A quest for the structural response through geometric representation of the design of built heritage

To ensure Cultural Heritage preservation it is necessary to understand its level of structural safety. When it comes to buildings with complex geometries, however, it is not easy to give an answer to this need: the current methods, require numerous inspections, time and economic resources. The goal of this study is to understand how to deal with the preliminary static study of an existing complex structure, starting with already available traditional 2D surveys. It is possible to achieve a 3D restitution of a building with a correct use of simple geometrical and graphic rules and with the help of the most common modeling digital software. The method works with various survey typologies, with increasing precision, but the descriptive geometry is that used originally, and brings with it the design idea and the original proportions. The method is applied to the apse of the Duomo of Milan, but is extendable and can be generalized for many buildings characterized by complex systems with arches, vaults and domes. The differences between the so represented ideal structure and the constructed real structure may be negligible for the purposes of the static analysis for which the method is used. The three-dimensional representation allows to derive the volumes and the weight of the construction elements and through the static method of limit analysis it is possible to study the structural response. In the case analyzed, the adequacy of the geometrical layout and the soundness of the structure designed 630 years ago has been demonstrated.