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PiPe StreSS engineering

byLiang-Chuan (L.C.) Peng and tsen-Loong (Alvin) PengPeng engineering, Houston, texas, USA

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CONTENTSAcknowledgments........................................................................................................................................ . xiPreface............................................................................................................................................. . xiiiNomenclature................................................................................................................................... . xv

Chapter.1Introduction....................................................................................................................................... . 11.1. Scope.of.Pipe.Stress.Analysis................................................................................................... . 21.2. Piping.Components.and.Connecting.Equipment..................................................................... . 41.3. Modes.of.Failure...................................................................................................................... . 9

1.3.1. Static.Stress.Rupture..................................................................................................... . 91.3.2. Fatigue.Failure............................................................................................................ . 121.3.3. Creep.Rupture............................................................................................................ . 141.3.4. Stability.Failure........................................................................................................... . 171.3.5. Miscellaneous.Modes.of.Failure................................................................................. . 18

1.4. Piping.Codes.......................................................................................................................... . 191.5. Industry.Practice.................................................................................................................... . 22

1.5.1. Load.Cases.................................................................................................................. . 231.5.2. Local.Support.Stresses................................................................................................ . 241.5.3. Local.Thermal.Stresses............................................................................................... . 241.5.4. Pressure.Effect.on.Flexibility...................................................................................... . 251.5.5. Stress.Intensification.for.Sustained.Loads.................................................................. . 251.5.6. Support.Friction......................................................................................................... . 251.5.7. Guide.and.Stop.Gaps.................................................................................................. . 261.5.8. Anchor.and.Restraint.Stiffness................................................................................... . 261.5.9. Small.Piping................................................................................................................ . 26

1.6. Design.Specification.............................................................................................................. . 261.6.1. Owner’s.Design.Specification..................................................................................... . 261.6.2. Project.Specification................................................................................................... . 28

1.7. Plant.Walk-down................................................................................................................... . 30

Chapter.2Strength.of.Materials.Basics............................................................................................................. . 332.1. Tensile.Strength..................................................................................................................... . 33

2.1.1. Modulus.of.Elasticity.................................................................................................. . 342.1.2. Proportional.Limit...................................................................................................... . 342.1.3. Yield.Strength,.Sy........................................................................................................ . 352.1.4. Ultimate.Strength,.Su.................................................................................................. . 352.1.5. Stresses.at.Skewed.Plane............................................................................................ . 352.1.6. Maximum.Shear.Stress,.Ss,max..................................................................................... . 362.1.7. Principal.Stresses........................................................................................................ . 36

2.2. Elastic.Relationship.of.Stress.and.Strain............................................................................... . 362.2.1. Poisson’s.Ratio........................................................................................................... . 372.2.2. Shear.Strain.and.Modulus.of.Rigidity......................................................................... . 38


iv. Contents

2.3. Static.Equilibrium.................................................................................................................. . 382.3.1. Free-Body.Diagram.................................................................................................... . 392.3.2. Static.Equilibrium....................................................................................................... . 40

2.4. Stresses.due.to.Moments........................................................................................................ . 402.4.1. Stresses.due.to.Bending.Moments.............................................................................. . 402.4.2. Moment.of.Inertia....................................................................................................... . 422.4.3. Polar.Moment.of.Inertia............................................................................................. . 422.4.4. Moment.of.Inertia.for.Circular.Cross-Sections.......................................................... . 432.4.5. Stresses.due.to.Torsion.Moment................................................................................ . 43

2.5. Stresses.in.Pipes..................................................................................................................... . 452.5.1. Stresses.due.to.Internal.Pressure................................................................................ . 452.5.2. Stresses.due.to.Forces.and.Moments.......................................................................... . 47

2.6. Evaluation.of.Multi-Dimensional.Stresses............................................................................. . 492.6.1. General.Two-Dimensional.Stress.Field...................................................................... . 492.6.2. Mohr’s.Circle.for.Combined.Stresses......................................................................... . 512.6.3. Theories.of.Failure...................................................................................................... . 522.6.4. Stress.Intensity.(Tresca.Stress)................................................................................... . 522.6.5. Effective.Stress.(von.Mises.Stress).............................................................................. . 53

2.7. Basic.Beam.Formulas............................................................................................................ . 532.7.1. Guided.Cantilever....................................................................................................... . 55

2.8. Analysis.of.Piping.Assembly.................................................................................................. . 552.8.1. Finite.Element............................................................................................................ . 562.8.2. Data.Points.and.Node.Points..................................................................................... . 572.8.3. Piping.Assembly......................................................................................................... . 58

Chapter.3Thermal.Expansion.and.Piping.Flexibility....................................................................................... . 613.1. Thermal.Expansion.Force.and.Stress.................................................................................... . 61

3.1.1. Ideal.Anchor.Evaluation............................................................................................. . 613.1.2. The.Real.Anchor......................................................................................................... . 62

3.2. Methods.of.Providing.Flexibility........................................................................................... . 633.2.1. Estimating.Leg.Length.Required................................................................................ . 633.2.2. Inherent.Flexibility..................................................................................................... . 653.2.3. Caution.Regarding.Quick.Check.Formulas................................................................ . 653.2.4. Wall.Thickness.and.Thermal.Expansion.Stress.......................................................... . 66

3.3. Self-Limiting.Stress................................................................................................................ . 663.3.1. Elastic.Equivalent.Stress............................................................................................. . 67

3.4. Stress.Intensification.and.Flexibility.Factors......................................................................... . 673.4.1. Ovalization.of.Curved.Pipes....................................................................................... . 683.4.2. Code.SIFs................................................................................................................... . 69

3.5. Allowable.Thermal.Expansion.Stress.Range......................................................................... . 713.6. Cold.Spring............................................................................................................................ . 76

3.6.1. Cold.Spring.Gap......................................................................................................... . 773.6.2. Location.of.Cold.Spring.Gap...................................................................................... . 783.6.3. Cold.Spring.Procedure................................................................................................ . 783.6.4. Multi-Branched.System.............................................................................................. . 793.6.5. Analysis.of.Cold.Sprung.Piping.System...................................................................... . 79

3.7. Pressure.Effects.on.Piping.Flexibility.................................................................................... . 803.7.1. Pressure.Elongation.................................................................................................... . 803.7.2. Potential.Twisting.at.Bends........................................................................................ . 81


Contents. v

3.7.3. Pressure.Elongation.Is.Self-Limiting.Load................................................................. . 823.7.4. Pressure.Effect.on.Bend.Flexibility.and.SIFs.............................................................. . 82

3.8. General.Procedure.of.Piping.Flexibility.Analysis.................................................................. . 833.8.1. Operating.Modes........................................................................................................ . 833.8.2. Anchor.Movements.................................................................................................... . 843.8.3. Assignments.of.Operating.Values............................................................................... . 843.8.4. Handling.of.Piping.Components................................................................................. . 853.8.5. The.Analysis............................................................................................................... . 86

