Sometimes a bridge pier is subjected to a heavy shove from the expansion of freezing ice; but the usual method of protecting the pier is to break up the ice immediately around the pier.
Resisting Forces. The force resisting sliding is the friction due to the combined weight of the train, the bridge, and the part of the pier above the section considered. For the greatest refinement, it would be necessary to compute the forces tending to slide the pier for two conditions, viz.: (1) with a wind of 50 lb. per sq. ft. on truss and pier, in which case the weight of the train should be omitted from the resisting forces; and (2) with a wind of 30 lb. per sq. ft. on truss, train, and pier, in which case the weight of a train of empty box cars should be included in the resisting forces. If the water can find its way under the foundation in hydrostatic condition, the weight of the part of the pier that is immersed in the water will be diminished by 621 lb. per cu. ft. by buoyancy; but if it finds its way under any section by absorption only, then no allowance need be made for buoyancy.
The forces resisting overturning are the weight of the pier above the section considered and the combined weight of the truss and the train.
Conclusion. The factor of safety against sliding and over turning can easily be computed similarly as for dams. However, in computing the maximum compressive stress in bridge piers the formulas employed for dams can not be applied, since they are appli cable only to elementary rectangular sections, while in computing the maximum compressive stress in bridge piers the entire cross section must be considered, and as a rule it is not a rectangle. Equations 1 and 2, page 354, are applicable to bridge piers, in which case I is the moment of inertia of the horizontal cross section about an axis through its center of gravity and perpendicular to its long axis.
In the former editions of this book an example was given of the method of computing the stability of a bridge pier. That investigation was made for an unusually high pier standing between two unusually long single-track railroad spans (Fig. 143, page 558), and the most dangerous conditions were assumed. The result of that computation was that any pier which has sufficient room on top for the bridge seat and which has a batter of 1 in 12 or 1 in 24 is safe against any mode of failure from longitudinal forces; in other words, the length required on the top for the bridge seat, together with a slight batter for appearance, generally give sufficient longi tudinal stability of a single-track pier against sliding, overturning, and crushing. This conclusion is especially true for a double-track
bridge, and for a pier of truly monolithic concrete.
Dynamic Action of Train. The locomotive in drawing a train, particularly up a steep approach, exerts a pull which must finally be balanced by the resistance of a pier to sliding and over turning in a direction opposite to the motion of the train; and if brakes are applied to the moving train while upon the bridge, a force will be developed which tends to slide and overturn a pier in the same direction as the motion of the train. The latter is the larger, since it may be one fifth of the weight of the entire train upon any one span. This force acts at the level of the rail. The moment of this force about the edge of any horizontal cross section is resisted by the moment of the combined weight of the truss, the train, and the pier.
Expansion of Bridge. The expansion or contraction of the bridge may exert a lateral pull on the pier. If the rollers or sliding plates at the free end of the bridge are in good working condition, this force is comparatively unimportant; but if the rollers become blocked by cinders and rust, as they frequently do, or if the sliding plates become rusted, as they often do, the force developed by the expansion or contraction of the bridge may be quite important. The . force developed is equal to the weight of the bridge multiplied by the coefficient of friction. This force may act either with or against the dynamic action of the.train; but of course the former is the condition to be considered.