Single-Span Deep Beams Subjected to Unsymmetrical Loads
Publication: Journal of Structural Engineering
Volume 135, Issue 3
Abstract
This paper investigates the effects of unsymmetrical loadings on the strength and behavior of simply supported deep beams. An experimental program consisting of 14 specimens has been carried out. Test results including crack patterns, load-deflection responses, steel and concrete strains, and failure loads are presented and discussed with the effects of load inequality (LI) and load asymmetry (LA). Conclusions are drawn on the effects of LI and LA on deep beam behavior. The ACI 318-05 strut-and-tie method is found to slightly overestimate the beam shear capacity. The writers proposed a direct strut-and-tie method (STM) for predicting the failure loads of unsymmetrically loaded deep beams. By adopting an interactive failure criterion, no preset empirical stress limit is required in the model. A load parameter Π is introduced such that the proposed STM can simulate both the effects of LI and LA. It is shown that the proposed STM is a generalized form that embodies the special cases of single-point and two-equal-point symmetric loading conditions. Besides, the model gives promising results in predicting the possible failure modes. The STM predictions are in good agreement with test results as well as finite-element predictions of 14 specimens.
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Acknowledgments
The writers would like to express their gratitude to the Nanyang Technological University for research account RG9/99. The first writer also acknowledges a scholarship from the Nanyang Technological University, Singapore.
References
American Concrete Institute (ACI). (2005). “Building code requirements for structural concrete (ACI 318–05) and commentary (ACI 318R-05).” ACI 318-05, American Concrete Institute, Farmington Hills, Mich.
An, X., Maekawa, K., and Okamura, H. (1997). “Numerical simulation of size effect in shear strength of RC beams.” J. Mater. Conc. Struct. Pavements, 35(564), 297–316.
Ashour, A. F. (2000). “Shear capacity of reinforced concrete deep beams.” J. Struct. Eng., 126(9), 1045–1052.
CEB-FIP model code 1990: Design code. (1993). Thomas Telford Ltd., London.
Foster, S. J., and Gilbert, R. I. (1998). “Experimental studies on high-strength concrete deep beams.” ACI Struct. J., 95(4), 382–390.
Foster, S. J., and Malik, A. R. (2002). “Evaluation of efficiency factor models used in strut-and-tie modeling of nonflexural members.” J. Struct. Eng., 128(5), 569–577.
Kong, F. K., Robins, P. J., Kirby, D. P., and Short, D. R. (1972). “Deep beams with inclined web reinforcement.” ACI J., 69(3), 172–176.
Maekawa, K., Pimanmas, A., and Okamura, H. (2003). Nonlinear mechanics of reinforced concrete, E & FN Spon, New York.
Oh, J.-K., and Shin, S.-W. (2001). “Shear strength of reinforced high-strength concrete deep beams.” ACI Struct. J., 98(2), 164–173.
Rogowsky, D. M., MacGregor, J. G., and Ong, S. Y. (1986). “Tests of reinforced concrete deep beams.” ACI J., 83(4), 614–623.
Russo, G., Somma, G., and Mitri, D. (2005). “Shear strength analysis and prediction for reinforced concrete beams without stirrups.” J. Struct. Eng., 131(1), 66–74.
Schlaich, J., Schaefer, K., and Jennewein, M. (1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–150.
Smith, K. N., and Vantsiotis, A. S. (1982). “Shear strength of deep beams.” ACI J., 79(3), 201–213.
Subedi, N. K. (1988). “Reinforced concrete deep beams: A method of analysis.” Proc. Inst. Civ. Eng., Part 2. Res. Theory, 85(2), 1–30.
Subedi, N. K., Vardy, A. E., and Kubota, N. (1986). “Reinforced concrete deep beams—Some test results.” Mag. Concrete Res., 38(137), 206–219.
Tan, K. H., and Cheng, G. H. (2006). “Size effect on shear strength of deep beams: Investigating with strut-and-tie model.” J. Struct. Eng., 132(5), 673–685.
Tan, K. H., Cheng, G. H., and Cheong, H. K. (2005). “Size effect in shear strength of large beams—Behaviour and finite element modelling.” Mag. Concrete Res., 57(8), 497–509.
Tan, K. H., Kong, F. K., Teng, S., and Guan, L. (1995). “High-strength concrete deep beams with effective span and shear span variations.” ACI Struct. J., 92(4), 395–405.
Tan, K. H., and Lu, H. Y. (1999). “Shear behavior of large reinforced concrete deep beams and code comparisons.” ACI Struct. J., 96(5), 836–845.
Tan, K. H., Teng, S., Kong, F. K., and Lu, H. Y. (1997a). “Main tension steel in high strength concrete deep and short beams.” ACI Struct. J., 94(6), 752–768.
Tan, K. H., Tong, K., and Tang, C. Y. (2001). “Direct strut-and-tie model for prestressed deep beams.” J. Struct. Eng., 127(9), 1076–1084.
Tan, K. H., Tong, K., and Tang, C. Y. (2003). “Consistent strut-and-tie modelling of deep beams with web openings.” Mag. Concrete Res., 55(1), 65–75.
Tan, K. H., Weng, L. W., and Teng, S. (1997b). “Strut-and-tie model for deep beams subjected to combined top-and-bottom loading.” Struct. Eng., 75(13), 215–221.
Tang, C. Y., and Tan, K. H. (2004). “Interactive mechanical model for shear strength of deep beams.” J. Struct. Eng., 130(10), 1534–1544.
Tsuchiya, S., Mishima, T., and Maekawa, K. (2002). “Shear failure and numerical performance evaluation for RC beam members made with high-strength materials.” Concr. Library Int., 40, 227–252.
Walraven, J., and Lehwalter, N. (1994). “Size effects in short beams loaded in shear.” ACI Struct. J., 91(5), 585–593.
Zhang, N., and Tan, K. H. (2007). “Direct strut-and-tie model for single and continuous deep beams.” Eng. Struct., 29(11), 2987–3001.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 135 • Issue 3 • March 2009
Pages: 239 - 252
Copyright
© 2009 ASCE.
History
Received: Oct 13, 2006
Accepted: Jul 1, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: Yahya C. Kurama
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