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A theoretical model to predict interface slip due to bending

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Abstract

Casting a new concrete layer on the tensile or compressive side of a reinforced concrete element is a common technique that is used to increase the flexural capacity of weak reinforced concrete elements. Until now however, a model has not been presented in the literature to evaluate the slip between the two components. Usually, in common practical design, slip is ignored and the strengthened element is assumed monolithic. This may not be a conservative assumption, as any slip would affect the ultimate resistance of the strengthened element. In the present paper, an analytical procedure is presented that predicts the distribution of slip strain, slip and shear stress along a reinforced or unreinforced interface between an initial beam and a new concrete layer. By following this process, the capacity of a strengthened beam is determined by taken slip into account. In addition, a step-by-step design procedure is presented and then applied to an experimental result. Good agreement if found. Further verification of the analytical procedure is performed by comparison with finite element analysis and very good agreement is found.

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Acknowledgments

The authors would like to thank Dr V. J. Moseley for his significant assistance during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Patras, 265 00, Patras, Greece

    O. T. Tsioulou & S. E. Dritsos

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  1. O. T. Tsioulou
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  2. S. E. Dritsos
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Correspondence to S. E. Dritsos.

Appendix 1

Appendix 1

1.1 Approximation of the interface shear stress distribution

In the absence of any experimental verification, several numerical analyses using ATENA finite element software [4] have been performed in order to define the type of shear stress distribution function along the interface. It was found that the shear stress distribution along the interface can be assumed as a cubic function of distance x. In the following, results of one of these analyses are presented.

A simply supported concrete beam strengthened with a new concrete layer on the tensile side (Fig. 18), has been analysed using [4] software. Details concerning ATENA modelling are presented in Sect. 7.2 above. Specific contact elements were used in this analysis to simulate the interface behaviour, with specific values for the coefficients of friction and adhesion.

Fig. 18
figure 18

Geometry and load condition for the beam strengthened with concrete layer on the tensile side

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The cross sectional dimensions of the initial beam were 250 mm by 400 mm and the span length was 5,000 mm. The longitudinal tensile reinforcement was four 12 mm diameter steel bars of 500 MPa yield strength and the concrete cover was 40 mm. The thickness of the additional layer was 100 mm and the additional reinforcement was two 14 mm diameter steel bars of 500 MPa yield strength, also with a concrete cover of 40 mm. The concrete strength of the beam was considered to equal 16.0 MPa, a common value for old structures that need strengthening. A concentrated load was applied at mid span.

Two specimens, S1 and S2, were examined. The differences between S1 and S2 were in the concrete strength of the additional layer and in the interface conditions. For specimen S1, the strengthening layer concrete strength was 16.0 MPa and μ and c at the interface were 0.5 and 0.5 MPa respectively. For specimen S2, strengthening layer concrete strength was 25.0 MPa and μ and c at the interface were 1.0 and 1.0 MPa respectively.

Taking into account the slip distribution derived from ATENA analysis and using Eq. 1a from above, the shear stress distribution along the interface of the strengthened beam was obtained, as shown in Fig. 19, together with the fitted curve described by the following equation:

Fig. 19
figure 19

Shear stress distribution along the interface of the strengthened beam

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$$ \tau_{x} = {\text{A}}1 \cdot x^{3} + {\text{B}}1 $$
(43)

where A1 = −0.043 and B1 = 0.67 for specimen S1, and A1 = −0,042 and B1 = 0.66 for specimen S2.

Therefore, in the present study, to initially start with, the interface shear stress distribution according to the general form of Eq. 43 was adopted.

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Tsioulou, O.T., Dritsos, S.E. A theoretical model to predict interface slip due to bending. Mater Struct 44, 825–843 (2011). https://doi.org/10.1617/s11527-010-9669-6

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