Question

A copper alloy cylinder 1.17 m long with a diameter of 32.39 mm is subjected to a tensile stress of 1,302 psi along its length. Assuming this applied stress is purely elastic calculate the diameter, in mm, of the cylinder under this load. For copper, the elastic modulus is 1,206,172 psi and the Poisson's ratio is 0.42.

Answer 1

Answer:

The diameter of cylinder under given load is 32.375 mm

Explanation:

First, we calculate the longitudinal strain in the cylinder:

Elastic Modulus = Stress/Longitudinal Strain

Longitudinal Strain = Stress/Elastic Modulus

Longitudinal Strain = 1302 psi/1206172 psi

Longitudinal Strain = 1.079 x 10^-3

Now, we find the lateral strain by using Poisson's Ratio:

Poisson's Ratio = - Lateral Strain/Longitudinal Strain

Lateral Strain = - (Poisson's Ratio)(Longitudinal Strain)

Lateral Strain = - (0.42)(1.079 x 10^-3)

Lateral Strain = - 4.5 x ^-4

Here, the negative sign shows a decrease in lateral dimensions.

Now, for the final diameter:

Lateral Strain = Change in Diameter/Original Diameter

Change in Diameter = (Lateral Strain)(Original Diameter)

Change in Diameter = (- 4.5 x 10^-4)(32.39 mm)

Change in Diameter = - 0.0145 mm

but,

Change in diameter = Final Diameter - Initial Diameter

Therefore,

Final Diameter = Change in diameter + Original or Initial Diameter

Final Diameter = - 0.015 mm + 32.39 mm

Final Diameter = 32.375 mm