On the influence of the rounded corners on the local stability of RHS members under axial force and biaxial bending

This paper presents the results of an investigation concerning the influence of corners with standard radii in the local buckling behaviour of thin-walled rectangular hollow section (RHS) members subjected to combinations of axial force and biaxial bending. The calculation of the half-wave length leading to the minimum critical bifurcation load is performed by means of a Generalized Beam Theory (GBT) specialization, developed taking advantage of the assumption that the stress resultants are uniform along the member length. This assumption makes it possible to obtain semi-analytical solutions, adopting half-wave sinusoidal amplitude functions for the GBT cross-section deformation modes, and leads to a numerical implementation that (i) is able to quickly solve a large number of problems and (ii) provides physical insight into the critical buckling mode mechanics, through a shell-like stress resultant-based energy criterion, as well as the modal decomposition features of the GBT semi-analytical solutions. Members with cross-sections belonging to the EN10219-2 database are analysed and their critical buckling coefficients are compared with those provided by available analytical expressions and/or currently included in steel design codes, namely Eurocode 3 and the North American Specification for Cold-Formed Steel Members. Analytical expressions are developed to take into account the (usually) beneficial influence of the rounded corners to the RHS member critical buckling stress.