For a hollow circular shaft transmitting torque T, the shear stress at the outer radius is:
Choose the correct answer
τ = T/J (no radius term)
τ = T×r_outer/J where J = π(D⁴-d⁴)/32 — maximum at outer surface of hollow shaft
τ = T×d/(2J) using inner radius
τ = 2T/(πD³) (solid shaft formula only)
Correct Answer
B. τ = T×r_outer/J where J = π(D⁴-d⁴)/32 — maximum at outer surface of hollow shaft
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Shear stress in shaft: τ = T×r/J where J = polar moment of inertia = π(D⁴-d⁴)/32 for hollow shaft (D=outer, d=inner dia), r = outer radius = D/2. Maximum shear stress at outer surface. Power transmitted: P = 2πNT/60 (P in W, N in rpm, T in N·m). Angle of twist: φ = TL/(GJ). Hollow shaft is more efficient than solid (same J for less material).
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