## 5 Sensitivity Analysis and Design Optimization of Parameters
### Result Analysis for a Single Index  
#### 5.1.1 Influence of Parameters on Maximum Stress  
The influence of changing parameters on maximum stress is illustrated in Figure 7. As can be seen from Figure 7, the maximum stresses decrease with the increase of box girder height and bifurcation diaphragm thickness, while the influences of the ramp radius and supporting condition are negligible. The growth of the box girder height increases the flexural rigidity to make the vertical bending stress smaller. Vertical bending stress plays the most important role in the normal stress of the top plate, which results in the decrease of the maximum stress. With the bifurcation diaphragm thickness increasing, the torsional stiffness of the bridge increases to resist the torsion and distortion, which decreases the maximum stress. According to range \(R\), it can be found that the influence degree of factors on the maximum stress is: box girder height > bifurcation diaphragm stiffness > ramp radius > supporting condition. The box girder height and bifurcation diaphragm stiffness are the major influencing factors for maximum stress. In the design of an irregularly-shaped bridge, the smaller maximum stress is conducive to bridge security. As can been seen from Table 7, the minimum value of the maximum stress index can be obtained when the box girder height is 2 m and the bifurcation  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test No.**} & \multicolumn{4}{c}{**Factor**} & \multicolumn{4}{c}{**Test index**} \\ \cline{2-7}  & **R (m)** & **\(D\) (m)** & **\(H\) (m)** & **\(U\)** & \(\sigma_{\text{max}}\) (MPa)** & \(\lambda\) & \(f_{d}\) (Hz) \\ \hline
1 & 30 & 1.2 & 1.6 & 1 & 2.95 & 1.76 & 7.7341 \\
2 & 30 & 1.6 & 1.8 & 2 & 2.36 & 1.66 & 7.8733 \\
3 & 30 & 2.0 & 2.0 & 3 & 1.99 & 1.57 & 5.2013 \\
4 & 40 & 1.2 & 1.8 & 3 & 2.66 & 1.85 & 5.0639 \\
5 & 40 & 1.6 & 2.0 & 1 & 2.14 & 1.78 & 8.3185 \\
6 & 40 & 2.0 & 1.6 & 2 & 2.64 & 1.47 & 8.2158 \\
7 & 50 & 1.2 & 2.0 & 2 & 2.35 & 1.90 & 8.3485 \\
8 & 50 & 1.6 & 1.6 & 3 & 2.70 & 1.61 & 5.0858 \\
9 & 50 & 2.0 & 1.8 & 1 & 2.24 & 1.51 & 8.4667 \\ \hline \hline \end{tabular}
\end{table}
Table 7: \(L_{9}(3^{4})\) orthogonal array testing for three indices.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Test Index**} & \multirow{2}{*}{**Item**} & \multicolumn{4}{c}{**Factor**} \\ \cline{3-5}  & & **R (m)** & **\(D\) (m)** & **\(H\) (m)** & **\(U\)** \\ \hline \multirow{4}{*}{Maximum stress} & \(k_{1}\) & 2.43 & 2.65 & 2.76 & 2.44 \\  & \(k_{2}\) & 2.48 & 2.40 & 2.42 & 2.45 \\  & \(k_{3}\) & 2.43 & 2.29 & 2.16 & 2.45 \\  & \(R\) & 0.05 & 0.36 & 0.60 & 0.01 \\ \hline \multirow{4}{*}{Stress variation coefficient} & \(k_{1}\) & 1.66 & 1.84 & 1.61 & 1.68 \\  & \(k_{2}\) & 1.70 & 1.68 & 1.67 & 1.67 \\  & \(k_{3}\) & 1.67 & 1.52 & 1.75 & 1.68 \\  & \(R\) & 0.04 & 0.32 & 0.14 & 0.01 \\ \hline \multirow{4}{*}{Torsion vibration fundamental frequency} & \(k_{1}\) & 6.9362 & 7.0488 & 7.0119 & 8.1731 \\  & \(k_{2}\) & 7.1994 & 7.0925 & 7.1346 & 8.1459 \\ \cline{1-1}  & \(k_{3}\) & 7.3003 & 7.2946 & 7.2894 & 5.1170 \\ \cline{1-1}  & \(R\) & 0.3641 & 0.2458 & 0.2775 & 3.0561 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Analysis of orthogonal test results.  
diaphrag thickness is 2 m. For the maximum stress index, the ramp radius and the supporting condition can adopt reasonable values due to their negligible influence.