What is the total number of independent strain-displacement relations in a three-dimensional elasticity problem?

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: