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Problem 11.4
a=100 mm
b=250 mm
p
1
=80 Mpa
p2=0
Given: A long closed cylinder has an internal
radius a = 100 mm and an external radisu b =
250 mm.
It is subjected to an internal
pressure p
1
= 80 MPa (p
2
= 0).
Find: the maximum radial, circumferential, and
axial stresses in the cylinder.
a
100 mm
⋅
:=
b
250 mm
⋅
:=
p
1
80 MPa
⋅
:=
p
2
0
:=
P0
:=
Eq. 11.20, 11.21, and 11.22
σ
rr
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
−
()
⋅
−
=
σ
zz
p
1
a
2
⋅
p
2
b
2
⋅
−
b
2
a
2
−
P
π
b
2
⋅
a
2
−
+
=
σ
θθ
p
1
a
2
⋅
p
2
b
2
⋅
−
b
2
a
2
−
a
2
b
2
⋅
r
2
b
2
a
2
−
()
⋅
p
1
p
2
−
()
⋅
+
=
Using p
2
= 0 and P=0 we get:
σ
rr
r
()
p
1
a
2
⋅
b
2
a
2
−
1
b
2
r
2
−
⎛
⎜
⎝
⎞
⎟
⎠
⋅
:=
σ
θθ
r
()
p
1
a
2
⋅
b
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Unformatted text preview: b 2 a 2 − 1 b 2 r 2 + ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ := σ zz r ( ) p 1 a 2 ⋅ b 2 a 2 − := The maximum stresses occur at r=a. σ rr a ( ) 80 − MPa ⋅ = σ θθ a ( ) 110.476 MPa ⋅ = σ zz a ( ) 15.238 MPa ⋅ = Defining a range variable for the radius: r a a 1 mm ⋅ + , b .. := then we can plot the stresses. 0.1 0.15 0.2 1 − 10 8 × 5 − 10 7 × 5 10 7 × 1 10 8 × 1.5 10 8 × σ rr r ( ) σ θθ r ( ) σ zz r ( ) r...
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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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