Question

A square steel bar has a length of 7.2 ft and a 2.5 in by 2.5 in cross section and is subjected to axial tension. The final length is 7.20532 ft . The final side length is 2.49946 in . What is Poisson's ratio for the material?Express your answer to three significant figures.ν = 0.292Part A - Calculate Poisson's ratio A square steel bar has a length of 5.3 ft and a 2.1 in by 2.1 in cross section and is subjected to axial tension. The final length is 5.30470 ft . The final side length is 2.09929 in . What is Poisson's ratio for the material?

Answer 1

Answer:

A) ν = 0.292

B) ν = 0.381

Explanation:

Poisson's ratio = - (Strain in the direction of the load)/(strain in the direction at right angle to the load)

In axial tension, the direction of the load is in the length's direction and the direction at right angle to the load is the side length

Strain = change in length/original length = (Δy)/y or (Δx)/x or (ΔL/L)

A) Strain in the direction of the load = (2.49946 - 2.5)/2.5 = - 0.000216

Strain in the direction at right angle to the load = (7.20532 - 7.2)/7.2 = 0.0007389

Poisson's ratio = - (-0.000216)/(0.0007389) = 0.292

B) Strain in the direction of the load = (2.09929 - 2.1)/2.1 = - 0.0003381

Strain in the direction at right angle to the load = (5.30470 - 5.3)/5.3 = 0.0008868

Poisson's ratio = - (-0.0003381)/(0.0008868) = 0.381