Stresses in a Layered Half-Plane

A general solution is given for the elastic stress distribution in a layered half-plane loaded normal to its boundary, both for plane stress and plane strain conditions. The solution has been developed using Fourier integrals. Detailed numerical work is done for an infinite beam resting on a half-plane loaded by a concentrated load at the top. The numerical work was chosen so as to determine the effect on the interface stresses of difference in Poisson's ratios of the beam and the foundation. The numerical results indicate that the effect of different Poisson's ratios between the beam and the foundation is predominantly on the shear stress, and not on the normal stress distribution at the interface, for both plane stress and strain conditions.