33407 2304-6295 3 123 2026 1-60

RAR RUS 12301-12301 H-9967-2013 16412815600 0000-0002-8588-3871 National Research University Moscow Power Engineering Institute Kirsanov Mikhail Nikolaevich mpei2004@yandex.ru

Moscow, Russian Federation

Formulas for calculating deformations of a cross-shaped tower The object of research is a spatially regular tower truss with a cross-shaped plan. The truss rod material is elastic, the rod cross-sections have equal stiffness, and hinges connect the rods. The trusses of the twelve lateral faces of the truss are planar diagonal lattices. The truss structure is statically determinate. The truss is loaded at the nodes. Method. Analytical dependencies of deflection on the number of panels are derived in the Maple computer mathematics system using the induction method. To determine the forces, a system of algebraic equilibrium equations for the nodes is constructed. Nodal displacements are calculated using the Maxwell-Mohr formula. The effect of uniformly distributed and concentrated lateral loads is considered. Results. Formulas for the dependence of node displacements on the load magnitude and the structure dimensions are polynomials in the number of panels. Asymptotic forms of the solutions and forces in individual, most critical rods are obtained. 10.4123/CUBS.123.1 69 Truss Deflection Tower Computer Mathematics System Analytical solution Asymptotics https://unistroy.spbstu.ru/article/2026.123.1/ 12301.pdf

RAR RUS 12302-12302 H-9967-2013 16412815600 0000-0002-8588-3871 National Research University Moscow Power Engineering Institute Kirsanov Mikhail Nikolaevich mpei2004@yandex.ru

Moscow, Russian Federation

Fundamental vibration frequency of a lattice truss with a lift The research object is a statically determinate plane lattice truss with an arbitrary number of panels, additional end supports, and a small uplift. Method. Equal masses model the inertial properties of the truss at its nodes. The forces in the bars are found by cutting out nodes in the Maple analytical computing system. A modified Dunkerley method is used to calculate the structure's first natural frequency analytically. The sum in this method's formula is calculated using the mean value theorem, which significantly simplifies the calculation and the final natural-frequency formula. The average frequency is taken as the half-sum of the oscillation frequencies of the middle nodes in the lower and upper chords of the truss. The rigidity of the structure is calculated using the Maxwell – Mohr's formula under the assumption that the rigidities of all rods are the same. Results. The coefficients in the final formula are obtained as simple polynomials in the number of panels no higher than the third degree. Compared with a numerical method that accounts for all system degrees of freedom, the proposed method provides good accuracy, slightly underestimating or overestimating the frequency depending on the number of panels. The proposed algorithm can be used for other regular statically determinate planar and spatial structures. 10.4123/CUBS.123.2 69 Truss Natural frequency Computer Mathematics System Simplified Dunkerley method Analytical solution Additional Supports https://unistroy.spbstu.ru/article/2026.123.2/ 12302.pdf

RAR RUS 12303-12303 Mkrtychev Oleg Vitalievich Bending calculation of rectangular beams using trigonometric series The object of research is the stress-strain state arising from the bending of a rectilinear beam. A beam with a rectangular cross-section is considered. The load is applied symmetrically to the top and bottom surfaces. The beam is loaded with a uniformly distributed load with stepwise intensity, with values changing regularly along the beam's length. Method. This study uses methods of classical elasticity theory and structural mechanics. The numerical-analytical solution utilizes the theory of trigonometric Fourier series. Results. A formula is given for the analytical determination of the stress arising from the bending of a rectilinear beam. To derive the formula, the given load was expanded into a Fourier series, followed by a well-known method for solving structural mechanics equations. 10.4123/CUBS.123.3 69 Bending Rectangular beam Analytical solution Fourier series Trigonometric series https://unistroy.spbstu.ru/article/2026.123.3/ 12303.pdf

RAR RUS 12304-12304 57210972600 0000-0001-6472-9413 Kazan State University of Architecture and Engineering (KSUAE) Shmelev Gennady Nikolaevich gn.shmelev@mail.ru

