Strain - Mechanical Properties of Solids Video Lecture - Class 11

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Part 2 before going ahead with part 3 so
now that we have covered stress and the
different types of stress we will move
on to strain what is strain so stress
and strain are very much related to each
other
so what is strain it is measure of
deformation of representing the
displacement between particles in the
body related to a reference length so
what a strain strain is a measure of
deformation so what the strain strain is
a measure of deformation representing
the displacement between particles in
the body relative to a reference length
what does this mean it means that just
now if we talk of stress what happened
when we have between a stress was
applied because of the stress we found
that there was some deformation in the
body you know there was a change in
length or there was a relative motion
between the opposite faces of the body
or there was something like contraction
of the body so there was some or the
other change in the shape of the body
either in terms of length or in terms of
displacement so strain is nothing but a
measure of the deformation that means
how much change in the shape in space so
strain basically measures what how and
what was it initially and how and what n
is now so that measurement is done by
strain so strain is a dimensionless
quantity because it is a ratio of two
quantities for example if we take the
example of the cylinder when you stretch
it from both ends the length increases
that is initially the length was this
much right now after being stretched the
new length
this much L - use this much so this
change in length is determined by strain
now while it strain a dimensionless
quantity that is because strain is
basically it is basically used to denote
the change in length AB divided by the
original length originally the length
was L the change in length is Delta L
which is equal to L dash - L divided by
L right so since it is the ratio of two
lengths therefore it is a dimensionless
quantity because both change in length
and length will have the same dimension
now we look at the types of string so
very similar to the types of stress we
have three types of strain longitudinal
strain shearing or tangential strain and
volume string it is very easy to
understand each of them because we have
already discussed the types of stress so
now let us discuss each of them in
detail so let's start with longitudinal
strength
what is longitudinal strain it is
basically the change in length to the
original length of the body due to
longitudinal stress that means when we
apply longitudinal stress in our body
there is a change in length of the body
that means either the body elongates or
the body gets compressed so longitudinal
strain basically measures to what extend
the change of length of the body of cut
that means longitudinal strain is equal
to change in length divided by the
original length for example the cylinder
gets elongated so let us suppose
initially the length was any after
elongation the length becomes L dash so
what is the change in length the change
in length would be a dash minus L so the
strain in this case is equal to Delta L
by M so you can you can understand it if
in this way that stream occurs as a
result of stress when there is a stress
we'll be a strain now let us look at
shearing strain very similar the name
itself might be telling you what is
happening right so shearing strain is
nothing but the measure of the relative
displacement of the opposite faces of
the body as a result of shearing stress
so what happened it just recall quickly
in your mind what happened during
shearing stress and shearing stress you
applied a force parallel to the cross
sectional area because of which there
was a displacement there was a relative
displacement between the opposite faces
right so this strain that the shearing
strain will measure the relative
displacement of the opposite faces it
will be a measure to what extent that
opposite faces opposite faces got
displaced relative to each other so
mathematically how can we write it let
us suppose initially this was the
position of the cylinder right now this
is the position of the cylinder
initially right now what happens the
cylinder gets displaced that means it
gets displaced by some angle theta let
us say this angle is Theta that means
initially it was something like this
later it got displaced by some angle
theta right and it is suppose this small
displacement which takes place is say X
so if this small displacement this
relative displacement is X and this
angle is Theta and let us suppose
initially the length of the cylinder was
L initially the length of the cylinder
was L so how do we define sheering
stream
shearing strain will be equal to the
relative displacement that is X divided
by the original length which was L so X
by L we can be also defined shearing
strain as this is equal to tan theta
because if you consider this angle as
theta so basically tan theta will be
equal to this X by L right so since this
theta is very very small since theta is
very small so we can say that tan theta
is approximately equal to theta
therefore whenever we talk of shearing
strain is a shearing strain is equal to
the relative displacement which takes
place that is X divided by L that is
original length or this is equal to
theta so this basically describes the
shearing strain in a body now let us
look at volume stream volume strain is
the ratio of change in volume to the
original volume as a result of hydraulic
stress as we saw in our example of
hydraulic stress when the stress is
applied or when the external force is
applied by a fluid there is there occurs
some change in volume of the body
without any change in its shape like we
saw the example of the ball what
happened to the bone initially this was
the bone was whatever shape it was it
was very clean shape after it went
inside the water because of the brake
force exerted by the water it contracted
that means the volume decreased so let
us suppose initially the volume was V
but after going inside because of the
hydraulic stress the volume reduced the
volume became free - that means there
was a change in volume which is given by
the initial volume minus the final
volume so there was some decrease in
volume so what is volume strain it is
basically the change in volume divided
by the original volume right so you saw
that in all the three cases the measure
of the deformation is done by strain
and stresses stress is the force per
unit area which causes the deformation
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