A paper mill processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50 m outside diameter (OD) x 22 cm inside diameter (ID) x 3.23-m long and is on a simply supported, hollow, steel shaft. Find the shaft ID needed to obtain a maximum deflection at the center of 3 mm if the shaft OD is 22 cm. Assume the shaft to be the same length between supports as the length of the paper roll.