Effects on the Plastic Region of RC Bridge Columns: Closed-Form Solution
Publication: Journal of Structural Engineering
Volume 142, Issue 11
Abstract
A closed-form solution to the effect of member deformations () on the inelastic response of RC bridge columns is presented. The formulation is based on an equivalent elastic structure with a constant flexural stiffness for the cracked RC section that enables the solution to be independent of the structural global displacements (). The ability of the proposed solution for predicting moment, curvature, and displacement profiles in RC columns is demonstrated and verified against experimental data from four half-scale test columns. The closed-form solution led to the identification of a dimensionless slenderness parameter that measures the susceptibility of RC columns to second-order effects. Simplified formulas for the spread of the plastic region () and the magnitude of moment are proposed for use in seismic design. The design formulas, derived from the mechanics-based solution, are shown to be able to predict experimental data on the effects with satisfactory accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research described in this paper was carried out with funding from the U.S. National Science Foundation under grant numbers CMMI-1000549 and CMMI-1000797. The authors thank Professors Michael Berry, Dawn Lehman, and Michael Eberhard for sharing test data for reported column B0815.
References
ACI (American Concrete Institute). (2011). “Building code requirements for structural concrete and commentary.” ACI 318-11, Farmington Hills, MI.
Aristizábal-Ochoa, J. (2004). “Large deflection stability of slender beam-columns with semirigid connections: Elastica approach.” J. Eng. Mech., 274–282.
Bae, S., and Bayrak, O. (2008a). “Plastic hinge length of reinforced concrete columns.” ACI Struct. J., 105(3), 290–300.
Bae, S., and Bayrak, O. (2008b). “Seismic performance of full-scale reinforced concrete columns.” ACI Struct. J., 105(2), 123–133.
Baker, A. L. L., and Amarakone, A. M. N. (1964). “Inelastic hyperstatic frames analysis.” Flexural Mech. Reinf. Concr., SP-12, 85–142.
Barrera, A. C., Bonet, J. L., Romero, M. L., and Miguel, P. F. (2011). “Experimental tests of slender reinforced concrete columns under combined axial load and lateral force.” Eng. Struct., 33(12), 3676–3689.
Barros, H., Silva, V. D., and Ferreira, C. (2010). “Second order effects in slender concrete columns—Reformulation of the Eurocode 2 method based on nominal curvature.” Eng. Struct., 32(12), 3989–3993.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford University Press, New York, 984.
Bažant, Z. P., and Xiang, Y. (1997). “Inelastic buckling of concrete column in braced frame.” J. Struct. Eng., 634–642.
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), 270–279, 238–239.
Bisshop, K. E., and Drucker, D. C. (1945). “Large deflections of cantilever beams.” Q. Appl. Math., 3(3), 272–275.
Bonet, J. L., Miguel, P. F., Fernandez, M. A., and Romero, M. L. (2004). “Biaxial bending moment magnifier method.” Eng. Struct., 26(13), 2007–2019.
Chen, L. (2010). “An integral approach for large deflection cantilever beams.” Int. J. Nonlinear Mech., 45(3), 301–305.
Chen, W. F., and Atsuta, T. (2007). Theory of beam-columns, volume 1: In-plane behavior and design, J. Ross, Fort Lauderdale, FL, 513.
Dodd, L., and Restrepo-Posada, J. (1995). “Model for predicting cyclic behavior of reinforcing steel.” J. Struct. Eng., 433–445.
Galambos, T. V., and Surovek, A. E. (2008). Structural stability of steel: Concepts and applications for structural engineers, Wiley, Hoboken, NJ, 373.
Hines, E. M. (2002). “Seismic performance of hollow rectangular reinforced concrete bridge piers with confined corner elements.” Ph.D. thesis, Univ. of California, San Diego.
Hines, E. M., Restrepo, J. I., and Seible, F. (2004). “Force-displacement characterization of well-confined bridge piers.” ACI Struct. J., 101(4), 537–548.
Kwak, H.-G., and Filippou, F. C. (1990). Finite element analysis of reinforced concrete structures under monotonic loads, Dept. of Civil Engineering, Univ. of California, CA.
Lai, S., and MacGregor, J. (1983). “Geometric nonlinearities in unbraced multistory frames.” J. Struct. Eng., 2528–2545.
