Stress & Strain PPT.ppt

stress strain

1. SUBJECT: FUNDAMENTAL OF MECHANICAL ENGINEERING
AND MECHATRONICS
Mr. Bodhisatwa Seal
Assistant Professor ( Mechanical Engineering Department)
IIMT Engineering College, Meerut

2. Unit -1

3. MECHANICS OF SOLID
Introduction to stress & strain
Types of stress & strain
Hook’s law
Poisson’s ratio
Elastic constant & their relationship
Stress & strain diagram for ductile material
Stress & strain diagram for brittle material
Factor of safety
Numerical based on stress & strain

4. whensomeexternalsystemof
loadactsonabody,the
internalforces(equal&
opposite)aresetupatvarious
sectionofthebody,which
resisttheexternalforce.This
forceperunitareaatany
sectionisknownasstress.
STRESS:
Letusconsiderarectangular
barofsomecross–sectional
areaandsubjectedtosome
loadorforce(inNewton’s)

5. Now,stressisdefinedastheforce
intensityorforceperunitarea.
Hereweuseasymboltorepresent
thestress
WhereAistheareaofthe
sectionX-X
ThebasicunitsofstressinS.Iunits
i.e.(Internationalsystem)are
N/m
2
(orPa)
MPa=N/mm
2
=10
6
Pa,N/mm
2
is
equivalenttoMPa
GPa=10
3
N/mm
2
=10
9
N/m
2
=
10
9
Pa
KPa=10
-3
N/mm
2
=10
3
Pa.

6. CLASSIFICATION OF STRESS

7. TYPES OF DIRECT STRESS:
Onlytwobasicstressesexist:
(1)Normalstress
(2)Shearstress.
Otherstresseseitheraresimilar
tothesebasicstressesorarea
combinationofthise.g.bending
stressisacombinationtensile,
compressiveandshearstresses.
Torsionalstress,asencountered
intwistingofashaftisa
shearingstress.

8. NormalStress(σ)
Whenaforceisappliedtoanelasticbody,thebodydeforms.The
wayinwhichthebodydeformsdependsuponthetypeofforce
appliedtoit.
Normalstressisthestresswhichactsinthedirection
perpendiculartothearea,itisrepresentedbysymbol‘σ’
( a ) Tensile Stress due to tensile
force
Atensilestressinducedina
body,whensubjectedtotwo
equal&oppositepullwhich
haveatendencytomakesthe
bodylongerorelongate

9. (b)CompressiveStressdueto
compressiveforce
Acompressivestressinducedina
body,whensubjectedtotwoequal
&oppositepushwhichhavea
tendencytomakesthebodyshorter
orshorten

10. SHEAR STRESS
Thestressinducedina
bodywhensubjectedto
twoequal&opposite
forceswhichareacting
tengentiallyacrossthe
resistingsection.Asa
resultofwhichbody
tendtoshearoffacross
thesection.Itisknown
asshearstress

11. Strain:Strainisthedeformationof
amaterialfromstress.Itissimplya
ratioofthechangeindimensiontothe
originaldimension.Deformationsthat
areappliedperpendiculartothecross
sectionarenormalstrains.
Stainisameasureofthemeasureof
thedeformationproducedinthe
memberbytheload.
IfarodoflengthLisintensionand
theelongationproducedisdL,
thenthedirectstrain=Elongation/
Originallength
Tensilestrainwillbepositive
compressivestrainwillbenegative.

