弯曲应力-纯弯曲

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1、材料力学ProfessorShibinWANG（王世斌）7.1ExamplesunderBendingLoading:Ch.7StressesinBeams受弯杆件的简化--悬臂梁Ch.7StressesinBeams7.1ExamplesunderBendingLoading:受弯杆件的简化--简支梁Ch.7StressesinBeams7.1ExamplesunderBendingLoading:受弯杆件的简化--外伸梁Ch.7StressesinBeams7.1ExamplesunderBendingLoading:Ch.7StressesinBeamsAFMModulesDime

2、nsion3100AFMTheworld'sbestsellingSPMsilicon-Si(111)2nm?7.1ExamplesunderBendingLoading:Ch.7StressesinBeamsScanningProbeMicroscopy(SPM)Components?7.1ExamplesunderBendingLoading:Ch.7StressesinBeamsCantileverSubstrateProbesThepropertiesanddimensionsofthecantileverplayanimportantroleindeterminingthes

3、ensitivityandresolutionoftheAFM.Cantilever--AFMProbeTip7.1ExamplesunderBendingLoading:Ch.7StressesinBeamsParis1889H=320mE=15000sG=70000KN70kmsightLaTourEiffer7.1ExamplesunderBendingLoading:PureBending:纯弯曲Ch.7StressesinBeams7.2LoadingTypesOtherLoadingTypesEccentricLoading:偏心加载TransverseLoading:横向力

4、作用Ch.7StressesinBeamsOtherLoadingTypesCh.7StressesinBeams7.3NormalStressesinBeamsP☻Ch.7StressesinBeamsdxxsxMMsxdx7.3NormalStressesinBeams☻Ch.7StressesinBeams应力分布应力公式变形应变分布平面假定物性关系静力方程7.3.1TheEngineeringBeamTheoryCh.7StressesinBeamsBendingDeformations平面假设？MM7.3.1TheEngineeringBeamTheoryxyMMABCDCom

5、pressionTensionNoStressNANeutralAxis中性轴zyy’y’A’B’C’D’y’Rdqdxsx=0ontheNeutralAxis.IngeneralwemustfindthepositionoftheNeutralAxis.Ch.7StressesinBeamsMM7.3.1TheEngineeringBeamTheoryxyMMABCDCompressionTensionNoStressNANeutralAxis中性轴y’A’B’C’D’y’RdqdxCh.7StressesinBeamsAssumptionsBeammaterialiselastic

6、Planesurfacesremainplaneandonly1GeometryofDeformation:Hooke’sLaw:andA’B’C’D’y’RdqMM7.3.1TheEngineeringBeamTheory1xyy’NANeutralAxis中性轴0+ve-veLinearDistributionofsx(Eqn)1dxNote:EisaMaterialPropertyisCurvature曲率xdxyMMsx7.3.1TheEngineeringBeamTheory7.3.1TheEngineeringBeamTheoryDeformationinaTransv

7、erseCrossSectionRRR´=R/zyxEquilibrium:xzyy’dAsxMArea,ALetButFirstMomentofArea面矩（静矩）Theny’ismeasuredfromthecentroidalaxisofthebeamcross-section.“NeutralAxis”coincideswiththeXZplanethroughthecentroid.y’y’NANeutralAxisCe