Lee, C., and Filippou, F. (2009). “Efficient beam-column element with variable inelastic end zones.” J. Struct. Eng., 1310–1319.
Lee, K. (2002). “Large deflections of cantilever beams of non-linear elastic material under a combined loading.” Int. J. Nonlinear Mech., 37(3), 439–443.
Lehman, D. E., and Moehle, J. P. (2000). “Seismic performance of well-confined concrete bridge columns.”, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
MacGregor, J. G., Breen, J. E., and Pfrang, E. O. (1970). “Design of slender concrete columns.” ACI J., 67(1), 6–28.
Mander, J., Priestley, M., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 1804–1826.
McGuire, W. (1968). Steel structures, Prentice Hall, Englewood Cliffs, NJ.
Mendis, P. (2001). “Plastic hinge lengths of normal and high-strength concrete in flexure.” Adv. Struct. Eng., 4(4), 189–195.
Mortezaei, A., and Ronagh, H. R. (2012). “Plastic hinge length of FRP strengthened reinforced concrete columns subjected to both far-fault and near-fault ground motions.” Scientia Iranica, 19(6), 1365–1378.
Neuenhofer, A., and Filippou, F. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 958–966.
Neuenhofer, A., and Filippou, F. (1998). “Geometrically nonlinear flexibility-based frame finite element.” J. Struct. Eng., 704–711.
Paulay, T., and Priestley, J. N. (1992). Seismic design of reinforced concrete and masonry buildings, Wiley, New York.
Priestley, M., and Park, R. (1987). “Strength and ductility of concrete bridge columns under seismic loading.” ACI Struct. J., 84(1), 61–76.
Priestley, M. J. N., Calvi, G. M., and Kowalsky, M. J. (2007). Displacement-based seismic design of structures, IUSS Press, Pravia, Italy.
Priestley, M. J. N., Seible, F., and Calvi, G. M. (1996). Seismic design and retrofit of bridges, Wiley, Canada.
Sakai, K., and Sheikh, S. A. (1989). “What do we know about confinement in reinforced concrete columns? (A critical review of previous work and code provisions).” ACI Struct. J., 86(2), 192–207.
Solano-Carrillo, E. (2009). “Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behaviour.” Int. J. Nonlinear Mech., 44(2), 253–256.
Spacone, E., Ciampi, V., and Filippou, F. C. (1996a). “Mixed formulation of nonlinear beam finite element.” Comput. Struct., 58(1), 71–83.
Spacone, E., Filippou, F. C., and Taucer, F. F. (1996b). “Fibre beam-column model for non-linear analysis of R/C frames: Part I. Formulation.” Earthquake Eng. Struct. Dyn., 25(7), 711–725.
Spacone, E., Filippou, F. C., and Taucer, F. F. (1996c). “Fibre beam-column model for non-linear analysis of R/C frames: Part II. Applications.” Earthquake Eng. Struct. Dyn., 25(7), 727–742.
Taucer, F., Spacone, E., and Filippou, F. C. (1991). A fiber beam-column element for seismic response analysis of reinforced concrete structures, Earthquake Engineering Research Center, College of Engineering, Univ. of California, Berkeley, CA.
Theil, H. (1961). Economic forecasts and policy, 2nd Revised Ed., North-Holland, Amsterdam, Netherlands.
Timoshenko, S. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, New York.
Wang, C.-K., Salmon, C. G., and Pincheira, J. A. (2006). Reinforced concrete design, 7th Ed., Wiley, Hoboken, NJ.
Wang, C. Y. (1981). “Large deflections of an inclined cantilever with an end load.” Int. J. Nonlinear Mech., 16(2), 155–164.
Youssf, O., ElGawady, M. A., and Mills, J. E. (2015). “Displacement and plastic hinge length of FRP-confined circular reinforced concrete columns.” Eng. Struct., 101, 465–476.
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.
Ziemian, R. D. (2010). Guide to stability design criteria for metal structures, Wiley, Hoboken, NJ.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Mar 5, 2015
Accepted: Apr 29, 2016
Published online: Jun 27, 2016
Published in print: Nov 1, 2016
Discussion open until: Nov 27, 2016
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.