Question

If a steel cable is rated to take 800-lb and the steel has a yield strength of 90,000psi, what is the diameter of the cable?

Answer 1

d = 2.69 mm

Step-by-step explanation:

Assuming the cable is rated with a factor of safety of 1.

The stress on the cable is:

σ = P/A

Where

σ = normal stress

P: load

A: cross section

The section area of a circle is:

A = π/4 * d^2

Then:

σ = 4*P / (π*d^2)

Rearranging:

d^2 = 4*P / (π*σ)

`d = √(4*P / (\pi*\sigma))`

Replacing:

`d = √(4*800 / (\pi*\90000)) = 0.106 inches`

0.106 inches = 2.69 mm