Arquitectura y Estructura: clase magistral de Ricardo Aroca

well good morning everyone good morning again most of us have seen each other since eight thirty we have the honor of having

ricardo

aroca

here because many of you because you are very young have not had the luck that others have had to have him as a teacher and as always We told you that he has taught us to love to be interested in the world of architectural structures, Riccardo Aroca and in summary, because what we want is to hear from him, you know that he has been a professor of structures at this school, he has trained many generations in that structural affection and he has been director of the school has changed many things in the school we were talking about the bar which was a parking lot that was a bit ugly not good he has been dean of the college of architects he has won many awards he has built a lot and he has had that generosity of teaching he is the author of tremendous books attractive things, not that they ask him to write, like the secret buildings of Madrid or the magical buildings, among many other notebooks of articles and everything, and well, he is always in the spotlight and will also tell us the latest news about the building in Spain.

Well, everyone, welcome. hitmen well to serve as advertising now I am writing something that I have been commissioned to call what is the use of an architect I hope that people learn to rely more on architects well first of all thank you for the invitation that five years after having left this house, they still sometimes call me to continue talking and thanks to you, for let's say act as an audience because it really is depressing to be talking when there are no people who can hear you. Well, they have asked me to do a lesson. which was already there last year, as I have never been able to teach the same class twice because if it doesn't interest me, then I suppose that the others don't either.

It's not a little changed from the previous version, I hope it has improved and within five In today's topic I will deal with a series of questions that are of the type that came before the chicken or the egg. We really tend to think that we think and then we say the Things that we have really thought are not at all clear. It is much more likely that we are capable of thinking because we know how to speak. Let's say that language is really not only the vehicle of thought but is the very essence and the very construction of thought happens.

The same with another series of things as we will now see, that is, you think about being educated as you are currently, in that when you are doing a project, first you have an idea and then you draw it and then you even build it, well out there it is not even the architects who They built it but the life of some drawings and then there are others who really build it. It has never been like that. It is not architecture that has not been drawn towards the Renaissance, that is, towards the Renaissance. It has been built without drawing.

No, drawing applied to architecture did not exist. and therefore it was built in a different way, fantastic buildings were built but no one drew the building before to build it, it was when perspective and the means of representation were formalized that painters began to actually like those that had been drawn by painters at a time After all, the painters replaced the architects and the builders because the painter could not make a drawing of what he was going to do and then get the order even if he did not know how to build it, then a little later in the 16th at the end of the 16th they started again the agents who built knew how to draw and things were channeled to those who painted began to know construction but there is a very curious topic, that is, the Renaissance building that many experts or many historians consider to be the most perfect, which is the Charles Palace.

Fifth in the Alhambra is designed and built by a painter who had never built anything before nor had he ever built anything after Machuca. He was a painter. His only work of architecture, well really, the path can be considered in another way, it can be considered the reverse path, which is the one that really followed the evolution of the construction from the materials it was built and from the construction, then the same architecture appears. I am clear about the Ammonian language, just as language is the essence of thought. Construction is the expression of architecture. That is, it is the language of architecture.

In architecture, historically, it is built and then we have learned to imagine it before building it, but for me There it is personally impossible for me to draw something without knowing and thinking at the same time how it is constructed and the language of construction is absolutely essential. I say what I say not because we are in a construction class but because I am completely convinced that it is like that and in In essence, the advantage that Spanish architects enjoy now that many of their colleagues are forced to emigrate abroad is that they know much more about construction than their competitors and therefore they have great success in international studies because there are people who master or have a notion that the language of construction is something is something important this misunderstanding or this issue of precedence that happens with language and language and thought construction and architecture we could say that it also exists to a large extent in the subject of structures in fact structure is something that really has to do with the management of forces but we really don't really know what a force is until Newton at the end of 17 until then there was no idea at all what it was a force then truly has been able to be built and things have been able to be done that are maintained without even knowing that it was a force and then we have learned what a force was and then and then after a series of avatars that I will later refer to well We start things the other way around, that is, we begin to explain to you what forces are and then, well, some with some lines, some springs, some little triangles and all that, that is the end of a story that began in another, in another completely different way, even since or as a consequence of the evolution of 19 in which concrete and new materials appear in steel and then the structural problems are resolved through a skeleton, we even associate the structure with something that physically exists that is a differentiating element of a building when it is not That is to say, the structure is nothing more than what we understand as a structure, it is nothing more than the fulfillment of a series of requirements that have to do with forces, fundamentally gravity, but then with other forces, and in addition, structures are only three things. balance, resistance and rigidity are nothing more than those three issues that sometimes need a differentiated system in a building but sometimes they do not need it.

I usually use the theme of a glass and a plastic glass, so the glass, as you see, is in balance and There is an important notion which is that of stable balance and the table on which it is placed could not be horizontal someone can push it a little so we say that the balance is stable when if it is separated slightly from the equilibrium position it tends to return to it. There is nothing and in that sense it is important in the issue of structures there are no absolutes, that is to say that there is nothing that is stable everything is relatively stable it is stable enough if something is pushed a lot the rigidity falls, well then it is worth it and I give balance the adjective stable because it tends to be understood in normal language when talking about balance when balance is difficult, that is to say, no, a tightrope walker is not called someone who sits solidly on a table, but someone who stands on a table. foot on a stool that is on top of a ball then but really a balance is a stable balance like mine in this case and the balance of the tightrope walker is an unstable balance naturally they have an example of stable and unstable balance or for example well if I place this upright, yes, because it is an unstable balance, the slightest thing falls.

We need stable balances and therefore any type of balance is not enough. Rigidity implies that when a thing is subjected to the conditions of use, it deforms. always but that it does not deform too much is to say that a thing, well, really in the case of the glass, one can even speak of there being a certain question of compromise while in stable equilibrium there is no compromise, a thing has to be stable in rigidity. Well, there may be a certain compromise when you buy that glass because you expect it to be quite rigid, but if you buy much cheaper glasses, then the glass is much less rigid, but since it has cost you less, you accept to pick it up with the edge or pick it up very carefully.

