Resolution of any stress system into uniform tension and shearing stress (contd...)

A cylinder or prism of any form, subjected to tension which is uniform over its plane ends and free from traction at the lateral surfaces. Then we can write,

(3.20)

Algebra:

Then from equation 3.15, state of strain can be written as,

(3.21)

where, we put,

(3.22)

The quantity obtained by dividing the simple longitudinal tension by the measure of the extension produced by it, is known as the Young's modulus . The number is the ratio of lateral contraction to longitudinal extension is called Poisson's ratio . is called shear modulus.

Furthermore, note the relations:

(3.23)