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In distortion energy theorem, if a unit cube is subjected to biaxial stress, then S(yt) is given by which of the following?

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In distortion energy theorem, if a unit cube is subjected to biaxial stress, then S(yt) is given by which of the following?

(a) √ (σ₁²- σ₁σ₂ +σ₂²)

(b) σ₁²- σ₁σ₂ +σ₂²

(c) √ (σ₁²+ σ₁σ₂ +σ₂²)

(d) σ₁²+ σ₁σ₂ +σ₂²

This question requires clarification and I found it by my college professor while I was bunking the class.

I encountered this question in the Couplings in part Shafts, Keys and Couplings of Machine Design

1 Answer

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The suitable answer is (a) √ (σ₁²- σ₁σ₂ +σ₂²)

Easy explanation: S(yt)=√[(σ₁ -σ₂)²+(σ₂ -σ₃)²+(σ₃ -σ₁)²]/2, for σ₃=0; expression a is obtained.

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