sm8 104

_______________________________________________________________________
PROBLEM (*8.104) A cylindrical thick-walled pipe having an inner radius a and outer radius b
is subjected to an internal pressure pi (Fig. P8.101). Determine:
(a) The ratio of the wall thickness to the inner radius, if the internal pressure is one-half of the maximum
tangential stress: pi = ½ ( t
σ
)max .
(b) The increase in inner radius of the pipe, if a = 2 ft, pi =1.2 ksi, E = 30 x 106 psi, and
ν
= 0.3.
*SOLUTION
(a) From Eq. (8.30a),
22
max 22
() 2
t
i
ab
pba
σ
+
==
−, 1.732ba
=
Then
1.732; 0.732
bat ta
aa
+
== =
So
0.732 0.732
ta
aa
==
(b) Using Eq. (8.29), with 2 12 24 .ra in
=
=× = and 1.732 41.57 .ba in
=
=:
22
22
()
i
ap ab
uEb a
ν
+
=+
−
32 2
622
24(1.2 10 ) 24 41.57
(0
.3)
3
2.21(10 ) .in
−
=
30 10 41.57 24
×+
=+
×−
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