Title:
Consideration of Stress-Strain Curve in Concrete Creep Theories
Author(s):
Vladimir Nikolaevich Elistratov
Publication:
Structural Journal
Volume:
123
Issue:
5
Appears on pages(s):
3-12
Keywords:
aging theory; concrete creep theory; creep coefficient; creep strain; elastic creep theory; elastic heredity theory; instantaneous strain; Sargin’s curve; stress-strain curve of concrete
DOI:
10.14359/51750734
Date:
9/1/2026
Abstract:
New refined theoretical models for the study of concrete creep were proposed, which jointly consider the nonlinear relationship between stresses and strains of concrete (nonlinear creep) and the nonlinear relationship between stresses and instantaneous strains of concrete (stress-strain curve). The fundamental theories of creep that needed to be refined were the elastic-creeping solid theory, elastic heredity theory, and aging theory. The relationship from Eurocode 2 (Sargin’s formula) was used as the analytical relationship for the stress-strain curve. Within the framework of the refined theory of concrete aging, the problem of determining the concrete creep coefficient in the study of compressed reinforced concrete columns was solved. The effect of the stress-strain curve on the formula for determining the concrete creep coefficient, which is used in American, European, and Russian standards to consider the loading duration of reinforced concrete structures, was revealed.
Related References:
1. Neville, A. M., Properties of Concrete, Pitman Publishing Limited, London, UK, 1977, 687 pp.
2. Neville, A. M., “A General Relation for Strengths of Concrete Specimens of Different Shapes and Sizes,” ACI Journal Proceedings, V. 63, No. 10, Oct. 1966, pp. 1095-1109. doi: 10.14359/7664
3. Neville, A. M., “Creep Recovery of Mortars Made with Different Cements,” ACI Journal Proceedings, V. 55, No. 9, Aug. 1959, pp. 963-984. doi: 10.14359/8090
4. Neville, A. M., and Dilger, W., Creep of Concrete: Plain, Reinforced, and Prestressed, North-Holland Publishing Company, Amsterdam, the Netherlands, 1970, 622 pp.
5. Nasser, K. W., and Neville, A. M., “Creep of Old Concrete at Normal and Elevated Temperatures,” ACI Journal Proceedings, V. 64, No. 2, Feb. 1967, pp. 97-103. doi: 10.14359/7546
6. Nasser, K. W., and Neville, A. M., “Creep of Concrete at Elevated Temperatures,” ACI Journal Proceedings, V. 62, No. 12, Dec. 1962, pp. 1567-1579. doi: 10.14359/7762
7. Neville, A. M., and Brooks, J. J., “Relaxation of Stress in Concrete and Its Relation to Creep,” ACI Journal Proceedings, V. 73, No. 4, Apr. 1976, pp. 227-232. doi: 10.14359/11070
8. Bažant, Z. P., Material Models for Structural Creep Analysis, Chapter 2, John Wiley and Sons, Chichester, UK, 1988, pp. 99-215.
9. Bažant, Z. P., and Jirásek, M., “Creep and Hygrothermal Effects in Concrete Structures,” Springer Science+Business Media, Luxembourg, 2018, 968 pp.
10. Bažant, Z. P.; Wendner, R.; and Hubler, M. H., “Comprehensive Database for Concrete Creep and Shrinkage: Analysis and Recommendations for Testing and Recording,” ACI Materials Journal, V. 112, No. 4, July-Aug. 2015, pp. 547-558. doi: 10.14359/51687453
11. Young, J. F., Physical Mechanisms and Their Mathematical Descriptions, Chapter 1, John Wiley and Sons, Chichester, UK, 1988, pp. 63-98.
12. Aleksandrovskiy, S. V., Calculation of Concrete and Reinforced Concrete Structures for Temperature and Humidity Changes with Consideration of Creep, Stroyizdat, Moscow, Russia, 1973, 432 pp. (in Russian)
13. Sheikin, A. E.; Chekhovsky, Y. V.; and Brusser, M. I., Structure and Properties of Cement Concretes, Stroyizdat, Moscow, Russia, 1979, 344 pp. (in Russian)
14. Bondarenko, V. M., “Some Questions of Non-linear Theory of Reinforced Concrete,” University of Kharkiv, Kharkiv, Ukraine, 1968, 323 pp. (in Russian)
15. Berg, O. Y., The Physical Foundations of the Theory of Strength of Concrete and Reinforced Concrete, The State Publishing House of Literature on Construction, Architecture and Building Materials, Moscow, Russia, 1961, 96 pp. (in Russian)
16. Sakhnovsky, K. V., Reinforced Concrete Structures, State Publishing House of Literature on Construction, Architecture and Building Materials, Moscow, Russia, 1961, 840 pp. (in Russian)
17. Ulitsky, I. I.; Zhang, Z.-Y.; and Golyshev, A. B., “Calculation of Reinforced Concrete Structures with Consideration of Long-Term Processes,” State Publishing House for Construction and Architecture of the Ukrainian SSR, Kiev, Ukraine, 1960, 495 pp. (in Russian)
18. ACI Committee 209, “Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete (ACI 209.2R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 46 pp.
