Beam Buckling by Finite Element Procedure

A finite element procedure for determining the critical buckling load for three-dimensional structures idealized by planar two-dimensional elements is presented. This procedure is applicable to structures whose instabilities involve small displacements and elastic behavior, i.e., linear elastic buckling. Local and overall structural instabilities may be treated together with complex loading and support conditions. The smallest eigenvalue corresponding to the smallest buckling load is determined by an inverse iteration procedure. The accuracy of this finite element procedure is evaluated by comparison with a number of problems for which classical solutions are available. A simply supported wide-flange beam with a stiffener, lateral restraints, and various rotational restraints is presented to illustrate the versatility of the procedure as well as the effect of the restraints on the buckling load. In addition, a comparison between the subject procedure and recent experimental results on a continuous wide-flange beam is presented.