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

Answer:

Poission Ratio = 0.2784

Step-by-step explanation:

we know that

Poission ratio is defined as

μ = $\frac{-lateral strain}{longitudinal strain}$

We also know that lateral strain =$\frac{Final width-Initial width}{Initial Width}$

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 = $\frac{2.89945-2.9}{2.9}$

Lateral strain =  $-1.8965X10^{-4}$

Similarly longitudinal strain = $\frac{Final Length-Initial Length}{Initial Length}$

Thus  longitudinal strain = $\frac{7.40504ft-7.4ft}{7.4ft}$

Longitudinal strain =  $6.8108X10^{-4}$

Thus by formula poission ratio =  $\frac{-(-1.8965X10^{-4}}{6.8108X10^{-4}}$

Poission Ratio = 0.2784