Question

An electrical conductor is composed of a steel core 1/16 inch in diameter surrounded by a 3/64 inch thick shell of copper. What tension can be applied to the conductor if the stresses are not to exceed 60 ksi and 24 ksi for the steel and copper respectively?

Answer 1

F_max = 184.08 lb

Step-by-step explanation:

Given:

- The diameter of steel core d = 1/16 inch

- The thickness of copper shell t = 3/64 inch

- The allowable stress for steel = 60 ksi

- The allowable stress for copper = 24 ksi

Find:

- What tension can be applied without exceeding allowable limits.

Solution:

- Compute the cross sectional areas of the each material.

A_steel = pi*d^2/4

A_steel = pi*(1/16)^2 / 4

A_steel = 3.06796*10^-3 in^2

A_copper = pi*((d+2t)^2 - d^2) / 4

A_copper = pi*((5/32)^2 - (1/16)^2) / 4

A_copper = 0.016107 in^2

- We will use the allowable stresses to calculate the maximum force possible for each component of wire:

F_steel = sigma_steel * A_steel

F_steel = 60,000 * 3.06796 * 10^-3

F_steel = 184.08 lb

F_copper = sigma_copper * A_copper

F_copper = 24,000 * 0.016107

F_steel = 386.56 lb

- Hence, the maximum possible force that can be applied is:

F_max = min ( 184.08 , 386.56 )

F_max = 184.08 lb