The Bending Equation is?

By K Balaji|Updated : October 6th, 2022
  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

The bending equation is M / I = σ /y = E / R. The pure bending is taken into consideration when bending moment is constant and rate of bending moment change is equal.

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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