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 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
The contact ratio is the ratio of

Length of arc of approach to the circular pitch
Length of path of contact to the circular pitch
Length of arc of recess to the circular pitch
Length of arc of contact to the circular pitch

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