Second-Order Collapse Load Analysis: LP Approach

The paper presents an iterative procedure for the analysis of elastic-plastic building frames to determine the failure load accounting for second-order effects due to axial forces and member deformations. The analysis procedure is essentially the reverse of historical load-deformation analysis in that it starts from an upper-bound estimate to the failure load as given by that found for rigid plastic (i.e., first-order) analysis. Secondary moments as well as axial force influences on plastic moment capacities and member flexibilities are accounted for. The procedure involves the iterative performance of a series of strength and deformation analyses as linear programming (LP) problems. Single-bay frames having one, four, eight, and fifteen stories are analyzed to illustrate the features and scope of application of the approach. Solution convergence is shown to be very good.