Deformations of the Rod Pyramid: An Analytical Solution

The object of the study is a spatial statically determinate pyramid-type covering truss. The truss has vertical support posts along the perimeter of the base. The corner nodes are fixed on spherical support, cylindrical, and rack. The truss has axial symmetry. The aim is to determine the analytical dependence of the deflection of the structure on the number of panels in its base. Two types of loads are considered: distributed along the edges and vertical loads concentrated at the vertex. Method. The Maxwell - Mohr formula is used to determine the deflection. The forces in the rods, together with the reactions of the supports, are found in their general system of the equilibrium equation of all nodes. The generalization of partial solutions to an arbitrary number of panels is obtained by induction using operators of the Maple computer mathematics system. Results. The dependence of the deflection on the number of panels is obtained in the form of a compact formula containing quadratic or linear polynomials in the number of panels. The inclined and horizontal asymptotes of the solutions are found. The existence of deflection minima depending on the number of panels is shown.