工程力學之張力的原理與應用

1Chapter1Stress21.1IntroductionMechanics*Rigidbodymechanics:statics,dynamics*Deformablebodymechanics:Mechanicsofmaterials,Elasticity,PlasticityFracturemechanics*Fluidmechanics3MechanicsofMaterials*Externalloadingsinternalforcesstresses*Deformationsstrains*Materialproperties*Designcriteria4UNITS5SISystem*Basicunits:mass-kg,length-m,time-sec*Derivedunits:velocitym/sec,accelerationm/sec2,

g=9.81m/sec2,forceN=kgm/sec2,stressN/m2,

workJ=Nm,powerW=J/sec=Nm/sec,etcUSFPSSystem*Basicunits:force-lb,length-ft,time-sec*Derivedunits:velocityft/sec,accelerationft/sec2,

g=32.17ft/sec2,massslug=lbsec2/ft,etc1slug=32.17lbm6USIPSSystem*Basicunits:force-lb,length-in,time-sec*Derivedunits:velocityin/sec,accelerationin/sec2,

g=386in/sec2,massblob=lbsec2/in,etc1blob=386lbmUnitConversion*Stayinthesameunitsystem.*Usecorrectunitformass7PrefixesFactor Prefix Symbol109 giga G106 mega M103 kilo k10-2 centi c10-3 milli m10-6 micro 10-9 nano n81.2EquilibriumofaDeformableBodyExternalLoads*Surfaceforces-causedbydirectcontact1.Concentratedforce2.Distributedforce*Bodyforce-gravity9SupportReactions*Supportreactionsarealsoexternalforces*Ifasupportpreventscertainmotion(translationorrotation),thereactionsfromthesupportareinthesamedirections(forceormoment).1011EquationofEquilibrium*Vectorequations

O–anypoint*Scalarequations*2-D(Coplanar)case12InternalLoadings*Cut(imaginarily)thebodyintotwoparts.*Internalforces–forces(moments)onthecutplaneappliedtoonepartfromanotherpart.13InternalForcesofabeam14ProcedureforAnalysis1.Drawfree-bodydiagram(FBD)fortheentirebody,

includingexternalforcesandsupportreactions.Writeequilibriumequations,andsolveforsupportreactions.2.Cutthebodyintotwoparts,andtakeonepart(simplerone).DrawFDBforthispart,includingexternalforces,supportreactions,andinternalforcesonthispart.3.Writeequilibriumequationsforthispart,andsolveforinternalforces.15

NormalforceNB–perpendiculartocross-sectionIttendstostretchorcompressthemember.ShearforceVB–tangent(parallel)tocross-sectionIttendstocutthememberintransversedirection.BendingmomentMB–couplemomentIttendstobendthemember.4.for2-Dcase,threeinternalforcesingeneral:16*ShearforceVrotatethepartclockwisely+counterclockwisely-SignConvention*NormalforceNtensile+,compressive-17Severalissues*Alwaysdrawinternalforcesinpositivedirections.Iftheresultisnegative,theactualdirectionisopposite.*Dependingonthesituation,oneortwoofthethreeinternalforcesmaybeabsent.*BendingmomentM

bendthepartconcaveupward+(likeabowl)Concavedownward-18192021ReplacedistributedforcebyconcentratedforceFR:

*ThemagnitudeofFRistheareaAunderw(x)curve.*FRpassesthroughthecentroidofareaA.22UniformLoading

w(x)=w=constant

FR=wL,FRisinthemiddleoftheloading.23Fortheloadingbelow,replaceitbythreeforces.24TriangularLoading

FR=Lw0/2

Thelocation

ofFRisshownbelow.252627EXAMPLE1.3

28EXAMPLE1.3(CONTINUED)

2930EXAMPLE1.4(CONTINUED)

311.3StressConceptofStress*Stress–internalforceperunitarea*Stressdependson(i)internalforceand(ii)area.*Largestressmaycausedamageofmaterial*Stressisthecriterionfordesign.32NormalStressInternalforce

FonAhasthreecomponents:

Fz–normaltoA,inz-direction

Fx–tangenttoA,inx-direction

Fy–tangenttoA,iny-directionNormalstress:

z

>0-tensilestress

z

<0-compresivestress33ShearStressSigndependsoncoordinatesystem34GeneralStateofStress356components:

normalstresses

x,

y,

z

shearstresses

xy,

yz,

zx

36ImportantIssues*Stressisapropertyofapoint.Differentpointsinthematerialhavedifferentstresses.*Stressdependsonthedirectionofthearea.Evenatthesamepoint,areasofdifferentdirectionshavedifferentstresses.*Stressisthemostimportantconceptinthiscourse,aswellasinmachinedesign.*Units:SIsystem:Pa=N/m2IPSsystem:psi=lb/in2

FPSsystem:lb/ft2371.4AverageNormalStressinanAxiallyLoadedBarAssumptions*Theaxialforcesareappliedatthecenterofthecross-section(centroid).*Thebarmaterialishomogeneous.(samematerialpropertiesatallpoints)*Onlyconsiderthepartfarfromtheends.38AverageNormalStress*IfAisconstant,isconstant.*IfAchanges,*Formultiplesegmentsandmanyexternalforces,(i)findinternalforcesfordifferentcross-sections,(i)determinethestresses.39Tensileandcompressivenormalstresses40EXAMPLE1.5

4142EXAMPLE1.6

43EXAMPLE1.6(CONTINUED)

44EXAMPLE1.7

45EXAMPLE1.7(CONTINUED)

46EXAMPLE1.8

47EXAMPLE1.8(CONTINUED)

481.5AverageShearStress*Internalforce:*Shearstress:*Procedure:(i)Findtheinternalshearforces,(ii)Determinetheshearstresses.49EXAMPLE1.9

5051EXAMPLE1.10

52EXAMPLE1.10(CONTINUED)

5354EXAMPLE1.11(CONTINUED)

551.6AllowableStressDesign*FailureloadFfail:

Ffail-

themaximumloadthemembercanstand

Ffaildependsonmaterialproperty.*AllowableloadFallow:

Fallow-themaximumallowableloadforthemembe