- STRUCTURAL MECHANICS
- A Probabilistic Analysis Of Operation Of A Flat Steel Frame Under Seismic Action
- UDC 624.04 DOI: 10.33622/0869-7019.2020.05.45-50

**Oleg V. MKRTYCHEV**, e-mail: MkrtychevOV@mgsu.ru

**Sergey V. BULUSHEV**, e-mail: BulushevSV@mgsu.ru

Moscow State University of Civil Engineering (National Research University), Yaroslavskoe shosse, 26, Moscow 129337, Russian Federation

**Abstract**. The seismic action is non-stationary random process. Calculation in the probabilistic setting makes it possible to most accurately assess the response of the system during an earthquake. In the work, the reliability of a flat steel frame under seismic action was estimated by the method of statistical tests when considering seismic action in the form of a non-stationary random process. The design cross-sections of the frame were adopted based on the results of the calculation of the seismic action of the design earthquake level in accordance with current design standards. When performing the probabilistic calculation, a deterministic solution implemented in the software package was used. The solution is based on direct integration of the equations of motion using explicit schemes. A method has been developed for determining the actual value of safety coefficient of load-bearing capacity of the frame. Considering the safety factor of the frame under seismic action as a random variable, a corresponding histogram is constructed using the criterion of non-collapse. Using the Pearson criterion, the closest theoretical distribution law to the obtained empirical distribution is determined. According to the theoretical laws produced, the assessment of the actual safety factor of the bearing capacity and the coefficients taking into account possible damage to buildings and structures with a given security. In addition, the probability of plastic deformations exceeding the value of 0.05 in the structural elements in case of accidental seismic impact of the maximum calculated earthquake level was established by statistical tests. The method is used to determine the seismic stability of structures with a given security, which makes it possible to provide the required level of reliability for all buildings and structures designed in seismic areas.

**Key words**: seismic stability, non-linear dynamic calculation method, earthquake accelerogram, non-stationary random process, explicit integration method, reliability theory of building structures, probabilistic calculation methods, statistical test method. - REFERENCES

1. Augustu G., Barata A., Kashiati F. Veroyatnostnye metody v stroitel'nom proektirovanii [Probabilistic methods in construction design]. Moscow, Stroyizdat Publ., 1988. 583 p. (In Russian).

2. Rayzer V.D. Veroyatnostnaya optimizatsiya urovnya nadezhnosti sooruzheniy [Probabilistic optimization of the reliability level of structures]. Stroitel'naya mekhanika i raschet sooruzhenij, 2008, no. 3, pp. 39-42. (In Russian).

3. Mkrtychev O. V., Bulushev S. V. Probabilistic Estimation Seismic Resistance of Plain Steel Frame. XXVIII R-P-S Seminar 2019 IOP Conference Series. Materials Science and Engineering, 2019, vol. 661, pp. 012016.

4. Bolotin V. V. Statisticheskie metody v stroitel'noy mekhanike [Statistical Methods in Structural Mechanics]. Moscow, Stroyizdat Publ.,1961. 203 p. (In Russian).

5. Rayzer V. D. Teoriya nadezhnosti sooruzheniy [Theory of reliability of structures]. Moscow, ASV Publ., 2010. 382 p. (In Russian).

6. Dzhinchvelashvili G. A. Nonlinear dynamic methods of calculation of buildings and structures with a given security seismic stability. Available at: http://www.dslib.net/stroj-mexanika/nelinejnye-dinamicheskie-metody-rascheta-zdanij-i-sooruzhenij-s-zadannoj.html (accessed 20.03.2020). (In Russian).

7. Aptikaev F. F. Instrumental'naya shkala seysmicheskoy intensivnosti [Instrumental scale of seismic intensity]. Moscow, Nauka i obrazovanie Publ. 2012. 176 p. (In Russian).

8. Aptikaev F. F., Erteleva O. O. Parameters of the response spectra. Sejsmostojkoe stroitel'stvo. Bezopasnost' sooruzhenij, 2008, no. 5, pp. 23-25. (In Russian).

9. Bolotin V. V., Radin V. P., Chirkov V. P. Modeling dynamic processes in the elements of building structures in case of earthquakes. Izvestiya vuzov, 1999, no. 5, pp. 17-21. (In Russian).

10. Mkrtychev O. V., Reshetov A. A. Method for determining initial characteristics of the most unfavorable accelerograms for linear systems with finite number of degrees of freedom. Vestnik MGSU, 2015, no. 8, pp. 80-91. (In Russian).

11. Mkrtychev O. V., Reshetov A. A. Representative set of earthquake accelerogramms for structural engineering of buildings and structures during earthquake effects. Vestnik MGSU, 2017, vol. 12, no. 7 (106), pp. 754-760. (In Russian).

12. Rayzer V. D. Problem of buildings and structures survivability. Stroitel'naya mekhanika i raschet sooruzhenij, 2012, no. 5, pp. 77-78. (In Russian).

13. Rayzer V. D. Optimization of reliability of structures based on survivability factor. Stroitel'naya mekhanika i raschet sooruzhenij, 2015, no.1, pp. 42-45. (In Russian).

14. Sturges H. A. The choice of a class interval. Journal of the American Statistical Association, 1926, no. 21(153), pp. 65-66.

15. Rzhanitsyn A. R. Teoriya rascheta stroitel'nykh konstruktsiy na nadezhnost' [Theory of calculation of building structures for reliability]. Moscow, Stroyizdat Publ., 1978. 239 p. (In Russian).

16. Venttsel' E. S. Teoriya veroyatnostey [Probability theory]. Moscow, Nauka Publ., 1963. 576 p. (In Russian).

17. Nemchinov Yu. I., Mar'enkov N. G., Khavkin A. K., Babik K. N. Proektirovanie zdaniy s zadannym urovnem obespecheniya seysmostoykosti (s uchetom rekomendatsiy Evrokoda 8, mezhdunarodnykh standartov i trebovaniy DBN) [Designing Buildings with a given level of seismic resistance (taking into account the recommendations of Eurocode 8, int. standards and DBN requirements)]. Kiev, Minregion Ukrainy Publ., GP NIISK Publ., 2012. 53 p. (In Russian).

18. Pshenichkina V. A., Zolina T. V., Drozdov V. V., Kharlanov V. L. Methods of estimating seismic reliability of high-rise buildings. Vestnik VolgGASU. Seriya: Stroitelstvo i arhitektura, 2011, no. 25, pp. 50-56. (In Russian).

19. Shablinskiy G. E., Dzhinchvelashvili G. A., Zubkov D. A. Seysmostoykost' stroitel'nykh konstruktsiy atomnykh elektrostantsiy [Earthquake resistance of building structures of nuclear power plants]. Moscow, ASV Publ., 2014. 216 p. (In Russian). **For citation**: Mkrtychev O. V., Bulushev S. V. A Probabilistic Analysis of Operation of a Flat Steel Frame under Seismic Action.*Promyshlennoe i grazhdanskoe stroitel'stvo*[Industrial and Civil Engineering], 2020, no. 5, pp. 45-50. (In Russian). DOI: 10.33622/0869-7019.2020.05.45-50.

BACK