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. concept of eccentric loading with the help of this
post. 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.

###
**
Concept
of eccentric loading**

Eccentric load is basically defined as the load
whose line of action does not pass through the axis of the column, but also
line of action of load passes through a point away from the axis of the column.

In simple, we can say that when a load will act away
from the axis of the column then that load will be termed as eccentric load.

Distance between the axis of the column and line of
action of eccentric load will be termed as eccentricity and eccentricity will
be indicated by e.

Now let us consider one column, as displayed in
following figure, which is fixed at one end and let us apply one load P to the
other end of the column at a distance e from the axis of the column.

In simple, we can say that column will be subjected
to an eccentric load as we have discussed above and line of action of this load
will be at a distance e from the axis of the column.

We have following information from above
figure

P = Eccentric load which is acting at a
distance e from the axis of the column

A= Area of cross section of the given
column

Area of cross section of the given
column = b x d, (For rectangular cross section)

b= Width of the cross section of the
given column

d= height or depth of the cross section
of the given column

I is the area moment of inertia of
the column rectangular section across the axis YY

I = db

^{3}/12
M = Moment formed by the load P

M= P x e

e = eccentricity of the load P

As we have already discussed that when a body will be subjected with an axial tensile or axial compressive load, there will be produced only direct stress in the body. Similarly, when a body will be subjected to a bending moment there will be produced only bending stress in the body.

Now let us think that a body is subjected to axial
tensile or compressive loads and also to bending moments, in this situation
there will be produced direct stress and bending stress in the body.

In case
of eccentric loading, there will be produced direct
stress as well as bending stress in the column.

As load P is acting over the column in downward
direction and other end of the column is fixed and hence there will be developed
direct compressive stress in the column.

###
**Direct stress**

Direct compressive stress developed in
the column

_{ }= Axial applied compressive load/ Area of cross section of the given column
σ

_{d }= P/ A
σ

_{d }= P/ (b x d)
Unit of Direct compressive stress = N/mm

^{2}###
**Bending
stress**

There will be developed one bending moment too because of eccentric load P which is acting at e distance from the axis of the column and that bending moment will be formulated as M = P x e.

Due to this bending moment, there will be developed
bending stress too in the column. Recall the concept of bending stress and we will write
here the expression for the bending stress developed in the body.

Where y is the distance of the point from neutral axis where bending stress is to be determined.We will see derivation for differential equation of elastic curve of abeam in our next post

Where y is the distance of the point from neutral axis where bending stress is to be determined.We will see derivation for differential equation of elastic curve of abeam in our next post

###
**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google