直杆轴向拉压的强度和变形Strengthanddeform

直杆轴向拉压的强度和变形Strengthanddeformationofstraightrodunderaxialtensionandcompression主讲人：王雅君12目录CONTENTS强度变形StrengthDeformation1拉、压的强度StrengthoftensionandcompressionONE一、拉、压的强度Strengthoftensionandcompression

一、拉、压的强度Strengthoftensionandcompression对于塑性材料，当应力达到屈服极限σs时，整个杆件都会发生比较大的变形且不能恢复，因此塑性材料以σs为极限应力;对于脆性材料，当应力达到强度极限σb时发生断裂，故对脆性材料以σb为极限应力。Forplasticmaterials,whenthestressreachestheyieldlimitσAts,theentirerodwillundergosignificantdeformationandcannotberestored,sotheplasticmaterialwillσSistheultimatestress;Forbrittlematerials,whenthestressreachesthestrengthlimitσFractureoccursattimeb,therefore,forbrittlematerialsσBistheultimatestress.一、材料力学的基本概念Basicconceptsofmaterialmechanics

σs一屈服极限

σs--yieldlimitns一安全系数，一般塑性材料ns=1.3~2.0Ns-safetyfactor,forgeneralplasticmaterials,ns=1.3-2.0一、材料力学的基本概念Basicconceptsofmaterialmechanics

σb一强度极限

σb-Strengthlimitnb一安全系数，脆性材料nb=2.0~3.5Nb-safetyfactor,brittlematerialsnb=2.0~3.5一、拉、压的强度Strengthoftensionandcompression因为断裂破坏比屈服破坏更危险，所以nb>ns。此外，安全系数的选取还要考虑对安全要求的高低和经济等因素的影响。Becausefracturefailureismoredangerousthanyieldfailure,nb>ns.Inaddition,theselectionofsafetyfactorsalsoneedstoconsidertheimpactoffactorssuchasthelevelofsafetyrequirementsandeconomy.一、拉、压的强度Strengthoftensionandcompression根据强度条件，可以解决三类强度计算问题Accordingtothestrengthconditions,threetypesofstrengthcalculationproblemscanbesolved1.强度校核Strengthverification确保危险点的最大工作应力不超过材料的容许正应力，就能保证杆件正常工作Toensurethatthemaximumworkingstressatthedangerouspointdoesnotexceedtheallowablenormalstressofthematerial,thenormaloperationoftherodcanbeensuredFNmax--杆的最大轴力，即危险截面上的轴力FNmax-Themaximumaxialforceoftherod,thatis,theaxialforceonthedangeroussection一、拉、压的强度Strengthoftensionandcompression

2拉、压的变形DeformationcausedbytensionandcompressionTWO二、拉、压的变形Deformationcausedbytensionandcompression

1.轴向变形Axialdeformation轴向变形量Axialdeformation

二、拉、压的变形Deformationcausedbytensionandcompression

轴向线应变:Axiallinearstrain:相对变形，表示轴向变形的程度。Relativedeformationrepresentsthedegreeofaxialdeformation.胡克定律推论:CorollarytoHooke'sLaw:对于同一种材料，当应力未超过某一极限时，应力与应变成正比Forthesamematerial,whenthestressdoesnotexceedacertainlimit,thestressisproportionaltothestrain.二、拉、压的变形Deformationcausedbytensionandcompression

二、拉、压的变形Deformationcausedbytensionandcompression

2.横向变形横向变形对于同一种材料，当应力未超过某一极限时，横向应变与轴向应变成正比:Forthesamematerial,whenthestressdoesnotexceedacertainlimit,thetransversestrainbecomesproportionaltotheaxialstrain:泊松比Poisson'sratioμ——量纲为1的量，其数值因材料而异，由实验测定μ——Aquantitywithadimensionof1,whosevaluevariesdependingonthematerialandisdeterminedexperimentally弹性模量E和泊松比μ都是材料的弹性常数。ElasticmodulusEandPoisson'sratioμAllaretheelasticconstantsofthematerial.二、拉、压的变形Deformationcausedbytensionandcompression

例:如下图所示变截面杆AC，AB段的截面积A1=5cm2，CB段的截面积A2=10cm2。在A、B两处的轴线上分别受到50kN和140kN的力的作用，材料E=200GPa。求总变形量.Example:Asshowninthefigurebelow,thecross-sectionalareaofthevariablecross-sectionrodAC,ABsectionA1=5cm2,andCBsectionA2=10cm2.Subjectedtoforcesof50kNand140kNrespectivelyontheaxesofAandB,materialE=200GPa.Findthetotaldeformation解:(1)计算轴力(画轴力图）Solution:(1)Calculatetheaxialforce(drawanaxisdiagram)

AB段:FN1=-50X103NCB段:FN2=140X103-50X103=90X103N二、拉、压的变形Deformationcausedbytensionandcompression二、轴向拉压的内力和应力Internalforcesandstressesunderaxialtensionandcompression(2)计算AB段、CB段的正应力CalculatethenormalstressofABandCBsegmentsAB段:ABsegment:CB段:CBsegment:

(3)计算AB段、CB段的变形量，进而计算总变形量CalculatethedeformationofABandCBsegments,andthencalculatethetotaldeformationAB段:ABsegment:

CB段:CBsegment:总变形量:Totaldeformation:

1自测题SELF-TEST图示结构，AC为50x50x5的等边角钢，面积A1=9.6cm2，AB为10号槽钢，面积A2=25.48cm2。α=30°，材料的许用应力[σ]=120MPa。确定许可载荷F。ThestructureshowninthediagramisanequilateralanglesteelwithanACof50x50x5,withanareaofA1=9.6cm2,andanABofchannelsteelwithanareaofA2=25.48cm2.α=30°,allowablestressofmaterial[σ]=120MPa.DeterminetheallowableloadF.1自测题SELF-TEST提示计算轴力Calculateaxialforce根据斜杆的强度，求许可载荷Calculatetheallowa