3.9. Problems.With.Excessive.Flexibility...................................................................................... . 863.9.1. Problems.Associated.With.Excessive.Flexibility........................................................ . 88

3.10. Field.Proven.Systems............................................................................................................. . 88

Chapter.4Code.Stress.Requirements................................................................................................................ . 914.1. “Design”.Chapter.of.the.Piping.Codes.................................................................................. . 914.2. Loadings.to.be.Considered.................................................................................................... . 92

4.2.1. Pressure...................................................................................................................... . 934.2.2. Temperature............................................................................................................... . 934.2.3. Weight.Effects............................................................................................................. . 954.2.4. Wind.Load.................................................................................................................. . 954.2.5. Earthquake.................................................................................................................. . 964.2.6. Dynamic.Fluid.Loads................................................................................................. . 964.2.7. Harmonic.Anchor.Displacement.Loads..................................................................... . 984.2.8. Passive.Loads.............................................................................................................. . 98

4.3. Basic.Allowable.Stresses........................................................................................................ . 984.3.1. Bases.for.Establishing.Allowable.Stresses................................................................... . 984.3.2. Code.Allowable.Stress.Tables..................................................................................... . 994.3.3. Weld.Strength.Reduction.Factor.............................................................................. . 100

4.4. Pressure.Design................................................................................................................... . 1014.4.1. Straight.Pipe............................................................................................................. . 1024.4.2. Curved.Segment.of.Pipe............................................................................................ . 1044.4.3. Miter.Bends.............................................................................................................. . 1064.4.4. Branch.Connections................................................................................................. . 1094.4.5. Pressure.Design.for.Other.Components................................................................... . 113

4.5. Stresses.of.Piping.Components............................................................................................ . 1134.5.1. Calculations.of.Component.Stresses......................................................................... . 1134.5.2. Sustained.Stresses..................................................................................................... . 1174.5.3. Occasional.Stresses................................................................................................... . 1194.5.4. Thermal.Expansion.and.Displacement.Stress.Range................................................ . 1214.5.5. Code.Stress.Compliance.Report............................................................................... . 124

4.6. Class.1.Nuclear.Piping......................................................................................................... . 125

Chapter.5Discontinuity.Stresses..................................................................................................................... . 1335.1. Differential.Equation.of.the.Beam.Deflection.Curve........................................................... . 1335.2. Infinite.Beam.on.Elastic.Foundation.With.Concentrated.Load........................................... . 1355.3. Semi-Infinite.Beam.on.Elastic.Foundation.......................................................................... . 1385.4. Application.of.Beam.on.Elastic.Foundation.to.Cylindrical.Shells....................................... . 1395.5. Effective.Widths................................................................................................................... . 1415.6. Choking.Model.................................................................................................................... . 142


vi. Contents

5.7. Stresses.at.Junctions.Between.Dissimilar.Materials............................................................ . 1435.7.1. Uniform.Pipes.With.Similar.Modulus.of.Elasticity................................................... . 1445.7.2. A.Pipe.Connected.to.a.Rigid.Section........................................................................ . 146

5.8. Vessel.Shell.Rotation........................................................................................................... . 147

Chapter.6Pipe.Supports.and.Restraints......................................................................................................... . 1516.1. Device.Terminology.and.Basic.Functions........................................................................... . 1516.2. Support.Spacing................................................................................................................... . 1576.3. Analysis.of.Piping.Systems.Resting.on.Supports................................................................. . 1596.4. Variable.Spring.and.Constant.Effort.Supports..................................................................... . 162

6.4.1. Variable.Spring.Hanger.Selection.Procedure............................................................ . 1636.4.2. Constant-Effort.Supports.......................................................................................... . 1656.4.3. Spring.Support.Types.and.Installations.................................................................... . 1666.4.4. Setting.of.Loads.—.Hot.Balance.and.Cold.Balance................................................. . 168

6.5. Support.of.Long.Risers........................................................................................................ . 1706.5.1. Support.Schemes...................................................................................................... . 1706.5.2. Support.Loads.......................................................................................................... . 1716.5.3. Analysis.Method....................................................................................................... . 172

6.6. Significance.of.Support.Friction.......................................................................................... . 1726.6.1. Effects.of.Support.Friction....................................................................................... . 1726.6.2. Method.of.Including.Friction.in.the.Analysis........................................................... . 1746.6.3. Application.of.Friction.Force................................................................................... . 1766.6.4. Methods.of.Reducing.Friction.Force........................................................................ . 176

6.7. Support.of.Large.Pipes......................................................................................................... . 1786.7.1. Saddle.Supports.Using.Roark’s.Formula.................................................................. . 1796.7.2. Ring.Girder.Supports................................................................................................ . 1806.7.3. Saddle.Supports.by.Zick’s.Method........................................................................... . 1856.7.4. Support.Types........................................................................................................... . 190

6.8. Pipe.Stresses.at.Integral.Support.Attachments.................................................................... . 1946.8.1. Power.Boiler.Formulas.for.Lug.Stresses................................................................... . 1946.8.2. Kellogg’s.Choking.Model......................................................................................... . 1986.8.3. WRC-107.Stress.Evaluation...................................................................................... . 202

6.9. Treatment.of.Support.Stiffness.and.Displacement............................................................... . 205

Chapter.7Flexible.Connections....................................................................................................................... . 2097.1. Basic.Flexible.Joint.Elements.and.Analytical.Tools............................................................ . 211

7.1.1. Generic.Flexible.Connections................................................................................... . 2117.1.2. Bellow.Elements....................................................................................................... . 213

7.2. Using.Catalog.Data.............................................................................................................. . 2187.2.1. Background.of.Catalog.Data.................................................................................... . 2187.2.2. Using.the.Catalog..................................................................................................... . 2197.2.3. Calculating.Operational.Movements........................................................................ . 2237.2.4. Cold.Spring.of.Expansion.Joint................................................................................ . 224

7.3. Applications.of.Bellow.Expansion.Joints............................................................................. . 2257.3.1. Application.of.Axial.Deformation............................................................................ . 2257.3.2. Lateral.Movement.and.Angular.Rotation................................................................. . 2307.3.3. Hinges.and.Gimbals.................................................................................................. . 232

7.4. Slip.Joints............................................................................................................................ . 235


Contents. vii

7.5. Flexible.Hoses...................................................................................................................... . 2377.5.1. Types.of.Metallic.Hoses............................................................................................ . 2377.5.2. Application.and.Analysis.of.Flexible.Hoses............................................................. . 2387.5.3. Analysis.of.Hose.Assembly....................................................................................... . 241

