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59.
Ladies and gentlemen.
This evening I will continue my series of talks, concentrating specifically
on engineering works and bridges. I have, again, brought with me
a brief statement to introduce the talk. It is a translation of a
brief sentence I chose from a letter of Vincent Van Gogh to his brother
Theo: |
60. If we consider engineering as an art --as I believe it is-- and if we go back to a time when there was no difference between the art of architecture and that of engineering, as I suggested we do at the beginning of my first talk, then we can consider that it is in ourselves, and especially in the new generation, that a rebirth of art happens. It is not only our heritage but also the mother of heritage that we must translate into action through our capacity to make buildings, reinventing them each time.
61. I would like to begin my second talk by showing another small object that is done using my children's toys. This one expresses another way of putting things together, hanging the same stone as in the previous case, but in this case, the forces are working parallel to each other; they do not cross. So, it is like a game in which you discover that the weight of an object has the capacity to express something and that it all depends upon the ordering of the forces.
62. I have not found a better way to introduce you to these thoughts on construction than through my own experience, and, somewhat like an author writing his first book, one always gets a little autobiographical.
63. One of the first buildings I designed was a warehouse for steel. In this project, the problem was how to design the beams of the roof, and how to do them as light as possible. I was just coming out of the school of engineering, and it was a challenge for me to achieve this with something like twenty-eight kilograms of steel per square meter, and a span of thirty meters across. The beams were made of corrugated metal because it was light and could handle the shear forces of the roof which, in this case, were very small. The reason is that most of the beams are arched on top. It took a lot of time to investigate how to bolt together the two corrugated metal plates that make the beam. I wanted to create a construction that works as a spatial frame, capable of handling lateral wind forces when another corrugated metal for the roof is put in place.
64. I have recently designed a bridge for Venice, the Piazza Roma footbridge, and in this bridge, I used a type of beam that is very similar to the ones I used for the warehouse, but expressed in another way. If you look at the bridge, you find all the elements of a traditional Venetian bridge, including the embank- ment and staircases on both sides. But the bridge itself is a very shallow arch, as a result of using these beams. I thought it important to achieve a certain simplicity of expression in the bridge and therefore, the bridge is effectively done using only two beams and making its form a function of the form of the beams. As the beams become wider at the center, the bridge becomes wider too. The details of the embankment and its complementary staircase reinforce not only the expression of the embankment's mass, but also, the pull of the bridge. I did not want to use the lower part of the arch as a compression element; only the two lateral ones. The lower element is just for stability.
65. A very early experiment was for a balcony I had to add to an existing house. In the beginning, many of my works were very simple. The existing balcony was very small --something like three feet deep. I had to extend it, using the existing reinforce- ment, to a depth of some ten feet. It is interesting that, in order to preserve this reinforcement, I had to find a complementary structure to build underneath. This new structure works like two half arches that are tied together through a tensional member. It supports a slab of concrete that cantilevers in a very daring way, about five feet from the end of this structure. This early experiment was the precedent for another work. A year later I had an opportunity to recreate this idea as a type of bridge in the Stadelhofen station of Zurich: a cantilever that is close to a wall.
66. In my opinion, the consideration of the static properties of a bridge is very important. The bridge's static equilibrium is probably its most essential part, so that if we think of a bridge like a body, this static condition is analogous to the heart. Of course, the body has other parts; in a bridge you have other properties. The central part of the whole problem is certainly very much about resolving the problem of how to bring the forces from one shore to another.
67. In the station of Stadelhofen bridges are an integral part of architecture and there are several types of bridges in addition to the balcony-bridge I just mentioned. For example, there is a kind of concrete platform that works as a bridge, and a steel bridge that springs from a very small support to connect into the upper promenade, and an additional bridge.
68. One of my last works is the new Orient Station in Lisbon. An existing berm that supported the train rails was translated into six bridges and four rows of metal trees over them; so that, what was previously an impossible barrier to cross, is now a rather transparent construction in concrete and steel. In this case the idea of the bridge is essential to the architecture of the station. It is no more a station that has bridges, but it is a station on bridges.
