A paper mill processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50 m outside dia (OD) by 0.22 m inside dia (ID) by 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.

Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.