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PROBLEM (9.73) Determine the normal stress at points A, B, D, and E of the tube seen in Fig.
P9.71,which has a constant t = 10-mm thickness.
Given: d = 50 mm, P = 150 kN
SOLUTION
See Figure S9.71 (Solution of Prob. 9.71).
We now have,
kNPmmdmmt 1505010
=
==
mkNPMmkNPM yz
⋅
=
=
⋅== 302.05.705.0
Therefore,
23
104.4)80(120)100(140 mmA ×=−=
33 64
1[100(140) 80(120) ] 11.35 10
12
y
I
mm=−=×
33 64
1[140(100) 120(80) ] 6.55 10
12
z
I
mm=−=×
Then
yz
xyz
Mz
M
yP
AI I
σ
=− ± ±
yields
33 3
36 6
150 10 3 10 (0.07) 7.5 10 (0.05)
4.4 10 11.35 10 6.55 10
A
σ
−− −
×× ×
=− + −
×× ×
MPa85.7225.575.181.34
−
=
−+−=
MPa
B9.10925.575.181.34
−
=
−
−
−=
σ
MPa
D65.4125.575.181.34
−
=
++−=
σ
MPa
E65.425.575.181.34
=
+
−
−=
σ
1
/
1
100%