Numerical Investigation of the Shear Strength of RC Deep Beams Using the Microplane Model
Publication: Journal of Structural Engineering
Volume 142, Issue 10
Abstract
Although much work has been done on the shear behavior of RC elements, current design provisions are still based on empirical data and their predictions, especially for deep beams, are not always reliable and can lead to unconservative results. This paper presents an extensive numerical investigation on the role of key parameters on the shear performance of RC deep beams using the microplane M4 material model. The model is validated against experimental results of 20 RC deep beams. A parametric study is then carried out to investigate the effect of shear span to depth ratio and concrete compressive strength for RC deep beams with and without shear reinforcement. Although a single strut mechanism is generally mobilized in deep beams, the presence of shear reinforcement can enable a more uniform distribution of shear stresses within the shear span and enhance the effectiveness of concrete cracked in tension. The study confirms that both shear span to depth ratio and concrete strength are the key parameters that affect the shear capacity of RC deep beams and should be taken into account in code equations.
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Acknowledgments
The authors acknowledge the financial support of the Human Capacity Development Program (HCDP) of the Ministry of Higher Education and Scientific Research, Kurdistan Regional Government for the Ph.D. studies of Kamaran S. Ismail.
References
Abaqus [Computer software]. Dassault Systèmes, Waltham, MA.
ACI (American Concrete Institute). (2014). “Building code requirements for structural concrete.” ACI 318M–14, Farmington Hills, MI.
Aguilar, G., Matamoros, A. B., Parra-Montesinos, G. J., Ramírez, J. A., and Wight, J. K. (2002). “Experimental evaluation of design procedures for shear strength of deep reinforced concrete beams.” ACI Struct. J., 99(4), 539–548.
Arabzadeh, A., Rahaie, A. R., and Aghayari, R. (2009). “A simple strut-and-tie model for prediction of ultimate shear strength of RC deep beams.” Int. J. Civ. Eng., 7(3), 141–153.
Batdorf, S. B., and Budiansky, B. (1949). “A mathematical theory of plasticity based on the concept of slip.”, National Advisory Committee for Aeronautics, Washington, DC.
Bazant, Z. P., Caner, F. C., Carol, I., Adley, M. D., and Akers, S. A. (2000). “Microplane model M4 for concrete—I: Formulation with work-conjugate deviatoric stress.” J. Eng. Mech., 944–953.
Bazant, Z. P., and Gambarova, P. G. (1984). “Crack shear in concrete: Crack band microplane model.” J. Struct. Eng., 2015–2035.
Bazant, Z. P., and Ožbolt, J. (1990). “Nonlocal microplane model for fracture, damage, and size effect in structures.” J. Eng. Mech., 2485–2505.
Bazant, Z. P., and Prat, P. C. (1988). “Microplane model for brittle-plastic material—I: Theory.” J. Eng. Mech., 1672–1688.
Bazant, Z. P., Xiang, Y., Adley, M. D., Prat, P. C., and Akers, S. A. (1996a). “Microplane model for concrete—II: Data delocalization and verification.” J. Eng. Mech., 255–262.
Bazant, Z. P., Xiang, Y., and Prat, P. C. (1996b). “Microplane model for concrete—I: Stress-strain boundaries and finite strain.” J. Eng. Mech., 245–254.
Bažant, P., and Oh, B. (1986). “Efficient numerical integration on the surface of a sphere.” J. Appl. Math. Mech., 66(1), 37–49.
British Standards Institution. (2004). “Design of concrete structures—Part 1-1: General rules and rules for buildings.” Eurocode 2, London.
Brown, M. D., and Bayrak, O. (2008a). “Design of deep beams using strut-and-tie models—Part I: Evaluating U.S. provisions.” ACI Struct. J., 105(4), 395–404.
Brown, M. D., and Bayrak, O. (2008b). “Design of deep beams using strut-and-tie models—Part II: Design recommendations.” ACI Struct. J., 105(4), 405–413.
Caner, F. C., and Bazant, Z. P. (2000). “Microplane model M4 for concrete—II: Algorithm and calibration.” J. Eng. Mech., 954–961.
Carol, I., Prat, P. C., and Bažant, Z. P. (1992). “New explicit microplane model for concrete: Theoretical aspects and numerical implementation.” Int. J. Solids Struct., 29(9), 1173–1191.
Červenka, J., Bažant, Z. P., and Wierer, M. (2005). “Equivalent localization element for crack band approach to mesh-sensitivity in microplane model.” Int. J. Numer. Methods Eng., 62(5), 700–726.
Collins, M. P., Bentz, E. C., and Sherwood, E. G. (2008). “Where is shear reinforcement required? Review of research results and design procedures.” ACI Struct. J., 105(5), 590–600.
Di Luzio, G. (2007). “A symmetric over-nonlocal microplane model M4 for fracture in concrete.” Int. J. Solids Struct., 44(13), 4418–4441.
Foster, S. J., and Gilbert, R. I. (1998). “Experimental studies on high-strength concrete deep beams.” ACI Struct. J., 95(4), 382–390.
Guadagnini, M. (2002). “Shear behaviour and design of FRP RC beams.” Ph.D. thesis, Univ. of Sheffield, Sheffield, U.K.
Kuchma, D., Yindeesuk, S., Nagle, T., Hart, J., and Lee, H. H. (2008). “Experimental validation of strut-and-tie method for complex regions.” ACI Struct. J., 105(5), 578–589.
Lubliner, J., Oliver, J., Oller, S., and Onate, E. (1989). “A plastic-damage model for concrete.” Int. J. Solids Struct., 25(3), 299–326.
Mohammad, M., Jumaat, M. Z. B., Chemrouk, M., Ghasemi, A., Hakim, S., and Najmeh, R. (2011). “An experimental investigation of the stress-strain distribution in high strength concrete deep beams.” Proc. Eng., 14(2011), 2141–2150.
Ožbolt, J., Li, Y., and Kožar, I. (2001). “Microplane model for concrete with relaxed kinematic constraint.” Int. J. Solids Struct., 38(16), 2683–2711.
Ožbolt, J., and Li, Y.-J. (2001). “Three-dimensional cyclic analysis of compressive diagonal shear failure.” ACI Spec. Publ., 205(4), 61–80.
Rashid, Y. (1968). “Ultimate strength analysis of prestressed concrete pressure vessels.” Nucl. Eng. Des., 7(4), 334–344.
Sagaseta, J., and Vollum, R. (2010). “Shear design of short-span beams.” Mag. Concr. Res., 62(4), 267–282.
Slobbe, A. T., Hendriks, M. A. N., and Rots, J. G. (2013). “Systematic assessment of directional mesh bias with periodic boundary conditions: Applied to the crack band model.” Eng. Fract. Mech., 109, 186–208.
Taylor, G. I. (1938). “Plastic strain in metals.” J. Inst. Met., 62, 307–324.
Tuchscherer, R. G., Birrcher, D. B., Williams, C. S., Deschenes, D. J., and Bayrak, O. (2014). “Evaluation of existing strut-and-tie methods and recommended improvements.” ACI Struct. J., 111(6), 1451–1460.
Wight, J. K., and MacGregor, J. G. (2009). Reinforced concrete: Mechanics and design, Pearson Education, Upper Saddle River, NJ.
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Published In
Journal of Structural Engineering
Volume 142 • Issue 10 • October 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 2, 2015
Accepted: Feb 25, 2016
Published online: Apr 29, 2016
Discussion open until: Sep 29, 2016
Published in print: Oct 1, 2016
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