## 4 FEA Data Construction  
### Database Construction  
To construct structural response data from the geometrically nonlinear analysis with imperfection (GNIA), several main design parameters were considered in this study, including various cross-sections of the bridges, torsional bracing stiffness (\(\beta_{b}\)), the number of bracings, the girder spacing to height ratio (\(S/d\)), the moment gradient factor (\(C_{bb}\)) within the brace points at target segments, the moment gradient factor (\(C_{bu}\)) of the entire span, and the yield strength of structural steels (\(f_{y}\)). Therefore, a total of 16,576 structural response data were constructed, as summarized in Table 4. This study uses 16 input variables, including the flange width (\(b_{f}\)), flange thickness (\(t_{f}\)), the height of the girder (\(d\)), the moment of inertia about the strong axis (\(I_{x}\)), the moment of inertia about the weak axis (\(I_{y}\)), span length (\(L\)), unbraced length (\(L_{b}\)), number of bracings, bracing stiffness (\(\beta_{T}\)), girder spacing (\(S\)), moment gradient factors (\(C_{bu}\), \(C_{bb}\)), the flexural strength of the bracing system (\(f_{bu}\)), the yielding strength of structural steels (\(f_{y}\)), the LTB strength of braced segments (\(F_{n,L_{b}}\)), and the LTB strength of nonbraced girders (\(F_{n,L}\)), whereas the maximum and minimum bracing moments (\(M_{br,max}\), \(M_{br,min}\)) and bracing force (\(F_{br}\)) are the target variables. In  
Figure 5: Bracing moments and internal forces acting on bracing members. addition, a detailed statistical analysis of the database, including the min, max, mean, median, variation (var), standard deviation (std), and skewness of variables, is presented in Table 5 for input variables and Table 6 for output variables. Finally, the histograms of the input and output variables used in this study are plotted in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Variable** & **Unit** & **Min** & **Max** & **Mean** & **Median** & **Var** & **Std** & **Skewness** \\ \hline \(M_{br,max}\) & N \(-\) mm & 0 & 9,208,109 & 723,113 & 396,654.7 & 8.62 \(\times 10^{11}\) & 928,189.1 & 2.88 \\ \(M_{br,min}\) & N \(-\) mm & 0 & 2,394,757 & 278,486.4 & 188,031.7 & 8.77 \(\times 10^{10}\) & 296,136.8 & 2.12 \\ \(F_{br}\) & N & 0 & 3421.2 & 525.8 & 376.6 & 250,172.9 & 500.2 & 1.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Ranges of design parameters for output parameters used in this study. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Section** & \(\beta_{b}\) &
\begin{tabular}{c} **No. of** \\ **Bracings** \\ \end{tabular} & \(S\)/\(d\) & \(C_{bu}\) & \(C_{bb}\) & \(\begin{array}{c}f_{y}\\ **(MPa)** \\ \end{tabular}\) & **Count** \\ \hline W920 \(\times\) 201 & & 1, 2, 3 & 1–1.471 & 1–1.67 & & 3360 \\ W920 \(\times\) 420 & & 2 & 1 & 1 & & 392 \\ W1000 \(\times\) 314 & & 2 & 1 & 1 & & 392 \\ W1000 \(\times\) 371 & & 2 & 1 & 1 & & 392 \\ W1100 \(\times\) 390 & & 1, 2, 3 & 1–1.471 & 1–1.67 & 235 & 3360 \\ W1100 \(\times\) 343 & & 8 cases from & 2 & 1 & 1 & 315 & 392 \\ BT-1 & 14 cases from & Table 1 & 1, 2, 3 & 1–1.471 & 1–1.67 & 345 & 3360 \\ BT-2 & Table 1 & 2 & 1 & 1 & 450 & 392 \\ BT-3 & & 2 & 1 & 1 & & 392 \\ BT-4 & & 1, 2, 3 & 1–1.471 & 1–1.67 & & 3360 \\ BT-5 & & 2 & 1 & 1 & & 392 \\ BT-6 & & 2 & 1 & 1 & & 392 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of structural response data based on major design parameters.