## 1 Introduction
### Validation of the Global FE Model of the Simply Supported Composite Beam Bridge  
The modal properties of the simply supported composite beam bridge, specifically its natural frequencies and mode shapes, are crucial for validating the global FE model and associated numerical modeling techniques. According to the General Design Specification for Highway Bridges and Culverts [26], the fundamental natural frequency of a simply supported beam bridge can be calculated by  
\[f_{1}=\frac{\pi}{2L^{2}}\sqrt{\frac{EI_{c}}{m_{c}}} \tag{1}\]  
where \(L\) is the calculated span of a simply supported beam bridge, \(E\) is the elastic modulus of the girder material, \(I_{c}\) is the moment of inertia of the girder section, and \(m_{c}\) is the mass per unit length of the girder. According to the composite section details of the simply supported beam bridge in Figure 3, the moment of inertia \(I_{c}\) and the mass per unit length \(m_{c}\) of the steel-concrete composite section are calculated. The theoretical value of the fundamental natural frequency of the simply supported composite beam bridge is then determined using Equation (1), yielding 3.25 Hz, corresponding to the first-order vertical bending mode of the girder. To validate the accuracy of the numerical modeling techniques employed in Section 3.3, the structural natural vibration characteristics were analyzed numerically using the established global FE model of the bridge. Through modal analysis, the fundamental natural frequency of the simply supported composite beam bridge is 2.97 Hz, which also corresponds to the first vertical bending mode of the girder (Figure 4c). The relative difference between the numerical result and the theoretical value of the first-order natural frequency is only 9.4%, which is deemed acceptable for practical engineering structures. The discrepancy may be attributed to the omission of ancillary components such as bridge deck pavement and guardrails in the theoretical calculation of the fundamental natural frequency (Equation (1)), resulting in a higher natural frequency for the simply supported composite beam bridge. In conclusion, the established global FE model of the simply supported composite beam bridge effectively captures its inherent characteristics with acceptable accuracy.  
In general, the best way to validate the established numerical model of the target simply supported composite beam bridge is with the aid of experimental data, which are fully representative of the real bridge structure. Due to the busy urban traffic demand, it is impossible to stop train operations to conduct load tests on the bridge. Thus, it is not feasible to validate the numerical model based on experimental data of the bridge. As an alternative measure, the design values of the dynamic characteristics of the simply supported composite beam bridge are adopted to validate the numerical model in the above  
Figure 4: Global FE model of the simply supported steel-concrete composite beam bridge on Shanghai Metro Line 3.  
context. It should be pointed out that the dynamic behaviors calculated using stationary techniques still have a limitation for the target bridge. The target bridge in service may undergo damage over time, and its actual dynamic characteristics might be different from the design values. The validation using the design values of the dynamic characteristics of bridges thus may affect the reliability of the established numerical model to a certain extent. It might be better to employ techniques, e.g., a band-variable filter [27], which are capable of assessing non-stationary dynamic behaviors of existing structures. However, compared with the design values of structural dynamic characteristics, the techniques to capture non-stationary dynamic behaviors of existing structures are too complex in principle, and the calculation process is also very cumbersome. Hence, using design values of structural dynamic characteristics to do calibration plays a role as a quick and effective means for numerical model validation.