities fully tried and demonstrated, before any 
 formidable competitor appeared in the field, it could not 
 be dislodged from its position, until a rival plan could 
 not only theoretically, but also practically demonstrate 
 its superior claim to public favor. 
 
 The result has been such as to show that even a very 
 considerable excess of action upon material, may be 
 overbalanced by more advantageous action of thrust 
 material, and greater simplicity and facility of construct- 
 tion ; insomuch that the Whipple Patent Arch Truss, 
 with trifling modifications from the original pattern, 
 has competed successfully with all other plans, for the 
 class of structures it was originally designed and re 
 commended for (common bridges of 50 to 100 feet), 
 during more than a quarter of a century, which has 
 been fruitful in efforts at improvement in iron bridge 
 construction. 
 
 COUNTER BRACING. 
 
 The elasticity of solid materials, is manifested 
 in bridge trusses, by their downward deflection under 
 
264 BRIDGE BUILDING. 
 
 load, and the recovery of their previous form and po 
 sition on the removal of the load. 
 
 Tins arises principally, from the temporary elonga 
 tion of parts exposed to tension, and the contraction 
 of those exposed to compression, according to laws 
 and principles supposed to be understood. 
 
 The deflection of trusses within the usual limits, 
 when properly proportioned, is not essentially detri 
 mental to their safety and durability ; but rather 
 enables them the better to resist sudden impulses, 
 except in case of a regular succession of impulses, at 
 intervals corresponding with those of the natural vi 
 brations of the structure, or with some multiple or 
 even division thereof; a result frequently noticeable, 
 and sometimes, to a degree somewhat unpleasant to 
 the eye. as well as suggestive of danger. Hence, 
 great emphasis is often employed, in expressing the sup 
 posed advantages of " counter bracing," as a means 
 of stiffening trusses, and preventing, or diminishing 
 their vibration. 
 
 What is technically called " counter-bracing," as ap 
 plied to bridge trusses, is the introduction of a set of 
 diagonal, or oblique pieces or members, to act in an 
 tagonism to the main diagonals, whether acting by 
 tension or thrust, which contribute toward sustaining the 
 weight of structure and load; the object being, to re 
 tain in the truss when unloaded, more or less of the 
 deflection produced by the load, when the truss is 
 loaded. 
 
 My object at the present time is, to exhibit the pro 
 cess and results of my investigations as to the theory 
 and effects of this counter-bracing, as usually practiced 
 in bridge building, and to state the conclusions arrived 
 
COUNTER BRACING. 
 
 265 
 
 at, as to the value of counter-braces, towards effecting 
 the object proposed. 
 
 FIG. 52. 
 a b c d e f fj h . i 
 
 I assume a truss (see Fig. 52) composed of horizon 
 tal chords (of equal lengths), at top and bottom, vertical 
 posts, and diagonal tension rods, inclined at 45, or at 
 any other given inclination, the truss being uni 
 formly loaded from end to end, and so proportioned 
 that all of the above named parts, in that condition of 
 the load, shall undergo an amount of extension or 
 compression, proportional to the respective lengths of 
 pans, multiplied by a constant factor (E), equal to the 
 elastic change effected in a length equal to that of the 
 uprights between centres of chords, which is assumed as 
 the unit of length for the occasion. Then, let L repre 
 sent the length of truss, P, the number of panels, ff, 
 equal to L-r- P, the horizontal reach of diagonals, and 
 D (equal to 2LE), the difference in length, occasioned 
 by extension of lower, and compression of upper chord. 
 
 Now, assuming no change in lengths of diagonals 
 and verticals, it is manifest that the chords assume, in 
 these circumstances, the forms of two similar and con 
 centric arcs of circles, of which the difference in length 
 is to the mean length, as the difference of radii is to 
 the mean radius, R. 
 
 But the difference of radii manifestly equals the 
 distance between chords, equal to L Using, then, 
 the representative signs before adopted, we have 
 
 D : L : : 1 : E; whence R = L-D. 
 
 34 
 
266 
 
 BRIDGE BUILDING. 
 
 the depression at the centre of the truss, is 
 evidently equal to the versed sine of half the arc made 
 by the chords, and is found with sufficient nearness, 
 by the equation . . Dep. =- (Lf -v- 2R, = JZ, 2 -r- R. 
 Then, substituting L -s- D for R, we have dep.= \U -r- 
 (Z, -s- D), = IDL. 
 
 Hence, if the length of truss equal 8 times the depth, 
 or 8, the deflection due to this cause, will equal the 
 difference in length of the two chords, produced by 
 their extension and compression. 
 
 Again, if length equal 6, then, dep.= JD x 6, == 
 3D -T- 4, = 9E. 
 
 The depression resulting from extension of diagonals, 
 may be illustrated as follows. 
 
 If the points a and b of a rectangular panel abed 
 (Fig. 53), be fixed, and ac be extended by an addition 
 FIG 53 equal to eh to its length, produced by 
 
 d the action of weight at c, either di- 
 g rectly, or through the upright dc ; the 
 points d and c will fall to g and h, 
 and the very small triangle ceh (eh 
 representing only the elastic stretch 
 of ac), will be essentially similar to abc ; 
 whence, ch : ac : : eh : ab y and eh : 
 ac : ab, : : V (1 + H 2 ) : 1 . . . Therefore, eh = 
 (1 -f H 2 ). But ch : ^ (1 + H 2 } : : eh : 1, : : 
 (1 -f H 2 ) : 1 ; consequently, . . ch = E + EH 2 . 
 Now, if this represent one of the end panels of a 
 truss, all parts of the truss between the end panels, 
 must descend through a space equal to ch, in conse 
 quence of the extension of diagonals in the two end 
 panels ; and so for each succeeding pair of diagonals, 
 to the centre of the truss. Therefore, the depression 
 
 E 
 
COUNTER BRACING. 2G7 
 
 iu the centre, due to the stretching of diagonals, must 
 be equal to JP x (1 + H 2 )E, = (JP + } PH 2 )E. 
 
 The depression in the centre of the truss, due to 
 compression of uprights, is simply equal to the aggre 
 gate compression of all the uprights on either side of 
 the centre one, and consequently, equal to %PE. This 
 amount added to that produced by extension of 
 diagonals, as above determined, makes, for up 
 rights and diagonals together, a depression equal to 
 
 The value of this last expression, length and depth 
 of truss being the same, varies slightly with variation 
 in number and width of panels, but not so as to be a 
 matter of practical importance. 
 
 Assuming L = 8w, = 8, we find that, 
 
 P = 2, and P = 16, make (P + J PR 2 )E = ISE. 
 
 P=4, andP = 8 " 
 
 P=6, makes " 
 
 6 panels, therefore, seem to produce the least deflec 
 tion. 
 
 The deflection resulting from changes in leng hs of 
 chords, has been shown to be equal to \LD ; and, 
 substituting PHfor L, & ZPHEior D, we have. . J- 
 LD JP J jfZ 2 j57, =deflectiou from change in chords. 
 
 The term E, then, with the following co-efficients, 
 expresses the depression at the centre of the truss, re 
 sulting from all changes in length of parts, namely, 
 for chords, JPJEP, for diagonals, ...... JP+JPl? 8 , and, 
 
 for uprights, JP. 
 
 Hence, the deflection of a truss, under the condi 
 tions here assumed, depends upon three simple ele 
 ments, represented by the letters, P, H, & E; and is 
 expressed in the following general formula ; 
 
 Deflection^ (iP 2 7P, + JP+ JPH 2 , + 
 
268 BRIDGE BUILDING. 
 
 The parts of this aggregate co-efficient of E, re 
 ferring respectively to chords, diagonals, and uprights, 
 are separated and distinguished by commas. 
 
 The formula just given is equally applicable in case 
 of thrust diagonals and tension verticals ; as will be 
 made obvious by a moment s examination of the 
 principles involved. 
 
 Now, if the truss could be anchored down, by ties 
 and anchorage absolutely unyielding, to the point of 
 its utmost deflection under load ; the load might be 
 removed, and replaced, without any rising or falling 
 of the truss, the load and the anchors alternately re 
 taining the deflection, and preserving a constant and 
 uniform strain upon the truss. 
 
 The same effect is partially produced by counter- 
 bracing ; and the object of the present investigation is, 
 to determine, approximately, at least, to what extent 
 this may be done, and what is the real advantage of 
 counter-braces, in trusses with parallel chords ; beyond 
 where they are necessary, to counteract the effects of 
 unequal variable load, upon the different parts of the 
 truss. 
 
 We have seen that deflection results from three 
 causes, all, of course, depending upon elasticity ; 
 namely ; difference effected in lengths of, first chords, 
 second, diagonals, and third, uprights. 
 
 The theory of counter-bracing is, that by the intro 
 duction of antagonistic diagonals, the material is pre 
 vented from regaining its normal state on removal of 
 the load ; and consequently, that it yields to the re- 
 imposition of load, to much less extent than it would 
 do, in the absence of counters. 
 
 As to the deflection due to the difference in lengths 
 of chords, equal, as shown by the general formula one 
 
COUNTER BRACING. 269 
 
 page back, to one-half of the whole, for a truss in which 
 L = 6/Z, and to more than half, when L is greater 
 than 611; the counter-diagonals have no tendency to 
 retain or diminish that difference, or the deflection 
 produced by it. The diagonals and counters, simply 
 contract or extend (according as they act by tension or 
 thrust), the two chords equally, without affecting the 
 difference between the two. 
 
 On the contrary, the action of the counter diagonal 
 tends to retain the tension (or thrust, in case of thrust 
 diagonals), of the main in the same panel, and also, 
 the compression (or tension), of uprights ; and, in as 
 far as that is accomplished, the deflection due to the 
 elasticity of those parts, is retained, on removal of load 
 from the truss. 
 
 Suppose, in a truss with tension diagonals, loaded 
 and depressed as already explained, and all parts ex 
 tended or contracted to the amount of E X respective 
 lengths ; a counter-diagonal to be inserted in each 
 panel, crossing the mains, as shown in the diagram 
 (Fig. 52), and of half the size of the latter, such being 
 the usual proportion for counters. 
 
 Now, the counters being adjusted so as not to act 
 while the load is on, but ready to act immediately, as 
 the main diagonals begin to contract, then, the load 
 being removed, the main will contract by its elasticity, 
 opposed by the counter, until they come to an equili 
 brium ; each sustaining the same amount of tension. 
 Still, the aggregate extension of the two beyond the 
 natural state, must be essentially the same as that of 
 the one, under the load; the one gaining, just as fast 
 as the other loses. 
 
 But the main, having a cross-section twice as great 
 as the counter (chords and uprights retaining the same 
 
270 BRIDGE BUILDING. 
 
 lengths), must lose two-thirds of its tension, while the 
 latter is acquiring strain enough to withstand the re 
 maining third. Hence, 2 thirds of the deflection due 
 to extension of diagonals, is recovered, on removal of 
 the load, while the counter-diagonal retains the other 
 1 third. 
 
 But the posts (the greater portion of them), do not 
 remain stationary as to length, as above assumed ; the 
 main and counter diagonals together, exerting, ob 
 viously, only f as much action upon them in the new 
 condition, as the former exert under load, they are re 
 lieved of J of their aggregate stress under load ; but 
 do not recover in the same degree, their original ag 
 gregate length ; for the relief falls mostly upon the 
 larger uprights, where the relative effects are less than 
 the average. 
 
 To illustrate the case as to uprights if equal 
 weights act at the nodes of the lower chord (Fig. 52), 
 the compressive action upon the posts at p, q, r, and s, 
 is obviously as 1, 3, 5, 7, respectively, or as 3ft, 9ft, 
 15??, 21rc. [See analysis of Fig. 12]. Then, Counter- 
 bracing, and removing load ; sa is relieved of two-thirds 
 of its stress, equal to 14??, while bs exerts a force of 7n 
 upon br, making with 5?? retained by bq, a total of 12ft 
 upon br, and showing a relief of 3ft. Again ; cq receives 
 5ft through cr, and 3ft through cp, = 8?i in all, being a 
 relief of In. But dp, receiving 3ft through dq, and In 
 retained by do, sustains 4n, being an increase of In. 
 
 Now, as these uprights are assumed to undergo the 
 same contraction under load, J of the deflection on ac 
 count uprights, is due to each. Therefore, sa being 
 relieved of 2-3ds of its action, restores . . 2-3ds of J, 
 (= 16.6 per C.), of that deflection. In like manner, br 
 restores l-5th of J, = 5 per C., and cq l-9th of J, or 2.8 
 
COUNTER BRACING. 271 
 
 per C., making, for the pieces together, 24.4 per C., re 
 stored. This is diminished by l-3d of J, or 8.3 per C. 
 (on account of increased compression upon c/p), leaving 
 a balance of 16.1 per C. only, of deflection from con 
 traction of uprights, which is restored in spite of 
 counter-diagonals, in the case under discussion. 
 
 Moreover, the main and counter diagonals, produc 
 ing more or less effect of contraction upon the chords, 
 according to the degree of inclination of the former, 
 and the cross-sections of the latter, it may, perhaps, be 
 reasonably assumed, that the contraction thus effected 
 in the horizontal, is a full offset to the 16 per C. of ex 
 pansion in the vertical sides of panels, as above shown; 
 BO that we may regard the whole deflection from up 
 rights, as being retained by counter-diagonals. 
 
 To state the full result of the foregoing investigation 
 then, we tind in case of Fig. 52, which is a fair repre 
 sentative of the average of trusses; that counter-brac 
 ing, obviates all the deflection due to compression of 
 uprights, together with J of that resulting from exten 
 sion of diagonals ; and, making H = 1, in the formula 
 for deflection (p. 267), we have deflection saved by 
 counter-diagonals, = (J X 8 -f 4) -*- 28, = a little less 
 than 24 per C. of the whole deflection. If //== 0.75 
 (truss 52), the result would be about 31J per C. saved. 
 
 But even these results are based upon condition^ 
 never occurring in practice. It has been assumed that 
 all parts of the truss undergo equal degrees of change 
 under a full load ; which may be nearly true with re 
 spect to chords, but not to other parts. The maximum 
 action upon od and dp (Fig. 52), requires those parts to 
 be 2J times as great, as they need be under full load ; 
 while pc and cq require more, and, qb and 6r, l-20th more 
 
272 BRIDGE BUILDING. 
 
 cross-section at the maximum, than under a full load 
 of the truss. 
 
 Now the deflection resulting from elasticity in these 
 parts, being less in proportion as the parts are greater, 
 the saving by counter-bracing, must be less in the same 
 degree, as far as it relates to such parts. This at once 
 reduces the above computations for deflection retained, 
 from 31 J and 24, to 25 and 19 per C., for the two cases 
 respectively ; and, considering the increase of section 
 required for uprights (in iron trusses), on account of 
 great length and small diameter, as heretofore alluded 
 to, it is deemed to have been fully demonstrated, that 
 the effects of counter-diagonals, of half the size of the 
 mains, are, to retain in the truss when unloaded, from 
 one-sixth or "less, to one-fourth of the deflection pro 
 duced by a full movable load. 
 
 But it has been seen in the progress of our investi 
 gations as to the action of load upon the different parts 
 of the truss, that counter-diagonals are required in one 
 or two panels on either side of the centre, and there, 
 they can not be safely omitted. But, beyond the point 
 where the weight of structure acting on the mains, be 
 gins to overbalance the effects of unequal and variable 
 load upon the counters, I do not consider the advan 
 tages of counter diagonals to be sufficient to warrant 
 their use. 
 
 In the case of rail road trains, gliding smoothly over 
 bridges of ordinary spans, a quarter or a half of an 
 inch more or less of deflection, is of slight importance, 
 while, in bridges for ordinary carriage travel, the only 
 objection to it is, that it slightly increases the degree 
 of vibration produced by successive impulses, as of the 
 trotting of animals, in time with the natural vibrations. 
 Now, counter-bracing tends to shorten the intervals of 
 
COUNTER BRACING. 273 
 
 the natural vibrations by diminishing their extent; but 
 can not destroy the liability to vibration ;.and the al 
 teration of interval produced, may as often bring the 
 vibrations nigher in tone with the gait of a trotting 
 horse, as otherwise. "In certain cases the effect would 
 be one way, and in others, the opposite; and in 
 general, the only result would be, to diminish the ex 
 tent of motion ; by one quarter, or less. 
 
 Such is the result of the best reasoning and science 
 that I have been able to bring to bear upon the subject 
 of counter-bracing. 
 
 To find the actual maximum deflection of a truss it 
 is only necessary to know the value of P and //, and 
 to assign to E a value determined by the character of 
 material, and the stress upon the several parts under 
 full load. 
 
 In Fig. 52, if II = 1 = 12|ft., and the tension of 
 wrought iron equal 15,0001bs. per square inch, the 
 value of E for that material, will be about 0.0075 ft. ; 
 and this will apply to the lower chord, and the obliques, 
 ar and li. But the average value of E for diagonals 
 of wrought iron, would be about 0.006ft. 
 
 For cast iron, ll,0001bs. to the square inch, requires 
 about the same value for E, as 15,000 upon wrought 
 I. ; and, as that is a fair working rate of compression 
 for cast iron in the upper chord, .0075ft. may be taken 
 as Ae value of E for chords, in general. Uprights, 
 for reasons heretofore explained, require a value for 
 E , not greater than .005ft. 
 
 The above values of E and H, substituted in the 
 formula (J P*H\ + JP + JP# 2 , + JP,) x E, it becomes 
 P*H*E+ (JP + PH*}E f + \PE, equal to J x 64 x 
 .0075, + (4 + 4) .006, + 4 x .005, =, 0.188ft. = about 
 2J inches. Hence, a well proportioned wrought and 
 35 
 
274 BRIDGE BUILDING. 
 
 cast iron truss, one hundred feet long, by 12J feet deep, 
 may be depressed 2J" in the centre by a distributed 
 load (including structure), with tension not exceeding 
 15, and thrust, not exceeding 11 thousand pounds to 
 the square inch in cross-section of iron. 
 
 WOODED BRIDGES. 
 
 STRENGTH OF TIMBER, &c. 
 
 CXL. The qualities of wood as a building material, 
 have been extensively treated of by authors whose 
 works have long been before the public, with a degree 
 of ability and research to which the present writer can 
 make no pretensions. He will therefore at this timo f 
 simply state the conclusions arrived at from reading 
 and observation (coupled with some experimental re 
 search) with respect to the average absolute strength, 
 positive, negative, transverse, and to resist splitting, in 
 certain cases ; of the timbers principally in use for 
 building purposes; as also, the forces they will bear 
 with safety under various circumstances ; leaving it, 
 of course, for others to adopt his views for their own 
 practice, or to modify and correct them, according as 
 their greater experience or better judgment may 
 dictate. 
 
 At the same time, the author may be allowed to ex 
 press his firm belief, that the views about to be pre 
 sented, if fairly observed, will lead to the adoption or 
 continuance of a safe and economical practice as to the 
 proportioning of timber work in bridge construction. 
 
 Pine timber in this country is perhaps to be ranked 
 as among the most valuable timber in use for building 
 purposes ; especially in bridge building. White oak, 
 
WOODEN BRIDGES. 275 
 
 and some other varieties, are preferred for certain pur 
 poses, as being harder, stiffer, and especially better 
 calculated to sustain a transverse action, whether 
 tending to bend or crush it. But in what follows, 
 reference will principally be had to the ordinary white 
 pine of this country ; and the deductions here made, 
 may readily be modified so as to apply to other mate 
 rials of known strength, when so required. 
 
 The absolute positive, or tensile strength of pine, 
 may be stated at about 10,OOOJbs. to the square inch 
 of cross-section. It might therefore seem to be safely 
 reliable in practice, at 15 or 16 hundred pounds to the 
 inch, upon that part of the section of which the fibres 
 are not separated in forming connections with other 
 parts of the structure. And so it probably would be, 
 when new, sound, and straight grained. But timber 
 in bridges, is usually more or less exposed to wetting 
 and drying, and deterioration in strength, especially 
 as it regards tension. Moreover, in forming connections 
 of parts and pieces in a structure, it is difficult to se 
 cure a uniform strain upon all the uncut fibres; one 
 side of the piece being often exposed to much greater 
 stress than the other. In view of such facts, it is 
 deemed advisable to seldom allow less than one square 
 inch section of unbroken fibre to each l,0001bs. of 
 tensile strain. 
 
 NEGATIVE STRENGTH OF TIMBER. 
 
 CXLI. The ability of pine to resist compression in 
 the direction of the length of piece, is from 4 to 5 thou 
 sand pounds to the square inch of section, and this 
 varies but little, whether the pieces be of length equal 
 to once, or five or six times the diameter. It moreover 
 
276 
 
 BRIDGE BUILDING. 
 
 diminishes only about one-third with an increase of 
 length up to 18 or 20 diameters. 
 
 !N"ow, if we take about | of the absolute strength, 
 say 800ft>s. to the inch for a length of 6 diameters, and 
 560 for 18 diameters, and substract 40ft>s. per inch for 
 every increase of 2 diameters in length, between 6 and 
 18 diameters; and from 18 to 40 diameters, compute 
 the quantities by the rule given [LXXXIX], in relation 
 to negative resistance of cast iron, we shall form a 
 table of negative resistances of timber, for a range of 
 lengths which will cover the principal cases that will 
 occur in bridge building, which the author feels confi 
 dent in recommending for the adoption of engineers 
 and practical bridge builders. If it be desired to ex 
 tend the table to greater lengths than 40 diameters, 
 the formula which makes the strength as the cube of 
 the diameter divided by the square of the length, may 
 properly be used. 
 
 The following brief table of negative resistance of 
 timber, has been constructed in the manner above in- 
 
 Table of Negative Resistance of Timber. 
 
 Diameters. 
 
 Pounds. 
 
 Diameters. 
 
 Pounds. 
 
 Diameters. 
 
 Pounds. 
 
 6 
 
 800 
 
 24 
 
 368 
 
 42 
 
 166 
 
 8 
 
 760 
 
 26 
 
 328 
 
 44 
 
 151 
 
 10 
 
 720 
 
 28 
 
 296 
 
 46 
 
 138 
 
 12 
 
 C80 
 
 30 
 
 269 
 
 48 
 
 127 
 
 14 
 
 640 
 
 32 
 
 246 
 
 50 
 
 117 
 
 16 
 
 600 
 
 34 
 
 227 
 
 52 
 
 108 
 
 18 
 
 560 
 
 36 
 
 210 
 
 54 
 
 100 
 
 20 
 
 479 
 
 38 
 
 195 
 
 57 
 
 90 
 
 22 
 
 416 
 
 40 
 
 183 
 
 60 
 
 81 
 
 dicated, and exhibits at a single view, the number of 
 pounds to the square inch of cross-section, which tim 
 bers of different lengths will bear with safety, at inter- 
 
WOODEN BRIDGES. 277 
 
 vals of 2 diameters in length, for all lengths between 6 
 and 60 diameters. The first column gives lengths in 
 diameters, and the second, the number of pounds to 
 the square inch, borne, with safety. 
 
 TRANSVERSE STRENGTH OF WOOD. 
 
 CXLII. Pine timber will bear a transverse strain of 
 1500 or 1600flbs. to the square inch of cross-section ; 
 that is, the projecting end of a beam will bear 1500Sbs. 
 for each square inch of its cross-section, applied at a 
 distance from the fulcrum equal to the depth of the 
 beam ; the force acting parallel with the sides. In 
 other words, a beam 1 inch square upon supports 2 
 inches apart, will sustain 3,000ft>s. midway of supports, 
 provided the timber be not split or crushed ; as would 
 certainly be the case with so short a leverage. 
 
 It will therefore be proper in practice, never to ex 
 pose this material to a greater transverse strain than 
 250Ibs. (upon a leverage of 1 diameter), to the square 
 inch ; and, to calculate the strength of a projecting 
 beam, this quantity should be multiplied by the cross- 
 section and the depth, and the product divided by the 
 distance of the load from the fulcrum, [xciv.] 
 
 For the safe load in the middle of a beam supported 
 near the ends, take four times the above quantity 
 (= l,000fbs.), multiply by cross-section and depth, and 
 divide by length between supports. 
 
 A beam will bear twice as much load uniformly dis 
 tributed over its length, as when it is concentrated in 
 the centre, in case the bea .n is supported at the ends, 
 or at the end in the case of a projecting beam. 
 
 But these are familiar principles and need not be 
 dwelt upon in this place. 
 
278 BRIDGE BUILDING. 
 
 CLEAVAGE. 
 
 CXLIII. In order that a piece of timber may act by 
 tension, it is necessary that a portion of its fibres be 
 separated, to form a heading for the stretching force to 
 act against; and, that the strength of the piece may 
 be made available for as great a part of its length as 
 may be, without having the head split off, it becomes 
 important to know the power of the material to resist 
 such a result. 
 