7.6. Examples.of.Improper.Installation.of.Expansion.Joints...................................................... . 2417.6.1. Direction.of.Anchor.Force....................................................................................... . 2417.6.2. Tie-Rods.and.Limit.Rods......................................................................................... . 2427.6.3. Improperly.Installed.Anchors................................................................................... . 244

Chapter.8Interface.with.Stationary.Equipment............................................................................................. . 2478.1. Flange.Leakage.Concern...................................................................................................... . 247

8.1.1. Standard.Flange.Design.Procedure.......................................................................... . 2488.1.2. Unofficial.Position.of.B31.3...................................................................................... . 2508.1.3. Equivalent.Pressure.Method..................................................................................... . 2518.1.4. Class.2.Nuclear.Piping.Rules.................................................................................... . 254

8.2. Sensitive.Valves.................................................................................................................... . 2558.3. Pressure.Vessel.Connections............................................................................................... . 256

8.3.1. Loadings.Imposed.to.Piping.from.Vessel................................................................. . 2578.3.2. Vessel.Shell.Flexibility.............................................................................................. . 2588.3.3. Allowable.Piping.Load.at.Vessel.Connections......................................................... . 2648.3.4. Heat.Exchanger.Connections................................................................................... . 265

8.4. Power.Boiler.and.Process.Heater.Connections................................................................... . 2658.5. Air-Cooled.Heat.Exchanger.Connections............................................................................ . 2688.6. Low-Type.Tank.Connections.............................................................................................. . 270

8.6.1. Displacement.and.Rotation.of.Tank.Connection..................................................... . 2708.6.2. Stiffness.Coefficients.of.Tank.Nozzle.Connection.................................................... . 2728.6.3. Allowable.Piping.Loads.at.Tank.Connections.......................................................... . 2748.6.4. Practical.Considerations.of.Tank.Piping.................................................................. . 280

Chapter.9Interface.with.Rotating.Equipment................................................................................................ . 2859.1. Brief.Background.of.Allowable.Piping.Load.on.Rotating.Equipment................................. . 286

9.1.1. When.Nobody.Knew.What.to.Do............................................................................. . 2869.1.2. First.Official.Set.of.Allowable.Piping.Loads............................................................. . 2879.1.3. Factors.Behind.the.Low.Allowable.Piping.Load...................................................... . 287

9.2. Evaluation.of.Piping.Load.on.Rotating.Equipment............................................................. . 2889.2.1. Effect.of.Piping.Loads............................................................................................... . 2889.2.2. Movements.of.Nozzle.Connection.Point.................................................................. . 2899.2.3. Analysis.Approach.................................................................................................... . 2909.2.4. Selecting.the.Spring.Hangers.to.Minimize.the.Weight.Load.................................... . 2929.2.5. Multi-Unit.Installation.............................................................................................. . 2939.2.6. Fit-up.the.Connection............................................................................................... . 294

9.3. Steam.Power.Turbine.......................................................................................................... . 2959.4. Mechanical.Drive.Steam.Turbines....................................................................................... . 296

9.4.1. Allowable.Loads.at.Individual.Connection.............................................................. . 2969.4.2. Allowable.for.Combined.Resultant.Loads................................................................ . 2979.4.3. Basic.Piping.Layout.Strategy.................................................................................... . 298

9.5. Centrifugal.Pumps............................................................................................................... . 300.9.5.1. Characteristics.Related.to.Piping.Interface.............................................................. . 300


viii. Contents

9.5.2. Basic.Piping.Support.Schemes.................................................................................. . 3029.5.3. Non-API.Pumps....................................................................................................... . 3039.5.4. API.Standard.610.Pumps......................................................................................... . 304

9.6. Centrifugal.Compressors...................................................................................................... . 3089.7. Reciprocating.Compressors.and.Pumps.............................................................................. . 313

9.7.1. Pulsating.Flow.......................................................................................................... . 3139.7.2. Pulsation.Pressure..................................................................................................... . 3159.7.3. Pulsation.Dampener.for.Reciprocating.Pumps......................................................... . 3169.7.4. Some.Notes.on.Piping.Connected.to.Reciprocating.Machine.................................. . 319

9.8. Problems.Associated.With.Some.Techniques.Used.in.Reducing.Piping.Loads.................. . 3219.8.1. Excessive.Flexibility.................................................................................................. . 3219.8.2. Improper.Expansion.Joint.Installations.................................................................... . 3229.8.3. Theoretical.Restraints............................................................................................... . 322

9.9. Example.Procedure.for.Designing.Rotation.Equipment.Piping........................................... . 324

Chapter.10Transportation.Pipeline.and.Buried.Piping.................................................................................... . 32910.1. Governing.Codes.and.General.Design.Requirements.......................................................... . 330

10.1.1. . B31.4.Liquid.Petroleum.Pipeline............................................................................ . 33110.1.2. . B31.8.Gas.Transmission.Pipeline........................................................................... . 333

10.2. Behavior.of.Long.Pipeline.................................................................................................... . 33510.2.1. . Pressure.Elongation................................................................................................ . 33510.2.2. . Anchor.Force.......................................................................................................... . 33510.2.3. . Potential.Movement.of.Free.Ends.......................................................................... . 33610.2.4. . Movement.of.Restrained.Ends................................................................................ . 33710.2.5. . Stresses.at.Fully.Restrained.Section........................................................................ . 337

10.3. Pipeline.Bends..................................................................................................................... . 33910.4. Basic.Elements.of.Soil.Mechanics....................................................................................... . 340

10.4.1. . Types.of.Soils.......................................................................................................... . 34010.4.2. . Friction.Angle......................................................................................................... . 34010.4.3. . Shearing.Stress........................................................................................................ . 34110.4.4. . Soil.Resistance.Against.Axial.Pipe.Movement....................................................... . 34110.4.5. . Lateral.Soil.Force................................................................................................... . 34310.4.6. . Soil-Pipe.Interaction............................................................................................... . 344

10.5. Example.Calculations.of.Basic.Pipeline.Behaviors.............................................................. . 34610.5.1. . Basic.Calculations................................................................................................... . 34610.5.2. . Soil-Pipe.Interaction............................................................................................... . 347

10.6. Simulation.of.Soil.Resistance............................................................................................... . 34810.7. Behavior.of.Large.Bends...................................................................................................... . 34910.8. Construction.of.Analytical.Model........................................................................................ . 35110.9. Anchor.and.Drag.Anchor.................................................................................................... . 353

Chapter.11Special.Thermal.Problems.............................................................................................................. . 35711.1. Thermal.Bowing................................................................................................................... . 357

