Page 374 - Marine Structural Design

350 Part III Fatigue and Fracture

18.3 Fatigue Stresses
18.3.1 General
As a preparation for Chapter 19, this Section presents three approaches for the estimation of
long-term fatigue stresses that will be used respectively by the subsequent chapters. They are:
Long-term fatigue stress based on Weibull distribution
Long-term fatigue stress based on deterministic approach
Long-term fatigue stress based on stochastic approach
18.3.2 Long Term Fatigue Stress Based on Weibull Distribution
The Weibull probability density function for long-term fatigue stress, S, may be described as:

(18.7)

where A is a scale parameter, and 5 is the shape parameter which is a function of the type of
structure and its location, see Table 18.1 for typical values for the shape parameter 5.

Table 18.3 Typical Weibull Shape Parameter Values for Simplified Fatigue Assessment
Typical Values for shape parameter 5
Fast cargo ships 5>1, maybe as high as 1.3 or a little more
Slower ships in equatorial waters <<I, and perhaps as low as 0.7
Gulf of Mexico fixed platforms 5~0.7

North Sea fixed platforms 5>1, maybe as high as 1.4 if the platform is
slender and dynamically active

The Weibull shape parameter is generally dependent on the load categories contributing to the
occurrence of cyclic stress.
The Webull distribution function is then:

(18.8)

The stress exceedance probability may then be expressed as:

(18.9)

If So is the expected extreme stress occurring once in a lifetime of No wave encounters (or
stress reversals), Eq.( 18.9) becomes