## 3 Results and Discussion
### Positive Bending Moment Distributions of Selected Points  
In the previous research, it is found that the maximum positive bending moments appear at rail seats of turnout bearers [12], which is similar to normal tracks [23; 24; 25; 26; 27]. The same idea is applied here while assessing the relation between unsupported bearers and positive bending moment distribution along a turnout. As reflected in Figure 22, the distribution of maximum positive bending moments of bearers at normal track section shows similarities with the distribution of force transferred via fastening system and maximum negative bending moments in previous section. Unsupported bearers have no significant positive bending moments and an increased number of unsupported bearers introduce higher bending moments on adjacent bearers. Similarly, the effect of different velocity is unclear. For instance, two unsupported bearers cause maximum positive bending moments of 8.5 kNm, 8.6 kNm, 8.5 kNm, 8.3 kNm and 8.7 kNm over one adjacent bearer at 10 m/s, 20 m/s, 30 m/s, 40 m/s and 50 m/s, respectively. Under the same condition, maximum positive bending moments over the other adjacent bearer are 8.4 kNm, 8.5 kNm, 8.3 kNm, 9.1 kNm and 10.6 kNm. Furthermore, the plot in a particular time also follows the similar pattern. The distribution becomes more uneven with unsupported bearers and transition the from adjacent bearer to the next fully supported bearer is sharp. A distribution of maximum positive bending moments owing to unsupported bearers is depicted in Figure 23 for switch panel bearers. Similar properties observed in normal track section are also valid for the bearers at switch panel. Apart from that, a small discrepancy could be observed in the case of three unsupported bearers, where one of the unsupported bearers, first one in moving direction, has positive bending moments due to additional rail that acts like a support. In numerical model, this bearer is the point before which the switch blades and stock rails just start to split. In general, the correlation remains between the force transferred via the fastening system and the maximum positive bending moments at this section. In all cases, the maximum positive bending moment take place at former adjacent bearer of unsupported bearers. Among them, highest maximum positive bending moment, 11.5 kNm, emerges at 50 m/s when three bearers are unsupported and lowest positive bending moment is 5.2 kNm at 10 m/s with two unsupported bearer. Considering the positive bending moment distributions in particular time, it is evident that the distribution looks similar to normal track section. The only difference is the positive bending moments seems to be distributed more evenly due to higher track stiffness. Figure 21: The distribution of negative bending moments over the bearers when the shortest bearer is unsupported: (**a**) at particular time when the front wheel is on the bearer with number 62; (**b**) when maximum occurs at each bearer. Figure 22: The distribution of positive bending moments over the bearers when unsupported bearers exist at normal track section: (**a**) at particular time when the front wheel is on the bearer with number 10; (**b**) when maximum occurs at each bearer. Figure 23: The distribution of positive 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. As can be seen from Figure 24, reflecting the effect of unsupported bearers at closure panel, the unsupported bearers are also exposed to important positive bending moments. It could be said that the results for all three cases is indistinct in terms of maximum positive bending moments at this section, despite a barely perceptible difference for adjacent bearers having slightly higher positive bending moments. According to [12], highest bending moments occur at closure panel under static loads or at lower speeds, when the impact forces are ineffective at crossing nose.