Problem 550 The hydrofoil boat has an A36 steel propeller sh

Problem 5.50 The hydrofoil boat has an A-36 steel propeller shaft that is 30 m long. It is connected to an in-line diesel engine that delivers a maximum power of 2500 kW and causes the shaft to rotate at 1700 rpm. The outer diameter of the shaft is 200 mm and the wall thickness is 10 mm G 75 GPa (Figure 1) Figure 1 r of t Part A Determine the maximum shear stress developed in the shaft. Express your answer to three significant figures and include the appropriate units. A Value Units I Submit My Answers Give Up Part B What is the \"wind up, or angle of twist in the shaft at full power? Express your answer using three significant figures

Solution

part (A)

shear stress= T x r / J

where T = Torque acting on the shaft

r = distance from the centre to the stressed surface

J = Polar moment of inertia

for a given problem maximum shear stress will be acting on the outer surface at maximum torque condition

max torque T = Max power x 60 / 2 x pi x N

max power = 2500 kw

N = 1700

Substituting given values ; max torque T = 14043 n-m

J = pi x (D⁴ - d⁴) / 32

where D = outer diameter = 200 mm

d = inner diameter = 180 mm

substituting given values we get J =5.4 x 10^-5

shear stress= T x r / J

substituting above calculated max torque (T) , J and r

we get Max shear stress = 26 Mpa

part (B)

Angle of twist = L x T / J x G

L = length of the shaft = 30 m

   T = max torque = 14043 n-m

   J = polar moment of inertia = 5.4 x 10^-5

   G = modulus of rigidity = 75 Gpa

substituting above values we get angle of twist = 0.104 radians

angle of twist = 5.96 deg