So really there is a margin of rigidity, let's say, of the means against expectations, etc., but well, it is not a fatal thing. The problem is not clear. If you build a house and it falls down, you have a problem, but only one if the house is little rigid and cracks in the partitions you give them the throwers of a lifetime, that is, it has that it is not fatal but it can be frightening in terms of art, they ride then things are reformed more or less depending on the forces that are applied and If they are tightened too much, then they break.

That is resistance. Resistance is not negotiable either. In other words, of the three conditions, the only one that is negotiable to a certain extent is the condition of rigidity. The condition of resistance and the condition of stable equilibrium are not negotiable, so of course. As I said before, from the beginning of 18 we can handle these things with a vocabulary and with the mathematical language that from then on was considered to be the best way to explain the world and the most compact and most effective way, but before those that humans, because anything that has a physical existence, encountered structural problems as nature solves or more resolved its structural problems, because through trial and error, that is, the genetic code has random variations, some random variations improve survival and transmitted to the entire species and over millions of years very final solutions are achieved.

You don't have a bone, look at the calcium carbonate ballast, the very nature of the bone, which is a mixture of rigid calcium carbonate with a series of proteins that give it They give ductility and prevent it from breaking easily, although sometimes the part that has friction and that has direct application of forces breaks. It has a greater density and is even capable of adapting, that is, if you exercise a lot, your bones become harder. If you don't exercise, your bones decalcify, which means that there really is even a certain capacity for adaptation that has occurred or been acquired over millions of years, an adaptation that varies with circumstances.

This is a section of an eagle bone from one of a bone from the wing of a vulture, notice how the vulture flies because then those weigh much less, it is much more hollow and then it has that adaptation. You can find very sharp examples and truly nature produces some fantastic solutions with several limitations. The first limitation is the materials have nature, it is incapable of using metals so it is forced to use calcium carbonate, chitin can improve it from but it cannot, it has not been able to integrate metals into the structural design, so it has lost, let's say, a certain capacity.

It has not even been able to use carbon in the solutions that we now have of carbon fiber or graphene etc. with extraordinary resistance. It has not been able to enter that path. The second issue is that things have to grow, so the The need for growth imposes certain limitations in terms of form, etc., etc., and the third issue is time, that is, our clients cannot wait millions of years for the structural solution of a green project to evolve; there is no choice but to turn to culture. culture is one in the second the first way of transmitting and accumulating and transmitting information has been adn the next the dna the next is the culture the culture has is much faster it can operate on things than on the experience of things that already have been done to others, the development of culture has been so rapid that since writing began a little over three thousand years ago, right now we would be capable of completely destroying the planet, something that nature has not been able to do.

In other words, culture moves very quickly and then culture organizes models, teaches, opens things. You have seen before the east bone of the vulture's wing. If you know that a triangulated beam works, you can see a triangulated beam like Mr. Darcy. tromp are in this that it takes a lot of imagination to see there is a triangulated beam but well to a certain extent what happens is that it is impossible but a triangulated life and if one knows that a triangular beam works by seeing how it really works, then it is said that the The digital camera, above all, works exactly the same as the eye, but the digital camera was not really invented by looking at the eye.

We have understood how the eye works after inventing the camera, so there is always that duality that came first. They have to observe things but they don't really know what they have to look at. It's not that easy to make observations, so culture achieves an accumulation of knowledge and thenIt works better and thanks to culture, we have learned to not only know why the structures that were already being made worked, but we have learned so much about the subject that now, unfortunately for you, we explain them backwards instead of explaining how things are and how they work we explain how they work and then if there is time what these are like the structures hello on the way to resolving the balance of forces well it has a material theme today we are going to talk about that and its relationship with architecture and so for that Well, we will have to dissect what things are important in the structural behavior, so the things that are important are very few, they are only 4 the material, the size and the shape, and within the shape, the scheme and the proportion, that is, with those four words, naturally returning to the The subject of the reverse with those four words, the vocabulary of truth, what matters in structures, independently of the processes of mathematical analysis, is absolutely sufficient to talk about structures.

It would really be the first thing we should tell you when talking to other structures, but it is not what we mean. we usually do what we usually do between one of the things among other things why it has been carried out for many years on the subject because of the difference in interests, let's say, between the teaching group and the student group that you try to find out and that it helps you to projecting to do things the teacher's interest is not to be evident in the class so when one prepares a class what worries one most is not to skip any sign that a cosine is not missing that things work and then they truly are conflicting interests or by at least the coincident ones and that probably means that the teaching process is not as effective as it should be.

On the other hand, an effective teaching process would probably start the other way around, that is, in class one spent time answering questions that The students had not asked themselves so when you have asked yourself a question you understand the answer much better. I remember that for a while and we taught the subject the other way around, that is, first we put the problems and then we recorded the theoretical class. There were very few students at that time. It was the world of specialty and when we began to see more in favor of our physical safety we returned to the usual path of first explaining how things were done and then asking them to do them but that was very effective, having to deal with something without knowing how because then They listened in a really avid way well then let's start from the list of things that I have said with the material the material can be spoken in simple terms about the material talking about bonds if the material is a liquid or a violent pool or a gas well no It has links from our point of view, things move with respect to each other and then the links can be internal and external, that is, a stone or a brick has internal links that make it a solid, let's say manageable, but on the other hand, the external links Because they can only really work against each other, the compression allows a series of issues and on the other hand, the external linking is enormously important on how it can be used to make the link more simple is the compression link the next link plus the compression another action not the next simplest link that shear and then of course the issue of flexion because the possibility of the material internally resisting attraction is required it is because the joint can resist traction it is To these bonding possibilities, let's say with bonds with materials that only allow compression and with the simple compression bond, because you can do the things that can be done with the bond.

There are materials that admit attraction, such as wood, but the bonds can be very complicated. in wooden joints they imply a very important loss of section and then, since very early in history, there have been extraordinarily refined links, that is, look, it is a rope, a thread is made of extremely small fibers, so if the fibers remember the twist it causes them to be compressed the compression produces friction and from very small fibers you can make a rope or you can make a mesh thread that historically have been produced extraordinarily ingenious links have been used and in addition to a non-elementary explanation the next important thing about the material It is the resistance, that is, with what forces the material breaks there, because the simplest in compression are more complicated materials that can resist fractions and then the resistance of the materials offers enormous variability.

