Formulas for Calculating Deformations of Power Line Supports

Abstract

In this work, we investigate the static deformations of the spatial model of a statically determined truss of a power line support. The tetrahedral truss has a pyramidal extension at the base and a cross-shaped lattice. Brackets for attaching the supporting cables are located at the top of the truss. A spherical support hinge, a cylindrical one, and two vertical posts are located at the four corners of the structure base. We consider two types of loads: wind, and force. Horizontal forces applied to the nodes of one face model the wind load. The horizontal force is applied to the top of the structure. We aim to derive formulas for the dependence of the deflections of the truss on the number of its panels. We use the Maxwell-Mohr formula to determine the deflection. We find the efforts in the structural elements and the reactions of the supports from the general system of linear equations of equilibrium of all nodes of the truss. A series of solutions for trusses with different numbers of panels are summarized by the induction method in the Maple computer mathematics system. The sought formulas for the dependence of the vertical deflection of the console and the displacement of the top of the mast on the number of panels were obtained in the form of polynomials in the number of panels of degree not higher than the fourth. Some asymptotics of solutions is found in the work.