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