1

PROF. WOLFGANG SCHUELLER

Building structures are defined by geometry, materials, load action, and construction as well as form, that

is, its abstract dimensions as taken into account by architecture. When a building has meaning by

expressing an idea or by being a special kind of place, it is called architecture. Although structure is a

necessary part of a building, it is not a necessary part of architecture; without structure, there is no

building, but depending on the design philosophy, architecture as an idea does not require structure.

The relationship of structure to architecture or the interdependence of architectural form and structures is

most critical for the broader understanding of structure and design of buildings in general. On the one hand,

the support structure may be exposed to be part of architecture. On the other hand, the structure may be

hidden by being disregarded in the form-giving process, as is often the case in postmodern buildings.

One may distinguish structure from its visual expression as: hidden structure vs. exposed structure vs. partially exposed structure decorative structure vs. tectonic structure vs. sculptural structure innovative structures vs. standard construction

The purpose of structure in buildings may be fourfold: Support. The structure must be stable and strong enough (i.e., provide necessary strength) to hold

the building up under any type of load action, so it does not collapse either on a local or global scale (e.g., due to buckling, instability, yielding, fracture, etc.). Structure makes the building and spaces within the building possible; it gives support to the material, and therefore is necessary.

Serviceability. The structure must be durable, and stiff enough to control the functional performance, such as: excessive deflections, vibrations and drift, as well as long-term deflections, expansion and contraction, etc.

Ordering system. The structure functions as a spatial and dimensional organizer besides identifying assembly or construction systems.

Form giver. The structure defines the spatial configuration, reflects other meanings and is part of aesthetics, i.e. aesthetics as a branch of philosophy.

There is no limit to the geometrical basis of buildings as is suggested in the slide about the visual study of

geometric patterns.

The theme of this presentation brings immediately to mind the spanning of bridges, stadiums, and other

large open-volume spaces. However, I am not concerned only with the more acrobatic dimension of the

large scale of spanning space, which is of primary concern to the structural engineer, but also the

dynamics of the intimate scale of the smaller span and smaller spaces.

The clear definition of the transition from short span, to medium span, to long span from the engineer's point of view, is not always that simple.

Long-span floor structures in high-rise buildings may be already be considered at 60 ft (c. 18 m) whereas the

long span of horizontal roof structures may start at 100 ft (c. 30 m). From a material point of view it is apparent that the long span of wood beams because of lower

strength and stiffness of the material is by far less than for prestressed concrete or steel beams.

SPANNING SPACE HORIZONTAL -SPAN BUILDING

STRUCTURES

2

Scale range:

Long-span stadium: e.g. Odate-wood dome, Odate, Japan, 1992, Toyo Ito/Takenaka, 178 m on oval plan

Atrium structure: e.g. San Franciscos War Memorial Opera House, long-span structure behavior investigation

High-rise floor framing: e.g. Tower, steel/concrete frame, using Etabs Parthenon, Athens, 430 BC

The Development of Long-span Structures:

The great domes of the past together with cylindrical barrel vaults and the intersection of vaults represent

the long-span structures of the past. The Gothic churches employed arch-like cloister and groin vaults,

where the pointed arches represent a good approximation of the funicular shape for a uniformly

distributed load and a point load at mid-span. Flat arches were used for Renaissance bridges in Italy.

Example of short span: Parthenon, 430 BC, Athens

The development of the wide-span structure

The Romans had achieved immense spans of 90 ft (27 m) and more with their vaults and as so powerfully demonstrated by the 143-ft (44 m) span of the Pantheon in Rome (c. 123 AD), which

was unequaled in Europe until the second half of the 19th century.

The series of domes of Justinian's Hagia Sofia in Constantinople (537 A.D), 112 ft (34 m), cause a dynamic flow of solid building elements together with an interior spaciousness quite different

from the more static Pantheon.

Taj Mahal (1647), Agra, India, 125 ft (38 m) span corbelled dome

St. Peters, Rome (1590): US Capitol, Washington (1865, double dome); Epcot Center, Orlando, geodesic dome; Georgia Astrodome, Atlanta (1980)

These early heavy-weight structures in compression were made from solid thick surfaces and/or ribs of stone, masonry or concrete.

The transition to modern long-span structures occurred primarily during the second half of the 19th century

with the light-weight steel skeleton structures for railway sheds, exhibition halls, bridges, etc. as

represented by:

Arches: 240-ft (73 m) span fixed trussed arches for St. Pancras Station, London (1868) 530-ft (162 m) span Garabit viaduct, 1884, Gustave Eiffel

Frames: 375-ft (114 m) span steel arches for the Galerie des Machines (1889), Contamin & Dutert

Domes: 207-ft (63 m) Schwedler dome (braced dome, 1874), Vienna Bridges:1595-ft (486 m) span Brooklyn Bridge, New York, (1883, Roebling)

Among other early modern long-span structures were also:

Thin-concrete shells, form-passive membranes in compression, tension and shear: 720-ft (219 m) span CNIT Exhibition Hall Paris, 1958

Space frames surface structures in compression, tension and bending; Jacob K. Javits Convention Center, New York, 1986, James Ingo Freed

Tensile membranes almost weightless i.e. form-active structures, e.g. Fabric domes and HP membranes: tent like roofs for Munich Olympics, 1972, Frei Otto

Air domes, cable reinforced fabric structures: Pontiac Silver Dome, Pontiac, 722 ft (220 m), 1975

Tensegrity fabric domes, tension cables + compression struts + fabrics: Georgia Dome, Atlanta, 770 ft (235 m), 1992

The Building Support Structure

Every building consists of the load-bearing structure and the non-load-bearing portion. The main load

bearing structure, in turn, is subdivided into:

Gravity structure consisting of floor/roof framing, slabs, trusses, columns, walls, foundations Lateral force-resisting structure consisting of walls, frames, trusses, diaphragms, foundations

Support structures may be classified as,

Horizontal-span structure systems: floor and roof structure, enclosure structures, bridges

Vertical building structure systems: walls, frames cores, etc. tall buildings

3

Horizontal-span Structure Systems

From a geometrical point of view, horizontal-span structures may consist of linear, planar, or spatial

elements. Two- and three-dimensional assemblies may be composed of linear or surface elements.

Two-dimensional (planar) assemblies may act as one- or two-way systems. For example, one-way floor or planar roof structures (or bridges) typically consist of linear elements spanning in one direction where the

loads are transferred from slab to secondary beams to primary beams. Two-way systems, on the other

hand, carry loads to the supports along different paths, that is in more than one direction; here members

interact and share the load resistance (e.g. to-way ribbed slabs, space frames).

Building enclosures may be two-dimensional assemblies of linear members (e.g. frames and arches), or the

may be three-dimensional assemblies of linear or surface elements. Whereas two-dimensional enclosure

systems may resist forces in bending and/or axial action, three-dimensional systems may be form-resistant

structures that use their profile to support loads primarily in axial action. Spatial structures are obviously

more efficient regarding material (i.e. require less weight) than flexural planar structures.

