# Performing Fatigue State Characterization in Railway Steel Bridges Using Digital Twin Models
## 4 Bridge Case Study
### Fatigue Analysis System Implementation  
As described in Chapter 2, of the four phases that are part of a global fatigue analysis process, the one that integrates the proposed DT model is the second phase based on LDAM (see Figure 4). This FAS was modified to meet the scope of the proposed DT model. The details of such steps and the modifications implemented for this present case study are presented in Figure 10. The modifications (in the \"standard FAS\") are fundamental to give new input conditions to the system regarding loads (traffic) and geometry. Thus, besides being a system that performs analyses (calculation of accumulated damage) for fixed conditions, it becomes flexible for various situations.  
Figure 10: Implemented FAS to reach the proposed digital twin.  
The above conditions' implementation and automation are achieved through implementing routines via APDL and MATLAB(r) v2021a. In terms of analyses that lead to obtaining nominal stresses in connection details, given that the speeds of the trains traveling over the bridge under study do not exceed 200 km/h, according to EC1-2 [28], dynamic analysis was dispensed, and static analysis was carried out through the implementation of influence lines for determining internal forces, bending moments, and stresses (Figures 10 and 11).  
If it were a dynamic analysis, modal superposition would be the most efficient methodology (see Figure 10, and a more in-depth approach to the methodologies can also be found in previous studies [1; 5]). The respective numerical model was based on finite elements implemented in the ANSYS(r) v.2021 software. Beam elements (BEAM 188) available in ANSYS APDL v.2021 [31] were used to design the model. This included the non-ballasted railway track, where the rail and wooden sleepers were also modeled using BEAM 188. Regarding the material properties (steel), two classes were considered depending on the type of metallic member: S355 (with yield strength, fy, equal to 355 MPa, Young's modulus, E, of 210 GPa, density, \(\rho\), of 7850 kg/m\({}^{3}\), and Poisson's ratio, v, equal to 0.27) and S235, with all properties similar to the S355, except for the yield stress, fy, which is equal to 235 Mpa.  
To validate the numerical model, which led to the computation of fatigue damage, and in the context of conducting a detailed analysis (not covered in this work), in addition to an ambient vibration test of the bridge, to obtain experimental vibration modes and frequencies and subsequent comparison with those obtained numerically (Table 2), a forced vibration campaign was conducted regarding the passage of a regular passenger train (composed of 12 axles with an average weight of 115 kN per axle) through the bridge, at a speed of 53 km/h. To this end, 14 strain gauges were installed to evaluate the stresses at locations of interest. Figure 12[32] shows the position of four sensors that are part of this set and the installation process of one of these. Figure 13[32] shows an overlap of numerical time history stress and experimental stresses in two of the four previously mentioned positions, calculated from strain values and considering a purely elastic material. As for the vibration modes, the numerical and experimental stress values show good agreement, which suggests that the model provides reliable and accurate results for stresses. For the vibration modes, the average percentage variation between the corresponding experimental and numerical frequencies (only for the frequencies presented here, out of a total of 28 obtained correspondences) is approximately 1.6%. A more in-depth discussion of this issue can be found in the previous study [32], which was solely concerned with the fatigue analysis of the same bridge.  
Figure 11: General scheme implemented for calculating fatigue damage via static analysis.