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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

SISTEMA DE EDIFICAÇÃO

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LATTICE GRID SHELL

ANNA TIMMERMANS

SANDER DELCHAMBRE

VINCENT MACRIS

JOÃO MENDINHOS


2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

ÍNDICE

1. Introdução 2. Evolução Histórica 2.1. Caracterização do Sistema Adoptado (Influências Conceptuais/Bases de Concepção/Desenho/Elementos/Materiais)‫‏‬ 2.2. Características Técnicas 2.3. Potencialidades de Uso/Rentabilidade

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3. Implementação em Projecto 3.1. Esboços e Ideias 3.2. Possibilidades Plásticas/Variantes/Limitações/Físicas/Geográficas/ Fenómenos Naturais 3.3. Inovações Possíveis (últimos 10 anos)‫‏‬ 3.4. Aspectos Construtivos Relevantes 3.5. Processo de Produção e Montagem (Construção)‫‏‬ 3.6. Avaliação do Comportamento/Patologias 3.7. Eventual Recuperação

Imagem 1 – Cable Railway, Innsbruck, Zaha Hadid

4. Duas Obras de Referências 4.1. Autores e Análise das Obras 4.2.Sistema Construtivo (Ideia/Bases de Concepção/Função/Escala/Materiais/ Variações)‫‏‬ 4.3. Abordagens Construtivas 4.4. Opções de Edificação

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Imagem 2 – Cable Railway, Innsbruck, Zaha Hadid Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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ÍNDICE

5. Modelo Homotético 5.1. Metodologia (Critérios de Execução dos Modelos Tridimensionais)‫‏‬ 5.2. Análise Estrutural (Sistemas Construtivos)‫‏‬ 5.3. Análise crítica (Processo de Produção das Maquetas e Problemas Encontrados)‫‏‬ 6. Conclusão

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7. Bibliografia

Imagem 3 – 3D Model

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Imagem 4 – Section & Homothetic Model of Analysis Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

INTRODUÇÃO

1. Introdução The Nordpark Cable Railway is comprising four new stations and a cable-stayed suspension bridge over the river Inn. It was opened in a ceremony at Loewenhaus Station, Rennweg, Innsbruck on 01 December 2007. Starting at the station of Congress in the centre of the city, the railway travels to Loewenhaus station before crossing the river, ascending the Nordkette Mountain north of Innsbruck to Alpenzoo station. The final station is at Hungerburg village, 288 metres above Innsbruck, where passengers can join the cable-car to the summit of the Seegrube Mountain Zaha Hadid Architects won the competition to create Nordpark Cable Railway in 2005 together with the contractor Strabag. The railway is the second project completed by Zaha Hadid in the city; the Bergisel Ski Jump by Hadid was completed in 2002 and awarded the Gold Medal for Design by the International Olympic Committee in 2005.

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Imagem 5 – Panoramic View of the Implementation

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Imagem 6 – Zaha Hadid – Architecture and Design Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

EVOLUÇÃO HISTÓRICA

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Imagem 7 – Planar wooden beams ready to be lifted

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2.1. Caracterização do Sistema Adoptado (Influências Conceptuais/Bases de Concepção/Desenho/Elementos/Materiais)‫‏‬ A lattice grid shell system is a structure that is based on a rectangular planar grid that is transformed to a more organic form with a double curvature which ensures the strength of it. The main original concept is to create a 2D grid of connected wooden beams on the ground and push them from the external ribs to the inside in such a way that the desired 3D form can be achieved. Unfortunately this method is only possible with wooden beams. The famous Russian engineer/scientist/architect Vladimir Shukhov pioneered a first fixed steel gridshell structure in Vyksa in 1896, it was the world s first double curvature gridshell. This innovative design changed the way of thinking about these kind of systems and different materials such as steel and later-on plastics were fitted into the system. After this evolution the modification of the grid became much more complex with the digital computing era. Computers make it possible to generate different and more difficult transformations in space.

