1358
THEORY AND PRACTICE OF ENGINEERING.
Rook II.
be multiplied, and very largetimbers used, which involvesa considerable and needlessexpense. It is now generallyacknowledged that the bestmethod of applying timberin bridges is to form archeswith courses of curved tim-bers bent over each other:this arrangement has beenpreferred, after several othershave been tried, which haveproved entirely defective,and the result of long ex-perience is justified by ananalysis of the differentsystems of carpentry in largearches.
Let A and B, fig. 2! 74. be two points of support, united by a large principal of carpentry,which principal, besides its own weight, is to carry that of the floor, which may be con-sidered as distributed uniformly throughout its length. The first idea which would presentitself is to establish on the two points of support a solid bearing in timber, the formof which shall be such that it resists this double effort equally in all its points, and ifwe recal the notions which have been given on solids of equal resistance, we shallimagine that this should present nearly the form of aCb, indicated in the figure : let usthen observe that if this solid should yield, the fibres situated on the upper surface wouldbe compressed, whilst those situated on the lower would be extended, so that we can tracein the interior of the solid two lines C a and C5, which shall separate the compressed fromthe extended fibres, and that the resistance of the solid exerts itself by means of the pressuredirected in the lines Pm, Pm, and of the tensions directed in the lines P'm', P'n', efforts inwhich this resistance consists solely, and which are the more considerable following eachof the lines Pm, Pn, P'm', P r n', as these lines are nearer the surface of the solid, and furtherremoved from the line aCb.
It is easy to draw conclusions from such an example : first, the pieces of which thesolids should be formed must be disposed in the direction of the lines, according to whichthe pressure and the tensions are exerted, for of all the applications of timber, the mostadvantageous is that where it is pressed or drawn in the direction of its length ; it mustbe observed also, that there is advantage in using the same quantity of pieces, in removingthem from each other, in not making the solid full, and in augmenting its height; in short,the effort of the weight which the solid supports may be assimilated to that of a certainweight suspended at the point C, and which decomposes itself into two forces, directedfrom this point towards the points of support A and B; when the point C is higherwith relation to the points A and B, the two components of weight, making a less angle,have a less considerable value, and produce pressures less strong. We are led by theseconsiderations to a system of carpentry represented in fig. 2175., which is that of thebridge of Schaffhausen and Wittingen : the principals of these bridges have the formwhich would suit a solid of equal resistance, and the timbers are disposed exactly in \hedirection of the pressures and tensions which they would exert in the solid; but thepieces which would be found in connection with aCb (fig. 2174.) are suppressed, because,having scarcely any effort to make, thev would increase the weight without having anyutility : we may remark that the pieces which resist the pressures are in much greaternumber than those which resist the tensions, which arises from the timber being drawnin the direction of its fibres, and consequently having much more strength than thatwhich is compressed in the same direction. The carpentry of these bridges bears on theabutments, but docs not exercise against them any effort which tends to overthrow them ;the thrusts being retained by the tensions of the interior girder, in rendering the abutmentscapable of resisting the thrusts, we may then, without changing the nature of the system,suppress the girder; this idea leads to the arrangement represented fig. 2176., which isthat of the bridge of Kandel. A slight modification in this arrangement gives the com-bination represented in fig. 2178., which is that of the bridge projected for Lyons;this latter has an advantage over the preceding, because the braces united and subjectedto each other form a rafter, and resist much better than when they are isolated, aboveall, if each of them were to be only of one piece ; but this advantage has its inconvenience,for the effort of the weight of the bridge may be considered as that of several weightsattached to pendant binding-pieces ; in the systems, figs. 2175, 2176. the efforts of theweights suspended to each binding-piece is carried back towards the points of support,and maintained almost entirely by the inclined piece, which abuts at the upper extremity
BAYS AND ARCHES.