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A Comprehensive Formula to Predict the Shear Contribution of FRP Sheets in Strengthened Reinforced Concrete Deep Beams

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Abstract

Retrofitting of reinforced concrete beams using fiber-reinforced polymer (FRP) sheets is one of the most commonly used methods to enhance shear and bending behavior. A comprehensive review shows that the presented formulas are insufficiently accurate to predict the shear contribution of FRP sheets. Researchers have also studied only 45° and 90° for the FRP sheets in previous research. This paper presents a comprehensive formula for evaluating the shear contribution of full- and U-wrap FRP sheets. For this purpose, experimental data are collected for angles of 45° and 90°. Then, two experimental tests are modeled using ABAQUS software. After verifying the models, the shear contribution of FRP sheets is determined for different values of the input parameters and at the angles of 30°, 60° and 75°. Therefore, to present a formula for evaluating the shear contribution of FRP sheets, multigene genetic programming is used. The results show that the presented formula has sufficient accuracy in computing the shear contribution of FRP sheets at angles of 30°, 45°, 60°, 75° and 90° in comparison with other existing formulas from codes and literature. The effect of width, thickness, the ultimate strain of FRP, effective depth of FRP, beam shear span length, the effective depth of the concrete beam, spacing between the FRP strips, compressive strengths, angle of FRP sheets, and elasticity modulus of FRP sheets is considered on computing the shear contribution of FRP sheets. The results show that the mean absolute percentage error (MAPE), root mean square error (RMSE), and R2 for the proposed formulas are 12.48, 9.84 and 0.98, respectively, which performs better than the other existing methods.

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Data availability

All data and material that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

All codes that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors would like to show their appreciation to the HPC center (Shahr-e-Kord University, Iran) for their collaboration in offering computational clusters, which was a great help in completing this work.

Funding

This study has not been funded.

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Authors and Affiliations

  1. Master of Science Student, Shahrekord University, Shahrekord, Iran

    Mehdi Omidi

  2. Faculty of Civil Engineering, Shahrekord University, Shahrekord, Iran

    Reza Kamgar & Ali Reza Jahangiri

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  1. Mehdi Omidi
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  2. Reza Kamgar
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  3. Ali Reza Jahangiri
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Contributions

Conceptualization, RK, MO and ARJ; methodology, RK, MO; software, RK, MO; validation, RK, MO and ARJ; formal analysis, RK, MO and ARJ; investigation, RK, MO and ARJ; writing—original draft preparation, RK and MO; writing—review and editing, RK and ARJ.

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Correspondence to Reza Kamgar.

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This article does not contain any studies with animal/human participants performed by any of the authors.

Appendix 1

Appendix 1

The collected and computed data (from the literature and ABAQUS software, respectively) for training and testing are indicated in Table 10. The testing data are marked with an asterisk (*).

Table 10 Collected data for training and testing
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Omidi, M., Kamgar, R. & Jahangiri, A. A Comprehensive Formula to Predict the Shear Contribution of FRP Sheets in Strengthened Reinforced Concrete Deep Beams. Iran J Sci Technol Trans Civ Eng 47, 2731–2751 (2023). https://doi.org/10.1007/s40996-023-01118-6

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