Machine Design
When a machine member is subjected to torsion, the torsional shear stress set up in the member is

Zero at the centroidal axis and maximum at the outer surface of the member
Zero at both the centroidal axis and outer surface of the member
Maximum at both the centroidal axis and outer surface of the member
Maximum at the centroidal axis and zero at the outer surface of the member

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

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
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 maximum principal stress in a biaxial stress system reaches the elastic limit of the material in a simple tension test
When the maximum shear stress in a biaxial stress system reaches the shear stress at elastic limit in a simple tension test

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Machine Design
A bolt of uniform strength can be developed by

Keeping the core diameter smaller than the diameter of the unthreaded portion
Keeping the nominal diameter of threads equal to the diameter of unthreaded portion of the bolt
Keeping the core diameter of threads equal to the diameter of unthreaded portion of the bolt
None of these

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