New Spread Plasticity Model for Reinforced Concrete Structural Elements Accounting for Both Gravity and Lateral Load Effects
Publication: Journal of Structural Engineering
Volume 144, Issue 5
Abstract
The spread plasticity models that are generally used for nonlinear analysis include the uniform, linear, and, more recently, power spread plasticity models. Because all of these models are formulated from a linear moment diagram subjected to lateral loading apart from the effect of gravity loading, it has been assumed that the predefined shape of their curvature extends from the two ends of the element. This assumption can lead to incorrect outcomes in nonlinear analysis. In this study, a distributed plasticity model is developed that considers the effects of both gravity and lateral loading. To derive the proposed model, the unit load theory based on the principle of virtual work is used, and a general formulation is prepared to achieve the stiffness matrix of each beam-column element with the different flexibility properties along it. To confirm the accuracy of the proposed methodology, seven numerical examples are assessed. It is demonstrated that the results of the proposed model differ from the linear flexibility model when using only one element for each member, although the difference can be decreased by subdividing the individual structural members into more than one element. The accuracy of the proposed model is corroborated through comparison with experimental results.
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References
Al-Haddad, M. S., and Wight, J. S. (1988). “Relocating beam plastic hinging zones for earthquake resistant design of reinforced concrete buildings.” Struct. J., 85(2), 123–133.
Alva, G. M. S., and de Cresce El, A. L. H. (2010). “Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures.” Eng. Struct., 32(4), 974–981.
Amorim, D. L. D. F., Proença, S. P., and Flórez-López, J. (2013). “A model of fracture in reinforced concrete arches based on lumped damage mechanics.” Int. J. Solids Struct., 50(24), 4070–4079.
Anderson, J. C., and Townsend, W. H. (1977). “Models for RC frames with degrading stiffness.” J. Struct. Div., 103(12), 2361–2376.
Aoyama, H., and Sugano, T. (1968). “A generalized inelastic analysis of reinforced concrete structures based on the tests of members.” Recent Researches of Structural Mechanics-Contributions in Honor of the 60-th Birthday of Prof. Y. Tsuboi, Uno Shoten, Tokyo.
Astroza, R., Ebrahimian, H., and Conte, J. P. (2015). “Material parameter identification in distributed plasticity FE models of frame-type structures using nonlinear stochastic filtering.” J. Eng. Mech., 04014149.
Au, F. T. K., and Bai, Z. Z. (2007). “Two-dimensional nonlinear finite element analysis of monotonically and non-reversed cyclically loaded RC beams.” Eng. Struct., 29(11), 2921–2934.
Babazadeh, A., Burgueño, R., and Silva, P. F. (2016). “Evaluation of the critical plastic region length in slender reinforced concrete bridge columns.” Eng. Struct., 125, 280–293.
Berry, M. P., Lehman, D. E., and Lowes, L. N. (2008). “Lumped-plasticity models for performance simulation of bridge columns.” ACI Struct. J., 105(3), 270.
Bhatti, M. A. (2006). Advanced topics in finite element analysis of structures: With Mathematica and MATLAB computations, Wiley, Hoboken, NJ.
Birely, A. C., Lowes, L. N., and Lehman, D. E. (2012). “A model for the practical nonlinear analysis of reinforced-concrete frames including joint flexibility.” Eng. Struct., 34, 455–465.
Caltrans. (1988). “Bridge design specifications.” Sacramento, CA.
Clough, R. W., and Johnston, R. B. (1966). Effect of stiffness degradation on earthquake ductility requirements, Dept. of Civil Engineering, Univ. of California, Berkeley, CA.
Dides, M. A., and De la Llera, J. C. (2005). “A comparative study of concentrated plasticity models in dynamic analysis of building structures.” Earthquake Eng. Struct. Dyn., 34(8), 1005–1026.
Emori, K., and Schnobrich, W. C. (1981). “Inelastic behavior of concrete frame-wall structures.” J. Struct. Div., 107(1), 145–164.
