Analysis of Reinforced Concrete Columns Subjected to Combined Axial, Flexure, Shear, and Torsional Loads
Publication: Journal of Structural Engineering
Volume 139, Issue 4
Abstract
This paper describes the implementation of a three-dimensional (3D) concrete constitutive model for fiber-based analysis of RC members subjected to combined loadings including torsion. The proposed model is formulated to address the interaction between the axial force, bidirectional shear, biaxial bending, and torsion. The shear mechanism along the beam is modeled using a Timoshenko beam approach with 3D frame elements with arbitrary cross-sectional geometry. The model considers the 3D equilibrium, compatibility, and constitutive laws of materials at the section and structural level. The concrete constitutive law follows the softened membrane model with a tangent-stiffness formulation. The emphasis of the paper is on evaluation of the effect of the different stress states on the global and local behavior of the member. The ability of the model to assess the ultimate strength, stiffness, energy dissipation, failure modes under 3D loading is evaluated by correlation of analytical results with experimental tests of RC specimens.
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Acknowledgments
The work presented in this paper was supported by funds from the National Science Foundation under Grant No. CMMI-0530737 and partially supported by the ASCE O.H. Ammann Research Fellowship. This support is gratefully acknowledged. The opinions expressed in this paper are those of the writers and do not necessarily reflect those of the sponsors.
References
AASHTO. (2000). Bridge design specifications, 2nd Ed., Washington, DC.
American Concrete Institute (ACI). (2002). “Building code requirements for reinforced concrete.” 318-02, Farmington Hills, MI.
Belarbi, A., and Hsu, T. T. C. (1994). “Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete.” ACI Struct. J., 91(4), 465–474.
Belarbi, A., and Hsu, T. T. C. (1995). “Constitutive laws of softened concrete in biaxial tension-compression.” Struct. J., 92(5), 562–573.
Elfgren, L., Karlsson, I., and Losberg, A. (1974). “Torsion-bending-shear interaction for concrete beams.” J. Struct. Div., 100(ST8), 1657–1676.
Ewida, A. A., and McMullen, A. E. (1982). “Concrete members under combined torsion and shear.” J. Struct. Div., 108(4), 911–928.
Gesund, H., and Boston, L. A. (1964). “Ultimate strength in combined bending and torsion of concrete beams containing only longitudinal reinforcement.” J. Struct. Div., 61(11), 1453–1472.
Gregori, J. N., Sosa, P. M., Prada, M. A. F., and Filippou, F. C. (2007). “A 3-D numerical model for reinforced and prestressed concrete elements subjected to combined axial, bending, shear and torsion loading.” Eng. Structures, 29(12), 3404–3419.
Hsu, T. T. C., and Zhang, L. X. (1996). “Tension stiffening in reinforced concrete membrane elements.” Struct. J., 93(1), 108–115.
Hsu, T. T. C., and Zhang, L. X. (1997). “Nonlinear analysis of membrane elements by fixed-angle softened-truss model.” Struct. J., 94(5), 483–492.
Hsu, T. T. C., and Zhu, R. R. H. (2002). “Softened membrane model for reinforced concrete elements in shear.” Struct. J., 99(4), 460–469.
Jeng, C. H., and Hsu, T. T. C. (2009). “A softened membrane model for torsion in reinforced concrete members.” Eng. Structures, 31(9), 1944–1954.
Kupfer, H. B., Hildorf, H. K., and Rusch, H. (1969). “Behavior of concrete under biaxial stresses.” Struct. J., 66(8), 656–666.
Lessig, N. N. (1959). Determination of load-carrying capacity of rectangular reinforced concrete elements subjected to flexure and torsion, Study No. 5, Institut Betona i Zhelezobetona [Institute of Concrete and Reinforced Concrete], Moscow, 5–28.
Mansur, M. A., and Paramasivam, P. (1984). “Reinforced concrete beams with small opening in bending and torsion.” ACI Struct. J., 81(2), 180–185.
Mullapudi, T. R. S. (2010). “Seismic analysis of reinforced concrete structures subjected to combined axial, bending, shear and torsional loads.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Houston, Houston.
Mullapudi, T. R. S., and Ayoub, A. S. (2010). “Modeling of the seismic behavior of shear-critical reinforced concrete columns.” J. Eng. Struct., 32(11), 3601–3615.
