Lateral-torsional buckling capacity of beams with varying cross-sections: an analytical approach

Purpose This study aims to develop an analytical approach to accurately predict the lateral-torsional buckling (LTB) capacity of beams with varying cross-sections (VCS) such as beams with web openings (e.g castellated and cellular beams) and beams with patch corrosion. Existing expressions for elastic critical moments are limited to beams with uniform cross-sections and do not capture the influence of geometric variations. Design/methodology/approach An explicit analytical formula for the elastic critical moment is derived using the energy (Rayleigh–Ritz) method, equating the strain energy during LTB to the external work done by loads. The derivation covers simply supported and fixed-ended beams subjected to end moments and extends to other loading conditions through moment modification factors. The analytical results are validated against existing experimental and finite element (FE) data for beams with web openings. Hence the corresponding design LTB moment capacities are established. Findings The analytical predictions show very good agreement with experimental and FE results for beams with web openings. The method provides slightly conservative predictions when distortional buckling interactions are present. The results confirm that the proposed formula effectively captures the physical LTB behaviour in beams with VCS. Originality/value This paper proposes, for the first time, an explicit energy-based analytical formulation for the elastic critical buckling moment of beams with VCS such as beams with web openings and beams with patch corrosion. The approach bridges theoretical understanding and design practice, providing a computationally efficient and physically consistent method suitable for assessing the structural integrity and reuse of existing steel structures.