sm8 103

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PROBLEM (8.103) A thick-walled cylindrical tank of inner radius a and outer radius b is made of
ASTM A-48 cast iron (see Table B.4) having an ultimate strength in tension u
σ
, modulus of elastcity
E, and Poisson’s ratio of
ν
. Determine the maximum radial displacement of the tank, if it is subjected to
an internal pressure of pi , as shown in Fig. P8.101.
Given: a = 0.5 m, b = 1 m, pi = 10 MPa, u
σ
= 170 MPa, E = 70 GPa,
ν
= 0.3
SOLUTION
The maximum radial displacement occurs at the inner edge of the tank.
max
u
So, Eq. (8.29) for r=a, results in
22
max 22
()
i
ap ab
uEba
ν
+
== +
−
Introducing the given data
22
max 922
(0.5) 0.5 1.0
(0
.3)
70(10 ) 1.0 0.5
u+ =+
−
3
0.14(10 ) 0.14mmm
−
==
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