土木工程英语2课件

1.2DeterminateandIndeterminateStructures

静定和超静定结构StaticallyDeterminateStructuresStructuresaresaidtobestaticallydeterminatewhentheforcesandreactionsproducedbyagivenloadingcanbecalculatedusingonlytheequationsofequilibrium.StaticallydeterminatestructureStaticallyDeterminateStructuresThesimplysupportedbeamshowninFigure1.3isstaticallydeterminate.Wecansolveforthethreeunknownreactionsusingtheequationsofequilibriumandthencalculatetheinternalforcessuchasbendingmoment,shearforce,andaxialforceatanygivenlocationalongthelengthofthebeam.StaticallydeterminatestructureStaticallyIndeterminateStructuresFourunknownreactionsThreeindependentequilibriumequations,StaticallyIndeterminateStructuresStaticallyindeterminatebeamSaticallyindeterminateframeSaticallyindeterminatecompositeStructuresForceMethod力法Theforcemethod(alsocalledtheflexibilitymethod)isusedtocalculateinternalforcesandreactionsinstaticallyindeterminatestructuresduetoloadsandimposeddeformations.ForceMethod力法Thestepsintheforcemethod1．Determinethedegreeofstaticalindeterminacyofthestructure.Parameternwillbeusedtodenotethedegreeofindeterminacy.确定超静定次数

FPFPFAxFAyMAX1静定结构AABBCCThestepsintheforcemethod2Transformthestructureintoastaticallydeterminatesystembyreleasinganumberofstaticalconstraintsequaltothedegreeofstaticalindeterminacy,n.FPFPFAxFAyMAX1基本体系AABBCCprimarysystemThestepsintheforcemethodThisisaccomplishedbyreleasingexternalsupportconditionscreatinginternalhinges.Thesystemthusformediscalledtheprimarysystem.Numberthereleasedconstraintsfrom1ton.primarysystemqqqAABBCCllX1X1b)基本体系a)一次超静定结构3．Foragivenreleasedconstraintj,introduceanunknownredundant[ri5dQndEnt]force

Xj

correspondingtothetypeanddirectionofthereleasedconstraint.多余未知力redundantforce

基本体系沿多余未知力方向的位移应与原结构位移相同FPFPFAxFAyMAX1基本体系AABBCCqqqAABBCCllX1X1X14．Applythegivenloadingorimposeddeformationtotheprimarysystem.Calculatedisplacements

duetothegivenloadingateachofthereleasedconstraintsintheprimarysystem.ThesedisplacementsarecalledΔ1P

,Δ2P

,ΔnP

..,.FPAABBCΔ1PX1ABX1=1d11Δ11

=d11X1FPABCEIl/2l/2X1基本体系(Δ1=ΔB=0)=+5．Foragivenreleasedconstraint

j,applyaunitload

Xj

=1

totheprimarysystem.Calculatedisplacementsdueto

Xj

=1

ateachofthereleasedconstraintsintheprimarysystem.Thesedisplacementsarecalled

，，ABX1=1d11FPABCEIl/2l/2X1基本体系(Δ1=ΔB=0)=FPAABBCΔ1PX1Δ11

=d11X1+unitload单位力,...,.

6.Solveforredundantforcesx1throughxnbyimposingthecompatibilityconditionsoftheoriginalstructure.Theseconditionstransformtheprimarysystembacktotheoriginalstructurebyfindingthecombinationofredundantforcesthatmakedisplacementateachofthereleasedconstraintsequaltozero.CalculateforceSatagivenlocationinthestructureusingForcecanbebendingmoment,shear,axialforce,orreaction.TheClassicalDisplacementMethodTheforcemethod:unknownsareforcequantities(theredundantforces)basedongeometricalconditions(compatibilityconditionsatthelocationofeachredundantforce).Theclassicaldisplacementmethodunknownsaredisplacementquantitiesbasedonstaticalconditions(equilibriumconditions).=Z1↷R211234↷134P↷R2P12234R22R12R11R1PZ2Thestepsintheclassicaldisplacementmethod1．Foragivenstructureandloading,considerthejointstobefullyfixedagainstrotation.PL1234EI=常数Z1Z2(a)(b)基本结构1234=Z1Z2↷R1=0=0PR2Thestepsintheclassicaldisplacementmethod2．Calculatethemomentsineachmemberofthestructureduetothegivenloads,R1P

,R2P,assumingfullfixityatthejoints.Thesemomentsarecalledfixed-endmoments.3.Calculatemomentsr11、r12attheendsofeachmemberduetounitdisplacementsofthejoints.4．Expressthetotalmomentateachendofagivenmemberasthesumofthefixed-endmoments

MP

,andtheproductofunknownjointdisplacements

z1,z2

timesthemomentsM1、M2

producedbyunitjointdisplacementsZ1,Z2,calculatedinStep3.5．Generateanequationofmomentequilibriumateachjoint.

基本结构在荷载等外因和结点位移的共同作用下，每一个附加联系中的附加反力矩或反力都应等于零(静力平衡条件)。6．Solvethesystemofequationsfortheunknownjointdisplacements.

7．CalculatethememberendmomentsusingtheexpressionsderivedinStep4andthevaluesofjointdisplacementscalculatedinStep6.r11Z1+r12Z2+R1P=0r21Z1+r22Z2+R2P=0r11Z1+r12Z2+R1P=0r21Z1+r22Z2+R2P=0R1=R11+R12+R1P=0R2=R21+R22+R2P=08．Calculateallremainingforcesinthestructure(shearforcesandaxialforces).Forcemethodcansolveallstaticallyindeterminatestructures.computationalcomplexityprohibitiveforstructureswithmorethanthreeunknownforces.Classicaldisplacementmethodallowsasolutionbasedonamember-by-memberprocedure,ratherthanonethatrequiresconsiderationofthestructureasawhole;basedonthepre-solutionofstandardcasesofintermediate媒介物loadanddisplacementreducethenumberofunknownsinagivensolution.MomentDistributionMethod

力矩分配法Themomentdistributionmethodisusedforstaticallyindeterminatebeamsandframesbysimplehandcalculations.Thisisbasicallyaniterative[5itErEtiv]迭代的process.Theprocedureinvolvesartificiallyrestrainingtemporarilyallthejointsagainstrotationandwritingdownthefixedendmomentsforallthemembers.restrainallthejointsagainstrotationWritedownthefixedendmomentsThejointsarethenreleasedonebyoneinsuccession[sEk5seFEn]连续.Ateachreleasedjointtheunbalancedmomentsaredistributedtoalltheendsofthemembersmeetingatthatjoint.Acertainfractionofthesedistributedmomentsarecarriedovertothefarendsofmembers.Thereleasedjointisagainrestrainedtemporarilybeforeproceedingtothenextjoint.Thesamesetofoperationsarecarriedoutateachjointtillal