Chap. XXIII.
I3G1
as the curve given to each rafter leaves nothing to fear from the transverse pressure towhich it is submitted, and there is even no necessity to consider these pressures.
Fig. 2203. represents an arch projected according to these principles for an opening of132 feet; the principals are at a distance of 6 feet 6 inches from centre to centre; thearch is composed of four courses of curves, tightened by bolts, and so placed thattheir joints do not meet, some being opposite the others; it carries the floor by meansof pendant binding-pieces, which it appears more proper to place vertically than per-pendicularly to the curve, and it may be admitted as a general principle, that each pieceshould always be placed exactly in the centre of what it supports ; these pendant binding-pieces are held by horizontal binding-pieces placed on centres, which prevent the spreadingout of the principals; courses of vertical and horizontal binding-pieces should never be atmore than 16 feet apart.
When the opening of the arch is considerable, the movement of carriages, and sometimeseven the action of the wind alone, occasions oscillations in the horizontal direction, whichinjure the carpentry, and might become very dangerous ; the greatest care should be takento prevent this, if an arch bend in the direction of its width, the horizontal binding-pieces, which were at first parallel between each other, would become normal to the curvewhich the arch would have taken ; they will then have changed position with relation toeach other; thus the flexion of the arch will be prevented, if pieces are so disposed as tomaintain these binding-pieces in their respective positions ; in the half-plan represented infig. 2203., braces are placed for this purpose in the interval of the courses of binding-pieces.
In the oscillations of an arch, the entire system of its carpentry may participate in themovement, or it may only be partial ; for example, the floor may to a certain point moveindependently of the arch ; still it is very important to oppose these effects; there aretherefore placed between the first course of pendant binding-pieces, near the springing,inclined struts which secure the union of the floor and the arch, and it appearsthat this disposition would give to the arch all the solidity and stability which could bedesired; it is scarcely necessary to observe that the framing of all these pieces should besecured by bolts, without which the union could not be obtained.
It is requisite to allude to the manner in which the thrust of the arches in carpentry,of the kind we have just indicated, should be considered, and on the settling, of whichthey are susceptible. If timber did not suffer any compression, and if the execution of thework could be sufficiently perfect for no voids to remain in the framing, and all the piecescould bear exactly one against the other, there could be no settlement; and the force ofthe timbers being regarded capable of resisting the load, no flexion would be produced;the centre would then be as a single piece placed upon two supports, and would haveno thrust; this perfection in the quality of the materials, and in the execution of thework, not existing, it happens that the moment an arch is placed and left to itself it hasa tendency to settle: if this movement could operate freely, and the chord of the archelongate without obstacle, until the framework was tightened, the settling would stop,and the arch would then have no more thrust; but it is always retained by obstacles,which do not permit the chord to be thus elongated, which obstacles necessarily experiencea certain pressure; the most simple manner of valuing this pressure is to assimilate thearch of carpentry to a wall of stone, and to examine the horizontal thrust which it wouldproduce, according to its weight and the relation of the yielding at the opening; weshall thus have, not the true value of the thrust of the centre, but a limit below whichthis thrust always remains, and according to which the dimensions of the piers andthe abutments may be regulated. Although the arches of carpentry be confined at theirspringing, and their chord not being able to lengthen itself the summit cannot sink,they experience a slight settlement, analogous to that of a vault in stone, and to whichregard must be had in construction. According to the observations of M. Wiebeking,by representing c as the opening of an arch, and/as its fleche or settlement, the lowering
f
at the middle, expressed in inches, is given bv the formula 002 -; but we must remark that
¥ c
these observations were made on bridges of fir timber; for centres in oak the settlementshould be less considerable. This formula gives the settlement immediately after building,but it increases from the effect of the alteration of the timber.
Floors and Parapets. — Floors of wooden bridges are constructed in various ways;formerly they were almost always covered with a pavement placed on a bed of sand; but ithas been ascertained that a very considerable weight was the result, and that the dampproduced on the planks tended to make them rapidly perish, as well as the girders onwhich they were carried; it is therefore preferable to cover them with a false floor, whichalso prevents them from being injured by the wheels of carriages, and can be renewed asoften as necessary.
Fig. 2204. represents the section of a floor disposed to receive a pavement; it is formedby timbers, from 7 to 8 inches square, slightly notched at the meeting of the main timbers,
4 S