Upper and lower bound solutions for lateral-torsional buckling of doubly symmetric members

Abstract

A family of three finite elements is developed for the lateral-torsional buckling analysis of thin-walled members with doubly symmetric cross-sections. The elements are based on a recently derived variational principle which incorporates shear deformation effects in conjunction with a special interpolation scheme ensuring C1 continuity. One of the elements is developed such that it consistently converges from above while another element is intended to consistently converge from below. The third element exhibits fast convergence characteristics compared to other shear deformable elements but cannot be guaranteed to provide either an upper or a lower bound solution. The formulation can incorporate any set of linear multi-point kinematic constraints. The validity of the solution is established through comparisons with other well-established numerical solutions. The elements are then used to solve practical problems involving simply supported beams, cantilevers and continuous beams under a variety of loading conditions including concentrated loads, linear bending moments and uniformly distributed loads. The effect of lateral and torsional restraints and the location of lateral restraint along the section height on lateral-torsional buckling capacity of beams are also examined through examples.