A shaft of length (L), loaded in torsion, must support a specified torque (T^{*}) without failing and

Question:

A shaft of length $L$, loaded in torsion, must support a specified torque $T^{*}$ without failing and be as cheap as possible. Section shape is a variable and 'failure' again means the first onset of plasticity. Derive the material index. The table summarizes the requirements.

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