There you have rectangles that can resist the same strength of different factory floor materials and concrete or wood that is you is the difference in section as opposed to area that requires some things and others but still in this small box if we make it larger then the steel profiles appear The steel as such, that is, a steel profile, has an apparent area like five times the real area of ​​steel due to instability issues and then lastly you have the cables and I have no longer put the carbon fiber etcetera because it would no longer fit and would force me to make other other other boxes so that the materials have on the one hand the issue of links and on the other hand the issue of resistance and finally the other quality of the materials in rigidity, that is, anything deforms when it is It subjects it to forces and there is a magic number for architecture that is 10 to the power of minus 3, one millimeter per meter, that is, what distinguishes the materials that we use in architectural construction is that they deform less than one millimeter per meter when they are subjected to forces or a milliliter per meter is the standard for steel and wood less than a millimeter per meter because they are concrete and factories, then there are more sophisticated solutions that I am not going to talk about today but I could talk about another time so it turns out that Well, steel, wood, concrete, and reinforced concrete can be handled practically indifferently because although steel is 20 times stronger than wood, it is 20 times more rigid so that a wooden beam has exactly the same depth as a equivalent steel beam in section is not the same but the depth is the same because the deformation under service load is exactly the same in steel as in wood and in iu and in concrete it is not a coincidence that is It is one of the things that the industry owes to us architects.

The architects drew the houses with wooden floors and when they wanted to sell them steel joists they told them, hey, you don't have to change the section of the building and then the architect agreed to change to zero. because I did not have to change the plans, not the same as when they sell plastic laminates, because they sell them with the appearance of wood so that people accept them because if they had something else, people are used to seeing the godmothers, concrete and steel have entered in construction replacing wood and because they could do it because they did not force the architect to change the plans, then the next thing that goes hand in hand with resistance is the size, that is, how the structures influence the size, there is a very easy way to compare the materials, that is, take a material and make a prism such that it reaches the resistance or its service tension at the base due to its own weight.

Yes, this immediately produces a classification of the materials that can be easily done in meters of So the factories allow you to make a prism of 50 or 100 meters high, the concrete of 300 to 500, the steel of 2100, the wood of 1500, that is, this gives an idea of ​​the structural capacity of the materials in a very simple parameter that They are the meters, of course, that's what you would tell them, that is, if a factory can make a tower at a premium between 50 and 100 meters high, there are factory towers that are taller, how can that be done? Well, if you cut the premium by half can be twice as tall if you cut it in the shape of a pyramid it can be three times as tall and it follows a logarithmic scale which is dividing each basic raw height dividing the area by the number which as you all know is 271 82 and in the base of natural logarithms and quantities of things appear by themselves because you can really make a tower of infinite height, it is the only case of a structure of a structural form that does not have the limit, it is in fact the one that whoever wants reasoning that is this short, that is, it is not necessary to go further for the number to appear, the number is as a result of a differential equation, it integrates a linear differential equation, that what they explain to you in mathematics sometimes serves a purpose and very few things of the which explains to them then the possibility was a tower of infinite height because it explains why when humanity tried to make a tower that would reach the sky because God sent them to the confusion of languages ​​so that they could not do it because it was a technically possible company so thank you very skillfully understanding that language was the essence of thought by making people speak different languages ​​because it managed to confuse them and prevent them from finishing the tower and therefore they could not reach the sky and be close to it, so we are left with the last ingredient in the form you can talk a lot about the form but I'm not going to do it, I'm going to do it in the simplest way, that is to say, the materials that we have handled are going to condition three basic types of structures, there really are no more cheeses, that is, when the link It is the only compression link.

The only way to make a structure is to make the balance occur through the accumulation of masses that in turn give weight and then you have to ensure that there are polygons of forces that reach the base that reach within the foundation of the building is the way to build with the simplest things, which are stones, bricks, etc., there are other types of modern structures, which are hanging themes, which is exactly the same but the other way around, that is to say, if a thing has very little, then and with elements that work in traction it works exactly the same as a thing that weighs a lot working in compression with the added problem because if the forces vary the shape changes etc. but this is not the case of today's lesson efe the topic is that there needs to be a balance general and then it is represented up there because the topic of local balance, that is, local balance is very simple and a multiplication of forces always occurs.

As you can see, the internal forces are much larger than the weight than the weight that they try to balance in each of the elements of the structure that we had this first type of structures that are structures that we could call balance and that allow the use of any type of material, stone is used, etc., but historically, the emperor Trajan built a bridge over the Danube River. with wooden arches of fifty-six meters of span, of which the arches still do not remain, but the stone abutments still remain. The author was Apollodorus of Damascus, of whom we will later have the opportunity to talk about the following time about structures.

It is what we call lintel structures require materials that can resist compression and shear traction, requires a material with more ties, historically requires the use of wood, which is the material that can do so, or the use of stone with very short spans with spans so short that practically at the bottom for a stone lintel to work there has to be an arch inside a viable arch inside so that this would be the second type of structures and the third type of structures more sophisticated that everything is also used by the Romans who In Trajan's column, which was made by Apollodorus himself, not only does the Danube Bridge appear, but some triangulated structures appear that the good Don Apollodoro already managed, so here compressed elements coexist that are represented in only compressed forms, it is not necessary that they be of that flexion. and tensile elements and really the conflict of all these things is in the joints.

It is the most effective type of structure, that is, the structure formed by compressed and extended bars is the most effective of all possible structural solutions. If you give me any structure and I I make them an equivalent structure of bars that weigh much less. In fact, it is a normal car. Basically, it is a structural series of sheet metal, a formula one car, since it is a set of compressed and extended tubes with some carbon fiber elements, etcetera, etcetera. so basically we have these three types of structures efe so that we have already talked about material we have talked about the influence of the material on the shape and then it remains in the proportion I am not going to go into a little more theoretical development either but the proportion is an extraordinarily element important, that is, you think and it is generally thought that the important thing about a structure is the drawing of the scheme, it is really more important in the proportion that the drawing has a bad scheme with an adequate proportion, resulting in a better structure than an excellent scheme with an excessively involved either the proportion has to do with the rigidity of the structure it has to do with the stability that is to say it is extraordinarily it is an extraordinarily important element to which we do not dedicate enough space when we are explaining how structures work it isenormously enormously important in fact because until the 19th century the verification that was carried out for the so-called structural verifications that were carried out in architecture were simply summarized in some rules of proportion the rules of proportion that were managed the result of the experience were sufficient to ensure The rigidity and stability of the buildings and in fact they allowed the façade of the Greek temple to evolve from wood by bringing the columns closer to the lintels is to solve the problem of what looks like a transformer house by putting a peristyle gives rise to a completely different thing with they continued managing the proportions they made things bigger or smaller they already knew that if one thing was proportional up or down from something else they had done it worked well that they learned early and they learned it they learned it Soon the same thing works with lintel structures that the same thing works with the arches so that this issue of proportion was the structural lifeline of architecture until Galileo operated an important conceptual change in 1638, exactly, I say a conceptual change because really for a couple For centuries, no one paid attention to him, but really, a Galilean who had just had some problems with the church because things revolved around the sun.

