## 4 Verification Analysis in Current Conditions (Step 1 of the Design Procedure)
### Time-History Verification and Performance Assessment Analysis  
The performance evaluation enquiry was carried out for the four reference seismic levels fixed in the Italian Standards [47], that is, Frequent Design Earthquake (FDE, with 81% probability of being exceeded over the reference time period \(V_{R}\)); Serviceability Design Earthquake (SDE, with 50%/\(V_{R}\) probability); Basic Design Earthquake (BDE, with 10%/\(V_{R}\) probability); and Maximum Considered Earthquake (MCE, with 5%/\(V_{R}\) probability). The \(V_{R}\) period is fixed at 75 years, which is obtained by multiplying the nominal structural life \(V_{N}\) of 50 years by a coefficient of use \(C_{tt}\) equal to 1.5, imposed to structures whose seismic resistance is of importance in view of the consequences associated with their possible collapse, like the case-study school gym building. By referring to topographic category T1 (flat surface) and B-type soil, the resulting peak ground accelerations for the four seismic levels referred to the city of Florence are as follows: 0.065 g (FDE), 0.078 g (SDE), 0.181 g (BDE), and 0.227 g (MCE). The relevant pseudo-acceleration elastic response spectra at linear viscous damping ratio \(\xi=5\%\) are plotted in Figure 8.  
Figure 7: View and reference coordinate system of the finite element model. Time-history analyses were developed by assuming artificial ground motions as inputs, generated in families of seven by the SIMQKE-II software [53] from the spectra above. As required by the Italian Standards [47], as well as by several other international seismic Codes and Regulations [36; 46], in each time-history analysis the accelerograms were assumed in groups of two simultaneous horizontal components, with the first one selected from the first generated family of seven motions, and the second one selected from the second family. The results of the analyses carried out at the FDE and the SDE are evaluated in terms of interlevel drift ratio (i.e., the ratio of the interlevel drift to the interlevel height of the columns) \(ILD_{r}\), which is equivalent to the interstorey drift ratio in the presence of a system of continuous intermediate beams, although without a floor. The maximum \(ILD_{r}\) values induced by the most severe among the seven groups of input motions, \(ILD_{r,max}\), are as follows: 0.07% (FDE), 0.09% (SDE) in \(X\), and 0.06% (FDE), 0.07% (SDE) in \(Y\), on the first level; 0.13% (FDE), 0.16% (SDE) in \(X\), and 0.53% (FDE), 0.64% (SDE) in \(Y\), on the second level. The drift ratios in \(X\) are far below the 0.33% limitation adopted by [47] at the Operational (OP) performance level for frame structures interacting with drift-sensitive non-structural elements, like the masonry infills on the first level and the curtain wall-type windows on the second level, for the main facades of the building, and the infills situated on both levels, for the side facades. The \(ILD_{r,max}\) values obtained on the second level in \(Y\) are 1.6 times (FDE) and about twice (SDE) the OP-related limit, and also greater than the drift threshold adopted by [47] for the Immediate Occupancy (IO) performance level, equal to 0.5%. The \(ILD_{r,max}\) values computed for the second level in \(Y\) are equal to 1.36% at the BDE, and 1.69% at the MCE, assessing moderate (BDE) to high (MCE) potential plastic demands on the columns--should an inelastic finite element analysis be carried out--and severe (BDE) to very severe (MCE) damage of infills and curtain-wall windows. Consequently, the performance level attained in terms of displacement response is Life Safety (LS), both for the BDE and the MCE. At the same time, \(ILD_{r,max}\) is no greater than 0.18% (BDE) and 0.22% (MCE) on the first level in \(Y\), i.e., only 13% of the second level values. This identifies a cantilever-like response of the structure along \(Y\), with structural and non-structural damage located on the second level.