## 3 Results and Discussion
### Negative Bending Moment Distributions of Selected Points  
Bending moment distributions along a turnout show quite complex behavior. In general, maximum positive bending moments occur at rail seats in contrast to maximum negative bending moments that could exist at any position along a bearer [12]. Therefore, it seems more suitable to select a specific position on the bearer to investigate negative bending moment behaviors. Indeed, it is a challenging task due to varying bearer lengths and additional rails such as switchblades. It is obvious that other ends of the bearers will have different coordinates due to varying lengths, regarding one-sided alignment of the bearers. A common approach is to select midpoints of bearers and rail seats while investigating the response of the system for normal track. The same idea is followed here with a small adaptation referring to above-mentioned challenge. Here, the element in the middle of two loaded rails is selected instead of mid-point of a bearer. Maximum negative bending moments of middle points of the bearers at normal track section are illustrated in Figure 16. It seems that the figure reveals the common characteristic behavior of unsupported bearers at normal track section. Unsupported bearers carry no significant force that results in no bending moments in contrast to supported adjacent bearers. Furthermore, the more unsupported track section expands, the higher negative bending moments occur over fully supported bearers. Maximum negative bending moments of supported bearers could reach 8.8 kNm, while three bearers are unsupported at 50 m/s. The changes in the velocity mostly cause higher bending moments as also found in [3]; however, the effect of velocity owing to unsupported bearers is unclear in comparison with the reference case. For instance, relative increase for one of the adjacent bearers are 33%, 35%, 27%, 34% and 45% at 10 m/s, 20 m/s, 30 m/s, 40 m/s and 50 m/s, respectively, in the case of one supported bearer. Figure 14: The distribution of rail seat force over the bearers when the longest bearer is unsupported: (**a**) at particular time when the front wheel is on the bearer with number 61; (**b**) when maximum occurs at each bearer. Figure 15: The distribution of rail seat force 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 16: The distribution of negative 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. A depiction of the results for the unsupported bearers laid under switchblades is given in Figure 17. What stands out in the figure is that the distributions of maximum negative moments for unsupported bearers show no distinct deviation from the reference case. The reason why unsupported bearers are subjected to a negative bending moment is that switch blades, specifically opened switch blade, act as a support that cause negative bending moments [12]. The maximum negative bending moments range from 3.1 kNm to 5.8 kNm for bearers under switch blades. Despite one different case when three bearers are unsupported, maximum negative bending moment is correlated to the number of unsupported bearers, in contrast to different speeds, in terms of bending moments of unsupported bearers. For instance, the magnitudes of bending moments of same bearer are 2.5, 2.8 and 3.1 kNm for one, two and three unsupported cases. Similar to switch panel, unsupported bearers also bear maximum negative bending moments when they are laid at closure panel, shown in Figure 18. It is clear that unsupported bearers amplify negative bending moments at closure panel.