In structural analysis, it is often necessary to determine the geometrical properties of cross section. The location of the shear center is greater importance for an arbitrary cross section. In this study, the problems of coupled shearing and torsional were analyzed by using the finite element method. Namely, the simultaneous equations with respect to the warping, shear deflection, angle of torsion and Lagrange’s multipliers are derived by finite element approximation. Solving them numerically, the matrix of the shearing rigidity and torsional rigidity is obtained. This matrix indicates the coupled shearing and torsional deflection. The shear center can be obtained determining the coordinate axes so as to eliminate the non-diagonal terms. Several numerical examples are performed and show that the present method gives excellent results for an arbitrary cross section.
References
[1]
Timoshenko, S.P. (1953) History of Strength of Materials. McGraw-Hill, New York.
[2]
Fung, Y.C. (1969) An Introduction to the Theory of Aeroelasticity. Dover, New York.
[3]
Trefftz, E. (1936) Uber den Schubmittelpunkt in einemdurcheine Einzellastgebogenen Balken. Zeitschrift für Angewandte Mathematik und Mechanik, 15, 220-225. http://dx.doi.org/10.1002/zamm.19350150405
[4]
Vlasov, V.Z. (1961) Thin-Walled Elastic Beams. Office of Technical Services, US Department of Commerce, Washington DC.
[5]
Katori, H. (2001) Consideration of the Problem of Shearing and Torsion of Thin-Walled Beams with Arbitrary Cross-Section. Thin-Walled Structures, 39, 671-684. http://dx.doi.org/10.1016/S0263-8231(01)00029-5
[6]
Katori, H. and Nishimura, T. (1993) A Boundary Element Analysis of Coupled Shearing and Torsional Deformation of Beams. Advances in Engineering Software, 17, 1-5. http://dx.doi.org/10.1016/0965-9978(93)90035-R
[7]
Timoshenko, S.P. and Goodier, J.N. (1984) Theory of Elasticity. 3rd Edition, McGraw-Hill, New York.
[8]
Kawai, F. and Fujitani, Y. (1972) Some Discussions of the Stress Center. Proceedings of the 14th JSASS/JSME Conference on Structural Strength, Fukuoka, 12-13 July 1972, 163-166. (In Japanese)
[9]
Stronge, W.J. and Zhang, T.G. (1993) Warping of Prismatic Bars in Torsion. International Journal of Solids and Structures, 30, 601-606. http://dx.doi.org/10.1016/0020-7683(93)90024-2
