Page 167 - Introduction to Naval Architecture

STRENGTH 153

In this case it is desired to find the value of bending moment
8
that is only likely to be exceeded once in 1.08 X 10 cycles, that is
8
8
its probability is (1/1.08) X Kr = 0.926 X 10~ .
Thus M e is given by:

Taking natural logarithms both sides of the equation:

The hogging moment will be the greater component at 60 per
cent. Hence the hogging moment that is only likely to be
exceeded once in the ship's life is 167MNm.

Statistical recording at sea
For many years a number of ships have been fitted with statistical strain
gauges. These have been of various types but most use electrical
resistance gauges to record the strain. They usually record the number
of times the strain lies in a certain range during recording periods of 20
or 30 minutes. From these data histograms can be produced and curves
can be fitted to them. Cumulative probability curves can then be
produced to show the likelihood that certain strain levels will be
exceeded.
The strain levels are usually converted to stress values based on a
knowledge of the scantlings of the structure. These are an approxima-
tion, involving assumptions as to the structure that can be included in
the section modulus. However, if the same guidelines are followed as
those used in designing the structure the data are valid for comparisons
with predictions. Direct comparison is not possible, only ones based on
statistical probabilities. Again to be of use it is necessary to record the
sea conditions applying during the recording period. With short
periods the conditions are likely to be sensibly constant. The sea
conditions are recorded on a basis of visual observation related to the
Beaufort scale. This was defined in the chapter on the environment but
for this purpose it is usual to take the Beaufort numbers in five groups
as in Table 7.3.
For a general picture of a ship's structural loading during its life the
recording periods should be decided in a completely random manner.
Otherwise there is the danger that results will be biased. If, for instance,
the records are taken when the master feels the conditions are leading
to significant strain the results will not adequately reflect the many