Effect of Shear on Simple Buckling Problem

Abstract

The present note studies the buckling behavior of a hinged‐hinged column, taking into consideration the effect of shear deformation. The approach taken is an extension of the method proposed by Timoshenko and Gere in 1961. In this approach, the axial force is assumed to act in the direction tangent to the deformed axis of the member, and the shear force is assumed to act in the direction normal to the deformed axis. The same constitutive equation as Timoshenko and Gere is used. Further analysis differs in the following: (1) a different shear‐correction factor was used; and (2) the assumption that displacements are small was not used. As a result of latter assumption, the differential equations presented in the note are nonlinear. The solution to this equation yields not only the critical force, but the buckled shape of the rod, as well. The buckled shape is obtained by numerical integration. It is shown that by decreasing the shear stiffness (under the constant compressive force) the maximum deflection increases and, at a certain value, the possibility for higher buckling modes appears.