One of two hollow drive shafts of a cruise ship is 180 ft lo

One of two hollow drive shafts of a cruise ship is 180 ft long, and its outer and inner diameters are 22 in. and 4 in., respectively. The shaft is made of a steel for which the allowable shear stress is 8500 psi and G = 11.2 × 106 psi. Knowing that the maximum speed of rotation of the shaft is 190 rpm, determine:
(a) the maximum power that can be transmitted by the one shaft to its propeller,
(b) the corresponding angle of twist of the shaft.

Solution

a)

Max. torque T = (pi/16) * Tau_max * (D^4 - d^4) / D

= (3.14/16) * 8500 * (22^4 - 4^4) / 22

= 17742784.1 lb-in

= 17742784.1 / 12 ft-lb

= 1478565 ft-lb

Power = 2*pi*N*T/60

= 2*3.14*190*1478565 / 60

= 29403736 ft-lb/s

= 29403736*60 ft-lb/min

= 1764224164 ft-lb/min

= 53461.3 hp

b)

Angular deflection = 32 L T / (G (D⁴- d⁴))

= 32*(180*12) * 17742784.1 / (11.2*10^6 * 3.14 * (22^4 - 4^4))

= 0.149 rad = 8.54 deg