Sistemas Reticulados 24/08/2008. Sistemas Reticulados. Treliças. Sistemas Estruturais Reticulados:

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1 PEF2602 Estruturas na Arquitetura I I - Sistemas Reticulados 2º Semestre 2008 Sistemas Reticulados EP-USP FAU-USP Grafos 24/08/2008 Sistemas Reticulados Treliças Diferentes Esquemas para um mesmo grafo: Sistema Reticulados: Grafos em que a posição geométrica dos nós é relevante Sistemas Estruturais Reticulados: sistemas estruturais cujos elementos podem ser bem representados por uma rede de nós interconectados por barras. Exemplo: * Sistema de Forças Centrais * Treliças Sistemas Estruturais Reticulados: Treliças Planas Treliças Espaciais Pórticos Grelhas Domos Árvores Redes de cabos Tensegrities Pantógrafos... Equilíbrio do Sistema: x x F + N = 0, i = 1,2,, n i n j i ij j= 1 xj xi

2 The idea for Quantum Cloud came from a comment about algebra made by Basil Hiley, quantum physicist (and long-time colleague of David Bohm), in which he said that "algebra is the relationship of relationships". The comment was made during a conversation between Gormley, Hiley and writer David Peat at a 1999 London gathering of artists and scientists, organized by Peat. Quantum Cloud Antony Gormley Londres, 1999

3 Fiera di Milano Exhibition Centre, Milan, Italy The Fiera di Milano exhibition and convention centre, designed by Massimiliano Fuksas, has given Italy's most stylish city a radical new makeover. Um mecanismo reticulado: pantógrafo Um domo pantográfico: (S. Pellegrino)

4 Teliças Planas: Módulo Básico - Triângulo Triângulo Módulo Básico das Treliças Planas (Triangulo de Sierspinski) Tetraedro Módulo Básico das Treliças Espaciais (Pirâmide de Sierspinski)

5 Treliça K Treliça Pettit. Treliça Baltimore. Treliça com banzo superior em partes inclinadas. Duas águas Treliça Duas águas, sem montantes

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9 Alexander Graham Bell and the Octet Truss "Climaxing Bell's architectural experiments with tetrahedral structures was an observation tower at Beinn Bhreagh, his summer estate near Baddeck, Nova Scotia. Each unit for this tower consisted of six 4-foot pieces of ordinary galvanized iron pipe and four connecting nuts; the units, themselves, were riveted together in the field by unskilled labor. Upon its completion in September 1907, the tower stood nearly 80 feet high."

10 Estruturas tensegrity Monument à la Forme Futile Emmerich, 1966 Needle Tower, Keneth Snelson, 1948

11 Monumento à Forma Fútil Monumento à Forma Fútil Y X Z Y X Z

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13 Toothpick Bridge Contest Winners The bridges become stronger and improved with the succession of experience, and the evolution begins with the adventure of the odd fellow. Year/Supported load 1997 The first competition 17.5 kgf The workof winner 1999 The third competition 47.5kgf 2000 The fourth competition 60.0kgf 2004 The eighth competition 190kgf 1998 The second competition 35.5kgf 1998 The second competition 35.5kgf 2000 The fourth competition 60.0kgf 2001 The fifth competition 85.0kgf 2005 The nineth competition 250kgf 1998 The second competition 35.5kgf 1999 The third competition 47.5kgf> 2002 The sixth competition 120kgf 2003 The seventh competition 120kgf 2005 The nineth competition 250kgf Torre Eiffel

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15 Sibelius Hall Finlândida Sibelius Hall The Sibelius Hall (Sibeliustalo) is a concert hall in Lahti, Finland, named after composer Jean Sibelius. The Hall was built in Architects Kimmo Lintula and Hannu Tikka designed the hall, which is made of wood. The acoustics were engineered by Artec Consultants, New York. Its acoustics are one of its strongest points, while it follows the Scandinavian tradition of sophisticated design. It has a capacity of 1,250 seats. The Hall is home to the Lahti Symphony Orchestra. Estádio Olímpico de Pequim Bird s Nest Março, 2008 Location: Beijing, China Broke ground: December 2003 Owner: Government of the People's Republic of China Construction cost: ~USD $500 million Architect: Herzog & de Meuron, ArupSport, CAG Capacity: 80,000 / 91,000 (Olympics)

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17 Complexo Aquático de Pequim Water Cube, ou H 2 O 3 ) Março, 2008

18 Estrutura de Kelvin: Arranjo compacto de Octaedros Truncados Designers: PTW Architects (Australia, Arup international engineering group, CSCEC (China State Construction Engineering Corporation) and the CSCEC Shenzhen Design Institute (CSCEC+DESIGN) Comprising a steel space frame, it is the largest ETFE clad structure in the world with over 100,000 m² of ETFE pillows that are only 0.2 mm (1/125 of an inch) in total thickness. The ETFE cladding allows more light and heat penetration than traditional glass, resulting in a 30% decrease in energy costs. The outer wall is based on the Weaire-Phelan structure, a structure devised from the natural formation of bubbles in soap foam.the complex Weaire-Phelan pattern was developed by slicing through bubbles in soap foam, resulting in more irregular, organic patterns than foam bubble structures proposed earlier by the scientist Kelvin Using the Weaire-Phelan geometry, the Water Cube's exterior is made of 4,000 ETFE bubbles, some as large as 9.14 meters (30 feet) across, with seven different sizes for the roof and 15 for the walls. The structure will have a capacity of 17,000 during the games that will be reduced to 6,000 afterwards. It also has a total land surface of 65,000 square meters and will cover a total of 32,000 square metres (7.9 acres). Although called the Water Cube, the aquatic center is really a rectangular box meters (584 feet) square and 31 meters (102 feet) high. Estrutura de Wearie-Phelan: Arranjo compacto de tetradecaedros (14 faces) e dodecaedros (12 faces) irregulares Um dodecaedro regular

19 The Weaire-Phelan foam provided not just a pretty surface for the walls, but the building s very structure. Imagine an enormous block of the foam, with steel beams outlining the edge of each bubble. Now carve out the center to form a building with 12-foot-thick walls and 24-foot thick ceilings. This is the weight-bearing structure of the Water Cube. The result is so strong, the engineers say, that the entire building could be turned on its side without collapsing. Furthermore, the remarkable effect is that they ve designed a building without triangles. Ordinarily, buildings rely on triangles to provide stiffness, since a triangle is the only two-dimensional shape that can t be deformed without changing the length of its sides. The engineers say that this lack of triangles will make the building more flexible and hence more able to withstand earthquakes. The special award for the most accomplished work in the section Atmosphere is awarded to the Australian architecture firm PTW Architects, CSCEC + Design and Arup for the project National Swimming Center, Beijing Olympic Green, China. The project demonstrates in a stunning way, how the deliberate morphing of molecular science, architecture and phenomenology can create an airy and misty atmosphere for a personal experience of water leisure Quote from the Jury report of the Official Awards 9th International Architecture Exhibition - METAMORPH, Venice Biennale A BUILDING OF BUBBLES By Julie Rehmeyer Web edition : Saturday, July 19th, 2008