# Shear Strength of Trapezoidal Corrugated Steel Webs for Horizontally Curved Girder Bridges
## 2 Elastic Global and Local Shear Buckling Stress of CSWs
### Elastic Global Shear Buckling Stress of CSWs
#### 2.2.2 Calculation of Coefficient \(k_{g}\)
In addition, the conclusion remains unchanged when changing the values of \(h^{2}/(Rd)\), \(\gamma\), and the boundary conditions. As a result, \(\beta=1.8\alpha\) is used further in this paper. Figure 3 shows the effect of the rigidity ratio \(D_{x}/D_{y}\) and the length to height ratio \(l/h\) on the global shear buckling coefficient \(k_{g,s}\) for a four-edge simple support. As we can see from Figure 3, the global shear buckling coefficient \(k_{g,s}\) increases with the increase of the rigidity ratio \(D_{x}/D_{y}\) and decreases with the increase of the length to height ratio \(l/h\) but only very little. When \(l/h\) is larger than \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(D_{\text{x}}/D_{y}\)} & \multicolumn{6}{c}{_l/h_} \\ \cline{2-7}  & & **1** & **2** & **3** & **4** & **5** \\ \hline \multirow{3}{*}{0.0005} & \(\beta=1.6\alpha\) & 5.0169 & 4.9471 & 4.9335 & 4.9292 & 4.9252 \\  & \(\beta=1.8\alpha\) & 5.0245 & 4.9547 & 4.9410 & 4.9367 & 4.9327 \\  & \(\beta=2.0\alpha\) & 5.0321 & 4.9623 & 4.9486 & 4.9442 & 4.9402 \\ \hline \multirow{3}{*}{0.0015} & \(\beta=1.6\alpha\) & 6.7307 & 6.5947 & 6.5643 & 6.5525 & 6.5470 \\  & \(\beta=1.8\alpha\) & 6.7489 & 6.6121 & 6.5816 & 6.5697 & 6.5642 \\  & \(\beta=2.0\alpha\) & 6.7671 & 6.6295 & 6.5989 & 6.5868 & 6.5813 \\ \hline \multirow{3}{*}{0.0025} & \(\beta=1.6\alpha\) & 7.7454 & 7.5645 & 7.5126 & 7.4963 & 7.4888 \\  & \(\beta=1.8\alpha\) & 7.7714 & 7.5901 & 7.5379 & 7.5214 & 7.5139 \\  & \(\beta=2.0\alpha\) & 7.7973 & 7.6151 & 7.5631 & 7.5465 & 7.5390 \\ \hline \multirow{3}{*}{0.0035} & \(\beta=1.6\alpha\) & 8.5136 & 8.2755 & 8.2214 & 8.2008 & 8.1909 \\  & \(\beta=1.8\alpha\) & 8.5485 & 8.3084 & 8.2539 & 8.2332 & 8.2232 \\  & \(\beta=2.0\alpha\) & 8.5834 & 8.3413 & 8.2865 & 8.2656 & 8.2555 \\ \hline \multirow{3}{*}{0.0050} & \(\beta=1.6\alpha\) & 9.5393 & 9.1230 & 9.0567 & 9.0301 & 9.0159 \\  & \(\beta=1.8\alpha\) & 9.5816 & 9.1656 & 9.0993 & 9.0721 & 9.0580 \\  & \(\beta=2.0\alpha\) & 9.6239 & 9.2081 & 9.1418 & 9.1141 & 9.1001 \\ \hline \multirow{3}{*}{0.0070} & \(\beta=1.6\alpha\) & 10.4099 & 10.0444 & 9.9332 & 9.8997 & 9.8847 \\  & \(\beta=1.8\alpha\) & 10.4672 & 10.1004 & 9.9878 & 9.9537 & 9.9386 \\ \cline{1-1}  & \(\beta=2.0\alpha\) & 10.5245 & 10.1557 & 10.0424 & 10.0077 & 9.9924 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The effect of \(\beta/\alpha\) on the global shear buckling coefficient \(k_{g,s}\) when \(h^{2}/(Rd)=5\) and \(\gamma=0.4\) for the four-edge simple support. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(h^{2}\)/(\(Rd\))} & \multicolumn{10}{c}{\(D_{\text{s}}\)/\(D_{\text{y}}\)} \\ \cline{2-13}  & **0.0005** & **0.001** & **0.0015** & **0.002** & **0.0025** & **0.003** & **0.0035** & **0.004** & **0.0045** & **0.005** & **0.006** & **0.007** \\ \hline
0 & 9.3514 & 11.1640 & 12.4009 & 13.3583 & 14.1615 & 14.8549 & 15.4721 & 16.0277 & 16.5369 & 17.0056 & 17.8537 & 18.6069 \\
5 & 9.3516 & 11.1643 & 12.4014 & 13.3590 & 14.1624 & 14.8561 & 15.4736 & 16.0295 & 16.5389 & 17.0079 & 17.8566 & 18.6104 \\
10 & 9.3520 & 11.1653 & 12.4030 & 13.3613 & 14.1654 & 14.8598 & 15.4781 & 16.0347 & 16.5450 & 17.0149 & 17.8655 & 18.6209 \\
15 & 9.3526 & 11.1668 & 12.4057 & 13.3650 & 14.1703 & 14.8659 & 15.4855 & 16.0434 & 16.5551 & 17.0265 & 17.8799 & 18.6384 \\
20 & 9.3536 & 11.1690 & 12.4095 & 13.3703 & 14.1772 & 12.8474 & 15.4959 & 16.0555 & 16.5693 & 17.0427 & 17.9001 & 18.6628 \\
25 & 9.3547 & 11.1718 & 12.4143 & 13.3770 & 14.1860 & 14.8854 & 15.5093 & 16.0710 & 16.5874 & 17.0635 & 17.9261 & 18.6938 \\
30 & 9.3562 & 11.1753 & 12.4202 & 13.3852 & 14.1968 & 14.8978 & 15.5255 & 16.0900 & 16.6095 & 17.0887 & 17.9575 & 18.7314 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Global shear buckling coefficient \(k_{g,fs}\) for various values of \(h^{2}\)/(\(Rd\)) and \(D_{\text{s}}\)/\(D_{\text{y}}\) when \(|\)/\(t\) = 5, \(\gamma\) = 0.4 and \(\beta\) = 1.8\(\alpha\) for the two edges constrained by flanges fixed and the other two edges simply supported.