Page 170 - Pipelines and Risers

Force Model and Wave Fatigue 143

For narrow banded response, the accumulated damage of a sea-state may be expressed in the
continuous form:
W)
D,=, E-&
=
N(S)
where n(S)dS represents the number of stress ranges between S and S+dS. If a stationary
response process of duration TEfe is assumed, the total number of stress cycles will be:

in which case, one can obtain:
n(S)dS = Np(S)dS = v,T,,p(S)dS

where p(S) is the probability density function for stress range S given by:
S
pfS)
4u
Then, one can obtain:

using notation:

and Gamma function:

We may get:

- Fatimue Damage for All Sea-States

From the damage equation for one sea-state, one may easily calculate the damage
accumulated for all sea-states. If the response process is wide banded process, the
Winching's Rain Flow Correction Factor is recommended to correct the conservatism due to
narrow banded assumption (Wirsching and Light, 1980).