结构力学英文课件 Chapter7.ppt

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1、Chapter7Slope-DeflectionMethodSection1IntroductionSlope-deflectionmethod(orsimplythedisplacementmethod)isanothermethodtoanalyzethestaticallyindeterminatestructure.Inthelastchapter(forcemethod),theunknownsofprimarystructureareforces.Afterobtainingunknownf

2、orce,displacementofthestructurecanbesolved.Infact,thedisplacement(ordeflection)canbeproducedundertheactionofexternalloads,sothedisplacementsofthestructurehaveinherentrelationtotheexternalload.Thatistosay,thedisplacementsofthestructurecanbealsousedasprima

3、ryunknowns.Thismethodisreferredtoasdisplacementmethod.Rotationdisplacementandtranslationdisplacementaregeneralizeddisplacement.Sothedisplacementmethodisalsocalledslope-deflectionmethod.EX.qClløBøBBA(a)CABqøBøB(b)ABCøBABqC(d)(c)Notice:(1)Theflexuraldeform

4、ationoftheflexuralmembersintheframeistakenintoaccount,buttheshearingandaxialdeformationsofwhichareneglected.(2)Straightmembersofconstantsectionbetweenthetwoendsareconsidered.Section2Determineunknownsandprimarystructure1、Primaryunknown(1)、Rotationdisplace

5、mentsunknown(2)、TranslationunknownABCDBCBC2、Basicassumptions(1)、Smalldisplacementissupposed.(2)、Axialforceandshearingforcearedisregarded.3、Howtodecidethenumberofprimaryunknowns(1)、Thenumberofrotationdisplacements()isequaltothenumberofrigidjoints.(2)、

6、Thenumberoftranslationunknowns()Themethodofdeterminingthetranslationunknownsisasfollowing.Allrigidjoints(includingfixedsupports)arechangedintohinges;calculatedegreeoffreedomofthenewstructure.Thedegreeoffreedomofthenewstructureisequaltothenumberoftranslat

7、ionunknownoftheoriginalstructure.HowtodecidethenumberofprimaryunknownsThereare4rigidjointsinFig.Sotherotationdisplacementunknownsare4.Fig(a)ischangedintoFig(b),degreeoffreedomofFig(b):sotranslationunknownsoforiginalstructureare2.4,DegreeofindeterminacyTh

8、edegreeofindeterminacy(n)is:5,PrimarystructureWhenindeterminatestructureisanalyzedbyusingdisplacementmethod,everymemberisconsideredasastaticallyindeterminatebeamwithsinglespan.Sotheprimarystructureisthateverymemberischange