## 3 Results and Discussion
### Comparison of the Results  
The comparison of the capacity curves for the structure before and after the application of the Resisto 5.9 Tube (Figure 11) demonstrates how the cold-formed exoskeleton improved the stiffness, ductility and strength of the existing RC buildings. The percentage variations in the key parameters of the seismic analysis, both before and after the retrofit, are summarized in Table 10.  
The efficacy of the Resisto 5.9 Tube for the seismic upgrading of existing RC buildings was assessed by comparing the seismic safety index \(\zeta_{\text{E}}\) before and after the retrofit intervention. The seismic safety index was evaluated according to the Italian Technical Standard as a ratio between the capacity and the demand in terms of the peak ground acceleration, as reported in Equation (3):  
\[\zeta_{\text{E}}=\frac{\text{PGA}_{\text{C}}}{\text{PGA}_{\text{D}}} \tag{3}\]  
This index represents the ratio between the seismic action that the building can sustain and the one that is requested for a new structure. To classify a retrofit intervention as seismic upgrading, the code requires that the seismic safety index must increase by at least 0.1. The cold-formed exoskeleton allowed for achieving an increase in \(\zeta_{\text{E}}\) value of 0.16 and, therefore, the seismic upgrade of the RC building was attained, as summarized in Table 11.  
Finally, a comparison was made in terms of the seismic risk classification according to the Italian Guidelines [35]. The seismic risk class of a building was determined based on two main parameters: the seismic safety index (IS-V), corresponding to the \(\zeta_{\text{E}}\) index, and the PAM value, which represents the expected annual loss. To each parameter a risk class ranging from A+ to G, with increasing levels of risk, was assigned. The seismic risk of the building was classified according to the lowest class between IS-V class and PAM one. The worst condition was represented by the annual loss (PAM class), which was evaluated as the area under the curve that depicted the direct economic losses as a function of the average annual frequency of an exceedance of the seismic event that causes the structure to reach the life safety limit state.  
For the analyzed building, the retrofit intervention led to an improvement by one risk class, from F to E, as shown in Table 12 and Figure 12.  
In conclusion, based on the results achieved, it is evident that the Resisto 5.9 enhanced the seismic performances of the existing building by improving the global seismic behavior of the bare structure similarly to other exoskeleton solutions [13; 36].  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Dir.** & **\(\Delta\)d\({}_{\text{v}}\)1** & **\(\Delta\)d\({}_{\text{cu}}\)1** & **\(\Delta\)F\({}_{\text{max}}\)1** & **\(\Delta\)K\({}^{\star}\)1** \\ \hline X & +9.3\% & +11.7\% & +18.5\% & +8.3\% \\ Y & +29.5\% & +10.2\% & +27.5\% & \(-1.5\%\) \\ \hline \end{tabular} \({}^{\dagger}\) Ultimate displacement (d\({}_{\text{cu}}\)) and maximum shear (F\({}_{\text{max}}\)). Asterisked terms indicate the equivalent bilinear yielding displacement (d\({}_{\text{v}}^{\star}\)) and stiffness (K\({}^{\star}\)).  
\end{table}
Table 10: Comparison of the seismic analysis results: percentage variation in the capacity curve’s parameters due to the application of the Resisto 5.9 Tube system.  
\begin{table}
\begin{tabular}{c c c c} \hline \(\zeta_{\text{E}}\) **Existing Building** & \(\zeta_{\text{E}}\) **Retrofitted Building** & \(\zeta_{\text{E}}\) **Increase** \\ \hline
0.26 & 0.42 & +0.16 \\ \hline \end{tabular}
\end{table}
Table 11: Seismic safety index \(\zeta_{\text{E}}\) before and after the retrofit intervention.