## 4 Fatigue Load Effects  
Fatigue damage in steel bridges can occur due to the cyclic loads, e.g., train loading. Therefore, it is necessary to acquire train information including daily numbers of passage, marshalling, axle weight, running speed and so on in the service history of the Baihe Bridge. A comprehensive investigation was carried out by [PERSON] et al. (2019) on 54 main railway lines in China including the Beijing-Tongliao line where the Baihe Bridge is located. In their study, the operating trains in the Beijing-Tongliao line were categorized into two types, i.e., passenger train and freight train. The passenger train consists of one locomotive and 20 cars with the axle weights = 23 t and 15.4 t, respectively. The freight train is comprised of one locomotive, 25 open-top cars, 11 covered cars, four tank cars, and three flat cars with the net axle weights = 23 t, 5.5 t, 6.0 t, 5.5 t, and 5.5 t, respectively. It should be noted that each type of freight car features several values of the actual axle weights depending on the amount of carried goods. Numbers of the passenger and freight train passage per day are 22 and 28 respectively. More information on the passenger and freight trains can be found in [PERSON] et al. (2019). During the field test in 2011, running speeds of the freight trains were measured. The average speed was found to be 60 km/h ([PERSON] et al., 2019). In addition, train speeds were increased in China's railway network after 1997 since a campaign aiming at speed-up of the national railway system was launched by the former Ministry of Railway. Consequently, it is assumed in this study that the freight trains ran at the speed of 40 km/h before 1997. Generally, passenger trains have higher speeds compared with the freight ones. Therefore, the speeds of passenger trains before and after 1997 are considered as 50 km/h and 70 km/h, respectively. Stress responses of the stringer-to-floor-beam bracket due to the abovementioned passenger and freight trains are computed through the multi-scale vibration analysis of the TTB system as discussed earlier. Figures 8 and 9 show the distribution of stresses on the stringer-to-floor-beam bracket analyzed (Figure 2) at two typical time instants induced by the passenger and freight trains of the two loading periods (i.e., 1980-1997 and after 1997). It can be seen in the figures that the stress amplitudes obtained from the operating trains differ significantly. However, in all scenarios the stress distributions in the bracket are similar. The highest stresses appear in the areas (red regions in Figures 8 and 9) around the end of welds connecting the vertical plate and the bottom flange of the stringer. This intense stress response in the high-stress areas is partly attributed to the stress concentration effects resulting from the geometric irregularity and discontinuity around the cope hole. The maximum stress is caused by the freight train with the speed = 60 km/h, reaching 348 MPa. Nevertheless, it is smaller compared with the material yield strength 430 MPa. Moreover, the stress variations associated with the high-stress area are also more significant than that observed in other areas of the stringer-to-floor-beam bracket. In addition, time-histories of the dynamic stresses associated with the high-stress area of the bracket are displayed in Figure 10. It is found in this figure that both the stress amplitudes and variations produced by the freight train are significantly larger compared with those by the passenger train. Therefore, the freight train will contribute the majority to the fatigue damage. No considerable differences in the amplitudes and variations of stress time-histories due to the passenger trains of 50 km/h and 70 km/h can be observed. Yet dynamic stress variations corresponding to the freight train with the speed = 60 km/h are more significant in comparison with that related to the freight train with the speed = 40 km/h.