## 3 Case-Study School Building
### Numerical Modeling, Seismic Hazard, and Records Selection  
An advanced nonlinear numerical model was developed to assess the seismic response of the case study school building, which was built around 1960-1970 and designed for gravity loads only, which likely anticipates relevant structural vulnerability due to the lack of seismic provisions. To account for potential structural deficiencies generally found in similar RC buildings in Italy, the modeling approach proposed by [PERSON] et al. [21] and [PERSON] et al. [22] for older RC frames was followed, as shown in Figure 3.  
The numerical model was developed using OpenSees [23], which integrates the structural behavior of flexural elements and joints. The flexural elements (i.e., beams and columns) were modeled through force-based beam-column elements with a modified Radau plastic hinge integration scheme, as suggested by [PERSON] and [PERSON] [24]. Likewise, to capture the nonlinear behavior of joints, a zero-length spring coupled with a rotational hinge was adopted. Although the shear behavior of flexural elements was considered elastic, a post-processing analysis was carried out to determine any possible shear failure, similar to the approach adopted by [PERSON] et al. [25]. Masonry infills were modeled using a single-equivalent-strut model, which reproduces the infill panel through one diagonal, compression-only nonlinear truss element for each direction. To account for the potential shear failure of columns and beams, as well as to capture the increment in the lateral stiffness and potential torsional modal behavior, the stair systems were modeled using a series of elastic frame elements. Moreover, the school building model foresaw a rigid floor slab, and second-order geometry effects (P-\(\Delta\)) were taken into account. Regarding damping, 5% tangent stiffness proportional to Rayleigh damping at the fundamental periods was adopted.  
Figure 2: Case-study school building: (**a**) plan layout, (**b**) satellite view (Google Earth), and (**c**) longitudinal elevation.  
It is worth mentioning that the school building analyzed herein was equipped with an advanced structural monitoring system aimed at continuous dynamic system identification through ambient vibration acquisitions, and the developed numerical model was validated in [PERSON] et al. [26], using ambient vibration acquisition data.  
OpenQuake [27] was used to perform seismic hazard computations. The analysis is based on the SHARE Project [28] source model and the ground motion model proposed by [PERSON] and [PERSON] [29]. The hazard curve in terms of the spectral acceleration corresponding to the AvgSa (0.1:0.1:2.0 s) for the city of Ancona (Italy) [30,31] is shown in Figure 4a. A total of 25 pairs of ground motion records in two horizontal components were selected, for each of the ten intensity measure levels (IM levels), from the PEER NGA-West database [32]. For this purpose, any other ground motion record database, such as a European one [33], could have been used. Figure 4b illustrates the target conditional spectra (CS) for IM level 6 (close to Life Safety limit states (NTC 2018 [34]) for the site of interest, together with the  
Figure 3: Case–study school building model in OpenSees [23] and illustration of the numerical modeling approach for masonry infill, frame elements, and beam–column joints.  
25 individual record spectra. More details on the record selection procedure are provided by [PERSON] et al. [30; 31].