Deformation of the Transmission Towers: Analytical Solution

The object of the study is a spatial model of a statically definable power line support truss. The four-sided truss has a cross-shaped lattice and a pyramidal extension at the base. In the upper part of the truss, there are consoles for attaching the carrier cables. The corner nodes in the base are attached to the ground by one spherical joint, a cylindrical joint, and two vertical posts. Two types of loads are considered: a horizontal load evenly distributed over the nodes of one face (wind), and a vertical load applied to one of the consoles. The aim is to determine the analytical dependence of the deflection of the structure on the number of mast panels in its middle part. Method. To determine the deflection, the Mohr integral is used. The forces in the rods are located simultaneously with the reactions of the supports from the general system of linear equilibrium equations of all nodes. Obtaining a solution and generalizing it to an arbitrary number of panels is obtained by induction in the Maple computer mathematics system. Results. The dependence of the deflection of the console and the displacement of the mast top on the number of panels is obtained in the form of a formula containing up to eight coefficients in the form of polynomials in the number of panels of degree no higher than the fourth. The analytical dependences of the forces in some rods as a function of the number of panels are determined.  Cubic asymptotics of the solutions is found.