Machine Design
Castle nut is a locking device in which

A slot is cut partly is middle of nut and then slot reduced by tightening a screw
One smaller nut is tightened over main nut and main nut tightened against smaller one by loosening, creating friction jamming
Through slots are made at top and a cotter pin is passed through these and a hole in the bolt, and cotter pin spitted and bent in reverse direction at other end
A hard fibre or nylon cotter is recessed in the nut and becomes threaded as the nut is screwed on the bolt causing a tight grip

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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 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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