The requirements for the bridge seats for the ends of the two spans resting on a pier, are usually such that a pier with a top as large as thus required, and with a proper batter to the faces, will have all the strength necessary for the external forces acting on the pier. For example, the channel pier of one of the large railroad bridges crossing the Mississippi River was capped by a course of stonework 14 feet wide and 29 feet long, besides two semi-circles with a radius of 7 feet. The footing of this pier was 30 feet wide by 70 feet long, and the total height from subsoil to top was about 170 feet. This pier, of course, was unusually large. For trusses of shorter span, the bridge seats are correspondingly smaller. The elements which affect stability are so easily computed that it is always proper, as a matter of precaution, to test every pier designed to fulfil the other usual requirements to see whether it is certainly safe against certain possible methods of failure. This is especially true when the piers are unusually high.

The requirements for supporting the truss are, fortunately, just such as give the pier the most favorable formation so that it offers the least obstruction to the flow of the current in the river. In other words, since the normal condition is for a bridge to cross a river at right angles, the bridge piers are always comparatively long (in the direction of the river) and narrow in a direction perpendicular to the flow of the current. The rectangular shape, however, is modified by making both the upper and the lower ends pointed. The pointing of the upper end serves the double purpose of deflecting the current, and thus offers less resistance to the flow of the water; and it also deflects the floating ice and timber, so that there is less danger of the formation of a jam during a freshet. The lower end should also be pointed in order to reduce the resistance to the flow of the water. The ends of the piers are sometimes made semicircular, but a better plan is to make them in the form of two arcs of circles which intersect at a point.

## 232. Possible Methods Of Failure

The forces tending to cause a bridge pier to fail in a direction perpendicular to the line of the bridge, include the action of wind on the pier itself, on the trusses, and on a train which may be crossing the bridge. They will also include the maximum possible effect of floating ice in the river and of the current due to a freshet. It is not at all improbable that all of these causes may combine to act together simultaneously. The least favorable condition for resisting such an effect is that produced by the weight of the bridge, together with that of a train of empty cars, and the weight of the masonry of the pier above any joint whose stability is in question. The effects of wind, ice, and current will tend to make the masonry slide on the horizontal joints. They will also increase the pressure on the subsoil on the downstream end of the foundation of a pier. They will tend to crush the masonry on the downstream side, and will tend to tip the pier over.

Another possible method of failure of a bridge pier arises from forces parallel with the length of the bridge. The stress produced on a bridge by the sudden stoppage of a train thereon, combined with a wind pressure parallel with the length of the bridge, will tend to cause the pier to fail in that direction (see Fig. 71). Although these forces are never so great as the other external forces, yet the resisting power of the pier in this direction is so very much less than that in the other direction, that the factor of safety against failure is probably less, even if there is no actual danger under any reasonable values for these external forces.

Fig. 71. Bridge Pier.