If, previous
to firing, the metal of the tube were free from any internal stresses,
then the resistance of the tube would be
R squared - r squared_0
P0 = U ----------- ,
R squared + r squared_0
or 2,115 atmospheres--that is, one-half that in the ideally perfect
cylinder. From this we perceive the great advantage of developing useful
initial stresses in the metal and of regulating the conditions of
manufacture accordingly. Unless due attention be paid to such
precautions, and injurious stresses be permitted to develop themselves
in the metal, then the resistance of the cylinder will always be less
than 2,115 atmospheres; besides which, when the initial stresses exceed
a certain intensity, the elastic limit will be exceeded, even without
the action of external pressures, so that the bore of the gun will not
be in a condition to withstand any pressure because the tensile stress
due to such pressure, and which acts tangentially to the circumference,
will increase the stress, already excessive, in the layers of the
cylinder; and this will occur, notwithstanding the circumstance that the
metal, according to the indications of test pieces taken from the bore,
possessed the high elastic limit of 3,000 atmospheres.
[Illustration: Fig. 1]
In order to understand more thoroughly the difference of the law of
distribution of useful internal stresses as applied to homogeneous or to
built-up cylinders, let us imagine the latter having the external and
internal radii of the same length as in the first case, but as being
composed of two layers--that is to say, made up of a tube with one hoop
shrunk on under the most favorable conditions--when the internal radius
of the hoop = sqrt(R v0) or 118.
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