Lecture11-Notes - ME 382 Lecture 11 von Mises yield...

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ME 382 Lecture 11 1 von Mises yield criterion (continued) Example: Cantilevered solid cylindrical beam of AISI 1020 steel ( σ 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 1 = 4 kN m T xx = T = Pd /2 + T 1 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 J xy = # Td J = # 16 $ d 3 Pd 2 + T 1 % & ' ( ) * Also, by inspection: σ yy = 0, σ zz = 0, τ zx = τ zy = 0 xx = 4 " 90 " 10 3 # " 0.1 ( ) 2 + 32 " 18 " 10 3 " 0.75 " 0.1 ( ) 3 = 148.97 MPa xy = # 16 % 0.1 ( ) 3 18 % 10 3 % 0.1 2 + 4 % 10 3 & ' ( ) * + = # 24.96 MPa Mohr’s Circle: Center = 74.49 MPa; Radius = 78.56 MPa
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ME 382 Lecture 11 2 " 1 = 153.05; 2 = # 4.07; 3 = 0.00 MPa Loading parameter: H = 1 2 153.05 + 4.07 ( ) 2 + 153.05 # 0 ( ) 2 + # 4.07 # 0 ( ) 2 [ ] = 155.13 MPa Safety factor is S f = ! Y H = 260 155.13 = 1.68 (by von Mises). (Or, 1.65 by Tresca) 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 σ Y
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Lecture11-Notes - ME 382 Lecture 11 von Mises yield...

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