Relationship between Modulus of Elasticity and Modulus of Rigidity

Modulus of elasticity (E) and the modulus of rigidity (G) are related by the following equation:

E=2G\left( 1+\nu\right)

Here, \nu represents a number called Poisson’s ratio given to the particular material. When the material is being stretched in one direction, it gets shortened in a perpendicular direction. In the direction that the material becomes elongated, the axial strain (\varepsilon_ais defined as the fractional increase in the length. In the direction that the material shortens, the transverse strain (\varepsilon_t) gives the fractional reduction in length. The diagram below illustrates these changes in shape:

Difference Between Modulus of Elasticity and Modulus of Rigidity - Poisson's_Ratio_Illustration

Defining Poisson’s ratio

In this diagram, the axial strain is:


The transverse strain is:


Note that since the object shortens in the direction perpendicular to the force, \varepsilon_t<0. Poisson’s ratio (\nu) is defined as:


The minus sign has been introduced to ensure that \nu takes a positive value.

Related Posts

Comments are closed.

© 2024 Mechanical Engineering - Theme by WPEnjoy · Powered by WordPress