Road Crossing (Highway)

Prepared by Youngtae Kim, P.E.

E-mail address: evergrowkim@gmail.com

This calculation provides design of buried pipeline for crossing highways or roads. The calculation was performed accordint to the reference [1].

Reference[1] API Recommended Practice 1102, Steel Pipelines Crossing Railroads and Highways , American Petroleum Institute, Washington, D.C.

Input data

Design parameters

Fluid type ≔Fluid “Natural Gas”

Operating pressure ≔p 9310 kPa

Installation temperature ≔T1 25 C

Maximum temperature ≔T2 85 C

Temperature derating factor ≔T “N/A”

Depth of burial ≔H 1800 mm

Design factor ≔F 0.6

Crossing type ≔Crossing “Open Cut”(Open Cut, Bored)

Pipe properties

Nominal outside diameter ≔D 762 mm

Wall thickness ≔wt 13.9 mm

Grade

SMYS ≔SMYS 448 MPa

Bored diameter

≔Bd

|

if

else if

else

＝Crossing “Open Cut”‖‖D

＝Crossing “Bored”‖‖ +D 51 mm

‖‖ “Error”

=Bd 762 mm

Longitudinal weld type ≔Weldtype “SMLS”

SMLS, ERW, SAW

page 1/11

Longitudinal weld factor

≔E if

else if

else

∨＝Weldtype “SMLS” ＝Weldtype “ERW”‖‖ 1

＝Weldtype “SAW”‖‖ 0.9

‖‖ “Error”

=E 1

Young's modulus ≔Es 207 GPa

Poisson's ratio ≔ν 0.3

Coeff. thermal expansion ≔α ⋅0.0000117 C−1

Soil properties

Soil density ≔γ ⋅18.1 kN m−3

Soil type ≔Soil “Soft to medium clays and silts, low ot medium plasticities”

Table A.1 Tables of Typical Values [Ref.1, Annex A.1]

Soil_Description

“Soft to medium clays and silts, high plasticities”

“Soft to medium clays and silts, low ot medium plasticities”

“Stiff to very stiff clays and silts”

“Loose sands and gravels”

“Medium dense sands and gravels”

“Dense to very dense sands and gravels”

Eprime

((MPa))

1.4

3.4

6.9

3.4

6.9

13.8

Er

((MPa))

34

34

69

69

69

138

Modulus of soil reaction

≔E' lookup ⎛⎝ ,,Soil Soil_Description Eprime⎞⎠0=E' 3.4 MPa

Resilient modulus

≔Er lookup ⎛⎝ ,,Soil Soil_Description Er⎞⎠0 =Er 34 MPa

Road properties

Single axle Wheel load ≔ps 53.4 kN

Tandem axle wheel load ≔pt 44.50 kN

Wheel load contact area ≔A 0.093 m2

Pavement type≔pave “Flexible”

"Non-Dirt", "Flexible", "Rigid"

page 2/11

Output data

1.0 Allowable Barlow Stress

Operating pressure =p 9.31 MPa

Outer diameter of pipe =D 762 mm

Wall thickness of pipe =wt 13.9 mm

Design factor =F 0.6

Longitudianl joint factor =E 1

Temperature derating factor ≔T if (( ,,＝T “N/A” 1 T))

Specified minimum yield stress =SMYS 448 MPa

LHS of Equation [Ref.1, Eq (8)]

≔LHS ――⋅p D

⋅2 wt=LHS 255.188 MPa

RHS of Equation [Ref.1, Eq (8)]

≔RHS ⋅⋅⋅F E T SMYS =RHS 268.8 MPa

Code check

≔CheckBarlow ||||||

if

else

≤LHS RHS‖‖ “OK”

‖‖ “Not OK”

=CheckBarlow “OK”

2.0 Circumferenctial Stress due to Earth Load

Wall thickness / diameter ≔WtoD =―wt

D0.018

Modulus of soil reaction =E' 3.4 MPa

Soil type

Depth / bored diameter

Excavation factor

Pipe outer diamter

≔KHe (( ,E' r)) |||||||||||||||

|

if

else if

else if

else if

else

＝E' 1.4 MPa‖‖‖ +−+−+−⋅2135428777338 r 6 ⋅626422293797 r 5 ⋅74464325065 r 4 ⋅4630383304 r 3 ⋅161759296 r 2 ⋅3112916 r 27419

