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Article 3.6 - Morison's Equation ~ [*36*#]
Section 3.6.6 - Forces on Multi-Hull Semisubmersibles: ~ [*366*#]
(i) Split Force.
(ii) Twist Moment on Two-Pontoon Semisubmersible.
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Section 3.6.6 - Forces on Multi-Hull Semisubmersibles.

Semisubmersibles with more hulls, legs or pontoons are sensitive to horizontal wave forces that tend to separate the hulls. Such forces must be taken up by cross bracings and by the connection to the deck structure. An approximate estimation of the maximum value of such forces may be carried out by Morison's equation. With ordinary dimensions the mass term in the Morison equation prevails over the drag force. This must, however, be checked in each particular case.

(i) Split Force. The split force is mainly caused by the horizontal acceleration of the wave. The horizontal acceleration is greatest in the nodal lines of the waves. The most unfavourable situation is therefore when the platform is riding on the crest of a wave with opposite hulls or pontoons situated in the middle between the crest and the adjacent wave troughs. See Figure 3.6.8. _

Figure 3.6.8: Phase of maximum split force on legs or pontoons of a semisubmersible platform.

If (lambda) is the wave length and B is the effective distance between opposite hulls, then the wave length of this critical wave is evidently
Equation (3 6.99).
When the platform is submerged in this position, it will not move significantly. As in the previous section, we may therefore calculate the wave forces as if the platform were fixed. The horizontal split force amplitude Fs is then evaluated from the inertia term in Morison's equation to be

Page 307. (3.6 - Morison's Equation)
Equation (3 6.100).
where V is the submerged volume of the hull, A is the wave amplitude and d is the effective draught. Forces on the vertical columns may be included in the volume V, adjusting the value for the effective draught d.

We may now for convenience introduce the wave slope
Equation (3 6.101).
The wave slope has a theoretical maximum value of 1/7. When s is introduced into (3.6.100), this gives the alternative form of the split force
Equation (3 6.102).
The term ((rho g V)) is the displaced water weight, or buoyancy force, on the hull under investigation. If the platform has N such hulls and a total weight of W, then (rho gV ~ W/N).

Choosing as characteristic values
Equation (3 6.103).
we find that the maximum split force is of order 33% of the buoyancy force on the hull under investigation.

For a conventional unit the characteristic width or diameter is about 75 m. This gives a critical wave 150 m long and 15 m high. Such waves may appear in storms with significant wave height of 8 m or more which is not particularly extreme. As a consequence of this, the extreme long term split force does increase slowly with the return period. The 20 years extreme force is only slightly larger than the 1 year extreme.

(ii) Twist Moment on Two-Pontoon Semisubmersible. For semisubmersible platforms with two long pontoons there will be a pitching moment on each hull. If the two pitching moments are in opposite phase, they will constitute a twist of the whole platform which must be considered in the design. See Figure 3.6.9. _

Figure 3.6.9: Twisting moment on a semisubmersible platform with two pontoons.

In this case the predominant forces are induced by the vertical acceleration of the water. The most unfavourable position is evidently when the platform is riding diagonally over a wave crest where the wave length (lambda) is related to the platform dimensions through

Page 308. (3.6 - Morison's Equation)

Equation (3 6.104).
L is the length of the hulls and B is the distance between the hulls. The twisting moment MT may then be evaluated by the inertia term in the Morison formula to be
Equation (3 6.105).
S is the cross section area of the pontoon and d is the effective draught as before. Introducing the wave steepness (s=2A/lambda) and the volume V of each pontoon, the moment becomes
Equation (3 6.106).
Introducing a maximum steepness of for instance s=1/7 we have obtained a rough formula for the extreme twisting moment, even without any use of statistics.

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