Hello, in this video, we are going
to see how to use the applet i-Cremona to obtain, in the same way that we
obtained them with the graphical statics, the internal forces in a
cable subjected to a load, as well as the forces at the supports.
So, we will successively see how to introduce a
load, this, you have already done it, how to introduce
a support, you have also already done it.
Then, we will see how to activate the funicular polygon
and how to control it, that is to say to give it the proper geometry.
Then, we will see how to read with the applet,
the internal forces which act on the structure.
In this applet, we have, as background, the
configuration of the cable with a centered load in the middle.
We introduce
both supports, one on the left, the other one on the right.
Let's try to accurately place them where the real supports are
and we introduce, as a force, in the middle, a load of 10 Newtons.
We can place it a little bit above the chain, we can
place it below the chain, we can place it in a symmetric way.
Anyway, when we move a load on its line
of action, it does not have any influence on the solving.
We now activate the button "funicular polygon" of the applet
to activate the automatic solving, by the Cremona method.
By default, the resolution starts from the first
support which we have introduced, it is the support here, on the left,
the one which, in our case, has a small
vertical line, the other support does not have any small vertical line
inside. That is from this support that the
slope is defined at 45 degrees by default in the applet.
Obviously, this is not that slope which interests us here.
So, we are going to use this button, the red ball,
which has the function to define the initial tangent.
We click once on this button, it stays pushed down, you can see, it has a gray tint.
Then, we come
here on the polygon, we click on it, we keep the
button of the mouse pushed down, and we can now move the polygon, and
you can see that we can move it until it is
exactly superimposed on the chain that we had on the blackboard.
You can see on the right, the Cremona diagram
which has been materialized, we recognize
the force of 10 Newtons, both internal forces of roughly 7 Newtons.
If we place the cursor on the intersection of both segments, we can see, in yellow,
the solving which enlightens on the right part,
that is to say, the three internal forces or forces which correspond to this configuration.
If, on the contrary, we place the cursor approximately in the middle of the segment between the support and
the first load, we can see that, on the right, this force enlightens in yellow,
and, its magnitude, which is not exactly 7, as we had it in
the accurate solving, but 6.81 and 6.96 on the right.
This is a small uncertainty but
which is not a particular problem.
We can, for example, make a parametric study,
that is to say that we are going to add a second load of 10 Newtons.
So, you can see that now, in the construction,
there are two loads on top of each other.
And, the internal force is now equal to 13, roughly 14
Newtons, which corresponds to what we have already seen.
In this configuration, we have as background,
the configuration of cable with an inclined and eccentric load.
We introduce
both supports, as usually. A load of 10
Newtons, which we position somewhere on the line of action of the force.
We now have to make it rotate.
If we activate the button "control" and if we grasp
the tail of the force, we can
rotate it without changing its magnitude and then, we
line it up quite well on the line of action which
we wanted to get.
We now activate the funicular polygon.
We must deactivate the button "control", otherwise we
will have some troubles. We click on the button "funicular
polygon" and on the button "initial tangent" to give
to our cable, the exact shape which we were looking for.
And we obtain the internal forces, on the left of 4.4, it was 4.5 before
if I remember well and of 8.47 instead of 8.5.
So, it also works very well, like the various other functionalities.
In this video, we have seen how
to use the applet i-Cremona to obtain the internal forces
in a cable with a load, whether it
be vertical or inclined, or whether it be centered of eccentric.
We have seen how to introduce the
fixed supports, how to introduce the load,
how to rotate the load for it to corresponds to what we want to do and
we have also seen how to activate the
funicular polygon and how to control its geometry.
Olivier L. BurdetDr
Aurelio Muttoni
