This is the question to ask now that the Napoli’s failure mechanism has been identified. We should therefore focus on the critical area where the accident occurred on the Napoli.
What we are looking for are ships with a similar arrangement in the transition from hold to engine room. It is customary to arrange the engine room with transverse stiffeners to support the shell plating. This is to ensure sufficient stiffness and support for the engines and ER equipment. In smaller container ships, the superstructure is normally right at the aft end of the ship. As the ships get bigger, the superstructure is moved forward, allowing more space for the engines and equipment. However, the hull girder bending moment increases towards the midship area. We need therefore to verify that this area has been properly taken into consideration when the ship was built.
Our initial criterion for selecting critical ships was thus to select ships with a container hold aft of the superstructure, i.e. ships of around 2500 TEU and bigger.
These ships were then subjected to technical screening, which is divided into two steps as shown in the illustration. In the first step, the “basic strength check”, the hull girder capacity is determined together with a buckling check of plating and stiffeners in the critical area, i.e. the forward engine room area where the longitudinal stiffening forward ends and the transverse stiffening in the ER begins.
STEP 1: Basic Strength Check
The hull girder cross section at this location is determined according to IACS Unified Requirement UR-S11 (which is the same for all IACS class societies). The DNV tool is the “Nauticus Section Scantlings” which calculates the cross-sectional properties of the hull girder. The required hull girder section modulus is established according to the same UR-S11. The design still water bending moment is taken from the approved trim and stability booklet. The “wave bending moment” (also according to UR-S11) and the “still water bending moment” provide the “total bending moment”. Combining this with the “allowable stress level” gives us the required “minimum section modulus”. The “as built section modulus” should have a higher value than this minimum value.
The buckling capacities of the plating and stiffeners of the double bottom and lower side shell are determined using a similar way of reasoning. Container ships are hogging ships, which means that the bottom and lower parts of the sides are always in compression and therefore prone to plate and stiffener buckling.
Critical buckling stress (the stress where the plate or stiffener collapses) is determined according to a Unified Requirement procedure (UR-S11). Usage factors are the actual stress divided by the critical buckling stress. A total of three local usage factors for plate buckling are determined in step 1, one for the shell plate in the double bottom, one for the inner bottom and one for the bilges. The following criteria are then used to evaluate whether step 2 is activated:
■ all three usage factors (σl/σc) are less than 1.0, no further action is necessary
■ the average usage factor is less than 0.90 , one usage factor is slightly above 1.0, no further action is necessary
■ two usage factors are greater than 1 or one single usage factor is much greater than 1, proceed to STEP 2
STEP 2: Ultimate Limit State
Buckling Check
If for instance there is a typical bottom structure with a plate field buckle and loose capacity, are the stiffeners able to withstand the loads without the plate support? If yes, then the structure still has redundant buckling capacity. In the ultimate state analysis, the various structural members making up the total buckling resistance are studied to determine the effectiveness of the various parts. This is similar to the effective breadth concept introduced by von Karman, but used on a global scale.
The PULSE code is a modern algorithm that calculates the ultimate state non-linear bi-axial buckling strength of typical plate and stiffener panels as pictured below. On the left, a longitudinal stiffened panel and on the right a transversely stiffened panel.
The local buckling capacities from the PULSE ultimate state analyses are then fed into Section Scantlings to determine the global “effective hull girder section modulus”. The “ultimate moment capacity” is then determined by multiplying the “effective section modulus” by the yield strength of the material in the plating. The ultimate hull girder capacity is determined by dividing the “actual design moments” by the “ultimate moment capacity”. This value must not exceed a limit, set at 0.9. If it does, corrective action is to be considered.
1)The effective hull girder section modulus Zeff is calculated using DNV Nauticus Section Scantlings, with effective local scantlings based on non-linear PULS buckling calculations.
2)The hull girder ultimate moment capacity Mu is calculated as the effective hull girder section modulus multiplied by the yieldstrength of the bottom plate Sigf:
Mu = Zeff * Sigf
3)The ultimate hull girder capacity in bending at the transition between the engine room and cargo area is found by comparing the actual design moments* to the ultimate moment capacity:
η= M/Mu
Where M = Ms + Mw
Ms= still water bending moments (sea condition, hogging) according to loading manual
Mw =standard rule wave at cross section considered, hogging condition
The capacity η should be 0.9 or lower in order for “no further action to be considered”.
