1406

THEORY AND PRACTICE OF ENGINEERING.

Book II.

formation as for those employed in the construction of the arch of a bridge. When thewidth of the tunnel and the earth which is to be removed will permit, a way may bedriven on each side, and a portion of the earth or rock left in the middle, or at the twosides, upon which the timber centre may rest until the entire arch it is intended to sup-port is completed . many tunnels have been cut through the chalk hills, with a paraboliccurve given to their centres, two masses of chalk having been left to support their lowertimbers.

In the former portion of the work, we have given the design and description of thecentres used at many of the bridges erected during the last century, and to them wemust refer the reader ; those used for the construction of the bridges of London andWaterloo are particularly worthy of observation.

On Pitot's manner ofdetermining the Strength

and Power of Cejitres -

One of the first consider-ations he gives this sub-ject is to determine theeffort which the centrewill have to make, inresisting the pressure at itsvarious parts; or what itwill have to bear, at dif-ferent portions of time,whilst the voussoirs arefixing; the centre notbeing at all times equallyloaded, the dimensions ofthe timbers must he pro-portioned to the burdensplaced upon them, and thisoften before the load is Fig. 2349 . centre for a tunnel.

equally distributed.

M. Pitot has calculated the scantlings of the timber ribs for a semicircular arch60 feet span, the stone ring that formed the first row of voussoirs being 7 feet inthickness. The timber was oak, and he states that a square inch will carry 8640 poundsweight with perfect security and for any length of time: hut as knots and shakes mayoccur, in order to be on the safe side, he only’ calculates upon 7200 pounds as themeasure of absolute strength. The entire weight resting on each rib or principal was707,520 pounds, the weight of a cube foot of stone being 160 pounds. M. Pitot hasin this case assumed a much more considerable weight than could occur in practice, as noarch of such a span could ever require a depth of voussoirs equal to what he has given.In a semicircular arch the voussoirs would not deposit much or any weight upon thecentre, until the joints began to form a greater angle than 30°, as before observed;consequently the pressure on each rib would be diminished at least three-fourths of theentire load, and 555,908 pounds of stone would be the quantity resting on one rib, or elevenparts out of the entire fourteen.

The dimensions of the timber forming one of the ribs were as follow : the exteriorcurved rib, cut to the form of the intrados, was in several lengths, no part less than afoot in width, and the whole 6 inches thick, all framed and bolted together; the mainstretching piece or horizontal tie-beam, as well as the under one, were each 12 inches square :the king-post 12 inches square; the upper struts 10 inches by 6, and the lower 10 inchesby 8; each rib has to carry 555,908 pounds, or of the entire weight of the stone ring,and as the lower portions of the arch on each side were nearly perpendicular, the curvedouter rib would have to bear 7200 pounds weight on every square inch of sectional area.The scantling being 12 inches by 6, the area is 72 square inches, and this multiplied by7200 gives 518,400 pounds as the quantity of support that each end of this timber willafford : the lower struts will, after the same calculation, sustain 576,000 pounds ; theirinclination has not been considered, as it does not materially affect them.

We shall find that the strength of the outer rib, or timber ring of this centre, willhave a power of sustaining 1,036,800 pounds; and if we add to this 576,000 poundsfor each of the four lower struts, we shall obtain 3,340,800 pounds strength to supporta load of 555,908 pounds. But as this load does not press perpendicularly on thesupports, it is necessary to carry the investigation further, and to determine the valueof the oblique forces, bv reducing them to a parallelogram, with sides proportionateto each force, and thus acquire the exact result. To do this a scale of equal parts maybe set out, from which may be taken the lengths of such sides as are proportionate to theexisting forces, and then measure the results by the same scale ; the scale should be divided