Note the convention:

• A shear force is termed POSITIVE if in acts on a positive face in a positive direction (or on a negative face in a negative direction). A positive shear force on the right-face - the positive x-face - acts upward, in the positive y-direction.
• A positive moment causes a beam to bend into a "happy face"-shape. A moment is POSITIVE if it acts on a positive face about a positive axis (or a negative face about a negative axis). Here, the moment on the right face acts on the +x-face, about the +z-axis, which is out of the plane (screen, paper).

When a beam is subjected to pure bending (constant moment), it deforms in the manner shown at right. Viewed from the side, the deflection takes the form of a circular arc with a radius of curvature of R (measured to the neutral axis of the beam). The neutral axis is a line along the beam axis that does not change length and so has zero strain.

From geometry, the strain in the beam must be:

• For a positive moment, the strain above the neutral axis (y > 0), the strain is negative (compressive);
• For a positive moment:, the strain below the neutral axis the strain is positive (tensile).
• Kappa, k = 1/R is the Curvature.

From Hooke's Law, the stress due to bending is related to the bending strain:

Applying the equilibrium conditions and making a couple of algebraic substitutions, the Bending Stress - a normal stress in the x-direction - is: