Shear Strength of RC Beams with Steel Stirrups
Publication: Journal of Structural Engineering
Volume 142, Issue 2
Abstract
Because of the complexity of the shear failure mechanism, most current design codes and guidelines are based on highly empirical approaches and consequently should only be used within the bounds of testing regimes from which they were derived. Hence this limitation restricts their applicability to innovative materials such as high-strength concrete and fiber-reinforced polymer (FRP) reinforcement. To solve this issue, a mechanics-based segmental approach, which can analyze a reinforced concrete (RC) beam with any type of concrete and reinforcement and which can explain the physical process of shear failure, has been developed to quantify the shear capacity of RC beams without stirrups. In this paper, with the partial interaction analysis of transverse reinforcements directly linked with that of longitudinal reinforcements, the segmental approach is extended by incorporating steel stirrups in the mechanics-based model; furthermore, a simplified closed form solution for design is derived. By evaluating the shear strength of 194 published test specimens, the proposed approaches are validated with good correlation between the predicted and measured strengths. In contrast to current empirical approaches which often assume the stirrups always yield, using the segmental approach it is shown that stirrups’ force rarely reaches the value calculated by the truss model. Furthermore, it is shown that direct contribution of the stirrups is less important than the increase in the concrete component of the shear capacity attributable to confinement by the stirrups. Being mechanics based, this approach has a great potential to be developed for all types of RC structures.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to acknowledge the support of the Australian Research Council ARC Discovery Project DP0985828 “A unified reinforced concrete model for flexure and shear” and ARC Discovery Project DP140103525 “A New Generic Approach for Assessing Blast Effects on Reinforced Concrete.” The first author also thanks the China Scholarship Council for financial support.
References
ACI (American Concrete Institute). (1992). “State of the art report on high-strength concrete.” ACI 363R-92, Detroit.
ACI (American Concrete Institute). (2008). “Building code requirements for structural concrete and commentary.” ACI 318-08, Farmington Hills, MI.
Anderson, N. S., and Ramirez, J. A. (1989). “Detailing of stirrup reinforcement.” ACI Struct. J., 86(5), 507–515.
Bažant, Z. P., and Sun, H.-H. (2011). “Size effect in diagonal shear failure: Influence of aggregate size and stirrups.” ACI Mater. J., 84(4), 259–272.
Bentz, E. C., Vecchio, F. J., and Collins, M. P. (2007). “Simplified modified compression field theory for calculating shear strength of reinforced concrete elements.” ACI Struct. J., 104(3), 378–379.
Bresler, B., and Scordelis, A. C. (1963). “Shear strength of reinforced concrete beams.” ACI J. Proc., 60(1), 51–74.
Bresler, B., and Scordelis, A. C. (1964). “Shear strength of reinforced concrete beams—Series II.”, Structures and Materials Research, Dept. of Civil Engineering, Univ. of California, Berkeley, CA.
Bresler, B., and Scordelis, A. C. (1966). “Shear strength of reinforced concrete beams—Series III.”, Structures and Materials Research, Dept. of Civil Engineering, Univ. of California, Berkeley, CA.
CEB (ComitØ Euro-International du Béton). (1992). “CEB-FIP model code 90.” London.
CEN. (1992). “Eurocode 2: Design of concrete structures—Part 1-1: General rules and rules for buildings.” EN 1992-1-1: 1992, Brussels, Belgium.
CEN. (2004). “Eurocode 2: Design of concrete structures—Part 1-1: General rules and rules for buildings.” EN 1992-1-1: 2004, Brussels, Belgium.
Choi, K.-K., Park, H.-G., and Wight, J. K. (2007). “Unified shear strength model for reinforced concrete beams—Part I: Development.” ACI Struct. J., 104(2), 142–152.
Cladera, A., and Marí, A. R. (2011). “Shear design procedure for reinforced normal and high-strength concrete beams using artificial neural networks. Part II: Beams with stirrups.” Eng. Struct., 26(7), 927–936.
Clark, A. P. (1951). “Diagonal tension in reinforced concrete beams.” ACI J. Proc., 48(10), 145–156.
Collins, M. P., Bentz, E. C., Sherwood, E. G., and Xie, L. (2008a). “An adequate theory for the shear strength of reinforced concrete structures.” Mag. Concr. Res., 60(9), 635–650.
Collins, M. P., Mitchell, D., Adebar, P., and Vecchio, F. J. (1996). “A general shear design method.” ACI Struct. J., 93(1), 36–45.
Collins, M. R., Bentz, E. C., and Sherwood, E. G. (2008b). “Where is shear reinforcement required? Review of research results and design procedures.” ACI Struct. J., 105(5), 590–600.
