Restrained torsion of open thin-walled beams including shear deformation effects |
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Authors: | Zhao-qiang Wang Jin-cheng Zhao Da-xu Zhang and Jing-hai Gong |
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Institution: | Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China |
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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. |
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