 Let ab Fig. 54 represent a heading by means of 
 which the stick is made to act by tension. Now, as the 
 timber is incapable of supporting upon the ends of its 
 fibres with safety, for a great length of time, a force of 
 more than 8 or 10 hundred pounds to the square inch, 
 the area ab should contain at least one square inch-for 
 each l,OOOIbs. to be applied to it. And, if the head 
 ab be too nigh the end of the stick, the part abed will 
 
 split off, and be thrust over the end of the timber. It 
 is found by experiment that to produce this effect upon 
 timber of sound and straight grain, requires a force of 
 nearly GOOEbs. to the square inch of cleavage in the area 
 efcb. It is therefore obviously necessary to safety, that 
 the head ab, be at a distance from the end, equal to at 
 least 10 times the depth (ae) of the head, that the area 
 of cleavage may be sufficient to stand as great a force 
 as the area of head can stand ; i. e., there should be 
 10 inches of cleavage surface to one inch of head surface. 
 
WOODEN BRIDGES. 279 
 
 If the heading be formed in the central part of the 
 Btick, as by a mortice or pin hole, two cleavages must 
 be made from the hole to the end in order that the 
 part may be forced out. Hence, the hole need be only 
 about five times the width of hole from the end ; that 
 is, an inch hole should be five inches, and a two inch 
 hole, 10 inches from the eud. 
 
 TRANSVERSE CRUSHING. 
 
 Timber is sometimes liable to be crushed by forces 
 acting transversely to the direction of its fibres. If 
 the pressure be applied to the whole sLle of the piece, 
 it should not exceed 150, or at most 2001bs. to the 
 square inch, in practice. If acting on one-half of the 
 surface, it may perhaps, be SOOSbs. to the inch, without 
 yielding very injuriously ; and, for a very small portion 
 of surface, as under a bolt head or washer, a pressure 
 of 500ft>9. to the inch may be admissible. These limits 
 are taken with reference to pine timber. Hard timbers, 
 will bear, probably, 25 to 50 per C. more with safety. 
 
 CONNECTIONS OF TENSION PIECES, AND PROPORTIONATE 
 AMOUNT OF AVAILABLE SECTION. 
 
 CXLIY. From what has been already said, it fol 
 lows that for a piece to act with the best advantage by 
 tension, if the connection be made all at one point in 
 the length, one-half of the fibres require to be cut off, 
 so as to form an area of heading equal to the cross-sec 
 tion of the remaining part of the stick ; since it has 
 been assumed that the power to resist tensile strain 
 with safety, is the same as the power to resist compres 
 sion upon the ends of fibres. But if several headings, 
 or shoulders be made at different points, or distances 
 
280 BRIDGE BUILDING. 
 
 from the end, a less portion of the fibres require to be 
 separated. 
 
 If, upon apiece 4 inches thick, instead of one shoulder 
 2 inches deep at 20 inches from the end, we make two 
 of one inch deep, each, the one at 10, and the other at 
 20 inches from the end, we have the same area of 
 shoulder, and 50 per C, more fibres to act by tension ; 
 which may be made available by another shoulder at 
 30 inches from the end. Thus a greater proportion of 
 the fibres, but a less proportion of the length is availa 
 ble. 
 
 In the same manner, if a piece be connected by 
 pinning, requiring 2 pins of 2 inches in diameter, at 
 10 inches from the end, fourl inch pins, two at 5, and 
 two at JO inches (if stiff enough), give the same shoulder 
 surface, and require the cutting of only half as many 
 fibres ; and, two more pins at 15 inches from the end 
 will give jths of the whole area of section available for 
 tension. In case the smaller pins be not stiff enough, 
 they may be of an oblong section in the direction of 
 the strain. 
 
 A still further reduction of depth of shoulder or 
 width of pin, will make a still larger proportion of the 
 fibres available, but not so much length ; and, experi 
 ence and judgment, with a little calculation, must dic 
 tate as to the proper medium in this respect. The 
 theoretical limit is, when the shoulders are infinitely 
 small, in which case, the whole cross-section becomes 
 available. But, as the resistance to cleavage must be 
 equal to the force of tension, it follows that the loss in 
 available length, is proportional to the amount of 
 cross-section available for tension. 
 
 In practice, it is usually not expedient to estimate 
 more than one-half or two thirds of the whole section 
 
WOODEN BRIDGES CONNECTING PINS. 281 
 
 as available for tension. This reduces the safe practi 
 cal strain for timbers sustaining tension, to from 500 
 to TOOlbs. to the square inch, for the whole cross-section ; 
 and the proper point between these limits should be de 
 termined by the mode of forming the connections in 
 specific cases. 
 
 PINS OF WOOD AND IRON, FOR CONNECTING TIMBERS 
 IN BRIDGE WORK. 
 
 CXLV. Perhaps no more suitable place will occur 
 for making a few general remarks upon the merits and 
 use of pins for connecting pieces of timber. 
 
 While it is readily admitted that the plank lattice 
 girder, put together exclusively with wooden pins, an 
 swered an excellent purpose in affording cheap and 
 serviceable bridges in this country when timber was 
 abundant, and the iron manufacture in its infancy, it 
 is nevertheless believed that the use of wooden pins in 
 bridge construction, is not destined to a long continu 
 ance. Where pins are required in wooden bridge 
 work, it is thought that iron may be used with a de 
 cided advantage over wood not in the lattice bridge 
 of the usual form, composed of a great number of dia 
 gonals, and a legion of connecting pins ; but in a modi- 
 lied form (as in Figures 13 and 19), with a greatly 
 reduced number of pieces, and points of connection. 
 
 Wooden pins for the purpose under consideration, 
 do not possess sufficient strength in proportion to the 
 surface, unless made so large as to require too much 
 cutting of the timber. Moreover, the action upon the 
 pin tends to crush it laterally, in which direction the 
 hardest timbers available for pins, scarcely offer as 
 much resistance as the ends of fibres to which they are 
 opposed. 
 
 36 
 
282 BRIDGE BUILDING. 
 
 Where pieces are connected with their fibres paral 
 lel, wooden pins or keys with cross-sections elongated 
 in the direction of the grain, to give them the necessary 
 strength, may be employed without too much cutting 
 of the timber. Bat, as just remarked, the key is liable 
 to yield before the cut ends of the fibres are taxed to 
 their full capacity. It is therefore poorly adapted to 
 the purpose in any case where great strength is required. 
 Moreover, when the pieces to be connected are placed 
 across one another, the hole will not admit of elonga 
 tion without too much cutting of at least one of the 
 pieces. 
 
 If it be required to connect a piece by a pin between 
 two other pieces as seen in Fig, 55, upper diagram, 
 the pin, as already seen, should be strong enough to 
 bear as much strain as the opposed surface can sustain. 
 Now, we have seen that this can scarcely be done by 
 wooden pins. Still if sufficiently stiff, they may yield 
 somewhat to compression, without material loss of 
 strength. 
 
 Taking the transverse strength of pin timber at 
 SOOfts. to the inch, with leverage equal to diameter, 
 the expression 4 x 3000rf -*- 1 (a representing the cross- 
 section, d, the diameter, and /, the length of pin, be 
 tween centres of outside bearings), gives the amount 
 which the pin will bear in the middle. 
 
 "Now, the two outside pieces, having each half the 
 thickness of the centre one,* I must equal 1J times 
 the thickness (0, of the middle piece ; while the effect 
 
 * The outside hearings may be regarded as concentrated at the centres 
 of thickness of the pieces, while the stress 
 of the pin in the centre, is the same as if 
 
 .T*;. . .. : .frjs-. . tne force exerted by the middle timber, 
 
 <:<: wore concentrated half and half at the 
 
 I - > >>- : ^> } centres of the two halves of the piece ; see 
 
 L - - ; - ^* diagram. 
 
WOODEN BRIDGES CONNECTING PINS. 283 
 
 of the force exerted by said middle piece, is two-thirds 
 of what the same force would produce, if concentrated 
 in the middle of the pin, and consequently, the pin 
 will hear 50 per C. more. Hence, we have 4xljx 
 30(W-r- lJ/,= 1200a</-5-<,= strength of the pin. 
 
 But the opposed surface will hear 1,000&/ ; and put 
 ting this expression equal to the former, and deducing 
 the value of d, in terms of t, it will show the smallest 
 diameter of a wooden pin, strong enough to hear as 
 much as the opposed surface. This equation gives 
 d = 1.03^;t whence, it appears that the wooden pin 
 should he 3 per C. greater in diameter than the thick 
 ness of the middle timber. 
 
 In the same manner, the strength of an iron pin in 
 the same circumstances, is respresented by 4xlJ 
 X5,000ad -*- 1J*, = 20,000ad -r- t, which made equal to 
 l,000fr/, gives d = 0.252, hence, the most economical 
 diameter for an iron pin in fastening one piece between 
 two others, is about Jth the thickness of the middle 
 piece; i. e., taking the stiffness of a round pin at 
 5,000ft)s. But reducing it to 4,500Ibs. as proposed in 
 another place [xcvm], it gives c? = 0.266^; whence, 
 even upon this basis, it will be safe in practice to make 
 d = |^, and the whole length of pin = 2, so that it may 
 extend into the outside pieces to the extent of half the 
 thickness of the middle piece. 
 
 Since the outside pieces (Fig. 55), require half the 
 thickness of the middle piece, and the pin requires a 
 diameter equal to \t = J the thickness of outside pieces, 
 it follows that in pinning or spiking a plank or timber 
 to the outside of a thicker piece, the pin or spike should 
 
 f Dividing tlie equation l2Q3ad--t =-1,000^, by lOOd and multiply 
 ing by t, give 12a I0t\ But 12<z 12x.7854d a , =9.4248d a , = 10t a - 
 whence, cf 1.06K 9 , and d v/TOGl?" = 1.03*. 
 
284 
 
 BRIDGE BUILDING. 
 
 have half the thickness of the piece attached, that it 
 may not bend with less force than the ends of the 
 severed fibres can bear ; and should extend into the 
 thicker timber at least 6 times its diameter. For, as 
 
 FIG. 55. 
 
 1 1 I \ 
 
 I 
 
 1 j 1 
 
 
 
 
 B331 
 
 | 
 
 \ ik 4K \ 
 
 
 ffcEEtt ...^ 
 
 
 the inner portion of the pin or spike, must act upon 
 the wood in the same direction as the part through the 
 attached piece, it requires the same amount of surface 
 to act upon, while the intermediate portion requires a 
 surface equal to that acting upon the two end portions. 
 And, even in this condition, the pressure is not uniform 
 upon all parts of the length of the pin, since there is a 
 neutral point, as represented by the upper dotted line 
 (lower diagram, Fig. 55), where the pressure changes 
 from one side to the other, and, near this point, must 
 be very light in both directions. Hence, for the most 
 perfect results, in such cases, the pin should probably 
 enter the thicker timber to a distance of 7 or 8 times 
 the diameter of the pin. 
 
 When the end bearings of the pin act transversely 
 to the grain, they require at least 50 per C. more ex 
 tent of bearing, or even twice as much, when practica 
 ble. At 50 per C. I = If/ , and the effect of the pressure 
 exerted by the middle piece, is ^ths that of the same 
 force at the centre of the pin. The equation for the 
 proper diameter of the pin, then, is 4x|x5,OOOfltfH-l} 
 = 1,000/d ; whence, d = 0.283*, and length of pin =2H 
 
WOODEN BRIDGES SPLICING. 285 
 
 SPLICING. 
 
 CXLYI. The term splicing, as applied to timber 
 work, may be defined to be the uniting of two pieces 
 of timber by their end portions, so as to form (in figure) 
 a continuous timber upon a straight axis. 
 
 The splicing of timber to withstand a thrust action, 
 requires only the meeting of the squared ends of pieces ; 
 or, a half lap, formed by removing the half of each for 
 a foot or two, more or less, from the end, and lapping 
 the remaining halves, so as to have the extreme end of 
 each, meet the shoulder of the other. 
 
 But the splicing of pieces to withstand tension, ob 
 viously requires a more complicated process ; and, 
 from what has already been said, [CXLIV,] it is clear 
 that only a part of the absolute section can be made 
 available to withstand a tensile strain. 
 
 FIG. 56. 
 
 In Fig. 56, we have the profile of a lock splice, by 
 which one-third of the section is available for tension ; 
 the depth of the locking being equal to one-third of 
 the thickness of timber. Now, that the locking may 
 not split off, we have seen that the lap should extend 
 10 times the depth of lock, each way, making a lap of 
 6 times the thickness of the timbers. 
 
 By slanting the timber to a thickness at the end equal 
 to that in the neck of the lock, we lose none of the 
 cleavage required to split off the hook, while we gain 
 in amount of section where it is required for bolt holes 
 to secure the splicing. Otherwise, the bolt holes would 
 
286 BRIDGE BUILDING. 
 
 reduce the available section below one-third of the 
 whole. 
 
 It is proper to observe with regard to this splice, 
 and also the succeeding one, that the power being ap 
 plied upon the reversed shoulder, or hook, out of the 
 line of the unbroken fibres which resist the power, 
 the tendency is to throw tfye ends outward, and pro 
 duce a degree of lateral action, which weakens the 
 timber to a somewhat greater degree than in proportion 
 to the amount of fibres severed. 
 
 FIG. 57. 
 
 With a double lock splice, as in Fig. 57, one-half of 
 the section is available. This requires a lap of 10 times 
 the thickness of the timber. 
 
 By three lockings upon the same principle, f of the 
 fibres may be utilized for tension, with a lap of 12 
 thicknesses (or 12.), and, by a lap 13J, we make two- 
 thirds of the fibres available. Finally, by a lap of 20. 
 and an infinite number of lockings the whole cross- 
 section would be available. 
 
 But this, of course, is a point not attainable in prac 
 tice. From J to J say an average of J, is as much 
 as can be reckoned on, and about as much as can usually 
 be made available for tension, at the end connections 
 of a single timber. 
 
 Splicing may also be effected by a plain scarf, with 
 bolting, pinning and spiking, as indicated in Fig. 58. 
 With bolts, pins and spikes properly arranged and pro 
 portioned, a strong splice may be formed in this 
 
WOODEN BRIDGES SPLICING. 287 
 
 manner, with a less lap than what is required in the 
 lock splice. In this case the fastenings should pass 
 
 FIG. 58. 
 
 through at right angles with the plane of the joint, that 
 they may not be slackened by a slight yielding of the 
 timber to pressure, in the holes. This, however, is a 
 device which will probably, seldom be resorted to in 
 bridge construction. 
 
 Timbers may also be shackled together end to end 
 by iron bolts and straps, as shewn in Fig. 59. The ag 
 gregate cross-section of straps should be about 1 square 
 inch to each 10 to 15 thousand pounds of strain which 
 the splice is intended to bear; and the diameter of 
 bolts fastening the straps, about one-fifth of the thick 
 ness of timber, to secure the greatest effect for the 
 amount of section destroyed in cutting the bolt hole. 
 
 FIG. 59 
 
 To connect two timbers 10x12 inches, so as make 
 half of the fibres available for tension, we may take 6 
 straps 2 feet long from hole to hole, and containing a 
 cross-section of about 1 square inch, each. Also 6 
 bolts of 2" in diameter, and arrange the straps and 
 bolts as shown in the figure, the straps being placed 
 upon the 12" sides. This will cost, say for ITOlbs. of 
 iron at 7cts., $11.90. 
 
288 BRIDGE BUILDING. 
 
 The expense of a double lock splice (Fig. 57), will 
 
 be about 7 cubic ft. of waste timber, $3.50 
 
 40Ibs. of iron bolts, washers and plates,... 2.80 
 Labor in fitting the timbers, say, 1. 
 
 Total,,.... $7.30. 
 
 showing the shackle connection to be from 4 to 5 dol 
 lars the more expensive. 
 
 CONSTRUCTION OF WOODEN TRUSSES. 
 
 CLVII. With a thorough comprehension of the 
 power of timber to resist the various kinds of strain to 
 which it may be liable in bridges, and other timber 
 structures, and of the general principles of forming 
 connections in timber work, as attempted to be ex 
 plained and get forth in the last few preceding pages ; 
 and a knowledge of the general forms of arrangement 
 for the several members in bridge trusses, or girders, 
 and of the manner of computing the stresses to which 
 the several parts are liable to be subjected, as treated 
 of in the first 100 pages or so, of this work, the details 
 of practical construction of wooden truss bridges may 
 be intelligently entered upon. 
 
 Nothing more elaborate will be here undertaken, 
 than a reference to general forms of trussing suitable 
 for wooden bridges of different spans, and a descrip 
 tion of what seem to be the most feasible methods of 
 forming connections at peculiar and specific points. 
 
 The method pursued will be, to proceed from the 
 shorter spans, and more simple combinations, to struct 
 ures of greater length, and requiring a greater number 
 and a more complex arrangements of parts. 
 
WOODEN BRIDGES. 289 
 
 Two PANEL TRUSSES. 
 
 CLVIIT. The form presented in Fig. 3, with rafter 
 braces ad and dc, and a tie or chord ac, together with 
 an iron tension member db (in 1 or 2 pieces), is proba 
 bly the best adapted to bridges from 20 to 25 feet in 
 length. The braces should meet with a vertical joint 
 at d (Fig. 3), and toe into the chord tie with two head 
 ings, and one or two small bolts, as in Fig. 60. 
 
 Fia. 60. 
 
 Assuming the brace to be capable of sustaining a 
 thrust of 500Ibs. to the inch of section, and the heading 
 l,000ft)s, to the inch, the aggregate depth of heading, 
 a/, and de, should be one-half the depth c6, of the brace ; 
 and, the point /, should fall below the point d, by 
 j\ ad, so as to give a length of cleavage /A, = lOaf or 
 10 dh. The shoulder de, then, should be, 
 
 (1),... de =J cb T V ad,~$cb hab + T V db. 
 
 We here speak of a d b as a straight horizontal line, 
 not shown. This is regarding of as equal to the verti 
 cal depth of cut at af; which will be sufficiently near 
 the truth for our present purpose, provided the brace 
 be not very steep. 
 
 But (2),...de = db. sin. dbe, ~db. sin. cab. 
 37 
 
290 BRIDGE BUILDING. 
 
 and, putting this value of de equal to the one above, 
 and changing vulgar to decimal fractions, we have, 
 
 (3), ..db. sin. cab =* 0.5 cb 0.106 + O.lr/6. 
 
 Then, transposing, and uniting co-efficients of db. 
 
 (4.). ..(sin. cab 0.1) </6 ==0.5c-6 0.106, whence, 
 
 ,-v ,, 0.5 cb 0.1 ab 
 
 Now, from equation (2) we derive 0*6= sin ca() , which 
 value of 0*6 being substituted in equation (5), we have 
 
 //>N de 0.5 cb Q.lab \ ,,. <, . , 
 
 u ( 6 ) - sh^Tb ~ sin.c^-o.1. whence, multiplying by 
 sin. c06. we derive, 
 
 (7),... de - - 5 ^~^/ 5 Then, substituting for 06, its 
 
 1 ^^_ * r __, 
 
 sin. cab 
 
 equal. sin cajb the last equation becomes, 
 
 
 s 
 
 Making the angle C06 = 2633J , which is regarded 
 as a suitable inclination for the brace, being one, ver 
 tical, and two, horizontal reach, sin. C06 = 0.447, which 
 substituted in (8), gives de .356^6, and af=* .144c-6. 
 
 This, it will be recollected, is deduced upon the 
 supposition that the brace will sustain a compression 
 of 500ft>s. to the inch, and no more ; which will depend 
 upon the length as compared with the least diameter. 
 If the brace be capable of bearing with safety, more or 
 less than 500ft>s. to the inch, the heading, or butting 
 surface should be more or less than half the area of 
 cross-section, in like proportion. For, if unnecessarily 
 large, it requires too much cutting of the chord, and 
 if too small, the pressure upon abutting surfaces be 
 comes too great. 
 
 With the inclination of brace above assumed, the 
 compression upon the brace obviously equals the weight 
 
WOODEN BRIDGES. 291 
 
 sustained multiplied by v/5 ; and, for a rail road bridge, 
 at 1J tons to the lineal foot, the weight upon each 
 brace, will be 6,250ft>s. = %w ; or say, J (w -f W*) = 
 7,500ibs. This by N/O, gives 16,770ft>s. = thrust of 
 brace, while 15,000ft>s. = tension of chord. Now, at 
 SOOIbs. to the square inch of gross section, the chord 
 requires 30 square inches, and the brace 33J inches* 
 being a little less than 6" square. But the length of 
 brace being about lift, or 22 diameters of a 6" stick, 
 we find by the table [CXLI], the brace is only capable 
 of bearing 416ifes. to the inch. Hence, with a 6" least 
 diameter, a section of 40.3 inches, or nearly 6" x 1", 
 becomes necessary. Still the butting surface required 
 is only 16.77 square inches a little less than 2|-" depth 
 (at right angles with the brace), by 7" in width. 
 
 This 2J inches in depth may be divided between the 
 two shoulders at a and d, in any manner that will leave 
 a length of cleavage from a to the end of the chord 
 equal to 10 a/, or more strictly 10 afx cos. cab, which 
 equals the vertical depth of cut at/. But the line df, 
 should preserve a descent, equal to J^-th of its length. 
 
 The depth of shoulder being thus reduced from Jc6 
 (= 3" in this case), to 2|", de is diminished in the same 
 degree, and from .356c6, becomes |x.356c 6 = .2966c6 ; 
 and, substituting 6" for c6, we have de = 1.78 inches. 
 In the meantime af becomes |x.!44c6, = .72". 
 
 The vertical depth of cut for de, = 1.78", is 1.78xcos. 
 cab, =1.78x.894, = 1.59". Add to this the vertical cut 
 at/, equal to .642" and it makes 2.233", = aggregate 
 vertical depth of cut in the chord, whence the distance 
 eg should be 22.33 inches, to afford the necessary re 
 sistance to cleavage. 
 
 Now, we require in the chord 15 square inches of 
 unsevered fibre, to withstand the horizontal thrust of 
 
292 
 
 BRIDGE BUILDING. 
 
 the brace while we require, as seen above, 1.59X 
 7 = 11.13 inches to be cat away to form foothold for 
 brace, making aggregate section of chord = 15+11.13 
 = 26.13 sqr. inches, equal to about 7" X 3", by strict 
 computation. 
 
 Timbers so small, however, although capable of sus 
 taining, without excessive stress, any action to which 
 a bridge is legitimately exposed, is not to be recom 
 mended in practice, as the structures might be de 
 stroyed by casualties which would but slightly affect 
 the large timbers required in heavier and longer struct- 
 tures. 
 
 The centre of bearing of the truss upon the abut 
 ment, should be directly under the point i, at the 
 meeting of central axes of the brace, and the unsevered 
 portion of the chord. Otherwise, an injurious lateral 
 strain would result to the chord at its weakest point. 
 
 The transverse beam at the centre of the truss, may 
 be placed above the chord or below, as preferred, and 
 sustained by 2 suspension bolts descend 
 ing divergently from a saddle, or double 
 washer at the vertex of the braces, pass 
 ing through the beam, and secured by 
 nuts and washers upon the under side of 
 the beam, as shown in Fig. 61. The 
 divergence of bolts should be from Jth 
 to Jth their length, and the section of 
 bolts, a trifle more than what is required 
 simply to sustain the weight, as they may 
 act unequally, in consequence of a small 
 lateral tendency of the braces. 
 
 A small bolt should pass vertically 
 through chord and beam, to preserve 
 them in place. Also, a small bolster, or corbel block 
 
 FIG. 61. 
 
WOODEN BRIDGES. 293 
 
 (j. Fig. 60 and 61), under the chord at the end, affords 
 some protection at the weak point in the chord. 
 
 A pair of horizontal X braces in each panel, between 
 beam and abutments, or plate timbers upon abutments, 
 are required to produce lateral steadiness in the struc 
 ture. 
 
 The idea of constructing the trusses of a rail road 
 bridge, even of 20 span, of 6" timbers, to persons in 
 the habit of seeing such bridges constructed with tim 
 bers 10 or 12 inches square, will undoubtedly suggest 
 visions of catastrophe, courts and coroners ; and, in 
 view of liability to casualty, fretting at joints, and per 
 haps surface decay, it may be advisable to use in such 
 structures, timbers somewhat larger than the above 
 computations indicate as sufficient to withstand deter 
 minate forces. 
 
