Nonlinear Analysis of Mixed Steel-Concrete Frames. I: Element Formulation
Publication: Journal of Structural Engineering
Volume 127, Issue 6
Abstract
A beam-column element for simulating the inelastic behavior of 3D mixed frame structures comprised of steel, reinforced concrete, and/or composite members is presented. The formulation makes use of the flexibility method for deriving the element stiffness equations. A stress-resultant bounding surface plasticity model provides the sectional properties, which are then integrated along the length to generate the stiffness matrices. For steel members, the plasticity model is based on two nested surfaces, whereas for composite and reinforced concrete members the inner loading surface is degenerated to a point. Stiffness degradation of reinforced concrete and composite members is incorporated as a function of dissipated strain energy. Implementation and verification of the models for static and dynamic time-history analyses of mixed steel-concrete space frames are presented in a companion paper.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Attala, M. R., Deierlein, G. G., and McGuire, W. (1994). “Spread of plasticity—Quasi-plastic-hinge approach.”J. Struct. Engrg., ASCE, 120(8), 2451–2473.
2.
Dafalias, Y. H., and Popov, E. P. ( 1977). “Cyclic loading for materials with vanishing elastic region.” Nuclear Engrg. and Des., 41(2), 293–302.
3.
Drucker, D. C. ( 1951). “A more fundamental approach to plastic stress-strain relations.” Proc. 1st U.S. Nat. Congress of Appl. Mech., ASME, New York, 487–491.
4.
El-Tawil, S., and Deierlein, G. G. ( 1996). “Inelastic dynamic analysis of mixed steel-concrete space frames.” Struct. Engrg. Rep. 96-6, School of Civ. and Envir. Engrg., Cornell University, Ithaca, N.Y.
5.
El-Tawil, S., and Deierlein, G. G. (1998). “Stress-resultant plasticity for frame structures.”J. Engrg. Mech., ASCE, 124(12), 1360–1370.
6.
El-Tawil, S., and Deierlein, G. G. (2001). “Nonlinear analysis of mixed steel-concrete Frames. II: Implementation and verification.”J. Struct. Engrg., ASCE, 127(6), 656–665.
7.
Hajjar, J. F., and Gourley, B. C. (1997). “A cyclic nonlinear model for concrete-filled Tubes. I: Formulation.”J. Struct. Engrg., ASCE, 123(6), 736–744.
8.
Hajjar, J. F., Gourley, B. C., and Olson, M. C. (1997). “A cyclic nonlinear model for concrete-filled tubes. II: Verification.”J. Struct. Engrg., 123(6), 745–754.
9.
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 Engrg., Theory and Applications, Proc., Intl. Conf., Balkema, Rotterdam, The Netherlands, 305–314.
10.
Konig, J. A. ( 1987). Shakedown of elastic plastic structures, Polish Scientific, Warsaw.
11.
Kunnath, S. K., and Reinhorn, A. M. ( 1989). “Inelastic three dimensional response analysis of reinforced concrete building structures (IDARC-3D) Part I—Modeling.” Tech. Rep. NCEER-89-0011. Nat. Ctr. for Earthquake Engrg. Res., State University of New York at Buffalo, N.Y.
12.
Lubliner, J. ( 1990). Plasticity theory, Macmillan, New York.
13.
Mroz, Z. ( 1967). “On the description of anisotropic workhardening.” J. Mech. and Physics of Solids, 15, 163–175.
14.
Nigam, N. C. (1970). “Yielding in framed structures under dynamic loads.”J. Engrg. Mech. Div., ASCE, 96(5), 687–709.
15.
Orbison, J. ( 1982). “Nonlinear static analysis of 3-D steel frames.” PhD thesis, School of Civ. and Envir. Engrg., Cornell University, Ithaca, N.Y.
16.
Phillips, A., and Weng, G. J. ( 1975). “An analytical study of an experimentally verified hardening law.” J. Appl. Mech., 42(6), 375–378.
17.
Porter, F. L., and Powell, G. H. ( 1971). “Static and dynamic analysis of inelastic frame structures.” EERC Rep. 71-3, Earthquake Engrg. Res. Ctr., University of California, Berkeley, Calif.
18.
Powell, G. H., and Chen, P. F. (1986). “3D beam-column element with generalized plastic hinges.”J. Engrg. Mech., ASCE, 112(7), 627–641.
19.
Prager, W. ( 1956). “A new method of analyzing stresses and strains in work-hardening plastic solids.” J. Appl. Mech., 23, 493–496.
20.
Sfakianakis, M., and Fardis, M. N. (1991). “Bounding surface model for cyclic biaxial bending of RC sections.”J. Engrg. Mech., ASCE, 117(12), 2748–2769.
21.
Takeda, T., Sozen, M. A., and Nielsen, N. (1970). “Reinforced concrete response to simulated earthquakes.”J. Struct. Engrg., ASCE, 96(12), 2557–2573.
22.
Takizawa, H., and Aoyama, H. ( 1976). “Biaxial effects in modeling earthquake response of RC structures.” Earthquake Engrg. and Struct. Dyn., 4(6), 523–552.
23.
Zhao, Y. ( 1993). “Modeling of inelastic cyclic behavior of members, connections, and joint panels of steel frames.” PhD thesis, School of Civ. and Envir. Engrg., Cornell University, Ithaca, N.Y.
24.
Ziegler, H. ( 1959). “A modification of Prager's hardening rule.” Quarterly Appl. Math., 17, 55–65.
25.
Zyczykowski, M. ( 1981). Combined loading in the theory of plasticity, Polish Scientific, Warsaw.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 127 • Issue 6 • June 2001
Pages: 647 - 655
History
Received: Aug 2, 2000
Published online: Jun 1, 2001
Published in print: Jun 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.