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A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is 100 MPa. The yield and ultimate strengths of the shaft material in tension are 300 MPa and 450 MPa, respectively. The factor of safety using maximum distortion energy (Von-Mises) theory is _______ .
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- 1.732
- 2.732
- 0.732
- 1.622
Correct Option: A
σ1 = 100 MPa
σ2 = 100 MPa
As per Von-mises yield theory.
n² [(σ1 - σ2)² + (σ2 - σ3²) + (σ1 - σ3²)]
≤ 2σ2²
2n²[σ1² + σ2² - σ1σ2] ≤ 2σy²
⇒ n²[(100)² + (100)² + (100)²]≤ (300)²
∴ n = 1.732
