Structural analysis and design of pipelines

different loadings

internal pressure (operating pressure)

external pressure (hydrostatic pressure of sea)

temperature changes (operating)

bending (construction, spans, upheaval)

concentrated loads (construction, accidents)

impact (accidents)

0.75 m

15 MPa

0.75 m

15 MPa

wall tension

1 m long

=

= (pressure)(area)

= (15 MN/m2)(0.75 m2 )

= 11.25 MN

= 1100 tonnes

vertical equilibrium of half pipe and half contentsresultant force must be zero

D

p

po

i

i

Do

t t

D

p

po

i

i

Do

t t

D

ps

i

Do

t t

H

i

po

sH

iiHoo DptsDp =+ 2

vertical equilibrium of unit length

p D s t p D

sp D p D

ts

o o H i i

Hi i o o

H

+ =

=−

2

2

rearrange

exact for mean value of

D/tt

tDpps

t

Dps

st

DpDps

ooiH

iH

H

ooiiH

of valueslfor typica small are sdifference

1996) (DnV 2

))((

(Barlow) 2

variants

of mean valuefor exact 2

−−=

=

−=

design

most codes require that the hoop stress is less than a prescribed fraction f1 of the yield stress Y

s f YH ≤ 1

stressUY

0.005 strain

f1Y

f1 is called the design factor (usage factor)

historically f1 was taken as 0.72 for pipelines, 0.60 or less for risers

those factors date back 70 years, to a time when standards of design, pipe manufacture, welding and construction were far inferior to today

recent thinking is that higher factors to and above 0.8 can be applied (provided that the governing code allows that change)

rearrange

Do is 762 mm (30 inches), pi is 20 MPa (200 bars, 2900 psi) po is 2 MPa (20 bars, 290.1 psi) Y is 413.7 MPa (N/mm2) (60000 psi,

X60), f1 is 0.83, t > 18.87 mm (0.743 inches)

)(2

)(2

)2(

2

1

00

01

i

i

ooiooiiH

pYf

Dppt

t

DptDp

t

DpDpsYf

+−≥

−−=−=≥

example

12 1 +

−

≥

oi pp

YfD

t

DnV 1996 formula

rearrange

D is 762 mm (30 inches), pi is 20 MPa (200 bars, 2900 psi) po is 2 MPa (20 bars, 290.1 psi) Y is 413.7 MPa (N/mm2) (60000 psi,

X60), f1 is 0.83, t > 19.46 mm (0.766 inches)

t

tDppsYf oi

H 2

))((1

−−=≥

s p pD D

D DpH i o

o i

o io= − +

−−( )

2 2

2 2

exact for linear elastic material, even for thick-walled tube

Lamé formula

allowed by some codes

Lamé formula

design

t Do= − −

12

1 14β

β = + +−

2 1 1f Y p

p po

i o

where

with the same values as in the previous example

t = 19.37 mm (0.763 inches)(compare with 18.87 mm from exact equation for mean stress, and 19.46 mm from DnV 1996)

p pp t

li eb

SC m

− ≤ ( )1

γ γ

γSC is a safety class reduction factor, listed in table 5-5 of the rules γm is a material resistance factor, listed in table 5-4

DnV 2000 and 2007 rules adopt a limit state approach

allowable pressure difference (inside – outside) is the burst pressure divided by two factors

where pb is the burst pressure

−−=

3

2

15.1

2,

3

22Min

U

tD

tY

tD

tpb

the burst pressure is

where

Y is the characteristic yield stress (fy in DNV 2007)

U is the characteristic ultimate tensile strength(ft in DNV 2007); Y governs if U > 1.15Y

stressUY

0.005 strain

−+

=

15.1,Min

3

2

)(

21

UY

pp

Dt

elimSCγγ

continuing the example, and taking

γsc 1.138 (safety class normal)γm 1.15Y 413.7 MPa (60000 psi)U >1.15Y (so that Y governs)

minimum wall thickness is 18.34 mm (0.722 inch)

(rearrange)

9092949698

100102104106

400 450 500 550 600

SMYS (MPa)

% c

ost (

refe

rred

to g

rade

48

3 ba

se c

ase)

120 bars

80 bars

high-strength steels

TransCanada (TCPL) started using grade 483 (X70) 30 years ago, now has 6300 kmstarted using grade 550 (X80) in 1991, now has 400 kmnow introducing grade 690 (X100), 1 km installed in 2002

project cost reduction by higher grades and higher operating pressure

external pressure

complex interaction between elastic circumferential bending, plastic circumferential bending and initial out-of-roundness

DnV 2007 clause 5D 401

ptRgpppppp YecrYecr )/(2))(( 22 =−−

pecr = 2E/(D/t)3(1-ν2) is the pressure at which the pipe would collapse if it remained elastic and yield did not occur

pY = 2Yαfab /(D/t) is the pressure at which the hoop stress would reach αfabY in compression if the pipe remained round and elastic instability did not occur

g is the out of roundness (max-min)/mean diameter, and >0.005αfab is a fabrication factor, 1 for seamless, 0.85 for UOE

p is the collapse pressure (and must be smaller than the smaller of pecr

and pY)

