Column on an Elastic foundation under vertical load

Abstract

The problem of buckling of a column standing on an elastic foundation has been posed exactly as an elastostatic mixed boundary value problem and solved by using Hankel Transform and Tranter's mehtod of dual equations. The effect of imbedding is ignored. An equation for the critical load for buckling is obtained which reduces to the well-known formula for the Euler column. Critical loads are determined in two cases which show a decrease in their values because of the elasticity of the foundation. Stresses under the foot of the column have been computed for loads less than the critical loads.