## 3 Structural Design and Optimization
### Design and Optimization of Structures  
Three-dimensional models of the structure are established; the original scheme is depicted in Figure 4. The improved configuration, when compared to the original scheme, introduces several changes. First, it eliminates the secondary crossbeams between the suspender crossbeams. Second, a layer of 10 mm-thick ordinary steel plate is added on top of the crossbeams. This steel plate serves multiple purposes--it acts as a protective layer and provides additional strength to the bridge deck.  
To ensure proper connection between the concrete and steel structures, improved PBL shear connectors are employed at the top of the steel plate. These connectors not only enhance the anti-slip capability but also replace the longitudinal steel bars used in the original scheme. This replacement partially compensates for the increased steel consumption resulting from the addition of the ordinary steel plate.  
Figure 4: The schematic diagram of the three-dimensional model of the original scheme.  
Figure 3: Schematic diagram of local optimization units.  
Figure 5 illustrates the improved configuration, showcasing the absence of secondary crossbeams and the inclusion of the steel plate. On the other hand, Figure 6 depicts the design of the improved PBL shear connectors.  
To analyze the structural response of the two configurations, FE models were created using the 2020 ABAQUS software. The steel bars were represented using one-dimensional truss elements (Truss), while solid elements (C3D8R) were utilized for the remaining parts of the model. The details of the model establishment are shown in Table 1.  
Hinge boundary conditions were applied to one end of the suspender crossbeams, while symmetric boundary conditions were applied to the other end. This setup allows for appropriate modeling of the structural behavior. In terms of loading, the concrete slab was subjected to a design load that is 1.2 times the load of a class-I highway vehicle. This  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Structures**} & \multicolumn{2}{c}{**Young’s**} & \multirow{2}{*}{**Poisson’s Ratio**} & \multirow{2}{*}{**Type of Meshes**} & \multicolumn{1}{c}{**Size of Meshes**} \\  & & **Modulus (GPa)** & & & **Meshes** & **(mm)** \\ \hline \multirow{2}{*}{Concrete} & Concrete & \multirow{2}{*}{34.5} & \multirow{2}{*}{0.2} & \multirow{2}{*}{C3D8R} & \multirow{2}{*}{150} \\  & overlay & & & & \\ \hline \multirow{4}{*}{Steel} & Rebar & 206 & 0.3 & Truss & 150 \\  & PBL shear & & & & \\ \cline{1-1}  & connectors & & & & \\ \cline{1-1}  & Stiffening rib & 206 & 0.3 & C3D8R & 150 \\ \cline{1-1}  & Steel beam & 206 & 0.3 & C3D8R & 150 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The details of model establishment.  
Figure 5: The three-dimensional schematic diagram of the improved configuration.  
Figure 6: The schematic diagram of the improved PBL shear connectors in the optimized configuration of the ordinary steel plate scheme.  
loading condition allows for a realistic simulation of the expected forces on the bridge. Table 2 presents the results obtained from the analysis, including the maximum tensile stress and vertical displacement of the concrete overlays, as well as the maximum stress and vertical displacement of the steel structures.  
According to Table 2, it can be observed that the improved design scheme effectively reduces the stress and displacement amplitudes of the structure without a significant increase in steel consumption, with a concrete saving of up to 20%. Furthermore, by altering the construction method of the concrete structure, it will effectively decrease construction costs and alleviate construction difficulty.