Page 390 - Marine Structural Design

366 Pari III Fatigue and Fracture

(19.9)

In Part III Chapter 18, it has been derived that:

(1 9.1 0)

Hence, it is obtained that the long-term cumulative damage may be written as (Almar-Naess,
1985):

(19.11)

where,
No = Total number of cycles in the long-term period (e.g. service life) considered
So = Expected maximum stress range in No cycles,
1
P(S > s,,) = - (fatigue stress range s exceeds S, once every N~ cycles)
No
5 = Shape parameter of the Weibull distribution for the stress cycles
K, m = Material parameters of the S-N curve

19.3.2 Weibull Stress Distribution Parameters
When the shape parameter, 6, equals to 1, the Weibull distribution yield to the Exponential
distribution. The value of 5 can be larger or smaller than 1. The higher the 5 values, the more
severe cyclic loading conditions are. The shape parameter is a function of the cyclic loading
environment in which the system exists, and how the system responds to this environment (e.g.
local loading effects, dynamic loading effects). A suitable value for the shape parameter
should be chosen based on fatigue analysis of similar structures in the same site. In order to
evaluate the accuracy of the selected shape parameters, the predicted fatigue damage
corresponding to given shape parameters shall be compared with the measured data or more
refined analysis (e.g. spectral fatigue analysis). Typical values for the Weibull shape parameter
5 are given in Table 18.1 for some commercial ships and offshore structures.
The spectral fatigue analysis and extensive fatigue damage data may be used to calibrate the
Weibull parameters for various types of ship and offshore structures. Luyties and Stoebner
(1998) presented a procedure to calibrate the MI simplified fatigue design method using
spectral fatigue analysis.

19.4 Simplified Fatigue Assessment for Bilinear S-N Curves
When the S-N curves are expressed as bilinear curves (see Part I11 Chapter 17), the fatigue
damage may be predicted using