Stress-strain curves of concrete under monotonic uniaxial compression: a systematic review
DOI:
https://doi.org/10.3989/ic.11.114Keywords:
Structural concrete, stress-strain curves, literature review, modellingAbstract
The existence of more than thirty different mathematical expressions that claims to represent the stress-strain relationship of a concrete specimen under monotonic and uniaxial compression (including those proposed in the official regulations of different countries that have regulated by law the use of concrete as structural material), seems to require an additional effort in formulating a universally accepted equation. As a first step toward that goal, in this paper we show and analyze systematically the different dynasties of equations that have been published, since the first proposals of Ritter and Bach (1897-1899), through the, more or less complicated, polynomial truncations of the Smith and Young’s equation (1956), continuing with the contributions based on statistical distributions of the damage model, and concluding with the analysis of the approach to the issue by the successive versions of the Model Code and the Spanish Structural Concrete Instruction (EHE-08).
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(1) Rosshändler, J. Die Basler Baukatastrophe u. Hennebique. Basler Nachrichten de 1 de septiembre de 1901, en Schindler, Y. V. (1995). Und Beton revolutionierte den Brückenbau gewaltig. Kunst and Architektur, 46: 181-189.
(2) Simonnet, C. (2009). Hormigón. Historia de un Material, Ed. Nerea, San Sebastián, . PMCid:3044547
(3) Ritter, K. W. (1899). Die Bauweise Hennebique. Schweizerische Bauzeitung, 33(7): 59-61.
(4) Mörsch, E. (1902). Der Eisenbetonbau, seine Anwendung und Theorie, Wayss & Freytag, Stuttgart.
(5) Rowe, G. W. (1965). An Introduction to the Principles of Metalworking, Edward Arnold Ltd., Londres. (Edición espa-ola: Conformado de los Metales, Urmo, Bilbao, 1972).
(6) Popovics, S. (1970). A review of stress-strain relationships for concrete. ACI Journal Proceedings, 67(3): 243-248.
(7) Walker, S. (1923). Modulus of elasticity of concrete. Proceedings of the American Society for Testing Materials, 19(Part II): 510-606.
(8) Smith, G. M. y Young, L. E. (1955). Ultimate theory by exponential function. ACI Journal Proceedings, 52(11): 349-359.
(9) Smith, G. M. y Young, L. E. (1956). Ultimate flexural analysis on stress-strain curves for cylinders. ACI Journal Proceedings, 53(12): 597-609.
(10) Yip, W. K. (1997). Generic form of stress-strain equations for concrete. Cement and Concrete Research, 28(4): 499-508. http://dx.doi.org/10.1016/S0008-8846(98)00039-8
(11) Desayi, P. y Krishnan, S. (1964). Equation for the stress-strain curve of concrete. ACI Journal Proceedings, 61(3): 345-350.
(12) Saenz, L. P. (1964). Discussion of "Equation for the stress-strain curve of concrete" by P. Desayi and S. Krishnan. ACI Journal Proceedings, 61(9): 1229-1235.
(13) Tulin, L. G. y Gerstle, K. H. (1964). Discussion of "Equation for the stress-strain curve of concrete" by P. Desayi and S. Krishnan. ACI Journal Proceedings, 61(9): 1236-1238.
(14) Popovics, S. (1973). A numerical approach to the complete stress-strain curve of concrete. Cement and Concrete Research, 3(5): 583-599. http://dx.doi.org/10.1016/0008-8846(73)90096-3
(15) Carreira, D. J. y Chu, K.-H. (1985). Stress-strain Relationship for plain concrete in compression. ACI Journal Proceedings, Vol. 82, n.º 6, pp. 797-804.
(16) Alexander, S. (1965). A single equation for the stress-strain curve of concrete. Indian Concrete Journal, 39(7): 247-277.
