Elasticity
13.0 Poisson’s Ratio
13.0 Poisson’s Ratio
When a long bar is stretched by a force along its length, then its length is increases and the diameter decreases as shown in Fig. E. 27.
The ratio of change in diameter $\Delta D$ to the original diameter ${D_i}$ is called lateral strain.
The ratio of change in diameter $\Delta D$ to the original diameter ${D_i}$ is called lateral strain.
$$Lateral\ Strain = \frac{{ - \Delta D}}{{{D_i}}}$$
where $\Delta D = {D_i} - {D_f}$. Negative sign indicated that the diameter is decreased.
The ratio of change in length $\Delta l$ to the original length $l$ is called longitudinal strain.
$$Longitudinal\ Strain = \frac{{\Delta l}}{l}$$
The ratio of lateral strain to the longitudinal strain is called Poissons’s ratio. It is denoted by sigma ($\sigma $).
So,
$${\text{Poission's Ratio = }}\frac{{\frac{{ - \Delta D}}{{{D_i}}}}}{{\frac{{\Delta l}}{l}}} = \frac{{ - l}}{{\Delta l}}.\frac{{\Delta D}}{{{D_i}}}$$
