A beam with section modulus Z = 2 × 106 mm3 is subjected to a bending moment of 10 kN-m. What is the maximum bending stress?
- A2.0 MPa
- B5 MPaCorrect
- C10 MPa
- D50 MPa
Solution
Concept
Maximum bending stress from moment and section modulus
Formula
σ = M / Z
Step-by-step solution
1. The flexure formula relates bending moment M, section modulus Z, and maximum bending stress σ. 2. Bending stress is expressed as σ = M / Z. 3. Applied bending moment M = 10 kN-m = 10 × 106 N-mm. 4. Section modulus Z = 2 × 106 mm3. 5. σ = (10 × 106 N-mm) / (2 × 106 mm3) = 5 N/mm2 = 5 MPa. Answer: B
Explanation
The maximum bending stress in a flexural member is computed from the flexure formula as σ = M / Z, where M is the applied bending moment and Z is the section modulus. For M = 10 kN-m = 10x106 N-mm and Z = 2x106 mm3: σ = 10x106 / (2x106) = 5 MPa.
Why the other options are wrong
A) 2.0 MPa results from inverting the ratio (Z / M). C) 10 MPa corresponds to Z = 1x106 mm3. D) 50 MPa results from unit conversion errors between kN-m and N-mm.
Shortcut
σ = M / Z = 10x106 / 2x106 = 5 MPa.
Common mistake
Dividing Z by M instead of M by Z.
Correct answer: B) 5 MPa