## 4 Parametric Study by Computational Analysis  
### Computation Model  
To investigate the impact of size parameters of the bi-directional U-ribbed stiffening plate (BUSP) on structural stress, finite element analysis (FEA) models were constructed for a portion of the bridge using the ABAQUS software. Two types of structural models were primarily established for this analysis. Both types of models incorporated the U-ribbed stiffening plate, which is depicted within the black box in Figure 9. The key difference between the two models lies in the crossbeams used. Structure 1 utilized optimized crossbeams, while Structure 2 retained the crossbeams from the original design. The purpose of creating these two variations of computational models is to further validate the effectiveness of the optimized crossbeams. Additionally, the computational results obtained from the two types of FEA models, with different size parameters, will be compared with the original structure. Figure 8: The schematic diagram of the improved PBL shear connectors in the optimized configuration for the BUSP scheme. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{2}{c}{**Stress (MPa)**} & \multicolumn{2}{c}{**Displacement (mm)**} & \multicolumn{2}{c}{**Material**} \\  & & & & & **Consumption** \\ \cline{2-7}  & **Concrete** & **Steel** & **Concrete** & **Steel** &
\begin{tabular}{c} **Concrete** \\ **(m3)** \\ \end{tabular} & **Steel (t)** \\ \hline Original Scheme & 1.28 & 63.81 & 4.95 & 7.01 & 92.96 & 161.50 \\ BUSP Solution & 0.90 & 56.88 & 3.87 & 6.29 & 75.16 & 163.51 \\ Amplitude of & \(-\)29.69 & \(-\)10.86 & \(-\)21.82 & \(-\)10.27 & \(-\)19.15 & 1.24 \\ Variation (\%) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: A comparative analysis between the original scheme and the BUSP scheme. In the U-ribbed stiffening plate, the size parameters include both individual U-rib characteristics and various spacing parameters between U-ribs. The size parameters of a single U-rib consist of the following: the height of the U-rib (\(h\)), the opening width of the U-rib (\(a\)), the bottom width of the U-rib (\(b\)), the thickness of the steel plate (\(t\)), and the angle between the side and bottom edges of the U-rib (\(\alpha\)). On the other hand, the spacing parameters between U-ribs comprise the spacing between longitudinal U-ribs along the transverse direction of the bridge (\(e\)) and the longitudinal spacing between transverse U-ribs (\(w\)). The meaning of these size parameters is shown in Table 4. And all these size parameters used in the FEA models are illustrated in Figure 10 for reference. In a single U-rib of the BUSP, there are five size parameters: \(a\), \(b\), \(\alpha\), \(h\), and \(t\). However, these parameters are not entirely independent. For instance, when \(b\) is kept constant, changing the value of \(a\) will correspondingly affect the value of \(\alpha\). This relationship between \(a\), \(b\), and \(\alpha\) indicates that \(\alpha\) is a non-independent parameter. Furthermore, since the bottom of the BUSP directly contacts the crossbeams, the size of the U-rib's bottom (\(b\)) must be consistent with the flange plate dimensions of the crossbeams. Therefore, the primary focus of this paper regarding the single U-rib size parameters is on \(a\), \(h\), and \(t\). The parameter \(b\) has been set as a constant value of 600 mm, matching the dimensions of the crossbeam flange. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Meaning** \\ \hline \(h\) & The height of the U-rib \\ \(a\) & The opening width of the U-rib \\ \(b\) & The bottom width of the U-rib \\ \(t\) & The thickness of the steel plate \\ \(\alpha\) & The angle between the side and bottom edges of the U-rib \\ \(e\) & The spacing between longitudinal U-ribs \\ \(w\) & The spacing between transverse U-ribs \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The meaning of the size parameters for the U-ribbed stiffening plate. Figure 9: Configuration of a structural model.