Shear Modulus Of Rigidity - Byju's

Shear modulus, also known as Modulus of rigidity, is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. PhysicsSolidDeformationShearModulusElasticModuli ShearModulusOfRigidity Shearmodulus,alsoknownasModulusofrigidity, isthemeasureoftherigidityofthebody,givenbytheratioofshearstresstoshearstrain.ItisoftendenotedbyGsometimesbySorμ. TableofContents WhatisShearModulus? ModulusofRigidityFormula ModulusofRigidity–Overview ExampleofModulusOfRigidity Calculation RelationBetweenElasticConstants FrequentlyAskedQuestions(FAQs) WhatisShearModulus? TheshearModulusofelasticityisoneofthemeasuresofthemechanicalpropertiesofsolids.OtherelasticmoduliareYoung’smodulusandbulkmodulus.Theshearmodulusofmaterialgivesustheratioofshearstresstoshearstraininabody. MeasuredusingtheSIunitpascalorPa. ThedimensionalformulaofshearmodulusisM1L-1T-2. ItisdenotedbyG. Itcanbeusedtoexplainhowamaterialresiststransversedeformationsbutthisispracticalforsmalldeformationsonly,followingwhichtheyareabletoreturntotheoriginalstate.Thisisbecauselargeshearingforcesleadtopermanentdeformations(nolongerelasticbody). ModulusOfRigidityFormula \(\begin{array}{l}G=\frac{\tau_{xy}}{\gamma_{xy}}=\frac{\left(\frac{F}{A}\right)}{\left(\frac{\Deltax}{l}\right)}=\frac{Fl}{A\Deltax}\end{array}\) Where, \(\begin{array}{l}\tau_{xy}=\frac{F}{A}\,is\,shear\,stress\end{array}\). Fistheforceactingontheobject. Aistheareaonwhichtheforceisacting. \(\begin{array}{l}\gamma_{xy}=\frac{\Deltax}{l}\,is\,the\,shear\,strain\end{array}\). \(\begin{array}{l}\Deltax\,is\,the\,transverse\,displacement.\end{array}\) listheinitiallength. Units: ThemodulusofrigidityismeasuredusingtheSIunitpascalorPa. CommonlyitisexpressedintermsofgigaPascal(GPa). Alternatively,itisalsoexpressedinpoundspersquareinch(PSI). ModulusOfRigidity–Overview: Themodulusofrigidityistheelasticcoefficientwhenashearforceisappliedresultinginlateraldeformation.Itgivesusameasureofhowrigidabodyis.Thetablegivenbelowbriefseverythingyouneedtoknowaboutrigiditymodulus. Definition Shearmodulusistheratioofshearstresstoshearstraininabody. Symbol GorSorμ SIunit Pascal(Pa),N/m2 Formula Shearstress/shearstrain Dimensionformula M1L-1T-2 Exampleof ModulusOfRigidity Thefollowingexamplewillgiveyouaclearunderstandingofhowtheshearmodulushelpsindefiningtherigidityofanymaterial. Shearmodulusofwoodis6.2×108Pa Shearmodulusofsteelis7.2×1010Pa Thus,itimpliesthatsteelisalotmore(reallyalotmore)rigidthanwood,around127timesmore! Calculation: Ablockofunknownmaterialkeptonatable(Thesquarefaceisplacedonthetable.),isunderashearingforce.Thefollowingdataisgiven,calculatetheshearmodulusofthematerial. Dimensionsoftheblock=60mmx60mmx20mm ShearingForce=0.245N Displacement=5mm Solution: Substitutingthevaluesintheformulaweget- Shearstress\(\begin{array}{l}=\frac{F}{A}=\frac{0.245}{60\times60\times10^{-6}}\end{array}\) \(\begin{array}{l}=\frac{2450}{36}\,N/m^2\end{array}\) Shearstrain\(\begin{array}{l}=\frac{\Deltax}{l}=\frac{5}{20}=\frac{1}{4}\end{array}\) Thus,shearmodulus,\(\begin{array}{l}G=\frac{Shear\;stress}{Shear\;strain}\end{array}\) \(\begin{array}{l}=\frac{2450\times4}{36}=\frac{2450}{9}\end{array}\) =272.22N/m2. Youmayalsowanttocheckoutthesetopicsgivenbelow! RelationBetweenYoung’sModulusAndBulkModulus Elastomers Thermalstress LongitudinalStrain RelationBetweenElasticConstants Theelasticmoduliofamaterial,likeYoung’sModulus,BulkModulus,andShearModulusarespecificformsofHooke’slaw,whichstatesthat,foranelasticmaterial,thestrainexperiencedbythecorrespondingstressappliedisproportionaltothatstress.Thus,wecanwritetherelationbetweenelasticconstantsbythefollowingequation: 2G(1+υ)=E=3K(1−2υ) Where, GistheShearModulus EistheYoung’sModulus KistheBulkModulus υisPoisson’sRatio FrequentlyAskedQuestions–FAQsIftheshearmodulusofmaterial1isxpascalsandMaterial2is30xpascals.Whatdoesitmean?Iftheshearmodulusofmaterial1isxpascalsandMaterial2is30xpascals.Itmeansthatmaterial2ismorerigidthanmaterial1.Whathappenstotheshearmodulusifappliedshearforceincreases?Thevalueofshearmodulusisconstantforagivenmaterialandisindependentoftheappliedshearforce.Howisrigiditymodulusrelatedtootherelasticmoduli?Theshearmodulusisrelatedtootherelasticmodulias2G(1+υ)=E=3K(1−2υ) where, GistheShearModulus EistheYoung’sModulus KistheBulkModulus υisPoisson’sRatioWhatismeantbythemodulusofrigidity?Themodulusofrigidityisdefinedastheratioofshearstresstoshearstraininabody.Whatistheunitofshearstrain?Shearstrainisadimensionlessphysicalquantityandhencehasnounit. StaytunedwithBYJU’Sformoresuchinterestingarticles.Ifyouwishtolearnmorephysicsconceptswiththehelpofinteractivevideolessons,downloadBYJU’S–TheLearningApp. Thevideoexplainsthegeneralstress-straingraphofanelasticmaterialexperiencingtensileload. --> TestyourknowledgeonShearModulusElasticModuli Q5 PutyourunderstandingofthisconcepttotestbyansweringafewMCQs.Click‘StartQuiz’tobegin! Selectthecorrectanswerandclickonthe“Finish”buttonCheckyourscoreandanswersattheendofthequiz StartQuiz Congrats! 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