The lecture is in support of:
(1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016.
(2) Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller. The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller
2. 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.
3. 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
4. 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.
5. 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.
7. 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.
8. 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
14. 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.
15. • 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)
19. Taj Mahal (1647, Quing Dynasty), Agra, India, 125 ft (38 m) span corbelled dome
20. St. Peters, Rome, 1590 US Capitol, Washington, 1865
Epcot Center, Orlando, 1982 Georgia Astrodome, Atlanta, 1980
21. 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)
28. 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
29. The Palace of Labor (49 x 49-m), Turin, Italy, 1961, Pier Luigi Nervi
30.
31. Thin-concrete shells, form-passive membranes in compression, tension and
shear: 720-ft (219 m) span CNIT Exhibition Hall, Paris, 1958, B. Zehrfuss
34. 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)
37. 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
38. 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.
40. 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)
42. 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
48. 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.
54. 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.
55. 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)
56. 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
57. 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.
58.
59.
60. 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.
61. 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.
62. 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.
67. 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
68. 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
69. 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.
70.
71. 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
72. 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.
79. 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.
80.
81. 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
83. 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
119. 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
142. 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.
143. Visual study of Olivetti Building,
Florence, Italy, 1973, Alberto Galardi
144. Visual study of Olivetti Building (5 floors), Florence, Italy, 1973, Alberto Galardi
154. Hongkong Bank (1985), Honkong, 180m, Foster + Arup, steel mast joined by suspension trusses
155.
156.
157. 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
216. 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
239. 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
242. 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
253. Joe and Etsuko Price
Residence, Corona del Mar,
California 1989, 1996
(addition) , Bart Prince Arch.
254. 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.
335. 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
425. Bac de Roda Felipe II Bridge,
1987, Barcelona, S. Calatrava
426. Bridge over the Rhein-Herne-Canal, BUGA 1997, Gelsenkirchen, Stefan Polónyi
427. 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
430. • 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
453. The Munich Airport Business Center, Munich, Germany, 1997, Helmut Jahn Arch
454.
455.
456. 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
457. 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
491. 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.
513. 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.
514. 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.
556. 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.
583. National Swimming Center, Beijing, 2008, Herzog de Meuron, Tristram Carfrae of
Arup structural engineers
584.
585.
586.
587.
588. 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).
597. 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.
632. 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
633. 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
663. 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
721. 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
724. 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.
740. 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
741. 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.
766. 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
767. 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
776. 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
778. 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
781. 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
782. 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
787. 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.
789. 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.
790. 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.
791. Georgia Dome, Atlanta, 1995,
Weidlinger, Structures such as the
Hypar-Tensegrity Dome, 234 m x 186 m
Editor's Notes
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 façade appear as a decorative element with symbolic meaning.
Geometric patterns
Odate-wood dome, Odate, Japan, 1992, Toyo Ito/Takenaka, 178 m on oval plan
San Francisco’s War Memorial Opera House (1932, 1989) long-span structure behavior investigation
Tower, steel/concrete frame, using Etabs
Parthenon, 430 BC, Athens
Glass Cube, Art Museum Stuttgart, 2005, Hascher und Jehle Arch.
Glass Cube, Art Museum Stuttgart, 2005, Hascher und Jehle Arch
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 Sophia in Constantinopel, used by the master builders Anthemius of Tralles and Isodore of Miletus (535 A.D) for the first time cause a rather dynamic flow of solid building elements together with an interior spaciousness that is quite different from the static Pantheon. The shallow main brick dome of 112-ft span is reinforced with ribs and almost entirely in compression, thus evades the tensile stresses in semicircular domes and the necessary increase in shell thickness, which may not have been feasible because of the low tensile capacity of the brick and the lost art of Roman technology. The dome sits on four gigantic pendentives that convert the round base to the square base below. The pendentives, in turn, are vertically supported by four huge circular arches. The lateral thrust, which is large for shallow domes (but not present for semicircular domes, where it is transformed into tensile stress bands along the bottom part of the dome), is resisted by two semidomes in one direction and massive corner buttresses in the other direction. The action of the buttresses was not fully understood and thus could not prevent several collapses of the roof.
Taj Mahal (1647), Agra, India, 125 ft (38 m) span corbelled dome
St. Peters, Rome (1590): US Capitol, Washington (1865, double dome); Epcot Center, Orlando, geodesic dome; Georgia Astrodome, Atlanta (1980)
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)
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, e.g. triangulated ribbed dome for asymmetrical loading
1595-ft (486 m) span Brooklyn Bridge, New York, (1883, Roebling)
The Palace of Labor, Turin, Italy, 1961, Pier Luigi Nervi; the structure consists of 16 statically independent mushroom units, each 131 x 131 ft wide supported by 66-ft high columns
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, Bernard Zehrfuss Arch, Nicolas Esquillon Eng.
Jacob K. Javits Convention Center, New York, 1986, James Ingo Freed
Munich Olympics, 1972, Frei Otto
Pontiac Silver Dome, Pontiac, 722 ft (220 m), 1975
Georgia Dome, Atlanta, 770 ft (235 m), 1992
Location of vertical support structure
The basic lateral load resisting structure systems
Stability of basic vertical structural building units
Possible location of units in building
Lateral stability of buildings
Typical span-to-depth ratios for bending members
Daniel Schodek:: Structures, 3rd ed., Prentice Hall 1908, Structure systems, preliminary design
Multi-bay long-span roof structures
Cantilever structures
Some roof support structures
Examples of horizontal-span roof structure systems
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 principal architect, Coyne et Bellier structural engineers
Petersbogen shopping center, Leipzig, 2001, HPP Hentrich-Petschnigg
The asymmetrical entrance metal-glass canopies of the National Gallery of Art, Stuttgart, J. Stirling (1984), counteract and relieve the traditional post-modern classicism of the monumental stone building; they are toy-like and witty but not beautiful.
Documentation Center Nazi Party Rally Grounds (Nuremberg, 2001, Guenther Domenig Architect) is located in the unfinished structure of the Congress Hall. It gives detailed information about the history of the Party Rallies and exposes them as manipulative rituals of Nazi propaganda. A glass and steel gangway penetrates the North wing of the Congress Hall like a shaft, the Documentation Center makes a clear contemporary architectural statement.
Floor/roof framing systems
Floor framing structures
RISA floor framing example
Chifley tower , Sydney, 1992, Kohn, Pederson, Fox, Travis McEwen Group , Plan shape rectangular with multiple setbacks and curved facade to the East with a central irregular polygon shaped core. - Number of stories 53 levels above ground, 4 levels basement and 5 service levels
Vertical loads, The load transfer strategy for the floor system is to transfer the load along the shorter direction to the perimeter of the building and to the central core. This strategy is carried out by using a two level structure - a concrete floor slab on permanent form work for the first level and the composite steel beams for the second. The first level thus consists of small span - varying from 2.5 m to 3.0 m - surface structures that provide a one-way transfer of distributed loads, and the second consists of large span linear elements that act compositely with the slab and transfer loads in the 10-15m direction. The loads reaching the perimeter are transferred through discrete point supports, and those reaching the central core are transferred through continuous supports.
The loads on the car park floors are transferred horizontally using a two-way load transfer strategy and then vertically using discrete point supports, to provide the required flexibility for parking and circulation within the car park. The live loads acting on the building are initially applied to the slab, which transfers it to the radial main beams by the shortest path - transverse to the beams. The loads are then transferred radially along the main beams to the two ends of the beams. Loads transferred by one set of alternate beams and reaching the perimeter of the building are transferred to the columns through pinned connections. The loads transferred by the other set of beams are initially transferred to perimeter beams, which then transfer the loads to the columns supporting each of them. The loads transferred to the core ends of the beams are transferred through steel brackets and embedded steel plates to the outer core wall. The dead loads also follow a similar path, but the magnitude of the dead load transferred increases as new elements enter the load path. The columns provide the vertical load paths at the perimeter of building and the core walls the vertical load paths at the centre. The perimeter column loads reaching the transfer trusses at level 39/40 are transferred to accommodate the ganging geometry of the building. Additional loads are also transferred to these columns and the core walls from the car park floors. Finally, the loads reach the footings of the columns and the core structure, are transferred to the foundation.
The live and dead loads acting on the car park floors are transferred by each of the floor panels to the supporting columns by two-way load transfer. There are, however, a number of possible load paths to the column from any point in the slab panel, with the load flow along any particular path being determined by the structural stiffness available along that path. The loads reaching the columns are taken vertically down to the footings and then to the foundation.
The vertical loads are collected by the composite floor system and transferred to the radial steel beams. The beams carry the load to the core on the inside and the columns on the outside. The core carries the load to the foundations. The columns carry the load to the foundation.
Designed and built from 1946 to 1951, Farnsworth House is considered a paradigm of international style architecture in America. The house's structure consists of precast concrete floor and roof slabs supported by a carefully crafted steel skeleton frame of beams, girders and columns. The facade is made of single panes of glass spanning from floor to ceiling, fastened to the structural system by steel mullions. The building is heated by radiant coils set in the concrete floor; natural cross ventilation and the shade of nearby trees provide minimal cooling. Though it proved difficult to live in, the Farnsworth House's elegant simplicity is still regarded as an important accomplishment of the international style.
3-D Model of skeleton frame and one way slabs
Residence, Aspen, Colorado, 2004, Voorsanger & Assoc., Weidlinger Struct. Eng.
