Stresses in Elastic Plates over Flexible Subgrades

Comparative studies are presented of the effect flexible surface layers have on the load-carrying capacity of the combined surface layer and subgrade. The analysis is based on the representation of the subgrade as a system of springs or, equivalently, as a heavy liquid. Approximate formulas are obtained for the maximum tensile stress in the surface layer and the maximum deflection of the surface layer that are produced by loads distributed uniformly in circular areas. A limit is established for the range of applicability of these formulas and this bound also determines the range of usefulness of the surface layer. In the range of usefulness, it is shown that reasonable nonuniformity of load distribution and built-in tensions of plausible magnitude are of secondary importance. Also, nonlinear effects caused by noninfinitesimal deflections are negligible if the deflections of the surface layer are no larger than approximately one-half the thickness of the surface layer.