Plastic Resistance of Pipe Sections: Upper Bound Solution
Publication: Journal of Structural Engineering
Volume 129, Issue 1
Abstract
In a previous paper, interaction relations based on the lower bound theorem of plasticity were derived for moderately thick pipes subjected to biaxial shear and bending, axial force, twisting moments, and internal or external pressure. The developments provided a lower bound solution based on assumed simplified stress fields. In this paper it is demonstrated that the assumptions made in the previous solution were indeed equilibrium requirements. Pipe interaction relations are obtained using the upper bound theorem of plasticity. Because (1) the assumed strain fields are based on the general solution of the compatibility equations; (2) the stress fields meet the equilibrium conditions; and (3) the yield condition is met over the whole pipe cross section, the interaction relations obtained are exact within the limitations of the formulation. The yield surface obtained meets the Drucker convexity requirement and is suitable as a potential surface characterizing the behavior of generalized plastic hinges in the elastoplastic analysis of pipe elements. The yield surface is mathematically described by two intrinsic functions. A simple mathematical procedure is devised in order to express the normality condition to the yield surface.
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References
American Institute for Steel Construction (AISC). (1999). “Load and resistance factor design specification for structural steel buildings.” AISC-LRFD, Chicago, Ill.
Boresi, A., and Sidebottom, O. (1985). Advanced mechanics of materials, 4th Ed., Wiley, New York.
Bruneau, M., Uang, C., and Whittaker, A. (1998). Ductile design of steel structures, McGraw-Hill, New York.
Canadian Standards Association (CSA). (1994). “Limit states design of steel structures.” CAN/CSA S16.1-94, Rexdale, Ontario, Canada.
Canadian Standards Association (CSA). (1996). “Oil and gas pipeline systems.” CAN/CSA Z662-96, Rexdale, Ontario, Canada.
Chen, W., and Atsuta, T.(1972). “Interaction equations for biaxially loaded sections.” J. Struct. Div., ASCE, 98(5), 1035–1052.
Det Norske Veritas. (1996). “Rules for submarine pipelines.” Oslo, Norway.
Drucker, D. C. (1951). “A more fundamental approach to plastic stress-strain relations.” Proc., 1st U.S. National Congress of Applied Mechanics, Chicago, 487–491.
Gaydon, F., and Nuttall, H.(1957). “On the combined bending and twisting of beams of various sections.” J. Mech. Phys. Solids, 6, 17–21.
Hill, R., and Seibel, M. P. L.(1953). “On the plastic distortion of solid bars by combined bending and twisting.” J. Mech. Phys. Solids, 1, 207–214.
Hodge, Ph. G. (1981). Plastic analysis of structures, R. E. Krieger, Malabar, Fla.
Hu, S. Z., Prion, H. G. L., and Birkemoe, P. C.(1993). “Influence of imperfections on the strength of unstiffened, fabricated, tubular beam-columns.” J. Constr. Steel Res., 25(1), 43–61.
Mohareb, M. (1995). “Deformational behaviour of line pipe.” PhD dissertation, Dept. of Civil Engineering, Univ. of Alberta, Edmonton, Alberta, Canada.
Mohareb, M.(2002). “Plastic interaction relations for pipe sections.” J. Eng. Mech., 128(1), 112–120.
Mohareb, M., Kulak, G. L., Elwi, A., and Murray, D. W.(2001). “Testing and analysis of steel pipe segments.” J. Transp. Eng.,408–417.
Mohareb, M., and Murray, D. W.(1999). “Mobilization of fully plastic moment capacity for pressurized pipes subjected to axial loading.” J. Offshore Mech. Arct. Eng., 121(4), 237–241.
Morris, G., and Fenves, S.(1969). “Approximate yield surface equations.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 95(EM4), 937–954.
Orbison, J., McGuire, W., and Abel, J.(1982). “Yield surface application of nonlinear steel frame analysis.” Comput. Methods Appl. Mech. Eng., 33, 557–573.
Powell, G., and Chen, P.(1986). “3D beam-column element with generalized plastic hinge.” J. Eng. Mech., 112(7), 627–641.
Prion, H., and Birkemoe, P. (1988). “Experimental behaviour of unstiffened fabricated tubular steel beam columns.” Pub. No. 88-03, Dept. of Civil Eng., Univ. of Toronto, Toronto.
Reisman, H., and Pawlik, P. (1980). Elasticity theory and applications, Wiley, New York, 111.
Schilling, C. G.(1965). “Buckling strength of circular tubes.” J. Struct. Div., ASCE, 91(5), 325–349.
Stewart, G., Klever, F., and Ritchie, D. (1994), “An analytical model to predict the burst capacity of pipelines.” 13th Int. Conf. on OMAE, Pipeline Technology, Houston, Vol. V, 177–188.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed., McGraw-Hill, New York, 342.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Jun 28, 2001
Accepted: Nov 13, 2001
Published online: Dec 13, 2002
Published in print: Jan 2003
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