SPANNING SPACE

HORIZONTAL-SPAN BUILDING STRUCTURES

BUILDING STRUCTURES are defined by,

geometry, materials, load action, construction 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.

BUILDING SHAPES and FORMS: there is no limit to building shapes ranging from boxy to compound hybrid to organic and

crystalline shapes. Most conventional buildings are derived from the rectangle, triangle, circle, trapezoid, cruciform, pinwheel,

letter shapes and other linked figures usually composed of rectangles. Traditional architecture shapes from the basic

geometrical solids the prism, pyramid, cylinder, cone, and sphere. Odd-shaped buildings may have irregular plans that may

change with height so that the floors are not repetitive anymore. The modernists invented an almost inexhaustible number of

new building shapes through transformation and arrangement of basic building shapes, through analogies with biology, the

human body, crystallography, machines, tinker toys, flow forms, and so on. Classical architecture, in contrast, lets the faade

appear as a decorative element with symbolic meaning.

Geometry as the basis of architecture

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.

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 (1932, 1989), long-span structure behavior investigation

High-rise floor framing

e.g. Tower, steel/concrete frame, using Etabs

Short span:

e.g. Parthenon, Athens, 430 BC

Long-span stadium: Odate-wood dome,

Odate, Japan, 1992, Toyo Ito/Takenaka, 178

m on oval plan

Atrium structure:

San Franciscos War (1932, 1989) Memorial

Opera House, long-

span structure behavior

investigation

High-rise floor framing: Tower, steel/concrete frame

Example of short span: Parthenon, Athens, 430 BC (Zhou Dynasty)

Glass Cube, Art Museum Stuttgart,

2005, Hascher und Jehle

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.

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

Pantheon, Rom, 143 ft, 44 m, c. 123 AD (HAN Dynasty)

Hagia Sofia, Constantinopel, 535 AD (Sui Dynasty), 112 ft (34 m)

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

St. Peters, Rome, 1590 US Capitol, Washington, 1865

Epcot Center, Orlando 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)

Domes: 207-ft (63 m) Schwedler dome (braced dome, 1874), Vienna

Bridges:1595-ft (486 m) span Brooklyn Bridge, New York, (1883, Roebling)

St. Pancras Station, London, 1868, 240 ft (73 m)

Garabit Viaduct, France, 530 ft (162 m), 1884, Gustave Eiffel

Galerie des Machines (375 ft, 114 m), Paris, 1889

Schwedler dome (braced dome, 1874), Vienna, 207-ft (63 m), e.g.

triangulated ribbed dome

Brooklyn Bridge (1595 ft, 486 m), New York, 1883,

Roebling

Among other early modern long-span structures (reflecting development of

structure systems) were also:

Mushroom concrete frame units (161x161-ft), the Palace of Labor, Turin, Italy, 1961, Pier Luigi Nervi

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: tentlike 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 Palace of Labor (49 x 49-m), Turin, Italy, 1961, Pier Luigi Nervi

Thin-concrete shells, form-passive membranes in compression, tension and

shear: 720-ft (219 m) span CNIT Exhibition Hall, Paris, 1958, B. Zehrfuss

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 (235m),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,

A. Horizontal-span structure systems: floor and roof structure

enclosure structures

bridges

B. Vertical building structure systems: walls, frames cores, etc.

tall buildings

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.

Horizontal gravity force flow

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, cable nets)

Some common rigid horizontal-span structure systems are

shown in 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

HORIZONTAL SPAN BUILDING STRUCTURES

rigid systems

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

composite systems

semi-rigid structures

flexible 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:

(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:

frames, braced frames, walls

Stability of basic vertical

structural building units

Possible location of

lateral force resisting

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)

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.

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 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.

Multi-bay long-span roof structures

Cantilever structures

Some roof support structures

EXAMPLES OF HORIZONTAL-SPAN

ROOF STRUCTURES

My presentation of cases is based on the following organization:

A. BEAMS

B. FRAMES

C. CABLE-STAYED ROOF STRUCTURES

D. FORM - PASSIVE SURFACE STRUCTURES

E. FORM - ACTIVE SURFACE STRUCTURES

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 Beam buildings Cable-supported beams and cable beams

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. 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.

