# Unified V. Integrated Approaches in Lateral-Torsional Buckling of Beams

*Lateral-torsional buckling of beams has been a topic of research for many years, yet a correct interpretation of the phenomenon under general conditions of moment and lateral end restraints is not well established. In the literature, Timoshenko's exact solution for the uniform buckling moment of a simply supported I-beam has been treated as a reference solution and the effects of moment gradient and lateral end restraint are modelled via an empirical modification factor which, when multiplied by the reference solution, gives the buckling moment under actual conditions. This approach has been continued for the last 40 years, and various studies have been published regarding the dependence of this modification factor on moment gradient assuming simple end conditions. The results of these studies are more or less similar because of the common underlying assumption of ignoring or approximating the warping rigidity of beams for simplicity of analysis. The need for a simple design formula rather than logic was the obvious motivation for extending Timoshenko's solution to the general cases of loading and end conditions. In the authors' opinion, current approaches simply ignore the fact that the lateral-torsional buckling is a superposition of two fundamental modes of deformation, i.e. lateral bending with warping and twisting, as outlined by Worthington. Thus the effects of boundary conditions regarding lateral displacement and twist combined with the moment gradient factor on the two modes should be studied separately and then superimposed according to certain rules. This interpretation advocates the need for two parameters to describe the effects of the stated factors on the two fundamental modes and their subsequent superposition to obtain the critical moment of the combined mode. This is in contrast to the current approach of using a single factor to incorporate the effects of all the variables.
M.D. Pandey and Professor A.N. Sherbourne*