19. Bažant, Z. P., “Prediction of Concrete Creep and Shrinkage: Past, Present and Future,” Nuclear Engineering and Design, V. 203, No. 1, 2001, pp. 27-38. doi: 10.1016/S0029-5493(00)00299-5
20. Chiorino, M. A., “Analysis of Structural Effects of Time-Dependent Behavior of Concrete: An Internationally Harmonized Format,” Bulletin of Science and Research Center of Construction, V. 16, No. 1, 2018, pp. 31-47.
21. Partov, D., and Kantchev, V., “Gardner and Lockman Model in Creep Analysis of Composite Steel-Concrete Sections,” ACI Structural Journal, V. 111, No. 1, Jan.-Feb. 2014, pp. 59-69. doi: 10.14359/51686430
22. Reddy, D. H.; Ramaswamy, A. “Experimental and Numerical Modeling of Creep in Different Types of Concrete,” Heliyon, V. 4, No. 7, 2018, pp. 1-47.
23. Santos, S. B.; Silva Filho, L. C. P.; and Calmon, J. L., “Early-Age Creep of Mass Concrete: Effects of Chemical and Mineral Admixtures,” ACI Materials Journal, V. 109, No. 5, Sept.-Oct. 2012, pp. 537-544. doi: 10.14359/51684085
24. Shurbert-Hetzel, C.; Daneshvar, D.; Robisson, A. and Shafei, B., “Data-Enabled Comparison of Six Prediction Models for Concrete Shrinkage and Creep,” Case Studies in Construction Materials, V. 19, 2023, p. e02406.
25. Sicaras, V. K., “A New Way to Predict Creep and Shrinkage,” Concrete International, V. 45, No. 10, Oct. 2023, pp. 51-53. doi: 10.14359/51739163
26. Beglov, A. D., and Sanzharovsky, R. S., European Standards and Non-linear Theory of Reinforced Concrete, Saint Petersburg, Russia, 2011, 309 pp.
27. Arutyunyan, N. K., Some Questions of Creep Theory, State Publisher of Technical and Theoretical Literature, Moscow-Saint Petersburg, Russia, 1952, 323 pp. (in Russian)
28. Vasil’ev, P. I., “Some Issues of Plastic Strains of Concrete,” Proceedings of the B. E. All-Union Scientific Research Institute of Hydraulic Engineering, Saint Petersburg, Russia, V. 49, 1953, pp. 83-113. (in Russian)
29. Livshits, Y. D., “Calculation of Reinforced Concrete Structures Taking into Account the Effects of Shrinkage and Creep of Concrete,” Publisher of Higher School, Kiev, Ukraine, 1976, 280 pp. (in Russian)
30. Mel’nik, R. A., “Application of the Stress Function of the Type f(σc) = aσcn to Determine the Values of Strains of Nonlinear Creep of Concrete,” Budivelnik Publishing House, Kiev, Ukraine, 1966, pp. 178-193. (in Russian)
31. Mel’nik, R. A., “Experimental Study of Non-Linear Creep of Concrete,” Collection of Scientific Papers, Publisher of the Kyiv Civil Engineering Institute, Issue 16, 1961, Kiev, Ukraine, pp. 117-133. (in Russian)
32. Popkova, O. M., “Experimental Study of Non-linear Creep of Aging Concrete under Compression,” Long-Term Deformative Processes in Concrete and Reinforced Concrete Structures, Materials of the Conference of Young Specialists, Moscow, Russia, 1970, pp. 23-37. (in Russian)
33. Ulitsky, I. I., “Effect of Long-Term Processes on the Stressed-Deformed State of Reinforced Concrete Structures,” Publisher of the Academy of Construction and Architecture of the Ukrainian SSR, Kiev, Ukraine, 1962, 36 pp. (in Russian)
34. Shchelkunov, V. G., “Long-Term Compression Strength of Reinforced Concrete Reinforced with High-Strength Reinforcement,” Collection of Scientific Papers of the Kiev Automobile Institute, Kiev, Ukraine, 1978, pp. 31-38. (in Russian)