The DNV 2007 notation is slightly different

α β αβ α α3 5 3 2 1 0( / ) ( / ) ( )( / )D t D t g D t− − + + =

where

α

β ν

=

= −

p

Y

Y

E

2

1 2( )

which is a quintic in D/t

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05

p/2Y

D/t

g=0.01

g=0.02

g=0.03

0 0 0 0 0 0 0

5

3

10

1 1

0123456

0 to5

5 to10

10to15

15to20

20to25

25to30

30to35

35to40

40to45

45to50

50to55

55to60

60to65

collapse pressure (MPa)

num

ber

of te

sts

calculated

alternatively

API RP1111

pp p

p p

ecr Y

ecr Y

=+2 2

which does not include out-of-roundness, but for reasonable values of g gives about the same collapse pressure as DnV 2000

sL

sH

hoop stress sH is statically determinate

longitudinal stress sL is not statically determinate, and depends on whether the pipeline moves longitudinally

quantify

idealise pipeline as thin-walled tube, radius R, wall thicknesst

elastic modulus E

Poisson’s ratio ν

thermal expansion coefficientα

operating temperature rise θ (operating - installation)

operating pressure p

Rt

material elastic, isotropic;

stress and strain tensile positive

general relationship for longitudinal strain

εν

αθLL Hs

E

s

E= − +

longitudinal hoop thermal

θαν

ε

Et

pRs

tpRtpDs

L

H

L

−=

===

then

on)idealisati (thin wall /2/and

0if

εν

αθLL Hs

E

s

E= − +

longitudinal hoop thermal

s longitudinalL

hoopsH

Y

Y

von Mises yield condition for biaxial combined stress

s longitudinalL

hoopsH

Y

Y

von Mises yield condition for biaxial combined stress

pressure

temperature

s longitudinalL

hoopsH

Y

Y

von Mises yield condition for biaxial combined stress

pressure +temperature

L

H

some older codes impose a second limit on a von Misesequivalent stress that includes both sH and sL

(sH2 - sHsL + sL

2)1/2 = seqvM < f3Y

s

s

0

5

10

15

20

25

0 50 100 150

temperature rise (deg C)

req

uir

ed w

all

thic

knes

s (m

m)

equivalent stresscondition

hoop stresscondition

example

OD 323.85 mm (nominal 12 inch), operating pressure 20 MPa (200 bars, 2900 psi), X60, no temperature derating of yield stress

the equivalent stress condition governs the design of constrained high-temperature pipelines, and leads to a big increase in wall thickness

recent thinking is that this condition is not necessary

some plastic strain occurs, but it is limited in magnitude and does not lead to instability or rupture

wall thickness can then be reduced

allowable-strain design permitted by ANSI B31.4, DnV 1996, DnV 2000, DnV 2007, BS 8010 Part 3, NEN3650, CSA Z662

safeguards:

limit magnitude of plastic strain

do not apply to large D/t (< 60 for BS8010, <45 for DnV 2007)

make sure welds have adequate ductility

take account of reduced flexural rigidity

curvature

bending moment

first yield

buckling

curvature localises

1

2

bending buckling

0.000

0.010

0.020

0.030

0.040

0 10 20 30 40 50 60

D/t

bu

cklin

g s

trai

n

tests

DNV (no pressure, alphafactors 1)

comparison between data and DNV formula (DNV 2007 5D 608) for buckling strain

external pressure reducesthe critical curvature at which pipe buckles

internal pressure increasesthe critical curvature at which pipe buckles

if bending and large external pressure occur together, another phenomenon becomes important

2/5

6

=R

tYpprop

propagation is initiated by a combination of bending and pressure

once started, the buckle can propagate at a lower pressure

propagation pressure is minimum pressure at which a buckle can continue to propagate

proportional to t5/2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 10 20 30 40 50

D/t

p/Y data

DNV formula (afab = 1)

comparison between data and DNV formula (DNV 2007 5D 501) for propagation pressure

alternative strategies to deal with buckle propagation

one

increase wall thickness so that

propagation pressure > maximum external pressure

two

accept possibility of propagation over short distances, but incorporate buckle arresters, so that buckle runs to arresters on either side and then stops

Sleeve arresterIntegral arrester

Ring arrester

Wierzbicki analysis

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50

deflection (mm)

inde

ntat

ion

forc

e (M

N)

theory

measured812.8 mm (32-inch), 19.05 mm wall, X65

impact

need to know when a missile will rupture a pipe

tests by Neilsen (AEA Winfrith)

U

D

t

d

for flat-ended missiles, the missile kinetic energy at which the pipe is just perforated is

3

50751751

kJ/mm 00560.cY

DdcYtE ...

=

= −

for schedule 40

pointed missiles perforate at lower energiesliquid-filled pipes perforate at lower energies

0

20

40

60

80

100

0 50 100 150 200

impact energy (kJ)

redu

ctio

n in

ID (

mm

)

on sand

on steel

1 23

8

7

6

54