BEAMS as FLEXURAL SYSTEMS

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

Individual Beams

Railway Station, Munich, Germany Atrium, Germanisches Museum, Nuremberg, Germany Pedestrian bridge Nuremberg Dresdner Bank, Verwaltungszentrum, Leipzig, 1997, Engel und Zimmermann Shanghai-Pudong International Airport, Paul Andreu principal architect 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.

Railway Station, Munich, Germany

Atrium, Germanisches Museum, Nuremberg, Germany

Pedestrian bridge Nuremberg

Dresdner Bank, Verwaltungszentrum, Leipzig, 1997, Engel und Zimmermann Arch

Shanghai-Pudong

International Airport,

2001, Paul Andreu

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. E. E European Court of Justice, Luxemburg, 1994, Atelier d'Architecture Paczowski Fritsch Associs

Central Beheer, Apeldorn, NL, Herman Hertzberger (1972): adjacent tower element about 27x 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. Kaifeng,

Xiangguo Si temple complex downtown Kaifeng

Floor/roof framing systems

FLOOR FRAMING STRUCTURES

floor framing example

Chifley tower , Sydney, 1992, Kohn, Pederson, Fox,

Farnsworth House, 1951, Mies van

der Rohe

Residence, Aspen, Colorado,

2004, Voorsanger & Assoc.,

European Court of Justice, Luxemburg, 1994, Atelier d'Architecture Paczowski

Fritsch & Associs

Central Beheer Insurance

Company, Apeldoorn, The

Netherlands, 1972, Herman

Herzberger

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, SOM Documentation Center Nazi Party Rally Grounds, Nuremberg,, 2001, G. Domenig Sobek House, Stuttgart Sony Center, Berlin, Rogers Petersbogen shopping center, Leipzig, 2001, HPP Hentrich-Petschnigg Tokyo Art Center, Vignoli Ski Jump Berg Isel, Innsbruck, 2002, Zaha Hadid

Beam trusses

Atrium, Germanisches Museum, Nuremberg, Germany

National Gallery of Art, East Wing, Washington, 1978, I.M. Pei

Library University of Bamberg

TU Munich

Library Gainesville, Florida

TU Stuttgart

San Francisco Terminal, 2001, SOM

Documentation Center Nazi Party Rally Grounds (Nuremberg, 2001, Guenther Domenig Architect)

Sobek House,

Stuttgart, 2001, Werner

Sobek

Integrated urban

buildings, Linkstr.

Potsdamer Platz),

Richard Rogers,

Berlin, 1998

Petersbogen shopping center, Leipzig, 2001, HPP Hentrich-Petschnigg

Petersbogen shopping

center, Leipzig, 2001, HPP

Hentrich-Petschnigg

Tokyo International Forum, 1997,

Rafael Vignoli Arch, Kunio

Watanabe Struct. Eng.

Ski Jump

Berg Isel,

Innsbruck,

Zaha Hadid,

2002

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, von Gerkan Berlin Stock Exchange, Berlin, Germany, 1999, Nick Grimshaw Centre George Pompidou, 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.

Visual study of Olivetti Building (5 floors), Florence, Italy, 1973, Alberto Galardi

Shanghai-Pudong Museum, Shanghai, (competition won 2002), von Gerkan

Berlin Stock Exchange,

Berlin, Germany, 1999,

Nick Grimshaw

Centre George Pompidou, Paris, 1978, Piano & Rogers

Hongkong Bank (1985), Honkong, 180m, Foster + Arup, steel mast joined by suspension trusses

Beam buildings

Visual study of beam buildings Seoul National University Museum, Rem Koolhaas, 2006 Clinton Library Landesvertretung von Baden-Wuertemberg, Berlin, Dietrich Bangert, 2000 Embassy UK, Berlin, Michael Wilford, 2000 Shanghai Grand Theater, Jean-Marie Charpentier, architect (1998): inverted cylindrical tensile shell

Lehrter Bahnhof, Berlin, 2006, von Gerkan, Marg and Partners Grand Arch de la Defense, Paris Fuji Sankei Building, Tokyo, 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

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, RWTH Aachen, Germany, 2008, Fritzer +

Pape , Schlaich, Bergermann & Partner

Super C, RWHA, Aachen, 2008

WDR

Arcades/Broad

casting House,

Cologne, 1996,

Gottfried Bhm

Shanghai Grand Theater, Jean-Marie Charpentier, 1998

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 Toronto, Canada, Alsop Architects, 2004

Porsche Museum, Stuttgart, Germany, 2009, Delugan Meissl

Abu Dhabi Performing Arts Centre

project, Zaha Hadid

Cable-Supported Beams and Cable Beams

Single-strut and multi-strut cable-supported beams

Erasmus Bridge, Rotterdam, architect 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. Shopping areas, Berlin, Linkstr., Rogers, 1998 Wilkhahn Factory, Bad Muender, Germany, 1992, Thomas Herzog Arch Merzedes-Benz Zentrale, Berlin, 1998, Rafael Moneo Shopping Center, Stuttgart Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove Arup Struct. Eng Lehrter Bahnhof, Berlin, 2006, von Gerkan, Marg and Partners Theater, Berlin, Renzo Piano, 1998 Shanghai-Pudong International Airport, Paul Andreu principal architect, Coyne et Bellier structural engineers, 2001

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

Single-strut and multi-

strut cable-supported

beams

Erasmus Bridge, Rotterdam, 1996, architect Ben Van Berkel

Golden Gate Bridge (one 2224 ft), 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

Shopping areas, Berlin, Linkstr., Richard Rogers, 1998

Wilkhahn-Moebelwerk, Bad Muender, 1992, Thomas Herzog

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 Str. Eng

Lehrter Bahnhof, Berlin, 2006, von Gerkan,

Marg and Partners

Debis Theater, Berlin, Renzo Piano, 1998

Shanghai-Pudong International Airport, 2001, Paul Andreu principal architect,

Coyne et Bellier structural engineers

Ski Jump Voightland Arena,

Klingenthal, 2007, m2r-architecture

B. Frames

FRAMES are flexural-axial systems in contrast to hinged trusses, which are axial systems, and beams, which are flexural systems. Flexural-axial

systems are identified by beam-column behavior that includes the effects of

biaxial bending, torsion, axial deformation, and biaxial shear deformations.

Here, two-dimensional skeleton structures composed of linear elements

are briefly investigated. The most common group of planar structure systems

includes

Portal frames, gable frames, etc. Arches

Portal Frames, Gable Frames, etc. Crown Hall, IIT, Chicago, 1955, Mies van der Rohe 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. Indeterminate portal frames under gravity loads Indeterminate portal frames under lateral load action Sainsbury Centre for Visual Arts, UK, 1978, Norman Foster 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, 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, Germany, 1985, Gottfried Boehm Miyagi Stadium, Sendai City, Japan, 2000, Atelier Hitoshi Abe

Visual study of single-

bay portal frames

Visual study of Frames and

arches

Crown Hall, IIT, Chicago, 1955, Mies van der Rohe

Postal Museum, Frankfurt, Germany, 1990, Guenter Behnisch Arch

Single-story, multi-bay frame

systems

Visual study of multiple-span frame structures

Indeterminate portal frames under gravity loads

Indeterminate portal frames under lateral load action

Sainsbury Centre for Visual Arts,

UK, 1978, Norman Foster

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

Barajas Airport, Madrid, Spain, 2004, Richard Rogers,

Anthony Hunt Associates (main structure), Arup (main

faade)

