Engineering Transactions, 69, 2, pp. 211–221, 2021
10.24423/EngTrans.1294.20210607

Estimation of the Torsional Rigidity of Orthotropic Solid Cross Section

István ECSEDI
University of Miskolc
Hungary

Attila BAKSA
University of Miskolc
Hungary

In this paper, two inequality relations are proven for the torsional rigidity of orthotropic elastic solid cross sections. By using the derived inequality relations, lower and upper bounds can be obtained for the torsional rigidity. All results of the paper follow from the Saint-Venant theory of uniform torsion. The presented bounding formulae are based on the mean value theorem of integral calculus.

Keywords: Saint-Venant torsion; orthotropic; torsional rigidity; Barta-type inequality
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).

References

Rand O., Rovenski V., Analytical Methods in Anisotropic Elasticity with Symbolic Computation Tools, Birkhäuser Basel, 2005, doi: 10.1007/b138765.

Lekhnitskii S.G., Theory of an Anisotropic Body [in Russian], Mir Publishers, Moscow, 1981.

Milne-Thomson L.M., Plane Elastic System, Springer Verlag, Berlin, 1960.

Lekhnitskii S.G., Torsion of Anisotropic and Non-homogeneous Beams [in Russian], Nauka, Moscow, 1971.

Barta J., On the estimation of torsional rigidity, Koninklijke Nederlandse Akademie van Wetenschappen. Series B, 58(1): 80–89, 1955.

Barta J., On the fundamental vibration of a membrane [in French: Sur la vibration fondamentale d’une membrane], Comptes Rendus de l'Académie des Sciences Paris, 204(7): 472–473, 1934.

Bandle C., Isoperimetric Inequalities and Applications, Pitman Publishing Inc., Boston, 1980.

Hersch J., On the fundamental frequency of a vibrating membrane: evaluations by defeat and principle of the maximum [in French: Sur la fréquence fondamentale d’une membrane vibrante: évaluations par défant et principle du maximum], Journal of Applied Mathematics and Physics (ZAMP), 11: 387–413, 1960, doi: 10.1007/BF01604498.

Barta J., On the estimation of the torsional stiffness of thin-walled multicell prisms [in French: Sur l’estimation de la rigidité de torsion des prismes multicellures à paois minces], Acta Technica Academiae Scientiarum Hungaricae, XII: 333–337, 1955.

Weber C., Günther W., Torsionstheorie [in German], Friedrich Vieweg & Sohn, Braunschweig, 1958.




DOI: 10.24423/EngTrans.1294.20210607