## 5 Nonlinear Time History Analyses
### Ground Motion Record Selection  
The NTHAs performed for the case-study structure use three unscaled ground motion records recently recorded in Italy and selected from the ITalian ACcelerometric Archive--ITACA [36]. The records are selected to be spectrum-compatible with the Uniform Hazard Spectrum (UHS) corresponding to a return period T\({}_{\text{R}}\) of 475 years and a rigid soil (cat. A) site located at long 45.419, lat 7.1536. Additionally, according to ECS [1] and NTC18 [31], for each period \(T_{\text{i}}\) included in a range between 0.02 s and 1.0 s, the average spectrum of the three selected records was greater than 90% of the UHS and lower than the 130% of the UHS, as indicated in Figure 8.  
First, only the Horizontal component H of the ground motion is applied to the two-dimensional (2D) structure; then, the horizontal and vertical components (H + V) are applied simultaneously. For each ground motion component, 15 s of the record is used in the analysis to reduce the computational effort. This interval time is selected based on the significant duration of the record and considering the time o  
Figure 8: Response spectra corresponding to the horizontal components of the spectrum-compatible. Upper and lower limits represent 130% and 90% of the UHS considered in this study.  
Figure 7: Crack pattern of the masonry wall corresponding to an IDR of the first level equal to 2% for (a) VL-a, (b) VL-b, and (c) VL-c.  
the total Arias Intensity between 5% and 95% is accumulated. Figure 9 shows the ground motion components H and V used for each record in this study.  
Table 4 reports the main seismological features of each selected record (Name, Moment Magnitude M\({}_{\rm w}\), Earthquake Date, Code of the Station, Site Class, and Epicentral Distance R) and the Peak Ground Acceleration of the selected horizontal component (PGA\({}_{\rm H}\)) and vertical components (PGAv).  
The ratios PGA\({}_{\rm V}\)/PGA\({}_{\rm H}\) of the records #1, #2, and #3 are equal to 0.94, 0.74, and 0.73, respectively.  
Figure 10 shows the response spectra of the H and V components of the three selected records and the corresponding ratio, V/H. These plots indicate that record #1 is characterized by a very high vertical spectral acceleration at T = 0.09 s, equal to S\({}_{\rm u,V}\) = 5.20 m/s\({}^{2}\). For the same period, the horizontal spectral acceleration, S\({}_{\rm a,H}\), is low; thus, the ratio at S\({}_{\rm a,V}\)/S\({}_{\rm a,H}\) is at its maximum in this period and is equal to 2.25. Analogous behaviour can be observed for records #2 and #3, whose maximum ratios S\({}_{\rm a,V}\)/S\({}_{\rm a,H}\) occur at T = 0.75 s and T = 0.59 s, respectively. As indicated in Section 3, the vertical period obtained for VL-c (T = 0.861 s) is very similar to the period corresponding to the maximum spectral amplification of record #1. This indicates that the effect of the vertical component of record #1 is, in this case, affected by an amplification due to the dynamic characteristics of the structure. This effect is negligible for the other records.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\#} & **Event** & **Event** & **Event** & **Station** & **EC8 Site** & **R** & **PGA\({}_{\rm H}\)** & **PGA\({}_{\rm V}\)** \\  & **Name** & **M\({}_{\rm w}\)** & **Date** & **ID** & **Class** & **(km)** & **(g)** & **(g)** \\ \hline
1 & Norcia & 6.5 & 2016/10/30 & CSC & B & 14.900 & 0.169 & 0.159 \\ \hline
2 & Norcia & 6.5 & 2016/10/30 & MMO & A & 19.200 & 0.189 & 0.140 \\ \hline
3 & Norcia & 6.5 & 2016/10/30 & T1215 & A & 20.100 & 0.089 & 0.065 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ground motion records.  
Figure 9: Horizontal (top row) and vertical (bottom row) recorded accelerograms: (**a**) earthquake #1, Norcia 30 October 2016, 14.9 km from the epicentre; (**b**) #2 Norcia 30 October 2016, 19.2 km from the epicentre; and (**c**) #3 Norcia 30 October 2016, 20 km from the epicentre.