Code: ASME VIII-1

Year: 2007

Addenda: 2009 File: PVEfea-4472.0

MAWP: 1500 psi Desc: Tri-Clamp FEA

MEAWP: 0 psi Dwg: PVEdwg-4472.0

Max. Temp.: 500 °F Date:

MDMT: -40 °F

MDMT Press.: 1500 psi

Min. Thk. (UG-16b): 0.0625 in

Corrosion Allowance: 0 in

Hydrotest: 2201 psi

Impact Testing: None

Impact Exemption: UHA-51(d)

Radiography: None

Internal Press.: Yes

External Press.: No

Vessel Weight: No

Weight of Attachments: No

Attachment of Internals: No

Attachment of Externals: No

Cyclic or Dynamic Reactions: No

Wind Loading: No

Seismic Loading: No

Fluid Impact Shock Reactions: No

Temperature Gradients: No

Differential Thermal Expansion: No Author: Cameron Moore

Abnormal Pressures: No Reviewer: Laurence Brundrett

Hydrotest Loads: No

Pressure Vessel Engineering Ltd.ASME Calculations - CRN Assistance - Vessel Design - Finite Element Analysis

Design Conditions

UG-22 Loadings Considered

Pressure Vessel Engineering Ltd.

120 Randall Drive, Suite B

Waterloo, Ontario, Canada, N2V 1C6

www.pveng.com

info@pveng.com

Phone 519-880-9808

Finite Element Analysis Report - VIII-1

Conclusion: The Tri-Clamp meets VIII-2 design rules

using VIII-1 allowable stresses and is acceptable.

August 16, 2010

PVEng

Table of Contents 23-Aug-10 Page 2 of 20

Description Page Description Page

Cover 1 Reaction Area 11

Table of Contents 2 Reaction Forces 12

Executive Summary 3 Displacement 13

Stress Limits 4 Stress 14

Model 5 Clamp Stress 15

Mesh 6 Ferrule Stress 16

Error 7 Stress Linearization 17

Restraints 8 Bolt Stress 18

Loads 9 Component Cycle Life 19

Bolt Loads 10

Rev Date By

0 16-Aug-10 CBM

Revision(s)

Description

Release

Executive Summary ver 4.00 Page 3 of 20

Goal:

Summary Conclusions:

Materials

Model Information

Restraints & Loads

Results

Analysis Conclusion:

Material strength properties used in this report are obtained from ASME IID, Table 1A, and are suitable

for VIII-1 components. The rules of ASME VIII-2 are used to set the stress limits.

The Tri-Clamp will be used under ASME VIII-1 service. This product cannot be calculated to code rules

due to the complexity of its geometry. Instead the rules of ASME VIII-2 are used with ASME VIII-1

allowable stresses to determine its acceptability.

The model used in the analysis represents 1/2 of the Tri-Clamp due to symmetry. A global mesh size of

0.09375" has been applied using 3D tetrahedral solid elements. The mesh size results in a reported error

of less than 5%.

The Tri-Clamp meets VIII-2 design rules using VIII-1 allowable stresses and is acceptable.

Through the FEA we found a 0.0009" maximum displacement as acceptable. A 22,817 psi peak stress

results in an infinite cycle life. All general areas are within the allowable stress limits.

A symmetry restraint is applied to compensate for the use of a 1/2 model. A single point on the clamp is

fixed to prevent rigid body motion in all directions. Internal pressure is applied up to the pressure

boundary and bolt loads simulated with a "bolt connector" feature. The resulting reaction forces closely

match the theoretical reaction forces. The model is in balance and may be used for displacement and

stress analysis.

1 Material Stress Limits ver 4.01 ASME VIII-2 Fig 5.1 Page 4 of 20

2 Material Input Chart:

3 500 Temperature [ºF]

4 Material 1 Material 2 Bolting 3 Material 4

5 Material = SA-182 F316L SA-403 316L SA-193 B7

6 Application = Clamps/Ferrules Pipe Caps Bolts

7 Sm [psi] = 14,800 14,800 25,000

8 Sy [psi] = 16,400 16,400 88,500

9 E1 = 1.0 1.0 1.0

10 E2 = 1.0 1.0 1.0

11 E [psi] = 25,900,000 25,900,000 27,400,000

12 v = 0.30 0.30 0.30

13 Coef [/˚F]=

14 Cond [btu/hr-ft-˚F]=15

16 Pm [psi] = 14,800 14,800 50,000

17 Pl [psi] = 22,200 22,200 0

18 Pl+Pb [psi] = 22,200 22,200 75,000

19 Pl+Pb+Q [psi] = 44,400 44,400 0

20 Material 5 Material 6 Material 7 Bolting 8

21 Material =

22 Application =

23 Sm [psi] =

24 Sy [psi] =

25 E1 =

26 E2 =

27 E [psi] =

28 v =

29 Coef [/˚F]=

30 Cond [btu/hr-ft-˚F]=31

32 Pm [psi] =

33 Pl [psi] =

34 Pl+Pb [psi] =

35 Pl+Pb+Q [psi] =

36 Comments

37 Variable Descriptions: VIII-2 5.13

38 Sm (basic allowable) E (modulus of elasticity) - IID Table TM-1

39 E1 (weld efficiency) v (Poison's ratio) - IID Table PRD

40 E2 (casting efficiency) Coef (coefficient of thermal expansion) - IID Table TE-1

41 Cond (Thermal Conductivity) - IID Table TCD

42 Stress Limit Equations: VIII-2 Figure 5.1

43 Pm =

44 Pl =

45 Pl+Pb =

46 Pl+Pb+Q =

47 Pl+Pb+Q+F = Use fatigue curves~~peak stress intensity limit

48 Comments: 49 (1) Sy material property is not required, more conservative Pl+Pb+Q limits might be computed without it.

50 (2) The thermal expansion and conductivity coefficients are only required for studies including thermal stresses

51 (3) Refer to VIII-2 5.15 Figure 5.1 and following for the Pm, Pl, Q and F stress limits

52 (4) Refer to VIII-2 5.14 Table 5.6 for the correct application of the calculated stress limits

53 (5) Use IID tables 5A and 5B for Sm for VIII-2 studies

54 (6) Use IID tables 1A and 1B for Sm values (S) for VIII-1 studies

55 (7) Use B31.1 Table A for Sm values for B31.1 studies

56 (8) Use B31.3 Table A for Sm values for B31.3 studies

E1*E2*Sm~~general primary membrane stress intensity limit

1.5*E1*E2*Sm~~local membrane stress intensity limit

1.5*E1*E2*Sm~~primary membrane + primary bending stress intensity limit

Max(3*E1*E2*Sm,2*E1*E2*Sy)~~primary + secondary stress intensity

1 Model Page 5 of 20

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Fig-B Due to symmetry, a half model will be analyzed. Ferrules have been capped to simulate loads

caused by a closed loop system. The nuts and bolts have been replaced by a "bolt connector" feature.

Fig-A An exploded view of the Tri-Clamp assembly.

The clamp, ferrules and bolts will be analyzed in this report.

Refer to drawing PVEdwg-4472.0 for details.

1 Mesh Page 6 of 20

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Fig-B A view of the mesh on the opposite side of the assembly. "No Penetration" contact sets are applied

between the two clamp faces and the ferrule to clamp interaction. The caps are treated as bonded to the

ferrules.

Fig-A A view of the mesh applied to the model. A global mesh size of 0.09375" is used with second order

tetrahedral solid elements.

1 Error Page 7 of 20

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52 Fig-B An alternative view of Fig-A.

Fig-A A view of Error plot, capped at 5% error

No general areas are observed in excess of 5% . Error results are acceptable, the mesh selected is

appropriate.

1 Restraints Page 8 of 20

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Fig-A A view of the symmetry restraint applied. This condition restrains the

sectioned faces to the "XY" plane wile permitting movement in the "X" & "Y" directions. This restraint

compensates for the use of a half model and provides results identical to a full model.

Fig-B A close-up of Fig-A.

