# 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 tra

251 views
in General
closed
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

by (30.1k points)
selected

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