结构稳定论文之钢结构设计英文版.docx
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结构稳定论文之钢结构设计英文版.docx
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结构稳定论文之钢结构设计英文版
GraduateCourseWork
SteelStructureStabilityDesign
Abstract
Steelstructurehasadvantagesoflightweight,highstrengthandhighdegreeofindustryali
zation,whichhasbeenwidelyusedintheconstructionengineering.Weoftenhearthistheaccidentcasecausedbyitsinstabilityandfailureofstructureofcasualtiesandpropertylosses,andthecauseofthefailureisusuallycausedbystructuredesignflaws.Thispapersaystheexperiencesinthedesignofstabilityofsteelstructurethroughthesummaryofthestabilityofsteelstructuredesignoftheconcept,principle,analysismethodandcombinationwithengineeringpractice.
Keywords:
steelstructure;stabilitydesign;detailstructure
SteelStructureStabilityDesign
StructurallystablesystemswereintroducedbyAleksandrAndronovandLevPontryaginin1937underthename"systèmesgrossières",orroughsystems.Theyannouncedacharacterizationofroughsystemsintheplane,theAndronov–Pontryagincriterion.Inthiscase,structurallystablesystemsaretypical,theyformanopendensesetinthespaceofallsystemsendowedwithappropriatetopology.Inhigherdimensions,thisisnolongertrue,indicatingthattypicaldynamicscanbeverycomplex(cfstrangeattractor).AnimportantclassofstructurallystablesystemsinarbitrarydimensionsisgivenbyAnosovdiffeomorphismsandflows.
Inmathematics,structuralstabilityisafundamentalpropertyofadynamicalsystemwhichmeansthatthequalitativebehaviorofthetrajectoriesisunaffectedbyC1-smallperturbations.Examplesofsuchqualitativepropertiesarenumbersoffixedpointsandperiodicorbits(butnottheirperiods).UnlikeLyapunovstability,whichconsidersperturbationsofinitialconditionsforafixedsystem,structuralstabilitydealswithperturbationsofthesystemitself.Variantsofthisnotionapplytosystemsofordinarydifferentialequations,vectorfieldsonsmoothmanifoldsandflowsgeneratedbythem,anddiffeomorphisms.
Thestabilityisoneofthecontentwhichneedstobeaddressedinthedesignofsteelstructureengineering.Threearemoreengineeringaccidentcaseduetothesteelstructureinstabilityinthereallife.Forexample,thestadium,inthecityofHartford92mby110mtotheplaneofspacetrussstructure,suddenlyfellonthegroundin1978.Thereasonisthecompressivebarbucklinginstability;13.2mby18.0msteeltruss,in1988,lackofstabilityofthewebmembercollapsedinconstructionprocessinChina;OnJanuary3,2010intheafternoon,38msteelstructurebridgeinKunmingNewacrosssuddenlycollapsed,killingsevenpeople,8peopleseriouslyinjured,26peopleslightlyinjured.Thereasonisthatthebridgesteelstructuresupportingsystemisoutofstability,suddenlyabridgecollapsingdownto8mtall.Wecanseefromtheabovecase,theusualcauseofinstabilityandfailureofsteelstructureistheunreasonablestructuraldesign,structuraldesigndefects.Tofundamentallypreventsuchaccidents,stabilityofsteelstructuredesignisthekey.
Structuralstabilityofthesystemprovidesajustificationforapplyingthequalitativetheoryofdynamicalsystemstoanalysisofconcretephysicalsystems.TheideaofsuchqualitativeanalysisgoesbacktotheworkofHenriPoincaréonthethree-bodyproblemincelestialmechanics.Aroundthesametime,AleksandrLyapunovrigorouslyinvestigatedstabilityofsmallperturbationsofanindividualsystem.Inpractice,theevolutionlawofthesystem(i.e.thedifferentialequations)isneverknownexactly,duetothepresenceofvarioussmallinteractions.Itis,therefore,crucialtoknowthatbasicfeaturesofthedynamicsarethesameforanysmallperturbationofthe"model"system,whoseevolutionisgovernedbyacertainknownphysicallaw.QualitativeanalysiswasfurtherdevelopedbyGeorgeBirkhoffinthe1920s,butwasfirstformalizedwithintroductionoftheconceptofroughsystembyAndronovandPontryaginin1937.ThiswasimmediatelyappliedtoanalysisofphysicalsystemswithoscillationsbyAndronov,Witt,andKhaikin.Theterm"structuralstability"isduetoSolomonLefschetz,whooversawtranslationoftheirmonographintoEnglish.IdeasofstructuralstabilityweretakenupbyStephenSmaleandhisschoolinthe1960sinthecontextofhyperbolicdynamics.Earlier,MarstonMorseandHasslerWhitneyinitiatedandRenéThomdevelopedaparalleltheoryofstabilityfordifferentiablemaps,whichformsakeypartofsingularitytheory.Thomenvisagedapplicationsofthistheorytobiologicalsystems.BothSmaleandThomworkedindirectcontactwithMaurícioPeixoto,whodevelopedPeixoto'stheoreminthelate1950's.
