Question

A 1.96 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 68,787 psi. If the tensile testing machine can apply no more than 797 lb of force to the specimen, calculate the maximum rod diameter that should be used for the specimen.

Answer 1

Step-by-step explanation:

The maximum normal stress that can be applied to the specimen is given by the ratio of applied force to the area of the cross section of the specimen:

stress = force / area

The area of the cross section of a rod is given by the formula for the area of a circle:

area = πr^2

where r is the radius of the rod. We are given the diameter of the rod, which is 1.96 inches, so the radius is half of that, or 0.98 inches.

The maximum normal stress that the specimen can withstand is 68,787 psi, and the maximum force that can be applied is 797 lb. Substituting these values into the equation for stress gives:

68,787 psi = 797 lb / πr^2

Solving for the radius r gives:

r = √(797 lb / (68,787 psi × π))

Substituting in the value for π and calculating gives:

r ≈ 0.330 inches

The maximum diameter of the rod is twice the radius, so the maximum diameter is:

d = 2r ≈ 0.660 inches

Therefore, the maximum rod diameter that should be used for the specimen is approximately 0.660 inches.