Space Grid Structures
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Space Grid Structures
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SPACE GRID STRUCTURES
OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI
Architectural PressAn imprint of Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP225 Wildwood Avenue, Woburn, MA 01801-2041A division of Reed Educational and Professional Publishing Ltd
A member of the Reed Elsevier plc group
First published 2000
© John Chilton 2000
All rights reserved. No part of this publication may be reproduced inany material form (including photocopying or storing in any medium byelectronic means and whether or not transiently or incidentally to someother use of this publication) without the written permission of thecopyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 9HE. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publishers
British Library Cataloguing in Publication DataChilton, John
Space Grid Structures1. Space frame structures – Design and constructionI. Title624.1'773
Library of Congress Cataloguing in Publication DataA catalogue record for this book is available from the Library of Congress
ISBN 0 7506 3275 5
Composition by Scribe Design, Gillingham, KentPrinted and bound in Great Britain
1 Early development of space grids 1
2 Space grid geometry – thinking in threedimensions 12
Why two-way spanning structures? 12Aspect ratio 14Space truss stability 15Stable polyhedral forms 16Advantages of using space grids 17Disadvantages 20Grid configurations 21Defining the grid 24Complex geometries 25Support locations 26‘Tree’ supports 27Edge profiles 28Multi-layer space grids 28
3 Materials and systems 30
Materials for space grids 30Space grid systems 30‘Piece-small’ systems 31Continuous chord systems 41Modules 43
4 Design and construction 52
Element structural behaviour 52Span/depth ratios for various support conditions 53Support details and thermal movement 53Dimensional accuracy 54Pre-camber 55Cladding and glazing 56Methods of erection 56Fire resistance of space grids 58Space grids in seismic zones 59
5 Case studies 61
Space frame for the ‘Symbol Zone’, Expo ’70, Osaka,Japan 61Nusatsum House, Bella Coola Valley, BritishColumbia, Canada 64The Crystal Cathedral, Garden Grove CommunityChurch, California, USA 67The National Exhibition Centre and BirminghamInternational Arena, Birmingham, UK 69
Meishusama Hall, Shiga Sacred Garden, Shigaraki,Shiga, Japan 71Jacob K. Javits Center, New York, USA 72Oguni Dome, Oguni-machi, Kumamoto Prefecture,Japan 75FFV Aerotech Hangar, Stansted Airport, UK 78Sant Jordi Sports Palace, Barcelona, Spain 81Biosphere 2, Sonoran Desert, Arizona, USA 88National Indoor Arena for Sport, Birmingham, UK 89Lan Chile, Maintenance Hangar, Aeropuerto ComodoroArturo Merino Benítez, Santiago, Chile 93Palafolls Sports Hall, Spain 94Space grids at Expo ’92, Seville, Spain 99Markethall, Eagle Centre, Derby, UK 104Barrel Vault Atrium, The Bentall Centre, Kingston uponThames, UK 106Terminal 2, Manchester Airport, UK 110Fantasy Island, Pyramid, Skegness, UK 112Roundwood timber space trusses 114Atlanta Pavilion (unbuilt project) 118Milan Fair, New Exhibition Facilities, Milan, Italy 118Stadium Australia, Sydney, Australia 126
6 Deployable, foldable and retractable space grids 131
Deployable and foldable space grids 131Emilio Pérez Piñero 131Venezuela Pavilion Expo ’92, Seville, Spain 135The ‘Pantadome’ erection system 139Folding roof for swimming pool, San Pablo, Seville,Spain 151Retractable roof structures 151
7 Future developments 156
Polyhedral space grid buildings 156High-rise and megastructures 156TRY 2004 160Composite floors 163Tensegrity and space grids 164Quasicrystal geometry: combining rods and plates 164What does the future hold? 166
Appendix 1: two-way spanning structures 169Appendix 2: list of manufacturers 169Further reading 171Index 173
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This book has been long in gestation. The original stim-ulus for it came about seven years ago out of my teach-ing about space structures to student architects, rein-forced by my earlier doctoral research into space gridstructures. When asked by students to suggest an appro-priate text where they might encounter information aboutthe geometry, design parameters, detailing and con-struction of space grids, I found the choice was ratherlimited (although there seemed to be many more booksdescribing the structural behaviour and analysis of suchstructures). At that time a book that I consistently rec-ommended was Space Grid Structures by John Borrego,which was published in 1968 by MIT Press (and, coin-cidentally, has the same title as this present volume).However, thirty years have passed since its publicationand the technology of space grids has developed con-siderably over this period. Therefore, from the outset myintention has been to create a text of similar utility forarchitects, engineers and builders who wish to under-stand the basics of space grid design and constructionin the late 1990s.
