Question

"For thestatic plane-stress state: x = 20 MPa,y = 100 MPa,xy = 20 MPa clockwise, assuming the yield stress of the material is 190 MPa,a. Draw the 3D Mohr’s circles to determine the maximum shear stress, and use the maximum shear stress criterion to determine the safety factor n. b. Use the Distortion Energy criterion to determine the safety factor n. "

Answer 1

Part No: Solution Atry Given plane stresses are, x = Ose=200MPa Y: 04 = 100 MPa. XY = Eary = 20 MPa. ) 17 .) 3D Moby Circle'. Calculating Principal stress cos, 101 = (* *03) + Jeojet =(120) + (-40)2 + 202 = 104.7213 MPa 0 = (00-04) - 11:0) 2n Bey - =(120) - }(40)2+(20)2 02= 15.27864 MPA + 0530 | Plane stess *. As condition. 30 Mohr clircle, may - 107 / 15.27864 1b4 72=512

Page Nc.: Cate: 1 - Maximum shear stress can be calculaled using Imax z oi-02 2 1047213 -15.2786 2 | max =_44.72.35 MPa ► Factor of Safety using Max. Shetty Shress theory: As per max. shear stress criteria the material caill fail when the maximum working shear stress exceeds allowable sheer Shess at yielding Here allowable shear stress at ylelding 05 (I go =gs MPa = 45 MP4 .. To calculate factor of safety using max. sheor Shees theory Working Max. oble Max. allowable at shear stress - yielding 44.72135 95 44.72135 (FS) = 95 FS = 2.1242 where, FS = factor of Safety, en.

Page Mic.: D Du: b) According to distortion energy theory tallere of material colll ocaure when max. distortion energy a point exceeds mox. distorkan energy at a point at yleiding ie. - 0,2 +62² - 0162 a ogled Max-distorkon energy at yield, (OR +6² +0,02) ooh oyieng. n = Oyield 02 + 02 -oo r = 1.9385 . Factor of Safety according to distortion energy Heory - 1.93851

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