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 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

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Machine Design
In replacing the V-belts, a complete set of new belts is used instead of replacing a single damaged belt because

Belts are available in sets
New and old belts will cause vibrations
The new belt will carry more than its share and result in short life
Only one belt cannot be fitted with other used belts

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