24/08/2008 • Sistemas Reticulados • Treliças Sistemas - LMC

Sistemas Reticulados
PEF2602
Estruturas na Arquitetura I I - Sistemas Reticulados
2º Semestre 2008
FAU-USP
EP-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
www.lmc.ep.usp.br/disciplinas/pef2602
Sistemas Estruturais Reticulados:
sistemas estruturais cujos elementos podem ser bem
representados por uma rede de nós interconectados por barras.
• Treliças Planas
• Treliças Espaciais
• Pórticos
• Grelhas
• Domos
• Árvores
• Redes de cabos
• Tensegrities
• Pantógrafos
•....
Exemplo:
* Sistema de Forças Centrais
* Treliças
Equilíbrio
do Sistema:
Sistemas Estruturais Reticulados:
n
x j − xi
j =1
x j − xi
Fi + ∑ N ij
= 0 , i = 1, 2,… , n
Quantum Cloud
Antony Gormley
Londres, 1999
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.
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)
Teliças Planas:
Módulo Básico - Triângulo
Triângulo – Módulo Básico das
Treliças Planas
(Triangulo de Sierspinski)
Tetraedro – Módulo Básico das
Treliças Espaciais
(Pirâmide de Sierspinski)
Treliça K
Treliça Baltimore.
Treliça Pettit.
Treliça com banzo superior em partes inclinadas.
“Duas águas”
Treliça “Duas águas”,
sem montantes
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."
Estruturas ‘tensegrity’
Monument à la Forme Futile
Emmerich, 1966
“Needle Tower”,
Keneth Snelson, 1948
Monumento à Forma Fútil
Y
X
Z
Monumento à Forma Fútil
Y
X
Z
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
1998
The second competition
35.5kgf
1998
The second competition
35.5kgf
1999
The third competition
47.5kgf
The workof winner
2004
The eighth competition
190kgf
2000
The fourth competition
60.0kgf
2000
The fourth competition
60.0kgf
2001
The fifth competition
85.0kgf
2005
The nineth competition
250kgf
2002
The sixth competition
120kgf
1998
The second competition
35.5kgf
1999
The third competition
47.5kgf>
2003
The seventh competition
120kgf
Torre Eiffel
2005
The nineth competition
250kgf
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 2000.
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)
Complexo Aquático de Pequim
“Water Cube” , ou “H2O3”)
Março, 2008
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 - 178 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…
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.
A BUILDING OF BUBBLES
By Julie Rehmeyer
Web edition : Saturday, July 19th, 2008
“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