Direct Stiffness Analysis of Lateral Buckling

Abstract

A direct stiffness method of analyzing the elastic ftexural-torsional buckling of rigid-jointed plane frames composed of l-section members and subjected to in-plane loads is presented. The in-plane stiffness matrix and the fixed-end resultants are obtained from the member stiffness matrices derived from the in-plane differential equations. These member stiffness matrices are assembled and solved, and their solutions are used to linearize the flexural-torsional buckling equations. The out-of-plane member stiffness matrices are then obtained numerically from the buckling equations by the method of finite integrals. The out-of-plane frame -stiffness matrix is assembled, and the critical loads are obtained when its determinant is zero. A computer program is developed which carries out either a first- or second-order in-plane analysis, and then determines the flexural-torsional buckling loads. The effects of in-plane deformations prior to buckling can be included. Very good agreement is obtained between the results computed by this program and known solutions, and its ability to analyze large complex frames is demonstrated.