Which describes the relationship between bending moment and curvature?

The relationship between bending moment and curvature is fundamentally linked through the concepts of beam theory and the mathematical principles of structural analysis. When a beam is subjected to bending, the deformation or deflection experienced by the beam can be described by its curvature.

Curvature in a beam is defined as the rate of change of the angle of the tangent to the beam's neutral axis with respect to the length of the beam. This curvature is directly influenced by the bending moment acting on the beam. When a positive bending moment is applied, it causes the beam to bend in a concave-upward manner, which creates positive curvature.

In more technical terms, the relationship can be represented mathematically by the formula ( M = EI \cdot \kappa ), where ( M ) is the moment, ( E ) is the modulus of elasticity, ( I ) is the moment of inertia, and ( \kappa ) is the curvature. In this context, a positive moment results in positive curvature because it causes the beam to bend upwards, aligning with the definition of positive curvature.

Conversely, negative bending moments lead to negative curvature, indicating that the beam is bent in the opposite direction. Understanding this relationship is crucial for analyzing and designing structural