त्रि-आयामी (three-dimensional) प्रत्यास्थता समस्या में स्वतंत्र विकृति-विस्थापन संबंधों (strain-displacement relations) की कुल संख्या कितनी होती है?

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: