382. The abutments and piers of wooden bridges are frequently executed in stone, in which case their construction falls within the mason's province; nevertheless, as they should be capable of sustaining the thrust when curved ribs are used without a horizontal tie, the following rule is given for finding the proper thickness; the abutments being rectangular, and the weight of a cubic foot of the masonry 120 lbs.

* 'Edinburgh Philosophical Journal,' No. 1, p. 191.

Rule. - Multiply the square of the height of the abutment by 160, and divide the product by the weight on a square foot of the arch, and by the rise of the arch; add unity to the quotient, and extract the square root.

Diminish the square root by unity, and multiply the root so diminished by half the span of the arch, and by the weight on a square foot of the arch.

Divide the last product by 120 times the height of the abutment, and the quotient will be the thickness of the abutment.

Example. - Let the height of the abutment from the base to the springing of the arch be 20 feet, half the span 100 feet, the weight of a square foot of the arch, including the greatest probable load upon it, 300 pounds, and the rise of the arch

18 feet. Then 16x20x20/300x18 = 11.852, and 11. 852 + 1 =

12.852. The square root of 12.852 is 3.6 nearly; and

3.6-1 = 2.6. Also 2.6x100x300/120x20= 32.5 feet, the thickness required.

The thickness of the abutment thus determined is one-fourth more than would barely resist the thrust of the ribs, not reckoning the additional stability it receives from that part of the height above the springing. In order to prevent any risk of sliding at the joints of the masonry, it would be an advantage to incline them towards the opening of the bridge, making the inclination less and less as it approaches the base. In the bridge, Plate XLVIII., the joints arc drawn in the manner proposed.

383. When piers are necessary, it is best to construct them of stone, as timber decays very rapidly when exposed alternately to dryness and moisture, which is the worst situation in which timber can be placed.

Stone piers have been used for wooden bridges in many situations, particularly the following: -

It will be seen that considerable latitude has been taken in fixing the dimensions of stone piers. If it be considered that they should be capable of withstanding the thrust of the arches, their thickness should be found by the same rule as that given for the abutments. The ends of stone piers should be formed by the intersection of two parabolic curves, in order that the water may glide easily past them.‡

384. When piers are constructed of timber, they may, in simple cases, be formed by driving a single row of piles for each pier in a line with the current of the river. The piles may be from 10 to 14 inches square, and placed at from 2 to 4 feet distance from one another. The piles should be strengthened by oblique braces. Fig. 118 represents a pier of this kind.

385. In a deep river, or where the height of the roadway is much above the surface of the water, it is difficult to get piles of sufficient length. In such a case the piles may be driven and cut off a little below low-water mark, and upon

* ' Quarterly Review,' vol. xix., p. 256.

†Gauthey, ' Construction des Ponts.'

‡ See Du Buat, ' Principes d'Hydraulique.' these piles posts may be placed for supporting the roadway. The joinings should be secured by means of horizontal pieces well bolted together. A, B, and C (Fig. 119), show how the upper and lower parts of the pier should be connected.

Fig. 118.

Fig. 110.

The piers of the Bridge of St. Clair, at Lyons, were constructed nearly in this manner,* and it has the advantage of giving a good hold to the piles, besides rendering them much easier to drive; it also cuts off the connection between the part of the pier which is constantly wet, therefore less liable to decay, and that which is alternately wet and dry, and the posts can be repaired or renewed with much greater facility.

386. When the depth of the river is very considerable, it would not be safe to trust to a single row of piles; in that case the lower part should consist of a double row, B B (Fig. 120), at about three feet apart from middle to middle, connected by the horizontal beams E E, and the cross pieces D D, for supporting the posts.

Fig. 120.

In order to secure the feet of the posts they must be clasped by two horizontal ties, C, C, and the whole well bolted together.

Figs. 118 and 121 show how the posts may be braced; and when their height is considerable, one or more courses

* Gautkey, ' Construction des Ponts.' of horizontal ties will be required in addition to the inclined braces.

Fig. 121.

387. Instead of driving piles for the piers or supports of a wooden bridge, another method has been adopted with perfect success by Telford on the river Severn, about eight miles below Shrewsbury. He makes choice of any convenient situation on the banks of the river for constructing the pier, which consists of an upright frame, having a grated platform attached so as to form the base, which extends on each side of the upright frame. The pier is then sunk in its proper situation, the bottom having been carefully levelled to receive it.

Through the spaces in the grated frame or platform short piles are driven to keep the whole secure in its place. The sides of the upright frame are covered with planking, and in order to add to the stability, the lower parts are filled with gravel and small stones.

To prevent ice, or other bodies carried down by the current, from injuring the piers, the edges of the frames which face the stream have triangular pieces of cast iron fixed upon them.* Fender piles also are sometimes driven so as to form a triangle at a little distance above and opposite to each pier.

388. When a river is subject to ice floods the piers should be protected by ice-breakers, which should be detached, in order that the bridge may not be injured by the shock of bodies descending with the current. Ice-breakers may consist of a single row of piles, connected by two horizontal beams, with an inclined capping, the edge of which is protected by a triangular prism of cast iron, or it may consist of two rows of inclined piles, the heads of which abut against an inclined capping, protected with iron as shown by Figs. 122 and 123. The inclined sides ought to be covered with planking, though not shown in Fig. 122.

Fig. 122

Fig. 123.

* ' Edinburgh Encyclopaedia,' art. Bridge.

In a large bridge there is little danger to be apprehended from connecting the ice-breaker with the pier.

389. Piles from 10 to 14 inches diameter require to be driven with a ram of from 1000 to 1700 lbs. weight.

Sheeting piles require a ram from 500 to 900 lbs. weight, and are about 8 or 9 inches wide and 3 or 4 inches thick.

Notwithstanding that every precaution is taken to ensure the durability of wooden piers, they are almost always found to be in a state of decay before the superior parts of the bridge; therefore wood should only be used when stone is difficult to procure.

390. In situations where timber is liable to be attacked by the worm, iron piles might be used with advantage, and where the soil is soft or sandy, the screw-pile invented by Mr. Alexander Mitchell is one of the best that could be devised; even in ordinary situations, a cast-iron screw may be used to form the base of the wood pile which is to support the bridge. The screw to have a socket end to project above the ground into which the foot of the wood pile can be stepped.

391. Fig. 89, Art. 287, and Figs. 112 and 117, Art. 344, show the methods of framing applicable to the piers of viaducts and aqueducts, which are usually of great height. Fig. 124 shows the method adopted in framing the trestles or supports of a lofty aqueduct near Smartsville, Yuba County, in California, described by Mr. J. A. Phillips in his work on the 'Mining and Metallurgy of Gold and Silver.'

Fig. 124.