Spanning Space, Horizontal-span Building Structures, Wolfgang Schueller

SPANNING SPACE
HORIZONTAL-SPAN BUILDING STRUCTURES
Prof. Wolfgang Schueller

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 o
crystalline shapes. Most conventional buildings are derived from the rectangle, triangle, circle, trapezoid, cruciform
letter shapes and other linked figures usually composed of rectangles. Traditional architecture shapes from the ba
geometrical solids the prism, pyramid, cylinder, cone, and sphere. Odd-shaped buildings may have irregular plans th
change with height so that the floors are not repetitive anymore. The modernists invented an almost inexhaustible n
new building shapes through transformation and arrangement of basic building shapes, through analogies with biol
human body, crystallography, machines, tinker toys, flow forms, and so on. Classical architecture, in contrast, le
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 Francisco’s 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 Francisco’s War
(1932, 1989) Memorial
Opera House, long-
span structure behavior

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, 1982 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

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

Schwedler dome (braced dome, 1874), Vienna, 207-ft (63 m), e.g.
triangulated ribbed dome using SAP2000

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

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.

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

composite systems
semi-rigidstructures

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

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.

The basic lateral load resisting structure systems:
frames, braced frames, walls

Lateral stability of buildings

Stability of basic vertical
structural building units

Possible location of
lateral force resisting
units in building

LOCATION OF VERTICAL
SUPPORT STRUCTURE

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.

EXAMPLES OF HORIZONTAL-SPAN
ROOF STRUCTURES

Multi-bay long-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, Δ, 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 ):
Δ ∞ 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, 1972

Atrium, Germanisches Museum, Nuremberg, Germany, 1993, me di um Arch.

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

The Building Erection: tower cranes

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 Associés
• 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

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

Tuskegee University
Chapel, Tuskegee,
Alabama, 1969, Paul
Rudolph Architect

The Niagara
Wintergarden, 1977,
Cesar Pelli

Farnsworth House, 1951, Mies van
der Rohe

Cummins Component Factory.
Darlington. 1971, Kevin Roche and John
Dinkeloo

Buffalo Metropolitan
Transportation Center, 1977, The
Cannon Partnership

Osaka Prefectural Rinkai Sports
Center, 1972, Maki & Assoc.

Residence, Aspen, Colorado,
2004, Voorsanger & Assoc.,

Athletic Facility, Phillips Exeter Academy,
Exeter, NH, 1970, Kallman & McKinnel

European Court of Justice, Luxemburg, 2008, Dominique Perrault

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

XL Center (Hartford Coliseum), Hartford, CONN, 1979, reconstruction, Ellerbe
Architects

Freeman Athletic Center, Wesleyan University, Middletown,
Conn., 1970, NewmanArchitects

Central Beheer Insurance
Company, Apeldoorn, The
Netherlands, 1972, Herman
Herzberger

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

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

Library 4, University of Bamberg,
2004, Meyer & Partner, Bayreuth

Main Library, Gainesville, FL, 1992, McKellips Assoc.

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

Tokyo International Forum, 1997,
Rafael Vignoli Arch, Kunio
Watanabe Struct. Eng.

Lyon National School of
Architecture, 1987, Jourda &
Perraudin

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,
Florence, Italy, 1973, Alberto Galardi

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

Greenhouse Pavilions, Parc André
Citroën, Paris, 1992, Patrick Berger
Arch, Veritas Struct.

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

Charles A. Dana
Creative Arts Center,
Colgate University,
Hamilton, New York,
1966, Paul Rudolph

Herbert F. Johnson Museum of Art, Cornell University, 1973, I. M. Pei, constructivist sculpture

Newhouse
Communications
Center I, Syracuse
University, 1964, I.M.
Pei with King & King

Uris Hall, Cornell University, Ithaca,
NY, 1973, Gordon Bunschaft
(Skidmore, Owings & Merrill)

Seoul National University Museum, Rem Koolhaas, 2006

William J. Clinton Presidential Center, Little Rock, AR, 2004, Polshek Partnership

Clinton Presidential Center Museum, Little Rock,
Ark, 2005, Polshek Arch, Leslie Robertson

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

WDR Arcades/Broadcasting House, Cologne, 1996, Gottfried Böhm

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

La Grande Arch, Paris, 1989, Fainsilber & P. 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

Rabat Grand
Theatre proposal,
2010, Zaha Hadid
Architects

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

Office building of the
European Investment
Bank, 2009, Luxembourg,
Ingenhoven Architects

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

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
Internation
al 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

Visual study of Frames and
arches

Visual study of single-
bay portal frames

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 giant’s 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

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

Joe and Etsuko Price
Residence, Corona del Mar,
California 1989, 1996
(addition) , Bart Prince Arch.