Imagem 8 – Homothetic Model of a Wooden Gridshell & V. Shukhov, Steel Gridshell Structure in Vyksa, 1896 Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

EVOLUÇÃO HISTÓRICA

Imagem 9 – Wooden Connections with Exterior Glass

2.2. Características Técnicas The difficulty of the techniques in grid shell structure are the connections between the nodes. Nodes are the most critical objects in a grid structure followed by the anchoring. Each grid shell structure will need its own system of connections for the different types of beams that are used, and likely or not a different material from wood, plastic, metal, … -elements. Once the main structure is built it’s still possible to cover this with glass, wood, zinc, aluminum, plastics or laminate, as well on the inside, outside or in between the structural beams. This all depends on the design, what is preferred and what the final outcome has to be. Manufacturing all the same elements in a symmetrical design will be an optimal, ecological and economical advantage. However this is not always the main goal of an architect, architect Zaha Hadid for example translates the form to a very conceptual design with no structural element being the same. In this case digital design and computing technology for calculating, printing, cutting and manufacturing will be used.

Imagem 10 – Principles of Connections & Surfaces Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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EVOLUÇÃO HISTÓRICA

There are two main deformations which can be used to make the desired form with a lattice grid. The first one is a method based on the repositioning of the nodes in the grid and making organic surfaces or roof/shells. The second one is based on the deformation of the grid elements itself, the beams, in this way more conceptual new solid forms can be designed. First Method: Repositioning the nodes of the lattice grid

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The idea of the system starts from one planar lattice grid of beams. To achieve the double curvature the nodes need to be moved upwards to finally get a dome or another organic form by pushing it from the outer parts. In this case the beams will just be the same but in different positions. By playing with the location of the different nodes we can manipulate the lattice grid and create some new innovated structures with it. A perfect example is a structure made by the engineer Laurent Ney, the grid is based on the internal forces of the total structure. He calculated and computed every point of the grid to be in the best place for optimizing the shape to it s strength. 2.3 Potencialidades de Uso/Rentabilidade The goal of a grid shell is to make a lightweight and thin structure that is used just for covering (like a shell) and not to bear heavy loads. If it is a system with a double curvature, a dome for example, it can provide a huge span without internal supports or columns and is therefore often used for roofing. It s possible to cover the structure with different materials such as wood, plastics or even glass to fill the spaces in between and permitting sunlight to pass trough. When glass is used the lightness of this system is truly recognizable.

Imagem 11 – Method 1

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Imagem 12 – Grid Calculation - Laurent Ney Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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EVOLUÇÃO HISTÓRICA

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Imagem 13 – Foster, Q. Elizabeth II Great Court, London

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Imagem 14 – Massimiliano Fuksas, Vela, Milan

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Imagem 16 – Rem Koolhaas CCTV Beijing

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Imagem 15 – Grid structure made with generative scripting

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Imagem 17 – Herzog & de Meuron Beijing Stadium

Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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Imagem 18 – descrição

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

EVOLUÇÃO HISTÓRICA

Second Method: Transforming and deforming the structural elements of the lattice grid The idea of this method also starts from one planar grid of beams but we don t explicitly move the nodes, however it s still possible, but we define the form of de grid elements themselves by deforming or transforming them. The goal of this method is to design specific forms, organic or not, for either a technical purpose or a conceptual approach. Boats for example, are designed to float on water with as few resistance as possible. Therefore the solution exists in creating such a smooth form with the use of this kind of lattice grid shell system.

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2.3 Potencialidades de Uso/Rentabilidade The problem of these structures is the manufacturing process. Because of each element being slightly different it s a quite difficult task to produce and make such an organic form. Not only the beams but also the connection between them is another important technical difficulty. It s noticeable that there are not many forms like these built yet, but future architects will be able to make this change. The implementation of digital design and scripting –which is the creation of mathematical functions to generate special 3D forms - makes it possible to create these conceptual forms. Nowadays it s not even a necessity anymore for an architect to draw sections of a structure like this and definitely not by hand. Because of the extraordinary shape of organic structures, each section would be different, even if it would be only a section made 10 cm further. Computers are being used to design the shape, calculate the deformations, transformations, size and form of each individual element. After it has been send to the new generation of printing and cutting machines it s ready to be produced.