 But, as an instance of what strength may be obtained 
 with very small timbers, properly proportioned and 
 put together, it may be here stated that a model of a 
 20 feet truss, upon a scale of 1 to 12, constructed as 
 above explained, of J" x T 6 2 " braces and chord, bore 
 without material injury, 350ft>s. at the centre, equiva 
 lent to 700ft)S. distributed, and representing 700x144 
 = 100,800ft>s. upon one truss, or over 100 net tons upon 
 a 20 f^eet bridge; being some four times as much as a 
 single track rail road bridge of that span is usually 
 subjected to. 
 
 With regard to the proper size of transverse beam, 
 the formula (see rule [CXLII]), 1^5 == W, (a represent 
 ing area of section, d, depth of beam, , length between 
 supports, and W, the load in the centre), gives a = 
 iOMd" Then, assuming I = 15 , W = 7,500ft>s, ( = 
 15,0001bs. distributed), and d = 14" ; we have a = 
 
294 BRIDGE BUILDING. 
 
 lowxi" = 96 4 square inches ; which divided bv de P th 
 (d), in inches, gives thickness (f), = 7 inches nearly. 
 
 Or the formula t = gives the required thickness 
 
 directly. But in this case, I and dmust express length 
 and depth in inches, since the co-efficient of d (1,000) 
 refers to square inches of section. Otherwise, the co 
 efficient must be multiplied by 144 to make it refer to 
 the square foot of section ; in which latter case the 
 value of t will be obtained in feet. 
 
 In the case of beams to sustain rail road track, we 
 may let V = length of beam exclusive of the portion 
 between rails, and W = weight upon the 2 rails. If 
 I = 120" and W = 25,000ft>s., and d =* 14" the above 
 
 formula becomes, * = _ _ 15 . 3 in . 
 
 THREE PANEL TRUSS. 
 
 CLIX. A three panel truss bridge of wood may be 
 constructed upon the plan shown in outline by Fig. 7. 
 The main braces a6and a b may connect with the chord 
 in the same manner as in the two panel truss described 
 in the last section, and illustrated by Fig. 60; while 
 the upper end may be square, and the whole bevel to 
 form the angle abb , given to the member bb . Or, the 
 bevel may be upon both members ; in which case the 
 saddle plates at b and b e should extend over the joint, 
 so as to throw a part of the weight directly upon the 
 brace. In case the bevel be all upon bb , the saddle 
 need not bear upon the brace. 
 
 The counter braces in the middle panel may box 
 into the chord and the horizontal W, in the manner 
 shown in Fig. 62, either by the black or the dotted 
 lines ; the upper end of the counter toeing against the 
 
WOODEN BRIDGES. 295 
 
 end of the main brace, when the form of connection 
 shown by the black line is used. 
 
 As the counter braces cross, or meet in the centre of 
 the panel, one may be in two pieces thrusting into the 
 other as at c Fig. 62 ; or one member may be in two 
 full length pieces, and the other a single brace between 
 the former, of such width vertically, as to possess the 
 required cross-section ; say 2J" x 6" for the outside, 
 and 4x8 for the middle one, and the whole connected 
 by a small transverse bolt at the crossing. 
 
 The stresses of the several parts of the truss may be 
 determined in the manner explained in section xvni, 
 and the timbers proportioned accordingly, and in con 
 formity to rules in relation to strength of timber [CXL 
 and CXLI]. For a truss of 30 feet to carry a gross load 
 of 15,000ft)3. to the panel, with a horizontal reach of 
 brace equal to twice the vertical chord and " strain 
 ing beam," (66 , Fig. 7), should be 7" deep x 9" wide ; 
 main braces 8" X 9". Counter-braces being subject to 
 only one-third of the movable panel load, may properly 
 be 4 X 8 or 5 X 6, if one be severed at the crossing, or 
 as above specified, if one member be in 2 full length 
 pieces. 
 
 Two counter-braces might cross one another side by 
 side, but this would not produce a well balanced action. 
 
296 BRIDGE BUILDING. 
 
 Bridges of this length of span are, moreover, often 
 built with counter braces omitted, for common road 
 purposes. But such practice is defective, unless extra 
 depth of section be given to the lower chord, so that 
 its stiffness may transfer a portion of weight over the 
 quadrangular middle panel ; and in no case is it ad 
 visable to dispense with counter braces in a rail road 
 bridge of three panels. 
 
 Beams may be suspended by divergent bolts as in 
 Fig. 61, and bolted to the chord; while horizontal x 
 ties or braces, as may be preferred, in each panel will 
 prevent lateral swaying of the structure. 
 
 The above is probably the simplest and best plan of 
 wooden truss for bridges of 30 to 35 feet span. 
 
 FOUR AND Six PANEL TRUSSES. 
 
 CLX. The same general arrangement, with the same 
 kind of connections, in trusses of 4 or 6 panels, accord 
 ing to length of span, may be used with good effect 
 for common road purposes, in any length up to 70 or 
 80 feet. In such cases, each panel should have one 
 main brace, and counter braces may be entirely omitted; 
 as the partial movable load is seldom so great as to 
 neutralize the action of weight of structure upon the 
 main braces. 
 
 In the 6 panel truss, the movable must exceed the 
 permanent panel load upon the two beams next either 
 end, with no movable load upon the other beams, in 
 order to neutralize the constant tendency to action 
 upon the central pair of main braces. This is obvious 
 from the fact that the greatest tendency to tension action 
 upon the latter, is 3i0", = Jt0, while the permonent load 
 gives a constant opposite tendency, equal to JM? . 
 Should such cases occur, the transverse stiffness of 
 
WOODEN BRIDGES. 
 
 297 
 
 both upper and low chords must he 
 overcome before a collapse could 
 take place. In the case of iron 
 trusses, the chords are supposed to 
 have no lateral stiffness at the 
 nodes; consequently, counterbraces, 
 or ties, as the case may be, are al 
 ways necessary in one or two panels 
 each side of the centre. 
 
 Fig. 63 represents a Six Panel 
 truss, as arranged and recommended 
 by the author 16 or 18 years ago, 
 and adopted by the Canal depart 
 ment of the State of ]$few York, 
 for farm and country road crossings 
 over the State canals, upon which 
 several hundreds of them are in use. 
 
 The arrangement of upper and 
 lower chord timbers, and the diver 
 gent suspension rods, to maintain 
 the erect position of trusses, as well 
 as the assignment of correct pro 
 portions to all the parts throughout, 
 are believed to have originated with 
 
 O 
 
 the author of this work. 
 
 The lower and longer portion of 
 the bottom chord, is usually in two 
 pieces, spliced with double locking 
 and bolting (see Fig. 57), over the 
 centre beam. Transfer blocks are 
 also inserted between upper and 
 lower timbers, to transfer a part of 
 the stress of the longer to the 
 shorter portion, and thus dimmish 
 the strain at the splicing. 
 
298 BRIDGE BUILDING. 
 
 The long portion of the upper chord may also be 
 in two pieces meeting with squared ends, or with a 
 plain half lap, of a foot or so. Transfer blocks or 
 packing pieces and bolts should likewise be inserted as 
 indicated in the figure. 
 
 The dimensions of the several members, of course, 
 will depend upon the length and depth of truss, and 
 the load it is required to bear. It is seen by pro 
 cesses explained heretofore [XL and LIII], that the 
 portion of chord under the triangular end panels, and 
 also the endniost sections of the upper chord, are liable 
 to action equal to 2JW-, in which expression "W = 
 w+w , h =the horizontal, and v = the vertical reach 
 of braces. The next sections (top and bottom), are 
 liable to 4W-, and the lower chord under the two 
 
 V 
 
 middle panels, to 4JW-. 
 
 The end braces are liable to 2JW \/A 2 -f v 2 -i-v,thQ 
 next braces, to (lOu/ +lJw ) v/A 2 -f v 2 -s- v, and the 
 
 middle ones, to (6w"+%w f ) V h? -f v 2 -* V, while the 
 verticals are exposed to 2JW for the endniost, 1W for 
 the middle, and 10 w" -f- IJw for the intermediates. 
 
 Now, we have only to assign specific values to w and 
 w , and to A and v, in order to obtain the actual maxi 
 mum stresses the several parts are liable to, from the 
 general expressions just found. 
 
 Let A = 12 , and v = 7 ; which, though not an eco 
 nomical proportion, as we have seen [LXIV], may be 
 admissible for bridges of light burthens, giving a better 
 appearance, and the structure being less top heavy. 
 
 The weight of a light superstructure of this descrip 
 tion, is 18 or 20 tons say, w = 3,000fbs. Then, as 
 suming w = 6,000ft)s. which will be sufficient for the 
 
WOODEN BRIDGES. 299 
 
 lighter class of private and country bridges. Then, - = 
 
 V = 1,714, and x//7~+~^H- v = 1.984. 
 
 Substituting these values in the above expressions 
 for stresses, we have 2J X 9,000 X 1.714, = 38,565, = 
 tension of end section of bottom chord. For the next 
 section, 4 X 9,000 X 1,714 = 61,704ft>s. ; and, for the 
 two middle sections, 69,417ft>s. ; while the compression 
 of the two portions of the upper chord, is 38.565flbs., 
 for the end, and 61,7041bs., for the middle sections. 
 
 The maximum compression of the three sets of 
 braces, is 44,653 for the ends, 14,880 for the middle 
 ones, and 28,760 for the intermediates. 
 
 The tension of suspension bolts, is, at the maximum, 
 for the endmost 22,500, for the middle ones, 9,000 
 ( = W), and for the intermediates 14,500. 
 
 The main portion of the lower chord, requires a lap 
 at the splice, equal to 10 times its depth, [CXLVI.] 
 Hence, the less depth, the less waste in splicing, and 
 the more lateral stiffness of truss. But this also in 
 volves greater required section in the lighter braces, 
 which become too thin, vertically, to act with advantage 
 under compression. 
 
 There is no ready means of determining the exact 
 optimum in the ratio of depth to width of timbers in 
 this case ; and we shall not err greatly by assuming a 
 ratio of width to depth as 3 to 2, or as 4 to 3 ; neither 
 to be rigidly adhered to. 
 
 The bottom chord may suffer tension in the second 
 panel, equal to nearly 62,000ft>s., requiring 62 inches 
 of net section ; while the second brace has a maximum 
 horizontal thrust of nearly 25,000ft>s., requiring the 
 severing of 25 inches, whence this part of the chord 
 should have a gross section of 62 + 25, = 87 inches. 
 
300 BRIDGE BUILDING. 
 
 This amount may be furnished nearly, by a section of 
 8" x 10", 8 x 11, or 7 x 12. Assuming the second, 
 the end braces should be 8-J X 11, the next 7 x 11, and 
 the middle ones, 5J x 11. 
 
 We have seen above, that 62,000ft>s. of tension, are 
 communicated to the long timbers of the lower chord, 
 while the splice at the middle is only good for 500ft>s., 
 to the inch of gross section, being 44,000ft)3. ; thus 
 leaving a deficiency of 18,000ft)3. to be sustained and 
 made up by the upper timber. In the mean time, 
 the middle braces exert about 8,OOOIbs. of horizontal 
 action upon this piece, under a full load of the truss, 
 and near 13,000ft>s. at the maximum action of those 
 braces. Hence that timber should have a mini n urn 
 net section of 26 inches, -f 18 inches to be severed for 
 the insertion of transfer blocks. The timber should 
 therefore be at least 4" deep. 
 
 The transfer blocks should be If " thick, in this case, 
 and 15 or 16 inches long, and be well fitted in position 
 as indicated in Fig. 63. This mode is preferable to that 
 of using blocks twice as thick, and letting one-half into 
 each timber by a square boxing; because it leaves a 
 larger section of timber opposite the middle of the 
 block where bolt-holes are required. Otherwise it 
 would be necessary to provide additional gross section 
 on account of bolt holes. The same reason applies in 
 the case of braces toeing into chords, &c. ; where the 
 boxing, instead of being as deep at the heel as at the 
 toe of the brace, should taper out to nothing at the heel. 
 See black line at foot of counter brace c, Fig. 62. 
 
 This case has been given in pretty full detail, since 
 the plan seems to merit, as it certainly enjoys, a high 
 degree of popularity, for small bridges for ordinary use. 
 
WOODEN BRIDGES. 301 
 
 By increasing the depth to at least Jth of the length 
 of truss, inserting counter braces in the two middle 
 panels, and proportioning members to the respective 
 strains to which they are liable ; this plan is undoubt 
 edly well adapted to rail road purposes in spans from 
 50 to 70 feet in length. 
 
 For greater spans than 70 feet for rail roads and 80 
 for common roads, higher trusses, with top connections 
 and lateral bracing or tying, should undoubtedly be 
 adopted. 
 
 CLXI. The bridge usually designated asBeardsley s 
 Bridge, is identical with the one shown in Fig. 63, 
 modified by the substitution of iron bottom chords, 
 composed of two parallel rods (to each truss) in 5 pieces 
 or parts corresponding in size with the stresses of 
 chords under respective panels. The middle and 
 largest part extending under the two middle panels, 
 and the others, each under one panel only. 
 
 These pieces or parts, being connected by turn-buck 
 les, or screw couplings, pass through cast iron shoes, 
 into and against which the several braces toe and 
 thrust ; the shoes being prevented from sliding out 
 ward upon the rods, by the couplings. 
 
 The shoe should in all cases be so formed and located 
 that the axes of action of chord, brace and vertical, 
 meet at the same point, as it regards the intermediates, 
 while as to those upon the abutments, the axes of chord 
 and brace should meet over the centre of bearing upon 
 abutments. 
 
 This arrangement (understood to have been the sug 
 gestion and device of Mr. Geo. Heath), gives very sat 
 isfactory results, and the only practical question with 
 regard to it, as compared with the one with wooden 
 
302 BRIDGE BUILDING. 
 
 chords, seems to be merely one of economy and con 
 venience. If suitable timbers for chords can be readily 
 and reasonably obtained, it is thought to be quite as 
 advantageous to use wooden chords. 
 
 THE HOWE BRIDGE. 
 
 CLXII. A very popular plan of wooden bridges, 
 which has, in fact, superseded most others in New York 
 and New England for rail-road purposes from the time 
 of the introduction of the rail road system, is known 
 as the Howe Bridge. 
 
 The trusses have upper and lower parallel chords, 
 together w r ith main and counter braces, of wood, tied 
 vertically by wrought iron tension rods from chord to 
 chord, the principle of action being the same as in the 
 plan shown in Fig. 63. 
 
 The braces act upon the chords and verticals through 
 the medium of cast iron shoes or skewbacks, with ribs 
 or flanges let into the chords to a sufficient depth to 
 sustain the horizontal thrust of braces, and with tubes, 
 or hollow processes, square externally, and having 
 round holes to receive the vertical bolts. These tubes 
 project downward through the lower, and upward 
 through upper chord, between the courses of timber 
 composing the chord, being boxed into the timber on 
 each side of the tube, so as to leave about an inch be 
 tween adjacent courses for ventilation ; the tubes, ex 
 tending through the chords, reach an iron plate upon 
 the opposite side, which serves as a washer, or bearing 
 for the nuts of the suspension bolts. 
 
 By this means the vertical action of braces is brought 
 directly upon the verticals, without a transverse crush 
 ing action upon the chord timbers. 
 
WOODEN BRIDGES. 
 
 303 
 
 The chords are formed of 3 or 4 courses of timber 
 side by side, with a depth equal to two or three times 
 the thickness; the joints in the several courses being 
 so distributed that no two courses may have a joint in 
 the same panel when avoidable. 
 
 Fig. 64, represents a side view in the upper, and a 
 top view in the lower diagram, of a portion of the bot- 
 
 FIG. 64. 
 
 torn chord. At t is represented a view of the tube of 
 the skewbackas it would appear with the outside chord 
 timber removed ; at m m, the seats of the main braces, 
 and c, the seat of the counter brace. Over a, is a 
 clamp, or lock piece, and bb r are transfer blocks, or 
 packing pieces, to secure the joint, and transfer the 
 strain from one to another of the chord timbers. The 
 transfer blocks may be placed obliquely as at 6, or 
 straight, as at & . The latter is the more usual, but 
 the former leaves the greater section of timber at the 
 point where the bolt holes occur. 
 
 The braces are usually placed with a horizontal about 
 half as great as the vertical reach, and extending across 
 one panel only. Counter braces used throughout, and 
 the upper chord made of equal leugth with the lower, 
 giving the truss a rectangular, instead of a Trape 
 zoidal form. 
 
304 BRIDGE BUILDING. 
 
 Now, it is obvious that in a rectangular truss, as 
 represented in Fig. 52, the end posts, and one panel- 
 length of the upper chord at each end, as well as one 
 counter-brace, are entirely useless, as it regards sus 
 taining weight of structure and load. It will readily 
 be seen, moreover, that no counter-braces except those 
 of the two middle panels, in the 8 panel truss, Fig. 52, 
 have any sustaining action, unless the variable exceed 
 4 times the permanent load of the truss. 
 
 It is furthermore manifest that there is a large 
 amount of surplus material in the portions of lower 
 chord toward the ends ; the tension of that chord being 
 in the several panels, preceding from the end (in the 
 case of Fig. 52), as 3J, 6, 7J and 8. Hence, over one- 
 fifth of the material in a chord of uniform section, is in 
 excess. 
 
 But the greatest sacrifice of economy in the Howe 
 Bridge as usually constructed, results from the steep pitch 
 of the braces. For, while, as was seen [LXVI], braces 
 act with about the same economy at an inclination 
 giving a horizontal reach equal to the vertical, as when 
 the former equals only one-half of the latter, that is, 
 with h = v and h =* Jy, it was shown in the succeeding 
 section, that the action upon verticals was nearly twice 
 as great in the latter, as in the former case. For in 
 stance, suppose Fig. 18 to represent a 16 panel trnss, 
 with thrust braces and tension verticals. Estimating 
 
 O 
 
 successively the action upon verticals with diagonals 
 crossing two panels, as in Fig. 18, and the same with 
 diagonals crossing but one panel, we find the action 
 over 85 per cent more in the latter than in the t former 
 case. 
 
 "With regard to chords, the horizontal effect is essen 
 tially the same in both cases, while the vertical thrust 
 
WOODEN BRIDGES. 305 
 
 of braces, being but little over half as great witb the 
 long, as with the short horizontal reach, may be sus 
 tained by the timber of the chord, thus obviating the 
 necessity of tubes extending through the chord from 
 the cast iron skewback; and furthermore, may enable 
 the iron shoe to be dispensed with altogether, in many 
 cases. Hence would result a still further saving in ex- 
 
 o 
 
 pense, as well as in weight of structure. 
 
 Take, for example a brace 10" square, capable of 
 resisting a tnrust of 50,0001bs. in the direction of its 
 length, and a vertical pressure of 35,0001bs. when in 
 clined at 45. "Whether the end be cut as at d, e, or/ 
 (Fig. 64), it covers a horizontal area of 141 square 
 inches, giving a square inch for every 250Ibs. of vertical 
 pressure. This does not much, if any, exeeed the ca 
 pacity of timber for resisting transverse crushing, as 
 estimated in section CXLIII, when acting upon a portion 
 of surface so limited with respect to the whole. 
 
 Perhaps, however, the propriety of dispensing with 
 the iron shoe, should not be too strenuously urged. 
 But there seems to be little excuse for incurring the 
 sacrifice of iron required in suspension bolts in case of 
 the steep braces, over what is required with the greater 
 inclination. The interference of bolts with braces, 
 when the latter reach across two panels, is perhaps the 
 greatest obstacle in the way of adopting the latter ar 
 rangement ; and this may be managed by either pass 
 ing the bolts through the intervening braces (which 
 does not materially impair their strength, when sup 
 ported at intervals by counter-braces), or between 
 main and counter braces, as may seem most favorable 
 in respective cases, 
 
 In view of the above considerations, the author can 
 not avoid regarding the usual practice in the construc 
 tion of Howe Bridges, as decidedly faulty. 
 
306 BRIDGE BUILDING. 
 
 TRAPEZOID WITHOUT VERTICALS.* 
 
 CLXIII. This form of truss, Figs. 13, 15 and 19, has 
 been shown [XLIV, &c.], to be liable to a less amount 
 of action upon materials, in sustaining a given load 
 under like general conditions, than any of the other 
 forms analyzed in this work; and this advantage may 
 be made practically available in wooden bridge con 
 struction, by a system of chords and diagonals con 
 nected by transverse iron bolts and pins at the nodes 
 of upper and lower chords. 
 
 The lower chords should be proportioned in their 
 several parts, nearly in accordance with the stresses to 
 which such parts are liable. This may be accomplished 
 by a pair of parallel courses of timber of uniform sec 
 tion upon the outsides of the chord from end to end, 
 placed at such distance asunder as to admit the ends 
 of diagonals between them, and also, to admit of addi 
 tional courses of chord timbers upon the inside of the 
 former, to be introduced as required toward the centre, 
 to give in each panel a section of chord, proportional 
 to the computed strain for such part. 
 
 The pieces composing the several courses, may 
 be spliced with the double lock, Fig. 57, usually with 
 the centre of the splice at the nodes, or connecting 
 points of chords with diagonals ; no two splices in the 
 same half-chord to occur at the same node. 
 
 The upper chord should be increased in section by 
 enlargement of the section rather than the number of 
 courses. Or, in some cases, timbers may taper in 
 thickness toward the ends of chords, either upper or 
 
 * The characteristic of this truss, is not that strictly speaking 1 it lias 
 no vertical members, but that there is no general alternate transfer of 
 weight from diagonals to verticals, and the contrary. 
 
WOODEN BRIDGES. 307 
 
 lower. For instance, if 5" in thickness be sufficient 
 in the end panel, and 7" be required in the next, a 
 timber extending over the width of two panels, 6" at 
 the smaller, and 8" at the larger end, will answer the 
 requirement with perhaps less waste of timber and 
 labor than would suffice under a different arrangement. 
 But such matters must be left to the judgment of the 
 designer. 
 
 The upper chord acting by compression, the timbers 
 may be connected by a half-lap of 1J or 2 feet at the 
 nodes, where the main connecting bolts will secure 
 the ends. 
 
 The diagonals which act principally by compression 
 (represented as the narrower ones in Figs. 65 and 66), 
 may be in pairs, while those mostly exposed to tension 
 (the wider ones), may be single, and placed between 
 the former. Thus usually three pieces are united at 
 each node. 
 
 FIG. 65. 
 
 
 .. 
 
 V ?/ \ 
 
 / w 
 
 In some cases where the thickness of diagonals ex 
 ceeds the space between half-chords, the thrust dia 
 gonals may be shouldered to fit a boxing upon the in 
 side of the chord ; as by either of the vertical dotted 
 lines, Fig. 65. Sometimes also, the boxing may ex 
 tend through the whole depth of the chord, so as to 
 require no cutting of the diagonal ; and again, the 
 thickness of the diagonals maybe reduced in the parts 
 
308 BRIDGE BUILDING. 
 
 between chords, and no cutting of chord timbers re 
 quired.. 
 
 "When cutting of timbers becomes necessary for pur 
 poses as above, it should be in the parts where the 
 greater surplus over the necessary net section occurs, 
 whether in chord or diagonals. Every part should 
 have a square inch of net available section for each 
 l,0001bs. of tension, and a square inch of bearing upon 
 bolt, pin, or shoulder, for each l,OOOSbs. of either ten 
 sion or thrust to which the part is liable ; and the 
 bearing upon bolts and pins should be estimated as 
 equal to the diameter multiplied by the length of hole 
 through the piece ; or, equal to the section of timber 
 severed by the hole. 
 
 CLXIY. Fig. 66 is a general representation of the 
 half of an 8 panel truss, suitable for a 100 foot common 
 road bridge. Let v 14 , = distance between centres 
 of upper and lower chords, and h = 12 J , = horizontal 
 width of panel. Then, assuming w 10,0001bs. 
 (= movable panel load), and w f = 4,000ft>s. (= perma 
 nent panel load), we have - = .893 (nearly), and D = 
 
 18.77 = length of diagonal; whence, D - = 1.34; and, 
 computing the stresses of the several parts and mem 
 bers by the process explained in sections [XLIV, &c.,], 
 the maximum vertical pressure at a equals 49,000ft>s. 
 giving a longitudinal compression upon ai 9 equal to 
 65,660Bbs., and a tension upon ab, equal to 43,750ft>s. 
 
 For the double member ai, 8" X 9" timbers are suf 
 ficient ; while 4" X 12" (in each half), would answer 
 for ab. But to give greater transverse stiffness for 
 supporting floor timbers, it is preferred to have the 
 outside course of lower chord timbers 5x12 inches. 
 
WOODEN BRIDGES. 309 
 
310 
 
 BRIDGE BUILDING. 
 
 The piece bj having no office but to fill the space at 
 b 9 and to give support to a i, may be of any convenient 
 dimensions. 
 