Felber, A. J. (1990). “RESPONSE: A program to determine the load-deformation response of reinforced concrete sections.” Univ. of Toronto, Toronto.
Giberson, M. F. (1967). “The response of nonlinear multi-story structures subjected to earthquake excitation.” Ph.D. dissertation, California Institute of Technology, Pasadena, CA.
Guyan, R. J. (1965). “Reduction of stiffness and mass matrices.” AIAA J., 3(2), 380.
Habibi, A., and Moharrami, H. (2010). “Nonlinear sensitivity analysis of reinforced concrete frames.” Finite Elem. Anal. Des., 46(7), 571–584.
Habibi, A. R. (2008). “Optimal seismic performance based design of 2D reinforced concrete frames.” Ph.D. thesis, Tarbiat Modarres Univ., Tehran, Iran.
Hajjar, J. F., Molodan, A., and Schiller, P. H. (1998a). “A distributed plasticity model for cyclic analysis of concrete-filled steel tube beam-columns and composite frames.” Eng. Struct., 20(4–6), 398–412.
Hajjar, J. F., Schiller, P. H., and Molodan, A. (1998b). “A distributed plasticity model for concrete-filled steel tube beam-columns with interlayer slip.” Eng. Struct., 20(8), 663–676.
He, R., and Zhong, H. (2012). “Large deflection elasto-plastic analysis of frames using the weak-form quadrature element method.” Finite Elem. Anal. Des., 50, 125–133.
He, Z., Liu, W., Wang, X., and Ye, A. (2016). “Optimal force-based beam-column element size for reinforced-concrete piles in bridges.” J. Bridge Eng., 06016006.
Inel, M., and Ozmen, H. B. (2006). “Effects of plastic hinge properties in nonlinear analysis of reinforced concrete buildings.” Eng. Struct., 28(11), 1494–1502.
Izadpanah, M., and Habibi, A. (2015). “Evaluating the spread plasticity model of IDARC for inelastic analysis of reinforced concrete frames.” Struct. Eng. Mech., 56(2), 169–188.
Jelenić, G., and Crisfield, M. A. (1996). “Non-linear ‘master-slave’ relationships for joints in 3-D beams with large rotations.” Comput. Methods Appl. Mech. Eng., 135(3–4), 211–228.
Kim, S. P., and Kurama, Y. C. (2008). “An alternative pushover analysis procedure to estimate seismic displacement demands.” Eng. Struct., 30(12), 3793–3807.
Kucukler, M., Gardner, L., and Macorini, L. (2014). “A stiffness reduction method for the in-plane design of structural steel elements.” Eng. Struct., 73, 72–84.
Kunnath, S. K., and Reinhorn, A. M. (1989). Inelastic three-dimensional response analysis of reinforced concrete building structures (IDARC-3D), National Center for Earthquake Engineering Research, Buffalo, NY.
Lee, C. L., and Filippou, F. C. (2009). “Efficient beam-column element with variable inelastic end zones.” J. Struct. Eng., 1310–1319.
Lee, H. S., and Woo, S. W. (2002). “Seismic performance of a 3-story RC frame in a low-seismicity region.” Eng. Struct., 24(6), 719–734.
Mahin, S. A., and Bertero, V. V. (1976). “Problems in establishing and predicting ductility in aseismic design.” Proc., Int. Symp. on Earthquake Structural Engineering, Univ. of Missouri, Rolla, MO, 613–628.
Mazza, F. (2014). “A distributed plasticity model to simulate the biaxial behaviour in the nonlinear analysis of spatial framed structures.” Comput. Struct., 135, 141–154.
Medić, S., Dolarević, S., and Ibrahimbegovic, A. (2013). “Beam model refinement and reduction.” Eng. Struct., 50, 158–169.
Mergos, P. E., and Kappos, A. J. (2012). “A gradual spread inelasticity model for R/C beam-columns, accounting for flexure, shear and anchorage slip.” Eng. Struct., 44, 94–106.
