## 2 Simplified Vulnerability Assessment Methods for Masonry and RC Building Structures
### Application of the Method of Group A and B to a Reduced Sample of Buildings  
Methods of Group B were applied to 14 masonry buildings, since only for these buildings all geometrical and mechanical data necessary for applying the methods were available. For the same dataset of buildings also methods of Group A were applied. For all methods, the design seismic action, PGA\({}_{\rm d}\), was again expressed by the design PGA for the return period of 475 years and subsoil type B. In particular, for the 14 examined buildings, the PGA\({}_{\rm d}\) varied in the range 0.18-0.21 g (i.e., corresponding to 0.15-0.18 g on rock). Based on the information gathered by the forms available in the digital platform, it was evidenced that all the examined masonry buildings were made of tuff stones with regular texture and floors were mainly made of RC elements and light bricks, while in a few cases were made of steel profiles and light bricks. The height of buildings was variable from 4.0 to 9.0 m; in particular, nine buildings had 1 or 2 floors, three buildings had 3 floors, and two buildings had 4 floors. The wall geometry was gathered by the digital platform too, in particular the areas of the resistant walls in the two directions were detected due to technical drawing of each floor available for these buildings. About the construction period, seven buildings were realized before 1960, four buildings between 1960 and 1975, and three buildings were built before 1945. Within the categories suggested by the annex document (Annex n. 7, 2019 [40]) to the Italian building code (NTC 2018), the typology'regular tuff masonry' was assigned to all 14 buildings. Physical and mechanical parameters of masonry were, thus, defined according to the ranges of values provided for existing masonry buildings in (Annex n. 7, 2019 [40]) and assuming a basic level of knowledge, i.e., LC1, for structural geometry, details, and materials. Such an assumption leads to assessing the design values of mechanical properties as equal to the lowest values of the provided ranges divided to the so called \"knowledge factor\", FC, which was 1.35 for the level of knowledge LC1. For'regular tuff masonry', the unit weight was assumed to be \(\gamma=16\) kN/m\({}^{3}\), while the lower bounds for the average shear strength without normal stresses were \(\tau_{0}=0.04\) MPa and \(f_{v0}=0.10\) MPa. Note that \(\tau_{0}\) was the shear strength for tensile failure in the masonry and was used in the Turnsek and Cacovic [31] formulation, while \(f_{v0}\) refers to a sliding failure along the joints and was used in the Mohr-Coulomb criterion. Thus, considering the level of knowledge LC1, the design values of the shear strength were:  
- \(\tau_{0d}=\tau_{0}\)/FC = 0.04/1.35 = 0.03 MPa,  
- \(f_{v0d}=f_{v0}\)/FC = 0.10/1.35 = 0.07 MPa. In order to uniform the values of the shear strength adopted by the examined methods and provide comparable judgments, the following assumptions have been done:  
* GNDT: \(\tau_{0k}\) = 0.03 MPa;
* RE.SIS.TO: \(\tau_{0}\) = 0.03 MPa;
* DPCM: \(\tau_{0l}\) = 0.03 MPa;
* L&R: \(f_{\mathrm{v0k}}\) = 0.07 MPa. When the Mohr-Coulomb criterion was used, i.e., in the only L&R method, for the friction angle of masonry, lacking specific information, the common value tan \(\varphi\) = 0.4 was assumed. For the floors, the unit weight of 4 kN/m\({}^{2}\) was assumed in all cases. Such a value, together with the unit weight of masonry, was used for evaluating the average normal stress acting in the masonry walls at each floor. Note that the methods Azizi, RE.SIS.TO, and GNDT of Group B allow one to express both a quantitative and a qualitative, i.e., linguistic, judgment (from 'low' to 'high') about the level of vulnerability of the buildings. Thus, in Section 3.4.1, the quantitative judgments in terms of capacity-to-demand ratio provided by methods RE.SIS.TO, GNDT, DPCM 9/2/2011, and L&R were presented and compared with each other.