An Atypical Flat Arch in Prato Cathedral: Some Remarks on the Non-standard Plastic Behaviour of Stone Structures

In this contribution the equilibrium of an intriguing case study is studied, which was inspired by the flat arch that crowns the transept portal in the Prato Cathedral. The 'wrong' shape of some voussoirs invites to reflect on the difficulties for the application of limit analysis techniques to determine the collapse conditions. Investigations on the minimum friction coefficient compatible with an equilibrium condition are conducted by means of different methods. At first, a semi-analytical approach combines static and kinematic analyses exploiting both a modern version of the ‘stability area method’ and the virtual work theorem. Then, the results thus obtained are compared with those derived from a FEA, which aims at simulating the construction process of the flat arch, and from DEM, which capture the collapse mechanisms; results are in a very good agreement. Finally, inconsistencies in adopting a limit state analysis based only on the lower limit theorem are highlighted. This research stresses the need for a critical viewpoint in the examination of the collapse behaviour of masonry structures.