## 4 Construction of the Index System and the Determination of Factors and Levels  
The irregularly-shaped bridge is a continuous structure with three spans. The top plate of the bifurcation diaphragm is under the effect of the hogging moment and tensile stress, which can easily result in cracking and breaking of the concrete in the top plate. Moreover, the bifurcation diaphragm is located at the croft of main bridge and ramp. It is affected by the coupling effect of constraints, torsion, and shear lag, which makes the distribution of tensile stress seriously uneven. Research on the maximum stress and uneven stress distribution in the top plate of the bifurcation diaphragm is essential to improve the design security of irregularly-shaped bridges. Meanwhile, the torsion vibration  
Figure 4: Plan view of a typical irregularly-shaped bridge. Figure 5: Finite element model of a typical irregularly-shaped bridge. fundamental frequency of the irregularly-shaped bridge should be greater than the external excitation frequency to avoid torsional resonance and improve its dynamic characteristics [5]. The middle section of the bifurcation diaphragm is selected and the nodes in the middle layer of the top plate are adopted as study objects, which are shown in Figure 6a. Taking into account the static and dynamic characteristics, the maximum stress (\(\sigma_{\text{max}}\)), the stress variation coefficient (\(\lambda\)) of selected nodes under a dead load condition, and the torsion vibration fundamental frequency (\(f_{d}\)) of the bridge are regarded as the indices to reflect the parameter influences on the mechanical properties. Hierarchical structure and index weights are listed in Table 4. The stress variation coefficient (\(\lambda\)) is the ratio of the maximum normal stress (\(\sigma_{\text{max}}\)) to the minimum normal stress (\(\sigma_{\text{min}}\)), which can be calculated by Equation (12). The calculation results are shown in Figure 6b. \[\lambda=\sigma_{\text{max}}/\sigma_{\text{min}} \tag{12}\]  
Based on the relative importance of maximum stress, the stress variation coefficient, and the torsion vibration fundamental frequency to the mechanical properties of the irregularly-shaped bridge, the comparative judgment matrix is established as follows:  
\[A=\left[ \begin{array}{ccc}1&1&1/2\\ 1&1&1/2\\ 2&2&1\end{array} \right] \tag{13}\]  
The eigenvector for matrix \(A\) can be calculated according to Equation (1), and is shown as follows:  
\[W=\left[ \begin{array}{ccc}1/4&1/4&1/2\end{array} \right]^{T} \tag{14}\]  
The consistency ratio \(CR\) is calculated by Equation (4). If \(CR<0.001\), then the extent of inconsistency for comparison judgment matrix is permitted. The orthogonal test is carried out for every index to investigate the influence of parameters. In practice, the span is an important factor affecting the strained condition of the bridge structure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Target Layer** & \multicolumn{3}{c}{**Mechanical Property of the Irregularly-Shaped Bridge**} \\ \hline Index layer & \(\sigma_{\text{max}}\) & \(\lambda\) & \(f_{d}\) \\ Weight & 0.25 & 0.25 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hierarchical structure and index weights. Figure 6: Node selection and normal stress distribution in the top plate of the bifurcation diaphragm. (**a**) Node selected in the top plate; and (**b**) the normal stress distribution of selected nodes. However, it is restricted by topographical conditions. Therefore, the influence of other parameters on mechanical properties is demonstrated for the irregularly-shaped bridge with a certain span. In this paper, ramp radius, bifurcation diaphragm stiffness, box girder height, and supporting condition, which can strongly affect the mechanical properties of an irregularly-shaped bridge, are selected as the influence factors for mechanical properties in the irregularly-shaped bridge design [3]. The change of the bifurcation diaphragm stiffness is simulated by thickness variation.