## 4 Results and Discussion
### Parametric Studies
#### 4.2.1 Effects of Train Speed
In Figure 6, the longitudinal bending moment distribution is displayed for a case when the vehicle runs over a track without irregularities. The bending moment distribution shows that maximum bending moments at lower speeds gradually increase with the sleeper length, with the exception of a small drop at the sleepers under the crossing nose. The relatively lower bending moments at the crossing panel could be a consequence of the increased total rail stiffness, which evenly distributes the load between sleepers. The distinct property of Figure 6 is that significant variations could be observed only at the crossing panel with no track irregularities. As can be seen from Figure 6, maximum positive bending moments as well as maximum negative bending moments mostly take place at sleepers close to the crossing nose and the deviation between the bending moments at minimum and maximum speeds is large. Another insight stemmed from Figure 6 is that the open switch blade increases the maximum negative bending moment; therefore, the maximum negative bending moment starts to increase a few sleepers before. In Figure 7, maximum positive and negative bending moments are presented for different vehicle speeds travelling on a track with irregularities. It is evident that the location of the maximum bending moment is related to vehicle speed. At lower speeds, maximum positive bending moments appear to occur at closure panels and the magnitudes of the positive bending moments are 10-15 kNm with reference to vehicle speed. Likewise, maximum negative bending moments take place in the vicinity of the location of the maximum positive bending moments, with magnitudes of around 7 kNm. For both moment directions Figure 7, there are fluctuations in the bending moments, which are as a result of track irregularities. Figure 5: Multibody responses: (**a**) Dynamic factors for two cases: track with no irregularities and with irregularities; (**b**) contact forces for minimum and maximum speed. Interestingly, higher train speeds produce a significant difference in the maximum positive bending moment distributions along the turnout. The location of the maximum positive and negative bending moments shifts from the closure panels to the crossing panels with higher speeds. The reason for this shift is that the effects of impact forces become more distinct, parallel to speed increments. The magnitude of the maximum bending moment is 20 kNm at the speed of 55 m/s., which is approximately four times higher than normal for that track section. Interestingly, track irregularities still produce higher bending moments and therefore, the maximum positive bending moments at closure panels are still significant. Nevertheless, these become insignificant when compared with the gain at the crossing panel. Similarly, the negative bending moments also distinctly seem to have shifted their location from the sleepers at the closure panel to the sleepers under the crossing nose. However, the maximum negative bending moments show smaller increases compared to the maximum positive bending moments. The contribution of the track irregularities to bending moments is clear by the comparison of Figures 6 and 7. Irregularities have a limited effect on the bending moments of the sleepers under the crossing nose, in contrast to other sleepers. For instance, the gap between maximum bending moments in two cases for sleeper 52 is 1 kNm; by contrast, it is 5 kNm for the sleeper 38. Another significant aspect of this comparison is that the standard deviation of the bending moments due to  
Figure 6: Longitudinal bending moment distribution with no track irregularities. Figure 7: Longitudinal bending moment distribution with track irregularities. track irregularities could be significant which is important in terms of fatigue damage. The fatigue damage occurs under cyclic loadings; the mean force and force amplitudes define the stress cycle [46]. In addition, this comparison gives another proof for the effects of track irregularities.