BMW Plant Leipzig, Central Building,

2004, Zaha Hadid

San Diego Library, 1970, William L. Pereira

798 Beijing Art Factory, Beijing, 1956

Suzhou Museum, China, 2007, Suzhou I. M. Pei

Bus Stop, Aachen, 1998, Peter Eisenman

Zueblin AG Headquarters, Stuttgart, 1985, Gottfried Boehm

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

Miyagi Stadium, Sendai ,Japan ,Atelier

Hitoshi Abe , 2000

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 United Airlines Terminal at OHare Airport, Chicago, 1987, H. Jahn Museum of Roman Art, Mrida, Spain 1985, Jose Rafael Moneo City of Arts & Sciences, Valencia ,Spain ,Santiago Calatrava, 2000 Geschwungene Holzbruecke bei Esslingen (Spannbandbruecke), 1986, R. Dietrich

La Defesa Footbridge, Ripoll, Spain, S. Calatrava, torsion Bridge over the Rhein-Herne-Canal, BUGA 1997, Gelsenkirchen, Stefan Polnyi

Rotterdam arch Kansai International Airport Terminal in Osaka, Japan, 1994 , Renzo Piano San Giovanni Rotondo, Italy, 2004, Renzo Piano Center Paul Klee, Bern, 2005, Renzo Piano Waterloo Terminal, London, Nicholas Grimshaw + Anthony Hunt

Traditional bridge, China

Salignatobel Bridge, Switzerland, 1930, Robert Maillart

Cathedral of Palma, Majorca - photoelastic Study by Robert Mark

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

Dresden Main Train Station, Dresden, 2006, Foster

Bodegas Protos,

Peafiel, Valladolid,

Spain, 2008, Richard

Rogers, Arup

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

Cathedral of Christ the Light, Oakland, CA, 2008, SOM

City of Arts & Sciences, Planetarium, Valencia ,Spain ,Santiago Calatrava, 2000

City of Arts & Sciences, Planetarium, Valencia, Spain, Santiago Calatrava, 2000

The Metro station at Blaak, Rotterdam, 1993, Harry Reijnders of Movares; the arch

spans 62.5 m, dome diameter is 35 m

Space Truss Arch Axial Force Flow

Kansai International

Airport Terminal in

Osaka, Japan, 1994 ,

Renzo Piano

Terminal 5 Roof Heathrow Airport, London, 2005, Rogers/Arup

Terminal 5 Roof Heathrow Airport, London, 2005, Rogers/Arup

Ningbo Air terminal

Ningbo Air terminal

Shenyang Taoxian International Airport

Chongqing Airport Terminal, 2005, Llewelyn Davies Yeang and Arup

San Giovanni Rotondo,

Foggia, Italy, 2004, Renzo

Piano

San Giovanni Rotondo, Italy, 2004, Renzo Piano

Center Paul Klee, Bern, Switzerland, 2007, Renzo Piano Building Workshop , Arup

Center Paul Klee, Bern, 2005, Renzo Piano, Paul Klee

Waterloo Terminal, London, 1993, Nicholas Grimshaw

+ Anthony Hunt

5.86'

27.32'10'

4.29'

10.1

0 k

7.70 k

Mmax

Mmin

BCE Place, Toronto, 1992, Santiago Calatrava

Subway Station to Allians Stadium, Froettmanning,

Munich, 2004, Bohn Architekten, fabric membranes

New TVG Station, Liege, Belgium, 2008,

Santiago Calatrava

Olympic Stadium Athens, 2004, Santiago Calatrava

Pedestrian bridge in Cologne,

Germany

Suspended arch wood bridge, Esslingen, Germany, 1986, R. Dietrich

La Devesa Footbridge, Ripoll, Spain, 1991, S. Calatrava, torsion

Bac de Roda Felipe II Bridge,

1987, Barcelona, S. Calatrava

Bridge over the Rhein-Herne-Canal, BUGA 1997, Gelsenkirchen, Stefan Polnyi

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

Visual study of cable-supported structures

Force flow in cable-supported roofs Patscenter, Princeton, 1984, Rogers/Rice, Fleetguard Factory, Quimper, France, 1981, Richard Rogers

