Elastic buckling formulae for web crippling of square and rectangular hollow sections under concentrated transverse forces

Formulae for determining the elastic buckling loads of structural steel rectangular hollow sections subjected to concentrated transverse forces are presented herein. The predicted elastic buckling load is bounded by a theoretical lower bound, where only the material within the bearing length is mobilised, and a practical upper bound, where the adjacent material is mobilised to its maximum extent. The lower bound is the elastic buckling load of a wide plate with a width equal to the bearing length and a length equal to the web depth, while the upper bound is determined from finite element (FE) analyses of various representative loading scenarios. The level of mobilisation of adjacent material (i.e., where a specific case lies between the lower and upper bounds) is quantified by introducing a coefficient ζ that is calibrated through FE analyses in the commercial package ABAQUS. The rotational stiffness afforded to the webs by the flanges is also captured. The four loading scenarios defined in the North American Specification and Australian/New Zealand Standard for the design of cold-formed steel structures, namely the Interior-Two-Flange (ITF), End-Two-Flange (ETF), Interior-One-Flange (IOF) and End-One-Flange (EOF) loading conditions, alongside their transitional cases, are considered. Rectangular hollow sections with a broad spectrum of cross-sectional geometric proportions and bearing lengths encompassing the aforementioned loading conditions are considered. It is found that the developed formulae for predicting the elastic buckling loads under concentrated transverse forces provide accurate results that are typically within 5% of the numerical values. Hence, the developed formulae can be employed as a convenient alternative to numerical methods in advanced structural design methodologies, such as the Direct Strength Method (DSM) and the Continuous Strength Method (CSM). • Elastic buckling loads of RHS profiles under concentrated transverse forces are determined. • Coefficient ζ quantifies extent of adjacent material mobilised by concentrated transverse forces. • Four standard loading conditions (ITF, ETF, EOF and IOF) and their transitional cases are considered. • Elastic buckling loads are typically predicted to within 5% of numerical results. • Developed formulae are suitable for use in advanced structural design methodologies (e.g., DSM and CSM).