Lecture11 - ME 382 Lecture 11 1/ii/06 1 von Mises yield...

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Unformatted text preview: ME 382 Lecture 11 1/ii/06 1 von Mises yield criterion (continued) Example : Cantilevered solid cylindrical beam of AISI 1020 steel ( Y = 260 MPa), built in as shown. What is factor of safety against yield at A? L = 0.75 m, d = 0.10 m, P = 18 kN, Q = 90 kN T = Pd/2 T xx = Pd /2 V xz = P M yy = PL N xx = Q A xx = ! d 2 /4; I yy = ! d 4 /64; J xx = ! d 4 /32 ! xx = N xx A xx + M yy d /2 I yy ! xx = 4 Q " d 2 + 32 PL " d 3 " xy = # T xx d /2 J ! xy = " Td /2 J = " 8 P # d 2 Also, by inspection: yy = 0, zz = 0, zx = zy = 0 ! xx = 4 " 90 " 10 3 # " 0.1 ( ) 2 + 32 " 18 " 10 3 " 0.75 # " 0.1 ( ) 3 = 148.97 MPa " xy = # 8 $ 18 $ 10 3 % $ 0.1 ( ) 2 = # 4.58 MPa Mohrs Circle : Center = 74.49 MPa; Radius = 74.63 MPa ME 382 Lecture 11 1/ii/06 2 " 1 = 149.12; " 2 = # 0.14; " 3 = 0.00 MPa Loading parameter: " H = 1 2 149.12 + 0.14 ( ) 2 + 149.12 # ( ) 2 + # 0.14 # ( ) 2 [ ] = 149.19 MPa Safety factor is S f = ! Y ! H = 260 149.19 = 1.7 H ARDNESS Push an indenter into the surface of a material Hardness defined as H = P / A where P is the load required to indent A is the area of the indent impression Complicated geometry gives a complicated 3-D stress state so that H 3 Y Provides a simple and non-destructive way of measuring...
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Lecture11 - ME 382 Lecture 11 1/ii/06 1 von Mises yield...

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