solved problems regarding torsion

For one propeller drive shaft, compute the torsional shear stress when it is transmitting a torque of 1.76 kNm. The shaft is a hollow tube having an outside diameter of 60 mm and an inside diameter of 40 mm. Find the stress at both the outer and inner surfaces.

Inside diameter of tube Di = 40 mm

Now, using the torsion equation

where J is polar moment of inertia

For hollow shaft

Torsional stress on outer surface is;

t₀ = T/J (D₀/2) = (1.76 × 1000 × 1000) * (60/2) / p/32 ((60)⁴ – (40)⁴)

→   t_i = 34.475 N/mm²               

Thus, the stresses on outer and inner surfaces are 51.713 N/mm² and 34.475 N/mm² respectively.