Tuesday, 1 September 2009
Sunday, 4 January 2009
In 2000, the Re-opened Formal Investigation (RFI) into the loss of the Derbyshire concluded that that the Tees built bulk carrier had been lost, during typhoon Orchid, as a result of significant hold flooding following the structural failure of the vessel’s main cargo hold hatch covers due to heavy seas.
The Court also concluded that although the vessel’s main cargo-hold hatch covers had been designed to meet the international strength standards applicable at the time she was built, those strength standards were severely deficient, and it was this regulatory deficiency that was crucial to the vessel’s loss.
Extracts from sections 7 and 16 in the final report of the RFI:
"7.16 At the time of the DERBYSHIRE’s last voyage her
hatch covers complied with the minimum strength requirements of ILLC 66 and of the Lloyd’s Register of Shipping Rules.
16.7 In so far as material to the loss of the “DERBYSHIRE” was the design of the hatch covers of the “DERBYSHIRE” in accordance with the standards applicable at the time she was built?
16.8 Is that design satisfactory in the light of what is now known?
- No: seriously deficient. The design strength was inadequate to withstand the green water loads likely to be sustained during extreme sea conditions, which a vessel might encounter during her service life."
The outcome of the RFI was, thus, able to deflect any suspicion of blame away from the vessel’s builders and the Classification Society, both of whom could have been subjected to hostile litigation, had the design or construction of the hatch covers been found to fall short of the required norms.
However, independent calculations show that the court’s conclusion, that the Derbyshire complied with the standards applicable at the time she was built, is not wholly correct. The results of these calculations are summarised in the pages that follow below.
Hatch Covers - applicable standards
It is unfortunate that the Derbyshire was not constructed to meet the version of Lloyd’s Rules that was in force prior to the introduction of their 1968 Rule amendments, as that earlier version (first introduced in 1963 and valid until 1967) contained more stringent requirements for ore carrying deep draught vessels such as the Derbyshire.
What is more unfortunate, however, is that, as our calculations show, she didn’t comply with the standards that were introduced later (i.e. at the time of her build). This latter non-compliance was not acknowledged during the course of the 2000 RFI, and whether or not the Derbyshire would have survived, had her hatch covers met the relevant standards, remains, therefore, debatable.
Extracts from Lloyd’s Rules 1967
designed for carrying ore
Para 6020 (page 254)
Steel hatch covers are to be in accordance with D 2326 and the
scantlings determined from the formulae given in table 43 note 6. When a draught in excess of the cargo ship draught is desired, the section modulus and moment of inertia of the stiffeners and thickness of the plating are to be increased by 15 per cent.”
In 1968, Lloyd’s rule requirements for hatch cover strength were reduced by 15% to bring them into line with the requirements of the 1966 Load Line Convention.
In the following pages the strength of the Derbyshire’s number one cargo-hold hatch covers has been evaluated and compared to the minimum strength required by both the Load Line convention and Lloyds Rules. The minimum strength requirements that were given within the Load Line Convention and Lloyd’s Rules were the ‘standards applicable at the time she was built’. No other standard is relevant.
The summarised results from the strength calculations that are given below include values obtained from classical manual calculation methods (simple beam theory), empirical methods (to give section modulus required by Lloyd’s rules) as well as finite element modelling and analysis.
The results from each of the above methods show that the Derbyshire’s No. 1 hatch covers did not meet the minimum strength ‘standards applicable at the time she was built’.
Derbyshire no.1 hatch cover construction (mild steel)
The Derbyshire’s number 1 cargo hold hatch opening was protected by two hatch covers arranged Port and Starboard of the vessel’s centreline which slid outboard to open and inboard to close. When closed, each hatch cover was supported on three of its sides by the upper deck hatch coaming structure. The fourth side of the port hatch cover mated with the fourth side of starboard hatch cover at the vessel’s centerline. There was no structural support for the fourth side of the hatch covers at the vessel’s centreline other than at their fore and aft ends where they sat upon the hatch coamings.
Each hatch cover panel was arranged with steel top plating and four side plates around its perimeter. Longitudinal and transverse stiffening members were provided on the underside, i.e. ten main, fore and aft longitudinal stiffeners and three main transversal girders (side, centre, side); these stiffening members were ‘simply supported’ at their ends by the four hatch cover side plates.
