Stresses caused by the bending moment are known as flexural or bending stresses. Consider a beam to be loaded as shown.
Consider a fiber at a distance from the neutral axis, because of the beam's curvature, as the effect of bending moment, the fiber is stretched by an amount of . Since the curvature of the beam is very small, and are considered as similar triangles. The strain on this fiber is
By Hooke's law, , then
which means that the stress is proportional to the distance from the neutral axis.
Considering a differential area at a distance from N.A., the force acting over the area is
The resultant of all the elemental moment about N.A. must be equal to the bending moment on the section.
but , then
where is the radius of curvature of the beam in mm (in), is the bending moment in N·mm (lb·in), is the flexural stress in MPa (psi), is the centroidal moment of inertia in mm4 (in4), and is the distance from the neutral axis to the outermost fiber in mm (in).