Technical Papers
Jul 2, 2014

Rational Approach to Prediction of Shear Capacity of RC Beam-Column Elements

Publication: Journal of Structural Engineering
Volume 141, Issue 2

Abstract

This paper presents a new predictive formula for the shear capacity evaluation of reinforced concrete members subjected to combined axial, bending, and shear forces. The formula is based on a tensorial approach to concrete shear resistance that is very similar to the one used in the shear-enhanced fiber beam element. The total shear resistance is broken down into the contribution of concrete and contribution of shear reinforcement. The concrete contribution to the shear resistance is calculated using a normal-shear stress failure envelope. Normal (longitudinal) stresses are calculated from axial and bending forces acting on the concrete member. In the formulation, a number of simplifications are made to keep the formula as simple as possible but still sufficiently accurate. The resulting formulation, although capable of accounting for all of the major variables that influence the shear strength, including size effect, remains particularly simple and with a compact notation. The predictions of the proposed formula are compared with those used by the American Concrete Institute (ACI), the European Committee for Standardization (CEN) Eurocode, and the International Federation for Structural Concrete (fib) model code, and its accuracy is checked against a vast experimental database available in the literature. Results and comparisons are very encouraging and confirm the soundness of the underlying mechanical model. The capability of this model to provide a unified approach for reinforced and unreinforced members opens up the possibility to extend the application of the proposed formula to engineered cementitious composites, such as fiber-reinforced concrete.