A point is restrained from translation in the Y and X directions. The model is now restrained from rigid body

motion in all directions.

1 Loads Page 9 of 20

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Fig-B A close-up of Fig-A.

Fig-A 1,500 psi is applied to all internal faces up to the pressure boundary.

1 Bolt Loads Page 10 of 20

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Fig-A Simulated bolt connectors are applied to the clamp. This simulates a bolt using beam elements rather

than including the bolt in the model. An axial preload of 1,262 lb has been applied. Refer to the bolt results

page for the preload calculation.

Fig-B A "No Penetration" contact set is applied. A friction factor of 0.7 for steel on steel is incorporated.

1 Reaction Area Page 11 of 20

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Fig-A The reaction normal to the XY plane is measured. This area is used to compute the reaction force

acting in the Z-direction.

Fig-B The reaction area measured in the Z-direction is 6.977 sq. in. This area will be multiplied by the

design pressure to determine the reaction force in the Z-direction.

1 Reaction Forces ver 4.08 Page 12 of 20

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27 1,500 P [psi] - Pressure

28 X Axis: reaction forces on the YZ plane caused by loads in the X direction

29 0.000 XArea [in2] - Pressurized area on YZ plane

30 0.0 XForce [lbs] - Added force in the X direction

31 -0.002 XReaction [lbs] - Reaction force in X direction reported by FEA program

32 TReactionX [lbs] = XArea*P+XForce ~~ Theoretical X reaction force 0*1500+0 = 033

34 Y Axis: reaction forces on the XZ plane caused by loads in the Y direction

35 0.000 YArea [in2] - Pressurized area on XZ plane

36 0.0 YForce [lbs] - Added force in the Y direction

37 0.008 YReaction [lbs] - Reaction force in Y direction reported by FEA program

38 TReactionY [lbs] = YArea*P+YForce ~~ Theoretical Y reaction force 0*1500+0 = 039

40 Z Axis: reaction forces on the XY plane caused by loads in the Z direction

41 6.977 ZArea [in2] - Pressurized area on XY plane

42 0.0 ZForce [lbs] - Added force in the Z direction

43 10467.000 ZReaction [lbs] - Reaction force in Z direction reported by FEA program

44 TReactionZ [lbs] = ZArea*P+ZForce ~~ Theoretical Z reaction force 6.977*1500+0 = 10,46645

46 Resultant of reaction forces in X, Y and Z:

47 TResultant [lbs] =

48 10,466

49 Resultant [lbs] =

50 10,467

51 Error [%] = 100*(TResultant-Resultant)/Resultant 100*(10466-10467)/10467 = 0.052 CheckError = abs(Error)<2 ~~ Error should be less than 2% ABS(0)<2 = Acceptable

53

SQRT(-0.002^2+0.008^2+10467^2) =

View showing Global Reaction Forces from analysis 'X' = -0.00158 lb, 'Y' = 0.0078 lb, 'Z' = 10467 lb

Calculated Reaction Forces = Analysis Reaction Forces within 2%

Model is balanced, results are valid.

sqrt(TReactionX^2+TReactionY^2+TReactionZ^2) ~~ Theoretical resultant

SQRT(0^2+0^2+10466^2) =

sqrt(XReaction^2+YReaction^2+ZReaction^2) ~~ Actual resultant

1 Displacement Page 13 of 20

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Fig-B A alternate view of Fig-A. The maximum displacement is 0.0009". Note the clamp displacement in

the bolt head region and joint separation begins to occur. The displacement direction is as expected and the

magnitude is acceptable.

Fig-A A view of the displacement plot with superimposed original geometry. Results are magnified 500x.

The ferrules elongate axially and displace radially outward. The clamps rotate about the center due to the

pulling force of the ferrules.

Joint separation

Axial Elongation

Radial Expansion

1 Stress Page 14 of 20

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Fig-B A sectioned view of Fig-A.

`A peak stress of 22,817 psi is located on the clamp face in contact with the ferrule. This stress will be used

to determine the cycle life of the design.

