## 6 Results and Discussion  
The results of all computations are summarized in Table 1. The column labeled LPF shows the maximum obtainable load proportional factor that can be obtained in relation to the result of the LBA, and the last column shows--if applicable--the relation of the obtained resistance factor of the imperfect and geometrical and material nonlinear structure \(R_{GMNIA}\) to the obtained resistance factor of the perfect shell without imperfections \(R_{GMNIA}\). Because it is not known a priori whether the amplitude has to be applied inwards or outwards to be most damaging, all calculations were performed probing both possibilities. In addition, all amplitudes were reduced by 10% as required by EN 1993-1-6 [3]. In order to keep Table 1 readable, only the lowest values of the respective computations are given.  
Three observations can be made regarding the eigenform-affine imperfections. First, the resulting ratios \(R_{GMNIA}/R_{GMNA}\) do not show significant differences (\(\Delta<7\%\)) for all investigated modes; second, the most damaging imperfection pattern of all investigated patterns  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Analysis** & **Imperfection** & **Buckling Mode** & **LPF** & \(R_{GMNIA}/R_{GMNA}\) \\ \hline
1 & LBA & none & - & 1.00 & - \\
2 & MNA & none & - & 1.18 & - \\
3 & GMA & none & - & 0.96 & - \\ \hline
4 & GMNIA & eigenmode & 1 & 0.43 & 0.58 \\
5 & GMNIA & eigenmode & 3 & 0.44 & 0.60 \\
6 & GMNIA & eigenmode & 5 & 0.45 & 0.58 \\
7 & GMNIA & eigenmode & 7 & 0.45 & 0.61 \\
8 & GMNIA & eigenmode & 20 & 0.45 & 0.60 \\
9 & GMNIA & eigenmode & 22 & 0.45 & 0.60 \\
10 & GMNIA & eigenmode & 186 & 0.46 & 0.61 \\ \hline
11 & GMNIA & collapse-affine & - & 0.58 & 0.78 \\ \hline
12 & GMNIA & quasi-collapse-affine & - & 0.48 & 0.65 \\ \hline
13 & GMNIA & post-buckling & - & 0.48 & 0.64 \\ \hline
14 & GMNIA & weld depression & pattern 2.1 & 0.46 & 0.62 \\ \hline
15 & GMNIA & weld depression & pattern 2.2 & 0.73 & 0.98 \\ \hline
16 & GMNIA & combined pattern & - & 0.47 & 0.64 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Load bearing capacity.  
Figure 14: Updated geometry due to imperfections on the panel and on the beam webs.  
seems to be eigenmode one or five; and third, the direction (not shown in Table 1) of the applied eigenform-affine imperfection has an insignificant influence on the resulting resistance values.  
Only the run with the collapse-affine imperfections stands out when comparing all results. When the mesh is perturbed according to the deformation state at the collapse in a GMNA, the damaging effect is relatively small compared with all other imperfections. As discussed earlier, the scaling of the whole imperfection results in a (globally) small deformation of the whole structure, which appears to be less damaging. If a quasi-collapse-affine imperfection pattern is derived from this deformation's state (Figure 12), the result are very similar to the ones obtained by introducing a post-buckling eigenshape obtained from a GMNA as an imperfection.  
In [36], as a sanity check, the authors propose to check the relation \(R_{GMNIA}/R_{MNA}\) against the dimensionless buckling knockdown factor \(\chi\) from the axial compression or bending capacity curves in prEN 1993-1-6 [29]. In the present work, this sanity check is performed against the curves in EN 1993-1-6 [3], as this version was used in the calculations. Therefore, the dimensionless slenderness \(\lambda\) was estimated to be \((R_{MNA}/R_{LBA})^{0.5}\), giving a value of \(\lambda_{check}\)= 1.087. This value was then inserted into the capacity curves in Annex D [3] for the cylinder in bending, which yielded a knockdown factor of \(\chi_{check}\) = 0.33 for a portion of the main girder spanning from bulkhead to bulkhead. This reference value was then compared with \(R_{GMNIA\_lowest}\)\(/\)\(R_{MNA}\) = 0.36, which appears to be sufficient.