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References

Adebar, P., and Collins, M. P. (1996). “Shear strength of members without transverse reinforcement.” Can. J. Civ. Eng., 23, 30–41.
Ahmad, S. H., Khaloo, A. R., and Poveda, A. (1986). “Shear capacity of reinforced high-strength concrete beams.” ACI J. Proc., 83(2), 297–305.
Al-Alusi, A. F. (1957). “Diagonal tension strength of reinforced concrete t-beams with varying shear span.” ACI J. Proc., 53, 1067–1077.
American Concrete Institute (ACI). (2005). “Building code requirements for structural concrete and commentary.”, Farmington Hills, MI.
Anderson, N. S., and Ramirez, J. A. (1989). “Detailing of stirrup reinforcement.” ACI Struct. J., 86(5), 507–515.
Angelakos, D., Bentz, E. C., and Collins, M. P. (2001). “Effect of concrete strength and minimum stirrups on shear strength of large members.” ACI Struct. J., 98(3), 290–300.
Aster, H., and Koch, R. (1974). “Schubtragfähigkeit dicker Stahlbetonplatten.” Beton-und-Stahlbetonbau, 69(11), 266–270.
Bahl, N. S. (1968). “Uber den Einfluss der Balkenhöhe auf Schubtragfähigeit von einfeldrigen Stahlbetonbalken mit und ohne Schubbewerhung.” Dissertation, Universität Stuttgart, Germany (in German).
Bažant, Z. P. (1984). “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech., 518–535.
Bažant, Z. P., and Yu, Q. (2005a). “Designing against size effect on shear strength of reinforced concrete beams without stirrups: I. formulation.” J. Struct. Eng., 1886–1897.
Bažant, Z. P., and Yu, Q. (2005b). “Designing against size effect on shear strength of reinforced concrete beams without stirrups: II. verification and calibration.” J. Struct. Eng., 1877–1885.
Bentz, E. C., Vecchio, F. J., and Collins, M. P. (2006). “Simplified modified compression field theory for calculating shear strength of reinforced concrete elements.” ACI Struct. J., 10(4), 614–624.
Bresler, B., and Scordelis, A. C. (1963). “Shear strength of reinforced concrete beams.” J. Am. Concr. Inst., 60(1), 51–72.
Bresler, B., and Scordelis, A. C. (1966). “Shear strength of reinforced concrete beams—Series III.”, Strucutres and materials Research, Dept. og Civil Engineering, Univ. of California, Berkeley, CA.
Canadian Codes Association. (2004). “Design of concrete structures.”, Ontario, Canada.
Chana, P. S. (1981). “Some aspects of modeling the behavior of reinforced concrete under shear loading.”, Cement and Concrete Association, Wexham Springs.
Collins, M. P., and Kuchma, D. (1999). “How Safe are our large, lightly reinforced concrete beams, slabs and footings?” ACI Struct. J., 96(4), 482–490.
Diaz de Cossio, R., and Siess, C.P. (1960). “Behavior and strength in shear of beams and frames without web reinforcement” ACI J., 31(8), 695–735.
Elzanaty, A. H., Nilson, A. H., and Slate, F. O. (1986). “Shear capacity of reinforced concrete beams using high strength concrete.” J. Am. Concr. Inst., 65(1), 290–296.
EN 1992-1-1:1993. (1993). “Design of concrete structures. Part 1-1: General rules for buildings.” Eurocode 2, UNI, Milan.
EN 1992-1-1:2005. (2005). “Design of concrete structures. Part 1-1: General rules for buildings.” Eurocode 2, UNI, Milan.
fib Bulletin 65: Model code 2010—Final draft, Volume 1.
fib Bulletin 66: Model code 2010—Final draft, Volume 2.
Feldman, A., and Siess, C. P. (1955). “Effect of Moment-shear ratio on diagonal tension cracking and strength in shear of reinforced concrete beams.” Univ. of Illinois Engineering Experiment Station, College of Engineering, Univ. of Illinois at Urbana-Champaign.
Frosch, R. J. (2000). “Behavior of large-scale reinforced concrete beams with minimum shear reinforcement.” ACI Struct. J., 97(6), 814–820.
Goode, C. D., and Helmy, M. A. (1967). “The strength on concrete under combined shear and direct stress.” Mag. Concr. Res., 19(59), 105–112.
Grimm, R. (1997). “Einfluß bruchmechanischer kenngrößen auf das biege- und schubtragverhalten hochfester betone.” Diss., Fachb. Konstr. Ingenieurbau der TH Darmstadt, und DafStb H.477, Beuth Verlag GmbH, Berlin.
Hallgren, M. (1994). “Shear tests on reinforced high and normal strength concrete beams without stirrups.” Dept. of Structural Engineering, Royal Institute of Technology, Stockholm, Sweden.
