Elastic buckling formulae for web crippling of square and rectangular hollow sections under concentrated transverse forces
File(s)
Published version
Author(s)
Dai, Ruikai
Gardner, Leroy
Wadee, M Ahmer
Type
Journal Article
Abstract
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).
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).
Date Issued
2025-10-01
Date Acceptance
2025-05-16
Citation
Thin-Walled Structures, 2025, 215 (Part A)
ISSN
0263-8231
Publisher
Elsevier BV
Journal / Book Title
Thin-Walled Structures
Volume
215
Issue
Part A
Copyright Statement
© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
10.1016/j.tws.2025.113469
Publication Status
Published
Article Number
113469
Date Publish Online
2025-06-02