Capacity of compressed reinforced concrete element under dynamic load considering effect of long-term preloading

The study provides an analytical solution to the problem of dynamic buckling of an eccentrically compressed reinforced concrete element with eccentricities of axial force in two planes. It takes into account the initial stress-strain state formed by the preceding long-term loading with a service load. The object of the study is the columns of reinforced concrete frames of buildings and structures subjected to dynamic loading as a result of the initial local failure in the structural system. The study is based on the analytical method under the following assumptions and limitations: before the formation of cracks, the strain is consistent with the Bernoulli hypothesis; the projections of the deformed axis of the column are approximated by sinusoids; the influence of short-term loads and their variability on the formation of the stress-strain state of the column at the time of a special design situation is not taken into account; a piecewise linear law of variation in time is assumed for the load and initial deflections. A combination of viscoelastic model of aging material and modified Maxwell model with consideration of nonlinear elastic relations of stresses and conventionally instantaneous strains is utilized as a model of concrete under the considered regime loading. Validation of the adopted material model on the background of experimental data is performed.

The paper presents the solution of the problem of determining the stress-strain state of a reinforced concrete column taking into account the adopted material model under static-dynamic loading considering the influence of creep.

1. Alshaikh I.M.H. et al. Experimental investigation of the progressive collapse of rein-forced concrete structures: An overview. Structures. 2020. Vol. 25. P. 881–900.

2. Kiakojouri F. et al. Experimental studies on the progressive collapse of building structures: A review and discussion on dynamic column removal techniques. Structures. 2023. Vol. 57.

3. Kiakojouri F. et al. Progressive collapse of framed building structures: Current knowledge and future prospects. Eng Struct. 2020. Vol. 206, № December 2019. P. 110061.

4. Adam J.M. et al. Research and practice on progressive collapse and robustness of building structures in the 21st century. Eng Struct. 2018. Vol. 173, № March. P. 122–149.

5. Caredda G. et al. Learning from the progressive collapse of buildings. Developments in the Built Environment. 2023. Vol. 15. P. 100194.

6. Fedorova N.V., Savin S.YU. Progressive collapse resistance of facilities experienced to localized structural damage - an analytical review. Building and reconstruction. 2021. Vol. 95, no. 3. P. 76–108.

7. Levtchitch V. et al. Seismic performance capacities of old concrete. 13 th World Conference on Earthquake Engineering, Vancouver, B.C., Canada. 2004. P. 1–15.

8. Bazhenov Yu.M. Concrete under dynamic loading. Moscow: Stroyizdat, 1970. 271 p.

9. Geniyev G.A. Method for determining dynamic strength of concrete. Concrete and reinforced concrete. 1998. No. 1. P. 18–19.

10. Nam J.W. et al. Analytical study of finite element models for FRP retrofitted concrete structure under blast loads. International Journal of Damage Mechanics. 2009. Vol. 18, № 5. P. 461–490.

11. Yu W., Jin L., Du X. Influence of pre-static loads on dynamic compression and corre-sponding size effect of concrete: Mesoscale analysis. Constr Build Mater. 2021. Vol. 300. P. 124302.

12. Kolchunov V.I. et al. Robustness of buildings and structures under accidental actions. Moscow: Publishing ASV, 2014. 208 p.

13. Tsvetkov K.A., Bazhenova S.I., Bezgodov I.M. Problem of construction of the deformation diagram for concrete under dynamic impact considering effects of static preloading. Vestnik MGSU. 2012. No. 7. P. 152–158.

14. Fedorova N.V., Medyankin M.D., Bushova O.B. Experimental determination of the parameters of the static-dynamic deformation of concrete under loading modal. Building and reconstruction. 2020. Vol. 89, № 3. P. 72–81.

15. Savin S.Yu., Medyankin M.D., Sharipov M.Z. Deformation of Fiber Concrete Under a Single Dynamic Impact Taking into Account the Influence of Initial Stresses from the Static Load. Building and reconstruction. 2022. Vol. 99, № 1. P. 76–88.

16. Savin S.Yu., Fedorova N.V. Viscoelastic Model of Fiber Concrete under Dynamic Loading Considering the Effect of Initial Stresses. Russian Journal of Building Con-struction and Architecture. 2024. № 2(62). P. 19–35.

17. Zhou Y. Concrete creep and thermal effects on the dynamic behavior of a concrete-filled steel tube arch bridge. Journal of Vybroengineering. 2014. Vol. 16, № 4. P. 1735–1744.

18. Tamrazyan A.G. Dynamic stability of compressed reinforced concrete element as a visco-elastic rod. Vestnik MGSU. 2011. Vol. 2, No. 1. P. 193–194.

19. Tamrazyan A.G. Survivability resource - the main criterion for the decisions of high-rise buildings. Zhilischnoe stroitelstvo. 2010. No. 1. P. 15–18.

20. Alekseytsev A.V. et al. Bearing capacity of emergencyly loaded reinforced concrete columns with initial imperfections. Building and reconstruction. 2022. Vol. 104, № 6. P. 104–115.

21. Alekseytsev A.V. Optimal design of steel frame structures subject to level of mechanical safety. Building and reconstruction. 2020. Vol. 89, № 3. P. 51–62.

22. Gemmerling A.V. Bar structural systems analysis. Moscow: Stroyizdat, 1974. 207 p. 23. FIB Model Code 2010. CEB and FIP, 2011.

23. Tamrazyan A.G., Esayan S.G. Mechanics of concrete creep. Moscow: Moscow State University of Civil Engineering, 2012. 524 p.

24. Chen Y. et al. Research on creep behaviour of UHPC based on experiments and visco-elastic modelling. Journal of Building Engineering. 2024. Vol. 84.

25. BS EN 1992-1-1. Eurocode 2: Design of concrete structures - Part 1-1 : General rules and rules for buildings. British Standards Institution. 2004.

26. Lai J., Sun W. Dynamic behaviour and visco-elastic damage model of ultra-high per-formance cementitious composite. Cem Concr Res. 2009. Vol. 39, № 11. P. 1044–1051.

27. Wang L. et al. Nonlinear Viscoelastic Constitutive Relations and Nonlinear Viscoe-lastic Wave Propagation for Polymers at High Strain Rates. 1996.

28. Wang F.C., Zhao H.Y. Experimental investigation on blast furnace slag aggregate concrete filled double skin tubular (CFDST) stub columns under sustained loading. Structures. 2020. Vol. 27, № May. P. 352–360.