 The maximum tension of other portions of the lower 
 chord is, for be, 56,250; for cd, 81,250, and for de, 
 93,750Ebs. For the upper chord, we have compression 
 ofih, hg and gf, 62,509ft>s., 87,500ft>., and 100,OOOR>s. re 
 spectively. 
 
 The diagonals and verticals are liable to maximum 
 tension and compression as shown in the following 
 statement ; and may properly be of dimensions as 
 marked opposite each in the right hand column below ; 
 in case of double members, the figures indicate the 
 width and thickness of each. 
 
 Parts. 
 
 Tension, Ibs. 
 
 Compression, libs. 
 
 Cross-Section, inches. 
 
 bi 
 
 28,000 
 
 
 double 3 X 11 
 
 d 
 
 28,140 
 
 
 single 5 X 12 
 
 dh 
 
 20,435 
 
 
 " 4 x 12 
 
 e 9 
 
 12,730 
 
 ,670 
 
 " 3 x 11 
 
 fd 
 
 6,700 
 
 6,700 
 
 d. 3x 6 
 
 yc 
 
 670 
 
 12,730 
 
 " 3x6 
 
 hb 
 
 
 20,425 
 
 " 3} x 7 
 
 fa 
 
 
 65,660 
 
 " 8x9 
 
 The inside course of lower chord timbers may be 
 a 4" x 12" piece extending from d across the two mid 
 dle panels of the truss, spliced at each end to a taper 
 ing piece 4 X 12 at d, and 2 X 12 at b ; and consequently, 
 3 X 12 at c. Then, leaving a space of 8" between half 
 chords at d and e, we have 10" at c, and 12" at b. 
 
 Each half of the upper chord should be 8" x 12", in 
 the two middle panels, and placed 9" apart ; connect 
 ing with a tapering piece each way, from 8 x 12 at g y 
 
WOODEN BHIDGES. 311 
 
 to 6 x 12 at i\ where the end should be beveled to a 
 line bisecting the angle aih, and abut against a beveled 
 shoulder upon the upper end of the king brace ai. 
 The king brace is also cut away upon the inside, leav 
 ing only 1" in thickness, to make up, with bi and z c, a 
 thickness equal to the space (13") between the half- 
 chords at i. 
 
 The parts thus meeting at i are to be fastened by 2 
 transverse bolts of at least 2J" in diameter. These 
 afford the requisite square inch of bearing surface for 
 each IjOOOfos. of pressure, with an unimportant de 
 ficiency for the member zc, which may be eked out with 
 a V pin through bi and ic only, if thought advisable, 
 thus giving 55 square inches for vertical and diagonal 
 together. 
 
 These members should extend at least 14" beyond 
 the centres of holes. 
 
 At h and <;, the three diagonal pieces just fill the 
 space between chord timbers, and require at A, two 
 bolts and one plain pin of If " in diameter, and at g, 
 the same number &c., of If" diameter. The diagram 
 shows only two bolts at each connection. 
 
 At the point /", where two pairs of braces meet, one 
 pair may be cut off at the meeting, and a 4 by 6 inch 
 piece introduced, lapping 2 feet between the cut pieces 
 (reduced each J inch in thickness, inside, to the extent 
 of the lap), and secured by 2 bolts and 1 pin of V 
 diameter; the upper end passing between the opposite 
 braces, the latter being boxed J" inside, to afford room 
 for the 4" piece ; and the whole secured by a single 
 1J" or 1 J" bolt through chord and braces. 
 
 The connections at the lower chord are somewhat 
 more complicated, but involve little difficulty. The 
 best connection at a, is made by cutting a vertical 
 
312 BRIDGE BUILDING. 
 
 shoulder or heading J" deep, upon both sides of the 
 half chord, as shown by the vertical dotted line in the 
 diagram A, Fig. 66; the brace being forked with 
 counter shoulders upon the inside. This affords 36 
 square inches of shoulder surface, which, assisted by 2 
 bolts of V diameter, give 50 square inches, to with 
 stand less than 44,0001bs. The end of the brace is 
 thus made to bear directly upon the abutment without 
 any crushing action upon the chord. 
 
 At 6, the space in the chord is 12", while the verti 
 cals descending parallel, would occupy 11". But giv 
 ing a divergence of 2J", and boxing f " upon the inside 
 of chord timbers, leaves a space of 6J" between verti 
 cals at b. Then, boxing bh J" upon the inside at the 
 crossing with ic 9 there will be a 3" space between 
 braces bh at 6, and a thickness of 4 J" (of the pieces bh) 
 between the verticals bi; also, a shoulder of 1J" upon 
 the outside, which may be made to act vertically in a 
 boxing upon the inside of fo , thus securing the requi 
 site bearing surface for the thrust of bh. Thus ar 
 ranged, the point should be fastened with 2 bolts and 
 1 pin of If" diameter. 
 
 The piece bj will have 3" in thickness at 6, and will 
 be furred out, if necessary, to fill the space atj. 
 
 The space at c is 10" ; and, eg being shouldered |" 
 at the upper side of the chord at c, and boxed J" at the 
 crossing with hd t the point c may be secured by 2 
 bolts and 1 pin of 1 J" or 2" diameter. 
 
 A J" boxing of df at rf, upon the inside, leaves a 
 thickness of 9", being 1" greater than the space in the 
 chord, and the pieces (//"therefore require a further re 
 duction in thickness upon the outside between chord 
 timbers, of J" upon each. The point d, requires If" 
 bolts and pin. 
 
WOODEN BRIDGES. 
 
 The two single diagonals meeting at e, may be 
 halved into one another at the crossing, and a 3x11 inch 
 piece lapped and locked on to each, as shown 
 Fid. 67. by a a in Fig.67 ; thus serving to fill the space 
 in the chord, and to restore strength to the 
 diagonals. The lap pieces are to be reduced 
 3* to 2J" in thickness below the lock at I. 
 
 ra 
 
 Two 1 J bolts are sufficient at the point e. 
 
 Transverse joists, or floor beams may 
 be placed upon, or suspended below either 
 the lower or upper chords. Sway bracing 
 may be locked and bolted upon the upper 
 chords, and iron X tie rods used at the lower 
 chords ; the beam timbers being shouldered 
 against the inside of cords, so as to strut 
 them apart against the action of the ties. 
 
 Angle braces from the king brace ai 9 to a transverse 
 beam from truss to truss at i, will aid in preserving the 
 erect position of trusses. These braces should usually 
 be lapped and bolted at the ends, so as to act by either 
 tension or thrust 
 
 The preceding specifications, it is hoped, will serve 
 to make the peculiarities of detail in the kind of truss 
 under consideration, properly understood. It may be 
 deemed advisable to adopt the rectangular, instead of 
 the Trapezoidal form of outline for the truss, by extend 
 ing the upper, to the same length with the lower chord, 
 inserting vertical posts at the ends, and exchanging the 
 double vertical bi, to a single diagonal meeting the up 
 per chord and end post at their point of junction ; thus 
 simplifying the connections at b and i. 
 
 This modification, unlike the case of the trapezoidw^A 
 verticals, involves no increase in amount of action upon 
 materials, though it increases the number of members, 
 and changes the manner of distribution of the action. 
 
314 BRIDGE BUILDING. 
 
 MODULUS OF STRENGTH, FOR BRIDGE 
 TRUSSES. 
 
 It is shown in preceding pages of this work, that, 
 knowing by experiment the strength of the materials 
 to be employed, we may calculate the necessary cross- 
 section of each part of a bridge truss, in order that it 
 may sustain a given load, with a given stress upon the 
 materials. 
 
 It is sometimes, however, a satisfaction to have a 
 confirmation of the correctness of our calculations, by 
 direct experiment upon the same combination com 
 plete, which we propose to employ for actual use. For 
 this purpose, instead of applying the test to a full sized 
 structure, which would involve a great deal of labor 
 and expense, the test may be applied to a model, made 
 in the true proportions, upon any scale. 
 
 Now, it is obvious that with the same combination 
 and arrangement of members, the stresses, whether 
 positive, negative or transverse, produced upon the 
 several parts by the acting forces, will be in proportion, 
 throughout, to the weight sustained, whatever be 
 the length of pieces ; such stresses being determined by 
 the positions and angles, and not by the lengths of 
 pieces. 
 
 It is further manifest that the ability of parts to 
 withstand the effects of the acting forces, must be as 
 the cross-sections of parts respectively ; and in similar 
 models, the parts, being similar solid figures, have their 
 cross-sections as the squares of the magnitude of scale 
 upon which they are respectively constructed, while 
 the bulk and weight of each corresponding part, and 
 of the combinations complete, are as the cubes of the 
 magnitude of scale. 
 
MODULUS OF STRENGTH. 315 
 
 Then, assuming two similar models, the scale of one 
 being m times as great as that of the other, the weights 
 which they will respectively bear, under the same 
 stress of material, will be as W to Wm 2 , while their re 
 spective weights will be as 1 to m 3 . 
 
 Now, dividing the sustaining power of each by its 
 
 own weight,the quotients are as "W toW - 3 or as W to 
 . But the lengths being as L to Lm, if we multiply 
 
 the quotients just found by respective lengths, we have 
 WL for the one, and Lm W -f- m, = WL for the other ; 
 showing that the length of a model truss by the num 
 ber of times its own weight which it can bear (with a 
 given stress), is a constant quantity, whatever be the 
 scale of such model. 
 
 Again, the quotients W, and , multiplied by the 
 
 lengths L and Lm, give the products WL, and -- X Lm, 
 
 equal to WL. Hence, the product of a truss medal into 
 the number of times its own weight which it is able 
 to sustain, is also constant, whatever be the relative 
 values of the two factors. 
 
 It follows, that making these two factors variable, 
 and representing them by Q and L, the one increases 
 at the same rate at which the other is diminished ; and, 
 when Q = 1, L must be equal to the greatest length 
 at which a truss of the same plan and proportions, and 
 under the same stress of materials, can sustain its own 
 weight alone. 
 
 This length, as we have seen, is determined for a 
 model upon any plan,, constructed upon whatever scale, 
 by multiplying the length of model by the number of 
 times its own weight it is capable of sustaining. 
 
316 BRIDGE BUILDING. 
 
 This product may be called the MODULUS OF STRENGTH, 
 and the plan of truss which gives the largest MODULUS, 
 may fairly be regarded as the strongest plan. 
 
 The Modulus may refer either to the actual break 
 ing load, as found by experiment, or to the load pro 
 ducing given rates of strain upon materials, as 
 determined by calculation. 
 
 EXAMPLES. 
 
 (1). A bar of cast iron 1 inch square and 12" between 
 supports, will bear (at 6,000rbs. to the inch of section, 
 upon a leverage equal to depth of beam), a distributed 
 load of 4,000116s. which divided by its weight, = say 
 3.12ft)s. gives Q = 1250 ; and L being 1 foot, the Modu 
 lus = QL, = 1,250 feet. 
 
 (2). A beam of pine timber 12 long and 6" square, 
 at l,500flbs. to the inch upon a leverage equal to depth, 
 as above, bears a distributed load of 18,0001bs. [CXLIL] 
 For the weight, say 3 cubic feet at 36ft>s. = 108ft>s. ; 
 
 1ft 000 
 
 whence, Q = ^ = 166.6, which multiplied by L 
 (= 12 ) gives Modulus equal to 2,000 ft. 
 
 By reducing the length of the beam just considered, 
 to 6 feet in length, retaining the same section, it would 
 give a Modulus of 4,000 feet, instead of 5,000, as given 
 in the Appendix to my former work ; the difference 
 arising from the assumption of a smaller specific 
 gravity for pine in the latter case. 
 
 (3). The two panel model with chord and rafter 
 braces, mentioned in the latter part of [CLVIII], 20" 
 long, and weighing 0.18rb. supported a load equiva 
 lent to 3,885 times its weight, while L = 1 feet ; 
 whence, 3,885 xlf = 6,475 feet, = its Modulus. 
 
MODULUS OF STRENGTH. 317 
 
 (4). A model wooden truss 4 feet long, made many 
 years ago by the author, on the plan of the truss Fig. 
 66, having 10 panels, and a depth equal to j\ of its 
 length, weighed 0.9Ibs, and bore a distributed load of 
 
 6001bs. Hence, the modulus of the truss was X 4 
 = 2,664 feet, being more than half a mile. 
 
 The model was somewhat strained but not broken ; 
 and recovered its normal shape and condition on re 
 moval of the load. It was subsequently sent to the 
 U. S. Patent Office. 
 
 These examples, however can not be taken as in 
 dices to the relative merits for general use, of the 
 different forms of truss to which they refer. Each 
 possesses qualities suited to special occasions. 
 
 (5). A model of a 6 feet Trapezoidal Iron Truss (the 
 first ever constructed], weight a little less than three 
 pounds, sustained TOOSbs. distributed, without any ap 
 pearance of overstraining ; thus showing a modulus of 
 
 12? x 6 = 1,400 feet, with an estimated stress upon the 
 
 chord, at the rate of about 16,OOOIbs. to the square 
 inch. The model represents a truss of 144 feet, upon 
 a scale of J inch to the foot. The sustaining power of 
 a full sized truss in the same proportions, would be 
 700 x 24 2 , = 403,200ft)s, while the weight of truss would 
 equal 3 X 24 3 = 41,472ft>s. Doubling this for two 
 trusses, and adding, say 10,0001bs, for beams, &c., we 
 have 92,944ft)s. for the weight of a 144 feet bridge, 
 capable of sustaining, at a stress of 16,000ft>s. to the 
 square inch upon the chords, over 356 net tons beside 
 weight of structure. 
 
DRAWBRIDGES. 
 
 CLXY. The present is undoubtedly distinguishable 
 from all preceding periods of history, by the increased 
 amount of locomotion, both of persons and property, 
 which takes place both by land and water. Hence, 
 the frequent crossing of one another by land and water 
 lines of transit, as well as the crossing by the former 
 of unnavigable waters, and of streets and ravines y 
 creates a large demand for the construction of BRIDGES ; 
 which forms the special subject of the present volume. 
 
 Furthermore, as convenience often requires that 
 these intersecting lines by land and water should oc 
 cupy so nearly the same elevation that both can not be 
 used at the same moment, a necessity arises for the 
 frequent construction of DRAW BRIDGES, which may be 
 temporarily withdrawn from over the water highway 
 during the passage of water craft, and replaced for the 
 transit of laud vehicles. 
 
 Cases requiring the construction of draw bridges 
 occur so frequently at the present day, that a treatise 
 upon bridge construction may be considered somewhat 
 incomplete, which does not embrace the construction 
 of Draw Bridges, as well as stationary structures. 
 
 The subject of Draw Bridges having been omitted 
 m the preceding edition of this work, it has come to 
 the knowledge of the author that such omission has 
 occasioned disappointment to some who have made 
 use of the book. In consideration of this, as well as 
 the fact that the author has originated some plans and 
 devices which he believes to be valuable and useful in 
 
320 BRIDGE BUILDING. 
 
 the construction of draw bridges, the current chapter 
 is introduced in the present edition, in order to make 
 the work as satisfactory and useful as may be to those 
 who may have occasion to consult its pages. 
 
 The present design is not a historical sketch of the 
 construction of draw bridges, but to give the author s 
 views, derived from experience, obserration and in 
 vestigation, as to the most direct, feasible, and conven 
 ient means of accomplishing the ends requiring the use 
 -of such works. 
 
 CLXVI. The indispensable requisites of a draw 
 bridge are, first, strength to sustain with safety the 
 weight of the land traffic, and second, mobility, ena 
 bling it to be withdrawn, so as to afford sufficient width 
 of unobstructed water way, and sufficient head room 
 for the passage of the water traffic. Hence, strength 
 combined with lightness is a desideratum. 
 
 Draw bridges, as hitherto constructed and used, 
 may be distinguished into three classes; Retractile, 
 Swing (or pivot), and Lift Draw Bridges. The former 
 
 FIG. 68. 
 
 are withdrawn bodily, either in the direct line of the 
 land traffic, or obliquely, so as not to come in conflict 
 with the stationary portion of the way ; as represented 
 
DRAW BRIDGES. 
 
 321 
 
 in Fig. 68, where CO shows the water channel, DD, the 
 draw closed, and D D , the draw open. 
 
 In case of direct retraction, the draw must either oc 
 cupy a higher position than the permanent way, so as 
 to be drawn back over a portion of it, and the two 
 planes connected by an inclined apron (a plan not 
 feasible for rail roads), or a portion, a (Fig. 69), of the 
 way at the heal of the draw proper, Z), withdrawn late 
 rally, as to the position of # , to make room for the 
 longitudinal withdrawal of the draw proper. 
 
 FIG. 69. 
 
 1 
 
 
 a 
 
 D 
 
 
 a 
 
 
 1 
 
 
 These movements are effected by having the mova 
 ble bodies mounted upon wheels or rollers, running 
 upon hard level ways, so as to reduce the amount of 
 friction, and consequently that of the required motive 
 power, to a minimum. 
 
 But retractile draws, though they may be still used 
 in a few cases, and under peculiar circumstances, must 
 be regarded as nearly obsolete, having been mostly 
 superseded by the swing draw, which has important 
 advantages in convenience of construction and opera 
 tion. No practical details, therefore, as to the con 
 struction of retractile draws, will be given at this 
 time, as such details if given, would be almost certain 
 never to be adopted in practice. 
 
 CLXYII. The Swing or Pivot draw is either mounted 
 upon a pivot P (Fig. 70), in the vertical line through 
 41 
 
322 
 
 BRIDGE BUILDING. 
 
 its centre of gravity, or upon wheels or rollers running 
 upon a horizontal circular way or track tt, with its 
 centre in said vertical line ; or what is more common, 
 the weight is divided between a central pivot and the 
 track and rollers. 
 
 FIG. 70. 
 
 ft 
 
 It will be seen that by this arrangement, the draw 
 has only to be gyrated through a quadrant, to bring it 
 to a position parallel with the side of the navigable 
 channel (7, and leave the latter unobstructed. It is also 
 obvious that the draw having its centre of gravity at P, 
 the moments (with respect to P), of the portions or 
 arms on opposite sides of P, must be equal, whatever 
 be the relative lengths of those portions; whence, in 
 general, the length of arm spanning the water channel 
 being given, the shorter the other arm, the greater 
 must be its weight, though the exact proportion will 
 depend upon the disposition of material, whether near 
 or remote from P. 
 
 It follows that it is usually little if any more expen- 
 
DRAW BRIDGES. 32S 
 
 sivc to constructor work a draw with two equal arms, 
 and covering two equal water channels (which is often 
 highly advantageous), than one having one short arm, 
 with extra weight as a counterpoise to the long arm. 
 This is not the case as to the retractile draw, which 
 shows one advantage in favor of the pivot draw. 
 
 Equal arms also serve to balance the action of wind 
 upon the pivot draw, which often effects a serious 
 drawback to the convenient working of the swing 
 bridge, and this would seem to give some advantage 
 to the .retractile draw, over the swin<? draw with une- 
 
 O 
 
 qual arms. 
 
 The portion extending over the water channel, in 
 both the retractile and the swing draw, require the 
 same weight of material, and the same counterpoise 
 toward the opposite end. Consequently, the weight 
 to be moved in working the draw, requires to be about 
 the same in both. But the retractile is to be moved 
 bodily, and if withdrawn obliquely at 45 with its 
 longitudinal axis, must move through a space equal to 
 the width of channel multiplied by \/2. If withdrawn 
 in the direct line of its length, it moves over the width 
 of channel, in addition to the movement required for 
 the displacement of the section of road (a. a , F. 69), 
 equal in length to said width of channel, making an 
 amount of movement about equal to that required in 
 ease of the oblique withdrawal. * 
 
 The swing draw, gyrating about its centre of gravity, 
 the amount of movement equals twice the weight of 
 the long arm (the one spanning the water channel), 
 moving through the quadrant of a circle with a radius 
 equal to the distance of the centre of gravity of said 
 long arm, from the centre of motion ; which distance 
 is about 55 per cent, of the width of channel, allowing 
 
324 BRIDGE BUILDING. 
 
 for the distance of the centre of motion back from the 
 water s edge. The length of the quadrant equals 
 about 1.57 Rad., and, denoting the width of channel by 
 C, and substituting 0.55C for Rad., we have 1.57 x 
 .550 X 2vvt. of long half of draw, = quantity of move 
 ment, == 0.8635C x wt. of draw ; assuming the weight 
 of draw to be equal to twice the weight of the long 
 half. If the short arm be heavier than the other, the 
 space traversed by its centre of gravity is less in like 
 proportion. 
 
 Hence, the quantity of movement in working the 
 retractile draw, is to .that of working the swing 
 draw, about as CV2 to 0.8635C; being some 63 
 per cent, greater for the former than for the latter. 
 The difference in the required power for working the 
 draws respectively, may be assumed to be about the 
 same, as the appliances for effecting the movement 
 have about equal advantages, and the resistance to mo 
 tion is about the same in the two cases. 
 
 This decided advantage in favor of the swing draw, 
 with no apparent offset in favor of the retractile, is 
 sufficient to account for the prevalent discardment of 
 the latter, and adoption of the former ; as well as for 
 its being here referred to as an obsolete device. 
 
 CLXVTH. The truss work of the swing draw when 
 in motion, being entirely supported by the pivot at the 
 centre of motion, and the wheels or rollers a few feet 
 therefrom, obviously suffers a reversed action in the 
 upper and lower members, from what they would 
 suffer if supported at the ends. That is, in the former 
 case, the upper members are exposed to tension, and 
 the lower, to compression, instead of the reverse, 
 which takes place in the latter case. 
 
SWING DRAW BRIDGES. 
 
 325 
 
 Two plans have been employed for meeting these 
 conditions ; one of which is the use of parallel chord 
 trusses, with the upper chord to sustain tension with 
 occasional compression upon the end portions, and the 
 lower chord to sustain compression, with occasional 
 tension upon parts toward the ends. 
 
 CLXIX. The other plan is, the construction of 
 trusses (ab Fig. 71), from the turn table T, to either end, 
 acting upon one another by compression at the lower 
 chord through or over the turn table, and sustained at 
 the outer ends by oblique suspension rods or cables, 
 eb and/d, descending from tower frames erected over 
 the turn table. 
 
 FIG. 71. 
 
 XX 
 
 \\xxxx 
 
 The trusses may be constructed upon any plan suita 
 ble for a stationary bridge of like span. But the lower 
 chord must be capable of sustaining compressive action 
 in the direction of its length, equal to the excess of 
 horizontal force of suspension rods eb and fd, over the 
 tension of respective parts of said lower chord, due to 
 weight of structure. 
 
 The horizontal action of eb, equals half the weight 
 
 of the long arm ab, multiplied by *&, and it is advisable 
 that the chord gb be able to sustain that amount of 
 
326 BRIDGE BUILDING. 
 
 compression throughout, though some deduction may 
 be made in the central portion in case economy can be 
 promoted thereby, as perhaps may not be the case to 
 any considerable extent. 
 
 The lower chord gb, is relieved of tension through 
 out its whole length by the action of eb, which must 
 continue nearly or quite at its maximum while loads 
 are in transit, as the end b will seldom be raised when 
 unloaded, so as to relieve eb to any considerable extent ; 
 while the tendency of load to elongate the lower chord, 
 will also tend to increase the tension eb, and may in 
 crease it considerably beyond what it endures from 
 simply sustaining half the weight of the truss. But 
 this point can not be precisely determined. 
 
 These facts may properly be considered in propor 
 tioning the lower chord ; but the matter should be 
 handled with caution, and with a constant leaning to 
 the side of safety, in case of any uncertainty in regard 
 to the amount and kind of stress upon the various 
 parts. 
 
 In case of unequal arms, as represented in the Figure, 
 the short arm will generally require a greater weight 
 to be thrown upon the king post fh than upon eg, upon 
 which two (regarding at present only one side of the 
 bridge), the weight of superstructure is concentrated. 
 It therefore becomes necessary, in order to a uniform 
 distribution of weight upon the turn table, that a por 
 tion of this excess be transferred from fh to eg, through 
 the tension of ce and ha, or by equivalent means. But 
 assuming that the reader is versed in the general modes 
 of calculating strains, as explained and illustrated in 
 this and other works treating of the subject, I shall 
 not go much into detail in that branch of the matter 
 in hand, at this time. 
 
