## 4 Analysis of Korea Container Crane
### Sensitivity Analysis for Container Crane  
The lower and upper bounds corresponding to 10 th and 90 th percentile values are calculated by the mean of the assumed normal distribution using the following equation [31]:  
\[X=\mu+Z\cdot\sigma, \tag{5}\]  
where \(\mu\) and \(\sigma\) are the mean and standard deviation of the variable \(X\) and \(Z\) is the value of the standard normal distribution for the desired percentile (i.e., \(Z\) is equal to \(-1.282\) and \(1.282\) for 10 th and 90 th percentile, respectively). All the input parameters are listed in Table 5. Notably, that the scaling factor (\(\alpha_{i}\)) in Table 5 is the ratio of the target acceleration spectrum (i.e., \(S_{a\ target}\) = 0.07 g, 0.13 g, and 0.21 g) to an i\({}^{\text{th}}\) acceleration spectrum, \(\alpha_{i}=S_{a\ target}/S_{ai}\).  
The swing analysis through \"tornado diagrams\" is shown in Figure 7. For the portal drift of the crane, the largest swing is associated with the ground motion intensity, which is approximately 0.4%. The second notable sensitivity is from the characteristics of the ground motion profile. The portal drift was from 0.32% to 0.42% (or a swing of around 0.1%). Of the structural properties, the damping, elastic modulus, and mass all have a low impact, with swing values of 0.043%, 0.035%, and 0.032%, respectively. The IM level plays a significant impact on the displacement of the structure in terms of portal drift. Under an IM level (S\({}_{\text{a}}\)) ranging from 0.07 g to 0.21 g, the drift at the top of the portal frame fluctuates from 0.22% to 0.62%.  
While the ground motion intensity is the most sensitive in terms of portal drift, mass has the highest effect on the vertical reaction of the crane legs. The oscillation of the vertical reaction along the seaside legs of the crane (for example, node 40 of the FE model, as shown in Figure 7b) is between 4628 to 5762 kN, corresponding to a swing of approximately 1134 kN. In contrast, the damping showed the lowest sensitivity, with a swing of roughly 13.5 kN, occupying around 1.2% compared to the effect of mass. The IM level also shows a remarkable effect on the increase of the axial reaction of the crane's legs compared to the ground motion profile and elastic modulus. The swing of ground motion intensity was around three times that of the ground motion profile and over four times that of the elastic modulus.  
Figure 7c describes the sensitivity analysis of the total base shear. Differently from Figure 7a,b, all the input parameters have their own contributions on the total base shear. The spectral acceleration parameter remains the highest with a swing of around 1120 kN compared to those of the mass, damping, ground motion profile, and elastic modulus of around 567, 383, 269, and 107 kN, respectively. The interesting point is from the effect of the damping ratio, it affects significantly on the total base shear, slightly on the drift, while it had almost no impact on the vertical reaction of the crane's legs.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Source of Uncertainty** & **Lower Bound** & **Median** & **Upper Bound** & **Remarks** \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{IM, Sa (g)} & 0.07 & 0.13 & 0.21 & Spectral \\  & & GM-17, 19 & GM-9, 11 & GM-9, 11 & \multirow{3}{*}{Ground motion} \\  & & 0.081, 0.092 & 0.552, 0.188 & 0.917, 0.313 & Scaling factor \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{Ground motion profile} & GM-16 & GM-9 & GM-14 & Ground motion \\  & & 0.111 & 0.552 & 0.178 & Scaling factor \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{Mass, M\({}_{\text{n}}\) (ton)} & \multirow{3}{*}{\(0.872\times\) M\({}_{\text{n}}\)} & \multirow{3}{*}{M\({}_{\text{n}}\)} & \multirow{3}{*}{\(1.128\times\) M\({}_{\text{n}}\)} & M\({}_{\text{n}}\): nominal \\  & & & & & mass = 1 \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{Damping ratio, \(\xi\) (\%)} & 0.92 & 1.50 & 2.08 & \multirow{3}{*}{} \\  & & 184.6 & 200 & 215.4 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters of the sensitivity study.