11.1.1. . Displacement.and.Stress.Produced.by.Thermal.Bowing......................................... . 35711.1.2. . Internal.Thermal.Stresses.Generated.by.Bowing.Temperature............................... . 35911.1.3. . Occurrences.of.Thermal.Bowing............................................................................. . 36011.1.4. . The.Problem.Created.by.a.Tiny.Line...................................................................... . 364

11.2. Refractory.Lined.Pipe.......................................................................................................... . 365


Contents. ix

11.2.1. . Equivalent.Modulus.of.Elasticity............................................................................ . 36511.2.2. . Hot-Cold.Pipe.Junction.......................................................................................... . 366

11.3. Un-Insulated.Flange.Connections....................................................................................... . 36911.4. Unmatched.Small.Branch.Connections............................................................................... . 36911.5. Socket-Welded.Connections................................................................................................ . 370

Chapter.12Dynamic.Analysis.—.Part.1:.SDOF.Systems.and.Basics................................................................. . 37312.1. Impact.and.Dynamic.Load.Factor....................................................................................... . 37312.2. SDOF.Structures.................................................................................................................. . 375

12.2.1. . Working.Formula.for.SDOF.Systems..................................................................... . 37612.2.2. . Un-Damped.SDOF.Systems................................................................................... . 37612.2.3. . Damped.SDOF.Systems......................................................................................... . 38212.2.4. . Summary.of.the.Characteristics.of.SDOF.Vibration............................................... . 386

12.3. Damping.............................................................................................................................. . 38712.4. Sonic.Velocity.Versus.Flow.Velocity................................................................................... . 389

12.4.1. . Sonic.Velocity......................................................................................................... . 39012.4.2. . Flow.Velocity.......................................................................................................... . 392

12.5. Shaking.Forces.due.to.Fluid.Flow....................................................................................... . 39512.6. Safety.Valve.Relieving.Forces.............................................................................................. . 397

12.6.1. . Open.Discharge.System.......................................................................................... . 39712.6.2. . Closed.Discharge.System........................................................................................ . 401

12.7. Steam.Turbine.Trip.Load.................................................................................................... . 403

Chapter.13Dynamic.Analysis.—.Part.2:.MDOF.Systems.and.Applications..................................................... . 40913.1. Lumped-Mass.Multi-Degree.of.Freedom.Systems............................................................... . 409

13.1.1. . Mass.Lumping........................................................................................................ . 41013.1.2. . Free.Vibration.and.Modal.Superposition............................................................... . 412

13.2. Piping.Subject.to.Ground.Motion........................................................................................ . 41313.2.1. . Response.Spectra.Method...................................................................................... . 41513.2.2. . Combination.of.Response.Spectra.Analysis.Results............................................... . 41713.2.3. . Comparison.of.Modal.Combination.Methods........................................................ . 41913.2.4. . Puzzles.of.Absolute.Closely.Spaced.Modal.Combination...................................... . 42113.2.5. . Compensation.for.the.Higher.Modes.Truncated.................................................... . 42213.2.6. . Design.Response.Spectra........................................................................................ . 423

13.3. Account.for.Uncertainties.................................................................................................... . 42613.4. Steady-State.Vibration.and.Harmonic.Analysis................................................................... . 428

13.4.1. . Basic.Vibration.Patterns......................................................................................... . 42813.4.2. . Allowable.Vibration.Displacement.and.Velocity.................................................... . 42913.4.3. . Formulation.of.Harmonic.Analysis......................................................................... . 43713.4.4. . Evaluation.of.Vibration.Stress................................................................................ . 444

13.5. Time-History.Analysis......................................................................................................... . 44613.5.1. . Treatment.of.Damping............................................................................................ . 44613.5.2. . Integration.Schemes................................................................................................ . 44813.5.3. . Time.Step,.Stability,.and.Accuracy......................................................................... . 45013.5.4. . Example.Time-History.Analysis............................................................................. . 451


x. Contents

Appendix.A..................................................................................................................................... . 459Appendix.B..................................................................................................................................... . 461Appendix.C..................................................................................................................................... . 462Appendix.D..................................................................................................................................... . 464Appendix.E..................................................................................................................................... . 466Appendix.F..................................................................................................................................... . 474

INDEX............................................................................................................................................ . 475


ACKNOWLEDGMENTSThis.book.is.essentially.the.summary.of.the.knowledge.accumulated.by.the.authors.through.40.years.of.practice.as.piping.mechanical.engineers..I,.the.senior.author,.would.like.to.use.this.opportunity.to.express.my.appreciation.and.gratitude.to.many.friends,.colleagues,.and.supervisors.for.providing.those.learning.opportunities.and.environments..First,.I.would.like.to.thank.Ron.Hollmeier.of.Pioneer.Service.&.Engineering.in.Chicago.for.offering.me.my.first.pipe.stress.job.developing.a.computer.pro-gram.for.pipe.stress.analysis.in.1967..This.job.allowed.me.to.stay.in.the.United.States.and.led.to.a.long,.interesting.career..I.am.grateful.to.Bechtel’s.Bill.Doble.and.Joe.Gilchrist,.who.did.not.hesitate.to.send.me.to.English.classes.and.put.me.on.interesting.jobs.such.as.the.Trans-Alaskan.pipeline.and.Black..Mesa. coal. slurry. pipeline. projects.. My. most. memorable. work. was. done. at. Nuclear. Services. Cor-poration.in.San.Jose..Working.as.part.of.a.team.that. included.Bob.Keever,.Randy.Broman,.Doug.Munson.and.myself,.and.with.help.from.Professor.Gram.Powell.of.University.of.California-Berkeley.and.valuable.inputs.from.Mel.Pedell.and.Dane.Shave.of.Stone.and.Webster,.we.created.the.NUPIPE.pipe.stress.software,.which.became.a.very.powerful.tool.in.the.design.of.nuclear.piping..I.am.greatly.indebted.to.Don.Mckeehan.and.Ed.Bissaillon.of.M..W..Kellogg.for.their.encouragement.and.imple-mentation.of.the.SIMFLEX.software..As.a.result.of.the.authors’.long.association.with.M..W..Kellogg,.this.book.is.noticeably.influenced.by.Kellogg’s.philosophy.and.approaches.mentioned.in.the.second.edition.of.the.Kellogg’s.book.—.Design of Piping Systems (1956,.John.Wiley.and.Sons)..Suggestions.from.Ray.Chao.and.David.Osage.of.Exxon.Research.were.very.helpful.during.the.development.of.the.PENGS.program..The.estimated.1000.engineers,.who.came.to.my.training.classes.conducted.in.a.dozen.countries,.have.greatly.widened.my.perspective.on.piping.mechanical.work..The.authors.are.very.grateful.to.ASME.Press.for.valuable.comments.and.excellent.editing..We.would.also.like.to.thank.the.twin.sisters.Lina.and.Linda.for.reading.the.manuscript..The.fact.that.these.two.non-technical.sis-ters.have.read.through.the.entire.draft.of.the.manuscript.has.greatly.encouraged.us.