Imagem 19 – Method 2

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Imagem 20 – AA DRL Pavilion Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

EVOLUÇÃO HISTÓRICA

Imagem 21 – Transformation of fuselage to wing, two similar systems

Influências Conceptuais/Bases de Concepção Because of this lightweight structure the link with the concept and production of airplanes is easily made. However both body and wings are two totally different structures they are actually derived from the same system. The concept of a fuselage (the body) is to protect the passengers from the outside weather and flying conditions and to fit in the aero dynamical design. This is possible by making it with a tubular grid shell system and defining the form which translates from the front to the back of the plane (images on the right). The fuselage differs from the wing because it’s necessary to have open space for loads and passengers in the tube, it has similar ribs of the same thickness with a few exceptions in crucial points and sections. So imagine if the fuselage didn’t need to be an open tube and the main ribs were connected to a solid part like the red surfaces shown in the image above. From this point of view you can transform this tube to the actual form of the wing. Arriving at the concept of an airplane wing it is now possible to achieve aerodynamic design by modeling and adapting the red solid surfaces to optimize the shape.

Imagem 22 – Fuselage Tubular Grid-shell /Digital Model Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

EVOLUÇÃO HISTÓRICA

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Imagem 23 – Hexagonal Grid Structure

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Imagem 24 – AA DRL Pavilion, Bedford Square

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Imagem 26 – Grid structure used in an aeroplane wing

Imagem 25 – Structural Elements, Z. Hadid, Innsbruck

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Imagem 27 – Grid structure used in a boat

Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

Imagem 28 – Grid Structure in Conceptual Design

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IMPLEMENTAÇÃO EM PROJECTO

Imagem 29 – Panoramic View of the Highest Station

3.1. Esboços e Ideias The concept for the four new stations is based on two contradictory elements ‘Shell & Shadow’. The lightweight organic roof structure floats on top of a heavily shaped concrete plinth. In each station the fluid language of natural ice formations is used, like a frozen stream on the mountainside. This artificial landscape describes the movement and circulation within. At the same time each station adapts to its own unique context, topography, altitude, and circulation. The flowing lines of the Congress Center station's roof, for example, are integrated in their environment, while at the Löwenhaus station the dynamic of the river Inn can be found in the undulating shape. The Alpenzoo station is characterized by a glass tower, the Hungerburg station by a curved S-shaped roof. Despite these differences, the formal links between all four locations are kept.

Imagem 30 – Global Concept: Ice Formation & Glaciers Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE  DE  ARQUITECTURA     UNIVERSIDADE  TÉCNICA  DE  LISBOA  

Imagem 31 – Hungerburg station & Congress Station                                                                

IMPLEMENTAÇÃO EM PROJECTO

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3.2. Possibilidades Plásticas/Variantes/Limitações/Físicas/Geográficas/Fenómenos Naturais The 1.8 km-long rack railway line from downtown Innsbruck up to the Nordkette alpine recreation area some 2,000 m above sea level includes four station buildings and the 242m-long cable-stayed bridge over the River Inn. Starting at the station of Congress in the centre of the city, the railway travels to Loewenhaus station before crossing the river, ascending the Nordkette Mountain north of Innsbruck to Alpenzoo station. The final station is at Hungerburg village, 288 meters above Innsbruck, where passengers can join the cable-car to the summit of the Seegrube Mountain. Each station is built by the same construction method but has his difference in the fluid shaped form. The forms are adapted to the surrounding landscape, for example the form of the Löwenhaus station is inspired by the movement of the nearby river Inn. With the construction method that is used here, fluid forms can be obtained.The condition of each form is that the structure must rest on at least three points (yet it seems like the structure floats). On this points the system is anchored in the concrete plinths and because the stations are just roof shells there are no big temperature differences that can effect the expension of the curved glass.