Encouragement to pursue this idea came in 1993, whenI attended the 4th Space Structures Conference at theUniversity of Surrey, where I tried to strike up a conver-sation with Stéphane du Château, one of the pioneers ofspace grid structures who sadly died this year, aged 92.He immediately asked if I was an engineer or an archi-tect and when I responded ‘engineer’, he at first was nottoo keen to talk to me but when I added that I taught ina School of Architecture he became very communicativeand eventually presented me with a signed copy of hisown book on structural morphology in which he wrote:
‘a Jean – John Chilton – pour l’inspirer des idéespas comme les autres – avec toute ma sympathie’
It was after much consideration that the title ‘Space
Grid Structures’ was chosen for this volume. Amongarchitects, engineers and others in the building and con-struction industry the generic term ‘space frame’ is com-monly used to describe three-dimensional structures thatmay be either frames or trusses in the engineering def-inition of the terms. In fact, practically all ‘space frames’are space trusses in the engineering sense. However,space grid is a widely accepted alternative name thatencompasses both structural systems and can be usedwhen describing features common to both. The morecorrect terms, space frame and space truss, may thenbe used where it is important to distinguish the differ-ences in their structural action.
Chapters 1 to 4 describe the history, geometry, designand construction of space grids. A selection of spacegrid structures of varying sizes, made from differentmaterials, using different systems and constructed overthe last thirty years are included in Chapter 5, in orderto show the wide potential for the use of this structuralform. Chapter 6 investigates the use of retractable,deployable and foldable space grids that, although hav-ing been developed early in the 1960s, have only recent-ly been exploited to any great extent in architectural appli-cations. Finally, in Chapter 7, some space grid conceptsthat have not yet been fully utilized are outlined togeth-er with some interesting developments that might beimplemented in the near future.
Some people who consider that the use of space gridsreached its zenith in the 1970s have commented thatthis might be a book of only historical interest. However,as the case studies in Chapter 5 demonstrate, spacegrids are still being used widely for medium and long-span structures of innovative form. Although their usemay diminish in the more developed countries of theworld, there is still a huge potential for their widespreaduse in developing countries where materials are expen-sive, labour is cheap and simple efficient structures arein demand.
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First and most importantly I must give my heartfelt thanksto my wife Gloria Llanos for her unfailing support andencouragement without which I doubt whether I wouldhave ever completed the task of writing this book. Notonly has she endured many lonely evenings and week-ends as I have laboured incarcerated in my study, butshe has also carried out many corrections and revisionsof the word-processed text.
Although I have ended this journey alone it did notstart thus. Therefore, I also give my sincere thanks toDr Richard McConnel, of Cambridge UniversityEngineering Department, who was initially my co-author,for his assistance in acquiring some of the informationincluded in the book and for the time that he spent read-ing and making very constructive comments on an earlydraft of the manuscript.
It would be difficult to produce a book of this charac-ter without the help and generosity of many people. Ofthose who have contributed I am particularly indebted toGraeme Barker for his excellent three-dimensional, com-puter-generated representations of space grid geometryused in Chapter 2 and to Glyn Halls, photographer inthe School of the Built Environment at the University ofNottingham for his assistance in the production of manyof the photographs. I am also extremely grateful to thefollowing who have given their permission for drawingsand/or photographs to be reproduced: ABBA SpaceStructures, Architectural Association Photo Library,British Steel Tubes Division, De Bondt, A. El-Sheikh,Félix Escrig, J. François Gabriel, Alastair Gardner, G. C.Giuliani/Redesco srl., Glyn Halls, H. Hendriks, Pieter
Huybers, N. M. T. Jackson, Mamoru Kawaguchi, L. A.Kubik, Matthys Levy, Mai Sky System Inc., CarlosMárquez, J. Martinez-Calzón, R. E. McConnel, Mero(UK), Orona S. Coop. Ltda., Fundación Piñero, TonyRobbin, Scogin Elam and Bray, Shimizu Corporation, R.G. Satterwhite, Space Decks Ltd, Kyo Takenouchi, R.Taylor, Peter Trebilcock, Ture Wester and YohArchitects.
Of those who have provided illustrations, listed above,a special mention must be made of Mamoru Kawaguchiwho very generously provided copious amounts of infor-mation, diagrams and photographs of the projects withwhich he has been associated, in particular those con-structed using the Pantadome system. In addition, I amvery grateful to Roland Howarth and Richard Porada –Space Decks Ltd; Ane Yarza – Orona S. Coop. Ltda.;Eddie Hole – British Steel Tubes Division; Jane Wernick– Ove Arup; K. Sugizaki – Shimizu Corporation; andStephen Morley – MODUS Consulting, all of whom haveassisted me in the acquisition of drawings, photographsand information. If I have omitted anyone, I apologize.
