sm8 101

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PROBLEM (8.101) A thick-walled, closed-ended cylinder of inner radius a and outer radius b is
subjected to an internal pressure p only (Fig. P8.101). The cylinder is made of a material with
permissible tensile strength all
σ
and shear strength all
τ
. Calculate the allowable value of pi.
Given: a = 0.8 m, b = 1.2 m, all
σ
= 100 MPa, all
τ
= 60 MPa
SOLUTION
Axial Stress, Eq. (8.32):
22
22 2 2
0.8 0.8 100
1.2 0.8
ii
ai
pa p p
ba
σ == ==
−− , 125
i
p
MPa
=
Tangential stress, Eq. (8.30a):
22 2 2
max 22 2 2
1.2 0.8
( ) 2.6 100
1.2 0.8
tii
ba
ppp
ba
σ
++
== ==
−− i
, 38.5
i
p
MPa=
Shear Stress, Eq. (8.31b):
22
max 22 2 2
1.2 60
1.2 0.8
ii
pb p
ba
τ == =
−−
Solving
33.3
iall
p
MPa p==
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