Abstract
The aim of this research was to determine the optimal dimensions of a tapered, bisymmetric, thin-walled, I-shaped cantilever for which, at a constant mass, the critical load causing the buckling of the beam reaches the maximum value. Optimal solutions were sought in a discrete set of admissible values of the taper coefficients of the I-bar’s web and/or flanges. A model of a thin-walled bar with an open cross-section, whose mathematical description was derived on the basis of the momentless theory of shells, was used to analyse the considered problem described by a system of four coupled differential equations with variable coefficients. The equations were solved using Chebyshev series of the first kind to approximate the generalized displacement functions, and the recurrence algorithm presented in earlier publications by the author(s). A tapered cantilever with a bisymmetric cross-section, subjected to the action of a uniformly distributed load, was analysed. The load can be applied to the I-bar’s upper flange or to its lower flange, or it can act in the centre of the web. The obtained critical load values were compared with those obtained using the finite element method and the commercial Sofistik software. In the set of linearly tapered cantilevers with a bisymmetric double-tee cross section, the cantilevers with the highest taper coefficients of the web and the flanges (the free end having the smallest possible dimensions) were found to be optimal (in their case, at a constant mass, the critical buckling load reaches its maximum value).