09 - Mechanical Design - Press
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Transcript of 09 - Mechanical Design - Press
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Shawn Kenny, Ph.D., P.Eng.Assistant Professor
Faculty of Engineering and Applied ScienceMemorial University of [email protected]
ENGI 8673 Subsea Pipeline
Engineering
Lecture 09: Mechanical Design PressureContainment: Part 2
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2 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Update Available DNV OS & RP
Educational Purposes Only
DNV OS-F101 Submarine Pipeline Systems DNV-RP-C205 Environmental Conditions and
Environmental Loads
DNV-RP-F105 Free Spanning Pipelines DNV-RP-F109 On-bottom Stability Design of
Submarine Pipelines
DNV-RP-F111 Interference between TrawlGear and Pipelines
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Lecture 09 Objective
To examine mechanical behaviour for
pressure containment of thick-walledpipelines
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4 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Pi
Pe
Thick-Walled Cylinders
Characteristics Through thickness (radial) variation of stress
Valid for D/t 20 t 0.10 inner pipe radius
Theory of Elasticity Lam Formula
Force equilibrium
- relationships
Compatibility equation -
relationships
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5 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Symmetry
No shear stress
Equilibrium equation
- relationship
0rr rd
Fdr r
+ + =
0r =
1 1, ,r r
du dv u dv du v
dr r d r dr r d r
= = + = +
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6 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Open End & Unconstrained
z = 0 Hookes law
( )1
r r
du
dr E
= =
0r =
( )1
r
u
r E
= =
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7 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Rearranging and Equating
Substitute intoForce Equilibrium
( )2 21 1r rE E du u
dr r
= + = +
( )2 21 1rE E u du
r dr
= + = +
0rr rd
Fdr r
+ + =
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8 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Equilibrium Equation of Motion
Radial and Tangential
Stress Equations
2
2 2
10
d u du u
dr r dr r + =2
1
c
Solution u c r r = +
( )1 22 21
11
r
Ec c
r
= +
( )1 22 21
11
Ec c
r
= + +
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9 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Constant Longitudinal Strain
plane sectionsremain plane
( )1 22 21
11rE
c c r
= +
( )1 22 21
11
Ec c
r
= + +
12
1r
Ec
+ =
( ) constantz rE
= + =
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Thick-Walled Cylinders (cont.)
Recall Open End and
Unconstrained Cylinder
c3 = z = 0
Substitute PressureBoundary Conditions
( ) ( )2 232 0b
zar dr c b a = =
2 2
1 2 21 i ea p b p c
E b a =
( )2 22 2 2
1 i ea b p p c
E b a
+=
a
bPi
Pe
Pi
Pe
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11 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Lam Equations
( )( )
2 22 2
2 2 2 2 2
i ei er
p p a b a p b p b a b a r
=
( )
( )
2 22 2
2 2 2 2 2
i ei ep p a b a p b p
b a b a r
= +
( ) ( )( )
2 2 2 2
2 2 2 2
1 1i e i ea p b p r p p a b uE b a E b a r
+= +
( )
( )
2 2
max 2 2 22
i erp p a b
b a r
= =
Conditions for largest max
?
a
bPi
Pe
Pi
Pe
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12 ENGI 8673 Subsea Pipeline Engineering Lecture 09 2008 S. Kenny, Ph.D., P.Eng.
Thick-Walled Cylinders (cont.)
Principal Stresses
r,
max on 45
Pressure to
Initiate Yielding(Tension)
a
bPi
Pe
Pi
Pe
max2
y =
( )2 22
2
y
y
b ap
b
=
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Hoop Stress Comparison
Through
Thickness
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Example 9-01
Calculate the minimum wall thickness using thin wall theory,Barlows equation and Lam equation using the outside diameter Do = 0.762; Pi = 20MPa; Pe = 2MPa; = 0.80
E = 205GPa; y = 448MPa; = 0.3
Thin wall theory tmin = 18.0mm
Barlow tmin = 21.2mm
Lam tmin = 19.1mm2
2
1 1 0
2 1 y eo o
i e
ttpD D
p p
+ =
+ +
( )min
2
i e o
y i
p p Dt
p
+
min2
i o
y
p Dt
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References
Ugural, A.C. and Fenster, S.K. (2003).
Advanced Strength and Applied Elasticity,4th Edition, Prentice Hall, 544p.