69. This is one of the early bridges I designed, for what is called a Diplom Arbeit, my diploma examinations work at the school of Zurich [ETH]. My conception of this bridge comes from two different ideas. The first one is a cantilever bridge --very simple-- and the second is one of those beautiful arch bridges in which the forces are expressed by the arch. In a cantilever example, the forces work in another way. You have tension here [through the top] and compression here [through the bottom], and then part of the bending moments are transferred into the shaft. So, I divided these elements in three, and I found that by leaving a hole at this point could be quite nice. I started with pillars that have a certain proportion --subdivided here-- and in fact, this pillar, if you look at it from the front, is like this. Then, the deck arrives here and the support is here. It may seem contradictory to make the support smaller in plan, rather than wider, but it emphasizes independence. This is a view from underneath. This emphasizes very much an independence between deck and pillar; the deck needs to stay wide, because it has to conserve the whole dimension [of the roadway] with the lower part working in compression. In fact, there are other studies that I did coming from the same idea. We can obtain this other idea, which is that a person is holding the bridge's deck in his hands over his head. This is how I arrived to these forms, in which there is an anthropomorphic understanding of the design.
70. The first bridge I built and would like to talk about is the Alamillo Bridge in Seville. For the World Exhibition of 1992, my thought was to do two symmetrical bridges; one on one side of the island and another on the other side, both linked by a viaduct. This is the viaduct under construction, and the landscape is very flat, and this example has the particularity of being on an island --meaning that you cross the river twice. The basic idea is this one: the distance between rivers is about one kilometer. If this had been a single river, a good solution would be to make a suspension bridge on pillars holding the whole span, like this; and build an object in the scale of this very flat and wide landscape. But in my opinion, this did not seem necessary, hence I created a viaduct here, with many supports, which is quite transparent, and then, I placed two bridges here, and there, in response to the scale of the place. I introduced a design where the mast is very important so as to create a reaction to this place that belongs in its scale.
71. Certainly, a bridge is a utilitarian object but at the time I thought it could also be an important element of the EXPO 92 and I wanted to use the two bridges to create a big sign in the scale of the island, by projecting laser beams from the shafts. However, I could build only one of the bridges for various reasons. There were two administrations, and one decided to do their bridge in another way. But originally the project was for two bridges.
72. The design of the bridge was original because, as far as I know, this kind of bridge had never been built before. Usually, in cable-stayed bridges there is always a compensation of the forces from one side to the other. But if you incline the pylon, the forces are not only compensated for by the cables behind but also by using the weight of the pylon itself. And if the pylon is inclined enough, and heavy enough, it can compensate the whole bridge purely by the pylon itself, and this is what I tried to do here.
73. It is important to understand this object mechanically, and this will be one of the few times I will come to this subject. You see, mechanically, what is happening, is that each segment of the bridge has a certain weight, and then force arrives here, and the resultant is at the interior [within the shaft]. The next element, has another force --another weight-- and we have this force, and the resultant adds to this here, staying in the mast; and goes all the way along with the different cables. Finally the resultant arrives here, and compensates with the horizontal force coming from the deck, and arrives as a pure vertical force into the foundation. The foundation is very small relative to the huge span of the bridge. And it is interesting that, if the dead load produces a resultant here, then, the live load will move it away. And then we have other problems, like the wind and many other things that we have to take into account in a cantilevering system.
74. Some details are important. The bridge from underneath is quite interesting as a spatial event, with concrete vaulting and openings for light. Also, it is important to take care of pedestrians. In big bridges, very often pedestrians are lost. In this bridge the walkway is over the torsion box girder, in the center between the cables. Another interesting thing is that there is a small meteorological center in the head of the pylon which is possible to access.
75. Now, I would like to return to my home town of Valencia and its river, the Turia. Valencia has a patrimony of bridges built in stone that, in my opinion, few other cities in this part of the world can claim; early Gothic, high Gothic, Renaissance bridges, all done using arches. These are magnificent works that we consider, without a doubt, as having architectural value. The Renaissance bridge is by the architect Juan de Herrera who also built the Escorial. In fact, if you look at the old stone gates of the city and the Gothic bridge that leads to these gates, you see that there is very little difference between the architectural language of the gate towers and that of the bridge. There is another bridge that has not only huge public stairs but also chapels, and another --a concrete bridge from the early twentieth century-- that has caryatids and other decoration executed by Terencio, a sculptor from the city.
