STATISTICAL EVALUATION OF THE FLEXURAL MOMENT CAPACITY OF BEAMS REINFORCED WITH FRP AND HYBRID FRP-STEEL REINFORCEMENT
DOI:
https://doi.org/10.30572/2018/KJE/170135Keywords:
Flexural Strength, FRP, Hybrid Reinforcement, Design Equation, Statistical AnalysisAbstract
Fiber reinforced polymer (FRP) bars are more commonly used as alternatives to conventional steel reinforcement because of their non-corrosive characteristics, especially in aggressive environments. Therefore, a large number of researchers have concentrated on studies involving the mechanical behavior of the flexural strength of concrete beams FSCB reinforced by FRP with regard to using FRP bars. In this paper, the flexural moment capacity of concrete beams reinforced with FRP bars and a combination of FRP and steel reinforcement are investigated. The authors carry out a statistical analysis using a database of 144 beam specimens, including 72 reinforced with FRP bars and 72 with hybrid FRP-steel reinforcement. The experimental flexural strength results were compared to theoretically predicted values obtained according to ACI 440.1R-2015, CSA S807-2012, and a hybrid reinforcement equation, in which the three models were analyzed with respect to their prediction accuracy and reliability. Mean, coefficient of variation (COV), standard deviation (SD), Mean Absolute Percentage Error (MAPE), Root-Mean-Square Error (RMSE), Pearson's r, and Nash -Sutcliffe efficiency index are some statistical metrics which were used to better compare the predictive performance of all the equations. The COV of the developed hybrid equations was 15.27 % and SD was 0.16. Contrarily, model ACI 440.1R-2015 presented such COV of 17.5% and SD = 0.17, whereas model CSA S807-2012 showed a COV of 17.11% and an SD = 0.15. It led to a 12% improvement in the prediction of error compared with both ACI 440.1R-2015 and CSA S807-2012, suggesting better precision and uniformity in predicting the bending resistance of reinforced concrete beams. These results highlight the accuracy of the predictive hybrid model, especially in the estimation of the most important parameters such as elastic modulus, FRP, concrete compressive strength, and reinforcement ratios
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References
American Concrete Institute (ACI) 363R-10, A. (2010). Report on High-Strength Concrete (ACI 363R-10), ACI.
American Concrete Institute (ACI) 318R-19 (2019). Building Code Requirements for Structural Concrete ACI 318-19 and Commentary 318R–19, Farmington Hills, MI, USA, American Concrete Institute.
American Concrete Institute (ACI) Committee-440 (2006) Guide for the Design and Construction of Concrete Reinforced with FRP Bars.(ACI) -440.1R-06. Committee Detroit, Michigan, USA DOI: https://doi.org/10.1061/40753(171)158
Abdullah, M. M. (2020). Flexural Behavior of Normal and High Strength Continuous Beams Reinforced by GFRP Bars. AL-Mustansiriayah University. https://doi.org/10.31272/jeasd.25.1.2 DOI: https://doi.org/10.31272/jeasd.25.1.2
Abed, F., Al-Mimar, M. & Ahmed, S. (2021). Performance of BFRP RC beams using high-strength concrete. Composites Part C: Open Access, 4, 100107. https://doi.org/10.1016/j.jcomc.2021.100107 DOI: https://doi.org/10.1016/j.jcomc.2021.100107
Adam, M. A., Said, M., Mahmoud, A. A. & Shanour, A. S. (2015. Analytical and experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars. Construction and building materials, 84, 354-366. https://doi.org/10.1016/j.conbuildmat.2015.03.057 DOI: https://doi.org/10.1016/j.conbuildmat.2015.03.057
Aiello, M. A. & Ombres, L. (2002). Structural performances of concrete beams with hybrid (fiber-reinforced polymer-steel) reinforcements. Journal of Composites for Construction, 6, 133-140. https://doi.org/10.1061/(ASCE)1090-0268(2002)6:2(133) DOI: https://doi.org/10.1061/(ASCE)1090-0268(2002)6:2(133)
Al-turihi, A. A. A. & Al-katib, H. A. A. (2024). Behavior of Hybrid Reinforced Concrete Beams on Flexural Strength. Kufa Journal of Engineering, 15, 27-38. DOI: https://doi.org/10.30572/2018/KJE/150203 DOI: https://doi.org/10.30572/2018/KJE/150203
Al-hawat, M. & Ashour, A. Bond strength between corroded steel reinforcement and recycled aggregate concrete. Structures, (2019). Elsevier, 369-385. https://doi.org/10.1016/j.istruc.2019.02.001 DOI: https://doi.org/10.1016/j.istruc.2019.02.001
Alshadidi, R. M., Hassan, H. F. & Mohammed, M. H. (2016). Shear behavior of high-strength concrete beams reinforced with GFRP bars and strengthened by CFRP sheets. Journal of Engineering and Sustainable Development, 20, 102-117.