35. Yatsenko E. A., “Experimental Studies of Non-Linear Creep of Concrete,” Collection of Scientific Papers of the Kiev Institute of Civil Engineering, Kiev, Ukraine, V. 20, 1962, pp. 74-90. (in Russian)
36. Yatsenko, E. A., “Creep of Concrete and Reinforced Concrete Structures,” Publishing House of the Dnepropetrovsk Institute of Railway Transport Engineers, Dnipropetrovsk, Ukraine, 1973, 97 pp. (in Russian)
37. Yatsenko, E. A., “Investigation of Prestress Losses From Shrinkage, Linear and Nonlinear Creep of Concrete, Taking into Account the Reversibility of Creep Strains,” Publishing House of the Odessa Institute of Civil Engineering, Odesa, Ukraine, 1963, 20 pp. (in Russian)
38. Carreira, D. J., and Chu, K.-H., “Stress-Strain Relationship for Plain Concrete in Compression,” ACI Journal Proceedings, V. 82, No. 6, Nov.-Dec. 1985, pp. 797-804. doi: 10.14359/10390
39. Chin, M. S.; Mansur, M. A.; and Wee, T. H., “Effects of Shape, Size, and Casting Direction of Specimens on Stress-Strain Curves of High-Strength Concrete,” ACI Materials Journal, V. 94, No. 3, May-June 1997, pp. 209-219. doi: 10.14359/301
40. Desayi, P., and Krishnan, S., “Equation for the Stress-Strain Curve of Concrete,” ACI Journal Proceedings, V. 61, No. 3, Mar. 1964, pp. 345-353. doi: 10.14359/7785
41. Eid, R.; Dancygier, A. N.; and Paultre, P., “Stress-Strain Curve for Concrete in Circular Columns Based on Elastoplastic Analysis,” Materials and Structures, V. 43, No. 1-2, 2010, pp. 63-79. doi: 10.1617/s11527-009-9470-6
42. Sargin, M., “Stress-Strain Relationships for Concrete and the Analysis of Structural Concrete Sections,” The University of Waterloo, Waterloo, ON, Canada, Study No. 4, 1971, 167 pp.
43. Radaikin, O. V., “Comparative Analysis of Various Diagrams of Concrete Strain According to the Criterion of Energy Consumption for Strain and Destruction,” Bulletin of Belgorod State Technological University, Belgorod, Russia, 2019, pp. 29-39. (in Russian)
44. Selyaev, V. P.; Selyaev, P. V.; Alimov, M. F. and Sorokin, E. V., “Analytical Description of Concrete Strain Diagrams for the Calculation of Plastic Surfaces from Nonlinearly Deformable Material,” Building and Reconstruction, Oryol, Russia, V. 3, 2018, pp. 22-30. (in Russian)
45. Baikov, V. N., “Calculation of Bendable Elements Taking into Account Experimental Dependences Between Stresses and Strains for Concrete and High-Strength Reinforcement,” Construction and Architecture, Novosibirsk, Russia, V. 5, 1981, pp. 26-32. (in Russian)
46. Varlamov, A. A.; Shishlonov, E. A.; Tkach, E. N.; Shumilin, M. S.; and Goncharov, D. V., “Patterns of Stress and Strain Coupling in Concrete,” Academy (Scientific and Methodological Journal), Moscow, Russia, V. 2, No. 5, 2016, pp. 7-17. (in Russian)
47. EN 1992-1-1, “Eurocode 2: Design of Concrete Structures—Part 1.1: General Rules and Rules for Buildings,” European Committee for Standardization, Brussels, Belgium, 2004, 91 pp.
48. ACI Committee 318, “Building Code for Structural Concrete—Code Requirements and Commentary (ACI CODE-318-25),” American Concrete Institute, Farmington Hills, MI, 2025, 701 pp.
49. SP 63.13330.2018, “Concrete and Reinforced Concrete Structures. General Provisions,” Standartinform, Moscow, Russia, 2019, 124 pp. (in Russian)