Liang-Chuan (L.C.) PengTsen-Loong (Alvin) Peng

xi



PREFACEPipe.stress.analysis.calculates.the.stress.in.a.piping.system.subject.to.normal.operating.loads.such.as.pressure,.weight,.and.thermal.expansion,.and.occasional.loads.such.as.wind,.earthquake,.and.water.hammer..Because.all.piping.systems.are.connected.to.equipment.such.as.vessels,.tanks,.pumps,.tur-bines,.and.compressors,.the.piping.stress.analysis.also.involves.evaluation.of.the.effect.of.the.piping.forces.and.moments.to.the.connecting.equipment..As.the.piping.stress.is.controlled.by.the.arrange-ment.of.the.supports.and.restraints,.the.scope.of.piping.stress.includes.also.pipe.supports..The.whole.scope.of.this.work.is.generally.referred.to.as.piping.mechanical.

Before.the.advent.of.the.electronic.computer,.pipe.stress.analysis.was.handled.by.very.specialized.engineers..Only.large.corporations.and.specialized.firms.had.the.personnel.to.do.the.job..It.normally.took.a.specialist.to.use.the.calculator.non-stop.for.a.couple.of.weeks.just.to.analyze.the.flexibility.of.a.moderately.complex.piping.system.to.absorb.the.thermal.expansion.of.the.pipe..Because.only.very.few.of.these.engineers.knew.how.to.analyze.piping.stress,.most.engineers.treated.it.as.some.type.of.a.mysterious.subject..Engineers.saw.there.were.expansion.loops,.offsets,.and.special.supports.such.as.spring.hangers.and.constant.effort.supports,.but.did.not.really.know.why.they.were.there..The.limited.scope.of.pipe.stress.analysis.dealing.with.the.piping.flexibility.for.absorbing.thermal.expansion.was.called.piping.flexibility.analysis.

With.the.arrival.of.the.electronic.computer.in.the.1970s,.and.especially.the.personal.computer.in.the.1980s,.suddenly.everybody.knew.how.to.analyze.pipe.stress..This.has.generated.even.more.mystery.about.the.field..Nowadays,.we.occasionally.see.an.electrical.engineer,.although.discouraged,.conduct-ing.the.analysis.just.as.proficiently.as.a.mechanical.or.a.structural.engineer..This.partly.stems.from.the.fact.that.colleges.and.universities.normally.do.not.offer.any.course.on.pipe.stress..This.leaves.the.knowledge.and.skill.of.pipe.stress.and.piping.engineering.to.be.learned.by.self-study.and.actual.prac-tice..Practitioners.who.obtain.the.best.computer.program.and.comprehend.the.manual.most.will.do.the.better.job.

With.the.rapid.advancement.in.computer.technology,.a.piping.flexibility.analysis.nowadays.takes.only.few.minutes.via.an.appropriate.computer.software..Therefore,.the.task.of.the.stress.engineer.has.been.shifted.from.the.traditional.stress.calculation.to.stress.engineering..The.emphasis.is.not.on.how.to.calculate.the.stress,.but.rather.on.how.to.utilize.the.analysis.tool.to.design.a.better.plant..However,.just.because.it.is.easy.to.get.the.stress.calculated,.engineers.often.depend.too.much.on.the.computer.and.forget.about. the. fundamentals.and.engineering.common.sense..Without. the. fundamentals.and.common.sense,.one.may.not.even.be.aware.of.the.unreasonable.results.produced.by.the.computer,.to.say.the.least.about.good.engineering..This.book.emphasizes.engineering.common.sense.as.well.as.the.basic.principles..The.following.are.some.examples.of.piping.problems.that.might.have.been.solved.by.just.good.engineering.common.sense:

.A.plant.operated.smoothly.for.the.first.10.years,.and.then.experienced.a.leakage.at.the.main.process.piping.about.every.4.months.after.a.major.revamping..Experts.were.con-sulted,.sophisticated.analyses.were.performed,.and.expensive.modifications.were.made.to.no.avail..Had.the.engineers.used.the.basic.thermal.stress.common.sense,.the.problem.would.have.been.solved.with.very.little.effort.(see.Section.11.2.2)..The.pressure.thrust.force.is.very.critical.at.a.bellow.expansion.joint..Anchors.are.often.needed. at. bellow. expansion. joint. installations. to. resist. the. pressure. thrust. force,. but.

•

•

xiii


sometimes.an.anchor.placed.at.the.wrong.location.may.just.be.the.cause.of.the.problem..The.wrong.anchor.had.been.contributing.to.severe.vibration.at.some.rotating.equipment..Had.we.known.that. the.pressure. thrust. force.at.an.expansion. joint. is.generally.much.higher.than.the.force.that.can.be.tolerated.by.the.rotating.equipment,.the.problem.would.not.have.occurred.(Chapters.7.and.9)..A.small.steam.purge. line. in.a. large.process.pipe.had.caused.the.plant.piping.to. twist.wildly,.breaking.many.connecting.leads..Several.major.re-routing.of.the.piping.systems.were.made,.but.the.problem.persisted..Had.the.involved.engineers.had.some.idea.about.thermal.bowing,.the.problem.could.have.been.easily.corrected.(see.Section.11.1.4).

Providing. the. knowledge. for. solving. the. problems. such. as. the. ones. listed. above. is. the. primary.goal.of.the.book..Chapter.1.summarizes.the.scopes.and.requirements.related.to.piping.mechanical.activities,.and.the.subsequent.chapters.discuss.how.to.deal.with.them..Chapter.1.contains.some.of.the.authors’.inside.views,.which.we.hope.will.help.the.readers.progress.more.confidently.and.comfortably.into.the.piping.mechanical.field.

Nowadays,.making.a.calculation.with.a.computer.is.so.fast.that.we.often.hear.about.the.“what-if”.approach.in.engineering..What.all.this.“what-if”.approach.accomplishes.is.making.numerous.random.trials.and.the.wish.that.one.of.these.trials.will.hit.the.mark.sooner.or.later..The.problem.is.that.after.a.few.trials,.most.people.lose.the.ability.to.make.sense.of.the.trials..The.more.they.try,.the.more.they.get.confused..In.contrast,.this.book.puts.emphasis.on.the.“what,.why,.and.how”.to.guide.the.readers.into.this.3-W.approach.—.that.is,.to.be.aware.of.the.problem,.understand.the.cause.of.the.problem,.and.to.solve.the.problem.or.prevent.it.from.happening.

