In our previous topics, we have seen
some important concepts such as Concepts of direct and bending stresses,
Middle third rule for rectangular section, Middle quarter rule for circular section, shear
stress distribution diagram and basic
concept of shear force and bending moment in our previous posts.

Now we will start here, in this post, another
important topic i.e. Deflection of beams and its various terms. If a beam will
be loaded with point load or uniformly distributed load, beam will be bent or
deflected from its initial position.

We will first discuss here the terminologies and
various terms used in deflection of beam with the help of this post and after
that we will see the amount by which beam will be deflected from its initial
state and also slope of the deflected beam under the action of load in our next
post.

So let us come to the main topic without wasting the
time and let us see here various terms used in the concept of deflection of
beam. Because without understanding the terms used in the deflection of beams,
we will not be able to secure the amount by which beam will be deflected from
its initial state and also slope of the deflected beam under the action of load.

Let us consider a beam AB of length L is simply
supported at A and B as displayed in following figure. Let us think that one
load P is acting at the midpoint of the beam.

As beam is loaded with load P at
the center of the beam and therefore beam will be subjected with bending moment
and hence beam will be bent or deflected from its initial position under this
load P.

###
**Deflection**

As we have seen above that beam is loaded with a
load P at the midpoint of the beam and hence beam will be subjected with a
bending moment and therefore beam will be bent in the form of a curvature or in
to a circular arc.

We have shown the initial position of the beam i.e.
before loading as ACB and deflected position of the beam i.e. after loading as
ADB.

Now the vertical distance CD will be termed as the
deflection of the beam under the action of the load P.

####
**
Let us define the deflection of the beam**

Deflection of beam is basically defined as the
vertical distance of beam measured before and after loading. Deflection of beam
will be denoted by “y” and its unit of measurement will be mm.

###
**Elastic
curve**

As we have seen above that beam is loaded with a
load P at the midpoint of the beam and hence beam will be subjected with a
bending moment and therefore beam will be bent in the form of a curvature or in
to a circular arc.

Curvature or circular arc of the beam, formed under
the action of load, will be termed as elastic curve.

Therefore, curvature ADB of the beam will be termed
here as elastic curve.

###
**Slope**

Slope in deflection of beam will be defined as the
angle turned by the beam under the action of load and hence under the action of
bending moment.

Slope in deflection of beam will be basically
defined as the angle made between the tangent drawn at the elastic curve and
original axis of the beam.

Slope will be measured in radian and will be
indicated by dy/dx or Î¸.

We will see the amount by which beam will be deflected from its initial state and also slope of the deflected beam under the action of load in our next post.

Please
comment your feedback and suggestions in comment box provided at the end of
this post.

###
**Reference:**

Strength
of material, By R. K. Bansal

Image
Courtesy: Google