Flexural Capacity Prediction for Reinforced Concrete Beams by Group Method of Data Handling Approach

Document Type : Original Article


1 Dept. of Civil Engineering, University of Birmingham, UK

2 University of Wollongong, New South Wales, Australia


Application of group method of data handling (GMDH) to predict the capacity of reinforced concrete beams strengthened with CFRP laminate has been investigated in this paper. The proposed model considers nine parameters including concrete compressive strength, width of beam, effective depth, area of tension reinforcement, area of compression reinforcement, yield strength of steel, modulus of elasticity of steel, width of CFRP sheet, length of CFRP sheet. There are fourteen second order polynomials in three middle layers and an output layer. The coefficients of these polynomials are determined based on a collection of experimental laboratory tests, which were collected from the literature. In addition, 66 datasets were used to estimate unknown coefficients of the polynomials. To validate the model, 17 datasets were considered from the collected database. The results of the proposed GMDH showed that it can use as a predictive model for determining the ultimate flexural capacity of reinforced concrete beams strengthened with CFRP laminates.


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[1]      Qu HC, Wu CQ, Chen LL. Numerical Analysis on the Load-Carrying Capacity for the FRP Reinforced Four-Point Bending Concrete Beam. Adv Mater Res 2011;287–290:1130–4. doi:10.4028/www.scientific.net/AMR.287-290.1130.
[2]      Xu X. Calculation Method and Analysis of Bearing Capacity of FRP Rebar Concrete Beam. ICTE 2011, Reston, VA: American Society of Civil Engineers; 2011, p. 1572–7. doi:10.1061/41184(419)260.
[3]      Kheyroddin A, Mirrashid M, Arshadi H. An Investigation on the Behavior of Concrete Cores in Suspended Tall Buildings. Iran J Sci Technol Trans Civ Eng 2017;41:383–8. doi:10.1007/s40996-017-0075-y.
[4]      Penelis GG, Penelis GG. Concrete Buildings in Seismic Regions. 2nd Ed. | Boca Raton : Taylor & Francis, CRC Press, 2018.: CRC Press; 2018. doi:10.1201/b22364.
[5]      Jafari M, Mirrashid M, Vahidnia A. Prediction of chloride penetration in the concrete containing magnetite aggregates by Adaptive Neural Fuzzy Inference System (ANFIS). 7th Internatinal Symp. Adv Sci Technol(5thsastech), Bandare Abbas, Iran 2013.
[6]      Mirrashid M. Earthquake magnitude prediction by adaptive neuro-fuzzy inference system (ANFIS) based on fuzzy C-means algorithm. Nat Hazards 2014;74:1577–93. doi:10.1007/s11069-014-1264-7.
[7]      Naderpour H, Mirrashid M. Shear Strength Prediction of RC Beams Using Adaptive Neuro-Fuzzy Inference System. Sci Iran 2018:0–0. doi:10.24200/sci.2018.50308.1624.
[8]      Naderpour H, Mirrashid M. An innovative approach for compressive strength estimation of mortars having calcium inosilicate minerals. J Build Eng 2018;19:205–15. doi:10.1016/j.jobe.2018.05.012.
[9]      Naderpour H, Rafiean AH, Fakharian P. Compressive strength prediction of environmentally friendly concrete using artificial neural networks. J Build Eng 2018;16:213–9. doi:10.1016/j.jobe.2018.01.007.
[10]    Naderpour H, Vahdani R, Mirrashid M. Soft Computing Research in Structural Control by Mass Damper (A review paper). 4st Int. Conf. Struct. Eng. Tehran, Iran, 2018.
[11]     Mirrashid M. Comparison study of soft computing approaches for estimation of the non-ductile RC joint shear strength. Soft Comput Civ Eng 2017;1:12–28.
[12]    Mirrashid M, Bigdeli S. Genetic Algorithm for Prediction the Compressive Strength of Mortar Containing Wollastonite. 1st Natl. Congr. Counstruction Eng. Proj. Assessment, Gorgan, Iran, 2014.
[13]    Mirrashid M, Givehchi M, Miri M, Madandoust R. Performance investigation of neuro-fuzzy system for earthquake prediction 2016.
[14]    Mirrashid M, Jafari M, Akhlaghi A, Vahidnia A. Prediction of compressive strength of concrete containing magnetite aggregates using Adaptive Neural Fuzzy Inference System (ANFIS) 2013.
