## 2 Discussion on the Working Conditions of a Bridge Restrainer
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case No.**} & \multirow{2}{*}{\begin{tabular}{c} **Location of Bridge** \\ **Restrainer** \\ **Setting** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Wave** \\ **Type** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Assuming the** \\ **Breaking of the** \\ **Pier Base?** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Working** \\ **Gap** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Assuming the** \\ **Breaking of the** \\ **Fixed Support?** \\ \end{tabular} } & \multicolumn{2}{c}{**Number Line: Maximum Displacement in Working Direction (m)**} \\  & & & & & & & **1A** & **2G** & **3G** & **4A** & **1P** & **2P** & **3P** & **4P** \\ \hline \multirow{8}{*}{3} & \multirow{4}{*}{\
\begin{tabular}{c} **Gider** \\ **to** \\ **Gider** \\ \end{tabular} } & 1 & & & & & - & - & - & - & - & - & - \\  & & 1 & & & & 0.263 & 0.112 & 0.074 & 0.250 & 0.620 & 0.381 & 0.886 & 0.337 \\  & & 2 & & & - & - & - & - & - & - & - & - \\  & & 3 & & & 0.255 & 0.063 & 0.007 & 0.269 & 0.646 & 0.201 & 0.727 & 0.193 \\  & & 3 & & 0.75 & & - & - & - & - & - & - & - \\ \cline{2-16}  & & 1 & & & Se & & - & - & - & - & - & - & - \\  & & 1 & & & & 0.263 & - & - & - & - & - & - \\  & & 2 & & & & & 0.255 & & 0.269 & 0.236 & 0.201 & 0.255 & 0.193 \\  & & Pier & 3 & & & & - & - & - & - & - & 0.587 \\ \hline \multirow{8}{*}{4} & \multirow{4}{*}{
\begin{tabular}{c} **Gider** \\ **to** \\ **Pier** \\ \end{tabular} } & 1 & & & & & - & - & - & - & - & - & - \\  & 2 & & & & 0.256 & 0.076 & 0.066 & 0.253 & 0.088 & 0.174 & 0.165 & 0.088 \\  & & 2 & & & 0.126 & - & - & - & - & - & - \\  & & 3 & & & 0.260 & 0.065 & 0.092 & 0.255 & 0.089 & 0.183 & 0.171 & 0.093 \\ \cline{2-16}  & & 3 & & & - & - & - & 0.24 & - & - & - & - \\ \cline{2-16}  & & 1 & & & & 0.255 & 0.072 & 0.022 & 0.264 & 0.090 & 0.171 & 0.179 & 0.086 \\ \cline{2-16}  & & 1 & & & Se & & - & - & - & - & - & - \\  & & 3 & & & & 0.256 & - & - & - & - & - & - \\ \cline{2-16}  & & 1 & & & Se & & 0.256 & - & - & - & - & - & - \\  & & 2 & & & & 0.256 & - & - & - & - & - & - \\  & & Pier & & & & & 0.260 & & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._  
As a result, when relative displacement exceeding the girder seating length occurred, it was judged as a collapsed bridge and the cell was filled with yellow. When it exceeded the working gap of the bridge restrainer, the cell was filled with blue to mean that the bridge restrainer has been activated. Breaking of both the pier base and the fixed support were not considered in Case 1. Therefore, unsurprisingly, the bridge restrainers did not work. The bridge restrainers did not work in Case 2 either, wherein all the fixed supports behaved as movable supports and were destroyed. The maximum relative displacement between the superstructure and substructure was 0.280 m (0.32 \(\times\) Se). In this case, although all the girders moved in one direction, the maximum gap on the opposite side was 80 mm \(\times\) 4 = 320 mm (0.37 \(\times\) Se). Then, it was argued that there was no chance that a bridge restrainer would work unless the relative displacement became very large, because of the large displacement of the top of the pier. In Case 3, considering an unexpected situation, the maximum relative displacement that approached the working displacement of the bridge restrainer was observed when the bridge restrainer was placed between the girder and the pier. Thereafter, a large relative displacement, indicating the collapse of a bridge, was confirmed when the bridge restrainer was placed between the girders. That is, the results indicate that there is a risk of bridge collapse when the bridge restrainer is placed between the girders under assumption. The results of Case 4, wherein the working gap was set to 0.3 \(\times\) Se based on the actual bridge value, indicate that the bridge restrainer worked when it was placed between the girder and the pier, even if the pier base was not assumed to break.