Page 83 - Marine Structural Design

Chapter 3 Loads and Dynamic Response for offsore Structures 59

k
q(x) = cxm exp(-px ) (3.17)
where, c, m, p, and k are four constant parameters to be determined by nonlinear least-squared
fitting:

=
Q = ln[-ln(l- P(x))~ lnc + mlnx - pxk (3.18)
Once the mathematical expression ofP (x) in Eq. (3.15) is obtained, the long-term PEV can be
determined by:
1
1 - P(xpEy) = - (3.19)
N
a
1 -P(x,,l ) = - (3.20)
a N
Here a, is the possibility level as in Eqs. (3.7) and (3.10) and N is the number of observations
or cycles related to the return period. In the design of offshore structures, a rehun period of
100 years is widely used for estimating the long-term extreme values.
When the wave scatter diagram is applied, P (x) from Eq. (3.15) can be obtained by using the
definition of probability density function of maxima:

(3.21)
where,
Pr(w~) = Normalized joint wave probability of (Hs(i),m)) or cell wg in Wave Scatter
Diagram, pr(wii ) = I
i.i
Pr(ak) = Probability of wave in direction ak, 1 Pr(ak ) = I
k
Pr(A/) = Probability (or percentage) of loading pattern A1 during service, EPr(h,) = I
I
nQk/ = Average number of responses in TS corresponding to cell wQ of Wave Scatter
Diagram, wave direction ak and loading pattern Ai. nijw can be computed by
Eq. (3.1 1)

j& = Average number of responses per unit of time of a short-term response
corresponding to cell WQ, wave direction ak and loading pattern AI, unit in
1hOUr. fiki = niikr/Ts
pQk&) = Probability density function of short-term response maxima corresponding to
cell WQ , wave direction ak and loading pattern AI. If the wave spreading (short-
crest sea) effect is considered, it should have been included in the responses as
shown in Eq. (3.8).
-
N, = Long-term based, average number of observations of responses in Ts,
-
N, = zngu P<w,)P<~,)P~(A,)=T, fqu ~r(w,)~r(a,)~r(~,) (3.22)
i.j.k.1 i.1.k.t