Pure bending

In solid mechanics, pure bending (also known as the theory of simple bending) is a condition of stress where a bending moment is applied to a beam without the simultaneous presence of axial, shear, or torsional forces. Pure bending occurs only under a constant bending moment ($M$) since the shear force ($V$), which is equal to $$\tfrac{dM}{dx},$$ has to be equal to zero. In reality, a state of pure bending does not practically exist, because such a state needs an absolutely weightless member. The state of pure bending is an approximation made to derive formulas.

Kinematics of pure bending

 * 1) In pure bending the axial lines bend to form circumferential lines and transverse lines remain straight and become radial lines.
 * 2) Axial lines that do not extend or contract form a neutral surface.

Assumptions made in the theory of Pure Bending
Notes: 1 Homogeneous means the material is of same kind throughout. 2 Isotropic means that the elastic properties in all directions are equal.
 * 1) The material of the beam is homogeneous1 and isotropic2.
 * 2) The value of Young's Modulus of Elasticity is same in tension and compression.
 * 3) The transverse sections which were plane before bending, remain plane after bending also.
 * 4) The beam is initially straight and all longitudinal filaments bend into circular arcs with a common centre of curvature.
 * 5) The radius of curvature is large as compared to the dimensions of the cross-section.
 * 6) Each layer of the beam is free to expand or contract, independently of the layer, above or below it.