Question

A solid shaft of 2 m diameter is used to transmit torque. The maximum shear stress induced to the shaft is 100 N/m² . Determine the maximum torque transmitted by the shaft.
1. 146 N-m
2. 188 N-m
3. 165 N-m
4. 157 N-m

Answer 1

Correct Answer - Option 4 : 157 N-m

Concept:

Using torsion equation:

\(\frac{T}{{{I_P}}} = \frac{{{{\rm{τ }}_{max}}}}{R} = \frac{{G\theta }}{L}\)

Where,

T = applied torque, IP = Polar section modulus, τmax = Maximum shear stress in the shaft material, R = Radius of the shaft, G = Modulus of Rigidity, θ = Angle of twist, L = Length of the shaft

\({I_P} = \frac{π }{{32}}{D^4}\)

R = \(\frac{D}{2}\)

From shear stress criteria:

\(\frac{{{{\rm{τ }}_{{\rm{max}}\left( {allowable} \right)}} \times 2}}{D} = \frac{T}{{{I_P}}}\)

Substituting the values of \({I_P} \) and R we get 

Torque (T) = \(\frac{π }{{16}}τ {d^3}\)

Calculation:

Given:

d = 2 m, τ = 100 N/m2

T = \(\frac{π }{{16}}τ {d^3}\) 

Taking π = 3.14

T = \(\frac{3.14\;\times\;100\;\times\;2^3}{16}\) = 157 N-m