76. This is to say that if you go back a little, you come to a time when architecture and bridge building were absolutely linked together. The bridge builders were very conscious of this particular relationship. They were also conscious of the seriousness of the act of constructing a bridge. Many of those bridges are five hundred, six hundred, years old and have resisted unbelievable floods. But even while taking into account the engineering needs of the bridge to resist floods, the builders also thought about making small chapels (maybe to pray in, so that they would not be swept away in the next flood).
77. In this context I built a contemporary arch bridge over the Turia, which I showed in my past lecture. It has a plaza below it with an underground station under the plaza. It is a pure steel bridge as much as the others were pure stone bridges.
78. I also built another bridge for Valencia, just outside of the city. Except for a few elements, the whole bridge is done in concrete. In this one I divided the bridge's ramp into two, because first, it had to be very wide for traffic, and second, I wanted not to distinguish the upper part of the bridge because it was the continuation of a boulevard that comes onto the bridge from one side. I chose to leave a void down the center of the bridge that corresponds to the space of the boulevard. In the space underneath the bridge, I wanted to emphasize the spatial effect. A pool of water is to be built in this lower space that will reflect light onto the underside of the bridge and also reflect the bridge itself. Light comes into this space from the sides and from above, between the pedestrian deck and the roadway. We have been studying very seriously the lighting for this lower part including lamps.
79. A third bridge for Valencia is close to the harbor. Here, the river almost leaves the city and there is an area of new development. This is a new project for a much wider part of the river. The span of the bridge, in this case, is something like two hundred and twenty meters. I chose a cable-stayed bridge for this case, and also a small platform that you can reach with an elevator that rises one hundred meters above the ground. Given that the city is very flat, this platform provides the opportunity to look at the city from above.
80. Next is the Felipe II bridge, built for the city of Barcelona. I would like to emphasize in particular with this bridge the capacity of a public work such as a bridge to generate infrastructure and in doing so, change the circumstances of a part of the city. For example, the Bach de Roda area where this bridge was built was a very poor neighborhood --a kind of bidonville. The people who were living there were moved into better apartments so that the area immediately adjacent to the bridge and the station below it could be turned into a series of parks. So, in a very rough part of Barcelona, you now have a place that has the potential, in my opinion, to become a significant part of the city, because it is a very wide open space and one that is very interesting from an urban point of view. In this case, the need to build a bridge and produce a link provided the impetus for regenerating a portion of the city. One of the ideas of this bridge was to make a place. Because of this, I made the bridge wider at the center, like a balcony, and the arches that span the railway tracks signify, not only the bridge itself, but also this place in the middle of this neighborhood. In this part of the city the landscape is not very romantic, but on the other hand, when I look at the mountains behind and the housing around, this space has huge potential to become a place of interest in Barcelona, especially now that there are green areas on both sides of the bridge.
81. I think that all cities need, very much, their public works to help them regenerate, especially now. During the '70s architectural and urban interests focused on the historical point of view which supported the regeneration of city centers to make them more habitable. Those interests also initiated the preservation of a lot of buildings that otherwise would have fallen victim to speculative development. But meanwhile, in those years, the development of the city's periphery began to become a very significant problem. So today, the problem is how to reform those parts of the city --and particularly European cities-- where the population has doubled or tripled during the last thirty or forty years. I think that public works like bridges and stations can become very significant forces in regenerating areas by creating and focusing urban activity.
82. These next projects explore the idea of the arch. The first is a trade exhibition hall in Tenerife, in the Canary Islands. Sometimes when you design a functional building that, like many of the bridges, has to be done for a very low cost, the idea of using the arch is important. It is very efficient for large spans. In this building there are many different types of arches: concrete half-arches, and, on the top, steel arches. A large arch spans 240 meters --something like 800 feet-- to support the whole roof.
83. A bridge in Mérida, the Lusitania, over the Guadiana river, is supported by an arch, but one that is much purer. In this case, the landscape was especially important. In Spain, the sensitivity for the landscape from the point of view of ecology is becoming important. This is quite a beautiful area with a Roman bridge that is just one kilometer away from the one that I did. The bridge is mostly in concrete with the central portion of the arch made in steel. In this case --as in the bridge in Seville-- I was very interested in the movement of pedestrians across the bridge because there are urban areas on both sides of the river at a distance of one kilometer apart from each other.
84. A much shorter and lighter pedestrian bridge, was done at Créteil near Paris. The span is approximately seventy meters and it was built to allow children to cross a major roadway to go to school. It is a very simple arch made with two tubular pipes, connecting members and cables.
