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 ( 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 = 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: 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 = # 8 $ 18 $ 10 3 % $ 0.1 ( ) 2 = # 4.58 MPa Mohr’s 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 σ Y • Provides a simple and non-destructive way of measuring...
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This note was uploaded on 01/26/2011 for the course ME 382 taught by Professor Garikipati during the Winter '08 term at University of Michigan.

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

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