Exact post‐buckling stiffness calculation of box section struts

Abstract

PurposeThe purpose of this paper is to develop and apply an exact finite strip (F‐a FSM) for the buckling and initial post‐buckling analyses of box section struts.Design/methodology/approachThe Von‐Karman's equilibrium equation is solved exactly to obtain the buckling loads and deflection modes for the struts. The investigation 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 are developed in terms of the unknown coefficient. These in‐plane and out‐of‐plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient.FindingsThe F‐a FSM is applied to analyze the buckling and initial post‐buckling behavior of some representative box sections for which the results were also obtained through the application of a semi‐energy finite strip method (S‐e FSM). For a given degree of accuracy in the results, however, the F‐a FSM analysis requires less computational effort.Research limitations/implicationsIn the present F‐a FSM, only one of the calculated deflection modes is used for the initial post‐buckling study.Practical implicationsA very useful and computationally economical methodology is developed for the initial design of struts which encounter post‐buckling.Originality/valueThe originality of the paper is the fact that by incorporating a rigorous buckling solution into the Von‐Karman's compatibility equation, and solving it, a fairly efficient method for post‐buckling stiffness calculation is achieved.