Full beam formulation for the lateral torsional buckling analysis of elastic frames by considering the structural detail of beam-to-column joint

Abstract

The total potential energy formulation plays an essential role in investigating the flexural–torsional instability of elastic plane frames composed of thin-walled members. However, the work conjugateness between the internal moments and rotation variables of typical frame member cannot be restored completely when applying the conventional potential energy approaches. This paper aims to fully consider the virtual work done by the induced conservative and nonconservative moments in the planar frame prone to lateral buckling. The proposed full beam formulation can help identify those neglected moments that are necessary for fulfilling the equilibrium at the critical state no matter which potential energy formulation is concerned. It has been found that the relative significance of the virtual work done by the neglected moments with respect to the first variation of total potential energy is served as an indicator as whether the conventional potential energy equation can be used for investigating the lateral torsional buckling behavior of the frame. In the out-of-plane buckling investigation of benchmark elastic frames, it has been demonstrated in cases where the neglection of non-zero virtual work done by the nonconservative moment or an approximate account of the induced bimoment through the kinematic warping model may result in incorrect critical load. The lateral torsional buckling strength of the elastic frames can only be correctly determined by taking into account the structural configuration of beam-to-column joint.