Question

The maximum deflection of a fixed beam of length \( l \) carrying a total load \( W \) being uniformly distributed over the entire length is

• A. \( \dfrac{Wl^3}{48EI} \)
• B. \( \dfrac{Wl^3}{96EI} \)
• C. \( \dfrac{Wl^3}{192EI} \)
• D. \( \dfrac{Wl^3}{384EI} \)

Hint:

Fixed beams have smaller deflection compared to simply supported beams under the same loading.

Answer 1

The Correct Option is C

Step 1: Understanding the beam condition.
The beam is fixed at both ends and carries a uniformly distributed load over its entire length. Fixed supports restrict both rotation and translation.
Step 2: Using standard deflection formula.
For a fixed beam under uniformly distributed load, the maximum deflection occurs at the centre of the beam.
Step 3: Writing the formula.
The maximum deflection is given by: \[ \delta_{\max} = \frac{Wl^3}{192EI} \]
Step 4: Conclusion.
The maximum deflection of the beam is \( \dfrac{Wl^3}{192EI} \).