Rayleigh Ritz formulation for moment modification factors on lateral torsional buckling

Lateral-torsional buckling is a major stability concern for long span flexural members, especially during construction and in the negative moment regions of composite I-girders. The classical solution for lateral-torsional buckling was formulated several decades ago for a simply-supported doubly-symmetric I-beam subjected to uniform moment. The classical solution was subsequently modified in order to design for other boundary conditions and loading scenarios, by the use of empirical equations for moment magnification factors. Finite element modelling to calculate lateral-torsional buckling capacities, though accurate, is not practical to implement in every design scenario. The use of empirical equations is also problematic, given that there are different equations for moment modification factors in literature and international design specifications for identical loading and boundary conditions. This paper shows that each of these equations is most accurate within a limited range of applicability. The authors derive the critical lateraltorsional buckling moment solutions using the Rayleigh-Ritz method for beams with both simply-supported and fixed boundary conditions, and subjected to different loading scenarios. Finally, these analytical solutions are shown to compare well with finite element models for a few sample cross-sections.

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