Stability of multispan rods

Objective. In the design of complex engineering structures, the problem of stability is now becoming especially relevant. With the need to meet the conditions of strength, rigidity in calculations and design, it is imperative to ensure the stability of equilibrium as the most important requirement. Regardless of the type of strength calculations (verification, design, load), the calculation of a structure for stability, even in the simplest formulation, is reduced to the determination of critical forces. This allows us to estimate the stability margin of the structure under a given load. The complexity of determining the critical parameters of the impact increases with the complexity of the system under consideration.

Method. The use of the finite difference method is a feature in solving systems of equations in problems with boundary conditions.

Result. The exact values of critical forces in non-classical problems of the stability of compressed rods are determined, which is proved by the obtained curve from the monitor screen.

Conclusion. The main points of the theory of calculation in the study of the stability of multi-span rods are outlined. To find the critical forces of a multi-span rod on elastic supports, a simple algorithm for solving problems is given.

1. Maslennikov A.M. Dynamics and Stability of Structures. Textbook and Practice for Higher Education Institutions. M.: Publishing house Yurait. 2016; 366. (In Russ)

2. Volmir A.S. Stability of deformable systems. Moscow : Nauka. 1967; 984. (In Russ)

3. Leontiev N.N. Fundamentals of Structural Mechanics of Rod Systems: Textbook for Building Specialties of Higher Education Institutions. / N.N. Leontiev, D.N. Sobolev, A.A. Amosov. Moscow: Publishing House ASV, 1996; 541. (In Russ)

4. Bezukhov N.I. Stability and Dynamics in Examples and Problems: Textbook for Building Specialties of Higher Education Institutions / N.I. Bezukhov, O.V. Luzhin, N.V. Kolkunov. - Moscow: High School, 1987; 264. (In Russ)

5. A.A. Kramarenko, Stability and Dynamics of Structures: Collection of Tasks for Independent Studying / Novosibirsk State Academy of Civil Engineering. Novosibirsk: NGAS, 1994; 36. (In Russ)

6. Samarsky A.A. Introduction in numerical methods. - 2nd edition. M.: Nauka. Main Editorial Office for Physical and Mathematical Literature, 1987. (In Russ)

7. Alfutov N.A. Fundamentals of calculating the stability of elastic systems. Moscow: Mashinostroenie. 1978;312. (In Russ)

8. Samarsky A.A., Gulin A.V. Numerical Methods. Moscow: Nauka, G. Ed. of Physics and Mathematics, 1989; 432. (In Russ)

9. Varvak P.M., Varvak L.P. Method of grids in the tasks of calculating building structures. Moscow: Stroyizdat. 1977; 154.

10. Karamansky T.D. Numerical methods of structural mechanics. M.: Stroyizdat. 1981; 436. (In Russ)

11. Sorin Micu, Ionel Rovenţa, Laurenţiu Emanuel Temereancă. Approximation of the controls for the linear beam equation. Springer-Verlag London, 2016. URL: researchgate.net/publication/294736245 Approximation of the controls for the linear beam equation.

12. Verzhbitsky V.M. Fundamentals of numerical methods. Moscow: High school, 2002; 840. (In Russ)

13. Ilyin V.P., Karpov V.V., Maslennikov A.M. Numerical methods of solving problems of structural mechanics. - Moscow: Publishing house ASV; Saint-Petersburg: Saint-Petersburg State University of Civil Engineering and Architecture, 2005; 425. (In Russ)

14. Kulterbaev Kh. P., Baragunova L.A., Shogenova M.M., Senov Kh. M. About a High-Precision Graphoanalytical Method of Determination of Critical Forces of an Oblate Rod. Proceedings 2018 IEEE International Conference "Quality Management, Transport and Information Security, Information Technologies" (IT&QM&IS). September, 24-28, 2018. St. Petersburg. Russia 2018; 794-796. (In Russ)

15. Kulterbaev Kh.P., Baragunova L.A. About realization of the problem of eigenvalues of a compressed-stretched rod on computer. Computer Technology in Construction: Proceedings of the All-Russian Scientific and Technical Conference. DSTU. - Makhachkala: Alef (IP Ovchinnikov), 2012; 90-94. (In Russ)

16. Shogenova M.M., Shogenov O.M., Baragunova L.A. Solving the Euler problem on the stability of a rod with non-classical boundary conditions. Engineering Herald of the Don. 2021, №11. URL: http://go.microsoft.com/fwlink/?LinkId=69157. (In Russ)

17. Litvinov S.V., Yazyev B.M., Beskopylny A.N., Ananyev I.V. Calculation of Stability of Rods from EDT-10 with Initial Death of Rod as S-Curve. Engineering Herald of the Don 2012, 1. URL: ivdon.ru/magazine/archive/n1y2012/620/.

18. Baragunova L.A. Stability of pre-compressed reinforcement in reinforced concrete beams. Engineering Herald of the Don 2016, №4. URL: ivdon.ru/magazine/archive/n1y2016/3797/.(In Russ)

19. Baragunova L.A. On the effect of elasticity of supports on the stability of compressed rods. Science. Technique. Technology (Polytechnic Bulletin). LLC "Publishing House-Yug", Kuban State University, 2013;1 – 2: 49 - 54. (In Russ)

20. Baragunova L.A., Shogenova M.M. Stability loss of a rod under unevenly distributed load. Engineering Herald of the Don. 2018;1. URL: ivdon.ru/ru/magazine/ archive/n1y2018/4810. (In Russ)