## 6 Numerical Study and Comparison
### Parametric Analysis and Comparison
Hence, changing the width of the inclined folds become greater than that of the longitudinal folds. This result illustrates that for global shear buckling of PCCSW with constant curvature radius and height, the denser the corrugation is, the larger the buckling strength is. It is worth pointing out that these conclusions remain accurate with different corrugation dimensions as the results of the other bridge conditions are qualitatively similar to those of Cognac Bridge. Figure 8: Finite element value \(\tau_{cr,F}\) versus theoretical value \(\tau_{cr,T}\) of global elastic shear buckling strength. AVE: average value; COV: covariance. Figure 7: Global elastic shear buckling strength \(\tau_{cr}\) versus web height-to-thickness ratio \(H/t\) (\(R\) = 110 m). As seen from Figures 10-12 and Tables 5 and 6, when the radius of curvature is constant at \(R\) = 110 m, it can be concluded that the global shear buckling stress of the PCCSW increases with the increase of the corrugation height \(h_{r}\). Additionally, the larger the web height-to-thickness ratio \(H/t\) is, the slower the growth trend is. Different angles, such as the outer corrugation angle \(\theta_{1}\), the intersection angle \(\theta\) of the central axis and the inner corrugation angle \(\theta_{2}\) of the PCCSW, also increase with the increase of the corrugation height \(h_{r}\). Note that the outer corrugation angle \(\theta_{1}\) is greater than the inner corrugation angle \(\theta_{2}\); that is, these angles satisfy the inequality \(\theta_{1}>\theta>\theta_{2}\), and the sum of \(\theta_{1}\) and \(\theta_{2}\) is slightly larger than two times \(\theta\). It can also be observed that the global shear buckling stress of the PCCSW increases with the increase of the inner and outer corrugation angles and it shows a steady increasing trend. It can also be confirmed that the critical finite element values of the global elastic shear buckling are well matched with the theoretical results, as can be noticed from Table 5.  
Figure 10: Global elastic shear buckling strength of PCCSW in theory \(\tau_{c,T}\) versus corrugation height \(h_{r}\) (\(R=110\) m). Figure 9: Global elastic shear buckling strength in theory \(\tau_{c,T}\) versus the ratios \(a/H\) and \(c/H\) (\(R=110\) m, \(H=4032\) mm). Figure 11: Different angles \(\theta_{1}\), \(\theta\) and \(\theta_{2}\) versus corrugation height \(h_{r}\) (\(R\) = 110 m). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Bridge** & \(h_{r}\) (mm) & \(H\) (mm) & \(t\) (mm) & \(\tau_{\sigma,T}\) (MPa) & \(\tau_{\sigma,F}\) (MPa) & \(\tau_{\sigma,F}\)/\(\tau_{\sigma,T}\) \\ \hline \multirow{4}{*}{Shinkai} & 130 & 2700 & 10 & 728.09 & 838.52 & 1.15 \\  & 140 & 2700 & 10 & 819.67 & 862.85 & 1.05 \\  & 150 & 2700 & 10 & 916.22 & 887.85 & 0.97 \\  & 160 & 2700 & 10 & 1017.79 & 902.33 & 0.89 \\ \hline \multirow{4}{*}{Maupre} & 140 & 3150 & 10 & 593.26 & 654.63 & 1.10 \\  & 150 & 3150 & 10 & 661.52 & 674.19 & 1.02 \\ \cline{1-1}  & 160 & 3150 & 10 & 733.11 & 691.87 & 0.94 \\ \cline{1-1}  & 170 & 3150 & 10 & 808.05 & 707.62 & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Global elastic shear buckling strength of PCCSW with varying corrugation height for \(R\) = 110 m.  
Figure 12: Global elastic shear buckling strength of PCCSW in theory \(\tau_{\sigma,T}\) versus different angles \(\theta_{1}\), \(\theta\) and \(\theta_{2}\) (\(R\) = 110 m).