PVEfea-3520.0...Symmetryisapplied tocompensatefor theuseofa1/4model,asinglefixedpointisapplied...

Sample Job #24

ABC-123-456

Finite Element Analysis (FEA) Report

Heat Exchanger Analysis

September 29, 2009

1 of 44

Derek Verstege C.TechLaurence Brundrett P. Eng.

PVE-3520

Table of Contents ver 4.00 of 44

Contents PageCover 1Table of Contents 2Executive Summary 3Section - Materials 4

SA-240 304 5SA-213 TP304 6

Section - Model Information 7Model 8Mesh 9Error 10

Section - Restraints & Loads 11Restraints 1 12Restraints 2 13Pressure Loads 14Thermal Loads 1 15Thermal Loads 2 16X-Axis Reaction Area 17Z-Axis Reaction Area 18Reaction Forces 19

Section - Results 20Case 1 - Displacement 21Case 1 - General Stress 22Case 1 - Local Stress 23Case 1 - Buckling 24Case 2 - Displacement 25Case 2 - General Stress 26Case 2 - Buckling 27Case 3 - Displacement 28Case 3 - General Stress 29Case 3 - Local Stress 30Case 3 - Buckling 31Case 4 - Displacement 32Case 4 - Stress SPS 33Case 4 - Buckling 34Case 5 - Displacement 35Case 5 - Stress SPS 36Case 5 - Buckling 37Case 6 - Displacement 38

Executive Summary ver 4.00 of 44

Project Information:

CustomerVessel / Component(s)Part NumberJobFEA Program UsedDate

Shell Side (psi) Tube Side (psi)

100 300Max Operating Temp (F) MDMT

300 -20

Goal:

Summary Conclusions:

Materials

Model Information

Restraints & Loads

Results

Analysis Conclusion:

A 1/4 model is used to simplify the analysis due to symmetry. A mesh size of 1" is applied globally, thetubesheet and adjacent shell are refined to 3/8" and 1/4" respectively. Reported error is < 5% for allgeneral areas. The mesh selected is acceptable.

The heat exchanger meets ASME VIII-2 code rules using ASME VIII-1 allowables. The design isacceptable.

Maximum Allowed Working Pressures

Maximum Design Metal Temperatures

Displacement direction is as expected, displacement magnitude is acceptable for all (7) load cases.

All observed stresses are below their respective allowable for all (7) loads cases.

No further analysis is required.

Symmetry is applied to compensate for the use of a 1/4 model, a single fixed point is applied to preventrigid body motion. (7) load cases are applied as per ASME VIII-1 UHX-13.4(a). Reported reactionforces closely match theoretical reaction forces. The model is in balance and may be used fordisplacement and stress analysis.

Material properties used in this analysis are obtained from ASME IID, and are suitable for VIII-1components. The rules of ASME VIII-2 are used to set the stress limits.

The tubesheet cannot be calculated to ASME VIII-1 UHX code rules due to the unusual tube pattern.Instead the rules of ASME VIII-2 are used with VIII-1allowed stresses to determine the acceptability ofthe design.

All (7) load cases as per ASME VIII-1 UHX are analyzed for the following components:

- The tubesheet- The shell adjacent to the tubesheet- The tubes

SolidWorks Simulation 200926-Jun-2009

XYZ Vessel Corp.Heat Exchanger

ABC-123-456PVE-3520

Materials ver 4.00 of 44

Summary:

Contents:

Material properties used in this analysis are obtained from ASME IID, and are suitable for VIII-1components. The rules of ASME VIII-2 are used to set the stress limits.

Material properties are obtained from:

- ASME IID, Table 1A (allowable stress)- Table TE-1 (modulus of elasticity)- Table TM-1 (thermal expansion coefficient)

The rules of VIII-2 have been applied to calculate the maximum allowable stresses.

