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

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
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

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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
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
Zero at both the centroidal axis and outer surface of the member

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Machine Design
In a hydrodynamic lubricated bearing

There is a thin film of lubricant between the journal and the bearing
The lubricant is forced between the journal and the bearing, by external pressure
There is no lubricant between the journal and the bearing
There is a thick film of lubricant between the journal and the bearing

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