Strut-and-Tie Model Based on Crack Band Theory for Deep Beams
Publication: Journal of Structural Engineering
Volume 137, Issue 10
Abstract
A simplified strut-and-tie model including size effect based on the crack band theory is proposed to evaluate the shear capacity of deep beams. Concrete struts are idealized as uniformly tapered prismatic members with a stress relief strip whereas horizontal and vertical shear reinforcements are assumed to be an internally statically indeterminate system. The shear transfer mechanism of concrete and shear reinforcement is then driven by using the energy equilibrium in the stress relief strip and crack band zone of concrete struts. The shear capacity predictions of deep beams obtained from the present models are in better agreement with 637 test results than those determined from strut-and-tie models proposed by ACI 318-08, EC-2, and Tan and Cheng. In addition, the trend of the shear capacity of deep beams against different parameters as predicted by the present models has a consistent agreement with that observed from experimental results. In particular, the present model shows that the normalized shear capacity of deep beams is proportional to , where = section overall depth.
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Acknowledgments
This work was supported by a grant from the Korean Ministry of Education, Science, and Technology (The Regional Core Research Program/Bio-housing Research Institute).
References
ACI Committee 318. (1999). “Building code requirements for structural concrete and commentary.” ACI 318-99, Detroit, MI.
ACI Committee 318. (2008). “Building code requirements for structural concrete and commentary.” ACI 318-08, Detroit, MI.
Ashour, A. F., and Yang, K. H. (2008). “Application of plasticity theory to reinforced concrete deep beams—A review.” Mag. Concr. Res., 60(9), 657–664.
Bažant, Z. P. (1982). “Crack band model for fracture of geomaterials.” Proc. of 4th Int. Conf. on Numerical Methods in Geomechanics, Vol. 3, Canadian Geotechnical Society, Rotterdam, Netherlands, 1137–1152.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC, New York.
Bažant, Z. P., and Sun, H. H. (1987). “Size effect in diagonal shear failure: Influence of aggregate size and stirrups.” ACI Mater. J., 84(4), 259–272.
British Standards Institution (BSI). (2004). “Eurocode 2: Design of concrete structures.” EN 1992-1-1:2004, London.
Comité Euro-International du Beton (CEB-FIP). (1993). “CEB-FIP model code 1990 for concrete structures.” Bulletin d’Information No. 213-214, CEB-FIP 90, Lausanne, Switzerland.
Cook, W. D., and Mitchell, D. (1988). “Studies of disturbed regions near discontinuities in reinforced concrete members.” ACI Struct. J., 85(2), 206–216.
Foster, S. J., and Malik, A. R. (2002). “Evaluation of efficiency factor models used in strut-and-tie modelling of nonflexural members.” J. Struct. Eng., 128(5), 569–577.
MacGregor, J. G., and Wight, J. K. (2006). Reinforced concrete: Mechanics and design, Prentice Hall, Pearson Education South Asia, Singapore.
Marti, P. (1985). “Basic tools of reinforced concrete beam design.” ACI Struct. J., 82(1), 46–56.
Matamoros, A. B., and Wong, K. H. (2003). “Design of simply supported deep beams using strut-and-tie models.” ACI Struct. J., 100(6), 704–712.
Schlaich, J., Schäfer, K., and Jennewein, M. (1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–150.
Smith, K. H., and Vantsiotis, A. S. (1982). “Shear strength of deep beams.” J. Am. Concr. Inst., 79(3), 201–213.
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., Kong, F. K., Teng, S., and Weng, L. W. (1997a). “Effect of web reinforcement on high-strength concrete deep beams.” ACI Struct. J., 94(5), 572–582.
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. (1997b). “Main tension steel in high strength concrete deep and short beams.” ACI Struct. J., 94(6), 752–768.
Yang, K. H., and Ashour, A. F. (2008). “Code modelling of reinforced concrete deep beam.” Mag. Concr. Res., 60(6), 441–454.
Yang, K. H., and Ashour, A. F., and Song, J. K. (2008 a). “Shear capacity of reinforced concrete beams using neural network.” Int. J. Concr. Struct. Mater., 1(1), 63–73.
Yang, K. H., Ashour, A. F., Song, J. K., and Lee, E. T. (2008 b). “Neural network modelling for shear strength of reinforced concrete deep beams.” Struct. Build., 161(1), 29–39.
Yang, K. H., Chung, H. S., and Ashour, A. F. (2007). “Influence of shear reinforcement on reinforced concrete continuous deep beams.” ACI Struct. J., 104(4), 420–429.
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© 2011 American Society of Civil Engineers.
History
Received: Feb 2, 2009
Accepted: Oct 24, 2010
Published online: Dec 3, 2010
Published in print: Oct 1, 2011
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