CSA (Canadian Standards Association). (2004). “Design of concrete structures.” CSA A23.3-04, Mississauga, ON, Canada.
EI-Chabib, H., Nehdi, M., and Saïd, A. (2006). “Predicting the effect of stirrups on shear strength of reinforced normal-strength concrete (NSC) and high-strength concrete (HSC) slender beams using artificial intelligence.” Can. J. Civ. Eng., 33(8), 933–944.
Elzanaty, A. H., Nilson, A. H., and Slate, F. O. (1986). “Shear capacity of reinforced concrete beams using high-strength concrete.” ACI J. Proc., 83(2), 290–296.
Fédération internationale du béton (fib). (2010a). “Model code 2010–First complete draft, fédération internationale du béton.”, Lausanne, Switzerland, 318.
Fédération internationale du béton (fib). (2010b). “Model code 2010—First complete draft, fédération internationale du béton.”, Lausanne, Switzerland, 312.
Fernández Ruiz, M., and Muttoni, A. (2009). “Applications of the critical shear crack theory to punching of R/C slabs with transverse reinforcement.” ACI Struct. J., 106(4), 485–494.
Frosch, R. J. (2000). “Behavior of large-scale reinforced concrete beams with minimum shear reinforcement.” ACI Struct. J., 97(6), 814–820.
Haskett, M., Oehlers, D. J., and Ali, M. S. M. (2008). “Local and global bond characteristics of steel reinforcing bars.” Eng. Struct., 30(2), 376–383.
Kim, J. K., and Park, Y. D. (1996). "Prediction of shear strength of reinforced concrete beams without web reinforcement." ACI Mater. J., 93(3), 213–222.
Knight, D., Visintin, P., Oehlers, D. J., and Jumaat, M. Z. (2013). "Incorporating residual strains in the flexural rigidity of RC members with varying degree of prestress and cracking." Adv. Struct. Eng., 16(10), 1701–1718.
Krefeld, W. J., and Thurston, C. W. (1966). “Studies of the shear and diagonal tension strength of simply supported reinforced concrete beams.” ACI J. Proc., 63(4), 451–476.
Lee, J.-Y., Choi, I.-J., and Kim, S.-W. (2011). “Shear behavior of reinforced concrete beams with high-strength stirrups.” ACI Struct. J., 108(5), 620–629.
Lee, J.-Y., and Hwang, H.-B. (2010). “Maximum shear reinforcement of reinforced concrete beams.” ACI Struct. J., 107(5), 580–588.
Loov, R. E. (1998). “Review of A23.3-94 simplified method of shear design and comparison with results using shear friction.” Can. J. Civ. Eng., 25(3), 437–450.
Lucas, W., Oehlers, D. J., and Ali, M. (2011). “Formulation of a shear resistance mechanism for inclined cracks in RC beams.” J. Struct. Eng., 1480–1488.
Lucas, W. D. (2011). “The discrete rotation behaviour of reinforced concrete beams under shear loading.” Ph.D. thesis, Univ. of Adelaide, Adelaide, Australia.
Mansour, M. Y., Dicleli, M., Lee, J. Y., and Zhang, J. (2004). “Predicting the shear strength of reinforced concrete beams using artificial neural networks.” Eng. Struct., 26(6), 781–799.
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.
Mphonde, A. G. (1989). “Use of stirrup effectiveness in shear design of concrete beams.” ACI Struct. J., 86(5), 541–545.
Mphonde, A. G., and Frantz, G. C. (1985). “Shear tests of high- and low-strength concrete beams with stirrups.” High strength concrete, American Concrete Institute, Farmington Hills, MI, 179–186.
Muhamad, R., Ali, M. S. M., Oehlers, D., and Sheikh, A. H. (2011). “Load-slip relationship of tension reinforcement in reinforced concrete members.” Eng. Struct., 33(4), 1098–1106.
Muhamad, R., Ali, M. S. M., Oehlers, D. J., and Griffith, M. (2012). “The tension stiffening mechanism in reinforced concrete prisms.” Adv. Struct. Eng., 15(12), 2053–2070.
Muttoni, A., and Fernández Ruiz, M. (2008). “Shear strength of members without transverse reinforcement as function of critical shear crack width.” ACI Struct. J., 105(2), 163–172.
Muttoni, A., and Fernández Ruiz, M. (2010). “MC2010: The critical shear crack theory as a mechanical model for punching shear design and its application to code provisions.” École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 31–60.
Oehlers, D. J., Ali, M. S. M., Haskett, M., Lucas, W., Muhamad, R., and Visintin, P. (2011a). “FRP-reinforced concrete beams: Unified approach based on IC theory.” J. Compos. Constr., 293–303.
