Determine the maximum shear stress and angle of twist:
A hollow circular shaft of 6 m length and inner & outer diameter ois equal to 80 mm and
100 mm is subjected to a torque of 20 kN-m. If G = 80 GPa, determine the maximum shear stress and the angle of twist.
Solution
l = 6 m; do = 100 mm; di = 80 mm
T = 20 kN-m = 20 × 10^{3 }N-m
G = 80 GPa = 0.8 × 10^{11} N/m^{2}
R = 50 mm
Z P = J / R = 5.8 × 10^{-6} /0.05 = 1.16 × 10^{- 4} m^{3}
T/ J = τ_{max} / R = G θ/ l
τ_{max} = T /Z_{P} = 20 × 10^{3} / 1.16 × 10^{- 4}
= 17.2 × 10^{7} N/m2
= 172 N/mm^{2}
θ= τ_{max} /R × (l/G) = 172 × 10 ^{6} /0.05 × (6/ (0.8 × 10^{11}))
= 0.258 radian = 14.78o.