I'm sorry, everyone knew it, but they couldn't tell us if he couldn't write at all, and then they banned him. He did not want him to write any of that, they even put a guard on him so that his soul would not suffer, he would not be condemned and so he dedicated himself to other things and then he made the first book of structures that is within the tell-tale dialogue of the new sciences Galileo called everything into question. Curiously, until the metric system there is no recognized unit system, Galileo He could not speak in 10 inches etc. because the size of the units of measurement differs in each town so he does it in terms of proportion and then he makes the observation that the volume of things and therefore their mass the heights were then known. which was mass but well its weight which was known depends on the cube of the proportion ratio and on the other hand the section depends on the square and so it says that the forces increase more quickly than the resistance and therefore the giants could not have existed does that drawing in comparison of the bones of a large and small animal does not really correspond to the correct relationship it is not that but there was not too much trick in the subject if in this way the bones are placed in a cantilever the proportion is exactly correct but they go The bones are not cantilevered, they are part of other systems.

In any case, Galileo's observation is perfectly correct, from which he deduces that the rules of proportion do not ensure the proper functioning of a structure so that things cannot be be increased indefinitely because they end up seeing a maximum size, which is one of the things that I have talked about in passing before, there is a maximum size except for the tower, there is a maximum size for any type of structure, really, Galileo, the notion of force did not exist. there was the notion of tension and then if they had existed as he was an extraordinarily lucid man he would have said something as simple as 'last the part of the tensions due to the self-weight of a structure increase linearly with size and then how it increases linearly in the Due to its own weight, there is less left for the rest and then there comes a time when things can only sustain themselves and then there are catastrophes that in fact have a limit but in practice nothing has been built except for hanging bridges.

Nothing has been built that exceeds 20 percent of the theoretical maximum size, which is more or less the rule of thumb that I have been able to find at this time. For example, I am not going to dwell on that. If you take a dome, the balance of a dome is very simple. and then the relationship between the stresses and the size of the dome is immediate so that in the extension of a dome it is the density of the material times the radius divided by two and it does not matter at all if the dome is more curious even thinner that is to say If the dome on scales resists more but weighs more and if they comply with it thinner, it resists less but weighs less, the domes are made thicker for reasons of local stability so that they do not rest like a ping pong ball, then from there it is You can find out what is the maximum radius in a factory in a factory dome the maximum radius is between 100 and 200 meters so that the pantheon, which is the largest dome built for centuries, is about 20 percent of the maximum size right now.

We make a steel dome, whether continuous or made of bars, the result is the same because it could have a maximum diameter of about 8 kilometers, so the maximum sizes have always been well above the needs of construction, so it is Galilean because it is not He paid no attention to anyone because he was right but it was not the problem, that is, the things that were being made were much smaller than the maximum size and then Galileo introduced the paradigm of resistance that at that time with the materials that were used was absolutely irrelevant the resistance paradigm begins to be right when you start making skeletal structures with minimum sections etc. then this is the pantheon and this is the observation that I have made before that the resistance was not when when you reach the structure of skeletons, then Galileo's reasoning is taken up and then we enter into the type of structures that we try to teach you in which resistance is important but it has never been, that is, what was important was that the balance was stable and in some In the case of floors, it was rigidity, the paradigm of resistance has never been important, but we have it so deep in our bodies that right now when one of these large consulting firms makes an opinion on a structure of load-bearing walls, it starts to fall into pieces. of walls and do wall resistance tests when the resistance of the wall is absolutely irrelevant to the problem being processed, you always think that this allows you to make the report bigger, so for now we leave the topic of the 19th century and then we return to what we It was at the beginning, that is to say, the theme of the mutual relations between structure and architecture and we go first to a story in which the management of the structure is put at the service of a purely architectural interest.

The story begins with the pantheon. The pantheon is built. by Trajan's architect Apollodorus of Damascus in the time of the emperor Hadrian and then it is curious because after building the pantheon Hadrian said to execute it but not because he had built the pantheon that continues to function perfectly but because he dared to say in public that Hadrian did not He was a good poet and then, since those things are forgiven much less than the building falling down because the pantheon ordered it to be executed, it is a fantastic work for a lot of things, first of all, the daring, that is to say, they had fundamentally made domes before. in the east but already some in Rome but no dome reached half the diameter of the pantheon was that it meant taking a leap twice as large as what had been done until then not the work the work is also built in 18 months so inside the pantheon well There is a sphere that fits in.

One of the curious things about the things that exist is that it is impossible to agree on the dimensions. That is, if you look at the dimension of the pantheon in various sources, you will find that the number is always different, but it is around Of the 44 meters in diameter, which is already a considerable size, the structure is very simple. It is a structure that works by gravity and then has the ability to make the wall on which it rests is hollow with a series of niches, the pressure line. becomes here it has a variable section, I will even be lightened that the upper elements were not needed and it is also balanced that it is perfectly maintained over the years.

It was lucky compared to other Roman temples that it was not destroyed by the Christians because it served for meet inside so they turned it into churches and in a way that it escaped thanks to its ability to house other types of functions which is an important issue also for architecture, you see the light enters through a dark central Mayak one of the problems of the dome of Those of us who will see the evolution now because it is where the light enters, the light enters through the large central oculus, water also enters when it rains but the pavement is subtly curved so that the water is collected on the perimeter and also if it rains little how air is coming out hot upwards almost no water enters it just has to be a heavy rain and the size is the size is you don't get any ideas about the size it has here is the section of the pantheon because it is on top of a street in the Salamanca neighborhood or of chamberí if this is a 15 meter street like those streets are and they are buildings 7 stories high then look what that meant in size that is an absolutely incredible topic it is such a simple shape that you don't have a notion of the enormous size of the construction, I think it is good to compare it with something that you physically know, that is, it is twice as high as the buildings and three times as wide as the street.