I have designed several bridges that I am only going to mention next.
Bridge Projects:
85. A bridge designed theoretically outside of Florence. It is the Cascine footbridge over the Arno river that was done for the Milan Triennial as a kind of design exercise. From the beginning, I have been very interested in the idea that form and construction (as pure as it needs to be for a bridge) are related to each other.
86. Ile Falcon double arched viaduct over the river Rhone, in the Alps, close to the city of Sierre, Switzerland. The viaduct's circulation passes through the arches.
87. Project for a shallow concrete bridge in Lake Lucerne, Switzerland.
88. Project for a steel bridge for the city of Basel constructed over existing stone supports. One of the reasons this bridge was not built was because the steel on the stone foundations seemed too daring to many people.
89. Project for a bridge for the city of Paris. It was one of the first times I tried to introduce an inclined arch using the torsional stiffness of the box girder that carries the roadway. It took me two additional experiences --some six to seven years-- before I could build the first torsional box girder for a wider bridge. I achieved it in Valencia.
90. Project for a very small bridge in the city of Bristol with glass roof and paving.
91. Proposition for a bridge crossing over the Thames in the east part of London, done for the Royal Fine Arts Commission. Its span is seventy meters (2300 feet).
92. Another project for the city of London done for the Royal Academy.
93. Footbridge in front of Saint Paul's in London.
94. Two propositions for a bridge competition in Öresund: one a cable-stayed bridge and the other an arch bridge with a major span. The entry took second prize.
95. These two bridges are original proposal and final design for a bridge in this beautiful fluvial landscape, for the city of Orléans. An arch bridge in steel is now under construction.
96. Three bridges in an urban landscape for Murcia, south of Valencia. A small existing bridge in concrete is transformed into a plaza and two lateral bridges are added for traffic. The symmetry of the two new inclined arch bridges creates the unity.
97. The Kroprinzen bridge in Berlin, now almost finished. It was the result of an international competition promoted by the European community, done as a gift to the city of Berlin. The original bridge on this site was destroyed because it was very close to the Wall. This bridge has a complex steel construction.
98. A pedestrian bridge between Salford and Manchester in England. The weight of the ramps arriving into the bridge compensate for the weight of the central span.
99. Sketches and drawings from my time as an assistant at the ETH when I was imagining cable-stayed bridges in the Alps. Those sketches influenced my early bridges very much.
100. Proposition for a bridge for the city of Lérida in Spain.
101. A cable-stayed bridge for Sweden.
102. A cable-stayed bridge between Geneva and France --very close to the frontier.
103. A study for a pedestrian path, the idea of the cantilever and the idea of one piece being supported in the next piece, for Bedford England.
104. A competition for Poole Harbour, England, in which I submitted two ideas for the same landscape: one is a cable-stayed bridge and the other an arch. In the latter one, I wanted to tie the elements together and block them down in order to emphasize the idea of jumping over the water --just touching the water and jumping over it.
105. Some movable bridges: a proposition for the city of Bordeaux. The bridge can turn to let the boats into the harbor.
106. Studies of a balancing bridge for the harbor of Barcelona and a rotating bridge.
107. This is a proposal for a pedestrian bridge for the city of Redding in California in a very beautiful site above the Sacramento River, where one is crossing from one small forest into another. We are designing this as a cable-stayed bridge in steel. Because it is a pedestrian bridge with a width of some twenty five feet, it was possible to make the mast as a box in steel, that takes, by flexion only, all the forces coming from the cables. Additionally, because the bridge is in a recreation park, and because it is oriented directly north-south, I wanted to make the mast into a kind of huge sundial for the school children and for the young people. So, the shadow of the mast can mark the hours of the day, and also the months of the year.
108. I would like now to talk about the inclined arch in particular, which I have explored in my work. The first example I will now show is the La Devesa Pedestrian Bridge in the city of Ripoll, which is in the northern part of Catalonia in the very dramatic landscape of the Spanish Pyrenees. In this area, we built a bridge to link the train station to a residential neighborhood located on the other side of the river Ter. The area between the bridge and the edge of the neighborhood was also transformed into a park, with a plaza and a series of interventions that were built by other architects. As I said earlier, bridges are very powerful when you want to regenerate a place, because they introduce a very good reason to restructure the surrounding area and, in so doing, make more livable these parts of the city that are rather lost like this one here in Ripoll.
