The safe bearing capacity of a floating ice sheet is usually determined by limiting the maximum tensile stress which occurs under the load at the bottom of the ice sheet. If the size of the load distribution is large compared to the ice thickness, the thin plate theory predicts these stresses correctly. However, if the size of the load distribution becomes small compared to the ice thickness, the plate theory overestimates the stresses. In this case the ice sheet should he treated as a three-dimensional elastic layer.
Previous investigators have solved the elastic-layer problem for loads distributed over a circular area, and have limited the results to the stress at the bottom of the ice sheet directly under the center of the load. In the present paper the stresses are evaluated at any radial position, and it is shown how these stresses approach those for the plate theory as the radial position becomes large. The solutions for the stresses are presented in integral form, as well as graphs from the numerical integration. These new results are significant for the superposition of stresses when two concentrated loads act near each other.
Similarly for loads distributed over a rectangular area, the plate theory will overestimate the stresses if the dimensions of the load becomes small compared to the ice thickness. For this case integral solutions are presented for the stresses, and are evaluated directly under the center of the load.