Neuenhofer, A., and Filippou, F. C. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 123(7), 958–966.
Nylander, H. (1945). Torsion and torsional restraint by concrete structures, Bull. D-19, Statens Kommittee för Byggnadsforskning, Stockholm, Sweden.
Pang, X. B., and Hsu, T. T. C. (1995). “Behavior of reinforced concrete membrane elements in shear.” Struct. J. 92(6), 665–679.
Pang, X. B., and Hsu, T. T. C. (1996). “Fixed-angle softened-truss model for reinforced concrete.” Struct. J. 93(2), 197–207.
Park, R., Priestley, M. J. N., and Gill, W. D. (1982). “Ductility of square confined concrete columns.” J. Struct. Div., 108(4), 929–950.
Prakash, S., Belarbi, A., and You, Y. (2010). “Seismic performance of circular RC columns subjected to axial force, bending, and torsion with low and moderate shear.” Eng. Struct., 32(1), 46–59.
Rahal, K. N., and Collins, M. P. (1995a). “Analysis of sections subjected to combined shear and torsion—a theoretical investigation.” ACI Struct. J., 92(4), 459–469.
Rahal, K. N., and Collins, M. P. (1995b). “Effect of thickness of concrete cover on shear-torsion interaction—an experimental investigation.” ACI Struct. J., 92(3), 334–342.
Rahal, K. N., and Collins, M. P. (2003a). “Combined torsion and bending in reinforced and prestressed concrete beams.” ACI Struct. J., 100(2), 157–165.
Rahal, K. N., and Collins, M. P. (2003b). “Experimental evaluation of ACI and AASHTO-LRFD design provisions for combined shear and torsion.” ACI Struct. J., 100(3), 277–282.
Spacone, E., Filippou, F. C., and Taucer, F. F. (1996). “Fiber beam-column model for nonlinear analysis of R/C frames, part I formulation.” Earthquake Eng. Struct. Dynam., 25(7), 711–725.
Taylor, R. L. (2005). FEAP user manual v2.0., Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA.
Tirasit, P., and Kawashima, K. (2008). “Effect of nonlinear seismic torsion on the performance of skewed bridge piers.” J. Earthquake Eng., 12(6), 980–998.
Tirasit, P., Kawashima, K., and Watanabe, G. (2005). “An experimental study on the performance of RC columns subjected to cyclic flexural-torsional loading.” Proc., 2nd Int. Conf. on Urban Earthquake Engineering, Tokyo Institute of Technology, Tokyo, 357–364.
Vecchio, F. J. (1992). “Finite element modeling of concrete expansion and confinement.” J. Struct. Eng., 118(9), 2390–2405.
Vecchio, F. J., and Collins, M. P. (1981). “Stress-strain characteristic of reinforced concrete in pure shear.” Proc., IABSE Colloquium, Advanced Mechanics of Reinforced Concrete, Delft, Final Rep., Int. Association of Bridge and Structural Engineering, Zurich, Switzerland, 221–225.
Vecchio, F. J., and Collins, M. P. (1986). “The modified compression field theory for reinforced concrete elements subjected to shear.” Struct. J., 83(2), 219–231.
Vecchio, F. J., and Selby, R. G. (1991). “Toward compression-field analysis of reinforced concrete solids.” J. Struct. Eng., 117(6), 1740–1758.
Yudin, V. K. (1962). “Determination of the load-carrying capacity of rectangular reinforced concrete elements subjected to combined torsion and bending.” Beton i Zhelezobeton [Concrete and Reinforced Concrete], Moscow, 6, 265–269 (in Russian).
Zhang, L. X., and Hsu, T. T. C. (1998). “Behavior and analysis of 100 MPa concrete membrane elements.” J. Struct. Eng., 124(1), 24–34.
Zhu, R. H., and Hsu, T. T. C. (2002). “Poisson effect of reinforced concrete membrane elements.” Struct. J., 99(5), 631–640.
Zhu, R. H., Hsu, T. T. C., and Lee, J. Y. (2001). “Rational shear modulus for smeared crack analysis of reinforced concrete.” Struct. J., 98(4), 443–450.
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Published In
Journal of Structural Engineering
Volume 139 • Issue 4 • April 2013
Pages: 561 - 573
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jan 10, 2012
Accepted: Jul 20, 2012
Published online: Aug 11, 2012
Published in print: Apr 1, 2013
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