WhenSmalestartedtodevelopthetheoryofhyperbolicdynamicalsystems,hehopedthatstructurallystablesystemswouldbe"typical".Thiswouldhavebeenconsistentwiththesituationinlowdimensions:
dimensiontwoforflowsanddimensiononefordiffeomorphisms.However,hesoonfoundexamplesofvectorfieldsonhigher-dimensionalmanifoldsthatcannotbemadestructurallystablebyanarbitrarilysmallperturbation(suchexampleshavebeenlaterconstructedonmanifoldsofdimensionthree).Thismeansthatinhigherdimensions,structurallystablesystemsarenotdense.Inaddition,astructurallystablesystemmayhavetransversalhomoclinictrajectoriesofhyperbolicsaddleclosedorbitsandinfinitelymanyperiodicorbits,eventhoughthephasespaceiscompact.Theclosesthigher-dimensionalanalogueofstructurallystablesystemsconsideredbyAndronovandPontryaginisgivenbytheMorse–Smalesystems.
Structuretheoryofstabilitystudywasconductedonthemathematicalmodeloftheideal,andtheactualstructureisnotasidealasmathematicalmodel,infact,weneedtoconsidertheinfluenceofvariousfactors.Forexample,forthecompressiverods,loadcouldnothaveabsolutealignmentsectioncenter;Therewillalwaysbesomeinitialbendingbaritself,theso-called"geometricdefects";Materialitselfinevitablyhassomekindof"defect",suchasthediscretenessofyieldstressandbarmanufacturingmethodscausedbytheresidualstress,etc.So,inadditiontothemodulusofelasticityandgeometrysizeofbar,alltheabove-mentionedfactorsaffectingthebearingcapacityofthepushrodindifferentdegrees,inthestructuredesignofthisinfluenceoftenshouldbeconsidered.Usuallywillbebasedontheidealmathematicalmodeltostudythestabilityofthetheoryiscalledbucklingtheory,basedontheactualbarstudyconsiderthevariousfactorsrelatedtothestabilityofthestabilityoftheultimatebearingcapacitytheorycalledthetheoryofcrushing.Practicalbar,componentorstructuredamageoccurredduringuseorastheloadingtestofthebucklingloadiscalledcrushingloadandultimatebearingcapacity.Forsimplicity,commonlyusedbucklingload.Aboutgeometricdefects,accordingtoalargenumberofexperimentalresults,itisgenerallybelievedtoassumeameniscuscurveanditsvectordegreesfortherodlengthof1/1000.Abouttissuedefects,inthenationalstandardformulaisnotthesame,allowthebucklingstresscurvegivenbytheverydifferentalso,someproblemsremaintobefurtherresearch.
1.Steelstructurestabilitydesignconcept
1.1.Thedifferencebetweenintensityandstability
Theintensityreferstothatthestructureorasinglecomponentmaximumstress(orinternalforce)causedbyloadinstableequilibriumstateismorethantheultimatestrengthofbuildingmaterials,soitisaquestionofthestress.Theultimatestrengthvalueisdifferentaccordingtothecharacteristicsofthematerialvaries.forsteel,itistheyieldpoint.Theresearchofstabilityismainlyistofindtheexternalloadandstructureunstableequilibriumbetweeninternalresistance.Thatistosay,deformationbegantorapidgrowthandweshouldtrytoavoidthestructureenteringthestate,soitisaquestionofdeformation.Forexample,foranaxialcompressioncolumns,intheconditioncolumninstability,thelateraldeflectionofthecolumnaddalotofadditionalbendingmoment,thusthefractureloadofpillarscanbefarlessthanitsaxialcompressionstrength.Atthispoint,theinstabilityisthemainreasonofthepillarfracture.
1.2.Theclassificationofthesteelstructureinstability
1)Thestabilityproblemwiththeequilibriumbifurcation(Branchpointinstability).
2)Theaxialcompressionbucklingoftheperfectstraightrodandtabletcompressionbucklingallbelongtothiscategory.
3)Thestabilityoftheequilibriumbifurcationproblem(Extremevaluepointinstability).
4)Theabilityofthelossofstabilityofeccentriccompressionmembermadeofconstructionsteelinplasticdevelopmenttoacertaindegree,fallintothiscategory.
5)Jumpinginstability
6)Jumpinginstabilityisakindofdifferentfromtheabovetwotypesofstabilityproblem.Itisajumptoanotherstableequilibriumstateafterlossofstabilitybalance.
2.Theprincipleofsteelstructurestabilitydesign
2.1.Forthesteelstructurearrangement,thewholesystemandthestabilityofthepartrequirementsmustbeconsidered,andmostofthecurrentsteelstructureisdesignedaccordingtoplanesystem,suchastrussandframe.Theoveralllayoutofstructurecanguaranteethattheflatstructuredoesnotappearout-of-planeinstability,suchasincreasingthenecessarysupportingartifacts,etc.Aplanarstructuresofplanestabilitycalculationisconsistentwiththestructurearrangement.
2.2.Structurecalculationdiagramshouldbeconsistentwithadiagramofapracticalcalculationmethodisbasedon.Whendesigningasinglelayerormultilayerframestructure,weusuallydonotmakeanalysisoftheframeworkstabilitybuttheframecolu
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