# FPSO Hull Structures with Sandwich Plate System in Cargo Tanks
## 4 Traditional Steel Structure Scantling
### Strength Criteria  
In any project, one of the crucial objectives is to design a product with the lowest cost as possible in order to make a profit. In the shipbuilding industry, this can be achieved by building a ship or a platform without over-dimensioning the whole structure. In this study, the optimal design is the one with the lightest structure that satisfies all the strength criteria (buckling, yield and ultimate strength [14]) imposed for both load conditions (static and dynamic) simultaneously. However, this is not a simple task. For example, in this primary section, there are 37 plates whose thickness can vary between the minimum value imposed by the rule and a maximum value, which is considered 32 mm. In this aspect alone, finding an optimal solution is complicated. In addition, each individual plate interferes directly with the strength criteria from the other plates, because they can modify the neutral axis height and the moment of inertia and, therefore, the normal and shear stress in the structure.  
Thus, the optimization problem used to obtain a feasible solution is described below.
* Objective Function \(\bigcirc\) & Minimize (total weight)
* Variables \(\bigcirc\) & Thickness from longitudinal plates
* Constraints \(\bigcirc\) & Strength criteria \(\bigcirc\) & Maximum thickness of 32 mm
* Minimum moment of inertia and section modulus
* Load Cases \(\bigcirc\) & Static: still water condition \(\bigcirc\) & Dynamic: still water + wave load conditions  
The results from the solver can be seen in Figure 5. The solution found complies with most of the strength criteria. The exception is the deck plates for the static load case, which are 3-5% higher than the allowed value (the maximum allowed is 355 \(\times\) 0.6 = 213 MPa). Despite this, the solution is feasible for two reasons. First, the condition in which this exceedance of the onboard safety factor takes place is not the worst of all. This helps as a reference for dimensioning, but the important thing is that the plates are able to withstand loads of the worst condition without exceeding the yield stress, which in fact happens. The second reason is that the vast majority of plates meet the buckling and yield requirements for the calm water condition and all of them are within the stipulated limits for the buckling, yield and ultimate strength criteria for the worst condition in which a large amount of calm waters plus waves exist.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **Plate Number** & **Gross Thickness [mm]** & **Structure** & **Plate Number** & **Gross Thickness [mm]** \\ \hline \multirow{4}{*}{Bottom} & Keel & 24 & & 22 S & 16 \\  & Cargo Area & 23 & Side Longitudinal & 23 S & 16 \\  & Ballast Tank & 22 & Bulkhead & 24 S & 16 \\ \hline \multirow{8}{*}{Side} & 5 & 19 & & 25 S & 16 \\  & 6 & 18 & & 5 H & 18 \\  & 7 & 18 & & 6 H & 18 \\  & 8 & 18 & & 7 H & 18 \\  & 9 & 18 & & 8 H & 18 \\  & 10 & 18 & & 9 H & 18 \\  & 11 & 18 & & 10 H & 18 \\  & 12 & 18 & & 17 T & 20 \\  & 13 & 19 & & 18 T & 19 \\ \hline \multirow{2}{*}{Deck} & 15 & 22 & & 19 T & 19 \\  & 16 & 23 & & 20 T & 18 \\ \hline \multirow{8}{*}{Longitudinal} & 17 & 20 & & 21 T & 17 \\  & 18 & 18 & & 22 T & 17 \\  & 19 & 17 & & 23 T & 17 \\  & 20 & 17 & & 24 T & 17 \\  & 21 & 17 & & 25 T & 17 \\ \cline{1-1}  & 22 & 17 & Web Frame Bottom & 1 & 23 \\ \cline{1-1} \cline{3-4}  & 23 & 17 & & 2 & 20 \\  & 24 & 17 & & 3 & 18 \\  & 25 & 16 & & 4 & 17 \\ \hline \multirow{4}{*}{Side Longitudinal} & 17 S & 22 & Web Frame Side & 5 & 16 \\  & 18 S & 19 & & 6 & 16 \\ \cline{1-1}  & 19 S & 17 & & 7 & 16 \\ \cline{1-1}  & 20 S & 16 & & 8 & 16 \\ \cline{1-1}  & 21 S & 16 & Web Frame Deck & 9 & 17 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Gross thickness obtained after the design based on the FPI guidelines [14].  
Moreover, most the of values range from 0.4 to 0.5 and 0.75 to 0.85 of the yield stress for the static and dynamic load cases, respectively. This indicates that the achieved solution is good because the structure is not over-dimensioned.