Tension Stiffness Model for Cracked Reinforced Concrete
Publication: Journal of Structural Engineering
Volume 117, Issue 3
Abstract
It is known that the consideration of tension stiffening effect resulting from bond slip between reinforcement and surrounding concrete is very effective for the deformation analysis of reinforced concrete members. In the paper, the crack strain is defined as the derivative of the bond slip. Bond characteristics between the concrete and the steel are directly related to the crack spacing and crack width. The tension stiffening effect is derived to be evaluated by the factor λ. Furthermore, constitutive equations of composite materials of concrete and reinforcement in a two‐dimensional stress field with multiple‐crack orientation are developed, using stress reduction and reinforcement tensors. The proposed model can successfully represent the nonlinear behavior of multiple‐cracked reinforced concrete resulting from damage by cracking, etc., and is formulated so that the material tensors are directly applicable to nonlinear finite element analysis through the use of the concept of the smeared crack model. The experimental results are compared with the theoretical calculations. Reasonable agreement is obtained.
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References
1.
Bažant, Z. P., and Gambaroba, P. B. (1980). “Rough cracks in reinforced concrete.” J. Struct. Div., ASCE, 106(4), 819–842.
2.
Bažant, Z. P., Belytschko, T. B., and Chang, T. P. (1984). “Continuum theory for strain‐softening.” J. Engrg. Mech., ASCE, 110(12), 1666–1692.
3.
Bažant, Z. P., and Lin, F. B. (1988). “Nonlocal smeared cracking model for concrete fracture.” J. Engrg. Mech., ASCE, 114(11), 2493–2510.
4.
Cervenka, V. (1985). “Constitutive model for cracked reinforced concrete.” J. Am. Concr. Inst., 82(6), 877–882.
5.
Foegl, H., and Mang, H. A. (1982). “Tension stiffening concept based on bond slip.” J. Struct. Div., ASCE, 108(12), 2681–2701.
6.
Gilbert, R. I., and Warner, R. F. (1978). “Tension stiffening in reinforced concrete slabs.” J. Struct. Div., ASCE, 104(12), 85–1899.
7.
Goto, Y. (1971). “Cracks formed in concrete around deformed tension bars.” J. Am. Concr. Inst., 68(4), 244–251.
8.
Lin, C. S., and Scordelis, A. C. (1975). “Nonlinear analysis of RC shells of general form.” J. Struct. Div., ASCE, 101(3), 523–538.
9.
Oesterle, R. G., and Russell, H. G. (1980). “Shear transfer in large scale reinforced concrete containment elements.” NUREG/CR‐1374, Construction Technology Laboratories, Apr.
10.
Ozaka, Y., Ohtsuka, K., and Matsumoto, Y. (1985). “Cracks formed in concrete prism with axial tension bars under influence of drying.” Concr. J., 23(3), 109–119.
11.
Powell, G. H., De Villiers, I. P., and Litton, R. W. (1979). “Implementation of endochronic theory for concrete with extensions to include cracking.” SMiRT 5, Berlin, Germany, Vol. M, Aug. 1979, M2–6.
12.
Rizkalla, S. H., and Hwang, L. S. (1984). “Crack prediction for members in uniaxial tension.” J. Am. Concr. Inst., 81(6), 572–579.
13.
Tanabe, T., Kawasumi, M., and Yamashita, Y. (1985). “Finite element modelling for the thermal stress analysis of massive concrete structures.” Proc. of Japan‐U.S. Science Seminar on Finite Element Analysis of Reinforced Concrete Structures, Tokyo, Japan, Vol. 2, May, 75–93.
14.
Vecchio, F., and Collins, M. P. (1981). “Stress‐strain characteristics of reinforced concrete in pure shear.” Colloquium on Advanced Mechanics of Reinforced Concrete, International Association of Bridge and Structural Engineers, Delft, the Netherlands, Jun., 211–255.
15.
Wu, Z. S., Yoshikawa, H., and Tanabe, T. (1989). “Nonlinear aspects of cracked reinforced concrete by the damage mechanics concept.” Proc. of the Second East Asia‐Pacific Conf. on Structural Engineering and Construction, Chiang Mai, Thailand, Jan., 481–486.
16.
Yamamoto, Y. (1973). “Study on bond stress of reinforcements, cracking and restoring characteristics of embedded tension bars.” Taisei Tech. Report 6, Technical Research Institute, Taisei Corp., 151–193.
17.
Yoshikawa, H., and Tanabe, T. (1985). “A finite element model for cracked reinforced concrete members introducing crack strain concept.” Proc. of Japan‐U.S. Science Seminar on Finite Element Analysis of Reinforced Concrete Structures, Tokyo, Japan, Vol. 2, May, 237–246.
18.
Yoshikawa, H., and Tanabe, T. (1986). “An analytical study for the tension stiffness of reinforced concrete members on the basis of bond slip mechanism.” Trans., of the Japan Concrete Institute, 473–480.
19.
Yoshikawa, H., Wu, Z. S., and Tanabe, T. (1989). “An analytical model for shear slip of cracked concrete.” J. Struct. Engrg., ASCE, 115(4), 771–788.
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Copyright © 1991 ASCE.
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Published online: Mar 1, 1991
Published in print: Mar 1991
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