450 Câble avec une charge : résolution avec i-Cremona

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來自 École Polytechnique Fédérale de Lausanne 的課程

L'art des structures 1 : Câbles et arcs

24 個評分

École Polytechnique Fédérale de Lausanne

L'art des structures 1 : Câbles et arcs

24 個評分

L'art des structures propose une découverte du fonctionnement des structures porteuses, telles que les bâtiments, les toitures ou les ponts. Ce cours présente les principes du dimensionnement et les structures en câbles et en arcs. Un deuxième cours présente les structures en treillis, en poutres et en cadres. Après avoir suivi ce cours, vous serez capable d'identifier les structures en câble, en arc et en arc et câble. Vous pourrez déterminer les efforts dans les éléments de structure principaux et procéder au choix de leurs dimensions en fonction du matériau de construction choisi. Votre maîtrise des constructions de statique graphique ainsi que de l'applet de calcul i-Cremona vous permettra de comparer diverses solutions et de choisir la forme la plus appropriée pour un type de structure donné. De manière générale, vous pourrez, en observant les structures autour de vous, reconnaître leur mode de fonctionnement, expliquer le choix de leurs dimensions et de leurs proportions.

從本節課中

Câbles avec une charge

Les câbles sont le premier type de structure que nous abordons. Il est très important que vous compreniez parfaitement toutes les leçons en rapport avec les câbles, car les concepts et les constructions graphiques que nous dériverons seront réutilisés dans toutes les leçons suivantes du cours. Nous commençons par le cas le plus simple, celui des câbles avec une seule force. Sur la base des conditions d'équilibre dans le plan, nous obtenons les efforts dans les divers tronçons du câble ainsi que les forces aux appuis. Il est ensuite possible de dimensionner le câble.

400 Les câbles2:17

410 Câble avec une charge centrée21:16

430 Câble avec une charge excentrée17:37

450 Câble avec une charge : résolution avec i-Cremona5:13

與講師見面

Olivier L. Burdet
Dr
Laboratoire de Construction en Béton
Aurelio Muttoni

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.

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