Page 375 - Marine Structural Design

Chapter 18 Fatigue Loading and Stresses 35 1

(18.10)

From the above equation, we may get (Almar-Naess, 1985):
A = S, (In N, )-A (18.11)

The special case of 5=1 is the well-known exponential distribution in which the log (n) plot of
stress exceedance is a straight line. Substituting Eq.(18.10) into Eq.(18.7), we may obtain:

(18.12)

From Eq.( 18.1 l), it may be obtained that

(1 8.13)

18.3.3 Long Term Stress Distribution Based on Deterministic Approach
This method is based on the deterministic calculation of wave force and it involves the
following steps (Almar-Naess, 1985):
Selection of major wave directions
4 to 8 major wave directions are selected for analysis. The selection of major wave
directions shall consider the directions that cause high stresses to key structural members.
All of the waves are distributed between these major directions.
Establishment of long-term distributions of waves
For each wave direction selected, a long-term distribution of wave height is established by
a set of regular waves, which adequately describes the directional long-term wave
distributions. The range of wave heights, that give the highest contribution to the fatigue
damage, should be given special attention. The most probable period may be taken as the
wave period.
Prediction of stress ranges
For each wave identified (direction, height, period), the stress range is predicted using a
deterministic method for hydrodynamic loads and structural response.
Selection of stress distribution
The long-term stress exceedance diagram from a wave exceedance diagram is as illustrated
in Figure 18.1, where boi and Hi denote the stress range and wave height.

A simplified fatigue analysis has been coded in API 2A-WSD(2001) assuming a relation
between the stress range S and wave height H obtained based on the deterministic approach
described in the above:
Aa = CH’ (1 8.14)