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

The Poisson's ratio for the material is 0.0134.

Explanation:

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

`\\u = -(\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* 10^(-4)\,in`

`\\u = - ((-4.7* 10^(-4)\,in))/(0.035\,in)`

`\\u = 0.0134`

The Poisson's ratio for the material is 0.0134.