Upper Bound Plastic Interaction Relations for Elliptical Hollow Sections
Publication: Journal of Engineering Mechanics
Volume 136, Issue 8
Abstract
A family of interaction expressions are developed for steel elliptical hollow sections (EHSs) subjected to combinations of axial force, biaxial bending moments, torsion, and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. The interaction expressions developed consist of a set of elliptical integrals which are cast in a dimensionless form applicable for EHS of general geometries. An iterative solution technique is developed to solve the resulting nonlinear relations. The applicability of the resulting interaction relations for conducting the cross-sectional check is illustrated through examples. A comparison with shell finite-element analysis results illustrates the validity of the interaction relations derived.
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Acknowledgments
This research was partly funded by the Natural Science and Research Council (NSERC) of Canada through a grant to the second writer. The writers also acknowledge the contribution of one of reviewers who proposed the simplified quadratic form of the interaction relations in Eq. (65).UNSPECIFIED
References
Benscoter, S. U. (1954). “A theory of torsion bending for multicell beams.” Trans. ASME, J. Appl. Mech., 21(1), 25–34.
Boresi, A., and Sidebottom, O. (1985). Advanced mechanics of materials, Wiley, New York.
Chan, T. M., and Gardner, L. (2008a). “Bending strength of hot-rolled elliptical hollow sections.” J. Constr. Steel Res., 64(9), 971–986.
Chan, T. M., and Gardner, L. (2008b). “Compressive resistance of hot-rolled elliptical hollow sections.” Eng. Struct., 30(2), 522–532.
Chen, W. F., and Atsuta, T. (1972). “Interaction equations for biaxially loaded sections.” J. Struct. Div., 98(5), 1035–1052.
Chen, Y. N., and Kempner, J. (1976). “Buckling of oval cylindrical-shell under compression and asymmetric bending.” AIAA J., 14(9), 1235–1240.
Feinstein, G., Erickson, B., and Kempner, J. (1971). “Stability of oval cylindrical shells.” Exp. Mech., 11(11), 514–520.
Gardner, L. (2005). “Structural behaviour of oval hollow sections.” 4th Int. Conf. on Advances in Steel Structures, Elsevier, New York, 517–522.
Gardner, L., and Chan, T. M. (2007). “Cross-section classification of elliptical hollow sections.” Steel Compos. Struct., 7(3), 185–200.
Gardner, L., Chan, T. M., and Wadee, M. A. (2008). “Shear response of elliptical hollow sections.” Proc. Inst. Civ. Eng., Struct. Build., 161(6), 301–309.
Gardner, L., and Ministro, A. (2004). Testing and numerical modelling of structural steel oval hollow sections, Imperial College, London.
Gaydon, F. A., and Nuttall, H. (1957). “On the combined bending and twisting of beams of various sections.” J. Mech. Phys. Solids, 6(1), 17–26.
Grigorenko, Y. M., and Rozhok, L. S. (2002). “Stress analysis of hollow elliptic cylinders with variable eccentricity and thickness.” Int. Appl. Mech., 38(8), 954–966.
Hill, R. (1967). The mathematical theory of plasticity, Clarendon, Oxford.
Hill, R., and Siebel, M. P. L. (1953). “On the plastic distortion of solid bars by combined bending and twisting.” J. Mech. Phys. Solids, 1(3), 207–214.
Hodge, P. G. (1981). Plastic analysis of structures, Krieger, Malabar, Fla.
Hutchinson, J. W. (1968). “Buckling and initial postbuckling behavior of oval cylindrical shells under axial compression.” Trans. ASME, J. Appl. Mech., 35(1), 66–72.
Kempner, J. (1962). “Some results on buckling and post-buckling of cylindrical shells.” NASA Rep. TN D-1510, Langley Research Center, Hampton, Va., 173–186.
Kempner, J., and Chen, Y. N. (1974). “Buckling and initial postbuckling of oval cylindrical-shells under combined axial-compression and bending.” Trans. N. Y. Acad. Sci., 36(2), 171–191.
Mohareb, M. (2001). “Exact yield hyper-surface for thin pipes.” Int. J. Pressure Vessels Piping, 78(7), 507–514.
Mohareb, M. (2003). “Plastic resistance of pipe sections: Upper bound solution.” J. Struct. Eng., 129(1), 41–48.
Nocedal, J., and Wright, S. J. (1999). Numerical optimization, Springer, New York.
Nowzartash, F. (2010). “Interaction relations for elliptical hollow sections.” Ph.D. thesis, Univ. of Ottawa, Ottawa.
Nowzartash, F., and Mohareb, M. (2009). “Plastic interaction relations for elliptical hollow sections.” Thin-Walled Struct., 47, 681–691.
Nowzartash, F., and Mohareb, M. (2010). “Plastic interaction relations for semi-elliptical hollow sections.” Thin-Walled Struct., 48, 42–54.
Ruiz-Teran, A. M., and Gardner, L. (2008). “Elastic buckling of elliptical tubes.” Thin-Walled Struct., 46(11), 1304–1318.
Silvestre, N. (2008). “Buckling behaviour of elliptical cylindrical shells and tubes under compression.” Int. J. Solids Struct., 45(16), 4427–4447.
SIMULIA. (2007). “Abaqus unified finite element analysis.” ⟨http://www.simulia.com/products/abaqus_fea.html⟩ (Apr. 2008).
Theofanous, M., Chan, T. M., and Gardner, L. (2009). “Structural response of stainless steel oval hollow section compression members.” Eng. Struct., 31(4), 922–934.
Willibald, S., Packer, J. A., and Martinez-Saucedo, G. (2006). “Behaviour of gusset plate connections to ends of round and elliptical hollow structural section members.” Can. J. Civ. Eng., 33(4), 373–383.
Zhu, Y., and Wilkinson, T. (2007). Finite element analysis of structural steel elliptical hollow sections in compression, University of Sydney, Sydney, Australia.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 8 • August 2010
Pages: 1015 - 1027
Copyright
© 2010 ASCE.
History
Received: May 15, 2009
Accepted: Jan 12, 2010
Published online: Jan 25, 2010
Published in print: Aug 2010
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