Forma trougla u arhitekturi fasada savremenih objekata

THE TRIANGULAR FORMS OF THE MODERN ARCHITECTURE BUILDINGS FACADESOlivera Nikoli, Vladan Nikoli, Petar Peji

ABSTRACT

Triangular forms, along with quadratic forms, are most commonly used as a design of the architectural structures facade plane, especially in modern architecture. Contemporary forms of architectural structures, increasingly, involve streamlined and simplified form, where the visual effect is achieved by treatment of the facade plane texture. The triangle, as a statically ideal figure, is very interesting in visual explorations of contemporary architects.

Triangular facade articulation occurs in several ways: as a form of faade plane, as a form created by visibility of structural elements in the plane of the facade, as an independent element of faade membrane structure and so on. This paper is an analysis of typical contemporary examples and gives a classification of triangular articulation of modern architectural building facades.Key words: triangle, form, element, faade, architecture, classification1. INTRODUCTION

In the recent years in contemporary architecture, one frequently encounters structures having pyramidal forms, or buildings where the faade planes are obtained by joining triangular panels. Starting from a simple form of the triangle, be it equilateral, isosceles or right, and by their combination, the architects achieve complex building forms.

In this paper will be analyzed manners of combining and joining of triangles, and the expression and importance of a pyramidal form, and made a classification of usage of triangular forms of contemporary architectonic structures.

The goal of the paper is to emphasize the importance of the design accomplished by usage of simple forms and to present new tendencies in treatment of faade planes.

2. BACKGROUNDThe form of a triangle, in historical perspective, is one of the most used forms in architecture. The shape of a triangle in the facade planes occurred in architecture and structure of dwellings of the Lepenski Vir site as early as in the Mesolithic period, 6000 BC.

Figure 1. Mesolithic House at Lepenski Vir, illustrations by Giovanni Caselli

The shape of a triangle in the design of facades, throughout history was used both in mundane and sacred architecture. Geometrical shape of a triangle was the favorite form of the Greek architecture and every ancient pediment has it. It is supposed to have originated from the Egyptian pyramids, where this form, in the old world, represented the aspiration to divinity. Later, in the Christian Middle Ages, the triangle is often seen in church architecture, and not only near the bell towers, which with their height and form represent a link between earth and sky. The symbolism of the triangle represents the starting point in designing modern spiritual structures such as e.g. San Josemara Escriv Mexico City Church, which was designed by architect Javier Sordo Madalena Bringas in 2008. Figure 2. a) The Great Pyramid of Giza in 4700 B.C. with proportions according to a "sacred ratio.", b) The Temple of Hephaistos in Athens, c) Cologne Cathedral - the largest church in Germany d) San Josemara Escriv church in Mexico City

3. CLASSIFICATION

Based on the analysis of the data collected on the characteristic buildings of contemporary architecture, a classification on the use of a triangle in formation of the faade plane form was made. The shape of a triangle can be found as:

- forms of the facade planes

- forms created by visibility of structural elements in the plane of the facade

- elements in plane of the facade skin

- elements of spatial facade skin

3.1. Triangle as a form of the facade planes

The triangular form was used for the compositions where one wants to create emphasis, which in the case of architectural structures means setting accents in space, because this form attracts the viewers attention and becomes the focus. No matter which side of the triangle is observed, it indicates something.

It is no coincidence then that this form is used in the design of monumental buildings or facilities used to emphasize the importance and achieve spatial dominance.

In recent years, construction of three pyramidal skyscrapers, where the main faade form is a triangle has started in Europe.

In London, until the beginning of the Olympic games in 2012, the tallest building in Western Europe will be built, the skyscraper called The Shard (Figure 3). The building was designed by architect Renzo Piano, and it represents a vertical city with office space, restaurants, hotels, exclusive apartments and panoramic views of 360 . It is 310m high. The investors concept, when designing the skyscrapers, was to direct the attention of the world at London Bridge Quarter. The facades are composed of eight irregular triangles which does not touch each other at the tops , and they were inspired by the London church towers and by the sails of ships sailing in the Thames. Figure 3. The Shard, London, arch. Renzo Piano

In Paris, another pyramid-shaped vertical city is under construction. "Le Projet Triangle", or the Parisian pyramid, as it came to be called, is situated at an important location in Paris. The skyscraper was designed by Swiss firm Herzog & de Meuron. It is 180 m high, and it includes 50 floors of different functions.

The designers emphasize that in the design of the building they took into account its volumetry and its impact on the environment, so the adopted pyramidal form is actually imposed as the best possible form, in order to protect the environment from the shadows and maximize using insolation and wind energy.

Figure 3. Le Projet Triangle, Paris, Herzog & de MeuronHowever, the question is whether this is the only reason or there is also the formalism, because the analysis of the recent work of this team leads to the conclusion that triangular shape is prominent, as in fact, in recent years the team has created several impressive structures using triangular shapes. Those are: Forum, the concert hall in Barcelona, Tate Modern, contemporary art gallery in London which has experienced redesign during the construction and became a high energy efficiency building, Tower for Basel II, the Roche pharmaceutical company headquarters in Basel.

Figure 4. a) Forum in Barcelona, b) Tate Modern, c) Tower for Basel II, Herzog & de MeuronIn Moscow, the construction of the tallest building in Europe (612.2 m) is in progress, the International Business Center, called , which means The Russia Tower. The building was designed by the architect Norman Foster. The construction will be completed by the end of 2012. The analyzing this structure, it can be concluded that the three skyscrapers have been combined into a single one, tapering towards the top, creating a pyramidal building form. The architects chose the pyramidal shape of the tower because of greater exposure to natural daylight of entire the building, which will reduce the amount of energy consumed by lighting and heating of the facility.

Figure 5. The Russia Tower, Moscow International Business Centre in Moscow, arch. Norman Foster3.2 The triangle as a form created by visibility of the structural elements in the facade planeShape of the structure is usually not random. Any structure must fulfill two basic conditions: to serve the function and be stable. Very often, the shape of the structure and of its parts determines its stability. The structural elements, connected so as to form a triangle, form, in fact, the strongest and most stable form, from the viewpoint of static stability.

Architects and engineers use patterns generated by algorithmic formulae, such as fractals, pinwheels, as well as cellular and reticulated structures to create the structural system of a building and triangle is the basic formal shape of these structures

and triangle is the basic formal shape of these structures.

The structural elements, designed to create together a triangle form are an integral part of the facade plane at Hearst Tower in New York, China National Tennis Center in Beijing and the Serpentine Pavilion of 2002 in London. Figure 6. a) Hearst Tower, New York City, arch. Norman Foster b) China National Tennis Center, Beijing, arch. Xu Lei,, c) Serpentine's pavilion in 2002, London, Toyo ItoFor this case study, a characteristic example is the Serpentine Pavilion of 2002. Toyo Ito designed the Serpentine Pavilion for the annual exhibition in the Hyde Park in London. The form of the structure is made up of, seemingly, randomly distributed triangles and a trapezoids, which are, in fact, derived from the algorithm of a cube.

The pavilion is used as the experiment of the architects checking the form and structure for the Tod's Omotesando Store facility, which was designed and constructed in 2005 in Tokyo.

Inspired by the idea of creating a "box with no pillars," the architect Toyo Ito and engineer Cecil Balmond created a space defined by a geometric series of triangles and trapezoids (glass, aluminum, etc..), and a structural framework that relied on an unconventional interdependency of parts. The formulated algorithm is the work of Cecil Balmond and it is reflected in the following steps: 1 Draw a square. 2. Draw a line from one half to one third of the adjacent side, clockwise 3. Repeat the procedure for each side 4. Extend the four lines in both directions out of the original square until it touches the new rotated square. 5. Repeat steps 1 through 4 in the new square. In this way, created the unique structural system is obtained, that is, at the same time, a facade frame.

INCLUDEPICTURE "http://www.thearchitect.lk/wp-content/uploads/2010/10/2-2.jpg" \* MERGEFORMATINET Figure 7. Serpentine pavilion 2002, algorithm animated3.3 Triangle as an individual element in the of faade membrane planeTriangle as a structural element in the faade membrane plane can occur in several ways, depending on the degree of surface curvature. Triangles as parts of the faade plane can be connected together so as to form:

- A flat surface of the facade

- Single curved surface of the facade

- Doubly curved surface of the faade 3.3.1 Triangle as an element in the plane of the flat surface facadeThe facade of La Cite du Design (The International Centre for Design) in Saint Etienne, France, is the simplest example of the use of the triangle as an element in the plane of the flat surface faade. It was designed by the architectural group of LIN architects in 2004, and built in 2009. The faade planes of the structure are typical in many ways. The fifth faade or the roof faade, is inseparable from the other four sides. The form of the faade planes was achieved by using 14 000 panels in the shape of equilateral triangles made of opaque and transparent materials, arranged in accordance with the needs of the exhibition center, in order to achieve a better control of light, temperature and air flow. Some of the triangle panels are photovoltaic panels that generate all the amount of energy required for operation of the facility. In this way a flexible and responsive high-tech faade is created.

Figure 8. The International Centre for Design, Saint Etienne, France, LIN architectsAnother specific example of this subspecies is the Federation Square building in Melbourne, the shopping mall, designed by Lab architecture studio. Construction of the center was completed in 2002. The building facade has a unique faade for which was necessary to use mathematics. The faade plane was made up of 22 073 panels in the form of equal right triangles, which differ only in terms of materials because the built-in panels were from sandstone, zinc and glass materials.

Formed the "pinwheel tiling", which was discovered by the mathematician John Conway, used on the facade, created a fractal faade. The sides of the triangles are in the ratio 1:2: 5. In order to form a network of panels, it is necessary to start from the basic right triangle with the mentioned triangle side ratio. They were then repeat five times and arranged to form the initial shape of a triangle, and the triangle formed is called a great super triangle". Then the newly created triangle again multiplied was five times to form a "supersuper" triangle. The procedure is reiterated until the entire wall is covered.

Figure 8. Illustration of how to make the pinwheel tiling

Figure 8. Federation Square, Melbourne, Lab architecture studio3.3.2 Triangle as an independent faade membrane element in the plane of single curved surfaces

The example of the Westhafen Tower, the office building in Frankfurt, is best for viewing the use of the triangle as an independent element of the facade skin of single curved surfaces. The building was built in 2004, and it was designed by the architects Schneider & Schumacher.

Glass panels, triangular in shape, 3556 of them, create a cylindrical form faade surface. In order to create as much curvature as possible with flat panels (which meant polygonal division of the faade planes around the circular floor slab), the tips of the triangle were alternately tilted slightly inward and outward. Due to these minimal inclinations every sheet of glass reflects the light in a different angle, creating a stunning multifaceted effect that resemble a cut gem. The triangular windows can be opened to supply natural ventilation to the offices. Figure 9. Westhafen Tower, Frankfurt, Schneider & Schumacher3.3.3 Triangle as an independent element in the plane of double curved surface of the faade membraneThe American engineer and architect Buckminster Fuller began with the use of the triangle as an independent element in the plane of the double curved surface of the faade, in the mid-twentieth century. His studies were mainly done on spherical shapes. One of his earliest works is the Geodesic Dome, installed in 1950, in Montreal, icosahedron structure made of aluminum tubes over which canvas vinyl is stretched. The Fuller's most famous work is the U.S. pavilion at the world exhibition Expo 67 in Montreal.Geodesic designs can be used to form any curved, enclosed space.

Figure 10. a)Geodesic Dome, drawing, b) Geodesic Dome, Montreal, Buckminster Fuller, c) US pavilion, Montreal, Buckminster Fuller

In modern architecture, geodesic design has a widespread application. It was used by Massimilano Fuksas when designing The MyZeil center in Frankfurt and The Admirant entrance building in Eindhoven in Holland, by Norman Foster to design for the UAE Pavilion at Shanghai Expo 2010, by HOK Architects to design a part of the facade of the Dali Museum in Florida.

Figure 11. a) The MyZeil center, Frankfurt, arch. Massimilano Fuksas b) The Admirant entrance building, Eindhoven in Holland, arch. Massimilano Fuksas

c) UAE Pavilion at Shanghai Expo 2010, arch. Norman Foster, d) Dali Museum in Florida, HOK Architects3.4 Triangle as an independent element of the spatial faade membraneThe Plasma studio was founded in London in 1999 by the architects Eva Castro and Holger Kin. Very soon they became known in the architecture public for its unique architecture based on simple forms and geometry or prismatic surfaces composed of triangular shapes. The progressive design and distinctive spatial structures in architecture of the Plasma studio are equally represented both in the installations and interior and in the external expression of commercial, residential and public buildings. Their facilities the best display the use of the triangle as an element of a dynamic, spatially playful facade membrane.

The design of the gate, exhibition hall and the Green Pavilion for the Xi'an international horticultural exhibition 2011 in China are among the latest works of Plasma Studio. The form of the complex facilities is obtained in the same way as in previous designs, highlighted by the geometry and acute angles. Triangular shapes are the base of the design. The facade fragments are triangular in shape, pointing in different directions, creating a unique form.

Figure 12. Xi'an International Horticultural Fair Complex, exhibition hall, Plasma studio

Figure 13. Xi'an International Horticultural Fair Complex, Guangyun Entrance, Plasma studio4. CONCLUSION

In this paper is emphasized the importance of using math and geometry for a remarkable architectural works, through the analysis of structures in which triangular form is implement in the treatment of the faade plane. In order to faade place faade elements proportionally well, and that the composition of the faade plane would have aesthetic value, although made from simple triangular shapes, it is necessary to know the fractal geometry, pinwheel and geodesic design. The form of modern architectural structures, increasingly, is based on these principles. Triangle has become a basic element of design and structures of facades, whatever form it may have.5. REFERENCES

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http://local.wasp.uwa.edu.au/~pbourke/texture_colour/nonperiodic/Olivera Nikoli, dipl. ing. arh., Phd student GAF Ni, saradnik u nastavi GAF Ni

Vladan Nikoli, dipl. ing. arh., Phd student GAF Ni, asistent GAF Ni

Petar Peji, dipl. ing. arh., Phd student GAF Ni, saradnik u nastavi GAF Ni

1 Rappaport, N., Deep Decoration, Decoration, 306090 Books Volume 10, September 2006, pp 95-105

2 Nikoli, O., Nikoli, V., Mobilnost, fleksibilnost i eksperimentalnost konstrukcije i forme - najznaajnije karakteristike savremenih paviljona, Zbornik radova Graevinsko-arhitektonskog fakulteta, Ni, 2011, br. 26, str. 69-79

3 Huylebrouck, D., Hammer, J.: From fractal geometry to fractured architecture: The federation square of Melbourne, Mathematical Intelligencer - MATH INTELL , vol. 28, no. 4, pp. 44-48, 2006

4 Binder, G., Tall Buildings of Europe, The Middle East And Africa, The Images Publishing Group, pp.68-69, 2006.