## 3 Case Studies
### Seismic Input  
The response of the bridge model was estimated through the employment of nonlinear static and dynamic analyses. The dynamic analyses were performed by adopting a set of seven ground motions (GMs) selected from the response spectra (RS) used to design the bridge; from the set of ground motions, a median response spectra (RSm) was defined. To select the set of GMs, the spectrum match for a relevant period range was adopted; this approach was considered sufficient to describe the seismic behavior of an individual structure [40; 41].  
The RS was defined according to the Italian technical code (NTC 2018): (a) The location was Reggio Calabria (a region characterized by high seismic hazard in Southern Italy), (b) the soil class was type B (very dense sand or gravel or very stiff clay, \(360\leq\mathrm{V_{s30}}\leq 800\)), and (c) the return period considered was Tr = 949 years (life safety limit state: \(\mathrm{P_{VR}}\) = 10%; \(\mathrm{a_{g}}\) = 0.35 g; \(\mathrm{T_{B}}\) = 0.172 s, \(\mathrm{T_{C}}\) = 0.516 s, \(\mathrm{T_{D}}\) = 3.035 s; \(\mathrm{F_{0}}\) = 2.464; \(\mathrm{S_{T}}\) = 1.0). Using Rexel [42], we selected a set of seven unscaled records, compatible on average with the target spectrum, and with the minimum dispersion of individual spectra: The average response spectrum matched the target spectrum at a specified period range that included all the periods considered relevant (participating mass \(>\)1% along the transverse direction of the bridge).  
The seven ground motions selected are listed in Table 2, and in Figure 8 are shown the 5% damped response spectra of the transverse component of the ground motions. The seven GMs were used to perform the NRHAs, and their mean spectrum (RSm) was used for the purpose of evaluating the pushover-based procedure (the performance point is evaluated, for each intensity level, adopting RSm for the seismic demand); in Figure 8, the RS used to design the bridges (RB and IB), together with RS1,..., RS7 (the response spectra of the seven GM) and their mean spectrum RSm (the one used for the nonlinear static analyses), is plotted.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Load** & **kN/m** & **kN** \\ \hline Dead & Self-weight & 200 & - \\ Live & Vehicle loads (Qik) & - & 1200 \\ Live & Distributed load (qik) & 54.5 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Loads and actions.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Eto ID** & **Earthquake Name** & **Waveform** & **Date** & **PGA (g)** \\ \hline
1635 & South Iceland & 4674-xa & 17/06/2000 & 0.31 \\
1635 & South Iceland & 4674-ya & 17/06/2000 & 0.31 \\
2309 & Bingol & 7142-xa & 01/05/2003 & 0.50 \\
2309 & Bingol & 7142-ya & 01/05/2003 & 0.50 \\
2142 & South Iceland & 6349-xa & 21/06/2000 & 0.72 \\  & (aftershock) & & & \\
2142 & South Iceland & 6332-ya & 21/06/2000 & 0.51 \\  & (aftershock) & & & \\
1635 & South Iceland & 6277-ya & 17/06/2000 & 0.35 \\ - & Mean & & - & 0.46 \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of the selected ground motions.  
In this paper (Section 4), analysis results are presented in terms of bridge capacity curve, i.e., monitoring point displacement versus seismic intensity, configuration of the deck drift profile, plastic hinges rotations and bending moments. Following Eurocode 8 recommendations, the independent damage parameter selected was the displacement of each pier top node (P1, P2 and P3).