Hallgren, M. (1996). “Punching shear capacity of reinforced high strength concrete slabs.” doctoral thesis, Royal Institute of Technology, Stockholm, Sweden, 206.
Hamadi, Y. D. (1976). “Force transfer across cracks in concrete structures.” Ph.D. Thesis, Polytechnic of Central London.
Hanson, J. A. (1958). “Shear strength of lightweight reinforced concrete beams.” J. Am. Concr. Inst., 30(3), 387–403.
Hanson, J. A. (1961). “Tensile strength and diagonal tension resistance of structural lightweight concrete.” ACI J. Proc., 58(1), 1–39.
Islam, M. S., Pam, H. J., and Kwan, A. K. H. (1998). “Shear capacity of high-strength concrete beams with their point of inflection within the shear span.” Proc. Inst. of Civ. Eng. Struct. Build., 128.
Johnson, M. K., and Ramirez, J. A. (1989). “Minimum Shear Reinforcement in Beams with HSC.” ACI Struct. J., 86(4), 376–382.
Kani, G.N. (1967). “How safe are our large concrete beams?” ACI J. Proc., 64(3), 128–141.
Karayiannis, C. G., and Chalioris, C. E. (1999). “Experimental investigation of the influence of stirrups on the shear failure mechanism of reinforced concrete beams.” Proc., 13th Hellenic Conf. on Concrete, Rethymnon, Greece, 133–141.
Kong, P. Y. L., and Rangan, B. V. (1998). “Shear strength of high-performance concrete beams.” ACI Struct. J., 95(6), 667–677.
Krefeld, W. J., and Thurston, C. W. (1966). “Studies of the shear and diagonal tension strength of simply reinforced concrete beams.” J. Am. Concr. Inst., 63(4), 451–476.
Kulkarni, S. M., and Shah, S. P. (1998). “Response of reinforced concrete beams at high strain rates.” ACI Struct. J., 95(6), 705–715.
Lambotte, H., and Taerwe, L. R. (1990). “Deflection and cracking of high-strength concrete beams and slabs.” SP 121-7, High-Strength Concrete, Second International Symposium, Weston T. Hester, ACI, 108–128.
Laupa, A., Seiss, C.P., and Newmark, N.M. (1953). “The shear strength of simple-span reinforced concrete beams without web reinforcement.”, Univ. of Illinois, Urbana.
Lehwalter, N. (1988). “The bearning capacity of concrete compression struts in truss-system, exemplified by the case of short beams.” Ph.D. thesis, Darmstadt, Germany.
Leonhardt, F., and Mönnig, E. (1984). Lectures on massive construction. Third part: Bases for reinforcing in the reinforced concrete construction, Springer, Berlin.
Leonhardt, F., and Walther, R. (1962). “Schubversuche an Einfeldrigen Stahlbeton-Balken mit und ohne Schubbewehrung zur Ermittlung der Schubtragfähigkeit und der Oberen Schubspannungsgrenze.” Heft 151, Deutcher Ausschuss für Stahlbeton, W. Ernst, u. Sohn, Berlin 66 (in German).
Mathey, R.G., and Watstein, D. (1963). “Shear strength of beams without web reinforcement containing deformed bars of different yield strengths.” ACI J. Proc., 63, 183–206.
Mattock, A. H., and Wang, Z. (1984). “Shear strength of reinforced concrete members subject to high axial compressive stress.” ACI Struct. J., 81, 287–298.
Moody, K. G., Viest, I. M., Elstner, R. C., and Hognestad, E. (1954). “Shear strength of reinforced concrete beams, Part-1: Tests of simple beams.” ACI J., 51(3), 317–332.
McGormley, J. C., Clearly, D. B., and Ramirez, J. A. (1996). “The performance of epoxy-coated shear reinforcement.” ACI Struct. J., 93(5), 531–537.
Morrow, J., and Viest, I. M. (1957). “Shear strength of reinforced concrete frame without web reinforcement.” ACI J. Proc., 28(9), 833–869.
Mphonde, A. G., and Frantz, G. G. (1985). “Shear tests of hogh-and-low-strength concrete beams with stirrups.” High-Strength concrete, SP-87, H. G. Russell, ed., American Concrete Institute, Farmington Hills, MI, 179–196.
Niwa, J., Yamada, K., Yokozawa, K., and Okamura, H. (1987). “Revaluation of the equation for shear strength of reinforced concrete beams without web reinforcement.” Concr. Lib. of JSCE, 9, 65–84.
Ožbolt, J. (1995). “Size effect and ductility of concrete and reinforced concrete structures.” Habilitation, Univ. Stuttgart, Stuttgart, Germany (in German).
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 Reinhardt, H. W. (2002). “Numerical study of mixed mode fracture in concrete.” Int. J. Fract., 118(2), 145–161.
Petrangeli, M., Pinto, P. E., and Ciampi, V. (1999a). “A fibre element for cyclic bending and shear. I: Theory.” J. Eng. Mech., 994–1001.
