daftar pustaka - institut teknologi...

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Daftar Pustaka

1. Bai, Yong. 2001. “Pipelines and Risers”. Amsterdam: Elsevier Science.

2. Dalrymple, Dean. 1991. “Water Wave Mechanics for Engineers and Scientist”. New Jersey: World

Scientific.

3. Ellenberger, Philip. 2005. “Piping Systems & Pipeline”. McGraw‐Hill Profesional Engineering.

4. Guo, Boyun. 2005. “Offshore Pipelines”. Massachussets: Elsevier Inc.

5. Heryanto, Julius. 2008. “Desain dan Analisis Struktur Pipa Bawah Laut”. Institut Teknologi Bandung.

6. McAllister, E.W.. 2002. “Pipeline Rules of Thumb Handbook”. Gulf Profesional Publishing.

7. Mouselli, A.H. 1985. “Offshore Pipelines Design, Analysis, and Method”. Oklahoma: Penn Well

Books.

8. Nakazawa, Kazuto. 1980. “Soil Mechanic and Foundation Engineering”. Pradnya Paramitha.

9. Palmer, Andrew C. and King, Roger A. 2004. “Subsea Pipeline Engineering”. PennWell Corporation.

10. Sam Kannappan, P.E. 1985. “Pipe Stress Analysis”. John Wiley & Sons.

11. Veritas Offshore Technology and Services A/S. April 1981. “DNV 1981 Rules for Submarine Pipelines

Systems”. Norway: DNV Publisher.

12. Veritas Offshore Technology and Services A/S. March 2002. “DNV RP F105 Free Spanning Pipelines”.

Norway: DNV Publisher.

13. Veritas Offshore Technology and Services A/S. August 2005. “DNV RP E305 On‐Bottom Stability

Design of Submarine Pipelines ”. Norway: DNV Publisher.

DESIGN DATA

Pipe OD , d = inches= mm

Concrete grade = kg/cm2

Tensile strength of steel , fy = kg/cm2

Density of concrete = kg/m3

Density of soil , γ = kg/m3

Angle of friction , φ = 0 Backfill materialφ 0 = 0 original soil

Cohession of soil, Ca = kg/m2 original soil

Fx = kgFy = kgFz = kgMx = kgmMy = kgmM

0

30.0

32.00812.8

2400

1754200

1800

200

radians0.520.61=35.0

= radians

2.150

00

20

4957

PERENCANAAN PIPA DAN EXPANSION SPOOL PADA PIPA PENYALUR SPM

ANCHOR BLOCK CALCULATION

Mz = kgm= m H2 = m

Assumed length of concrete block , L1 = m L2 = m= m

Depth of pipe from top of concrete , db = mDepth of pipe from top of soil , hp = m

Hence volume of concrete block = m3

Volume due to pipe = m3

Hence effective volume of concrete block = -= m3

PLAN

SECTION X-X SETION Z-Z

2.7

L1

H1

0.41

Assumed total height of concrete block , H1

0.41

hp

1.00

0.800.80

centre line of pipe - X

1.102.40

0

H2centre line of pipe

B

Assumed total width of concrete block , B

B

2.00

2.72

0.40

2.31

L2

Z

db

L2

H1



Total block weight , W = m3 x kg/m3

W = kg

Total soil weight above the block , Ws = (( B x L ) x ( hp - db ) + (L2-L1) x ( hp - db + H1 )) x γ

Ws = kg

CHECK FOR UPLIFT

Vertical uplift force from pipe, Fv = ( Fy + sqrt (( Mx/B)2 + (Mz/L)2))

= kg

Factor of safety against uplift = /

= > Hence OK

PASSIVE EARTH PRESSURE

Pp = γ x H x Kp

553.2278

10.00

5760

2400

5532

0 2

2.0

10.00

55322.305

where , Kp = ( 1 - sin φ ) / ( 1 + sin φ ) =

Pp = γ x (hp-db+H2) x Kp

= kg/cm2

Fp = 0.5 x Pp x (B x H2 - 0.25 x pi x OD^2)= kg

CHECK FOR SLIDING

Coefficient of friction , μ 0 = tan ( φ0 ) =

Resistance to sliding = ( 0.7 x Ca x ( L2 x B ) + ( μ0 x ( W + Ws - Fy ))

= ( x x ( x x )

= kg

Factor of safety against sliding = ( Resistance to sliding ) / {(sqrt ( Fx2 + Fz

2 )) - Fp }

= /

= > Hence OK

CHECK FOR OVERTUNING

Height of centre of pipe from base , Hm = m

Overtuning moment due to pipe load = ( sqrt (Fx2 + Fz

2 ) x Hm ) + My

= kgm

Stabilizing moment due to block weight & passive pressure is given as= ((W - Fy ) x (L2 - x) )

= kgm

Factor of safety against overtuning = /

= > Hence OK

20

13550.73

6586.8

4259.98

697

6586.80

1.546

9.311

1.5

0.7

829

11292.32.40 2.00 ) + (

0.58

0.58

0.27

1455.375

2.0

13550.73

0.29

1455



x

I

0.80

1.11

m

1.10

0.90

0.41

0.221.20

X V *X

y

V*Y

0.80

=

0.70 1.5361.728

2 21.11

x1 y1 =3.2642 2

= 1.20 m=

2.40

1.44 1.20 0.15

x1

2.72

1.28V Y

3.264

y1

CHECK FOR BEARING CAPACITY

Ultimate Bearing capacity = t/m2

Actual bearing pressure = ( W - Fy ) / ( area of bottom anchor block )

= t/m2 < Ultimate Bearing capacity

REINFORCEMENT

Reinforcement Data :fy = t/m2 Dia. of bar = = cm2

fc' = t/m2 fy rebar = t/m2

Shear Check :

Effect. thickness of conc. block t = m

Shear Force Vu = tVu

Vc = 0.85 x 0.53 x fc'0.5 x B x d = t Vu < Vc OK !