European Court of Justice, Luxemburg, 1994, Atelier d'Architecture Paczowski Fritsch & Associés
European Court of Justice, Luxemburg, 1994, Atelier d'Architecture Paczowski Fritsch & Associés
Office building for 'Centraal Beheer' Insurance Company, Apeldoorn, The Netherlands, 1972, Herman Herzberger
Office building Central Beheer, Apedoorn, The Netherlands, Herman Hertzberger, 1987
Xiangguo Si temple complex, downtown Kaifeng
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
National Gallery of Art, East Wing, Washington, 1978, I.M. Pei
Library, University of Bamberg
TU Munich
Library Gainesville, FL
TU Stuttgart
San Francisco Terminal, 2001, SOM
Documentation Center Nazi Party Rally Grounds (Nuremberg, 2001, Guenther Domenig Architect)
Sobek House, 2001, Stuttgart, 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
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
Berlin Stock Exchange, Berlin, Germany, 1999, Nick Grimshaw: the building reminds one of an armadillo; it is suspended from arches, i.e. the upper floors are suspended from arches on steel hangers so the bottom two stories are free of vertical structure to allow connection between life of building and the city outside.
Centre George Pompidou,1978, Paris, Piano & Rogers
Centre George Pompidou, Paris, 1978, Piano & Rogers
KM, Hongkong Bank (1985), Honkong, 180m, Foster + Arup, steel mast joined by suspension trusses
acting in portal frame action
Hongkong Bank (180 m), Honkong, 1985, Foster + Arup, steel mast joined by suspension trussesacting in portal frame action
Beam buildings
Herbert F. Johnson Museum of Ar, Cornell University. Ithaca, 1973, I.M. Pei
Seoul National University Museum, Rem Koolhaas, 2006
William J. Clinton Presidential Center, Little Rock, AR, 2004, Polshek Partnership
The 5-story building is420’ long and 46’ wide and is supported by a pair of 37’ deep trusses. The trusses cantilever 90’ at each end of the building and are supported at three locations with a maximum clear span of 150’ between supports.
Landesvertretung von Baden-Wuertemberg, Berlin, Dietrich Bangert, 2000
Embassy UK, Berlin, Michael Wilford, 2000
Super C, RWTH Aachen, Germany, Fritzer + Pape , Schlaich, Bergermann & Partner . heating and cooling through a 2.500 m deep probe linked to a geothermal heat pump , Four 31-metre steel girders carry the entire top floor. The supports weigh a total of 45 tonnes and form a 16-metre overhanging half-timbered construction. Vibration absorbers in the cantilever eliminate possible future oscillations. The extreme overhang is made possible by 22-metre long steel cables, so-called monostrands. These monostrands support the steel frames of the upper floors by connecting them with the foundations, similar to the principle of a prestressed concrete bridge.
Super C, RWTH Aachen, Germany, Fritzer + Pape , Schlaich, Bergermann & Partner
WDR Arcades/Broadcasting House, Cologne, 1996, Gottfried Böhm; this buildings hiuses the Radio and television production studios of the largest German broadcasting station. The WDR-Arkaden are architecturally one of the most interesting buildings in Cologne. The shopping arcade was benn designed by Gottfried Böhm. Some people characterise it as some batched container.
WDR Arcades/Broadcasting House, Cologne, 1996, Gottfried Böhm; this buildings hiuses the Radio and television production studios of the largest German broadcasting station. The WDR-Arkaden are architecturally one of the most interesting buildings in Cologne. The shopping arcade was benn designed by Gottfried Böhm. Some people characterise it as some batched container.
WDR Arcades/Broadcasting House, Cologne, 1996, Gottfried Böhm; this buildings hiuses the Radio and television production studios of the largest German broadcasting station. The WDR-Arkaden are architecturally one of the most interesting buildings in Cologne. The shopping arcade was benn designed by Gottfried Böhm. Some people characterise it as some batched container.
Shanghai Grand Theater, Jean-Marie Charpentier, architect (1998): inverted cylindrical tensile shell
Lehrter Bahnhof, Berlin, 2006, von Gerkan, Marg and Partners
La Grande Arche, Paris, 1989, Johan Otto von Sprechelsen/ Peter Rice for the canopy
Fuji Sankei Building, Tokyo, 1996, Kenco Tange
The Sharp Centre for Design, Ontario College of Art & Design, 100 McCaul Street, Toront, Ontario, Canada, Alsop Architects, 2004, With the addition of the Sharp Centre for Design at the Ontario College of Art and Design, Will Alsop cleverly addresses the complicated notion of expansion in a dense urban setting with his soaring black and white box. The building stitches a connection between existing buildings while providing new space in the rectangular volume that proudly soars above.
Sharp Centre for Design, Ontario College of Art & Design, Toronto, Canada, 2004, Alsop Architects
Porsche Museum building: images authorised by Delugan Meissl Architects 2007
Abu Dhabi Performing Arts Centre, Zaha Hadid, the centre,2007 presented to the public, will be 62 metres tall and include five theatres.It appears to be an organic, almost living element given soul by the movement of people.
Single-strut and multi-strut cable-supported beams
Erasmus Bridge, Rotterdam, architect Ben Van Berkel, measuring 33 m (109 ft) in width, totalling over 800 m (2630 ft) in length.
The kink in the pylon was designed to resist the enormous forces resulting resulting from the high bend load; because of the twisted shape of the pylon, tremendous moments are created at the location of the twist
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: the elegance and lightness of the the 40-m (135-ft) span glass and steel lattice roof is articulated through the transparency of roof skin and the almost non-existence of the diagonal arches which are cable- supported by a single post at their intersection at center span. This new technology features construction with its own aesthetics reflecting a play between artistic, architectural mathematical, and engineering worlds. The depth of the box arches is reduced by the central compression strut (flying column) carried by the suspended tension rods. The arches, in turn, are supported by tubular trusses on each side, which separate the roof from the buildings.
Kempinski Hotel, Munich, Germany, 1997, H. Jahn/Schlaich: the elegance and lightness of the the 40-m (135-ft) span glass and steel lattice roof is articulated through the transparency of roof skin and the almost non-existence of the diagonal arches which are cable- supported by a single post at their intersection at center span. This new technology features construction with its own aesthetics reflecting a play between artistic, architectural mathematical, and engineering worlds. The depth of the box arches is reduced by the central compression strut (flying column) carried by the suspended tension rods. The arches, in turn, are supported by tubular trusses on each side, which separate the roof from the buildings.
Shopping areas, Berlin, Linkstr., Richard Rogers, 1998
The main structure for the Wilkhahn Factory, Bad Muender, Germany, 1992, by Thomas Herzog Arch., is parallel to the façade (i.e. longitudinal); the building integrates function, construction, ecological concern and architecture. The 5.4 m wide (18 ft) tower structures that contain the offices and service zones, are centered at 30 m (98 ft) and give support to the long spans of the cable-supported beams (24.6 m/81 ft). The formal configuration of the cables (1.5 m deep) convincingly reflects the moment flow of continuous beams under gravity load action. The diagonal bracing of the towers seems to give lateral support to the post-beam timber structure to resist wind with a minimum effort.
Wilkhahn-Moebelwerk, 1992, Thomas Herzog
Mercedes-Benz Center am Salzufer, Berlin, 2000, Lamm, Weber, Donath und Partner
Mercedes-Benz Center am Salzufer, Berlin, 2000, Lamm, Weber, Donath und Partner
Shopping Center, Stuttgart
Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng
Lehrter Bahnhof, Berlin, 2006, von Gerkan, Marg and Partners
Debis Theater, Berlin, 1998, Renzo Piano
Shanghai-Pudong International Airport, 2001, Paul Andreu principal architect, Coyne et Bellier structural engineers
Shanghai-Pudong International Airport, 2001, Paul Andreu principal architect, Coyne et Bellier structural engineers
Shanghai-Pudong International Airport, 2001, Paul Andreu principal architect, Coyne et Bellier structural engineers
Crown Hall, IIT, Chicago, 1955, Mies van der Rohe; the 120-ft (37 m) span building has become a symbol for the celebration of the portal frame; Mies articulated the power and beauty of the post-beam structure by exposing the lightness of the steel skeleton as contrasted by the glass surface; the roof platform is suspended from the welded plate girders that are spaced at 60 ft (18 m).
Crown Hall, IIT, Chicago, 1955, Mies van der Rohe; the 120-ft (37 m) span building has become a symbol for the celebration of the portal frame; Mies articulated the power and beauty of the post-beam structure by exposing the lightness of the steel skeleton as contrasted by the glass surface; the roof platform is suspended from the welded plate girders that are spaced at 60 ft (18 m).
Postal Museum, Frankfurt, Germany, 1990, Guenter Behnisch Arch.: space dynamics through fragmentation
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
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 façade). This new airport terminal building reflects Madrid's commitment to becoming a major international hub. The building is in three sections: a parking station comprising six five-level modules, the terminal with three areas for domestic and European flights and a satellite in two parts for international flights. The terminal and satellite are built using the same construction principle: the sinuous main beams of the roof are supported by metal bearers resting on a reinforced concrete structure. The main beams are up to 72 metres long; they rest on Y-shaped elliptical tube posts at each end. The secondary beams at 3.5-metre intervals form an arch between the main beams.
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
The Barajas project is the largest so far undertaken by the practice - more than one million square metres of buildings with a budget of around one billion Euros. The new terminal and satellite are designed to handle up to 35 million passengers annually, establishing Madrid as a major European hub, and are located some distance to the north-west of the existing terminal complex.
The new terminal features a clear progression of spaces for departing and arriving travellers. The building's legible, modular design creates a repeating sequence of waves formed by vast wings of prefabricated steel. Supported on central 'trees', the great roof is punctuated by roof lights providing carefully controlled natural light throughout the upper level of the terminal. Light-filled 'canyons' divide the parallel floors that accommodate the various stages of passenger processing - from point of arrival, through check-in and passport and security controls to departure lounges and, finally, to the aircraft.
