On the evaluation of elastic critical moments in doubly and singly symmetric I-section cantilevers

Abstract

The so-called 3-factor formula is one of the most commonly employed general formulae to estimate the elastic critical moment of steel beams prone to lateral-torsional buckling. This work extends its domain of application to I-section cantilevers (i) with equal or unequal flanges, (ii) fully built-in or free to warp at the support and (iii) acted on by uniformly distributed or concentrated tip loads (applied either at the shear centre or at one of the flanges). The paper includes (i) a discussion of the theoretical basis of elastic lateral-torsional buckling, (ii) the description of the main steps involved in posing the buckling problem in a non-dimensional form over a fixed reference domain, features that are particularly convenient for the purpose of this work, (iii) the numerical results of a parametric study, obtained by the Rayleigh–Ritz method, and (iv) their use for the development of approximate analytical expressions for the C 1 , C 2 and C 3 factors appearing in the aforementioned formula.