The effect of cross-section geometry on the lateral–torsional behavior of thin-walled beams: Analytical and numerical studies

Abstract

In this paper, the elastic lateral–torsional behavior of simple beams is discussed by presenting a novel analytical solution and performing numerical studies. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, significantly different when the second-order nonlinear behavior of beams with initial imperfections is analyzed. To understand and explain the observed differences, a novel analytical model is worked out for the geometrically nonlinear analysis of beams with initial geometric imperfections. The advancement in the presented analytical solution is the explicit consideration of the changing geometry as the load increases. The most important steps of the derivations are summarized, and the resulting formulae are briefly discussed. The derivations are done for general cross-sections, however, the bending is assumed to act in one of the principal planes. Numerical studies are also presented, focusing on mono-symmetric cross-sections. As part of the numerical studies, first, the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae can capture the most essential elements of the behavior observed in the shell finite element calculations, justifying that the cross-section shape might have a significant effect on the nonlinear lateral–torsional behavior of beams. Then the effect of the lateral–torsional buckling is predicted by calculating buckling reduction factors, using the results of the geometrically nonlinear finite element calculations. The capacity prediction results, again, justify that the cross-section shape, as well as the sign of the assumed geometric imperfection, might have a non-negligible effect on the buckling reduction factors, and on the capacity of the member.