The Bending Equation is?

Bending Equation Derivation

The following is the equation for simple bending:

M / I = σ /y = E / R

where I = Moment of Inertia,

E = Modulus of Elasticity,

σ = Stress at any fibre at a distance of y from the neutral axis,

M = Bending moment and

R = Radius of curvature.

When the bending moment is constant and the shear force or rate of bending moment change is equal, the equation of pure bending applies.

S.F = (dM/dx) = 0

The assumptions behind the idea of Simple Bending are as follows:

1. The beam’s substance is uniform and isotropic.
2. The longitudinal fibers of the beam first bend in a straight line with a common center of curvature.
3. Members are bent toward symmetry and have symmetric cross-sections.
4. The effect of shear is ignored, and the beam is only subjected to pure bending.
5. After bending, plane portions through a beam that are taken normally to the axis of the beam stay plane.
6. Concerning the beam’s diameter, the radius of curvature is considerable.

Summary:

The Bending Equation is 1. M / I = σ /y = E / R 2. I / M = σ / y = E / R 3. I / M = y / σ = E /R 4. M / I = σ / y = R / E

M / I = σ /y = E / R is the formula for simple bending. The equation of pure bending is considered when bending moment is constant and shear force or rate of bending moment change is equal.

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