## 5 Examples
### Appropriate Matching Location of Fixed Bearing with Rer
#### 5.2.2 Longer Continuous Beam  
The continuous beams with the lengths of 180 to 300 m are studied with an interval of 30 m as examples of a longer length. The locations of RER are, respectively, above the left and right ends of the  
Figure 11: Additional force of rail along its length, with the fixed bearing located at three different positions for the length of 150 m of continuous beam. Figure 12: Longitudinal displacement of rail along its length, with the fixed bearing located at three different positions for the length of 150 m of continuous beam. continuous beam, and they remain unchanged. The curves of the maximum additional compression and tension forces of rail with the change of the location of the fixed bearing can be obtained by using Step (8) in Section 4, and they are plotted in Figure 13, in which the abscissa represents the distance between the fixed bearing and the left end of the continuous beam. The figure shows that the change of the maximum additional tension force (TF) can be ignored, but that of the maximum additional compression force (CF) depends on the locations of RER and the fixed bearing. It can be seen from the figure that there is indeed an upper limit value for the maximum additional tension force of rail mentioned in Section 5.1. When RER is located above the left end of the continuous beam, regardless of the length of the beam, the change of CF can be ignored, for example, when the fixed bearing is located within 58 m of the right end of the beam; the number 58 is marked in Figure 13a-e. In the other locations, the change of CF is significant, and the closer the fixed bearing is to the left end of the beam, the greater the CF will be. When RER is located above the right end of the continuous beam, the change of CF can be ignored, with the fixed bearing located within 26 m near the left end of the beam. In fact, the distance between the fixed bearing of the continuous beam and the fixed bearing of the left simple beam neighbor to the continuous beam is also equal to 58 m, and it is the same as the range mentioned above. Similarly, the number 26 is marked in Figure 13a-e. At other locations, the change of CF is obvious, and the closer the fixed bearing is to the right end of the beam, the greater the CF will be. Therefore, if RER is set above the left end of the continuous beam, the fixed bearing of the continuous beam should be arranged close to the right end of the continuous beam. Conversely, if RER is set above the right end, the fixed bearing should be arranged near the left end. This matching arrangement can reduce the maximum additional compression force of rail. Here, three different locations are considered with the \(l_{\text{lb}}\) of 100, 122, and 150 m for a continuous beam with the length of 180 m; RERs are located above the left end of the continuous beam. Figure 14 shows the corresponding additional force of rail along its length. The abscissa in Figure 14 represents the distance between a certain section and the left end of the rail. Three curves with RER are shown in Figure 14; the maximum additional tension forces of rail in the three curves are almost equal to each other, but the maximum additional compression forces are different. For \(l_{\text{lb}}\) of 122 m, the additional compression force of rail above the right end of the continuous beam is equal to that above the right end of the last simple beam adjacent to the embankment, and they are the maximum compression force corresponding to \(l_{\text{lb}}\) of 122 m. When \(l_{\text{lb}}\) is smaller than 122 m, the force above the right end of the continuous beam is maximum, and it increases with the reduction of the distance. It is the significantly changed part of Figure 13a. When \(l_{\text{lb}}\) is greater than 122 m, the force above the right end of the last simple beam adjacent to embankment is maximum, and it is not affected by the change of \(l_{\text{lb}}\). It is the unchanging part of Figure 13a.