Page 378 - Marine Structural Design

354 Part III Fatigue and Fracture

The long-term distribution of the stress range may be estimated by a weighted sum over all sea
states as

where pi is the probability of occurrence of the ith sea state and the weighted coefficient is

(18.25)

The obtained long-term distribution of the stress range may be described using a probability
function, e.g. Weibull distribution function in which the Weibull parameters are determined
through curve fitting.

18.4 Fatigue Loading Defined Using Scatter Diagrams
18.4.1 General
A "short-term" description of the sea (or sea state) means the significant wave height and the
mean wave period are assumed to be constant during the time period considered. To construct
a "long-term" description of the sea, we need scatter diagrams. The scatter diagrams are used
for spectral fatigue analysis and time-domain fatigue analysis, where waves and currents are
defined using wave scatter diagram and current scatter diagrams respectively. The
environmental criteria are defined as combinations of directional sea, swell, winds and
currents as well as their combinations that the structure will be subject to through its life cycle.
Unless the mean stress is very large (e.g. for TLP tethers), the effect of mean stress is ignored.
Hence, steady current is normally not given attention except its effect on nonlinear dynamic
response. The current scatter diagram is mainly used for the prediction of vortex-induced
vibrations.

The joint frequency of significant wave height H, and spectral wave period T, are defined
using the wave scatter diagram. Each cell of the diagram represents a particular combination
of Hs , T, and its probability of occurrence. The fatigue analysis involves a random sea
analysis for each sea state in the scatter diagram and then summing the calculated fatigue
damages based on the probability of occurrence for the corresponding sea-state. From motion
analysis, the stress amplitude operator (RAO) is obtained for a particular reference sea state.
Long-term directionality effects are also accounted for using wave scatter diagrams in which
the probability of each direction is defined. For each set of the significant wave height H, and
spectral wave period T, , the total probability for all directions should then be equal to 1 .O.

18.4.2 Mooring and Riser Induced Damping in Fatigue Seastates
Viscous damping due to drag on mooring lines and risers may significantly affect the motion
of deepwater floating structures. Traditionally, the motion response of moored floating
structures has been evaluated by modeling the mooring lines and risers as massless springs. In
this un-coupled approach, the inertia, damping and stiffness of the mooring lines and risers
have not been properly included in the prediction of the vessel motions.