A complete treatise on stone bridging would be of little practical value to the American engineer, and would occupy too much of the necessarily small space allowed here. The object in the present chapter is to give the manner of dimensioning stone arches of from ten to sixty feet span, and of proportioning retaining walls, piers, and abutments.
CONTRACTION OF THE WATER-WAY.
246. In building a bridge across a stream, we must be careful not to obstruct the water-way so as to prevent free passage to the highest floods. Regard must be had to this in fixing the size of the spans, and the thickness and number of the piers. By contracting the width of the stream the velocity is increased beneath the arches, the same amount of water being obliged to pass through a smaller space, and when the bottom is of such a nature as to yield to this action, there is danger of the foundation being undermined. If the form and size of the piers be so arranged as not to increase the velocity, such danger will be avoided and floods will pass without harm. In bridges crossing navigable streams, if the bottom is not destroyed the velocity may be made so great as to impede navigation.
247. The following table is from Gauthey, Construction des Ponts, showing the velocities which are just in equilibrium with the material composing the bottom of the stream.
| State of the water. | Velocity in feet per second. | Nature of bottom. |
|---|---|---|
| Torrents, | 10′ 0″ | Large rocks. |
| Floods, | 3′ 3″ | Loose rocks. |
| Common, | 3′ 0″ | Gravel and stones. |
| Regular, | 2′ 0″ | Fine gravel. |
| Moderate, | 1′ 0″ | Sand. |
| Slow, | 0′ 6″ | Clay. |
| Very slow, | 0′ 3″ | Common earth. |
248. If b represents the width of the natural water-way; c, that as reduced by the structure; V, the velocity of the stream in the natural state; then the augmented velocity is expressed by
W = mVb
c;
and c = mbV
W;
where m is a constant quantity expressing the contraction which takes place in passing the narrow place, which, according to Du-Buat, is 1.09; but depending somewhat upon the form of the bridge piers; adopting which value, we have
W = 1.09Vb
c;