On energy based flexural-torsional buckling criteria of double-tee shape elastic thin-walled members

Abstract

Double-tee shaped steel beam-columns under compression and major axis bending (about the section stronger principal axis) are generally sensitive to flexural-torsional buckling when insufficiently restrained against lateral-torsional deformations. Depending upon the section inertia properties about principal axes, out-of-plane restraining conditions and a ratio of the dimensionless compressive axial force and the maximum bending moment, the influence of prebuckling in-plane displacements and the in-plane buckling effect on the flexural-torsional resistance become more or less important, or even negligible. The energy formulations dedicated to the elastic flexural-torsional buckling analysis of I- or H-section steel members are usually based on the Vlasov theory of thin-walled structures in the form of linear buckling analysis. In such a classical approach, only the effect of prebuckling stress resultants is taken into account in the energy formulation, and the buckling analysis may be converted to the linear eigenproblem analysis. When nonlinear rotation terms of the displacement field components, and consequently the curvature strain components, maintain rigorously the trigonometric functions of the twist rotation, a more accurate buckling energy equations and corresponding differential equilibrium equations may be obtained. As a result, the buckling analysis may be converted to the nonlinear eigenproblem analysis. In this paper, formulations of the displacement field and the energy equation, leading to the elastic flexural-torsonal buckling criteria are widely discussed. Conclusions are drawn with regard to the utilization of obtained solutions in engineering practice.In memory of the late Professor Nicholas Snowden Trahair