A square steel bar has a length of 8.4 ft and a 2.1 in by 2.1 in cross section and is subjected to axial tension. The final length is 8.40392 ft. The final side length is 2.09967 in. What is Poisson's ratio for the material

Poissons ratio = - 0.3367

Explanation:

Poissons ratio = Lateral Strain / Longitudinal Strain

In this case, the longitudinal strain will be:

Strain (longitudinal) = Change in length / total length

Strain (longitudinal) = (8.40392 - 8.4) / 8.4

Strain (longitudinal) = 4.666 * 10^ (-4)

While the lateral strain will be:

Strain (Lateral) = Change in length / total length

Strain (Lateral) = (2.09967 - 2.1) / 2.1

Strain (Lateral) = - 1.571 * 10^ (-4)

Solving the poisson equation at the top we get:

Poissons ratio = - 1.571 / 4.666 (10^ (-4) cancels out)

Poissons ratio = - 0.3367