Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

649 Pages·2010·4.62 MB·English

by  T.H.G. Megson

An Introduction to Aircraft
Structural Analysis
T. H. G. Megson
AMSTERDAM•BOSTON•HEIDELBERG•LONDON
NEWYORK•OXFORD•PARIS•SANDIEGO
SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO

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LibraryofCongressCataloging-in-PublicationData
Megson,T.H.G.(ThomasHenryGordon)
Anintroductiontoaircraftstructuralanalysis/T.H.G.Megson.
p.cm.
Rev.ed.of:Aircraftstructuresforengineeringstudents/T.H.G.Megson.4thed.2007.
Includesbibliographicalreferencesandindex.
ISBN978-1-85617-932-4(alk.paper)
1.Airframes.2.Structuralanalysis(Engineering)I.Title.
TL671.6.M362010
629.134’31–dc22
2009050354
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Contents
Preface ............................................................................................. vii
PART A FUNDAMENTALS OF STRUCTURAL ANALYSIS
CHAPTER1 BasicElasticity........................................................................... 3
1.1 Stress.................................................................................................. 3
1.2 NotationforForcesandStresses................................................................... 5
1.3 EquationsofEquilibrium ........................................................................... 7
1.4 PlaneStress........................................................................................... 9
1.5 BoundaryConditions................................................................................ 9
1.6 DeterminationofStressesonInclinedPlanes.................................................... 10
1.7 PrincipalStresses .................................................................................... 14
1.8 Mohr’sCircleofStress.............................................................................. 16
1.9 Strain.................................................................................................. 20
1.10 CompatibilityEquations ............................................................................ 24
1.11 PlaneStrain........................................................................................... 25
1.12 DeterminationofStrainsonInclinedPlanes...................................................... 25
1.13 PrincipalStrains...................................................................................... 27
1.14 Mohr’sCircleofStrain.............................................................................. 28
1.15 Stress–StrainRelationships......................................................................... 28
1.16 ExperimentalMeasurementofSurfaceStrains................................................... 37
Problems.............................................................................................. 41
CHAPTER2 Two-DimensionalProblemsinElasticity.............................................. 45
2.1 Two-DimensionalProblems........................................................................ 45
2.2 StressFunctions...................................................................................... 47
2.3 InverseandSemi-InverseMethods ................................................................ 48
2.4 St.Venant’sPrinciple................................................................................ 53
2.5 Displacements........................................................................................ 54
2.6 BendingofanEnd-LoadedCantilever ............................................................ 55
Problems.............................................................................................. 60
CHAPTER3 TorsionofSolidSections............................................................... 65
3.1 PrandtlStressFunctionSolution................................................................... 65
3.2 St.VenantWarpingFunctionSolution ............................................................ 75
3.3 TheMembraneAnalogy ............................................................................ 77
3.4 TorsionofaNarrowRectangularStrip............................................................ 79
Problems.............................................................................................. 82
CHAPTER4 VirtualWorkandEnergyMethods..................................................... 85
4.1 Work................................................................................................... 85
4.2 PrincipleofVirtualWork ........................................................................... 86
4.3 ApplicationsofthePrincipleofVirtualWork.................................................... 99
Problems.............................................................................................. 107
CHAPTER5 EnergyMethods.......................................................................... 111
5.1 StrainEnergyandComplementaryEnergy....................................................... 111
5.2 ThePrincipleoftheStationaryValueoftheTotalComplementaryEnergy.................. 113
iii
iv Contents
5.3 ApplicationtoDeflectionProblems ............................................................... 114
5.4 ApplicationtotheSolutionofStaticallyIndeterminateSystems............................... 122
5.5 UnitLoadMethod ................................................................................... 138
5.6 FlexibilityMethod................................................................................... 141
5.7 TotalPotentialEnergy............................................................................... 147
5.8 ThePrincipleoftheStationaryValueoftheTotalPotentialEnergy........................... 148
5.9 PrincipleofSuperposition .......................................................................... 151
5.10 TheReciprocalTheorem............................................................................ 151
5.11 TemperatureEffects ................................................................................. 156
Problems.............................................................................................. 158
CHAPTER6 MatrixMethods........................................................................... 169
6.1 Notation............................................................................................... 170
6.2 StiffnessMatrixforanElasticSpring............................................................. 171
6.3 StiffnessMatrixforTwoElasticSpringsinLine................................................. 172
6.4 MatrixAnalysisofPin-jointedFrameworks...................................................... 176
6.5 ApplicationtoStaticallyIndeterminateFrameworks............................................ 183
6.6 MatrixAnalysisofSpaceFrames.................................................................. 183
6.7 StiffnessMatrixforaUniformBeam.............................................................. 185
6.8 FiniteElementMethodforContinuumStructures............................................... 193
