Bending Moment at Point of Contraflexure

The concept of a point of contraflexure is crucial in the analysis of beams and structures. It represents a specific location along the length of a beam where the bending moment undergoes a change in sign.

Understanding Point of Contraflexure

A point of contraflexure, also sometimes referred to as a point of inflection, is a point on the bending moment diagram where the bending moment changes its direction. This change implies that the curvature of the beam also reverses at this point.

• When a beam is subjected to various loads, it experiences internal bending moments. These moments can be positive (causing sagging) or negative (causing hogging).
• As we move along the beam, the bending moment can transition from positive to negative, or vice versa.
• The exact location where this transition occurs, and the bending moment passes through zero, is defined as the point of contraflexure.

Value of Bending Moment

Because the point of contraflexure marks the exact location where the bending moment changes its sign, it logically follows that the value of the bending moment at this precise point must be zero. It's the moment when the beam is neither under a positive (sagging) bending stress nor a negative (hogging) bending stress, but is in a state of transition.

Consider a continuous beam or a beam with overhangs. These types of beams commonly exhibit points of contraflexure. For example, in a simply supported beam with an overhang, the bending moment changes from negative (overhang) to positive (mid-span), passing through zero at the support or somewhere within the span, which would be the point of contraflexure.

Therefore, when analyzing a bending moment diagram, if you identify a point where the diagram crosses the zero axis (the neutral axis for bending moment), that point signifies a point of contraflexure, and the bending moment at that location is zero.