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

Now
we are going ahead to start new topic i.e. Assumptions made in the theory of
simple bending in
strength of material with the help of this post.

###
**A****ssumptions made in the theory of
simple bending **

Before
understanding the theory of simple bending, we must have to be aware about the
various assumptions made, as mentioned here, in the theory of simple bending.

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

####
**First assumption**

Material
of the beam will be homogenous and isentropic.

Now
you might be thinking that what is the meaning of the terms homogeneous and
isentropic used here in first assumption.

Homogeneous
term is used here to indicate that material of the beam will be same throughout
or we can say more specifically that material composition of the beam will be
same throughout the beam i.e. material of the beam will not be changing
throughout.

Isentropic
term used here to indicate that elastic properties of the material will be same
in all the directions i.e. modulus of elasticity of the material will be same
in X-direction, in Y-direction and in Z-direction.

####
**Second assumption**

Young’s
modulus of elasticity of the material of the beam will be same in tension and
compression.

As
we have discussed in our previous post that due to bending action, top portion
of the beam will be in compression whereas bottom portion of the beam will be
in tension. Value of Young’s modulus of elasticity of material of the beam will be same
for tension and compression.

####
**
Third assumption**

Beam
will be straight before loading and will remain straight once load will be
removed.

Let us
assume that we have following horizontal beam AB as displayed here. Beam AB is
straight before loading, now once load W will be applied over the simply
supported horizontal beam AB as displayed here, beam AB will be bending in the
form of a curve.

If we have
removed the load W, beam AB must be straight i.e. there must be elastic
deformation.

####
**Fourth assumption**

The sections
of the beam which were plane before bending, must remain plain after bending
too.

####
**Fifth assumption**

Beam material
must be stressed within its elastic limit and therefore beam material must
follow the principle of Hooke’s law.

Bending
stress developed in the beam, once beam will be loaded, must be within elastic
limit or we can say that there must be elastic deformation in the beam.

####
**
Sixth assumption**

The radius
of curvature, during bending of the beam, will be large as compared with the
dimensions of the cross-section of the beam and beam will have symmetrical
cross-section.

####
**Seventh assumption**

Beam will
be subjected with the pure bending action.

As we have
already discussed that when horizontal simply supported beam AB will be loaded
with a load, there might be shearing action and beam might be sheared.

We will
not have to consider here the shearing action, but also we will consider here
only bending action i.e. we have assumed that beam AB will be loaded with a
load and there will be only bending action.

####
**Eighth assumption**

Load will
be applied in the plane of bending and each layer of the beam will be free to expand
or contract, independently of the layer, above or below it.

We will
discuss 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