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An evolutionary approach for modeling of shear strength of RC deep beams

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Abstract

In this study, a new variant of genetic programming, namely gene expression programming (GEP) is utilized to predict the shear strength of reinforced concrete (RC) deep beams. A constitutive relationship was obtained correlating the ultimate load with seven mechanical and geometrical parameters. The model was developed using 214 experimental test results obtained from previously published papers. A comparative study was conducted between the results obtained by the proposed model and those of the American Concrete Institute (ACI) and Canadian Standard Association (CSA) models, as well as an Artificial Neural Network (ANN)-based model. A subsequent parametric analysis was carried out and the trends of the results were confirmed via some previous laboratory studies. The results indicate that the GEP model gives precise estimations of the shear strength of RC deep beams. The prediction performance of the model is significantly better than the ACI and CSA models and has a very good agreement with the ANN results. The derived design equation provides a valuable analysis tool accessible to practicing engineers.

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References

  1. Kong FK (2002) Reinforced concrete deep beams. Taylor & Francis, New York

    Google Scholar 

  2. Raju NK (2005) Advanced reinforced concrete design. CBS Publishers & Distributors, New Delhi

    Google Scholar 

  3. Tang CY, Tan KH (2004) Interactive mechanical model for shear strength of deep beams. J Struct Eng 130(10):1534–1544

    Article  Google Scholar 

  4. Mau ST, Hsu TTC (1989) A formula for the shear strength of deep beams. ACI Struct J 86(5):516–523

    Google Scholar 

  5. Averbuch D, de Buhan P (1999) Shear design of reinforced concrete deep beams: a numerical approach. J Struct Eng 125(3):309–318

    Article  Google Scholar 

  6. Matamoros AB, Wong KH (2003) Design of simply supported deep beams using strut-and-tie models. ACI Struct J 100(6):704–712

    Google Scholar 

  7. Park JW, Kuchma D (2007) Strut-and-tie model analysis for strength prediction of deep beams. ACI Struct J 104(6):657–666

    Google Scholar 

  8. Yang KH, Ashour AF (2011) Strut-and-tie model based on crack band theory for deep beams. J Struct Eng 137(10):1030–1038

    Article  Google Scholar 

  9. Oreta AWC (2004) Simulating size effect on shear strength of RC beams without stirrups using neural networks. Eng Struct 26(5):681–691

    Article  Google Scholar 

  10. Tang CW (2006) Using radial basis function neural networks to model torsional strength of reinforced concrete beams. Comput Concr 3(5):335–355

    Article  Google Scholar 

  11. Elbahy YI, Nehdi M, Youssef MA (2010) Artificial neural network model for deflection analysis of superelastic shape memory alloy reinforced concrete beams. Can J Civil Eng 37(6):855–865

    Article  Google Scholar 

  12. Goh ATC (1995) Prediction of ultimate shear-strength of deep beams using neural networks. ACI Struct J 92(1):28–32

    MathSciNet  Google Scholar 

  13. Sanad A, Saka MP (2001) Prediction of ultimate shear strength of reinforced-concrete deep beams using neural networks. J Struct Eng 127(7):818–828

    Article  Google Scholar 

  14. Yang KH et al (2008) Neural network modelling for shear strength of reinforced concrete deep beams. Struct Build 161(1):29–39

    Article  Google Scholar 

  15. Pal M, Deswal S (2011) Support vector regression based shear strength modelling of deep beams. Comput Struct 89(13–14):1430–1439

    Article  Google Scholar 

  16. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge

    MATH  Google Scholar 

  17. Ashour AF, Alvarez LF, Toropov VV (2003) Empirical modelling of shear strength of RC deep beams by genetic programming. Comput Struct 81(5):331–338

    Article  Google Scholar 

  18. Gandomi AH, Alavi AH, Yun GJ (2011) Nonlinear modeling of shear strength of SFRC beams using linear genetic programming. Struct Eng Mech 38(1):1–25

    Article  Google Scholar 

  19. Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst 13(2):87–129

    MATH  Google Scholar 

  20. Gandomi AH et al (2011) A new prediction model for the load capacity of castellated steel beams. J Constr Steel Res 67(7):1096–1105

    Article  Google Scholar 

  21. Gesoglu M et al (2010) Modeling the mechanical properties of rubberized concretes by neural network and genetic programming. Mater Struct 43(1–2):31–45

