Stiffness analysis of locally-buckled thin-walled continuous beams

Abstract

A direct iterative numerical method is presented for predicting the post-local-buckling response of thin-walled continuous structures. Nonlinearities due to local buckling and non-linear material properties are accounted for by the nonlinear moment-curvature relations of the section derived with the aid of effective width concept. Since the effective width of the compression element decreases as the stress borne by the element edge increases, the effective flexural rigidity of the cross-section varies along the member length depending upon the magnitude of the moment at the section. In the post-buckling range, the member is treated as a nonprismatic section. For continuous thin-walled structures, it is further complicated by the fact that the bending moment distribution throughout the structure and the member stiffnesses are interdependent. The proposed direct iterative solution scheme includes a stiffness matrix method of analysis in conjunction with a numerical integration procedure for evaluating the member stiffnesses. The method is employed to analyze continuous beams in the post-buckling range. Using the moment distribution of an elastic prismatic continuous beam based on the nonbuckling analysis as a first approximation, it has been found that the iterative solution scheme converges rapidly. An excellent agreement has been obtained between the results based on the method presented and from an earlier study for continuous beams. The stiffness formulation is direct and is well suited for the analysis of continuous thin-walled structures.