From a structural point of view, horizontal-span structures may be organized as,

Axial systems (e.g. trusses, space frames, cables) Flexural systems (e.g. one-way and two-way beams, trusses, floor grids) Flexural-axial systems (e.g. frames, arches) Form-resistant structures, axial-shear systems: (folded plates, shells, tensile membranes)

One may distinguish between,

Compressive systems (arches, domes, shells) Tensile systems (suspended cables, textile fabric membranes,

Some common rigid horizontal-span structure systems are shown on the following slide:

Straight, folded and bent line elements: beams, columns, struts, hangars Straight and folded surface elements: one- or two-way slabs, folded plates, etc. Curved surface elements of synclastic shape: shell beams, domes, etc. Curved surface elements of anticlastic shape: hyperbolic paraboloids

Common semi-rigid composite tension-compression systems and flexible or soft tensile membranes are

organized as:

Single-layer, simply suspended cable roofs: single-curvature and dish-shaped (synclastic) hanging roofs

Prestressed tensile membranes and cable nets edge-supported saddle roofs

mast-supported conical saddle roofs

arch-supported saddle roofs

air supported structures and air-inflated structures (air members)

Cable-supported structures cable-supported beams and arched beams

cable-stayed bridges

cable-stayed roof structures

Tensegrity structures planar open and closed tensegrity systems:

cable beams, cable trusses, cable frames

spatial open tensegrity systems: cable domes

spatial closed tensegrity systems: polyhedral twist units

Hybrid structures: combination of the above systems Some typical examples of horizontal-span structures are,

Examples of horizontal-span roof structure systems Multi-bay long-span roof structures Cantilever structures

Lateral Stability: Every building consists of the load-bearing structure and the non-load-bearing portion. The main load-bearing structure, in turn, is subdivided into:

4

(a) The gravity load resisting structure system (GRLS), which consists of the horizontal and vertical subsystems: Foor/roof framing and concrete slabs, Walls, frames (e.g., columns, beams), braced frames, etc., and foundations

(b) The lateral load resisting structure system (LLRS), which supports gravity loads besides providing lateral stability to the building. It consists of walls, frames, braced frames, diaphragms, foundations, and can be subdivided into horizontal and vertical structure subsystems: Floor diaphragm structures (FD) are typically horizontal floor structure systems; they transfer

horizontal forces typically induced by wind or earthquake to the lateral load resisting vertical structures, which then take the forces to the ground. diaphragms are like large beams (usually horizontal beams). They typically act like large simply supported beams spanning between vertical systems.

Vertical structure systems typically act like large cantilevers spanning vertically out of the ground. Common vertical structure systems are frameworks and walls.

(c) The non-load-bearing structure, which includes wind bracing as well as the curtains, ceilings, and partitions that cover the structure and subdivide the space.

Location of vertical support structure The basic lateral load resisting structure systems Stability of basic vertical structural building units Possible location of units in building Lateral stability of buildings

Basic Concepts of Span: One must keep in mind that with increase in span the weight increases rapidly while the live loads may be

treated as constant; a linear increase of span does not result merely in a linear increase of beam size and

construction method. With increase of scale new design determinants enter.

The effect of scale is known from nature, where animal skeletons become much bulkier with increase of

size as reflected by the change from the tiny ant to the delicate gazelle and finally to the massive elephant.

While the ant can support a multiple of its own weight, it could not even carry itself if its size were

proportionally increased to the size of an elephant, since the weight increases with the cube, while the

supporting area only increases with the square as the dimensions are linearly increased. Thus the

dimensions are not in linear relationship to each other; the weight increases much faster than the

corresponding cross-sectional area. Hence, either the proportions of the ant's skeleton would have to be changed, or the material made lighter, or the strength and stiffness of the bones increased. It is also

interesting to note that the bones of a mouse make up only about 8% of the total mass in contrast to about

18% for the human body. We may conclude that structure proportions in nature are derived from

behavioral considerations and cannot remain constant.

This phenomenon of scale is taken into account by the various structure members and systems as well as by

the building structure types as related to the horizontal span, and vertical span or height. With increase of

span or height, material, member proportions, member structure, and structure layout must be

altered and optimized to achieve higher strength and stiffness with less weight.

For example, for the following long-span systems (rather than cellular construction where some of the

high-rise systems are applicable) starting at approximately 40- to 50-span (12 to 15 m) and ranging usually

to roughly the following spans,

Deep beam structures: flat wood truss 120 ft (37 m) Deep beam structures: flat steel truss 300 ft (91 m) Timber frames and arches 250 ft (76 m) Folded plates 120 ft (37 m) Cylindrical shell beams 180 ft (55 m) Thin shell domes 250 ft (76 m) Space frames, skeletal domes 400 ft (122 m) Two-way trussed box mega-arches 400 ft (122 m) Two-way cable supported strutted mega-arches 500 ft (152 m) Composite tensegrity fabric structures 800 ft (244 m)

5

This change of structure systems with increase of span can also be seen, for example, in bridge design,

where the longer span bridges use the cantilever principle. The change may be approximated from simple

span beam bridges to cantilever span suspension bridges, as follows,

beam bridges 200 ft (61 m) box girder bridges truss bridges arch bridges 1,000 ft (305 m) cable-stayed bridges suspension bridges (center span) 7,000 ft (2134 m)

total span of AKASHI KAIKO BRIDGE (1998), 13,000 ft (4000 m)

Typical empirical design aids as expressed in span-to-depth ratios have been developed from experience

for preliminary design purposes in response to various structure system, keeping in mind that member

proportions may not be controlled by structural requirements but by dimensional, environmental, and

esthetic considerations. For example,

Deep beams, e.g. trusses, girders L/t 12 or t L/12 Shallow beams, e.g. average floor framing L/t 24 Slabs, e.g. concrete slabs L/t 36 Vaults and arches L/t 60 Shell beams L/t 100 Reinforced concrete shells L/t 400 Lightweight cable or prestressed fabric structures not an issue

The effect of scale is demonstrated by the decrease of member thickness (t) as the members become

smaller, that is change from deep beams to shallow beams to slabs to envelope systems. Each system is

applicable for a certain scale range only, specific structure systems constitute an optimum solution as

determined by the efficient use of the strength-to-weight and stiffness-to-weight ratios.

The thickness (t) of shells is by far less than that of the other systems since they resist loads through geometry as membranes in axial and shear action (i.e. strength through form), in contrast to other

structures, which are flexural systems.

The systems shown are rigid systems and gain weight rapidly as the span increases, so it may be more

efficient to replace them at a certain point by flexible lightweight cable or fabric structures.

