## 1 Introduction  
Italy is the country with the highest number of cultural heritage structures in the world. As well as the fifty-three UNESCO World Heritage Sites, the official online database \"Vincoli in rete\" (VIR) [1], launched in 2012 by the Italian government and currently under development, reports more than 12,000 archaeological sites and monuments, as well as about 200,000 architectural heritage properties distributed all over the country. One of the main issues concerning the Italian cultural heritage is definitely its seismic risk. The most valuable buildings are often located in medium-high hazard territories that, even recently, have been shaken by severe earthquakes able to produce catastrophic damage scenarios. Among these,the 2009 L'Aquila [2; 3; 4], the 2012 Emilia [5], and the 2016 Central Italy earthquakes [6] are certainly worth mentioning. Moreover, these buildings were built without any type of design regulation and present significant sources of vulnerability, often exacerbated by the various transformations that have occurred over the centuries [7; 8; 9; 10]. In addition to the fact that some of these buildings often host a high number of people, they present a high architectonic value and contain precious artworks that need to be protected in order to avoid irremediable losses. Among these buildings, a large proportion of the immovable Italian cultural heritage is made of fortified architecture. Indeed, more than 3800 castles, 1000 fortresses, and 4400 towers are currently listed in the VIR database, but, according to other unofficial statistics, there are more than 20,000 fortified properties in the country. Indeed, fortified constructions represent a significant part of the national architectural heritage and need to be analyzed as a particular class of construction from the seismic vulnerability standpoint. Castles and fortress were generally built for residential and/or military purposes and are characterized by massive structures conceived for defensive purposes. Nowadays, large parts of the existing castles are the results of manipulations carried out over the centuries to adapt them to residential functions [11]. Consequently, many transformations can be observed in the internal spatial distribution and, most of all, in the opening position. According to recent studies [12; 13], the seismic vulnerability of castles and fortresses depends not only on the in-plane and out-of-plane capacity of the masonry walls, floors, and vaults, as for ordinary buildings, but it is also affected by the non-regularities, both in plane and in elevation, the corner positions of the towers--which are often not continuous and not aligned with the perimeter walls--and the different heights and slenderness of the curtain walls. In addition, their seismic capacity is also affected by the behavior of specific elements, for instance merlons, corbels, and outstanding elements such as spires that must be carefully evaluated [14]. [PERSON] et al. [13] found that the most recurrent fragilities are related to (i) the tower-to-perimeter wall interactions; (ii) the behavior of the main body of the tower (i.e., at the base of the tower due to combined compressive and bending cracks); (iii) in-plane and out-of-plane failures of the tops of towers, (e.g., flexural or shear cracks in the merlons, overturning of the merlons, mechanisms affecting the bell gable piers, etc. ); and (iv) damage mechanisms involving the roof (e.g., due to the roof thrust in the tower corners). As a matter of fact, the seismic behavior of castles is characterized by local collapse mechanisms rather than global failures and their detection is not straightforward. Among the different methods and modeling approaches for the assessment of historic constructions subjected to seismic actions [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27], this study focused on force-based assessment (FBA) and computational RBLA [28; 29; 30; 31; 32].