- Concrete block rebar :

Ld = ( L1 - .075 ) = m

= of gross section area

b' = m (analysis per 1 m width)

= 0.15% * Ld * b' = cm2/m

Rebar : D16mm - mm

m0.412.72

x1 y12.72

1.20 m

0.725

L1

4.957

27.33

10.88

0.15% L2

150

Amin

Amin

Hence OK

0.73

3.46

2.4 D16mm 1.986

1

hf

H1

1750 42000

15



- Punching Shear :

Vc = bo * d * [ φ * ( 0.34 ) * sqrt( fc' ) ]

bo = 2 * [(a + d) + b ] = m

d = hf - cover = m

Vc = MN Vu = V = MN

Thickness of footing slab is OK

- Flexture Rebar for footing slab :

fmax = t/m2

s1 = (L2-L1)/2 = m

Mu = 1/2 * fmax * s12

= t.m

b' = m (analysis per 1 m width)

hf

6.05

==

fmax

s1

L2

0 0028

L1 + d

15.000

1.629

* [ 1 sqrt( 1 2 * R / ( 0 85 * f ' ) ) ]

0.030

L1

0.8

>

0.225

= 111 5470.85 * fc't/ 2

1

R =Mu

4.800

ρuse = As = ρuse * d * b' = cm2/m

Rebar : D16mm - mm

== 0.0028* [ 1 - sqrt( 1 - 2 Ru / ( 0.85 fc ) ) ]

0.013fy (MN/m2) fy 600 + fy

( β ) * 600 =0.75 *0.85 * fc' *

1.4=

= 111.547φ * b' * d2 fy

0.003401 7.653

200

ρmin = 0.003401 ρmax =

ct/m2 ρRu =

BUCKLING AND COLLAPSEDURING INSTALLATION

Condition : Installation stage is assumed as the most critical time that buckling andcollapse could occur. At installation stage, there is no internal pressure tocounteract hydrostatic head. Pressure design is assumed as zero pressure, socalculation will produce a conservative result.

K = C

INPUT DATA:

Maximum Water Depth dmax 81.2ft:=

Minimum Water Depth dmin 0ft:= *

Seawater Density ρsw 64lb

ft3

:=

Maximum External Pressure Pe_max ρsw g⋅ dmax⋅:=

Pe_max 36.089 psi=

Minimum External Pressure Pe_min ρsw g⋅ dmin⋅:= *Pe_min 0=

Outside Diameter D 32in:=

Wall Thickness t 0.45in:=

Internal Diameter ID D 2t−:= *ID 31.1 in=

Material Grade : API 5L X‐52

Spesified Minimum Yield Stress SMYS 52000psi:=

Steel Density ρs 490.1lb

ft3

:=

Poissons Ratio υ 0.3:=

Modulus Elasticity E 3.01 107psi⋅:= *

Coefficient of Thermal Expansion α 1.17 105−

⋅ C1−

:= *Permissible Usage Factor ηxp 0.96:=

Permissible Usage Factor ηyp 0.82:=

Operating Data :

Design Pressure Pd 0psi:= *Contain Density ρcont 0lb ft

3−⋅:= *

Max. Operating Temp Ti 82.222C:=

Installation temp Tins 25C:=

CALCULATIONS:

Axial Stress

Axial Stress Due To End Effect σend Pd

π

4ID2

π D2ID2−( )⋅

4

⋅:= *

σend 0=

Axial Stress Due To Poisson Effect σpoissons υ−Pd ID⋅ Pe_min D⋅−

2t⎛⎜⎝

⎞⎟⎠

⋅:= *

σpoissons 0=

Longitudinal / axial strain byinternal pressure σp σend σpoissons+:= *

σp 0=

Thermal stress

σt E α⋅ Ti Tins−( )⋅:= * σt 2.015 104

× psi=

Total Axial Stress σtot σp σt+:= *σtot 2.015 10

4× psi=

Buckling Check :

Longitudinal StressDue To Axial Component σx_N σtot:=

σx_N 2.015 104

× psi=Longitudinal StressDue To Moment σx_M 0psi:= *Longitudinal Stress σx σx_N σx_M+:= *

σx 2.015 104

× psi=

Critical Longitudinal Stress (N Act Alone)

σxcrn_N SMYSD

t20<if

SMYS 1 0.001D

t20−⎛⎜

⎝⎞⎟⎠

−⎡⎢⎣

⎤⎥⎦

⋅ 20D

t< 100<if

:= *

σxcrn_N 4.934 104

× psi=

σxcr_M SMYS 1.35 0.0045D

t⋅−⎛⎜

⎝⎞⎟⎠

⋅:= * σxcr_M 5.356 104

× psi=

Critical Longitudinal Stress

σxcrσx_N

σxσxcrn_N⋅

σx_M

σxσxcr_M⋅+:= *

σxcr 4.934 104

× psi=

Hoop Stress σyPd Pe_max−

2 t⋅D⋅:=

σy 1.283− 103

× psi=

Hoop Stress Elastic σyE Et

D t−⎛⎜⎝

⎞⎟⎠

2⋅:= *

σyE 6.123 103

× psi=Critical Hoop Stress

σycr σyE σyE2

3SMYS⋅≤if

SMYS 11

3

2SMYS

3 σyE⋅⎛⎜⎝

⎞⎟⎠

2⋅−

⎡⎢⎣

⎤⎥⎦

⋅2

3

σyE

SMYS<if

:= *

σycr 6.123 103

× psi=

α 1300

D

t

σy

σycr⋅⎛

⎜⎜⎝

⎞⎟⎟⎠

+:= α 0.116=

ifσx

ηxp σxcr⋅⎛⎜⎝

⎞⎟⎠

ασy

ηyp σycr⋅+

⎡⎢⎣

⎤⎥⎦

1≤ "OK", "Need More Thickness",⎡⎢⎣

⎤⎥⎦

"OK"=

σx

ηxp σxcr⋅⎛⎜⎝

⎞⎟⎠

ασy

ηyp σycr⋅+

⎡⎢⎣

⎤⎥⎦

0.65= "OK, karena ratio nya < 1"

