Question

If the engineering strain in a tensile bar is 0.0025 and Poisson’s ratio is 0.33, find the original length and the original diameter if the length and diameter under load are 2.333 ft. and 1.005 in. respectively.

Answer 1

To find the original length and diameter, we can use the formula for engineering strain and Poisson's ratio. The original length is approximately 2.3278 ft, and the original diameter is approximately 101.515 ft.

Step-by-step explanation:

To find the original length and diameter, we need to use the formula for engineering strain:

Engineering Strain = Change in Length / Original Length

Given that the engineering strain is 0.0025 and the length under load is 2.333 ft, we can rearrange the formula to solve for the original length:

Original Length = Length under load / (1 + Engineering Strain)

Substituting the values:

Original Length = 2.333 ft / (1 + 0.0025) = 2.3278 ft

Next, we can find the original diameter using Poisson's ratio. Poisson's ratio relates the strain in the axial direction (lengthwise) to the strain in the transverse direction (diameter). The formula is:

Poisson's Ratio = Lateral Strain / Axial Strain

Since we know the engineering strain in the axial direction is 0.0025, we can rearrange the formula to solve for the lateral strain:

Lateral Strain = Poisson's Ratio * Axial Strain

Substituting the values:

Lateral Strain = 0.33 * 0.0025 = 0.000825

The lateral strain is equal to the change in diameter divided by the original diameter:

Lateral Strain = Change in Diameter / Original Diameter

Rearranging the formula to solve for the original diameter:

Original Diameter = Change in Diameter / Lateral Strain

Substituting the values:

Original Diameter = 1.005 in / 0.000825 = 1218.18 in ~ 101.515 ft