**Flexure Formula**

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

substituting

then

and

The bending stress due to beams curvature is

The beam curvature is:

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 mm^{4} (in^{4}), and is the distance from the neutral axis to the outermost fiber in mm (in).

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