Shopping Center, Nantes, France, 1988, Rogers/Rice Horst Korber Sports Center, Berlin, 1990, Christoph Langhof, The Charlety Stadium, Cite Universitaire, Paris, 1994, Henri and Bruno Gaudin Lufthansa Hangar, Munich, 1992, Buechl + Angerer Bridge, Hoofddorp, Netherlands, S. 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

Patcenter, Princeton, 1984, Richard Rogers

Fleetguard Factory, Quimper, France, 1981, Richard Rogers

Shopping Center (1988), Nantes, France, Rogers/Rice

Horst Korber Sports Center

(1990), Berlin, Christoph

Langhof

The Charlety Stadium at the

City University in Paris, 1994,

Henri and Bruno Gaudin

Lufthansa Hangar (153 m), Munich, 1992, Buechl + Angerer

Bridge, Hoofddorp, Netherlands,

2004, Santiago Calatrava

The University of Chicago Gerald Ratner

Athletic Center, Cesar Pelli, 2002

Melbourne Cricket Ground Southern Stand, 1992, Jolimont, Victoria, Tomkins Shaw & Evans

Gravitational load systems

Radial lateral load resisting system

Uplift resisting system

Bruce Stadium , Philip Cox, Taylor and Partners ,1977, Bruce , Australian Capital Territory

City of Manchester Stadium, UK, 2003, Arup

The Munich Airport Business Center, Munich, Germany, 1997, Helmut Jahn Arch

D. FORM-PASSIVE SURFACE STRUCTURES

Slabs Folded Plates Space frames Tree columns supporting surfaces Skeleton dome structures Thin shells: rotational, synclastic forms vs. translational, anticlastic surfaces

Slabs Visual study of floor/ roof structures Slab analogy and slab support Multi-story building in concrete and steel Hospital, Dachau, Germany Ramp (STRAP) for parking garage Government building, Berlin Government building, Berlin 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

Visual study of floor/ roof structures

Visual study of floor/ roof

structures

Stress flow, multi-story building in concrete and steel

Stress flow, Hospital, Dachau, Germany

Computer modelling, ramp for parking garage

Glasshouse, 1949, Philip Johnson

New National Gallery, Berlin, 1968, Mies van der Rohe

Sichuan University, Chengdu,

College for Basic Studies, 2002

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

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

Phaeno Science Center, 2005, Wolfsburg, Germany, Zaha Hadid

Folded Plates

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 Baller 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

Salone Agnelli, Turin Exhibition Hall, 1948, Pier Luigi Nervi Kimmel Center for the Performing Arts, Philadelphia, 2001, Rafael Vinoly Sydney Olympic Train Station, 1998, Homebush, Hassell Pty. Ltd Arch, vaulted leaf roof truss

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

Visual study of folded plate structures

Folded plate structure systems

Alte Kurhaus, Aachen, Germany

St. Foillan, Aachen,, Leo Hugot

Institute for Philosophy, Free University,

Berlin, 1980s, Hinrich and Inken Balle

Church of the Pilgrimage, Neviges, Germany,

Gottfried Boehm, 1963, 1964-68, Velbert,

Germany

Air force Academy Chapel, Colorado Springs, 1961, Walter Netsch (SOM); trusses

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

Salone Agnelli, Turin Exhibition

Hall, 1948, Pier Luigi Nervi

Kimmel Center for the Performing Arts,

Philadelphia, Rafael Vinoly, 2001

Sydney Olympic Train Station, 1998,

Homebush, Hassell Pty. Ltd Arch

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

Space Frames

Polyhedral roof structures Single-layer three-dimensional frameworks 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

Structural 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 Tomochi Forestry Hall, Kumamoto, Japan, 2005, Taira Nishizawa Architects National Swimming Center, Beijing, 2008, Arup Arch and Eng.

Three-dimensional structures may be organized as follows:

Spatial frameworks: such as space truss beams, derricks, building cores, towers, guyed structures, etc

Single-layer three-dimensional frameworks are folded or bent latticed surface structures such as folded plate planar trusses,

polyhedral dome-like structures and other synclastic and anticlastic

surface structures. They obtain their strength through spatial geometry

that is their profile.

