Question

A square steel bar has a length of 5.1 ft and a 2.7 in by 2.7 in cross section and is subjected to axial tension. The final length is 5.10295 ft . The final side length is 2.69953 in . What is Poisson's ratio for the material

Answer 1

Answer:

The Poisson's ratio for the material is 0.0134.

Step-by-step explanation:

The Poisson's ratio ($\nu$), no unit, is the ratio of transversal strain ($\epsilon_{t}$), in inches, to axial strain ($\epsilon_{a}$), in inches:

$\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}$ (1)

$\epsilon_{a} = l_{a,f}-l_{a,o}$ (2)

$\epsilon_{t} = l_{t,f}-l_{t,o}$ (3)

Where:

$l_{a,o}$ - Initial axial length, in inches.

$l_{a,f}$ - Final axial length, in inches.

$l_{t,o}$ - Initial transversal length, in inches.

$l_{t,f}$ - Final transversal length, in inches.

If we know that $l_{a,o} = 61.2\,in$, $l_{a,f} = 61.235\,in$, $l_{t,o} = 2.7\,in$ and $l_{t,f} = 2.69953\,in$, then the Poisson's ratio is:

$\epsilon_{a} = 61.235\,in - 61.2\,in$

$\epsilon_{a} = 0.035\,in$

$\epsilon_{t} = 2.69953\,in - 2.7\,in$

$\epsilon_{t} = -4.7\times 10^{-4}\,in$

$\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}$

$\nu = 0.0134$

The Poisson's ratio for the material is 0.0134.