(17) Tsai, W. T. (1988). Uniaxial compressional stress-strain relation of concrete. Journal of Structural Engineering, 14(9): 2133-2136. http://dx.doi.org/10.1061/(ASCE)0733-9445(1988)114:9(2133)
(18) Sargin, M. 1971. Stress-strain Relationships for Concrete and the Analysis of Structural Concrete Sections, Solid Mechanics Division, University of Waterloo, Waterloo, Ontario.
(19) Wang, P. T., Shah, S. P. y Naaman, A. E. (1978). Stress-strain curves of normal and lightweight concrete in compression. ACI Journal Proceedings, 75(11): 603-611.
(20) Pantazopoulou, S. J. y Mills, R. H. (1995). Microstructural aspects of the mechanical response of plain concrete. ACI Materials Journal, 92(6): 605-616.
(21) Kachanov, L. M. (1958). On the time to rupture under creep conditions. Izv. Akad. Nauk SSSR. Otd. Tekhn. Nauk, 8: 26-31.
(22) Rabotnov, Y. N. (1959). A mechanism of a long time failure, in Creep Problems in Structural Members, USSR Academy of Sci. Publ., Moscú.
(23) Shah, S. P. y Winter, G. (1966). Inelastic behavior and fracture of concrete. ACI Journal Proceedings, 63(9): 925-930.
(24) Weibull, W. (1939). A statistical theory of the strength of materials. Ingeniors Vetenskaps Akademien, 151: 1-45.
(25) Weibull, W. (1951). A statistical distribution function of wide applicability. J. Appl. Mech., 18: 293-297.
(26) Blechman, I. (1988). Stage model of stress-strain relationship for concrete under short-term load. Part 1: Ascending branch. Cement and Concrete Research, 18: 863-873. http://dx.doi.org/10.1016/0008-8846(88)90022-1
(27) Blechman, I. (1989). Stage model of stress-strain relationship for concrete under short-term load. Part 2: Nature of concrete atrophy. Cement and Concrete Research, 19: 7-15. http://dx.doi.org/10.1016/0008-8846(89)90060-4
(28) Blechman, I. (1989). Stage model of stress-strain relationship for concrete under short-term load. Part 3: Descending branch. Cement and Concrete Research, 19: 203-215. http://dx.doi.org/10.1016/0008-8846(89)90085-9
(29) Collins, M. P., Mitchell, D. y MacGregor, J. G. (1993). Structural design considerations for highstrength concrete. Concrete International: Design and Construction, 15(5): 27-34.
(30) Tasnimi, A. (2004). A. Mathematical model for complete stress-strain curve prediction of normal, light-weight and high-strength concretes. Magazine of concrete Research, 56(1): 23-34. http://dx.doi.org/10.1680/macr.2004.56.1.23
(31) Comité Euro-International du Béton. CEB-FIP Model Code for Concrete Structures (CEB, Lausana, 1978).
(32) Comité Técnico AEN/CTN 140 Eurocódigos Estructurales. (2010). UNE-EN 1992-1-1:2010 Eurocódigo 2: Proyecto de estructuras de hormigón. Parte 1-1: Reglas generales y reglas para edificación. AENOR.
(33) Comité Técnico AEN/CTN 140 Eurocódigos Estructurales. (2011). UNE-EN 1992-1-1:2010 ERRATUM: 2011 Eurocódigo 2: Proyecto de estructuras de hormigón. Parte 1-1: Reglas generales y reglas para edificación. AENOR.
(34) Comité Euro-International du Béton. CBE-FIP Model Code 90, Thomas Telford, Londres, 1991.
(35) CEB Working Group on HSC/HPC. (1995). High performance concrete, Recommended Extensions to the MC 90 Research Needs. Bulletin d'Information CEB, (228):140.
(36) Van Gysel, A. y Taerwe, L. (1996). Analytical formulation of the complete stress-strain curve for high strength concrete. Materials and Structures, 29: 529-533. http://dx.doi.org/10.1007/BF02485952
(37) CEB-FIP. Model Code 2010. (2011). Final approved version. Volume 1. fib Bulletin, (65).
(38) CEB-FIP. Model Code 2010. (2011). Final approved version. Volume 2. fib Bulletin, (56).
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