Page 389 - Marine Structural Design
P. 389
Chapter 19 Simplified Fatigue Assesment 365
19.3 Simplified Fatigue Assessment
19.3.1 Calculation of Accumulated Damage
It is assumed that the linear cumulative Palmgren-Miner Law is applicable, and may be written
as:
(19.2)
where,
No = Total number of cycles in the long-term period considered
f (S) = probability density function for the stress range (which means that the number
of cycles for the stress range S is N,,f(S)dS)
.
As discussed in Chapter 16, S-N curves may be expressed as N = KS-'" Substituting this
equation into Eq.(19.2), we may get:
(1 9.3)
For marine structures, the probability density function of stress range may be represented by a
two-parameter Weibull distribution.
(19.4)
where A and 5 denote a scale parameter and a shape parameter respectively. Combining
Eq.(19.3) and Eq.(l9.4), we may get:
(19.5)
.=(:) 6
Introducing
(19.6)
we may get
(19.7)
The Gamma fimction is defined as:
r(ic) = ge-xxk-'dx (1 9.8)
Combining Eq.(19.7) and Eq.(19.8), the long-term cumulative damage may be written as:
