The flexure (bending) equation relates the bending moment acting on a beam's cross-section to the normal stress induced at any point in that section, derived from geometric compatibility of deformation combined with equilibrium of internal forces. Under the assumptions of pure bending, plane symmetric cross-sections, and the "plane sections remain plane" hypothesis, strain and stress vary linearly with distance from a neutral axis passing through the centroid of the cross-section, giving the relation M/I = E/ρ = -σ/y. This is a foundational topic in mechanics of materials/solid mechanics, extending the equilibrium analysis of shear force and bending moment diagrams into stress analysis of beams, and it is the beam analog of the torsion formula for shafts.
The flexure (bending) equation relates the bending moment acting on a beam's cross-section to the normal stress induced at any point in that section, derived from geometric compatibility of deformati…