You can put it anywhere and see what it does then first The question is why the light is not going to enter because the light enters through the side is a very simple issue, in addition to one even a play of light which I also do not have time to take care of taking care of now if we are like this the issue of light and the other An important question in architecture is how it looks from the outside or if a building is made not only to use it but to demonstrate the power of the one who makes it and then from the outside, well, it has a façade, well, the façade already had a problem and The columns were brought from Egypt and so the initial columns were too big even for the Romans and so they had to make them a little shorter even so because each column of those weights is something like 100 tons for sure because that's how they brought them from Aswan they are of a piece but you can see that it was reduced, there was a budget reduction and one but when you look at it from another point of view the issue is depressing that is the appearance of the building it has nothing to do with the interior, let alone on average It has two problems: one is where the light enters, which really prevents you from seeing the dome.

If it is a sunny day, the ray that enters is a fantastic effect but to a certain extent distorting, and then, from the outside, the building does not have the magnificent appearance that one would expect. The one who previously had marble coverings has collaborated, they removed them and all that, but despite everything you can see that it is not very successful, so the scene with the 43 44 meters of light really has a fantastic route because it is almost 600 Years later the sphere appears again in a moment of splendor of the Eastern Roman Empire and then the emperor Justinian resurrects the sphere and in fact and then it appears, then Hagia Sophia in Hagia Sophia is not such a large dome but it measures diagonally The same as the pantheon measures in circumference so what happens then is that it searches for there is a much greater complexity, the pantheon can be seen perfectly how it stands.

Saint Sofia is made with great skill so that the first thing one does not understand That is how that is held because there are two, for us, two with half domes and then there are, see, where the ones in the dome are counteracted by two, the barrel vaults on some against forts and on other sides with half spheres, it was not A layout, let's say very good, was made by two mathematicians Artemio in suits and without mileto pain and it was not a very suitable layout for the site where it is built. In fact, it has fallen a couple of times as a result of the earthquake.

The dome we hope to return to do it then. First of all, the dome is the smallest dome in the construction. It is much more complex but it has a different way of seeing where the light enters. The light enters not through the center but enters the bottom part of the dome in a way. that the dome remains this dome that is floating in the middle of light that enters the building from all sides, not only through the central eye, which from the point of view of light entry represents an advance, let's say a tremendous advance compared to the pantheon in terms of the way in which a more complex structure is achieved to achieve that rolling effect of the most impressive buildings that one has the joy of being able to see from the inside that the issue of light is resolved in the pantheon the issue of the exterior appearance not so much the dome is also sheet metal and then the effect of the exterior is a bit variegated and complex and now and then the minarets that the Turkish conquerors put up are added so that we really already have it associated with the image of that of Santa Sofia but that were obviously not original and then the next attempt appears in Florence, they propose to make a large cathedral, there was a small one, a modest church, as befitted the town as it grew in economic power, so they decided to make a larger one. so that its construction was compatible with the small one and there comes a time when the powerful wool guild says we will take care oflacathedral and then they say well we are going to make a much larger dome and do a strange thing because proposing a dome that covers the three naves instead of this one in relation to the central nave and that is the size of the pantheon again has them trying again which was the model and then they begin to build the church without knowing how they are going to solve the dome.

In the end they call an architectural competition and declare that there is no winner but they commission him to build the dome for a ski can be discussed can also be talked about. more on the subject but I am not going to talk and then due to a law that proposes a dome that has the problem that it is much higher than that of the pantheon, the one in the pantheon is below, the one in Santa Sofia relatively below, the one in this one has many more problems and So what occurs to him is to make a double-leaf dome with some arches so that the dome is really eight arches that intersect with each other and there is a double interior and exterior dome to resolve the duality of how the dome looks from the outside.

Inside, we do not interpret that it is not convenient for it to be very pointed and on the other hand, on the outside, it is convenient for it to be more pointed and then it makes this double dome. The pointing of the dome allows a lantern to be placed in such a way and brings together the two things, those of the Santa thing. sofía that the light enters through the edge and the pantheon that the light enters from above but a more nuanced light that enters through the dome is not resolved with the rotundity of santa sofía but in the exterior image it is fantastic that it resolves combines the two ways of entering the light, but above all it resolves the issue of the external image of an extraordinary power with the pointed dome.

This inspires the creation of the dome of San Pedro. Pedro, in the different projects, it becomes more and more pointed, each time it becomes more pointed and it ends up being, well, the dome that you know that is less tense is an ellipsoid instead of being an arc of circumference that is less tense, let alone less powerful. than the one in Santamaría de Flores, but it is, but it really is a powerful dome. It is also a little smaller so that you have an idea, that is the telephone inside the San Pedro dome. There is still a good distance above it so that the entire telephone can fit. then the policy had certain problems that we are not going to go into and then the last solution is the San Pablo in London in which it is no longer a double dome but a triple dome so that there is a dome inside so that you can see a sphere, an intermediate choir that supports the dome and then a dome on the outside so that you can see that it is made of wood.

The next issue we see about mutual influence. I don't know if I'm going overboard. I think we didn't have an hour and a half, which is why I say well, the next one. The question is the other way around, that is, how a constructive architectural discovery has a brutal influence on architecture. Here we have seen how over centuries the knowledge they had about structures gives answers to a series of architectural problems. This is the other way around, it is the birth. of the Gothic, that is to say, the domes, the structures, the structures are in balance because they require very large counter remains, so the way to do more is to not spend so much material on the counter remains, because it is to make nuances of the structure, that is, if within that of a dome inside a vault because we make a series of thicker areas, they are more rigid and then they came from a series of buttresses, you can avoid part of the amount of material that is in a wall with a thick wall then the Romans anyway and finds another solution which is the groin vault and then and then the basin and then using two barrel vaults because you can obtain a solution, let's say that it can even support at points and that is permeable in two directions but that has the problem that the meeting of the two coria is an ellipse and then gives rise to complex constructive problems, then at a given moment they appear through a series of questions, let's say attempts, but truly curiously the Gothic is in the hands of the constructive systems or architectural, whatever you want to call it, it has an exact date of July 18, 1140.

