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The total strain energy for a unit cube subjected to three principal stresses is given by?

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+1 vote
in Machine Design by (86.7k points)
The total strain energy for a unit cube subjected to three principal stresses is given by?

(a) U= [(σέ) ₁ + (σέ) ₂+ (σέ) ₃]/3

(b) U= [(σ₁²+σ₂²+σ₃²)/2E] – (σ₁σ₂+σ₂σ₃+σ₃σ₁)2μ

(c) U= [(σέ) ₁ + (σέ) ₂+ (σέ) ₃]/4

(d) None of the mentioned

I got this question in a dream while sleeping.

I encountered this question in the Principal Stresses & Theories of Elastic Failure concept in unit Design Against Static Load of Machine Design

1 Answer

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ago by (48.2k points)
Best answer is (b) U= [(σ₁²+σ₂²+σ₃²)/2E] – (σ₁σ₂+σ₂σ₃+σ₃σ₁)2μ

Easy explanation: U= [(σέ) ₁ + (σέ) ₂+ (σέ) ₃]/2 is the basic formula. After substituting values of έ₁, έ₂ and έ₃, we get the expression b.

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