The coefficient of rolling friction for bridge rollers in good con dition, or of sliding plates in good condition is comparatively small; but if the rollers fail to work or the plates become rusted, the bridge is compelled to slide, when the coefficient of friction may become 0.15 to 0.20 or even more for high unit pressures.
Wind on Side of Pier. The amount and point of applica tion of the force of the wind against a pier has been considered in 1091, and hence nothing need be said here on that subject.
Resultant Stability. The resultant tendency to slide is equal to the square root of the sum of the squares of the longitudinal and of the transverse forces tending to produce sliding.
Similarly, the resultant force tending to overturn the pier is equal to the square root of the sum of the squares of the longitudinal and of the transverse forces; but ordinarily the factor of safety for the resultant moment will be greater than that for the transverse moment, because the arm of the resisting moment is considerably greater, being half of a diagonal diameter of the pier instead of half of the shortest diameter.
Strictly, the formula for the maximum crushing stress (equation 1, page 354) should be applied in the plane of the resultant moment, in which case I would represent the moment of inertia of the hori zontal cross section with reference to an axis through the center of gravity of the section and perpendicular to the plane of the resultant moment; but ordinarily the following approximate solution is sufficient. The maximum compressive stress due to the forces acting longitudinally upon the pier occurs at the down-stream end of a horizontal section, and that due to the forces acting transversely upon the pier occur at one side of a horizontal section; and there fore the resultant compressive stress will be approximately the sum of the maximum longitudinal and of the maximum transverse forces.
If the down-stream end of the horizontal cross section is square, this approximate solution will be more nearly correct than if the down-stream end is pointed.