On July 18, 1140, a part of the bay of Saint Denis was inaugurated with the presence of the king for a long time, which is when the way of building that thing jumps, let's say. to public opinion so that 60 years later certain Gothic centers were being built despite the difference and the difficulty of transmitting information that existed at the time. The idea is very simple in a double-barrel crossing vault because the course of the cannons in a shipment, a line is to convert that line into an arc into a physical arc, then that line is converted into a physical arc and since it is difficult to make a holistic arc, a semicircular arc is made about two arcs ago. semicircular that are easy to shape and it already has a beginning of structure problem that it has because it on the diagonal of a square because it is one with four times the side and then the side because it is a smaller arc and then if one It makes a semicircular arc on the diagonal, ellipses appear again at the ends, so the skill is to say, well, since I have cut stones to make the arc of the ski, I don't use them on the other sides and then the arc comes out pointed.

The pointed arch is a consequence of a constructive simplicity of making all the two sails the same. Actually, in the Gothic they took the stone and made the voussoir of the size that the stone gave them and then they adjusted the key, they took advantage of the material, but as I said before, if it is a previous drawing when you start drawing the renaissance all the novels are the same but then it is no longer about using the stone but rather doing things as in the drawing then the result is this two crossed semicircular arches some pointed arches that balance each other putting a larger stone on top and then there are little triangles that can be made with anything, so this has a brutal advantage to begin with, it weighs much less, it requires much less auxiliary support and it pushes at points that are easier to counteract, it is such a fantastic thing that Using the same stone it is possible to do the same thing with a quarter of the stone of what was done before, let's say in the entire history of construction there has not been a technical advance similar to Gothic construction so this gives rise to more or less complex solutions but they also allow you to make very tall elements.

They also knew that the further you take the straight counter, the easier it is to counteract and then a whole series of interior constructions appear because we said, I do this with a quarter of the price but So instead of making things cheaper, what they did was spend the same things and make them more sumptuous. You can't make them taller. You can put vivieras. You can put 11 ago. The interior is truly fantastic with depressing exteriors. We are really used to seeing the first Gothic cathedral. like a spider crab or something like that or it has been explained and here I am doing this and also the scaffolding was left in place that is what it is in fact even God you tell them that he invents the Gothic again there were houses tucked in around it and you could only see of the chairs on the cover because the other one was already considered to be the scaffolding but they had left it there because there was no way to remove it because they would fall down with one.

A very subtle balance. The equipment is very useful but I think they have been standing for almost a thousand years and they work. and they continue to work perfectly, it is not a technical and impressive advance and it is and comes not from trying to do something but from taking advantage of a way of building, that is, it is a consequence not of the will, not of the architectural will but of the constructive will. so much so that when the Renaissance arrives they repudiate the Gothic system, the Gothic is a contemptuous oar that put a bazaar and that way of building and they wanted to build again like the Romans with terrible resistance on the part of the builders who did not want to.

For a long time there was a kind of understanding so that the architect who had gone to Rome was allowed to build a Renaissance façade and then the interior was made Gothic by the builder who was cheaper then but well well in the end the issue ended up disappearing with these fantastic interiors consequences of taking advantage of a construction system in architecture, also taking advantage of architecture without architects and now there are no known Gothic architects except in Italy, then everything becomes more complicated and then each time the ribs are more complicated and they return to them again. make shells that with the nerves hanging down because of course the end novelty ends in the need for novelty digs absolutely perverting things the same as we have talked about evolution and influence in a sense and choice now we are going to talk about mutual influence mutual influence that appears when there are new materials when there are new materials on the one hand the materials allow us to do other things things that initially architecture did not demand the first appearance of the new materials you can see it there in the annunciation of fra angelico it is possible to make these graphic arches Because there is a steel brace inserted at the bottom, the brace naturally does not appear in the architects' drawings and is not even placed in an orderly manner in relation to the capitals.

They did not paint it black, in addition, so that it would give little prestige, as an addition, but a good one, it is already beginning to take shape. iron appears in fact the dome of San Pedro because it is stable thanks to a series of points and chains because at 100 meters high it was impossible to function exclusively by gravity and then well you plus the initial relationship of iron and steel with architecture, but it then began in the middle of the 19th century, because not only was the steel made better, but these unions began. It was unions, who knows how then the roblon appears and then systematic ways of joining first of producing steel and then of joining the steel in a safe and reliable way and then we begin to use steel in construction in parallel because even a little earlier the analysis instruments that Galileo had started were developed and then we learn to predict the behavior of these new steel structures as of course it happens that while in stone and wood there had been centuries of sedimentation and it is still fed in proportions in the steel because everything appears very soon each structure must be previously verified separately and we continue at it when really the steel concrete etc. are susceptible to being handled with rules of proportions exactly the same as things have always been handled in architecture in a way that I still hope we will get there but we have not yet managed to assimilate the new materials in a way that they are handled in an architecture how The ancients handled it by leaving sizes, proportions instead of numbers because geometry is really our language and with geometry you can reach practically any place, so steel allows you to make a section of steel because it allows you to spend half of material, that is, it allows the section to be modulated, it is necessary because steel is expensive and is also enormously resistant, 720 times more resistant than wood, since you cannot use a billet, you have to be more refined in the use of steel.

The beginning of steel, since it appears from use, themes appear that have little to do with the architecture that appears in the appearance of the large greenhouses of the Universal Exhibition and then the train stations, the train stations had to have that fantastic size so that the smoke would not suffocate the travelers. Right now it continues to get just as big even though it is electric and a canopy was enough. These are those things that are going to drag away from the magnificence and one sees some absurd bird stations that are a calamity, but there really was no need at all. nothing, nothing of that, but well the precept to these enormous things and then the steel, well, the construction enters slowly because a key element of the entry of steel in constructions where there are elevators is if there is no elevator, why make buildings very tall and with factories could be made and curiously the key element in the development of the elevator is not the machinery to go up but it is the one that stops automatically when the rope that holds the elevator breaks, that is, it does not begin to be used until Mr.

