Inelastic stability of tapered, singly-symmetric beam-columns.

Abstract

The purpose of this study is to determine the inelastic lateraltorsional buckling load of a linearly web-tapered member having unequal flanges and subjected to unequal end moments and axial load. Triangular residual stress patterns in flanges and uniform tensile stress across the web are assumed to exist. The total potential energy functional for such a member is developed and the inelastic effects are included. Using the standard techniques of calculus of variations, the three differential equations describing the behavior of the member are derived and the natural and force boundary conditions are determined. Two of these equations, which are coupled, describe the out-of-plane behavior of the member. Central difference expressions are used to transform these two equations into difference equations. In order to determine the yield pattern at each station along the member, a new method based on the solution of the equations of equilibrium is proposed. By solving these two simultaneous, nonlinear equations, the yield parameters are computed. The section properties of the partially yielded cross-sections are computed using the yield parameters. The section properties are used to satisfy the difference equations at different nodes along the member. The value of the determinant of these equations is tested for different trial values of the buckling load until a zero value is found which insures buckling. The buckling mode shape is then obtained by assuming one of the displacements equal to unity, cancelling one equation and solving the rest of the equations using Gauss-Jordan elimination method.

The results of the analysis are compared with solutions available in the literature and also with those of a limited experimental study. Good agreement is shown to exist. The effect of the curvature of the neutral axis and the contribution of the yielded portions in lateral-torsional buckling are explained. The results of the study are used to develop a design criterion for singly-symmetric, tapered members and an interaction-type equation is developed in Load Resistance Factor Design format.