The absolute bending moment in a simply supported beam of span 10 m due to a moving load of 40 kN/m spanning over 5 m is
- A375 kN m at 2.5 m from end A
- B375 kN m at midpointCorrect
- C375 kN m at 3.75 m from end A
- D500 kN m at midspan
Solution
Concept
Absolute maximum moment for a moving UDL
Formula
Place the load symmetrically for max moment at mid-span
Step-by-step solution
1. Load 40 kN/m × 5 m = 200 kN; place it symmetrically about the centre. 2. R = 100 kN. 3. M at midspan = 100 × 5 − 40 × 2.5 × 1.25 = 500 − 125 = 375 kN·m.
Explanation
When a UDL shorter than the span moves across, the absolute maximum moment occurs at mid-span with the load centred.
Why the other options are wrong
375 kN·m at other positions is not the maximum; 500 kN·m ignores the load's own moment.
Shortcut
Centre the load; M = R × L/2 − w a²/8.
Common mistake
Forgetting the load's own moment.
Correct answer: B) 375 kN m at midpoint