Annex - An Example of Alternative Intact Stability Criteria for Twin-Pontoon Column-Stabilized Semisubmersible Units
Clasification Society 2023 - Version 9.38
Statutory Documents - IMO Publications and Documents - Resolutions - Assembly - IMO Resolution A.650(16) – An Example of Alternative Intact Stability Criteria for Twin-Pontoon Column-Stabilized Semisubmersible Units – (Adopted 19 October 1989) - Annex - An Example of Alternative Intact Stability Criteria for Twin-Pontoon Column-Stabilized Semisubmersible Units

# Annex - An Example of Alternative Intact Stability Criteria for Twin-Pontoon Column-Stabilized Semisubmersible Units

1.1 The criteria hereunder constitute alternative intact stability criteria for column-stabilized units under the provisions of section 3.3.3 of the Code for the Construction and Equipment of Mobile Offshore Drilling Units, 1989 (1989 MODU Code). These criteria apply only to twin-pontoon column-stabilized semisubmersible units in severe storm conditions which fall within the following range of parameters:

 Vp/Vt is between 0.48 and 0.58 Awp/(Vc)2/3 is between 0.72 and 1.00 lwp/[Vc× (Lptn/2)] is between 0.40 and 0.70

The parameters used in the above equations are defined in paragraph 1.3.

1.2 Intact stability criteria

The stability of a unit in the survival mode of operation should meet the following criteria:

• .1 Capsize criteria

These criteria are based on the wind heeling moment and righting moment curves calculated as shown in section 3.2 of the 1989 MODU Code at the survival draught. The reserve energy area 'B' must be greater than 10% of the dynamic response area 'A' as shown in figure 1.1.

Area 'B'/Area 'A' ≥ 0.10

where
• Area 'A' is the area under the righting arm curve measured from θ1 to (θ1 + 1.15 θdyn)
• Area 'B' is the area under the righting arm curve measured from (θ1 + 1.15 θdyn) to θ2
• θ1 is the first intercept with the 100 knot wind moment curve
• θ2 is the second intercept with the 100 knot wind moment curve
• θdyn is the dynamic response angle due to waves and fluctuating wind
• θdyn = (10.3 + 17.8C)/(1 + GM/(1.46 + + 0.28BM))
• C = (Lptn 5/3 * VCPw1 * Aw * Vp * Vc 1/3)/(l wp 5/3 * Vt)

Parameters used in the above equations are defined in paragraph 1.3.

• .2 Down flooding criteria

These criteria are based on the physical dimensions of the unit and the relative motion of the unit about a static inclination due to a 75 knot wind measured at the survival draught. The initial downflooding distance (DFDo) must be greater than the reduction in downflooding distance at the survival draught as shown in figure 1.2.

DFDo - RDFD > 0.0

Where:
• DFDo = initial downflooding distance to Dm in metres
• RDFD = reduction in downflooding distance in metres
• = SF (k * QSD1 + RMW)
• SF = 1.10, which is a safety factor to account for uncertainties in the analysis, such as non-linear effects.
• k (correlation factor) = 0.55 + 0.08 (a - 4.0) + 0.056 (1.52 - GM)
• a = (FBDo/Dm)(Sptn * Lccc)/Awp

(a cannot be taken to be less than 4.0)

(GM cannot be taken to be greater than 2.44 m)

• QSD1 = DFDo - Quasi-static downflooding distance at θ1 in metres, but not to be taken less than 3.0 m.
• RMW = Relative motion due to waves about 01 in metres
• = 9.3+0.11(X-12.19)
• X = Dm(Vt/Vp)(Awp 2/l wp)( Lccc/Lptn)
• (X cannot be taken to be less than 12.19 m)

The parameters used in the above equations are defined in paragraph 1.3.