1 Material Stress Limits ver 4.00 ASME VIII-2 Fig 4-130.1 of 44

2 Material:3 Material4 Application

5 Strength Properties:6 Source of strength properties7 300 T [ºF] temperature8 18,900 Sm [psi] basic allowable stress at temperature T9 22,400 Sy [psi] yield stress at temperature T (optional)10 1.0 k [] - stress intensity k factor11 1.00 E1 [] - weld efficiency factor12 1.00 E2 [] - casting efficiency factor

13 FEA Properties:14 Source of FEA properties15 27,000,000 E [psi] - modulus of elasticity (at temperature)16 0.31 v [] - Poison's ratio17 9.2 E-006 Coef [in/in/ºF]- coefficient of thermal expansion (for thermal stress studies only)

18 Stress Limits:19 Pm =20 18,900

21 Pl =22 28,350

23 Pl+Pb =24 28,350

25 Pl+Pb+Q =26 56,700

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

28 Comments:29 (1) Sy material property is not required, more conservative Pl+Pb+Q limits might be computed without it.30 (2) Refer to VIII-2 Table AD-150.1 for k values31 (3) The thermal expansion coeficient is only required for studies including thermal stresses32 (4) Refer to VIII-2 App 4-130 and following for the Pm, Pl, Q and F stress limits33 (5) Refer to VIII-2 App 4-130 Table 4-120.1 for the correct application of the calculated stress limits34 (6) Use IID tables 2A and 2B for Sm for VIII-2 studies35 (7) Use IID tables 1A and 2A for Sm values (S) for VIII-1 studies36 (8) Use B31.1 Table A for Sm values for B31.1 studies37 (9) Use B31.3 Table A for Sm values for B31.3 studies

SA-240 304

ASME VIII-IID, 2007 Ed, 2008 Add.

Shell, Head, Tubesheet, Bellows


k*E1*E2*Sm~~general primary membrane stress intensity limit1*1*1*18900 =

1.5*k*E1*E2*Sm~~local membrane stress intensity limit1.5*1*1*1*18900 =

1.5*k*E1*E2*Sm~~primary membrane + primary bending stress intensity limit1.5*1*1*1*18900 =

Max(3*E1*E2*Sm,2*E1*E2*Sy)~~primary + secondary stress intensityMAX(3*1*1*18900,2*1*1*22400) =

1 Material Stress Limits ver 4.00 ASME VIII-2 Fig 4-130.1 of 44

2 Material:3 Material4 Application

5 Strength Properties:6 Source of strength properties7 300 T [ºF] temperature8 18,900 Sm [psi] basic allowable stress at temperature T9 22,400 Sy [psi] yield stress at temperature T (optional)10 1.0 k [] - stress intensity k factor11 1.00 E1 [] - weld efficiency factor12 1.00 E2 [] - casting efficiency factor

13 FEA Properties:14 Source of FEA properties15 27,000,000 E [psi] - modulus of elasticity (at temperature)16 0.31 v [] - Poison's ratio17 9.2 E-006 Coef [in/in/ºF]- coefficient of thermal expansion (for thermal stress studies only)

18 Stress Limits:19 Pm =20 18,900

21 Pl =22 28,350

23 Pl+Pb =24 28,350

25 Pl+Pb+Q =26 56,700

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

28 Comments:29 (1) Sy material property is not required, more conservative Pl+Pb+Q limits might be computed without it.30 (2) Refer to VIII-2 Table AD-150.1 for k values31 (3) The thermal expansion coeficient is only required for studies including thermal stresses32 (4) Refer to VIII-2 App 4-130 and following for the Pm, Pl, Q and F stress limits33 (5) Refer to VIII-2 App 4-130 Table 4-120.1 for the correct application of the calculated stress limits34 (6) Use IID tables 2A and 2B for Sm for VIII-2 studies35 (7) Use IID tables 1A and 2A for Sm values (S) for VIII-1 studies36 (8) Use B31.1 Table A for Sm values for B31.1 studies37 (9) Use B31.3 Table A for Sm values for B31.3 studies

SA-213 TP304


Tubes


k*E1*E2*Sm~~general primary membrane stress intensity limit1*1*1*18900 =

1.5*k*E1*E2*Sm~~local membrane stress intensity limit1.5*1*1*1*18900 =

1.5*k*E1*E2*Sm~~primary membrane + primary bending stress intensity limit1.5*1*1*1*18900 =

Max(3*E1*E2*Sm,2*E1*E2*Sy)~~primary + secondary stress intensityMAX(3*1*1*18900,2*1*1*22400) =

Model Information ver 4.00 of 44

Summary:

Contents:

Model

Mesh

Error Plot

Reference Information:

A 1/4 model was used to simplify the analysis due to symmetry. 1/2 of the bellows is included and positioned at mid length of the shell to compensate for the use of symmetry.

