## 2 Target Structure and Numerical Modeling
### Initial Load and Boundary Conditions  
To assess the structural performance of each major bridge component such as pylon, deck, and cables, initial compressive forces and tensile forces of the components should be considered. During the application of tension to the stay cables, compressive forces result in the pylon and deck while tensile forces are generated in the cables as shown in Figure 6a. The distribution of compressive forces along the bridge's length is depicted in Figure 6b. Since the compressive forces which are transferred from each stay cable are accumulated, compression of the deck section gradually increases as it approaches the pylon. In another point of view, a very small amount of compression results on the deck section of the center of the mid-span. The deck segment of the current numerical analysis is located at the center of the mid-span, and the design compression of the section is approximately 1.8% of the maximum compression of the deck, according to the design documents [23; 28]. Therefore, the compressive force of the considered segment is regarded as negligible, and only the self-weight of the segment is considered as the initial load. Figure 6: Axial force in cable-stayed bridge: (**a**) axial force paths and (**b**) axial force in deck. \begin{table}
\begin{tabular}{c c c} \hline
**Part** & **Category** & **Input Parameter** \\ \hline \multirow{2}{*}{Concrete} & \multirow{2}{*}{Deck, Pylon} & \(\mathrm{f_{ck}}=39.23\) MPa, \(\mathrm{E}=33.107\) GPa, \\  & & \(\mathrm{p}=2,300\) kg/m\({}^{3}\), ERODE \(=1.05\) \\ \hline \multirow{4}{*}{Steel plate} & \multirow{2}{*}{Girder (Thickness 0–16 mm)} & \(\mathrm{f_{y}}=365\) MPa, \(\mathrm{f_{ta}}=520\) MPa, \(\mathrm{E}=210\) GPa, \(\mathrm{p}=7850\) kg/m\({}^{3}\), \\  & & \(\mathrm{\epsilon_{fail}}=0.15\), \(\mathrm{C}=5.67\times 10^{4}\) s\({}^{-1}\), \(\mathrm{p}=5\) \\ \cline{2-3}  & \multirow{2}{*}{Girder (Thickness 17–40 mm)} & \(\mathrm{f_{y}}=355\) MPa, \(\mathrm{f_{ta}}=520\) MPa, \(\mathrm{E}=210\) GPa, \(\mathrm{p}=7850\) kg/m\({}^{3}\), \\  & & \(\mathrm{\epsilon_{fail}}=0.19\), \(\mathrm{C}=4.99\times 10^{4}\) s\({}^{-1}\), \(\mathrm{p}=5\) \\ \cline{2-3}  & \multirow{2}{*}{Girder (Thickness 41–75 mm)} & \(\mathrm{f_{y}}=335\) MPa, \(\mathrm{f_{ta}}=520\) MPa, \(\mathrm{E}=210\) GPa, \(\mathrm{p}=7850\) kg/m\({}^{3}\), \\  & & \(\mathrm{\epsilon_{fail}}=0.21\), \(\mathrm{C}=3.69\times 10^{4}\) s\({}^{-1}\), \(\mathrm{p}=5\) \\ \hline \multirow{2}{*}{Rebar} & \multirow{2}{*}{Deck, Pylon} & \(\mathrm{f_{y}}=400\) MPa, \(\mathrm{f_{ta}}=560\) MPa, \(\mathrm{E}=200\) GPa, \(\mathrm{p}=7850\) kg/m\({}^{3}\), \\  & & \(\mathrm{\epsilon_{fail}}=0.16\), \(\mathrm{C}=8.21\times 10^{4}\) s\({}^{-1}\), \(\mathrm{p}=5\) \\ \hline \multirow{2}{*}{Cable (BS-5896 Super Grade)} & \multirow{2}{*}{Stay Cable} & \(\mathrm{f_{y}}=1569\) MPa, \(\mathrm{f_{ta}}=1765\) MPa, \(\mathrm{E}=200\) GPa, \(\mathrm{p}=7850\) kg/m\({}^{3}\), \\  & & \(\mathrm{\epsilon_{fail}}=0.035\), \(\mathrm{C}=6.65\times 10^{6}\) s\({}^{-1}\), \(\mathrm{p}=5\) \\ \hline \end{tabular}
\end{table} 
Table 3: Material model input parameters. Initial loads and boundary conditions of each numerical model of the bridge components are shown in Figure 7. As previously mentioned, only self-weight is considered as the initial load for the deck model. As a boundary condition of the deck model, the longitudinal symmetry condition is considered, and the z-directional translation is constrained at the location of cable anchorage. For the cable models, translational DOFs of surface nodes at each end region are constrained considering the anchored length. Thermal load is utilized to apply the initial stresses of each cable model of nos. 37, 53, and 68, which are 415, 556, and 665 MPa, respectively. For thermal load analysis, the temperature change is calculated using the thermal stress Equation (2) with the general thermal expansion coefficient of steel, \(1.2\times 10^{-5}\)/\({}^{\circ}\)C. The calculated temperature drops are \(-\)173, \(-\)232, and \(-\)277 \({}^{\circ}\)C for Cable nos.