Press Fit Pressure
The circumferential strains in the copper and steel must be the same because they are both subject to the same interference of 0.005” when the sleeve is pressed into the head. Having said that, the radial deformation of each is not the same (because of the different E values and stresses in each) and this can be calculated as follows.
Remembering that E = Stress / Strain and Strain = Extension / Original length – then substituting and rearranging gives - Extension = Stress x Original length / E
So for the steel head we have - Ext(steel) = 10714 x 2.0 / 30 x 10^6 = 0.0007”
And for the copper we have – Ext(copper) = -21428 x 2.0 / 10 x 10^6 = -0.0043”
therefore the inside diameter of the steel head has increased from 2.000” to 2.000 + 0.0007 = 2.0007”, while the outside diameter of the copper sleeve has reduced from 2.005” to 2.005 – 0.0043 = 2.0007”
By the way did you spot my deliberate mistake in posting 10480 ? I calculated the radial stresses by dividing by the diameter, when it should have been the radius, giving a radial stress of 1340lb/in^2 and not 670lb/in^2. You may have picked this up as the formula was correct, just my numbers that were wrong.