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Thick Cylinders
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Stress distribution
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Strains and Changes in Dimensions
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Change in diameter
Change in internal volume
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Problem:
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Compound Cylinders
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If this compound cylinder is subjected to internal pressure, the resultant hoop stresses will be the algebraic
sum of those resulting from internal pressure and those resulting from shrinkage. Therefore, the cylinders are
often built up by shrinking one tube on to the outside of another.
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for each condition, the hoop and
radial stresses at any radius can be
evaluated and the principle of
superposition applied. This means
that the various stresses can
simply be added up to compute
the stresses in a compound
cylinder subject to both shrinkage
and internal pressure
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Shrinkage or Interference Allowance
The difference in diameter at the mating surfaces is called the shrinkage or interference allowance for compound
cylinders produced by shrinking (normal process) or force fit procedure respectively.
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Problem: A compound cylinder is formed by shrinking a tube of 250 mm inside diameter and 300 mm
outside diameter onto another smaller tube of 200 mm inside diameter and 250 mm outside
diameter
(nominal
dimensions).
Both
tubes
are
manufactured
from
steel.
The
interference
pressure at the junction is 10 MPa. If the compound cylinder is then subjected to an internal
pressure of 80 MPa, calculate the hoop stress distribution and shrinkage/ interference allowance.
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Problem:
A compound tube is made by shrinking one tube of 100 mm internal diameter and 25 mm wall thickness on to
another tube of 100 mm external diameter and 25 mm wall thickness. The shrinkage allowance, based on radius, is
0.01 mm. If both tubes are of steel (with E = 208 GN/m2), calculate the radial pressure set up at the junction owing
to shrinkage.
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The tube (a) is subjected to internal pressure past its elastic limit (b), leaving an inner layer of compressively
stressed metal (c).
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