poissons ratio

 Poisson's ratio:

Introduction:

The Poisson's ratio is identified (defined) as the ratio of lateral strain to axial strain.

(or)

It can also be stated as the ratio of unit strain in lateral (transverse) direction to

the unit strain in axial direction. its denoted by

the symbol μ.

μ =Lateral Strain/Axial Strain

Derivation of Poisson's Ratio

Consider, a steel bar of length (L) , and diameter D, as shown in the below

figure.

When this steel bar is not subjected to any load, its dimensions (L and D) remain the same.

When a tensile load is applied to the bar, the bar habits a change in its dimensions. The tensile

load act-the bar, increases the length of the bar in axial direction. Due to the increase in length,

the diameter of e bar decreases and thus the cross sectional area of the bar changes i.e., the bar exhibits a change in its dimensions in lateral or transverse direction. Thus due to load, the bar experiences strain in axial direction as well as in lateral direction.

Axial strain, Σa =Change in length/original length =ΔL/L

Lateral strain, Σl = Change in diameter/original diameter = -ΔD/D