Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)3156410.22363/1815-5235-2022-18-2-93-103Research ArticleNonlinear and linear analysis of the overall stability of the load-bearing system of a high-rise building with a load-bearing trunkInozemtsevaOlga V.<p>Candidate of Technical Sciences, leading designer</p>olga.inozemtseva@yandex.ruhttps://orcid.org/0000-0002-6608-7458InozemtsevVyacheslav K.<p>Doctor of Technical Sciences, Professor, Department of Building Materials, Structures and Technologies</p>aditi2003@mail.ruhttps://orcid.org/0000-0003-2817-0426Construction Bureau “SmartProekt”Saratov State Technical University named after Yu.A. Gagarin200720221829310320072022Copyright © 2022, Inozemtseva O.V., Inozemtsev V.K.2022<p style="text-align: justify;">The results of numerical calculations can and should be verified, but testing a complex and detailed computational model is problematic. This possibility is provided by simplified models represented by simple computational schemes that are available for qualitative analysis, and the numerical results obtained are predictable. Such calculation schemes, as a rule, describe individual calculation tasks facing designers. For example, linear stability analysis is offered by the American Institute of Steel Structures (AISC). One of these models is discussed. The model under consideration is based on a linear analysis of the stability of a cantilever rack, which can be considered as a simple model of the bearing trunk of a high-rise building. A comparison of critical loads based on nonlinear and linear analysis of the stability of the cantilever rack is carried out. It is concluded that the considered linear model makes it possible to obtain a preliminary estimate of the critical load to verify the results of computer calculations using more complex models of the general stability of the equilibrium of the bearing trunk of a high-altitude object.</p>high-altitude objectgeneral stabilitytesting of resultsnonlinear stability modellinear stability modelcritical loadвысотный объектобщая устойчивостьтестирование результатовнелинейная модель устойчивостилинейная модель устойчивостикритическая нагрузка[Zhestkova S.A., Inozemtsev V.K. Bifurcation problems of stability of high-rise buildings. Structural Mechanics of Engineering Constructions and Buildings. 2016;(4):53–57. (In Russ.)][Zhestkova S.A., Inozemtseva O.V., Inozemtsev V.K. List''s deformations of high-rise building on deformable slab. Structural Mechanics of Engineering Constructions and Buildings. 2017;(2):74–78. (In Russ.)][Zhestkova S.A., Inozemtseva O.V., Inozemtsev V.K., Redkov V.I. Calculation of overall sustainability of structures with the high centre of gravity. Structural Mechanics of Engineering Constructions and Buildings. 2017;(5):61–65. (In Russ.) https://doi.org/10.22363/1815-5235-2017-5-61-65][Zhestkova S.A., Inozemtsev V.K. General stability of a system with a highly located center of gravity. Bulletin of the Volga Regional Branch of the Russian Academy of Architecture and Building Sciences. 2018;(21):156–159. (In Russ.)][Inozemtseva O.V., Inozemtsev V.K., Murtazina G.R. Roll-over stability as a problem of high-rise buildings’ designing. Structural Mechanics of Engineering Constructions and Buildings. 2021;17(3):228–247. https://doi.org/10.22363/1815-5235-2021-17-3-228-247][Perelmuter A.V., Slivker V.I. Stability of the equilibrium of structures and related problems. Moscow: SCUD SOFT Publ.; 2010. (In Russ.)][Bazant Z.P., Cedolin L. Stability of structures: elastic, inelastic, fracture, and damage theories. Mineola: Dover Publications Inc., 2003.][Sadd M.H. Elasticity: theory, application and numerics. 4th ed. Academic Press, 2020.][Patel A. Geotechnical investigations and improvement of ground conditions. 1st ed. Woodhead Publishing, 2019.][Ratner L.W. Non-linear theory of elasticity and optimal design. 1st ed. Elsevier Science, 2003.][Levi-Civita T., Amaldi U. Lezioni di meccanica razionale (vol. 1, part 2). Bologna: Zanichelli; 1923.][Rabinovich I.M. Questions of the theory of static analysis from structures with one-way connections. Moscow: Stroiizdat Publ.; 1975. (In Russ.)][Schulz M., Pellegrino S. Equilibrium paths of mechanical systems with unilateral constraints. Part I. Theory. Proceeding of the Royal Society. Ser. A. 2000;456(8):2223–2242. https://doi.org/10.1098/rspa.2000.0610][Perelmuter A.V., Slivker V.I. Equilibrium stability of structures and related problems (vol. II). Moscow: SKAD SOFT Publ.; 2011. (In Russ.)][Engel H. Carrier systems (R. Rapson, Preface; L.A. Andreeva, Transl.). Moscow: AST Publ., Astrel Publ.; 2007. (In Russ.)]