We were discussing basic concept of shear force and bending moment in our
previous session. We have also discussed strain energy and expression for strain
energy due to various types of loading such strain
energy stored due to gradual applied load.

Now we
are going ahead to start new topic in strength of material and that is bending
stress. First we will understand here the meaning and importance of bending
stress.

###
**Bending Stress**

We have
already seen various types of stress in strength of materials such as tensile
stress, compressive stress and shear stress. Today we will see another type of
stress in loaded member i.e. bending stress.

Let us go
ahead step by step for easy understanding, however if there is any issue we can
discuss it in comment box which is provided below this post.

Let us
consider one structural member such as beam with rectangular cross section, we
can select any type of cross section for beam but we have considered here that
following beam has rectangular cross section.

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

Let us
think that a load W is applied over the beam AB as displayed in above figure,
now someone want to ask one question that what you will see when load W will be
applied over the beam AB?

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

As we have
seen above that horizontal beam AB will be bending due to the load W which is
applied over the beam AB and therefore we can say that load W will be the
responsible for the bending action of the horizontal beam AB.

Now,
material of the horizontal beam AB will resist the bending action of load W and
hence material of the horizontal beam will provide the internal resistance against
load W and this internal resistance per unit area will be termed as bending
stress.

Therefore we
can define bending stress as the internal resistance per unit area developed by
material of the beam against the external load.

###
**Formula and unit of bending stress**

Unit of
bending stress will be similar as the unit of stress i.e. N/m

^{2}.
We have
shown above one small section of the beam AB after loading condition i.e. after
bending of the beam. We have used few letters above in diagram of small section
of the beam; let us see the nomenclature of those terms/letters.

R: Radius
of curvature

N.A:
Neutral axis of the beam AB

We must
note it here that due to bending action, top portion of the beam will be in
compression whereas bottom portion of the beam AB will be in tension and we
have displayed it in above figure.

We will
discuss assumptions made in the theory of simple bending in the category of strength
of material in our next post.

###
**Reference:**

Strength
of material, By R. K. Bansal

Image
Courtesy: Google