Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: conventional and constrained finite strip methods

The objective of this paper is to provide the theoretical background and illustrative examples for elastic buckling analysis of cold-formed steel members with general boundary conditions as implemented in the forthcoming update to CUFSM. CUFSM is an open source finite strip elastic stability analysis program freely distributed by the senior author. Although the finite strip method presents a general methodology, the conventional implementation (e.g. CUFSM v 3.13 or earlier) employs only simply-supported boundary conditions. In this paper, utilizing specially selected longitudinal shape functions, the conventional finite strip method is extended to general boundary conditions, including the conventional case: simply-simply supported, as well as: clamped-clamped, clamped-simply supported, clamped-free, and clamped-guided. The solution remains semi-analytical as the elastic and geometric stiffness matrices are derived in a general form with only specific integrals depending on the boundary conditions. An example of the stability solution is provided. The selection of longitudinal terms to be included in the analysis is discussed in terms of balancing accuracy with computational efficiency. Also herein, the constrained finite strip method is extended to general boundary conditions. Both modal decomposition and identification can be carried out based on the new bases developed for the constrained finite strip method, and illustrative examples are provided. This extension of CUFSM is intended to aid the implementation of the direct strength method to the case of general boundary conditions.