Hello, in this video, we will see the
concepts of internal force and of stress which
will enable us to understand what
happens inside the components of a structure.
On the basis of the example of a person,
standing on a stool, we will see how
the weight of this person is in
equilibrium with the gravitational force that this
person exerts on Earth, through the stool.
In this video, I stand up on a stool.
My weight of 800 Newtons is not directly borne by the ground anymore.
It is obvious that I still exert a gravitational
force on Earth of 800 Newtons too.
Then, these two forces must be in equilibrium.
But now, between us, there is the stool.
In order to sketch rather than to look at myself on the stool, we can
simply, sketch.
I am standing, on the stool which is directly standing, on Earth.
Acts on me, my weight, a gravitational force of 800 Newtons.
Acts on Earth, the gravitational force that I exert on
Earth, which is equal and opposite, of 800 Newtons.
And now, what interests us in this lecture, is what
happens, is what happens inside the stool ?
To answer this, we are going to isolate three free-bodies.
One for the man, one for Earth.
Well, it is not complete, but we include all Earth below.
And then, finally, one for the stool.
The forces that we
already know, are the weight of the person, 800 Newtons, and the gravitational
force that the man exerts on Earth, of 800 Newtons as well.
For that free-body "man" to be in equilibrium,
it is necessary that the stool exerts on him,
a force equal and opposite to his weight
of 800 Newtons, and on the same line of action.
Thus,
we have, here, 800 Newtons which are
the stool's effect on
the man. Likewise, below the stool,
we must have a force of 800 Newtons
which is the effect of the stool on the Earth.
Our two free-bodies of the man and of the Earth are now in equilibrium,
and now we have to deal with the free-body of the stool.
The stool is subjected to a
force of 800 Newtons which is the effect of the man on the stool.
And then, below,
also to a force of 800 Newtons which is the effect
of the Earth on the stool. If we disregard, what
is a reasonable hypothesis, the weight of the stool,
we can see that the stool, which has no weight, is nevertheless
subjected to forces which pass through it. These forces, inside
a structure, we call them internal forces.
This is the way I give you the following definition : an internal force is
a force inside
a structure. And, to be able to see
this force, it is necessary to use a free-body.
Then, we say that it is... this force is
revealed by the cut of a
free-body. Looking at an example,
hum, of a man who is now on the top of a column.
His weight is still 800 Newtons. And if we draw
a free-body which passes just under his feet,
it is obvious that, there must be an internal force in the column, of 800
Newtons, upwards, for the the man to be in equilibrium.
Thereafter, once again, we are going to... it is a little bit
less easy to admit, but we are going to do it anyway.
We are going to disregard the weight of the column.
If I take a free-body, in the middle of the column,