Iterative system buckling analysis, considering a fictitious axial force to determine effective length factors for multi-story frames

Traditional elastic buckling analysis, based on the system buckling approach, is a convenient tool for the evaluation of effective length factors of columns, in the stability design of multi-story frames. This method is superior to other analytical approaches, such as the isolated subassembly and story-based approaches, in that the inter-story and inter-column interactions are inherently taken into account. Nevertheless, use of the conventional critical load expression, in combination with results of elastic buckling analysis, may yield an excessively large effective length in members having relatively small axial forces. The present paper proposes an iterative elastic buckling analysis to determine reasonable effective length factors of columns in multi-story frames. In this paper, numerical procedures for an iterative buckling analysis using a modified geometric stiffness matrix, are described to obtain the effective length factors of the columns in multi-story frames. The axial force term in the geometric stiffness matrix is modified by adding a fictitious axial force to make the columns buckle along with the overall buckling of the frame. Iterative eigenvalue analysis is performed using the modified geometric stiffness matrix, to obtain the effective length factors of each column using the critical load expression. Example frames presented in this paper demonstrate that the proposed method not only provides excellent outcomes by amending the weakness associated with traditional elastic buckling analysis for determining the effective length factor, but is also a competitive alternative in the design of multi-story frames.