Ortiz whose descendants are still manufacturing elevators, he does not invent the class procedure or separate, he does it in a spectacular way at a universal exhibition using a platform loaded with things attached to a rope and with an ax he cuts the ropes to demonstrate that the elevator has the inertia brake It worked and the elevator stops then curiously the important thing about the elevator is not how it works but how it stops and if the steel enters the construction not through other things but through the elevator then the steel already allows us to do other things allows in larger spans it enters very very slowly it enters very slowly but it enters slowly and in fact it appears inside the factory walls the windows continue to be made the same it takes a long time for someone specifically le corbusier to realize that the windows can be made in a different way if the structure is simply a series of supports as you know you want to know le corbusier was a french architect well he was notA Swiss painter then Le Corbusier realized that things could be done differently then the Villa Savoy East Manifesto appears in which all the stories of the exact modulation of supports appear that is not the case inside, it is only for facades inside.

They are placed in a much more dispersed way and then, well, it is more than a building, it is a manifesto. You see how the supports are placed inside, which do not follow the same law, and then, well, there are things as wonderful as that support at the foot of the bed that It must be great when one rises from the kings but well it is a manifesto it is not something to avoid although I said that they are a vitter in this process of mutual relations because there is a prominent place in the opera designated with a misunderstanding of something that is It is ahead of its time and takes much longer to build, costs ten times more than planned, etc., but it is a success because it has a good image and then it gives rise to this certain architecture of the image and a more or less evolution. let's say painful in that there is the opera design in it and it is weighed down by the desire for a sound of authenticity and for what is seen as with you care and has no desire for authenticity, what is inside is done on the one hand what is outside On the other hand, you can put anything in between, no matter how complex it is, but there is also a whole period of mutual influences of what can be done and what you want to do with solutions, let's say more or less clean or less clean. this one or cleaner ones like these can be but we can already see that the series of things that can be done is expanding enormously, something else is what can be done and another thing is what would be reasonable to do sometimes with a kind of berlin in alexanderplatz and then that huge truss that is in front of the windows I suppose not from the directors of the company that rents that because it is a manifesto that we come on there was a hotel there was a controversy about whether it could be demolished or not they left a piece of hotel and then that is the demonstration that this piece of hotel that is below is supported that it really could have been done in 10,000 ways so that it could not be seen but they wanted not only to support the building and that it without walking so that it could be seen that it was had done and obviously it is seen that it is done with all the intention or even the date is on the outside which is even more complicated to solve what they wanted to solve what you see naturally is not the truss but what you see It is the in the fire protection of the triangulated beam, that fantastic and canonical one is inserted with other beams since they are less visible from the inside and that must delight the man who has the back window.

Finally, we have talked about architecture, structure and the Last question before moving on to a topic that will still give me time to be current is the topic of representation. In recent years, not so recent, it appears at the entrance to the computer in architecture. You will think that it is because it allows you to analyze any type. of structure is really not so much that as it allows us to represent anything, that is, a problem to build something right now in the current era in which things are produced industrially, to build something you have to draw it and you have to know what size it is, so you don't know The day that was before, that is, when one made a geodesic dome, calculating by hand, calculating was not the problem of fixing the dome, which was idiotic, but it was that they were never very big, what I had to do without the problem was calculate the length of the bars and I tried to make sections in which there were as few different bars as possible because each bar was torture when calculating its precise length, then suddenly the computer not only allows you to analyze anything but also allows you to draw anything and see what size it is and then that radically changed the paradigm of how things are done so the issue of what can be done and therefore of the stupidities that can be carried out increases in a way the panorama increased in an extraordinary way that is This is impossible to do if you can't, but you can draw and put those things in any way, well look if instead of on a plane, if instead of putting the structural elements as they should, they put them at random, it's simply putting double of iron, if this is done in three dimensions, simply put triple the amount of iron and it is triple, not afterwards, simply put the triple amount of iron and put them in any way, then you can do these things of extraordinary and unnecessary complexity Of course, if you really look at it within this, it seems that the triangulation wing of the era of the vulture of Darth and Thomson does not appear again, although I did not want to do things randomly, it is impossible no matter how crazy one wants to do, there are points in what to do something reasonable but within that it can seem like randomness quite well you can do things like this that they left theoretically it can be extraordinarily clean in practice it is solid iron inside really to support that and on top of that with psychic problems because it is God's, not that, but it can be done, it can be done if you don't mind that everything is full of iron and that it costs a fortune, but hey, but it appears, it appears everywhere, you can see that what had to appear in the drawing is put on top of something that has nothing to do with that, there you have it is the real complexity of things there are other complex things but the most reasonable how is this and then to degrease this topic and to return to a topical topic let's to the building of Spain let's go to the building of Spain and the topic of what it has to do with the structures of the building Spain, as you see, that building with a height of one hundred and something meters and a floor also of one hundred and something meters, that is, almost one hectare of surface and then, well, that building was protected, then it stopped being protected except for the façade and then there is an immovable official provision for the moment that says that we must preserve that, that is, the edge here, this with this fold, this piece that is set back a little. and this little piece above but but not the building that is the situation the current situation of the topic so well that there was reasonably already set to pull the end of integers and make a new building and that Madrid would have a new icon but well the reality is that They have come to that and there were some gentlemen who asked precisely that since they asked that only the façade be protected and the interior could be modified, then that problem appears, that problem is a consequence of a story that starts from Felipe Segundo and Felipe Segundo establishes how It had to be the houses of Madrid so that they could accommodate their courtiers and then he was very thorough and described everything with extraordinary detail, including what the facades had to be like but not what the interior walls of Mary had to be like, since then the arbiter of the sea. and the facades are incorporated and stable as Felipe Segundo requested and the interior in any case that makes the interiors function very badly after the running water appeared and then to preserve the buildings the solution is reached: you can preserve the facades that They were maintained and so there is a certain tradition, let's say a conservation officer, hey, you can touch everything except the façade, the portal and the staircase, sometimes you have to keep some stairs shot with all the steps, different software, but that's what it is, what happens is that they don't where to maintain this that a 107 meter high façade that is also attached to the structure is made of fabric etc. then the same gentlemen who ask the same technicians who signed that they could pull the interior and leave the façade then make another paper saying that the façade cannot be torn down, we have to go inside because the façades fall, things are quite reasonable and then it appears, let's say how the façade is made, there is a concrete structure, there is half a foot of brick, although The factory on the outside appears standing but it is made with a rope brick and then another brick cut so that it looks like a foot but it is not, and then another part because it is a half foot of double hollow with an artificial stone thing glued on. mesh that is not a particularly consistent thing as you can see and also on top because the recessed part is made by the procedure that there are some beams perpendicular to facades and others that start above but the supports of facades are not in front of those of behind the area that bad beam for the other beam that goes for the supports at the back is a salad that has stood for 70 years without any problems and the façade is also good because it is one thing then the city council comes to me for a moment question, hey, is it possible to maintain the façade, so I study the issue to know if it is possible to do one thing, the only solution that is possible is to do it, and then I proposed the following: the building, if you are going to see it, what it has are large patios. open towards the back that reach very close to the façade and then the problem of maintaining the façade right now the building maintains the façade if other things are built behind it it continues to remain on the façade because it is rigid and is heavy enough without problems they are like I said before, balance resistance and rigidity, that is, it is sufficiently rigid and it will be rigid again.