Imagem 32 – alpenzoo station Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

Löwenhaus Station

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

IMPLEMENTAÇÃO EM PROJECTO

3.3. Inovações Possíveis (últimos 10 anos) Zaha Hadid One of the possible solutions to new innovations concerning this principle of grid structures can be found in the project of Zaha Hadid. The typical theoretical form of grid structures is usually adapted to big projects, for instance domes, sport complexes, concert halls etc... In these projects the originality usually depends on the form of the complete structure. Hereby the actual structure is rather functional, depending on the internal and external forces that are to be expected. The structure is only the basis of the architectural form, it s not an innovation at itself (apart from the fact that every grid structure has it s specific demands and thereby is original in it s own way). In contrary to this stereotypic definition, this project is innovative in it s structure itself, because the structural form has become an architectural form. The grid structure itself is no longer existing out of a great number of separated, but equal pieces. The structure has become organic by connecting all the different (organic) pieces. The shell that surrounds the structure isn t more than a shell, as a shiny coating. In the end the shell (,what we eventually see,) reveals the structure. So in a certain way we could say that the structure has become visual. The second example of Hadid s work that follows this trend is the Contemporary Exhibition Pavilion for Chanel. The grid principle is the same, however there is one difference, instead of a linear array the grid in this project is based on a rotational arry. The form, a torus (geometrical name for doughnut), is cut into 36 different pieces, each with an angle of 10°. Instead of a linear array the grid in this example is based on a rotational array.

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Imagem 33 – Nordpark Cable Railway - Alpenzoo by Zaha Hadid

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Imagem 34 – Chanel Exhibition Pavilion by Zaha Hadid Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

IMPLEMENTAÇÃO EM PROJECTO

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Imagem 35 – Linear Array

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Imagem 36 – Structural Linear Elements

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Imagem 38 – Rotational Array

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Imagem 39 – Zaha Hadid, Chanel Exhibition

Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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Imagem 37 – Zaha Hadid, Cable Railway, Innsbruck

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Imagem 40 – 3D Model, Zaha Hadid, Chanel Exhibition

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

IMPLEMENTAÇÃO EM PROJECTO

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Imagem 41 – rendering Swoosh summer pavilion

AA’s ‘Swoosh’ summer pavilion (student Valeria Garcia) This year’s (2008) AA summer pavilion competition was won by student Valeria Garcia. She created an elliptical pavilion where people would be able to walk through, sit on, relax… The project was made with a principal quite similar to Hadid’s higher mentioned grid structure. Due to the use of different material, wood in stet of steel, the distance between beam and columns (which exist out of vertical beams) is much smaller. Because of the shape of this project each beam points out towards a center point, and therefore none of them is parallel. Because of the form, each beam or column, which are all different, had to be cut using the CNC cutting system. This renewing project shows even more of the structure (because is has got no shell) then Hadid’s projects and therefore is a very good example of an architectural structure.

Imagem 42 – up: plan drawing | down: rendering Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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IMPLEMENTAÇÃO EM PROJECTO

3.4. Aspectos Construtivos Relevantes To translate the 3D digital models directly into the cutting apparates for the steel plates, CNC milling is used. The milling machine is digitally automated via CNC. CNC stands for computer numerical control and is a computer controller that reads G-code and Mcode. CNC machines today are controlled directly from files created bij CAM software packages so that a part or assembly can go directly from design to manufacturing so that there was an economic assembly process and the number of working drawings and convention plans are minimalised. A milling machine is a machine tool that was used for shaping the steel ribs. Its basic form is that of a rotating cutter which rotates about the spindle axis (similar to a drill), and a table to which the workpiece is affixed. In contrast to drilling, where the drill is moved exclusively along its axis, the milling operation involves movement of the rotating cutter sideways as well as 'in and out'. The cutter and workpiece move relative to each other, generating a toolpath along which material is removed. The movement is precisely controlled, usually with slides and leadscrews or analogous technology. Often the movement is achieved by moving the table while the cutter rotates in one place, but regardless of how the parts of the machine slide, the result that matters is the relative motion between cutter and workpiece. CNC machines can exist in virtually any of the forms of manual machinery, like horizontal mills. The most advanced CNC milling-machines, the 5-axis machines, add two more axes in addition to the three normal axes (XYZ). Horizontal milling machines also have a C or Q axis, allowing the horizontally mounted workpiece to be rotated, essentially allowing asymmetric and eccentric turning. The fifth axis (B axis) controls the tilt of the tool itself. When all of these axes are used in conjunction with each other, extremely complicated geometries, even organic geometries can be made with relative ease. Thermoforming is when a plastic sheet or film is converted into a formed, finished part. In the thermoforming process the plastic sheet or film is fed from a roll or from an extruder into a set of indexing chains that incorporate pins, or spikes, that pierce the sheet and gets heated in an oven to its forming temperature. For the sheet heating quartz heaters or radiant-panel heaters are used. This makes it also easy to control it zonely. The heated sheet then indexes into a form station where a mating mold and pressure-box close on the sheet, with vacuum then applied to remove trapped air and to pull the material into or onto the mold along with pressurized air to form the plastic to the detailed shape of the mold. The CNC milling and thermoforming are new production methods witch are also used in the automotive industry. Those two methods are applied to create the streamlined aesthetics of each station.

