A Shear Deformable Finite Element Formulation for the Elastic Lateral Torsional Buckling Analyses of Steel Beams

The present study develops a shear deformable finite element (FE) formulation for the analysis of the elastic lateral torsional buckling (LTB) of steel beams. Four governing displacement fields are proposed to describe the LTB deformation. The buckling strains/stresses and the total buckling potential energy of the system are subsequently expressed in terms of the governing displacements. The theory considers the contributions of local and global warping deformations and shear deformations. A FE formulation is then developed by using linear and cubic shape functions. Based on the validations conducted in four examples, the buckling loads/modes of single and continuous span steel beams predicted by the present solutions are observed to excellently agree with those predicted by other analytical, experimental, numerical solutions. The buckling loads evaluated by using standard moment modification factors are also discussed to clarify the restrictions of the evaluation method. The effects of shear deformations, different loading conditions, and span ratios on the buckling responses of various steel beams are also investigated in the present study.