310 Strength Comparison of Hollow and Solid Steel Shafts of Equal Outside Diameters

Hollow circular shaft:
$\tau_{max-hollow} = \dfrac{16TD}{\pi(D^4 - d^4)}$

$\tau_{max-hollow} = \dfrac{16TD}{\pi \, [ \, D^4 - (\frac{1}{2}D)^4 \, ]}$

$\tau_{max-hollow} = \dfrac{16TD}{\pi (\frac{15}{16}D^4)}$

$\tau_{max-hollow} = \dfrac{16^2T}{15\pi D^3}$
 

Solid circular shaft:
$\tau_{max-solid} = \dfrac{16T}{\pi D^3}$

$\tau_{max-solid} = \dfrac{15}{16} \left[ \dfrac{16^2 T}{15\pi D^3} \right]$

$\tau_{max-solid} = \frac{15}{16} \times \tau_{max-hollow}$      (okay!)