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在线教务辅导网HTTP/WWWSHANGFUWANGCOM更多课程配套课件资源请访问在线教务辅导网12DETERMINATEANDINDETERMINATESTRUCTURES静定和超静定结构2018/1/102STATICALLYDETERMINATESTRUCTURESNSTRUCTURESARESAIDTOBESTATICALLYDETERMINATEWHENTHEFORCESANDREACTIONSPRODUCEDBYAGIVENLOADINGCANBECALCULATEDUSINGONLYTHEEQUATIONSOFEQUILIBRIUMSTATICALLYDETERMINATESTRUCTURESTATICALLYDETERMINATESTRUCTURESNTHESIMPLYSUPPORTEDBEAMSHOWNINFIGURE13ISSTATICALLYDETERMINATEWECANSOLVEFORTHETHREEUNKNOWNREACTIONSUSINGTHEEQUATIONSOFEQUILIBRIUMANDTHENCALCULATETHEINTERNALFORCESSUCHASBENDINGMOMENT,SHEARFORCE,ANDAXIALFORCEATANYGIVENLOCATIONALONGTHELENGTHOFTHEBEAMSTATICALLYDETERMINATESTRUCTURESTATICALLYINDETERMINATESTRUCTURESNFOURUNKNOWNREACTIONSNTHREEINDEPENDENTEQUILIBRIUMEQUATIONS,STATICALLYINDETERMINATESTRUCTURESSTATICALLYINDETERMINATEBEAMSATICALLYINDETERMINATEFRAMESATICALLYINDETERMINATECOMPOSITESTRUCTURESFORCEMETHOD力法NTHEFORCEMETHODALSOCALLEDTHEFLEXIBILITYMETHODISUSEDTOCALCULATEINTERNALFORCESANDREACTIONSINSTATICALLYINDETERMINATESTRUCTURESDUETOLOADSANDIMPOSEDDEFORMATIONSFORCEMETHOD力法NTHESTEPSINTHEFORCEMETHOD1DETERMINETHEDEGREEOFSTATICALINDETERMINACYOFTHESTRUCTUREPARAMETERNWILLBEUSEDTODENOTETHEDEGREEOFINDETERMINACYN确定超静定次数FPFPFAXFAYMAX1静定结构AABBCCNTHESTEPSINTHEFORCEMETHOD2TRANSFORMTHESTRUCTUREINTOASTATICALLYDETERMINATESYSTEMBYRELEASINGANUMBEROFSTATICALCONSTRAINTSEQUALTOTHEDEGREEOFSTATICALINDETERMINACY,NFPFPFAXFAYMAX1基本体系AABBCCPRIMARYSYSTEMNTHESTEPSINTHEFORCEMETHODTHISISACCOMPLISHEDBYNRELEASINGEXTERNALSUPPORTCONDITIONSNCREATINGINTERNALHINGESTHESYSTEMTHUSFORMEDISCALLEDTHEPRIMARYSYSTEMNUMBERTHERELEASEDCONSTRAINTSFROM1TONPRIMARYSYSTEMQQQAABBCCLLX1X1B基本体系A一次超静定结构N3FORAGIVENRELEASEDCONSTRAINTJ,INTRODUCEANUNKNOWNREDUNDANTRI5DQNDENTFORCEXJCORRESPONDINGTOTHETYPEANDDIRECTIONOFTHERELEASEDCONSTRAINT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AABBCCQQQAABBCCLLX1X1X1N4APPLYTHEGIVENLOADINGORIMPOSEDDEFORMATIONTOTHEPRIMARYSYSTEMCALCULATEDISPLACEMENTSDUETOTHEGIVENLOADINGATEACHOFTHERELEASEDCONSTRAINTSINTHEPRIMARYSYSTEMTHESEDISPLACEMENTSARECALLED1P,2P,NP,FPAABBC1PX1ABX11D1111D11X1FPABCEIL/2L/2X1基本体系1B0N5FORAGIVENRELEASEDCONSTRAINTJ,APPLYAUNITLOADXJ1TOTHEPRIMARYSYSTEMCALCULATEDISPLACEMENTSDUETOXJ1ATEACHOFTHERELEASEDCONSTRAINTSINTHEPRIMARYSYSTEMTHESEDISPLACEMENTSARECALLED,ABX11D11FPABCEIL/2L/2X1基本体系1B0FPAABBC1PX111D11X1UNITLOAD单位力,N6SOLVEFORREDUNDANTFORCESX1THROUGHXNBYIMPOSINGTHECOMPATIBILITYCONDITIONSOFTHEORIGINALSTRUCTURETHESECONDITIONSTRANSFORMTHEPRIMARYSYSTEMBACKTOTHEORIGINALSTRUCTUREBYFINDINGTHECOMBINATIONOFREDUNDANTFORCESTHATMAKEDISPLACEMENTATEACHOFTHERELEASEDCONSTRAINTSEQUALTOZERONCALCULATEFORCESATAGIVENLOCATIONINTHESTRUCTUREUSINGNFORCECANBEBENDINGMOMENT,SHEAR,AXIALFORCE,ORREACTIONTHECLASSICALDISPLACEMENTMETHODNTHEFORCEMETHODUNKNOWNSAREFORCEQUANTITIESTHEREDUNDANTFORCESBASEDONGEOMETRICALCONDITIONSCOMPATIBILITYCONDITIONSATTHELOCATIONOFEACHREDUNDANTFORCENTHECLASSICALDISPLACEMENTMETHODUNKNOWNSAREDISPLACEMENTQUANTITIESBASEDONSTATICALCONDITIONSEQUILIBRIUMCONDITIONSZ1R211234134PR2P12234R22R12R11R1PZ2NTHESTEPSINTHECLASSICALDISPLACEMENTMETHOD1FORAGIVENSTRUCTUREANDLOADING,CONSIDERTHEJOINTSTOBEFULLYFIXEDAGAINSTROTATIONPL1234EI常数Z1Z2AB基本结构1234Z1Z2R100PR2NTHESTEPSINTHECLASSICALDISPLACEMENTMETHOD2CALCULATETHEMOMENTSINEACHMEMBEROFTHESTRUCTUREDUETOTHEGIVENLOADS,R1P,R2P,ASSUMINGFULLFIXITYATTHEJOINTSTHESEMOMENTSARECALLEDFIXEDENDMOMENTSN3CALCULATEMOMENTSR11、R12ATTHEENDSOFEACHMEMBERDUETOUNITDISPLACEMENTSOFTHEJOINTSN4EXPRESSTHETOTALMOMENTATEACHENDOFAGIVENMEMBERASTHESUMOFTHEFIXEDENDMOMENTSMP,ANDTHEPRODUCTOFUNKNOWNJOINTDISPLACEMENTSZ1,Z2TIMESTHEMOMENTSM1、M2PRODUCEDBYUNITJOINTDISPLACEMENTSZ1,Z2,CALCULATEDINSTEP3N5GENERATEANEQUATIONOFMOMENTEQUILIBRIUMATEACHJOINT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。N6SOLVETHESYSTEMOFEQUATIONSFORTHEUNKNOWNJOINTDISPLACEMENTSN7CALCULATETHEMEMBERENDMOMENTSUSINGTHEEXPRESSIONSDERIVEDINSTEP4ANDTHEVALUESOFJOINTDISPLACEMENTSCALCULATEDINSTEP6R11Z1R12Z2R1P0R21Z1R22Z2R2P0R11Z1R12Z2R1P0R21Z1R22Z2R2P0R1R11R12R1P0R2R21R22R2P0N8CALCULATEALLREMAININGFORCESINTHESTRUCTURESHEARFORCESANDAXIALFORCESNFORCEMETHODCANSOLVEALLSTATICALLYINDETERMINATESTRUCTURESCOMPUTATIONALCOMPLEXITYPROHIBITIVEFORSTRUCTURESWITHMORETHANTHREEUNKNOWNFORCESNCLASSICALDISPLACEMENTMETHODALLOWSASOLUTIONBASEDONAMEMBERBYMEMBERPROCEDURE,RATHERTHANONETHATREQUIRESCONSIDERATIONOFTHESTRUCTUREASAWHOLEBASEDONTHEPRESOLUTIONOFSTANDARDCASESOFINTERMEDIATE媒介物LOADANDDISPLACEMENTREDUCETHENUMBEROFUNKNOWNSINAGIVENSOLUTIONMOMENTDISTRIBUTIONMETHOD力矩分配法NTHEMOMENTDISTRIBUTIONMETHODISUSEDFORSTATICALLYINDETERMINATEBEAMSANDFRAMESBYSIMPLEHANDCALCULATIONSNTHISISBASICALLYANITERATIVE5ITERETIV迭代的PROCESSNTHEPROCEDUREINVOLVESARTIFICIALLYRESTRAININGTEMPORARILYALLTHEJOINTSAGAINSTROTATIONANDWRITINGDOWNTHEFIXEDENDMOMENTSFORALLTHEMEMBERSRESTRAINALLTHEJOINTSAGAINSTROTATIONWRITEDOWNTHEFIXEDENDMOMENTSNTHEJOINTSARETHENRELEASEDONEBYONEINSUCCESSIONSEK5SEFEN连续ATEACHRELEASEDJOINTTHEUNBALANCEDMOMENTSAREDISTRIBUTEDTOALLTHEENDSOFTHEMEMBERSMEETINGATTHATJOINTNACERTAINFRACTIONOFTHESEDISTRIBUTEDMOMENTSARECARRIEDOVERTOTHEFARENDSOFMEMBERSTHERELEASEDJOINTISAGAINRESTRAINEDTEMP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