1.3 Geometric parameters

 Awp is the waterplane area at the survival draught including the effects of bracing members as applicable (in square metres). Aw is the effective wind area with the unit in the upright position (i.e. the product of projected area, shape coefficient and height coefficient) (in square metres). BM is the vertical distance from the metacentre to the centre of buoyancy with the unit in the upright position (in metres). Dm is the initial survival draught (in metres). FBDo is the vertical distance from Dm to the top of the upper exposed weathertight deck at the side (in metres). GM for paragraph 1.2.1.1 , GM is the metacentric height measured about the roll or diagonal axis, whichever gives the minimum restoring energy ratio, 'B'/'A'. This axis is usually the diagonal axis as it possesses a characteristically larger projected wind area which influences the three characteristic angles mentioned above. GM for paragraph 1.2.1.2, GM is the metacentric height measured about the axis which gives the minimum downflooding distance margin (i.e. generally the direction that gives the largest QSD1) (in metres). l wp is the waterplane second moment of inertia at the survival draught including the effects of bracing members as applicable (in metres to the power of 4). Lccc is the longitudinal distance between centres of the corner columns (in metres). Lptn is the length of each pontoon (in metres) Sptn is the transverse distance between the centreline of the pontoons (in metres). Vc is the total volume of all columns from the top of the pontoons to the top of the column structure, except for any volume included in the upper deck (in cubic metres). Vp is the total combined volume of both pontoons (in cubic metres). Vt is the total volume of the structures (pontoons, columns and bracings) contributing to the buoyancy of the unit, from its baseline to the top of the column structure, except for any volume included in the upper deck (in cubic metres). VCPw1 is the vertical centre of wind pressure above Dm, (in metres). Figure 1.1 Righting moment and heeling moment curves Figure 1.2 Definition of downflooding distance and relative motion

1.4 Capesize criteria assessment form

 Input data GM __________________________________________ = ________ m BM __________________________________________ = ________ m VCPw1 __________________________________________ = ________ m Aw __________________________________________ = ________ m2 Vt __________________________________________ = ________ m3 Vc __________________________________________ = ________ m3 Vp __________________________________________ = ________ m3 l wp __________________________________________ = ________ m4 Lptn __________________________________________ = ________ m Determine θ1 __________________________________________ = ________ deg θ2 __________________________________________ = ________ deg C=(Lptn 5/3 * VCPw1 * Aw * Vp * Vc 1/3)/l wp 5/3 * Vt) m-1 θdyn (10.3+17.8C)/(1.0+GM/(1.46+0.28BM)) __________ = ________ deg Area 'A' __________________________________________ = ________ m-deg Area 'B' __________________________________________ = ________ m-deg Results Reserve energy ration: 'B'/'A' = _____________ (min=0.10) GM = __________ m (KG=__________ m)

Note:

The minimum GM is that which produces a 'B'/'A' ratio = 0.10

1.5 Downflooding criteria assessment form

 DFDo _________________________________________ = _______ m FBDo _________________________________________ = _______ m GM _________________________________________ = _______ m Dm _________________________________________ = _______ m Vt _________________________________________ = _______ m3 Vp _________________________________________ = _______ m3 Awp _________________________________________ = _______ m2 l wp _________________________________________ = _______ m4 Lccc _________________________________________ = _______ m Lptn _________________________________________ = _______ m Sptn _________________________________________ = _______ m SF _________________________________________ = _______ 1.10 Determine θ1 ____________________________________________________ deg DFD1 ____________________________________________________ m QSD1 ____________________________________________________ m a=(FBDo/DM)(Sptn * Lccc)/Awp = ____ (AMIN=4.0) k=0.55+0.08(a-4.0)+0.056(1.52–GM)= ____ (GMMAX=2.44 m) X=Dm(Vt/Vp)(Awp 2/l wp)(Lccc/Lptn)= ____ m = (XMIN=12.19 m) RMW=9.3+0.11(X-12.19) = _______ m RDFD=SF (k * QSD1+RMW) = _______ m Results downflooding margin: DFDo-RDFD= __________ (min=0.0 m) GM= ____ m (KG= ____ m)

Note:

The minimum GM is that which produces a downflooding margin = 0.0 m.

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