Journal of Mechanical Science and Technology

, Volume 24, Issue 6, pp 1273–1278 | Cite as

Formulation of elastic modulus of concrete using linear genetic programming

  • Amir Hossein GandomiEmail author
  • Amir Hossein Alavi
  • Mohammad Ghasem Sahab
  • Parvin Arjmandi


This paper proposes a novel approach for the formulation of elastic modulus of both normal-strength concrete (NSC) and high-strength concrete (HSC) using a variant of genetic programming (GP), namely linear genetic programming (LGP). LGP-based models relate the modulus of elasticity of NSC and HSC to the compressive strength, as similarly presented in several codes of practice. The models are developed based on experimental results collected from the literature. A subsequent parametric analysis is further carried out to evaluate the sensitivity of the elastic modulus to the compressive strength variations. The results demonstrate that the proposed formulas can predict the elastic modulus with an acceptable degree of accuracy. The LGP results are found to be more accurate than those obtained using the buildings codes and various solutions reported in the literature. The LGP-based formulas are quite simple and straightforward and can be used reliably for routine design practice.


Tangent elastic modulus Linear genetic programming Compressive strength Normal and high strength concrete Formulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Khan et al., Early age compressive stress-strain properties of low, medium and high strength concretes, ACI Mater. J., 92(6) (1995) 617–624.Google Scholar
  2. [2]
    H. Mesbah et al., Determination of elastic properties of high-performance concrete at early age, ACI Mater. J., 99(1) (2002) 37–41.Google Scholar
  3. [3]
    A. D. McNaught and A. Wilkinson, Compendium of Chemical Terminology, (2nd Ed.), IUPAC, Blackwell Scientific Publications, Oxford, (1997).Google Scholar
  4. [4]
    A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, (5th Ed.), John Wiley & Sons, (1997).Google Scholar
  5. [5]
    P. M. Ferguson et al., Reinforced Concrete Fundamentals, (5th Ed.), John Wiley & Sons, (1988).Google Scholar
  6. [6]
    ASTM C 469. Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression, Annual Book of ASTM standards, (1994).Google Scholar
  7. [7]
    F. Demir, A new way of prediction elastic modulus of normal and high strength concrete-fuzzy logic, Cem. Conc. Res. 35(8) (2005) 1531–1538.CrossRefGoogle Scholar
  8. [8]
    F. Demir, Prediction of elastic modulus of normal and high strength concrete by artificial neural networks, Constr. Build. Mater., 22(7) (2008) 1428–1435.CrossRefGoogle Scholar
  9. [9]
    J. R. Koza, Genetic Programming: On the Programming of Computers by means of Natural Selection, MIT Press, Cambridge (MA), (1992).zbMATHGoogle Scholar
  10. [10]
    W. Banzhaf et al., Genetic Programming — An Introduction. On the Automatic Evolution of Computer Programs and its Application, dpunkt/Morgan Kaufmann, Heidelberg/San Francisco, (1998).Google Scholar
  11. [11]
    A. H. Alavi et al., Multi Expression Programming: A New Approach to Formulation of Soil Classification, Eng. Comput., 26 (2010) 111–118.CrossRefGoogle Scholar
  12. [12]
    M. Brameier and W. Banzhaf, Linear Genetic Programming, Springer Science+Business Media, New York, (2007).zbMATHGoogle Scholar
  13. [13]
    M. Oltean and C. Grosan, A comparison of several linear genetic programming techniques, Adv. Complex Syst., 14(4) (2003) 1–29.MathSciNetGoogle Scholar
  14. [14]
    A. H. Gandomi et al., New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming, Mater. Struct. (2010) in press.Google Scholar
  15. [15]
    A. H. Alavi and A. H. Gandomi, Energy-based numerical correlations for soil liquefaction assessment, Comput. Geotech. (2010) in press.Google Scholar
  16. [16]
    NBS, Analysis and Design of Reinforced Concrete Buildings, National Building Standard, Part 9, Iran, (2006).Google Scholar
  17. [17]
    ACI 318-95, Building Code Requirements for Structural Concrete, ACI Manual of Concrete Practice Part 3: Use of concrete in Buildings -Design, Specifications, and Related Topics. Detroit, Michigan, (1996).Google Scholar
  18. [18]
    L. J. Parrott, A Literature Review of High Strength Concrete Properties, British Cement Association, ISBN 0 7210 13724, (1988).Google Scholar
  19. [19]
    CSA A23.3-94, Design of Concrete Structures, Canadian Standard Association, Rexdale, Ontario, Canada, (1995).Google Scholar
  20. [20]
    NS 3473, Norwegian Council for Building Standardization, Concrete Structures Design Rules, Stockholm, (1992).Google Scholar
  21. [21]
    TS 500, Requirements for Design and Construction of Reinforced Concrete Structures, Turkish Standardization Institute, Ankara, (2000).Google Scholar
  22. [22]
    T. H. Wee et al., Stress-strain relationship of high strength concrete in compression, J. Mater. Civ. Eng., 8(2) (1994) 70–76.CrossRefGoogle Scholar
  23. [23]
    D. Mostofinejad and M. Nozhati, Prediction of the modulus of elasticity of high strength concrete, Iranian J. Sci. Tech., Trans. B Eng., 2005 29(B3) 85–99.Google Scholar
  24. [24]
    T. Ozturan, An Investigation of Concrete Abrasion as Two Phase Material, Thesis (PhD), Istanbul, Faculty of Civil Engineering, Istanbul Technical University (in Turkish), (1984).Google Scholar
  25. [25]
    M. Gesoglu et al., Effects of end conditions on compressive strength and static elastic modulus of very high strength concrete, Cem. Conc. Res., 32(10) (2002) 1545–1550.CrossRefGoogle Scholar
  26. [26]
    M. J. Shannag, High strength concrete containing natural pozzolan and silica fume, Cem. Conc. Comp., 22(8) (2000) 399–406.CrossRefGoogle Scholar
  27. [27]
    M. Turan, Iren M. Strain stress relationship of concrete, J. Eng. Arch., 12(1) (1997) 76–81.Google Scholar
  28. [28]
    A. H. Gandomi et al., Discussion on Genetic programming for retrieving missing information in wave records along the west coast of India, Appl. Oce. Res., 30 (2008) 338–339.CrossRefGoogle Scholar
  29. [29]
    M. Conrads et al., Discipulus-Fast Genetic Programming Based on AIM Learning Technology, Register Machine Learning Technologies Inc., Littleton, CO., (2004).Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Amir Hossein Gandomi
    • 1
    Email author
  • Amir Hossein Alavi
    • 2
  • Mohammad Ghasem Sahab
    • 1
  • Parvin Arjmandi
    • 1
  1. 1.Structural Health Monitoring Research Group, College of Civil EngineeringTafresh UniversityTafreshIran
  2. 2.College of Civil EngineeringIran University of Science & TechnologyNarmakTehran, Iran

Personalised recommendations