A prismatic beam fixed at both ends carries a uniformly distributed load. The ratio of bending moment at supports to bending moment at mid-span is
- A0.5
- B1.0
- C1.5
- D2.0Correct
Solution
Concept
Bending moments in a fixed beam with UDL
Formula
Msupport = wL²/12 (hogging); Mmid = wL²/24 (sagging)
Step-by-step solution
1. Support moment = wL²/12. 2. Mid-span moment = wL²/8 − wL²/12 = wL²/24. 3. Ratio = (wL²/12) / (wL²/24) = 2.
Explanation
For a fixed beam under a UDL the end moments are twice the central moment, so the ratio of the support moment to the mid-span moment is 2.0.
Shortcut
Fixed beam UDL: ends wL²/12, centre wL²/24, ratio 2.
Common mistake
Inverting the ratio.
Correct answer: D) 2.0