Araba, A. M. & Ashour, A. F. (2018). Flexural performance of hybrid GFRP-Steel reinforced concrete continuous beams. Composites Part B: Engineering, 154, 321-336. https://doi.org/10.1016/j.compositesb.2018.08.077 DOI: https://doi.org/10.1016/j.compositesb.2018.08.077
Benmokrane & Masmoudi (1996). Flexural response of concrete beams reinforced with FRP reinforcing bars. Structural Journal, 93, 46-55. DOI: 10.14359/9839 DOI: https://doi.org/10.14359/9839
Bischoff, P. H. (2005). Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber-reinforced polymer bars. Journal of Structural Engineering, 131, 752-767. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(752) DOI: https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(752)
Bischoff, P. H. & Sacanlon, A. (2007). Effective moment of inertia for calculating deflections of concrete members containing steel reinforcement and fiber-reinforced polymer reinforcement. ACI Structural Journal, 104, 68. DOI: https://doi.org/10.14359/18434
Cai, J., Pan, J. & Zhou, X. (2017). Flexural behavior of basalt FRP reinforced ECC and concrete beams. Construction and Building Materials, 142, 423-430. https://doi.org/10.1016/j.conbuildmat.2017.03.087 DOI: https://doi.org/10.1016/j.conbuildmat.2017.03.087
Chaallal, O. & Benmokrane, B. (1996). Fiber-reinforced plastic rebars for concrete applications. Composites Part B: Engineering, 27, 245-252. https://doi.org/10.1016/1359-8368(95)00023-2 DOI: https://doi.org/10.1016/1359-8368(95)00023-2
Dong, H.-L., Zhou, W. & Wang, Z. (2019). Flexural performance of concrete beams reinforced with FRP bars grouted in corrugated sleeves. Composite Structures, 215, 49-59. https://doi.org/10.1016/j.compstruct.2019.02.052 DOI: https://doi.org/10.1016/j.compstruct.2019.02.052
Douglas, D. (2012). An Investigation into the Flexural Behavior of GFRP Reinforced Concrete Beams [MSc thesis]. Canada Univ. Toronto.
El Refai, A., Abed, F. & AL-Rahmani, A. (2015). Structural performance and serviceability of concrete beams reinforced with hybrid (GFRP and steel) bars. Construction and Building Materials, 96, 518-529. https://doi.org/10.1016/j.conbuildmat.2015.08.063 DOI: https://doi.org/10.1016/j.conbuildmat.2015.08.063
EL-Messalami, N., EL Refai, A. & Abed, F. (2019). Fiber-reinforced polymer bars for compression reinforcement: A promising alternative to steel bars. Construction and Building Materials, 209, 725-737. https://doi.org/10.1016/j.conbuildmat.2019.03.105 DOI: https://doi.org/10.1016/j.conbuildmat.2019.03.105
Ftnan, A. H. & Makki, R. F. (2022). Behavior of Recycled Aggregate Concrete Beams Strengthened with FRP. Kufa Journal of Engineering, 13, 13-24. https://doi.org/10.30572/2018/KJE/130402 DOI: https://doi.org/10.30572/2018/KJE/130402
GE, W., Zhang, J., Cao, D. & TU, Y. (2015). Flexural behaviors of hybrid concrete beams reinforced with BFRP bars and steel bars. Construction and Building Materials, 87, 28-37.https://doi.org/10.1016/j.conbuildmat.2015.03.113 DOI: https://doi.org/10.1016/j.conbuildmat.2015.03.113
Grace, N. F., Sayed, G., Soliman, A. & Saleh, K. (1999). Strengthening reinforced concrete beams using fiber-reinforced polymer (FRP) laminates. ACI Structural Journal-American Concrete Institute, 96, 865-874. DOI: https://doi.org/10.14359/741
Gravina, R. J. & Smith, S. T. (2008). Flexural behaviour of indeterminate concrete beams reinforced with FRP bars. Engineering Structures, 30, 2370-2380. https://doi.org/10.1016/j.engstruct.2007.12.019 DOI: https://doi.org/10.1016/j.engstruct.2007.12.019
Habeeb, M. & Ashour, A. F. (2008). Flexural behavior of continuous GFRP reinforced concrete beams. Journal of composites for construction, 12, 115-124. https://doi.org/10.1061/(ASCE)1090-0268(2008)12:2(115) DOI: https://doi.org/10.1061/(ASCE)1090-0268(2008)12:2(115)
Japan Society of Civil Engineers (JSCE),(1997). Recommendation for Design and Construction of Concrete Structures using Continuous Fiber Reinforcing Materials. Concrete Engineering Series. Tokyo, Japan.
