Stress Calculator

Young's modulus (stress vs strain) OmniCalculatorlogoWe’rehiring!EmbedShareviaStressCalculatorCreatedbyBognaSzykReviewedbyStevenWoodingLastupdated:Apr14,2022Tableofcontents:HowtocalculatestrainandstressYoung'smodulus(stressvsstrain)AnexampleofcalculationsModulusofelasticityunitsFAQThisstresscalculatorwillhelpyousolvetheproblemsinmechanicsinvolvingstress,strainandYoung'smodulus.Inafewsimplesteps,youwilllearnthestressvsstrainrelationshipforanymaterialthatremainselastic.Wewillalsoteachyouhowtocalculatestrainandhowtoapplythestressequation. Howtocalculatestrainandstress Strainisdefinedasthemeasureofdeformation-aproportionbetweenthechangeoflengthandoriginallengthofanobject.Forexample,ifyoutakeanelasticbandandstretchitsothatitistwicelongerthaninitially,thenthestrainwillbeequalto1(100%). Theformulaforstrainis: ε=ΔL/L₁=(L₂-L₁)/L₁ L₁denotestheinitiallength,L₂-thefinallength,andΔListhechangeinlength.Notethatstrainisdimensionless. Stress,ontheotherhand,isthemeasureofpressurethattheparticlesofamaterialexertoneachother.Itisdefinedastheforceactingontheobjectperunitarea.Itisdifferentfromthepressure,though;whencalculatingstress,theareaconsideredmustbesosmallthattheanalyzedparticlesareassumedtobehomogeneous.Ifwetakeintoaccountabiggerarea,thecalculatedstressisusuallytheaveragevalue. Thestressequationis: σ=F/A FdenotestheforceactingonabodyandAdenotesthearea.Unitsofstressarethesameasunitsofpressure-Pascals(symbol:Pa)orNewtonspersquaredmeter. Positivestressmeansthattheobjectisintension-it"wants"toelongate.Negativestressmeansthatitisincompressionand"wants"tobecomeshorter. Young'smodulus(stressvsstrain) Ifthematerialislinearlyelastic,thenthestressandstrainaredirectlyrelatedwiththefollowingformula: E=σ/ε Eisthemodulusofelasticity,ortheYoung'smodulus.Itisamaterialconstant,differentforeachsubstance. Whatexactlyisalinearelasticbehaviorofamaterial?Ifweapplystresstoamaterial,strainincreasesproportionally.Thismaybetrueforsomerangeofstressonly-afterwereachacertainvalue,thematerialmaybreakoryield.Yieldingistheincreaseofstraininaconstantstressstate. Anexampleofcalculations Let'sassumewewanttofindtheYoung'smodulusofsteel.Todoit,wepreparedasteelrodthatwaspulledwithahighforce. Wedecidethattheforceusedtopulltherodwillbeequalto30kN(30*10³N). Wedeterminethedimensionsoftherod.Let'sassumethelengthof2m(2,000mm)andacross-sectionalareaof1cm²(1*10⁻⁴m²). Weobservedthattherodelongatedby3mm. Wecalculatethestrainistherodaccordingtotheformula:ε=ΔL/L₁=3/2000=0.0015. Wecalculatethestress,usingthestressformula:σ=F/A=30*10³/(1*10⁻⁴)=300*10⁶=300MPa. Finally,wedividethestressbystraintofindtheYoung'smodulusofsteel:E=σ/ε=300*10⁶/0.0015=200*10⁹=200GPa. Modulusofelasticityunits TheunitsoftheYoung'smodulusarethesameastheunitsofpressureandstress:Pascalsornewtonspersquaremeter.InSIunits, 1Pa=1N/1m²=1kg·m/s²/m²=1kg/(m·s²) Ifyouareinterestedinmechanics,trythetorquecalculatoraswell.Orexploremohr'scirclecalculatortounderstanddifferenttypesofstresses. FAQ WhatdoesitmeanifYoung'smodulusishigh? Thehigherthemodulusofelasticity,orYoung'smodulus,thestifferthematerial.Thismeansitcanwithstandagreateramountofstress. Whattypeofstressactsonapillar'sparticularcross-sectionduetosegmentaboveit? Thestressonapillar'scross-sectionisnegativeorcompressivestress,duetotheweightofthesegmentabovesaidcross-section. HowdoIestimatethestressataparticularcross-sectionofapillar? Toestimatethestressataparticularcross-sectionofapillar: Findtheweightofthesegmentaboveit. Substitutethevalueofweightforforceintheformulaforstress,σ=F/A,whereFistheforceandAistheareaofcross-section. Yay!Youjustfoundoutthestressactingonthecross-section! Whatisthedifferencebetweenyieldandultimatetensilestrength? Asolidmaterial'syieldstrengthisthemaximumtensilestressitcanhandlebeforepermanentdeformationoccurs.Ultimatestrengthisthemaximumstressitcanwithstandbeforefailure. BognaSzykArea(A)ft²Force(F)lbfStress(σ)psiStraincalculationsInitiallength(L₁)ftFinallength(L₂)ftChangeinlength(ΔL)ftStrain(ε)Young'smodulus(E)psiCheckout71similarclassicalmechanicscalculators⚙️AccelerationBankangleBeltlength…68moreBMR-Harris-BenedictequationHarris-BenedictcalculatorusesoneofthethreemostpopularBMRformulas.KnowingyourBMR(basalmetabolicweight)mayhelpyoumakeimportantdecisionsaboutyourdietandlifestyle.Harris-BenedictCalculator(TotalDailyEnergyExpenditure)BlackFridayHowtogetbestdealsonBlackFriday?Thestruggleisreal,letushelpyouwiththisBlackFridaycalculator!BlackFridayCalculatorBridgerectifierYoucanusethisbridgerectifiercalculatortocomputevariousrectificationattributesoftheconversionofAC(alternatingcurrent)intoDC(directcurrent).BridgeRectifierCalculatorIdealgaslawUsetheidealgaslawcalculatortofindthepressure,volumeandtemperatureofagas.IdealGasLawCalculator