Question

If the hinged end of a propped cantilever of span \( L \) settles by an amount \( \delta \), then the rotation of the hinged end will be

• A. \( \frac{\delta}{L} \)
• B. \( \frac{1.5 \delta}{L} \)
• C. \( \frac{2 \delta}{L} \)
• D. Zero

Hint:

- For propped cantilevers, settlement at the hinge leads to double the deflection ratio.

Answer 1

The Correct Option is C

Step 1: Understanding support settlement. - When the hinged end of a propped cantilever settles, the beam undergoes rotation at the hinge. Step 2: Applying the slope-deflection method. - The rotation \( \theta \) at the hinge due to settlement is given by: \[ \theta = \frac{2\delta}{L} \] Step 3: Selecting the correct option. Since the rotation at the hinge is \( \frac{2\delta}{L} \), the correct answer is (C).