Mohr's Circle.pdf

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University at Buffalo
Engineering & Applied Sciences
EAS 209
Christine Human

. is positive xy ) σaxis τy τxy , -τy σ σ and σ x will therefore σ τy axis. . As shown, − τxy τaxes to the same scale Usecotheenoiofn:yiwnoσry about the sign , where line XY crosses the avg Notplot below thee EAS 2SprocedTurPt1o:Dlottrmoher’hIitclr:Christine Humant point X with coordinatR = half-length of line XY2dius R By the end of today’s Lecture 25 is a graphical approach to finding Mohr’s Circle for Plane Stress DeptriDetAdd stress statest any orientation EAS 209-SpriMohr’s Circlecorowhr(Instructors: Christilectir•l,tud• •’s shoForsadMiticMalhielp understanding Mohr’s circle 0 P A = =2 x x τ = TcJ y ' ± = σ = x = σ x min σ max, σ o =5 p = Tc J θ xy = ,rom poit Y or X = τxy ± o σ 0 = =0 , = Max shear ptress is given bycur at P A σy τmax 2 x =x EAS 20Srin2l4 ohxa’s ciesleffMrocen’ssccar:irsle amangsion(a)loadi(b) 3/17/2014 4 s p θ =0) θ τ -axis ( -axis is 2 σ σ from circle σmin , max σ is defined by the top of the circle max τ EAS 209-Spring 2014 STEP 6: DetermineT:DeeanrmleibetwreentXtonaondprincipal axesdavxemtcm lshiesrs 23 EAS 2MSpigim1um shear stress Instructors: Christine Human 3/17/2014 6 EAS 20SriF2oshto(rc,riarctplailreConstruction of Mohr’s circle planes and stresses 3/17/2014 5 . MPa MPa 2 80 2 52 = = = 48 20 60 FX2 = 4 + 2 2+ 48 XF CF. °lockwise 100 2+ = =7 . Pa =-48 MPa = () 20) p p 33 BC M
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