Analytical investigation of lateral-torsional buckling of tapered cantilevers with I-section

I-section steel profiles are commonly used as cantilever beams in steel structures. They are loaded to resist bending about their strong axes for efficient material utilisation. When subjected to bending along the strong axis, I-section cantilevers experience out-of-plane lateral deformation and torsion at a certain critical load, leading to a loss of stability. This failure mode is known as lateral-torsional buckling. This global stability loss, which may occur before yielding the cross-section, should be considered in structural design. The lateral-torsional buckling behaviour of slender columns, beams, cantilevers, and axially loaded beams has been extensively investigated in the literature via analytical, numerical, and experimental methods. Compared to simply supported beams, the lateral-torsional buckling mode of cantilever beams is more complex, often making the derivation of closed-form solutions impractical and requiring numerical approaches. This study developed an analytical procedure based on the energy method to calculate the lateral-torsional buckling loads of web and/or flanges tapered cantilevers with symmetric I-section. The proposed analytical method considers all influential factors, including the tapering levels of the flange and/or web, slenderness, transverse load type, and the position of the transverse load on the cross-section. The analytical solutions have been validated using finite element analyses with one-dimensional (1D) beam elements incorporating warping effects. The lateral-torsional buckling behaviour of webs and/or flanges tapered cantilevers with symmetric I-sections has been thoroughly examined and interpreted in detail.