Point of contraflexure (inflection point) occurs in which beams under usual loading?

Introduction / Context:
The point of contraflexure (inflection) is where the bending moment changes sign, and the curvature of the beam changes from sagging to hogging or vice versa. Recognizing beam types that exhibit this is essential for reinforcement and section design.

Given Data / Assumptions:

• Usual static load cases (point loads, UDL, UVL).
• Beam behavior is linear elastic.
• We consider typical “textbook” loadings.

Concept / Approach:
Simply supported beams under common symmetrical loads have positive bending moment within span and zero at supports—no sign change within the span. Cantilevers typically have one sign of bending throughout. Overhanging beams can have positive midspan and negative near supports, creating a sign change. Fixed beams often have negative moments at supports and positive toward midspan, producing two inflection points.

Step-by-Step Solution:

Verification / Alternative check:
For a fixed–fixed beam with UDL, analytical M(x) shows negative at ends, positive at midspan, guaranteeing two zeros within the span.

Why Other Options Are Wrong:
Cantilevers and simply supported beams (typical loadings) lack an internal sign change. “No real beam” is false; “all beams” is overgeneralized.

Common Pitfalls:
Confusing zero moment at supports of simply supported beams with an internal inflection point; forgetting that overhangs and fixity modify end moments.

Final Answer:
Overhanging and fixed beams (where bending moment changes sign)