Finally, I wish to thank my father who, although nei-ther architect nor engineer, read and commented on thealmost completed manuscript (without the benefit of thefigures to aid his understanding) and my mother for herpatience in listening as he read her sections of the text.I owe them the most, for without their nurture, supportand encouragement I should never have embarked onmy career as an engineer and would not have had theopportunity to write this book. It is dedicated to themboth.
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Architects and engineers are always seeking new waysof solving the problem of space enclosure. With theindustrialization and development of the modern worldthere is a demand for efficient and adaptable long-spanstructures. Space grid structures are a valuable tool forthe architect or engineer in the search for new forms,owing to their wide diversity and flexibility. Before enter-ing into a discussion of the design and use of spacegrids in the late twentieth century, it is useful to lookback at the early use of three-dimensional structures.
Until the middle of the eighteenth century the mainconstruction materials available to architects and engi-neers were stone, wood and brick. Metals, being in rel-atively short supply, were used mainly for jointing of theother materials. Of the widely available materials, stoneand brick are strong in compression but weak in tension.Thus they are suitable for three-dimensional structuralforms such as domes and vaults. Impressive feats ofvaulting were achieved by medieval masons but thelargest span masonry domes, St Peter’s Basilica in Rome(1588–93) and Santa Maria del Fiore in Florence(1420–34) are both approximately 42 m diameter at thebase.1 Good quality timber has strength in tension andcompression but is naturally available only in limitedlengths and with limited cross-section. For large-scalethree-dimensional structures jointing of timber becomesa major problem. Nevertheless, the Todai-ji temple atNara in Japan, the largest historic timber building in theworld, is 57 m by 50 m and 47 m high. The present build-ing dates from 1708 and replaces the original, even larg-er, structure which was destroyed by fire. Although thesematerials were used to produce impressive large-scalestructures, the spans were limited and the constructionheavy. However, with the Industrial Revolution came thewider production of iron and then steel, high-strengthmaterials that permitted the construction of more deli-cate structures of longer span or greater height. Atapproximately the same time, mathematical techniqueswere being developed to describe and predict structur-al behaviour and understanding of the strength of mate-rials was advancing rapidly. Equally, with the advent ofthe Railway Age and the industrialization of commodityproduction came an increasing demand for longer spanstructures for bridges, stations, storage buildings and fac-tories. With the wider availability of iron and steel andthe demand for larger spans, there came a period ofdevelopment of new structural forms, initially a multiplicity
of different truss configurations and eventually three-dimensional space grids.
Many structural forms including most space gridassemblies are modular. The concept and efficiency ofmodular building construction was dramatically illustrat-ed, almost 150 years ago, by the design, fabrication andassembly of the metal framework of the Crystal Palacein Hyde Park, London, for the Great Exhibition of 1851.The whole process, from the submission of the tenderby Fox Henderson & Co. and Joseph Paxton to the pos-session of the completed building, was accomplished inapproximately six months – a feat that would probablytax the abilities of today’s construction industry.
Landmark structures such as the Eiffel Tower in Parisconstructed from wrought iron between 1897 and 1899,bear witness to the stability and durability of modular three-dimensional metal construction. The tower, built as a sym-bol for the centenary celebration of the French Revolution,and conceived as a temporary structure, has already sur-vived over 100 years. Sadly, the magnificent 114 m spanGalerie des Machines by Contamin and Dutert, built atthe same time adjacent to the tower, has not. Such struc-tures demonstrated the possibilities for the use of iron andsteel in high-rise and long-span buildings and challengedthe ingenuity of architects and engineers to discover newand more efficient ways for their construction.
Probably the earliest examples of what we now com-monly call space frames or space grids (light, strong,three-dimensional, mass-produced, modular structures)were developed by the inventor of the telephone,Alexander Graham Bell (1847–1922). In the first decadeof the twentieth century he experimented with spacetrusses composed of octahedral and tetrahedral units(Figure 1.1). In his article on kite construction in theNational Geographic Magazine,2 in 1903, Bell com-mented:
Of course, the use of a tetrahedral cell is not limitedto the construction of a framework for kites and fly-ing-machines. It is applicable to any kind of struc-ture whatever in which it is desirable to combine thequalities of strength and lightness. Just as we canbuild houses of all kinds out of bricks, so we canbuild structures of all sorts out of tetrahedral framesand the structures can be so formed as to possessthe same qualities of strength and lightness whichare characteristic of the individual cells.
