Question

The shear force at the fixed end of a cantilever beam of length \( l \) carrying a uniformly distributed load \( w \) per unit length is

• A. zero
• B. \( \dfrac{wl}{4} \)
• C. \( \dfrac{wl}{2} \)
• D. \( wl \)

Hint:

For a cantilever with UDL, maximum shear force always occurs at the fixed end.

Answer 1

The Correct Option is D

Step 1: Understanding the loading condition.
A cantilever beam is fixed at one end and free at the other. The uniformly distributed load \( w \) acts over the entire length \( l \) of the beam.
Step 2: Calculating the total load.
The total load acting on the beam is: \[ W = w \times l \]
Step 3: Shear force at the fixed end.
The fixed end must balance the entire applied load. Hence, the shear force at the fixed end is equal to the total load: \[ V = wl \]
Step 4: Conclusion.
The shear force at the fixed end of the cantilever beam is \( wl \).