In a metal forming operation when the material has just started yielding- the principal stresses are - 1 - -180 MPa- - 2 - - 100 MPa- - 3 - 0-Following von Mises criterion- the yield stress is MPa-

Safe condition for design as per von Mises criterion, σ_1^2+σ_2^2 σ_1σ_2 ≤ ( S_ytN )^2 When yielding occurs, N = 1 σ_1^2+σ _2^2 σ_2 σ_2=(S_yt)^2 (180)^2+( 100 ...

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Strength of Materials

Maximum Distortion Energy Theory

In a metal fo...

Question

In a metal forming operation when the material has just started yielding, the principal stresses are $σ_{1} = + 180 M P a, σ_{2} = - 100 M P a, σ_{3} = 0.$
Following von Mises criterion, the yield stress is ______ MPa.
245.7641

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Solution

The correct option is A 245.7641
Safe condition for design as per von-Mises criterion,
$σ_{1}^{2} + σ_{2}^{2} - σ_{1} σ_{2} \leq {(\frac{S_{y t}}{N})}^{2}$

When yielding occurs, $N = 1$

$σ_{1}^{2} + σ_{2}^{2} - σ_{2} σ_{2} = (S_{y t})^{2}$
$(180)^{2} + (- 100)^{2} - (180) (- 100) = (S_{y t})^{2}$

$S_{y t} = 245.7641 M P a$

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In a metal forming operation when the material has just started yielding, the principal stresses are σ1=+180 MPa,σ2=−100 MPa,σ3=0. Following von Mises criterion, the yield stress is ______ MPa.245.7641

The correct option is A 245.7641Safe condition for design as per von-Mises criterion, σ21+σ22−σ1σ2≤(SytN)2 When yielding occurs, N=1 σ21+σ22−σ2σ2=(Syt)2 (180)2+(−100)2−(180)(−100)=(Syt)2 Syt=245.7641MPa

In a metal forming operation when the material has just started yielding, the principal stresses are $σ_{1} = + 180 M P a, σ_{2} = - 100 M P a, σ_{3} = 0.$
Following von Mises criterion, the yield stress is ______ MPa.
245.7641