Kabashi, N., Avdyli, B., Krasniqi, E. & Kepuska, A. (2020). Comparative approach to flexural behavior of reinforced beams with GFRP, CFRP, and steel bars. Civil Engineering Journal, 6, 50-59. DOI: 10.28991/cej-2020-03091452 DOI: https://doi.org/10.28991/cej-2020-03091452
Kadhim, M. Q. & Hassan, H. F. (2024). Revisiting the Code Design Equations for Concrete Columns Reinforced with GFRP Bars. Journal of Engineering and Sustainable Development, 28, 664-674. https://doi.org/10.31272/jeasd.28.5.12 DOI: https://doi.org/10.31272/jeasd.28.5.12
Kadhima, A. J. & Zinkaaha, O. H. (2024). Flexural behaviour of hybrid (FRP/steel) reinforced concrete beams: a review. Muthanna J. Eng. Technol, 12, 31-42. DOI:10.52113/3/eng/mjet/2024-12-01/31-42 DOI: https://doi.org/10.52113/3/eng/mjet/2024-12-01/31-42
Kara, I. F. & Ashour, A. F. (2012). Flexural performance of FRP reinforced concrete beams. Composite structures, 94, 1616-1625. https://doi.org/10.1016/j.compstruct.2011.12.012 DOI: https://doi.org/10.1016/j.compstruct.2011.12.012
Kara, I. F., Ashour, A. F. & Koroglu, M. A. (2015). Flexural behavior of hybrid FRP/steel reinforced concrete beams. Composite Structures, 129, 111-121. https://doi.org/10.1016/j.compstruct.2015.03.073 DOI: https://doi.org/10.1016/j.compstruct.2015.03.073
Karpiuk, V., Tselikova, A., Khudobych, A., Kostyuk, A. & Karpiuk, I. (2020). Study of strength, deformability property, and crack resistance of beams with BFRP. Восточно-Европейский журнал передовых технологий, 4, 42-53. DOI:10.15587/1729-4061.2020.209378 DOI: https://doi.org/10.15587/1729-4061.2020.209378
Kassem, C., Farghaly, A. S. & Benmokrane, B. (2011). Evaluation of flexural behavior and serviceability performance of concrete beams reinforced with FRP bars. Journal of composites for construction, 15, 682-695. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000216 DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000216
Khalid, N., Shallal, M., Naji H. & Hasson, A. (2025). An Experimental Investigation on Improving the Bond Behavior of Glass Fiber Reinforced Polymer Bars in Concrete. Kufa Journal of Engineering, 16, 81-95. DOI: https://doi.org/10.30572/2018/KJE/160205 DOI: https://doi.org/10.30572/2018/KJE/160205
Lapko, A. & Urbanski, M. (2015). Experimental and theoretical analysis of deflections of concrete beams reinforced with basalt rebar. Archives of Civil and Mechanical Engineering, 15, 223-230. https://doi.org/10.1016/j.acme.2014.03.008 DOI: https://doi.org/10.1016/j.acme.2014.03.008
Lau, D. & Pam, H. J. (2010). Experimental study of hybrid FRP reinforced concrete beams. Engineering Structures, 32, 3857-3865.https://doi.org/10.1016/j.engstruct.2010.08.028 DOI: https://doi.org/10.1016/j.engstruct.2010.08.028
Leung, H. & Balendran, R. (2003). Flexural behaviour of concrete beams internally reinforced with GFRP rods and steel rebars. Structural Survey, 21, 146-157.https://doi.org/10.1108/02630800310507159 DOI: https://doi.org/10.1108/02630800310507159
Lu, C., Li, H., Xu, K., Xuan, G. & Abdullah, W.(2020) Experimental study of flexural behavior and serviceability of hybrid concrete beams reinforced by steel and G/BFRP bars. IOP Conference Series: Materials Science and Engineering, . IOP Publishing, 012007. https://doi.org/10.1088/1757-899X/770/1/012007 DOI: https://doi.org/10.1088/1757-899X/770/1/012007
Nanni, A., De Luca, A. & Zadeh, H. (2014). Reinforced concrete with FRP bars. Reinforced Concrete with FRP Bars. CRC Press, London, United Kingdom. doi, 10, b16669. DOI: https://doi.org/10.1201/b16669
Nguyen, P. D., Dang, V. H. & Vu, N. A. (2020). Performance of concrete beams reinforced with various ratios of hybrid GFRP/steel bars. Civil Engineering Journal, 6, 1652-1669.http://dx.doi.org/10.28.991/cej-2020-03091572 DOI: https://doi.org/10.28991/cej-2020-03091572
Pang, L., Qu, W., Zhu, P. & Xu, J. (2016). Design propositions for hybrid FRP-steel reinforced concrete beams. Journal of Composites for Construction, 20, 04015086. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000654 DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000654