A simple palette of materials and straightforward detailing reinforce the direct character of the architecture. Internally, the roof is clad in bamboo strips, giving it a smooth and seamless appearance. In contrast, the structural 'trees' are painted to create a kilometre-long vista of graduated colour. The lower levels of the building house baggage handling, storage and plant areas, and offer a striking contrast with the lightweight transparency of the passenger areas above
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Der bedeutendste britische Architekturpreis, der "Stirling Prize", geht in diesem Jahr an den Madrider Flughafen Barajas. Allein das schiere Ausmaß und die Vielschichtigkeit des 1,2 Kilometer langen farbenfrohen Gebäudes könne nicht "genügend gewürdigt" werden, begründeten die Juroren des Royal Institute of British Architects (RIBA) am Samstag ihre Entscheidung. Entworfen wurde der Flughafen von dem britischen Architekten Richard Rogers, der gemeinsam mit Renzo Piano auch das Pariser Centre Pompidou gebaut hatte. Machen Sie sich ein Bild von den architektonischen Meisterwerke, die mit Sicherheit eine Reise wert sind:
Airport Madrid, Spain, 2005, Richard Rogers
Bamboo roof detail Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade), detail view of the scalloped roof edge
Barajas Airport, Madrid, Spain, 2004, Richard Rogers, Anthony Hunt Associates (main structure), Arup (main façade)
BMW Plant Leipzig, Central Building, 2004, Zaha Hadid
BMW Plant Leipzig, Central Building, 2004, Zaha Hadid
San Diego Library, 1970, William L. Pereira
San Diego Library, 1970, William L. Pereira
798 Beijing Art Factory, Beijing, 1956, the shape of the supporting frames (i.e. roof shape) depends on ventilation and lighting of the sheds.
Suzhou Museum, Suzhou, China, 2007, I.M. Pei
Suzhou Museum, Suzhou, China, 2007, I.M. Pei
Suzhou Museum, Suzhou, China, 2007, I.M. Pei
Suzhou Museum, Suzhou, China, 2007, I.M. Pei
Suzhou Museum, Suzhou, China, 2007, I.M. Pei
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, 1985, Gottfried Boehm: hollow central glass-covered atrium space between solid building masses; stair towers and pedestrian bridges as interior connectors; celebration of articulated precast concrete cladding
Zueblin AG Headquarters, Stuttgart, 1985, Gottfried Boehm: hollow central glass-covered atrium space between solid building masses; stair towers and pedestrian bridges as interior connectors; celebration of articulated precast concrete cladding
Miyagi Stadium, Sendai City, Japan, 2000, Atelier Hitoshi Abe. It is partially built into a green hillock, and its shape is symbolic. When viewed from the air, the sweeping, crescent-shaped roof evokes the image of a warrior's battle helmet from the days of the Date clan of the Japanese feudal period. The roof of the main stand is 360 meters long and incorporates a frame comprising 2,500 tons of steel trusses. Like the string against which an arrow is nocked, a gigantic prestressed concrete tie-beam buried in the ground pulls both edges of the roof toward the center of the stand with 3,000 tons of force, to stabilize the shape and create a beautiful, flowing line. The external perimeter is formed of a lattice of countless criss-crossing pylons in a complex structure, much like a gigantic scaffold. The bulk of the structure involved pouring the pylons on site and took up most of the three-year construction period. A total of 100,000 cubic meters of concrete was used. The undressed concrete is rough and stark, but imparts a sense of solidity--and even warmth--to the structure.
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, a secondary transfer structure was introduced to transfer loads from the membrane to the top chord of the station roof’s old steel arches. The fragile arches had little resistance to horizontal forces, so reactions in the longitudinal direction are transferred to braced end bays, which act as 10 m wide trusses. Additional cables underneath the fabric ensure overall stability.
The refurbishment of the main roof of Dresden Railway Station (Foster + Happold) is an outstanding example of the use of 21st Century technology to respect and conserve an unaltered, historic 19th century structure.
The original 120m x 240m structure was formed with elegant, three span, filigree arches, with the central arch spanning 59 metres at a height of 30 metres. Material testing and surveys revealed extensive corrosion of the original structure due to poor post war repairs. In some locations, wartime damage had resulted in several arches being distorted and out of alignment. It was clear that the existing structure could not support the weight of a reinstated glazed roof along the 240 metre long and 120 metre wide station. The use of an innovative sculptured fabric roof has enabled the existing structure to be retained in its original form and function, a key objective for any conservation project…”
Bodegas Protos, Peñafiel, Valladolid, Spain, 2008, Richard Rogers, Arup; The design of the delicate roof structure was also based on off site industrialised fabrication and simple and rapid in-situ assembly. This modular system starts with laminated timber arches that span 18 metres across the access level, with triangular steel base connections to the concrete structure.
Lanxess Arena, Cologne, 1998, Peter Böhm Architekten
Lanxess Arena, Cologne, 1998, Peter Böhm Architekten
United Airlines Terminal at O’Hare Airport, Chicago, 1987, H. Jahn, the corridor roofs are supported by perforated arched bents that span a maximum distance of 50 ft (15 m) and are supported on multi-pipe, battened, column assemblies of sculptural appearance.
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. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
Cathedral of Christ the Light, Oakland, CA, 2008, SOM. The Cathedral's strength is achieved through the creation of glued-laminated timber beams (glulam) and steel rod space frames. The frame is constructed with 26, 10-3/4 inch wide by 99 foot -9 inch long glulam ribs that vary in depth from 30 inches at the base to 19-1/2 inches at the top. Between each rib are 32, 5-1/8-inch-wide glulam louvers varying in depth from 22-1/2 inches to 39 inches. The louvers are installed at 7 different angles to optimize the light effects. The roof of the cathedral is composed of a tension-free glass oculus supported by a steel compression ring which resists the horizontal thrust of the glulam ribs. Parallel to each rib is a glulam mullion 10-3/4 inches wide by 15 inches deep and 103 feet long. The mullions are installed 80 degrees from horizontal and are connected to the wooden vaults by turned glulam struts with tapered ends of lengths varying from 2 feet to 15 feet.The space frame's diagonal members are made with pre-tensioned high strength steel rods installed such that in an earthquake they will always be in tension. The building is subdivided into five levels where fixed connections tie the louvers to the ribs completing the structural frame.
City of Arts & Sciences, Valencia ,Spain ,Santiago Calatrava, 2000; the planetarium , as an eye to the skies , was designed in the form of a huge lens.
City of Arts & Sciences, Valencia ,Spain ,Santiago Calatrava, 2000; the planetarium , as an eye to the skies , was designed in the form of a huge lens.
The Metro station at Blaak, Rotterdam, 1993, Harry Reijnders of Movares; the arch spans 62.5 m, dome diameter is 35 m
The Metro station at Blaak, Rotterdam, 1993, Harry Reijnders of Movares; the arch spans 62.5 m, dome diameter is 35 m
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 Piano
Kansai International Airport Terminal in Osaka, Japan, 1994 , Renzo Piano
Chongqing Airport Terminal, 2005, Llewelyn Davies Yeang and Arup
Chongqing Airport Terminal, 2005, Llewelyn Davies Yeang and Arup
Chongqing Air Terminal
San Giovanni Rotondo is one of the most-visited pilgrimage destinations in Italy. Every year, several hundreds of thousands of pilgrims gather here to pay homage to the memory of Saint Padre Pio, a monk from a monastery famous for his stigmata.To accommodate the ever-increasing number of followers, the monks decided to build a larger place of worship. The project consisted of building a larger church, not far from the site where the existing church and monastery are located.The major challenge for such a building was in creating a space that would be open and inviting. Rather than intimidate the followers, it had to incite a desire to draw closer. That explains why the church was given an immense but low-lying dome shape.From above, the structure appears spiral shaped, converging at a central dome. When approached from ground level, the building reaches its highest point at the edge overhanging the square. At that point, the dome tapers slightly, as if bidding visitors welcome. Nearly 6000 others may actually be seated inside the place of worship itself, while 30,000 people can take part in religious services from the piazza outside.To maintain the sense of welcome, the paving on the square will extend into the church, integrating the inside and the outside of the structure, and making it into a kind of "open house".The dome is supported by about twenty arches, made up of the same mountain stone, the largest arch being 18 meters high and 50 meters long. Centuries after being the main structural element of Gothic cathedrals, this material has been subjected to new experiments, drawing on leading-edge technology (computerized structural designs, laser-based cross-sectional images, etc.). As the main structural material used at San Giovanni Rotondo, it is the stone that gives the overall structure its distinctive unity. The construction is completed with other natural or everlasting treated material: stainless steel for the props supporting the top, laminated larch timber for the upper beams, pre-oxidized copper for the roof finishing.
San Giovanni Rotondo, 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 is not someone you can simply contain inside an ordinary building. An artist with so much depth needs plenty of scope. That’s why we tried to express Paul Klee’s creative nature through an unusual, gentle architecture which in turn plays with nature.” Renzo Piano
Paul Klee is not someone you can simply contain inside an ordinary building. An artist with so much depth needs plenty of scope. That’s why we tried to express Paul Klee’s creative nature through an unusual, gentle architecture which in turn plays with nature.” Renzo Piano
Waterloo Terminal, London, 1993, Nicholas Grimshaw + Anthony Hunt
Waterloo Terminal, London, Nicholas Grimshaw + Anthony Hunt
Waterloo Terminal, London, Nicholas Grimshaw + Anthony Hunt
For preliminary design purposes, investigate the following asymmetrical arch systems using a 20-ft radius as derived from a 40-ft diameter circle, with respect to the effect of load arrangement on intensity of force flow by studying bending moment distribution, axial force flow, deflections, and the reactions. Assume Lb/L = 0.05 about the minor axis.