The Hysolar Institute at the University of Stuttgart, Germany (1988, G. Behnish and Frank Stepper) reflects
the spirit of deconstruction, it looks like a picture puzzle of a building - it is a playful open style of building
with modern light materials. It reflects a play of irregular spaces like a collage using oblique angles causing
the structure to look for order. The building consists of two rows of prefabricated stacked metal
containers arranged in some haphazard twisted fashion, together with a structural framework
enclosed with sun collectors. The interior space is open at the ends and covered by a sloped roof
structure. The bent linear element gives the illusion of an arch with unimportant almost ugly
anchorage to the ground.

Hysolar Institute, University of
Stuttgart, Germany, 1988, G.
Behnish and Frank Stepper

Response of typical gable frame roof enclosures to gravity loading

Project for Fiumicino Airport, Rome, 1957, Nervi etc

The Novotel Belfort, Belfort,
France, 1994, Bouchez

The International Congress Center,
Berlin, R. Schuler Architect

EDP Center, Friuli,
Italy, A.
Mangiarotti Arch.

Wuppertal Ohligsmühle, suspension railway station, 1982, Rathke Architekten

EDP Center, Friuli, Italy, A.
Mangiarotti Arch.

Rosenthal Glass Factory, Amberg, Germany, 1967,
The Architects Collaborative , Walter Gropius

Barajas Airport, Madrid, Spain, 2004, Richard Rogers,
Anthony Hunt Associates (main structure), Arup (main
façade)

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

Single-layer space frame roofs

The M-House, Los Angeles, 2000, Michael Jantzen, Advanced Structures Inc.

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 O’Hare Airport, Chicago, 1987, H. Jahn
• Museum of Roman Art, Mérida, 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
Polónyi
• 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

Salignatobel Bridge, Switzerland, 1930, Robert Maillart

Cathedral of Palma, Majorca - photoelastic Study by Robert Mark

New Beijing Planetarium,
2005, AmphibianArc –
Nanchi Wang

Visual study of lateral thrust

Satolas Airport TGV Train
Station, Lyons, France, 1995,
Santiago Calatrava

German National Museum, Nuremberg,
1993, me di um Architects

Chiesa di Santa Maria Assunta, Riola,
Italy, 1978, Alvar Aalto

Olympic Stadium Montreal,
1975, Roger Taillibert

Dresden Main Train Station, Dresden, 2006, Foster

Bodegas Protos,
Peñafiel, Valladolid,
Spain, 2008, Richard
Rogers, Arup

Lanxess Arena, Cologne, 1998, Peter Böhm Architekten

United Airlines Terminal at
O’Hare Airport, Chicago,
1987, H. Jahn

Museum of Roman Art, Mérida,
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

Kansai International Airport
Terminal in Osaka, Japan, 1994 ,
Renzo Pia

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

Shenyang Taoxian International Airport, 2002

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, 2005, Renzo Piano, Paul Klee

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

Waterloo Terminal, London, 1993,
Nicholas Grimshaw + Anthony Hunt

5.86'
27.32'10'
4.29'
10.10k
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

Mediapark Cologne, bridge over the lake, 1992

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 Polónyi

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

Renault Distribution Center
Norman Foster Quimper,
France 1980 Swindon,
England

Fleetguard Factory, Quimper, France, 1981, Richard Rogers

Shopping Center St. Herblain, 1988, Nantes, France, Rogers/Rice

Igus Headquarters and
Factory, Cologne, Germany,
2000, Nicholas Grimshaw &
Partners

Horst Korber Sports Center
(1990), Berlin, Christoph
Langhof

The International School,
Lyon, France, 1993, Jourda
& Perraudin Arch.

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

in 2004 three bridges designed by the
Spanish architect Santiago Calatrava were
opened.

The University of Chicago Gerald Ratner
Athletic Center, Cesar Pelli, 2002

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

Radial lateral load 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, New
Canaan, Conn., 1949,
Philip Johnson

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

Sichuan University, Chengdu,
College for Basic Studies, 2002

Paul Löbe and Marie-Elisabeth
Lüders 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,
2009, Make Architects

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.