12. TYPESOFSTRAINACCORDING TOFORCE
TensileStrain:ifthereissomeincreaseinlengthofabodydueto
externalforcethentheratioofincreaseoflengthtotheoriginallength
ofbodyisknownastensilestrain.
Compressivestrain:ifthereissomedecreaseinlengthofbody.Then
theratioofdecreaseoflengthofthebodytotheoriginallengthis
knownascompressivestrain

13. VolumetricStrainisdefinedastheratioofchangeinvolumetotheinitial
volume.

14. Shearstrainisdefinedasthestrainaccompanyingashearingaction.Itis
theangleinradianmeasurethroughwhichthebodygetsdistortedwhen
subjectedtoanexternalshearingaction.ItisdenotedbyΦ
ConsideracubeABCDsubjectedtoequalandoppositeforcesQacross
thetopandbottomforcesABandCD.Ifthebottomfaceistakenfixed,
thecubegetsdistortedthroughangleΦtotheshapeABC’D’.Now
strainordeformationperunitlengthis
Shearstrainofcube=CC’/CD=CC’/BC=Φradian

15. ACCORDING TO DIRECTION

16. LateralStrain:
Lateralstrainofadeformed
bodyisdefinedastheratio
ofthechangeinlength
(breadthofarectangularbar
ordiameterofacircularbar)
ofthebodyduetothe
deformationtoitsoriginal
length(breadthofa
rectangularbarordiameter
ofacircularbar)inthe
directionperpendicularof
theforce

17. Whenanexternalforceisappliedonabodyanditundergoes
somedeformation.Ifthebodyreturnsbacktoitsoriginalshape
andsizeoncompleteremovaloftheload,thebodyiscalled
elasticbody.
Elasticity:Thepropertyofamaterialbywhichitreturnsbacktoits
originalposition(i.e.shapeandsize)ontheremovalofexternal
forceorload,iscalledelasticity.
ElasticLimit:Itisdefinedasthevalueofstressuptoandwithin
whichthematerialreturnbacktotheiroriginalposition(i.e.shape
andsize)ontheremovalofexternalforce.
Ifthevalueofexternalforceissuchthatitexceedstheelasticlimit,
thanthebodywillnotcompletelyregainitsoriginalposition.The
bodylosesitspropertyofelasticitytosomeextent.Andifthe
externalforceactingonthebodyisremoved,inthatconditionthe
bodywillnotreturntoitsoriginalshapeandsizeandtherewillbe
aresidualdeformationinthematerial
Elasticity & Elastic limit

19. Hooke’slawstatedthatwhena
materialisloadedwithinelasticlimit,
stressisdirectlyproportionaltostrain
Inwhich
“σ”istheaxialstress
“ε”istheaxialstrain
“E”isaconstantofproportionality
knownasthemodulusofelasticityfor
thematerial.
Themodulusofelasticityistheslope
ofthestress-straindiagraminthe
linearlyelasticregion.
Theequationσ=Eεiscommonly
knownasHooke’slaw
Hook’s law:

20. Whenanelasticbody
issubjectedtostress,a
proportionateamount
ofstrainisproduced.
Theratiooftheapplied
stressestothestrains
generatedwillalways
beconstantandis
known aselastic
constant. Elastic
constantrepresentsthe
elasticbehaviourof
objects.
ELASTIC CONSTANT & THEIR RELATION SHIP
Elastic Constants
Different elastic constants are as
follows :
1.Young’s modulus or Modulus of
elasticity, E
2.Bulk modulus
3.Modulus of rigidity or shear modulus
4.Poisson’s ratio

21. Young’sModulus
AccordingtoHooke’slaw,when
abodyissubjectedtotensile
stressorcompressivestress,
thestressappliedisdirectly
proportionaltothestrainwithin
theelasticlimitsofthatbody.
Theratioofappliedstresstothe
strainisconstantandisknown
asYoung’smodulusormodulus
ofelasticity.
Young’smodulusisdenotedby
letter“E”.Theunitofmodulusof
elasticityisthesameastheunit
ofstresswhichismegapascal
(Mpa).1Mpaisequalto1

22. BulkModulus(B)or
K
Whenabodyissubjectedto
mutuallyperpendiculardirect
stresseswhicharealikeand
equal,withinitselasticlimits,
theratioofdirectstressto
thecorrespondingvolumetric
strainisfoundtobeconstant.
Thisratioiscalledbulk
modulusandisrepresented
byletter“K”.UnitofBulk
modulusisMpa.