Oehlers, D. J., Haskett, M., Ali, M. S. M., Lucas, W., and Muhamad, R. (2011b). “Our obsession with curvature in RC beam modelling.” Adv. Struct. Eng., 14(3), 391–404.
Park, H.-G., Choi, K.-K., and Wight, J. K. (2006). “Strain-based shear strength model for slender beams without web reinforcement.” ACI Struct. J., 103(6), 783–793.
Placas, A., and Regan, P. E. (1971). “Shear failure of reinforced concrete beams.” ACI J. Proc., 68(10), 763–773.
Rebeiz, K. S. (1999). “Shear strength prediction for concrete members.” J. Struct. Eng., 301–308.
Regan, P. E., and Yu, C. W. (1973). Limit state design of structural concrete, Chatto & Windus, London.
Russo, G., and Puleri, G. (1997). “Stirrup effectiveness in reinforced concrete beams under flexure and shear.” ACI Struct. J., 94(3), 227–238.
Saqan, E. I., and Frosch, R. J. (2009). “Influence of flexural reinforcement on shear strength of prestressed concrete beams.” ACI Struct. J., 106(1), 60–68.
Sarsam, K. F., and Al-Musawi, J. M. S. (1992). “Shear design of high- and normal strength concrete beams with web reinforcement.” ACI Struct. J., 89(6), 658–664.
Standards Australia. (2009). “Concrete structures.” AS 3600-2009, Sydney, Australia.
Swamy, R. N., and Andriopoulos, A. D. (1974). “Contribution of aggregate interlock and dowel forces to the shear resistance of reinforced beams with web reinforcement.” Shear in reinforced concrete, American Concrete Institute, Farmington Hills, MI, 129–166.
Tompos, E. J., and Frosch, R. J. (2002). “Influence of beam size, longitudinal reinforcement, and stirrup effectiveness on concrete shear strength.” ACI Struct. J., 99(5), 559–567.
Tureyen, A. K., and Frosch, R. J. (2003). “Concrete shear strength: Another perspective.” ACI Struct. J., 100(5), 609–615.
Visintin, P., Oehlers, D. J., Haskett, M., and Wu, C. (2012a). “Mechanics based hinge for reinforced concrete columns.” J. Struct. Eng., 139(11), 1973–1980.
Visintin, P., Oehlers, D. J., Muhamad, R., and Wu, C. (2013). “Partial-interaction short term serviceability deflection of RC beams.” Eng. Struct., 56, 993–1006.
Visintin, P., Oehlers, D. J., Wu, C., and Haskett, M. (2012c). “A mechanics solution for hinges in RC beams with multiple cracks.” Eng. Struct., 36, 61–69.
Wei, W., Che, Y., and Gong, J. (2011). “Shear strength model for reinforced concrete beams with web reinforcement.” Mag. Concr. Res., 63(6), 423–431.
Xie, Y., Ahmad, S. H., Yu, T., Hino, S., and Chung, W. (1994). “Shear ductility of reinforced concrete beams of normal and high-strength concrete.” ACI Struct. J., 91(2), 140–149.
Yoon, Y.-S., Cook, W. D., and Mitchell, D. (1996). “Minimum shear reinforcement in normal, medium, and high-strength concrete beams.” ACI Struct. J., 93(5), 576–584.
Yu, Q., and Bažant, Z. P. (2011). “Can stirrups suppress size effect on shear strength of RC beams?” J. Struct. Eng., 607–617.
Zhang, J. P. (1997). “Diagonal cracking and shear strength of reinforced concrete beams.” Mag. Concr. Res., 49(178), 55–65.
Zhang, T. (2013). “A mechanics based approach for shear strength of RC beams without web reinforcement.”, Univ. of Adelaide, Adelaide, Australia.
Zhang, T., Oehlers, D. J., and Visintin, P. (2014a). “Shear strength of FRP RC beams and one-way slabs without stirrups.” J. Compos. Constr., 04014007.
Zhang, T., Visintin, P., and Oehlers, D. J. (2014b). “A semi-mechanical model for tension-stiffening.”, Univ. of Adelaide, Adelaide, Australia.
Zhang, T., Visintin, P., Oehlers, D. J., and Griffith, M. C. (2014c). “Presliding shear failure in prestressed RC beams. I: Partial-interaction mechanism.” J. Struct. Eng., 140(10), 04014069.
Zhang, T., Visintin, P., Oehlers, D. J., and Griffith, M. C. (2014d). “Presliding shear failure in prestressed RC beams. II: Behavior.” J. Struct. Eng., 140(10), 04014069.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 142 • Issue 2 • February 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 14, 2014
Accepted: Jul 17, 2015
Published online: Sep 18, 2015
Published in print: Feb 1, 2016
Discussion open until: Feb 18, 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.