直桿軸向拉壓的強(qiáng)度和變形Strengthanddeform

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

一、拉、壓的強(qiáng)度Strengthoftensionandcompression對(duì)于塑性材料，當(dāng)應(yīng)力達(dá)到屈服極限σs時(shí)，整個(gè)桿件都會(huì)發(fā)生比較大的變形且不能恢復(fù)，因此塑性材料以σs為極限應(yīng)力;對(duì)于脆性材料，當(dāng)應(yīng)力達(dá)到強(qiáng)度極限σb時(shí)發(fā)生斷裂，故對(duì)脆性材料以σb為極限應(yīng)力。Forplasticmaterials,whenthestressreachestheyieldlimitσAts,theentirerodwillundergosignificantdeformationandcannotberestored,sotheplasticmaterialwillσSistheultimatestress;Forbrittlematerials,whenthestressreachesthestrengthlimitσFractureoccursattimeb,therefore,forbrittlematerialsσBistheultimatestress.一、材料力學(xué)的基本概念Basicconceptsofmaterialmechanics

σs一屈服極限

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

σb一強(qiáng)度極限

σb-Strengthlimitnb一安全系數(shù)，脆性材料nb=2.0~3.5Nb-safetyfactor,brittlematerialsnb=2.0~3.5一、拉、壓的強(qiáng)度Strengthoftensionandcompression因?yàn)閿嗔哑茐谋惹茐母ｋU(xiǎn)，所以nb>ns。此外，安全系數(shù)的選取還要考慮對(duì)安全要求的高低和經(jīng)濟(jì)等因素的影響。Becausefracturefailureismoredangerousthanyieldfailure,nb>ns.Inaddition,theselectionofsafetyfactorsalsoneedstoconsidertheimpactoffactorssuchasthelevelofsafetyrequirementsandeconomy.一、拉、壓的強(qiáng)度Strengthoftensionandcompression根據(jù)強(qiáng)度條件，可以解決三類(lèi)強(qiáng)度計(jì)算問(wèn)題Accordingtothestrengthconditions,threetypesofstrengthcalculationproblemscanbesolved1.強(qiáng)度校核Strengthverification確保危險(xiǎn)點(diǎn)的最大工作應(yīng)力不超過(guò)材料的容許正應(yīng)力，就能保證桿件正常工作Toensurethatthemaximumworkingstressatthedangerouspointdoesnotexceedtheallowablenormalstressofthematerial,thenormaloperationoftherodcanbeensuredFNmax--桿的最大軸力，即危險(xiǎn)截面上的軸力FNmax-Themaximumaxialforceoftherod,thatis,theaxialforceonthedangeroussection一、拉、壓的強(qiáng)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(yīng)變:Axiallinearstrain:相對(duì)變形，表示軸向變形的程度。Relativedeformationrepresentsthedegreeofaxialdeformation.胡克定律推論:CorollarytoHooke'sLaw:對(duì)于同一種材料，當(dāng)應(yīng)力未超過(guò)某一極限時(shí)，應(yīng)力與應(yīng)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(duì)于同一種材料，當(dāng)應(yīng)力未超過(guò)某一極限時(shí)，橫向應(yīng)變與軸向應(yīng)變成正比:Forthesamematerial,whenthestressdoesnotexceedacertainlimit,thetransversestrainbecomesproportionaltotheaxialstrain:泊松比Poisson'sratioμ——量綱為1的量，其數(shù)值因材料而異，由實(shí)驗(yàn)測(cè)定μ——Aquantitywithadimensionof1,whosevaluevariesdependingonthematerialandisdeterminedexperimentally彈性模量E和泊松比μ都是材料的彈性常數(shù)。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(jì)算軸力(畫(huà)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(nèi)力和應(yīng)力Internalforcesandstressesunderaxialtensionandcompression(2)計(jì)算AB段、CB段的正應(yīng)力CalculatethenormalstressofABandCBsegmentsAB段:ABsegment:CB段:CBsegment:

(3)計(jì)算AB段、CB段的變形量，進(jìn)而計(jì)算總變形量CalculatethedeformationofABandCBsegments,andthencalculatethetotaldeformationAB段:ABsegment:

CB段:CBsegment:總變形量:Totaldeformation:

1自測(cè)題SELF-TEST圖示結(jié)構(gòu)，AC為50x50x5的等邊角鋼，面積A1=9.6cm2，AB為10號(hào)槽鋼，面積A2=25.48cm2。α=30°，材料的許用應(yīng)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(cè)題SELF-TEST提示計(jì)算軸力Calculateaxialforce根據(jù)斜桿的強(qiáng)度，求許可載荷Calculatetheallowa