山农双语材力9.ppt

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1、Chapter9Stabilityofcompressedcolumns1Chapter9Stabilityofcompressedcolumns§9–1Conceptsofstabilityofcompressedcolumns§9–2Euler'sformulaofthecriticalforceofslendercompressedcolumns§9–3ScopeofapplicationofEuler'sformulaandempiricalformula§9–4Stabilitycheckandmeasuresofincreasingstabilit

2、y2§9–1CONCEPTSOFSTABILITYOFCOMPRESSEDCOLUMNSTheload-carryingcapacityofstructuremembers：①Strength②Rigidity③StabilitySomestructuremembersinengineeringhaveenoughstrengthandrigiditybuttheyareunabletoworksafelyandreliably.3P456易拉罐压缩失稳71、Stableandinstableequilibrium：1).instableequilibrium

3、82).Stableequilibrium93).Stableandinstableequilibrium102、Lossofstabilityandthecriticalpressureofthecolumn：1).Idealcompressivecolumns：thematerialisabsolutelyideal；theaxisisabsolutelystraight；thecompressiveforceisabsolutelyalongtheaxisofthecolumn.2).Stableandinstableequilibriumofcompr

4、essivecolumns：InstableequilibriumStableequilibrium113).lossofstabilityofcompressedcolumn：4).CriticalpressureofcompressedcolumnsStableequilibriumInstableequilibriumCriticalstateCriticalpressure:Fcrcorrespondingpressureintermediatestate12§9–2Euler'sformulaofthecriticalforceofslenderco

5、mpressedcolumns1、Criticalpressureforthecolumnwithtwohingedends:①bendingmoment：②ApproximatedifferentialequationofthedeflectioncurveFFxyPMSupposethepressurehasreachedthecriticalvalueandthecolumnhasbeenintinybendingstateasshowninthefigure.Starttodeterminethecriticalforcewiththedeflecti

6、vecurve.FxL13③Solutionofthedifferentialequation：④Determinetheintegralconstants：ThecriticalforceFcristhesmallestpressureundertinybending，thereforeweonlytaken=1andthecolumnwillbendabouttheaxiswiththesmallestmomentofinertia.Thatis142、Applicationrangeoftheformula：3、Euler’sformulaofthecr

7、iticalpressureforthecolumnwithotherendconditions:1).Idealcompressivecolumns；2).Inlinearelasticrange；3).Theendsofthecolumnaresupportedbyhinges.—Lengthcoefficient（orconstraintcoefficient）Euler’sformulaofthecriticalpressureforthecompressivecolumnwithtwohingedendsGeneralformofEuler’sfo

8、rmulaofthecriticalp