Torsion of Shafts MCQ with answer and solution

Concept

Torsional shear stress in solid circular shaft

Formula

τ_max = 16 × T / (π × d³)

Step-by-step solution

1. For a solid circular shaft of diameter d = 50 mm, the polar section modulus is Z_p = (π × d³) / 16. 2. Z_p = (π × 50³) / 16 = (π × 125,000) / 16 = 24,543.7 mm³. 3. Applied torque T = 0.3 kN-m = 300,000 N-mm. 4. Maximum torsional shear stress τ_max = T / Z_p = 300,000 / 24,543.7 = 12.22 MPa = 12 MPa. Answer: A

Explanation

For a solid circular shaft of diameter d = 50 mm, the polar section modulus is Z_p = (π × d³) / 16 = (π × 50³) / 16 = 24,544 mm³. Under an applied torque T = 0.3 kN-m = 300,000 N-mm, the maximum torsional shear stress at the outer surface is τ_max = T / Z_p = 300,000 / 24,544 = 12.22 MPa = 12 MPa.

Why the other options are wrong

B) 14 MPa is an overestimation from rounded constants. C) 6 MPa results from using 32 in the numerator instead of 16. D) 18 MPa is an arithmetic error.

Shortcut

τ_max = 16·T / (π·d³) = (16 × 300,000) / (π × 125,000) = 4800 / 392.7 = 12.22 MPa = 12 MPa.

Common mistake

Using rectangular section modulus or polar moment of inertia J instead of section modulus Z_p.