Bending theory: In a loaded beam, the point of contraflexure is located at the section where the bending moment is zero and changes sign. Identify the correct description.

Introduction / Context:
The point of contraflexure is a fundamental concept in beam analysis, indicating where the curvature of the elastic axis changes from sagging to hogging or vice versa. Recognizing this point is important for reinforcement detailing and for understanding the internal force distribution under complex loading.

Given Data / Assumptions:

• Beam is prismatic and behaves elastically.
• Bending moment and shear force diagrams are well-defined for the applied loads.
• Sign convention: sagging positive, hogging negative (or vice versa consistently).

Concept / Approach:
Bending curvature is proportional to bending moment divided by E * I. If the bending moment passes through zero and changes sign, the curvature changes sign, and hence a point of contraflexure exists. This concept does not depend on the shear force magnitude at that location; it is purely linked to the bending moment sign change.

Step-by-Step Solution:
1) Construct the bending moment diagram from the loading.2) Identify where M crosses the zero axis.3) Confirm that M changes sign across that crossing; that section is the point of contraflexure.

Verification / Alternative check:
In continuous beams or cantilevers with overhangs, there are often one or more points where the moment flips sign. Design codes may require tension reinforcement on the face that becomes tensile across this point, reflecting the change in curvature.

Why Other Options Are Wrong:
Minimum or maximum bending moment points need not be zero.Shear force extrema have no necessary correlation with contraflexure points.

Common Pitfalls:
Confusing zero shear locations with contraflexure points; neglecting sign conventions and concluding incorrectly about curvature change.

Final Answer:
Bending moment is zero or changes sign