    Article  Google Scholar 

  22. Gandomi AH et al (2011) Nonlinear genetic-based models for prediction of flow number of asphalt mixtures. J Mater Civil Eng 23(3):248–263

    Article  Google Scholar 

  23. Gandomi AH, Alavi AH (2013) Expression programming techniques for formulation of structural engineering systems. In: Gandomi AH et al (eds) Metaheuristic applications in structures and infrastructures. Elsevier, Waltham

    Google Scholar 

  24. Alavi AH, Gandomi AH (2011) A robust data mining approach for formulation of geotechnical engineering systems. Eng Comput 28(3–4):242–274

    Article  Google Scholar 

  25. Ferreira C (2006) Gene expression programming: mathematical modeling by an artificial intelligence, 2nd edn. Springer, Germany

    Google Scholar 

  26. GEPSOFT (2006) GeneXpro tools. GEPSOFT, Bristol

    Google Scholar 

  27. Gandomi AH et al (2012) A novel approach to strength modeling of concrete under triaxial compression. J Mater Civil Eng 24(9):1132–1143

    Article  Google Scholar 

  28. Zararis PD (2003) Shear compression failure in reinforced concrete deep beams. J Struct Eng 129(4):544–553

    Article  Google Scholar 

  29. Aguilar G et al (2002) Experimental evaluation of design procedures for shear strength of deep reinforced concrete beams. ACI Struct J 99(4):539–548

    Google Scholar 

  30. Anderson NS, Ramirez JA (1989) Detailing of stirrup reinforcement. ACI Struct J 86(5):507–515

    Google Scholar 

  31. Clark AP (1951) Diagonal tension in reinforced concrete beams. ACI J 48(10):145–156

    Google Scholar 

  32. Kong FK, Robins PJ, Cole DF (1970) Web reinforcement effects on deep beams. ACI J 67(12):1010–1017

    Google Scholar 

  33. Oh JK, Shin SW (2001) Shear strength of reinforced high-strength concrete deep beams. ACI Struct J 98(2):164–173

    MathSciNet  Google Scholar 

  34. Quintero-Febres CG, Parra-Montesinos G, Wight JK (2006) Strength of struts in deep concrete members designed using strut-and-tie method. ACI Struct J 103(4):577–586

    Google Scholar 

  35. Smith KN, Vantsiotis AS (1982) Shear-strength of deep beams. J Am Concr Inst 79(3):201–213

    Google Scholar 

  36. Tan KH et al (1995) High-strength concrete deep beams with effective span and shear span variations. ACI Struct J 92(4):395–405

    Google Scholar 

  37. Baykasoglu A et al (2008) Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst Appl 35(1–2):111–123

    Article  Google Scholar 

  38. Smith GN (1986) Probability and statistics in civil engineering. Collins, London

    Google Scholar 

  39. Frank IE, Todeschini R (1994) The data analysis handbook. Elsevier, Amsterdam

    Google Scholar 

  40. Golbraikh A, Tropsha A (2002) Beware of q(2)! J Mol Graph Model 20(4):269–276

    Article  Google Scholar 

  41. Roy PP, Roy K (2008) On some aspects of variable selection for partial least squares regression models. QSAR Comb Sci 27(3):302–313

    Article  Google Scholar 

  42. Kuo YL et al (2009) ANN-based model for predicting the bearing capacity of strip footing on multi-layered cohesive soil. Comput Geotech 36(3):503–516

    Article  Google Scholar 

  43. Tan KH, Cheng GH (2006) Size effect on shear strength of deep beams: investigating with strut-and-tie model. J Struct Eng 132(5):673–685

    Article  Google Scholar 

  44. Ashour AF (2000) Shear capacity of reinforced concrete deep beams. J Struct Eng 126(9):1045–1052

    Article  Google Scholar 

  45. ACI (2005) Committee 318, building code requirements for structural concrete (ACI 318–05) and commentary (318R–05). American Concrete Institute, Farmington Hills

    Google Scholar 

  46. CSA (1994) A23.3, C.C. design of concrete structures: structures (design)—a national standard of Canada. Canadian Standards Association, Toronto

    Google Scholar 

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Correspondence to Gun Jin Yun.

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Gandomi, A.H., Yun, G.J. & Alavi, A.H. An evolutionary approach for modeling of shear strength of RC deep beams. Mater Struct 46, 2109–2119 (2013). https://doi.org/10.1617/s11527-013-0039-z

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