Assessment Of Fundamental Lateral Torsional Buckling As The Minimum Critical Case

Abstract

Critical buckling moment is a fundamental property of the flexural resistance of laterally unsupported steel beams. In principle, it is easy to calculate the fundamental critical buckling moment (critical buckling moment for simply supported steel beams with doubly symmetric cross-section subjected to uniform moment). Still, the actual elastic critical moment strongly depends on both the bending moment distribution and restrictions at end supports. Standards estimate the actual critical buckling moment as a multiplier "Moment Gradient Factor" of the fundamental critical buckling moment as what was thought as the most severe case. It is believed that the fundamental critical moment is the minimum critical case for these reasons. First, researchers thought that the fundamental critical moment is the most severe case because studies find that if the moment gradient factor equals one, it tends to be conservative. second, the fundamental critical moment is not more than actual critical moment under a linear moment, distributed load, and concentrated loads. To the authors’ knowledge, no study finds cases where the actual critical LTB is less than the critical buckling moment of uniform bending moments due to variation in moment diagram and boundary condition. This paper studies if the fundamental moment is the minimum critical case by investigating the lateral torsional buckling of twenty representative I-shaped beams subjected to an intermediate moment and two inverted loads with different in-plane and out-of-plane boundary conditions. The actual critical moments are determined numerically using LTBeam and ANSYS, free and commercial software, respectively. The results prove that the fundamental moment is not the minimum critical case under specific loading conditions and show the need to study the cases of critical buckling moments that led to moment gradient factor values of less than one. Further work is required to find cases like this and apply the same loading pattern on single symmetric and cold formed sections to provide a suitable moment gradient factor formula