## 3 Results and Discussion
### Positive Bending Moment Distributions of Selected Points
Relative bending moments range from -1.3 kNm to 1 kNm for unsupported bearers at different speeds. Likewise, relative bending moments for adjacent bearers vary from -0.72 kNm to 2.01 kNm, associated with vehicle speed and number of unsupported bearers. Here, negative sign indicates that bending moments in reference case could be higher, regarding the previously made definition of'relative'. Apart from that, the plot of bending moments in particular time shows that the bending moments reach maximum when the wheel is on the top of unsupported bearer. What is more, the bending moment value for that bearer exceeds the other values where rear wheel contribution takes place. Hence, it is expected that unsupported bearers underneath the closure panel is likely to be damaged quickly. In Figure 25, maximum positive bending moments as a result of unsupported bearers under crossing nose are presented. Two distinct properties are striking. First, unsupported bearers at lower speeds have relatively small bending moments due to lower contact forces, which is similar to negative bending moments. As aforementioned, adjacent bearers have relatively higher load distribution due to insignificant impact loads at lower speeds. The combination of this uneven load distribution and length of the bearers result in higher bending moments. Hence, adjacent bearers are affected from relatively higher bending moments regarding the reference case. Adjacent bearer have up to 26%, 51% and 78% increase ratio for one, two and three unsupported bearer. On the other hand, higher speeds induce significant impact forces. Those impact forces result in higher bending moments at unsupported bearer or bearers after crossing nose with reference to different velocities. As a result, the gap between adjacent bearer and unsupported bearer closes. Interestingly, the unsupported bearers have positive effect to mitigate impact forces at crossing nose. The reduction in positive bending moments could be up to 56% at 10 m/s and 21% at 50 m/s. This behavior seems to be different for concrete bearers, which will be mentioned in later in this paper. Maximum positive bending moments are given in Figure 26, for unsupported longest bearer and its neighbor bearers. Even though the track is relatively separated from diverging track, unsupported bearers are still subjected to positive bending moments that are lower in the magnitude and more, adjacent bearers have relatively higher bending moments. Magnitudes for adjacent bearers vary from 4.8 to 11.7 kNm with respect to different velocities. For unsupported bearers, it is between 3.2 and 6.2 kNm. As clearly seen in the figure, one of the unsupported bearers (shortest bearer) carries no positive bending moments, which is due to independency from diverging route. Another perceptible difference is that longest adjacent bearers are subjected to more bending moments in comparison to shortest adjacent bearer as a result higher track stiffness. As demonstrated in Figure 27, shortest bearers have lower maximum positive bending moments owing to their shorter lengths. The distribution characteristic is similar to normal bearers. The unsupported bearers have almost no bending moments and the number of unsupported bearers significantly affects the bending moments of adjacent bearers. The maximum positive bending moment is observed with a magnitude of 12.3 kNm at 50 m/s in the case of three unsupported bearers. Similarly, the effect of vehicle velocity is also unclear at this section. For instance, the magnitudes of maximum positive bending moments are 9.5, 7.3, 8.5, 10 and 12.3 kNm from 10 m/s to 50 m/s, respectively, for one of the adjacent sleepers in three unsupported case. Figure 24: The distribution of positive 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.