Rheological equations of concrete state and relaxation of stress

Cover Page

Cite item

Full Text

Abstract

Some approaches to the derivation of rheological equations of the mechanical state of concrete are considered and the principle of superposition of fraction deformations is justified in a nonlinear statement. In linear creep theory, this principle is known as L. Boltzmann’s superposition principle of fraction creep deformations. The concept of the strength structure of the constructive material is the basis for substantiating the statements given in this work. The statistical distribution of the strength of the fractions forming a structural element in the union allows the derivation of nonlinear equations of state. At the same time, the so-called structural stresses of fractions that capable to force resistance are considered. The overlay principle of fraction deformations in non-linear statement is justified. This means the modification of L. Boltzmann’s principle of superposition allowing its applicability also under the nonlinear dependence of deformations on stresses. It is established that the integral equation of state, which is nonlinear with respect to calculated stresses, is linear with respect to structural stresses. It is this circumstance that permits its reduction to a simple linear differential equation, which, in particular, simplifies the solution of relaxation problems. These problems are closely related to the calculation of structures for long-term safety.

About the authors

Evgeny A. Larionov

Peoples’ Friendship University of Russia (RUDN University)

Email: evgenylarionov39@yandex.ru
ORCID iD: 0000-0002-4906-5919

Doctor of Technical Sciences, Professor of the Department of Construction, Academy of Engineering

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Marina I. Rynkovskaya

Peoples’ Friendship University of Russia (RUDN University)

Email: rynkovskaya-mi@rudn.ru
ORCID iD: 0000-0003-2206-2563

PhD, Docent, Director of the Department of Civil Engineering, Academy of Engineering

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Elena A. Grinko

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: grinko-ea@rudn.ru
ORCID iD: 0000-0002-0459-8359

Head of the Materials Resistance Laboratory, Department of Construction, Academy of Engineering

