chapter six stiffness：六章刚度

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1、ChapterSix:stiffness6.1MemberendreleasesJointstiffnessisexpressedinthemastermatrixforastructure,buttwosituationsexistthatmaycausethemtovary.First,ajointthatisbeingutilizedasasupportmaybereleased.Forexample,thesupportbecomesslottedorpinned.Second,amembercanbephysicallyreleasedfromajointforoneormoreof

2、thesixpossibleenddisplacements.Whenlookingatajointrelease,thejointisfullydesignedasasupportbeforetherelease.Thiscreatesthereactioncomponents.Whenamemberreleaseoccurs,thememberisreleasedinsomedirectionandthestiffnesscontributionthatmemberwasmakingtothejointchangesorgoestozero.Takenotethatthememberisr

3、eleasedinthelocalsystem.Example6.1-1Example6.1-26.2Non-prismaticmembers6.2.1RotationandTranslationStiffness-26FromCastigliano’s:SinceIvaries,let:Therefore:Stiffness-26Inmatrixform,theflexibilitymatrix:SolvingforPA&MAbythecofactormethod:InStiffnessform:TransmittotheBend:Byequilibrium:Stiffness-26Carr

4、y-overfactor:Withrotationonly:Thedistributionfactorisaratiooftherotationalstiffnessofamembertothesumoftherotationalstiffnessofallmembersatthejoint.Rotationalstiffness,thestiffnessduetorotationatpointA:DistributionFactor:Stiffness-26RotationanddeflectionatpointBcanbederivedusingthesamemethod.Thestiff

5、nessmatrixissymmetric:InStiffnessform:TransmittotheBend:Byequilibrium:Stiffness-26Carry-overfactor:Withrotationonly:Thedistributionfactorisaratiooftherotationalstiffnessofamembertothesumoftherotationalstiffnessofallmembersatthejoint.Rotationalstiffness,thestiffnessduetorotationatpointA:DistributionF

6、actor:Stiffness-266.1.2Fixed-endMomentsUniformlydistributedload:Stiffness-26let,therefore,Byequilibrium:Stiffness-26And,Uniformlydistributedload:ConcentratedLoad:Stiffness-26Foreithercase,let,Inmatrixform:Stiffness-26Byequilibrium:Example6.2.2-1Example6.2.2-2Example6.2.2-3Example6.2.2-4TotalTwo-Dime

7、nsionalNon-PrismaticStiffnessMatrixX-Z6.1Shearstiffness6.1.1ShearstiffnessStiffness-26Stiffness-26Fromstatics,Example6.3.-1Example6.3.-2Two-DimensionalShearStiffnessMatrixThree-DimensionalShearStiffne