AlfaBuild

RAR RUS 3801-3801 H-9967-2013 16412815600 0000-0002-8588-3871 Moscow Power Engineering Institute Kirsanov Mikhail Nikolaevich mpei2004@yandex.ru

Moscow, Russian Federation

Model of a spatial cantilever truss and formulas for calculating its deformations The object of research is a spatial lattice statically determinate regular cantilever truss formed by connecting eight plane trusses. The truss is loaded at its nodes. The longitudinal stiffness of the bars is assumed to be equal. Formulas are derived for the dependence of the truss end deflection on its dimensions and the number of panels. Method. The forces in the bars are found in analytical form using computer mathematics methods by solving a system of algebraic equations. The Maxwell - Mohr formula is used. Generalization of the solutions to the case of an arbitrary number of panels is performed by induction. Results. The resulting formulas for the deflections have the form of polynomials in the number of panels. Formulas are derived for the forces in individual, most critical bars. Asymptotic forms of the solutions are found. 10.57728/ALF.38.1 69 Space truss Maxwell-Mohr formula Induction Maple Analytical solution Deflection Asymptotics https://alfabuild.spbstu.ru/article/2026.38.1/ 3801.pdf

RAR RUS 3802-3802 Peter the Great St. Petersburg Polytechnic University Zimin Sergey Sergeevich zimin_sergei@mail.ru

St. Petersburg, Russia

Orlovich Roman Boleslavovich Dimitrieva Sofia Olegovna Zimina Elena Andreevna Influence of backfilling of masonry vault grooves on their load-bearing capacity In static calculations of stone vaults, backfill is usually considered only as a gravitational load, and its actual interaction with the vault structure is often not taken into account. The object of research is the stress state of stone vaults. The influence of backfill on the load-bearing capacity of stone vaults is analyzed. Methods. A numerical analysis was conducted using the finite element method for vaults with a span of 8.0 m and a thickness of 0.25 m. Two materials for backfilling were considered: sand (E = 120 MPa, density 1500 kg/m³) and expanded clay (E = 15 MPa, density 250 kg/m³). The ratio of the vault height to the span f/L varied from 0.1 to 0.5. Two calculation schemes were compared: taking into account the interaction of the vault with the backfill and without it. Results. It has been found that the inclusion of backfill in the design model reduces the tensile stresses in the vault. The positive effect increases with the ratio of the vault height to the span and is more pronounced for cylindrical vaults than for cross vaults. Sand backfill provides a more significant reduction in stresses due to its higher stiffness, but it also increases the overall load on the vault. The share of the horizontal распорной нагрузки H, perceived by the backfill, reaches 43% for sand and 37% for expanded clay in semicircular vaults (f/L = 0.5). Conclusions. To reduce the static load, it is recommended to use lightweight backfill materials (such as expanded clay), while maintaining a positive interaction with the vault. The effectiveness of lightweight backfill can be improved by using layer-by-layer consolidation with cement mortar or polymer composite reinforcement. ***ARTICLE IN PRESS*** 10.57728/ALF.38.2 69 Cylindrical vaults Cross vaults Filling of vault cavities Stressed state of vaults Masonry structures Vaulted https://alfabuild.spbstu.ru/article/2026.38.2/ 3802.pdf