[15]    Naderpour H, Mirrashid M. Application of soft computing to reinforced concrete beams strengthened with fibre reinforced polymers: a state-of-the-art review. Comput Tech Civ Struct Eng 2015;38:305–23.
[16]    Naderpour H, Mirrashid M. Compressive Strength of Mortars Admixed with Wollastonite and Microsilica. Mater Sci Forum 2017;890:415–8. doi:10.4028/www.scientific.net/MSF.890.415.
[17]    Naderpour H, Mirrashid M. Ultimate Capacity Prediction of Concrete Slabs Reinforced with FRP Bars. 3rd Int. 7th Natl. Conf. Mod. Mater. Struct. Civ. Eng. Bu-Ali Sina Univ. Hamedan, IRAN, 2018.
[18]    Naderpour H, Mirrashid M. Application of group method of data handling to Estimate the Shear Strength of RC Beams Reinforced with FRP Bars. 3rd Int. 7th Natl. Conf. Mod. Mater. Struct. Civ. Eng. Bu-Ali Sina Univ. Hamedan, IRAN, 2018.
[19]    Ivakhnenko AG. Polynomial Theory of Complex Systems. IEEE Trans Syst Man Cybern 1971;SMC-1:364–78. doi:10.1109/TSMC.1971.4308320.
[20]    HAJELA P, BERKE L. Neurobiological Computational Models in Structural Analysis and Design. 31st Struct. Struct. Dyn. Mater. Conf., Reston, Virigina: American Institute of Aeronautics and Astronautics; 1990. doi:10.2514/6.1990-1133.
[21]    Saadatmanesh H, Ehsani MR. RC Beams Strengthened with GFRP Plates. I: Experimental Study. J Struct Eng 1991;117:3417–33. doi:10.1061/(ASCE)0733-9445(1991)117:11(3417).
[22]    Ross CA, Jerome DM, Tedesco JW, Hughes ML. Strengthening of reinforced concrete beams with externally bonded composite laminates. Struct J 1999;96:212–20.
[23]    Ni H-G, Wang J-Z. Prediction of compressive strength of concrete by neural networks. Cem Concr Res 2000;30:1245–50. doi:10.1016/S0008-8846(00)00345-8.
[24]    Béton. F. I.Du. Externally bonded FRP reinforcement for RC structures, Bulletin FIB 2001;14:138.
[25]    Sanad A, Saka MP. Prediction of Ultimate Shear Strength of Reinforced-Concrete Deep Beams Using Neural Networks. J Struct Eng 2001;127:818–28. doi:10.1061/(ASCE)0733-9445(2001)127:7(818).
[26]    Dong Y, Zhao M, Ansari F. Failure characteristics of reinforced concrete beams repaired with CFRP composites. Strain 2002;304:12–7.
[27]    Dai JG, Ueda T, Sato Y, Ito T. Flexural strengthening of RC beams using externally bonded FRP sheets through flexible adhesive bonding. Int. Symp. Bond Behav. FRP Struct. (BBFS 2005), Hong Kong, 2005, p. 7–9.
[28]    Ebead UA, Marzouk H. Tension-stiffening model for FRP-strenghened RC concrete two-way slabs. Mater Struct 2005;38:193–200. doi:10.1007/BF02479344.
[29]    Kotynia R. Debonding failures of RC beams strengthened with externally bonded strips. Proc. Int. Symp. Bond Behav. FRP Struct. (BBFS 2005), 2005.
[30]    Lundqvist J, Nordin H, Täljsten B, Olofsson T. Numerical analysis of concrete beams strengthened with CFRP: a study of anchorage lengths. Int. Symp. Bond Behav. FRP Struct. 07/12/2005-09/12/2005, International Institute for FRP in Construction; 2005, p. 239–46.
[31]    Maalej M, Leong KS. Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRP-strengthened beams. Compos Sci Technol 2005;65:1148–58. doi:10.1016/j.compscitech.2004.11.010.
[32]    Coronado CA, Lopez MM. Sensitivity analysis of reinforced concrete beams strengthened with FRP laminates. Cem Concr Compos 2006;28:102–14. doi:10.1016/j.cemconcomp.2005.07.005.
[33]    Reeve BZ. Effect of adhesive stiffness and CFRP geometry on the behavior of externally bonded CFRP retrofit measures subject to monotonic loads 2006.
[34]    Abdalla JA, Elsanosi A, Abdelwahab A. Modeling and simulation of shear resistance of R/C beams using artificial neural network. J Franklin Inst 2007;344:741–56. doi:10.1016/j.jfranklin.2005.12.005.
[35]    Esfahani MR, Kianoush MR, Tajari AR. Flexural behaviour of reinforced concrete beams strengthened by CFRP sheets. Eng Struct 2007;29:2428–44. doi:10.1016/j.engstruct.2006.12.008.
[36]    Neagoe CA. Concrete beams reinforced with CFRP laminates 2011.