Page 384 - Marine Structural Design

360 Part 111 Fatigue and Fracture

Note that N is the number of cycles exceeding a given wave height, forces and stress range in
one year. A stress range exceedance diagram may be plotted based on the S - Log N relation
in the table.
Example 18.2: Long-term Stress Range Distribution - Spectral Approach
Problem:
Determine the long-term stress range distribution of the spanned riser considered in Example
18.1 using spectral approach. This example is chosen to illustrate the spectral approach for the
determination of long-term stress range described in Section 18.3.4 (Almar-Nsess, 1985).
Solution :
The long-term stress range distribution is obtaining using Eq. (18.21) summing up the short-
term distribution for a number of sea states. In the following, the procedure used to derive
short-term stress distribution as per Eq.(18.20) is illustrated. The most probable wave period
for a given wave height is:
277
T = - 0.7 + 4.2H0.4
=
w
The transfer function may be expressed as

where c,(w) is the maximum stress cased by wave frequency o.

Consider again the wave height H=llm, T=11.7 sec and w =0.539. From deterministic
analysis, we may find that
M,(w = 0.539) = 4698Nm, CT,,(W = 0.539) = 6.9MPa

The transfer function may then be calculated using the above value of cmx (w) and H. This
calculation is repeated for a set of wave periods between 3 and 25 to derive the relationship
between H,(w) and a.

When the relationship between unit wave height and stresses, “the transfer function H, (m(O)”,
is established, the stress spectrum may be given as:

The nth spectral moment of the stress response may be described for the ith sea state as:
mOi = I S, (m)dW = 1 1 5.6MPa2

mZi = ~O~S~(O)~O 35.74(~~a/sec)~
=
The average stress cycle period is thus
I