# Impact Evaluation of Track Girder Bearing on Yeongjong Grand Bridge
## 4 Finite Element Analysis
### Behavior of the Track Girder According to the Bearing Type
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Component** & **Material** & **Category** & \begin{tabular}{c} **Generated** \\ **Stress (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Minimum Yield** \\ **Stress (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Safety** \\ **Factor** \\ \end{tabular} \\ \hline \multirow{4}{*}{ECB} & Top plate & SM355 & \begin{tabular}{c} Vertical \\ \end{tabular} & \(177.85\) & \(295\) & \(1.66\) \\ \cline{3-6}  & \multirow{2}{*}{\begin{tabular}{c} Top plate \\ \end{tabular} } & \multirow{2}{*}{EP} & Horizontal & \(46.679\) & \(295\) & \(6.32\) \\ \cline{3-6}  & & & Vertical & \(45.152\) & \(80\) & \(1.77\) \\ \cline{3-6}  & \multirow{2}{*}{\begin{tabular}{c} Main cylinder \\ \end{tabular} } & \multirow{2}{*}{EP} & Horizontal & \(40.465\) & \(80\) & \(1.98\) \\ \cline{3-6}  & & & Vertical & - & - & - \\ \cline{3-6}  & \multirow{2}{*}{\begin{tabular}{c} Bolt \\ \end{tabular} } & \multirow{2}{*}{10.9 G} & Horizontal & \(24.508\) & \(900\) & \(36.72\) \\ \cline{3-6}  & & & Vertical & \(31.192\) & \(295\) & \(9.46\) \\ \cline{3-6}  & \multirow{2}{*}{\begin{tabular}{c} Low plate \\ \end{tabular} } & \multirow{2}{*}{SM355} & Horizontal & \(41.545\) & \(295\) & \(7.10\) \\ \hline \multirow{4}{*}{Line bearing} & Top plate & SC450 & Vertical & \(282.44\) & \(225\) & \(0.80\) \\ \cline{3-6}  & & Horizontal & \(78.974\) & \(225\) & \(2.85\) \\ \cline{3-6}  & \multirow{2}{*}{\begin{tabular}{c} Control plate \\ \end{tabular} } & \multirow{2}{*}{SC450} & Vertical & \(12.233\) & \(225\) & \(18.39\) \\ \cline{3-6}  & & Horizontal & - & - & - \\ \cline{3-6}  & \multirow{2}{*}{\begin{tabular}{c} Shear key \\ \end{tabular} } & \multirow{2}{*}{SC450} & Vertical & - & - & - \\ \cline{3-6}  & & Horizontal & \(160.45\) & \(225\) & \(1.40\) \\ \cline{3-6}  & \multirow{2}{*}{\
\begin{tabular}{c} Bolt \\ \end{tabular} } & \multirow{2}{*}{10.9 G} & Vertical & - & - & - \\ \cline{3-6}  & & Horizontal & \(57.204\) & \(900\) & \(15.73\) \\ \cline{3-6}  & \multirow{2}{*}{
\begin{tabular}{c} Low plate \\ \end{tabular} } & \multirow{2}{*}{SS275} & Vertical & \(14.856\) & \(235\) & \(15.82\) \\ \cline{3-6}  & & Horizontal & \(174.92\) & \(235\) & \(1.34\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Review of stress by member. To apply the damping value, the damping method was applied as the proportional strain energy. The damping ratio was applied as 1.45% for vertical structures, as 2% for the steel line bearings, and as 5% for the PTFE-based ECBs. In addition, to obtain more accurate results reflecting the effects of the continuous rail and adjacent tracks, it was modeled in three spans, and the results were calculated for the track and the rail located at the center as shown in Figure 18. The results are shown in Table 5.  
As shown in Figure 19a, the vertical displacement of the supporting point of the track girder was not affected by the change of bearings, regardless of the change in speed. ECBs with elastic members for shock absorption were found to have a relatively greater vertical displacement than line bearings. This is due to the elastic displacement (compression displacement) of the elastic material, not the vertical lifting phenomenon of the bearings such as the line bearings. It was confirmed that ECBs can reduce the impact and vibration on the main bridge of the Yeongjong Grand Bridge, supporting the track girder. As a result of the upward displacement analysis of the track support, the numerical results showed that the upward displacement of the support rarely occurred, regardless of the train speed, as shown in Figure 20. On the other hand, an upward displacement of about 0.21-0.38 mm was measured by field measurements in the track-supporting point with line bearings. The analysis results could underestimate the behavior of the actual track supporting points. Figure 17: KTX time history function example (at a speed of 200 km/h).