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

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 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 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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Machine Design
In case of thick cylinders, the tangential stress across the thickness of cylinder is

Maximum at the inner surface and zero at the outer surface
Maximum at the outer surface and zero at the inner surface
Maximum at the inner surface and minimum at the outer surface
Maximum at the outer surface and minimum at the inner surface

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