The.authors.will.try.to.explain.all.the.necessary.tasks.of.pipe.stress.engineering.with.basic.funda-mentals..Although.only.a. few.very. fundamental.equations.are. introduced,. theoretical.backgrounds.will.be.covered.in.as.much.detail.as.possible..The.book.is.titled.Pipe Stress Engineering.to.distinguish.it.from.a.regular.pipe.stress.analysis.book,.which.normally.lacks.the.coverage.of.the.engineering.aspects..Although.this.book.is.intended.for.piping.mechanical.engineers,.it.is.also.a.suitable.reference.book.for.piping.designers,.plant.engineers,.and.civil-mechanical.engineers..The.book.can.be.used.as.the.textbook.for.a.one-.or.two-semester.elective.course.given.at.the.senior.or.graduate.level.

•

xiv. Preface


NOMENCLATURE(All.are.in.consistent.units..Special.usages.and.non-consistent.units.are.noted.in.the.main.text..Ab-breviations.are.listed.at.the.end)

A. Cross-section.areaA. Thickness.allowance.including.corrosion,.thread,.etc.A. Flow.areaAb. Total.net.cross-section.area.of.flange.boltsAc. Corrosion.allowance.of.pipe.thicknessAm. Manufacturing.under-tolerance.of.pipe.thicknessAp. Pressure.area.encircled.by.the.bolt.circle.of.flangeAT. Nozzle.throat.area.or.valve.orifice.areaa. Bellow.effective.pressure.thrust.areaa. Sonic.speeda. Tank.nozzle.radiusB. Flange.inside.diameterB. Tank.bottom.plate.thermal.expansion.factorb. Flange.effective.gasket.widthb. Thickness.of.support.saddle,.in.pipe.axial.directionb. Width.of.the.beam.cross-sectionb. Width.of.a.small.element.or.stripC. Cold.spring.factorC. Flange.bolt.circle.diameterC. Thermal.bowing.local.stress.factor,.defined.in.Figure.11.2[C ]. Damping.matrix.of.the.structural.systemC1,.C2. integration.constants.to.be.determined.by.boundary.conditionsC2,.K2. ASME.Class-1.nuclear.piping.stress.indices.for.displacement.loadingCED. End.coefficient.with.respect.to.vibration.displacement,.defined.in.Eq..(13.43)CEV. End.coefficient.with.respect.to.vibration.velocity,.defined.in.Eq..(13.52)CK. Kármán.force.coefficient.on.vortex.shedding.forceCw. Ratio.of.total.pipe.weight,.including.pipe.metal.weight,.content,.and.insulation,.to.pipe.

metal.weightCX. Vibration.stress.amplification.factor.due.to.concentrated.weightc. Soil.cohesion.stressc. Viscous.dampingcp. Specific.heat.of.gas.under.constant.pressure.conditioncv. specific.heat.of.gas.under.constant.volume.conditionD. Diameter.of.pipe.or.circular.cross-sectionD. Diameter.of.vessel.shell.or.run.pipe{D}. Displacement.vector.in.global.coordinates,.for.both.element.and.overall.structures{D¢}. Element.displacement.vector.in.local.coordinatesDc. Combined.equivalent.diameter.of.all.the.nozzles.at.rotating.equipmentDe. Equivalent.diameter.of.an.individual.nozzle.at.rotating.equipment

xv


DLF. Dynamic.load.factord. Displacementd. Diameterd. Diameter.of.branch.pipede. Elastic.displacement.limit.of.an.elastic-plastic.restraintdp. Pitch.diameter.of.bellowE. Modulus.of.elasticityE. Longitudinal.joint.efficiency,.normally.expressed.with.allowable.stress.as.(SE)Ee. Equivalent.modulus.of.elasticity.for.composite.pipee. Strainecom. Combined.total.equivalent.axial.bellow.deformation.per.convolutionex. Axial.bellow.deformation.per.convolutioney. Equivalent.axial.bellow.deformation.per.convolution.due.to.lateral.displacement.yeθ. Equivalent.axial.bellow.deformation.per.convolution.due.to.rotation.θF. ForceF. Gas.pipeline.design.factor.(defined.in.Table.10.2)F. Pipeline.anchor.force,.or.potential.expansion.force{F}. Force.vector.in.global.coordinates,.for.both.element.and.overall.structures{F ¢}. Element.force.vector.in.local.coordinates|F|. Absolute.value.of.force.FF1. Force.equivalent.to.total.impulse.function.=.ρAV 2.+.PA{FC}. Vector.of.cosine.components.of.the.harmonic.forceFK. Kármán.force.or.vortex.shedding.forceFmax. Net.maximum.peak.shaking.force.of.a.given.piping.legFn. Normal.forceFnS. Pressure.force.at.point.n.due.to.standing.pressure.waveFnT. Pressure.force.at.point.n.due.to.traveling.pressure.waveFP. Tank.nozzle.pressure.force.defined.in.Eq..(8.30)FR. Radial.forceFR. Resultant.forceFs. Shear.force{FS}. Vector.of.sine.components.of.the.harmonic.forceF(t). Force.as.function.of.timeFRX. Rotation.spring.constant.about.x.axis.for.a.generic.flexible.jointFRY. Rotation.spring.constant.about.y.axis.for.a.generic.flexible.joint.FRZ. Rotation.spring.constant.about.z.axis.for.a.generic.flexible.jointFTX. Translation.spring.constant.in.x.axis.for.a.generic.flexible.jointFTY. Translation.spring.constant.in.y-.axis.for.a.generic.flexible.jointFTZ. Translation.spring.constant.in.z-.axis.for.a.generic.flexible.jointf. Line.force.per.unit.length.of.active.line.in.an.attachmentf. Natural.frequency.of.the.structural.system,.or.frequency.of.a.vibrationf. Pipeline.friction.force.per.unit.length.of.pipef. Stress.range.factor.for.calculating.allowable.expansion.stress.rangef. Support.friction.forcef1(βx). Beam.on.elastic.foundation.function.defined.by.Eq..(5.17a)f2(βx). Beam.on.elastic.foundation.function.defined.by.Eq..(5.17b)f3(βx). Beam.on.elastic.foundation.function.defined.by.Eq..(5.17c)f4(βx). Beam.on.elastic.foundation.function.defined.by.Eq..(5.17d)fw. Working.(nominal).axial.spring.constant.per.bellow.convolutionG. Flange.gasket.load.reaction.circle.diameterG. Shear.modulus.of.elasticity,.modulus.of.rigidity

