Parametric Design of Triangulated Tensile Spoke-Wheels With Bi-Convex Profile for Roof Structures on Elliptical Stadium Stands

Identifier:  imarina:9389462

Handle: https://hdl.handle.net/20.500.11797/imarina9389462

Authors:  Martin-Saiz, Rodrigo; Herrera, Blas

Abstract:
In this article, we make an analytical development of the step-by-step of a parametric design procedure for triangulated tensile spoke-wheels with bi-convex profile for roof structures on elliptical stadium stands. Through this procedure it is possible to define the geometric shape and the distribution of the pre-stressing forces necessary to achieve optimal conditions for the cross-section sizing of the outer ring, while considering its non-circularity. These optimal conditions are achieved when, under permanent loads, an in-plane homothetic deformation occurs. In each step of the procedure we formulate system of equations that describe the relationship between the geometric shape and the mechanical behavior, and we define the numerical methods to solve them. From the ground plan shape of several Roman amphitheaters, we develop application examples and we show the reasonable geometric limits of the design procedure. Finally, in an analysis model, we verify how, effectively, a structure designed according to this procedure deforms homothetically under permanent loads.