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Problem 11.23
Given: Two cylinders are slipfitted together to form a composite open cylinder.
Both cylinders are
made of a steel having a yield stress Y=700 MPa. The inner cylinder has inner and outer diameters of
100 and 150+ mm, respectively.
The outer cylinder has inner an outer diameters of 150 and 300 mm ,
respectively.
Find: a) the shrink pressure p
s
and maximum internal pressure p
1
that can be appplied to the cylinder if
it has been designed with a factor of safety of SF = 1.85 for simultaneous initiation of yielding at the
inner radii of the inner and outer cylinders.
Use maximum shearstress criterion of failure.
b) Determine the outer diameter of the inner cylinder required for the design.
E=200 GPa and
ν
=0.29.
Solution:
Note that Units are not used because it interferes with the MathCad solve block for some reason.
a
0.050
:=
b
0.150
:=
c
0.075
:=
P0
:=
SF
1.85
:=
E
200000
:=
ν
0.29
:=
Y
700
:=
Eq. 11.20
σ
rr
ra
,
b
,
p
1
,
p
2
,
()
p
1
a
2
⋅
p
2
b
2
⋅
−
b
2
a
2
−
a
2
b
2
⋅
p
1
p
2
−
⋅
r
2
b
2
a
2
−
⋅
−
⎡
⎢
⎢
⎣
⎤
⎥
⎥
⎦
:=
Eq. 11.21
σ
θθ
,
b
,
p
1
,
p
2
,
p
1
a
2
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This note was uploaded on 01/11/2011 for the course MAE 3040 taught by Professor Mechanicsofsolids during the Spring '10 term at Utah State University.
 Spring '10
 MechanicsofSolids
 Stress

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