xvi. Nomenclature


g1. Flange.hub.thickness.at.back.of.flangegx,.gy,.gz. Cold.spring.gap.in.x,.y,.z.directions,.respectivelyH. Depth.of.soil.cover,.from.top.of.pipe.to.soil.surfaceH. Height.of.the.beam.cross-sectionH. Ring.force.per.unit.circumferential.breadthh. Flexibility.characteristic.of.piping.component,.defined.in.Table.3.1h. Safety.valve.height,.defined.in.Fig..12.17h. Soil.depth.at.an.arbitrary.pointI. Moment.of.inertia.of.a.pipe.or.beam.cross-section[I ]D. Identity.matrix,.or.unit.diagonal.matrix,.with.1.on.diagonal.and.0.at.elsewhereIp. Polar.moment.of.inertiai. Stress.intensification.factori. Imaginary.number,.square.root.of.-1iC. Stress.intensification.factor.for.circumferential.stressiL. Stress.intensification.factor.for.longitudinal.stressK. Bulk.modulus.of.the.liquid.=.-dp/(dv/v)K. Stiffness.or.spring.constant.of.support.structure[K ]. Stiffness.matrix.in.global.coordinates,.for.both.element.and.overall.structures[K¢]. Element.stiffness.matrix.in.local.coordinatesKA. Coefficient.of.active.lateral.soil.pressureKh. Spring.constant.per.unit.pipe.length.for.horizontal.soil.resistanceKL. EJMA.bellow.lateral.spring.rate.=.KV

KN. Napier.constant.for.steam.flowKR. EJMA.bellow.rotational.spring.rate.=.KRθKRy. Bellow.rotational.spring.rate.due.to.lateral.end.deflectionKRθ. Bellow. rotational. spring. rate. due. to. end. rotation,. when. free. lateral. deflection. is..

allowedKV. Bellow.lateral.spring.rate.due.to.lateral.end.deflection..End.moment.also.createdKv. Spring.constant.per.unit.pipe.length.for.vertical.soil.resistanceKx. Bellow.axial.spring.ratek. Flexibility.factor.of.piping.componentk. Ratio.of.specific.heats.=.cp/cv

k. Spring.constant.and.directional.stiffnessk. Spring.constant.of.foundation.per.unit.length.of.beamL. Distance.from.the.center.of.tank.nozzle.to.tank.bottomL. LengthL. Pipeline.active.lengthL. Support.spacing[L]. Transformation.matrix.between.local.coordinates.and.global.coordinatesLMP. Larson-Miller.parameter.defined.in.Eq..(1.2)ℓ. Elongationℓ. Support.lug.lengthℓ. Length.of.elementM. MassM. Moment[M ]. Mass.matrix.of.the.structural.systemMmass. Concentrated.massMC. Circumferential.momentML. Longitudinal.momentMR. Resultant.momentMt. Torsion.moment

Nomenclature. xvii


Mw. Molecular.weightMy. Moment.produced.by.bellow.lateral.displacement.without.free.end.rotationMθ. Moment.produced.by.bellow.rotation.with.free.lateral.displacementM(θ.+.D). Moment.produced.by.bellow.rotation.without.free.lateral.displacementm. Flange.gasket.factorm. Mass.per.unit.length.of.pipe ̇m. Mass.flow.rateN. Circumferential.force.per.unit.length.of.pipeN. Number.of.bellow.convolutionsN. Number.of.operating.cyclesNS. Strouhal.number.on.vortex.shedding.frequency;.NS.=.fD/Vn. Number.of.stiffening.rings.at.each.support.saddleP. PressurePd. Flange.design.pressurePe. Equivalent.pressure.due.to.force.and.moment.acting.on.a.flangePS. Pressure.amplitude.of.a.standing.wavePT. Pressure.amplitude.of.a.traveling.wavep. Pressurep*. Critical.pressure.at.sonic.velocity.stateQ. Pipeline.end.resistance.forceQ. Total.support.loadQ. Volumetric.flow.rate[Q]. Influence.or.relation.matrix.relating.ground.motion.to.every.part.of.the.structureq. Distributed.external.force.per.unit.length.of.beamq. Pitch.of.bellow.convolutionqa. Deformed.pitch.at.centerline.of.bellowqc. Compressed.pitch.at.pitch.diameter.of.bellowqe. Extended.pitch.at.pitch.diameter.of.bellowqh. Horizontal.soil.resistance.force.per.unit.length.of.pipeqv. Vertical.soil.resistance.force.per.unit.length.of.pipeR. Bend.radiusR. Gas.constant.=.R/Mw

R. Radius.of.curvatureR. Radius.of.circular.cross-sectionR. Radius.of.vessel.shellR. Reaction.forceR. Universal.gas.constantRa. Acceleration.response.spectraRaj. Acceleration.response.spectra.of.jth.independent.support.motionRC. Radius.of.the.crown.on.a.vessel.headRd. Displacement.response.spectraRv. Velocity.response.spectrar. Radius.of.an.arbitrary.circular.ringr. Radius.of.pipe.cross-sectionr. Radius.of.round.attachmentr. Rotationrm. Mean.radius.of.pipe.cross-sectionS. Basic.allowable.stress.for.pipelineS. StressSA. Basic.allowable.thermal.expansion.stress.rangeSb. Flange.bolt.stress

xviii. Nomenclature


Sc. Allowable.stress.of.pipe.material.at.cold.ambient.conditionSE. Expansion.stressSEB. Benchmark.expansion.stress.rangeSel. Endurance.strength.of.pipe.materialSelA. Allowable.endurance.strengthSF. Flange.gasket.stress.due.to.axial.force{Sg}. Vector.of.independent.support.motion.componentsSh. Allowable.stress.of.pipe.material.at.hot.operating.conditionSh. Pressure.hoop.stressShp. Hoop.pressure.stressSi. Stress.intensity.(=twice.of.the.maximum.shear.stress)Slp. Longitudinal.pressure.stressSM. Flange.gasket.stress.due.to.bending.momentSMYS. Specified.Minimum.Yield.StrengthSP. Flange.gasket.stress.due.to.pressureSPW. Longitudinal.pipe.stress.due.to.pressure.and.weightST. Local.thermal.stress.due.to.thermal.bowingSu. Ultimate.strengthSy. Yield.strengthSyc. Yield.strength.at.cold.conditionSyhx. The.lesser.of.yield.strength.at.hot.condition.and.160%.of.the.stress.producing.0.01%.

creep.in.1000.hours.at.the.operating.temperatureT. Absolute.temperature,.K.(=273.+.°C).or.R.(=460.+.°F)T. Period.of.vibrationT. TemperatureT. Vessel.thickness.or.run.pipe.thicknessT*. Critical.absolute.temperature.at.sonic.velocity.statet. Thickness.of.bellowt. Thickness.of.branch.pipet. Thickness.of.pipe,.generict. Thickness.of.tank.shell.at.nozzle.locationt. Timetd. Time.duration.of.an.impulse.loadingto. Effective.valve.opening.timeV. Bellow.lateral.forceV. VelocityV. VolumeV. Tangential.shear.force.per.unit.circumferential.breadthv. Shear.forcev. Specific.volumeW. Total.flange.bolt.loadW. Total.shear.force.at.pipe.cross-sectionW. Weight.load.in.force.unitW. Weight.of.the.free.body,.or.weight.loadW. Weld.strength.reduction.factorWp. Weight.of.pipe.per.unit.length.of.pipeWs. Weight.of.soil.cover.per.unit.length.of.pipew. Weight.per.unit.length{X }. Displacement.vector.of.the.structural.system.XA. Distance.between.the.top.of.nozzle.and.tank.bottom.plateXB. Distance.between.the.bottom.of.nozzle.and.tank.bottom.plate

