CLC number: O342; TU311.1
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2012-03-08
Cited: 3
Clicked: 5789
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.
@article{title="Restrained torsion of open thin-walled beams including shear deformation effects",
author="Zhao-qiang Wang, Jin-cheng Zhao, Da-xu Zhang, Jing-hai Gong",
journal="Journal of Zhejiang University Science A",
volume="13",
number="4",
pages="260-273",
year="2012",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1100149"
}
%0 Journal Article
%T Restrained torsion of open thin-walled beams including shear deformation effects
%A Zhao-qiang Wang
%A Jin-cheng Zhao
%A Da-xu Zhang
%A Jing-hai Gong
%J Journal of Zhejiang University SCIENCE A
%V 13
%N 4
%P 260-273
%@ 1673-565X
%D 2012
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1100149
TY - JOUR
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
IS - 4
SP - 260
EP - 273
%@ 1673-565X
Y1 - 2012
PB - Zhejiang University Press & Springer
ER -
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.
[1]Back, S.Y., Will, K.M., 1998. A shear-flexible element with warping for thin-walled open beams. International Journal for Numerical Methods in Engineering, 43(7):1173-1191.
[2]Back, S.Y., Will, K.M., 2008. Shear-flexible thin-walled element for composite I-beams. Engineering Structures, 30(5):1447-1458.
[3]Chen, B.Z., Hu, Y.R., 1998. Thin-Walled Structrual Mechanics. Shanghai Jiao Tong University Press, Shanghai, China, p.51-67 (in Chinese).
[4]El Fatmi, R.E., 2007a. Non-uniform warping including the effects of torsion and shear forces. Part I: a general beam theory. International Journal of Solids and Structures, 44(18-19):5912-5929.
[5]El Fatmi, R.E., 2007b. Non-uniform warping including the effects of torsion and shear forces. Part II: analytical and numerical applications. International Journal of Solids and Structures, 44(18-19):5930-5952.
[6]Erkmen, E.R., Mohareb, M., 2006. Torsion analysis of thin-walled beams including shear deformation effects. Thin-Walled Structures, 44(10):1096-1108.
[7]Gjelsvik, A., 1981. The Theory of Thin-Walled Bars. John Wiley & Sons Inc., New York, p.1-10.
[8]Kim, N.I., 2011. Shear deformable doubly- and mono-symmetric composite I-beams. International Journal of Mechanical Sciences, 53(1):31-41.
[9]Kim, N.I., Kim, M.Y., 2005. Exact dynamic/static stiffness matrices of non-symmetric thin-walled beams considering coupled shear deformation effects. Thin-Walled Structures, 43(5):701-734.
[10]Lee, J., 2005. Flexural analysis of thin-walled composite beams using shear-deformable beam theory. Composite Structures, 70(2):212-222.
[11]Librescu, L., Song, O., 2006. Thin-Walled Composite Beams: Theory and Application. Springer, Berlin, p.xxi-xxvi.
[12]Mohareb, M., Nowzartash, F., 2003. Exact finite element for nonuniform torsion of open sections. Journal of Structural Engineering, 129(2):215-223.
[13]Mokos, V.G., Sapountzakis, E.J., 2011. Secondary torsional moment deformation effect by BEM. International Journal of Mechanical Sciences, 53(10):897-909.
[14]Park, S.W., Fujii, D., Fujitani, Y., 1997. A finite element analysis of discontinuous thin-walled beams considering nonuniform shear warping deformation. Computers & Structures, 65(1):17-27.
[15]Pavazza, R., 2005. Torsion of thin-walled beams of open cross-section with influence of shear. International Journal of Mechanical Sciences, 47(7):1099-1122.
[16]Reddy, J.N., Wang, C.M., Lee, K.H., 1997. Relationships between bending solutions of classical and shear deformation beam theories. International Journal of Solids and Structures, 34(26):3373-3384.
[17]Roberts, T.M., Al-Ubaidi, H., 2001. Influence of shear deformation on restrained torsional warping of pultruded FRP bars of open cross-section. Thin-Walled Structures, 39(5):395-414.
[18]Saadé, K., Espion, B., Warzee, G., 2004. Non-uniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections. Thin-Walled Structures, 42(6):857-881.
[19]Shakourzadeh, H., Guo, Y.Q., Batoz, J.L., 1994. A torsion bending element for thin-walled beams with open and closed cross sections. Computers & Structures, 55(6):1045-1054.
[20]Vlasov, V.Z., 1961. Thin-Walled Elastic Beams. Israel Program for Scientific Translations, Jerusalem, p.7-10.
[21]Wang, C.M., 1995. Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions. Journal of Engineering Mechanics, 121(6):763-765.
[22]Yang, Q.S., Wang, X.F., 2010. A geometrical and physical nonlinear finite element model for spatial thin-walled beams with arbitrary section. Science China Technological Sciences, 53(3):829-838.
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