310 Résultante de deux forces concourantes

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來自 École Polytechnique Fédérale de Lausanne 的課程

L'art des structures 1 : Câbles et arcs

23 個評分

École Polytechnique Fédérale de Lausanne

L'art des structures 1 : Câbles et arcs

23 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

Equilibre dans le plan

Après avoir vu comment les structures unidimensionnelles (sur une seule ligne) sont en équilibre et peuvent être dimensionnées, nous passons aux structures bidimensionnelles, qui se situent dans un plan. Les conditions d'équilibre sont présentées.

310 Résultante de deux forces concourantes4:54

320 Equilibre de trois forces15:45

330 Frottement12:33

350 Tir à la corde11:30

360 Equilibre de trois forces : résolution avec i-Cremona4:26

與講師見面

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

Hello.

In this video, we will introduce the concept of resultant,

and we will see how to get the resultant of two converging forces.

The resultant of two or several forces, is a force whose effect

on the structure is the same than the one of the group of force which we consider.

That is to say that this force, it will have as

magnitude, the vectorial sum, the magnitude of the

vectorial sum of the forces, and we will see

how to determine the position of its line of action.

We have here an example of a real system with

two forces, force one, and force two.

We also want to draw

to better see it, the line of action of each of these two forces.

I drew, on the left, these two forces with their accurate position, and their

magnitude, although the magnitude does not need

to be necessarily accurate in the real system.

And then, on the right, in the polygon of forces, I am going to copy

these two forces with their accurate

magnitude, to construct their vectorial sum.

So, force number one,

first, then force number two.

The resultant of these two forces,

is simply constructed like the vectorial sum.

And, we denote, usually, the resultant by R.

For the rest of this course, I will use

very generally, the color orange to identify the resultant.

Now, we have got the magnitude of this resultant.

We can measure it in centimeters, since we actually have a

scale drawing in the polygon of forces on the right.

But now, the question is, where does this resultant act ?

Well, we want it to act

so that it produces the same effect than the two other forces.

Thus, we cannot make it act anywhere,

we have to determine where its line of action is located.

So, I am going to draw the direction of

the line of action in the polygon of forces.

And now, we want to copy this line

of action in the real system. And for these two forces

to have the same effect on the system, it

is necessary that this line of action should pass by the intersection of

of the lines of action of

forces one and two, in the real system.

Thus, we have, here, this intersection, between the

lines of action of force one, and force two.

And we get, in this way, the line of action of the resultant.

And we can, of course, copy this resultant with

its magnitude, which we will have measured in the polygon of forces.

So, but as we do not need to draw it

to scale, here, it is enough to copy it in this way.

Of course, you can see that there is a limitation to this construction.

It is that both forces should be converging.

That is what we had in the title of the lecture.

We will revisit

several times the theme of the resultant, particularly for the case of

several forces, and for the case of forces which are not converging.

For example, forces which are parallel, or else which

would cross, let's say outside of our sheet of paper.

We have seen in this video, that the resultant

is obtained by making the vectorial sum of the forces.

But, for the

resultant to have the same effect, we also have to

take into account the intersection of the lines of action of the

forces, which will enable us

to determine, one point on the line of action of

the resultant, with which we will be able to trace in the real system.

I repeat, in the real system, we draw the position of the forces to

scale, but the forces

do not need to be necessarily to scale.

In the polygon of forces, the

forces must be drawn accurately to scale,

and obviously, with the good orientation.

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