A mathematica code for evaluating lateral-torsional buckling of tapered cantilevers

Abstract

Lateral-torsional buckling (LTB) is the primary failure mode where slender cantilevers experience nonuniform twisting and buckling about their weak axes. The studies focused on the elastic LTB load of cantilevers are limited, most of which are numerical since the LTB failure mode of cantilevers is much more complicated than those of simply supported beams. Furthermore, there are only a few studies of the LTB of tapered I-section cantilevers, which are aesthetic and structurally efficient. Structural designers tend to evaluate the LTB of tapered cantilevers using finite element simulations, but it requires specific experience and computational effort. The present study intends to close the gap in the literature related to tapered cantilevers, establish an analytical procedure providing rapid treatment, and develop a code for the solution. The analytical model considers first-order moment gradient through the cantilever, load position along the cross-section, mono-symmetry property of I-section, tapering of web, flange, or simultaneously web and flange to assess LTB of tapered cantilevers. The developed Mathematica code based on the analytical model has been verified with 3D finite element analysis, and it is demonstrated that the proposed code can be safely used to assess the LTB of tapered cantilevers.