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 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 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

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Machine Design
Stress concentration is caused due to

Variation in properties of material from point to point in a member
Pitting at points or areas at which loads on a member are applied
All of these
Abrupt change of section

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Machine Design
The elasticity is the property of a material which enables it to

Resists fracture due to high impact loads
Regains its original shape after deformation when the external forces are removed
Draw into wires by the application of a tensile force
Retain deformation produced under load permanently

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