Machine Design
A plate with an elliptical hole in the centre, with semi-major axis (a) perpendicular to the direction of loading and semi-minor axis (b) along the direction of loading, is subjected to a pull P. The maximum stress induced at the edge of the hole is equal to (where σ = Stress for a plate with no hole i.e. nominal stress)

σ [1 + (b/3a)]
σ [1 + (2a/b)]
σ [1 + (b/2a)]
σ [1 + (3a/b)]

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

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 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 principal stress in a biaxial stress system reaches the elastic limit of the material in a simple tension test

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