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Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method
The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to invest...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8838607/ https://www.ncbi.nlm.nih.gov/pubmed/35159883 http://dx.doi.org/10.3390/nano12030538 |
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author | Pan, Wen-Hao Zhao, Chuan-Hao Tian, Yuan Lin, Kai-Qi |
author_facet | Pan, Wen-Hao Zhao, Chuan-Hao Tian, Yuan Lin, Kai-Qi |
author_sort | Pan, Wen-Hao |
collection | PubMed |
description | The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method. |
format | Online Article Text |
id | pubmed-8838607 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-88386072022-02-13 Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method Pan, Wen-Hao Zhao, Chuan-Hao Tian, Yuan Lin, Kai-Qi Nanomaterials (Basel) Article The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method. MDPI 2022-02-04 /pmc/articles/PMC8838607/ /pubmed/35159883 http://dx.doi.org/10.3390/nano12030538 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Pan, Wen-Hao Zhao, Chuan-Hao Tian, Yuan Lin, Kai-Qi Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method |
title | Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method |
title_full | Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method |
title_fullStr | Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method |
title_full_unstemmed | Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method |
title_short | Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method |
title_sort | exact solutions for torsion and warping of axial-loaded beam-columns based on matrix stiffness method |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8838607/ https://www.ncbi.nlm.nih.gov/pubmed/35159883 http://dx.doi.org/10.3390/nano12030538 |
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