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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