Question

A square steel bar has a length of 9.7 ft and a 2.9 in by 2.9 in cross section and is subjected to axial tension. The final length is 9.70710 ft . The final side length is 2.89933 in . What is Poisson's ratio for the material? Express your answer to three significant figures.

Answer 1

The Poisson's ratio definition is given as the change in lateral deformation over longitudinal deformation. Mathematically it could be expressed like this,

$\upsilon = \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$

$\upsilon = \frac{(\delta a/a)}{(\delta l/l)}$

Replacing with our values we would have to,

$\upsilon = \frac{(2.89933-2.9/2.9)}{(9.70710-9.7/97)}$

$\upsilon = 0.1977$

Therefore Poisson's ratio is 0.1977.