# Dynamic Behavior of Track Bridge on Serviced Long-Span Road/Railway Bridge
## 4 Results and Discussions
### Rail and Girder Displacement  
An example of the numerical analysis results and measurements of the vertical displacement of the rail and track girder are provided in Figure 5.  
Figure 4: Sensor installation.  
The vertical displacement analysis of the rail and track girder revealed errors between the displacements measured at a passing speed of approximately 98 km/h on the actual Yeongjong Bridge and the results obtained from the numerical analysis (100 km/h) of 3.6% and 4.8% for the rail and track girder displacements, respectively. These results indicate that the numerical analysis model predicts the displacement well, and is considered a valid model.  
After verifying its validity, the full-scale model of the Yeongjong Bridge was used to calculate the rail and track girder vertical and horizontal displacements with increasing KTX speed (up to 200 km/h). As shown in Figure 6, the measured results of KTX were found to be closer to the finite element analysis results of KTX than the measured results of the airport railway express (AREX).  
According to the results obtained with increasing KTX speed, the vertical (Figure 6) and horizontal displacements of the rail and track girder were similar to those measured in the field for speeds  
Figure 5: Comparison of rail and track girder vertical displacements. (**a**) Rail vertical displacement (100 km/h, numerical analysis); (**b**) Rail vertical displacement (98 km/h, field measurement); (**c**) Track girder vertical displacement (100 km/h, numerical analysis); (**d**) Track girder vertical displacement (98 km/h, field measurement).  
Figure 6: Analytical results of vertical displacements of rail and track girder. (**a**) Rail vertical displacement; (**b**) Track girder vertical displacement.  
below 100 km/h. Furthermore, the vertical displacement decreased as the speed approached 200 km/h. However, the horizontal displacements of the rail and track girder increased by approximately 1.5 times and two times, respectively. This occurs because of the influence of the hunting oscillation (swaying motion) when the train speed increased. However, this effect is marginal when compared to the lateral displacement standard of 4 mm. Therefore, we predict that the vertical and horizontal displacements of the rail and track girder will not be negatively affected by increases in train speed.  
Twist (or cant) refers to an operational safety standard, whose reference value varies with train speed. The conventional method of expressing it (i.e., 3.0 mm/m (transverse direction)/3 m (longitudinal direction)) is somewhat confusing, and can result in misconceptions or errors. According to an SNCF-1 expert, the above expression implies the following: \"The variation in cant measured on a 3 m scale should not exceed 3.0 mm (i.e., 1 mm/m).\" However, this criterion should be modified according to speed as follows. In the French standard and in Korea's bridge design manual (BRDM), it is stipulated that 0.4 mm/m should be considered for high-speed trains, depending on the actual train load [10; 11].  
In addition, the total change in cant (i.e., cant variation owing to load + existing cant variation owing to the track transition curve, etc.) should not exceed 2.5 mm/m (equivalent to a cant change of 7.5 mm/m on a 3 m track). The twist (the most important item to evaluate) exhibited a maximum deflection of 3.69 mm at the center of the girder and 2.60 mm at a distance of 3 m from the center; a variation of approximately 1.09 mm. Accordingly, the twist at a distance of 3 m was below the permissible reference value of 3.0 mm (Korean standard, 120 km/h \(<\) V \(\leq\) 220 km/h). This indicates that there should be no safety concerns associated with twist in the bridge deck when the train speed is \(\leq\)200 km/h.