A shaft is required to transmit 1 MW power at 240 rpm. The shaft must not twist more than 1 degree on a length of one meter. If the modulus of rigidity for the material of shaft is 80 kN/mm2. Find the diameter of shaft and shear stress induced on it.

 Torque transmitted by the shaft

T= Px60/2π N= 1X106X60/2 π x240

 = 39783.58 Nm

 =39783.58 x 103 N.mm

We know that T/J=GΘ/L or J=TXL/GXΘ

 π/32xd⁴ = 39783.58x103x1000/80x103x0.0174

 = 28580158

 d⁴= 28580158x32/ π= 291077357

 d= 103.73 mm

say110mm=130.74mm

Say 135mm

Shear stress induced in the shaft

Torque transmitted by the shaft T = π/16 x τ xd³= 

put d=135mm

39783.58x10³ = π/16 x τ x(110)³

τ = 148.15N/mm²=148.15 MPa=82.36MPa