1. The problem statement, all variables and given/known data A steel ring has a diameter of 75 mm at 20 deg C. how much must it be heated in order to mount on a brass shaft of dia 75.05 Then both are cooled. how must they be cooled so the ring will fall off? 2. Relevant equations Thermal elongation coefficient of steel: 12E-6 Thermal elongation coefficient of brass: 20E-6 Expansion of area under heating/cooling: ##A=A_0(1+2\alpha \Delta t)## 3. The attempt at a solution Heating: $$\pi\cdot 75.05^2=\pi\cdot 75^2 (1+2\cdot 12E-6\cdot\Delta t)\rightarrow \Delta t=55.6^0C$$ It's too low, isn't it? For cooling i consider as if the ring isn' t mounted on the shaft, it's aside of it: $$\pi\cdot 75.05^2(1-2\cdot 20E-6\cdot\Delta t)=\pi\cdot 75^2 (1-2\cdot 12E-6\cdot\Delta t)\rightarrow \Delta t=83.1^0C$$ Also too small, isn't it? Is it correct what i have done, taking the ring aside? i didn't know how to solve it with the ring mounted, i don't know if to calculate efforts or not and how to do it. i know the formula for stress due to heating in a straight bar.