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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 × 103 N-m
G = 80 GPa = 0.8 × 1011 N/m2
R = 50 mm
Z P = J / R = 5.8 × 10-6 /0.05 = 1.16 × 10- 4 m3
T/ J = τmax / R = G θ/ l
τmax = T /ZP = 20 × 103 / 1.16 × 10- 4
= 17.2 × 107 N/m2
= 172 N/mm2
θ= τmax /R × (l/G) = 172 × 10 6 /0.05 × (6/ (0.8 × 1011))
= 0.258 radian = 14.78o.
r
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