Page 166 - Introduction to Naval Architecture

2 STRENGTH

total. The ship spends 300 days at sea each year and has a life of
25 years. The average period of encounter during its life is six
seconds. Calculate the value of the bending moment that is only
likely to be exceeded once in the life of the ship.

Solution
The bending moment spectrum can be found by multiplying the
wave spectrum ordinate by the square of the appropriate RAO.
For the overall response the area under the spectrum is needed,
This is best done in tabular form using Simpson's First Rule.

Table 7.2

5(o)J RAO (RAO) 2 E(ti>J ASimpson's multiplier Product
(l> e

0 0 0 0 0 1 0
0,4 0.106 103 10609 1124.6 4 4498,4
0.8 0.325 120 14400 4680.0 2 9360.0
1,2 0.300 106 11236 3370.8 4 13483.2
1.6 0.145 95 9025 1308.6 2 2617.2
2.0 0.060 77 5929 355.7 4 1422.8
2.4 0 64 4096 0 1 0
Summation 31381.6

In the Table 7.2, E(ft> e) is the ordinate of the bending moment
spectrum. The total area under the spectrum is given by:

The total number of stress cycles during the ship's life:

Assuming the bending moment follows a Rayleigh distribution,
the probability that it will exceed some value M^. is given by:

where 2a is the area under the spectrum.