Strength of Materials & Engineering Mechanics - UNIT 1.pdf

Strength of Materials & Engineering Mechanics

1. 20AG302
STRENGTH OF MATERIALS
AND
ENGINEERING MECHANICS
Handled by,
Dr. P. DINESHKUMAR M.E., Ph.D.,
Assistant Professor,
Department of Agricultural Engineering,
KongunaduCollege of Engineering and Technology

3. TEXT BOOKS & REFERENCE BOOKS

4. UNIT –1
STRESS, STRAIN AND DEFORMATION OF SOLIDS
Rigidbodiesanddeformablesolids–Tension,
CompressionandShearStresses–Deformationof
simpleandcompoundbars–Thermalstresses–Elastic
constants–Volumetricstrains–Stressesoninclined
planes–principalstressesandprincipalplanes–
Mohr’scircleofstress.

5. INTRODUCTION
Engineering science is usually subdivided into number of topics
such as
1. Solid Mechanics.
2. Fluid Mechanics.
3. Heat Transfer.
4. Properties of materials.

6. SOLID MECHANICS
Thesolidmechanicsasasubjectmaybedefinedasabranchof
appliedmechanicsthatdealswithbehaviorsofsolidbodies
subjectedtovarioustypesofloadings.
Thisisusuallysubdividedintofurthertwostreams
1.MechanicsofRigidbodiesorsimplyMechanics
2.MechanicsofDeformablesolids.

7. SOLID MECHANICS
Thesolidmechanicsasasubjectmaybedefinedasabranchof
appliedmechanicsthatdealswithbehaviorsofsolidbodies
subjectedtovarioustypesofloadings.
Thisisusuallysubdividedintofurthertwostreams
1.MechanicsofRigidbodiesorsimplyMechanics
2.MechanicsofDeformablesolids.

8. MECHANICS OF RIGID BODIES
Themechanicsofrigidbodiesisprimarilyconcernedwiththestatic
anddynamicbehaviorunderexternalforcesofengineering
componentsandsystemswhicharetreatedasinfinitelystrongand
undeformable,primarilywedealherewiththeforcesandmotions
associatedwithparticlesandrigidbodies.
“Arigidbodyisdefinedasabodyonwhichthedistancebetween
twopointsneverchangeswhateverbetheforceappliedonit”
Forexample:Abridgedoesnotdeformundertheweightofasinglemanbutitmay
deformundertheloadofatruckortentrucks.However,thedeformationissmall.

9. MECHANICS OF DEFORMABLE SOLIDS
•Themechanicsofdeformablesolidsismoreconcernedwiththe
internalforcesandassociatedchangesinthegeometryofthe
componentsinvolved.
•Theimportancearethepropertiesofthematerialsused,thestrengthof
whichwilldeterminewhetherthecomponentsfailbybreakingin
service,andthestiffnessofwhichwilldeterminewhethertheamount
ofdeformationtheysufferisacceptable.
•Therefore,thesubjectofmechanicsofmaterialsorstrengthof
materialsiscentraltothewholeactivityofengineeringdesign.
•Usuallytheobjectivesinanalysisherewillbethedeterminationofthe
stresses,strains,anddeflectionsproducedbyloads.Theoretical
analysesandexperimentalresultshaveequalrolesinthisfield.

10. TYPES OF STRESSES
1.Normal Stress
2.Shear stress

11. NORMAL STRESS
Normalstressisstresswhichactsinadirectionperpendiculartothe
area.Thenormalstressisfurtherdividedinto
•Tensilestress
•Compressivestress

12. Thisisalsoknownasuniaxialstateofstress,becausethestressesactsonlyin
onedirectionhowever,suchastaterarelyexists,thereforewehavebiaxialand
triaxialstateofstresseswhereeitherthetwomutuallyperpendicularnormal
stressesactsorthreemutuallyperpendicularnormalstresses.
Uni –axial Stress Bi -axial Stress Tri -axial Stress

13. TENSILE STRESS
Thestressinducedinabody,whensubjectedtotwoequaland
oppositepullsasaresultofwhichthereisanincreaseinlengthis
knownastensilestress.

14. COMPRESSIVE STRESS
Thestressinducedinabody,whensubjectedtotwoequaland
oppositepushesasaresultofwhichthereisandecreaseinlengthis
knownascompressivestress.

15. SHEAR STRESS
Theshearstressinducedinabody,whensubjectedtotwoequaland
oppositeforceswhichareactingtangentiallyacrosstheresisting
actionasaresultofwhichthebodytendstoshearoffacrossthe
sectionisknownasshearstress.Itisdenotedbyτ.

16. ELASTICITY
Whenanexternalforceactsonabody,thebodytendstoundergo
somedeformation.Iftheexternalforceisremovedandthebody
comesbacktoitsoriginalshapeandsize(whichmeansthe
deformationdisappearscompletely),thebodyisknownaselastic
body.Thepropertyiscalledelasticity.

17. ELASTIC LIMIT
Thebodywillregainitsperviousshapeandsizeonlywhenthe
deformationcausedbytheexternalforce,iswithinacertainlimit.
Thusthereisalimitingvalueofforceuptiandwithinwhich,the
deformationcompletelydisappearsontheremovaloftheforce.The
valueofstresscorrespondingtothislimitingforceisknownasthe
elasticlimitofthematerial.

18. HOOKE’S LAW
Hooke’slawstatesthatwhenamaterialisloadedwithinproportional
limit,thestressisproportionaltothestrain.
Thismeanstheratioofthestresstothecorrespondingstrainisa
constantwithintheproportionallimit.
ThisconstantisknownasModulusofElasticity(or)Modulusof
Rigidity.

19. MODULUS OF ELASTICITY
•

20. MODULUS OF RIGIDITY
•

21. Whenabodyissubjectedtoanaxialtensileload,thereisanincrease
inthelengthofthebody.Butatthesametimethereisadecreasein
otherdimensionsofthebodyatrightanglestothelineofactionof
theappliedload.Thusthebodyishavingaxialdeformationandalso
deformationatrightanglestothelineofactionoftheappliedload.

22. LONGITUDINAL STRAIN
Theratioofaxialdeformationtotheoriginallengthofthe
bodyisknownaslongitudinal(orlinear)strain.

23. LATERAL STRAIN
Thestrainatrightanglestothedirectionofappliedloadisknownas
lateralstrain.

24. POISSON’S RATIO
Theratiooflateralstraintolongitudinalstrainisaconstantfora
givenmaterial,whenthematerialisstressedwithinproportional
limit.ThisratioiscalledPoisson’sratio.

25. Stress -Strain Relations