FIINCTIONS OF A BRIDGE PIER. A bridge pier has two functions: (1) it must support the bridge, and (2) it must permit water to pass with the least possible disturbance to that water. The first concerns the stability of the pier, which depends upon its vertical cross section; and the second concerns the form of the horizontal cross section of the pier.
A bridge pier may fail in either of two ways: (1) by sliding or overturning down stream, i.e., longi tudinally, or (2) by sliding or overturning laterally.
Effect of Wind. The pressure of the wind against the truss alone is usually taken at 50 lb. per sq. ft. against twice the vertical projection of one truss, which for well-proportioned trusses will average about 10 sq. ft. per linear foot of span. The pressure of the wind against the truss and train together is usually taken at 30 lb. per sq. ft. of truss and train. The train exposes about 10 sq. ft. of surface per linear foot. The pressure of the wind against any other than a flat surface is not known with any certainty; for a cylinder, it is usually assumed that the pressure is two thirds of that against its vertical projection.
The center of pressure of the wind on the truss is practically at the middle of its height; that of the wind on the train is 7 to 9 feet above the top of the rail, according to whether the train is for freight or passengers; and that of the wind on the pier is at the middle of the exposed part.
Effect of Current. For the pressure of the current of water against an obstruction, Weisbach's Mechanics of Engineering (page 1,030 of Coxe's edition) gives the formula, in which P is the pressure in pounds, s the exposed surface in sq. ft., k a coefficient depending upon the ratio of width to length of the pier, to the weight of a cubic foot of water, v the velocity in ft. per sec., and g the acceleration of gravity. For piers with rectangular cross section, k varies between 1.47 and 1.33, the first being for square piers and the latter for those 3 times as long as wide; for cylinders, k = about 0.73. The law of the variation of the velocity with depth is not certainly known; but it is probable that the velocity varies as the ordinates of an ellipse, the greatest velocity being a little below the surface. Of course, the water has its maximum
effect when at its highest stage.
The center of pressure of the current is not easily determined, since the law of the variation of the velocity with the depth is not accurately known; but it will probably be safe to take it at one third the depth.
Floating Ice. The pier is also liable to a horizon:;al pressure due to floating ice. The formulas for impact are not applicable to this case. The assumption is sometimes made that the field of ice which may rest against the pier will simply increase the surface exposed to the pressure of the current. The greatest pressure possible will occur when a field of ice, so large that it is not stopped by the impact, strikes the pier and plows past, crushing a channel through it equal to the greatest width of the pier. The resulting horizontal pressure is equal to the area crushed multiplied by the crushing strength of the ice. The latter varies with the temperature; but since ice will move down stream in fields only when melting, we desire its minimum strength. The crushing strength of floating ice is some times put at 20 tons per sq. ft. (300 lb. per sq. in.); but in com puting the stability of the piers of the St. Louis steel-arch bridge, it was taken at 600 lb. per sq. in. (43 tons per sq. ft.). According to experiments made under the author's direction,* the crushing strength of ice at 23° F., varies between , 370 and 760 lbs. per sq. in.
The arm for the pressure of the ice should be measured from high water.
Occasionally a gorge of ice may form between the piers and dam the water back. The resulting horizontal pressure on a pier will then be equal to the hydrostatic pressure on the width of the pier and half the span on either side, due to the difference between the level of the water immediately above and below the bridge opening. A pier is also liable to blows from rafts, boats, etc.; but as these can not occur simultaneously with a field of ice, and will probably be smaller than that, it will not generally be necessary to consider them.