Energy formulation for flexural - Torsional buckling of thin-walled column with open cross- section

Abstract

In this work, the problem of flexural - torsional buckling analysis of thin-walled column with open cross-section has been formulated using energy methods. Thin-walled column with open cross-section of arbitrary slope was considered. The deformation taking place during elastic buckling was assumed to consist of a combination of twisting and bending about two axes of the cross-section. The total potential energy functional was derived as the sum of the strain energy and the potential energy of the loads. Euler - Lagrange differential equations were used to obtain the differential equations corresponding to the conditions for the minimization of the total potential energy functional. It was found that the integral formulation reduced to a boundary value problem represented by a system of three coupled differential equations in terms of three unknowns which were the three displacement variables, two translational displacements u(z), v(z) and one rotational displacement θ(z).