SWING DRAW BRIDGES. 827 
 
 The trusses being constructed upon any approved 
 plau from turn table to adjacent abutments or piers, 
 and proportioned as for stationary bridge spans, with 
 the exception of the rigid lower chord as above re 
 ferred to, extending across the turn table; and the 
 tower frame erected, the rod or cable eb must have sec 
 tion sufficient to bear a tension equal at least to half 
 the weight of the arm ab, multiplied by . The rod 
 fd will have tension determined by the disposition and 
 amount of ballast upon the arm cd, as well as the 
 weight of the arm cd itself. The tension of fd will 
 generally exert less horizontal action than eb, and the 
 deficiency of horizontal action must be made up by 
 the horizontal action of ec and ah, in order to brinsc 
 
 O 
 
 the centre of pressure over the centre of the table. 
 The horizontal action of ef (equal to its full tension), 
 must be equal to that of eb, less that of ec ; or, equal to 
 the horizontal action of fd. 
 
 But these several stresses are easy of calculation by 
 modes, it is believed, clearly explained in the present 
 work, and from such calculations the following results 
 are readily obtained. 
 
 CLXX. Representing the constant panel weight of 
 the arm ab by w f , the maximum variable panel load by 
 w, and w+w f by W, as usual in this work ; also, making 
 r = ag, ae, and h = horizontal panel width, we have 
 the horizontal action of eb equal to 5?//x -^-,=2510 ^ . 
 
 The stress of gb due to a maximum gross load, in the 
 two middle panels, equals 11W-. That in the next 
 
 panel each way, = 9W-?, and in the next, 6JW-S while 
 the stress of the two remaining panels on the right, 
 equals 4JW-*, and on the left 2VW~, and zero, respect- 
 
328 BRIDGE BUILDING. 
 
 ively. Then, assuming W = 4iv , the stresses of res 
 pective portions of lower chord due to a max. gross 
 load, in terms of io f , equal w 7 ^ with the coefficients 
 44, 36, 26, 18, 10 and 0; showing that the tension of 
 eb counteracts over J the tendency toward tension on 
 lower chord, as to the two middle panels, over f as to 
 the two next panels, and substantially the whole, as to 
 the remaining parts of said chord, in a structure ar 
 ranged as in Fig. 71, and with w = 3w . 
 
 On the other hand, the minimum tendency to ten 
 sion on the two middle panel lengths of lower chord, 
 
 is HM; . Hence the compression of 25w/ upon those 
 parts, due to the horizontal action of eb, is reduced (by 
 such tendency to tension), to (25-ll)i0 r , = 
 
 and, to (25-9) ?/; -,=16w/- upon succeeding panel- 
 lengths, either way, while for succeeding panel-lengths 
 toward 6, the coefficients of w -^ are 18 J, 20J and 20J, 
 and for those toward g, 18J, 22J and 25. * 
 
 The maximum thrust and tension for successive por 
 tions of the lower chord, beginning at the turn table, 
 are, for part over turn table, and first panel-length from 
 
 O m Comp. 25?(/ Tension 
 
 2d panel, " 22 J- " " 
 
 3d and 8th " 18J " " lw -% 
 
 4th " 7th " 16J " " 11 " 
 
 5th " 6th " 14 " " 19 " 
 
 9th " 10th " 20J " " " 
 
 The other members of the truss ab are subject to the 
 same stresses as if it were a stationary bridge truss; 
 and, if the structure have equal arms, the stresses upon 
 members of the opposite arm, will of course be the 
 same as upon corresponding members of the arm ab. 
 
SWING DRAW BRIDGES. 
 
 CLXXI. If cd have half the length of ab, its weight 
 will balance the half (gC), of ab next the turn table,. 
 while the half Cb must be counterpoised by extra weight 
 upon cd, having moment equal to that of Cb, with res 
 pect to a transverse axis through the centre of motion ; 
 and the stress of fd will be determined by its length, 
 and the weight sustained by it. In case the extra 
 weight be uniformly disposed upon the two outer pan 
 els, J of it, together with J the weight of the arm cd, 
 (= 2Jw/), must be sustained by c/f, and the weight of 
 
 ballast will be 5w f x 7 ff + ffi, j of which, added to 
 
 4/4 -f fa 
 
 2J?*/, equals the weight sustained by fd, whence we 
 obtain the tension of fd, its horizontal action, and the 
 complementary horizontal action of ce, required to ba 
 lance that of cb. 
 
 In this case, the members meeting at the points e 
 and/, should have unyielding connections by pins and 
 eyes, or screws and nuts. But in case of equal arms, 
 dfeb may be continuous cables (usually one on each 
 side of each truss), attached at b and d, and acting by 
 simple pressure at e and /, those points being strutted 
 apart by a force equal to SM? (=* vertical pressure at e), 
 
 x ^. The piece ac should have loose connections at 
 
 the ends (so as to act by thrust only), or what is better, 
 should be omitted entirely, and the single pair of diag 
 onals inserted as indicated by the dotted lines fg and 
 ch, instead of shorter ones, ce, etc., so as to give free 
 and independent action to the trusses either way, by 
 a slight springing of the long king posts, as the trusses 
 are deflected by load. 
 
 The tension of fd modifies that due to the chord hd r 
 on the same principle explained with regard to eb and 
 gb, and to an extent determined b} the length of dh y 
 42 
 
330 
 
 BRIDGE BUILDING. 
 
 and other conditions, and which can not be expressed 
 in a general formula. 
 
 CLXXII. Proceeding to the other case mentioned, 
 and which may be illustrated with reference to Fig. 72, 
 both upper and lower chords require to be so con 
 structed as to be able to act both by tension and thrust, 
 except as to the part across the turn-table, and one, 
 two, or three panels either way therefrom, as circum 
 stances may require. 
 
 FIG. 72. 
 
 When out of contact with the abutment at I, the 
 diagonal In sustains (using the accustomed symbols), 
 \w , and 7co, etc. to bx, sustain respectively and succes 
 sively w r with the coefficients 1, 1}, 2, 2J, 3, 3J, 4, 4-J 
 and 5. These weights determine the stresses of those 
 members, due to weight of structure (and also show 
 for xy, a tension of 50M? -^, including the horizontal 
 action of xz, if any), and show for several of them 
 toward the right, their maximum stresses. But when 
 the end I touches the abutment, and is in position for 
 the transit of loads, and weight is imposed upon any 
 part between a and 6, the materials yielding more or 
 less in consequence of elasticity, a portion of such 
 weight bears at , and the remainder at a. 
 
 If the upper chord were relaxed between x and ?/, 
 the respective portions of weight bearing at a and I 
 could be readily determined, being the same as in case 
 
SWING DRAW BRIDGES. 831 
 
 of an ordinary truss. But the portion of chord xy 
 being under tension equal to 50w , as already stated 
 (regarding the abutment as sustaining no weight of 
 structure), the truss must act in the manner of abeam 
 continuous over one support, and discontinuous at the 
 next, so that, when loaded, there will be a neutral 
 point where the action upon chords changes from ten 
 sion to thrust and the contrary. 
 
 Now the tension of :ry-|-hor. action of xz, equal to 
 oOw/ , must be exhausted by the hor. ac. of bx, ex etc., 
 before any compressive action can take place upon the 
 upper chord. In other words, diagonals inclining to 
 the left, with truss fully loaded from a to I, must exert 
 a hor. action at the upper chord greater than those 
 inclining to the right (including with the latter the- 
 hor. thrust of /m), by 50w . 
 
 Then, assuming all the weight at the points ,J, /:, 
 and J of that at //, to bear at /, and all at the six points 
 from g to b inclusive (except J W at y\ to bear at tf , 
 the horizontal action toward the left upon the upper 
 chord, equals IW- ; and that toward the left, 
 
 the difference being 12JW ; and if W = 4w , then 
 12JW = 50i# , showing that the action toward the right, 
 upon the upper chord, is just equal to that toward the 
 left, including in the latter, the action of xy and xz 
 Hence it will be seen that under the conditions here 
 assumed, the horizontal action of m?, mj, mi and ng, is 
 just equal to that of gr, fs and et in the opposite direc 
 tion, and consequently, tm alone of the upper chord is 
 subject to compression, and el alone of the lower chord,. 
 subject to tension, while dc and ut are neutral ; ad al 
 ways under compression, and wj always under tension ; 
 since this condition of load obviously throws a greater 
 
332 BRIDGE BUILDING. 
 
 bearing at I than can occur when the opposite arm is 
 wholly or partially loaded, so as to bring greater ten 
 sion upon xy, and exert greater counterpoise action 
 upon the arm al. Hence this condition gives the max 
 imum compression upon the upper, and the maximum 
 tension upon the lower chord. 
 
 CLXXIIL What the difference in amount of bear 
 ing at I may be with both arms fully loaded, can not 
 easily be determined with precision. But as to Fig. 
 72, it is deemed entirely safe to assume that at least 
 all the weight at j and k will bear at , in all cases of 
 load sufficient to produce a maximum strain upon any 
 part of the structure on the right from the point a ; 
 and that all the weight from b to i, including those 
 points, may bear at a. This will depend somewhat 
 upon the firmness with which the ends are brought to 
 bear upon abutments when in position for use, but 
 without load. 
 
 Under the above supposition as to bearing at l s the 
 obliques ml and mj would exert horizontal action equal 
 to 3W , and equal to that of ig, and half that of gr in 
 the opposite direction ; whence gl alone of the lower 
 chord is under tension, and rm of the upper chord, 
 under compression ; but in neither case under maxi 
 mum stress. On the contrary, ag is under compres 
 sion, and rx under tension, being in each case a maxi 
 mum stress upon a considerable portion of those parts, 
 as will be determined by comparing the strains of 
 respective parts in the present assumed conditions, 
 with those obtained while the structure swings clear 
 of abutments. 
 
 Representing, as usual in this work, the long diag 
 onal by D, and the short and steep ones by D , we have 
 
SWING DRAW BRIDGES. 333 
 
 ^- and |p factors in expressions of stresses of those 
 classes of members respectively, and for convenience, we 
 will substitute m for-? and n for^-. Then, stress of iq 
 
 and gr, in case of full load upon both arms, equals 
 AVm, for each; That of fs and et equals 2Wm, that 
 ofrfw an ex equals 3Wm, and that of bx equals 4Wn. 
 
 CLXXIV. As to the stress of chords, half the hori 
 zontal action of gr, being taken by the excess of thrust 
 
 of mr over hor. action of iq,* the other half, fW J, is 
 opposed by tension of rs, and compression of gf. This 
 added to 4Wp for hor. action of/sf (making ~ = p), 
 
 makes 5AVp = tension of st,= comp. offe. Add 4Wp 
 for action of et, and it makes 9Wp = tension of tu, 
 comp. of ed. Adding again 6~Wp for hor. action of du, 
 gives 15 Wp = tension of ux, = comp. of dc. Then, 
 adding 6Wp for action of ex, gives 21Wp = comp. of 
 be, and lastly, adding 4Wp for action of bx, we have 
 25TV~p = comp. of baza , = horizontal action of xy and 
 xz. This all falls upon xy in case of equal arms. 
 
 In one or other of the three cases above considered 
 (namely : first, arm swung clear and without load ; 
 second, arm xl fully loaded; third, both arms fully 
 loaded), every part of the arm xl undergoes its great 
 est strain, which may be determined by comparing the 
 results obtained by computing the strains produced in 
 
 * The 2W upon ml, and 1W upon jm, produce thrust equal to 
 o W upon mq, which equals the horizontal action of iq, -j- half that 
 
 of gr in the opposite direction, leaving W to be opposed by tension 
 of rs. 
 
 \fs sustaining 2W, its horizontal action = 4W . 
 
334 BRIDGE BUILDING. 
 
 the several cases ; except that ep and fo may snffer 
 a nominal stress, not precisely determinable, under a 
 load progressing from a to L Also gn may sustain 
 some more weight with Lj and k unloaded, than with 
 the truss fully loaded. It is deemed safe to provide 
 that gn be able to sustain a weight of |W; /o, to sus 
 tain JW, and ep, JW, a little more or less as the judg 
 ment or calculations of the designer may dictate. 
 
 The preceding explanations are thought to be suffi 
 cient to guide as to the computation of stresses upon 
 the other arm of the bridge, whether equal or unequal 
 to the arm al. 
 
 The superstructures of swing bridges should be 
 thoroughly cross-tied and braced laterally, and the 
 king posts (represented by ax and yz), well secured by 
 arch braces or other efficient means transversely : and 
 if the space az be too great for floor joists or rail string 
 ers without intermediate support, an intermediate beam 
 may be suspended from the crossing point of ay and 
 xz, or stringers may be trussed. 
 
 CLXXY. Whatever advantages either of these plans 
 (Figs. 71 and 72), may have over the other, are pro 
 bably not very great. I find a greater amount of ac 
 tion (stress into length of parts), upon material in 
 chords of the long arm, in plan Fig. 71, including the 
 suspension rod eb, than in that of Fig. 72, by some 5 
 
 It will be seen that tu is under less tension strain (as 2Sw p to 
 Mw p), and ts under greater strain (as 21 to 20), when the truss is on 
 the swing, than when fully loaded on both arms (upon the above 
 assumptions of w=s d-w f , and 2W bearing at I), and that tn has the 
 max. tension with bridge on the swing, while tx has its maximum 
 with bridge fully loaded, inn is always under compression. In the 
 lower chord, e is the changing point, and parts at the left have their 
 max. comp. with bridge fully loaded, and those on the right, when, 
 on the swing. 
 
DRAW BRIDGES. 335 
 
 per cent. And while the action upon diagonals and 
 verticals may be a little greater in case of the latter, 
 the extra material in the tower frame of the former, is 
 thought to be an overbalance for any such excess, even 
 including the greater thrust and tension in the con 
 tinuation of chords over the turn-table, which takes 
 place in plan Fig. 72. 
 
 In regard to convenience of construction and appear 
 ance of structure, also, as well as economy of material, 
 the latter plan is thought to possess some advantage. 
 Still opinions and tastes may vary as to this, as well as- 
 in regard to other matters. 
 
 Regarding the ratio of length to depth of truss, the 
 same rules should govern in plan 71, as in the case of 
 stationary bridges of like span. In spanning channel* 
 of 50 or 60 feet in width, on plan 72, the head room 
 required for the traffic will govern, and depth from 15 
 to 18 feet, according to span, and the purposes of the 
 bridge, whether for common or railroad travel, wilS 
 probably be found expedient. In general, circum 
 stances will probably dictate a variation of ratio (of 
 depth of truss to length of span), ranging from J to J. 
 
 TURN TABLE. 
 
 CLXXVI. The same plan of turn table is applicable 
 with equal advantage to either of the two above de 
 scribed plans of swing bridge trussing. 
 
 A common, perhaps the most common, form of turn 
 table for draw bridges, is composed of rollers act, 
 Fig. 73, arranged in circular form, and rolling between 
 two metallic circular rails, of which one, 66, is fastened 
 to the supporting pier />, and the other, cc, inverted, 
 and attached to the under side of the bridge super 
 structure. 
 
336 
 
 UP.IDGE BUILDING. 
 
 The rollers are in the form of conic frusta, or seg 
 ments of cones having their vertices meeting at the 
 axis of motion of the bridge ; and are retained in posi 
 tion by arms radiating from a central hub, and serving 
 as axles for the rollers; or secured by a circular frame, 
 
 FIG. 73. 
 
 B 
 
 ff, formed of two concentric iron rings (shown com 
 plete in the upper, but only in section in the lower 
 diagram of Fig. 73), one inside, and the other outside 
 
TURN-TABLES. 337 
 
 of the circle of rollers. The rollers may either turn 
 upon pins through their centres, and through said rings, 
 or the pin or shaft may be fast in the roller, and turn 
 with it upon journals running in gudgeon boxes 
 attached to or formed in the circular frame /. The 
 pins or axles may be quite small (say V to 1 J in dia 
 meter), as they support but a nominal weight, and are 
 only required to maintain the proper positions and 
 directions of the axes of the rollers. 
 
 The roller frame, as well as the upper circular rail 
 running upon the rollers, must be connected with a 
 central hub for each (as they do not turn together), 
 turning upon a journal or pivot attached to the ma 
 sonry of the supporting pier. The rails, or surfaces 
 between which the rollers work, are beveled to fit the 
 conical faces of the rollers, and, in order to work in 
 the most perfect manner, they should be of cast iron, 
 and turned off by a tool carried by the arm of a heavy 
 revolving vertical shaft. 
 
 The diameter of the circle should not probably be 
 less than J to \ the span of the water channel, nor less 
 than to ^ the width of superstructure, and the dia 
 meter of the rollers, not greater than T V to J of the 
 radius of the circle upon which they travel. Greater 
 diameter would give so much obliquity of face as to 
 produce too strong a centrifugal tendency. The face 
 of the rail should have a width of 2J to 3 inches 
 generally, and for some 30 opposite each king post 
 (transversely of the bridge) when the draw is in position, 
 a width about twice as great, and as great as the face 
 of the rollers. This is to give sufficient bearing surface 
 while loads are passing, when nearly the whole weight 
 will be concentrated upon two or three rollers near 
 each of those positions. 
 13 
 
338 BRIDGE BUILDING. 
 
 The lower rail should have a depth (if of cast iron), 
 of 4 to 5 inches, according to size of bridge ; and the 
 upper and inverted one, of one to two feet (the deeper 
 the stiffer), and in both cases, they will generally be 
 cast in segments, and those of the upper one, bolted 
 together by flanges, so as to form a rigid hoop, over 
 which one or more strong beams, BB, crossing at quad- 
 ran tal points ee, etc. (or at the angular points of any 
 rectangle inscribed in the circle), should form supports 
 for the king posts (ag, and ch, Fig. 71), the space gh, being 
 adjusted to an equality with the side of the inscribed 
 square or rectangle of the rail circle. And, the nearer 
 the transverse distance between king posts comes to 
 the length of the other sides of the said inscribed square 
 or rectangle, the less stiffness of beams, BB, is required ; 
 that is, (7(7, F. 73 representing truss chords, and dd, the 
 positions of king posts, the nearer the d points come 
 to the e points, the less is the transverse action upon 
 the beams BB. Hence it is desirable that the circle of 
 rollers should pass directly under the points dd, etc. 
 
 CLXXVHL An intermediate beam may be in 
 serted between BB, and over the centre pivot, resting 
 upon the circle cc, to support floor joists or rail 
 stringers over the long stretch between BB. Or very 
 stiff diagonal girders ee, and e e , firmly attached by 
 the ends to the circle cc, meeting a common nucleus at 
 II, and so arranged as to have an adjustable bearing 
 upon the centre pivot (5 or 6 inches in diameter, as to 
 size of draw), enabling any desired amount of the 
 weight of structure which such girders can support, to 
 be thrown upon said pivot, and thereby relieving the 
 rollers, a, of a like amount of pressure. These girders 
 should have the greatest practicable depth, so as to sus- 
 
TURN-TABLES. 339 
 
 tain as great a proportion of the weight of superstruc 
 ture as may be. But the skill and judgment of engineers 
 in charge of specific cases respectively, will dictate as 
 to the minutiae of these devices, and more precise de 
 tail will not be attempted in this place. 
 
 CLXXIX. This plan of turn table, as well as the 
 one hereafter to be described, is worked by a vertical 
 shaft attached to the superstructure, and turned by one 
 or more sweep levers, with a pinion at the lower end, 
 taking into toothed segments attached to the circular 
 track 6, or to the masonry of the pier p ; and, in case 
 more power be required, a gear wheel takes place of 
 the sweeps above mentioned, and these are transferred 
 to a second shaft and pinion working into said gear 
 wheel. 
 
 The table above described, with slight modifications, 
 is extensively in use, and, when well constructed, un 
 doubtedly works as easily and satisfactorily as can be 
 expected. Still, it is liable to some objections, among 
 which may be named the great weight of the ring cc, 
 constituting or carrying the inverted rail, and the great 
 number of rollers, , so few of which can act with much 
 effect at the same time. For, it is obvious that about 
 two rollers under each king post, support essentially 
 the whole weight. It is therefore proper that when 
 the bridge is in place, each king post should stand cen 
 trally between two consecutive rollers ; and, that the 
 rollers be at equal distances apart. Then there will 
 be at least 8 rollers under equal pressure at all times 
 when loads are in transit, and when rollers receive their 
 greatest pressure. But without discussing this plan 
 further at present, I proceed to describe another swing 
 bridge turn-table devised many years ago by myself, 
 
340 
 
 BRIDGE BUILDING. 
 
 and used in a considerable number of cases with most 
 satisfactory results. 
 
 FIG. 74. 
 
 THE WHIPPLE TURN TABLE. 
 
 CXXX. Is arranged with a two wheeled truck a, 
 Fig. 74, directly under each king post, and the four 
 connected in pairs diagonally by an inverted triangular 
 truss to each pair. These trusses consist of a hollow 
 
TURN-TABLES. 341 
 
 cylindrical (or conic segmental) brace 6, running from 
 each truck frame obliquely downward to an abutting 
 block c, which is common to the two trusses, with 
 chords or ties </, from truck to truck for each pair. 
 
 The truck wheels are from 20 to 24 inches in dia 
 meter, with 5 to 6 inches width of rim, and with short 
 axles or shafts, 3 to 4 inches in diameter, according to 
 dimensions of bridge. The axles run in journal boxes 
 fitted to the truck-frame so as to bring the axles in the 
 direction of radii to the circular track t, upon which 
 the trucks are to run. 
 
 The truck frame consists of two cast iron side plates 
 (of which g and h present an outside and an inside view), 
 of an I formed cross section, and contour as seen at g. 
 These plates upon the insides, have projecting portions 
 as shown by the dark surface of diagram A, meeting 
 from opposite plates, in the centre of the frame at a 
 common surface of contact, and forming continuous 
 tubes or sockets through the frame, which serve as 
 media through which the ties d, act upon the cylindri 
 cal braces 6, thus forming a rigid truss, which should 
 be so proportioned as to be able to support (upon the 
 two trusses), the whole weight of superstructure, throw 
 ing it upon the centre block c. 
 
 The chord ties d, of the two trusses, crossing one 
 another upon the same level, are kept from mutual in 
 terference by cutting out the middle portion of one 
 set, and replacing the removed part with two pieces to 
 each tie bar, one passing above and the other below the 
 single continuous rods of the other set, as shown at/. 
 
 The block c has a cylindrical cavity in the under side, 
 10 to 12 inches in diameter, and about 7 inches deep, 
 into which is fitted (loosely) a solid cylinder entering 
 about 4 inches into the cavity, and leaving a space of 
 
342 BRIDGE BUILDIXG. 
 
 structure to be raised essentially free from bearing up- 
 some 3 inches in thickness above, to be occupied by 
 the nuts of a number of set screws s, intended to force 
 clown said internal cylinder upon the bed plate i, and 
 thus relieve the truck wheels from nearly all the weight 
 of superstructure. 
 
 The bed plate- z, has a socket or step f of an inch 
 deep, or thereabouts, with a hardened steel plate in the 
 bottom, to receive the lower part of the cylinder bear 
 ing upon the plate i, where the diameter of cylinder 
 and socket should be graduated to the proportion most 
 favorable for reducing the amount of friction. A di 
 ameter of 6 to 8 inches is thought to be suitable for 
 draws of 60 to 100 feet opening, while the part of the 
 pivot block within the block c should have a diameter 
 of 10 or 12 inches, in order to afford sufficient surface 
 for the set screws s to act upon. 
 
 The bed plate i. should have a rim about the step to re 
 tain oil, and the surfaces above and below the steel plate 
 should have radial grooves to allow the penetration of 
 oil; and these (grooves) should be so situated as to admit 
 of their being probed, to prevent their getting clogged. 
 
 The pivot block should have guides to prevent its 
 turning in the cavity of the block c ; otherwise it might 
 stick in the step, and the set screws slide upon its upper 
 surface ; which has been the case in some instances. 
 
 A groove should be formed in the under side of the 
 block c, near the edge, to keep the water from the pivot ; 
 and the screws- s, should be kept secluded from water 
 by a tin, or galvanized iron cap shutting over a rim or 
 ring cast upon the block c, outside of the screw hole?. 
 Sufficient vertical movement (1J or 2 inches), should 
 be allowed to the pivot cylinder, to enable the elasticity 
 of the braces and ties, b and d, to be taken up, and the 
 
TURN-TABLES. 343 
 
 on the wheels e, as the bridge will move much more 
 easily with the bearing upon the centre pivot, than up. 
 on the truck wheels. 
 
 The king posts should be placed over the centres of 
 trucks, or, when this can not be done, they should bear 
 upon transverse beams which bear upon centres of 
 trucks. In all cases, the bearing upon trucks should 
 be through the medium of bolster plates so formed up 
 on the under side as to touch the truck frame only up 
 on a space an inch wide or less, square across the centre, 
 as indicated by the parallel lines across the. trucks in 
 the large diagram of the Figure 74. Were the pressure 
 applied in a line diagonally across the truck, it would 
 act unequally upon the journals, and produce a tortion 
 strain upon the truck frame, which the latter might 
 not be able to bear. 
 
