sm9 11

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PROBLEM (9.11) A thin-walled cylindrical tank of radius r and thickness t is subjected to an
internal pressure p, axial compression P , and a torque T applied to the tank through the rigid end plates
(Fig. P9.11). Calculate the maximum principal stress in the cylinder wall.
Given: d = 10 in, t = 0.2 in., p = 400 ksi, P = 5 kips, T = 250 kip⋅in.
SOLUTION
2dr=
2Art
π
=
y
σ
y
3
2Jrt
π
=
Stresses are:
2
xPpr
At
σ =− +
50.4(5)
4.2 ksi
2 (5)(0.2) 2(0.2)
π
=− + =
0.4(5) 10
0.2
ypr ksi
t
σ == =
22
250 7.96
2 2 (5) (0.2)
xy Tr T ksi
Jrt
τππ =− =− =− =−
Maximum principal stress is then
22
14.2 10 4.2 10
( ) ( 7.96) 15.57
22 ksi
σ
+−
=+ +−=
x
σ
x
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