Post Lateral-Torsional Buckling Behaviour of a Simply-Supported Beam Subjected to Midspan Point Load

Lateral-torsional buckling (LTB) is a critical instability phenomenon in slender beams subjected to major axis bending, involving both lateral displacement and torsional rotation. Although the critical buckling load has been widely studied, the nonlinear post-buckling response of beams has gathered less attention. This thesis investigates the LTB behavior of simply-supported European rolled I-section (IPE) beams subjected to midspan point load. Beam profiles of IPE 120 to IPE 300 with unbraced span lengths varying from 2.0 m to 6.0 m and with “fork-type” restraint, that prevents twist of cross-section, are examined. The study examines both the critical buckling load and the post-buckling response of the beams neglecting cross-section warping. Two analytical models employing energy-based formulations derived from the principle of minimum potential energy assuming circular and parabolic deformation paths are employed with a goal of developing accurate analytical solutions. These models provide expressions for load as a function of displacement and twist, offering insight into the beam’s buckling and post-buckling behavior. In parallel, a nonlinear numerical finite element model (FEM) is developed in OpenSeesPy to simulate the LTB behavior. The study includes a comparison of critical buckling load obtained from analytical methods, the developed numerical model and the Eurocode formulation. The emphasis of the work is placed on a comparison of post-buckling response from the analytical methods and FEM with the responses from OpenSeesPy simulations served as reliable numerical benchmark. Results obtained for various IPE sections and beam spans indicate that while the analytical circular deformation path model provides a critical buckling load expression which exhibits a strong resemblance with the Eurocode formulation, it tends to overestimate the critical load by roughly 105% compared to the numerical model. Moreover, its post-buckling response shows softening behavior unlike the numerical model and its deformed shapes completely disagree with the numerical solutions, even though they are qualitatively similar. In contrast, Eurocode critical buckling load predictions, used alongside the numerical and analytical results for comparison, underestimate the numerical results by about 12%. A parabolic deformation path model is developed, with a coefficient determined based on the numerical critical load, to solve the problem of unmatching critical load and post-buckling behavior of the circular path model. Post-buckling responses are examined using load-deflection and load-twist curves. The post-buckling response results from the numerical model shows hardening behavior with a nearly elliptical deformed shape while the responses from the parabolic path with the calibrated coefficients shows hardening behavior with deformed shapes converging initially towards the numerical results for intermediate beam cross-sections and spans. Overall, this study highlights the capabilities and limitations of simplified analytical models for capturing post-LTB behavior, offering valuable comparisons with code-based and numerical simulation. With further study including material nonlinearity, warping effects, and other imperfections it can be applied for practical analysis and design.