＝E' 3.4 MPa‖‖‖ +−+−−+⋅−171895178210 r 6 ⋅45672296715 r 5 ⋅3658564781 r 4 ⋅15402952 r 3 ⋅16170266 r 2 ⋅784602 r 12469

＝E' 6.9 MPa‖‖‖ +−+−+−⋅51414913562 r 6 ⋅7538533859 r 5 ⋅474831992 r 4 ⋅74684102 r 3 ⋅8976558 r 2 ⋅443668 r 8106

＝E' 13.8 MPa‖‖‖ +−+−+−⋅894176204422 r 6 ⋅242587612255 r 5 ⋅25949787583 r 4 ⋅1408204803 r 3 ⋅42302933 r 2 ⋅746819 r 7674

‖‖‖ “Error”

=KHe (( ,E' WtoD)) 3124.713

page 3/11

≔rr , ‥0 0.001 0.08

20003000400050006000700080009000

1000011000

01000

12000

0.02 0.03 0.04 0.05 0.06 0.070 0.01 0.08

rr

KHe (( ,1.4 MPa rr))

KHe (( ,3.4 MPa rr))

KHe (( ,6.9 MPa rr))

KHe (( ,13.8 MPa rr))

Soil type

≔Typesoil ⎛⎝ ,E' Er⎞⎠ ||||||||||||||||

if

else if

else if

else if

else

＝E' 1.4 MPa‖‖‖

if ⎛⎝ ,,＝Er 34 MPa “A” “B”⎞⎠

＝E' 3.4 MPa‖‖‖

if ⎛⎝ ,,＝Er 34 MPa “A” “B”⎞⎠

＝E' 6.9 MPa‖‖‖ “B”

＝E' 13.8 MPa‖‖‖ “B”

‖‖‖ “Error”

≔Typesoil =Typesoil ⎛⎝ ,E' Er⎞⎠ “A”

Depth of Burial / borred diameter ≔HtoD =―H

Bd2.362

Burial factor

≔Be ⎛⎝ ,Typesoil r⎞⎠ ||||||||||

if

else if

else

＝Typesoil “A”‖‖‖ ++−+−+⋅−0.0000000258669 r 6 ⋅0.000003017677 r 5 ⋅0.0001432545 r 4 ⋅0.003581486 r 3 ⋅0.0507431 r 2 ⋅0.396878 r 0.00152735

＝Typesoil “B”‖‖‖ ++−+−+⋅−0.0000000419772 r 6 ⋅0.00000466458 r 5 0.000206857 r 4 ⋅0.00470306 r 3 ⋅0.0586974 r 2 ⋅0.394459 r 0.00891192

‖‖‖ “Error”

=Be ⎛⎝ ,Typesoil HtoD⎞⎠ 0.699

≔rr , ‥0 0.1 32

1

0

0.5

1.5

6 9 12 15 18 21 24 270 3 30

rr

Be (( ,“A” rr))

Be (( ,“B” rr))

page 4/11

Bored diameter / diameter ≔BDtoD =―Bd

D1

Excavation factor

≔Ee ((r))‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||

|

←Ee +−+⋅−1.1111 r 3 ⋅5.2429 r 2 ⋅5.7265 r 2.4259||||||||||

|

if

else

＝Crossing “Open Cut”‖‖‖ 1

‖‖‖‖‖‖‖‖

||||||

if

else

>Ee 1.4‖‖‖ 1.4

‖‖‖ Ee

=Ee ((BDtoD)) 1

Soil density =γ 18.1 ――kN

m3

Outer diameter of pipe =D 762 mm

Circumferential stress at the pipeline invert caused by earth load

≔KHe KHe (( ,E' WtoD))

≔Ee Ee ((BDtoD))

≔Be Be ⎛⎝ ,Typesoil HtoD⎞⎠

≔SHe ⋅⋅⋅⋅KHe Be Ee γ D =SHe 30.118 MPa

page 5/11

3.0 Impact Factor and Applied Design Surface Pressure [Ref.1, 4.7.2.2]

Design axle configuration

≔AxleConfig ⎛⎝ ,,,,H D ps pt pave⎞⎠ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

|

if

else if

else

∧＝ps 53.4 kN ＝pt 44.5 kN‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||

if

else

∧<H 1200 mm ≤D 305 mm‖‖‖‖‖‖‖‖‖‖

|||||||||

if

else if

else if

＝pave “Flexibile”‖‖ “Tandem”

＝pave “Non-dirt”‖‖ “Single”

＝pave “Rigid”‖‖ “Tandem”

‖‖ “Tandem”

