Beam bending (cantilever with end load): When a cantilever beam is loaded at its free end by a downward force, where does the maximum compressive bending stress occur at the fixed support cross-section?

Introduction / Context:Bending stress distribution in beams depends on load type and support conditions. For cantilevers, identifying the fibres in tension versus compression is key for safe design and detailing (e.g., reinforcement placement in concrete).

Given Data / Assumptions:

• Prismatic cantilever beam fixed at one end and free at the other.
• Downward point load applied at the free end.
• Linear elastic behavior; small deflections.

Concept / Approach:Under a downward end load, the cantilever deflects downward, producing a sagging curvature (concave upward). In sagging, the top fibres are in compression and bottom fibres are in tension. Bending stress magnitude at a section is sigma = My / I, largest at extreme fibres (maximum y).

Step-by-Step Solution:

Verification / Alternative check:Draw a qualitative bending moment diagram: a triangle from zero at free end to maximum at the fixed end; check sign conventions—sagging indicates compression at the top for a horizontal beam with downward load.

Why Other Options Are Wrong:

• Bottom fibre: carries maximum tension, not compression.
• Neutral axis: zero bending stress by definition.
• Centre of gravity: coincides with neutral axis for symmetric sections; stress is zero there.

Common Pitfalls:Confusing sign conventions for sagging/hogging; assuming the same behaviour as simply supported beams at midspan without considering boundary conditions.

Final Answer:Top fibre