# FPSO Hull Structures with Sandwich Plate System in Cargo Tanks
## 6 Ultimate Strength Analysis
### Ultimate Loads  
A ship's hull in intact condition sustains the applied loads smaller than the design values. In normal seagoing and cargo loading conditions, it will not suffer any structural damages (e.g., buckling and collapse). However, the loads are uncertain due to the nature of rough seas, as well as human errors leading to unusual loading/unloading of cargo [23]. Therefore, the ultimate hull girder strength needs to be accurately evaluated when taking into consideration the structural safety of the hull. However, closed-form methods, especially from classification societies, tend to underestimate the real ultimate bending capacity of structures in order to achieve a safety design [22]. Thus, the FEA is a powerful tool to estimate the ultimate BM of the hull. \begin{table}
\begin{tabular}{c c} \hline \hline
**Structure** & **Condition: Sagging** \\ \hline Steel & 154 \\ Composite & 130 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Static displacement. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Comparison** & \multicolumn{3}{c}{**Steel**} & \multicolumn{3}{c}{**SPS**} \\ \hline
**Parameter** & **FEM** & **Reference** & **Parameter** & **FEM** & **Reference** & **Parameter** \\ \hline Neutral Axis [m] & 15.64 & 15.47 & Neutral Axis [m] & 15.64 & 15.47 & Neutral Axis [m] \\ \hline \(\sigma\) bottom [MPa] & 210 & 208 & \(\sigma\) bottom [MPa] & 210 & 208 & \(\sigma\) bottom [MPa] \\ \hline \(\sigma\) deck [MPa] & \(-\)220 & \(-\)226 & \(\sigma\) deck [MPa] & \(-\)220 & \(-\)226 & \(\sigma\) deck [MPa] \\ \hline Spring Reaction & 0.2\% & 0.3\% & Spring Reaction & 0.2\% & 0.3\% & Spring Reaction \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of the static load case for both arrangements. Moreover, the ultimate strength load is obtained by increasing the load from the static load gradually until the structure reaches either a stress value near 665 MPa, which is the maximum stress from the true stress--true strain curve of DH36 steel--or there is a collapse due to classical plate buckling. This is because the applied loads are beyond their design values, structural members buckle in compression and yield in tension. The hull girder can normally carry further loading beyond the onset of limited buckling / yielding, but the structural effectiveness clearly decreases, and the individual stiffness can even become \"negative\" [23]. It is important to notice that this is a simplistic simulation once it used the model of the equivalent plate and not the stiffened panels. This could change the buckling behavior of the plates. The FEA showed that the steel structure and the structure with SPS could withstand 1.94 and 2.45 times the static load, which is a 26% increase. This can be explained by the moment of inertia, which is inversely proportional to the normal stress. Therefore, the bigger the inertia, the bigger the bending moment required to reach a specific value. Furthermore, since the SPS structure has a bigger one than the steel structure (almost 10% bigger), this structure can reach higher values of bending moments. Table 12 summarizes this information. Moreover, the moment-curvature graphic was also plotted to compare the ultimate bending capacity between the classification society rules (ABS/DNV) with the finite element results (see Figure 10). This graph shows the ULS for both types of arrangements and the location each plate starts to buckle as well. As it can be observed, the ULS for the steel and SPS according to the FEA are 11% and 24% higher, respectively, than the ones proposed by the classification society rules, which are more conservative about the estimation. Comparing the values obtained with the same comparison made in [23], they \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure** & **Static Bending Moment [kNm]** & **Multiplier** & **Ultimate Bending Moment [kNm]** \\ \hline Steel & \(-\)29,453,568 & 1.94 & \(-\)57,139,922 \\ \hline Composite & & 2.45 & \(-\)72,161,242 \\ \hline \hline \end{tabular}
\end{table}