Pure bending

In solid mechanics, 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 since the shear force, which is equal to 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

• 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==

Assumptions made in the theory of Pure Bending

• The material of the beam is homogeneous1 and isotropic2. • The material is linearly elastic and obeys Hooke’s Law within the range of stresses produced by bending. • 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. ==References==

Source: Wikipedia ↗

tickerdossier.com tickerdossier.substack.com