GATE 2021 PI – Question 28
Steel has uniaxial tensile and compressive yield strength 700 MPa. Under pure shear its ordered principal stresses are σ₁ = σ, σ₂ = 0, σ₃ = −σ. Find σ at initial yield under von Mises, in MPa to two decimals.
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Correct answer: 404.00 to 405.00
Explanation
Equivalent stress is $\sqrt{[(\sigma-0)^2+(0+\sigma)^2+(-\sigma-\sigma)^2]/2}=\sqrt3\sigma$. Set this to 700 MPa: $\sigma=700/\sqrt3=\mathbf{404.15}$ MPa.