Shear Capacity of Reinforced Concrete Deep Beams
Publication: Journal of Structural Engineering
Volume 126, Issue 9
Abstract
A mechanism analysis of shear failure of simply supported reinforced concrete deep beams is presented. Concrete and steel reinforcement are modeled as rigid perfectly plastic materials. The failure modes are idealized as an assemblage of rigid blocks separated by failure zones of displacement discontinuity. The shear strength of deep beams is derived as a function of the location of the instantaneous center of relative rotation of moving blocks. Minimization of the developed function gives the shear capacity of deep beams. Comparisons of the predicted shear capacity of numerous deep beams show good agreement with results obtained from experiments. A parametric study of main variables affecting shear strength of deep beams is conducted. The present model shows that the shear-span-to-depth ratio has more influence on the shear capacity than the span-to-depth ratio and as the former increases, the shear strength decreases. Increasing main longitudinal bottom reinforcement increases the shear capacity up to a certain limit beyond which no shear strength improvement could be achieved. The relative effectiveness of horizontal and vertical web reinforcement on the load capacity is mainly influenced by the shear-span-to-depth ratio; the deeper the beam, the more effective the horizontal web reinforcement and the less effective the vertical web reinforcement.
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References
1.
American Concrete Institute (ACI). (1995). “Building code requirements for reinforced concrete and commentary.” ACI 318-95, Detroit.
2.
Ashour, A. F. (1999). “Upper bound analysis for reinforced concrete deep beams with fixed end supports.” ACI Struct. J., 96(2), 167–173.
3.
Ashour, A. F., and Morley, C. T. (1994). “The numerical determination of shear failure mechanisms in reinforced-concrete beams.” The Struct. Engr., London, 72(23–24), 395–400.
4.
Ashour, A. F., and Morley, C. T. (1996). “Effectiveness factor of concrete in continuous deep beams.”J. Struct. Engrg., ASCE, 122(2), 169–178.
5.
Averbuch, D., and de Buhan, P. (1999). “Shear failure design of reinforced concrete deep beams: A numerical approach.”J. Struct. Engrg., ASCE, 125(3), 309–318.
6.
Chen, W. F. (1982). Plasticity in reinforced concrete, McGraw-Hill, New York.
7.
de Paiva, H. A., and Siess, C. P. (1965). “Strength and behavior of deep beams in shear.”J. Struct. Div., ASCE, 91(5), 19–41.
8.
Grob, J., and Thürlimann, B. (1976). “Ultimate strength and design of reinforced concrete beams under bending and shear.” IABSE Periodica, Zurich, 36-II, 105–120.
9.
Jensen, J. F. (1982). “Discussion of `An upper-bound rigid-plastic solution for the shear failure of concrete beams without shear reinforcement' by K. O. Kemp and M. T. Al-Safi.” Mag. of Concrete Res., London, 34(119), 100–103.
10.
Kong, F. K., Robins, P. J., and Cole, D. F. (1970). “Web reinforcement effects on deep beams.” ACI J., 67(December), 1010–1017.
11.
Kong, F. K., Robins, P. J., Kirby, D. P., and Short, D. R. (1972). “Deep beams with inclined web reinforcement.” ACI J., 69(March), 172–176.
12.
Manuel, R. F., Slight, B. W., and Suter, G. T. (1971). “Deep beam behavior affected by length and shear span variations.” ACI J., 68(December), 954–958.
13.
Marti, P. (1985). “Basic tools of reinforced concrete beam design.” ACI Struct. J., 82(1), 46–56.
14.
Nielsen, M. P. (1984). Limit analysis and concrete plasticity, Prentice-Hall, Englewood Cliffs, N.J.
15.
Nielsen, M. P., Bræstrup, M. W., and Bach, F. (1978). “Rational analysis of shear in reinforced concrete beams.” IABSE Proc., 2, P-15/78.
16.
Over Arup and Partners (OAP) and Construction Industry Research and Information Association (CIRIA). (1977). “The design of deep beams in reinforced concrete.” CIRIA guide 2, London.
17.
Ramakrishnan, V., and Ananthanarayana, Y. (1968). “Ultimate strength of deep beams in shear.” ACI J., 65(February), 87–98.
18.
Regan, P. E. (1993). “Research on shear: A benefit to humanity or a waste of time?” The Struct. Engr., London, 71(19), 337–346.
19.
Rogowsky, D. M., and MacGregor, J. G. (1986). “Design of reinforced concrete deep beams.” Concrete Int., 83(August), 49–58.
20.
Rogowsky, D. M., MacGregor, J. G., and Ong, S. Y. (1986). “Test of reinforced concrete deep beams.” ACI Struct. J., 83(July–August), 614–623.
21.
Schlaich, J., Schäfer, K., and Jennewein, M. (1987). “Toward a consistent design of structural concrete.” PCI J., 32(May–June), 74–150.
22.
Sio, W. B. (1993). “Strut-and-tie model for shear behavior in deep beams and pile caps failing in diagonal splitting.” ACI Struct. J., 90(4), 356–363.
23.
Smith, K. N., and Vantsiotis, A. S. (1982). “Shear strength of deep beams.” ACI J., 79(May–June), 201–213.
24.
Subdei, N. K. (1988). “Reinforced concrete deep beams: A method of analysis.” Proc., Instn. of Civ. Engrs., 85(March), 1–30.
25.
Subedi, N. K., Vardy, A. E., and Kubota, N. (1986). “Reinforced concrete deep beams—Some test results.” Mag. of Concrete Res., 38(137), 206–219.
26.
Suter, G. T., and Manuel, R. F. (1971). “Diagonal crack width control in short beams.” ACI J., 68(June), 451–455.
27.
Tan, K. H., and Lu, H. Y. (1999). “Shear behaviour of large reinforced concrete deep beams and code comparisons.” ACI Struct. J., 96(5), 836–845.
28.
Tan, K. H., Weng, L. W., and Teng, S. (1997). “A strut-and-tie model for deep beams subjected to combined top-and-bottom loading.” The Struct. Engr., London, 75(13), 215–225.
29.
Wang, W., Jiang, D., and Hsu, C. T. (1993). “Shear strength of reinforced concrete deep beams.”J. Struct. Engrg., ASCE, 119(8), 2294–2312.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 126 • Issue 9 • September 2000
Pages: 1045 - 1052
History
Received: Nov 1, 1999
Published online: Sep 1, 2000
Published in print: Sep 2000
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