69439 AlfaBuild AlfaBuild 2658-5553 1 10.57728/ALF.38.1 Model of a spatial cantilever truss and formulas for calculating its deformations Model of a spatial cantilever truss and formulas for calculating its deformations 0000-0002-8588-3871 16412815600 H-9967-2013 Kirsanov Mikhail Nikolaevich mpei2004@yandex.ru Moscow Power Engineering Institute 16 02 2026 38 2 38 3801 3801

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.

 Space truss Maxwell-Mohr formula Induction Maple Analytical solution Deflection Asymptotics References 1         Zhang, D., Zhao, Q., Li, F., Tao, J. and Gao, Y. (2018) Torsional Behavior of a Hybrid FRP-Aluminum Space Truss Bridge: Experimental and Numerical Study. Engineering Structures, Elsevier Ltd, 157, 132–143. https://doi.org/10.1016/j.engstruct.2017.12.013 2         Grishanina, T.V. and Shklyarchuk, F.N. (2022) Numerical-Analytical Method for Calculating the Oscillations of Regular Structures. Mechanics of composite materials and structures, 28, 175–186. https://elibrary.ru/item.asp?id=49026364 3         Embaby, M. and El Naggar, M.H. (2025) Experimental and Analytical Investigation for Modular Double Truss Bridge. Engineering Structures, Elsevier, 322, 119087. https://doi.org/10.1016/J.ENGSTRUCT.2024.119087 4         Komerzan E.V. and Maslov A.N. (2023) Estimation of the L-Shaped Spatial Truss Fundamental Frequency Oscillations. Structural mechanics and structures, 37, 35–45. https://doi.org/10.36622/VSTU.2023.37.2.004 5         Komerzan, E. V. and Maslov, A.N. (2023) Analytical Evaluation of a Regular Truss Natural Oscillations Fundamental Frequency. Structural Mechanics and Structures, 37, 17–26. https://doi.org/10.36622/VSTU.2023.37.2.002 6         Goloskokov, D.P. and Matrosov, A. V. (2018) Approximate Analytical Approach in Analyzing an Orthotropic Rectangular Plate with a Crack. Materials Physics and Mechanics, 36, 137–141. https://doi.org/10.18720/MPM.3612018_15 7         Goloskokov, D.P. and Matrosov, A. V. (2018) Approximate Analytical Solutions in the Analysis of Thin Elastic Plates. AIP Conference Proceedings. https://doi.org/10.1063/1.5034687 8         Kirsanov, M.N. and Xuan, J. (2023) Kinematic Analysis, Spectrum of Natural Frequencies, and Formula for the First Frequency of a Planar Truss. AlfaBuild, 27, 2703. https://doi.org/10.57728/ALF.27.3 9         Zotos, K. (2007) Performance Comparison of Maple and Mathematica. Applied Mathematics and Computation, Elsevier, 188, 1426–1429. https://doi.org/10.1016/j.amc.2006.11.008 10       Luong, C.L. (2024) Dependence of the Region of Resonantly Safe Frequencies on the Dimensions of a Statically Determinate Flat Truss. Structural Mechanics and Structures, 41, 16–26. https://doi.org/10.36622/2219-1038.2024.41.2.002 11       Shchigol, E.D. (2023) The Formula for the Lower Estimate of the Natural Oscillations of a Flat Regular Girder Truss with a Rectilinear Upper Belt. Structural Mechanics and Structures, 37, 46–53. https://doi.org/10.36622/VSTU.2023.37.2.005 12       Tinkov, D. V. (2016) The Optimum Geometry of the Flat Diagonal Truss Taking into Account the Linear Creep. Magazine of Civil Engineering, 61, 25–32. https://doi.org/10.5862/MCE.61.3 13       Kazmiruk, I.Yu. (2016) On the Arch Truss Deformation under the Action of Lateral Load. Science Almanac, 17, 75–78. https://doi.org/10.17117/na.2016.03.03.075 14       Belyankin, N.A. and Boyko, A.Y. (2019) Formula for Deflection of a Girder with an Arbitrary Number of Panels under the Uniform Load. Structural Mechanics and Structures, 1, 21–29. https://www.elibrary.ru/download/elibrary_37105069_21945931.pdf 15       Ovsyannikova, V.M. (2020) Dependence of Deformations of a Trapezous Truss Beam on the Number of Panels. Structural Mechanics and Structures, 26, 13–20. https://www.elibrary.ru/item.asp?id=44110286 16       Kirsanov, M.N. and Luong, C.L. (2023) Natural Frequency Spectra of Spatial Structure. Construction of Unique Buildings and Structures, 107, 10604–10604. https://doi.org/10.4123/CUBS.106.04 17       Astakhov, S.V. (2024) Analytical Assessment of the Deflection of the Rod Model of a Four-Slope Roof Frame. Structural mechanics and structures, 43, 34–41. https://doi.org/10.36622/2219-1038.2024.43.4.003 18       Luong, C.L. (2024) Estimates of Deflection and Natural Frequency of Vibrations of a Hinged-Rod Truss with an Arbitrary Number of Panels. Structural mechanics and structures, 43, 42–53. https://doi.org/10.36622/2219-1038.2024.43.4.004 19       Luong, C.L. (2024) Resonance Safety Zones of a Truss Structure with an Arbitrary Number of Panels. Construction of Unique Buildings and Structures, 113, 11304. https://doi.org/10.4123/CUBS.113 20       Gribova O.V. (2025) Formulas for Calculation of Deflection and Natural Frequency of a Flat Truss with an Arbitrary Number of Panels. Structural Mechanics and Structures, 44, 31–39. https://doi.org/10.36622/2219-1038.2025.44.1.003 21       Hutchinson, R.G. and Fleck, N.A. (2005) Microarchitectured Cellular Solids - The Hunt for Statically Determinate Periodic Trusses. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 85, 607–617. https://doi.org/10.1002/zamm.200410208 22       Hutchinson, R.G. and Fleck, N.A. (2006) The Structural Performance of the Periodic Truss. Journal of the Mechanics and Physics of Solids, Pergamon, 54, 756–782. https://doi.org/10.1016/j.jmps.2005.10.008 23       Kaveh, A. and Talatahari, S. (2009) Particle Swarm Optimizer, Ant Colony Strategy and Harmony Search Scheme Hybridized for Optimization of Truss Structures. Computers & Structures., 87, 267–283. https://doi.org/10.1016/j.compstruc.2009.01.003 24       Kaveh, A. and Zolghadr, A. (2018) Meta-Heuristic Methods for Optimization of Truss Structures with Vibration Frequency Constraints. Acta Mechanica, 229, 3971–3992. https://doi.org/10.1007/s00707-018-2234-z 25       Kirsanov, M.N. (2023) Model of a Hexagonal Prismatic Truss. Oscillation Frequency Spectrum. Construction of Unique Buildings and Structures, 106, 10601. https://doi.org/10.4123/CUBS.106.01