80 mm
D
o
= ?
Problem 11.19
Given:
A closed cylinder is made of a ductile steel that has a
yield stress Y = 600 MPa.
The inside diameter of the cylinder
is 80 mm.
Determine the outside diameter of the cylinder if the
cylinder is subjected to an internal pressure of p
1
= 140 MPa
and the cylinder is designed using a factor of safety of SF =
1.75 based on the maximum shearstress criterion of failure.
Solution:
a
80 mm
⋅
2
:=
p
1
140 MPa
⋅
:=
p
2
0 MPa
⋅
:=
P0
:=
SF
1.75
:=
Y
600 MPa
⋅
:=
Using Eq. 11.20 at at r=a gives:
σ
rr
p
1
−
140
−
MPa
⋅
=
:=
Assume that
σ
rr
σ
zz
<
σ
θθ
<
so that
SF
Y
2
σ
θθ
σ
rr
−
2
⎛
⎜
⎝
⎞
⎟
⎠
=
Y
σ
θθ
σ
rr
−
()
=
Thus:
σ
θθ
Y
SF
σ
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 Spring '10
 MechanicsofSolids
 Stress, MPa, σzz, 80 mm, σθθ

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