Cantilever with end load — location of failure under increasing load: When a vertical cantilever beam carries a load at its free end, where does failure initiate as the load is increased?

Introduction:
Bending failure typically initiates where bending moment is maximum. For a cantilever with an end load, recognizing the bending moment distribution is key.

Given Data / Assumptions:

• Cantilever of length l; point load at the free end.
• Linear elastic behavior up to failure.

Concept / Approach:
Maximum bending moment occurs at the fixed support for a cantilever with end load. Extreme fiber stress is largest there, so yielding/crack initiation starts at the fixed end section.

Step-by-Step Solution:

Verification / Alternative check:
Comparative check of stress magnitudes along the beam confirms the fixed section is critical.

Why Other Options Are Wrong:

• Free end / middle / 2l/3: bending moment is smaller away from the fixed support.
• Uniformly along the span: bending stresses are not uniform.

Common Pitfalls:
Confusing maximum deflection (free end) with maximum bending stress (fixed end).

Final Answer: