Some Simplified Solutions for Relatively Stiff Beams on Elastic Foundations

Abstract

Maximum bending moments, rotations, and deflections of beams resting on elastic foundations and subject to central forces and bending moments are computed on the basis of a linear approximation to the foundation reaction. This reaction is determined from the rigid-body motion of the beam, and is thus statically determinate. The results of these approximate analyses are compared with those obtained from the exact theory in terms of the “characteristic parameter” of the beam, which is a function of the relative stiffnesses of the beam and the foundation. It is shown that the approximate analysis introduces very little error if the beam is stiff as compared to the foundation on which it rests.