Lateral buckling analysis of beams of arbitrary cross section by BEM

Abstract

In this paper, the lateral buckling analysis of beams of arbitrary cross section is presented taking into account moderate large displacements and employing nonlinear relationships between bending moments and curvatures. The beam is supported by the most general boundary conditions including elastic support or restraint. Starting from a displacement field without any simplifying assumptions about the angle of twist amplitude and based on the total potential energy principle, the stability criterion is formulated taking into account the warping effects, the prebuckling displacements and the Wagner’s coefficients due to the asymmetric character of the cross section. The stability criterion is based on the positive definiteness of the second variation of the total potential energy and is established using the Analog Equation Method (AEM), a BEM based method. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint–Venant’s torsional constant. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The effects of both the load height and prebuckling deflections as well as the discrepancy of the Eurocode 3 standard solutions are discussed.