Hello.
We start today the lecture on the arches.
When we talk about this kind of structure, we often think about the vaults of Antiquity.
What you can see here, for example, they are
vaults of the Roman thermal baths which have been built around
twenty centuries ago, by builders who did not
know the principles of statics and who did not know,
of course, how to calculate the structures.
The purpose of this lecture today is precisely to learn these principles.
The experience of builders of Antiquity were particularly based on what
they have seen during the construction of the vaults, and
also during the collapsing of these structures, indeed there
were lots of them which collapsed in the past.
We have here a model which reproduces quite well a masonry vault.
We can see,
very well, for example, how such a vault can deform.
We can see here, for example, that we have the opening of
joints between the arch stones which compose the vault, and we can
see very well by where passes the pressure
line, that is to say the internal force inside the vault.
The study of the geometry of this pressure line is
fundamental to understand what is the ideal shape of a vault.
And that is what we are going to study, in this lecture.
That is from the moment when we have better
understood the functioning of this type of structure, that
we have developed graphical and analytical tools
which enable to determine the ideal shape of the vaults.
And it is from this moment that the architects and the engineers
have been able to design structures as for example the arch that you can see here,
it a structure of the 19th century, no longer only based on the experience,
but also on graphical and analytical methods.
It has also enabled to progress
towards much thinner structures like the reinforced
concrete shell that you can see here, it is only
a few centimeters thick, or this one, it is also a reinforced concrete
shell of ten centimeters thickness, which I have designed a few year ago.
The learning center, this structures that the students
of EPFL know very well, it is also an example
of reinforced concrete shell which works exactly with
the principles that we are going to study in this lecture.