Typical span-to-depth ratios for bending members Structure systems, preliminary design

The large scale of long-span structures because of lack of redundancy may require unique building

configurations quite different from traditional forms, as well as other materials and systems with more

reserve capacity and unconventional detailing techniques as compared to small-scale buildings.

It requires a more precise evaluation of loading conditions as just provided by codes. This includes the

placement of expansion joints as well as the consideration of secondary stresses due to deformation of

members and their intersection, which cannot be ignored anymore as for small-scale structures.

Furthermore a much more comprehensive field inspection is required to control the quality during the

erection phase; post-construction building maintenance and periodic inspection are necessary to monitor

the effects of loading and weather on member behavior in addition to the potential deterioration of the

materials. In other words, the potential failure and protection of life makes it mandatory that special

care is taken in the design of long-span structures.

Today, there is a trend away from pure structure systems towards hybrid solutions, as expressed in geometry, material, structure layout, and building use. Interactive computer-aided design ideally makes a

team approach to design and construction possible, allowing the designer to stay abreast of new

construction technology at an early design stage. In the search for more efficient structural solutions a new

generation of hybrid systems has developed with the aid of computers. These new structures do not

necessarily follow the traditional classification presented before.

Currently, the selection of a structure system, as based on the basic variables of material and the type and

location of structure, is no longer a simple choice between a limited number of possibilities. The computer

software simulates the effectiveness of a support system, so that the form and structure layout as well as

6

material can be optimized and nonessential members can be eliminated to obtain the stiffest structure

with a minimum amount of material.

From this discussion it is clear that with increase of span, to reduce weight, new structure systems must be

invented and structures must change from linear beams to arched members to spatial surface shapes to

spatial pre-stressed tensile structures to take fully advantage of geometry and the strength of material.

In my presentation I will follow this organization by presenting structural systems in various context. The

examples will show that architecture cannot be defined simply by engineering line diagrams. To

present the multiplicity of horizontal-span structures is not a simple undertaking. Some roof structures

shown in the drawings, can only suggest the many possible support systems.

Examples of horizontal-span roof structure systems The cases may indicate the difficulty in classifying structure systems considering the richness of the actual

architecture rather than only structural line diagrams.

A. BEAMS

One-way and two-way floor/roof framing systems (bottom supported and top supported), shallow beams,

deep beams (trusses, girders, joist-trusses, Vierendeel beams, prestressed concrete T-beams), etc.

Individual beams Floor/roof framing Large-scale beams including trusses Supports for tensile columns Cable-supported beams Cable beams

There is a wide variety of spans ranging from,

Short-span beams are controlled by shear, V, where shear is a function of the span, L, and the

cross-sectional area, A: V A Medium-span beams are controlled by flexure, where M increases with the square of the span,

L2,and the cross-section depends on the section modulus, S: M S Long-span beams are controlled by deflection, , where deflection increases to the forth power of

L, (L4) and the cross-section depends on the moment of inertia I and the modulus of elasticity E

(i.e. elastic stiffness EI ): EI

The following examples clearly demonstrate that engineering line diagrams cannot define the full richness

of architecture. The visual expression of beams ranges from structural expressionism (tectonics),

construction, minimalism to post-modern symbolism. The visual expression of beams ranges from structural expressionism (tectonics), construction, minimalism to post-modern symbolism. They may be,

planar beams spatial beams (e.g. folded plate, shell beams , corrugated sections) space trusses.

They may be not only the typical rigid beams but may be flexible beams such as

cable beams. The longitudinal profile of beams may be shaped as a funicular form in response to a particular force

action, which is usually gravity loading; that is, the beam shape matches the shape of the moment diagram

to achieve constant maximum stresses.

Beams may be part of a repetitive grid (e.g. parallel or two-way joist system) or may represent individual

members; they may support ordinary floor and roof structures or span a stadium; they may form a stair, a bridge, or an entire building. In other words, there is no limit to the application of the beam principle.

Individual Beams: - Railway Station, Munich, Germany Atrium, Germanisches Museum, Nuremberg, Germany Pedestrian bridge Nuremberg Dresdner Bank, Verwaltungszentrum, Leipzig, 1997, Engel und Zimmermann Arch

7

Shanghai-Pudong International Airport, 2001, Paul Andreu principal architect, Coyne et Bellier structural engineers

Petersbogen shopping center, Leipzig, 2001, HPP Hentrich-Petschnigg The asymmetrical entrance metal-glass canopies of the National Gallery of Art, Stuttgart, J. Stirling (1984), counteract and relieve the traditional post-modern classicism of the

monumental stone building; they are toy-like and witty but not beautiful. Documentation Center Nazi Party Rally Grounds (Nuremberg, 2001, Guenther Domenig

Architect) is located in the unfinished structure of the Congress Hall. It gives detailed information

about the history of the Party Rallies and exposes them as manipulative rituals of Nazi

propaganda. A glass and steel gangway penetrates the North wing of the Congress Hall like a

shaft, the Documentation Center makes a clear contemporary architectural statement.

Floor/ Roof Framing Floor/ roof framing systems Floor framing structures RISA floor framing example Chifley tower , Sydney, 1992, Kohn, Pederson, Fox Farnsworth House, Mies van der Rohe, Plano, Ill (1950), USA, welded steel frame Residence, Aspen, Colorado, 2004, Voorsanger & Assoc., Weidlinger Struct. Eng. European Court of Justice, Luxemburg, 1994, Atelier d'Architecture Paczowski Fritsch Associs Central Beheer, Apeldorn, NL, Herman Hertzberger (1972): adjacent tower element about 27

x 27 ft (8.23 m) square with 9 ft wide spaces between, where basic square grid unit is about

9 ft (2.74 m); precast concrete elements; people create their own environments.

Xiangguo Si temple complex, downtown Kaifeng

Large-scale beams including trusses: Beam trusses Atrium, Germanisches Museum, Nuremberg, Germany: the bridge acts not just as connector but

also interior space articulation.

National Gallery of Art, East Wing, Washington, 1978, I.M. Pei Library, University of Bamberg TU Munich Library Gainesville, FL TU Stuttgart San Francisco Terminal, 2001, SOM Documentation Center Nazi Party Rally Grounds, Nuremberg,, 2001, Guenther Domenig Sobek House, 2001, Stuttgart, Werner Sobek Integrated urban buildings, Linkstr. Potsdamer Platz), Richard Rogers, Berlin, 1998 Petersbogen shopping center, Leipzig, 2001, HPP Hentrich-Petschnigg Tokyo International Forum, 1997, Rafael Vignoli Arch, Kunio Watanabe Struct. Eng. Ski Jump Berg Isel, Innsbruck, 2002, Zaha Hadid

Supports for tensile columns 5-story Olivetti Office Building, Florence, Italy, Alberto Galardi, 1971: suspended construction

with prestressed concrete hangers sits on two towers supporting trusses, which in turn carry the

cross-trusses

Shanghai-Pudong Museum, Shanghai, (competition won 2002), von Gerkan Berlin Stock Exchange, Berlin, Germany, 1999, Nick Grimshaw Centre George Pompidou, 1978, Paris, Piano & Rogers 43-story Hongkong Bank, Hong Kong, 1985, Foster/Arup: The stacked bridge-like structure

allows opening up of the central space with vertically stacked atria and diagonal escalator bridges

by placing structural towers with elevators and mechanical modules along the sides of the

building. This approach is quite opposite to the central core idea of conventional high-rise

buildings. The building celebrates technology and architecture of science as art. It expresses the

performance of the building and the movement of people. The support structure is clearly

expressed by the clusters of 8 towers forming 4 parallel mega-frames. A mega-frame consists of

2 towers connected by cantilever suspension trusses supporting the vertical hangers which, in

turn,support the floor beams. Obviously, the structure does not express structural efficiency.