Multi-layer space frames are generated by adding polyhedral units to form three-dimensional building blocks. In contrast to single-layer

systems, the multi-layer structure has bending stiffness and does not

need to be curved; a familiar example are the flat, double-layer space

frame roofs and the sub-tensioned floor/ roof structures.

Visual study of polyhedral roof structures

Visual study of single-layer

three-dimensional

frameworks

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, Arup Arch and Eng.; RANDOM ARRANGEMENT OF SOAP BUBBLES

Strurctural behavior of double-layer

space frames

Common space

frame joints

Case study of flat space frame roofs

Other space frame types

Example Hohensyburg, Germany

a.

b. c.

Robson Square, Vancouver, 1980, Arthur Erickson

Jacob K. Javits Convention Center, New York, 1986, James Ingo Freed

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

Serpentine Gallery 2002, London, England Toyo Ito + Cecil Balmond

National Swimming Center, Beijing, 2008, Herzog de Meuron, Tristram Carfrae of

Arup structural engineers

Tree Columns

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).

Ningbo Air Terminal

Shenyang Airport Terminal

Stanted Airport, London, UK, 1991, Norman Foster/ Arup

Terminal 1, Stuttgart Airport, 1991, von Gerkan & Marg

concept of tree

geometry

Skeleton Dome Structures typical domes, inverted domes, segments of dome assembly, etc.

Major skeleton dome systems Dome shells on polygonal base 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.

Major skeleton dome systems

Dome structure cases

Little Sports Palace, 1960 Olympic Games, Rome, Italy, Pier Luigi Nervi,

Biosphere, Toronto, Expo 67, Buckminster Fuller, 76 m, double-layer space frame

Jkai Baseball Stadium, Odate,

Japan

Philological Library of Freie Universitaet Berlin, 2005, Foster

National Grand Theater, Beijing, 2007, Paul Andreu

Visual study of bent

surface structures

Grand Louvre, Paris, 1993, I. M. Pei

MUDAM, Museum of Modern Art, Luxembourg, 2006, I.M. Pei

Vacation home,

Sedona, Arizona, 1995

Ice Stadium, Davos, Switzerland

Reichstag, Berlin, Germany, 1999, Norman Foster Arch. Leonhardt & Andrae Struct. Eng

Beijing National

Stadium, 2008, Herzog

and De Meuron Arch,

Arup Eng

RIGID SURFACES: Thin Shells, GRID 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 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 Alnwick Gardens Visitor Center roof, UK, 2006, Hopkins Arch., Happold Struct. Eng. Museum Courtyard Roof, Hamburg, 1989, von Gerkan Marg und Partner DZ Bank, glass roof, Berlin, Gehry + Schlaich Exhibition hall Leipzig, Germany, 1996, von Gerkan, GMP, in cooperation with Ian Ritchie

Surface

structures in

nature

Surface classification 1

Surface classification 2

Suspended models of Isler Soap models of Frei Otto

Examples of shell form development through experimentation

Basic concepts related to barrel shells

Basic concepts related to barrel shells

Cylindrical shell-beam

structure

Vaults and short cylindrical shells

Cylindrical grid structures

Various cylindrical

shell types

Cologne Cathedral (1248 19th. Cent.), Germany

St. Lorenz, Nuremberg,

Germany, 14th cent

Airplane hangar, Orvieto 1, 1939, Pier Luigi Nervi

Zarzuela Hippodrome, Madrid, 1935, Eduardo Torroja

Kimball Museum, Fort Worth, 1972, Louis Kahn

Orly Airport, section E, with an elliptical vault

made out of concrete, 2004, Paul Andreu

Wood and steel diagrid shell-lattice supports the Alnwick Gardens Visitor Center

roof, UK, 2006, Hopkins Arch., Happold Struct. Eng.

