## 5 Conclusions  
In this paper, a multidisciplinary approach useful for the evaluation of the seismic performance of historic constructions characterised by complex geometries is discussed. In particular, two iconic case studies located in different areas of Italy were analysed: (i) the basilica of Santa Maria di Collemaggio; and (ii) the basilica of Santa Maria Novella in Florence. The starting point of the project involved the reconstruction of their geometry based on the data obtained from a series of complete laser scanner surveys. Subsequently, finite element models of the two churches were developed using plate elements to represent the walls, the facades, the vaults, the dome, and the beam elements to schematie the main pillars of both the transport area and the naive columns. An Eigenvalue analysis was performed to define the dynamic behaviour of the basilicas. This analysis has revealed that the vibration mode shapes of the main fundamental natural periods are analogous between the two case studies. This phenomenon can be attributed to their structural configurations: both exhibit a significant eccentricity between the gravity centre and the stiffness centre, resulting in the presence of torsional effects.  
To evaluate the seismic vulnerability of the two churches, a series of non-linear time history analyses were carried out using seven spectrum-compatible accelerograms obtained from the PEER database and considering the approach reported in [39]. The obtained results were quantified by means of risk indices defined by the ratio between the value of the peak ground acceleration that leads to the collapse of the first monitored structural elements and the design peak ground acceleration calculated as reported in [33] for the life safety limit state. Both the case studies were characterised by risk index values less than 1 (0.287 for Santa Maria di Collemaggio and 0.267 for Santa Maria Novella), which highlights the high seismic vulnerability of the two buildings.  
According to the considerations on the basilicas' structural configurations, the first elements to collapse are the main pillars of the transport area. This hypothesis is supported by the partial collapse observed at Santa Maria di Collemaggio during the 2009 L'Aquila earthquake.  
Finally, it is important to highlight that the collapse mechanism observed in the two case studies can apply to all historic churches with a similar structural layout. This is due to the presence of a significant eccentricity between the gravity centre and the stiffness centre. This aspect can be useful for planning the correct structural interventions to improve the seismic performance of historic churches while taking care not to develop collapse mechanisms in other structural elements, such as the facade or the naive columns.  
Conceptualization, M.Z., E.R. and A.C.; methodology, M.Z., E.R., E.V. and V.P.; software, M.Z., E.V. and A.D.; validation, E.R., V.P. and A.C.; formal analysis, M.Z. and A.D.; investigation, E.R., V.P. and A.D.; data curation, V.P. and A.D.; writing--original draft preparation, M.Z., E.V. and V.P.; writing--review and editing, E.R. and A.C.; and supervision, A.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.