LTBWTB: A Mathematica Software to Evaluate the Lateral-Torsional Buckling Load of Web-Tapered Mono-Symmetric I-Section Beams

Web-tapered beams with I-sections, which are aesthetic and structurally efficient, have been widely used in steel structures. Web-tapered I-section beams bent about the strong axis may undergo out-of-plane buckling through lateral deflection and twisting. This primary stability failure mode in slender beams is known as lateral-torsional buckling (LTB). Unlike prismatic I-beams, the complex mode shape of web-tapered I-section beams makes it challenging or even impossible to derive a closed-form expression for the LTB load under certain transverse loading conditions. Therefore, the LTB assessment of web-tapered I-section beams is primarily performed using finite element analysis (FEA). However, this method involves multiple steps, requires specialized expertise, and demands significant computational resources, making it impractical in certain cases. This study proposes an analytical approach based on the Ritz method to evaluate the LTB of simply supported web-tapered beams with doubly or mono-symmetric I-sections. The proposed analytical method accounts for web tapering, I-section mono-symmetry, types and positions of transverse loads, and beam slenderness. The method was implemented in Mathematica to allow the rapid evaluation of the LTB capacity of web-tapered I-beams. The study validates the LTB loads computed using the developed Mathematica package against results from shell-based FEA. An excellent agreement was observed between the analytically and numerically calculated LTB loads.