Buckling of columns. Allowance for axial shortening

Abstract

This paper investigates the effect of axial shortening on (i) the elastic buckling of columns with a continuous elastic restraint, (ii) the elastic buckling of rotating columns and (iii) the free vibration of columns under a static axial load. These column problems may be solved in a unified approach because the resulting energy functional is similar. The field differential equation is derived by minimizing the energy functional with respect to the lateral displacement function via calculus of variations. The buckling load or fundamental frequency may be obtained by solving analytically the two-point boundary value problem. It was found that the boundary conditions and the restraint parameter or angular velocity parameter affect the influence of axial shortening on the buckling load. In vibrating columns, tensile forces enhance the effect of axial stretching on the fundamental frequency.