Elastic Critical Loads on Multistory Rigid Frames

Abstract

A direct matrix method for the calculation of the elastic critical loads on rigid frames is presented. The effect of the secondary axial forces in columns is readily included. The procedure leads to a linear eigenvalue problem where the smallest root from a product matrix represents the critical load. The computational aspects of the method are considered, and the analysis is reduced to the setting up of two main matrixes. The first matrix is directly evaluated from the geometrical and loading properties, and the second is the linear elastic stiffness matrix under a fictitious system of transverse forces. Economy in the setting up of the stiffness matrix is achieved by treating individual columns as substructures. The method is applied to three example frames, and the numerical results are compared with those obtained from stability-function solutions.