Nonlinear Analysis of Shear-Critical Reinforced Concrete Beams Using Fixed Angle Theory
Publication: Journal of Structural Engineering
Volume 137, Issue 10
Abstract
This paper proposes a solution methodology for the application of the fixed-angle theory to predict the shear response of reinforced concrete (RC) beams subjected to the combined actions of shear and flexure. The proposed solution, based on the fixed-angle theory, takes into account the effect of flexural moment on the shear strength of RC beams and calculates the concrete constitutive relationships by transforming the concrete stresses and strains from the principal direction of concrete stresses to that of the applied stresses. To verify the effectiveness of the proposed solution method, seven shear-critical RC beams were tested and their corresponding experimental shear stress-strain relationships were compared with the predicted ones by using the proposed methodology. Furthermore, the shear strengths of 150 RC test beams, reported in the literature with various shear span-to-depth ratios, steel reinforcing ratios, and support conditions, were compared with the predicted shear strengths obtained by the proposed method and other existing truss models. The results presented in this paper show that the proposed formulation can predict the shear response of RC beams with reasonable accuracy.
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Acknowledgments
This work was supported by Mid-Career Researcher Program through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education, Science and Technology (MEST) (UNSPECIFIED2009-0078981) of Korea. In addition, this research was also financially supported by Priority Research Centers Program through the NRF funded by MEST (UNSPECIFIED2010-0028289).
References
Al-Alusi, A. F. (1957). “Diagonal tension strength of reinforced concrete T-beams with varying shear span.” ACI J. Proc., 53(5), 1067–1077.
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.” ACI Struct. J., 92(5), 562–573.
Bentz, E. C. (2000). “Sectional analysis of reinforced concrete members.” Ph.D. thesis, Univ. of Toronto, Toronto.
Bernander, K. G. (1957). “An investigation of the shear strength of concrete beams without stirrups or diagonal bars, reinforced with high tensile steel with various rib patterns.” Proc., RILEM Symposium on Bond and Crack Formation in Reinforced Concrete, Stockholm, Sweden, 211–214.
Clark, A. P. (1951). “Diagonal tension in reinforced concrete beams.” ACI J. Proc., 48(10), 145–156.
Collins, M. P., and Mitchell, D. (1991). “Prestressed concrete structures.” Prentice Hall, Englewood Cliffs, NJ.
Elstner, R. C., Moody, K. G., Viest, I. M., and Hognestad, E. (1955). “Shear strength of reinforced concrete beams. Part 3—Tests of restrained beams with web reinforcement.” ACI J. Proc., 51(2), 525–539.
Fukuhara, M., and Kokusho, S. (1982). “Effectiveness of high tension shear reinforcement in reinforced concrete members.” J. Struct. Constr. Eng., AIJ (320), 12–20 (in Japanese).
Gupta, P. R., and Collins, M. P. (2001). “Evaluation of shear design procedures for reinforced concrete members under axial compression.” ACI Struct. J., 98(4), 537–547.
Guralnick, S. A. (1960). “High-strength deformed steel bars for concrete reinforcement.” ACI J. Proc., 57(9), 241–282.
Haddadin, M. J., Hong, S.-T., and Mattock, A. H. (1971). “Stirrup effectiveness in reinforced concrete beams with axial force.” J. Struct. Div., 97(ST9), 2277–2297.
Hsu, T. T. C. (1988). “Softened truss model theory for shear and torsion.” ACI Struct. J., 85(6), 624–635.
Hsu, T. T. C., and Zhang, L. X. (1997). “Nonlinear analysis of membrane elements by fixed-angle softened-truss model.” ACI Struct. J., 94(5), 483–492.
Kim, S.-W., and Lee, J.-Y. (2002). “Shear behavior prediction of reinforced concrete beams by transformation angle truss model considered bending moment effect.” J. Korea Concr. Inst., 14(6), 910–921 (in Korean).
Kokusho, S., Kobayashe, K., Mitsugi, S., and Kumagai, H. (1987). “Ultimate shear strength of RC beams with high tension shear reinforcement and high strength concrete.” J. Struct. Constr. Eng., AIJ (373), 83–91 (in Japanese).
Kong, P. Y. L., and Rangan, B. V. (1998). “Shear strength of high-performance concrete beams.” ACI Struct. J., 95(6), 677–688.
Lee, J.-Y., and Watanabe, F. (2000). “Shear design of reinforced concrete beams with shear reinforcement considering failure modes.” ACI Struct. J., 97(3), 477–484.
Li, B., Maekawa, K., and Okamura, H. (1989). “Contact density model for stress transfer across cracks in concrete.” J. Faculty Eng., Univ. of Tokyo, 40(1), 9–52.
Matsuzaki, Y., Nakano, K., Iso, M., and Watanabe, H. (1990). “Experimental study on the shear characteristic of RC beams with high tension shear reinforcement.” Proc. JCI, 12(2), 325–328 (in Japanese).
Mattock, A. H., and Wang, Z. (1984). “Shear strength of reinforced concrete members subject to high axial compressive stress.” ACI J. Proc., 81(3), 287–298.
Nishiura, N., Makitani, E., and Shindou, K. (1993). “Shear resistance of concrete beams with high strength web reinforcements.” Proc. JCI, 15(2), 461–466 (in Japanese).
Pang, X. B., and Hsu, T. T. C. (1995). “Behavior of reinforced concrete membrane elements in shear.” ACI Struct. J., 92(6), 665–679.
Pang, X. B., and Hsu, T. T. C. (1996). “Fixed angle softened truss model for reinforced concrete.” ACI Struct. J., 93(2), 197–207.
Placas, A., and Regan, P. E. (1971). “Shear failure of reinforced concrete beams.” ACI J. Proc., 68(10), 763–773.
Rahal, K. N., and Collins, M. P. (1995). “Analysis of sections subjected to combined shear and torsion—A theoretical model.” ACI Struct. J., 92(4), 459–469.
Rodriguez, J. J., Bianchini, A. C., Viest, I. M., and Kesler, C. E. (1959). “Shear strength of two-span continuous reinforced concrete beams.” ACI J. Proc., 55(4), 1089–1130.
Takagi, H., Okude, H., and Nitta, T. (1989). “Shear strength of beam depending the strength of web reinforcements.” Proc., JCI, 11(2), 75–80 (in Japanese).
Vecchio, F. J., and Collins, M. P. (1982). “The response of reinforced concrete to in-plane shear and normal stresses.” Publication No. 82-03, Dept. of Civil Eng., Univ. of Toronto, Toronto.
Vecchio, F. J., and Collins, M. P. (1986). “The modified compression-field theory for reinforced concrete elements subjected to shear.” ACI J. Proc., 83(2), 219–231.
Vecchio, F. J., and Collins, M. P. (1988). “Predicting the response of reinforced concrete beams subjected to shear using the modified compression field theory.” ACI Struct. J., 85(3), 258–268.
Wilby, C. B. (1951). “The strength of reinforced concrete beams in shear.” Mag. Concr. Res. (7), 23–30.
Zhang, L. X. (1995). “Constitutive laws of reinforced concrete elements with high strength concrete.” Ph.D. thesis, Univ. of Houston, Houston.
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Published In
Journal of Structural Engineering
Volume 137 • Issue 10 • October 2011
Pages: 1017 - 1029
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Nov 27, 2008
Accepted: Oct 24, 2010
Published online: Nov 16, 2010
Published in print: Oct 1, 2011
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