Q.8.5
Two thick walled, closed –ended cylinders of the same dimensions are subjected
to internal and external pressure, respectively. The outer diameter of each is twice the
inner diameter. What is the ratio of the pressures for the following case?(a) The
maximum tangential stress has the same absolute value in each cylinder.(b) The
maximum tangential strain has the same absolute value in each cylinder. Take
3
1
=
n
Solution
:
First, we write the expression for tangential stress for a cylinder subjected to
internal pressure only.
+

=
r
b
a
b
p
a
i
2
2
2
2
2
1
1
.
s
q
Where,
p
i
is the internal pressure applied to the cylinder
a, b are the inner and outer radii of the cylinder respectively.
Now, we substitute b = 2a……….
.as given in the data.
+

=
∴
r
a
a
a
p
a
i
2
2
2
2
2
1
)
2
(
1
)
2
(
.
s
q
+
=
∴
r
a
p
i
2
2
1
4
1
3
s
q
Now, we note that this attains a maximum value at r = a, which is
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 Fall '09
 Law
 Ratio, tangential stress, εθ

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