Gaussian Beam–Column Element Formulation for Large-Deflection Analysis of Steel Members with Open Sections Subjected to Torsion
Publication: Journal of Structural Engineering
Volume 147, Issue 12
Abstract
The beam–column element analysis method has been extensively adopted in practice, relying on the robustness of its element formulation. Steel members with open sections are commonly used; their cross-sectional shapes are usually nonsymmetric to improve material efficiency. Nevertheless, an offset exists between the shear center and the centroid of a nonsymmetric section. If the applied loads do not act at the shear center, torsion can be induced; this is sometimes unavoidable. When a member is subject to torsion, the inclined angle between the local axes of the cross section and the element is varied along the element length, complicating the summating of the cross section’s stiffness to form an element stiffness matrix. This study developed a new beam–column element formulation based on the nonsymmetric section assumption and a Gaussian quadrature procedure to formulate the element stiffness matrix of being concise in expressing formulation. The updated Lagrangian method was modified to consider large deflections. This method permitted the use of fewer elements to simulate a member under torsion, leading to a significant improvement in numerical efficiency. Detailed derivations and verification examples are given in the paper.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The last author is grateful for financial support from the Research Grant Council of the Hong Kong Special Administrative Region on the projects “Joint-based second order direct analysis for domed structures allowing for finite joint stiffness (PolyU 152039/18E)” and “Second-order analysis and design of scaffolds with scissor braces and allowing for kink imperfections (PolyU 152035/20E).” The third author would like to express his gratitude to the National Science Foundation for Young Scientists of China (Grant No. 52008410). The third author would like to express his gratitude to Bucknell University for providing an excellent research environment for conducting this research.
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Published In
Journal of Structural Engineering
Volume 147 • Issue 12 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jun 30, 2020
Accepted: Jul 20, 2021
Published online: Sep 24, 2021
Published in print: Dec 1, 2021
Discussion open until: Feb 24, 2022
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