## 6 Numerical Study and Comparison
### Parametric Analysis and Comparison  
To analyze the pure shear global elastic shear buckling behavior of PCCSW, the corrugation dimensions of CSWs for existing bridges [8], given in Table 3, are used. The ratios of parameters for the current analysis of the global shear buckling are:  
Figure 6: Longitudinal section of a single wavelength PCCSW. * Corrugation height-to-thickness ratio: \(h_{r}/t=8\)-28;
* Web height-to-thickness ratio: \(H/t=136\)-750;
* Ratio of the bending rigidity in the \(y\)-direction to that in the \(x\)-direction: \(D_{y}/D_{x}=139\)-1483;
* Angle of the inclined panel in relation to the tangent line of the longitudinal axis: \(\theta=23.62^{\circ}\)-39.14\({}^{\circ}\);
* Outer folded angle: \(\theta_{1}=23.83^{\circ}\)-39.33\({}^{\circ}\);
* Inner folded angle: \(\theta_{2}=23.48^{\circ}\)-39.02\({}^{\circ}\);  
Radius of curvature: \(R=30\) m-110 m (30 m is the smallest curvature radius of a steel-concrete composite curved bridge [33], which is the most challenging curvature radius for a curved girder bridge with CSWs in the future; 110 m is the minimum curvature radius of the existing curved girder bridge with CSWs, which has already been built in China, namely, Yuwotou Bridge [34] located in Guangzhou, Guangdong). In the range of the above ratios of parameters, considering the relatively high web height of the bridge, the overall buckling is easy to occur. Additionally, local buckling and interactive buckling are not the main points discussed in this paper, so they are omitted in the data analysis. It can clearly be observed from Table 4 and Figure 7 that the critical shear stress of the global elastic shear buckling of PCCSW (e.g., for \(R=110\) m) increases with the increase of panel thickness \(t\) and with the reduction of both the height \(H\) and the height-to-thickness ratio (\(H/t\)). The greater \(H/t\) is, the smaller the absolute difference between the theory and finite element values is. Moreover, theoretical values \(\tau_{cr,T}\) of the 63 sets of data are in good agreement with the corresponding finite element values \(\tau_{cr,F}\) as shown in Table 4 and Figure 8; the mean of the \(\tau_{cr,F}/\tau_{cr,T}\) ratios is 1.00, and the covariance is 0.09, and the max and min values are 1.15 and 0.84, respectively. Thus, the accuracy of the theoretical values is verified. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Bridge** & \(H\) **(mm)** & \(t\) **(mm)** & \(H/t\) & \(h_{r}/t\) & \(\tau_{cr,T}\) **(MPa)** & \(\tau_{cr,F}\) **(MPa)** & \(\tau_{cr,F}\)**(MPa)** \\ \hline \multirow{8}{*}{Shinkai} & 2500 & 10 & 250 & 15 & 1067.81 & 914.28 & 0.86 \\  & 2500 & 12 & 208 & 13 & 1171.43 & 1157.80 & 0.99 \\  & 2500 & 14 & 179 & 11 & 1267.46 & 1416.00 & 1.12 \\  & 2700 & 10 & 270 & 15 & 916.22 & 887.85 & 0.97 \\  & 2700 & 12 & 225 & 13 & 1005.13 & 1126.23 & 1.12 \\  & 3000 & 8 & 375 & 19 & 664.07 & 635.54 & 0.96 \\  & 3000 & 10 & 300 & 15 & 743.34 & 850.87 & 1.14 \\  & 3500 & 6 & 583 & 25 & 423.83 & 410.31 & 0.97 \\ \hline \multirow{8}{*}{Maupre} & 2500 & 14 & 179 & 11 & 1242.19 & 1133.89 & 0.91 \\  & 2500 & 16 & 156 & 9 & 1330.58 & 1349.98 & 1.01 \\ \cline{1-1}  & 2500 & 18 & 139 & 8 & 1414.45 & 1577.02 & 1.11 \\ \cline{1-1}  & 3150 & 8 & 394 & 19 & 590.98 & 504.48 & 0.85 \\ \cline{1-1}  & 3150 & 10 & 315 & 15 & 661.52 & 674.19 & 1.02 \\ \cline{1-1}  & 3500 & 8 & 438 & 19 & 480.16 & 484.50 & 1.01 \\ \cline{1-1}  & 4000 & 6 & 667 & 25 & 320.08 & 315.94 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Global elastic shear buckling strength of PCCSW with varying height and thickness for \(R=110\) m. AVE: average value; COV: covariance.