Apply the gravity loads on the horizontal roof projection (this includes the dead load for preliminary design purposes) and the wind loads on the vertical roof projection. Use wD = 0.5 k/ft = 7,30 kN/m (DL case), wL = 0.5 k/ft (LLFULL = full loading , LLRIGHT = loading on right span, and LLLEFT = loading on left span), wW = 0.4 k/ft = 5,84 kN/m (WL case). Consider COMB1 (DL + LLFULL), COMB2 (DL + LLRIGHT), COMB3 (DL + LLLEFT), COMB4 (DL + LLFULL + WL) 0.75, COMB5 (DL + LLRIGHT + WL) 0.75, and COMB6 (DL + LLLEFT + WL)0.75. But for the design of the arches replace the factor of 0.75 by 1.0 because SAP by default reduces the wind load combination by 0.75!
1) Investigate a two-hinge arch (i.e. Fig. 7.11a but without crown hinge) trying W12 sections (W12x45, W12x40, etc.) using A36 steel. What loading condition does control? Run the program again by using one section for the arch rather than various ones as based on AUTOSELECT. Try to check approximately some of the answers manually.
Investigate the asymmetrical three-hinge arch (Fig. 7.12a) trying W12 sections (W12x45, W12x40, etc.) using A36 steel. What loading condition does control? Try to check approximately some of the answers manually.
3) Investigate the three-hinge, trussed arch (Fig.7.12b) trying as a first approach 1.25-in (3,18 cm) rods as tension members, Pxx4 (4.5-in. = 11,43 cm) pipes for the compression chord members and Pxx3 (3.5-in. = 8,89 cm) pipes for the web compression members. What loading condition does control? Try to check approximately some of the answers manually. Construct the right truss by subdividing the bottom chord into six equal parts.
To model the geometry of the three arches in SAP the following values are selected:
Global grid system: grid spacing in X direction: 2.5 ft using 20 spaces
grid spacing in Y direction: 5 ft using 20 spaces
grid spacing in Z direction: 5 ft using 15 spaces
In order to construct the trusses additional grid lines must be
chosen at a later stage.
Cylindrical grid system: grid spacing along Radius: 20 ft using 1 space
radial angles along Theta: 15 deg using 10 spaces
spacing of curves along Z direction: 20 ft using 1 space
BCE Place, Toronto, 1992, Santiago Calatrava
BCE Place, Toronto, 1992, Santiago Calatrava
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
Railroad Station, Liege, Belgium, 2008, Santiago Calatrava
In accordance to architectural study performed by Sandiago Calatrava, the newly built roof partially covers the Olympic Stadium in Athens, mainly the terraces, covering a total area of 25,000 sq m.The bearing construction is made of two double steel arcs, which are positioned at the same height in pairs and are connected with extended cables. A system of diagonal connectors further trusses the structure.The bearing construction is completed with the transversal girders, which are connected to the lower arc and form the grid on which the laminated polycarbonate is fitted.
Olympic Stadium Athens, 2004, Santiago Calatrava
Pedestrian bridge in Cologne
Geschwungene Holzbruecke bei Esslingen (Spannbandbruecke), 1986, R. Dietrich
La Devesa Footbridge, Ripoll, Spain, 1991, S. Calatrava, torsion
La Devesa Footbridge, Ripoll, Spain, 1991, S. Calatrava, torsion
Bac de Roda Felipe II Bridge, 1987, west Barcelona, Santiago Calatrava, Architect
Bridge over the Rhein-Herne-Canal, BUGA 1997, Gelsenkirchen, Stefan Polónyi
Visual study of cable-supported structures
Force flow in cable-supported roofs
Patcenter, Princeton, 1984, Rogers; cable-stayed double-cantilever central spine – A-frames support cables – ring plate connections – center struts are tubes (uplift), outer ones are rods (suspension)
Fleetguard Factory, Quimper, France, 1981, Richard Rogers
Fleetguard Factory, Quimper, France, 1981, Richard Rogers
Shopping Center (1988), Nantes, France, Rogers/Rice, 94-ft (29 m) high tubular masts support the 94-ft (29 m) framework in a spatial fashion from above without penetration of the roof. Only certain combinations of the 3-dimensional network of tension rods and compression struts are activated under various load actions.
Horst Korber Sports Center (1990), Berlin, Christoph Langhof, quite different in spirit are the slender and minimal abstract planar, tree-like c.30-m high masts with their five branches linked by cables from which the light cable roof trusses are hung. The symmetrical abstract forms of the masts are completely opposite in expression from the tectonic shapes of most other examples.
The Charlety Stadium at the Cite Universitaire in Paris (1994, Henri and Bruno Gaudin):
Lufthansa Hangar (1992), Munich, Buechl + Angerer, the immense 153-m span roof is supported by the diagonal cables suspended from the c.56-m tall concrete pylons
Bridge, Hoofddorp, Netherlands, 2004, S. Calatrava; in 2004 three bridges designed by the Spanish architect Santiago Calatrava were opened. The bridges span the main canal of the Haarlemmermeer and are named after three string instruments; Harp, Cittern, and Lute.
in 2004 three bridges designed by the Spanish architect Santiago Calatrava were opened. The bridges span the main canal of the Haarlemmermeer and are named after three string instruments; Harp, Cittern, and Lute.
The University of Chicago Gerald Ratner Athletic Center, Cesar Pelli, 2002, 160 x 125 ft column free space in the gymnasium, 130 x 200 ft in the auditorium
Melbourne Cricket Ground Southern Stand , Tomkins Shaw & Evans / Daryl Jackson Pty Ltd. Arch, Connell Wagner Struct. Eng, 1992, Jolimont, Victoria
Type Spectator stand form Form - Plan shape Elliptical arc- 324 m x 27 m (main seating deck) - Height to roof base 30.3 m - Basic roof module Top hung cantilever - Number of modules 28 Seating capacity 48,000 Relationship to ground 2 levels below ground, 5 above
Primary Structure
Material Steel Roof structure type - type Cantilevered truss - pattern Supported at 12 m centres around ellipse Support structures Tubular steel frame Footings Mainly reinforced concrete pad footings
Gravitational load systems
Structural subsystem: bowstring trusses, steel roof frame, box beams, concrete frame, steel columns, concrete footings.
Load transfer system: The roof structure comprises triangular section bowstring trusses centrally supported by a steel frame, which transfers loads to the upper deck box beam, which transfers the loads down to the concrete frame. The radial nature of the building necessitates the major loads being concentrated as far forward as possible, where spans between the radiating lines of columns are shortest, while minimizing the number of columns, freeing spectator sight lines. The 11.4m cantilever of the two lower seating decks is carried on the twin bay stabilizing frames and the smaller cantilever of 5.3m to the rear of the upper deck is carried on single columns at greater spacing. The concrete frames transfer the loads to the footings.
Radial lateral load resisting system
Structural subsystem: steel roof bracing and roof frame, main concrete frame, concrete footings.
Load transfer strategy: All radial loads are transferred to the concrete stabilizing frame. The concrete stabilizing frame, consisting of 29 rigid reinforced concrete frames, resists loads through rigid joints connecting to columns at 7 m centres. The columns are linked by concrete floor slabs and two 2m deep post-tensioned back span beams anchoring each steel cantilevered box beam. Circumferential lateral load resisting system
Structural subsystem: steel roof bracing, main concrete frame and concrete footings
Load transfer strategy: The circumferential loads are carried along the plane of the roof through a steel roof brace to its connection, with the cantilevering box beams, then to the concrete stabilizing frame and down to the footings. The concrete stabilizing frame carries the circumferential loads by rigid frame action. These frames are five bays deep, linked with band beams supporting the floor.
Uplift resisting system
Structural subsystem: bowstring trusses, steel roof frame, box beams, concrete frame, steel columns, concrete footings.
Load transfer strategy: As the structure acts as a frame, the uplift load transfer mechanism is essentially the same as for the gravitational load transfer system, except it acts in reverse.
National Athletics Stadium , known as Bruce Stadium , Philip Cox, Taylor and Partners ,1977, Bruce , Australian Capital Territory
The structural system chosen for the roof consists of a steel frame with 100mm concrete slab on permanent metal decking formwork . This is then suspended from 35mm steel cables held up by 5 tapered masts and back stayed with 52mm cables to ground anchors . Each mast is pin jointed to a tapered steel column , allowing for rotation during erection . The seating structure chosen was based on an in-situ concrete frame with precast units spanning between the frames to support the main seating . The framing for the seating provides stability for the whole structure and acts as a portal frame in taking the lateral loads . The main in-situ transverse concrete frames are at approximately 8m centres and support in-situ beam and slab construction found at the lower levels as well as precast seating units at the viewing level .
City of Manchester Stadium, UK, 2003, Arup, 12 support masts, tensile forces are maintained in the cable net under loading conditions
The Munich Airport Business Center, Munich, Germany, 1997, Helmut Jahn Arch.: also is an open public atrium as transition between building blocks or walled boundaries to form a square which is covered by 6 arch-supported membrane leaves. In other words, a transparent roof is carried by spatial triangular column frames. Here a minimum of structure gives a strong identity to space.
The Munich Airport Business Center, Munich, Germany, 1997, Helmut Jahn Arch.: also is an open public atrium as transition between building blocks or walled boundaries to form a square which is covered by 6 arch-supported membrane leaves. In other words, a transparent roof is carried by spatial triangular column frames. Here a minimum of structure gives a strong identity to space.
