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外文翻译--应力应变.doc

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外文翻译--应力应变.doc

五、外文资料翻译StressandStrain1.IntroductiontoMechanicsofMaterialsMechanicsofmaterialsisabranchofappliedmechanicsthatdealswiththebehaviorofsolidbodiessubjectedtovarioustypesofloading.Itisafieldofstudythatisknownbyavarietyofnames,includingstrengthofmaterialsandmechanicsofdeformablebodies.Thesolidbodiesconsideredinthisbookincludeaxiallyloadedbars,shafts,beams,andcolumns,aswellasstructuresthatareassembliesofthesecomponents.Usuallytheobjectiveofouranalysiswillbethedeterminationofthestresses,strains,anddeformationsproducedbytheloadsifthesequantitiescanbefoundforallvaluesofloaduptothefailureload,thenwewillhaveobtainedacompletepictureofthemechanicsbehaviorofthebody.Theoreticalanalysesandexperimentalresultshaveequallyimportantrolesinthestudyofmechanicsofmaterials.Onmanyoccasionwewillmakelogicalderivationstoobtainformulasandequationsforpredictingmechanicsbehavior,butatthesametimewemustrecognizethattheseformulascannotbeusedinarealisticwayunlesscertainpropertiesofthebeenmadeinthelaboratory.Also,manyproblemsofimportanceinengineeringcannotbehandledefficientlybytheoreticalmeans,andexperimentalmeasurementsbecomeapracticalnecessity.Thehistoricaldevelopmentofmechanicsofmaterialsisafascinatingblendofboththeoryandexperiment,withexperimentspointingthewaytousefulresultsinsomeinstancesandwiththeorydoingsoinothers①.SuchfamousmenasLeonardodaVinci14521519andGalileoGalilei15641642madeexperimentstoadequatetodeterminethestrengthofwires,bars,andbeams,althoughtheydidnotdevelopanyadequatetheoriesbytodaysstandardstoexplaintheirtestresults.Bycontrast,thefamousmathematicianLeonhardEuler17071783developedthemathematicaltheoryanyofcolumnsandcalculatedthecriticalloadofacolumnin1744,longbeforeanyexperimentalevidenceexistedtoshowthesignificanceofhisresults②.Thus,Eulerstheoreticalresultsremainedunusedformanyyears,althoughtodaytheyformthebasisofcolumntheory.Theimportanceofcombiningtheoreticalderivationswithexperimentallydeterminedpropertiesofmaterialswillbeevidenttheoreticalderivationswithexperimentallydeterminedpropertiesofmaterialswillbeevidentasweproceedwithourstudyofthesubject③.Inthissectionwewillbeginbydiscussingsomefundamentalconcepts,suchasstressandstrain,andthenwewillinvestigatebathebehavingofsimplestructuralelementssubjectedtotension,compression,andshear.2.StressTheconceptsofstressandstraincanbeillustratedinelementarywaybyconsideringtheextensionofaprismaticbarseeFig.1.4a.Aprismaticbarisonethathascrosssectionthroughoutitslengthandastraightaxis.InthisillustrationthebarisassumedtobeloadedatitsendsbyaxisforcesPthatproduceauniformstretching,ortension,ofthebar.Bymakinganartificialcutsectionmmthroughthebaratrightanglestoitsaxis,wecanisolatepartofthebarasafreebodyFig.1.4b.AttherighthandendtheforcePisapplied,andattheotherendthereareforcesrepresentingtheactionoftheremovedportionofthebaruponthepartthatremain.Theseforceswillbecontinuouslydistributedoverthecrosssection,analogoustothecontinuousdistributionofhydrostaticpressureoverasubmergedsurface.Theintensityofforce,thatis,theperunitarea,iscalledthestressandiscommonlydenotedbytheGreekletterб.AssumingthatthestresshasauniformdistributionoverthecrosssectionseeFig.1.4b,wecanreadilyseethatitsresultantisequaltotheintensityбtimesthecrosssectionalareaAofthebar.Furthermore,fromtheequilibriumofthebodyshowinFig.1.4b,Fig.1.4PrismaticbarintensionwecanalsoseethatthisresultantmustbeequalinmagnitudeandoppositeindirectiontotheforceP.Hence,weobtainбP/A1.3astheequationfortheuniformstressinaprismaticbar.Thisequationshowsthatstresshasunitsofforcedividedbyareaforexample,NewtonspersquaremillimeterN/mm²orpoundsofpersquareinchpsi.WhenthebarisbeingstretchedbytheforcesP,asshowninthefigure,theresultingstressisatensilestressiftheforcearereversedindirection,causingthebattobecompressed,theyarecalledcompressivestress.AnecessaryconditionforEq.1.3tobevalidisthatthestressбmustbeuniformoverthecrosssectionofthebat.Thisconditionwillberealizediftheaxialforcepactsthroughthecentroidofthecrosssection,ascanbedemonstratedbystatics.WhentheloadPdosesnotactatthuscentroid,bendingofthebarwillresult,andamorecomplicatedanalysisisnecessary.Throughoutthisbook,however,itisassumedthatallaxialforcesareappliedatthecentroidofthecrosssectionunlessspecificallystatedtothecontrary④.Also,unlessstatedotherwise,itisgenerallyassumedthattheweightoftheobjectitselfisneglected,aswasdonewhendiscussingthisbarinFig.1.4.3.StrainThetotalelongationofabarcarryingforcewillbedenotedbytheGreekletterбseeFig.1.4a,andtheelongationperunitlength,orstrain,isthendeterminedbytheequationεδ/L1.4WhereListhetotallengthofthebar.Nowthatthestrainεisanondimensionalquantity.ItcanbeobtainedaccuratelyformEq.1.4aslongasthestrainisuniformthroughoutthelengthofthebar.Ifthebarisintension,thestrainisatensilestrain,representinganelongationorastretchingofthematerialifthebarisincompression,thestrainisacompressivestrain,whichmeansthatadjacentcrosssectionofthebarmoveclosertooneanother.SelectedfromStephenP.TimoshenkoandJamesM.Gere,MechanicsofMaterials,VanNostrandReinholdCompanyLtd.,1978.应力应变1、材料力学的介绍材料力学是应用力学的分支,它是研究受到各种类型载荷作用的固体物。材料力学所用的方面就我们所知道的类型名称包括材料强度和可变形物体的力学。在本书中考虑的固体物有受轴向载荷的杆、轴、梁和柱以及用这些构件所组成的结构。通常我们分析物体由于载荷所引起的应力集中、应变和变形作为目的。如果这些是能够获得增长直到超载的重要性。我们就能够获得这种物体的完整的机械行为图。理论分析和实验结论是研究材料力学的相当重要的角色。在许多场合,我们要做出逻辑推理获得机械行为的公式和方程。但是同时我们必须认识到这些公式除非已知这些材料的性质,否则不能用于实际方法中,这些性质只有通过一些合适的实验之后才能用。同样的,许多重要的问题也不能用理论的方法有效的处理,只有通过实验测量才能实际应用。材料力学的发展历史是理论与实验极有趣的结合。在一些情况下是指明了得以有用结果的道路,在另一些情况下则是理论来做这些事。例如著名人物莱昂纳多·达·芬奇(14521519)和伽利略·加能(15641642)做实验以确定铁丝、杆、梁的强度。尽管他们没有得出足够的理论(以今天的标准)来解释他们的那些实验结果。相反的,著名的数学家利昴哈德·尤勒(17071783)在1744年就提出了柱体的数学理论计算出其极限载荷,而过了很久才有实验证明其结果的重要性。虽然其理论结果并没有留存多少年,但是在今天他仍是柱体理论的基本形式。随着研究的不断深入,把理论推导和在实验上已确定的材料性质结合起来形容的重要性是很显然的。然后,调查研究简单结构元件承受拉力、压力和剪切的性质。2、应力应力和应变的概念可以用图解这种方法。考虑等截面杆发生的延伸。如图1.4a.等截面杆沿长度方向和轴线方向延伸。在这个图中的杆假设在它的两端承受轴向载荷P致使产生一致的延伸,即杆的拉力。通过杆的假想(mm)截面是垂直于轴的直角面。我们可以分离出杆的一个自由体作为研究对象图1.4b.在右边的端点上是拉力P的作用,而在另一端是被移走的杆上的一部分作用在这部分上的力。这些力分布在水的表面上。强度就是单位面积上的载荷叫应力,用希腊字母σ表示。假设应力均匀连续分布在横截面上看图1.4b。而且在图1.4b中看到物体的平衡,我们能够得出这样的合力在大小上必须等于相反方向的载荷P。我们得到等截面杆的应力均匀分布的方程式σP/A

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