The Effect of Torsional Rigidity and Approximations in Analytical Solutions for the Critical Moment of Beams Considering Prebuckling Deflections

Solutions for the critical moment of lateral-torsional buckling of beams commonly used in design codes, are based on initially straight undeflected beams. However, studies indicate that when the weak-to-strong moment of inertia ratio is sufficiently high, prebuckling deformations can significantly impact critical loads. The proposed formulae in the literature often vary, and discussions on the effect of torsional rigidity are limited, with most studies focusing on open sections. This study provides a comprehensive review of the problem and relevant literature, exploring variations and simplifications used to derive closed-form solutions for the critical moment, while accounting for prebuckling deformations through the energy method. Several variations of the critical moment formula are presented and compared, with a detailed investigation into the influence of torsional rigidity. Prebuckling deformations were confirmed to have a significant effect on the critical moment for specific sections, and the conditions for appropriate simplifications were identified. Additionally, torsional rigidity was found to exert a non-negligible influence, with closed sections demonstrating a greater effect of prebuckling deformations.