# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 3 Small-Scale Approaches
### Finite Element Methods
#### 3.2.1 FEM Modelling: Strategies and Issues Applied to Cultural Heritage
Dealing with highly deformable structures, neglecting the floor contribution is more realistic than assuming a completely rigid plane [167]: the influence of the modelling strategy for timber frame floors was investigated by [PERSON], [PERSON] [161], comparing the effects when considering them as (i) all deformable, (ii) partially deformable and partially rigid (as the surveyed situation), (iii) or all rigid in their plane. [PERSON] and [PERSON] [189] proposed the use of two diagonal trusses with St. Andrew's cross configuration to represent deformable floors; the diagonal axial stiffness of the diagonals was calibrated on the actual floor in-plane stiffness. Alternatively, the adoption of a bidimensional shell element was suggested, accounting for the floor's in-plane stiffness by calibrating proper orthotropic materials. Timber floors as equivalent plates (i.e., plates with the same stiffness as the timber frames) were also adopted by [PERSON], [PERSON] [190]. Vaulted surfaces can be modelled according to their real shape both through shell elements [161, 186] and solid elements [173, 184]. The thrust effect of the vaults on the confining walls is properly evaluated, but the computational effort and meshing drawbacks are relevant when dealing with a high number of vaults. When aiming at assessing the structural capacity of a whole building, it is commonly accepted in the literature to model vaults as equivalent plates [190, 191, 192, 193, 194, 195], therefore strongly limiting numerical and meshing issues. Indeed, when the aim is the analysis of a masonry vault, the numerical model shall include both the vault (properly modelled) and the surrounding bearing structures since the seismic behaviour of the building strongly influences that of the vaults within it, as demonstrated by [PERSON], [PERSON] [173]. Modelling of the 'In-Aggregate' Effect  
When dealing with non-isolated buildings or when there is the need for modelling only a building portion, FE models of historical constructions shall face the issue of representing the interaction with adjacent structures. This condition is quite common since historical buildings are often part of an urban fabric resulting from progressive additions, demolitions and modifications, which frequently determine a connection among adjacent constructions or even within portions of the same construction. Depending on the toothing level between adjacent structural parts and the following reciprocal constraint established, fully connected [188] and not connected [158] configurations may be adopted as limit conditions, but intermediate situations may be even caught. [PERSON] and [PERSON] [166] modelled the Reggio Emilia cathedral by accounting for a portion of the surrounding buildings, calibrating the model through dynamic tests. The comparison of natural frequencies and modal shapes of the two extreme conditions above-mentioned was performed even in the analysis of the San Felice sul Panaro fortress [172], later updated through the modelling of the main tower of the fortress together with some portions of the adjacent elements, while simulating the remaining parts through section surfaces properly implemented by varying the Young's modulus. [PERSON], [PERSON] [188] analysed the influence of the boundary conditions regarding a portion of the Palazzo dei Musei (Modena, Italy) and four different cases: the presence of translational springs with low stiffness and the presence of translational springs with high stiffness, besides the two limits conditions of a not connected and fully connected building. In the two intermediate situations, the elastic stiffness for the spring elements used to simulate the non-modelled part was determined based on a reliable range of fundamental periods. A similar approach was used by [PERSON], [PERSON] [196] for the Sciri Tower in Perugia (Italy).