DEFORMATIONS AND DISPLACEMENTS OF WOODEN TRUSSES IN THE CATHEDRAL OF SAN PIETRO IN BOLOGNA THROUGH REVERSE ENGINEERING METHODS

The main topic of this work is the most recent step of a wider research project that has analyzed a few wooden roofing structures in the area of Bologna. These case studies are represented by a set of important churches in Bologna, all built between the 16th and 18th centuries, whose pitched roofs are supported by timber trusses. The most interesting roofing is in the Cathedral of Saint Peter whose trusses were possibly the biggest in Italy – and perhaps in Europe – at the time of construction. Having approximately 26 meters of span, 7 meters of height for nearly 9 tons of weight these trusses have a complex static conception with the coexistence of an external nondeformable triangle and an internal virtual discharging arc. The research protocol includes an acquisition step followed by the digital rendering of the acquired data. This last step provides many outputs (photos, drawings, graphs and 3D models) that constitute the operative tools to define and correctly interpret the behavior of the constructive systems studied. Results interpretation therefore allows us to suggest the most coherent design solutions, disengaging them, where necessary, from usual and standardized techniques. To avoid operating with excessive approximations, it was decided to transform the point cloud into 3D models using parametric modeling tools such as Grasshopper generative algorithms that once created for a single truss, allow to automatically generate 3D models of all trusses, changing only input parameters. The first result of this process is a basic 3D model representing the truss rendered with a limited number of sections. Number and position of the sections used has been decided in order to have the best-fitted 3D model with the lowest number of sections. Furthermore, it is possible to define an ideal 3D model, created through a series of robust theoretical assumptions, representing a reasonable original truss condition at construction time and used for displacement and deformations analyses. This is useful for analyzing the current static condition of the truss highlighting all undergone changes during its service life. The basic principle is to bring the basic 3D model to a pre-condition without displacements and deformations. In other words, to what it is supposed to be the original condition at construction time. The study proposed here is based on an accurate geometric and material survey of all constructive elements but above all, on the attempt to clearly understand the original implementation methods through the "rational" use of reverse engineering software and techniques. On the one hand, the analysis aims to give importance to this kind of constructive elements, neglected in the literature, identifying also new functional types, on the other it is used as an effective investigation protocol, with high diagnostic capability due to the wide use of technologies. This investigation protocol has been set up in order to systematize the analysis of these roofing systems and aims at accelerating modeling procedures as well as bringing on new tools for analyzing these structural systems surveyed through laser scanning devices.