∧＝ps 0 kN ＝pt 0 kN‖‖ “Single”

‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||||||||||||||||||||||||||||||

if

else

∧<H 1200 mm ≤D 305 mm‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||||||||||||||||

if

else if

else if

else

＝pave “Flexibile”‖‖‖‖‖‖‖‖‖‖‖

||||||||

|

if

else if

>―ps

pt1.34809

‖‖ “Single”

<―ps

pt1.34809

‖‖ “Tandem”

＝pave “Non-dirt”‖‖‖‖‖‖‖‖‖‖‖

||||||||

|

if

else if

>―ps

pt1.15576

‖‖ “Single”

<―ps

pt1.15576

‖‖ “Tandem”

＝pave “Rigid”‖‖‖‖‖‖‖‖‖‖‖

||||||||

|

if

else if

>―ps

pt1.5656

‖‖ “Single”

<―ps

pt1.5656

‖‖ “Tandem”

‖‖ “Tandem”

‖‖‖‖‖‖‖‖‖‖‖

||||||||

|

if

else if

>―ps

pt1.5718

‖‖ “Single”

<―ps

pt1.5718

‖‖ “Tandem”

≔AxleConfig AxleConfig ⎛⎝ ,,,,H D ps pt pave⎞⎠ =AxleConfig “Tandem”

page 6/11

Impact factor

≔FI ((H)) |||||||||

if

else

≤H 1150 mm‖‖ 1.5

‖‖‖‖‖

―――――

⎛⎜⎝

−―H

m16.535

⎞⎟⎠

−9.99

≔FI =FI ((H)) 1.475

Applied surface pressure

≔w |||||||||

if

else

＝AxleConfig “Single”‖‖‖‖

―ps

A

‖‖‖‖

―pt

A

=w 478.495 ⋅――1

m2kN

4.0 Cyclic Circumferential Stress due to Highway Load

Highway stiffness factor for cyclic circumferential stress [Ref.1, Figure 14]

≔KHh ⎛⎝ ,Er r⎞⎠ |||||||||

|

if

else if

else if

＝Er 34 MPa‖‖‖ −+−+−+−3.2237076 ⋅4638.0648 r ⋅310450.79 r 2 ⋅9107523.6 r 3 ⋅139837400 r 4 ⋅1099231400 r 5 ⋅3495727500 r 6

＝Er 69 MPa‖‖‖ −+−+−+−15.737318 ⋅5526.0815 r ⋅366382.76 r 2 ⋅11397948 r 3 ⋅187956810 r 4 ⋅1581992000 r 5 ⋅5344515500 r 6

＝Er 138 MPa‖‖‖ −+−+−+−6.3340025 ⋅2156.7579 r ⋅106523.74 r 2 ⋅2489665.1 r 3 ⋅32478904 r 4 ⋅230952800 r 5 ⋅703855050 r 6

≔rr , ‥0.01 0.011 0.08

79.512

14.517

19.522

24.5

24.5

27

0.03 0.04 0.05 0.06 0.07 0.080.01 0.02 0.09rr

KHh (( ,34 MPa rr))

KHh (( ,69 MPa rr))

KHh (( ,138 MPa rr))

≔KHh =KHh ⎛⎝ ,Er WtoD⎞⎠ 19.968

≔GHh (( ,H D))‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

|||||||||||||||||||||||||

←D ―D

m||||||||||||||||||||||

if

else if

else if

else if

else

≤≤900 mm H 1200 mm‖‖‖ −+−+−+1.24153 ⋅0.00563546 D ⋅0.0000417 D 2 ⋅1.18948 10 −7 D 3 ⋅⋅1.67785 10 −10 D 4 ⋅⋅1.16317 10 −13 D 5 ⋅3.16416 10 −17 D 6

＝H 1800 mm‖‖‖ −+−+−+0.967184 ⋅0.00379373 D ⋅0.0000249 D 2 ⋅6.42453 10 −8 D 3 ⋅⋅8.47467 10 −11 D 4 ⋅⋅5.62638 10 −14 D 5 ⋅1.49144 10 −17 D 6

＝H 2400 mm‖‖‖ −+−+−+0.7559 ⋅0.002596 D 0.0000155 D 2 ⋅3.88584 10 −8 D 3 ⋅⋅5.11916 10 −11 D 4 ⋅⋅3.42041 10 −14 D 5 ⋅9.12247 10 −18 D 6

