Maximum Permissible Load on Tube: Mechanics Problem

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PROBLEM (9.71) The tube shown in Fig. P9.71 is of constant t = 20-mm thickness. Determine the
maximum permissible load P.
Given: d = 30 mm, ( t
σ
)all = 80 MPa, ( c
σ
)all = 120 MPa,
SOLUTION
mmdmmt 3020
=
=
PMPM zy 05.004.0
=
=
33
100(140) 60(100)
12
y
I− =
46
1087.17 mm×=
)60(100)100(140
−
=
A
23
108 mm×=
33
140(100) 100(60)
12
z
I− =
46
1087.9 mm×=
Maximum tensile stress occurs at D:
yz
Dyz
Mz
M
yP
AI I
σ =− + +
666
0.04 (0.07) 0.05 (0.05)
80 10 0.008 17.87 10 9.87 10
PP P
−−
×=− + +
××
PPP 25.0157.0125.01080 3−−−=× ; kNP 7.283
=
Maximum compressive stress is at B:
PPP 25.0157.0125.010120 3−−−=×− ; kNP 6.255
=
Thus,
kNPall 6.255=
x
D
y
M
y
M
z
z
140 m
m
100 mm
P
P
t
Figure S9.71
A
E
B
d