Of plans for the construction of bridges, perhaps the following are the most useful. Fig. 103 shows a method of constructing wooden bridges where the banks of the river are high enough to permit the use of the tie-beam, a b. The upright pieces, c d, are notched and bolted on in pairs, for the support of the tie-beam. A bridge of this construction exerts no lateral pressure upon the abutments. This method may be employed even where the banks of the river are low, by letting the timbers for the roadway rest immediately upon the tie-beam. In this case the irame-work above will serve the purpose of a railing.
Fig. 104 exhibits a wooden bridge without a tie-beam. Where staunch buttresses can be obtained this method may be recommended; but if there is any doubt of their stability, it should not be attempted, as it is evident that such a system of framing is capable of a tremendous lateral thrust.
243. - Bridges: Built-Rib. - Fig. 105 represents a bridge with a built-rib (see Art. 231) as a chief support. The curve of equilibrium will not differ much from that of a parabola; this, therefore, may be used - especially if the rib is made gradually a little stronger as it approaches the buttresses. As it is desirable that a bridge be kept low, the following table is given to show the least rise that may be given to the rib.
Span in Feet.
Least Rise in Feet
Span in Feet.
Least Rise in Feet
Span in Feet.
Least Rise in Feel
The rise should never be made less than this, but in all cases greater if practicable; as a small rise requires a greater quantity of timber to make the bridge equally strong. The greatest uniform weight with which a bridge is likely to be loaded is, probably, that of a dense crowd of people. This may be estimated at 70 pounds per square foot, and the framing and gravelled roadway at 230 pounds more; which amounts to 300 pounds on a square foot. The following rule, based upon this estimate, may be useful in determining the area of the ribs.
Rule LXVII - Multiply the width of the bridge by the square of half the span, both in feet, and divide this product by the rise in feet multiplied by the number of ribs; the quotient multiplied by the decimal 0.0011 will give the area of each rib in feet. When the roadway is only planked, use the decimal 0.0007 instead of 0.0011,
Example. - What should be the area of the ribs for a bridge of 200 feet span, to rise 15 feet and be 30 feet wide, with three curved ribs? The half of the span is 100, and its square is 10000; this multiplied by 30 gives 300000, and 15 multiplied by 3 gives 45; then 300000 divided by 45 gives 6666 2/3, which multiplied by 0.0011 gives 7.333 feet or 1056 inches for the area of each rib. Such a rib may be 24 inches thick by 44 inches deep, and composed of 6 pieces, 2 in width and 3 in depth.
The above rule gives the area of a rib that would be requisite to support the greatest possible uniform load. But in large bridges, a variable load, such as a heavy wagon, is capable of exerting much greater strains; in such cases, therefore, the rib should be made larger.*
In constructing these ribs, if the span be not over 50 feet, each rib may be made in two or three thicknesses of timber (three thicknesses is preferable), of convenient lengths bolted together; but in larger spans, where the rib will be such as to render it difficult to procure timber of sufficient breadth, they may be constructed by bending the pieces to the proper curve and bolting them together. In this case, where timber of sufficient length to span the opening cannot be obtained, and scarfing is necessary, such joints must be made as will resist both tension and compression (see Fig. 114). To ascertain the greatest depth for the pieces which compose the rib, so that the process of bending may not injure their elasticity, multiply the radius of curvature in feet by the decimal 0.05, and the product will be the depth in inches. Example. - Suppose the curve of the rib to be described with a radius of 100 feet, then what should be the depth? The radius in feet, 100, multiplied by 0.05 gives a product of 5 inches. White pine or oak timber 5 inches thick would freely bend to the above curve; and if the required depth of such a rib be 20 inches, it would have to be composed of at least 4 pieces. Pitch pine is not quite so elastic as white pine or oak - its thickness may be found by using the decimal 0.046 instead of 0.05.
* See Tredgold's Carpentry by Hurst, Arts. 174 to 177.
244. - Bridges: Framed Rib. - In spans of over 250 feet, a framed rib, as in Fig. 106, would be preferable to the foregoing. Of this, the upper and the lower edges are formed as just described, by bending the timber to the proper curve. The pieces that tend to the centre of the curve, called radials, are notched and bolted on in pairs, and the cross-braces are halved together in the middle, and abut end to end between the radials. The distance between the ribs of a bridge should not exceed about 8 feet. The roadway should be supported by vertical standards bolted to the ribs at about every 10 to 15 feet. At the place where they rest on the ribs, a double, horizontal tie should be notched and bolted on the back of the ribs, and also another on the underside; and diagonal braces should be framed between the standards, over the space between the ribs, to prevent lateral motion. The timbers for the roadway may be as light as their situation will admit, as all useless timber is only an unnecessary load upon the arch.
245. - Bridges: Roadway. - If a roadway be 18 feet wide, two carriages can pass without inconvenience. Its width, therefore, should be either 9, 18, 27, or 36 feet, according to the amount of travel. The width of the footpath should be two feet for every person. When a stream of water has a rapid current, as few piers as practicable should be allowed to obstruct its course; otherwise the bridge will be liable to be swept away by freshets. When the span is not over 300 feet, and the banks of the river are of sufficient height to admit of it, only one arch should be employed. The rise of the arch is limited by the form of the roadway, and by the height of the banks of the river (see Art. 243). The rise of the roadway should not exceed one in 24 feet, but as the framing settles about one in 72, the roadway should be framed to rise one in 18, that it may be one in 24 after settling. The commencement of the arch at the abutments - the spring, as it is termed - should not be below high-water mark; and the bridge should be placed at right angles with the course of the current.
246. - Bridges: Abutments. - The best material for the abutments and piers of a bridge is stone; and no other should be used. The following rule is to determine the extent of the abutments, they being rectangular, and built with stone weighing 120 pounds to a cubic foot.
Rule LXVIII - Multiply the square of the height of the abutment by 160, and divide this product by the weight of 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 of 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 possible load upon it, 300 pounds, and the rise of the arch 18 feet: what should be its thickness? The square of the height of the abutment, 400, multiplied by 160 gives 64000, and 300 by 18 gives 5400; 64000 divided by 5400 gives a quotient of 11.852; one added to this makes 12.852, the square root of which is 3.6; this, less one is 2.6; this multiplied by 100 gives 260, and this again by 300 gives 78000; this divided by 120 times the height of the abutment, 2400, gives 32 feet 6 inches, the thickness required.
The dimensions of a pier will be found by the same rule; for, although the thrust of an arch may be balanced by an adjoining arch when the bridge is finished, and while it remains uninjured, yet, during the erection, and in the event of one arch being destroyed, the pier should be capable of sustaining the entire thrust of the other.
Piers are sometimes constructed of timber their principal strength depending on piles driven into the earth; but such piers should never be adopted where it is possible to avoid them; for, being alternately wet and dry, they decay much sooner than the upper parts of the bridge. Spruce and elm are considered good for piles. Where the height from the bottom of the river to the roadway is great, it is a good plan to cut them off at a little below low-water mark, cap them with a horizontal tie, and upon this erect the posts for the support of the roadway. This method cuts off the part that is continually wet from that which is only occasionally so, and thus affords an opportunity for replacing the upper part. The pieces which are immersed will last a great length of time, especially when of elm; for it is a well-established fact that timber is less durable when subject to alternate dryness and moisture than when it is either continually wet or continually dry. It has been ascertained that the piles under London Bridge, after having been driven about 600 years, were not materially decayed. These piles are chiefly of elm, and wholly immersed.