An exact finite strip for the calculation of relative post-buckling stiffness of I-section struts

Abstract

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of I-section struts. The so-called exact strip is developed based on the concept that it is effectively a plate. The presented method, which is designated by the name Full-analytical Finite Strip Method, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman's equilibrium equation is solved exactly to obtain the buckling loads and mode shapes for the I-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. The current post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. 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. Finally, the developed method is subsequently applied to analyze the initial post-buckling behavior of some representative I-sections for which the results were also obtained through the application of a Semi-energy Finite Strip Method [Ovesy HR. The development and application of a semi-energy post-local buckling finite strip. PhD dissertation, Cranfield University, UK, 1998]. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.