## 2 Multi-Scale Bridge FE Model
### Multi-Scale FE Modeling of the Baihe Bridge  
A global FE model of the Baihe Bridge was established by [PERSON] et al. [15]. Nevertheless, this model was purely composed of beam elements, aiming at dynamic stress analysis and fatigue damage evaluation at the primary truss member level. Although all of the section data of the beam elements were determined based on the cross-section dimensions of members in the design drawing, structural details such as the gusset plates of the main truss and component-to-component connections were ignored after considering both the analysis needs and computation costs. As a result, the beam element model cannot meet the requirements of enhanced fatigue evaluation associated with the abovementioned structural details. A refined FE model employing shell elements or solid elements for the entire bridge, however, could be inefficient due to huge computation efforts, especially in dynamic time-history analyses, which generally require small time steps. In the preliminary fatigue analysis, the stringers around joint E\({}_{16}\) (Figure 2) were identified as the fatigue-prone members [16]. The end configurations of stringers include the stringer-to-floor-beam bracket and connection angle with high-strength bolts as shown in Figure 3. The fatigue detail associated with the high-strength bolt connection angle was examined using the nominal stress-based S-N approach in [16]. However, fatigue cracks were discovered in the brackets at the position of joint E\({}_{16}\) through the bridge routine inspection [19]. In consideration of the abovementioned information, the bracket is more critical from the fatigue point of view and a detailed local model shown in Figure 4 was developed within a longitudinal distance of about 22 m between the truss joint E\({}_{14}\) and joint E\({}_{18}\) using the ANSYS software [20]. In this local model, truss members, stringers, floor beams, longitudinal bracings, gusset plates, component-to-component connections and so on are simulated using the Shell181 elements with a fine mesh and as-built geometric configurations. Specially, smaller meshing sizes (about 20 mm) are adopted in the vicinity of the critical stringer-to-floor-beam connection brackets compared with other areas (about 150 mm) as shown in Figure 4. The size of 20 mm is determined on the basis that the stress results remain stable when the meshing size of the bracket is smaller than 30 mm. In addition, considering the sufficient rigidity of the high-strength bolt connection among the bracket vertical plate, stringer bottom flange, and floor beam web, identical nodes are used at the interfaces of the bracket, stringer, and floor beam. The local model consists of 24,897 shell elements and 26,594 nodes. The remaining parts of the Baihe Bridge are treated with Beam188 elements. The wooden sleepers and steel rails on the open deck are properly modeled in the present study (Figure 4), whereas only the mass of these two components were taken into account in [PERSON] et al. [15] by uniformly distributing it to the stringer and floor beam. Appropriate connections between the local shell model and the beam model are needed to produce a reliable multi-scale bridge FE model. In this study, all the translation and rotation DOFs of the nodes in shell elements are coupled with the associated DOFs of the end nodes in beam elements at the interface of the shell and beam models (Figure 4). As a result, displacement compatibility and stress equilibrium can be expected to be achieved near the interface. In order to reduce the impact on stress computation accuracies due to the transition from beam elements to shell elements, the following aspects have been considered: (a) set sufficient distances in both longitudinal and vertical directions between the interface and the stringer-to-floor-beam connection bracket under investigation; and (b)avoid placing the interface in the locations that are subjected to intense and complex stress conditions such as the main truss joints.