The tubesheet and adjacent shell are solid models, all other components are modeled as surfaces.

Please refer to Drawing PVE-3520.0 for details.

A 1/4 model is used to simplify the analysis due to symmetry. A mesh size of 1" is applied globally, the tubesheet and adjacent shell are refined to 3/8" and 1/4" respectively. Reported error is < 5% for allgeneral areas. The mesh selected is acceptable.

1" 2nd order shell elements are applied to all surfaces. A 2nd order tetrahedral solid mesh was applied to the tubesheet and adjacent shell and refined to 3/8" and 1/4" respectively.

Reported error is < %5 for all general areas. Error in excess of %5 is limited to locations of discontinuityand does not affect the results.

The error plot justifies the mesh selected. The model may be used for analysis.

Please refer to the following links for additional information;

Including reference components in an FEA to provide appropriate boundary and load conditions.http://www.pveng.com/documents/content_80.pdf

The use and effects of 2nd order integration elements.http://www.pveng.com/documents/content_151.pdf

Mesh Refinement Using the Error Function Results for Areas at Discontinuities.http://www.pveng.com/documents/content_250.pdf

Mesh Refinement Using the Error Function Results for Areas near Discontinuities.http://www.pveng.com/documents/content_251.pdf

Error Plots for Bolt Heads and Surface to Surface Contacts Areas.http://www.pveng.com/documents/content_248.pdf

FEA Software Validation - A comparison to theoretical results.http://www.pveng.com/documents/content_249.pdf

COSMOSWorks Validation Examples.http://www.pveng.com/documents/content_247.pdf

http://www.pveng.com/documents/content_80.pdf







1 Model Ver 4.06 of 442

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Fig-B An alternative view of Fig-A.The tubesheet and shell are modeled as "solid" bodies; all other components are modeled as "surfaces".

The shell is shown as transparent for clarity.

Fig-A A view of the Heat Exchanger model.A 1/4 model was used to simplify the analysis due to symmetry.

Refer to drawing PVE-3520.0 for details.

Baffles SA-240 304

Bellows SA-240 304Head SA-240 304

Shell SA-240 304

Tubes SA-213 TP304

Tubesheet SA-240 304

Solid bodies

1 Mesh Ver 4.07 of 442

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Fig-B A close up of Fig-A.All components are treated as "bonded" and meshed as a single body.

Fig-A A view of the mesh applied to the model.A 1" shell mesh is applied to all surfaces, solid elements are refined to 3/8" for the tubesheet and 1/4" for the

adjacent shell.

1" Shell Mesh

3/8" Solid Mesh

1/4" Solid Mesh

1 Error Ver 4.06 of 442

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Fig-B An alternative view of Fig-A, with mesh overlaid.Error results are acceptable, the mesh may be used for analysis.

Fig-A A view of the Error plot, scale set to 5% Error.Areas of error greater than 5% are limited to locations of discontinuity within (1) element of change.

Error > %5 limitedto (1) element of change

Restraints & Loads ver 4.00 of 44

Summary:

Contents:

Restraints

Loads

Reaction Forces

Symmetry is applied to compensate for the use of a 1/4 model, a single fixed point is applied to preventrigid body motion. (7) load cases are applied as per ASME VIII-1 UHX-13.4(a). Reported reaction forcesclosely match theoretical reaction forces. The model is in balance and may be used for displacement and stress analysis.

A symmetry condition is applied to all faces & edges along symmetry planes. This compensates for the use of a 1/4 model and provides results identical to that of a full analysis. A single point is restrained to prevent rigid body motion in all directions.