The Munich Airport Business Center, Munich, Germany, 1997, Helmut Jahn Arch.: also is an open public atrium as transition between building blocks or walled boundaries to form a square which is covered by 6 arch-supported membrane leaves. In other words, a transparent roof is carried by spatial triangular column frames. Here a minimum of structure gives a strong identity to space.
Visual study of floor/ roof structures
Slab analogy and slab support Slab analogy and slab support
Multi-story building in concrete and steel
Hospital, Dachau, Germany
Ramp (STRAP) for parking garage
Glasshouse, 1949, Philip Johnson
New National Gallery, Berlin, 1968, Mies van der Rohe, here a 210-ft (64 m) square, flat, two-way, 6-ft (1.83 m) deep steel girder system that forms a nearly 12-ft (3.66 m) grid is pin-connected to eight flanged cruciform columns on the perimeter.
New National Gallery, Berlin, 1968, Mies van der Rohe, here a 210-ft (64 m) square, flat, two-way, 6-ft (1.83 m) deep steel girder system that forms a nearly 12-ft (3.66 m) grid is pin-connected to eight flanged cruciform columns on the perimeter.
Sichuan University, Chengdu, College for Basic Studies (2002)
Sichuan University, Chengdu, College for Basic Studies, 2002
Paul Löbe and Marie-Elisabeth Lüders House in the German Government Building, Berlin, 2001, Stephan Braunfels,
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
Science and Technology Museum Shanghai, 2002, RTKL/Arup
Science and Technology Museum Shanghai, 2002, RTKL/Arup
Wolf Prix and Helmut Swiczinsky, the Austrian architects who founded Coop Himmelblau in 1968, have waited an unusually long time for a U.S. debut. It finally arrives next week, when the firm's soaring, audaciously sculptural new wing for the Akron Art Museum opens to the public. Made of steel, glass, concrete and aluminum panels, the $35-million building is attached to the museum's existing home, a Renaissance Revival post office built in 1899, like a spaceship hitched to a locomotive. After all, Coop Himmelblau — German for "Blue-sky Collective," a name that suggests the dreamy nature of its work, if little of its toughness — has had a strong presence in Los Angeles for years. Prix taught for a decade at the Southern California Institute of Architecture and still has close ties there and at Pasadena's Art Center College of Design. He has been a friend and mentor to local architects Thom Mayne and Eric Owen Moss. Coop Himmelblau was hired by the Los Angeles Unified School District, with a push and a donation from Eli Broad, to design a performing arts high school on Grand Avenue. But it won't be ready until next year at the earliest.
Akron Art Museum, Akron, 2007, Wolf Prix and Helmut Swiczinsky (Himmelblau). Post architecture critic Philip Kennicott likens the new building to Transformers, the popular line of robot characters. He writes, "With its metal-mesh encased arms, its chrysalis glass core and its long thorax of aluminum-covered gallery space, [the addition] feels biomorphic and mechanical at the same time."
BMW Welt, Munich, 2007, Coop Himmelblau
“Set against a backdrop of hulking factory sheds and 1970s office towers, the BMW Welt, this car company’s fancy new delivery center in Munich, weaves together the detritus of a postwar industrial landscape, imbuing it with a more inclusive spirit,” writes Nicolai Ouroussoff. “Its undulating steel forms, suggesting the magical qualities of liquid mercury, may be the closest yet that architecture has come to alchemy.”
"An hourglass-shaped events hall grounds the building at one end, its torqued glass-and-steel form evoking a tornado drilling into the earth, sucking up energy from the passing cars. From here, the roof unfolds like a gigantic carpet draped over the main hall. Its curvaceous form billows up at some points and then sags at others, echoing the contours of the nearby park. A vertical band of glass cut into the main facade is set on an axis with the corporate tower across the street, locking the composition into its surroundings.”
Phaeno Science Center, 2005, Wolfsburg, Germany, Zaha Hadid
Phaeno Science Center, 2005, Wolfsburg, Germany, Zaha Hadid
Folded plate structures Folded plate structures
Folded plate structure systems
Alte Kurhaus, Aachen, Germany
St. Foillan, Aachen,, Leo Hugot Arch.
Institute for Philosophy, Free University, Berlin, 1980s, Hinrich and Inken Balle. Glass, openness, and light-flooded rooms: the architects Hinrich and Inken Baller created transparency in the 1980s in the design of the new building for the Institute for Philosophy in Habelschwerdter Allee. This building was the first university institute designed in the style of a villa to fit in with the single-family-house character of the district of Dahlem.
Church of the Pilgrimage, Neviges, Germany, Gottfried Boehm, 1963, 1964-68, Velbert, Germany
Air force Academy Chapel, Colorado Springs, 1961, Walter Netsch (SOM); truss, folded surfaces
Center Le Corbusier, Zurich, 1967, Le Corbusier, hipped and inverted hipped roof, each composed of four square steel panels
21_21 Design Sight,Tokyo, 2007, Tadao Ando; the building is a low-rise structure consisting of one ground floor and one underground floor. Most of the volume of the building, which has a unique form featuring a roof made from giant steel plates that slope gently down to the ground, is buried underground. Once inside, the space opens out on a scale unimaginable given the building's unobtrusive exterior. The ground floor houses the entrance and reception area, while the underground floor houses two galleries and a triangular sunken court. A feature of the building is that it is encased in the longest section of double-glazing in Japan.
21_21 Design Sight,Tokyo, 2007, Tadao Ando; the building is a low-rise structure consisting of one ground floor and one underground floor. Most of the volume of the building, which has a unique form featuring a roof made from giant steel plates that slope gently down to the ground, is buried underground. Once inside, the space opens out on a scale unimaginable given the building's unobtrusive exterior. The ground floor houses the entrance and reception area, while the underground floor houses two galleries and a triangular sunken court. A feature of the building is that it is encased in the longest section of double-glazing in Japan.
Salone Agnelli, Turin Exhibition Hall, 1948, Pier Luigi Nervi
Kimmel Center for the Performing Arts, Philadelphia, Rafael Vinoly, 2001, steel-and-glass barrel vault (160 ft high), the roof structure uses the depth of the vaulted section to creat a vierendeel truss that arches across the atrium, the trusses are propped against each adjacent element to provide a folded plate action that resists the longitudinal wind loads
Sydney Olympic Train Station, Homebush, Hassell Pty. Ltd Arch, Tierney & Partners Struct. Eng., 1998, single span vaulted 'leaf' roof truss, repeated folded vault configuration , Plan shape rectangular - 200m x 35m, 18 modules spaced at 12m , 14m long arched entrance canopy, 5.5m wide side awning, support structures columns, buttresses, arched trusses
Combining the use of an arch with that of a truss resulted in two layers. First, the two arches in each truss, which use arch action to span a large distance and provide a column, free space. Secondly, the truss to provide depth (to take bending moments) in the roof plane which is important to resist asymmetric loads under wind pressure in addition to resisting uplift forces. To cater for gravitational and uplift forces, the arched truss is designed to cater for both compression as well as tension.
Arched roof truss members: 355CHS twin arch at the ridge (centre of leaf) and 355CHS inclined arches at the bottom (leaf's border). Each arch is composed of three sections joined together.
Truss web members: 200 x 100 RHS with tubular bracing, link top and bottom arches.
Roof cladding: speed deck 500, zincalume finish ribbed cladding.
Internal roof lining: perforated aluminium sheets.
Under the vertical loads the arched roof truss functions axially as an arch, hence there are two actions in the arches, a horizontal action outwards away from the centre of the arch, and a vertical action downwards.
The cantilevered continuous roof on both the northern and southern ends provides no stability to the main structure, and occurs between the modules of the main arched roof trusses. The 5.5m wide sections are rigidly joined (welded) along one edge (their length) to universal steel beams which are joined to the "double V" pin joints at both ends. Along the other edge, they are tied back to the truss chords with high strength steel bars .The rigid joint between the steel beam and the roof sections resists the downward gravitational force, which is also resisted, by the bars. Under this condition, the supporting steel bars are in tension. In the case of uplift, the rigid joint provides downward reactions, and the high strength steel bar becomes in compression. Both stabilise the cantilevered structure.
The arched truss, also referred to as the vaulted "leaf" roof truss, was used because it allows a clear span of 35m throughout the building between the northern and southern ends. Each arched truss is joined to a mirrored arched truss to produce the "leaf" module which is repeated along the length of the building at 12m spacings thus producing 18 leaves. In between these modules sit the vaulted roofs which are supported by universal beams. The end universal beam for each vaulted roof supports a cantilever side roof, which is also supported by a high strength steel bar attached to the top arch of the arched truss.
The entrance canopy cantilevered off the first bay on the western end is constituted of two additional arched members with connecting web members, which form a truss. These arched members are tied back to the main roof by RHS and fabricated T-sections, which extend from the first truss web.
Under lateral loads in the longitudinal direction the two arches with connecting webs act as a truss which varies in depth across the span, from zero at supports ( double "V" pin joints) where the bending moment is zero to a maximum of 3 meters at the midspan where the bending moment is maximum, and both compression forces (in higher member) and tension forces (in lower member) are highest.
Loads are transferred axially through the arched chords of the truss to the pin joints. These joints transfer the loads down vertically to the foundation.
Maximum shear forces occur at the ends of the truss and reduce down to zero at the centre of the truss. Lateral stability of these trusses is achieved by universal beams horizontally linking bottom arches of adjacent leaves and forming an infill barrel-vaulted roof. Bracing occurs within these trusses to provide lateral stability under lateral loads. These universal beams also transfer loads from the roof sheeting mounted on top of them to the pin joints which inturn transfer them vertically down. Under lateral loads in the transverse direction the two arches with connecting webs act as a truss which varies in depth across the span, from zero at supports where the bending moment is zero to a maximum of 3 meters at the midspan where the bending moment is maximum. Loads are transferred through the truss chords to the pin joints which transfer them to the footings through the columns.
