Beam-buckling analysis via automated Rayleigh-Ritz method

Abstract

This paper presents an automated Rayleigh-Ritz method for the elastic buckling analysis of doubly symmetric I-beams subjected to arbitrary loading conditions. Moreover, the beams may have various types of end-supporting conditions, internal discrete rigid braces, and internal supports. The automation and the method's versatility are attributed to a general Ritz function consisting of the product of a polynomial function and the functions expressing the geometric restraint conditions. The method is simple and may be readily implemented on a personal computer. The solutions obtained are shown to be accurate provided a sufficient number of polynomial terms is taken. Buckling solutions of I-beams under a variety of loading and boundary conditions are obtained to illustrate the generality of the method and serve as design charts.