1 Early development of space grids
As can be seen from this quotation, Bell appreciated thedual properties of high strength and light weight exhib-ited by the rigid three-dimensional tetrahedral forms andincorporated them into many of his projects. One of thefirst steel space grid structures, using cast nodes andtubular members, the observation tower at BeinnBhreagh, USA, was constructed by Bell in 1907.
Despite Bell’s development of lightweight three-dimen-sional space trusses early in the century, they were notused in architecture until the introduction of the MEROsystem, in 1943. This was the first space grid systemwidely available commercially and was developed inGermany by Dr Ing. Max Mengeringhausen (1903–88).Using what is still probably the most common method ofspace truss construction, the system consists of individ-ual tubular members connected at ‘ball’-shaped nodejoints. The aesthetic appeal and popularity of this sys-tem has endured to the present day, as confirmed bythe many alternative tube and ball systems now avail-able.
An alternative popular method of constructing double-layer grids uses prefabricated modules. In the UK, dur-ing the 1950s, Denings of Chard developed the SpaceDeck system, based on bolting together prefabricatedsteel pyramidal modules (1.22 m � 1.22 m in plan and1.05 m or 0.61 m deep respectively). With only slightmodifications to module dimensions and materials,Space Deck has been widely and successfully used forroof and floor structures ever since. The system isdescribed in detail in Chapter 3. A similar module, withthe same plan dimensions but overall depth of 600 mm,was adopted for roof and floor construction in the Nenkmodular building system.3 The Nenk system was devel-oped by the former Ministry of Public Building and Worksin the UK in collaboration with Denings and was usedin the construction of army barrack blocks in the early1960s. It could span 12.2 m (40 feet) with normal floorloads and 26.8 m (88 feet) with normal roof load. Spacegrids were used to allow freedom of column location andspace planning on the floor below. Precast concrete floor
2 Space Grid Structures
1.1Early experimentalspace grid structuredeveloped byAlexander GrahamBell in the firstdecade of thiscentury
1.2Close-packing of spheres as studied by R. Buckminster Fuller. (Drawing: John Chilton)
slabs, set on preformed strips of polystyrene orpolyurethane, were used within the square upper grid ofthe modules to form the floor plates.
During the 1950s and 1960s, space grid systems wereproliferating all over the world as architects explored therelatively new aesthetic of the modular grid and engi-neers experimented with alternative jointing systems,materials and configurations. In the USA, RichardBuckminster Fuller (1895–1981), following his study ofthe closest packing of spheres, developed the OctetTruss system.4,5,6 The name Octet Truss derives fromthe octahedron-tetrahedron geometry formed by the lineslinking the centres of spheres packed together in a con-tinuum so that each sphere is surrounded by twelve morein close contact (see Figure 1.2). Members of the spacegrid then follow these lines. The Ford Rotunda Building,Ford River Rouge Plant, Dearborn, Michigan, construct-ed in 1953, used aluminium Octet Truss grids to formthe faces of a 28.4 m diameter geodesic dome weigh-ing only 8.5 tonnes (Figure 1.3). This space grid is of‘nodeless’ construction as the X-shaped ends of themembers allow them to be bolted directly to each otherat the intersections without the use of a separate nodecomponent. An exhibition of Buckminster Fuller’s workat the Museum of Modern Art, New York, in 1959, fea-tured a 1.22 m deep Octet Truss structure 10.7 m wideand 30.5 m long (consisting of two cantilevers of 18.3 mand 12.2 m) made from 51 mm diameter aluminiumtubes.
Konrad Wachsmann (1901–80) was appointed in 1959to develop a space grid system for large span aircrafthangars, for the United States Air Force. The briefdemanded great flexibility in construction, geometry andbuilding type, whilst also asking that the components
Early development of space grids 3
1.3Dome of the FordRotunda Building,Dearborn, Michigan,USA constructedusing 20 960members assembledinto Octet trusses asdeveloped by R.Buckminster Fuller
1.4Konrad Wachsmann’s universal connector made from acombination of four standard die forged elements which allowed upto twenty tubular members to be connected at each joint
should be demountable and reusable in the same orother configurations. Wachsmann’s system7 incorporat-ed a relatively complicated universal connector madefrom a combination of four standard die forged elementswhich allowed up to twenty tubular members to be con-nected at each joint, (Figure 1.4). Two diameters of tubewere employed, one for the continuous top and bottomchords of the grid made from 9.1 m lengths joined usinga flush connector and smaller diameter tubes for thediagonals. The joints between chords and diagonals weredesigned in such a way that on site, only a hammer wasrequired for assembly. This was necessary to drive threesoft steel wedges through notches to lock the connec-tors into position on the main chord members.
