Angle of Twist of a Hollow Steel Shaft

Equation: the angle of twist of a shaft is φ = T·L / (G·J), in radians. For a hollow circular section, J = π(do⁴ − di⁴)/32. Values: T = 1.5 kN·m = 1500 N·m is the torque. L = 2 m is the shaft length. G = 80 GPa = 80 × 10⁹ Pa is the shear modulus of steel. do = 0.060 m and di = 0.040 m give J. Step 1: J = π(0.060⁴ − 0.040⁴)/32 = 1.021 × 10⁻⁶ m⁴. Step 2: φ = 1500 × 2 / (80 × 10⁹ × 1.021 × 10⁻⁶) = 0.0367 rad. Step 3: convert to degrees, 0.0367 × 180/π = 2.10°. Leaving the answer in radians (0.0367) or slipping a decimal (0.21°) are the common errors; 4.20° doubles the length.