(7) load cases are analyzed as per ASME VIII-1 UHX 13.4(a)

1-TP (Tube pressure only)2-SP (Shell pressure only)3-TP+SP (Tube pressure + shell pressure)4-T (Thermal loads only)5-T+TP (Thermal loads + tube pressure)6-T+SP (Thermal loads + shell pressure)7-T+TP+SP (Thermal loads + tube pressure + shell pressure)

The above load cases are all run and analyzed individually.

The reported reaction forces closely match the theoretical reaction forces in all directions. The model is inbalance and can be used to calculate expected displacements and stresses.

1 Restraints Ver 4.06 of 442

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Fig-B A view of the symmetry restraint applied to all solid faces on the symmetry plane.These restraints prevent ridged body motion in the "X" direction.

Fig-A A view of the symmetry restraint applied to all shell edges on the symmetry plane.This restraint compensates for the use of a 1/4 model and provides results identical to a complete analysis.

1 Restraints Ver 4.06 of 442

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Fig-B A view of the no translation condition applied to a point on the model.This restraint prevent ridged body motion in the "Y" direction.

The model is now fully restrained from ridged body motion in all directions.

Fig-A A view of the symmetry restraint applied to the midlength edges of the bellows and shell.Note only 1/2 of the bellows is included and positioned at mid-length to compensate symmetry.

This restraint prevents ridged body motion in the "Z" direction.

1 Loads Ver 4.06 of 442

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Fig-B A view of the shell side pressure (100 psi) applied.

Fig-A A view of the tube side pressure (300 psi) applied.


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Fig-B A view of tube side faces set to 250°F.

Fig-A A view of the shell side components set to the operating temperature of 200°F.Thermal expansion will be calculated based on the temperature differential between 70°F ambient to the

respective components temperature as shown in the following images.


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Fig-A A view of tubes set to 250°F.An average temperature of 225°F is taken between the shell side and the tube side.

1 X-Axis Reaction Area Ver 4.02 of 442

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Fig-B A view showing the shellside pressure area on the X-Axis.This area will be used on the following pages to calculate reaction forces.

Area = 504.6 in^2

Fig-A A view showing the tubeside pressure area on the X-Axis.This area will be used on the following pages to calculate reaction forces.

Area = 682.8 in^2

1 Z-Axis Reaction Area Ver 4.02 of 442

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Fig-B A view showing the shellside pressure area on the Z-Axis.This area will be used on the following pages to calculate reaction forces.

Area =92.8 in^2

Fig-A A view showing the tubeside pressure area on the Z-Axis.This area will be used on the following pages to calculate reaction forces.

Area =60.4 in^2

1 Reaction Forces ver 4.08 of 442

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27 Applied Pressure:28 100 Ps [psi] - Pressure applied to the shell side29 300 Pt [psi] - Pressure applied to the tube side

30 X Axis: reaction forces on the YZ plane caused by loads in the X direction31 505.94 XArea1 [in2] - Pressurized area on YZ plane (Shell Side)32 682.80 XArea2 [in2] - Pressureized area on YZ plane (Tube Side)33 0 XForce [lbs] - Added force in the X direction34 255,920 XReaction [lbs] - Reaction force in X direction reported by FEA program35 TReactionX [lbs] =36 255,434

37 Z Axis: reaction forces on the XY plane caused by loads in the Z direction38 92.80 ZArea1 [in2] - Pressurized area on XY plane (Shell Side)39 60.38 ZArea2 [in2] - Pressurized area on XY plane (Tube Side)40 0 ZForce [lbs] - Added force in the Z direction41 -26,608 ZReaction [lbs] - Reaction force in Z direction reported by FEA program42 TReactionZ [lbs] =43 27,393

44 Resultant of reaction forces in X, Y and Z:45 TResultant [lbs] =46 256,89847 Resultant [lbs] =48 257,29949 Error [%] =50 0.251 CheckError = abs(Error)<2 ~~ Error should be less than 2% ABS(0.2)<2 = Acceptable52

ABS(100*(TResultant-Resultant)/Resultant)ABS(100*(256898-257299)/257299) =

SQRT(255920^2+-26608^2) =

View showing global reaction forces from analysis "X" = 255,920 lb, "Y" = 25.521 lb, "Z" = -26,608 lbReported reaction forces = theorectical reaction forces within 2%.

