Funicular solutions for masonry vaults: a review of recent and past numerical methods

The great engineers, architects and master builders of 17th and 19th centuries constructed the most amazing vaults in the entire world. Considering that the advanced technologies were massively developed only in the 20th century, the traditional approach for constructing masonry vaults were based in the geometry. As Heyman said, the correct shape of a masonry structure ensures its safety. Nowadays, it can be consider that their practice was a success because many of these vaults still stand after all these years. This thesis describes the considerable existing approaches about funicular solution for masonry vaults with the principal features of each method and their extensions. All methods derives compression-only structural lower-bound solutions, which guarantees the safety of the vaulted structures with at least one admissible equilibrium state given its geometry and boundary conditions. The review comprehends the old methods, Graphic Statics and Limit Analysis that are a strong base to the recent ones, also presented in this paper, Thrust Network Method, Force Density Method, Thrust Network Analysis and Thrust Surface Method. In 2007, the Thrust Network Analysis was introduced by Block and Ochsendorf, since then some extensions of their work were brought up to the scientific community and they are summarized in this thesis due to the importance for upcoming improved methods. Lastly, it is presented an application of the software RhinoVAULT 2 for funicular form-finding using the Thrust Network Analysis approach. The project designed is the "Tettoia Nervi", placed in Bologna, Italy.