Machine Design
Slenderness ratio is the ratio of

Effective length of column to width of column
Effective length of column to least radius of gyration of the column
Maximum size of column to minimum size of column
Width of column to depth of column

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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 stress in a biaxial stress system reaches the elastic limit of the material 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 maximum shear stress in a biaxial stress system reaches the shear stress at elastic limit in a simple tension test

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