Problem 11.11
Given:
A composite aluminum alloy (E = 72 GPa and
ν
=
0.33) cylinder is made up of an inner cylinder with inner
an outer diameters of 80 and 120+ mm, respectively, and
an outer cylinder with inner and outer diameters of 120
and 240 mm, respectively.
The composite cylinder is
subjected to an internal pressure of 160 MPa.
What
must the outside diameter of the inner cylinder be if the
circumferential stress at the inside of the composite
cylinder is equal to 130 MPa.
Solution:
a
80 mm
⋅
2
:=
b
240 mm
⋅
2
:=
c
120 mm
⋅
2
:=
p
1
160 MPa
⋅
:=
p
2
0 MPa
⋅
:=
P0
:=
Using Eq. 11.21, evaluate
σ
θθ
for the One Piece Solution (OPS) at at r=a:
σ
θθ
OPS
p
1
a
2
⋅
p
2
b
2
⋅
−
b
2
a
2
−
a
2
b
2
⋅
a
2
b
2
a
2
−
()
⋅
p
1
p
2
−
⋅
+
200 MPa
⋅
=
:=
The total stress is computed from:
σ
θθ
Total
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 Spring '10
 MechanicsofSolids
 MPa, inner cylinder

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