Pawlowski, D. & SZUMIGAŁA, M.(2015). Flexural behaviour of full-scale basalt FRP RC beams–experimental and numerical studies. Procedia engineering, 108, 518-525. https://doi.org/10.1016/j.proeng.2015.06.114 DOI: https://doi.org/10.1016/j.proeng.2015.06.114
Qin, R., Zhou, A. & Lau, D. (2017). Effect of reinforcement ratio on the flexural performance of hybrid FRP reinforced concrete beams. Composites Part B: Engineering, 108, 200-209. https://doi.org/10.1016/j.compositesb.2016.09.054 DOI: https://doi.org/10.1016/j.compositesb.2016.09.054
Qu, W., Zhang, X. & Huang, H. (2009). Flexural behavior of concrete beams reinforced with hybrid (GFRP and steel) bars. Journal of Composites for Construction, 13, 350-359. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000035 DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000035
Sam, A. R. M. & Swamy , R. N. (2005). Flexural behaviour of concrete beams reinforced with glass fibre reinforced polymer bars. Malaysian Journal of Civil Engineering, 17. DOI: https://doi.org/10.11113/mjce.v17.15672 DOI: https://doi.org/10.11113/mjce.v17.15672
Sun, Z., Fu, L., Feng, D.-C., Vatuloka, A. R., Wei, Y. & Wu, G. (2019). Experimental study on the flexural behavior of concrete beams reinforced with bundled hybrid steel/FRP bars.Engineering,Structures,197,109443.https://doi.org/10.1016/j.engstruct.2019.109443 DOI: https://doi.org/10.1016/j.engstruct.2019.109443
Theriault, M. & Benmokrane, B. (1998). Effects of FRP reinforcement ratio and concrete strength on flexural behavior of concrete beams. Journal of composites for construction, 2, 7-16. doi/abs/10.1061/(ASCE)1090-0268(1998)2:1(7) DOI: https://doi.org/10.1061/(ASCE)1090-0268(1998)2:1(7)
Tomlinson, D. & Fam, A. (2015). Performance of concrete beams reinforced with basalt FRP for flexure and shear. Journal of composites for construction, 19, 04014036. doi/abs/10.1061/(ASCE)CC.1943-5614.0000491 DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000491
Vu, H. D. & Phan, D. N. (2021). Experimental and theoretical analysis of the cracking moment of concrete beams reinforced with hybrid fiber-reinforced polymer and steel rebars. Advances in Technology Innovation, 6, 222.doi.org/10.46604/aiti.2021.7330 DOI: https://doi.org/10.46604/aiti.2021.7330
Xue, W., Peng, F. & Zheng, Q. (2016). Design equations for the flexural capacity of concrete beams reinforced with glass fiber–reinforced polymer bars. Journal of Composites for Construction, 20, 04015069. doi/abs/10.1061/(ASCE)CC.1943-5614.0000630 DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000630
Yang, Y., Sun, Z.-Y., Wu, G., Cao, D.-F. & Zhang, Z.-Q. (2020). Flexural capacity and design of hybrid FRP-steel-reinforced concrete beams. Advances in Structural Engineering, 23, 1290-1304. doi/abs/10.1177/1369433219894236 DOI: https://doi.org/10.1177/1369433219894236
Yoon, Y.-S., Yang, J.-M., Min, K.-H. & Shin, H.-O. (2011). Flexural strength and deflection characteristics of high-strength concrete beams with hybrid FRP and steel bar reinforcement. Special Publication, 275, 1-22.
Zinkaah, O. H., Ashour, A. & Sheehan, T. (2019). Experimental tests of two-span continuous concrete deep beams reinforced with GFRP bars and strut-and-tie method evaluation. Composite Structures, 216, 112-126. https://doi.org/10.1016/j.compstruct.2019.02.078 DOI: https://doi.org/10.1016/j.compstruct.2019.02.078
American Concrete Institute ACI-440.1R-15 (2015). Guide for the design and construction of structural concrete reinforced with FRP bars. American Concrete Institute
Canadian Standareds Association CAN/CSA-S806-12 (2012). Design and Construction of Building Structures with Fiber Reinforced Polymers (CAN/CSA), Rexdale, ON, Canada, Canadian Standards Association.
Canadian Standareds Association CAN/CSA-S6-14 (2014). Canadian highway bridge design code. CAN/CSA-S6-14.
American Concrete Institute (ACI) 440.11-22, A. (2022). Building Code Requirements for Structural Concrete Reinforced with Glass Fiber-Reinforced Polymer (GFRP) Bars – Code and Commentary, American Concrete Institute.
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