Museum Courtyard Roof (1989), Hamburg, glass-covered grid shell over L-shaped

courtyard, Architect von Gerkan Marg und Partner

DZ Bank, glass roof, Berlin, Gehry + Schlaich

Exhibition Hall, Leipzig, Germany, 1996, von Gerkan, GMP, Ian Ritchie

P&C Luebeck, Luebeck, 2005, Ingenhoven und Partner, Werner Sobek

Central Railway Station Cologne, Germany

CNIT Exhibition Hall, Paris, 1958, Bernard Zehrfuss Arch, Nicolas Esquillon Eng

Other Shell Forms

Dome shells on polygonal base Keramion Ceramics Museum, Frechen, 1971, Peter Neufert Arch., the building reflects the nature of cera. Kresge Auditorium, MIT, Eero Saarinen/Amman Whitney, 1955, on three supports

Eden Project in Cornwall/England Humid Tropics Biome, Nicholas Grimshaw, Hunt 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., 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 Metropol Parasol", Jrgen Mayer Arch

Dome shells on

polygonal base

Keramion Ceramics Museum, Frechen, 1971, Peter Neufert Arch.

Kresge Auditorium, MIT, Eero

Saarinen/Amman Whitney, 1955, on three

supports

Ecological Center, St. Austell, Cornwall,

England,1996, Nicholas Grimshaw,

Anthony Hunt

Delft University of Technology Aula Congress Centre, 1966, Bakema

Social Center of the Federal Mail, Stuttgart, 1989, Architect Ostertag

Hyperbolic paraboloids

Hypar units on square grids

Case study of hypar roofs

Membrane forces in a basic hypar unit

Some hypar

characteristics

Hypar examples

Felix Candela, Mexico

Bus shelter, Schweinfurt

Greenwich Playhouse, 2002,

Austin/Patterson/ Diston Architects

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

Multi Hall Mannheim, 1975, Timber Lattice

Roof , Frei Otto

DG Bank, Berlin, Germany

2001, Frank Gehry, Schlaich

Phaeno Science Centre, Wolfsburg, Germany, 2005, Zaha Zadid, Adams Kara Taylor

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

Metropol Parasol, Seville, Spain, 2008, Jrgen Mayer

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

Hybrid tensile surface structures possibly including tensegrity

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

Methods for stabilizing cable

structures

Anchorage of tension forces

Suspended Surfaces

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.

Simply-suspended structures

Dulles Airport, Washington, 1962, Eero Saarinen/ Fred Severud, 161-ft (49 m)

suspended tensile vault

Trade Fair Hall 26, Hanover, suspension roof structure, timber panels on steel tie

members, 1996, Architect Herzog + Partner, Mnchen; Schlaich Bergermann.

National Indoor Sports and Training Centre , Philip Cox and Partners, 1981

Olympic Stadium, 1964, Tokyo, Kenzo Tange/ Y. Tsuboi

Anticlastic Tensile 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, Paul Andreu Olympic Stadium, Munich, 1972, Behnich/Frei Otto/Leonardt 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 International Airport Terminal, Denver, 1994, Horst Berger/

Hybrid tensile surface structures

Tensile Membrane 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 synclstic pneumatic structures are tensioned by air

pressure.

Dorton (Raleigh) Arena, 1952,

North Carolina, Matthew Nowicki,

with Frederick Severud

Tent architecture

Subway Station Froettmanning, Munich, 2005, Bohn Architect, PTFE-Glass roof

IAA 95 motor show,

Frankfurt, BMW

New roof for the Olympic Stadium Montreal, 1975, Roger Taillibert

Grand Arch de la Defense, Paris, 1989, Paul Andreu, Peter Rice

Olympic Stadium, Munich, Germany, 1972, Frei Otto, Leonhardt-Andrae

Soap models by Frei Otto

Stadium Roof, Riyadh, Saudi Arabia, 1984, Architect Fraser Robert, Geiger & 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