Main fore and aft hatch cover stiffeners – strength and stress calculation
1. Stress calculation using simple beam theory:
The stresses within the hatch stiffener can be calculated from the section properties that are detailed above in conjunction with the loading that is given within the Load Line Convention:
The fore and aft stiffeners are simply supported at their ends by the hatch coamings:
(1) For mild steel, maximum allowable stress = 4100/4.25 = 965 kg/cm2
Hatch cover fore and aft stiffener spacing = 0.994 m
Total pressure load on one stiffener = W = 14.72 x 0.994 x 1.75 = 25.605 tonnes
Approximate self weight of one stiffener = Section Area of 1 stiffener x L x density:
Self weight of stiffener = (0.994 x 0.011 + (0.61 + 0.46)/2) x 0.0105 + 0.28 x 0.025) x 14.72 x 7.8 = 0.351 x 7.86 = 2.725 tonnes
From simple bending theory: the maximum bending moment in the stiffener is at its mid point = WL/8
M = (25.605 + 2.725) x 14.72/8 = 52.1272 tonne metres
Simple bending theory:
M/I = σ/Y = E/R => stress = σ = bending moment/section modulus
Maximum bending stress = 52.1272 x 105/4799.43 = 1086.11 kg/cm2 (this exceeds the maximum allowable stress in (1) above)
Load Line Convention requirements:
The minimum required Section Modulus (I/Y) to give stresses below 965 kg/cm2 can be easily determined:
From simple bending theory (M/I = σ/Y) => M/σ = I/Y = 5212720/965 = 5402 cm3
Summary of strength standards:
The table below provides a summary of the strength standards that were current during the period in which the Derbyshire was designed and built. The shortfall in the required strength of the hatch cover stiffeners is also indicated.
* It would appear that the Lloyd’s Register formulation for minimum section modulus does not include an element for the stiffener’s self-weight. This implies that their rules at that time would consistently give strength requirements that would fall below that set to meet the stress criteria of the 1966 Load Line Convention. The strength required to support the stiffener’s own self weight is significant (on the Derbyshire each stiffener weighed approximately 2.5 tonnes and was 14.7m long); neglecting this factor would mean an approximate 10% shortfall in required strength when the Lloyds formulation was used.
Although the percentages shown in the above table do not appear to be dramatic, it should be noted that these are shortfalls on a strength standard that is meant to provide a statutory minimum. There is no reason, other than cost savings, why designers should not exceed this statutory minimum by a comfortable margin.
The above concludes the summary of the traditional ‘rule - based’ approach to determining hatch cover strength requirements.
2. Strength and stress analysis of the Derbyshire’s hatch covers using the finite element method
It should be noted that the hatch covers on the Derbyshire were not solely provided with fore and aft ‘I’ section stiffening members (as discussed and examined previously) in addition three deep transverse girders were provided, arranged as indicated in the sketch on page 3. Effectively, this arrangement of longitudinal stiffeners and transverse girders formed what is known as a ‘grillage’ in structural analysis terminology.
ii) The port side hatch cover model
Undeformed stiffener model viewed from underside
Undeformed stiffener model viewed from above
Deformed model with seawater loading at 1.75 Tonnes/m2 (plus self weight) - Viewed from above
Deformed model with seawater loading at 1.75 Tonnes/m2 (plus self weight) - Viewed from the underside
Port side hatch cover model: this model revealed that the three main transverse girders were effective in reducing stresses in the longitudinal stiffeners to satisfactory levels. However, the girders themselves, together with the inboard hatch cover side plate to which they were attached, were not strong enough to take the additional loads that had been shed from the 10 longitudinal stiffeners. Stress maxima in the region of 1300 kg/cm2 were developed in the two transverse side girders, stress maxima in the region of 1400 kg/cm2 were developed in the single transverse girder, and stress maxima in the region of 1350 kg/cm2 were developed in the main inboard hatch cover side plate.
Undeformed hatch cover model viewed from above
Hatch cover - original and deformed structure
Hatch cover - original and deformed structure
Hatch cover - deformed structure - views
Hatch cover - deformed structure - view from above
Hatch cover - deformed structure - view of the underside
The stress levels in the transverse girders and longitudinal inboard side plate, as revealed by the FE analysis, significantly exceed the allowable stress levels that are given within the 1966 Load Line Convention. It is notable, that the stress levels in some areas are more than 40% above the statutory maxima. Elevated stress levels indicate that the hatch cover’s factor of safety against catastrophic collapse may have been significantly reduced. And a failure in the longitudinal inboard side plate could lead to a domino-like collapse of the remaining hatch structure.
On the basis of the calculations summarised above, it is clear that the strength of the Derbyshire’s hatch covers did not comply with the standards that were applicable at the time she was constructed, and that, therefore, the RFI statement to the contrary was incorrect.
 Re: Strength
i) The required ‘strength’ standard within the 1966 Load Line Convention was the minimum strength that, when the hatch covers were loaded at a rate of 1.75 tonnes/m2, would produce stresses below the ultimate breaking strength of mild steel divided by 4.25 (a notional factor of safety of 4.25).
ii) The required strength standard that was contained within Lloyd’s Register’s construction rules was expressed as ‘minimum required section modulus’ - the rule requirements allowed the maximum stress values, that were permitted by the Load Line Convention, to be governed by a single parameter which could be calculated for each girder in each hatch cover ie if the main hatch girders had a section modulus that exceeded xxxx cm3 then the maximum stress levels within that girder would not exceed the values permitted by the load Line Convention when the cover was loaded at 1.75 tonnes/m2.