Question

A 60 mm dia shaft is subjected to a torque of 6 kN-m. G = 8 x 10⁴ N/mm².

The maximum shear stress induced in the shaft is – 
1. \(\frac{{4000}}{{9\pi }}\;MPa\)
2. \(\frac{{8000}}{{9\pi }}\;MPa\)
3. \(\frac{{12000}}{{9\pi }}\;MPa\)
4. \(\frac{{16000}}{{9\pi }}\;MPa\)

Answer 1

Correct Answer - Option 1 : \(\frac{{4000}}{{9\pi }}\;MPa\)

Diameter, D = 60 mm

Torque, T = 6 kN-m

From torsion equation, \(\frac{T}{J} = \frac{\tau }{r}\)

\(\tau = \frac{T}{{{Z_P}}} = \frac{{16T}}{{\pi {D^3}}} = \frac{{16 \times 6 \times {{10}^6}}}{{\pi \times {{60}^3}}} = \frac{{4000}}{{9\pi }}\;MPa\)