An exact finite strip for the initial postbuckling analysis of channel section struts

Abstract

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of channel section struts. The presented method provides an efficient and extremely accurate buckling solution. The Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and mode shapes for the channel section struts. The investigation of buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. Through the solution of the Von-Karman’s compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. All the displacement functions are then substituted in the total strain energy expressions. The theorem of minimum total potential energy is subsequently applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial post-buckling behavior of some representative channel sections for which the results were also obtained through the application of a semi-energy finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.