Beam buildings

8

Visual study of beam buildings Seoul National University Museum, Rem Koolhaas, 2006 William J. Clinton Presidential Center, Little Rock, AR, 2004, Polshek Partnership Landesvertretung von Baden-Wuertemberg, Berlin, Dietrich Bangert, 2000 Embassy UK, Berlin, Michael Wilford, 2000 Super C, RWHA, Aachen, 2008 WDR Arcades/Broadcasting House, Cologne, 1996, Gottfried Bhm; this buildings hiuses the

Radio and television production studios of the largest German broadcasting station. The WDR-

Arkaden are architecturally one of the most interesting buildings in Cologne. The shopping arcade

was benn designed by Gottfried Bhm. Some people characterise it as some batched container.

Shanghai Grand Theater, Jean-Marie Charpentier, architect (1998): inverted cylindrical tensile shell

Lehrter Bahnhof, Berlin, 2006, von Gerkan, Marg and Partners La Grande Arche, Paris, 1989, Johan Otto von Sprechelsen/ Peter Rice for the canopy Fuji Sankei Building, Tokyo, 1996, Kenco Tange Sharp Centre for Design, Ontario College of Art & Design, Toronto, Canada, 2004, Alsop

Architects

Porsche Museum building: images authorised by Delugan Meissl Architects 2007 Abu Dhabi Performing Arts Centre, Zaha Hadid, the centre,2007

Cable-supported beams and cable beams Single-strut and multi-strut cable-supported beams Erasmusbridge, Rotterdam, 1996, Ben Van Berkel Golden Gate Bridge, San Francisco, 1936, C.H. Purcell Old Federal Reserve Bank Building, Minneapolis, 1973, Gunnar Birkerts, 273-ft (83 m) span truss

at top

World Trade Center, Amsterdam, 2003 (?), Kohn, Pedersen & Fox Luxembourg, 2007 Kempinski Hotel, Munich, Germany, 1997, H. Jahn/Schlaich. Also here, the hotels open grand

atrium is more than a lobby. The new technology of the 40-m span glass and steel roof features a

construction with its own aesthetics reflecting a play between artistic, architectural mathematical,

and engineering worlds. The depth of the diagonal arches is reduced by the central compression

strut (flying column) carried by the suspended tension rods. The arches, in turn, are supported by

tubular trusses on each side, which separate the roof from the buildings.

Shopping areas, Berlin, Linkstr., Rogers, 1998 The main structure for the Wilkhahn Factory, Bad Muender, Germany, 1992, by Thomas Herzog

Arch., is parallel to the faade (i.e. longitudinal); the building integrates function, construction,

ecological concern and architecture. The 5.4 m wide (18 ft) tower structures that contain the

offices and service zones, are centered at 30 m (98 ft) and give support to the long spans of the

cable-supported beams (24.6 m/81 ft). The formal configuration of the cables (1.5 m deep)

convincingly reflects the moment flow of continuous beams under gravity load action. The

diagonal bracing of the towers seems to give lateral support to the post-beam timber structure to

resist wind with a minimum effort.

Mercedes-Benz Center am Salzufer, Berlin, 2000, Lamm, Weber, Donath und Partner Shopping Center, Stuttgart Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng Lehrter Bahnhof, Berlin, 2006, von Gerkan, Marg and Partners Debis Theater, Berlin, 1998, Renzo Piano Shanghai-Pudong International Airport, 2001, Paul Andreu principal architect, Coyne et Bellier

structural engineers

Ski Jump Voightland Arena, Klingenthal, 2007, m2r-architecture

B. FRAMES

Gables, A-frames, Arches, Glass enclosures, etc.: parallel, two-way, spatial/polyhedral, trees Crown Hall, IIT, Chicago, 1955, Mies van der Rohe; the 120-ft (37 m) span building has become a

symbol for the celebration of the portal frame; Mies articulated the power and beauty of the post-

beam structure by exposing the lightness of the steel skeleton as contrasted by the glass surface;

the roof platform is suspended from the welded plate girders that are spaced at 60 ft (18 m).

9

Visual study of single-bay portal frames Single-story, multi-bay frame systems Visual study of multiple-span frame structures Postal Museum, Frankfurt, Germany, 1990, Guenter Behnisch Arch.: space dynamics through

fragmentation

Indeterminate portal frames under gravity loads Indeterminate portal frames under lateral load action Sainsbury Centre for Visual Arts, UK, 1978, Norman Foster Glass Cube, Art Museum Stuttgart, 2005, Hascher und Jehle Arch Visual study of Frames and arches Response of typical gable frame roof enclosures to gravity loading Pitched roof structures Joist roof construction Rafter roof construction Inclined frame structures Project for Fiumicino Airport, Rome, 1957, Nervi etc. The Novotel Belfort, Belfort, France, 1994, Bouchez BMW Plant Leipzig, Central Building, 2004, Zaha Hadid San Diego Library, 1970, William L. Pereira 798 Beijing Art Factory, Beijing, 1956, the shape of the supporting frames (i.e. roof shape)

depends on ventilation and lighting of the sheds.

Bus Stop Aachen, 1998, Peter Eisenman, folded steel structure that resembles a giants claw grasping the paving, or the folded steel shelter perches crablike on the square

Zueblin AG Headquarters, Stuttgart, 1985, Gottfried Boehm: hollow central glass-covered atrium space between solid building masses; stair towers and pedestrian bridges as interior connectors;

celebration of articulated precast concrete cladding.

