Question

A hollow circular shaft has an outer diameter of \(100\,\mathrm{mm}\) and a wall thickness of \(25\,\mathrm{mm}\). Allowable shear stress in the shaft is \(125\,\mathrm{MPa}\). The maximum torque the shaft can transmit is

• A. \(46\,\mathrm{kN\!-\!m}\)
• B. \(24.5\,\mathrm{kN\!-\!m}\)
• C. \(23\,\mathrm{kN\!-\!m}\)
• D. \(11.5\,\mathrm{kN\!-\!m}\)

Hint:

For a hollow circular shaft, \[ \boxed{ T= \frac{\pi}{16}\tau \frac{D^4-d^4}{D}. } \]

Answer 1

The Correct Option is C

Step 1: Determine the shaft dimensions. Outer diameter, \[ D=100\,\mathrm{mm} \] Wall thickness, \[ t=25\,\mathrm{mm} \] Inner diameter, \[ d=D-2t=100-50=50\,\mathrm{mm}. \]

Step 2: Use the torsion equation. \[ T=\frac{\pi}{16}\, \tau\, \frac{D^4-d^4}{D}, \] where \[ \tau=125\,\mathrm{MPa}. \] Substituting the values, \[ T = \frac{\pi}{16}(125) \frac{100^4-50^4}{100} \approx 23\times10^6\,\mathrm{N\,mm} = 23\,\mathrm{kN\!-\!m}. \] Hence, \[ \boxed{23\,\mathrm{kN\!-\!m}} \] is the correct answer. Therefore, \[ \boxed{(C)} \] is the correct answer.