Fig-A A view of the stress plot (von Mises) capped at the primary general membrane allowable of 14,800

psi.

1 Stress Page 15 of 20

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Fig-A A view of the clamp only stress plot (von Mises) capped at the primary general membrane allowable

of 14,800 psi.

Fig-B An "ISO Clipped" view of Fig-A capped at 14,800 psi.

The only stresses in excess of 14,800 psi are in peak areas. A fatigue life will be based on the maximum

peak stress.

1 Stress Page 16 of 20

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Fig-A A view of the ferrule only stress plot (von Mises) capped at the primary general membrane allowable

of 14,800 psi.

Fig-B An "ISO Clipped" view of Fig-A capped at 14,800 psi.

Stresses in the hub region in excess of 14,800 psi will be further analyzed through a stress

linearization study on the following page.

1 Stress Linearization ver 2.37 Page 17 of 20

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44 Stress Check:

45 General Stress Classification

46 SA-182 F316L Material

47 Allowed Actual Check

48 Pm [psi] = 14,800 2,692 Acceptable

49 Pb [psi] = 11,727

50 Pl+Pb [psi] = 22,200 13,376 Acceptable

51 Peak [psi] = 17,123

Fig-A The stress classification line is taken through the ferrule hub. The membrane stress is 2,692 psi

and the membrane plus bending stress is 13,376 psi. These stresses are within the allowable limits and

are acceptable.

4 nodes found on the stress classification line

0.1533 units long - cubic spline interpolated to 71

equally spaced nodes.

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

25,000

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Stre

ss

Distance i to j

von Mises with all Components

Sn

St

Sh

Tnt

Tnh

Tth

von Mises

Pm

Pm+Pb

Peak

Stress Classification Line

1 Bolt Stress ver 4.10 Page 18 of 20

2 Description

3 Inputs:

4 Preload + Operating Load type

5 UNC Bolt Type

6 1/4 Dia [in] Nominal Bolt Size (UNC)

7 25,000 Sm [psi] Allowable Bolt Stress

8 File Location

9 RDia [in] = PVELookup("BoltDia","Lookup","Root Dia",Dia) ~~ Root Diameter 0.189

10 HDia [in] = PVELookup("BoltDia","Lookup","AF",Dia) ~~ Head Diameter 0.438

11 A [in^2] = (π*RDia^2)/4 ~~cross sectional area (3.142*0.189^2)/4 = 0.028

12 Spl1 [psi] = 2*0.9*Sm ~~ bolt preload stress 2*0.9*25000 = 45,000

13 Spl2 [psi] = 45000/(SQRT(Dia)) ~~bolt preload stress per App. S 45000/(SQRT(0)) = 90,000

14 PL [lb] =

15 1,262

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31 Type X Y Z Resultant

32 SF (lb) 0.00 0.00 -0.09 0.09 Shear Force

33 AF (lb) 0.00 1293.90 4.87 1293.90 Axial Force

34 BM (lb-in) -1.58 0.00 0.00 1.58 Bend Moment

35 Shear Stress: Maximum Stressed Connector

36 SSx [psi] = SFx/A 0/0.028 = 0

37 SSy [psi] = SFy/A 0/0.028 = 0

38 SSz [psi] = SFz/A -0.09/0.028 = -3

39 Axial Stress: Maximum Stressed Connector

40 SAx [psi] = AFx/A 0/0.028 = 0

41 SAy [psi] = AFy/A 1293.9/0.028 = 46,120

42 SAz [psi] = AFz/A 4.87/0.028 = 174

43 Von Mises - Average Stress Across Bolt: Maximum Stressed Connector

44 σ [psi] =

45 46,033

46 Checkσ = σ<= 2*Sm ~~ ASME Section VIII-2 5.7.2(a) 46033<= 2*25000 = Acceptable

47 Bending Stress: Maximum Stressed Connector

48 M [lb-in] = 1.58 = 2

49 SB [psi] = M*(RDia/2)/((π*(RDia/2)^4)/4) 2*(0.189/2)/((3.142*(0.189/2)^4)/4) = 2,381

50 PmPb [psi] =

51 48414

52 CheckPmPb = PmPb<= 3*Sm ~~ ASME Section VIII-2 5.7.2(b) 48414<= 3*25000 = Acceptable

if(Spl2<(2*Sm),Spl2*A,Spl1*A) ~~bolt preload force used for fea

IF(90000<(2*25000),90000*0.028,45000*0.028) =

All connectors are below the allowables

Max(abs(σ+SB),abs(σ-SB))

