Keywords: average stress-strain, tension-stiffening, cracking, biaxial tension, reinforced concrete.

The weak tensile strength of concrete results in the nonlinear response of RC structures which can be divided into three ranges of behavior: the uncracked elastic stage, the crack propagation of concrete and the plastic (yielding of steel or crushing of concrete) stage. The post-cracking behavior of RC structures also depends on many influencing factors (the tensile strength of concrete, anchorage length of embedded reinforcing bars, concrete cover, and steel spacing, etc.) which are deeply related to the bond characteristics between concrete and steel. Accordingly, to verify the nonlinear behavior of RC structures including the bond-slip mechanism, many experimental and numerical studies have been conducted [1,2].

A review of the literature reveals that several models have been introduced to predict the post-cracking behavior of RC structures. In earlier studies, characterization itself of the tension stiffening effect due to the non-negligible contribution of cracked concrete was the main objective. Recently, following the introduction of nonlinear fracture mechanics in RC theory [3], more advanced analytical approaches have been conducted [4], and many numerical models which can implement the tension stiffening effect into the stress-strain relation of concrete have been proposed [1,2]. Besides, the ACI committee 224 [5] and CEB-FIP [6] predict, in an empirical manner, the average stress-strain curves of a RC element subject to biaxial loadings.

Two basically different approaches have been used in defining the strain softening part in the tension region: (1) a modified stiffness approach based on a repeated modification of stiffness according to the strain history [1,2]; and (2) a bond-slip based model constructed from the force equilibrium and strain compatibility condition at the cracked concrete matrix with the assumed bond stress distribution [1,2]. Even though the second approach is broadly adopted in finite element formulation, there are 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 behavior of RC structures is introduced in this paper. Unlike previous approaches based on the assumed bond stress distribution function, the strain distribution of concrete, which is abruptly changed after cracking occurs, is defined with a polynomial function satisfying the boundary conditions at the crack face and at the inner end of the transfer length. In advance, the polynomial order is determined from the energy equilibrium condition before and after cracking. The validity of the introduced approach is established by comparing the analytical predictions for RC tension members with results from experimental and previous analytical studies. Moreover, numerical analyses for idealized RC panels are conducted to verify the applicability of the constructed tension stiffening model to RC containments subject to internal pressure.

1

ASCE Task Committee on Finite Element Analysis of Reinforced Concrete Structures. State-of-the-art report on finite element analysis of reinforced concrete. New York: ASCE, 1982.

2

CEB. RC elements under cyclic loading: state of the art report. London: Thomas Telford Services Ltd., 1996.

3

Ouyang C, Wollrab E, Kulkarni SM, Shah SP. Prediction of cracking response of reinforced concrete tensile members. J. Struct. Eng. ASCE 1997;123:70-78. doi:10.1061/(ASCE)0733-9445(1997)123:1(70)

4

Salem HM, Maekawa K. Pre- and postyield finite element method simulation of bond of ribbed reinforcing bars. J. Struct. Eng. ASCE 2004;130;671-680. doi:10.1061/(ASCE)0733-9445(2004)130:4(671)

5

ACI Committee 224. Cracking of concrete members in direct tension. ACI Manual of Concrete Practice, Part 2, pp. 224.2R-1-12., 2002

6

CEB. CEB-FIP model code 1990. London: Thomas Telford Services Ltd., 1993.

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