Maximum shear forces occur at the ends of the truss and reduce down to zero at the centre of the truss. Accordingly, lateral stability of these trusses is achieved by universal beams horizontally linking bottom arches of adjacent leaves and forming an infill barrel-vaulted roof. Bracing occurs within these trusses to provide lateral stability under lateral loads.
Addition to Denver Art Museum, 2006, Daniel Libeskind/ Arup Eng.
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
Professor Weaire and his research assistant Dr Phelan at Trinity College, Dublin, that provided us with the answer for the Water Cube. The curious thing about Weaire Phelan foam is that, despite its complete regularity, when viewed at an arbitrary angle it appears to be random and organic. To construct the geometry of the structure of our building, we start with an infinite array of foam (oriented in a particular way) and then carve out a block equal to the size of our building – 177 x 177 x 31 cubic metres. The three major internal volumes are subtracted from this foam block and the result is the geometry of the structure. The structure is then clad with ETFE pillows inside and out to achieve the desired organic look and to work as an efficient insulated greenhouse. So, in searching for the most efficient way of subdividing space, we found a structure based on the geometry of soap bubbles, and clad with plastic pillows that look like bubbles. And inside, all the water of a swimming centre! We were confident that we had a winning scheme; our next challenge was to convey the idea accurately to the judges. We decided to build an accurate physical model of all 22,000 structural elements and 4,000 (different) cladding panels. The only way to do this seemed to be Rapid Prototyping machinery, commonly used in the manufacturing and automobile industries. It took us many weeks to learn enough about the CAD modelling and the data translation required just to make the structural model. With two days left, the structural model was flown from Melbourne to Beijing, where it was joined to a handmade plastic skin (we just couldn’t draw all the different pillow shapes in time), and the model was complete. In July 2003, we were announced as the winners of the competition and
Strurctural behavior of double-layer space frames
Common space frame joints
Case study of flat space frame roofs
Other space frame types
Example Hohensyburg
Spaceframe structure in SAP2000
Robson Square, Vancouver, 1980, Arthur Erickson
Robson Square, Vancouver, 1980, Arthur Erickson
Jacob K. Javits Convention Center, New York, 1986, James Ingo Freed
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.
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.
The Serpentine Gallery Pavilion 2002 appeared to be an extremely complex random pattern that proved, upon careful examination, to derive from an algorithm of a cube that expanded as it rotated. The numerous triangles and trapezoids formed by this system of intersecting lines were clad to be either transparent or translucent giving a sense of infinitely repeated motion.
6
Serpentine Gallery 2002, London, England - Toyo Ito & Associates, Cecil Balmond
Serpentine Gallery summer pavilion, London, Toyo Ito and Cecil Balmond offered a glimpse into a possible architectural future in London's Hyde Park, The Serpentine Gallery Pavilion 2002 appeared to be an extremely complex random pattern that proved, upon careful examination, to derive from an algorithm of a cube that expanded as it rotated.The numerous triangles and trapezoids formed by this system of intersecting lines were clad to be either transparent or translucent, giving a sense of infinitely repeated motion.
Mathematics and design have long been intertwined, dating back to ancient studies of techne and craft. Techne, understood as the creation of art or craft through the implementation of practical knowledge, has clear implications in architecture and engineering. For example, the study of the Golden Section has fascinated designers for ages, harkening back to ancient Greek, Roman, and renaissance architecture. A formula whose calculations provide a seemingly perfect and beautiful proportion, the golden section is one of the earliest examples of mathematics creating art. Over time, other mathematical theories have influenced artistic development including the statistical characteristics of fractals and irregular processes of chaos theory. In particular, fractals have significantly influenced current design rationale. These irregular patterns and structures found in nature and repeated at infinite smaller scales produce irregular shapes and surfaces, which have been impossible to define with classical geometry. Recently, the use of computer modeling has enabled engineers such as Balmond to better understand and use fractals as a design tool.
National Swimming Center, Beijing, Herzog de Meuron; Engineer: Tristram Carfrae of Arup, The Beijing National Swimming Centre, better known as the 'Water Cube', Arup Arch and Eng., will be one of the most dramatic and exciting venues to feature sporting events for the 2008 Olympics.The structure of the Water Cube is based on the most effective sub-division of three-dimensional space - the fundamental arrangement of organic cells and the natural formation of soap bubbles. The random-looking structure is based on the formation of soap bubbles – the most efficient sub-division of three-dimensional space.
Professor Weaire and his research assistant Dr Phelan at Trinity College, Dublin, that provided us with the answer for the Water Cube. The curious thing about Weaire Phelan foam is that, despite its complete regularity, when viewed at an arbitrary angle it appears to be random and organic. To construct the geometry of the structure of our building, we start with an infinite array of foam (oriented in a particular way) and then carve out a block equal to the size of our building – 177 x 177 x 31 cubic metres. The three major internal volumes are subtracted from this foam block and the result is the geometry of the structure. The structure is then clad with ETFE pillows inside and out to achieve the desired organic look and to work as an efficient insulated greenhouse. So, in searching for the most efficient way of subdividing space, we found a structure based on the geometry of soap bubbles, and clad with plastic pillows that look like bubbles. And inside, all the water of a swimming centre! We were confident that we had a winning scheme; our next challenge was to convey the idea accurately to the judges. We decided to build an accurate physical model of all 22,000 structural elements and 4,000 (different) cladding panels. The only way to do this seemed to be Rapid Prototyping machinery, commonly used in the manufacturing and automobile industries. It took us many weeks to learn enough about the CAD modelling and the data translation required just to make the structural model. With two days left, the structural model was flown from Melbourne to Beijing, where it was joined to a handmade plastic skin (we just couldn’t draw all the different pillow shapes in time), and the model was complete. In July 2003, we were announced as the winners of the competition and
Ningbo Air Terminal
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).
Entwicklung der Baum-Geometrie auf Raster 17m / 7 Die zur Verfügung gestellte Geometrie wurde auf ein einheitliches Rastermaß 17m / 7 = 2,43 m angepasst. Dabei wurde eine Aufteilung der Äste jeweils in den Winkelhalbierenden berücksichtigt, so dass eine nahezu nur auf Normalkraft beanspruchte Struktur ermöglicht wird. Die Konstruktion trägt die Lasten vornehmlich über Längskräfte ab. Die gesamte Baumstruktur ist druckbeansprucht, während der Trägerrost in Dachebene Zugkräfte aufnehmen muss.
Momente Die größten Momente treten im Bereich der Auflager und bei der 1. Verästelung auf.
Major skeleton dome systems
Dome structure cases
Pier Luigi Nervi,s famous Little Sports Palace for the 1960 Olympic Games, Rome, Italy, uses a 197-ft-span curved lamella dome consisting of diamond-shaped precast concrete panels of 13 different sizes, which acted as formwork for the cast-in-place concrete topping. The undulating dome edge is not a concrete ring, it only collects the curved lamella ribs and redirect them to the column supports. Thus the dome surface is continuous with 36 inclined forked buttresses with vertical legs. These buttresses are, in turn, carried by a tension ring below ground, which also function as their foundation. ( KM)
Pier Luigi Nervi's famous Little Sports Palace for the 1960 Olympic Games, Rome, Italy, uses a 197-ft-span curved lamella dome consisting of diamond-shaped precast concrete panels of 13 different sizes, which acted as formwork for the cast-in-place concrete topping. The undulating dome edge is not a concrete ring, it only collects the curved lamella ribs and redirect them to the column supports. Thus the dome surface is continuous with 36 inclined forked buttresses with vertical legs. These buttresses are, in turn, carried by a tension ring below ground, which also function as their foundation. ( KM)
Biosphere, Toronto, Expo 67, Buckminster Fuller, 250 ft (76 m) diameter ¾ sphere, double-layer space frame
Jkai Baseball Stadium, Odate, Japan
Exterior View of the Philological Library
The new building, which adopts the form of a brain, has provided a new home for 700,000 books in eleven sublibraries. The governing mayor of Berlin, Klaus Wowereit, and Sir Lord Norman Foster attended the ceremonial opening of the new building, which took place on September 14, 2005. The spectacular new building in its central location among the humanities and social sciences departments has become a Freie Universitaet campus landmark.
Philological Library
Since 2005 Berlin has a new architectural landmark: the Philological Library of Freie Universitaet Berlin, designed by the renowned British architect Lord Norman Foster. The new Philological Library offers scholars and students modern working places: 650 wireless internet-accessible reading places on 5 levels including 100 Internet research terminals and 14 workstations. An innovative environmental concept based on natural ventilation and heat recovery reduces energy use in the new building. The Philological Library is a reference library with mainly open stacks, containing approx. 700,000 books and 800 journal subscriptions. Through its various events and exhibitions, the new library provides a public space for exchange, discussion, and information.
National Grand Theater, Beijing, 2007, Paul Andreu
National Grand Theater, Beijing, 2007, Paul Andreu
One of the most controversial new buildings is the new National Theatre, designed by French architect Paul Andreu and nicknamed the 'Eggshell,' on the west side of the Great Hall of the People at Tian'anmen Square. Paul Andreu's previous works include the Osaka Maritime Museum
Bent surface structures
Grand Louvre, Paris, 1993, I. M. Pei
Grand Louvre, Paris, 1993, I. M. Pei
View of the Grand Duke Jean Museum of Modern Art in Luxembourg, I.M. Pei, If from some angles the museum's exterior itself evokes a fortress, it is one topped by an angular, 100-foot-high glass cupola.