Miyagi Stadium, Sendai City, Japan, 2000, Atelier Hitoshi Abe

Arches Study of curvilinear patterns Arches as enclosures Visual study of arches Visual study of lateral thrust Olympic Stadium Montreal, 1975, Roger Taillibert Dresden Main Train Station, Dresden, 2006, Foster Lanxess Arena, Cologne, 1998, Peter Bhm Architekten United Airlines Terminal at OHare Airport, Chicago, 1987, H. Jahn Museum of Roman Art, Mrida, Spain 1985, Jose Rafael Moneo 'Glass Worm' building - new Peek & Cloppenburg store, Cologne, Renzo Piano, 2005 City of Arts & Sciences, Valencia ,Spain ,Santiago Calatrava, 2000 Geschwungene Holzbruecke bei Esslingen (Spannbandbruecke), 1986, R. Dietrich La Devesa Footbridge, Ripoll, Spain, 1991, S. Calatrava, torsion Bac de Roda Felipe II Bridge, 1987, west Barcelona, Santiago Calatrava, Architect Bridge over the Rhein-Herne-Canal, BUGA 1997, Gelsenkirchen, Stefan Polnyi The Metro station at Blaak, Rotterdam, 1993, Harry Reijnders of Movares; the arch spans 62.5 m,

dome diameter is 35 m

Kansai International Airport Terminal in Osaka, Japan, 1994 , Renzo Piano Terminal 5 Roof Heathrow Airport, London, 2005, Rogers/Arup Ningbo Air terminal Shenyang Taoxian International Airport Chongqing Airport Terminal, 2005, Llewelyn Davies Yeang and Arup San Giovanni Rotondo, Italy, 2004, Renzo Piano Center Paul Klee, Bern, 2005, Renzo Piano Waterloo Terminal, London, 1993, Nicholas Grimshaw + Anthony Hunt BCE Place, Toronto, 1992, Santiago Calatrava Subway Station to Allians Stadium, Froettmanning, Munich, 2004, Bohn Architekten, fabric

membranes

Olympic Stadium Athens, 2004, Santiago Calatrava New TVG Station, Liege, Belgium, 2008, Santiago Calatrava

10

C. CABLE-STAYED ROOF STRUCTURES

Examples of cable-stayed roof structures range from long-span structures for stadiums, grandstands,

hangars, and exhibition centers, to smaller scale buildings for shopping centers, production or research

facilities, to personal experiments with tension and compression. Many of the general concepts of cable-stayed bridges, as discussed in the previous section, can be transferred to the design of cable-stayed roof

structures. Typical guyed structures, used either as planar or spatial stay systems, are the following:

Cable-stayed, double-cantilever roofs for central spinal buildings

Cable-stayed, single-cantilever roofs as used for hangars and grandstands

Cable-stayed beam structures supported by masts from the outside

Spatially guyed, multidirectional composite roof structures

Visual study of cable-supported structures Force flow in cable-supported roofs Patscenter, Princeton, 1984, Rogers/Rice, the building consists of parallel planar guyed structures

along the central spine consisting of c. 9m wide portal frames set 11 m on center that support on

top c. 15-m high A-frames which consist of inclined pipe columns connected to a large ring plate

from which are suspended steel rods to other ring plates on each side of the spine. Inverted truss

action is required for wind uplift where the central tubular hangers act in compression.

Fleetguard Factory, Quimper, France, 1981, Richard Rogers Shopping Center, Nantes, France, 1988, Rogers/Rice, 94-ft (29 m) high tubular masts support the

94-ft (29 m) framework in a spatial fashion from above without penetration of the roof. Only

certain combinations of the 3-dimensional network of tension rods and compression struts are

activated under various load actions.

Horst Korber Sports Center, Berlin, 1990, Christoph Langhof, quite different in spirit are the slender and minimal abstract planar, tree-like c.30-m high masts with their five branches linked by

cables from which the light cable roof trusses are hung. The symmetrical abstract forms of the masts are completely opposite in expression from the tectonic shapes of most other examples.

The Charlety Stadium, Cite Universitaire, Paris, 1994, Henri and Bruno Gaudin Lufthansa Hangar, Munich, 1992, Buechl + Angerer, the immense 153-m span roof is supported

by the diagonal cables suspended from the c.56-m tall concrete pylons

Bridge, Hoofddorp, Netherlands, 2004, Santiago Calatrava The University of Chicago Gerald Ratner Athletic Center, Chicago, 2002, Cesar Pelli Melbourne Cricket Ground Southern Stand , 1992, Tomkins Shaw & Evans / Daryl Jackson Pty Lt Bruce Stadium , Australian Capital Territory, 1977, Philip Cox, Taylor and Partners City of Manchester Stadium, UK, 2003, Arup Munich Airport Center, Munich, Germany, 1997, Helmut Jahn Arch.: the open public atrium as

transition, building blocks form walled boundaries to a square which is covered by a transparent roof hanging from stayed cables, with a minimum of structure that gives a strong identity to space

- the new technology features construction with its own aesthetics reflecting a play between

artistic, architectural mathematical, and engineering worlds.

D. FORM-PASSIVE SURFACE STRUCTURES: hard shells (rotational, synclastic forms vs. translational, anticlastic surfaces)

Slabs Folded plates Space frames Tree columns Dome structures Thin shells Ribbed shells

Slabs Visual study of floor/ roof structures 1, 2

11

Stress flow, multi-story building in concrete and steel Stress flow, Hospital, Dachau, Germany Computer modelling, ramp for parking garage Paul Lbe and Marie-Elisabeth Lders House in the German Government Building, Berlin, 2001,

Stephan Braunfels

Government building, Berlin, 2001 Federal Chancellery Building, Berlin, 2001, Axel Schultes and Charlotte Frank Glasshouse, 1949, Philip Johnson New National Gallery, Berlin, 1968, Mies van der Rohe Sichuan University, Chengdu, College for Basic Studies, 2002 Civic Center, Shenzhen Science and Technology Museum Shanghai, 2002, RTKL/Arup Akron Art Museum, Akron, 2007, Wolf Prix and Helmut Swiczinsky (Himmelblau) BMW Welt, Munich, 2007, Coop Himmelblau

Folded Plates: trussed vs. concrete, parallel vs. triangular folds, flat vs. warped surfaces, two-way warped surfaces

Folded plate structures Folded plate structure systems Alte Kurhaus, Aachen, Germany St. Foillan, Aachen, Leo Hugot Arch. Institute for Philosophy, Free University, Berlin, 1980s, Hinrich and Inken Balle. Glass, openness,

and light-flooded rooms: the architects Hinrich and Inken Baller created transparency in the 1980s

in the design of the new building for the Institute for Philosophy in Habelschwerdter Allee. This

building was the first university institute designed in the style of a villa to fit in with the single-

family-house character of the district of Dahlem.

Church of the Pilgrimage, Neviges, Germany, Gottfried Boehm, 1968, Velbert, Germany Air force Academy Chapel, Colorado Springs, 1961, Walter Netsch (SOM) Center Le Corbusier, Zurich, 1967, Le Corbusier, hipped and inverted hipped roof, each composed

of four square steel panels

21_21 Design Sight, Tokyo, 2007, Tadao Ando; the building is a low-rise structure consisting of one ground floor and one underground floor. Most of the volume of the building, which has a

unique form featuring a roof made from giant steel plates that slope gently down to the ground, is

buried underground. Once inside, the space opens out on a scale unimaginable given the building's

unobtrusive exterior. The ground floor houses the entrance and reception area, while the

underground floor houses two galleries and a triangular sunken court. A feature of the building is

that it is encased in the longest section of double-glazing in Japan.

