asme calculations - crn assistance - vessel design...
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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
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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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+
06
1.0
E+
07
1.0
E+
08
1.0
E+
09
1.0
E+
10
1.0
E+
11
Str
es
s
Cycles
Stress vs. Cycles