304 Maximum Shearing Stress and Angle of Twist of a Steel Shaft

$\tau_{max} = \dfrac{16T}{\pi D^3} = \dfrac{16(15)(1000)(12)}{\pi (4^3)}$

$\tau_{max} = 14 324 \, \text{psi}$

$\tau_{max} = 14.3 \, \text{ksi}$           answer
 

$\theta = \dfrac{TL}{JG} = \dfrac{15(3)(1000)(12^2)}{\frac{1}{32} \pi (4^4)(12 \times 10^6)}$

$\theta = 0.0215 \, \text{rad}$

$\theta = 1.23^\circ$           answer