Salone Agnelli, Turin Exhibition Hall, 1948, Pier Luigi Nervi Kimmel Center for the Performing Arts, Philadelphia, Rafael Vinoly, 2001, steel-and-glass barrel

vault (160 ft high), the roof structure uses the depth of the vaulted section to creat a vierendeel

truss that arches across the atrium, the trusses are propped against each adjacent element to

provide a folded plate action that resists the longitudinal wind loads Sydney Olympic Train Station, Homebush, Hassell Pty. Ltd Arch, Tierney & Partners Struct.

Eng., 1998, single span vaulted 'leaf' roof truss, repeated folded vault configuration , Plan shape

rectangular - 200m x 35m, 18 modules spaced at 12m , 14m long arched entrance canopy, 5.5m

wide side awning, support structures columns, buttresses, arched trusses Combining the use of

an arch with that of a truss resulted in two layers. First, the two arches in each truss, which use

arch action to span a large distance and provide a column, free space. Secondly, the truss to

provide depth (to take bending moments) in the roof plane which is important to resist asymmetric

loads under wind pressure in addition to resisting uplift forces. To cater for gravitational and uplift

forces, the arched truss is designed to cater for both compression as well as tension. Arched roof

truss members: 355CHS twin arch at the ridge (centre of leaf) and 355CHS inclined arches at the

bottom (leaf's border). Each arch is composed of three sections joined together. Truss web

members: 200 x 100 RHS with tubular bracing, link top and bottom arches. Roof cladding: speed deck 500, zincalume finish ribbed cladding. Internal roof lining: perforated aluminium sheets.

Addition to Denver Art Museum, 2006, Daniel Libeskind/ Arup Eng.

Space Frames Polyhedral roof structures Single-layer three-dimensional frameworks

12

Double-layer space frame systems 1 Double-layer space frame systems 2 Common polyhedra derived from cube Generation of space grids by overlapping planar networks National Swimming Center, Beijing, RANDOM ARRANGEMENT OF SOAP BUBBLES Professor Weaire and his research assistant Dr Phelan at Trinity College, Dublin, that provided us

with the answer for the Water Cube. The curious thing about Weaire Phelan foam is that, despite

its complete regularity, when viewed at an arbitrary angle it appears to be random and organic.

To construct the geometry of the structure of our building, we start with an infinite array of foam

(oriented in a particular way) and then carve out a block equal to the size of our building 177 x 177 x 31 cubic metres. The three major internal volumes are subtracted from this foam block and

the result is the geometry of the structure. The structure is then clad with ETFE pillows inside and

out to achieve the desired organic look and to work as an efficient insulated greenhouse. So, in

searching for the most efficient way of subdividing space, we found a structure based on the

geometry of soap bubbles, and clad with plastic pillows that look like bubbles. And inside, all the

water of a swimming centre! We were confident that we had a winning scheme; our next challenge

was to convey the idea accurately to the judges. We decided to build an accurate physical

model of all 22,000 structural elements and 4,000 (different) cladding panels. The only way to do this seemed to be Rapid Prototyping machinery, commonly used in the manufacturing and

automobile industries. It took us many weeks to learn enough about the CAD modelling and the

data translation required just to make the structural model. With two days left, the structural model

was flown from Melbourne to Beijing, where it was joined to a handmade plastic skin (we just

couldnt draw all the different pillow shapes in time), and the model was complete. In July 2003, we were announced as the winners of the competition and

Strurctural behavior of double-layer space frames Common space frame joints Case study of flat space frame roofs Other space frame types Example Hohensyburg Robson Square, Vancouver, 1980, Arthur Erickson Jacob K. Javits Convention Center, New York, 1986, James Ingo Freed/ Weidlinger Dvg-Administration, Hannover, 2000, Hascher/Jehle Crystal Cathedral, Garden Grove, CA, 1980, Philip Johnson Kyoto JR Station, Kyoto, Japan, 1998, Hiroshi Hara Arch.: the urban mega-atrium. The building

has the scale of a horizontal skyscraper - it forms an urban mega-complex. The urban landscape

includes not only the huge complex of the station, but also a department store, hotel, cultural

center, shopping center, etc. The central concourse or atrium is 470 m long, 27 m wide, and 60 m

high. It is covered by a large glass canopy that is supported by a space-frame. This space acts a

gateway to the city as real mega-connection.

Tomochi Forestry Hall, Kumamoto, Japan, 2005, Taira Nishizawa Architects National Swimming Center, Beijing, 2008, Herzog de Meuron; Engineer: Tristram Carfrae of

Arup, The Beijing National Swimming Centre, better known as the 'Water Cube', Arup Arch and

Eng., will be one of the most dramatic and exciting venues to feature sporting events for the 2008

Olympics. The structure of the Water Cube is based on the most effective sub-division of three-

dimensional space - the fundamental arrangement of organic cells and the natural formation of

soap bubbles. The random-looking structure is based on the formation of soap bubbles the most efficient sub-division of three-dimensional space.

Tree Columns: parallel, two-way, spatial/polyhedral, trees Ningbo Air Terminal Shenyang Airport Terminal Stanted Airport, London, UK, 1991, Norman Foster/ Arup Terminal 1 at Stuttgart Airport, 1991, von Gerkan & Marg. The huge steel trees of the Stuttgart

Airport Terminal, Stuttgart, Germany with their spatial strut work of slender branches give a continuous arched support to the roof structure thereby eliminating the separation between column

and slab. The tree columns put tension on the roof plate and compression in the branches; they are

spaced on a grid of about 21 x 32 m (70 x 106 ft).

Dome Structures: typical domes, inverted domes, segments of dome assembly, etc. Major skeleton dome systems

13

Dome structure cases Little Sports Palace, Rome, Italy, 1960 Olympic Games, Pier Luigi Nervi U.S. Pavilion, Toronto, Canada, Expo 67, Buckminster Fuller, 250 ft (76 m) diameter sphere,

double-layer space frame

Jkai Baseball Stadium, Odate, Japan Philological Library, Free University, Berlin, 2005, N. Foster National Grand Theater, Beijing, 2006, Paul Andreu Bent surface structures Grand Louvre, Paris, 1993, I. M. Pei MUDAM, Museum of Modern Art, Luxembourg, 2006, I.M. Pei The dome used for dwelling Ice Stadium, Davos, Switzerland Reichstag, Berlin, Germany, 1999, Norman Foster Arch/ Leonhardt & Andrae Struct. Eng. Beijing National Stadium, Beijing, 2008, Herzog and De Meuron Arch/ Arup Eng. The Bird's

Nest was designed by the Swiss firm Herzog & De Meuron. This firm's previous projects include

the renovation of an old power station on the banks of the Thames in London, which was turned

into the Tate Modern Art Museum. Herzog & De Meuron also won last year's Sterling Prize for

Architecture for their design of the Laban Dance Centre in a rundown area of London.

