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.