Propagation Buckling Check :

Ppr π1.15SMYSt

D t−⎛⎜⎝

⎞⎟⎠

2⋅:= * Ppr 38.219 psi=

Pe_max 36.089 psi= "OK, karena Ppr > Pe_max"

kPe_max

1.15πSMYS:= k 0.014=

Minimum Wall Thickness Due To Propagating Pressure

tnomk D⋅

1 k+:= tnom 0.437 in=

Collapse Pressure Check :

Cit

D⎛⎜⎝

⎞⎟⎠

32 E⋅

1 υ2

−

⎛⎜⎝

⎞⎟⎠

⋅:= * Ci 183.968 psi=

Constant of the quadratic equation are:

a 1:=

b 2SMYSt

D⋅ 1 0.03

D

t⋅+⎛⎜

⎝⎞⎟⎠Ci+⎡⎢

⎣⎤⎥⎦

−:= * b 2.039− 103

× psi=

c 2SMYSt

D⋅ Ci⋅:= * c 5.775 10

12×

lb2

ft2s4

⋅=

Det b2

4 a⋅ c⋅−:= Det 1.755 103

× psi=

x1b− Det+

2 a⋅:= x1 1.897 10

3× psi=

x2b− Det−

2a:= x2 141.823 psi=

Critical Collapse Pressure Is The Least Positif Root, Therefore

Pcr x1 x1 x2<if

x2 otherwise

:=Pcr 141.823 psi=

Pe_max 36.089 psi=

if Pcr Pe_max≤ "more thickness", "OK",( ) "OK"=

Safety Factor AgainstPressure Collapse SF

Pcr

Pe_max:=

SF 3.93= "OK, karena safety yangdidapatkan sangat besar"

"Digunakan wall thickness setebal 0.45 inch. Hal ini dikarenakan, saat memakai wallthickness sebesar 0.336 inch (hasil dari perhitungan akibat pressure containment),struktur pipa tidak kuat terhadap buckling."

FREE SPAN CALCULATIONDURING HYDROTEST PHASE

Equivalent ConditionPhase : HydrotestWave & Current Data : 1 year return period wave and current

pcflb

ft3

:=

INPUT DATA :

Pipeline Properties :

Outer Diameter

Wall Thickness

Corrosion Coating Thickness

Corrosion Coating Density

Concrete Coating Density

Content Density

Steel Density

Concrete Coating Thickness

Design Pressure

Structural Damping

Modulus Elasticity

SMYS

D 32in:=

t 0.45in:=

tcorr 0.125in:=

ρcorr 87.4pcf:=

ρcc 189.8pcf:=

ρcont 64pcf:=

ρst 490.1pcf:=

tcc 3in:=

Po 403.75psi:=

δ 0.126:=

E 3 107psi⋅:=

SMYS 52000psi:=

Environmental Parameter :

Hs 2.1m:=Significant Wave Height

Tp 11.01sec:=Spectral Peak Period

d 20m:=Water Depth

Ur 0.62ft sec1−

⋅:=Seabed Steady Current Velocity

Zr 2m:=

Seawater Density ρsw 64pcf:=

Kinematic Viscosity of Seawater ν 1.03 105−

⋅ ft2sec

1−⋅:=

Angle Between Wave Direction And Pipeline Direction φwave 90deg:=

Angle Between Current Direction And Pipeline Direction φcurr 90deg:=

CALCULATION :

Effective Weight :

This section calculates provided weight by pipeline properties section

Total Outside Diameter Dcc D 2tcorr+ 2tcc+:=

Dcc 38.25in=

Internal Diameter ID D 2t−:=

ID 31.1 in=

Corrosion Coating Diameter Dcorr D 2tcorr+:=

Dcorr 32.25in=

Steel Weight Wst 0.25π D2

ID2

−( )⋅ ρst⋅:=

Wst 151.804lb

ft=

Corrosion Coating Weight Wcorr 0.25π Dcorr2

D2

−( )⋅ ρcorr⋅:=

Wcorr 7.657lb

ft=

Concrete Coating Weight Wcc 0.25π Dcc2

Dcorr2

−( )⋅ ρcc⋅:=

Wcc 437.889lb

ft=

Content Weight Wcont 0.25π ID2

⋅ ρcont⋅:=

Wcont 337.62lb

ft=

Buoyancy B 0.25π Dcc2

⋅ ρsw⋅:=

B 510.705lb

ft=

Effective Weight Weff Wst Wcorr+ Wcc+ Wcont+ B+:=

Weff 1.446 103

×lb

ft=

External Pressure Pe ρsw g⋅ d⋅:=

Pe 29.163 psi=

Pressure Difference ΔP Po Pe−:=

ΔP 374.587 psi=

Elastic Modulus EI Eπ64

D4

ID4

−( )⋅⎡⎢⎣

⎤⎥⎦

⋅:=

EI 3.721 1010

×lb ft

3⋅

s2

=

Inertia Iπ64

D4

ID4

−( )⋅⎡⎢⎣

⎤⎥⎦

:=

I 0.268 ft4

=

Hydrodynamic Force Acting On Pipeline :

Minimum Required Submerged Weight Calculation According To DNV RP E305

Natural Period Parameter AccordingTo DNV RP E305 Figure 2.2 Tn

d

g:=

Tn 1.428 s=

Tn

Tp0.13= φ

Tp

Hs:= φ 7.598

s

m0.5

=

Peakness Parameter γ 5 φ 3.6s

m0.5

≤if

1 φ 5s

m0.5

≥if

3.3 otherwise

:=

γ 1=

Assuming There's No Reduction For Directional And Spreading Factor R = 1, Us* = Us

Wave Induced Current Velocity Perpendicular To The Pipe According To DNV RP E305Figure 2.1

