Question

A ¼-in. diameter rod must be machined on a lathe to a smaller diameter for use as a specimen in a tension test. The rod material is expected to break at a normal stress of 63,750 psi. If the tensile testing machine can apply no more than 925 lb of force to the specimen, calculate the maximum rod diameter that should be used for the specimen (precision of 0.000).

Answer 1

Answer: 0.136 inches

Step-by-step explanation:

To find the maximum diameter of the rod that can be used for the specimen, we first need to determine the cross-sectional area of the rod that will result in a maximum force of 925 lb when subjected to a normal stress of 63,750 psi.

Formula to calculate the cross-sectional area (A) based on force (F) and normal stress (σ) is:

A = F / σ

Given the force F = 925 lb and normal stress σ = 63,750 psi, we can calculate the required cross-sectional area:

A = 925 lb / 63,750 psi ≈ 0.0145 square inches

Now, we need to find the diameter (d) that corresponds to this cross-sectional area. The formula for the cross-sectional area of a circle is:

A = π * (d/2)^2

Solving for d, we get:

d = 2 * sqrt(A / π)

Substituting the value of A into the equation:

d = 2 * sqrt(0.0145 / π) ≈ 0.1356 inches

Therefore, the maximum rod diameter that should be used for the specimen is approximately 0.136 inches (rounded to the nearest thousandth).