 Particular care should be taken to provide convenient 
 means for keeping the working parts thoroughly oiled. 
 
 The superstructure being properly adjusted and 
 balanced upon this turn-table, and the set screws s, 
 forced down until all the truck wheels can be easily 
 made to slide upon the rail by the use of a light crow 
 bar, the structure will turn upon its centre pivot, 
 steadied by contact of truck wheels upon the rail, 
 with the least practicable resistance, and, during the 
 transit of moving loads, the wheels, beincr in contact 
 
 O O 
 
 with the rail, are in readiness to sustain the additional 
 weight without increase of pressure upon the pivot, or 
 increased strain upon the diagonal trusses. 
 
 The modes and means for the application of power 
 in working this table, as well as the preceding one, have 
 already been described, [CLXXIX], and the description 
 need not be repeated. They need no illustration by dia 
 gram, and are not shown in the drawings. 
 
344 BRIDGE BUILDING. 
 
 The plan, Fig. 74, requires the middle portion of the 
 supporting pier to be depressed 1J to 2 feet, as shown 
 at p, where a vertical section of the upper part of the 
 pier is represented; and, under the bed plate z, should 
 be a large and firmly bedded stone capable of sustain 
 ing the whole weight of superstructure. 
 
 This plan appears to answer all the requisites of a 
 draw-bridge turn-table by the most direct and economi 
 cal means. 
 
 LIFT DRAW BRIDGES. 
 
 CLXXXI. Under this designation may be included 
 all movable bridges which are withdrawn from position 
 by being raised, instead of moved horizontally out of 
 place. 
 
 Lift bridges, though not much in use at the present 
 day, have been constructed to be raised bodily, being 
 counterpoised by weights acting over pulleys or sheaves ; 
 a plan scarcely feasible upon waters navigated by mast 
 vessels, or steamers with high smoke stacks ; as must 
 be obvious on a moment s reflection. 
 
 The more common device for lift draws, is, to raise 
 the platform from a horizontal to a vertical position, by 
 lifting one end, while the other turns upon a hinge 
 joint ; the operation being like the raising of a trap 
 door. 
 
 This plan is feasible over narrow channels, where 
 vessels may be slowly warped through. But the pro 
 cess requires so much time as to seriously impede the 
 land traffic. A bridge may be so balanced as to turn 
 upon a horizontal axis about as easily as a swing bridge 
 turns upon a vertical one. But the means available 
 
LIFT DRAW BRIDGES. 345 
 
 for applying the counterpoise are far less convenient, 
 being usually the action of weights over sheaves, and, 
 the resistance constantly diminishing as the bridge 
 rises, it requires a complicated arrangement to graduate 
 the action of the counterpoise to an equality with the 
 resistance at all stages of the movement. Still, the 
 thing may be practicable, were the object of sufficient 
 utility to warrant the undertaking. For instance, the 
 counterpoise may be permanently attached to the draw 
 in such position as to bring the common centre of 
 gravity in the line of the axis of motion ; when the 
 only resistance would be the friction of the journals at 
 the hinge joint. Again, a counterpoise acting upon a 
 windlass might raise the draw by chains winding upon 
 a fusee, with radius increasing as resistance diminishes. 
 Or, weight might be mounted upon wheels, and run 
 down upon a curved incline, so adjusted as to diminish 
 its action to an equality with the resistance at the dif 
 ferent stages. 
 
 But none of these devices are suitable for effecting 
 more than very small openings, and are not likely to 
 be often adopted. They will therefore be passed by 
 with a mere allusion. 
 
 Lift bridges have also been constructed to open in 
 the middle and lift both ways. By this means wider 
 openings may be effected. 
 
 But, as the middle portion of the bridge and passing 
 loads must be sustained by the lifting chains, this plan 
 is not well adapted to any but light traffic. Such a 
 structure over the Albany Basin broke down many 
 years ago with fatal results. Perhaps, however, the 
 catastrophe resulted rather from the imperfect condi 
 tion or faulty construction of the bridge, than from in 
 herent defects of the general plan. 
 44 
 
346 BRIDGE BUILDING. 
 
 Still, this can hardly be classed as among the availa 
 ble plans of draw-bridge construction in the present 
 state of advancement in civil engineering. 
 
 Finally, unless some advantage can be derived from 
 the use of the Whipple Patent Lift Drawbridge, which 
 is now about to be described, we may fairly conclude 
 that Lift Draw-bridges, like retractile ones, are to be 
 regarded as practically obsolete. 
 
 CLXXXII. In the case of artificial navigation by 
 horse power, where only head room of 10 or 12 feet is 
 required, and where convenience requires the grade 
 upon which the land traffic is carried on to be but little 
 above the water surface, it is only necessary to effect 
 a vertical movement of a few feet, to afford the re 
 quisite head room. And to meet such cases, a plan 
 has lately been devised by myself, for which Letters 
 Patent of the U. S. have been granted. 
 
 WHIPPLE S PATENT LIFT DRAW BRIDGE. 
 
 This plan is, to construct over the navigable channel, 
 stationary trusses (with the necessary struts, stays and 
 braces, at the ends and upper chords, to secure per- 
 manance and steadiness laterally), upon corner posts or 
 towers (a, Fig. 75) of stone, wood or iron, high enough 
 to allow the required head room for navigation under 
 the truss chords; the towers having sufficient width 
 of base, or other provision to ensure stability. To 
 the parts thus prepared, instead of a stationary travel- 
 way, a movable way, cradle, or track, 6, (extending to 
 the edge of the towing path J), is adapted by means of 
 the suspension rods r, to the upper ends of which, 
 
347 
 
 t 
 
 ? 3 
 
 5" | 
 
348 BRIDGE BUILDING. 
 
 near the lower chords, are/connected the chains or 
 ropes c, passing over the sheaves or pulleys e, and con 
 necting with counterpoise weights iv, extending over 
 the whole length of cradle, and so adjusted as to just 
 balance the weight of cradle. 
 
 The rods r, except those near the abutment, pass 
 vertically through the connecting blocks of the truss 
 chords, and screw into cap pieces which are imme 
 diately above, and rest upon said blocks, when the 
 cradle is down, and serve to prevent the cradle from 
 descending below its proper level, and to sustain the 
 weight of transient loads without additional stress 
 upon the chains or pulleys. 
 
 The cap-piece is furnished with a loop, or a socket, 
 as may be required, for the connection of the chain or 
 wire rope <?, passing up inside of the hollow truss 
 post standing upon the connecting block; the post 
 having a slot, or opening near the upper end upon the 
 inner side, to receive a segment of the sheave reaching 
 the centre of the post. 
 
 The sheaves, except the endmost on the left (in the 
 diagram), are about 3 feet in diameter, and made fast 
 upon longitudinal line shafts I, one on each side of 
 the bridge, hung in composition journal boxes, one 
 upon each side of each sheave, suspended from cross 
 beams h. The sheave next the end of truss, is about 
 6 inches less in diameter than the others, and thrown 
 inward to avoid interference with the diagonal rods of 
 the truss. 
 
 Upon each line shaft near the centre, is a bevel gear 
 wheel #, about 3 feet in diameter, into which works a 
 pinion upon either end of the transverse shaft /, to 
 which (shaft) the power is applied for raising and 
 
LIFT DRAW BRIDGES. 849 
 
 lowering the cradle 6; and, it will be seen that on 
 such application of power sufficient to overcome the 
 friction of the working parts, the cradle being exactly 
 balanced by the weights w, the two line shafts, with 
 the sheaves upon them respectively, must revolve uni 
 formly, carrying the ropes along in the grooves of the 
 sheaves, and raising or lowering all parts of the cradle 
 uniformly, while the balance weights w, move in the 
 opposite direction. 
 
 It is therefore only necessary to reverse the motion 
 of the shaft/, to move the cradle up and down alter 
 nately as often as required. 
 
 The sheaves not connected with the line shafts, move 
 with the others, the cradle being stiff enough to over 
 come the small resistance at those points, since the 
 endmost sheaves sustain only half as much weight as 
 the intermediates. 
 
 Working loose upon the shaft/, is the large gear 
 wheel n, attatched to the winding drum m, and carry 
 ing a reversible spring catch (not shown) which plays 
 into the teeth of the ratchet wheel o, made fast on the 
 shaft/. Then, by applying power to the wheel 7?, 
 with the catch in the proper position, a line is made 
 to wind upon the drum m, (in either direction, as re 
 quired) so as to raise a power weighty, capable by its 
 descent, of raising or lowering the cradle through the 
 required space in a few seconds of time. The line 
 raising the weight p, is carried from the drum m, by 
 means of sheaves s, to any convenient position. 
 
 One movement of the cradle being effected, the 
 catch is reversed, the weight p is immediately wound 
 up in the opposite direction, and retained by a catch 
 or bolt until the draw requires another movement. 
 Then, the weight is disengaged, and the movement 
 
350 BRIDGE BUILDING. 
 
 effected in the least admissible time. Ten seconds, 
 with a properly adjusted power weight, is estimated to 
 be sufficient for a movement of the cradle through a 
 space of 12 feet, while the winding up of the weight 
 may require two or three minutes labor of a man. The 
 operator is thus enabled to condense the labor of 
 several minutes into only a few seconds. 
 
 It is proposed to give the power weight twice the 
 force necessary to overcome the friction, allowing one- 
 half to overcome inertia, and act as an accelerating 
 force ; the weight being made to run down and be 
 arrested when half the movement has been effected, 
 leaving the acquired momentum to be destroyed by 
 the friction during the other half of the movement. 
 Thus the motion will stop at the right time without 
 concussive shock. 
 
 The wheel n, to which the winding power is applied,, 
 may be a bevel gear wheel driven by a pinion upon the 
 vertical shaft of a tread-wheel or a sweep-lever, or a 
 spur gear wheel impelled by a pinion upon a horizon 
 tal counter-shaft ; and this also furnished with a large 
 gear wheel to be driven by a pinion upon a third shaft 
 furnished with a hand crank; thus reducing the 
 power to be applied to tne crank to any required de 
 gree. Further detail is not deemod necessary on this 
 occasion. The plan is expected soon to be subjected 
 to a practical test of its capabilities. 
 
 The advantages promised by the adoption of this 
 device, in the situations admitting of its use, are, first, 
 it is more cheaply constructed than a swing bridge of 
 like span. Second, it requires no more space for ita 
 operation than a stationary bridge, while the swing 
 draw requires several times as much. Third, its move 
 ment is effected in a fraction of the time required by 
 
LIFT DRAW BRIDGES. 351 
 
 any other draw bridge, whence It occasions less inter 
 ruption to the traffic over and beneath it. This last 
 advantage results from the fact that there is not more 
 than one-third as much weight to be put in motion, 
 and that is required to move over little if any more 
 than one quarter (say f ) of the space of the average 
 movement of the material of a swing draw of the same 
 spun. Hence, the inertia to be overcome in starting 
 and stopping the latter, is much greater than in case 
 of the former. For, the resistance of inertia being as 
 the mass into the square of the velocity to be commu 
 nicated in a given time, to give to thrice the mass, 3J 
 times the velocity, as required to shift these draws re 
 spectively in the same time, would give a resistance of 
 inertia more than 36 times as great in one case as in 
 the other, and require 36 times as much power to 
 generate the velocity in the given time. But an ac 
 celerating force equal to the friction, acting through 
 half the time of the movement, generates a momentum 
 in the lift draw, sufficient to overcome the friction for 
 the other half; and, the friction of the swing draw 
 being little if any greater for the whole movement 
 than that of the lift draw, it would only destroy J 8 part 
 of the momentum generated in the swing draw during 
 the first half of the movement, by a force capable of 
 producing that movement in the same time required 
 by the lift draw. The other || of the acquired 
 momentum must be destroyed without useful effect, 
 in order to avoid severe concussion at the stopping 
 point, while in the other case the whole acquired mo 
 mentum may be utilized in overcoming necessary 
 friction, so that no power need be wasted. Therefore, 
 without extending this discussion, already, perhaps, 
 carried too far, it may safely be pronounced practically 
 
352 . BRIDGE BUILDING. 
 
 impossible to effect the movement of the swing draw, 
 in the time in which that of the lift draw may be ac 
 complished. 
 
 After all, practical test is generally the only satisfac 
 tory means of determining the value and utility of any 
 mechanical device. 
 
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 Royal 8vo, 664 pp. Cloth. $12.50. 
 
 THE THEOKY OF STRAINS IN GIRDERS and Similar Strae- 
 tures, with Observations on the Application of Theory to Practice, 
 and Tables of Strength and other Properties of Materials. By 
 BINDON B. STONEY, B. A. 
 
 Roebling s Bridges. 
 
 Imperial folio. Cloth. $25.00. 
 
 LONG AND SHORT SPAN RAILWAY BRIDGES. By JOHW 
 A. ROEBLING, C. E. Illustrated with large copperplate engrav 
 ings of plans and views. 
 
 List of Plates 
 
 1. Parabolic Truss Railway Bridge. 2, 3, 4, 5, 6. Details of Parabolic 
 Truss, with centre span 500 feet in the clear. 7. Plan and View of a Bridge 
 over the Mississippi River, at St. Louis, for railway and common travel. 8, 9, 
 10, 11, 12. Details and View of St. Louis Bridge. 13. Railroad Bridge over 
 the Ohio. 
 
 Diedrichs Theory of Strains. 
 
 8vo. Cloth. $5.00. 
 
 A Compendium for the Calculation and Construction of Bridges, 
 Roofs, and Cranes, with the Application of Trigonometrical 
 Notes. Containing the most comprehensive information in re 
 gard to the Resulting Strains for a permanent Load, as also for 
 a combined (Permanent and Rolling) Load. In two sections 
 adapted to the requirements of the present time. By JOHN Dim>- 
 KICHS. Illustrated by numerous plates and diagrams. 
 
 " The want of a compact, universal and popular treatise on the Construc 
 tion of Roofs and Bridges especially one treating of the influence of a varia 
 ble load and the unsatisfactory essays of different authors on the subject, 
 induced me to prepare this work." 
 
D. VAN NOSTRAND. 
 
 Whilden s Strength, of Materials, 
 
 12ra<x Cloth. $2,00, 
 
 ON THE. STRENGTH OF MATERIALS used in Engineering 
 Construction. By J. K. WHILDEN, 
 
 C ampin on Iron Roofs. 
 
 Large 8vo. Cloth. $2,00. 
 
 ON THE CONSTRUCTION OF IRON ROOFS. A Theoretical 
 and Practical Treatise. By FEAXCIS CAMPIN. With wood-cuts 
 and plates of Roofs lately executed. 
 
 " The mathematical formulas are of an elementary kind, and the process 
 admits of an easy extension so as to embrace the prominent varieties of iron, 
 truss bridges. The treatise, though of a practical scientific character, may be 
 easily mastered by any one familiar with elementary mechanics and plane 
 trigonometry." 
 
 Holley s Railway Practice. 
 
 1 voL folio. Cloth. $12.00. 
 
 AMERICAN AND EUROPEAN RAILWAY PRACTICE, in 
 
 the Economical Generation of Steam, including the materials 
 and construction of Coal-burning Boilers, Combustion, the Varia 
 ble Blast, Vaporization, Circulation, Super-heating, Supplying 
 and Heating Feed- water, &c., and the adaptation of Wood and 
 Coke-burning Engines to Coal-burning ; and in Permanent Way, 
 including Road-bed, Sleepers, Rails, Joint Fastenings, Street 
 Railways, &c., &c. By ALEXANDER L. HOLLEY, B. P. With 77 
 lithographed plates. 
 
 " This is an elaborate treatise by one of our ablest civil engineers, on the con 
 struction and use of locomotives, with a few chapters on the building of Rail 
 roads. * * * All these subjects are treated by the author, who is a 
 first-class railroad engineer, in both an intelligent and intelligible manner. The 
 facts and ideas are well arranged, and presented in a clear and simple style, 
 accompanied by beautiful engravings, and we presume the work will be regard 
 ed as indispensable by all who are interested in a knowledge of the construc 
 tion of railroads and rolling stock, or the working of locomotives." Scientific 
 American. 
 
8 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Henrici s Skeleton Structures. 
 
 8vo. Cloth. $1.50. 
 
 SKELETON STEUCTUEES, especially in their Application to 
 the building of Steel and Iron Bridges. By OLAUS HEXRICI. 
 With folding plates and diagrams. 
 
 By presenting these general examinations on Skeleton Structures, with 
 particular application for Suspended Bridges, to Engineers, I venture to ex 
 press the hope that they will receive these theoretical results with some confi 
 dence, even although an opportunity is wanting to compare them with practi 
 cal results. 0. H. 
 
 Useful Information for Railway Men. 
 
 Pocket form. Morocco, gilt, $2.00. 
 
 Compiled by W. Gr. HAMILTON, Engineer. Fifth edition, revised 
 and enlarged. 570 pages. 
 
 " It embodies many valuable formulae and recipes useful for railway men, 
 and, indeed, for almost every class of persons in the world. The informa 
 tion comprises some valuable formulae and rules for the construction of 
 boilers and engines, masonry, properties of steel and iron, and the strength 
 of materials generally." Railroad Gazette, Chicago. 
 
 Brooklyn Water Works. 
 
 1 vol. folio. Cloth. $25.00. 
 
 A DESCEIPTIVE ACCOUNT OF THE CONSTEUCTION OF 
 THE WOEKS, and also Eeports on the Brooklyn, Hartford, 
 Belleville, and Cambridge Pumping Engines. Prepared and 
 printed by order of the Board of Water Commissioners. With 
 59 illustrations. 
 
 CONTENTS. Supply Ponds The Conduit -Ridgewood Engine House and 
 Pump Well Ridgewood Engines Force Mains Ridgewood Reservoir 
 Pipe Distribution Mount Prospect Reservoir Mount Prospect Engine 
 House and Engine Drainage Grounds Sewerage "Works Appendix. 
 
D. VAN XOSTRAND. 
 
 Kirkwood on Filtration. 
 
 4to. Cloth. $15.00. 
 
 REPORT ON THE FILTRATION OF EIVER WATERS, for 
 
 the Supply of Cities, as practised in Europe, made to the Board 
 of Water Commissioners of the City of St. Louis. By JAMES P. 
 KIRKWOOD. Illustrated by 30 double-plate engravings. 
 
 CONTENTS. Report on Filtration London Works, General Chelsea 
 Water Works and Filters Lambeth Water Works and Filters Southwark 
 and Vauxhull Water Works and Filters Grand Junction Water Works and 
 Filters West Middlesex Water Works and Filters New River Water 
 Works and Filters East London Water Works and Filters Leicester Water 
 Works and Filters York Water Works and Filters Liverpool Water Works 
 and Filters Edinburgh Water Works and Filters Dublin Water Works 
 and Filters Perth Water Works and Filtering- Gallery Berlin Water 
 Works and Filters Hamburg Water Works and Reservoirs Altona Water 
 Works and Filters Tours Water Works and Filtering Canal Angers Water 
 Works and Filtering Galleries Nantes Water Works and Filters Lyons 
 Water Works and Filtering Galleries Toulouse Water Works and Filtering 
 Galleries Marseilles Water Works and Filters Genoa Water Works and 
 Filtering Galleries Leghorn Water Works and Cisterns Wakefield Water 
 Works and Filters Appendix. 
 
 Tnnner on Roll-Turning. 
 
 1 vol. 8vo. and 1 vol. plates. $10.00. 
 
 A TREATISE ON ROLL-TURNING FOR THE MANUFAC 
 TURE OF IRON. By PETER TUNNER. Translated and adapted. 
 By JOHN B. PEARSE, of the Pennsylvania Steel Works. With 
 numerous wood-cuts, 8vo., together with a folio atlas of 10 litho 
 graphed plates of Rolls, Measurements, &c. 
 
 " We commend this book as a clear, elaborate, and practical treatise upon 
 the department of iron manufacturing operations to which it is devoted. 
 The writer states in his preface, that for twenty-five years he has felt the 
 necessity of such a work, and has evidently brought to its preparation the 
 fruits of experience, a painstaking regard for accuracy of statement, and a 
 desire to furnish information in a style readily understood. The book should 
 be in the hands of every one interested, either in the general practice of 
 mechanical engineering, or the special branch of manufacturing operations to 
 which the work relates. American Artisan. 
 
10 SCIENTIFIC BOOKS PUBLISHED BY 
 
 G-lynn on the Power of Water. 
 
 12mo. Cloth. $1.00. 
 
 A TREATISE ON THE POWER OF WATER, as applied to 
 drive Flour Mills, and to give motion to Turbines and other 
 Hydrostatic Engines. By JOSEPH GLYNN, F.R. S. Third edition, 
 revised and enlarged, with numerous illustrations. 
 
 Hewson on Embankments. 
 
 Svo. Cloth. $2.00. 
 
 PRINCIPLES AND PRACTICE OF EMBANKING LANDS 
 
 from River Floods, as applied to the Levees of the Mississippi. 
 By WILLIAM HEWSON, Civil Engineer. 
 
 " This is a valuable treatise on the principles and practice of embanking 
 lands from river floods, as applied to the Levees of the Mississippi, by a highly 
 intelligent and experienced engineer. The author says it is a first attempt 
 to reduce to order and to rule the design, execution, and measurement of the 
 Levees of the Mississippi. It is a most useful and needed contribution to 
 scientific literature. Philadelphia Evening Journal. 
 
 G-riiner on Steel. 
 
 8vo. Cloth. $3.50. 
 
 THE MANUFACTURE OF STEEL. By M. L. GRFNEII, trans 
 lated from the French. By Lenox Smith, A. M., E. M., with an 
 appendix on the Bessemer Process in the United States, by the 
 translator. Illustrated by lithographed drawings and wood-cuts. 
 
 " The purpose of the work is to present a careful, elaborate, and at the 
 same time practical examination into the physical properties of steel, as well 
 as a description of the new processes and mechanical appliances for its manufac 
 ture. The information which it contains, gathered from many trustworthy 
 sources, will be found of much value to the American steel manufacturer, 
 who may thus acquaint himself with the results of careful and elaborate ex 
 periments in other countries, and better prepare himself for successful com 
 petition in this important industry with foreign makers. The fact that this 
 volume i.s from the pen of one of the ablest metallurgists of the present day, 
 cannot fail, we think, to secure for it a favorable consideration. Iron Age. 
 
D. VAN NOSTRAND. 11 
 
 Bauerman on Iron. 
 
 12mo. Cloth. $3.00. 
 
 TEEATISE ON THE METALLURGY OF IEON. Contain 
 ing outlines of the History of Iron Manufacture, methods of 
 Assay, and analysis of Iron Ores, processes of manufacture of 
 Iron and Steel, etc., etc. By H. BATTEEMA.N. First American 
 edition. Revised and enlarged, with an appendix on the Martin 
 Process for making Steel, from the report of Abrani S. Hewitt. 
 Illustrated with numerous wood engravings. 
 
 " This is an important addition to the stock of technical works published in 
 this country. It embodies the latest facts, discoveries, and processes con 
 nected with the manufacture of iron and steel, and should be in the hands of 
 every person interested in the subject, as well as in all technical and scientific 
 libraries." Scientific A merican. 
 
 Link and Valve Motions, by W. S. 
 Auchincloss. 
 
 8vo. Cloth. $3.00. 
 
 APPLICATION OF THE SLIDE VALVE and Link Motion to 
 Stationary, Portable, Locomotive and Marine Engines, with netv 
 and simple methods for proportioning the parts. By WILLIAM 
 S. AUCHINCLOSS, Civil and Mechanical Engineer. Designed as 
 a hand-book for Mechanical Engineers, Master Mechanics, 
 Draughtsmen and Students of Steam Engineering. All dimen 
 sions of the valve are found with the greatest ease by means of 
 a Printed Scale, and proportions of the link determined without 
 the assistance of a model. Illustrated by 37 wood-cuts and 21 
 lithographic plates, together with a copperplate engraving of the 
 Travel Soale. 
 
 All the matters we have mentioned are treated with a clearness and absence 
 of unnecessary verbiage which renders the work a peculiarly valuable one. 
 The Travel Scale only requires. to be known to bo appreciated. Mr. A. writes 
 so ably on his subject, we wish he had written more. London En 
 gineering. 
 
 We have never opened a work relating to steam which seemed to us better 
 calculated to give an intelligent mind a clear understanding of the depart 
 ment it discusses. Scientific American. 
 
12 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Slide Valve by Eccentrics, by Prof. 
 C, W. MacCord. 
 
 4to. Illustrated. Cloth, $4.00. 
 
