The total strain energy stored in a solid shaft of volume V due to torsion is given by (where τ is maximum shear stress and G is modulus of rigidity):

When a bar of length l and uniform cross-section is rigidly fixed at the upper end and hangs freely, the total elongation produced in the bar due to its own weight is given by (where w = weight per unit volume and E = Modulus of Elasticity):

The hoop stress set up in a thin cylinder subjected to internal fluid pressure is: