Salvatore Sergio Ligaro

The web bridge

Abstract Optimal cable arrangements for tensile structures, for bridges in particular, are determined by drawing inspiration from the wrinkling behavior of flat elastic membranes stretched in their plane. The underlying rationale for the approach consists in the fact that wrinkle patterns naturally develop according to a “maximum-stiffness” criterion. By way of illustration, a two-dimensional theory is proposed to model the wrinkling phenomenon in membranes subjected to general in plane loading, and an iterative procedure is then presented for solving numerically the governing set of non-linear equilibrium equations in a finite-element framework. The numerical results show good agreement with experiments performed on thin polyethylene sheets. An idealized web bridge is then conceived of, in which the deck is regarded as being sustained by an elastic membrane. A simple criterion is then used to pass from the continuous natural wrinkled equilibrium configuration of the membrane to a discrete layout, formed by a cable net, exploitable in the design of a real bridge. By changing the parameters controlling the shape of the web, various “optimal” cable arrangements are determined. These turn out to resemble classical cable-stayed bridges or mixed suspended and cable-stayed “hybrid” solutions.

The Problem of Additional Load of Minimum Work in a Thin Plate

A rectangular elastic plate is simply supported along its boundary. A flexural couple is exerted on one of its sides, while the others remain unloaded. The question is posed, assuming the ability to produce couples along the side opposite the already loaded one, of determining the values of these latter couples which would minimize the elastic strain energy of the system.