Page 400 - Marine Structural Design
P. 400
376 Part 111 Fatime and Fracture
(20.12)
where, pi = Probability of occurrence of the ith seastate
Based on Eq. (20.12), the transformation of a stress range spectrum to fatigue damage is
straightforward. Applying a spectral fatigue analysis, analytical expressions may be derived as
transfer functions from wave spectra to response amplitude spectra and finally to stress range
spectrum. Using the root mean square stress cri , the accumulated damage equation (Eq.(20.12)
may be re-expressed as,
(20.13)
When wave direction is also accounted for in defining the sea states, the probability of each
sea state may be expressed as pii where j denotes the jth direction.
(20.14)
When the S-N curves are defined using bi-linear curves, the accumulated fatigue damage may
be determined as:
(20.15)
where the incomplete Gamma functions are defined as:
r(k,+ 5 me-xxk-'dx (20.16)
z
e
ro(k,z) = joz xk-'& (20.17)
--x
and
(20.18)
where S, is the stress range at the crossing of two S-N curves (e.g. corresponding to fatigue
life of io7).
The formulation for spectral fatigue assessment based on bi-linear S-N curves appeared in
DNV Classification Note 30.7 for ship structures and DNV (2000) for steel offshore structures.
