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- STRUCTURAL MECHANICS
- Algorithm For Numerical And Analytical Evaluation Of Inertial Effects In Building Structures
- UDC 004.41/42:519.8:531/534:539.2/6:624.042:624.044

doi: 10.33622/0869-7019.2023.02.04-09

**Vladimir L. MONDRUS**^{1}, mondrus@mail.ru

**Vladimir G. KULIKOV**^{1}, kulikov-miit@mail.ru

**Muhamed I. MAGOMEDOV**^{2}, magomedov.mi@progress.dsk1.ru

^{1}Moscow State University of Civil Engineering (National Research University), Yaroslavskoe shosse, 26, Moscow 129337, Russian Federation

^{2}Pervy DSK, ul. Rozanova, 6, str. 7, Moscow 123007, Russian Federation

**Abstract**. The paper proposes a non-standard approach to estimating the stochastic behavior of structural elements of buildings of large-panel housing construction and their nodes from pulsed dynamic external influences. An assessment of the reactive inertial resistance of the constructives of buildings and structures to complex kinetics in form and content is presented. A criterion has been developed for evaluating the behavior of constructives in the form of a symmetric matrix, the elements of which are moments of inertia in the coordinate system proposed by L. Euler that determines the kinetics of precession, nutation and angles of proper rotation of structural elements of buildings and structures, as well as their nodes. The calculation scheme for determining the inertia tensor for a typical reinforced concrete panel of large-panel housing construction is given. The terminology of "group theory" for engineering evaluation of the probabilistic reactive response of structural elements of buildings to external and internal impulse dynamic effects is considered. The practical significance of the study consists in the graph-analytical method proposed in the work, which makes it possible to predict the deformative behavior of the studied objects in known confidence intervals.

**Keywords**: large-panel housing construction, dynamic impulse effects, vector space, moments of inertia, inertia tensor, algebraic object, graph-analytical method - REFERENCES

1. Lesdon L. S. Optimizaciya bol'shih sistem [Optimization of large systems]. Moscow, Nauka Publ., 1975. 432 p. (In Russ.).

2. Nurminskiy E. A. Chislennye metody resheniya determinirovannyh i stohasticheskih minimaksnyh zadach [Numerical methods for solving deterministic and stochastic minimax problems]. Kiev, Naukova dumka Publ.,1979. 161p. (In Russ.).

3. Adamovich V. V., Barhin B. G. et al. Arhitekturnoe proektirovanie obshchestvennyh zdaniy i sooruzheniy [Architectural design of public buildings and structures]. Moscow, Stroyizdat Publ., 1984. 543 p. (In Russ.).

4. Gordeev V. N., Lantuh-Lyashchenko A. I., Pashinskiy V. A. et al. Nagruzki i vozdejstviya na zdaniya i sooruzheniya [Loads and impacts on buildings and structures]. Moscow, ASV Publ., 2017. 528 p. (In Russ.).

5. Borisenko A. I., Tarapov I. E. Vektorny analiz i nachala tenzornogo ischisleniya [Vector analysis and the beginnings of tensor calculus]. Har'kov,Vishcha shkola Publ., 1978. 216 p. (In Russ.).

6. Galadzhev R. S., Katar'yan E. S. Geometricheskie harakteristiki ploskih secheniy [Geometric characteristics of plane sections]. Moscow, 2001. 184 p. (In Russ.).

7. Karpilovskiy V. S., Kriksunov E. Z., Malyarenko A. A., Perel'muter A. V., Perel'muter M. A. SCAD Office. Formirovanie sechenij i raschet ih geometricheskih harakteristik [SCAD Office. Formation of sections and calculation of their geometric characteristics]. Moscow, ASV Publ., 2008. 990 p. (In Russ.).

8. Boher M. Vvedenie v vysshuyu algebru [Introduction to Higher Algebra]. Moscow, 2008. 296 p. (In Russ.).

9. Artamonov V. A., Slovohotov Yu. L. Gruppy i ih prilozheniya v fizike, himii, kristallografii [Groups and their applications in physics, chemistry, crystallography]. Moscow, Akademiya Publ., 2005. 512 p. (In Russ.).

10. Hovanskiy A. G. Teoriya Galua, nakrytiya i rimanovy poverhnosti [Galois theory, coverings and Riemann surfaces]. Moscow, MCNMO Publ., 2007. 392 p. (In Russ.). **For citation**: Mondrus V. L., Kulikov V. G., Magomedov M. I. Algorithm for Numerical and Analytical Evaluation of Inertial Effects in Building Structures.*Promyshlennoe i grazhdanskoe stroitel'stvo*[Industrial and Civil Engineering], 2023, no. 2, рp. 4-9 (In Russ.). doi: 10.33622/0869-7019.2023.02.04-09

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