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The principal stresses developed at a point are +30, -30, 0 MPa. Using shear strain energy theory, a factor of safety obtained is √6. What is yield stress of the material?
  • a)
    90√2 MPa
  • b)
    120 MPa
  • c)
    60√3 MPa
  • d)
    180 MPa
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The principal stresses developed at a point are +30, -30, 0 MPa. Using...
As per maximum shear strain energy theory,


σy = 90√2 MPa 
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Most Upvoted Answer
The principal stresses developed at a point are +30, -30, 0 MPa. Using...
Given Data:
Principal stresses: +30, -30, 0 MPa
Factor of safety: √6

Calculations:
- The maximum principal stress is +30 MPa.
- The minimum principal stress is -30 MPa.
- Using the formula for factor of safety (FoS) in shear strain energy theory:
FoS = Yield stress / (σ₁ - σ₂)
√6 = Yield stress / (30 - (-30))
√6 = Yield stress / 60
Yield stress = 60√6 MPa

Final Answer:
Therefore, the yield stress of the material is 60√6 MPa, which simplifies to approximately 90√2 MPa. Hence, the correct answer is option 'A'.
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