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© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
ThinWalled Pressure Vessels
Cylindrical
pressure vessel
Spherical
pressure vessel
© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
ThinWalled Pressure Vessels
Assume
:
Thinwalled
pressure vessels.
•
t
< 0.1
r
•S
t
r
e
s
s
is approximately
constant across
the thickness of the wall.
Assume
:
Weight
of vessel and contents is
negligible
(compared to stresses).
t
r
e
s
s
is approximately
constant around
the tank and from end to end.
© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
Cylindrical Pressure Vessel
xy
σ
≠
x
=
a
axial stress
or
meridional stress
However,
y
=
h
hoop stress
τ
xy
= 0
nx
≠
0
nt
≠
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© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
Cylindrical Vessels (cont)
Cut tank on “meridional” plane
(without letting the gas pressure escape!)
(
)
(
)
2
20
a
rt
p
r
σ
ππ
−=
0:
x
F
→=
∑
2
a
pr
t
=
© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
Cylindrical Vessels (cont)
Cut segment from side of tank on “meridional”
and “axial” planes (without letting the gas
pressure escape!)
x
F
∑
()()
22
0
h
Lt
p
rL
h
pr
t
=
In a cylindrical tank, the hoop stress is equal to
twice the axial stress.
© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
Spherical Pressure Vessel
x
=
y
=
n
meridional stress
τ
xy
=
nt
= 0
Because of symmetry of
loading and geometry,
the normal stress is the
same in every direction.
3
© 20022003, L.D. Sturges
EM 324
Mechanics of Materials
Spherical Vessels (cont)
Cut tank in half (without letting
the gas pressure escape!)
(
)
(
)
2
20
a
rt
p
r
σ
ππ
−=
0:
x
F
→=
∑
2
a
pr
t
=
The stress in a spherical pressure tank is the
same as the axial stress in a cylindrical tank.
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This note was uploaded on 03/27/2008 for the course EM 324 taught by Professor Boylan during the Spring '08 term at Iowa State.
 Spring '08
 Boylan

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