109. I will now focus on the cross section of the bridge. The cross-section of the bridge looks like this; handrails and pedestrian path are here. Now, in fact we have a global resultant of the forces acting here, at this point, and we could transport this force here, and then, this is transformed into a torsional moment. You see it here 'M' and the force by itself will get divided into two components: one component is here and the other one is here. So, the activation of the deck is necessary. You will see this in a slide before I show it to you in finished form. Then, there is a truss here, so that in plan this looks like this. Then I have the ribs and a membrane here, and then I put the torsional moment in this pipe. The pipe, on the other hand, is tied by the tension generated by this plane here, through this force; and it is interesting that the pipe is very, very tiny. In my first bridge in Mérida, I was so afraid of the effect of buckling that I made a huge arch over here. While here instead, I took the buckling through the ribs, which have stiffness. After that time, in Valencia, we transformed the pipe into the whole deck. In the case of Ondárroa we have a lateral box and then here, a cantilevering pedestrian walkway, and we hold the arch with the ribs, having tensional members. In Orléans, where we are currently building the arch, it goes here; this is held by cables.
110. So, there is a kind of progression, beginning with case number one --the bridge of Mérida whose section is a big arch and the deck is like this, with a torsion member, a big arch with three chords-- to case number two, Ripoll --which for me was a kind of experiment to control it in a span of seventy meters [230 feet], and make it feasible at a low cost and a very simple case, because the deck is only fifteen feet, or a little bit more-- continuing with the case of Ondárroa, with a real traffic load (we will see) and going to the case of Valencia, with four lanes of traffic, and finally the case of Orléans, with a major span, four lanes and pedestrians on both sides.
111. What is interesting in this type of bridge is the fact that the torsion of many of the regular sections that we see in bridges --the torsional stiffness that we have in the box girder that supports the roadway-- is almost unused as soon as bridges are upright, because you have only the unilateral load. What I have tried to explore is [precisely] the phenomenon of the torsion; how to exploit the torsional resistance of the roadway to create a certain asymmetry in the bridge, which permits me, for example, to emphasize the position of the bridge in relationship to the city around it --or, to the direction of the water, or, even the position of the sun-- and to sensitize the bridge itself as a phenomenon set into the surrounding landscape.
112. The landscape of Ondárroa is very picturesque with the Atlantic ocean in front, a small harbor, and fishing boats. For the Puerto Bridge, I tried to take advantage of local conditions and materials, using the stone of the area to build the embankments, for example. Many people walk across this bridge to Ondárroa's only beach, so it was necessary to provide an ample walkway. This brought me to the idea of making a big balcony on one side of the bridge. There is another pedestrian walkway on the other side of the bridge, but this one is given major importance by separating it from the roadway. With the hangers of the walkway, I made the bracing for the arch, which supports the bridge with cables.
113. In Ondárroa, there are very large changes in the tides and many people come with their boats to this area where the bridge is. For this, I added big staircases going down into the water as part of the embankments. As with the bridge in Valencia, and others, I was interested in the space underneath the bridge. I separated the parts of the bridge so that the light can filter through, to the space underneath, and this, together with the embankments, makes a very interesting space.
114. I want to add this other case because this is a unilateral inclined arch bridge with four lanes of traffic and pedestrian paths on both sides. In this case, of course, the whole bridge is uncompensated, but the torsional stiffness of the regular deck --of the box-- is so big, that we can hold it like this, and we achieve in fact, a very oblong, a very long thing. Proportionally, the box is something like this, and this height is something like six feet. And then, we also curve it as seen here. And this is covering the plaza over the underground station that I showed before. This shows an interesting part, you see, the torsion box is limited from here to there and the pedestrian walkway is cantilevering, and also the backside is also cantilevering, and those are the steel ribs. There is a hole here to go all the way along.