Nomenclature. xix


XC. Distance.between.the.center.of.nozzle.and.tank.bottom.plate{X}g. Ground.motion.displacement.vectorx. Axial.displacement.of.beam.or.bellowx,.y,.z. Coordinates.in.x,.y,.z.directions,.respectively YC. Allowable.coefficient,.Fig..8.25,.for.circumferential.moment.on.tank.nozzle YF. Allowable.coefficient,.Fig..8.25,.for.axial.force.on.tank.nozzle YL. Allowable.coefficient,.Fig..8.25,.for.longitudinal.moment.on.tank.nozzley. Adjustment.coefficient.(see.Table.4.1).for.pipe.thickness.calculationy. Flange.gasket.seating.stressy. Local.lateral.displacement.of.beam.or.bellowy. Pipeline.end.axial.movementy. Radial.displacement.of.pipe.shellZ. Section.modulus.of.a.pipe.or.beam.cross-sectionZp. Polar.section.modulusZPA. Zero.period.acceleration.of.the.response.spectra.curvez. Compressibility.of.real.gas.=.pv/(RT )

Greek.symbolsa. Constant.defining.participation.of.mass.in.damping,.see.Eq..(13.76)a. Vibration.allowable.stress.reduction.factor,.1.3.for.carbon.and.low.alloy.steels.and.1.0.

for.austenitic.stainless.and.high.alloy.steelsa. Thermal.expansion.rate,.as.expansion.per.unit.length.per.unit.temperatureβ. Angle.from.top.of.pipe.to.edge.of.saddleβ. Angle.of.branch.intersectionβ. Branch/run.diameter.ratioβ. Characteristic.parameter.of.beam.on.elastic.foundation,.defined.by.Eq..(5.26)β. Constant.defining.participation.of.stiffness.in.damping,.see.Eq..(13.76)β. Frequency.ratio.of.the.applied.frequency.to.the.natural.frequency.of.the.systemγ. Rotational.deformationD. Clearance.between.tube.and.tube.sheet.holeD. DeflectionD... Difference.of...DA. Amplitude.decay.due.to.step-by-step.time-history.analysisDT. Period.elongation.due.to.step-by-step.time-history.analysisDt. Integration.time.step.for.time-history.analysisζ. Damping.ratio,.the.ratio.of.damping.to.critical.dampingη. Nozzle.flow.efficiencyθ. Angle.of.circular.wedgeθ. Angle.of.miterθ. Angle.of.the.inclining.planeθ. Rotationθ. Support.saddle.anglel. Tank.geometrical.parameter.defined.in.Eq..(8.30)µ. Friction.coefficientν. Poisson.ratioξ. Coordinate.or.coefficient.of.normal.mode.space,.i.e.,.{X}.=.[F]{ξ}{ξC}. Cosine.component.of.modal.coordinate.vector.of.harmonic.response{ξS}. Sine.component.of.modal.coordinate.vector.of.harmonic.responseπ. 3.141592ρ. Angle.of.the.maximum.bending.moment.location.at.a.support.ringρ. Density,.mass.per.unit.volume

xx. Nomenclature


å. Summation.oft. Shear.stressυ. Flow.velocity{F}. Eigenvector,.or.natural.vibration.shape[F]. Eigenvector.matrix.with.eigenvectors.as.columnsφ. Angle.from.top.of.pipeφ. Bellow.rotation.per.convolutionφ. Soil.internal.friction.angleω. Circular.frequency,.or.rotational.speedωd. Circular.natural.frequency.for.damped.systemωn. Circular.natural.frequency.for.un-damped.(and.also.damped).system

Subscripts0. At.origin0. initial.state0,.1,.2,…. At.location.0,.1,.2,…,.etc.,.or.at.condition.0,.1,.2,…,.etc.a. Allowableallow. Allowablea,.b,…. at.point.a,.b,…,.etc.b. bendingb. branch.pipec. circumferential.directionc. cold.or.ambient.temperaturec. critical.conditionD. discharge.sidee. equivalentf. frictionH. hoop.directionh. hub.of.flangeh. hot.or.operating.temperaturehp. hoop.pressurei. in-planei. inside.surface.of.the.pipeL. longitudinal.directionl. longitudinal.directionlp. longitudinal.pressurem. mean.valuemax. maximum.valuen. natural.vibrationn. nominaln. normalo. out-planeo. outside.surface.of.the.pipep. pressureR. radial.directionR. resultantR. rigid.body.responseR. run.piper. ring.stiffenerr. run.pipe

Nomenclature. xxi


s. suction.sides. shearst. staticT. test.conditiont. tangentialt. torsionxy. on.x.plane.and.in.y.directionx,.y,.z. components.in.x,.y,.and.z.directions,.respectivelyy. yield.conditiony. at.y.distance.away

AbbreviationsABS. absoluteANSI. American.National.Standards.InstituteAPI. American.Petroleum.InstituteASME. American.Society.of.Mechanical.EngineersASTM. American.Society.of.Testing.and.MaterialsAWWA. American.Water.Work.Works.AssociationB&PV. Boiler.and.Pressure.VesselCEN. Comité.Européen.de.Normalisation.(European.Standard).cps. cycles.per.secondDLF. dynamic.load.factorft. foot.or.feetin.. inch.or.inchesHz. Hertz.=.cycles.per.secondK. Kelvin.=.273.+.°Cksi. kilo.pounds.per.square.inch.=.1000.psilb. pound.(weight.or.force)lbf. pound.forcem. meterMDOF. multi.degrees.of.freedomMSS. Manufacturer.Standardization.Society.of.the.Valve.and.Fitting.IndustryN. NewtonNRC. Nuclear.Regulatory.CommissionPa. Pascal.=.N/m2

psi. pounds.per.squire.inchR. Rankin.=.460.+.°FRPM. revolution.per.minuteSDOF. single.degree.of.freedomSIF. stress.intensification.factorSRSS. square.root.sum.of.the.squaresWRC. Welding.Research.Council

xxii. Nomenclature


Documents

PiPe StreSS engineering - Ebooksebooks.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/... · PiPe StreSS engineering by Liang-Chuan (L.C.) ... Local.Support.Stresses