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Question

A machine element develops principal stresses of magnitudes 2P and P. What is the maximum magnitude of P before the material reaches the yield stress fy as per Distortion Shear Energy Theory?

A
fy
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B
fy2
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C
fy23
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D
fy3
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Solution

The correct option is D fy3
As per distortion energy theory:

12[(σ1σ2)2+(σ2σ3)2+(σ3σ1)2]f2y

12[(2PP)2+(P0)2+(02P)2]f2y

12[P2+P2+4P2]f2y

Pfy3


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