Keywords: tension-stiffening, post-cracking models, numerical analysis, finite element method, modelling of cracked concrete.

In recent years, following the introduction of nonlinear finite element analysis of reinforced concrete elements, various analytical models which incorporate the tension-stiffening effect into the stress-strain relation of concrete in tension have been proposed by various investigators. Most of these models were calibrated for normal-strength concrete and only few studies have examined higher strength ranges.

Based on axial tension tests of both normal- and high-strength concrete, HSC was found to loose its tensile strength more rapidly than NSC, leading to a sharper declination in the post-cracking tensile response with less tension-stiffening strain capacity for HSC than NSC. This phenomenon was also observed in the present study when plotting tension-stiffening models extracted from tested specimens with different concrete grade on the same chart with and without normalization.

For purpose of accurately predicting the overall behaviour of the member using nonlinear finite element analysis, the onset of cracking is controlled by a maximum principal tensile stress criterion, while linear elastic behaviour prior to cracking is assumed. The limiting tensile stresses required to define the onset of cracking for states of triaxial tensile stress and for combination of tension and compression principal stresses and the material constitutive cracked matrices are presented.

Based on experimental studies, various forms of average tensile stress-strain relationships after cracking were suggested in literature to represent the gradual release of tensile stresses normal to the cracked plane through different tension-stiffening models. Such models exhibited considerable scatter, particularly when applied to different grades of concrete. Therefore, a new tension-stiffening model is developed which takes into account the concrete strength and consequently to be applicable to members having any grade of concrete. The model is verified by comparison with available experimental data as well as with other models.

To verify the soundness of the model, sixteen reinforced concrete beams made of both normal- and high-strength concrete tested by various researchers were selected to conduct a correlation study with other tension-stiffening models as well as with experimental results. The investigated beams have a concrete compressive strength ranging from 21.7 MPa to 101.8 MPa. A three dimensional nonlinear finite element program developed by the authors was used to analyze the investigated beams.

It was found that the finite element prediction of the ultimate load using all studied tension-stiffening models was generally in good agreement with the experimental results for NSC beams. However, they overestimated the ultimate loads for HSC beams, except for the proposed model which agreed well with the experimental results for both NSC and HSC beams. Similarly, the model presented appears to give the closet prediction with regard to the experimental load-deflection response for two selected NSC and HSC beams.

It is concluded that the inclusion of tension-stiffening effect has a considerable influence on determining the entire behaviour of reinforced concrete members, thus a correct average tensile stress-strain relationship of concrete is very important for finite element analysis.

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