 A PRACTICAL TREATISE ON TH SLIDE VALVE BY 
 
 ECCENTRICS, examining by methods, the action of the Eccen 
 tric upon the Slide Valve, and explaining the practical proces 
 ses of laying out the movements, adapting the valve for its 
 various duties in the steam-engine. For the use of Engineers, 
 Draughtsmen, Machinists, and Students of valve motions in 
 general. By C. "W. MACCORD, A. M., Professor of Mechanical 
 Drawing, Stevens Institute of Technology, Hoboken, N J. 
 
 Stillman s Steam-Engine Indicator. 
 
 12mo. Cloth. $1.00. 
 
 THE STEAM-ENGINE INDICATOR, and the Improved Mano 
 meter Steam arid Vacuum Gauges ; their utility and application 
 By PAUL STILLMAN. New edition. 
 
 Bacon s Steam-Engine Indicator. 
 
 12mo. Cloth. $1.00. Mor. $1.50. 
 
 A TREATISE ON THE RICHARDS STEAM-ENGINE IN 
 DICATOR, with directions for its use. By CHARLES T. PORTER. 
 Revised, with notes and large additions as developed by Amer 
 ican Practice, with an Appendix containing useful formula) and 
 rules for Engineers. By F. W. BACON, M. E., Member of the 
 American Society of Civil Engineers. Illustrated. Second Edition 
 
 In this work. Mr. Porter s book has been taken as the basis, but Mr. Bacon 
 has adapted it to American Practice, and has conferred a great boon on 
 American Engineers. Artisan. 
 
 Bartol on Marine Boilers. 
 
 8vo. Cloth. $1.50. 
 
 TREATISE ON THE MARINE BOILERS OF THE UNITED 
 STATES. By H. B. BARTOL. Illustrated. 
 
D. VAN NOSTRAND. 13 
 
 Gillmore s Limes and Cements. 
 
 Fourth Edition. Revised and Enlargd. 
 
 8vo. Cloth. $4.00. 
 
 PRACTICAL TREATISE ON LIMES, HYDRAULIC CE 
 MENTS, AND MORTARS. Papers on Practical Engineering, 
 
 , U. S. Engineer Department, No. 9, containing Reports of 
 numerous experiments conducted in New York City, during the 
 years 1858 to 1861, inclusive. By Q. A. GILLMORE, Brig-General 
 U. S. Volunteers, and Major U. S. Corps of Engineers. With 
 numerous illustrations. 
 
 " This work contains a record of certain experiments and researches made, 
 under the authority of the Engineer Bureau of the "War Department from 
 1858 to 1861, upon the various hydraulic cements of the United States, and 
 the materials for their manufacture. The experiments were carefully made, 
 and are well reported and compiled. Journal Franklin Institute. 
 
 Gillmore s Ooignet Beton. 
 
 8vo. Cloth. $2.50. 
 
 COIGNET BETON AND OTHER ARTIFICIAL STONE. By 
 Q. A. GILLMORE. 9 Plates, Views, etc. 
 
 This work describes with considerable minuteness of detail the several kinds 
 of artificial stone in most general use in Europe and now beginning to be 
 introduced in the United States, discusses their properties, relative merits, 
 and cost, and describes the materials of which they are composed. .... 
 The subject is one of special and growing interest, and wo commend the work, 
 embodying as it does the matured opinions of an experienced engineer and 
 expert. 
 
 Williamson s Practical Tables. 
 
 : 4to. Flexible Cloth. $2.50. 
 
 PRACTICAL TABLES IN METEOROLOGY AND HYPSO- 
 METRY, in connection with the use of the Barometer. By Col. 
 R. S. WILLIAMSOM, U. S. A. 
 
14 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Williamson on the Barometer. 
 
 4to. Cloth. $15.00. 
 
 ON THE USE OF THE BAROMETER ON SURVEYS AND 
 RECONNAISSANCES. Part I. Meteorology in its Connec 
 tion with Hypsometry. Part II.. Barometric Hypsometry. By 
 R. S. WILLIAMSON, Bvt. Lieut-Col. U. S. A., Major Corps of 
 Engineers. With Illustrative Tables and Engravings. Paper 1 
 No. 15, Professional Papers, Corps of Engineers. 
 
 " SAN FRANCISCO, CAL., Feb. 27, 1867. 
 " Gen. A. A. HUMPHREYS, Chief of Engineers, U. S. Army : 
 
 " GENERAL, I nave the honor to submit to you, in the following pages, the 
 results of my investigations in meteorology and hypsometry, made -with the 
 view of ascertaining how far the barometer can be used as a reliable instru 
 ment for determining altitudes on extended lines of survey and reconnais 
 sances. These investigations have occupied the leisure permitted roe from my 
 professional duties during the last ten years, and I hope the results will be 
 deemed of sufficient value to have a place assigned them among the printed 
 professional papers of the United States Corps of Engineers. 
 " Very respectfully, your obedient servant, 
 
 "R. S. WILLIAMSON, 
 " Bvt. Lt.-Col. U. S. A., Major Corps of U. S. Engineers." 
 
 Yon Cotta s Ore Deposits. 
 
 8vo. Cloth. $4.00. 
 
 TREATISE ON OEE DEPOSITS. By BERNHARD Vox GOTTA, 
 Professor of Geology in the Royal School of Mines, Freidberg, 
 Saxony. Translated from the second German edition, by 
 FREDERICK PRIME, Jr., Mining Engineer, and revised by the 
 author, with numerous illustrations. 
 
 " Prof. Von Cotta of the Freiberg School of Mines, is the author of the 
 best modern treatise on ore deposits, and we are heartily glad that this ad 
 mirable \vork has been translated and published in this country. The trans 
 lator, Mr. Frederick Prime, Jr., a graduate of Freiberg, has had in his work 
 the great advantage of a revision by the author himself, who declares in a 
 prefatory note that this may be considered as a new edition (the third, of his 
 own book. 
 
 " It is a timely and welcome contribution to the literature of mining in 
 this country, and we are grateful to the translator for his enterprise and good 
 judgment in undertaking its preparation ; while we recognize with equal cor 
 diality the liberality of the author in granting both permission and assist- 
 aace." Extract from Review in Engineering and Mining Journal. 
 
7>. VAN NO STRAND. 15 
 
 Plattner s Blow-Pipe Analysis. 
 
 Second edition. Revised. 8vo. Cloth. $7.50. 
 
 PLATTNER S MANUAL OF QUALITATIVE AND QUAN 
 TITATIVE ANALYSIS WITH THE BLOW-PIPE. Prom 
 the last German edition Revised and enlarged. By Prof. TH. 
 RICHTER, of the Royal Saxon Mining Academy. Translated by 
 Prof. II. B. CORNWALL, Assistant in the Columbia School of 
 Mines, New York ; assisted by JOHN H. CASWELL. Illustrated 
 with eighty-seven wood-cuts and one Lithographic Plate. 560 
 pages. 
 
 " Plattner s celebrated work has long been recognized as the only complete 
 book on Blow-Pipe Analysis. The fourth German edition, edited by Prof. 
 Kichter, fully sustains the reputation which the earlier editions acquired dur 
 ing the lifetime of the author, and it is a source of great satisfaction to us to 
 know that Prof. Kichter has co-operated with the translator in issuing the 
 American edition of the work, which is in fact a fifth edition of the original 
 work, being far more complete than the last German edition." SillimarSs 
 Journal. 
 
 There is nothing so complete to be found in the English language. Platt 
 ner s book is not a mere pocket edition ; it is ivitended as a comprehensive guide 
 to all that is at present known on the blow-pipe, and as such is really indis 
 pensable to teachers and advanced pupils. 
 
 " Mr. Cornwall s edition is something more than a translation, as it contains 
 many corrections, emendations and additions not to be found in the original. 
 It is a decided improvement on the work in it* German dress." Journal of 
 Applied Chemistry. 
 
 Egleston s Mineralogy. 
 
 8rq. Illustrated with 34 Lithographic Plates. Cloth. $4.50. 
 
 LECTUEES ON DESCRIPTIVE MINERALOGY, Delivered 
 at the School of Mines, Columbia College. 13 r PIIOFESSOJJ T. 
 EGLESTON. 
 
 These lectures are what their title indicates, the lectures on Mineralogy 
 delivered at the School of Minca of Columbia College. They have beea 
 printed for the students, in order that more time might be given to the vari 
 ous methods of examining and determining minerals. The second part has 
 only been printed. The first part, comprising crystallography and physical 
 mineralogy, will be printed at some future time. 
 
16 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Pynchon s Chemical Physics. 
 
 New Edition. Revised and Enlarged. 
 
 Crown 8vo. Cloth. 
 
 INTRODUCTION TO CHEMICAL PHYSICS, Designed for the 
 Use of Academies, Colleges, and High Schools. Illustrated with 
 numerous engravings, and containing copious experiments with 
 directions for preparing them. By THOMAS RUGGLES PYNCHON, 
 M. A., Professor of Chemistry and the Natural Sciences, Trinity 
 College, Hartford. 
 
 Hitherto, no work suitable for general use, treating of all these subjects 
 within the limits of a single volume, could be found ; consequently ths atten 
 tion they have received has not been at all proportionate to their importance. 
 It is believed that a book containing so much valuable information within so 
 small a compass, cannot fail to meet with a ready sale among ail intelligent 
 persons, while Professional men, Physicians, Medical Students, Photograph 
 ers, Telegraphers, Engineers, and Artisans generally, will find it specially 
 valuable, if not nearly indispensable, as a book of reference. 
 
 " We strongly recommend this able treatise to our readers as the first 
 work ever published on the subject free from perplexing technicalities. In 
 style it is pure, in description graphic, and its typographical appearance is 
 artistic. It is altogether a most excellent work." Eclectic Medical Journal. 
 
 " It treats fully of Photography, Telegraphy, Steam Engines, and the 
 various applications of Electricity. In short, it is a carefully prepared 
 volume, abreast with the latest scientific discoveries and inventions. Hart 
 ford Courant. 
 
 Plympton s Blow-Pipe Analysis. 
 
 12mo. Cloth. $2.00. 
 
 THE BLOW-PIPE : A System of Instruction in its practical use 
 being a graduated course of Analysis for the use of students, 
 and all those engaged in the Examination of Metallic Combina 
 tions. Second edition, with an appendix and a copious index. 
 By GEORGE "W- PLYMPTON, of the Polytechnic Institute, Brooklyn. 
 
 " This mamial probably has no superior in the English language as a text 
 book for beginners, or as a guide to the student working without a teacher. 
 To the latter many illustrations of the utensils and apparatus required in 
 using the blow-pipe, as well as the fully illustrated description of the blow 
 pipe flame, will be especially serviceable." New York Teaclwr. 
 
. VAN JFOSTRAJSTD. 
 
 lire s Dictionary. 
 
 Sixth Edition. 
 
 London, 1872. 
 3 vols. 8vo. Cloth, $25.00. Half Russia, $32.50. 
 
 DICTTONAEY OF AETS, MANUFACTURES, AND MINES. 
 By ANDREW URE, M.D. Sixth edition. Edited by BOBERT HUNT, 
 F.E.S., greatly enlarged and rewritten. 
 
 Brande and Cox s Dictionary. 
 
 Neiv Edition. 
 
 London, 1872. 
 3 rols. 8vo. Cloth, $20.00. Half Morocco, $27.50. 
 
 A Dictionary of Science, Literature, and Art. Edited by \V. T. 
 BRANDE and Eev. GEO. W. Cox. New and enlarged edition. 
 
 Watt s Dictionary of Chemistry. 
 
 Supplementary Volume. 
 
 8vo. Cloth. $9.00. . 
 
 This volume brings the Record of Chemical Discovery down to the end of 
 the year 1869, including also several additions to, and corrections of, former 
 results which have appeared in 1870 and 1871. 
 
 * # * Complete Sets of the Work, New and Revised edition, including- above 
 supplement C vols. 8vo. Cloth. $62.00. 
 
 Rammelsberg s Chemical Analysis. 
 
 8vo. Cloth. $2.25. 
 
 GUIDE TO A COUESE OF QUANTITATIVE CHEMICAL 
 ANALYSIS, ESPECIALLY OF MINERALS AND FUR 
 NACE PEODUCTS. Illustrated by Examples. By C. F. 
 Translated by J. TOWLER, M.D. 
 
 This work has been translated, and is now published expressly for those 
 students in chemistry whose time and other studies in colleges do not permit 
 them to enter "upon the more elaborate and expensive treatises of Fresenius 
 and others. It is the condensed labor of a master in chemistry and of a prac 
 tical analyst. 
 
18 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Eliot and Storer s Qualitative 
 Chemical Analysis. 
 
 New Edition, Revised. 
 
 12mo. Illustrated. Cloth. $1.50. 
 
 A COMPENDIOUS MANUAL OF QUALITATIVE CHEMI 
 CAL ANALYSIS. By CHARLES W. ELIOT and FRA^K H. STORER. 
 Revised with the Cooperation of the Authors, by WILLIAM RIP- 
 LEY NICHOLS, Professor of Chemistry in the Massachusetts Insti 
 tute of Technology. 
 
 " This Manual has great merits as a practical introduction to the science 
 and the art of which it treats. It contains enough of the theory and practice 
 of qualitative analysis, " in the wet way," to bring- out all the reasoning in 
 volved in the science, and to present clearly to the student the most approved 
 methods of the art. It is specially adapted for exercises and experiments in 
 the laboratory; and yet its classifications and manner of treatment are so 
 systematic and logical throughout, as to adapt it in a high degree to that 
 higher class of students generally who desire an accurate knowledge of the 
 practical methods of arriving at scientific facts." Lutfieran Observer. 
 
 " We wish every academical class in the land could have the benefit of the 
 fifty exercises of two hours each necessary to master this book. Chemistry 
 would cease to be a mere matter of memory, and become a pleasant experi 
 mental and intellectual recreation. We heartily commend this little volume 
 to the notice of those teachers who believe in using the sciences as means of 
 mental discipline." College Courant. 
 
 Craig s Decimal System. 
 
 Square 32mo. Limp. 50c. 
 
 WEIGHTS AND MEASURES. An Account of the Decimal 
 System, with Tables of Conversion for Commercial and Scientific 
 Uses. By B. F. CRAIG, M. D. 
 
 " The most lucid, accurate, and useful of all the hand-books on this subject 
 that we have yet seen. It gives forty-seven tables of comparison between the 
 English and French denominations of length, area, capacity, weight, and the 
 Centigrade and Fahrenheit thermometers, with clear instructions how to use 
 them ; and to this practical portion, which helps to make the transition as 
 easy as possible, is prefixed a scientific explanation of the errors in the metric 
 system, and how they may be corrected in the laboratory." Nation. 
 
D. VAN NOSTRAND. 19 
 
 Nugent on Optics. 
 
 12mo. Cloth, $2:00 
 
 TREATISE ON OPTICS ; or, Light and Sight, theoretically and 
 practically treated ; with the application to Fine Art and Indus 
 trial Pursuits. By E. NUGENT. With one hundred and three 
 illustrations. 
 
 " This book is of a practical rather than a theoretical kind, and is de 
 signed to afford accurate and complete information to all interested in appli 
 cations of the science." Hound Table. 
 
 Barnard s Metric System. 
 
 8vo. Brown cloth. $3.00. 
 
 THE METRIC SYSTEM OF WEIGHTS AND MEASURES. 
 
 An Address delivered before the .Convocation of the University of 
 the State of New York, at Albany, August, 1871. By FREDERICK 
 A. P. BARNARD, President of Columbia College, New York City. 
 Second edition from the Revised edition printed for the Trustees 
 of Columbia College. Tinted paper. 
 
 * It is the best summary of the arguments in favor of the metric weights 
 and measures with which we are acquainted, not only because it contains in 
 small space the leading facts of the case, but because it puts the advocacy of 
 that system on the only tenable grounds, namely, the great convenience of a 
 decimal notation of weight and measure as well as money, the value of inter 
 national uniformity in the matter, and the fact that this metric system is 
 adopted and hi general use by the majority of civilized nations." Tlie Nation* 
 
 The Young Mechanic. 
 
 Illustrated. 12mo. Cloth. $1.75. 
 
 THE YOUNG MECHANIC. Containing directions for the use 
 of all kinds of tools, and for the construction of steam engines 
 and mechanical models, including the Art of Turning in Wood 
 and Metal. By the author of "The Lathe and its Uses," etc 
 From the English edition, with corrections. 
 
20 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Harrison s Mechanic s Tool-Book. 
 
 12mo. Cloth. $1.50, 
 
 MECHANIC S TOOL BOOK, with practical rules and suggestions, 
 for the use of Machinists, Iron Workers, and others. By \V. B. 
 HARRISON, Associate Editor of the " American Artisan." Illustra 
 ted with 44 engravings. 
 
 " This work is specially adapted to meet the wants of Machinists and work 
 ers in iron generally. It is made up of the \rork-day experience of an intelli 
 gent and ingenious mechanic, who had the faculty of adapting tools to various 
 purposes. The practicability of his plans and suggestions are made apparent 
 even to the unpractised eye by a series of well-executed wood engravings." 
 Philadelphia Inquirer. 
 
 Pope s Modern Practice of the Elec 
 tric Telegraph. 
 
 Eighth Edition. 8vo. Cloth $2.00. 
 
 A Hand-book for Electricians and Operators. By FBANK L. POPS. 
 Seventh edition. Revised and enlarged, and fully illustrated. 
 
 Extract from Letter of Prof. Morse. 
 
 " I have had time only cursorily to examine its contents, but this examina 
 tion has resulted in great gratification, especially at the fairness and unpre 
 judiced tone of your whole work. 
 
 " Your illustrated diagrams are admirable and beautifully executed. 
 
 " I think all your instructions in the use of the telegraph apparatus judi 
 cious and correct, and I most cordially wish you success." 
 
 Extract from Letter of Prof. O. W. Hough, of the Dudley Observatory. 
 
 " There is no other work of this kind in the English language that con 
 tains in so small a compass so much practical information in the application 
 of galvanic electricity to telegraphy. It should be in the hands of every one 
 interested in telegraphy, or the use of Batteries for other purposes." 
 
 Morse s Telegraphic Apparatus. 
 
 Illustrated. 8vo. Cloth. $2.00. 
 
 EXAMINATION OF THE TELEGRAPHIC APPARATUS 
 AND THE PROCESSES IN TELEGAPHY. By SAMUEL F. 
 B. MOBSE, LL.D., United States Commissioner Paris Universal 
 Exposition, 1867. 
 
D, VAN tfOSTXAND. 21 
 
 Sabine s History of the Telegraph. 
 
 12mo. Cloth. $1.25. 
 
 HISTORY AND PROGRESS OF THE ELECTRIC TELE- 
 f GRAPH, with Descriptions of some of the Apparatus. By 
 ROBEBT SAJBINE, C. E. Second edition, with additions. 
 
 CONTENTS. I. Early Observations of Electrical Phenomena. II. Tele 
 graphs by Fractional Electricity. III. Telegraphs by Voltaic Electricity. 
 IV. Telegraphs by Electro-Magnetism and Magneto-Electricity. V. Tele 
 graphs now in use. VI. Overhead Lines. VII. Submarine Telegraph Lines. 
 VIII. Underground Telegraphs. IX. Atmospheric Electricity. 
 
 Haskins* Galvanometer, 
 
 Pocket form. Illustrated. Morocco tucks. $2.00. 
 
 THE GALVANOMETER, AND ITS USES; a Manual for 
 Electricians and Students. By 0. H. HASKINS. 
 
 " We hope this excellent little work will meet with the sale its merits 
 entitle it to. To every telegrapher who owns, or uses a Galvanometer, or 
 ever expects to, it will be quite indispensable." The Telegrapher. 
 
 Culley s Hand-Book of Telegraphy. 
 
 8vo. Cloth. $6.00. 
 
 A HAND-BOOK OF PRACTICAL TELEGRAPHY. By 
 R. S. CULLEY, Engineer to the Electric and International 
 Telegraph Company. Fifth edition, revised and enlarged. 
 
 -Fuivdl 8 f ioJJ r r Q a iljLxbf i j ; i 
 
 Foster s Submarine Blasting. 
 
 4to. Cloth. $3.50. 
 
 SUBMARINE BLASTING in Boston Harbor, Massachusetts- 
 Removal of Tower and Corwin Rocks. By JOHN G. FOSTEB, 
 Lieutenant-Colonel of Engineers, and Brevet Major- General, U. 
 S. Army. Illustrated with seven plates. 
 
 LIST OF PLATES. 1. Sketch of the Narrows, Boston Harbor. 2. 
 Townsend s Submarine Drilling Machine, and Working Vessel attending. 
 3. Submarine Drilling Machine employed. 4. Details of Drilling Machine 
 employed. 5. Cartridges and Tamping used. 6. Fuses and Insulated Wires 
 used. 7. Portable Friction Battery used. 
 
22 SCIENTIFIC BOOKS PUBLISHED BY 
 
 "X, 
 
 Barnes Submarine Warfare. 
 
 8. Cloth. $5.00. 
 
 SUBMARINE WARFARE, DEFENSIVE AND OFFENSIVE. 
 
 Comprising a full and complete History of the Invention of the 
 Torpedo, its employment in War and results of its use. De 
 scriptions of the yarious forms of Torpedoes, Submarine Batteries 
 and Torpeclo Boats actually used in War. Methods of Ignition 
 by Machinery, Contact Fuzes, and Electricity, and a full account 
 of experiments made to determine the Explosive Force of Gun 
 powder under Water. Also a discussion of the Offensive Torpedo 
 system, its effect upon Iron-Clad Ship systems, and influence upon 
 Future Naval Wars. By Lieut. -Commander Joux S. BAEXES, 
 IT. S. N. With twenty lithographic plates and many wood-cuts. 
 
 " A book important to military men, and especially so to engineers and ar 
 tillerists. It consists of an examination of the various offensive and defensive 
 engines that have been contrived for submarine hostilities, including a discus 
 sion of the torpedo system, its effects upon iron-clad ship-systems, and its 
 probable influence upon future naval wars. Plates of a valuable character 
 accompany the treatise, which affords a useful history of the momentous sub 
 ject it discusses. A great deal of useful information is collected in its pages, 
 especially concerning the inventions of SCIIOI.L ad VEIIDU, and of JONES 
 and HUNT S batteries, as well as of other similar machines, and the use in 
 submarine operations of gun-cotton and nitro-glycerine." N* T. Times* 
 
 Randall s Quartz Operator s Hand- 
 Book. 
 
 12mo. Cloth. $2.00. 
 
 QUARTZ OPERATOR S HAND-BOOK. By P. M. RANDALL. 
 
 New edition, revised and enlarged. Fully illustrated. 
 
 The object of this work has been to present a clear and comprehensive ex 
 position of mineral veins, ami the means and modes chiefly employed for the 
 mining and working of their ores more especially those containing gold and 
 silver. 
 
D. VAN NOSTRAND. 23 
 
 Mitchell s Manual of Assaying. 
 
 8vo. Cloth. $10.00, 
 
 A MANUAL OF PEACTICAL ASSAYING. By JOHN MITCHELL. 
 Third edition. Edited by WILLIAM CKOOKES, F.E.S. 
 
 In this edition are incorporated all the late important discoveries in Assay 
 ing made in this country and abroad, and special care is devoted to the very 
 important Volumetric and Colorimetric Assays, as well as to the Blow-Pipe 
 
 Benet s Chronoscope. 
 
 Second Edition. 
 
 Illustrated. 4to. Cloth. $3.00. 
 
 ELECTEO-BALLISTIC MACHINES, and the Schultz Chrono- 
 scope. By Lieutenant-Colonel S. V. BEN ET, Captain of Ordnance, 
 U. S. Army. 
 
 CONTENTS.1. Ballistic Pendulum. 2. Gun Pendulum. 3. Use of Elec 
 tricity. 4. Navez Machine. 5. Vignotti s Machine, with Plates. 6. Benton s 
 Electro-Ballistic Pendulum, with Plates. 7. Leur s Tro-Pendulum Machine 
 8. Schultz s Chronoscope, with two Plates. 
 
 Michaelis Chronograph. 
 
 4to. Illustrated. Cloth. $3.00. 
 
 THE LE BOULENGE CHEONOGEAPH. With three litho 
 graphed folding plates of illustrations. By Brevet Captain E. 
 MICHAELIS, First Lieutenant Ordnance Corps, U. S. Army. 
 
 " The excellent monograph of Captain Michaelis enters minutely into the 
 details of construction and management, and gives tables of the times of flight 
 calculated upon a given fall of the chronometer for all distances. < 
 Michaelis has done good service in presenting this work to his brother officers, 
 describing, as it does, an instrument which bids fair to be in constant use in 
 our future ballistic experiments. ^^ and Navy Journal. 
 
