Problemas asociados al equilibrio en estructuras de membrana con bordes rígidos y cables

This paper presents the equilibrium analysis of a membrane with rigid and cable boundaries for the so called prestressing phase. The idea of using membranes in Civil Engineering applications such as footbridges, a new technology being developed in Spain, implies higher structural responsibility and more accurate analysis procedure. The membrane and its boundary are respectively identified to a regular and negative gaussian curvature surface and a set of regular curves whose curvature depends on the structural elements, rigid or cable. Equilibrium is directly expressed by means of boundary differential problems, in terms of the membrane shape and its stress tensor. We must outline that membrane-cable interface equilibrium leads to take into account a singular condition that makes the problem more difficult. Therefore, starting from the equilibrium equations, two dual problems can be considered namely direct problem and dual problem. Both problems will be defined and analyzed, studying their principal qualitative aspects. Particularly, for the direct problem a numerical resolution procedure is proposed, in order to obtain practical results.