Us0.01 Hs⋅

Tn:= Us 0.015

m

s=

Zero Up Crossing Period According To DNV RP E305 Figure 2.2

Tu 1.35 Tp⋅:= Tu 14.864 s=

From The Soil Parameter Data

Roughness Zo 5.21 106−

⋅ m:=

A1Dcc

Zo:= A1 1.865 10

5×=

B1Zo

Dcc:= B1 5.363 10

6−×=

Average Velocity To Reference Velocity Ratio

Ud1

lnZr

Zo1+⎛⎜

⎝⎞⎟⎠

1 B1+( ) ln A1 1+( )⋅ 1−⎡⎣ ⎤⎦⋅⎡⎢⎢⎣

⎤⎥⎥⎦

Ur⋅:=

Ud 0.164m

s=

Significant Acceleration As 2πUs

Tu:=

As 6.216 103−

×m

s2

=

Using Simplified Static Stability Method According To DNV RP E305

Current To Wave Velocity Ratio MUd

Us:= M 11.13=

Keulegan Carpenter Number KCUs Tu⋅Dcc

:= KC 0.225=

REUd Us+( ) Dcc⋅

ν:= RE 1.811 10

5×=

Hidrodynamic Force Coefficients

Drag Coefficient CD 1.2 RE 3 105−

⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=

Lift Coefficient CL 0.9:=

Inertia Coefficient CM 3.29:=

Hydrodynamic Forces

Phase Angle Range i 0 90..:=

θi i deg⋅:=

Drag Force FD θ( ) 0.5ρswg

Dcc⋅ CD⋅ Us cos θ( )⋅ Ud+( ) 2⋅:=

Inertia Force FI θ( ) 0.25ρswg

π⋅ Dcc2

⋅ CM⋅ As⋅ sin θ( )⋅:=

Fw max FD θ( ) FI θ( )+( ):= Fw 1.711lb

ft= Fh Fw

2:=

0 20 40 60 80 1001

1.5

2

2.5

3

FD θ( ) FI θ( )+

θdeg

Dynamic Free Span :

Stability Number Ks2 Weff⋅ δ⋅

ρsw Dcc2

⋅:=

Ks 0.56=

Weff value can be changed depend on operation/installation phase (full/empty) + addedmass

In Line Analysis

Reduced Velocity According To DNV 1981 Graphic A.3 Vr 1.85:=

Note:

Con1 "In Line Oscillation":=

Con2 "Cross Flow Oscillation":=

Type of Oscillation Otype Con1 1 Vr< 3.5< Ks 1.8<∧if

Con2 otherwise

:=

Otype "In Line Oscillation"=

Strouhal Number According To DNV 1981 Graphic A.2 St 0.2:=

Vortex Shedding Frequency fvSt Ud Us+( )⋅

Dcc:=

fv 0.037Hz=

Condition At Both Ends of Span (Pinned To Pinned) C1 9.87:=

Critical Pipe Span Length LcrC1

2π

EI

Weff⋅ Dcc⋅

Vr

Us Ud+⋅:=

Lcr 86.372m=

Cross Flow Analysis

Reduced Velocity (Onset) According To DNV 1981 Graphic A.5 VrC1 4.9:=

LcrC1C1

2π

EI

Weff⋅ Dcc⋅

VrC1

Us Ud+⋅:=

LcrC1 140.568m=

Reduced Velocity (Peak) According To DNV 1981 Graphic A.5 VrC2 5.8:=

LcrC2C1

2π

EI

Weff⋅ Dcc⋅

VrC2

Us Ud+⋅:=

LcrC2 152.934m=

Static Free Span :

C2 8:=

Hoop Stress σhPo Pe− D⋅

2 t⋅:=

σh 1.332 104

× psi=

Yield Requirement

j 1 100..:= Lj j m⋅:=

Longitudinal Stress (End Cap Effect) σepσh2

:=

σep 6.659 103

× psi=

Total Longitudinal Stress

σx L( ) Weff B−( ) 2 Fh+⎡⎣

⎤⎦ L

2⋅ D⋅ g⋅

2 C2⋅ I⋅

⎡⎢⎣

⎤⎥⎦

σep+⎡⎢⎣

⎤⎥⎦

:=

0 20 40 60 80 1000

1 .105

2 .105

3 .105

4 .105

5 .105

σx L( )

psi

L

m

Allowable Stress (%)

Limiting Longitudinal Stress σxa L( ) 0.8SMYS:=

σxa L( ) 4.16 104

× psi=

Lcrit L( ) L 1m←

Lcrit L 1m−←

L L 1m+←

σx L 1m−( ) σxa L( )<while

Lcrit

:=

Lcrit L( ) 28m=

von Mises σe σx Lcrit L( )( ) 2 σh2

+:=

σe 4.289 104

× psi=

Limiting Equivalent Stress σxe L( ) 0.9SMYS:=

σxe L( ) 4.68 104

× psi=

if σe σxe L( )≤ "OK!", "Reduce The Length of Allowable Free Span",( ) "OK!"=

SUMMARY :

Critical Pipe Span Due To VIV In‐Line (Dynamic) Lcr 86.372m=

Critical Pipe Span Due To Cross‐Flow (Dynamic) LcrC1 140.568m=

Critical Pipe Span Due To Static Analysis Lcrit L( ) 28m=

FREE SPAN CALCULATIONDURING INSTALLATION PHASE

Equivalent ConditionPhase : InstallationWave & Current Data : 1 year return period wave and current

pcflb

ft3

:=

INPUT DATA :


Outer Diameter

Wall Thickness




Content Density

Steel Density


Design Pressure

Structural Damping

Modulus Elasticity

SMYS

D 32in:=

t 0.45in:=

tcorr 0.125in:=

ρcorr 87.4pcf:=

ρcc 189.8pcf:=

ρcont 0pcf:=

ρst 490.1pcf:=

tcc 3in:=

Po 0psi:=

δ 0.126:=

E 3 107psi⋅:=

SMYS 52000psi:=




d 20m:=Water Depth

Ur 0.62ft sec1−


Zr 2m:=



⋅ ft2sec

1−⋅:=



CALCULATION :