Thin shells Shell shapes may be classified as follows:

Geometrical, mathematical shapes Conventional or basic shapes: single-curvature surfaces (e.g. cylinder, cone), double-

curvature surfaces (e.g. synclastic surfaces such as elliptic paraboloid, domes, and

anticlastic surfaces such as hyperbolic paraboloid, conoid, hyperboloid of revolution)

Segments of basic shapes, additions of segments, etc. Translation and/or rotation of lines or surfaces Corrugated surfaces Complex surfaces such as catastrophe surfaces

Structural shapes Minimal surfaces, with the least surface area for a given boundary,

constant skin stress, and constant mean curvature

Funicular surfaces, which is determined under the predominant load Optimal surfaces, resulting in weight minimization Free-form shells, may be derived from experimentation Composed or sculptural shapes

Introduction to shells and cylindrical shells Surface structures in nature Surface classification 1 and 2 Examples of shell form development through experimentation Basic concepts related to barrel shells Slab action vs. beam action Cylindrical shell-beam structure Vaults and short cylindrical shells Cylindrical grid structures Various cylindrical shell types Cologne Cathedral, Germany St. Lorenz, Nuremberg, Germany, 14th cent Airplane hangar, Orvieto 1, 1939, Pier Luigi Nervi Zarzuela Hippodrome, Madrid, 1935, Eduardo Torroja Kimbell Art Museum, Fort Worth, 1972, Louis Kahn Terminal 2F, Orly Airport, Paris, 2002, Paul Andreu, elliptical concrete vault. As for section E,

while the public area is identical to the one of section F, the boarding area consists in a long hall-

way, with an elliptical vault made out of concrete. Passengers are more likely to encounter longer

walking distances in this case, than in Terminal 2F. I should underscore the fact that these two designs recall the ones of the two terminals at Orly airport.

Alnwick Gardens Visitor Center roof, UK, 2006, Hopkins Arch., Happold Struct. Eng. History Museum Courtyard Roof, Hamburg, 1989, von Gerkan Marg und Partner Dz Bank, glass roof, Berlin, 2001, Gehry + Schlaich

14

Exhibition hall Leipzig, Germany, 1996, von Gerkan, GMP, in cooperation with Ian Ritchie P&C Luebeck, Luebeck, 2005, Ingenhoven und Partner, Werner Sobek, At the very heart of

Lbeck's historical centre a new commercial building was constructed. The building had to be

inserted very carefully into the UNESCO-listed Old Town. For this reason the roof played a major

role in the design concept. The roof consists of 16 shells in reinforced concrete that have a

thickness of 14 cm each. In plan view the shells are trapezoids that are arranged in alternating alignments. The shells span 8.75 m in cross direction and up to 28 m in machine direction.

Central Railway Station Cologne, Germany CNIT Exhibition Hall Paris, 1958, Bernard Zehrfuss Arch, Nicolas Esquillon Eng. Thin-concrete

shells, form-passive membranes in compression, tension and shear: 720-ft (219 m) span

Other shell forms Dome shells on polygonal base Keramion Ceramics Museum, Frechen, 1971, Peter Neufert Arch., the building reflects the nature

of ceramics

Kresge Auditorium, MIT, Eero Saarinen/Amman Whitney (1955), on three supports Ecological Center, St. Austell, Cornwall, England,1996, Nicholas Grimshaw, Anthony Hunt; the

biomes are constructed from a tubular steel frame with mostly hexagonal transparent panels (there

are a few pentagonal ones) made from a complex plastic known as ETFE (it was decided very

early on that glass was out of the question, being too heavy and potentially dangerous). The "panes" of the biome are created from a triple layer of thin UV-transparent ETFE film, inflated to

create a large space between the two sides and trapping heat like double-glazed windows. The

plastic is resistant to most stains, which simply wipe off in the rain, although if required, cleaning

is performed by abseilers. Although the plastic is prone to punctures, these can be fixed with

ETFE tape. The structure is completely self-supporting, with no internal supports, and takes the

form of a geodesic structure. The panels vary in size up to 9 m across, with the largest at the top of

the structure.

Delft University of Technology Aula Congress Centre, 1966, Bakema Hyperbolic paraboloids Hypar units on square grids Case study of hypar roofs Membrane forces in a basic hypar unit Some hypar characteristics Examples Felix Candela, Mexico Bus shelter, Schweinfurt Greenwich Playhouse, 2002, Austin/Patterson/Diston Architects folded plate behavior Garden Exhibition Shell Roof, Stuttgart, 1977, Jrg Schlaich Expo Roof, Hannover, EXPO 2000, 2000, Thomas Herzog Intersecting shells Other surface structures TWA Terminal, New York, 1962, Saarinen Sydney Opera House, Australia, 1972, Joern Utzon/ Ove Arup Mannheim Exhibition, 1975, Frei Otto etc., the catenary surface geometry of the wooden grid

shell was derived by inverting a hanging chain model to a standing position and thus is curved

primarily synclastically

DZ Bank, amoeba-like auditorium, Berlin, 2001, Gehry + Schlaich Phaeno Science Centre Wolfsburg, Germany, 2005, Zaha Hadid BMW Welt, Munich, 2007, Coop Himmelblau Centre Pompidou-Metz, 2008, architects Shigeru Ban and Jean de Gastines Fisher Center, Bard College, NY, Frank Gehry, DeSimone, 2004 A model of the London Olympic Aquatic Center, 2004 by Zaha Hadid. Congress Center EUR District, Rome, Italy, Massimiliano Fuksa. Congress Center EUR District,

Rome, Italy, Massimiliano Fuksa. The building is basically large, 30 meters high, translucent container that extends lengthways. On each side a square opens on to the immediate area and the

city. The first converses directly continuously with the local area and can be crossed from viale

Europa to viale Shakespeare. The second, a space that can be composed freely using moveable

structures, is for welcoming conference participants and accompanying them to the various rooms

in the center. Inside this shell, a 3,500 square meter steel and teflon cloud, suspended above a

surface area of 10.000 square meter, is designed to hold a 2.000 square meter auditorium and

various meeting rooms. When the cloud, supported by a thick network of steel cables and

15

suspended between the floor and the ceiling of the main conference hall, is lit up, the building

seems to vibrate. The construction also changes completely depending on the viewpoint of the

observer.

Metropol Parasol", Jrgen Mayer Arch, a redevelopment project by J. Mayer H. for Plaza de la Encarnacion in Seville, Spain is one of the most striking projects I've seen in ages. Amazingly, it's

under construction and is expected to be complete this year.

