A square steel bar has a length of 8.2 ft and a 2.9 in by 2.9 in cross section and is subjected to axial tension. The final length is 8.20312 ftnt . The final side length is 2.89966 in . What is Poisson's ratio for the material?

ν=0.308

Explanation:

Poisson's ratio can be found using not the elongations and contractions, but the strain of the material in the longitudinal and lateral directions.

In the given question, we can calculate axial strain εa as:

εa=(8.20312-8.2)/8.2=3.805*10^(-4) ft/ft

For the lateral strain, we can repeat calculations:

εl=(2.89966-2.9)/2.9=-1.172*10^(-4) in/in

Then, the Poisson's ratio ν can be found as:

ν=-εl/εa=-(-1.172*10^(-4))/(3.805*10^-4)=0.308

Note that negative sign means, that the deformations will have opposite directions and the final answer is positive for the coefficient.