# Influence of Lower Lateral Bracing on the Seismic Pounding Damage to Slab-On-Girder Steel Bridges
## 2 Bridge Model and Ground Motion
### Element and Material Properties  
The finite element model was established and implicit dynamics analysis were performed using the general finite element software Abaqus [18]. To fine-simulate the seismic behavior of and local damage to the slab-on-girder steel bridge, plate elements are used for the steel beams and bridge deck, and solid elements are used for abutments and pier columns. However, this fined model is computationally expensive; as such, further adoption of a multiscale model is a better solution [19]. In this model, plate elements are used to simulate steel beams that may undergo local deformation; beam elements are used to simulate the concrete bridge deck. The space grillage method was used to model the beam model to ensure the continuous stiffness of the bridge deck in all directions. At the interface of the plate and beam elements, the transmission of translational and rotational degrees of freedom was handled according to the principles of displacement coordination and flat section, respectively. The interface and deformation relationship between the two elements is shown in Figure 4. In this study, the contact relationship between steel beams and the concrete bridge deck is simulated based on the hypothesis of tight bonding; that is, it is considered that the two do not produce relative slip and adopt the tie constraint. For concrete beams and steel beams in the model, there is a binding connection between the two parts. Since the bounding only occurs at the beam ends, the beam in the middle part always remains elastic, this simplification is reasonable.  
A global diagram of the bridge FE model is shown in Figure 5a. The eight key positions of the bridge model are named Locations 1 to 8 for convenience. The components of the corresponding locations are also named Gap A 1, Steel Key 2, etc. Figure 5b shows a top view of the bridge model, revealing the positional relationships of steel beams, steel diaphragms, and lateral bracings.  
Figure 4: Deformation relationships of plate and beam elements. (**a**) Interface relationship; (**b**) under axial force; (**c**) under moment.  
Figure 5: _Cont._In addition, the meshing size of the plate element was carefully considered. Numerical convergence tests on multiple mesh sizes (25, 50, and 100 mm) revealed that the results from 50 mm and smaller mesh were similar but computationally inexpensive. To keep the calculation cost as low as possible, the 50 mm finest mesh was only suitable for the length range of a steel beam 0.25 m from the steel beam's ends. The fine mesh (100 mm), medium mesh (200 mm), and rough mesh (500 mm) were also set in the model. Figure 5c-e shows the scheme of gradient mesh sizes at different positions, respectively.  
The steel beam adopts Q345 qE steel, which is a low-alloy high-strength structural steel commonly used in China, with a yield strength of not less than 345 MPa. For the simulation of the beam steel (Q345 qE), a high-precision hysteresis constitutive model was adopted, considering the mixed hardening effect of steel. The constitutive model includes nonlinear isotropic and kinematic hardening. Researchers have widely used this constitutive model, which has proven to be a good predictor of nonlinear mechanical responses in steel [20]. Table 1 shows the material parameters of the steel material [21]. The [PERSON]'s modulus, density, and Poisson's ratio of the steel material are 2.06 \(\times\) 10\({}^{5}\) MPa, 7850 kg/m\({}^{3}\), and 0.2, respectively. In this study, since the main focus is on the seismic-induced bounding failure of steel beams, only the elastic behavior of concrete materials is considered. The [PERSON]'s modulus, density, and Poisson's ratio of the concrete material are 3.45 \(\times\) 10\({}^{4}\), 2600 kg/m\({}^{3}\), and 0.2, respectively.