MAX(ABS(46033+2381),ABS(46033-2381)) =

Tri Clamp Bolt

SQRT(((SAx-SAy)^2+(SAy-SAz)^2+(SAz-SAx)^2+6*(SSx^2+SSy^2+SSz^2))/2)

SQRT(((0-46120)^2+(46120-174)^2+(174-0)^2+6*(0^2+0^2+-3^2))/2) =

J:\4000-4999\4400-4499\4472 PVE Tri Clamp\bolt data.csv

Connector

Counterbore with Nut-1

0

10000

20000

30000

40000

50000

60000

70000

80000

1 2

Str

ess (

psi)

Connector

Bolt Stresses - All Connectors

Pm

Pm+Pb

Pm-Pb

Max Conn

Sm

2 x Sm

3 x Sm

1 Cycle Life ver 5.10 Page 19 of 20

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43 The above chart represents the top differential von Mises stresses. These stresses are determined according to the

44 equations listed in ASMIE VIII-2 5.5.3.2. Stresses converging to infinity tend to lie at discontinuities and are not used for cycle

45 life calculations.

46 9287 Node - first node of a consecutive set47 ΔSpk [psi] =48 22,817 49 Not Linearized Stress result .50 Table3.F.4CurveA Material coefficient table51 Series 3xx High Alloy Steels, Ni-Cr-Fe Alloy, Ni-Fe-Cr Alloy, and Ni-Cu Alloy for temperatures not exceeding 800°F

52 Sa <= 28.2ksi, Curve A - Areas not heat, affected (Pl+Pb+Q) range <= 27.2ksi

vlookup(nodeselect,stressresult,2,False)

vlookup(nodeselect,stressresult,2,FALSE) =

Fig-A The 22,817 psi peak stress is used to determine the cycle life. An equivalent alternating stress of

12,465 psi is calculated which results in an infinite cycle life.

0.00E+00

5.00E+03

1.00E+04

1.50E+04

2.00E+04

2.50E+04

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Str

ess D

iffe

ren

tial

Rank

Stress Ranking

Cycle Life ver 5.10 Page 20 of 20

1 Inputs: VIII-2, 5.5.3

2 1.00 Kf - fatigue strength reduction factor3 14,800 Sa [psi] - material allowable4 16,400 Sy [psi] - material yield strength5 500 Tav [°F] - average cycle temperature6 25,900,000 Et [psi] - modulus of elasticity at Tav

7 Alternating Equivalent Stress: VIII-2, 5.5.3.2

8 Sps [psi] = max(3*Sa,2*Sy) MAX(3*14800,2*16400) = 44,400 9 Kek = if(ΔSpk<=Sps,1,"Linearize") 1.00 10 Kek = if(Sn1k <= Sps, 1,"ERROR") 1.00 11 Saltk = (Kf*Kek*ΔSpk)/2 (1*1*22817)/2 = 11,408 12 EG [psi] = PVELookup("EgTable","Lookup","Eg","CL_Fig511022A") 28,300,000 13 Se [psi] = Saltk*EG/Et 11408*28300000/25900000 = 12,465 14 Cycles = PVELookup("CL_Fig511022A","CycleLifeLookup",Se) 100,000,000,000

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24 PVELookup("","CycleLifeLookup",Se)

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1,000

10,000

100,000

1.0

E+

00

1.0

E+

01

1.0

E+

02

1.0

E+

03

1.0

E+

04

1.0

E+

05

1.0

E+

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1.0

E+

07

1.0

E+

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1.0

E+

09

1.0

E+

10

1.0

E+

11

Str

es

s

Cycles

Stress vs. Cycles