A copper pipe with an outside diameter = 4 inch and inside diameter = 2 5/8 inch is used as an electrical conductor in an energy conversion device that is subjected to a high axial compression load of 55 kips. To prevent this high compression load from buckling the copper pipe, a solid steel support of 2 1/2 inch diameter is placed inside the copper pipe. The copper pipe is 8.000 inches long. The steel support is 8.0001 inches (exactly 1 mil = 1/1000 inch longer).
The additional length for the steel is supposed to cause the steel to fully support the compression load. Unfortunately, it appears as if the large 55 kips load is compressing the steel more than 0.001 inch, so that some of the load is falling on the copper pipe as well.
Therefore, it is desired to determine the following:
(1) negative elongation of the steel cylinder, (2) negative elongation of the copper pipe (should be exactly 0.001 inch less than the steel value), (3) axial force on the steel cylinder, (4) axial force on the copper pipe, (5) axial stress on the steel cylinder, (6) axial stress on the copper pipe, (7) whether the proportional limit is exceeding for either material.
The following values are given: Young's modulus (E) for steel = 30000 ksi, Young's modulus (E) for copper = 17000 ksi, Proportional limit for steel (including safety factor) = 30 ksi, Proportional limit for copper (including safety factor) = 17 ksi.