Effective Weight :



Dcc 38.25in=


ID 31.1 in=


Dcorr 32.25in=


ID2

−( )⋅ ρst⋅:=

Wst 151.804lb

ft=


D2

−( )⋅ ρcorr⋅:=

Wcorr 7.657lb

ft=


Dcorr2

−( )⋅ ρcc⋅:=

Wcc 437.889lb

ft=


⋅ ρcont⋅:=

Wcont 0=


⋅ ρsw⋅:=

B 510.705lb

ft=


Weff 1.108 103

×lb

ft=


Pe 29.163 psi=


ΔP 29.163 psi=


D4

ID4

−( )⋅⎡⎢⎣

⎤⎥⎦

⋅:=

EI 3.721 1010

×lb ft

3⋅

s2

=

Inertia Iπ64

D4

ID4

−( )⋅⎡⎢⎣

⎤⎥⎦

:=

I 0.268 ft4

=




d

g:=

Tn 1.428 s=

Tn

Tp0.13= φ

Tp

Hs:= φ 7.598

s

m0.5

=


m0.5

≤if

1 φ 5s

m0.5

≥if

3.3 otherwise

:=

γ 1=



Us0.01 Hs⋅

Tn:= Us 0.015

m

s=


Tu 1.35 Tp⋅:= Tu 14.864 s=



⋅ m:=

A1Dcc

Zo:= A1 1.865 10

5×=

B1Zo

Dcc:= B1 5.363 10

6−×=


Ud1

lnZr

Zo1+⎛⎜

⎝⎞⎟⎠

1 B1+( ) ln A1 1+( )⋅ 1−⎡⎣ ⎤⎦⋅⎡⎢⎢⎣

⎤⎥⎥⎦

Ur⋅:=

Ud 0.164m

s=


Tu:=

As 6.216 103−

×m

s2

=



Us:= M 11.13=


:= KC 0.225=

REUd Us+( ) Dcc⋅

ν:= RE 1.811 10

5×=



⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=



Hydrodynamic Forces


θi i deg⋅:=


Dcc⋅ CD⋅ Us cos θ( )⋅ Ud+( ) 2⋅:=


π⋅ Dcc2

⋅ CM⋅ As⋅ sin θ( )⋅:=


ft= Fh Fw

2:=

0 20 40 60 80 1001

1.5

2

2.5

3

FD θ( ) FI θ( )+kg

m

θdeg

Dynamic Free Span :


ρsw Dcc2

⋅:=

Ks 0.429=


In Line Analysis


Note:




Con2 otherwise

:=




Dcc:=

fv 0.037Hz=



2π

EI

Weff⋅ Dcc⋅

Vr

Us Ud+⋅:=

Lcr 88.489m=

Cross Flow Analysis


LcrC1C1

2π

EI

Weff⋅ Dcc⋅

VrC1

Us Ud+⋅:=

LcrC1 150.233m=


LcrC2C1

2π

EI

Weff⋅ Dcc⋅

VrC2

Us Ud+⋅:=

LcrC2 163.448m=

Static Free Span :

C2 8:=


2 t⋅:=

σh 1.037 103

× psi=

Yield Requirement

j 1 100..:= Lj j m⋅:=


:=

σep 518.454 psi=


σx L( ) Weff B−( ) 2 Fh+⎡⎣

⎤⎦ L

2⋅ D⋅ g⋅

2 C2⋅ I⋅

⎡⎢⎣

⎤⎥⎦

σep+⎡⎢⎣

⎤⎥⎦

:=

0 20 40 60 80 1000

5.5 .104

1.1 .105

1.65 .105

2.2 .105

2.75 .105

σx L( )

psi

L

m



σxa L( ) 4.16 104

× psi=

Lcrit L( ) L 1m←

Lcrit L 1m−←

L L 1m+←


Lcrit

:=

Lcrit L( ) 38m=


+:=

σe 4.068 104

× psi=


σxe L( ) 4.68 104

× psi=


SUMMARY :




FREE SPAN CALCULATIONDURING OPERATION PHASE

Equivalent ConditionPhase : OperationWave & Current Data : 100 year return period wave and current

pcflb

ft3

:=

INPUT DATA :


Outer Diameter

Wall Thickness




Content Density

Steel Density


Design Pressure

Structural Damping

Modulus Elasticity

SMYS

D 32in:=

t 0.45in:=

tcorr 0.125in:=

ρcorr 87.4pcf:=

ρcc 189.8pcf:=

ρcont 54pcf:=

ρst 490.1pcf:=

tcc 3in:=

Po 323psi:=

δ 0.126:=

E 3 107psi⋅:=

SMYS 52000psi:=




d 20m:=Water Depth

Ur 1.27ft sec1−


Zr 2m:=



⋅ ft2sec

1−⋅:=



CALCULATION :

Effective Weight :



Dcc 38.25in=


ID 31.1 in=


Dcorr 32.25in=


ID2

−( )⋅ ρst⋅:=

Wst 151.804lb

ft=


D2

−( )⋅ ρcorr⋅:=

Wcorr 7.657lb

ft=


Dcorr2

−( )⋅ ρcc⋅:=

Wcc 437.889lb

ft=


⋅ ρcont⋅:=

Wcont 284.867lb

ft=


⋅ ρsw⋅:=

B 510.705lb

ft=


Weff 1.393 103

×lb

ft=


Pe 29.163 psi=


ΔP 293.837 psi=


D4

ID4

−( )⋅⎡⎢⎣

⎤⎥⎦

⋅:=

EI 3.721 1010

×lb ft

3⋅

s2

=

Inertia Iπ64

D4

ID4

−( )⋅⎡⎢⎣

⎤⎥⎦

:=

I 0.268 ft4

=Hydrodynamic Force Acting On Pipeline :



