A Fixed beam of span L is loaded with uniformly distributed load of intensity w/unit length, all through the span. Bending moment at fixed end is
- AwL²/8
- BwL²/2
- CwL²/12Correct
- DwL²/24
Solution
Concept
Fixed end bending moment under uniform load
Formula
M = wL2/12
Step-by-step solution
1. A fixed beam of length L carrying a full uniformly distributed load w experiences fixed-end restraint moments at both ends. 2. The magnitude of the fixed-end bending moment is calculated as M = wL²/12. 3. The mid-span bending moment for the same loading condition is wL²/24. Answer: C
Explanation
For a fully fixed beam subjected to a uniform distributed load w across span L, end restraint moments develop to prevent rotation at the supports. Standard structural analysis shows that these fixed-end moments reach a magnitude of wL²/12 at both ends. By contrast, the mid-span moment for the same beam is wL²/24.
Why the other options are wrong
A) wL²/8 is the maximum bending moment at the center of a simply supported beam under UDL. B) wL²/2 is the maximum bending moment at the fixed support of a cantilever beam under UDL. D) wL²/24 is the bending moment at the center of a fixed beam under UDL.
Shortcut
Fixed beam under UDL: End bending moment = wL²/12 (Center bending moment = wL²/24).
Common mistake
Confusing the fixed end moment formula (wL²/12) with the simply supported maximum moment (wL²/8) or fixed mid-span moment (wL²/24).
Correct answer: C) wL²/12