Machine Design
The shear stress at a point in a shaft subjected to a torque is

Directly proportional to the applied torque and the polar moment of inertia
Directly proportional to the polar moment of inertia and to the distance of the point from the axis
Inversely proportional to the applied torque and the polar moment of inertia
Directly proportional to the applied torque and inversely proportional to the polar moment of inertia

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Machine Design
According to Rankine's theory, the failure occurs at a point in a member

When the maximum shear stress in a biaxial stress system reaches the shear stress at elastic limit in a simple tension test
When the maximum principal stress in a biaxial stress system reaches the elastic limit of the material in a simple tension test
When the maximum principal strain in a biaxial stress system reaches the strain at the elastic limit as determined from a simple tension test
When the strain energy per unit volume in a biaxial stress system reaches the strain energy at the elastic limit per unit volume as determined from a simple tension test

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