Diseño de anillos de compresión no circulares y distribución óptima de fuerzas en el plano

Resumen

At the beginning of times, technique was used to reduce the physical stress of any work undertaken by the mankind; this was done without taking into consideration any saving of the resources used. Indeed, it was the other way around, as more energy was required to develop more ambitious projects. In addition to this, as the physical stress was not any more an issue, the amount of resources being mobilised was increased. From some time now, we have understood that the resources are not infinite, and that their consumption could cause irreversible damage to the system. For this reason, anything that can reduce the consumption of material and energy is now welcomed. In the construction industry, material resources become the final product: a building, a bridge, a dam, etc. To build means to extract, to transform and to assemble these materials on site. Energy is required to develop each one of these processes. Generally, this energy is directly related the amount of each specific material used. There are two exceptions to this rule: when the material is extracted and transformed in the same site (as it does not require transport). When the material is recycled from another site (as it implies less transformation or it does not require it at all). In addition to this, each material has different performance properties an requires different quantity of energy for its transformation. Therefore, if the aim is to save material, and therefore energy, the focus should be put on replacing the conventional construction techniques and technologies by those ones that allow building lighter structures. The tensile structures are the lighter structural solution currently available, with a design challenge: the internal loads balance. If this problem is properly taken into consideration and solved, then the efficiency, which is the relation between the structural performance (span and capacity) versus the resources used (material and energy), can be increased considerably. This is especially relevant on long-span roofs. By doing this, a good design can be achieved, and therefore, on the use of proper use of technology to save material and energy. On long-span and tensile roof systems it is better to provide the equilibrium of the inner loads by a self-balancing system based on rigid elements, rather than the use of external structural elements. The rigid element provides a closed loads path that converts the internally statically indeterminate structure on an externally statically determinate structure. In the case of a spatial structure, these elements are compression rings or polygons. The most efficient ones are those that under permanent loading conditions do not need to resist bending forces. This is because their geometry matches the funicular of the in-plane loads transferred by the cables or membranes, together with the fact that they are being restrained against buckling by the same tensile elements. Compression rings with circular shape under the reactions produced by membranes with uniform tension forces have to resist axial compression forces only. In addition to this, the membrane provides total bucking restraint (at least in-plane). On the other hand, in circular compression rings with isotensioned and equidistant spokes, the same forces diagrams and buckling conditions apply to the each of the ring sections. This research is focused on the design of non-circular compression rings and how to achieve an optimum distribution of in-plane loads, so that they can get closer, or even match, those design conditions that apply to circular compression rings. In order to do so, three general cases have been analysed: rings with uniform loads, rigid polygons and rings with punctual loads. For each case, a design method is defined, as well as the optimum or ideal distribution of the in-plane loads