MUDAM, Museum of Modern Art, Luxembourg, I.M. Pei, 2006. The structure is an impressive modern building and is described as the most ambitious architectural project ever undertaken in Luxembourg. The huge glass construction is designed to highlight the modern art pieces housed within it, through its contemporary architecture and stunning appearance. Inside, this glass palace creates a sense of space and openness and the owners have worked hard to fill the building with a selection of art which suitably compliments and accentuates the main features of the museum.
When David Walske, a 50-year-old writer, and his partner, Rick Goldstein, a 51-year-old film editor, built their vacation dome in the mid-1990s on a one-acre lot in the Arizona desert (Sedona), they saw it as a symbol of anarchy, Mr. Walske said, or at the very least, “doing your own thing.”
Ice Stadium, Davos, Switzerland
Reichstag, Berlin, Germany, (1999, Norman Foster Arch. Leonhardt & Andrae Struct. Eng.): The 25-m high steel glass dome, 40 m in diameter, consists of 24 slender ribs made of steel sections and plates to minimize their dimensions as to maximize the effect of transparency. An inverted cone, fully clad with adjustable mirrors, literally throws light into the parliament hall at ground level. Against the the curved glass skin, two ramps above each other wind their way to an outlook platform at the top.
See-thru Parliament
2008 Olympics Beijing, Herzog & De Meuron
The Bird's Nest was designed by the Swiss firm Herzog & De Meuron. This firm's previous projects include the renovation of an old power station on the banks of the Thames in London, which was turned into the Tate Modern Art Museum. Herzog & De Meuron also won last year's Sterling Prize for Architecture for their design of the Laban Dance Centre in a rundown area of London.
2008 Olympics Beijing, Herzog & De Meuron
The Bird's Nest was designed by the Swiss firm Herzog & De Meuron. This firm's previous projects include the renovation of an old power station on the banks of the Thames in London, which was turned into the Tate Modern Art Museum. Herzog & De Meuron also won last year's Sterling Prize for Architecture for their design of the Laban Dance Centre in a rundown area of London.
2008 Olympics Beijing, Herzog & De Meuron
The Bird's Nest was designed by the Swiss firm Herzog & De Meuron. This firm's previous projects include the renovation of an old power station on the banks of the Thames in London, which was turned into the Tate Modern Art Museum. Herzog & De Meuron also won last year's Sterling Prize for Architecture for their design of the Laban Dance Centre in a rundown area of London.
2008 Olympics Beijing, Herzog & De Meuron
The Bird's Nest was designed by the Swiss firm Herzog & De Meuron. This firm's previous projects include the renovation of an old power station on the banks of the Thames in London, which was turned into the Tate Modern Art Museum. Herzog & De Meuron also won last year's Sterling Prize for Architecture for their design of the Laban Dance Centre in a rundown area of London.
Beijing National Stadium, Herzog and De Meuron Arch, Arup Eng., The structural form of the roof is described as a ''nest''. The interwoven structural elements of the facade produce a single surface, upon which further elements are arranged in a chaotic manner to blur the distinction between the primary structure and the secondary structure.The roof is saddle-shaped, and the geometry is developed from a base ellipse of which the major and minor axes are 313 metres and 266 metres respectively. The outer surface of the facade is inclined at approximately 13° to the vertical.
Structural Modelling: the building’s distinctive façade was conceived in order to disguise the large parallel steel, girders required to support the retractable roof that was specified in the original design, program. (Lubow, 2006) The geometry of the seemingly random elements was defined using the geometrical constraints dictated by the usage and capacity of the structure (as outlined in section 2.0) and formalized using modeling software designed by Arupsport. (“Beijing,” 2006)
In defining the geometry of the structure, lines representing members were extended outward from the projected plan of the athletic field, along the roof and wall surfaces to the ground in one continuous gesture (Figure 3, blue lines). The angles of these lines were planned so that they intersect at ground level in 24 points spaced at regular intervals around the elliptical building footprint. This allows the vertical components of the structural members to be prefabricated in truss-columns of a roughly pyramidal shape (Figures 4 and
5). Conversely, the diagonal lines created by the staircases placed around the perimeter are traced continuously from the ground, along the roof, and down the other side (Figure 3, yellow lines). The remaining infill members balance the aesthetic of the façade (Figure 3, red
lines). (Stacey, 2004)
SAP2000 structural models
Surface structures in nature
Surface classification 1
Surface classification 2
Examples of shell form development through experimentation
Basic concepts related to barrel shells
Slab action vs. beam action Slab action vs. beam action
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
As for section E, while the public area is identical to the one of section F, the boarding
area consists in a long hall-way, with an elliptical vault made out of concrete.
Passengers are more likely to encounter longer walking distances in this case, than in
Terminal 2F. I should underscore the fact that these two designs recall the ones of the
two terminals at Orly airport.
The long, tubular structure was designed by Paul Andreu, who was at the time Director of Architecture for the Aéroports de Paris, or ADP. Before the collapse, a crack appeared in the departure lounge roof at the point where an intermediate steel section meant to connect the exterior glass shell to the inner concrete shell transpierced the concrete. Concrete began to fall and the southern lateral supporting beam ruptured. The folding of the shell brought the entire arched-section down. One reason was that the steel sections were embedded too deeply into the concrete. The report also cited inadequate or badly positioned reinforcing within the concrete. A lack of redundancy meant that stress was carried to the weakest points of the structure. The horizontal concrete beams on which the shell rested were weakened by the passage of ventilation ducts. Finally, the exterior metal structure was not sufficiently resistant to temperature changes. On the morning of the collapse the temperature dropped sharply to 4.1° C, from 25° C during the week.
Wood and steel diagrid shell-lattice supports the Alnwick Gardens Visitor Center roof, a translucent skin of ETFE pillows, 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,This grid shell over a L-shaped courtyard has two barrel-vaulted sections with a smooth transition between them. The structure consists of a quadrangular grid 1,2 x 1,2m braced by prestressed diagonal cables and of directly glazed flat bars 60 x 40cm. The somewhat softer areas of the barrel vault are stiffened with "spoked wheels" constisting of cables radiating from a "hub". Spans 14 to 17 m, single glazing Completed 1989
Dz Bank, glass roof, Berlin, Gehry + Schlaich
Exhibition hall • Leipzig, Germany, 1996, von Gerkan, GMP, in cooperation with Ian Ritchie
P&C Luebeck, Luebeck, 2005, Ingenhoven und Partner, Werner Sobek, At the very heart of Lübeck's historical centre a new commercial building was constructed. The building had to be inserted very carefully into the UNESCO-listed Old Town. For this reason the roof played a major role in the design concept. The roof consists of 16 shells in reinforced concrete that have a thickness of 14 cm each. In plan view the shells are trapezoids that are arranged in alternating alignments. The shells span 8.75 m in cross direction and up to 28 m in machine direction.
P&C Luebeck, Luebeck, 2005, Ingenhoven und Partner, Werner Sobek
Central Railway Station Cologne, Germany
Thin-concrete shells, form-passive membranes in compression, tension and shear: 720-ft (219 m) span, CNIT Exhibition Hall Paris, 1958, Bernard Zehrfuss Arch, Nicolas Esquillon Eng
Dome shells on polygonal base
Keramion Ceramics Museum, Frechen, 1971, Peter Neufert Arch., the building reflects the nature of ceramics
Kresge Auditorium, MIT, Eero Saarinen/Amman Whitney, 1955, on three supports
Ecological Center, St. Austell, Cornwall, England,1996, Nicholas Grimshaw, Anthony Hunt; the biomes are constructed from a tubular steel frame with mostly hexagonal transparent panels (there are a few pentagonal ones) made from a complex plastic known as ETFE (it was decided very early on that glass was out of the question, being too heavy and potentially dangerous). The "panes" of the biome are created from a triple layer of thin UV -transparent ETFE film , inflated to create a large space between the two sides and trapping heat like double-glazed windows. The plastic is resistant to most stains, which simply wipe off in the rain, although if required, cleaning is performed by abseilers . Although the plastic is prone to punctures, these can be fixed with ETFE tape. The structure is completely self-supporting, with no internal supports, and takes the form of a geodesic structure. The panels vary in size up to 9 m across, with the largest at the top of the structure.
Eden Project in Cornwall/England Humid Tropics Biome, The original vision of the project came from the anthropologist and archeologist Tim Smit. The architectural design was done by Nicholas Grimshaw and Partners (London) after a statical pre-design by MERO. more about Eden Project... Dlubal software
Delft University of Technology Aula Congress Centre, 1966, Bakema
Social Center of the Federal Mail, Stuttgart, concrete structure with prestressed floor slabs, central concrete shell, 1989, Architect Ostertag und Partner, Stuttgart/Isernhagen
Garden Exhibition Shell Roof, Stuttgart, eight prefabricated joint glass-fibre cement hypar shell, 1977, Jörg Schlaich at University of Stuttgart Architect Hans Luz und Partner. Shells have a curved surface and gain their unusual strength from their shape. Thus they can be very thin, much less than reinforced concrete permits, which needs to be at least 6 to 8 cm thick. The new material Glass Fibre Reinforced Concrete (GRC) appears to be ideal for shells. Alcali-resistant glass fibres are sprayed (gunnited) or mixed with the mortar, resulting in a concrete which, in addition to its compressive strength, has a permanent tensile strength. The thickness of the shell thus may follow its forces. The Stuttgart shell is composed out of 8 hypar-units with an average thickness of 15 mm. They were subsequently gunnited against one formwork. Since the weight of one unit was 2500 kg only, a standard crane was sufficient to lift and place it. After placing the units into their final position, their joints were cast using GRC-Mix. Supports Stainless steel balls on reinforced concrete abutments
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
Sydney Opera House Building Information Model from 2007 of the Sydney Opera House (1957–73), Jorn Utzon, with Ove Arup.
