A steel collar whose outside diameter = 3.000 in at room temperature is to be shrink fitted onto a steel shaft by heating it to an elevated temperature while the shaft remains at room temperature. The shaft diameter = 1.500 in. For ease of assembly when the collar is heated to an elevated temperature of 1000°F, the clearance between the shaft and the collar is to be 0.007 in. Determine
(a) the initial inside diameter of the collar at room temperature so that this clearance is satisfied,
(b) the radial pressure and
(c) maximum effective stress on the resulting interference fit at room temperature (70°F). For steel, the elastic modulus = 30,000,000 lb/in2 and coefficient of thermal expansion = 6 × 10-6 in/in per °F.