直桿軸向拉壓的強度和變形Strengthanddeformationofstraightrodunderaxialtensionandcompression主講人：王雅君12目錄CONTENTS強度變形StrengthDeformation1拉、壓的強度StrengthoftensionandcompressionONE一、拉、壓的強度Strengthoftensionandcompression

一、拉、壓的強度Strengthoftensionandcompression對于塑性材料，當應力達到屈服極限σs時，整個桿件都會發生比較大的變形且不能恢復，因此塑性材料以σs為極限應力;對于脆性材料，當應力達到強度極限σb時發生斷裂，故對脆性材料以σb為極限應力。Forplasticmaterials,whenthestressreachestheyieldlimitσAts,theentirerodwillundergosignificantdeformationandcannotberestored,sotheplasticmaterialwillσSistheultimatestress;Forbrittlematerials,whenthestressreachesthestrengthlimitσFractureoccursattimeb,therefore,forbrittlematerialsσBistheultimatestress.一、材料力學的基本概念Basicconceptsofmaterialmechanics

σs一屈服極限

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

σb一強度極限

σb-Strengthlimitnb一安全系數，脆性材料nb=2.0~3.5Nb-safetyfactor,brittlematerialsnb=2.0~3.5一、拉、壓的強度Strengthoftensionandcompression因為斷裂破壞比屈服破壞更危險，所以nb>ns。此外，安全系數的選取還要考慮對安全要求的高低和經濟等因素的影響。Becausefracturefailureismoredangerousthanyieldfailure,nb>ns.Inaddition,theselectionofsafetyfactorsalsoneedstoconsidertheimpactoffactorssuchasthelevelofsafetyrequirementsandeconomy.一、拉、壓的強度Strengthoftensionandcompression根據強度條件，可以解決三類強度計算問題Accordingtothestrengthconditions,threetypesofstrengthcalculationproblemscanbesolved1.強度校核Strengthverification確保危險點的最大工作應力不超過材料的容許正應力，就能保證桿件正常工作Toensurethatthemaximumworkingstressatthedangerouspointdoesnotexceedtheallowablenormalstressofthematerial,thenormaloperationoftherodcanbeensuredFNmax--桿的最大軸力，即危險截面上的軸力FNmax-Themaximumaxialforceoftherod,thatis,theaxialforceonthedangeroussection一、拉、壓的強度Strengthoftensionandcompression

2拉、壓的變形DeformationcausedbytensionandcompressionTWO二、拉、壓的變形Deformationcausedbytensionandcompression

1.軸向變形Axialdeformation軸向變形量Axialdeformation

二、拉、壓的變形Deformationcausedbytensionandcompression

軸向線應變:Axiallinearstrain:相對變形，表示軸向變形的程度。Relativedeformationrepresentsthedegreeofaxialdeformation.胡克定律推論:CorollarytoHooke'sLaw:對于同一種材料，當應力未超過某一極限時，應力與應變成正比Forthesamematerial,whenthestressdoesnotexceedacertainlimit,thestressisproportionaltothestrain.二、拉、壓的變形Deformationcausedbytensionandcompression

二、拉、壓的變形Deformationcausedbytensionandcompression

2.橫向變形橫向變形對于同一種材料，當應力未超過某一極限時，橫向應變與軸向應變成正比:Forthesamematerial,whenthestressdoesnotexceedacertainlimit,thetransversestrainbecomesproportionaltotheaxialstrain:泊松比Poisson'sratioμ——量綱為1的量，其數值因材料而異，由實驗測定μ——Aquantitywithadimensionof1,whosevaluevariesdependingonthematerialandisdeterminedexperimentally彈性模量E和泊松比μ都是材料的彈性常數。ElasticmodulusEandPoisson'sratioμAllaretheelasticconstantsofthematerial.二、拉、壓的變形Deformationcausedbytensionandcompression

例:如下圖所示變截面桿AC，AB段的截面積A1=5cm2，CB段的截面積A2=10cm2。在A、B兩處的軸線上分別受到50kN和140kN的力的作用，材料E=200GPa。求總變形量.Example:Asshowninthefigurebelow,thecross-sectionalareaofthevariablecross-sectionrodAC,ABsectionA1=5cm2,andCBsectionA2=10cm2.Subjectedtoforcesof50kNand140kNrespectivelyontheaxesofAandB,materialE=200GPa.Findthetotaldeformation解:(1)計算軸力(畫軸力圖）Solution:(1)Calculatetheaxialforce(drawanaxisdiagram)

AB段:FN1=-50X103NCB段:FN2=140X103-50X103=90X103N二、拉、壓的變形Deformationcausedbytensionandcompression二、軸向拉壓的內力和應力Internalforcesandstressesunderaxialtensionandcompression(2)計算AB段、CB段的正應力CalculatethenormalstressofABandCBsegmentsAB段:ABsegment:CB段:CBsegment:

(3)計算AB段、CB段的變形量，進而計算總變形量CalculatethedeformationofABandCBsegments,andthencalculatethetotaldeformationAB段:ABsegment:

CB段:CBsegment:總變形量:Totaldeformation:

1自測題SELF-TEST圖示結構，AC為50x50x5的等邊角鋼，面積A1=9.6cm2，AB為10號槽鋼，面積A2=25.48cm2。α=30°，材料的許用應力[σ]=120MPa。確定許可載荷F。ThestructureshowninthediagramisanequilateralanglesteelwithanACof50x50x5,withanareaofA1=9.6cm2,andanABofchannelsteelwithanareaofA2=25.48cm2.α=30°,allowablestressofmaterial[σ]=120MPa.DeterminetheallowableloadF.1自測題SELF-TEST提示計算軸力Calculateaxialforce根據斜桿的強度，求許可載荷Calculatetheallowa