＝H 3000 mm‖‖‖ −+−+−+0.60320 ⋅0.0021969 D ⋅0.00001298 D 2 ⋅3.135 10 −8 D 3 ⋅⋅3.8854 10 −11 D 4 ⋅⋅2.3985 10 −14 D 5 ⋅5.819 10 −18 D 6

‖‖‖‖‖‖‖

|||||||

if ∧>H 1200 mm <H 1800 mm‖‖‖‖‖‖

←a −+−+−+1.24153 ⋅0.00563546 D ⋅0.0000417 D 2 ⋅1.18948 10 −7 D 3 ⋅⋅1.67785 10 −10 D 4 ⋅⋅1.16317 10 −13 D 5 ⋅3.16416 10 −17 D 6

←b −+−+−+0.967184 ⋅0.00379373 D ⋅0.0000249 D 2 ⋅6.42453 10 −8 D 3 ⋅⋅8.47467 10 −11 D 4 ⋅⋅5.62638 10 −14 D 5 ⋅1.49144 10 −17 D 6

←aa 1200 mm1800 mm

⎡⎢⎣

⎤⎥⎦

Highway geometry factor for cyclic circumferential stress [Ref.1, Figure 15]

page 7/11

‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

|||||||||||||||||||||||||||||

|

||||||||||||||||||||||||||||||

‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||||||

|

else if

else if

‖‖‖‖‖‖

←aa1800 mm

⎡⎢⎣

⎤⎥⎦

←bb ab

⎡⎢⎣

⎤⎥⎦

linterp (( ,,aa bb H))

∧>H 1800 mm <H 2400 mm‖‖‖‖‖‖‖‖‖‖‖

‖‖‖‖‖‖‖‖‖‖

||||||||

|

←a −+−+−+0.967184 ⋅0.00379373 D ⋅0.0000249 D 2 ⋅6.42453 10 −8 D 3 ⋅⋅8.47467 10 −11 D 4 ⋅⋅5.62638 10 −14 D 5 ⋅1.49144 10 −17 D 6

←b −+−+−+0.7559 ⋅0.002596 D 0.0000155 D 2 ⋅3.88584 10 −8 D 3 ⋅⋅5.11916 10 −11 D 4 ⋅⋅3.42041 10 −14 D 5 ⋅9.12247 10 −18 D 6

←aa 1800 mm2400 mm

⎡⎢⎣

⎤⎥⎦

←bb ab

⎡⎢⎣

⎤⎥⎦

linterp (( ,,aa bb H))

∧>H 2400 mm <H 3000 mm‖‖‖‖‖‖‖‖‖‖‖

‖‖‖‖‖‖‖‖‖‖

||||||||

|

←a −+−+−+0.7559 ⋅0.002596 D 0.0000155 D 2 ⋅3.88584 10 −8 D 3 ⋅⋅5.11916 10 −11 D 4 ⋅⋅3.42041 10 −14 D 5 ⋅9.12247 10 −18 D 6

←b −+−+−+0.60320 ⋅0.0021969 D ⋅0.00001298 D 2 ⋅3.135 10 −8 D 3 ⋅⋅3.8854 10 −11 D 4 ⋅⋅2.3985 10 −14 D 5 ⋅5.819 10 −18 D 6

←aa 2400 mm3000 mm

⎡⎢⎣

⎤⎥⎦

←bb ab

⎡⎢⎣

⎤⎥⎦

linterp (( ,,aa bb H))

≔xx , ‥1 m 2 m 1100 m

0.60.70.80.9

11.11.21.31.41.51.6

0.40.5

1.7

399 598 797 9961 200 1195

0.788

762

GHh (( ,1.2 m xx))

GHh (( ,1.8 m xx))

GHh (( ,2.4 m xx))

GHh (( ,3.0 m xx))

xx ((m))

≔GHh =GHh (( ,H ⋅D 1000)) 0.788

Highway pavement type factors [Ref.1, Table2]

