Question:hard

A fixed beam of span \(L\) rises by \(\Delta\) upwards at right hand support. The fixed end moment at right hand support will be

Show Hint

Support settlement in a fixed beam: \[ \boxed{ M=\frac{6EI\Delta}{L^2} } \] The direction depends on whether the support rises or settles.
Updated On: Jul 23, 2026
  • \(\dfrac{6EI\Delta}{L^2}\) clockwise
  • \(\dfrac{6EI\Delta}{L^2}\) anticlockwise
  • \(\dfrac{3EI\Delta}{L^2}\) clockwise
  • \(\dfrac{3EI\Delta}{L^2}\) anticlockwise
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Recall the standard result for support movement.
For a fixed beam of span $L$, if one support moves by $\Delta$ relative to the other while both ends stay fixed against rotation, equal fixed end moments develop at both supports, given by \[ M = \frac{6EI\Delta}{L^2} \]
Step 2: Understand why this happens.
The relative rise of the support forces the originally straight beam axis to rotate slightly at both ends even though the joints themselves don't rotate freely, and this chord rotation is what the moment formula captures.
Step 3: Fix the direction at the right support.
With the right support rising relative to the left one, the beam's chord rotates in a sense that produces a clockwise moment at the right end to hold that end fixed.
\[ \boxed{\dfrac{6EI\Delta}{L^2}\ \text{clockwise}} \]
Was this answer helpful?
0