d

g:=

Tn 1.428 s=

Tn

Tp0.094= φ

Tp

Hs:= φ 4.542

s

m0.5

=


m0.5

≤if

1 φ 5s

m0.5

≥if

3.3 otherwise

:=

γ 3.3=



Us0.02 Hs⋅

Tn:= Us 0.157

m

s=


Tu 1.25 Tp⋅:= Tu 19 s=



⋅ m:=

A1Dcc

Zo:= A1 1.865 10

5×=

B1Zo

Dcc:= B1 5.363 10

6−×=


Ud1

lnZr

Zo1+⎛⎜

⎝⎞⎟⎠

1 B1+( ) ln A1 1+( )⋅ 1−⎡⎣ ⎤⎦⋅⎡⎢⎢⎣

⎤⎥⎥⎦

Ur⋅:=

Ud 0.335m

s=


Tu:=

As 0.052m

s2

=



Us:= M 2.137=


:= KC 3.067=

REUd Us+( ) Dcc⋅

ν:= RE 4.996 10

5×=



⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=



Hydrodynamic Forces


θi i deg⋅:=


Dcc⋅ CD⋅ Us cos θ( )⋅ Ud+( ) 2⋅:=


π⋅ Dcc2

⋅ CM⋅ As⋅ sin θ( )⋅:=


ft= Fh Fw

2:=

0 20 40 60 80 1005

10

15

20

FD θ( ) FI θ( )+

θdeg

Dynamic Free Span :


ρsw Dcc2

⋅:=

Ks 0.54=


In Line Analysis


Note:




Con2 otherwise

:=




Dcc:=

fv 0.114Hz=



2π

EI

Weff⋅ Dcc⋅

Vr

Us Ud+⋅:=

Lcr 50.313m=

Cross Flow Analysis


LcrC1C1

2π

EI

Weff⋅ Dcc⋅

VrC1

Us Ud+⋅:=

LcrC1 83.658m=


LcrC2C1

2π

EI

Weff⋅ Dcc⋅

VrC2

Us Ud+⋅:=

LcrC2 92.532m=

Static Free Span :

C2 8:=


2 t⋅:=

σh 1.045 104

× psi=

Yield Requirement

j 1 100..:= Lj j m⋅:=


:=

σep 5.224 103

× psi=


σx L( ) Weff B−( ) 2 Fh+⎡⎣

⎤⎦ L

2⋅ D⋅ g⋅

2 C2⋅ I⋅

⎡⎢⎣

⎤⎥⎦

σep+⎡⎢⎣

⎤⎥⎦

:=

0 20 40 60 80 1000

1 .109

2 .109

3 .109

σx L( )

L

m



σxa L( ) 4.16 104

× psi=

Lcrit L( ) L 1m←

Lcrit L 1m−←

L L 1m+←


Lcrit

:=

Lcrit L( ) 29m=


+:=

σe 4.111 104

× psi=


σxe L( ) 4.68 104

× psi=


SUMMARY :




ON-BOTTOM STABILITY CALCULATIONDURING INSTALLATION PHASE

Equivalent ConditionPhase : InstallationWave & Current Data : 1 year return period wave and current

pcflb

ft3

:=

INPUT DATA :


Outer Diameter

Wall Thickness




Content Density

Steel Density


D 32in:=

t 0.45in:=

tcorr 0.125in:=

ρcorr 87.4pcf:=

ρcc 189.8pcf:=

ρcont 0pcf:=

ρst 490.1pcf:=

tcc 3in:=

Environmental Parameter :Hs 2.2m:=Significant Wave HeightTp 11.01sec:=Spectral Peak Periodd 20m:=Water DepthUr 0.62ft sec

1−⋅:=Seabed Steady Current Velocity

Zr 2m:=


Kinematic Viscosity of Seawater ν 1.03 10 5−⋅ ft

2sec

1−⋅:=



CALCULATIONS :

Submerged Weight :



Dcc 38.25 in=


ID 31.1 in=


Dcorr 32.25 in=


ID2

−( )⋅ ρst⋅:=

Wst 225.91kg

m=


D2

−( )⋅ ρcorr⋅:=

Wcorr 11.395kg

m=


Dcorr2

−( )⋅ ρcc⋅:=

Wcc 651.651kg

m=


⋅ ρcont⋅:=

Wcont 0=


⋅ ρsw⋅:=

B 760.013kg

m=

Submerged Weight Wsub Wst Wcorr+ Wcc+ Wcont+ B−:=

Wsub 128.942kg

m=

Vertical Stability :

Specific Gravity VSWsub B+

B:= VS 1.1≥

VS 1.17=

if VS 1.1< "Need More Thickness", "OK!",( ) "OK!"=




d

g:=

Tn 1.428 s=

Tn

Tp0.13= φ

Tp

Hs:= φ 7.423

s

m0.5

=


m0.5

≤if

1 φ 5s

m0.5

≥if

3.3 otherwise

:=

γ 1=


Wave Induced Current Velocity Perpendicular To The Pipe According To DNV RP E305 Figure 2.1

Us0.01 Hs⋅

Tn:= Us 0.015

m

s=


Tu 1.35 Tp⋅:= Tu 14.864 s=


Roughness Zo 5.21 10 6−⋅ m:=

A1Dcc

Zo:= A1 1.865 105

×=

B1Zo

Dcc:= B1 5.363 10 6−

×=


Ud1

lnZr

Zo1+⎛⎜

⎝⎞⎟⎠

1 B1+( ) ln A1 1+( )⋅ 1−⎡⎣ ⎤⎦⋅⎡⎢⎢⎣

⎤⎥⎥⎦

Ur⋅:=

Ud 0.164m

s=


Tu:=

As 6.512 10 3−×

m

s2

=



Us:= M 10.624=

Keulegan Carpenter Number KCUs Tu⋅

Dcc:= KC 0.236=

REUd Us+( ) Dcc⋅

ν:= RE 1.818 105

×=


Drag Coefficient CD 1.2 RE 3 10 5−⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=