Meyer, C., Roufaiel, M. S., and Arzoumanidis, S. G. (1983). “Analysis of damaged concrete frames for cyclic loads.” Earthquake Eng. Struct. Dyn., 11(2), 207–228.
Neuenhofer, A., and Filippou, F. C. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 958–966.
Nguyen, P. C., and Kim, S. E. (2014). “Distributed plasticity approach for time-history analysis of steel frames including nonlinear connections.” J. Constr. Steel Res., 100, 36–49.
OpenSees [Computer software]. PEER, Berkeley, CA.
Otani, S., and Sozen, M. A. (1972). Behavior of multistory reinforced concrete frames during earthquakes, Univ. of Illinois, Urbana, IL, 551.
Pan, W. H., Tao, M. X., and Nie, J. G. (2016). “Fiber beam-column element model considering reinforcement anchorage slip in the footing.” Bull. Earthquake Eng., 15(3), 991–1018.
Park, Y. J., Reinhorn, A. M., and Kunnath, S. K. (1987). IDARC: Inelastic damage analysis of reinforced concrete frame-shear-wall structures, National Center for Earthquake Engineering Research, Buffalo, NY.
Powell, G. (1975). “Supplement to computer program DRAIN-2D.” DRAIN-2D user’s guide, Univ. of California, Berkeley, CA.
Rahai, A. R., and Nafari, S. F. (2013). “A comparison between lumped and distributed plasticity approaches in the pushover analysis results of a pc frame bridge.” Int. J. Civ. Eng., 11(4), 217–225.
Reinhorn, A. M., et al. (2009). “IDARC 2D version 7.0: A program for the inelastic damage analysis of structures.”, Univ. at Buffalo—State Univ. of New York, Buffalo, NY.
Roh, H., Reinhorn, A. M., and Lee, J. S. (2012). “Power spread plasticity model for inelastic analysis of reinforced concrete structures.” Eng. Struct., 39, 148–161.
Roufaiel, M. S., and Meyer, C. (1987). “Analytical modeling of hysteretic behavior of R/C frames.” J. Struct. Eng., 429–444.
Scott, M. H., and Fenves, G. L. (2006). “Plastic hinge integration methods for force-based beam-column elements.” J. Struct. Eng., 244–252.
Soleimani, D., Popov, E. P., and Bertero, V. V. (1979). “Nonlinear beam model for R/C frame analysis.” Electronic computation, ASCE, New York, 483–509.
Stone, W. C., and Cheok, G. S. (1989). “Inelastic behavior of full-scale bridge columns subjected to cyclic loading.”, National Institute of Standards and Technology, Gaitherburg, MD.
Takizawa, H. (1973). “Strong motion response analysis of reinforced concrete buildings.” Concr. J. Jpn. Nat. Counc. Concr., 11(2), 10–21.
Tang, Y. Q., Zhou, Z. H., and Chan, S. L. (2015). “Nonlinear beam-column element under consistent deformation.” Int. J. Struct. Stab. Dyn., 15(5), 1450068.
Wen, R. K., and Janssen, J. G. (1965). “Dynamic analysis of elasto-inelastic frames.” Proc., 3rd World Conf. on Earthquake Engineering, Vol. 2, Wellington, New Zealand, 713–729.
Zhao, X., Wu, Y. F., Leung, A. Y., and Lam, H. F. (2011). “Plastic hinge length in reinforced concrete flexural members.” Procedia Eng., 14, 1266–1274.
Zhao, X. M., Wu, Y. F., and Leung, A. Y. T. (2012). “Analyses of plastic hinge regions in reinforced concrete beams under monotonic loading.” Eng. Struct., 34, 466–482.
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Published In
Journal of Structural Engineering
Volume 144 • Issue 5 • May 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Feb 14, 2017
Accepted: Oct 23, 2017
Published online: Feb 22, 2018
Published in print: May 1, 2018
Discussion open until: Jul 22, 2018
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