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A shaft with a circular cross-section is subjected to a pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is

1. 2.0
2. 1.0
3. 0.5
4. 0

Correct answer: 0.5

Solution

Under pure torsion, the stress state at a point is pure shear with maximum shear stress $\tau_{max} = \tau$. The principal stresses are $\sigma_1 = \tau$ and $\sigma_2 = -\tau$, so the largest principal stress is $\tau$. Therefore, the ratio of maximum shear stress to largest principal stress is 0.5.

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