Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T01:00:01.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Closed-Form Approximate Formulas for Torsional Analysis of Hollow Tubes with Straight and Circular Edges

Published online by Cambridge University Press:  05 May 2011

A. Doostfatemeh ,
M. R. Hematiyan  and
S. Arghavan
A. Doostfatemeh*
Affiliation:
Department of Mechanical Engineering, School of Engineering 71345, Shiraz University, Shiraz, Iran
M. R. Hematiyan*
Affiliation:
Department of Mechanical Engineering, School of Engineering 71345, Shiraz University, Shiraz, Iran
S. Arghavan*
Affiliation:
Department of Mechanical Engineering, School of Engineering 71345, Shiraz University, Shiraz, Iran
*
*Master of Science
**Associate Professor, corresponding author
***Graduate Student
Get access

Abstract

Some analytical formulas are presented for torsional analysis of homogeneous hollow tubes. The cross section is supposed to consist of straight and circular segments. Thicknesses of segments of the cross section can be different. The problem is formulated in terms of Prandtl's stress function. The derived approximate formulas are so simple that computations can be carried out by a simple calculator. Several examples are presented to validate the formulation. The accuracy of formulas is verified by accurate finite element method solutions. It is seen that the error of the formulation is small and the formulas can be used for analysis of thin to moderately thick-walled hollow tubes.

Keywords

TorsionHollow tubesHomogenousArbitrary shapes.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 4 , December 2009 , pp. 401 - 409
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Beer, F. P. and Johnston, E. R., Mechanics of Materials, 2nd Ed., McGraw-Hill, New York (1992).Google Scholar
2.Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, McGraw-Hill, New York (1970).Google Scholar
3.Baron, F. M., “Torsion of Multi-Connected Thin Walled Cylinders,” J Appl Mech, 9, pp. 72–74 (1942).Google Scholar
4.Nguyen, S. H., “An Accurate Finite Element Formulation for Linear Elastic Torsion Calculations,” Comput Struct, 42, pp. 707–711 (1992).Google Scholar
5.Wang, C. Y., “Torsion of a Flattened Tube,” Meccanica, 30, pp. 221–227 (1995).CrossRefGoogle Scholar
6.Wang, C. Y., “Torsion of Tubes of Arbitrary Shape,” Int J Solids Struct, 35, pp. 719–731 (1998).Google Scholar
7.Li, Z., Ko, J. M. and Ni, Y. Q., “Torsional Rigidity of Reinforced Concrete Bars with Arbitrary Sectional Shape,” Finite Elem Anal Des, 35, pp. 349–361 (2000).Google Scholar
8.Sapountzakis, E. J., “Nonuniform Torsion of Multi-Material Composite Bars by the Boundary Element Method,” Comput Struct, 79, pp. 2805–2816 (2001).Google Scholar
9.Sapountzakis, E. J. and Mokos, V. G., “Warping Shear Stresses in Nonuniform Torsion of Composite Bars by BEM,” Comput Method Appl M, 192, pp. 4337–4353 (2003).Google Scholar
10.Sapountzakis, E. J. and Mokos, V. G., “Nonuniform Torsion of Bars of Variable Cross Section,” Comput Struct, 82, pp. 703–715 (2004).Google Scholar
11.Sapountzakis, E. J. and Mokos, V. G., “Nonuniform Torsion of Composite Bars of Variable Thickness by BEM,” Int J Solids Struct, 41, pp. 1753–1771 (2004).Google Scholar
12.Hassenpflug, W. C., “Torsion of Uniform Bars with Polygon Cross-Section,” Comput Math Appl, 46, pp. 313–392 (2003).Google Scholar
13.Kolodziej, J. A. and Fraska, A., “Elastic Torsion of Bars Possessing Regular Polygon in Cross-Section Using BCM,” Comput Struct, 84, pp. 78–91 (2005).Google Scholar
14.Hematiyan, M. R. and Doostfatemeh, A., “Torsion of Moderately Thick Hollow Tubes with Polygonal Shapes,” Mech Res Commun, 34, pp. 528–537 (2007).Google Scholar
15.Sadd, M. H., Elasticity, Elsevier, Burlington (2005).Google Scholar
16.Reddy, J. N., Finite Element Method, 2nd Ed., McGraw-Hill, New York (1993).Google Scholar