Page 184 - Introduction to Naval Architecture

170 STRENGTH

suitable material must be chosen. For a steel ship this means a steel with
adequate notch toughness in the temperatures and at the strain rates
expected during service. Allowance must be made for residual stresses
arising from the fabrication methods. Welding processes must be
defined and controlled to give acceptable weld quality, to avoid undue
plate distortion and defects in the weld. Openings must be arranged to
reduce stress concentrations to a minimum. Allowance must be made
lor corrosion.
Even with these safeguards there will be many reasons why actual
stresses might differ from those calculated. There remain a number of
simplifying assumptions regarding structural geometry made in the
calculations although with the modern analytical tools available these
are much less significant than formerly. The plating will not be exactly
the thickness specified because of rolling tolerances. Material proper-
ties will not be exactly those specified. Fabrication will lead to
departures from the intended geometry. Intercostal structure will not
be exactly in line either side of a bulkhead, say. Structure will become
dented and damaged during service. All these introduce some
uncertainty in the calculated stress values.
Then the loading experienced may differ from that assumed in the
design. The ship may go into areas not originally planned. Weather
conditions may not be as anticipated. Whilst many of these variations
will average out over a ship's life it is always possible that a ship will
experience some unusually severe combination of environmental
conditions.
Using the concept of load-shortening curves for the hull elements it
is possible to determine a realistic value of the ultimate bending
moment a hull can develop before it fails. The designer can combine
information on the likelihood of meeting different weather conditions
with its responses to those conditions, to find the loading that is likely
to be exceeded only once in a ship's life. However, one would be unwise
to regard these values as fixed because of the uncertainties discussed
above. Instead it is prudent to regard both loading and strength as
probability distributions as in Figure 7.23. In this figure load and
strength must be expressed in the same way and this would usually be
in terms of bending moment.
In Figure 7.23 the area under the loading curve to the right of point
A represents the probability that the applied load will exceed the
strength at A. The area under the strength curve to the left of A
represents the probability that the strength will be less than required to
withstand the load at A. The tails of the actual probability distributions
of load and strength are difficult to define from recorded data unless
assumptions are made as to their mathematical form. Many authorities
assume that the distributions are Rayleigh or Gaussian so that the tails