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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 51

Cracking Analysis of Reinforced Concrete Tension Members using Polynomial Strain Distribution Function

H.G. Kwak and J.Y. Song

Department of Civil Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea

Full Bibliographic Reference for this paper
H.G. Kwak, J.Y. Song, "Cracking Analysis of Reinforced Concrete Tension Members using Polynomial Strain Distribution Function", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 51, 2001. doi:10.4203/ccp.73.51
Keywords: crack strength, tension stiffening model, strain distribution function, elongation, tension member, bond-slip, reinforced concrete.

Summary
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.

References
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