Soil Friction Coefficient

Soil Type: Sand

μ 0.7:=

Calibration Factor According To DNV RP E305 Figure 5.12

M 10.624=

KC 0.236=

Fw 1:=

Hydrodynamic Forces vs Required Submerged Weight :


θ i i deg⋅:=

Lift Force FL θ( ) 0.5ρsw

gDcc⋅ CL⋅ Us cos θ( )⋅ Ud+( )2⋅:=

Drag Force FD θ( ) 0.5ρsw

gDcc⋅ CD⋅ Us cos θ( )⋅ Ud+( )2⋅:=

Inertia Force FI θ( ) 0.25ρsw

gπ⋅ Dcc

2⋅ CM⋅ As⋅ sin θ( )⋅:=

Required Submerged Weight Ws θ( ) FwFD θ( ) FI θ( )+ μ FL θ( )⋅+

μ⎛⎜⎝

⎞⎟⎠

⋅:=

0 20 40 60 80 1002

2.5

3

3.5

Ws θ( )lb

ft

θdeg

Wreq max Ws θ( )( ):=

Wreq 5.007kg

m= Wsub 128.942

kg

m=

if Wsub Wreq≤ "Need More Thickness", "OK!",( ) "OK!"=

Safety Factor For Submerged Weight Due To Requirement Weight

SFwWsub

Wreq:= SFw 25.752=

ON-BOTTOM STABILITY CALCULATIONDURING OPERATION CORRODED PHASE

Equivalent ConditionPhase : Operation CorrodedWave & Current Data : 100 year return period wave and current

pcflb

ft3

:=

INPUT DATA :


Outer Diameter

Wall Thickness




Content Density

Steel Density


Corrosion Allowance

D 32in:=

t 0.45in:=

tcorr 0.125in:=

ρcorr 87.4pcf:=

ρcc 189.8pcf:=

ρcont 54pcf:=

ρst 490.1pcf:=

tcc 3in:=

ca 0.125in:=

CA 0.7 ca⋅:=

Environmental Parameter :Hs 11.2m:=Significant Wave HeightTp 15.2sec:=Spectral Peak Periodd 20m:=Water Depth

Seabed Steady Current Velocity Ur 1.27ft sec1−

⋅:=

Zr 2m:=



2sec

1−⋅:=



CALCULATION :

Submerged Weight :


Total Outside Diameter Dcc D 2tcorr+ 2tcc+:=Dcc 38.25 in=

Internal Diameter ID D 2t− 2 CA⋅+:=ID 31.275 in=

Corrosion Coating Diameter Dcorr D 2tcorr+:=Dcorr 32.25 in=


ID2

−( )⋅ ρst⋅:=

Wst 182.487kg

m=


D2

−( )⋅ ρcorr⋅:=

Wcorr 11.395kg

m=


Dcorr2

−( )⋅ ρcc⋅:=

Wcc 651.651kg

m=


⋅ ρcont⋅:=

Wcont 428.713kg

m=


⋅ ρsw⋅:=

B 760.013kg

m=


Wsub 514.233kg

m=



B:= VS 1.1≥

VS 1.677=





d

g:=

Tn 1.428 s=

Tn

Tp0.094= φ

Tp

Hs:= φ 4.542

s

m0.5

=


m0.5

≤if

1 φ 5s

m0.5

≥if

3.3 otherwise

:=

γ 3.3=



Us0.02 Hs⋅

Tn:= Us 0.157

m

s=


Tu 1.25 Tp⋅:= Tu 19 s=



A1Dcc

Zo:= A1 1.865 105

×=

B1Zo

Dcc:= B1 5.363 10 6−

×=


Ud1

lnZr

Zo1+⎛⎜

⎝⎞⎟⎠

1 B1+( ) ln A1 1+( )⋅ 1−⎡⎣ ⎤⎦⋅⎡⎢⎢⎣

⎤⎥⎥⎦

Ur⋅:=

Ud 0.335m

s=


Tu:=

As 0.052m

s2

=



Us:= M 2.137=


Dcc:= KC 3.067=

REUd Us+( ) Dcc⋅

ν:= RE 4.996 105

×=



0.7 otherwise

:=

CD 0.7=



Soil Friction Coefficient According To Soil Properties Data

Soil Type: Sand

μ 0.7:=


M 2.137=

KC 3.067=

Fw 1:=

Hydrodynamic Forces And Required Submerged Weight


θ i i deg⋅:=






gπ⋅ Dcc

2⋅ CM⋅ As⋅ sin θ( )⋅:=


μ⎛⎜⎝

⎞⎟⎠

⋅:=

Plot Submerged Weight vs Phase Angle

0 20 40 60 80 10014

16

18

20

22

24

Ws θ( )lb

ft

θdeg


Wreq 32.925kg

m= Wsub 514.233

kg

m=



SFwWsub

Wreq:= SFw 15.618=

ON-BOTTOM STABILITY CALCULATIONDURING OPERATION PHASE

Equivalent ConditionPhase : OperationWave & Current Data : 100 year return period wave and current

pcflb

ft3

:=

INPUT DATA :


Outer Diameter

Wall Thickness




Content Density

Steel Density


D 32in:=

t 0.45in:=

tcorr 0.125in:=

ρcorr 87.4pcf:=

ρcc 189.8pcf:=

ρcont 54pcf:=

ρst 490.1pcf:=

tcc 3in:=

Environmental Parameter :Hs 11.2m:=Significant Wave HeightTp 15.2sec:=Spectral Peak Periodd 20m:=Water DepthUr 1.27ft sec

1−⋅:=Seabed Steady Current Velocity

Zr 2m:=



2sec

1−⋅:=



CALCULATIONS :

Submerged Weight :



