Abstract
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.
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References
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.
H. Mesbah et al., Determination of elastic properties of high-performance concrete at early age, ACI Mater. J., 99(1) (2002) 37–41.
A. D. McNaught and A. Wilkinson, Compendium of Chemical Terminology, (2nd Ed.), IUPAC, Blackwell Scientific Publications, Oxford, (1997).
A. C. Ugural and S. K. Fenster, Advanced Strength and Applied Elasticity, (5th Ed.), John Wiley & Sons, (1997).
P. M. Ferguson et al., Reinforced Concrete Fundamentals, (5th Ed.), John Wiley & Sons, (1988).
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).
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.
F. Demir, Prediction of elastic modulus of normal and high strength concrete by artificial neural networks, Constr. Build. Mater., 22(7) (2008) 1428–1435.
J. R. Koza, Genetic Programming: On the Programming of Computers by means of Natural Selection, MIT Press, Cambridge (MA), (1992).
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).
A. H. Alavi et al., Multi Expression Programming: A New Approach to Formulation of Soil Classification, Eng. Comput., 26 (2010) 111–118.
M. Brameier and W. Banzhaf, Linear Genetic Programming, Springer Science+Business Media, New York, (2007).
M. Oltean and C. Grosan, A comparison of several linear genetic programming techniques, Adv. Complex Syst., 14(4) (2003) 1–29.
A. H. Gandomi et al., New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming, Mater. Struct. (2010) in press.
A. H. Alavi and A. H. Gandomi, Energy-based numerical correlations for soil liquefaction assessment, Comput. Geotech. (2010) in press.
NBS, Analysis and Design of Reinforced Concrete Buildings, National Building Standard, Part 9, Iran, (2006).
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).
L. J. Parrott, A Literature Review of High Strength Concrete Properties, British Cement Association, ISBN 0 7210 13724, (1988).
CSA A23.3-94, Design of Concrete Structures, Canadian Standard Association, Rexdale, Ontario, Canada, (1995).
NS 3473, Norwegian Council for Building Standardization, Concrete Structures Design Rules, Stockholm, (1992).
TS 500, Requirements for Design and Construction of Reinforced Concrete Structures, Turkish Standardization Institute, Ankara, (2000).
T. H. Wee et al., Stress-strain relationship of high strength concrete in compression, J. Mater. Civ. Eng., 8(2) (1994) 70–76.
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.
T. Ozturan, An Investigation of Concrete Abrasion as Two Phase Material, Thesis (PhD), Istanbul, Faculty of Civil Engineering, Istanbul Technical University (in Turkish), (1984).
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.
M. J. Shannag, High strength concrete containing natural pozzolan and silica fume, Cem. Conc. Comp., 22(8) (2000) 399–406.
M. Turan, Iren M. Strain stress relationship of concrete, J. Eng. Arch., 12(1) (1997) 76–81.
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.
M. Conrads et al., Discipulus-Fast Genetic Programming Based on AIM Learning Technology, Register Machine Learning Technologies Inc., Littleton, CO., (2004).
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This paper was recommended for publication in revised form by Associate Editor Chang-Wan Kim
Amir Hossein Gandomi received his B.Sc. and M.Sc. degrees in Civil and Structural Engineering from Iran University of Science & Technology and Tafresh University, respectively. He is currently a lecturer at Tafresh University and serves as a researcher in National Elites Foundation in Iran. His research interests include Structural Health Monitoring, and Artificial Intelligence Application in Civil Engineering.
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Gandomi, A.H., Alavi, A.H., Sahab, M.G. et al. Formulation of elastic modulus of concrete using linear genetic programming. J Mech Sci Technol 24, 1273–1278 (2010). https://doi.org/10.1007/s12206-010-0330-7
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DOI: https://doi.org/10.1007/s12206-010-0330-7