Bending of a Cantilever Plate Supported From an Elastic Half Space

A solution is obtained for an infinitely long cantilever plate supported from an elastic half space. The junction conditions between the elasticity approach for the half space and the classical plate theory (no-shear) approach for the plate are based upon the use of assumed equilibrium surface tractions for the half space. The formal Fourier integral results for the example of a concentrated free-edge load are evaluated using an IBM 704 computer. The correlation with the deflection results of a steel model test is shown to be very good. The small deviations from the theoretical values are primarily due to shear effects in the model. It is also shown that, except for very stubby plates, it is sufficiently accurate to neglect the shear effects along the half space, and to assume that the rotation is proportional to the moment in the conventional “Winkler” sense.