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

References

  1. Boltzmann L.E. Zur Theorie der Elastischen Nachwirkung. Sitzungsberichte Kaiserliche Akademie Wissenhaft Wien Mathematische-Naturwissenhaft. 1874;70:275–306.
  2. Bondarenko V.M., Bondarenko S.V. Engineering methods of the nonlinear theory of reinforced concrete. Moscow: Stroyizdat Publ.; 1982. (In Russ.)
  3. Aleksandrovskii S.V., Vasilev P.I. Experimental study of creep of concrete. Creep and Shrinkage of Concrete and Reinforced Concrete Structures. Moscow: Stroiizdat Publ.; 1976. p. 97–152. (In Russ.)
  4. Arutyunyan N.Kh. Creep of aging materials. Mechanics of Solids. 1967;6:200. (In Russ.)
  5. Arutyunyan N.H., Kolmanovskii V.B. Theory of creep of inhomogeneous bodies. Moscow: Nauka Publ.; 1983. (In Russ.)
  6. Gvozdev A.A. Remark on the nonlinear theory of concrete creep under uniaxial compression. Izvestiya AN SSSR, MTT. 1972;(5):33. (In Russ.)
  7. Rabotnov Yu.N. Creep of construction elements. Moscow: Nauka Publ.; 1966. (In Russ.)
  8. Rzhanitsyn A.R. The creep theory. Moscow; 1968. (In Russ.)
  9. Aleksandrovskii S.V., Solomonov V.V. Dependence of creep deformations of concrete on the initial level of stress. Intersectoral Issues of Construction. Domestic Experience: an Abstract Collection. 1972;(6):6–12. (In Russ.)
  10. Nazarenko V.G. Development of the fundamentals of the theory of calculation of reinforced concrete structures taking into account the peculiarities of regime loading (dissertation of the Doctor of Technical Sciences). Moscow; 1988. (In Russ.)
  11. Vasilyev P.I. On the question of choosing a phenomenological theory of concrete creep. Creep of Building Materials and Structures. Moscow; 1964. p. 106–114. (In Russ.)
  12. Sanjarovskii R.S., Ter-Emmanuilyan T.N., Manchenko M.M. Superposition principle as the fundamental error of the creep theory and standards of the reinforced concrete. Structural Mechanics of Engineering Constructions and Buildings. 2018;14(2):92–104. (In Russ.) http://doi.org/10.22363/1815-5235-2018-14-2-92-104
  13. Sanzarovsky R.S., Manchenko M.M. The creep of concrete and its instantaneous nonlinearity of deformation in the structural calculations. Structural Mechanics of Engineering Constructions and Buildings. 2015;(2):33–40. (In Russ.)
  14. Nazarenko V.G., Zvezdov A.I., Larionov E.A., Kvasnikov A.A. Some aspects of the concrete creep theory. Concrete and Reinforced Concrete Magazine. 2021;(1(603)):40–43. (In Russ.)
  15. Ciorino M.A. Analysis structural effects time-dependent behavior of concrete an internationally harmonized format. Plenary Papers of All-Russian (International) Conference on Concrete and Reinforced Concrete. 2014;7:338–350.
  16. Galustov K.Z. Nonlinear theory of concrete creep and calculation of reinforced concrete structures. Moscow: Fizmatlit Publ.; 2006. (In Russ.)
  17. Sanjarovskii R.S. Non-linear hereditary creep theory. Structural Mechanics of Engineering Constructions and Buildings. 2014;(1):63–68. (In Russ.)
  18. Wiebull W. A statistical representation of fatigue failures in solids. Trsan. Roy. Inst. Techn. 1949;27:51.
  19. Kholmyanskiy M.M. Concrete and reinforced concrete: deformability and strength. Moscow: Stroyizdat Publ.; 1997. (In Russ.)
  20. Bolotin V.V. Some questions of the theory of brittle fracture. Strength Calculations. 1962;(8):36–52 p. (In Russ.)
  21. Kharlab V.D. Generalization of the Weibull statistical theory of brittle fracture. Mekhanika Sterzhnevykh Sistem i Sploshnykh Sred. 1987;(11):150–152.
  22. Bondarenko V.M., Larionov E.A. Strains superposition principle when construction elements have structural damages. Structural Mechanics of Engineering Constructions and Buildings. 2011;(2):16–22. (In Russ.)
  23. Larionov E.A., Rimshin V.I., Zhdanova T.V. Principle of the overlay deformations in the theory of creep. Structural Mechanics of Engineering Constructions and Buildings. 2019;15(6):483–496. http://dx.doi.org/10.22363/1815-5235-2019-15-6-483-496
  24. Larionov E.A., Larionov A.E. Nonlinear creep theory. Structural Mechanics and Analysis of Constructions. 2015;(2):58–65. (In Russ.)
  25. Larionov E.A., Larionov A.E. The theory of nonlinear creep of materials. Structural Mechanics and Analysis of Constructions. 2017;(4):35–39. (In Russ.)
  26. Vasilkova N.T., Bashcatova M.E., Larionov E.A. Stress relaxation of reinforced concrete beam under axial load. Structural Mechanics of Engineering Construction and Buildings. 2012;(1):24–29.
  27. Larionov E., Zveryaev E. Stress relaxation of construction elements. MATEC. Web of Conferences. 2017;117:00101.
  28. Persoz B. Le principe de superposition de Boltzmann. Cahier groupe Franc, etudes rheol. 1957;2(1):126–151.
  29. Sanjarovsky R.S., Ter-Emmnilyan T.N., Manchenko M.M. Insolvent nays of development of the modern theory of reinforced concrete. Structural Mechanics of Engineering Construction and Buildings. 2018;14(5):379–389. https://doi.org/10.22363/1815-5235-2018-14-5-379-389

Copyright (c) 2022 Larionov E.A., Rynkovskaya M.I., Grinko E.A.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies