# Numerical Assessment of the Seismic Vulnerability of Bridges within the Italian Road Network
## 2 Case Studies and Modeling
### Modeling  
All structures have been modeled using Seismostruct [29; 30]. Columns and connecting elements of the piers have been modeled using inelastic force-based frame elements. In \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case Study** & **Year** & \begin{tabular}{c} **Structural** \\ **Scheme** \\ \end{tabular} & **Bearings** & \begin{tabular}{c} **Number of** \\ **Spans** \\ \end{tabular} & \begin{tabular}{c} **Total Length** \\ **[m]** \\ \end{tabular} & \begin{tabular}{c} **Soil Category** \\ **(NTC2018)** \\ \end{tabular} \\ \hline Bridge 1 & 1960 & \begin{tabular}{c} Continuous \\ beams with \\ Gerber saddles \\ \end{tabular} & Neoprene & 13 & 421.1 & A \\ \hline Bridge 2 & 1969 & \begin{tabular}{c} Simple support \\ beams \\ \end{tabular} & Neoprene and & 4 & 124 & A \\ \hline Bridge 3 & 1973 & \begin{tabular}{c} Simple support \\ beams with \\ Gerber saddles \\ \end{tabular} & PTFE-Steel & 5 & 157 & B \\ \hline Bridge 4 & 1969 & \
\begin{tabular}{c} Simple support \\ beams \\ \end{tabular} & Neoprene and & 3 & 87.8 & A \\ \hline Bridge 5 & - &
\begin{tabular}{c} Simple support \\ beams \\ \end{tabular} & Neoprene and & 4 & 50 & A \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of the case studies. particular, the Seismonstruct elements employed in this study are the \"infrmFB\". This type of element is able to capture the inelastic behavior along the entire length of a structural element and is the most accurate among the inelastic frame elements available in Seismonstruct. The sectional stress-strain curve is obtained by integrating the uni-axial response of the individual fibers in which the section has been discretized [30]. The number of fibers and integration sections in the elements, for each model, has been defined after performing a convergence analysis. For each section of inelastic elements, the reinforcement effectively present in the section has been defined to obtain structural models as accurately as possible. The deck has been modeled using elastic frames. This is a common choice and can be justified considering that, in general, bridge decks are less vulnerable than piers and tend to have an elastic response. The same simplification has been made for the modeling of abutments. The Soil-Structure Interaction was not specifically modeled in this study, and consequently, all the results are based on the assumption of fixed base nodes. Uni-axial constitutive models employed for the fiber section of inelastic elements are based on the [PERSON] et al. [31] concrete model and on the Menegotto-Pinto [32] steel model. In particular, the concrete and steel models employed in the study are defined in Seismonstruct as \"con_ma\" and \"stl_mp\", respectively. The confinement effects in the concrete are taken into account assuming that the confining pressure is constant through the entire stress-strain range. The steel model, which includes isotropic hardening rules, is suitable for modeling R.C. structures in presence of complex loading histories where significant load reversals might occur [30]. Bearing devices have been modeled employing link elements. These elements are 3D links with uncoupled axial, shear, and moment actions. The link elements connect two initially coincident structural nodes and require the definition of an independent force-displacement (or moment-rotation) response curve for each of its local six degrees of freedom [30]. For neoprene pad bearings and reinforced neoprene pad bearings, it has been assumed that the rotational stiffness was negligible. The calculation of vertical and lateral stiffness was performed following the indications of Australian Standard AS 5100.4:2017 [33]. The force-deformation law employed for lateral stiffness was linear elastic. This assumption can be justified considering that the energy dissipated by these devices is negligible and that they behave linearly until failure. A different approach has been followed for the PTFE-steel devices.