Imagem 43 - 5-axis machining center with rotating table and computer interface

Imagem 44 – 4 different CNC machines Intl. Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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IMPLEMENTAÇÃO EM PROJECTO

3.5. Processo de Produção e Montagem (Construção)‫‏‬ The loadbearing structure is a grid with a dept of three meters. The grid exist of vertical steel ribs with a thickness of eight and twelve milimeters, on a distance of 1.25 meters center to center (the maximum for capicity). The structure follows the line of the skin with between the two a spacing from 60 milimeters. The roof is beared by elliptical vertical and circular horizontal supports, that are anchored in the surrounding concrete structure. The skin is continuous and homogeneous without obtrusive joints and fixings (to obtain zaha hadid s typical seamless fluidity). To achieve these qualities and the special thermal standards, glass is used. The first layer of glass is a support for the actual panel, and his form is bent this way. On the inside, the float glass is covered with polyurethane resin. The resin is not only applied for the coloration but also when breakage should happen there will stay a residual loadbearing strenght. The glas bears on the cross-ribs. The panes are supported on two, three or four edges, depending on the loading and position. At the end of the roof and where there are great differences in the height of the ribs, there are supports in the longitudinal direction. In case of snow loads, additional steel ribs were adhesively fixed to the inside face of the panes of glass. To connect the steel to the glass, the steel sheets are clasped (omklemd) with a continuous linear polythene section. Because structure follows the skin, this polythene had to be indivually made. The sections are cut from flat sheets, with a five – axis cutting tool (CNC cutting). To connect the glass with the polythene sections, compact T-shaped sheet-metal elements from 20 cm long were used. The T-element is in one side fixed to the inside face of the glass and on the other side bolted to the polythene sections. This main principle is adapted to the form of each station.

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Imagem 45 – construction of NCR- Loewenhaus by Zaha Hadid

Imagem 46 – Isometric of steel-rib roof structure NCR- hungerburg Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE  DE  ARQUITECTURA     UNIVERSIDADE  TÉCNICA  DE  LISBOA  

IMPLEMENTAÇÃO EM PROJECTO

Imagem 47  –  hungerburg  sta@on  in  snow@me      

3.6. Avaliação do  Comportamento/Patologias The grid is especially infected by the extreme climate events, like very heavy snow load and windstorms. Because the system mostly is borne by steel-framed glass, inherent problems can occur. The structure for the station buildings are covered with high – gloss thermo-melded glass roofs. Under it, it is covered with polyurethane resin. This resin makes sure that when makes sure that when the system should collapse under the snow weight or wind pressure the glass will not break and remain whole while giving a residual load bearing strength. For giving extra support to the system in snow/wind circumstances there are additional steel ribs fixed under the glas spanels. In case of rainstorm, a sufficient drainage system is developed underneath the panels. 3.7. Eventual Recuperação A project like this with a lattice grid shell system includes a very recent and new way of design. Therefore it s obvious that no damage is found to inspect and analyse at this time. Brand new technologies like these will definitely assure the durability of future projects and in case of damage to a piece they will just be reproduced and replaced. The intern structure is well protected by the shell elements around it which will endure the roughest circumstances. The most attention has to go to the internal expansion or shrinking of the steel and plastic beams, especially for the connections because these are the most critical points in such a project.

Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

Imagem 48  –  close-­‐up  skin      

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DUAS OBRAS DE REFERÊNCIAS

Imagem 49 – Repsol Service Station, Foster & Partners

4.1. Autores e Análise das Obras When the Spanish oil and gas company Repsol commissioned the practice to design a new service station system, the challenge was to update the companys distinctive roadside identity while delivering a highly flexible solution capable of adaptation to suit the more than 200 sites planned around Spain. In an elegant way the architect Norman Foster designed the Repsol gasoline station which is recognizable from its high-rise elements in the shape of an inverted pyramid. The modular canopy system provides the number needed for each station and the three signature colors from Repsol will be proudly represented; red, orange and white. Clusters of these structures form overlapping umbrellas sheltering each station forecourt. The umbrellas vary in number, height and in the degree of overlap between them, according to the size and specifics of each site. The canopies are arranged according to a pre-determined sequence, which ensures that a red one is always the tallest. This brightly coloured combination creates a strong three-dimensional image. Even from the air Repsols identity is clearly announced. On the road the stations are identifiable from a distance and are vivid and inviting when approached. The associated shop unit, car wash, petrol pumps and signage elements all belong to a related family of pure, box-like forms. Together, this kit of parts provides the maximum flexibility in planning and can respond to virtually any site configuration. All these lightweight elements are factory made and easily transported and installed on site, providing cost benefits while ensuring consistently high quality standards and rapid delivery. Imagem 50 – Repsol Service Station, Foster & Partners Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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DUAS OBRAS DE REFERÊNCIAS

Imagem 51 – Transformation of Grid to a Pyramid

4.2. Sistema Construtivo (Ideia/Bases de Concepção/Função/Escala/Materiais/Variações)‫‏‬ 4.3. Abordagens Construtivas 4.4. Opções de Edificação When the structures of the project from Hadid in Innsbruck and Foster’s Repsol station will be compared it’s clear enough to see that they both have a lattice grid shell system. However it’s not completely the same and one is more organic than the other they have much in common. Differences: The first difference that is noticeable are the lines of the basic grid, two diagonals have been added to achieve a pyramid shaped form. When these diagonals are connected with squares following the grid (red), they may also be considered as a result the system with a rotational array, comparable to the ‘Chanel’ project from Hadid. Foster’s design is more symmetrical compared with the very conceptual and innovating structures from Hadid. But besides this, Foster uses only one connection for each modular canopy to the ground, one fixed point. Foster’s design also includes a prefabricated product assembled on site, but one to produce several times for each station, with variations in height, number and degree of overlap with each other. Similarities: The idea of one fixed point is used into the homothetic model for further analysis, the link between Hadid and Foster’s project will be too easy to understand with the only big difference being the smoothness of the form, organic vs. rigidity. Imagem 52 – Principle Foster & Homothetic Model Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

MODELO HOMOTÉTICO

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Imagem 53 – animation from the build-up of the homothetic model 5.1. Metodologia (Critérios de Execução dos Modelos Tridimensionais) The intention of making a three-dimensional model is showing the way the actual structure(s) work. To do this, an own design was‫‏‬ made, with the intention of creating a comparable organic form, that uses the same principle of handling with the external (and internal ) forces. One of the most important things involved using a light, yet very strong and rigid material. The next criteria was a rigid connection , because having bad connections (between beams and columns) would result in a non-stiff model, which is an absolute must for these kind of projects. To fulfill these principles a handmade wooden structure was made, with a precision of 1 mm. At first a 3D generated model was made digitally, involving several 3D animations (renderings) and plans, followed by the print of it. Then the printed version was .copied onto a wooden panel. At last the pieces were cut out the panel, and put together. The whole model is handmade To make it easy to be transported and to minimalise the work, the model was made demountable and connected without any glue or whatsoever. Imagem 54 – model | plan | rendering Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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MODELO HOMOTÉTICO

