(Solved): 12. Figure \( 12.1 \) shows a motor driving a machine through a drive shaft \( A B \). The solid d ...

12. Figure \( 12.1 \) shows a motor driving a machine through a drive shaft \( A B \). The solid drive shaft has a diameter of \( 30 \mathrm{~mm} \) and the material used to fabricate the shaft has a modulus of rigidity of \( 80 \mathrm{GPa} \). a) Determine the torque which the shaft can transmit for an allowable shear stress of \( 85 \mathrm{MPa} \) in the shaft. b) Determine the internal torque in segment \( A B \) of the shaft. Draw the relevant free body diagram. (c) Determine the power transmitted by the shaft when it is rotating at 1500 rpm. (d) Determine the length of the shaft if the angle of twist between \( A \) and \( B \) is \( 2.028^{\circ} \) (Answer : \( 450.62 \mathrm{Nm}, 450.62 \mathrm{Nm}, 70.78 \mathrm{~kW}, 0.5 \mathrm{~m} \) )