Denver International Airport Terminal, 1994, Denver, Horst Berger/ Severud

Hybrid tensile surface structures

Pneumatic Structures

Air supported structures

Air-inflated structures

Classificati

on of

pneumatic

structures

Air-supported structures

high-profile ground-mounted air structures

berm- or wall-mounted air domes

low-profile roof membranes

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 Metrodome, Minneapolis, 1981, SOM

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 partioned 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. Air-supported structures may be

organized as

Pneumatic structures

Low-profile, long-span roof structures

Soap bubbles

To house a touring exhibition

Examples of pneumatic structures

Kiss the Frog: the Art of Transformation, inflatable pavilion for Norways National Galery, Oslo, 2001, Magne Magler Wiggen Architect,

Effect of wind loading on

spherical membrane

shapes

Metrodome, Minneapolis, 1981, SOM

Airinflated 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, air cussion, ca 100 m dia. Roman Arena Inflated Roof, Nimes, France, Schlaich Festo A.G. Stuttgart

Expo02 Neuchatel, air cussion, ca 100 m dia.

Roman Arena Inflated Roof, Nimes, France, removable

membrane pneu with outer steel, 1988, Architect Finn

Geipel, Nicolas Michelin, Paris; Schlaich Bergermann und

Partne.internal pressure 0.40.55 kN/m2

Festo A.G. Stuttgart

Tensegrity Structures

PLANAR OPEN TENSEGRITY SYSTEMS

SPATIAL OPEN TENSEGRITY SYSTEMS

SPATIAL CLOSED TENSEGRITY SYSTEMS

Buckminster Fuller:

small islands of compression in a sea of

tension

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

Tensegrity sculptures by K. Snelson

Tensegrity by Karl Ioganson, 1920, Russian

artist

TENSEGRITY TRIPOD

TENSEGRITY

tensile integrity

DOUBLE - LAYER TENSEGRITY DOME

Examples of the spatial open tensegrity

systems are the tensegrity domes. David

Geiger invented a new generation of low-

profile domes, which he called cable domes.

He derived the concept from Buckminster

Fullers aspension (ascending suspension) tensegrity domes, which are triangle based

and consist of discontinuous radial trusses

tied together by ascending concentric tension

rings; but the roof was not conceived as

made of fabric.

Olympic Fencing and Gymnastics Arenas,

Seoul, 1989, Geiger

The worlds largest cable dome is currently Atlantas Georgia Dome (1992), designed by engineer Mattys Levy of Weidlinger Associates.

Levy developed for this enormous 770- x 610-ft oval roof the hypar

tensegrity dome, which required three concentric tension hoops. He

used the name because the triangular-shaped roof panels form

diamonds that are saddle shaped.

In contrast to Geigers radial configuration primarily for round cable domes, Levy used triangular geometry, which works well for

noncircular structures and offers more redundancy, but also results in

a more complex design and erection process. An elliptical roof differs

from a circular one in that the tension along the hoops is not constant

under uniform gravity load action. Furthermore, while in radial cable

domes, the unbalanced loads are resisted first by the radial trusses

and then distributed through deflection of the network, in triangulated

tensegrity domes, loads are distributed more evenly.

The oval plan configuration of the roof consists of two radial circular

segments at the ends, with a planar, 184-ft long tension cable truss at

the long axis that pulls the roofs two foci together. The reinforced-concrete compression ring beam is a hollow box girder 26 ft wide and

5 ft deep that rests on Teflon bearing pads on top of the concrete

columns to accommodate movements.

The Teflon-coated fiberglass membrane, consisting of the fused

diamond-shaped fabric panels approximately 1/16 in. thick, is

supported by the cable network but works independently of it (i.e.

filler panels); it acts solely as a roof membrane but does contribute to

the dome stiffness. The total dead load of the roof is 8 psf.

The roof erection, using simultaneous lift of the entire giant roof

network from the stadium floor to a height of 250 ft, was an

impressive achievement of Birdair, Inc.

Georgia Dome, Atlanta, 1995,

Weidlinger, Structures such as the

Hypar-Tensegrity Dome, 234 m x 186 m