Question

a hollow circular shaft of OD 50mm is to transmit a torque of 250Nm. determine the internal diameter of the shaft if the maximum shear stress is limited to 50MPa. Answer in mm.

Answer 1

Given,

Outer diameter of shaft, D = 50 mm

Torque, T_max = 250 Nm

Maximum shear stress,τ_max = 50 Mpa

Solution:

Let, The inner diameter = d

The formula for maximum torque is given by,

T_max = (π/16)* τ_max*(D⁴ – d⁴)/D         ------ > (1)

Substituting given values in equation (1),

            250 = (π/16)* 50*10⁶*(0.050⁴ – d⁴)/0.050

            d⁴ = 4.9767*10^-6

            d = 0.04723 m = 47.23 mm     (Ans)   

Hence, inner diameter of the hollow shaft should be less than 47.23 mm to avoid failure.