Folded plate structure systems

Visual study of folded plate structures

UNESCO Building, Paris, 1953, Marcel
Breuer/Bernard Zehrfuss/Pier Luigi Nervi

Saratoga
Performing Arts
Center, 1966,
Saratoga
Springs, NY,
Vollmer Assoc.

Neue Kurhaus addendum, Aachen, Germany

St. Foillan, Aachen, 1958,
Leo Hugot

Institute for Philosophy, Free University,
Berlin, 1980s, Hinrich and Inken Balle

Church of the
Pilgrimage, Neviges,
Germany, Gottfried
Boehm, 1972, 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

Case study of flat space frame roofs

Currigan Hall, Chicago, 1969, Michow Ream & Larson, demolished 2001

McCormic Place, Chicago,
1971, C.F. Murphy Assoc

Omni Coliseum, Atlanta GA,
1972, Thompson, Ventulett &
Stainbeck Inc, demolished
1997

McMaster Health
Sciences Centre,
Hamilton, Ontario,
1972, Craig, Zeidler,
Strong Arch.

George Washington Bridge Bus Station,
Pier Luigi Nervi, 1963.

Wells College Library, Aurora NY,
1968, Walter Netch SOM

St. Benedict’s Abbey Church, Benet Lake,
Wisconsin, 1972, Stanley Tigerman Arch.

Palais Omnisports de
Paris-Bercy, 1983, Jean
Prouvé, Pierre Parat &
Michel Andrault

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).

Shenyang Taoxian International Airport, 2002, Klaus Kohlstrung

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

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

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 ¾ 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.

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

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

Climatron, Missouri Botanical
Garden, St. Louis, 1959,
Buckminster Fuller concept

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

Guangzhou Opera House, Guangzhou, 2010, Zaha Hadid

Vacation home,
Sedona, Arizona, 1995

Vaillant Arena , Davos, 1979, 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

Suspended models of Isler Soap models of Frei Otto
Examples of shell form development through experimentation

Basic concepts related to barrel shells

Cylindrical shell-beam
structure

Vaults and short cylindrical shells

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

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, 1990,
Germany Busmann and Haberer
Architects

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, Jörg 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

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

Eden Project in
Cornwall/England Humid
Tropics Biome

Delft University of Technology Aula Congress Centre, 1966, Bakema

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

Membrane forces in a basic hypar unit

The Flynn Recreation
Complex at Boston College
Daniel F. Tully Arch.

Almacen de Rio, Lindavista, D.F., Mexico, 1954, Felix Candela

Rossmarkt square, modern bus terminal, Schweinfurt, Germany

Greenwich Playhouse, 2002,
Austin/Patterson/ Diston Architects

Garden Exhibition Shell Roof, Stuttgart, 1977, Jörg Schlaich

Expo Roof, Hannover, EXPO 2000,
Thomas Herzog

Cathedral of St. Mary of the
Assumption, San Francisco, 1967,
Pietro Belluschi Arch, Pier Luigi Nervi

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, 2011, Jürgen Mayer +
Arup

Heydar Aliyev Center, Bacu, Azerbaijan, 2012,
Zaha Hadid Architects

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

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.

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, München; Schlaich Bergermann.

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

Stadthalle Bremen,
Germany, 1964,
Ronald Rainer Arch.

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

Sho-Hondo Temple ,
FUJINOMIYA, Japan,
1972, Kimio Yokoyama,
1998 demolished

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

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

Motorway Church,
Florence, 1964,
Giovanni Michelucci

Church Of San
Giovanni Battista,
Florence, Italy,
Giovanni Michelucci,
1964

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
• Norway’s 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 don’t 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

Low-profile, long-span roof structures

Examples of pneumatic structures

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

Effect of wind loading on
spherical membrane
shapes

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
• Expo’02 Neuchatel, air cussion, ca 100 m dia.
• Roman Arena Inflated Roof, Nimes, France, Schlaich
• Festo A.G. Stuttgart

Expo’02 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 0.4…0.55 kN/m2

Airtecture Exibition
Hall, Esslingen, 1996,
Festo Eng.

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:
• Planar closed tensegrity systems
• Spatial open tensegrity systems
• Spatial closed tensegrity systems

Tensegrity sculptures by
K. Snelson and others

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
Fuller’s 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 world’s largest cable dome is currently Atlanta’s 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 Geiger’s 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 roof’s 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

Spanning Space, Horizontal-span Building Structures, Wolfgang Schueller

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