Plastic Hinge Development of Frame Members Using a Nonlinear Hardening Rule
Publication: Journal of Structural Engineering
Volume 131, Issue 8
Abstract
A nonlinear hardening rule that defines a yield surface translation for homogeneous frame member materials is proposed. The rule is defined as a nonlinear constitutive relationship that examines material behavior through a postelastic perspective. The gradual development of the postelastic states of a beam along its length and through its section thickness is analyzed. The model uses a hardening index parameter to guide the nonlinear stress–strain relationship, and a smooth function to model the web–flange intersection of frame members. As such, nonlinear curvature distributions with continuous derivatives are determined along the length of the member, which enables lateral displacements to be accurately predicted. Plastic hinge lengths and finite-element displacements are subsequently determined, and a nonlinear stiffness is derived. The model is formulated on a constitutive level and applies a smoothed-over cross section to derive a single internal moment expression for any postelastic state. Results are verified through experimental published literature.
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References
Attalla, M., Deierlein, G., and McGuire, W. (1994). “Spread of plasticity—quasi-plastic-hinge approach.” J. Struct. Eng., 120(8), 2451–2473.
Attard, T. (2003). “Modeling of higher-mode effects in various frame structures using a pushover analysis.” Doctoral Dissertation, Arizona State University, Tempe, Ariz.
Ballio, G., and Perotti, F. (1987). “Cyclic behaviour of axailly loaded members: numerical simulation and experimental verification.” J. Constr. Steel Res., 7(1), 3–41.
Barsan, G., and Chiorean, C. (1999). “Computer program for large deflection elasto-plastic analysis of semi-rigid steel frameworks.” Comput. Struct., 72(6), 699–711.
Bayrak, O., and Sheikh, S. (2001). “Plastic hinge analysis.” J. Struct. Eng., 127(9), 1092–1100.
Brunig, M. (1998). “Nonlinear finite element analysis based on a large strain deformation theory of plasticity.” Comput. Struct., 69(1), 117–128.
Carnicero, A., Perera, R., and Alarcon, E. (1999). “Simplified model of low cycle fatigue for RC frames.” J. Struct. Eng., 125(10), 1200–1202.
Chen, P., and Powell, G. (1982). “Generalized plastic hinge concepts for 3D beam-column elements.” EERC Rep. No. 80/20, Univ. of California, Berkeley, Calif.
Clarke, M., Bridge, R., Hancock, G., and Trahair, N. (1991). “Design using advanced analysis.” SSRC Annual Tech. Session Proc., Lehigh Univ., Bethlehem, Pa., 27–40.
Dafalias, Y., and Popov, E. (1975). “A model of nonlinearly hardening materials for complex loading.” Acta Mech., 21(3), 173–192.
Elnashai, A., and Elghazouli, A. (1993). “Performance of composite steel/concrete members under earthquake loading. Part I: Analytical Model.” Earthquake Eng. Struct. Dyn., 22(4), 315–345.
Elnashai, A., and Izzuddin, B. (1993). “Modeling of material nonlinearities in steel structures subjected to transient dynamic loading.” Earthquake Eng. Struct. Dyn., 22(6), 509–532.
Englekirk, R. (1994). Steel structures: Controlling behavior through design, Wiley, New York.
Gao, L., and Haldar, A. (1995). “Nonlinear seismic analysis of space structures with partially restrained connections.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 32(5), 240A–240A.
Goldsworthy, H., and Stevens, L. (1992). “Energy dissipation in determinate steel beams.” J. Struct. Eng., 118(1), 1–17.
Iwan, W. D. (1967). “On a class of models for the yielding behavior of continuous and composite systems.” J. Appl. Mech., 34(3), 612–617.
Jiang, W. (1999). “General kinematic-isotropic hardening model.” J. Eng. Mech., 125(4), 487–490.
Jiang, X., Chen, H., and Liew, J. Y. R. (2002). “Spread of plasticity analysis of three-dimensional steel frames.” J. Constr. Steel Res., 58(2), 193–212.
Karabinis, A., and Kiousis, P. (2001). “Plasticity model for reinforced concrete elements subjected to overloads.” J. Struct. Eng., 127(11), 1251–1256.
Kim, S., and Lee, J. (2001). “Improved refined plastic-hinge analysis accounting for local buckling.” Eng. Struct., 23(8), 1031–1042.
Kratzig, W., and Niemann, H. (1996). Dynamics of civil engineering structures, A. A. Balkema, Rotterdam, The Netherlands.
Liew, J., Chen, H., Shanmugam, N., and Chen, W. (2000). “Improved nonlinear plastic hinge analysis of space frame structures.” Eng. Struct., 22(10), 1324–1338.
Liew, J., Yu, C., Ng, Y., and Shanmugam, N. (1997). “Testing of semi-rigid, unbraced frames for calibration of 2nd order inelastic analysis.” J. Constr. Steel Res., 41(2/3), 159–195.
Marcon, A., Bittencourt, E., and Creus, G. (1999). “On the integration of stresses in large deformations plasticity.” Eng. Comput., 16(1), 49–69.
Martin, J. B. (1975). Plasticity: Fundamentals and general results, MIT Press, Cambridge, Mass.
Mendleson, A. (1968). Plasticity: Theory and application, Macmillan, New York.
Needleman, A. (1985). “On finite element formulations for large elastic-plastic deformations.” Comput. Struct., 20(1–3), 247–257.
Petersson, H., and Popov, E. (1977). “Constitutive relations for generalized loading.” J. Eng. Mech. Div., 103(4), 611–627.
Phillips, A., and Lee, C. (1979). “Yield surfaces and loading surfaces. Experiments and recommendations.” Int. J. Solids Struct., 15(9), 715–729.
Popov, E. (1987). “Panel zone flexibility in seismic moment joints.” J. Constr. Steel Res., 8, 91–118.
Prager, W. (1955). “The theory of plasticity: A survey of recent achievements.” Proc. Inst. Mech. Eng., 169, 41–57.
Shames, I., and Cozzarelli, F. (1992). Elastic and inelastic stress analysis, Prentice-Hall, Englewood Cliffs, N.J.
Shen, C., Mamaghani, I., Mizuno, E., and Usami, T. (1995). “Cyclic behavior of structural steels. II: Theory.” J. Eng. Mech., 121(11), 1165–1172.
Uniform Building Code. (1997). International Conf. of Building Officials, Pasadena, Calif.
Usami, T., Gao, S., and Ge, H. (2000). “Elastoplastic analysis of steel members and frames subjected to cyclic loading.” Eng. Struct., 22(2), 135–145.
White, D. (1985). “Material and geometric nonlinear analysis of local planar behavior in steel frames using interactive computer graphics.” MS thesis, Cornell Univ., Ithaca, N.Y.
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© 2005 ASCE.
History
Received: Nov 8, 2002
Accepted: Nov 19, 2004
Published online: Aug 1, 2005
Published in print: Aug 2005
Notes
Note. Associate Editor: Enrico Spacone
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