Problems.............................................................................................. 211
CHAPTER7 BendingofThinPlates.................................................................. 219
7.1 PureBendingofThinPlates........................................................................ 219
7.2 PlatesSubjectedtoBendingandTwisting........................................................ 223
7.3 PlatesSubjectedtoaDistributedTransverseLoad............................................... 227
7.4 CombinedBendingandIn-PlaneLoadingofaThinRectangularPlate....................... 236
7.5 BendingofThinPlatesHavingaSmallInitialCurvature....................................... 240
7.6 EnergyMethodfortheBendingofThinPlates .................................................. 241
Problems.............................................................................................. 250
CHAPTER8 Columns................................................................................... 253
8.1 EulerBucklingofColumns......................................................................... 253
8.2 InelasticBuckling.................................................................................... 259
8.3 EffectofInitialImperfections...................................................................... 263
8.4 StabilityofBeamsunderTransverseandAxialLoads.......................................... 266
8.5 EnergyMethodfortheCalculationofBucklingLoadsinColumns........................... 270
8.6 Flexural–TorsionalBucklingofThin-WalledColumns......................................... 274
Problems.............................................................................................. 287
CHAPTER9 ThinPlates................................................................................ 293
9.1 BucklingofThinPlates............................................................................. 293
9.2 InelasticBucklingofPlates......................................................................... 296
9.3 ExperimentalDeterminationofCriticalLoadforaFlatPlate.................................. 298
9.4 LocalInstability...................................................................................... 299
9.5 InstabilityofStiffenedPanels...................................................................... 300
9.6 FailureStressinPlatesandStiffenedPanels...................................................... 302
9.7 TensionFieldBeams ................................................................................ 304
Problems.............................................................................................. 320
Contents v
PART B ANALYSIS OF AIRCRAFT STRUCTURES
CHAPTER10 Materials.................................................................................. 327
10.1 AluminumAlloys.................................................................................... 327
10.2 Steel ................................................................................................... 329
10.3 Titanium............................................................................................... 330
10.4 Plastics................................................................................................ 331
10.5 Glass................................................................................................... 331
10.6 CompositeMaterials................................................................................. 331
10.7 PropertiesofMaterials.............................................................................. 333
Problems.............................................................................................. 349
CHAPTER11 StructuralComponentsofAircraft ..................................................... 351
11.1 LoadsonStructuralComponents .................................................................. 351
11.2 FunctionofStructuralComponents................................................................ 354
11.3 FabricationofStructuralComponents............................................................. 359
11.4 Connections........................................................................................... 363
Problems.............................................................................................. 370
CHAPTER12 Airworthiness............................................................................. 373
12.1 FactorsofSafety-FlightEnvelope ................................................................. 373
12.2 LoadFactorDetermination......................................................................... 375
CHAPTER13 AirframeLoads........................................................................... 379
13.1 AircraftInertiaLoads................................................................................ 379
13.2 SymmetricManeuverLoads........................................................................ 386
13.3 NormalAccelerationsAssociatedwithVariousTypesofManeuver .......................... 391
13.4 GustLoads............................................................................................ 393
Problems.............................................................................................. 399
CHAPTER14 Fatigue .................................................................................... 403
14.1 SafeLifeandFail-SafeStructures................................................................. 403
14.2 DesigningAgainstFatigue.......................................................................... 404
14.3 FatigueStrengthofComponents................................................................... 405
14.4 PredictionofAircraftFatigueLife................................................................. 409
14.5 CrackPropagation................................................................................... 414
Problems.............................................................................................. 420
CHAPTER15 BendingofOpenandClosed,Thin-WalledBeams................................... 423
15.1 SymmetricalBending................................................................................ 424
15.2 UnsymmetricalBending ............................................................................ 433
15.3 DeflectionsduetoBending......................................................................... 441
15.4 CalculationofSectionProperties.................................................................. 456
15.5 ApplicabilityofBendingTheory................................................................... 466
15.6 TemperatureEffects ................................................................................. 466
Problems.............................................................................................. 471
CHAPTER16 ShearofBeams .......................................................................... 479
16.1 GeneralStress,Strain,andDisplacementRelationshipsforOpen
andSingleCellClosedSectionThin-WalledBeams............................................ 479
