Question

A square steel bar has a length of 7.4 ft and a 2.9 in by 2.9 in cross section and is subjected to axial tension. The final length is 7.40504 ft . The final side length is 2.89945 in . What is Poisson's ratio for the material?

Answer 1

Poission Ratio = 0.2784

Explanation:

we know that

Poission ratio is defined as

μ =
`(-lateral strain)/(longitudinal strain)`

We also know that lateral strain =
`(Final width-Initial width)/(Initial Width)`

In our case

Final width = 2.89945 in

Initial width = 2.9 in (Area of cross section (width x depth) = 2.9 in x 2.9 in)

Thus lateral strain =
`(2.89945-2.9)/(2.9)`

Lateral strain =
`-1.8965X10^(-4)`

Similarly longitudinal strain =
`(Final Length-Initial Length)/(Initial Length)`

Thus longitudinal strain =
`(7.40504ft-7.4ft)/(7.4ft)`

Longitudinal strain =
`6.8108X10^(-4)`

Thus by formula poission ratio =
`(-(-1.8965X10^(-4))/(6.8108X10^(-4))`

Poission Ratio = 0.2784