## 9 Conclusions  
The structural performance of a reinforced concrete arch bridge subjected to the action of earthquake ground motion was investigated in this study. The finite element model used here was developed based on the design criteria in the AASHTO [19] specifications. An eigenvalue analysis, together with a series of dynamic time history analyses, was performed to clarify the details of the seismic behavior of this type of bridge. The concept of Demand to Capacity Ratios (DCR) was also evaluated in order to provide an initial estimate of the seismic performance of RC arch bridges and the effect of the vertical component of ground motion on the dynamic characteristics of such bridges was considered. Based on the results obtained, the following conclusions can be drawn:  
1. The eigenvalue analysis demonstrated that an unexpectedly high number of modes of vibration contributed to the seismic behavior of the model RC arch bridge. In order to achieve the 90% modal contribution recommended by the AASHTO [19] specifications, it was necessary to include 1850 modes of vibration. 2. The DCR less than unity indicated that the arch bridge modeled in this study showed no sign of gross damage under either near- or far-field ground motion, although insignificant hazard levels for the DCR were reported for two piers. This is likely due to installing fixed bearings at both ends of the model bridge. 3. A significant relative difference between the deck and arch displacement can be observed in longitudinal direction, while the deck and arch displacement in the other directions show almost identical results for the time history analysis. This indicates that no significant residual deck displacement remains at the end of the analysis; hence, no damage has occurred in either the piers or the arch, which play the greatest role in supporting the internal forces of the deck. 4. The diagram representing the distribution of axial forces and out-of-plane bending moments along the main arch shows that for both near- and far-field ground motions, the average of maximum values calculated from the time history analyses has increased with a rather steep gradient near the abutment of the RC arch. The distribution of the in-plane shear force is almost uniform along the RC arch. 5. The average discrepancies, 53%, for displacement in vertical direction and up to 16% in DCR were observed when considering the vertical component of earthquake in dynamic analysis. It was concluded that ignoring the effect of the vertical component of ground motion highlighted the importance of including this effect when modeling the dynamic responses of long-span arch bridges. Hence, it is strongly recommended that this be taken into account when designing RC arch bridges. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake Name**} & & \multicolumn{2}{c}{**Three**} & \multicolumn{2}{c}{**Two**} \\  & & **Orthogonal** & **Horizontal** & **(\%)** \\  & & **Accelerations** & **Accelerations** & **Accelerations** & **(\%)** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Kobe \\ (Takarazuka) \\ \end{tabular} } & Arch & L & 0.105 & 0.098 & 6.70 \\  & & T & 0.596 & 0.535 & 10.2 \\  & & V & 0.165 & 0.041 & 75.2 \\ \cline{2-5}  & & L & 0.103 & 0.095 & 7.76 \\  & & T & 0.483 & 0.442 & 8.50 \\  & & V & 0.165 & 0.045 & 72.7 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Tabas \\ (Ferdows) \\ \end{tabular} } & Arch & L & 0.077 & 0.070 & 9.10 \\  & & T & 0.353 & 0.322 & 8.78 \\ \cline{1-1}  & & V & 0.148 & 0.038 & 74.3 \\ \cline{1-1} \cline{2-5}  & & L & 0.127 & 0.116 & 8.66 \\ \cline{1-1}  & & T & 0.451 & 0.418 & 7.31 \\ \cline{1-1}  & & V & 0.150 & 0.039 & 74.00 \\ \hline \hline \end{tabular}  
* L: Longitudinal, T: Transverse, V: Vertical directions.  
\end{table} 
Table 8: Effect of vertical component displacement of the deck and arch crown (DCR). **Author Contributions:** [PERSON] designed and coordinated the study. [PERSON] performed theoretical and numerical study under the supervision of J.K., [PERSON] and T.H.-K.K.