A rectangular simply supported beam of span 4 m is 300 mm × 700 mm in cross section and is reinforced with 3 bars of 20 mm on tension side at an effective cover of 50 mm. The beam experiences an imposed working load of 20 kN/m. Assume the density of concrete as 25 kN/m³ (excluding self-weight). What is the maximum bending moment?
- A5.05 kNm
- B50.5 kNmCorrect
- C55.0 kNm
- D5.5 kNm
Solution
Concept
Total load = imposed load + self-weight of beam. For a simply supported beam under UDL, Mmax = wL2/8.
Formula
wself = b × D × γc ; Mmax = wL2/8
Step-by-step solution
1. Self-weight = 0.3 × 0.7 × 25 = 5.25 kN/m 2. Imposed load = 20 kN/m 3. Total load w = 20 + 5.25 = 25.25 kN/m 4. Mmax = wL2/8 = 25.25 × 42 / 8 5. Mmax = 25.25 × 16 / 8 = 50.5 kNm
Explanation
The beam carries its own weight and the imposed load. Self-weight is 5.25 kN/m, so the total load is 25.25 kN/m. For a simply supported beam under UDL, the maximum moment at mid-span is wL2/8 = 50.5 kNm.
Why the other options are wrong
A (5.05) and D (5.5) are wrong by a factor of 10. C (55.0) does not match wL2/8 for any correct load. 40 kNm (imposed load only) is not given as an option.
Shortcut
wL2/8 with L = 4 m is simply 2w, so M = 2 × 25.25 = 50.5 kNm.
Common mistake
Forgetting self-weight gives 40 kNm. Also, the reinforcement and cover data are not needed for this.
Correct answer: B) 50.5 kNm