Elastic lateral-torsional buckling of restrained web-tapered I-beams

This paper presents an investigation on the elastic lateral-torsional buckling behaviour of discretely restrained tapered beams. Through a model problem consisting of a doubly symmetric web-tapered I-section cantilever acted by a tip load, it is shown how the effects of linearly elastic or rigid restraints can be included in the one-dimensional model previously developed by the authors to characterize the elastic buckling behaviour of thin-walled tapered beams. The restraints may have a translational, torsional, minor axis bending and/or warping character. The resulting self-adjoint eigenproblem is cast in non-dimensional form over a fixed reference domain, a process that leads to the identification of a complete set of independent non-dimensional parameters. It is then reformulated as a standard inhomogeneous boundary value problem and solved numerically with the collocation package colnew. A parametric study is carried out in order to examine in some detail (i) the effectiveness of different types of restraint, (ii) the influence of the restraint stiffness and (iii) the interplay between these two aspects and the degree of web tapering. This study provides insight into the peculiarities of the lateral-torsional buckling behaviour of tapered beams and some seemingly paradoxical results are given a physical explanation.