Model is in balance and may be used for stress and displacement analysis.

sqrt(TReactionX^2+TReactionZ^2) ~~ Theoretical resultantSQRT(255434^2+27393^2) =

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

(ZArea1*Ps)+(ZArea2*Pt)+ZForce ~~ Theoretical Z reaction force(92.8*100)+(60.38*300)+0 =

(XArea1*Ps)+(XArea2*Pt)+XForce ~~ Theoretical X reaction force(505.94*100)+(682.8*300)+0 =

Results ver 4.00 of 44

Summary:

Contents:

Displacement Plots

Stress Plots

Case Sa Result Cycle Life1 TP Acceptable NR2 SP Acceptable NR3 TP+SP Acceptable NR4 T Acceptable NR5 TP+T Acceptable NR6 SP+T Acceptable NR7 TP+SP+T Acceptable NR



No further analysis is required.



Tubesheet Results

18,900 psi

56,700 psi(Sps)

1 Case 1 TP Displacement of 442

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Fig-B An alternative view of Fig-A.The tubesheet observes bending do to the tubeside pressure acting on the head pulling it outwards while the

tubes restrain it at center.

Fig-A A view of the displacement plot, results magnified 100X.Maximum displacement is 0.019"

Tube bending

Tube bending

1 Case 1 TP Stress of 442

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Fig-B An "ISO clipped" view of Fig-A, clipped at 18,900 psi.The only areas or error in excess of the general membrane allowable are limited to local regions.

These stresses will be further analyzed on the following page.

Fig-A A view of the stress plot (von Mises), capped at the general membrane allowable of 18,900 psi.Maximum stresses are observed at the shell to tubesheet junction.

Shell to tubesheet junction

Local region


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Fig-B An "ISO clipped" view of Fig-A, clipped at 28,350 psi.No stresses in excess of 28,350 psi are observed.

No further analysis is required, results are acceptable.

Fig-A A view of the stress plot (von Mises), capped at the local membrane allowable of 28,350 psi.

1 Case 1 TP Buckling of 442

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Fig-B An "ISO clipped" view of Fig-A, clipped at -10,706 psi.No stresses in excess of -10,706 psi are observed in the tubes.


Fig-A A view of the stress plot in the "Z" direction capped at the tube buckling allowable of -10,706 psi.

1 Case 2 SP Displacement of 442

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Fig-B An alternative view of Fig-A.The shell observes radial expansion due to shell side pressure. The tubesheet observes bending do to the

shell side pressure forcing it outwards while the tubes restrain it at center.


Tube bending

Tube bending

1 Case 2 SP Stress of 442

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Fig-A A view of the stress plot (von Mises), capped at the general membrane allowable of 18,900 psi.Maximum stresses are observed at the shell.

Shell

1 Case 2 SP Buckling of 442

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No furhter analysis is required, results are acceptable.


1 Case 3 TP + SP Displacement of 442

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Fig-B An alternative view of Fig-A.The shell observes radial expansion due to shell side pressure. The tubesheet observes bending do to

combined shell side and tubeside pressure forcing it outwards while the tubes restrain it at center.


Tube bending

Tube bending

1 Case 3 TP + SP Stress of 442

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Fig-B An "ISO clipped" view of Fig-A, clipped at 18,900 psi.The only areas or error in excess of the general membrane allowable are limited to local regions.

These stresses will be further analyzed on the following page.

Fig-A A view of the stress plot (von Mises), capped at the general membrane allowable of 18,900 psi.Maximum stresses are observed at the shell to tubesheet junction.

Shell to tubesheet junction

Local region

1 Case 3 TP + SP Stress of 442

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Fig-A A view of the stress plot (von Mises), capped at the local membrane allowable of 28,350 psi.

1 Case 3 TP + SP Buckling of 442

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1 Case 4 TP Displacement of 442

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Fig-B An alternative view of Fig-A, with superimposed original geometry.The heat exchanger observes axial elongation due to thermal expansion.



