Calculation of Poisson's Ratio

Poisson's ratio (ν) is defined as the ratio of transverse strain to the longitudinal strain in a material subjected to tensile loading. It is given by the following formula:

ν = - (lateral strain/longitudinal strain)

where lateral strain is the strain in the transverse direction and longitudinal strain is the strain in the direction of the applied load.

Given Data

Young's modulus (E) = 200 GN/m2
Modulus of rigidity (G) = 80 GN/m2

Solution

We know that Young's modulus is related to modulus of rigidity and Poisson's ratio by the following equations:

E = 2G(1 + ν)
ν = (E/2G) - 1

Substituting the given values in the above equations, we get:

ν = (200 GN/m2)/(2 x 80 GN/m2) - 1
ν = 0.25

Therefore, the value of Poisson's ratio is 0.25.

Explanation

Young's modulus is a measure of the stiffness of a material under tensile loading, while modulus of rigidity is a measure of the material's resistance to shear deformation. Poisson's ratio is a measure of the material's tendency to contract in the transverse direction when stretched in the longitudinal direction.

The relationship between these three parameters is described by the equations above. By knowing two of these parameters, we can calculate the third. In this case, we were given Young's modulus and modulus of rigidity, so we were able to calculate Poisson's ratio using the equation ν = (E/2G) - 1.

Poisson's ratio is an important material property that is used in many engineering applications, such as the design of structures and the analysis of material behavior under different loading conditions.

E=2G(1+m)
m=E/2G -1
m=200/80*2 -1
m=0.25