Strain-stress analysis of reinforced concrete beams strengthened without unloading by exterior reinforcement/Apkrautų gelžbetoninių sijų, stiprinamų papildoma armatūra, įtempių-deformacijų būvio analizė
The mostly used method for strengthening flexural concrete members is mounting exterior reinforcing bars. When applying the strengthening by exterior reinforcing, the problem of assessing the remaining carrying capacity of the member being strengthened and estimating the actual stress in the reinforcement placed in the tensile zone of the member is to be solved.
In the paper a method for the analysis of the flexural concrete members strengthened by exterior reinforcing bars is proposed. The method allows to design the exterior reinforcement by taking account of the remaining carrying capacity of the member being strengthened. Moreover, the method proposed enables one to assess a redistribution of stress between the originally placed reinforcement and the exterior reinforcement used to strengthen the member.
The redistribution of stress has a considerable influence on the carrying capacity of the member as well as on its bending stiffness. The stress-strain relationships of the both reinforcements are necessary for assessing the redistribution of stress between them, and these relationships are input for the analysis method proposed in this paper.
In opposite to other methods suggested in the literature and used for the analysis of the flexural members strengthened in the way described above, the method proposed in the present paper allows one to take account of the pastiche deformations of concrete and steel in the member being strengthened. In addition, the proposed method is less complicated to apply when compared to methods suggested to date.
The method proposed is represented by the formula (9), which expresses the bending capacity of the flexural member after its strengthening. The main idea of the proposed method is to replace the design strengths of the reinforcement cast in concrete and mounted outside the member, R s , by the reduced strength σ s, redwhich is assigned to the both reinforcements. The reduced strength σs, red was introduced in order to take account of the plastic deformations of reinforcing steel.
The proposed method was verified by a series of experiments with simple reinforced concrete beams. The aim of the experiments was an investigation of the redistribution of stress inside the normal section of the member analysed and the assessment of the influence of the stress-strain state in the member before strengthening on the characteristics of its tensile zone after the member is strengthened. The results of the experiments are shown in Fig 7. In this figure, the experimental relationship between the deflection of the beams being investigated, f, and the reduced bending stress M/M u is depicted, where M is the stress applied and M u is the carrying capacity of the beam. One can see from the polygons shown in Fig 7 that the exceedance of the yield stress in the reinforcement cast in concrete has a considerable influence on the carrying capacity and the bending stiffness of the beams under investigation.
Another results obtained from the experiments with the beams strengthened by the exterior reinforcement is shown in Fig 10. This figure demonstrates the dependence of the strain in the reinforcement cast in concrete and the exterior reinforcement, ϵ, on the reduced bending stress M/M u . From Fig 10, one can conclude that the strain in both reinforcements is influenced by the stress-strain state available in the member before strengthening.
In Table 1, the bending capacities measured in the experiments just mentioned are compared with the ones calculated by applying the formula (9), which utilises the reduced strength σ s, red , and also the formula (1), which expresses the bending capacity through the design strengths R s . The formula (1) represents one of the methods suggested to date for the prediction of the bending carrying after strengthening of flexural members by exterior reinforcement. The comparison of the experimental results with the ones obtained from formulas (1) and (9) demonstrates that the method represented by the formula (1) has the unconservative difference in bending capacity of 11 %, whereas the proposed method represented by the formula (9) yields a conservative difference of only 2%. The results of experiments may be applied to predict the redistribution of stress in the statically indetermined structures.
First Published Online: 26 Jul 2012
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