Plastic Hinge Integration Methods for Force-Based Beam–Column Elements
Publication: Journal of Structural Engineering
Volume 132, Issue 2
Abstract
A new plastic hinge integration method overcomes the problems with nonobjective response caused by strain-softening behavior in force-based beam–column finite elements. The integration method uses the common concept of a plastic hinge length in a numerically consistent manner. The method, derived from the Gauss–Radau quadrature rule, integrates deformations over specified plastic hinge lengths at the ends of the beam–column element, and it has the desirable property that it reduces to the exact solution for linear problems. Numerical examples show the effect of plastic hinge integration on the response of force-based beam–column elements for both strain-hardening and strain-softening section behavior in the plastic hinge regions. The incorporation of a plastic hinge length in the element integration method ensures objective element and section response, which is important for strain-softening behavior in reinforced concrete structures. Plastic rotations are defined in a consistent manner and clearly related to deformations in the plastic hinges.
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Acknowledgment
This work and the development of OpenSees has been supported by the Pacific Earthquake Engineering Research Center under Grant No. NSFEEC-9701568 from the National Science Foundation to the University of California, Berkeley, Calif.
References
Bazant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC, Boca Raton, Fla.
Clough, R. W., Benuska, K. L., and Wilson, E. L. (1965). “Inelastic earthquake response of tall buildings.” Proc., 3rd World Conf. on Earthquake Engineering, Wellington, New Zealand.
Coleman, J., and Spacone, E. (2001). “Localization issues in force-based frame elements.” J. Struct. Eng., 127(11), 1257–1265.
de Borst, R., Feenstra, P. H., Pamin, J., and Sluys, L. J. (1994). “Some current issues in computational mechanics of concrete structures.” Computer Modelling of Concrete Structures, Proc., EURO-C, H. Mang, N. Bićanić, and R. de Borst, eds., Swansea, U.K.
El-Tawil, S., and Deierlein, G. G. (1998). “Stress-resultant plasticity for frame structures.” J. Eng. Mech., 124(12), 1360–1370.
Federal Emergency Management Agency (FEMA). (2000). “Prestandard and commentary for the seismic rehabilitation of buildings.” FEMA 356, Washington, D. C.
Filippou, F. C., and Fenves, G. L. (2004). “Methods of analysis for earthquake-resistant structures.” Earthquake engineering: From engineering seismology to performance-based engineering, Y. Bozorgnia and V. V. Bertero, eds., Chap. 6, CRC, Boca Raton, Fla.
Giberson, M. F. (1967). “The response of nonlinear multistory structures subjected to earthquake excitation.” PhD thesis, California Institute of Technology, Pasadena, Calif.
Hildebrand, F. B. (1974). Introduction to numerical analysis, McGraw-Hill, New York.
Hilmy, S. I., and Abel, J. F. (1985). “A strain-hardening concentrated plasticity model for nonlinear dynamic analysis of steel buildings.” NUMETA85, Numerical methods in engineering, theory and applications, Vol. 1, 305–314, Rotterdam, Boston.
Hughes, T. J. R. (1987). The finite element method, Prentice-Hall, Englewood Cliffs, N.J.
Kent, D. C., and Park, R. (1971). “Flexural members with confined concrete.” J. Struct. Div. ASCE, 97(7), 1969–1990.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress–strain model for confined concrete.” J. Struct. Eng., 114(8), 1804–1826.
McKenna, F., Fenves, G. L., Scott, M. H., and Jeremić, B. (2000). “Open system for earthquake engineering simulation ⟨http://opensees.berkeley.edu⟩
Neuenhofer, A., and Filippou, F. C. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 123(7), 958–966.
Paulay, T., and Priestley, M. J. N. (1992). Seismic design of reinforced concrete and masonry buildings, Wiley, New York.
Powell, G. H., and Chen, P. F. (1986). “3D beam-column element with generalized plastic hinges.” J. Eng. Mech., 112(7), 627–641.
Simo, J. C., and Hughes, T. J. R. (1998). Computational inelasticity, Springer-Verlag, New York.
Spacone, E., Ciampi, V., and Filippou, F. C. (1996). “Mixed formulation of nonlinear beam finite element.” Comput. Struct., 58, 71–83.
Stoer, J., and Bulirsch, R. (1993). Introduction to numerical analysis, 2nd Ed., Springer, New York.
Tanaka, H., and Park, R. (1990). “Effect of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns.” Rep. No. 90-2, Dept. of Civil Engineering, Univ. of Canterbury, Canterbury, U.K.
Zienkiewicz, O. C., and Taylor, R. L. (2000). The finite element method: The basis, 5th Ed., Vol. 1, Butterworth, Stoneham, Mass.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 132 • Issue 2 • February 2006
Pages: 244 - 252
Copyright
© 2006 ASCE.
History
Received: Oct 26, 2004
Accepted: Mar 24, 2005
Published online: Feb 1, 2006
Published in print: Feb 2006
Notes
Note. Associate Editor: Keith D. Hjelmstad
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