Question

A hollow steel shaft has outside diameter d and inside diameter d/2. The value of d for the shaft, if it has to transmit 200 hp at 105 rpm with a working shear stress of $420kg/c{m}^2$, is

• A. 5.6 cm
• B. 2.6 cm
• C. 12.1 cm
• D. 15.5 cm

Answer 1

The correct option is C 12.1 cm

P = 200 hp = 146.14 kW

$Power,P=\frac{2\pi NT}{60}$

$\therefore$ T = 13.563 kNm = 13563 N-m

For hollow cross-section

${\tau }_{max}=\frac{16T}{\pi d_0^3[1-{\left(\frac{d_i}{d_o}\right)}^4]}$

$420\times 9.81\times {10}^4=\frac{16\times 13563}{\pi d_0^3[1-{\left(\frac{1}{2}\right)}^4]}$

$\therefore d=0.121m=12.1cm$