Likewise, the internal force in the lower bar

is given by this same part of the graphical construction,

sometimes with additional elements, but most of the time directly.

We can see that the order of magnitude of these internal forces is again the same.

If we look at the internal force in the right part of the truss,

it is given on the upper part

of the construction.

And again, the values are quite similar.

There is a big similarity

between the results obtain for the arch-cable

and the various types of trusses which we have seen till now.

Don't forget that these structures obviously have the same span,

the same height, and they are subjected to the same loads.

In this diagram,

I have gathered together the resolution for three trusses :

the truss with 5 nodes which we have already seen together,

a truss which is similar to the first one but with half the height

and a truss which is also similar to the first one but with twice the height.

As before, let's look at

what happens in the Cremona diagram.

Here, we get the internal forces in the left diagonal

which is the most loaded.

When we divide the height by 2,

we can see that the horizontal scale turns out to be the double.

However, the vertical scale is defined by Newtons.

The loads being the same, this vertical scale remains identical.

Horizontaly, the drawing lengthens, which means that the triangle becomes flatter.

What we can see is that these elements here,

the horizontal elements, got twice longer

so the internal forces double from 10.1 to 20.2N.

However, in the diagonal, we go from -20 to -26N

because, trigonometrically,

the hypotenuse increases less than the cathetus which doubles.

In a similar way, if we take an interest in the right part,

we have doubled the height of the truss and we have kept the same vertical forces,

this triangle becomes much smaller, actually half size,

it is classical, we go from 10.1 to 5.1N, it is a rounded 5.05,

then we decrease the internal forces in the horizontal elements

by a factor 2.

However, for the diagonal elements,

the internal force goes from 20.2 to 18.2, in compression, reciprocally.

As we had already seen it for the arch-cable

and for other types of structures,

the height that we give to a truss has a big influence.

If the figure becomes smaller, less high, the internal forces increase.

That means that we will use more matter.

If, conversely, the structures becomes higher,

the internal forces decrease and we will be able to save matter.

In this lecture,

we have seen that the truss with 5 nodes is statically determinate,

we have solved it

starting by a node on which there was support forces.

These support forces are independantely determined.

We have determined the internal forces for each of the bars of this truss

and we have compared them, on the one hand, to the ones

of the other types of structures which we had seen till here,

the arch-cable and the various types of trusses with 4 nodes,

and then we have carried out a variations study,

changing the height.

We have seen how this change of height

had repercussions on the Cremona diagram

and thus on the internal forces which act on the structure.