115. The bridge that I built for Bilbao [Campo Volantin] is one of the last bridges that I have finished. It is interesting because it is somewhat the antitheses of what I had learned, or thought, was a classical bridge especially in terms of the embankments. If you think of a classical bridge, like the bridges in Venice, you have an arch and then all the forces of the arch are brought directly into the ground at the embankment which is solid. This event is signified with a staircase that permits the people to descend to the canal. So, the people can walk under the bridge along the canal or walk over the bridge. This embankment is a classical element of the bridge. It is the way the bridge touches the ground as a continuation of the forces. Then also, the bridges are usually straight in plan and, very often, symmetric. If there is an arch, it will probably be in the center along the axis of symmetry. This is the case in the bridge we did for Venice --we have two structural members that run the length of the bridge that are symmetric in relationship to the bridge.
116. In Bilbao, first of all, I tried to support the bridge on cantilevered sections, that rise up from the bank of the river, running parallel to the river, on both sides and the bridge deck is on these supports which are like arms. The bridge is in fact, held like this, so there is no embankment. There is a void here. And this emphasizes a longitudinal direction. You have one part of the bridge here, and this is the other, and the void is somewhere here and there. Directionality is clearly expressed by the bridge. A second point is that I wanted to indicate the curve in plan, in a very simple way, because I have a flow of pedestrians moving in this direction, and hence, the idea of the straight line disappears. And a third point is the following. Because this is an asymmetric structure, I wanted to create an element holding it that would be completely asymmetric; but one which optically, let's say, could compensate the situation. But in spite of these features, the torsion pipe is straight. The description of these two particular points was for me very important, where the arch and the torsion pipe come together, but the resultant of the forces is here, and the vertical force will appear there, so the support is only here. So, there are some situations in the bridge which are quite paradoxical, in which, let's say the arch arrives to this point, but the arch is in fact supported three or four feet away --apart. However, it is nonetheless centered, you see? And so, I tried to play formally, if you want, with a very pure understanding of the way forces and construction work in this bridge. So, for example, if you look at the bridge in plan, in fact you see torsion. Torsion is compensated globally, because this part of the deck is equal to this part of the deck in surface. So that at the end, we have the same torsion forces; and what is also interesting, is that the only degree of freedom that belongs here, is if the section was like this. I decided to put somewhere (to shift) the arch, so that sometimes the arch is outside of the bridge, and then is just tied by cables. Then I had to adapt the handrails to this situation. However, the arch is flat and touches the support here.
117. The span of the bridge is seventy-five meters (246 feet) and it is connected to the bank by ramps. The only two supports for the bridge are at the end of these ramps on both sides of the river. The bridge is blocked for torsion on one side only --one side is fixed and the other side is able to slide in one direction. The deck of the bridge is in laminated glass which also permitted us to light the bridge from underneath.
118. We opened the bridge on a working day so that, people gathered at the site. One of the big satisfactions of public works is that they are truly public. They are done for everyone. And, I think making bridges has this significance: many, many people enjoy them every day, with no effort and for no cost. Today we have lost the idealism of the '60s when architecture was very much devoted to social problems. In fact, today we ignore these problems, yet we live in a world in which a third of the people do not get enough to eat every day. I mean, it is quite dramatic. Can you imagine how much infrastructure is still needed?
119. If you think back to the heroic times of engineering, when people arrived at new places, imagine what it took just to bring water to a place; or to stop a flooding river, or to create sanitation infrastructure. I think you still feel the strength of this need when you build bridges --especially bridges in cities. I also think that the potential of bridges and bridge design has not yet been achieved. The vitality of bridges comes both from necessity and from the fact that they are unbelievably significant --even though they are ignored-- elements of the city. Significant because; could you imagine New York, for example, without those magnificent bridges? What if the George Washington bridge was a multi-span bridge, instead of being this gesture, jumping over 1,000 meters--more than half a mile-- when the previous span had been just half of that, or even less? Engineering can still provoke very wild and strong responses from gestures like these.
120. If you look at the engineering design of the nineteenth century, you will see that engineers took a lot of care in designing the handrails and the lighting. There are those great watercolor drawings where all the details were drawn. They were conscious that to take care of the details was to give more to the bridge. There are people who say, "architecture is all that you can take away from a bridge to leave the bridge standing." This is not true. Architecture is the bridge itself because the bridge is dedicated to man. All that gives satisfaction to man is good for a bridge.
121. These are some views of the construction. We built the bridge on one side, and then, using a boat with a rotating support, we turned it out over the river. Once it was turned, we elevated it and then translated it into the definitive position. Something like four maneuvers were needed to put this bridge in place. These are my last slides. I thank you very much for your attention.