Parametric design of non-conventional diagrid systems for tall buildings

Abstract

Geometric patterns inspired in historical Islamic ornamental art have attracted the attention of contemporary designers worldwide. The large variety of shapes, symmetries and combinations is a source of inspiration, but at the same time makes it difficult to provide general rules when used in a technological application. Structural small-scale applications have been object of research, but there are potential applications at larger scales that deserved attention. In view of some recent proposals of Islamic patterns as structural grids for tall building skins, the question of their structural efficiency, especially compared to conventional grids, arises. The purpose of this research is to assess the performance of structural grids based on geometric Islamic patterns as outer skins of tall buildings. For this purpose, several historic patterns have been classified. An equivalent meta-material has been defined for each pattern, based on the homogenization method for a series of saturations or beam sizes. Their response in different orientations has been studied to identify their structural behaviour based on the pattern geometry. Their relative performance has been assessed for all patterns against themselves and against the conventional diagrid system. All this process has been collected and summarized in a predesign tool made of graphs, pictures and tables Finally, the predesign tool accuracy has been assessed and applied to three tall buildings. All those steps have been structured in three distinctive levels: At the method level, the conclusion is that the developed predesign tool is a success as it provides a higher level of accuracy than modelling all the beams. It is also faster and easier to implement, than modelling all the beam elements, to compare alternatives in early stages as the complexity of modelling the patterns is postponed to later stages. As the saturation decreases and the effective beam length influence in the beam model results diminishes, the beam model will become more reliable than the predesign tool and vice versa. At the pattern level, the most interesting finding is that the patterns with square symmetry (symmetry directions at 90º) display a perpendicular isotropic behaviour, whereas the patterns with pentagonal symmetry (symmetry directions at 72ª) display an orthotropic behaviour, and the patterns with hexagonal symmetry (symmetry directions at 60ª) display an isotropic behaviour. It has also been studied the effect that would have filling the stars as an alternative to building the patterns as an assembly of beams. At the building level, it has been found a few geometric Islamic patterns that could be suitable alternatives to the conventional diagrid systems, a pattern with a similar performance and even a pattern with a higher structural performance than the conventional diagrids. This highly performing pattern is currently been used for some architects such as Shigeru Ban in their parametric designs. In this regard, it can be concluded that the objective of finding suitable alternatives to conventional diagrid systems has also been a success and it can affect some designers engineering judgement. The homogenization process obtained an equivalent ideal material corresponding to a plane infinite panel that will not correspond with the built structural grid. The use of complex geometries and its application to tall buildings introduce effects not considered in the homogenization that will disrupt the expected structural performance. Those effects are minimized in the case of other shells structures such as domes but can be important in the case of tall buildings. It is not advisable to account for the squeezing effect by adapting the saturation with the change of the modulus size in the x-direction as the relative beam depth has a greater impact in the overall stiffness than the change of geometry due to the squeezing effect. The distortion effect cannot be accounted for directly and it depends on the angle of the distortion and the pattern. However, in the studied case it has been found a required correction factor of 1.2-1.3, in line with other uncertainty factors used in practice. Finally, the intermediate supports can have a great influence in the final drift. It depends on the pattern used and the number of diaphragms inside the module. Nevertheless, the use of intermediate supports is always beneficial and not considering them will always lead to more conservative solutions. In conclusion, this document successfully bridges the knowledge gap regarding the structural behaviour of historic Islamic patterns, with comparative tables. It identifies the best performing patterns and their best orientation, and it provides a useful tool for the decision making in the design process of in-plane bearing geometric Islamic patterns.