Lateral Buckling of Nonprismatic Cantilevers Using Weighted Residuals

Abstract

This paper presents a general weighted residual formulation (both collocation and Galerkin) for the problem of the lateral buckling of nonprismatic cantilevers. The approach is first validated against exact solutions to the linear elastic, prismatic case, and then against the available data for the elastic stability of beams with a linear taper. Complete results are given for both rectangular and inverted T sections with linear and parabolic web tapers subjected to either a distributed load or an end point load, for a number of span to depth ratios; the effect of applying the load through the top fiber, rather than the centroid, is also studied. For the limiting cases where results have been cited by others, the values obtained are shown to compare well. Finally, the technique is used to study buckling of inverted T sections when material nonlinearity is included. This is achieved by providing functional forms for the degradation of flexural and torsional stiffness with load, the aim being purely to assess the relevance of buckling as an ultimate limit state.