Aircraft Structures By Megson

An Introduction to Aircraft Structural Analysis T. H. G. Megson AMSTERDAM•BOSTON•HEIDELBERG•LONDON NEWYORK•OXFORD•PARIS•SANDIEGO SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO Butterworth-HeinemannisanimprintofElsevier Butterworth-HeinemannisanimprintofElsevier 30CorporateDrive,Suite400 Burlington,MA01803,USA TheBoulevard,LangfordLane Kidlington,Oxford,OX51GB,UK Copyright©2010,T.H.G.Megson.PublishedbyElsevierLtd.Allrightsreserved. TherightofT.H.G.Megsontobeidenti?edastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,Designsand PatentsAct1988. 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ISBN978-1-85617-932-4(alk.paper) 1.Airframes.2.Structuralanalysis(Engineering)I.Title. TL671.6.M362010 629.134’31–dc22 2009050354 ForinformationonallButterworth-Heinemannpublications visitourWebsiteatwww.elsevierdirect.com PrintedintheUnitedStatesofAmerica 1011121314 10987654321 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 ApplicationtoDe?ectionProblems ............................................................... 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 De?ectionsduetoBending......................................................................... 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 vi Contents 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 De?ectionofOpenandClosedSectionBeams .................................................. 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 De?ections............................................................................................ 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,theyarenoweitheroutofdateortoospecializedincontenttoful?lltherequire- 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”to?ndtheWebsite 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. Please visit www.textbooks.elsevier.com and follow the registration instructions to access this material,whichisintendedforusebylecturersandtutors. vii Thispageintentionallyleftblank PART A Fundamentals of Structural Analysis