Pure 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 , has to be equal to zero. In reality, this 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
- In pure bending the axial lines bend to form circumferential lines and transverse lines remain straight and become radial lines.
- Axial lines that do not extend or contract form a neutral surface.
Assumptions made in the theory of Pure Bending
- The material of the beam is homogeneous1 and isotropic2.
- The value of Young's Modulus of Elasticity is same in tension and compression.
- The transverse sections which were plane before bending, remain plane after bending also.
- The beam is initially straight and all longitudinal filaments bend into circular arcs with a common centre of curvature.
- The radius of curvature is large as compared to the dimensions of the cross-section.
- Each layer of the beam is free to expand or contract, independently of the layer, above or below it.
Notes: 1 Homogeneous means the material is of same kind throughout. 2 Isotropic means that the elastic properties in all directions are equal.
- E P Popov; Sammurthy Nagarajan; Z A Lu. "Mechanics of Material". Englewood Cliffs, N.J. : Prentice-Hall, ©1976, p. 119, "Pure Bending of Beams", ISBN 0-87692-187-10