Introduction to aircraft structural analysis PDF
Preview Introduction to aircraft structural analysis
Introduction to Aircraft Structural Analysis Third Edition Introduction to Aircraft Structural Analysis Third Edition T.H.G. Megson Butterworth-HeinemannisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright#2018T.H.G.Megson.PublishedbyElsevierLtd.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe Publisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearance CenterandtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher (otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperience broadenourunderstanding,changesinresearchmethods,professionalpractices,ormedicaltreatment maybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingand usinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationor methodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhom theyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeany liabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceor otherwise,orfromanyuseoroperationofanymethods,products,instructions,orideascontainedinthe materialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-08-102076-0 ForinformationonallButterworth-Heinemannpublicationsvisit ourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:KateyBirtcher AcquisitionEditor:SteveMerken EditorialProjectManager:PeterJardim ProductionProjectManager:SruthiSatheesh CoverDesigner:ChristianBilbow TypesetbySPiGlobal,India To the memory of my darling wife, Margaret. Preface to the Third Edition During my experience of teaching aircraft structures, I felt the need for a textbook written specifi- cally for students of aeronautical engineering. Although there were a number of books available on the subject they were either out of date or too specialized in content to fulfill the requirements of an undergraduate textbook. With that in mind I wrote Aircraft Structures for Engineering Students. After a period of years users of that text commented that a briefer version of the book might be desirable particularly for programs that did not have time to cover all the material in the “big”book.That feedback, together withasurveycarriedoutbythe publisher, resulted inAnIntro- ductiontoAircraftStructuralAnalysisdesignedtomeettheneedsofmoretime-constrainedcourses. Tothisendthechapteron“Vibrationofstructures”wasremovedfromthe“big”booktogetherwith thesectionson“Structuralandloadingdiscontinuities”and“Aeroelasticity.”Thereaderinterestedin learningmoreonthesetopicsshouldrefertothe“big”book.Also,intheinterestofsavingspace,the appendix on “Design of a rear fuselage” was omitted but is available for download from the book’s companion website, http://booksite.elsevier.com/9780080982014/. The publication of a third edition has enabled me to include more worked examples and end-of- chapterexercisesofanessentiallypracticalnatureandalsotoextendtheworkoncompositemateri- alsandstructurestoaconsiderationofmulti-plylaminates.Inthisthemethodofspecifyingdifferent plylay-upsisincludedtogetherwiththeeffectsofsymmetryandreinforcementorientation.Thecal- culationofequivalentelasticconstantsispresentedforthecaseofin-planeloadingonlysincethisis normally the situation in the thin skins of aircraft structures. The calculation of the distribution of stresses across the thickness of a laminate isillustrated by an example and the strength oflaminates investigated using the maximum stress theory. Finally,thepublicationofathirdeditionhasenabledmetoreviewthetextandcorrecttheprint- ing errors, mainly in cross-referencing, which had, unfortunately, crept into the second edition. T.H.G. Megson SUPPORTING MATERIAL TO ACCOMPANY THIS BOOK Forinstructorsusingthistextintheircourse,afullsetofworkedsolutionsandelectronicimagesofthefiguresin thetextareavailablebyregisteringat:www.textbooks.elsevier.com xiii Fundamentoafl s structaunraally sis SECTION Elasticity Chapt1e r Basiecl asticity .. 5 Chapt2e r Two-dimenpsrioobnlaielnm es l asticity 47 Chapt3e r Torsiojos no lsiedc tions 69 CHAPTER 1 Basic elasticity Weconsider,inthischapter,thebasicideasandrelationshipsofthetheoryofelasticity.Thetreatment isdividedintothreebroadsections:stress,strain,andstress–strainrelationships.Thethirdsectionis deferred until the end of the chapter to emphasize the fact that the analysis of stress and strain, for example, the equations of equilibrium and compatibility, does not assume a particular stress–strain law.Inotherwords,therelationshipsderivedinSections1.1–1.14areapplicabletononlinearaswell as linearly elastic bodies. 1.1 STRESS Considerthearbitrarilyshaped,three-dimensionalbodyshowninFig.1.1.Thebodyisinequilibrium undertheactionofexternallyappliedforcesP ,P ,... andisassumedtoconstituteacontinuousand 1 2 deformable material, so that the forces are transmitted throughout its volume. It follows that, at any internal point O, there is a resultant force dP. The particle of material at O subjected to the force dP is in equilibrium, so that there must be an equal but opposite force dP (shown dotted in Fig.1.1)actingontheparticleatthesametime.Ifwenowdividethebodybyanyplanenncontaining O,thenthesetwoforcesdPmaybeconsideredasbeinguniformlydistributedoverasmallareadAof each face of the plane at the correspondingpoint O, as in Fig. 1.2. The stress at O is defined by the equation dP Stress¼ lim (1.1) dA!0dA ThedirectionsoftheforcesdPinFig.1.2aresuchastoproducetensilestressesonthefacesofthe planenn.Itmustberealizedherethat,whilethedirectionofdPisabsolute,thechoiceofplaneisarbitrary, sothat,althoughthedirectionofthestressatOisalwaysinthedirectionofdP,itsmagnitudedepends upontheactualplanechosen,sinceadifferentplanehasadifferentinclinationandthereforeadifferent valuefortheareadA.Thismaybemoreeasilyunderstoodbyreferencetothebarinsimpletensionin Fig.1.3.Onthecross-sectionalplanemm,theuniformstressisgivenbyP/A,whileontheinclinedplane m0m0 thestressisofmagnitudeP/A0.Inbothcases,thestressesareparalleltothedirectionofP. Generally,thedirectionofdPisnotnormaltotheareadA,inwhichcase,itisusualtoresolvedP intotwocomponents:one,dP ,normaltotheplaneandtheother,dP,actingintheplaneitself(see n s Fig.1.2).Notethat,inFig.1.2,theplanecontainingdPisperpendiculartodA.Thestressesassociated with these components are a normal ordirect stress defined as dP s¼ lim n (1.2) dA!0 dA 5 IntroductiontoAircraftStructuralAnalysis,ThirdEdition.http://dx.doi.org/10.1016/B978-0-08-102076-0.00001-4 Copyright©2018T.H.G.Megson.PublishedbyElsevierLtd.Allrightsreserved. 6 CHAPTER 1 Basic elasticity FIGURE1.1 InternalForceataPointinanArbitrarilyShapedBody FIGURE1.2 InternalForceComponentsatthePointO and ashear stress defined as dP t¼ lim s (1.3) dA!0 dA Theresultantstressiscomputedfromitscomponentsbythenormalrulesofvectoraddition,i.e.: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Resultant stress¼ s2þt2 Generally, however, asindicated previously,we are interested inthe separate effects ofsand t. However, to be strictly accurate, stress is not a vector quantity for, in addition to magnitude and direction,wemustspecifytheplaneonwhichthestressacts.Stressisthereforeatensor,itscomplete description dependingon the two vectors of force andsurface ofaction.
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