## 7 Conclusions  
This study examined the effects of the aspect ratios of a bridge and the characteristics of ground motion on the seismic response of a bridge. For this, nonlinear static analysis, or pushover analysis, was first performed to derive the shear force and displacement relationship of piers and evaluate the yield and ultimate displacement capacities. The yield displacement was determined using the effective stiffness approximation method, and the ultimate displacement was determined from a strain value corresponding to a 15% decrease in stress in the critical section of the pier. The initial stiffness of the pier decreased with a decreasing aspect ratio, which resulted in a decrease in the yield displacement capacity and an increase in the maximum shear force capacity. The ultimate displacement, determined from a constant strain of the confined concrete, increased with an increasing aspect ratio of the pier. The maximum displacement of the bridge was compared with the displacement spectrum according to the bridge height and ground motion. As the aspect ratio of the pier increased, the tendency of an increase or decrease in the maximum displacement of the bridge was similar to that of the displacement spectrum. This indicates that the displacement response would be affected mainly by the characteristics of ground motion. However, the rate of increase or decrease in the displacement response was larger than that of the response spectrum. Some differences between the maximum displacement and displacement spectrum could be attributed to the effects of the aspect ratio of the bridge. Compared with the displacement capacity of the bridge, far-fault ground motion produced the maximum displacement within approximately 22.5% of the yield displacement capacity. On the other hand, when subjected to near-fault ground motion with the forward-directional pulse, the maximum displacement response was within 80.6% of the yield displacement capacity. Fling-step near-fault ground motion significantly increased the maximum displacement of the bridge, which was close to or larger than the yield displacement capacity. For the maximum moment response of the bridge, this study proposed the dynamic response ratio (\(DR\)), which is defined as the ratio of the maximum displacement to the yield displacement capacity. The maximum moment of the bridge tends to increase as the \(DR\) increases, but the rate of increase in the maximum moment decreases when the \(DR\) exceeds approximately 80%. Regression curve fitting showed a good relationship between the proposed \(DR\) and the maximum moment of a bridge. The maximum moment under far-fault ground motion occurred within 25% of the \(DR\). Near-fault ground motion with forward directivity produced the maximum moment at approximately 80%  
Figure 15: Relationship between the decrease in the natural frequency and the dynamic response ratio (\(DR\)): (**a,b**) The decrease in the natural frequency and the dynamic response ratio at each ground motions. of the \(DR\). In the fling-step ground motion condition, the maximum moment reached as much as approximately 160% of the \(DR\). This study also investigated the changes in the natural frequency of bridges caused by ground motions. The post-earthquake natural frequency of the bridge decreased only in some ground motions. Therefore, the proposed \(DR\) was employed to analyze the decrease in the natural frequency of the bridge and the characteristics of ground motion. Compared with the far-fault ground motion, the near-fault ground motion showed a greater decrease in the natural frequency with the increase in the \(DR\). The rate of decrease in the natural frequency with an increasing \(DR\) was similar in near-fault and far-fault ground motions. [PERSON] and [PERSON] planned this study; [PERSON] performed the modeling; [PERSON][PERSON], [PERSON], and [PERSON] analyzed the data; and [PERSON]-[PERSON] and [PERSON] wrote and revised the paper. All authors have read and agreed to the published version of the manuscript.