23. RigidityModulus(G)
Whenabodyissubjectedto
shearstresstheshapeofthe
bodygetschanged,theratio
ofshearstresstothe
correspondingshearstrainis
calledrigiditymodulusor
modulusofrigidity.Itis
denotedbytheletters“G”or
“C”or“N”.Unitofrigidity
modulusisMpa

24. Poisson’s ratio
With in the elastic limit, the ratio of lateral strain to longitudinal strain or
linear strain is called Poisson's ratio
Poisson’sratioismaximumforanidealelasticincompressiblematerial
anditsvalueis0.5.Formostoftheengineeringmaterials,Poisson’s
ratioliesbetween0.25and0.33.Ithasnounits.

25. Relationship between Elastic Constants
1. The relationship between Young’s modulus (E), rigidity
modulus (G) and Poisson’s ratio (µ) is expressed as :
2.The relationship between Young’s modulus (E), bulk modulus
(K) and Poisson’s ratio (µ) is expressed as :

26. 3.Young’smoduluscanbeexpressedintermsofbulk
modulus(K)andrigiditymodulus(G)as:
4.Poisson’sratiocanbeexpressedintermsofbulkmodulus
(K)andrigiditymodulus(G)as:

27. Definition offactor of safety
It is the ratio of the ultimate strength of a member or piece of
material (as in an airplane) to the actual working stress or the
maximum permissible stress when in use

28. STRESS STRAIN DIAGRAM
Therelationbetweenstressandstrainisgenerallyshownby
plottingastress-strain(σ-ϵ)diagram.Stressisplottedonordinate
(verticalaxis)andstrainonabscissa(horizontalaxis).Such
diagramsaremostcommoninstrengthofmaterialsfor
understandingthebehaviourofmaterials.Stress-straindiagrams
aredrawnfordifferentloadings.
Stress-StrainCurves(Tension)
Whenabarorspecimenissubjectedtoagraduallyincreasing
axialtensileload,thestressesandstrainscanbefoundoutfor
numberofloadingconditionsandacurveisplotteduptothepoint
atwhichthespecimenfails.givingwhatisknownasstress-strain
curve.
Stress-straincarvesforductilematerials:Amaterialissaidto
beductileinnature,ifitelongatesappreciablybeforefracture.
Onesuchmaterialismildsteel.Theshapeofstress-strain
diagramforthemildsteelisshowninFig.(a)

29. STRESS STRAIN DIAGRAM

30. STRESS STRAIN DIAGRAM
PortionOA:Thisportionisabsolutely
straight,wherethestressis
proportionaltostrainandthematerial
obeysHooke’slaw(σ=Eϵ).Thevalue
ofstressatpointAiscalled
proportionallimit.
PortionAB:Inthisportion,Hook’s
lawisnotobeyed,althoughthe
materialmaystillbeelastic.Thepoint
Bindicatestheelasticlimit.

31. STRESS STRAIN DIAGRAM
PortionBC:Inthisportion,themetal
showsastrainevenwithoutincreasein
stressandthestrainisnotfullyreturn
whenloadisremoved.
PortionCD:Yieldingstartinthis
portionandthereisadropofstressat
thepointDdirectlyafteryielding
beginsatC.ThepointDistermedas
loweryieldpointandCiscalledupper
yieldpoint.

32. STRESS STRAIN DIAGRAM
PortionDE:Afteryieldinghastaken
placeatD,furtherstrainingtakesplace
atthisportionbyincreasingthestress
andthestress–straincurvecontinuesto
riseuptothepointE.Straininthis
portionisabout100timesthatof
portionO-A.AtthepointE,thebar
beginstoformalocalneck.Thepoint
Eistermedasultimatetensilestress
point.

33. STRESS STRAIN DIAGRAM
PortionEF:Inthisportion,theloadis
fallingofffromthemaximumand
fractureatFtakesplace.ThepointFis
termedasfractureorbreakingpoint
andtheidenticalstressiscalled
breakingstress.

