In structural analysis, the point of contraflexure along a beam is defined as the location where which characteristic of the bending moment (B.M.) diagram occurs?

Introduction / Context:
The point of contraflexure (also called the inflection point) is central to understanding beam behavior, especially in indeterminate structures or members with variable loading. It indicates a change in curvature and is relevant for reinforcement detailing and splicing decisions.

Given Data / Assumptions:

• We consider typical beam behavior with continuous or varying loads.
• The bending moment diagram (B.M. diagram) may pass through zero between positive and negative regions.

Concept / Approach:
Beam curvature is proportional to bending moment (for prismatic, linear-elastic beams: curvature κ ≈ M / (E I)). A change in sign of M implies a change in curvature direction (sagging to hogging or vice versa). The location where M = 0 within the span (not at a free end with zero moment by boundary) is the point of contraflexure.

Step-by-Step Solution:
1) Plot or envision the B.M. diagram for the given loading.2) Identify where M crosses zero within the member length.3) Mark that location as the point of contraflexure.4) Recognize that curvature changes sign there, indicating a shift from sagging to hogging or vice versa.

Verification / Alternative check:
In continuous beams over multiple supports, points of contraflexure commonly occur between supports where the B.M. diagram transitions through zero between negative and positive peaks.

Why Other Options Are Wrong:

• B.M. maximum/minimum: These are extremum points where shear force is zero, not necessarily points of sign change.
• S.F. is zero: Zero shear indicates a B.M. extremum, not inherently a sign change.

Common Pitfalls:

• Confusing zero shear (extreme B.M.) with zero moment (contraflexure).
• Marking support ends (where M = 0 by boundary) as contraflexure without a sign change in the span.

Final Answer:
B.M. changes sign.