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Imagem 55 – downward traction 5.2. Análise Estrutural (Sistemas Construtivos)‫‏‬ The applied external forces were taken at the endpoints, because the structure is only as strong as its weakest point. Which are the endpoints in this case, from where the distance is the biggest to the center , and where the thickness is at its lowest. )Downward traction (image 55 & 58‫‏‬ When pulling down on of the endpoints, obviously a different in height is recognizable. This is the maximum amplitude of deformation in this direction. The further towards the center, the less the deformation. This due to the height of the beam, and as higher mentioned to its length. Torsion (image 56 & 58) When pulling at both ends in opposite direction an axial deformation is visual. The deformation again is the biggest at the ends. In the center the deformation is less visual because it’s the stiffest point. Towards the ends the grid transforms from the original squares and rectangles to diamonds. Imagem 56 – torsion | wind load Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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MODELO HOMOTÉTICO

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Imagem 57 – external loads (extra weight) )external loads (extra weight‫‏‬ Because of the shape, that is intended to deduct the forces towards the ground at the middle, the center point is able to take the biggest loads. That’s why the surface is the biggest in this area. At the ends, due to its weakness, both height and width are very restrained, so it would never take too big loads. Because of the fact that the homothetic model is out of proportion, the loads on the model are not exactly comparable to real structures. But it shows however the strength of the construction. In image 57 the external loads go from 5kg (5L water) up to 7kg (5L water and 4 books). In image 59 a total load of around 10 kg up 12kg to has been put to the test.

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Imagem 58 – downward traction | torsion (a-a ) Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

MODELO HOMOTÉTICO

Imagem 59 – external loads (extra weight) 5.3. Análise crítica (Processo de Produção das Maquetas e Problemas Encontrados)‫‏‬ In the process of the development towards the final model, most of the problems were found in inventing an aesthetic, yet strong, not to heavy and representing model. The first models in cardboard dealt with lack of stiffness or breakage caused by too deep incisions. The final model had to be made very precise, to make each part fit into the other, which cost a lot of time and effort. Some strength problems showed up around the fixing in the base plate. But it the end it was made possible to make a very strong fixing, without glue or any other fittings but wood. The model isn’t 100% stiff and strong at each point because it was handmade, and some of the fittings (incisions) were a little bit too big, what causes the possibility to move.

Imagem 60 – development of model Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

CONCLUSÃO

6. Conclusão Each grid structure is unique in it’s own way. All the projects, based on these kind of principles are to be calculated, generated and seen in their context, usage and concept. Such architectural and not to be forgotten, ingenuous creations are only approachable in a theoretical way, but never a completely correct way. Each system has it’s own thickness, length, width, height… No context nor concept is the same. But comparisons based on the structural system can be a good reference to future projects.

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Imagem 61 – Hadid

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Imagem 62 – Hadid Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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2008|09 FACULDADE DE ARQUITECTURA UNIVERSIDADE TÉCNICA DE LISBOA

BIBLIOGRAFIA

7. Bibliografia Internet: www.detail.de www.archi-europe.com http://architect.com www.anc-d.fukui-u.ac.jp www.zaha-hadid.com www.pushpullbar.com www.flickr.com www.deviantart.com http://thomasmayerarchive.de http://www.arcspace.com/architects/hadid/nordpark/nordpark.html http://www.e-architect.co.uk/austria/nordpark_zaha_hadid.htm http://www.worldbuildingsdirectory.com/project.cfm?id=48 http://digitoolbox.wikidot.com/design-to-production http://www.thecoolhunter.co.uk/architecture/2/ http://thomasmayerarchive.de/categories.php?cat_id=1473&sessionid=60de55662b8cb2b6c08dbc9da85f6404&l=english http://www.bdonline.co.uk/story.asp?storycode=3110779 http://www.skyscrapercity.com/showthread.php?t=678936

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Imagem 61 – Hadid

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Imagem 62 – Hadid Anna Timmermans Sander Delchambre Vincent Macris joão Mendinhos

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SISTEMA DE EDIFICAÇÃO  

Analysis of a lattice grid shell

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