IL 13 Multihalle Mannheim - Multi Hall Mannheim, Mitteilungen des Instituts ... 1975, Timber Lattice Roof for the Mannheim Bundesgartenschau, Shells constructed by lifting a flat square lattice into a doubly curved shape are a recent form of construction. Such a shell of four times greater span than any previous examples had to be completed in 18 months for an exhibition.
The 5-story DG Bank, Berlin, Germany (2001, Frank Gehry; Schlaich, Bergemann und Partners, structural engineers for skylights and interior glass system): In an effort to respect the surrounding architecture on Pariser Platz, which is dominated by the Brandenburg Gate, the building meets the surrounding traditional architecture, but the sculptural drama typical of Gehry's happens intside. Here, Gehry has stuffed the building with an amoeba-like auditorium, that is vaguely like a fish, covered with steel and glass. It is a definitively weird structure. It's as if a glass and chrome tumor erupted in the middle of a bank's grand lobby.
Phaeno Science Centre • Wolfsburg, Germany, 2005 Zaha Hadid Architects The Phaeno Science Centre, looking like a huge futuristic concrete-shelled beast escaped from a scene in Star Wars, is situated on a large landscaped square to immediately arouse the curiosity of visitors with its original shapes. On the south façade, 39 prefabricated concrete panels are set over a steel framework.
Metal structure, supported by concrete pillars, forms a geometry that is orthogonal or trapezoidal. The Vierendeel girders covers large spaces without an intermediate column and enables the passage of fluids.
"An hourglass-shaped events hall grounds the building at one end, its torqued glass-and-steel form evoking a tornado drilling into the earth, sucking up energy from the passing cars. From here, the roof unfolds like a gigantic carpet draped over the main hall. Its curvaceous form billows up at some points and then sags at others, echoing the contours of the nearby park. A vertical band of glass cut into the main facade is set on an axis with the corporate tower across the street, locking the composition into its surroundings.”
Centre Pompidou-Metz, 2008, architects Shigeru Ban and Jean de Gastines,
Fisher Center, Bard College, NY, Frank Gehry, DeSimone, 2004
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. The building is basically large, 30 meters high, translucent container that extends lengthways. On each side a square opens on to the immediate area and the city. The first converses directly continuously with the local area and can be crossed from viale Europa to viale Shakespeare.The second, a space that can be composed freely using moveable structures, is for welcoming conference participants and accompanying them to the various rooms in the center. Inside this shell, a 3,500 square meter steel and teflon cloud, suspended above a surface area of 10.000 square meter, is designed to hold a 2.000 square meter auditorium and various meeting rooms. When the cloud, supported by a thick network of steel cables and suspended between the floor and the ceiling of the main conference hall, is lit up, the building seems to vibrate. The construction also changes completely depending on the viewpoint of the observer.
Metropol Parasol", Jürgen Mayer Arch, a redevelopment project by J. Mayer H. for Plaza de la Encarnacion in Seville, Spain is one of the most striking projects I've seen in ages. Amazingly, it's under construction and is expected to be complete this year.
Trade Fair Hall 26, Hanover, suspension roof structure, timber panels on steel tie members, 1996, Architect Herzog + Partner, München; Schlaich Bergermann. Covering a total area of 22000 m², arranged in three equal sections, the elegant suspension roof of the exhibition hall 26 combines climatic ideas like natural ventilation with the minimized structural approach of handling large spans by hanging elements. Wooden sandwich panels are fixed on flexible flat sections 300x40mm that are spanning 60m between inclined truss girders. These girders are fixed with hinges a A-shaped strut and tie supports at different heights (14 and 26.5m) shaping the natural hanging curve of the roof under dead weight. The building gets its light appearance also by large glass facade areas. All services are organized in 6 separate concrete containers cladded with wood on the outside.
National Indoor Sports and Training Centre , Philip Cox and Partners Pty Ltd. , 1981
The roof area which is totally covered by the concrete panels is a total of 6400 square metres. Consisting of 276 panels, the joints between these panels and therefore the role they play in the distribution of load and behaviour to uplift loads is important. Due to the grid already set up by the cable and mast system the panels were of a fixed dimension so to speak, of 3.75m by 6.2m by50 mm thick. Because the weight of the panels had to exceed a certain wind load uplift,the target weight of the units was finally established at 2kPa. That is a total of 1200 tonnes of concrete. An average thickness of 75mm of concrete over the whole roof areas was required to provide the necessary weight to overcome any uplift instability. Too much weight would have caused unnecessary sag and overload of the cables.
The concrete used in these panels were lightweight concrete, batched using expanded shale and normal sand for aggregate achieved 20Mpa with a density of 1800kg/cubic metre. In addition to the concrete panels, 300mm deep pre-stressed ribs prestressed with 9.5mm strands were used to maintain stiffness.
The cast in situ joints between the pre-cast panels are designed to provide for the articulation necessary to accommodate small changes in the roof profile from wind forces, temperature variations and live load. There is about 65 cubic metres of concrete in the 3km of joints. So as to compensate for the possible 4% overweight in the panels,the lightweight concrete was used in conjunction with a 75mm diameter void former in the joints.
The 150mm by 150mm joint was formed with an asbestos cement sheet soffit and poured with wheel barrows and a purpose made rickshaw with a bottom dump to place the concrete in the joints.
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.
Olympic Arena, Tokyo, 1964, Kenzo Tange, swooping roof suspended on two 13" steel cables
Yoyogi National Stadium, Gymnasium, Tange
Olympic Stadium for 1964 Olympics, Tokyo, Kenzo Tange/Y. Tsuboi
Olympic Stadium for 1964 Olympics, Tokyo, Kenzo Tange/Y. Tsuboi
Constructed for the 1964 Tokyo Olympics, Kenzo Tange’s Yoyogi National Stadium is a true masterwork. Its image is iconic and its scale and engineering are epic – especially considering it was built before the age of computers.
Dorton (Raleigh) Arena (1952), North Carolina, Matthew Nowicki, with Frederick Severud
Tent architecture
Subway Station to Allianz Arena, Stadium Railway Station Froettmanning, Munich, 2005, Bohn Architect, PTFE-Glass roof
For the IAA 95 motor show in Frankfurt BMW abandoned the idea of a conventional exhibition stand placed within the exhibition halls in favour of a free--standing pavilion erected on a central square between the Frankfurt exhibition buildings. On a surface of 100 x 50 m this pavilion was to provide large--scale, technically perfect and bright accommodation for the vehicles on show, especially the new 5-series.The pavilion consisted of a prestressed roof membrane supported by five centrally located masts and anchored along the edge by a number of guy cables. 1/4
New roof for the Olympic Stadium Montrea, 1975, Roger Taillibert
Grand Arch de la Defense, Paris, 1989, Paul Andreu, Peter Rice
Structural study model for the Munich Olympic Stadium (1972), Behnisch Architekten, with Frei Otto
Stadium Roof, Riyadh, Saudi Arabia, membrane roof of PTFE-glass fiber, suspended by cables and steel pylons, 1984, Architect Fraser Roberts + Partner, London; Geiger, Berger, New York, Cooperation Geiger + Berger, New York, Schlaich Bergermann
San Diego Convention Center, 1989, Arthur Erickson/ Horst Berger
Schlumberger Research Center, Cambridge, UK (1985, Hopkins/Hunt); The ship like masts and rigging support the spatial domelike undulating tensile fabric membrane. The high level technology and detailing reminds one of Roger's earlier work. The central portion of the building is subdivided by four parallel exposed portal steel frames into three bays, each 24 x 18 m (79 x 59 ft) in size. It consists of horizontal 24-m (79-ft) open triangulated truss girders and nearly 8-ft (c.2.5 m) wide vertical trusses which support two pairs of upper and lower booms. The two inclined upper tubular masts are supported by tie rods which are braced by lower masts (struts). Cables are suspended from the masts to give support to two parallel ridge cables at certain pick-up points. The translucent Teflon coated fiberglass membrane is clamped and stretched between ridge cables and steel work.
Denver International Airport Terminal (1994), Denver, Horst Berger/Severud,the folded Teflon-coated fiberglass membrane spans about 220 ft (67 m), the roof weighs less than 2 psf (96 Pa)
Hybrid tensile surface structures
Classification of pneumatic structures
Pneumatic structures
Low-profile, long-span roof structures
Soap bubbles Soap bubbles
To house a touring exhibition
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
Expo’02 Neuchatel, 2002, 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
Festo A.G. Stuttgart
Tensegrity sculptures by Kenneth Snelson
Tensegrity by Karl Ioganson, 1920, Russian artist
TENSEGRITY TRIPOD
Olympic Fencing and Gymnastics Arenas, Seoul, 1989, Geiger
Georgia Dome, Atlanta, Weidlinger, Structures such as the Hypar-Tensegrity Dome require special analysis and could not have been realized without the availability of computers and nonlinear programs. The world's largest cable dome, was completed for the 1992 football season in Atlanta, was the centerpiece of the 1996 Olympic Games. Spanning 766 ft x 610 ft (233.5 m x 186 m), it will be the first Hypar-Tensegrity Dome. This new cable supported teflon-coated fabric roof is based on the tensegrity principles first enunciated by Buckminster Fuller and Kenneth Snelson. Because of the large deformation characteristics of this type of structures, special geometric nonlinear analysis is required.