Keywords: crack strength, tension stiffening model, strain distribution function, elongation, tension member, bond-slip, reinforced concrete.

Since concrete is relatively weak and brittle in tension, cracking is expected when significant tensile stress is induced in a member. Mild reinforcement and/or prestressing steel can be used to provide the necessary tensile strength of a structural member. Especially, the tensile strength of concrete represents negligibly small contribution to the ultimate strength of a structural member, so that it was generally ignored in both design and numerical analysis of reinforced concrete (RC) structures. However, increasing needs to the assessment of the strength and serviceability of existing structures and newly designed critical structures in recent years have encouraged the development of advanced analytical methods capable of representing the cracking behaviour of RC structures under all possible loading conditions.

The post-cracking behaviour of RC structures depends on many influence factors (the tensile strength of concrete, anchorage length of embedded reinforcing bars, concrete cover, and steel spacing), which are deeply related to the bond characteristics between concrete and steel. In earlier studies, characterization itself of the tension stiffening effect due to the non-negligible contribution of cracked concrete was the main objective.

Two basically different approaches have been used in defining the strain softening part in the tension region: (1) the modified stiffness approach based on a repeated modification of stiffness according to the strain history; and (2) the bond-slip based model constructed from the force equilibrium and strain compatibility condition at the cracked concrete matrix with the assumed bond stress distribution. Even though the second approaches is broadly adopted in finite element formulation, there is still some limitations in application because this approach requires the assumption of bond stress distribution function along the reinforcement axis, and it follows a series of complex integration and derivation procedures to calculate the elongation and strain increment of steel and accompanying relative slip. To address this limitation in adopting the bond-slip based tension stiffening model, an analytical approach to predict the post-cracking behaviour of RC structures is introduced in this paper. Unlike the classical approaches using the bond stress-slip relationship or the assumed bond stress distribution, the tension stiffening effect at post-cracking stage is quantified on the basis of polynomial strain distribution functions of steel and concrete, and its contribution is implemented into the reinforcing steel. The loads carried by concrete and by reinforcing steel along the member axis can be directly evaluated on the basis of the introduced model. The prediction of cracking loads and elongations of reinforced steel using the introduced model shows good agreements with results from previous analytical studies and experimental data.

1

ACI Committee 224, "Cracking of concrete members in direct tension", J. of ACI, Vol.83, No.1, pp.3-13, 1986.

2

Blackman, J. S., Smith, G., and Young, L. E., "Stress Distribution Affects Ultimate Tensile Strength", ACI J., Vol.55, No. 6, pp.679-684, 1958.

3

CEB, CEB-FIP Model Code for Concrete Structures, Paris, France, 1978.

4

CEB, Cracking and deformation, Bulletin d'information No. 158, Paris, France, 1985.

5

Chan, H. C., Cheung, Y. K. and Huang, Y. P., "Crack Analysis of Reinforced Concrete Tension Members", J. of Structural Engineering, ASCE, Vol. 118, No. 8, pp. 2118-2132 doi:10.1061/(ASCE)0733-9445(1992)118:8(2118)

6

Gerstle, W., Ingraffera, A. R., and Gergely, P., "Tension Stiffening: A Fracture Mechanics Approach", Bond in Concrete, Applied Science Publishers, London, U.K., 1978.

7

Massicotte, B., Elwi, A. E., and Macgregor, J. G., "Tension-Stiffening Model for Planar Reinforced Concrete Members", J. of Structural Engineering, ASCE, Vol.116, No. 11, pp.3039-3058, 1990. doi:10.1061/(ASCE)0733-9445(1990)116:11(3039)

8

Mirza, S. M., and Houde, J., "Study of Bond Stress-Slip Relationships in Reinforce Concrete", ACI J., Vol.76, No.1, pp.19-45, 1979.

9

Okamura, H. and Maekawa, K, Nonlinear Analysis and Constitutive Models of Reinforced Concrete, Gihodo-Shuppan, Tokyo, Japan, 1991.

10

Ouyang, C., Kulkarni, S. M. and Shah, S. P., "Prediction of Cracking Response of Reinforced Concrete Tensile Members", J. of Structural Engineering, Vol.123, No.1, pp.70-78, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:1(70)

11

Somayaji, S. and Shah, S. P., "Bond Stress Versus Slip Relationship and Cracking Response of Tension Members", ACI J., Vol.78, No. 3, pp.217-225, 1981.

12

Vecchio, F. J., and Collins, M. P., "The Modified Compression Field Theory for Reinforced Concrete Members subjected to Shear", ACI J., Vol. 83, No. 2, pp. 219-231, 1986.

13

Yang, S. and Chen, J., "Bond Slip and Crack Width Calculation of Tension Members", ACI Struct. J., Vol.85, No.7, pp.414-422, 1988.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £122 +P&P)