Formulas for calculating deformations of a cross-shaped tower

Building constructions, buildings and structures
Authors:
Kirsanov, Mikhail Nikolaevich
Abstract:

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.

Key words:
TrussDeflectionTowerComputer Mathematics SystemAnalytical solutionAsymptotics
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