结构稳定概述

陈伟球交通工程研究所2008年4月13日结构的稳定性分析概述Theproofofthepuddinginanytheoryofengineeringscienceliesintheeating,thepracticalapplicationtopertinentproblems,andIbelievethetheoryofbucklingofstructureshaspassedthiscrucialtestwithhonours.———W.T.Koiter,1974KoiterWT.(1976)Currenttrendsinthetheoryofbuckling.In:BucklingofStructures,ITUMASymposium1974,editedbyBudiansky,B.Berlin:Springer.(1914-1997)1968TimoshenkomedalwinnerDeeBridge,Chester,UK,trussedgirderbridge,failureduetotorsionalinstability,killing5personson25May,1847InstabilityFailureofBridgesInstabilityFailureofBridgesQuebecBridge,Ste-Foy,Quebec,crossSaintLawrence(mainspan549m),Failuretoupdateconstructionmethodologywithanincreaseinthesizeandthereforeweightofsteelsectionsasdesignprogressedledtoanoverstressingofthecantileverarms.Thebridgecollapsedat5:32pmonAugust29,1907killing75people.MilfordHavenBridge,Pembrokeshire,Wales,UnitedKingdomSteelgirderbridge,collapsingduetoplatebucklingduringconstructionkillingfourmenon2June1970.InstabilityFailureofBridgesWestGateBridge,Melbourne,Victoria,Australia,Steelspancollapsesduringconstructionkilling35.FailureofBuildingStructuresduetoBucklingBuckledcolumnanddeformedbeamsina14-storeyofficeblockontheBroadgatedevelopmentinLondonafterafirein1990.LateralwebbeambucklingcausedfailureofroofatshoppingcenterCollapsingofWTC,911BazantZP,ZhouY.(2002).WhydidtheWorldTradeCentercollapse?Simpleanalysis.ASCEJournalofEngineeringMechanics,128:2.Oncemorethanhalfofthecolumnsinthecriticalfloor..sufferbuckling(stage3),theweightoftheupperpartofthestructureabovethisfloorcannolongerbesupported,andsotheupperpartstartsfallingdownontothelowerpartbelow…OtherBucklingPhenomenaAbucklingtreefailure.BucklingrailduetotemperatureHistoryofTheoryofStabilityTounderstandscienceitisnecessarytoknowitshistoryAugusteComte(1798-1857)•HeroofAlexandria(c.100B.C.):Whythestrengthofapieceofwoodreducesasitslengthincreases?•LeonardodaVinci(1452-1519)providedtwoempiricalrulesforthestrengthofcolumnsincompression.•TheJesuitM.Mersenne(1588-1648)observedthat‘iron,copperandothermetals,evensinglebodies,whensubjecttoaforceorweight,curveandbendtotheformofanarchbeforebreaking’•PetrusvanMusschenbroek(1692–1761)confirmedMersenne’sconclusionsbyexperiments.•JacobBernoulli(1654–1705)constructedtheequationofaflexiblebardeformedintheplaneconsideringfinitedeflectionandanonlinear(parabolic)dependencebetweencurvatureandbendingmoment.BeforeEuler’sWorkEuler’sinnovativeworkonstabilityTherefore,unlesstheloadPtobebornebegreaterthanCp2/4l2,therewillbeabsolutelynofearofbending;ontheotherhand,iftheweightPbegreater,thecolumnwillbeunabletoresistbending.Nowwhentheelasticityofthecolumnandlikewiseitsthicknessremainthesame,theweightPwhichitcancarrywithoutdangerwillbeinverselyproportionaltothesquareoftheheightofthecolumn;andacolumntwiceashighwillbeabletobearonlyone-fourthoftheload.EulerL.(1744)Methodusinveniendilineascurvas…224crCPlpPPAdvancesinStabilityinthe18thand19thcenturies•Lagrange(1736–1813)providedthelastsignificantcontributiontothetheoryofelasticstabilityinthe18thcentury,responsibleforintroducingthenotionofbifurcationthatconnectslinearizedandfullynonlinearsolutions.•ThomasYoung(1773-1829)treatedthelateralbucklingofacolumnwithvariablecross-section.•Navier(1785-1836)derivedthecorrectdifferentialequationforathinplatesubjecttouniformcompressiveforces.•G.R.Kirchhoff(1824-1887)proposedaneleganttheoryforslenderrodsexperiencinglargedisplacementandsmallstrain.•H.Poincaré(1854-1912)discoveredageneralmethodfordynamicalsystemsinvolvingseriesprovedconvergentforallvaluesoftime.•M.A.Liapunov(1857-1918)proposedacompletelyapriorimethodforassessingstabilitythatdependsuponthetimeevolutionofacertainauxiliaryfunction.•A.Föppl(1854-1924)andvonKármán(1881-1963)derivedasystemoftwoequationsdescribingthelargedeflectionofathinplatewithstressesactinginthemiddleplane.TragedyofScienceCertainstructuresareabletowithstandloadssignificantlyabovethebucklingload.Experimentallydeterminedbucklingloadsofaxiallycompressedthin-walledcylindersareconsiderablybelowthetheoreticalstabilitylimit.AbeautifultheorykilledbytheuglyfactsThomasHuxley(1825-1895)Itisnotwhoisright,butwhatisright,thatisofimportance.Itisthecustomaryfateofnewtruths,tobeginasheresies,andtoendassuperstitions.Patienceandtenacityareworthmorethantwicetheirweightofcleverness.•E.Reissner(1913-1996)relaxedsomeofthesimplifyingassumptionsofFöppl-vonKármán’stheory.•H.L.Cox(1940)performednonlinearanalysisofbucklingproblemsofthinflatplateswhichhavearewardingstablepost-bucklingbehaviorwithasignificantload-carryingcapacity.•vonKármán,L.G.DunnandH.S.Tsien(1940)pioneeredtheinvestigationsofnonlinearimperfection-sensitivecolumnmodels.•W.Koiter(1945)finishedhisPh.D.thesis,markinganeweraofbucklingofstructures.•J.L.Ericksen(1966)succeededinseparatingthethermaleffectsfromthemechanicalaspectsforestablishingtheenergycriterionofstabilityinitspurelymechanicalform.Reissner:1973Timoshenkomedal;Ericksen:1979TimoshenkomedalAdvancesinStabilityinthe20thcenturySome