Propped cantilever of span L is subjected to a moment +M at the propped end, the fixed end moment at the fixed end will be
- A–M
- B+M/2Correct
- C–M/2
- D+M
Solution
Concept
When a bending moment is applied at the simple support of a propped cantilever beam, a portion of this moment is carried over to the far fixed support.
Formula
Carry-over moment = Carry-over factor × Applied moment Carry-over factor for far end fixed = +1/2
Step-by-step solution
1. Understand the beam supports: one end is propped (simple support) and the other end is fixed. 2. Applied moment at the propped end = +M. 3. The carry-over factor from a hinged/propped end to a fixed end is +1/2. 4. Fixed end moment = (+1/2) × (+M) = +M/2. Answer: (B) +M/2
Explanation
Applying a moment +M at the propped end rotates that end. The far fixed end prevents rotation, developing a resisting moment of half the applied magnitude with the same sign. Thus, the carried-over fixed end moment is +M/2.
Why the other options are wrong
A: Incorrect carry-over factor and sign. C: Incorrect sign; the carried-over moment has the same sign as the applied moment. D: Incorrect value; full moment is not transferred to the fixed end.
Shortcut
Remember the carry-over factor for a far-end fixed support is always +1/2.
Common mistake
Confusing the sign or taking the carry-over factor as -1/2 or 1 instead of +1/2.
Correct answer: B) +M/2