## 3 Behavior Analysis of the Bridge Longitudinal Displacements
### Long-Term Characteristics of the Longitudinal Displacements of the Bridge  
The long-term analysis of monitoring data can indicate the importance of understanding bridge responses and show the spatio-temporal characteristics of the structural behaviors of in-service bridges. Figure 7 shows the trend in the longitudinal displacements at the south girder end (Pier 7) of the bridge from June to December in 2017 and includes the trend of atmospheric temperature for comparison. The dashed line (in color) denotes the longitudinal displacement data, and the solid line (in black) represents the temperature data. The temperature data exhibits missing time windows, with only six periods of temperature data measured from June to December. The time series cross-correlation of the displacement and temperature data in these six documented periods is analyzed, and the time delay ratios between the displacement and temperature sequences in the six periods are (0, 0, 0, 0, less than 0.5%, less than 0.5%). The time lag effect between the longitudinal displacement and environmental temperature is small. This phenomenon may be because bearings and expansion devices can directly release temperature-induced longitudinal displacements (the secondary effect and nonlinear behavior are not obvious). Figure 8 shows the long-term correlation between longitudinal displacement of the bearings and expansion joints at the south girder end and the atmospheric temperature over the seven-month study period. The R in Figure 8 indicates the correlation coefficient of the data points. The first decomposition part of the EWT results slightly increases the temperature correlation when compared with original longitudinal displacement data, because the original data include some nonlinear effects of the operation loads. However, the correlation between the original longitudinal displacement data and the atmospheric temperature is already quite high. As shown in Figures 7 and 8, the longitudinal displacements of the bearing and the expansion joint both have a high correlation with environmental temperature. This result is due to the use of modified ultra-high molecular weight polyethylene (Modified UHMWPE) in the sliding plate structure of the bearings and expansion devices, which effectively releases the longitudinal displacements of the bridge during operation. Figure 7: Trend of longitudinal displacements at the south girder end from June to December in 2017 (compared with the trend of atmospheric temperature): (**a**) bearing (B-7-11); (**b**) expansion joint (E)-7-1). Figure 9 shows the longitudinal displacement of the bearingss on Piers 1-3 and 5-7 versus the distance of each pier from Pier 4. In this figure, each value for a pier is the mean of the two side bearings on the same pier. Figure 9a is the average value for 2015, and Figure 9b is the linear fitting line for all of the data at 1600 s sampling intervals in 2015. As shown in Figure 9a, the longitudinal displacement is linearly related to the distance from Pier 4. As shown in Figure 9b, the longitudinal displacements have high values (absolute) for 8-10 months of the one year, and the bearings at the girder ends (Piers 1 and 7) have the highest values (greater than 150 mm) compared with the bearings on the other piers. It is worth noting that the bearings at the girder ends have the lowest capacity (20 MN) and the highest longitudinal displacement. The sliding limit of a bearing is positively correlated with the capacity of the bearing: the higher the capacity of the bearing, the larger the size of the bearing, and the higher its sliding limit. Hence, the low-capacity bearing at the girder end must be checked in the bridge design and maintenance. The general limit of the longitudinal sliding displacement of bearings with 20 MN capacity is \(\pm\)200 mm, and in this case, the longitudinal displacement of the bearings in the girder ends is close to this limit.