E. FORM-ACTIVE SURFACE STRUCTURES: soft shells, TENSILE MEMBRANES, textile fabric membranes, cable net

structures, tensegrity fabric composite structures

Suspended surfaces (parallel, radial)

Anticlastic, pre-stressed structures Edge-supported saddle roofs

Mast-supported conical saddle roofs

Arch-supported saddle roofs

Pneumatic structures Air-supported structures

Air-inflated structures (air members)

Hybrid air structures

Tensegrity structures

In contrast to traditional surface structures, tensile cablenet and textile structures lack stiffness and weight.

Whereas conventional hard and stiff structures can form linear surfaces, soft and flexible structures must

form double-curvature anticlastic surfaces that must be prestressed (i.e. with built-in tension) unless they

are pneumatic structures. In other words, the typical prestressed membrane will have two principal

directions of curvature, one convex and one concave, where the cables and/or yarn fibers of the fabric are

generally oriented parallel to these principal directions. The fabric resists the applied loads biaxially; the

stress in one principal direction will resist the load (i.e. load carrying action), whereas the stress in the perpendicular direction will provide stability to the surface structure (i.e. prestress action). Anticlastic

surfaces are directly prestressed, while synclastic pneumatic structures are tensioned by air pressure. The

basic prestressed tensile membranes and cable net surface structures are

Suspended Surfaces: parallel, radial Simply-suspended structures Dulles Airport, Washington, 1962, Eero Saarinen/Fred Severud, 161-ft suspended tensile vault Trade Fair Hall 26, Hanover, 1996, Herzog/ Schlaich National Indoor Sports and Training Centre, Australia, 1981, Philip Cox Olympic Stadium for 1964 Olympics, Tokyo, Kenzo Tange/Y. Tsuboi, the roof is supported by

heavy steel cables stretched between concrete towers and tied down to anchorage blocks.

Anticlastic, Prestressed Membranes Tent architecture Dorton (Raleigh) Arena (1952), North Carolina, Matthew Nowicki, with Frederick Severud Subway Station to Allianz Arena, Stadium Railway Station Froettmanning, Munich IAA 95 motor show, Frankfurt New roof for the Olympic Stadium Montreal, 1975, Roger Taillibert Grand Arch de la Defense, Paris, 1989, Paul Andreu Olympic Stadium, Munich, 1972, Behnich/Frei Otto/Leonardt, saddle-shaped prestressed

membranes

King Fahd International Stadium, Riyadh, Saudi Arabia, 1986, Horst Berger Canada Place, Vancouver, 1986, Eberhard Zeidler/ Horst Berger San Diego Convention Center, 1989, Arthur Erickson/ Horst Berger Schlumberger Research Center, Cambridge, UK (1985, Hopkins/Hunt); The ship like masts and

rigging support the spatial domelike undulating tensile fabric membrane. The high level technology and detailing reminds one of Roger's earlier work. The central portion of the building

is subdivided by four parallel exposed portal steel frames into three bays, each 24 x 18 m (79 x 59

ft) in size. It consists of horizontal 24-m (79-ft) open triangulated truss girders and nearly 8-ft

16

(c.2.5 m) wide vertical trusses which support two pairs of upper and lower booms. The two

inclined upper tubular masts are supported by tie rods which are braced by lower masts (struts).

Cables are suspended from the masts to give support to two parallel ridge cables at certain pick-up

points. The translucent Teflon coated fiberglass membrane is clamped and stretched between ridge

cables and steel work.

Denver International Airport Terminal, Denver, 1994, Horst Berger/ Severud,the folded Teflon-coated fiberglass membrane spans about 220 ft (67 m), the roof weighs less than 2 psf (96 Pa)

Hybrid tensile surface structures

Pneumatic structures

Air-supported structures high-profile ground-mounted air structures

berm- or wall-mounted air domes

low-profile roof membranes

Air-supported structures form synclastic, single-membrane structures, such as the typical basic domical

and cylindrical forms, where the interior is pressurized; they are often called low-pressure systems

because only a small pressure is needed to hold the skin up and the occupants dont notice it.

Pressure can be positive causing a convex response of the tensile membrane or it can be negative (i.e.

suction) resulting in a concave shape. The basic shapes can be combined in infinitely many ways and

can be partitioned by interior tensile columns or membranes to form chambered pneus.

The typical normal operating pressure for air-supported membranes in the USA is in the range of 4.5 to

8 psf (22 kg/m2 to 39 kg/m2) or roughly 1.0 to 1.5 inches of water as read from a water-pressure gage.

Pneumatic structures Low-profile, long-span roof structures Soap bubbles To house a touring exhibition Examples of pneumatic structures Norways National Galery, Oslo, 2001, Magne Magler Wiggen Architect Effect of wind loading on spherical membrane shapes Eden Project in Cornwall/England Humid Tropics Biome, 1996, Nicholas Grimshaw, A. Hunt Metrodome, Minneapolis, 1981, SOM

Air inflated structures: air members Air inflated structures or simply air members, are typically,

high-pressure tubes lower-pressure cellular mats: air cushions

Air members may act as columns, arches, beams, frames, mats, and so on; they need a much higher

internal pressure than air-supported membranes.

Expo02 Neuchatel, 2002, air cussion, ca 100 m dia. Roman Arena Inflated Roof, Nimes, France, 1988, Schlaich Festo A.G. Stuttgart

Tensegrity Structures

Buckminster Fuller described tensegrity as, small islands of compression in a sea of tension. Ideal tensegrity structures are self-stressed systems, where few non-touching straight compression struts are

suspended in a continuous cable network of tension members. The pretensioned cable structures may be

either self-balancing that is the forces are balanced internally or non-self-balancing where the forces are

resisted externally by the support structure. Tensegrity structures may be organized as

Planar open tensegrity systems: cable beams, cable trusses, cable frames

Planar closed tensegrity systems: cable beams, cable trusses, cable frames

Spatial open tensegrity systems

Spatial closed tensegrity systems

17

Tensegrity sculptures by Kenneth Snelson Karl Ioganson, 1920, Russian artist TENSEGRITY TRIPOD DOUBLE - LAYER TENSEGRITY DOME Olympic Fencing and Gymnastics Arenas, Seoul, 1989, Geiger Georgia Dome, Atlanta, 1992, Levi/Weidlinger, hypar-tensegrity dome. Georgia Dome, Atlanta,

Weidlinger, Structures such as the Hypar-Tensegrity Dome require special analysis and could not

have been realized without the availability of computers and nonlinear programs. The world's

largest cable dome, was completed for the 1992 football season in Atlanta, was the centerpiece of

the 1996 Olympic Games. Spanning 766 ft x 610 ft (233.5 m x 186 m), it will be the first Hypar-

Tensegrity Dome. This new cable supported teflon-coated fabric roof is based on the tensegrity

principles first enunciated by Buckminster Fuller and Kenneth Snelson. Because of the large

deformation characteristics of this type of structures, special geometric nonlinear analysis is

required.