# Analytical and Measured Effects of Short and Heavy Rail Cars on Railway Bridges in the USA
## 3 Results of Case Studies  
### Riveted Truss Spans  
#### 3.1.1 FEM Modeling and Analysis of Truss Bridge  
A variety of loads can be applied to a structure at the same time. For instance, dead load and live load, impact, centrifugal force, temperature, and the wind should be considered in the analysis [16]. Therefore, with a proper FEM model validated with field measurements, the analysis can be carried out with additional load cases to examine bridge structural behavior. The 3D FEM model of the existing bridge that contains all components and connections can predict stress concentration in places that are difficult to measure in the field. In this study, the analytical calculations were performed to guide the test plan. The effects of railcar lengths on truss span members depend on the type and location of the member, as well as the type and length of the truss. To evaluate the load effects, a 3D FEM model was developed in LUSAS software, Bridge Plus 2020 [17]. The advantage of a 3D model is that it contains all components and connections that can closely replicate the actual behavior of the structure. The bridge model was created using 3D beam and shell elements. The beam elements, with appropriate cross-sections, were used for all truss members that carry primarily axial forces. The floor beams and stringers were modeled using shell elements appropriate for members in which one dimension, the thickness, is significantly smaller than the other dimensions. The stringer-to-floor-beam connections were defined to replicate the continuous behavior of the stringers. However, the focus of the analysis was to find load effects on the main bridge components, not connections. Figure 4: Investigated deck plate girder (DPG) bridge dimensions and strain gauge locations (1 ft = 0.305 m). The bridge models were created both with and without the deck and ballasted track. The analytical results that match the stresses calculated from measured strains were obtained using the model without the deck and ballasted track (Figure 5). The load was applied directly onto the stringers. When the track components, i.e., rail, sleepers (ties), and ballast (modeled as a volume), were added to the model, the stresses in the bottom flange of stringers were much lower than the test data. It seems likely that the ballast used in the model was not only distributing the load but also influencing the stress distribution in the cross-section of the stringer. It is recommended to investigate further this issue by measuring strains in the components of the floor system with a focus on connection behavior and potential composite action of stringers and floor-beam with the track system. The ballast distribution can be easily introduced by replacing each point force corresponding to an axle load with a set of point forces distributed over three adjacent sleepers (Figure 6). More options of the axle load distribution and the effect of axle load spreading through the ballast as well as the effect of support stiffness were investigated on short-span railway bridges by [PERSON] et al. (2018). Figure 5: FEM model of investigated truss bridge. Figure 6: Set of forces corresponding to axles load. Stresses were calculated under moving loads for the entire span using common 16.2-m (53-ft) railcars and short 12.8-m (42-ft) railcars. Figure 7 presents examples of stress histories on selected bridge members due to a moving set of railcars. The calculated stresses in the 61-m (200-ft) truss due to short railcars were 15 to 25% higher than for common length railcars in most of the primary members such as end posts, primary diagonals (U1L2), and top and bottom chords. The intermediate diagonals L2U3 and U3L4 experienced 13 and 7% higher stresses, respectively, due to common length railcars when compared to the short railcars. Figure 8 presents a comparison of predicted peak stresses for the main bridge components on the 61-m (200-ft) and the 33.5-m (110-ft) spans.