Question

Point of contra-flexure is a

• A. Point where Shear force is maximum
• B. Point where Bending moment is maximum
• C. Point where Bending moment is zero
• D. Point where Bending moment is zero but also changes sign from positive to negative

Hint:

Do not confuse “zero bending moment” with “contra-flexure”. Contra-flexure occurs only when bending moment becomes zero {and} changes sign across that point.

Answer 1

The Correct Option is D

Contra-flexure refers to a beam reversing its curvature from sagging (concave up) to hogging (concave down), or vice versa, somewhere along its span, typically in overhanging or continuous beams.

1. Max shear force: Unrelated to bending moment sign changes.
2. Max bending moment: Occurs where shear is zero, the opposite of a zero-moment condition.
3. Zero bending moment: Necessary but not sufficient, simply-supported end points also have zero moment without any sign reversal.
4. Zero bending moment with sign reversal: The complete, correct description, the moment passes through zero and switches from sagging to hogging (or the reverse).

Answer 2

Picture the bending moment diagram as a continuous curve along the beam's length; wherever this curve crosses the horizontal (zero) axis, going from above it to below it (or the reverse), that crossing point is where curvature reverses.

1. Max shear force: This corresponds to a point of steepest slope on the bending moment diagram, not a zero crossing.
2. Max bending moment: This corresponds to a peak or trough of the bending moment curve, where its slope (the shear force) is momentarily zero, not where the curve crosses the axis.
3. Zero bending moment: Describes any point the curve touches the axis, including endpoints of a simply supported span where the curve simply starts or ends at zero without crossing through it.
4. Zero bending moment with sign change: Describes specifically the curve crossing through the axis, moving from positive to negative territory (or vice versa), which is what actually causes the beam's curvature to flip, the true point of contra-flexure.

Therefore, the correct answer is point where bending moment is zero but also changes sign from positive to negative.