## 2 Case Study  
The case study is a six-story residential building located in Tolmezzo, Italy. The building plan is rectangular with dimensions of 18.15 m \(\times\) 11.90 m (Figure 1) and is the same for all five floors. The interstory height is 3.00 m, except for the ground floor, which is 3.30 m high. The bearing structure against seismic actions is made by RC walls placed along the building perimeter (walls S1-S6 in Figure 2) and on the sides of the stairwell and the elevator shaft parallel to the \(Y\) direction (S7-S8 and A1-A2 in Figure 2). The resistance against vertical loads is provided by both walls and columns (P1-P9 in Figure 2). Columns and walls are connected at floor level by beams oriented along the building's main directions (\(X\) and \(Y\) in Figure 1), following the dotted grid in Figure 2. Walls S7-S8, A1-A2 rise above the flat rooftop, as shown in Figure 3, to allow the access to the roof and the housing of the elevator technical compartment. According to the dimensions shown in Figures 1 and 3, the slenderness of the building is calculated as the ratio between the building's height and the width of its base, which is equal to approximately 1 in the \(X\) direction and 1.5 in the \(Y\) direction. A building can be considered a skyscraper if this ratio is at least almost 10. Hence, the considered case study falls in the range of medium- or even low-rise buildings. The cross-sections of vertical elements stay the same for all the storys; only the walls' longitudinal reinforcements are reduced from the fourth floor upward, where steel bars of diameter \(\phi\) 20 change to \(\phi\) 16. The dimensions of structural members cross-sections are shown in Table 1. The reinforcement layouts at the base of vertical elements are shown in Figure 4. Floors are made by RC joists with a depth of 20 cm, a 5 cm thick RC slab at the top, and hollow bricks as lightening elements. The building foundations are made of a RC slab with dimensions of 19.15 m \(\times\) 12.90 m \(\times\) 0.80 m. The materials used for the building design are concrete of Italian grade C35/45, with characteristic compressive strength \(f_{ck}\) = 35 MPa and [PERSON]'s modulus \(E_{c}\) = 34 GPa, and reinforcing steel of Italian grade B450C, with characteristic yield strength \(f_{yk}\) = 450 MPa and [PERSON]'s modulus \(E_{s}\) = 210 GPa. Both concrete and steel are assumed to be linear materials in the finite element model of the building. The design of the RC structure against seismic actions was performed according to the dissipative behavior required by the Italian Building Code [41] for ductile wall structures, corresponding to a behavior factor \(q=3\). The finite element model (FEM) of the building was made using the software SAP2000 [42]. Beams and columns were modeled through frame elements, while shell elements were used for wall modeling (Table 1). Floors were assumed to behave as rigid diaphragms. The effects of cracking on structural members were taken into account by reducing the shear and flexural stiffnesses of cross-sections by 20% for vertical elements and by 50% for beams. The considered cracking is mainly due to the vertical loads for beams and to the horizontal loads for columns. In no case were  
Figure 4: Reinforcement layouts in vertical structural elements at the ground floor. Figure 3: Building elevation in \(X\) direction on the left, and \(Y\) direction on the right. Figure 2: Plan view of vertical structural elements. these cracks considered to be connected to a non-linear behavior of the structural elements, which are assumed to still be subjected to elastic deformations even after cracking. Gravity loads per unit area applied to the FEM of the building are resumed in Table 2, where \(g_{1,k}\) and \(g_{2,k}\) are the permanent structural and non-structural characteristic loads, respectively, and \(q_{k}\) is the characteristic variable load. A distributed load of 5.6  kN/m was applied to the perimeter beams to consider the self-weight of masonry external infills.