≔L (( ,,,H D pave AxleConfig)) |||||||||||||||||||||||||||||||

if

else

∧<H 1200 mm ≤D 305 mm‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||

if

else if

else

＝pave “Flexible”‖‖‖‖‖‖‖

||||||

if

else

＝AxleConfig “Tandem”‖‖ 1

‖‖ 0.75

＝pave “Non-dirt”‖‖‖‖‖‖‖

||||||

if

else

＝AxleConfig “Tandem”‖‖ 1

‖‖ 0.8

‖‖‖‖‖‖‖

||||||

if

else

＝AxleConfig “Tandem”‖‖ 1

‖‖ 0.65

‖‖‖

|||

if ＝AxleConfig “Tandem”‖‖ 1

≔R (( ,,,H D pave AxleConfig)) |||||||||||||||||||||||||||

if

else

∧<H 1200 mm ≤D 305 mm‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||

if

else if

else

＝pave “Flexible”‖‖ 1

＝pave “Non-dirt”‖‖‖‖‖‖‖

||||||

if

else

＝AxleConfig “Tandem”‖‖ 1.1

‖‖ 1.2

‖‖ 0.9

‖‖‖‖‖‖‖‖‖‖‖

|||||||||

if

else if

else

＝pave “Flexible”‖‖ 1

＝pave “Non-dirt”‖‖ 1.1

‖‖ 0.9

page 8/11

|||||

‖‖‖‖‖‖

|||||

else

‖‖ 1

‖‖ 0.9

≔R =R (( ,,,H D pave AxleConfig)) 1

≔L =L (( ,,,H D pave AxleConfig)) 1

Cyclic Circumferential Stress

≔ΔSHh ⋅⋅⋅⋅⋅KHh GHh R L FI w =ΔSHh 11.106 MPa

5.0 Cyclic Longitudinal Stress due to Highway Load

Highway stiffness factor for cyclic longitudinal stress [Ref.1, Figure 16]

≔KLh ⎛⎝ ,Er r⎞⎠ ||||||||||

if

else if

else if

＝Er 34 MPa‖‖‖ +−+−+7.059 ⋅1410.747 r ⋅82059.309 r 2 ⋅1849409 r 3 ⋅18907932 r 4 ⋅73024879 r 5

＝Er 69 MPa‖‖‖ −+−+−+3.887 ⋅1249.947 r ⋅85701.79 r 2 ⋅2592859 r 3 ⋅41346904 r 4 ⋅337216600 r 5 ⋅1105249400 r 6

＝Er 138 MPa‖‖‖ +−+−+0.9494 ⋅862.899 r ⋅43728.055 r 2 ⋅915470 r 3 ⋅8919603 r 4 ⋅33371469 r 5

68.511

13.516

18.521

23.5

13.5

26

0.03 0.04 0.05 0.06 0.07 0.080.01 0.02 0.09rr

KLh (( ,34 MPa rr))

KLh (( ,69 MPa rr))

KLh (( ,138 MPa rr))

≔KLh =KLh ⎛⎝ ,Er WtoD⎞⎠ 14.767

≔GLh (( ,H D))‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||||||||

←D ―D

m|||||||||||||||||||||||||||

if

else if

else if

else if

else

≤≤900 mm H 1200 mm‖‖‖

⎛⎝ +−12.41862 ⎛⎝ ⋅11.822553 D 0.0199224⎞⎠⎞⎠−1

＝H 1800 mm‖‖‖

⎛⎝ +−7.0602784 ⎛⎝ ⋅6.3002565 D 0.041841633⎞⎠⎞⎠−1

＝H 2400 mm‖‖‖

⎛⎝ +−5.4787163 ⎛⎝ ⋅4.5795368 D 0.061905445⎞⎠⎞⎠−1

＝H 3000 mm‖‖‖

⎛⎝ +−0.85388192 ⎛⎝ ⋅0.4044552 D 0.2817535⎞⎠⎞⎠−1

‖‖‖‖‖‖‖‖‖‖

|||||||||

if ∧>H 1200 mm <H 1800 mm‖‖‖‖‖‖‖‖

←a ⎛⎝ +−12.418 .62 ⎛⎝ ⋅11.822553 D 0.0199224⎞⎠⎞⎠−1

←b ⎛⎝ +−7.0602784 ⎛⎝ ⋅6.3002565 D 0.041841633⎞⎠⎞⎠−1

←aa 1200 mm1800 mm

⎡⎢⎣

⎤⎥⎦

bb a⎡ ⎤

Highway geometry factor for cyclic circumferential stress [Ref.1, Figure 17]

=GLh (( ,H D)) −1.203

page 9/11

‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||||||||||

|||||||||||||||||||||||||||||||

‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖‖

||||||||||||||||||||||||||||||

|

else if

else if

‖‖‖‖‖‖

⎣ ⎦

←bb ab

⎡⎢⎣

⎤⎥⎦

linterp (( ,,aa bb H))

