TECHNICAL PAPERS
Jul 1, 1986

3D Beam‐Column Element with Generalized Plastic Hinges

Publication: Journal of Engineering Mechanics
Volume 112, Issue 7

Abstract

Beam‐column elements in which plastic hinges may form are commonly used for elastic‐plastic analysis of frames. The concept of a zero‐length plastic hinge (lumped plasticity) is a mathematical abstraction, because it implies infinite strains. Nevertheless, the concept is convenient computationally, and can be sufficiently accurate for many practical applications. For simple beams, plastic hinges can be introduced easily into a mathematical model. For 3D beam‐columns, however, the concept of a “generalized” hinge is needed, accounting for interaction among axial, torsional and biaxial bending effects. A theory and computational procedure based on plasticity concepts are presented. Numerical examples indicate how the element might be used, and show that results in agreement with more elaborate models can be obtained. Because the lumped plasticity assumption is not necessarily accurate, caution is advised in use of the element.

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References

1.
Chen, P. F.‐S., and Powell, G. H., “Generalized Plastic Hinge Concepts for 3D Beam‐Column Elements,” Report No. UCB/EERC 82‐20, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif., Nov., 1982.
2.
Clough, R. W., Benuska, K. L., and Wilson, E. L., “Inelastic Earthquake Response of Tall Building,” Proceedings, 3rd World Conference on Earthquake Engineering, Vol. II, Session II, New Zealand, 1965, pp. 68–89.
3.
Giberson, M. F., “The Response of Nonlinear Multistory Structures Subjected to Earthquake Excitation,” Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, Calif., May, 1967.
4.
Litton, R. W., “A Contribution to the Analysis of Concrete Structures Under Cyclic Loading,” thesis presented to The University of California, at Berkeley, Calif., in 1975, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
5.
Mahasuverachai, M., and Powell, G. H., “Inelastic Analysis of Piping and Tubular Structures,” Report No. UCB/EERC 82‐27, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif., Nov., 1982.
6.
Mosaddad, B., and Powell, G. H., “Computational Models for Cyclic Plasticity, Rate Dependence, and Creep in Finite Element Analysis,” Report No. UCB/EERC 82‐26, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif., Nov., 1982.
7.
Mroz, Z., “On the Description of Anisotropic Workhardening,” Journal of Mechanical Physics and Solids, Vol. 15, 1967, pp. 163–175.
8.
Mroz, Z., “An Attempt to Describe the Behavior of Metals Under Cyclic Loads Using a More General Workhardening Model,” Acta Mechanica, Vol. 7, Nos. 2–3, 1969, pp. 199–212.
9.
Porter, F. L., and Powell, G. H., “Static and Dynamic Analysis of Inelastic Frame Structures,” Report No. UCB/EERC 71‐3, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif., 1971.
10.
Powell, G. H., Chen, P. F.‐S., et al., “WIPS: Computer Code for Whip and Impact Analysis of Piping Systems,” NUREG/OR‐3686 (4 volumes), U.S. Nuclear Regulatory Commission, 1984.
11.
Prager, W., “The Theory of Plasticity: A Survey of Recent Achievement,” Proceedings, Institute of Mechanical Engineers, Vol. 169, 1955, pp. 41–57.
12.
Riahi, A., Row, D. G., and Powell, G. H., “Beam Column Elements for the ANSR‐I Program,” Report No. UCB/EERC 78‐08, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif., Apr., 1978.
13.
Sherman and Morrison, Numerical Methods, Prentice‐Hall, Englewood Cliffs, N.J., 1974, 161 pp.
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Takizawa, H., and Aoyama, H., “Biaxial Effects in Modelling Earthquake Response of R/C Structures,” International Journal of Earthquake Engineering and Structural Dynamics, Vol. 4, 1976.
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Thorn, C. W., “The Effects of Inelastic Shear on the Seismic Response of Structures,” thesis presented to the University of Auckland, at New Zealand, in 1983, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
16.
Ziegler, H., “A Modification of Prager's Hardening Rule,” Quarterly of Applied Math, Vol. 17, 1959, p. 45.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 112Issue 7July 1986
Pages: 627 - 641

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Published online: Jul 1, 1986
Published in print: Jul 1986

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Authors

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Graham H. Powell, M. ASCE
Prof. of Civ. Engrg., Univ. of California, Berkeley, CA 94720
Paul Fu‐Song Chen
Consultant, SSD Inc., Berkeley, CA

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