sm9 47

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PROBLEM (9.47) A closed-ended cylinder of r = 6 in. radius and t = ½ in. wall thickness
is subjected to an internal pressure of p = 500 psi and an eccentricity e = 4-in. off-center axial
load P (Fig. P9.47). Determine the largest permissible value of P if ( t
σ
)all = 6 ksi and ( c
σ
)all
= 4.2 ksi.
SOLUTION
B
P 1 m
2Art
π
=
22
p
rPMc
tAI
σ =+−
p
r
t
1 m
12
p
rPMc
tAI
σ =++
3
22JrtI π
=
=
4 in.
A
P
t
2
r
A
B
We have
500(6) 3 0.053
22(0.5) 2(6)(0.5)
pr P P
ksi P
tA
π
== = =
3
(4)(6.5) 0.077
(6.0) (0.5)
Mc P P
I
π
==
Tension at A:
33
6 10 3 10 0.053 0.077, 23.08PP×=×+ + = kips
ips
ips
Compression at B:
33
4.2 10 3 10 0.053 0.0779 , 300PPPk−× =× + − =
Thus,
23.08
all
Pk=
Since 10rt≥, cylinder is thin-walled:
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