Rigidity and safety optimization of 3-dimensional repetitive frame systems as bar-joint building with graphs

Abstract

We explore options for improving the rigidity of a framework if the modeled building presents cubic symmetries. Braces are used to provide resistance to lateral loads in the framework. These cubic symmetries allow us to use a graph theoretical model and the possibility of a more accurate prediction of the rigidity of the braced cubic structure. Fixed joints attach the three-dimensional cubic grid structure as Scaffolding its base face and its lateral face to the planar ground and a planar lateral wall, respectively. Inserting some short or long bracing elements, we make the framework of the Scaffolding rigid. We suggest the revision of the sample scaffolding one of the standards. We provide a convenient method to determine if a braced structure as an n-story building with a core is rigid or flexible. This result is also useful from the algorithmic point of view, and it is applicable in structural and safety engineering, which could be a useful input of simulation and topology optimization. When the simulation is expensive, the Bar and Joint model could work at a low computational cost. The presented results provide the base of the algorithms which contribute to the development of a better characterization of the structures which are discretized as Bar and Joint Scaffolding frames or can be subdivided to those.