材料力学第五版刘鸿文第四章 弯曲内力ppt

MechanicsofMaterialsChapter4Internalforcesinbeams(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平§4-1弯曲的概念和实例(Basicconceptsandexamplesofbending)第四章弯曲内力(Internalforcesinbeams)§4-3剪力和弯矩(Shear-forceandbending-momentinbeams)§4-2受弯杆件的简化(Representingarealbeambyanidealizedmodel)(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平§4-6平面曲杆的内力图（Diagramsofinternalforcesforplane-curvedbars)§4-5载荷集度与剪力、弯矩间的关系(Relationshipsamongload,shearforceandbendingmoment)§4-4剪力方程和弯矩方程·剪力图和弯矩图(Shear-force&bending-momentequations;shear-force&bending-momentdiagrams)(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平一.工程实例（Engineeringexamples)§4-1基本概念及工程实例(Basicconceptsandexamples)(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平二、基本概念（Basicconcepts)2、梁(Beam)以弯曲变形为主的杆件外力（包括力偶）的作用线垂直于杆轴线.(1)受力特征(2)变形特征变形前为直线的轴线，变形后成为曲线.1、弯曲变形（Deflection)3、对称弯曲(Symmetricalbending)作用于梁上的所有外力都在纵向对称面内,弯曲变形后的轴线是一条在该纵向对称面内的平面曲线,这种弯曲称为对称弯曲.(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平AB纵向对称面梁变形后的轴线与外力在同一平面内梁的轴线RAF1F2RB(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平3支座的类型1梁的简化通常取梁的轴线来代替梁。2载荷类型集中力（concentratedforce)集中力偶（concentratedmoment)分布载荷（distributedload)（1）可动铰支座（rollersupport)RAAAAA§4-2受弯杆件的简化(Representingarealbeambyanidealizedmodel)(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平（2）固定铰支座(pinsupport)（3）固定端(clampedsupportorfixedend)AAAYAAXAVHM(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平4、静定梁的基本形式(Basictypesofstaticallydeterminatebeams)悬臂梁(cantileverbeam)外伸梁(overhangingbeam)简支梁(simplysupportedbeam)(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平例1贮液罐如图示，罐长L=5m，内径D=1m，壁厚t=10mm,钢的密度为：7.8g/cm³，液体的密度为：1g/cm³,液面高0.8m，外伸端长1m，试求贮液罐的计算简图.解：F—均布力(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平一、内力计算（Calculatinginternalforce)[举例]已知如图，F，a，l.求距A端x处截面上内力.解:求支座反力§4-3梁的剪力和弯矩(Shear-forceandbending-momentinbeams)BAalFRAXARBABFlalFRFlFaRmXFAyBAAx)(,0,00,0(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平求内力——截面法弯曲构件内力剪力弯矩1、弯矩(Bendingmoment)M构件受弯时，横截面上其作用面垂直于截面的内力偶矩.MYAXARBABFmmxYAFSCFRBFSCMxRMmlalFRFFACAy,0)(s,02、剪力(Shearforce)FS构件受弯时，横截面上其作用线平行于截面的内力.(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平1、剪力符号(Signconventionforshearforce)使dx微段有左端向上而右端向下的相对错动时,横截面m-m上的剪力为正。或使dx微段有顺时针转动趋势的剪力为正。对于左段，向上的外力产生正的剪力。二、内力的符号规定（Signconventionforinternalforce)使dx微段有左端向下而右端向上的相对错动时，横截面m-m上的剪力为负，或使dx微段有逆时针转动趋势的剪力为负。对于左段，向下的外力产生负的剪力。FSdxF+mmdxF-mm(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平当dx微段的弯曲下凸（即该段的下半部受拉）时，横截面m-m上的弯矩为正；或使左段有逆时针转动趋势的弯矩为正；对于左段，顺时针方向的外力偶产生正的弯矩。2、弯矩符号（Signconventionforbendingmoment)当dx微段的弯曲上凸（即该段的下半部受拉压）时，横截面m-m上的弯矩为负；或使右段有逆时针转动趋势的弯矩为负；对于右段，顺时针方向的外力偶产生负的弯矩。mm（受压）-+（受拉）MeMmm(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平解(1)求梁的支反力RA和RB例题2图示梁的计算简图。已知F1、F2，且F2F1，尺寸a、b、c和l亦均为已知.试求梁在E、F点处横截面处的剪力和弯矩.0mARBBdEDAabclCFF1F2RA021bFaFlRB0mB0)()(21blFalFlRAlblFalFRA)()(21lbFaFRB21(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平记E截面处的剪力为FSE和弯矩ME，且假设FSE和弯矩ME的指向和转向均为正值.BdEDAabclCFF1F2RAAEcFSERAME00SEAyFR,F0,0cRMmAEE解得AERFScRMAE(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平AEcFSERAMEa-cb-cCDl-cBEFSEF1F2MERB取右段为研究对象0yF021SFFRFBE0ME0)()()(21McbFcaFclREB解得++cRMAEAERFS(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平计算F点横截面处的剪力FS和弯矩MF.BdEDAabclCFF1F2RAFdBFSFMFRB0,00,0SdRMmRFFBFFBFy解得：-+RFBFSdRMBF(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平左侧梁段：向上的外力引起正值的剪力向下的外力引起负值的剪力右侧梁段：向下的外力引起正值的剪力向上的外力引起负值的剪力三、计算规律（Simplemethodforcalculatingshear-forceandbending-moment)1、剪力(Shearforce)niiSFF左（右）1(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平不论在截面的左侧或右侧向上的外力均将引起正值的弯矩,而向下的外力则引起负值的弯矩.2、弯矩（Bendingmoment)左侧梁段顺时针转向的外力偶引起正值的弯矩逆时针转向的外力偶引起负值的弯矩右侧梁段逆时针转向的外力偶引起正值的弯矩顺时针转向的外力偶引起负值的弯矩mkkiniiMaFM左（右）左（右）11(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平例题3轴的计例算简图如图所示，已知F1=F2=F=60kN，a=230mm,b=100mm和c=1000mm.求C、D点处横截面上的剪力和弯矩.F2=FACDBbacF1=FRARB解(1)求支座反力kN60FRRBA(Chapter4:InternalForcesinBeams)SCHOOLOFMECHANICALANDELECTRICALENGINEERINGMechanicsofMaterials韩光平(2)计算C横截面上的剪