## 3 Results and Discussion
### Negative Bending Moment Distributions of Selected Points
More interestingly, they are subjected to considerable negative bending moments and the contribution of vehicle speed to negative bending moments is imperative compared to other sections; whereas force transferred via fastening system is the lowest at this section with no significant effect of vehicle speed, as indicated previously. The highest magnitudes of maximum negative bending moment occur at bearer 37 in most cases. The exception is the case when three unsupported bearer exist and vehicle velocity is 50m /s. That time maximum negative bending moment shifts to the bearer with number 38, which is the worst case with a magnitude of 6.5 kNm that is 58% higher than reference case. What is more interesting is that the adjacent bearers of unsupported bearers are exposed to lower bending moments than unsupported bearers (Figure 18b), which is mostly vice versa in other cases. Figure 19 compares the outcomes of the simulations in terms of maximum negative bending moments of the bearers at crossing panel when the unsupported bearers are assumed to occur under the crossing nose. It is apparent from the figure that there is a difference between lower and higher speeds. At lower speeds such as 10 m/s, the impact forces are relatively ineffective and behavior of bearers is akin to normal track sections where the unsupported bearers are subjected to relatively no bending moments. Therefore, adjacent bearers are affected more from maximum negative bending moments. It should also be emphasized that an idle closure rail between two rails, producing negative bending moments, disappears at this section. On the other hand, the magnitude of impact forces escalates with higher velocities, which result in higher negative bending moments. Nevertheless, they are still lower than the reference case. In the worst case, maximum negative moment is 30% below the reference case. As there is no additional rail between two loaded rails, maximum negative bending moments at the selected point of longest bearer show similar behavior to normal similar (Figure 20). Unsupported bearers carry insignificant loads. The striking difference is that negative bending moments for longest adjacent bearers of unsupported bearers are lower than the shortest adjacent bearers. For instance, the magnitudes of maximum negative bending moments are 2.7/3.8, 3.4/4.3 and 4.5/6.04 kNm for longest/shortest adjacent bearers in one, two and three unsupported bearer cases, respectively. The reason could be explained by two factors. As previously mentioned, the load distribution is asymmetrical in this case, resulting in higher forces on the shortest bearers. Moreover, the actual maximum negative bending moments could occur on diverging route due to support conditions whereas the maximum negative bending moment depicted above is valid for bearer section located in the middle of two tracks. Although the results in Figure 20a seem to contradict with the outcome in previous sentences, it should be stressed that the results in Figure 20a is plotted when the front wheel is on the top of an unsupported bearer. As a consequence, the rear wheel also has a share in the negative bending moments of longest adjacent bearer at the particular time. Figure 17: The distribution of negative bending moments over the bearers when unsupported bearers exist under switchblades: (**a**) at particular time when the front wheel is on the bearer with number 20; (**b**) when maximum occurs at each bearer. Figure 18: The distribution of negative bending moments over the bearers when unsupported bearers exist at closure panel: (**a**) at particular time when the front wheel is on the bearer with number 37; (**b**) when maximum occurs at each bearer. Figure 19: The distribution of negative bending moments over the bearers when unsupported bearers exist under crossing nose: (**a**) at particular time when the front wheel is on the bearer with number 53; (**b**) when maximum occurs at each bearer.