Page 373 - Marine Structural Design

Chapter I8 Fatigue Loading and Stresses 349

2-N Y
B,=(M,,+~,(M,),)-++BM,,- (18.1)
4 IH
In hogging condition for minimum internal cargo or ballast loads
2-N
OL =(MSW +'$mn('WY)H)-+B MryH- Y (18.2)
1, IH
where
1, and I, : moment of inertia of a cross-section about the horizontal neutral axis, and
vertical neutral axis respectively,

N and z: vertical distance from the keel line to the neutral axis, and from the keel line to
the load point, respectively.
y: horizontal distance from the load point to the centerline,
(MW), and (MW)" : vertical wave bending moment for sagging and hogging conditions
respectively, according to IACS requirements.

A- , and B: Coefficients are defined in Table 18.2.
The local loads include the static sea pressure and internal cargo or ballast loads. The stress
ranges for full laden load conditions may be estimated as:
(18.3)

Similarly, the stress ranges for ballast load conditions may be estimated as:
(1 8.4)

The long-term distribution of the hull girder stress range may be represented by a two-
parameter Weibull distribution. When a long-term analysis of the ship behavior at sea is
performed enabling to determine the long-term distribution of hull girder bending stress, the
shape parameter 6 may be determined as follows (BV, 1998):

(18.5)

where c ~ ~ ~ . ~o,o-I are extreme hull girder bending stress for a probability of exceedance
and
probability of 10" and 10" respectively.
If no direct analysis of the ship behavior at sea is performed, a first approximation of the shape
parameter 6 for ocean-going steel vessels, may be taken from IACS (1999) as:

6 = 1.1 -0.35- L-loo where L is ship length in m (1 8.6)
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