Formulae for calculating elastic buckling loads for web crippling of rectangular hollow sections

Formulae for determining the elastic buckling loads of structural steel rectangular hollow sections (RHS) 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 is quantified by introducing a coefficient ζ that is calibrated through FE analyses in the commercial package ABAQUS, with the rotational stiffness afforded to the webs by the flanges also being captured. The four loading scenarios defined in the North American Specification (NAS) and Australian/New Zealand Standard (AS/NZS) 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).