Deflection of beams: For a cantilever beam of length l carrying a uniformly distributed load w per unit length, the location of maximum deflection is where?

Introduction / Context:
Determining where the maximum deflection occurs helps in serviceability checks and control of deflections in structures. For common loadings on standard supports, locations are well known and can be derived from beam theory.

Given Data / Assumptions:

• Cantilever of length l, fixed at one end and free at the other.
• Uniformly distributed load w over the entire span.
• Linear elastic behavior, small deflections.

Concept / Approach:
Deflection curves y(x) are obtained by integrating the moment–curvature relationship: EI * d^2y/dx^2 = M(x). For a UDL on a cantilever, the slope and deflection increase monotonically toward the free end, so maximum deflection occurs at the free tip.

Step-by-Step Solution:

Verification / Alternative check:
Closed-form maximum deflection magnitude: y_max = wl^4 / (8E*I) for UDL on a cantilever, which occurs at the free end.

Why Other Options Are Wrong:

• Fixed end or midspan: deflection there is smaller; at the fixed end it is zero by boundary condition.
• l/3 from fixed end: not the correct extremum for UDL on cantilever.

Common Pitfalls:
Confusing locations for different load cases (e.g., concentrated end load versus UDL); mixing up simply supported and cantilever cases.

Final Answer:
At the free end