34. STRESS STRAIN DIAGRAM
StressStrainCurvesforBrittleMaterials
Materialswhichshowverysmallelongation
beforetheyfracturearecalledbrittle
materials.Theshapeofcurveforhigh
carbonsteel,concreteandhighstrength
lightalloysoranybrittlematerialsisshown
infig.Formostbrittlematerialsthe
permanentelongation(i.e.increasein
length)islessthan10%.Principal
mechanicalpropertiesThecharacteristicsof
thematerialswhichdescribetheirbehaviour

35. PRINCIPLE MECHANICAL
PROPERTIES
1-Elasticity
Elasticityofamaterialispowerofcomingbacktooriginalpositionwhen
thestressorloadisremoved.Thegreateststressthatamaterialcan
withstandwithoutpermanentdistortioniscalledelasticlimit.
2-Plasticity
Theplasticityofamaterialisabilitytoundergosomepermanent
deformationwithoutfailure.Plasticdeformationwilltakeplaceonlyafter
theelasticrangehasbeenexceeded,beyond(pointc).
Plasticityisanimportantpropertyandwidelyusedinseveralmechanical
processeslikeforming,shaping,extrudingandmanyotherhotandcold
workingprocesses.Ingeneral,plasticityincreaseswithincreasing
temperature.
Duetothispropertyvariousmetalscanbetransformedintodifferent
productsofrequiredshapeandsize.Thisconversionintodesiredshape
andsizeiseffectedeitherbytheapplicationofpressureorheatorboth.

36. PRINCIPLE MECHANICAL
PROPERTIES
3-Ductility
Ductilityofamaterialtheirenablestodrawoutintothinwirewith
applicationtheload.Ductilematerialsuchasmildsteel,wiresofgold,
silver,copper,aluminium,etc.aredrawnbyextrusionorbypulling
throughaholeinadieduetotheductileproperty.Theductilitydecreases
withincreaseoftemperature.Thepercentelongationandthereductionin
areaintensionareoftenusedasempiricalmeasuresofductility.
4-Strength
Itistheresistanceofferedbyamaterialwhensubjectedtoexternal
loading,sostrongerthematerialcanbewithstandwithgreatertheload.
Dependinguponthetypeofloadappliedthestrengthcanbetensile,
compressive,shearortorsionalstrength.Themaximumstressthatany
materialwillwithstandbeforedestructioniscalleditsultimatestrength
(pointEasshowninFig.1).

37. PRINCIPLE MECHANICAL
PROPERTIES
5-Brittleness
Thebrittlenessofamaterialisthepropertyofbreakingwithoutmuch
permanentdistortion.Therearemanymaterials,whichbreakorfailbefore
muchdeformationtakeplace,suchasglass,castiron,etc.Therefore,a
non-ductilematerialissaidtobeabrittlematerial.Abrittlematerial
shouldnotbeconsideredaslackinginstrength,itisonlyshowsthelack
ofelasticity.Onstress-straindiagram,thesematerialsdon’thaveyield
pointandvalueofEissmall.
6-Toughness
Thetoughnessofamaterialisabilitytowithstandbothplasticandelastic
deformations.Itisahighlydesirablequalityforstructuralandmachine
partstowithstandtoshockandvibration.Manganesesteel,mildsteelsare
toughmaterials.ForEx:Ifaloadissuddenlyappliedtoapieceofmild
steelandthentoapieceofglassthemildsteelwillabsorbmuchmore
energybeforefailureoccurs.Thus,mildsteelissaidtobemuchtougher
thanaglass.

38. PRINCIPLE MECHANICAL
PROPERTIES
7-Hardness
Hardnessiscloselyrelatedtostrength.Itistheabilityofamaterialto
resistscratching,abrasion,penetrationwithapplyexternalload.
8-Stiffness(Rigidity)
Theresistanceofamaterialtodeflectioniscalledstiffnessorrigidity.
Steelisstifferormorerigidthanaluminium.Stiffnessismeasuredby
Young’smodulusE.ThehighervalueoftheYoung’smodulusthismean
stifferthematerial.Eistheratioofstressoverstrainandisgivenbythe
slopeoflineO–A.