FLEXURE FORMULA FOR BEAMS

We were discussing basic concept of bending stress in our previous session. We have also discussed a ssumptions made in the theory of simple bending and expression for bending stress in pure bending during our last session.

Now we are going ahead to start new topic i.e. Flexural formula or flexural bending equation with the help of this post.

Flexural formula

Let us assume that following beam PQ is horizontal and supported at its two extreme ends i.e. at end P and at end Q, therefore we can say that we have considered here the condition of simply supported beam.

Once load W will be applied over the simply supported horizontal beam PQ as displayed above, beam PQ will be bending in the form of a curve and we have tried to show the condition of bending of beam PQ due to load W in the above figure.

Flexural formula or flexural bending equation for a beam which is subjected to pure bending is as displayed in following figure.

Where,

M = Bending moment (N-mm)

I = Area moment of inertia for beam (mm⁴)

σ= Bending stress (N/mm²)

y= Distance of layer of the beam from neutral axis of the beam which is subjected to pure bending

E = Young’s modulus of elasticity of the material of the beam (N/mm²)
R = Radius of curvature of the beam (m)
Above formula will be used in calculation of various parameters when a beam will be subjected to pure bending.

We will discuss another topic i.e. derivation of flexural formula or bending equation for pure bending in the category of strength of material in our next post.