# Model Updating of Bridges Using Measured Influence Lines
## 2 Materials and Methods
### Finite Element (FE) Model
#### 2.3.2 Interactions and Boundary Conditions  
Piers were connected to the superstructure with elastomeric bearings modelled as wires (spring-dashpot assemblies). \"Cartesian + Rotation\" connector sections were assigned to these wires (assemblies), which connected reference points on the pier-girder contact surfaces. Stiffness properties were obtained from the design documentation [27] and are shown in Table 4. Unidirectional pot bearings, which connected the superstructure to the abutments, were not modelled as wires. Instead, the bearing surface was assigned a boundary condition with restrained movements in the Y and Z directions. A fixed boundary condition, which restrains displacements in all directions, was assigned to the bottom surfaces of all piers.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Translational**} & \multicolumn{1}{c}{**Vertical**} & \multicolumn{1}{c}{**Rotational**} \\ \cline{3-6}  & & \multicolumn{1}{c}{**Stiffness**} & \multicolumn{1}{c}{**Stiffness**} & \multicolumn{1}{c}{**Stiffness**} \\ \cline{3-6}
**Bearing** & **Position** & \multicolumn{1}{c}{**(kN/m)**} & \multicolumn{1}{c}{**(kN/m)**} & \multicolumn{1}{c}{**(kNm)**} \\ \cline{3-6}  & **(Abutment, Pier)** & \multicolumn{1}{c}{**X**} & \multicolumn{1}{c}{**Y**} & & \\ \cline{3-6}  & & **Direction** & \multicolumn{1}{c}{**Direction**} & & \\ \hline Elastomeric bearing type 1 & P1, P6 & \(3.18\times 10^{3}\) & \(3.18\times 10^{3}\) & \(1.77\times 10^{6}\) & \(3.41\times 10^{4}\) \\ Elastomeric bearing type 2 & P2, P3 & \(3.61\times 10^{3}\) & \(3.61\times 10^{3}\) & \(2.01\times 10^{6}\) & \(3.90\times 10^{4}\) \\ Elastomeric bearing type 3 & P4, P5 & \(4.19\times 10^{3}\) & \(4.19\times 10^{3}\) & \(2.33\times 10^{6}\) & \(4.55\times 10^{4}\) \\ Unidirectional pot bearing & ABUT1, ABUT2 & Free & Rigid & Rigid & Free (\textless{}0.01\lx@math@degree\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Properties of bearings according to design documentation [27].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multirow{2}{*}{**Abbreviation**} & \multicolumn{2}{c}{**Young’s Modulus**} & \multicolumn{1}{c}{**Poisson**} & \multicolumn{1}{c}{**Density**} \\  & & **(GPa)** & **Ratio** & **(t/m\({}^{3}\))** \\ \hline Asphalt & ASPH & 8.00 & 0.35 & 2.582 \\ Edge beam 1 & EB1 & 31.00 & 0.20 & 2.710 \\ Edge beam 2 & EB2 & 31.00 & 0.20 & 2.580 \\ Main girder 1 & MG1 & 35.00 & 0.20 & 2.500 \\ Main girder 2 & MG2 & 35.00 & 0.20 & 2.500 \\ Slab 1 & SLAB1 & 35.00 & 0.20 & 2.500 \\ Slab 2 & SLAB2 & 35.00 & 0.20 & 2.500 \\ Slab 3 & SLAB3 & 35.00 & 0.20 & 2.500 \\ Slab 4 & SLAB4 & 35.00 & 0.20 & 3.573 \\ Slab 5 & SLAB5 & 14.59 & 0.20 & 1.177 \\ Pier & PIER\_BOTTOM & 31.00 & 0.20 & 2.500 \\ (bottom part) 1 & PIER\_BOTTOM & & & \\ (upper part, bearing region) 1 & PIER\_TOP & 34.00 & 0.20 & 2.500 \\ Cross girder & CG & 35.00 & 0.20 & 2.500 \\ \hline \hline \end{tabular} \({}^{1}\)PIER\_BOTTOM represents the bottom parts, and PIER\_TOP represents the top parts (bearing region) of all pier pairs: P1, P2, P3, P4, P5, and P6.  
\end{table}
Table 3: Material properties of structural elements according to design documentation [24; 25; 26; 27].