Point of contraflexure — where bending moment changes sign In which types of beams can a point of contraflexure (a location where bending moment changes sign and curvature reverses) occur under typical loading?

Introduction / Context:
The point of contraflexure is significant for detailing reinforcement and checking sign changes in bending stress. It is where bending moment shifts from positive (sagging) to negative (hogging) or vice versa.

Given Data / Assumptions:

• Standard loading scenarios for common beam types.
• Prismatic members and small deflection theory.

Concept / Approach:
In a simply supported prismatic beam without overhangs, the bending moment diagram maintains a single sign between supports (no sign change), so no point of contraflexure exists. In overhanging beams and continuous beams, the bending moment diagram typically crosses zero between regions of positive and negative moment, creating one or more points of contraflexure.

Step-by-Step Solution:

Verification / Alternative check:
Plot basic M–x diagrams for the cases to confirm sign behavior; contraflexure points occur where M(x) = 0 between two regions of opposite sign.

Why Other Options Are Wrong:

• Only cantilevers/only continuous/only overhanging: each omits valid cases.
• All beam types including simple simply supported: incorrect, as a plain simply supported beam does not have a sign change under usual loads.

Common Pitfalls:
Confusing zero bending moment at a support with a point of contraflexure inside the span.

Final Answer:
Overhanging and continuous beams (not in a simple prismatic cantilever under usual loads)