∧>H 1800 mm <H 2400 mm‖‖‖‖‖‖‖‖‖‖‖‖‖

‖‖‖‖‖‖‖‖‖‖‖‖

|||||||||||

←a ⎛⎝ +−7.0602784 ⎛⎝ ⋅6.3002565 D 0.041841633⎞⎠⎞⎠−1

←b ⎛⎝ +−5.4787163 ⎛⎝ ⋅4.5795368 D 0.061905445⎞⎠⎞⎠−1

←aa 1800 mm2400 mm

⎡⎢⎣

⎤⎥⎦

←bb ab

⎡⎢⎣

⎤⎥⎦

linterp (( ,,aa bb H))

∧>H 2400 mm <H 3000 mm‖‖‖‖‖‖‖‖‖‖‖‖‖

‖‖‖‖‖‖‖‖‖‖‖‖

|||||||||||

←a ⎛⎝ +−5.4787163 ⎛⎝ ⋅4.5795368 D 0.061905445⎞⎠⎞⎠−1

←b ⎛⎝ +−0.85388192 ⎛⎝ ⋅0.4044552 D 0.2817535⎞⎠⎞⎠−1

←aa 2400 mm3000 mm

⎡⎢⎣

⎤⎥⎦

←bb ab

⎡⎢⎣

⎤⎥⎦

linterp (( ,,aa bb H))

0.9

1.15

1.4

1.65

1.9

2.15

2.4

2.65

2.9

0.4

0.65

3.15

199 298 397 496 595 694 793 892 991 10901 100 1189

0.796

762

GLh (( ,1.2 m xx))

GLh (( ,1.8 m xx))

GLh (( ,2.4 m xx))

GLh (( ,3.0 m xx))

xx ((m))

≔GLh =GLh (( ,1.8 m ⋅D 1000)) 0.796

Cyclic Circumferential Stress

≔ΔSLh ⋅⋅⋅⋅⋅KLh GLh R L FI w =ΔSLh 8.296 MPa

6.0 Circumferential Stress due to Internal Pressure [Ref.1, Sec.4.7.3]

≔SHi ――――⋅p (( −D wt))

2 wt=SHi 250.533 MPa

7.0 Total Effective Stress [Ref.1, Sec.4.8.1.2]

Earth load stress =SHe 30.118 MPa

Cyclic circumferential stress =ΔSHh 11.106 MPa

Cyclic longitudinal stress =ΔSLh 8.296 MPa

Circumferential stress due to int. pressure =SHi 250.533 MPa

Maximum circumferential stress

≔S1 ++SHe ΔSHh SHi =S1 291.757 MPa

page 10/11

Maximum longitudinal stress

≔S2 +−ΔSLh ⋅⋅Es α ⎛⎝ −T2 T1⎞⎠ ⋅ν ⎛⎝ +SHe SHi⎞⎠ =S2 −52.823 MPa

Maximum radial stress

≔S3 −p =S3 −9.31 MPa

Total effective stress [Ref.1, 4.8.1.3]

≔Seff‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾―1

2

⎛⎝ ++⎛⎝ −S1 S2⎞⎠

2⎛⎝ −S2 S3⎞⎠

2⎛⎝ −S3 S1⎞⎠

2 ⎞⎠ =Seff 325.015 MPa

Factored specified minimum yield strength =⋅F SMYS 268.8 MPa

Code check [Ref.1, 4.8.1.3]

≔Checkeff ||||||

if

else

≤Seff ⋅F SMYS‖‖ “OK”

‖‖ “Not OK”

=Checkeff “Not OK”

8.0 Girth Weld Fatigue Check [Ref.1, Sec.4.8.2.1.2]

Fatigue endurance limit ≔SFG 82.737 MPa

Code check [Ref.1, Eq 17]

≔Checkgirth ||||||

if

else

≤ΔSLh ⋅F SFG‖‖ “OK”

‖‖ “Not OK”

=Checkgirth “OK”

9.0 Longitudinal Weld Fatigue Check [Ref.1, Sec.4.8.2.2.3]

Fatigue endurance limit ≔SFL 158.579 MPa

Code check [Ref.1, Eq 17]

≔Checklongweld ||||||

if

else

≤ΔSHh ⋅F SFL‖‖ “OK”

‖‖ “Not OK”

=Checklongweld “OK”

10.0 Results Summary

=CheckBarlow “OK”Barlow Stress

Total Effective Stress =Checkeff “Not OK”

Girth Weld Fatigue Check =Checkgirth “OK”

Longitudinal Weld Fatigue Check =Checklongweld “OK”

page 11/11