Page 377 - Marine Structural Design

Chapter 18 Fatigue Loading and Stresses 353

Combine the results for all sea states in order to derive the long-term distribution of stress
range. In the following, a formulation is used to further illustrate the spectral approach @NV,
1998).
A wave scatter diagram may be used to describe the wave climate for fatigue damaged
assessment. The wave scatter diagram is represented by the distribution of H, and T, . The
environmental wave spectrum S,(w)for the different sea states can be defined, e.g. applying
the Pierson-Moskowitz wave spectrum (see Chapter 2).
When the relationship between unit wave height and stresses, "the transfer hction H, (wlB)",
is established, the stress spectrum S, (@)may be obtained as:

(1 8.1 7)
The nth spectral moment of the stress response may be described as:
m, = 1 wn . S, (cob@ (1 8.18)

A spreading function may be used to include wave spreading,

f(B) = k COS" (8) (1 8.1 9)
e+90°
where k is selected such that cf(B) I. Normally n=2. The spectral moment may then be
=
e-9oo
expressed as:
(18.20)

where mo is the 0th spectral moment. The average stress cycle period is thus

I
(18.21)

and the number of cycles within the sea state of period is
T.
n. =L (1 8.22)
' T02i
Nonlinear effects due to large amplitude motions and large waves can be neglected in the
fatigue assessment since the stress ranges at lower load levels contribute relatively more to the
cumulative fatigue damage. In cases where linearization is required, it is recommended that
the linearization is performed at a load level representative of the stress ranges that contribute
the most to fatigue damage, i.e. stresses at probability levels of exceedance between lo-* to
lo4. The stress range response may be assumed to be Rayleigh distributed within each sea
state as

(18.23)