# Seismic Isolation Devices for Protecting RC Buildings: The Frangipane School in Reggio Calabria
## 5 Retrofit Intervention (MIS Configuration)
### Seismic Performance Assessment  
The site seismic hazard was considered for a reference period \(V_{R}\) of 75 years (Nominal Life \(V_{N}=50\) years and Coefficient of Use \(C_{U}=1.5\)), in accordance with [31,32]. As such, the following Limit States were considered: Operativity Limit State (OLS), Damage (DLS), Life-Safety (LSLS) and Collapse Limit State (CLS). In particular, being the examined structure associated with Class III, according to the provisions of LR Calabria n. 35 [33], it was first necessary to calculate the local seismic response of the construction site. For each Limit State, reference spectra have been thus calculated based on the online available REXEL data sheet by assuming a total of 7 accelerometers for each Limit State [39]. In the selection of the accelerograms, earthquake events with a magnitude between 5 and 6.5 were taken into account, with an epicentral distance between 5 and 25 km and a duration between 15 and 25 s. The so-calculated response spectra can be seen in Figure 15.  
In accordance with [31,32], both the superstructure and substructure were numerically described in Midas software as systems with non-dissipative linear elastic behaviour, while the isolation system was modelled as a linear equivalent one (see Figure 16). In detail, Figure 16 shows the top and axonometric views of the studied building, with evidence of fundamental longitudinal, transverse and torsional mode shapes, respectively. In this case, it is worth noting that 99% part of the total mass of the building (cumulative effective modal mass) is represented, which corresponds to the 100% part of the superstructure mass. Figure 14: Detail of seismic joint in the region of emergency stairway: (**a**) plan view (dimensions in cm) and (**b**) vertical cross-section (detail of foundation level). Overall, in accordance with section 7.10.5.2 in [31], the following conditions were met:  
1. the equivalent stiffness of the isolation system was measured as greater than the 50% part of the secant stiffness for cycles with displacement equal to a 20% part of the reference displacement;
2. the equivalent linear damping of the isolation system was less than 30%;
3. the force-displacement characteristics of the isolation system must not be subject to deviations of more than 10% due to variations in the deformation velocity, the vertical action on the devices;
4. the increase of the strength in the isolation system for displacements between 0.5 times the design displacement and its maximum amplitude must be at least equal to 2.5% of the total weight of the superstructure. This request involves the use of a radius of curvature limited to 20 times the value of the project shift. Figure 15: Scales spectra for the site of Reggio Calabria, Mean spectra and code spectra for a soil type B, with evidence of (**a**) Operational Limit State (OLS), (**b**) Damage Limit State (DLS), (**c**) Life-Safety Limit State (LSLS) and (**d**) Collapse Limit State (CLS). As is evident in Figure 16, the superstructure clearly behaves like a rigid body (\(T_{\text{1,IB}}=2.24\) s the vibration period of the isolated system). The maximum displacement calculated for the superstructure was estimated at less than 280 mm, for CLS. According to national code [31; 32], the maximum displacement at CLS for the \"Corpo C\" system (i.e., a non-isolated building--\({}_{Dmax,NB,CLS}\)) can be thus calculated as:  
\[d_{max,NB,CLS}=\frac{H_{NB}}{100}\frac{a_{g}}{g}\cdot S=\frac{15.20}{100}\cdot 0.421\cdot 1=0.0639\;\text{m}=64\;\text{mm} \tag{1}\]  
in which:  
* \(a_{g}\) is the maximum horizontal acceleration at the considered Limit State;
* \(g\) is the acceleration due to gravity;
* \(S\) is a coefficient that takes into account the category of subsoil and topographical conditions; and
* \(H_{NB}\) is the height of \"Corpo C\". Figure 16: Fundamental vibration modes of the MIS system (Midas): top view and axonometric view: (**a**) longitudinal; (**b**) transverse; (**c**) torsional mode shapes.