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

Step 1: Define the point of contra-flexure.
The point of contra-flexure is the point on a beam where the bending moment changes its sign.
This means the curvature of the beam changes from sagging to hogging (or vice-versa).
Step 2: Connect sign change with bending moment value.
For bending moment to change sign, it must pass through zero at some location.
So, at the point of contra-flexure:
- Bending moment is zero, and
- It changes sign across that point (positive to negative or negative to positive).
Step 3: Analyze the options.
(A) Point where Shear force is maximum: Incorrect, because contra-flexure is related to bending moment sign change, not maximum shear force.
(B) Point where Bending moment is maximum: Incorrect, because contra-flexure occurs at zero bending moment, not maximum.
(C) Point where Bending moment is zero: Incomplete, because bending moment can be zero at supports in simply supported beams, but that does not necessarily indicate a sign change.
(D) Point where Bending moment is zero but also changes sign from positive to negative: Correct, this captures both necessary conditions for contra-flexure.
Step 4: Conclusion.
Hence, the point of contra-flexure is correctly described by option (D).

Answer 2

The point of contra-flexure marks where the curvature of a beam reverses, which has a precise meaning in terms of the bending moment diagram. Let's check each option.

1. Point where shear force is maximum: The location of maximum shear force is unrelated to where the bending moment crosses zero and changes sign; these are generally different points on the beam.
2. Point where bending moment is maximum: A point of maximum bending moment is where the shear force (the derivative of the bending moment) is zero, the opposite condition from where the bending moment itself is zero, so this does not describe contra-flexure.
3. Point where bending moment is zero: This is a necessary condition for contra-flexure, but not sufficient on its own, a beam can have a bending moment of exactly zero at its simply supported ends without that being a point of contra-flexure, since the moment doesn't reverse sign there.
4. Point where bending moment is zero but also changes sign from positive to negative: This captures both the necessary condition (zero bending moment) and the defining feature of contra-flexure (an actual reversal of curvature/sign), making it the complete and correct description.

A true point of contra-flexure requires both a zero bending moment and an actual sign change across that point, distinguishing it from an end support where the moment is zero without reversing.

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