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Fig-A A view of the stress plot (von Mises), capped at the secondary membrane allowable of 56,700 psi.

1 Case 4 T Buckling of 442

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Fig-B An "ISO clipped" view of Fig-A, clipped at -10,706 psi.Stresses in excess of -10,706 psi in the tubes are limited to a short length from the tubesheet.



1 Case 5 TP + T Displacement of 442

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Fig-B An alternative view of Fig-A.The tubesheet observes bending do to the tubeside pressure acting on the head pulling it outwards while

the tubes restrain it at center.


Tube bending

Tube bending

1 Case 5 TP + T Stress of 442

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1 Case 5 TP + T Buckling of 442

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1 Case 6 SP + T Displacement of 442

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Fig-B An alternative view of Fig-A.The shell observes radial expansion due to shell side pressure. The tubesheet observes bending do to the

shell side pressure forcing it outwards while the tubes restrain it at center.


Tube bending

Tube bending

1 Case 6 SP + T Stress of 442

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1 Case 6 SP + T Buckling of 442

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1 Case 7 TP + SP + T Displacement of 442

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Fig-B An alternative view of Fig-A.The shell observes radial expansion due to shell side pressure. The tubesheet observes bending do to

combined shell side and tubeside pressure forcing it outwards while the tubes restrain it at center.


Tube bending

Tube bending

1 Case 7 TP + SP + T Stress of 442

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1 Tube Buckling ver 4.00 ASME VIII-1 UHX-13.5.9(b)(3)(a) Page 14 of 192

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27 Inputs: VIII-1 UHX-13.328 SA-213 TP304 Mat - Tube material29 1.500 dt [in] - Tube OD30 0.109 tt [in] - Tube wall31 27,000,000 Et [psi] - Tube modulus of elasticity at design temp32 22,400 Sy [psi] - Tube yield strength at design temp33 18,900 St [psi] - Tube allowable stress at design temp34 16.750 l [in] - Unsupported length of tube35 0.800 k - Support configuration

36 Variables:37 lt [in] = k*l ~~ UHX-13.5.9(b)(1) Effective unsupported tube length 0.8*16.75 = 13.40038 rt [in] =39 0.98740 Ft = lt/rt ~~ UHX-13.5.9(b)(2) 13.4/0.987 = 13.58241 Ct = sqrt((2* ^2*Et)/Sy) ~~ UHX-13.5.9(b)(2) SQRT((2*3^2*27000000)/22400) = 154.17142 Fs = 2.0 ~~ UHX-13.5.9(b)(2) 2.0 = 2.000

43 Allowable Stress: UHX-13.5.9(b)(3)(a)44 Stb1 [psi] =45 1890046 Stb2 [psi] =47 1070748 Stb [psi] =49 1070750

51 *The reported tube axial compression stress (not von Mises equivalent) must be < Stb

MIN((22400/2)*(1-(13.582/(2*154.171))),18900) =

View showing the tube axial compression stress capped at the buckling allowable of 10,707 psi.Reported tube axial compression stress is less than the allowable.

Tube design is acceptable.

min(( ^2*Et)/(Fs*Ft^2),St) ~~ UHX-13.5.9(b)(2)MIN((3^2*27000000)/(2*13.582^2),18900) =

min((Sy/Fs)*(1-(Ft/(2*Ct))),St) ~~ UHX-13.5.9(b)(2)

sqrt((dt^2+(dt-2*tt)^2)/4) ~~ UHX-13.5.9(b)(2)SQRT((1.5^2+(1.5-2*0.109)^2)/4) =

if(Ct<=Ft, Stb1, Stb2) ~~ UHX-13.5.9(b)(2)IF(154.171<=13.582, 18900, 10707) =

PVEfea-3520.0...Symmetryisapplied tocompensatefor theuseofa1/4model,asinglefixedpointisapplied...

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Transcript of PVEfea-3520.0...Symmetryisapplied tocompensatefor theuseofa1/4model,asinglefixedpointisapplied...