Elastic Buckling Strengths of Unbraced Steel Frames Subjected to Variable Loadings

The problem of determining the elastic buckling strengths of unbraced steel frames subjected to variable loadings can be expressed as a pair of maximization and minimization problems with stability constraints based on the concept of storey-based buckling which accounts for the lateral stiffness interaction among columns in a storey while resisting applied loads. The maximization and minimization problems can be solved by either linear programming method or nonlinear programming method depends on whether an approximation on the column stiffness being applied or not. Compared with the nonlinear programming method, the linear programming method based on Taylor series approximation on column stiffness is considerably simpler and more suitable for engineering practice but the frame buckling strengths may be overestimated in some cases, which may result in unconservative designs. In this study, a secant approximation of the column stiffness is introduced. Then, a modified linear programming method based on the secant approximation is proposed. Four unbraced steel frames are investigated to illustrate that the linear programming method in light of the secant approximation can yield conservative results and maintain simplicity.