16.2 ShearofOpenSectionBeams...................................................................... 483
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16.3 ShearofClosedSectionBeams.................................................................... 488
Problems.............................................................................................. 496
CHAPTER17 TorsionofBeams ........................................................................ 503
17.1 TorsionofClosedSectionBeams.................................................................. 503
17.2 TorsionofOpenSectionBeams.................................................................... 514
Problems.............................................................................................. 521
CHAPTER18 CombinedOpenandClosedSectionBeams.......................................... 529
18.1 Bending ............................................................................................... 529
18.2 Shear................................................................................................... 529
18.3 Torsion ................................................................................................ 533
Problems.............................................................................................. 534
CHAPTER19 StructuralIdealization .................................................................. 537
19.1 Principle............................................................................................... 537
19.2 IdealizationofaPanel............................................................................... 538
19.3 EffectofIdealizationontheAnalysisofOpenandClosedSectionBeams................... 541
19.4 DeflectionofOpenandClosedSectionBeams .................................................. 553
Problems.............................................................................................. 556
CHAPTER20 WingSparsandBoxBeams ............................................................ 561
20.1 TaperedWingSpar................................................................................... 561
20.2 OpenandClosedSectionBeams................................................................... 565
20.3 BeamsHavingVariableStringerAreas............................................................ 571
Problems.............................................................................................. 574
CHAPTER21 Fuselages................................................................................. 577
21.1 Bending ............................................................................................... 577
21.2 Shear................................................................................................... 578
21.3 Torsion ................................................................................................ 581
21.4 CutoutsinFuselages................................................................................. 584
Problems.............................................................................................. 585
CHAPTER22 Wings...................................................................................... 587
22.1 Three-BoomShell ................................................................................... 587
22.2 Bending ............................................................................................... 588
22.3 Torsion ................................................................................................ 590
22.4 Shear................................................................................................... 594
22.5 ShearCenter.......................................................................................... 599
22.6 TaperedWings........................................................................................ 600
22.7 Deflections............................................................................................ 603
22.8 CutoutsinWings..................................................................................... 605
Problems.............................................................................................. 613
CHAPTER23 FuselageFramesandWingRibs....................................................... 619
23.1 PrinciplesofStiffener/WebConstruction......................................................... 619
23.2 FuselageFrames ..................................................................................... 625
23.3 WingRibs............................................................................................. 626
Problems.............................................................................................. 630
Index.............................................................................................. 633
Preface
Duringmyexperienceofteachingaircraftstructures,Ihavefelttheneedforatextbookwrittenspecif-
icallyforstudentsofaeronauticalengineering.Althoughtherehavebeenanumberofexcellentbooks
writtenonthesubject,theyarenoweitheroutofdateortoospecializedincontenttofulfilltherequire-
ments of an undergraduate textbook. With that in mind, I wrote Aircraft Structures for Engineering
Students,thetextonwhichthisoneisbased.Usersofthattexthavesuppliedmanyusefulcommentsto
thepublisher,includingcommentsthatabrieferversionofthebookmightbedesirable,particularlyfor
programsthatdonothavethetimetocoverallthematerialinthe“big”book.Thatfeedback,alongwith
asurveydonebythepublisher,resultedinthisbook, AnIntroductiontoAircraftStructuralAnalysis,
designedtomeettheneedsofmoretime-constrainedcourses.
MuchofthecontentofthisbookissimilartothatofAircraftStructuresforEngineeringStudents,but
thechapteron“VibrationofStructures”hasbeenremovedsincethisismostoftencoveredinaseparate
standalonecourse.ThetopicofAeroelasticityhasalsobeenremoved,leavingdetailedtreatmenttothe
graduate-levelcurriculum.Thesectionon“StructuralLoadingandDiscontinuities”remainsinthebig
bookbutnotthis“intro”one.Whilethesetopicshelpdevelopadeeperunderstandingofloadtransfer
andconstrainteffectsinaircraftstructures,theyareoftenoutsidethescopeofanundergraduatetext.
Thereaderinterestedinlearningmoreonthosetopicsshouldrefertothe“big”book.Intheinterestof
savingspace,theappendixon“DesignofaRearFuselage”isavailablefordownloadfromthebook’s
companionWebsite.Pleasevisitwww.elsevierdirect.comandsearchon“Megson”tofindtheWebsite
andthedownloadablecontent.
Supplementarymaterials,includingsolutionstoend-of-chapterproblems,areavailableforregistered
instructorswhoadoptthisbookasacoursetext.Pleasevisitwww.textbooks.elsevier.comforinformation
andtoregisterforaccesstotheseresources.
The help of Tom Lacy, Associate Professor of Mechanical and Aerospace Engineering at Missis-
sippiStateUniversity,isgratefullyacknowledgedinthedevelopmentofthisbook.
T.H.G.Megson
Supportingmaterialaccompanyingthisbook
Afullsetofworkedsolutionsforthisbookareavailableforteachingpurposes.
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vii
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PART
A
Fundamentals
of Structural
Analysis