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CLC number: O342; TU311.1

On-line Access: 2012-04-06

Received: 2011-05-29

Revision Accepted: 2011-11-04

Crosschecked: 2012-03-08

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Journal of Zhejiang University SCIENCE A 2012 Vol.13 No.4 P.260-273

10.1631/jzus.A1100149


Restrained torsion of open thin-walled beams including shear deformation effects


Author(s):  Zhao-qiang Wang, Jin-cheng Zhao, Da-xu Zhang, Jing-hai Gong

Affiliation(s):  Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding email(s):   zqwang2007@yahoo.com

Key Words:  Thin-walled beam, Restrained torsion, Shear deformation, Warping, Shear coefficient


Zhao-qiang Wang, Jin-cheng Zhao, Da-xu Zhang, Jing-hai Gong. Restrained torsion of open thin-walled beams including shear deformation effects[J]. Journal of Zhejiang University Science A, 2012, 13(4): 260-273.

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author="Zhao-qiang Wang, Jin-cheng Zhao, Da-xu Zhang, Jing-hai Gong",
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%A Jin-cheng Zhao
%A Da-xu Zhang
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%J Journal of Zhejiang University SCIENCE A
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1100149

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T1 - Restrained torsion of open thin-walled beams including shear deformation effects
A1 - Zhao-qiang Wang
A1 - Jin-cheng Zhao
A1 - Da-xu Zhang
A1 - Jing-hai Gong
J0 - Journal of Zhejiang University Science A
VL - 13
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1100149


Abstract: 
A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation is established by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium, the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to solve the equation. The relationship between total rotation and free warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition, under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated to validate the current approach and the results of the current theory are compared with those of some other available methods. The results of comparison show that the current theory provides more accurate results. In the example of a channel-shaped cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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