Bending Stress MCQ with answer and solution

Concept

Elastic section modulus and maximum bending stress

Formula

σ = M / Z = 6 × M / (b × d²)

Step-by-step solution

1. A rectangular beam cross section has width b = 200 mm and depth d = 300 mm. 2. The section modulus is Z = (b × d²) / 6 = (200 × 300²) / 6 = (200 × 90000) / 6 = 3,000,000 mm³ = 3x10⁶ mm³. 3. Applied bending moment M = 30 kN-m = 30 × 10⁶ N-mm. 4. Maximum bending stress σ = M / Z = (30 × 10⁶) / (3 × 10⁶) = 10 MPa. Answer: A

Explanation

For a rectangular cross section with width b = 200 mm and depth d = 300 mm, the elastic section modulus is Z = (b × d²) / 6 = (200 × 300²) / 6 = 3,000,000 mm³. Under a bending moment M = 30 kN-m = 30x10⁶ N-mm, the maximum bending stress is σ = M / Z = 30x10⁶ / (3x10⁶) = 10 MPa.

Why the other options are wrong

B) 20 MPa results from using Z = b·d²/12. C) 30 MPa results from dividing moment by cross-sectional area. D) 40 MPa is an arithmetic error.

Shortcut

Z = b·d²/6 = 3x10⁶ mm³ => σ = M/Z = 30x10⁶ / 3x10⁶ = 10 MPa.

Common mistake

Forgetting to square the depth d or misconverting kN-m to N-mm.