Question

A cantilever beam is subjected to a uniformly distributed load. At what point along the beam's length does the maximum deflection occur?

• A. At the fixed end
• B. At the midpoint of the beam
• C. At a quarter span from the free end
• D. At the free end

Hint:

For any cantilever configuration with downward loads, the fixed end has zero slope and zero deflection, while the free end always experiences the maximum deflection and maximum slope.

Answer 1

The Correct Option is D

Step 1: Recall the boundary conditions of a cantilever.
A cantilever is rigidly fixed at one end, so at that end both the deflection and the slope of the beam must be zero. At the other, unsupported end, neither condition applies.
Step 2: Think about how deflection builds up along the span.
Deflection accumulates as the curvature, bending moment divided by flexural rigidity, is integrated twice while moving away from the fixed end. Since the slope stays zero only at the fixed end and keeps growing as you move outward, deflection increases the whole way along the length for a cantilever under a uniformly distributed load, unlike a simply supported beam where deflection rises then falls back to zero at both supports.
Step 3: Locate the maximum.
Because deflection increases continuously from the fixed support and there is no second support to pull it back down, the largest value must occur exactly at the tip, giving the standard result \( \delta_{max} = \dfrac{wL^4}{8EI} \) at the free end.
\[ \boxed{\text{At the free end}} \]