Question

The cables of a power line are copper-coated steel wire. The overall diameter of the wire is 5/8 in. The steel core has a diameter of 1/2 in.
If the maximum tension in a wire is 8000 lb, what are the stresses in the steel and the copper?

Answer 1

Answer:

The stresses in steel and the copper are, 128 ksi and 72.44 ksi, respectively.

Explanation:

In this case, we need to calculate the area of both portions separately.

Thus, we know that:

Inner Radius = Rin = (1/2 in)/2 = 0.25 in

Outer Radius = Rout = (5/8 in)/2 = 0.3125 in

FOR STEEL CORE:

Area of steel core = As = π(Rin)² = π(0.25 in)² = 0.0625 in²

Hence, the stress will be:

σs = Force / As

σs = 8000 lb/ 0.0625 in²

σs = 128 ksi

FOR COPPER:

Area of copper = Ac = π[(Rout)² - (Rin)²]

Ac = π[(0.3125 in)² - (0.25 in)²] = 0.11044 in²

Hence, the stress will be:

σc = Force / Ac

σc = 8000 lb/ 0.11044 in²

σc = 72.44 ksi