## 4 Case Study: The Sports Hall  
The case study building is a sports hall located in the municipality of Mazzano, Northern Italy, built between 1969 and 1972. Two images of the geometric survey carried out through laser scanning are shown in Figure 6.  
Figure 5: Comparison between NTC-2018 and [PERSON]’s formulation of the spectral reduction factor \(\eta\). The structure consists of a reinforced concrete frame 28.0 m long, 17.0 m wide, and 8.3 m high. The column grid provides seven spans of 4.0 m and two of 8.5 m in the longitudinal (X) and transversal (Y) directions, respectively. According to the original technical drawings, the columns feature a rectangular 25 \(\times\) 35 cm cross-section with 4\(\updownarrow\)16 longitudinal steel rebars and stirrups of \(\updownarrow\)8/20 cm (see Figure 7b). The roof has double-sloped casted RC beams with a height of 80 cm at the supports and 180 cm at the mid-span, including \(\updownarrow\)20 longitudinal rebars and stirrups of \(\updownarrow\)8/20 cm. At the foundation level, the plinths are connected through inverted beams. Figure 6: Three-dimensional model of the building obtained through laser scanner technique: views of the (**a**) southwest and (**b**) southeast corners. Figure 7: Propagatetic interventions: (**a**) planar arrangement of the dissipative braces, columns with jacketing, and seismic joint for separation from adjacent service rooms; (**b**) as-built column cross-section;  
(c) jacketing of the columns framing the dissipative braces; (d) for other columns, shear strengthening at the nodes with \"masonry equivalent struts\"; (e) foundation enlargement and insertion of diagonal braces at roof level to create a horizontal rigid diaphragm. An edge RC beam (cross-section 25 \(\times\) 25 cm with 4\(\upmu\)16) links the columns at 4.25 m from the ground, delimiting the bottom masonry infills from the above glazed curtain walls, which are composed of modular elements of 1.35 \(\times\) 2.00 m.  
Based on the geometric parameters and the presence of openings, seven different types of masonry infill can be distinguished (see Table 1): (1) a bottom full panel in the X direction; (2) a bottom full panel in the Y direction; (3) a top full panel in the Y direction; (4) a bottom panel with an opening (door) in the X direction; (5) a bottom panel with an opening (door) in the Y direction; (6) a bottom panel with an opening for plants in the Y direction; and (7) a top panel with an opening for plants in the Y direction. Based on a dedicated survey, the material knowledge level LC2, which implies a safety factor for the reduction of characteristic strengths FC = 1.20 [25], is assumed hereafter for the concrete and steel rebars employed in RC elements. From the original technical drawings, smooth rebars made of AQ50 steel were used for the RC structural elements. To be on the safe side, the minimum mechanical properties for this obsolete steel grade were adopted [49]: (i) yield strength \(f_{yd}=270 MPa/F.C.=225 MPa\); (ii) ultimate strength \(f_{ud}=500 MPa/F.C.=417 MPa\); and (iii) elongation at failure \(\varepsilon_{ud}=0.16/F.C.=0.13\). The concrete compressive strength was measured experimentally on seven specimens according to the EN 12390-3:2009 [50]. The identified compression strength was \(f_{cd}=f_{cm,exp}/F.C.=18.8 MPa\), i.e., comparable to that of the modern C16/20, which is assumed hereinafter for FEM calculations. Note that due to the wide spacing of the original stirrups (see Figure 7b), the confinement effect can be neglected. Concerning the masonry infills, the removal of a portion of plaster disclosed hollow masonry bricks of 25 cm thickness. Because characterization tests were not carried out, the relevant mechanical properties were defined based on the recommendations of the Commentary Notes (Table C8.5.) [26] of the Italian Building Code.