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.
535 Systèmes de prétension
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From the course by École Polytechnique Fédérale de Lausanne
L'art des structures 1 : Câbles et arcs
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From the lesson
Câbles avec charges réparties
Les câbles avec charges réparties sont des câbles soumis à une charge qui agit partout sur la longueur du câble. C'est le cas par exemple du poids propre du câble, que nous avons négligé jusqu'ici. Il est possible de résoudre ce cas en remplaçant la charge répartie par un grand nombre de charges ponctuelles.
Meet the Instructors
Olivier L. BurdetDr
Laboratoire de Construction en Béton
Aurelio Muttoni
Hello. We have seen in the previous video
that a pretensioning cable is an efficient system to stabilize a cable.
In this video, we are going to see some
additional examples about shapes that the pretensioning
cables can take, particularly
we will finish with an expansion to the
third dimension, which is very interesting, since it
offers the possibility to cover spaces.
In this previous video, we have seen that the combination of a
load-bearing cable, we cannot really see well here, and
of a pretensioning cable, enables
to stabilize
a structure, decreasing its deformations,
which happens, for example, during
the accumulation of snow or when the wind blows on the roof.
Here, we have another example which
is a small concrete pedestrian footbridge.
The structure itself, it is a concrete strip,
we call it a ribbon, which is very,
very thin, and then its weight would not be sufficient
to limit the vibrations created by persons crossing it.
It is also very thin, which means that its stiffness is not enough
to consider it as a stiffening
beam, at least not completely.
So, what we have, in addition, on this footbridge,
is a stiffening cable, we see
it better here, in the elevation. Thus the footbridge itself,
the concrete part, in which there are cables, is in tension.
It is the same solution than the solution used
by Freyssinet for the Youth House in
Firminy-Vert, except that in this case here, it has been
designed for the people to walk on the cable,
and, as in the solution of the cables beam, the stiffening
is providing by a number of small diagonal cables, but
all these cables being in tension, are almost invisible,
if we look at the photo, it is difficult to distinguish them.
Here, we can see in the lower part that the construction
to which the cables are anchored is also monolithic, and is
fixed to the rest of the abutment, but it could be independent.
We can thus have a system of
independent cables which also stabilizes a cable which needs it.
This configuration, with multiple cables, which
is characterized by a significant transparency,
has been used for greenhouses, that is to say places which need to let
enter a maximum of light. They are vertical elements
which are essentially exposed to the wind pressure.
The effect of the wind is a pressure
which has the kiloNewton per square meter as unit of measure, we are not going to
make any calculations here, but there are two types of configuration.
When the wind blows towards the facade,
we have a pressures which presses where the
wind presses on the facade, and in this case,
the structure which we have here horizontally
works in the following way : the cable which is inside, I draw it
in red, it is the load-bearing cable, and
the cable which is outside, I draw
it in orange, it is the pretensioning cable.
Then, between these two elements,
we have here compression.
If, reversely, the wind blows in the other direction, we
have an effect of suction, then the wind pulls on
the facade, it can be a very important effect, especially
for lightwight structures like this type of glass facades.
Then, we have an inversion of the internal forces, the load-bearing cable becomes
the one which is outside,
and the cable inside
works as pretensioning cable. The
elements between these two cables
are still in compression.
If we consider the rest of the length of
these elements, when the wind presses on the facade, these elements are
in compression, these small elements here, as well as these
parts here, while if the wind pulls on the facade, the elements are in tension.
We can see that we have a part of the element which is in
compression, and the other part which is in tension, it is absolutely possible.
Note that
for these loads to be vertically transfer into the ground, we have on the left and
on the right, maybe I am going to draw them in pink to avoid
the confusion, we have on the left and on the right, similar structures which
also work with pretensioning cables and load-bearing cables.
This structure is a much more complex
structure in which we really use the third dimension.
It is
the Olympic skating rink in Munich, built in 1983.
First, there is an element which we have not seen yet in this course,
but as we are going to see it very soon,
it is not a problem to introduce it.
It is an arch, an element which works in
compression, that is why I draw it in blue.
Afterward, we have a series of cables.
The cables which have curvature upwards
are load-bearing
cables. And,
to prevent their movement, they are stabilized by cables
which pull downwards, which are thus pretensioning cables.
With all this, we have a network of cables which cross each other, but we do not have
yet something which enables us to
be sheltered to attend a match of
hockey, and we can see in the picture on the right how it has been solved, we have put an
fabric, above this network of cables which
has hugged its shape and which offered watertightness
when it was raining and where it was snowing, the spectators under were
not wet, since the water was evacuated onto the edges.
There are also some elements whose we did not have seen the function.
All the load-bearing cables and the pretensioning cables, are anchored into
the edges, into these cables that I draw here in green, which are
edge cables.
They are normal cables which are subjected to forces which comes
from the internal forces in the load-bearing and pretensioning cables, and which
are themselves supported by a system with elements here in tension,
and elements
in compression. We maybe should also add that there
are also here edge cables, and small hangers
which hang up the ends of these cables to the edge of the arch.
With this, we have explained how this part here works.
You can notice that there are lots of cables,
and this, it is a problem with this kind
of constructions, knowing that in addition, it will be necessary to carry out,
to avoid that it moves, it will be necessary to carry out
connections at the intersection of each of the cables.
Thus, it becomes a relatively complex construction, and we have
quite quickly searched how to simplify it, and this is the way we can
simplify it : instead of using a real network of cables, we can directly
use the fabric which we envisaged to stretch above as bearing element.
Obviously, it will be necessary to reinforce it. By the way, we can notice that there
are reinforcing bands in the fabric I have taken
here as illustration, but let's look at the
various bearing elements of this structure.
We have a central pillar, which goes up until here and which hold this ring.
We also have inclined lateral pillars,
also one here, an so forth. We have cables which catch hold of
these pillars. It looks a lot like the details which we
had on the edge of the skating rink of Munich. We also have edge cables.
And then, all the rest of the structure
is constituted by this membrane,
which is made in a fabric which can resist to
tension in several directions, there is tension in the direction where
we would normally have load-bearing cables, and then we also have
tension in the direction where we would have pretensioning cables.
Altogether this yields a quite light structure, very
transparent since it has just very few
bearing elements, and the construction
cost is also radically lower since we did not have
had to make all these cables and all these intersections of cables.
We are going to summarize here the various pretensioning systems which we have seen.
The first solution with an external cable and hangers in tension.
The second solution that we have seen for the greenhouses
of the "Parc Citroën", we have a second cable, which uses the same supports,
and then connecting components which are in compression.
The third solution, it is a combination of these
two solutions, that is to say a cable which is sometimes below,
so with hangers in tension, sometimes above, so
with elements in compression to transfer the pretension.
Fundamentally, it is a solution between the first one and the second one.
We can also have a solution in which we call on external supports,
to anchor the cables which are going to stabilize the structure, and finally,
we can call on a three-dimensional system, as we have seen it.
(here I make a sketch which looks a little bit like a camping tent,
but it can be something more sophisticated as you
have seen it), which enables the stiffening by means of networks of cables
or of membranes.
In this lecture, we have seen how to stabilize a cable by means of various
pretensioning system, noticing that we could use multiple
cables, and position them in various ways
in relation to the load-bearing cables, it
had as consequence that we would have either
hangers, either elements in compression
to introduce the internal forces.
We have also seen that it is possible to make a three-dimensional stabilization
using cables which are not on the same plane, but which are on
perpendicular planes to the load-bearing cables, and
that we can even use a
membrane system, which is a well stabilized
system when it is put in tension.
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