Drive shafts in cars are generally made of steel. An automobile manufacturer is seriously thinking of changing the material to a composite material. The reasons for changing the material to composite materials are that composites: reduce the weight of the drive shaft and thus reduce energy consumption, are fatigue resistant and thus have a long life, are noncorrosive and thus reduce maintenance costs and increase life of the drive shaft, allow single piece manufacturing and thus reduce manufacturing cost. The design constraints are as follows: 1. Based on the engine overload torque of 140 N-m, the drive shaft needs to withstand a torque of 550 N-m. 2. The shaft needs to withstand torsional buckling. 3. The shaft has a minimum bending natural frequency of at least 80 Hz. 4. Outside radius of drive shaft = 50 mm. 5. Length of drive shaft = 148 cm. 6. Factor of safety = 3. 7. Only 0, +45, 45, +60, 60, and 90 plies can be used. For steel, use the following properties: Youngs modulus E = 210 GPa, Poissons ratio = 0.3, Density of steel = 7800 kg/m3, Ultimate shear strength ult = 80 MPa. For the composite, use properties of glass/epoxy from Table 2.1 and Table 3.1 and assume that ply thickness is 0.125 mm. (A). Design the drive shaft using: 1. Steel 2. Glass/epoxy 3. Graphite/epoxy laminate with ply properties given in Table 2.1. (B). If minimizing mass is still an issue, would a graphite/epoxy laminate be a better choice than glass/epoxy? (C). If cost is the only issue, is glass/epoxy laminate, steel, or graphite/epoxy the best choice? Assume total manufacturing cost of graphite/epoxy is five times that of glass/epoxy on a per-unit mass basis and that the glass/epoxy and steel cost the same on a per-unit-mass basis