In our previous topics, we have seen some important
concepts such as deflection
and slope of a cantilever beam with point load at free end , deflection
and slope of a cantilever beam loaded with uniformly distributed load, bending
stress in beams, basic
concept of shear force and bending moment, strain
energy stored in body, beam
bending equation, bending
stress of composite beam, shear
stress distribution diagram for various sections.

Today we will see here one very important topic in
strength of material i.e. Assumptions made in the Euler’s column theory with
the help of this post.

###
**Assumptions
made in the ****Euler’s
column theory**

Before
understanding the Euler’s column theory, we must have to be aware about the
various assumptions made, as mentioned here, in the Euler’s
column theory.

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**

The column
will be initially perfectly straight and load will be applied axially.

Column
will be initially perfectly straight i.e. column is not bend before loading but
also column will be completely straight before loading.

Load which
is applied over the column will pass through the axis of the column i.e. load
will not be eccentric.

###
**Second
assumption**

Material
of the column will be homogenous and isentropic.

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

Homogeneous
term is used here to indicate that material of the column will be same
throughout or we can say more specifically that material composition of the column
will be same throughout the column i.e. material of the column 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.

###
**Third
assumption**

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

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

###
**Fourth assumption**

Direct
stress developed in the column will be very small as compared with the bending
stress.

When a
column will be loaded axially, there will be produced compressive stress in the
column as one end of the column will be fixed and load will be applied axially
on the other end of the column. But this compressive stress developed in the
column will be negligible as compared to bending stress.

In simple,
we can say that Euler had neglected the direct compression of the column.

###
**Fifth
assumption**

Length of
the column will be very large as compared with other dimensions of the column i.e.
length of the column will be very large as compared with lateral dimensions of
the column.

###
**Sixth
assumption**

Self
weight of the column will be negligible i.e. Euler had neglected the own weight
of the column.

###
**Seventh
assumption**

Column will
fail by buckling alone

###
**Eighth
assumption**

Cross-section
of the column will remain uniform throughout the length of the column.

We will
discuss failure of column and difference between column and strut in the category of strength of material in our next
post.

###
**Reference:**

Strength
of material, By R. K. Bansal

Image
Courtesy: Google