Page 208 - Practical Design Ships and Floating Structures

183

is
where T'" (unit in hours) is the duration of service T,, 0, the long-term based, average fatigue
damage caused by cell wy of WSD in T, ; is the average number of cycles per unit time of a short-
term response corresponding to cell wV of WSD, wave direction a, and loading pattern AI&., = nqkjTs
(unit in lhour). With Eq. 6, D can be further simplified. For a two-segment S-N curve as shown in
Figure 10, the total damage in T, (unit in years) can be represented by
m
DzTf,2' r(F + 1) I: fi/uk~u~~~ Pr(U&)Pr(A/ X20ij~)~ (8)
Pr(Wg)
K i,j.k.l
y(?+ I,u)-K(%h'y(-+ ' 1.u)
in which P,,~/ = I- K'& , integral y(p,x) = jrp-1 exp(-r)dr is the incomplete
'(5 + I) O
I
gamma function, and u=uiikl =-(--") S 2 . in which the rain flow correction
2"ijkl
h(m,eiikl) = a(m) + (1 - a(m)}(l -E~~)~(~) introduced to improve the counting of cycles of
been
has
the stress fluctuation. h can be determined by curve fitting (Wirsching, 1980) as
a(m) = 0.926 - 0.033m and b(m) = 1 S87m - 2.323. The two-segment S-N curve consists of the first
segment (K' , m') for 0 I s 5 s,, and the second segment (K, m) for s 2sq, where m' = m + Am . For a
one-segment S-N curve, pqk, = I.

From Eq. 7 or 8, the annualized fatigue damage D can be determined by letting T,=l year. When D =
1, T, (T',) becomes the fatigue life TL. Therefore, after considering the safety factorf, the fatigue life
can be represented as
1
r, =- (9)
fsD
Table 5 lists the fatigue life and annualized fatigue damage with respect to the wave environments
W156 and W391 using the JONSWAP and Bretschneider wave spectra, respectively. In this example,
the S-N curve in Figure 10 is utilized. It is found that the fatigue life under a more severe environment
(W156, in the North Sea) is much shorter than that under a more benign one (W391, in the Gulf of
Mexico). Also, the choice of wave spectrum can have significant effects on the fatigue damage. The
fatigue life predicted by using the JONSWAP spectrum is shorter (worse) than that predicted by using
the Bretschneider spectrum in this example.