工程力学之材料的力学特性拓展

Chapter3MechanicalPropertiesofMaterials13.6Poisson’sRatioWhencompressed,thebarisshortenedlongitudinally,butexpandsinlateraldirection.2Undertensionforce,thebarincreasesitslengthby

,andtheradiusreducesby

.Thestrainsinlongitudinalandlateraldirectionsare3S.D.Poissonfound(1880s)that,withintheelasticrangeandforahomogeneousandisotropicmaterial,*Since

longand

lathaveoppositesigns,

ispositive.*

isanon-dimensionalquantity.*Formostnonporoussolids,

isintherangeof1/4~1/3.*Itwasprovedtheoretically

max=1/2.Thus01/24563.7TheShearStress-StrainDiagramTestscanbeconductedforpureshearcase,anddraw

-

curve.7*Hooke’slawforshear:*G–shearmodulusmodulusofrigidity*G,E,

,

-sameunitforce/area*Relationship:891011Chapter5Torsion125.1TorsionalDeformationofaCircularShaftConceptofTorsion*Torque–amomenttendingtotwistamemberaboutitslongitudinalaxis.*Shaftoraxis–transmittorquefrommotortodrivemachine*Torsion–deformationduetotorque13Observation*Everycross-sectionremainsplanarandcircular.*Radiallinesremainstraight,androtatethroughthesameangle.*Longitudinallinesaretwisted.*Thelengthandradiusremainunchanged.14AngleofTwist*Radiallineonacross-sectionrotatethroughanangle

(x).*Theangleoftwistisafunctionofx.

=0atafixedend(x=0)*Sincetheangleischanged,thereisshearstrain.*Shearstrainisthelargestatoutersurface.155.2TheTorsionFormulaTorsionFormula*Shearstrainandshearstressareproportionaltoradius.*Atthecenter,theyarezero,andAtoutersurfacetheyaremaximum.16J–polarmomentofinertiaofthecross-section17SolidShaft18TabularShaft19202122232425265.3PowerTransmission27ConceptsofWorkandPower*WorkUnit-SIsystem:J,FPS:lbft,IPS:lbinUnit-SIsystem:W,FPS:ftlb/s,IPS:inlb/shp=550ftlb/s*Power–workdoneperunittime28PowerTransmission

–angularvelocity,circularfrequency,radians/secondf–f=2

,frequency,Hz,cycles/secondNote:Ifthespeedisgivenasnrpm(revolutionsperminute),then29ShaftDesign

allow–frommaterial,c,J–fromgeometryT–fromworkingrequirement*Givenmaterial(

allow),todeterminethesize.*Givesize,todeterminethematerial.3031325.4AngleofTwistAngleofTwist33

-angleoftwistofoneend(x=L)withrespecttotheotherend(x=0),measuredinradiansT(x)–internaltorquesatlocationxJ(x)–polarmomentofinertiaatxG–shearmodulusoftheshaftmaterial34ConstantTorqueandCross-SectionAreaGcanbedeterminedfrompuresheartests.35MultipleTorquesSignConventionUseright-handrule:Thumbisdirectedoutward.FingercurlgivespositiveTand