24 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Silversmith s Hand-Book. 
 
 Fourth Edition. 
 
 Illustrated. 12mo. Cloth. $3,00. 
 
 A PRACTICAL HAND-BOOK FOE MINERS, Metallurgists, 
 and Assayers, comprising the most recent improvements in the 
 disintegration, amalgamation, smelting, and parting of the 
 Precious Ores, with a Comprehensive Digest of the Mining 
 Laws. Greatly augmented, revised, and corrected. By JULIUS 
 SILVERSMITH. Fourth edition. Profusely illustrated. 1 vol. 
 12mo. Cloth. $3.00. 
 
 One of the most important features of this work is that in which the 
 metallurgy of the precious metals is treated of. In it the author has endeav 
 ored to embody all the processes for the reduction and manipulation of the 
 precious ores heretofore successfully employed in Grermany, England, Mexico, 
 and the United States, together with such as have been more recently invented, 
 and not yet fully tested all of which are profusely illustrated and easy of 
 comprehension. 
 
 Simms Levelling. 
 
 8vo. Cloth. $2.50. 
 
 A TREATISE ON THE PRINCIPLES AND PRACTICE OF 
 LEVELLING, showing its application to purposes of Railway 
 Engineering and the Construction of Roads, &c. By FREDERICK 
 W. SIMMS, C. E. From the fifth London edition, revised and 
 corrected, with the addition of Mr. Law s Practical Examples for 
 Setting Out Railway Curves. Illustrated with three lithographic 
 plates and numerous wood-cuts. 
 
 " One of the most important text-books for the general surveyor, and there 
 is scarcely a question connected with levelling for which a solution would be 
 sought, but that would be satisfactorily answered by consulting this volume." 
 Mining Jvumal. 
 
 " The text-book on levelling in most of our engineering schools and col 
 leges." -Engineers. 
 
 " The publishers have rendered a substantial service to the profession, 
 especially to the younger members, by bringing out the present edition of 
 MJ. Simms useful work." Engineering. 
 
D. VAN NO STRAND. 25 
 
 Stuart s Successful Engineer. 
 
 18mo. Boards. 50 cents. 
 
 HOW TO BECOME A SUCCESSFUL ENGINEER: Being 
 Hints to Youths intending to adopt the Profession. By 
 BERNARD STUART, Engineer. Sixth Edition. 
 
 "A valuable little book of sound, sensible advice to young men who 
 wish to rise in the most important of the professions." Scientific American. 
 
 Stuart s Naval Dry Docks. 
 
 Twenty-four engravings on steel. 
 Fourth Edition. 
 
 4to. Cloth. $6.00. 
 
 THE NAVAL DRY DOCKS OF THE UNITED STATES. 
 By CHARLES B. STUAET. Engineer in Chief of the United IS tales 
 
 Navy. 
 
 List of Illustrations. 
 
 Pumping Engine and Pumps Plan of Dry Dock and Pump- Well -Sec 
 tions of Dry Dock Engine House Iron Flpating Gate Details of Floating 
 Gate Iron Turning Gate Plan of Turning Gate Culvert Gate Filling 
 Culvert Gates Engine Bed Plate, Pumps, and Culvert Engine House 
 Roof Floating Sectional Dock Details of Section, and Plan of Turn-Tables 
 Plan of Basin and Marine Railways Plan of Sliding Frame, and Elevation 
 of Pumps Hydraulic Cylinder Plan of Gearing for Pumps and End Floats 
 Perspective View of Dock, Basin, and Railway Plan of Basin of Ports 
 mouth Dry Dock Floating Balance Dock Elevation of Trusses and the Ma 
 chinery Perspective View of Balance Dry Dock 
 
 Free Hand Drawing. 
 
 Profusely Illustrated. 18mo. Boards. 50 centa. 
 
 A GUIDE TO ORNAMENTAL, Figure, and Landscape Draw 
 ing. By an Art Student. 
 
 CONTENTS. Materials employed in Drawing, and how to use them On 
 Lines and how to Draw them-^On Shading Concerning lines and shading, 
 with applications of them to simple elementary subjects Sketches from Na 
 ture. 
 
26 SCIENTIFIC BOOKS PUBLISHED BY 
 
 \ \ 
 
 Minifie s Mechanical Drawing. 
 
 Eighth Edition. 
 
 Royal 8vo. Cloth. $4.00. 
 
 A TEXT-BOOK OF GEOMETRICAL DBAWING- for the use 
 of Mechanics and Schools, in which the Definitions and Bales of 
 Geometry are familiarly explained ; the Practical Problems are 
 arranged, from the most simple to the more complex, and in their 
 description technicalities are avoided as much as possible. With 
 illustrations for Drawing Plans, Sections, and Elevations of 
 Buildings and Machinery ; an Introduction to Isornetrical Draw 
 ing, and an Essay on Linear Perspective and Shadows. Illus 
 trated with over 2(K) diagrams engraved on steel. By WM. 
 MINIFIE, Architect. Eighth Edition. With an Appendix on the 
 Theory and Application of Colors. 
 
 " It is the best work on Drawing 1 that we have ever seen, and is especially a 
 text-book of Geometrical Drawing 1 for the use of Mechanics and Schools. No 
 young Mechanic, such as a Machinist, Engineer, Cabinet-Maker, Millwright, 
 or Carpenter, should be without it." Scientific American. 
 
 " One of the most comprehensive works of the kind ever published, and can 
 not but possess great value to builders. The style is at once elegant and sub 
 stantial. Pennsylvania Inquirer. 
 
 " Whatever is said is rendered perfectly intelligible by remarkably well- 
 executed diagrams on steel, leaving nothing for mere vague supposition ; and 
 the addition of an introduction to isometrical drawing, linear perspective, and 
 the projection of shadows, winding up with a useful index to technical terms." 
 Glasgow Mechanics Journal. 
 
 B3?F The British Government has authorized the use of this book in their 
 schools of art at Somerset House, London, and throughout the kingdom. 
 
 Minifie s Geometrical Drawing. 
 
 New Edition. Enlarged. 
 
 12mo. Cloth. $2.00. 
 
 GEOMETEICAL DEAWING. Abridged from the octavo edition, 
 for the use of Schools. Illustrated with 48 steel plates. New 
 edition, enlarged. 
 
 " It i well adapted as a text-book of drawing to be used in our High Schools 
 and Academies where this useful branch of the fine arts has been hitherto too 
 much neglected." Boston Journal. 
 
D. VAN NOSTRANJ). 27 
 
 Bell on Iron Smelting. 
 
 8vo. Cloth. $6.0J. 
 
 CHEMICAL PHENOMENA OF IRON SMELTING. An ex 
 perimental and practical examination of the circumstances which 
 determine the capacity of the Blast Furnace, the Temperature 
 of the Air, and the Proper Condition of the Materials to be 
 operated upon. By I. LOWTHIAN BELL. 
 
 " The reactions -which take place in every foot of the blast-furnace have 
 been investigated, and the nature of every step in the process, from the intro 
 duction of the raw material into the furnace to the production of the pig iron, 
 has been carefully ascertained, and recorded so fully that any one in the trade 
 can readily avail themselves of the knowledge acquired ; and we have no hes 
 itation in saying that the judicious application of such knowledge will do 
 much to facilitate the introduction of arrangements which will still further 
 economize fuel, and at the same time permit of the quality of the resulting 
 metal being maintained, if not improved. The volume is one which no prac 
 tical pig iron manufacturer can afford to be without if he be desirous of en 
 tering upon that competition which nowadays is essential to progress, and 
 in issuing such a work Mr. Bell has entitled himself to the best thanks of 
 every member of the trade." London Mining Journal. 
 
 Zing s Notes on Steam. 
 
 Thirteenth Edition. 
 
 8vo. Cloth. $2.00. 
 
 LESSONS AND PEACTICAL NOTES ON STEAM, the Steam- 
 Engine, Propellers, &c., &c., for Young Engineers, Students, and 
 others. By the late W. R. KING, U. S. N. Revised by Chief- 
 Engineer J. W. KIXG, U. S. Navy. 
 
 " This is one of the best, because eminently plain and practical treatises on 
 the Steam Engine ever published. Philadelphia Press. 
 
 This is the thirteenth edition of a valuable work of the late W. H. King, 
 U. S. N. It contains lessons and practical notes on Steam and the Steam En 
 gine, Propellers, etc. It is calculated to be of great use to young marine en 
 gineers, students, and others. The text is illustrated and explained by nu 
 merous diagrams and representations of machinery . Boston Daily Adver 
 tiser. 
 
 Text-book at the U. S. Naval Academy, Annapolis. 
 
28 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Burgh s Modern Marine Engineering. 
 
 One thick 4to vol. Cloth. $25.00. Half morocco. $30.00. 
 
 MODEEN MARINE ENGINEERING, applied to Paddlo and 
 Screw Propulsion. Consisting of 36 Colored Plates, 259 Practical 
 Wood-cut Illustrations, and 403 pages of Descriptive Matter, the 
 whole being an exposition of the present practice of the follow 
 ing firms : Messrs. J. Penn & Sons ; Messrs. Maudslay, Sons & 
 Field ; Messrs. James Watt & Co. ; Messrs. J. & Gr. Ronnie ; 
 Messrs. R. Napier & Sons ; Messrs. J. & W. Dudgeon ; Messrs. 
 Ravenhill & Hodgson ; Messrs. Humphreys & Tenant ; Mr. 
 J. T. Spencer, and Messrs. Forrester & Co. By N. P. BURGH, 
 Engineer. 
 
 PRINCIPAL CONTENTS. General Arrangements of Engines, 11 examples 
 General Arrangement of Boilers, 14 examples General Arrangement of 
 Superheaters, 11 examples Details of Oscillating Paddlo Engines, 04 ex 
 amples Condensers for Screw Engines, both Injection and Surface, 20 ex 
 amples Details of Screw Engines, 20 examples Cylinders and Details of 
 Screw Engines, 21 examples Slide Valves and Detail?, 7 examples Slide 
 Valve, Link Motion, 7 examples Expansion Valves and Gear, 10 exam 
 ples Details in General, 30 exam pies --Screw Propeller and Fittings, 13 ex 
 amples Engine and Boiler Fittings, 28 examples In relation to the Princi 
 ples of the Marine Engine and Boiler, 33 examples. 
 
 Notices of the Press. 
 
 " Every conceivable detail of the Marine Engine, under all its various 
 forms, is profusely, and we must add, admirably illustrated by a multitude 
 of engravings, selected from the best and most modern practice of the first 
 Marine Engineers of the day. The chapter on Condensers is peculiarly valu 
 able. In one word, there is no other work in exist*, nee which will bear a 
 moment s comparison with it as an exponent of the skill, talent and practical 
 experience to which is duo the splendid reputation enjoyed by many British 
 Marine Engineers." - Engineer. 
 
 " This very comprehensive work, which was issued in Monthly parts, has 
 just been completed. It contains large and full drawings and copious de 
 scriptions of most of the best examples of Modern Marine .Engines, and it is 
 a complete theoretical and practical treatise on the subject of Marine Engi 
 neering." American Artisan. 
 
 This is the only edition of th above work with the beautifully colored 
 plates, and it is out of print in England. 
 
J). VAN NOSTRAND. 29 
 
 Bourne s Treatise on the Steam En 
 gine. 
 
 Ninth Edition. 
 
 Illustrated. 4to. Cloth. $15.00. 
 
 TREATISE ON THE STEAM ENGINE in its various applica 
 tions to Mines, Mills, Steam Navigation, Railways, and Agricul 
 ture, with the theoretical investigations respecting the Motive 
 Power of Heat and the proper Proportions of Steam Engines. 
 Elaborate Tables of the right dimensions of every -part, and 
 Practical Instructions for the Manufacture and Management of 
 every species of Engine in actual use. By JOHN BOUKNE, being 
 the ninth edition of " A Treatise on the Steam Engine," by 
 the " Artisan Club." Illustrated by thirty-eight plates and five 
 hundred and forty-six wood-cuts. 
 
 As Mr. Bourne s work has the great merit of avoiding unsound and imma 
 ture views, it may safely be consulted by all who are really desirous of ac 
 quiring trustworthy information on the subject of which it treats. During 
 the twenty-two years which have elapsed from the issue of the first edition, 
 the improvements introduced in the construction of the steam engine have 
 been both numerous and important, and of these Mr. Bourne has taken care 
 to point out the more prominent, and to furnish the reader with such infor 
 mation as shall enable him readily to judge of their relative value. This edi 
 tion has been thoroughly modernized, and made to accord with the opinions 
 and practice of the more successful engineers of the present day. All that 
 the book professes to give is given with ability and evident care. The scien 
 tific principles which are permanent are admirably explained, and reference 
 is made to many of the more valuable of the recently introduced engines. To 
 express an opinion of the value and utility of such a work as The Artisan 
 Club s Treatise on the Steam Engine, which has passed through eight editions 
 already, woxild bo superfluous ; but it may be safely staged that the work is 
 worthy the attentive study of aM. either engaged in the manufacture of Bteam 
 engines or interested in economizing the use of steam. Mining Journal. 
 
 Islierwood s Engineering Precedents. 
 
 Two Vols. in One. 8vo. Cloth. $2.50. 
 
 ENGINEERING PRECEDENTS FOR STEAM MACHINERY. 
 Arranged in the most practical and useful manner for Engineers. 
 By B. F. ISHEKWOOD, Civil Engineer, U. S. Navy. With illus 
 trations. 
 
30 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Ward s Steam for the Million. 
 
 New and Revised Edition. 
 
 8vo. Cloth. $1.00. 
 
 STEAM FOE THE MILLION. A Popular Treatise on Steam 
 and its Application to the Useful Arts, especially to Naviga 
 tion. By J. H. WAED, Commander U. S. Navy. New and re 
 vised edition. 
 
 A most excellent work for the young engineer and general reader. Many 
 facts relating to the management of the boiler and engine -are set forth with a 
 simplicity of language and perfection of. detail that bring the subject home 
 to the reader. American Engineer. 
 
 Walker s Screw Propulsion. 
 
 8vo. Cloth. 75 cents. 
 
 NOTES ON SCREW PROPULSION, its Rise and History. By 
 Capt. W. H. WALKER, U. S. Navy. 
 
 Commander Walker s book contains an immense amount of concise practi 
 cal data, and every item of information recorded fully proves that the various 
 points bearing upon it have been well considered previously to expressing an 
 opinion. Tendon Mining Journal. 
 
 Page s Earth s Crust. 
 
 18mo. Cloth. 75 cents. 
 
 THE EARTH S CRUST : a Handy Outline of Geology. By 
 DAVID PAGE. 
 
 " Such a work as this was much wanted a work giving in clear and intel 
 ligible outline the leading facts of the science, without amplification or irk 
 some details. It is admirable in arrangement, and clear and easy, and, at the 
 same time, forcible in style. It will lead, wo hope, to the introduction of 
 Geology into many schools that have neither time nor room for the study of 
 large treatises." TJie Museum. 
 
D. VA N NOS TRA ND. 3 1 
 
 Rogers G-eology of Pennsylvania. 
 
 3 Vols. 4to, with Portfolio of Maps. Cloth. $30.00. 
 
 THE GEOLOGY OF PENNSYLVANIA. A Government Sur 
 rey. With a general view of the Geology of the United States, 
 Essays on the Coal Formation and its Fossils, and a description 
 of the Coal Fields of North America and Great Britain. By 
 HENRY DAHWIN ROGERS, Late State Geologist of Pennsylvania. 
 Splendidly illustrated with Plates and Engravings in the Text. 
 
 It certainly should be in every public library ^nroughout the country, and 
 likewise in the possession of all students of Geology. After the final sale of 
 these copies, the work will, of course, become more valuable. 
 
 The work for the last five years has been entirely out of the market, but a 
 few copies that remained in the hands of Prof. Rogers, in Scotland, at the 
 time of his death, are now offered to the public, at a price which is even 
 below what it was originally sold for when first published. 
 
 Morfit on Pure Fertilizers. 
 
 "With 28 Illustrative Plates. 8vo. Cloth. $20.00. 
 
 A PRACTICAL TREATISE ON PURE FERTILIZERS, and 
 
 the Chemical Conversion of Rock Guanos, Marlstones, Coprolites, 
 and the Crude Phosphates of Lime and Alumina Generally, into 
 yarious Valuable Products. By CAMPBELL MORFIT, M.D., F.C.S. 
 
 Sweet s Report on Coal. 
 
 8vo. Cloth. $3.00. 
 
 SPECIAL REPORT ON COAL ; showing its Distribution, Classi 
 fication, and Cost delivered over different routes to various points 
 in the State of New York, and the principal cities on the Atlantic 
 Coast. By S. H. SWEET. With maps. 
 
 Colburn s Gas Works of London. 
 
 I2ino. Boards. 60 cents. 
 GAS WORKS OF LONDON. By ZEBAH COLBUWT. 
 
32 SCIENTIFIC BOOKS PUBLISHED BY 
 
 The Useful Metals and their Alloys ; 
 Scoffren, Truran, and others. 
 
 Fifth Edition. 
 
 8vo. Half calf. $3.75. 
 
 THE USEFUL METALS AND THEIR ALLOYS, including 
 MINING VENTILATION, MINING JURISPRUDENCE 
 AND METALLURGIC CHEMISTRY employed in the conver 
 sion of IRON, COPPER, TIN, ZINC, ANTIMONY, AND 
 LEAD ORES, with their applications to THE INDUSTRIAL 
 ARTS. By JOHN SCOFFKEN, WILLIAM TRTJRAN, WILLIAM CLAY, 
 ROBERT OXLAND, WILLIAM FAIRBAIBN, W. C. AITKIN, and WIL 
 LIAM VOSE PICKETT. 
 
 Collins 1 Useful Alloys. 
 
 18mo. Flexible. 75 cents. 
 
 THE PRIVATE BOOK OF USEFUL ALLOYS and Memo 
 randa for Goldsmiths, Jewellers, etc. By JAMES E. COLLINS 
 
 This little book is compiled from notes made by the Author from the 
 papers of one of the largest and most eminent Manufacturing Goldsmiths and 
 Jewellers in this country, and as the firm is now no longer in existence, and the 
 Author is at present engaged in some other undertaking, he now offers to the 
 public the benefit of his experience, and in so doing he begs to state that all 
 the alloys, etc., given in these pages may be confidently relied on as being 
 thoroughly practicable. 
 
 The Memoranda and Receipts throughout this book are also compiled 
 from practice, and will no doubt be found useful to the practical jeweller. 
 Shirley, July, 1871. 
 
 Joynsorfs Metals Used in Construction. 
 
 12mo. Cloth. 75 cents. 
 
 THE METALS USED IN CONSTRUCTION : Iron, Steel, 
 Bessemer Metal, etc., etc. By FRANCIS HERBERT JOYNSON. Il 
 lustrated. 
 
 " In the interests of practical science, we are bound to notice this work ; 
 and to those who wish further information, we should say, buy it ; and the 
 outlay, we honestly believe, will be considered well spent." Scientific 
 Review. 
 
D. VAN NOSTRAND. 33 
 
 Holley s Ordnance and Armor. 
 
 493 Engravings, Half Roan, $10.00. Half Russia, $12.00. 
 
 A TEEATISE ON ORDNANCE AND ARMOR Embracing 
 Descriptions, Discussions, and Professional Opinions concerning 
 the MATERIAL, FABRICATION, Requirements, Capabilities, and En 
 durance of European and American Guns, for Naval, Sea Coast, 
 and Iron-clad Warfare, and their RIFLING, PROJECTILES, and 
 BREECH-LOADING; also, Results of Experiments against Armor, 
 from Official Records, with an Appendix referring to Gun-Cotton, 
 Hooped Guns, etc., etc. By ALEXANDER L. HOLLEY, B. P. 948 
 pages, 493 Engravings, and 147 Tables of Results, etc. 
 
 CONTENTS. 
 
 CHAPTER I. Standard Guns and their Fabrication Described: Section 1. 
 Hooped Guns ; Section 2. Solid Wrought Iron Guns ; Section 3. Solid Steel 
 Guns; Section 4. Cast-Iron Guns. CHAPTER II. The Requirements of Guns, 
 Armor: Section 1. The Work to be done; Section 2. Heavy Shot at Low Ve 
 locities; Sections. Small Shot at High Velocities; Section 4. The two Sys 
 tems Combined ; Section 5. Breaching Masonry. CHAPTER III. The Strains 
 and Structure of Guns: Section 1. Resistance to Elastic Pressure; Section 2. 
 The Effects of Vibration; Section 3. The Effects of Heat. CHAPTER IV. 
 Cannon Metals and Processes of Fabrication: Section 1. Elasticity and Ductil. 
 ity; Section 2. Cast-Iron; Section 3. Wrought Iron; Section 4. Steel; Sec 
 tion 5. Bronze ; Section 6. Other Alloys. CHAPTER V. Rifling and Projec 
 tiles ; Standard Forms and Practice Described ; Early Experiments ; The 
 Centring System ; The Compressing System ; The Expansion System ; Armor 
 Punching Projectiles ; Shells for Molten Metal ; Competitive Trial of Rifled 
 Guns, 1862; Duty of Rifled Guns: General Uses, Accuracy, Range, Velocity, 
 Strain, Liability of Projectile to Injury ; Firing Spherical Shot from Rifled 
 Guns ; Material for Armor-Punching Projectiles ; Shape of Armor-Punching 
 Projectiles; Capacity and Destructiveness of Shells; Elongated Shot from 
 Smooth Bores; Conclusions; Velocity of Projectiles (Tabled CHAPTER VI. 
 Breech-Loading Advantages and Defects of the System ; Rapid Firing and 
 Cooling Guns by Machinery ; Standard Breech-Loaders Described. Part Sec 
 ond : Experiments against Armor ; Account of Experiments from Official 
 Records in Chronological Order. APPENDIX. Report on the Application of 
 Gun-Cotton to Warlike Purposes British Association, 1863; Manufacture and 
 Experiments in England ; Guns Hooped with Initial Tension History; How 
 Guns Burst, by Wiard, Lyman s Accelerating Gun ; Endurance of Parrott 
 and Whitworth Guns at Charleston ; Hooping old United States Cast-Iron 
 Guns; Endurance and Accuracy of the Armstrong 600-pounder; Competitive 
 Trials with 7-inch Guns. 
 
34 SCIENTIFIC BOOKS PUBLISHED BY 
 
 Peirce s Analytic Mechanics. 
 
 4to. Cloth. $10.00. 
 
 SYSTEM OF ANALYTIC MECHANICS. Physical and Celestial 
 Mechanics. By BENJAMIN PEIRCK, Perkins Professor of Astronomy 
 and Mathematics in Harvard University, and Consulting As 
 tronomer of the American Ephemeris and Nautical Almanac. 
 Developed in four systems of Analytic Mechanics, Celestial 
 Mechanics, Potential Physics, and Analytic Morphology. 
 
 * I have re-examined the memoirs of the great geometers, and have striven 
 to consolidate their latest researches and their most exalted forms of thought 
 into a consistent and uniform treatise. If I have hereby succeeded in Open 
 ing to the students of my country a readier access to these choice jewels of 
 intellect ; if their brilliancy is not impaired in this attempt to reset them ; if, 
 in their own constellation, they illustrate each other, and concentrate 
 a stronger light upon the names of their discoverers , and, still more, if any 
 gem which I may have presumed to add is not wholly lustreless in the collec- 
 t\on, I shall feel that my work has not been in vain." Extract from the Pr& 
 face. 
 
 Bnrt s Key to Solar Compass. 
 
 Second Edition. 
 
 Pocket Book Form. Tuck. $2.50. <-; 
 
 KEY TO THE SOLAR COMPASS, and Surveyor s Companion ; 
 comprising all the Holes necessary for use in the field; also, 
 Description of the Linear Surveys and Public Land System of 
 the United States, Notes on the Barometer, Suggestions for an 
 outfit for a Survey of four months, etc., etc., etc. By W. A. 
 BUST, U. S. Deputy Surveyor. Second edition. 
 
 Chauvenet s Lunar Distances. 
 
 8vo. Cloth. $2.00. 
 
 NEW METHOD OF COERECTING LUNAR DISTANCES, 
 and Improved Method of Finding the Error and Rate of a Chro 
 nometer, by equal altitudes. By WM. CHAUVENET, LL.D., Chan 
 cellor of Washington University of St. Louis. 
 

 Jefiers Nautical Surveying. 
 
 Illustrated with 9 Copperplates and 31 Wood-cut Illustrations. 8vo 
 Cloth. $5,00. 
 
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D. VAST NOSTRAND. 37 
 
 
 
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