Dcc 38.25 in=


ID 31.1 in=


Dcorr 32.25 in=


ID2

−( )⋅ ρst⋅:=

Wst 225.91kg

m=


D2

−( )⋅ ρcorr⋅:=

Wcorr 11.395kg

m=


Dcorr2

−( )⋅ ρcc⋅:=

Wcc 651.651kg

m=


⋅ ρcont⋅:=

Wcont 423.929kg

m=


⋅ ρsw⋅:=

B 760.013kg

m=


Wsub 552.87kg

m=



B:= VS 1.1≥

VS 1.727=





d

g:=

Tn 1.428 s=

Tn

Tp0.094= φ

Tp

Hs:= φ 4.542

s

m0.5

=


m0.5

≤if

1 φ 5s

m0.5

≥if

3.3 otherwise

:=

γ 3.3=



Us0.01 Hs⋅

Tn:= Us 0.078

m

s=


Tu 1.35 Tp⋅:= Tu 20.52 s=



A1Dcc

Zo:= A1 1.865 105

×=

B1Zo

Dcc:= B1 5.363 10 6−

×=


Ud1

lnZr

Zo1+⎛⎜

⎝⎞⎟⎠

1 B1+( ) ln A1 1+( )⋅ 1−⎡⎣ ⎤⎦⋅⎡⎢⎢⎣

⎤⎥⎥⎦

Ur⋅:=

Ud 0.335m

s=


Tu:=

As 0.024m

s2

=



Us:= M 4.275=


Dcc:= KC 1.656=

REUd Us+( ) Dcc⋅

ν:= RE 4.2 105

×=



0.7 otherwise

:=

CD 0.7=



Soil Friction Coefficient

Soil Type: Sand

μ 0.7:=


M 4.275=

KC 1.656=

Fw 1:=

Hydrodynamic Forces vs Required Submerged Weight :


θ i i deg⋅:=






gπ⋅ Dcc

2⋅ CM⋅ As⋅ sin θ( )⋅:=


μ⎛⎜⎝

⎞⎟⎠

⋅:=

0 20 40 60 80 10011

12

13

14

15

Ws θ( )lb

ft

θdeg


Wreq 21.12kg

m= Wsub 552.87

kg

m=



SFwWsub

Wreq:= SFw 26.177=

WALL THICKNESS CALCULATIONDURING HYDROTEST CONDITION

DATA INPUT:

Nominal Water Depth (MSL) dnom 65.6ft:=

Highest Astronomical Tide HAT 12.5ft:=

Storm Surge (1 year) SS 0ft:=

Maximum Wave Height Hmax 6.2ft:=

Maximum Water Depth dmax dnom HAT+ SS+Hmax

2+:=

dmax 81.2 ft=

Minimum Water Depth dmin 0ft:=

Usage Factor (according to DNV 81Section 4 Table 4.1)

ηh_1 0.72:=

ηh_2 0.5:=

Gravity g 32.174ft

s2

=

Temperatur Derating Faktor kt 1:=


ft3

:=


Pe_max 36.089 psi=

Minimum External Presure Pe_min ρsw g⋅ dmin⋅:=

Pe_min 0=

Pressure Design (hidrotes) Pd 403.75psi:=


Corrosion Allowance CA 0.125in:=

Tsweet 0.7 CA⋅:=

Material API 5L X‐52


Modulus Elasticity E 3.01 107

× psi:=

CALCULATIONS:

1. Standard DNV 81

Zone 1

Minimum Req. Wall Thickness tDNV_1Pd Pe_min−( ) D⋅

2 ηh_1⋅ SMYS⋅ kt⋅:=

tDNV_1 0.173 in=

Nominal Wall Thickness tnom_1_DNV_sw tDNV_1 Tsweet+:=

tnom_1_DNV_sw 0.26 in=

Zone 2tDNV_2

Pd Pe_min−( ) D⋅

2 ηh_2⋅ SMYS⋅ kt⋅:=Minimum Req. Wall Thickness

tDNV_2 0.248 in=



2. STANDARD ASME B31.8

Longitudinal Joint Factor E1 1:=

S1 0.72 E1⋅ SMYS⋅:= S1 3.744 104

× psi=

Design Hoop Stress

Minimum Wall Thickness tASMEPd D⋅

2 S1⋅:= tASME 0.173 in=

Nominal Wall Thickness tnom_ASME_sw tASME Tsweet+:=

tnom_ASME_sw 0.26 in=

SUMMARY AND CONCLUSION:

DNV 81

Zone 1 tnom_1_DNV_sw 0.26 in=


ASME B31.8


WALL THICKNESS CALCULATIONDURING INSTALLATION CONDITION

DATA INPUT:






2+:=

dmax 81.2 ft=



ηh_1 0.72:=

ηh_2 0.5:=

Gravity g 32.174ft

s2

=



ft3

:=


Pe_max 36.089 psi=


Pe_min 0=

Pressure Design (hidrotes) Pd 323psi:=



Tsweet 0.7 CA⋅:=




× psi:=

CALCULATIONS:

1. Standard DNV 81

Zone 1



tDNV_1 0.138 in=



Zone 2tDNV_2



tDNV_2 0.199 in=





S1 0.72 E1⋅ SMYS⋅:= S1 3.744 104

× psi=

Design Hoop Stress


2 S1⋅:= tASME 0.138 in=




DNV 81



ASME B31.8


WALL THICKNESS CALCULATIONDURING OPERATION CONDITION

DATA INPUT:






2+:=

dmax 83.7 ft=



ηh_1 0.72:=

ηh_2 0.5:=

Gravity g 32.174ft

s2

=



ft3

:=


Pe_max 37.2 psi=


Pe_min 0=

Pressure Design (hidrotes) Pd 323psi:=



Tsweet 0.7 CA⋅:=




× psi:=

CALCULATIONS:

1. Standard DNV 81

Zone 1



tDNV_1 0.138 in=



Zone 2tDNV_2



tDNV_2 0.199 in=





S1 0.72 E1⋅ SMYS⋅:= S1 3.744 104

× psi=

Design Hoop Stress


2 S1⋅:= tASME 0.138 in=




DNV 81



ASME B31.8


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