The problem is that it is done in the meantime, whatever is achieved, that in the meantime, from the time the old building is removed until the building is put back up, it is still heavy enough so that there is a sufficiently rigid and sufficiently resistant balance, that is the problem, so I say well, if powerful vertical concrete elements are made in the patios that are the supports of the future building, meanwhile, the façade can be attached to these elements in such a way. Actually, the issue in principle is possible problems, no, it is not difficult to build that before starting to demolish the building, then on the façade, you can place some elements behind it and then fasten it, and once the façades are perfectly fastened, you can proceed. to the demolition and the new construction, taking into account that the project has to include those elements or something similar, then those screens can be as perforated as you want, that is in elevation, that is to say that it admits a large amount in a coordination with what you want to do but obviously it is impossible to conserve the façade if when making the project you do not take into account that you have to conserve the façade then what are the numbers the numbers are three images of these first of all the balance and the wind on that surface produces a moment of one million kilos newton-meter which is not bad to start with then a million then the first question is to see if it is possible to balance a million chelonians two meters with screens that have a base of 25 meters since it supposes a weight of 8 iu with an average height of 70 meters give 5,250 cubic meters of concrete of more than 10 and a half so that balance is possible.

The second question is whether the resistance condition is met because there you can also make some very easy numbers if you take You put the 10 screens together because it is like a section of concrete 3 meters wide and 25 meters deep. The module is resistant and to do it in cubic centimeters is a bit crazy and then it is very recent. The resident module of 300 meters is in cubic meters. cubics you divide the moment by the resistant module and it comes out in three thousand three hundred kilos minutes per square meter which is 33 kilos per centimeters now so that there are no distance resistance problems it is possible rigidity problems in the relative arrow of a cantilever it is the unitary deformation by the tedh divided by two so I have made the numbers for the screens it turns out that the head of the kicks would move 50 millimeters which is perfectly visible so that balance strength and rigidity are met in the more numbers than these are needed to to see if it is viable to maintain the building, then the constructive questions come about how to convert the screens into porticos so that the side elements continue to have light, that is, there is then how to support if the structure is removed, how will it support this part that is set back? which can be done using triangulated beams that occupy an entire floor placed on loads using hydraulic jacks, that is to say, there are a series of technical issues but you do not obtain 15 meters of light that can be used for garages and for anything you want and that They allow you to make either intermediate structures or use the 15 meters of light if you want or really so that if you accept some small conditions for the final project it is perfectly possible to maintain the façade which is reasonable or not. an issue that is a matter of another and that was not asked by the city council nor that they asked me on the day if the façade could be maintained.

I don't know if we have it. I'm not afraid that we have arrived exactly at the right time. I always have more things in case. Maybe because one of the recurring dreams I have has never happened to me but one of the recurring dreams I have is that I am teaching a class and there comes a time when I have nothing more to say and then there is stilltime and it is horrible, it has never happened to me and then I always add a queue to be sure that I can continue talking for as long as it takes, no, but yes, well, hey, I dream about it from time to time, I still don't teach classes anymore, it still happens to me, well, well Thank you very much for your attention.

Sometimes there is a temptation to become like a television screen. It is important that your prose is true. your mind and after your green from your point of view it is reasonable technically it is possible but it is reasonable let's see if there is truth there is a series of options we would say the three fundamental options is the one that the city council closed the previous heritage commission It has been defined that the façade is saved, the option that the Chinese offer, which is to tear down the façade and do it again, they call it not demolishing but dismantling the façade because that is what appears in the law and then building a new building.

I would prefer a building. new and still the truth is that foster is also involved in the project since there is already a good foster building in one of those but well what seems abominable to me is the option of tearing down the façade and doing it again the same and then it is because There is a subtle difference that I had always wondered what the difference is between the station throw them and then one you probably many of you do not know who Ramón Vásquez was and so I encourage you to look in architecture magazines from a fantastic architect and this csc He said one day he had a little house in Pontevedra, the estuary in flight and next to the sea in a place that is naturally now illegal in the interior maritime-terrestrial area and underneath he had a little boat that lied to him and every year the storm damaged the little boat and Ramón He was very crafty and so every year he repaired the boat, the damaged ones, etc., and then he told me there is no left.

I think there is not even an original piece of wood left, but in the same boat, if one had offered a reproduction of his boat made again, he would have said that It was not the same boat, it was an imitation of its cargo, so it is not a façade. It may be the same, but it is not the same. Time has passed through it. There is a continuity of things that have been done. If the directors do not mean that it cannot be done. replace things and the garment there are better windows so change the window if it is better I don't know what is changed but it is not done like a theater set but it is still one that we would say is the option I would prefer but I get the impression that on the other hand A controversy has already been launched and it seems to me that in the public opinion it would be very difficult to build a building apart from the legal problems because it was a question that the general plan says that 12,000 or 14,000 square meters are needed instead of 65,000 square meters.

If they don't demolish the building they will be left with a quarter of the buildability, which doesn't seem to be what they want, so the controversy is there and then really the state in which things were, well now I have had a series of conversations with the Chinese and I am trying to convince him that the façade can indeed be preserved, thank you very much Ricardo and this