# Calculation of Reasonable Tension Value for Longitudinal Connecting Reinforcement of CRTSII
## 4 Mechanical Analysis in Tensioning Process  
Each longitudinal connecting reinforcement provided 50 kN tension force when the longitudinal connecting reinforcement of the ballastless track was stretched. The tension force was simulated by dropping the temperature, and the equivalent formula is  
\[\Delta t=\frac{\Delta l}{la}=\frac{F}{AE\alpha}, \tag{3}\]  
where \(\Delta t\) is the scale of drop in temperature, \(\Delta l\) is the length change of the wide joint, \(l\) is the length of the wide joint, \(\alpha\) is the coefficient of linear expansion, \(F\) is the tension value, \(A\) is the section area of the longitudinal connecting reinforcement, and \(E\) is the elastic modulus of the longitudinal connecting reinforcement. The ballastless track is affected by the temperature load after the longitudinal reinforcement is stretched and before the casting of the wide joint, so only the temperature gradient load caused by daily temperature change was considered due to the short time interval between casting and stretching. Taking the common temperature gradient load into consideration, the positive temperature gradient load was 50 \({}^{\circ}\)C/m and the negative temperature gradient load was \(-\)25 \({}^{\circ}\)C/m. Temperature gradient loads were applied after the longitudinal reinforcement was tensioned. The designed tension load was 300 kN so, here, four calculation conditions of 100, 200, 300, and 400 kN were selected to analyze the influence of tension load. The vertical displacement of the bottom side of the track slab, after the longitudinally connected reinforcement was tensioned, is shown in Figure 9. It can be seen that due to the narrow joint, the longitudinal connecting reinforcement puts the track slab under eccentric compression after stretching. When the narrow joint position is under compression, the track slab tends to arch upward. The arch displacement of the track slab increases from the position of the slab edge to the position 0.7 m away from the slab edge. The arch displacement of the track slab begins to decrease gradually and then tends to be very small from the position of 0.7 m away from the slab edge to the position of 2 m away from the slab edge. The larger the tensile force, the larger the arch displacement, and the relationship between the arch displacement and tensile force is nearly linear. The arch displacement of the track slab is very small (0.002 mm) for ballastless track structure. Figure 10 shows the damage at the interface between the track slab and CA mortar under the action of positive temperature gradient load with different tensile force values. It can be seen that the position of the interface damage is located 0.7 m away from the edge of the track slab and the edge of the track slab that corresponds to the outer reinforcement under the action of positive temperature  
Figure 9: Vertical displacement of the track slab after the longitudinal connecting reinforcement is tensioned. (**a**) Track slab longitudinal path. (**b**) Testing result. gradient load. Both the damage value and the damage area increase with the increase of the tension force value. The position where the damage first appears is 0.7 m away from the edge of the track slab (point B), and the temperature gradient load value when the interface damage occurs is reduced from 46 to 40 \({}^{\circ}\)C/m when the tension force value increases from 100 to 300 kN (shown in Figure 11). However, when the tension force value is 400 kN, the first damage area at the edge of the track slab (point A) and the corresponding temperature gradient load value is 20 \({}^{\circ}\)C/m, which suggests that the large tension force value is unfavorable to the interface at the end of the track slab. The stress condition of the element node at points A and B are shown in Figures 12 and 13. It is longitudinal shear stress rather than the vertical normal stress and transverse shear stress that is most affected by tension force value.