1360

THEORY AND PRACTICE OF ENGINEERING.

Book II.

In the system of two inclined timbers abutting against each other, it is easy to imaginethat the load will separate in pressures in the direction of their length, following two linesdrawn from each side of the summit of the principal to the springing; the resistance ofthese timbers must make an equilibrium to these pressures, and in order to appreciate thisresistance, we must consider the timbers as placed upright, and loaded vertically with aweight equal to the pressures. According to this consideration, it is evident how disad-vantageous it is that the two halves of a principal should be divided into a great numberof articulations, forming so many points of rupture, leaving them no resistance but thatwhich arises from the strength of the framing; it may be easy to give to the framings at eacharticulation sufficient force to render the system invariable in form, but, as experience hasproved, it is very difficult, and even impossible, when the number of levers is considerable, tofortify them sufficiently to procure for each half of the centre a resistance capable of makingequilibrium to the pressure which it exercises in the direction of the length : it is for thisreason that the systems figs. 2178, 2179. become more disadvantageous as the number ofthe timbers augments, and terminates by being entirely impossible of execution.

A more solid combination is obtained by disposing inclined timbers, as seen in fig.2180., in polygons, some of the angles of which answer to the middles of the sides ofthe others, because if each half of the arch yielded to the pressures which exert themselvesfrom the summit to the springings, not only the framing of the articulations would bend,but the timbers would break in the middle of their length: we must observe that thecourses of the inclined timbers not being solidly framed, touch by a very small number ofpoints ; a certain flexion may therefore be produced in the whole without each piece sensiblybending; this may happen, should each binding-piece diverge a little from its position,so that tlie pieces of the polygon situated on the side of the concave face are not shortened,and those of the polygon situated on the convex face are not lengthened, as they would be,on account of the flexion, if they were perfectly united. It is impossible to executethe notches of the binding-pieces with the perfection necessary to prevent this divergingfrom taking place : thus the system fig. 2180., although very preferable to that of fig. 2179.,is far from perfect; the system fig. 2180. was that which Perronet used for the centres ofstone bridges. But if, instead of forming the timbers with straight pieces, which canonly touch each other at their extremities and in the middle of their length, the wholeof which may yield together without each piece in particular being obliged to bend, weuse, as in fig. 2181., curved pieces in juxta-position, united and tightened by binding-piecesand bolts, the joints of the extremities of which do not unite opposite to each other, thenature of the system will be found totally changed, and it will receive a very great im-provement, for the centre (fig. 2181.) cannot bend without all the pieces of which it isformed yielding : the strength of the framework of the extremities of these pieces no longer

Fig. 2203.

BRIDGE FORMED OP CURVED TIMBERS.

opposes itself alone, to the flexion of each half of the centre ; the resistance presented by thetimbers is a second obstacle to the flexion, more powerful than the first, rendering allbending impossible, if this resistance be sufficient, even if we discard all consideration otthe manner in which the framework of the ends is executed.

Arches formed of bent timbers have been adopted for some of the viaducts constructedon our railways, and where sufficient caution has been taken to prevent too much motionfrom their elasticity, are found to answer very well: the reparation of such bridges isdifficult, should any of the timbers exhibit decay ; but this disadvantage has been over-come in some instances by making the bolts and straps that hold the curved timbersmovable, so that one timber can be taken out without disturbing the others, which lieabove or below it.

The disposition fig. 2181. offers, with regard to the force with which each half of thecentre resists the longitudinal pressure exerted upon it, the same resistance as the systemfig. 2176.; it is equally invariable in form with the latter, and much more advantageous,