Petrangeli, M., Pinto, P. E., and Ciampi, V. (1999b). “A fibre element for cyclic bending and shear. II: Verification.” J. Eng. Mech., 1002–1009.
Placas, A., and Regan, P. E. (1971). “Shear failure of reinforced concrete beams.” Proc., J. Am. Concr. Inst., 68(10), 763–773.
Podgorniak-Stanik, B. (1998). “The influence of concrete strength, distribution of longitudinal reinforcement, amount of transverse reinforcement, and member size on shear strength of reinforced concrete members.” M.A.Sc. thesis, Dept. of Civil Engineering, Univ. of Toronto.
Rajagopalan, K. S., and Ferguson, P. M. (1968). “Exploratory shear tests emphasizing percentage of longitudinal steel.” ACI J. Proc., 65(9), 634–638.
Reineck, K.-H., Koch, R., and Schlaich, J. (1978). “Shear tests on reinforced concrete beams with axial compression for offshore structures.” Institut für Massivbau, Universität Stuttgart (unveröff. Berichte für den Auftraggeber) .
Reineck, K. H., Kuchma, D. A., and Fitik, B. (2010). “Extended databases with shear tests on structural concrete beams without and with stirrups for the assessment of shear design procedures.” Research Report of Institute for Lightweight Structures Conceptual and Structural Design (ILEK), Univ. of Stuttgart, Germany.
Reineck, K.-H., Kuchma, D. A., Kim, K. S., and Marx, S. (2003). “Shear database for reinforced concrete members without shear reinforcement.” ACI Struct. J., 100, 240–249.
Remmel, G. (1991). “Zum Zugtragverhalten hochfester Betone und seinem Einfluß auf die Querkrafttragfähigkeit von schlanken Bauteilen ohne Schubbewehrung.” Dissertation, Technische Hochschule Damstadt.
Roller, J. J., and Russell, H. G. (1990). “Shear strength of high-strength concrete beams with web reinforcement.” ACI Struct. J., 87(2), 191–198.
Ruesch, H., Haugli, F. R., and Mayer, H. (1962). “Schubversuche an Stahlbeton-Rechteckbalken mit gleichmaessig verteilter Belastung.” Deutscher Ausschuss für Stahlbeton, Heft 145, 3–30.
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.
Shah, A., and Ahmad, S. (2007). “An experimental investigation into shear capacity of high strength concrete beams.” Asian J. Civ. Eng., 8(5), 549–562.
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.” J. Am. Concr. Inst., 42, 129–166.
Taylor, H. P. J. (1968). “Shear stresses in reinforced concrete beams without shear reinforcement.” Technical Rep. TRA407, Cement and Concrete Association, London.
Taylor, H. P. J. (1972). “Shear strength of large beams.” ASCE J. Struct. Div., 98, 2473–2490.
Thorenfeldt, E., and Drangshold, G. (1990). “Shear capacity of reinforced high-strength concrete beams.” ACI Special Publication, SP-121, 129–154.
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.
Vecchio, F. J., and Collins, M. P. (1986). “The modified compression field theory for reinforced concrete elements subjected to shear.” ACI Struct. J., 83(2), 219–231.
Walraven, J. C. (1978). “The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement.”, Delft Univ. of Technology.
Xie, Y., Ahmad, S. H., Yu, T., Hino, S., Chung, W. (1994). “Shear ductility of reinforced concrete beams of normal and high-strength concrete.” ACI Struct. J., 91(2), 140–149.
Yoon, Y., 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.
Zararis, P. D., and Papadakis, G. (1999). “Influence of the arrangement of reinforcement on the shear strength of RC beams.” Proc., 13th Hellenic Conf. on Concrete, Vol. I, Rethymnon, Greece, 110–119 (in Greek).

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 141Issue 2February 2015

History

Received: Mar 19, 2013
Accepted: Jan 23, 2014
Published online: Jul 2, 2014
Discussion open until: Dec 2, 2014
Published in print: Feb 1, 2015

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Paola Rita Marcantonio, Ph.D. [email protected]
Dept. of Engineering and Geotechnical, Univ. of Pescara, Viale Pindaro 42, 65127 Pescara, Italy. E-mail: [email protected]
Joško Ožbolt [email protected]
Professor, Institute of Construction Materials, Univ. of Stuttgart, Pfaffenwaldring 4, 70560 Stuttgart, Germany (corresponding author). E-mail: [email protected]
Marco Petrangeli [email protected]
Professor, Dept. of Engineering and Geotechnical, Univ. of Pescara, Viale Pindaro 42, 65127 Pescara, Italy. E-mail: [email protected]

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