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Journal Articles International Journal of Solids and Structures Year : 2023

Elastoplastic bifurcation analysis for the lateral–torsional buckling of straight beams

Abstract

This paper deals with the lateral–torsional buckling of elastoplastic steel beams under pure bending considering various cross-section geometries. Critical buckling moment expressions for elastic beams are well documented. In contrast, less attention has been devoted to the lateral–torsional buckling phenomenon in elastoplastic regime. When considering short beams (with sufficiently low slenderness), plastic zones will develop before buckling occurs. The problem being faced here is however much more complex than the classical problem of an elastoplastic beam subjected to an axial compressive force. Under such loading, plasticity occurs instantaneously and evolves uniformly over the cross-section and along the beam length whereas, in the other case, plasticity will spread gradually and the plastic zones will change with the loading. The main objective of the present paper is to develop original analytical solutions for the elastoplastic lateral–torsional buckling of perfectly straight beams. A general formulation based on a previously developed 3D plastic bifurcation theory is first proposed and then applied to the cases of two specific cross-section geometries, namely rectangular and I profiles. For the sake of simplicity, transverse shear strains are neglected in the analysis. The von Mises yield criterion with a linear isotropic hardening is adopted. In the case of a rectangular cross-section, closed-form solutions are obtained for the elastoplastic critical buckling moment, which is shown to depend on the geometric and material parameters of the beam, including the yield stress. For validation purposes, all the analytical solutions are compared against the results of numerical computations performed with an in-house program based on a shell finite element formulation. Analytical and numerical results are in very good accordance, making the analytical method presented here an efficient and precise tool to analyze the elastoplastic lateral–torsional buckling phenomenon.
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hal-03971167 , version 1 (16-02-2023)

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Chedid Saade, Philippe Le Grognec, Maël Couchaux, Mohammed Hjiaj. Elastoplastic bifurcation analysis for the lateral–torsional buckling of straight beams. International Journal of Solids and Structures, 2023, 264, pp.112106. ⟨10.1016/j.ijsolstr.2023.112106⟩. ⟨hal-03971167⟩
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