Russian Federation, Tatarstan republic, Kazan, Zelenaya Str., 1

Sagdullin Aizat Ramilevich Metal frame of modular collapsible wedge scaffolding: Stress–strain state under cable pre-stress The object of research is mobile collapsible metal structures based on modular wedge scaffolding, widely used for the construction of temporary structures (stands, stage structures, enclosing walls) during mass events. This work aims to identify shortcomings in operating prefabricated metal structures based on wedge scaffolding and develop methods to improve their efficiency. The work is relevant because mobile rod systems for temporary structures are increasingly used, but their operation and the impact of joint gaps remain insufficiently studied. Method. The static analysis of the tribune fragment was performed using the LIRA-SAPR 2013 R3 software (type 5 scheme) with the use of beam finite elements (finite element type 10). The length of each element was divided into 5 equal segments (approximately 0.4 m per segment, depending on the element length). The actual semi‑rigid behaviour of the connections between the crossbeam and the deck was taken into account by assigning hinges of finite rigidity based on the bending moment diagram. The foundation was modelled as an elastic support (single‑node FE type 56 with automatic iterative calculation of subgrade reaction coefficients). The applied loading included self‑weight (γf =1.05), a live load of 4.0 kN/m² from spectators (γf =1.2), and static wind loads along the ±Y directions for terrain categories A and B. The analysis was limited to static conditions because the goal was to compare ties under primary loads; crowd dynamics are not considered and are noted as a limitation. Results. The main results of the study are as follows: using the example of the Kazanka facility (Kazan, Russian Federation), the study identified an uneven distribution of forces and the significant influence of foundation settlements. The study numerically demonstrated the high efficiency of introducing pre-stressed flexible connections (cable ties) into the rod system. The findings suggest that their use can reduce uneven support settlements by up to 42%, allow lightly loaded crossbars, and regulate force distribution. For freestanding walls, rational schemes for combining standard diagonals and ties have been developed and compared, reducing movements by 43% and metal consumption by 19%. 10.4123/CUBS.123.4 69 Modular scaffolding Wedge connection Pre-stressing Cable tightening Stress-strain state Prefabricated structure Numerical modeling https://unistroy.spbstu.ru/article/2026.123.4/ 12304.pdf

RAR RUS 12306-12306 Daryani Mohammad 0000-0003-2626-2626 Peter the Great St. Petersburg Polytechnic University Kotov Evgeny Vladimirovich ekotov.cfd@gmail.com

St. Petersburg, Russian Federation

Geometric and operational parameters in narrow vertical solar chimneys: Theoretical modelling and statistical analysis The object of research is a narrow vertical solar chimney designed for passive building ventilation, specifically focusing on the interplay of geometric and operational parameters within the narrow chimney regime (gap-to-height ratio ≤ 0.2). The purpose of this work is to systematically optimize the absorber height, air gap (set equal to the inlet height), and solar radiation intensity to maximize the volumetric airflow rate and air changes per hour (ACH), thereby providing a computationally efficient alternative to complex numerical simulations. Method. A steady-state analytical model, solving coupled energy balances for the glass cover, air stream, and absorber wall, was developed and implemented as a rapid, open-source predictive tool in Python. The model was first validated against established theoretical data, yielding a mean absolute percentage error of 5.3% (R² = 0.98). Subsequently, a Taguchi L16 orthogonal array was employed to evaluate the main effects of the selected parameters (absorber height: 800–1500 mm; air gap/inlet height: 50–150 mm; solar radiation: 250–700 W/m²), followed by Analysis of Variance (ANOVA) to quantify their statistical significance and relative percentage contributions. Results. The ANOVA revealed that the air gap is the most influential factor, contributing approximately 68% to the total variation in airflow, followed by solar radiation intensity (17%) and absorber height (14%). The optimal configuration for maximizing ventilation within the studied design space corresponds to the highest tested levels of all three parameters (1500 mm height, 150 mm gap, and 700 W/m²), yielding a volumetric flow rate of 0.0307 m³/s (approximately 4.1 ACH for a 27 m³ room). The findings confirm that, for narrow chimneys, monotonically increasing the air gap and inlet height while keeping them equal consistently improves performance, validating empirical design recommendations and establishing a robust, fast predictive framework for small-scale solar chimney optimization. ***ARTICLE IN PRESS*** 10.4123/CUBS.123.6 69 Solar chimney Natural ventilation Theoretical modeling Taguchi method Narrow chimney Air gap optimization Air changes per hour (ACH) https://unistroy.spbstu.ru/article/2026.123.5/