TECHNICAL PAPERS
May 1, 2006

Size Effect on Shear Strength of Deep Beams: Investigating with Strut-and-Tie Model

Publication: Journal of Structural Engineering
Volume 132, Issue 5

Abstract

Since a diagonally cracked deep beam behaves as a tied arch, the conventional plane section remaining plane approach is not applicable to analyses of deep beams. Besides, for beams without web reinforcement, it has been shown that shear strength decreases as member size increases. This is associated with a phenomenon called size effect. In this study, the causes of size effect on shear strength of deep beams are investigated using both the strut-and-tie model (STM) and finite element model. The study shows that size effect in concrete beam arises primarily from an inappropriate adoption of the shear transfer concept for steel beams. In addition, size effect also depends on secondary factors such as the geometry of strut, and the spacing and diameter of web reinforcement. The modified STM is verified with three published case studies comprising a total of 36 beams. Generally, the predictions are accurate and consistent, with a uniform safety margin for different member sizes considered.

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References

Alshegeir, A., and Ramirez, J. A. (1990). “Analysis of disturbed regions with strut-and-tie models.” Structural Engineering Rep. No. CE-STR-90-1, Purdue Univ., West Lafayette, Ind.
American Concrete Institute and American Society of Civil Engineers (ACI/ASCE). (1974). “The shear strength of reinforced concrete members.” ASCE Committee 426 Publication No. 426 R-74, Vol. 99, ACI, Farmington Hills, Mich., 1091–1187.
American Concrete Institute and American Society of Civil Engineers (ACI/ASCE). (1999). “Recent approaches to shear design of structural concrete.” ASCE Committee 445, ACI, Farmington Hills, Mich.
An, X. H., Maekawa, K., and Okamura, H. (1997). “Numerical simulation of size effect in shear strength of RC beams.” J. Mater. Concr. Struct. Pavement, JSCE, 35(564), 297–316.
Bazant Z. P., and Kim, J. K. (1984). “Size effect in shear failure of longitudinally reinforced beams.” ACI Struct. J., 81(5), 456–468.
Bazant, Z. P., Ozbolt, J., and Eligehausen, R. (1994). “Fracture size effect: Review of evidence for concrete structures.” J. Struct. Eng., 120(8), 2377–2398.
Bazant, Z. P., and Xiang, Y. (1997). “Size effect in compression fracture: Splitting crack band propagation.” J. Eng. Mech., 123(2), 162–172.
Bergmeister, K., Breen, J. E., and Jirsa, J. O. (1991). “Dimensioning of the nodes and development of reinforcement.” Rep. on IABSE Colloquium on Structural Concrete, IABSE, Zurich, Switzerland, 551–564.
Canadian Standards Association (CSA). (1994). “Design of concrete structures: Structures (design)—A national standard of Canada.” CAN-A23.3-94, CSA, Toronto.
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.
Collins, M. P., and Mitchell, D. (1986). “A rational approach to shear design—The 1984 Canadian code provisions.” ACI Struct. J., 83(80), 925–933.
Kani, G. N. J. (1967). “How safe are our large reinforced concrete beams?” ACI J., 64(3), 128–141.
Kim, J. K., Yi, S. T., Park, C. K., and Eo, S. H. (1999). “Size effect on compressive strength of plain and spirally reinforced concrete cylinders.” ACI Struct. J., 96(1), 88–94.
Kotsovos, M. D., and Pavlovic, M. N. (1994). “A possible explanation for size effects in structural concrete.” Arch. Civil Eng., XL, 2, 243–261.
Kotsovos, M. D., and Palovic, M. N. (1997). “Size effect in structural concrete: A numerical experiment.” Comput. Struct., 64(1–4), 285–295.
Marti, P. (1985). “Basic tools of reinforced concrete beam design.” ACI Struct. J., 82(4), 46–56.
Ramirez, J. A., and Breen, J. E. (1991). “Evaluation of a modified truss-model approach for beams in shear.” ACI Struct. J., 85(S58), 562–571.
Reinhardt, H. W. (1981). “Similitude of brittle fracture of structural concrete.” Proc. Advanced Mechanics of Reinforced Concrete, IABSE Colloquium, Delft, The Netherlands, 175–184.
Schlaich, J., Schafer, K., and Jennewein, M. (1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–151.
Shioya, T., and Akiyama, H. (1993). “Application to design of size effect in reinforced concrete structures.” Proc., JCI Int. Workshop on Size Effect in Concrete Structures, 327–334.
Tan, K. H., Cheng, G. H., and Cheong, H. K. (2003a). “Size effect in shear strength of large beams—Behavior and finite element modeling.” Mag. Concrete Res., to be published.
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., Lu, H. Y., and Teng, S. (1999). “Size effect in large prestressed concrete deep beams.” ACI Struct. J., 96(6), 937–946.
Tan, K. H., Tang, C. Y., and Tong K. (2003b). “A direct method for deep beams with web reinforcement.” Mag. Concrete Res., 55(1), 53–63.
Tan, K. H, Tong, K., and Tang, C. Y. (2001). “Direct strut-and-tie model for prestressed deep beams.” J. Struct. Eng., 127(9), 1076–1084.
Tan, K. H., Tong, K., and Tang C. Y. (2003c). “Consistent strut-and-tie modeling of deep beams with web openings.” Mag. Concrete Res., 55(1), 65–75.
Taylor, H. P. J. (1972). “Shear strength of large beams.” J. Struct. Div. ASCE, 98(11), 2473–2490.
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., and Lehwalter, N. (1994). “Size effects in short beams loaded in shear.” ACI Struct. J., 91(5), 585–593.
Weibull, W. (1939). “Phenomenon of rupture in solids.” Ingen.-skapsakad. Handl., 153, 1–55.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 132Issue 5May 2006
Pages: 673 - 685

History

Received: Mar 11, 2003
Accepted: Jul 28, 2005
Published online: May 1, 2006
Published in print: May 2006

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Notes

Note. Associate Editor: Khalid M. Mosalam

Authors

Affiliations

Associate Professor, School of Civil and Structural Engineering, Nanyang Technological Univ., Singapore 639798, Singapore (corresponding author). E-mail: [email protected]
G. H. Cheng
Research Scholar, School of Civil and Structural Engineering, Nanyang Technological Univ., Singapore 639798, Singapore.

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