The theory of pure bending can be expressed by ______?

Explanation :

 The equation for simple bending is given by:

\(\frac{M}{I}=\frac{f_{y}}{R}=\frac{E}{R}\)

where I = Moment of Inertia, E = Modulus of Elasticity, F = Stress at any fiber at a distance of y from the neutral axis, M = Bending moment and R = Radius of curvature.

For a circle, the radius is constant, hence for pure bending, the arc bend into a circle.

Following are the assumptions made in the theory of Pure Bending:

1. The material of the beam is homogenous and isotropic.

2. The beam is initially straight, and all the longitudinal fibres bend in circular arcs with a common centre of curvature.

3. Members have symmetric cross-sections and are subjected to bending in the plane of symmetry.

4. The beam is subjected to pure bending and the effect of shear is neglected.

5. Plane sections through a beam, taken normal to the axis of the beam remain plane after the beam is subjected to bending.

6. The radius of curvature is large as compared to the dimensions of the beam.

7. The beam materials are stressed within their elastic limit and, thus, obey Hook's law.

8. In pure bending every layer has a different radius of curvature but the same centre of curvature.