In France, Stéphane du Château (1967–1999) devel-oped Tridirectionelle S.D.C. (1957) which required work-shop or site welding of tubular members to the connec-tors, (Figure 1.5(a)). Subsequently, du Château alsodeveloped a system using triangular, square or hexag-onal based pyramidal modules, Pyramitec (1960),(Figure 1.5(b)). This was the forerunner of the Unibatsystem (1962; see Figure 1.6) which used similar mod-ules, but in this case was bolted together only at the cor-ners.8,9 Du Château also developed Tridimatic (1965), asystem of interconnected prefabricated plane trusses andSpherobat (1984), which uses two-part hollow sphericalnodes through which bolts connect to the end of tubu-lar members.
In Canada, the Triodetic system, predominantly usingaluminium as the material for the bars and joints, wasintroduced on a commercial basis in 1960, by FentimanBros. of Ottawa, Ontario, Canada.10 The system, wasinnovative in its use of extruded tubular members, flat-tened or coined at their ends and a solid extruded alu-minium hub with slots that matched the coining of thetubes (Figure 1.7). Development started in 1953 follow-ing the construction of a prototype, in wood, of an octa-hedral-tetrahedral grid. An early experimental use wasfor a totally demountable aircraft hangar (21 m wide,20 m deep and 9.8 m high) that was developed for theRoyal Canadian Air Force and which could be packedinto three crates 1.5 m by 1.5 m by 3.7 m long. The fullydemountable Netherlands Pavilion at Expo ’67, Montreal,74 m long, 22.5 m wide and 18.3 m high and erectedwithout scaffolding, was constructed using an externalstructure of Triodetic space grid. It used approximately52 000 aluminium tubes of 38, 51 and 76 mm diameter,5000 steel tubes of 76 mm diameter for highly loadedmembers and around 17 500 aluminium connectors.
Recognition of the innovative work of RichardBuckminster Fuller and the growing acceptance of spacegrid structures came in the adoption of a 76 m diameter,three-quarter sphere, geodesic dome for the US pavilionfor Expo ’67 in Montreal, Canada. Designed by Fuller inconjunction with Sadao Inc., Geometrics Inc., andSimpson, Gumpertz and Heger Inc., the dome was a dou-
4 Space Grid Structures
1.5(a)Tridirectionelle S.D.C. (1957) which required workshop or sitewelding of tubular members to the connectors, developed byStéphane du Château (Drawing: John Chilton after S. du Château)
1.5(b)Pyramitec (1960) a system using triangular, square or hexagonalbased pyramidal modules, developed by Stéphane du Château(Drawing: John Chilton after S. du Château)
ble-layer tubular steel space grid having a triangular geo-desic grid for the outer layer and a hexagonal grid for theinner layer (Figure 1.8). At the same Montreal Expo, two massive theme pavilions, ‘Man the Explorer’ and ‘Man the Producer’ (Architects: Affleck, Desbarats,Dimakopoulos, Lebensold, Sise (CCWE)) were also con-structed using modular three-dimensional space grids.These multi-layer grids were one of the early attempts todemonstrate the feasibility of inhabited mega-structures
constructed from a modular system of small elements.The pavilions (Figure 1.9) were constructed from around400 000 members composed of paired steel angles, using2.5 million bolts and 100 000 connecting nodes, totallingapproximately 7500 tonnes of steelwork. Large wall andfloor sections were assembled using grids based on thegeometry of a regular truncated tetrahedron of side length1 m (see Figure 1.10(a)). The truncated tetrahedron isone of the few regular space-filling polyhedra thus these
Early development of space grids 5
1.6The pyramidal modules of Unibat arebolted together at the corners (Photographcourtesy R. Taylor)
1.7Triodetic system introduced in 1960, byFentiman Bros. of Ottawa, using aluminiumfor the bars and solid hub joints(Photograph courtesy Glyn Halls)
basic modules could be nested in such a way that twoparallel surfaces were formed (see Figure 1.10(b)). Theresulting buildings had floors configured as shown in theplan view of Figure 1.10(c) and walls that were inclined
inwards at an angle of 71 degrees to the horizontal. Atypical elevation is shown in Figure 1.11.
The centrepiece of the Fairground at Expo ’67, inMontreal, was a multi-layer space grid 65.5 m high
6 Space Grid Structures
1.8Richard BuckminsterFuller’s 76 m diameter,three-quarter sphere,double-layer spacegrid geodesic domefor the US pavilion atExpo ’67 in Montreal,Canada (Photographcourtesy AlastairGardner)
1.9Modular multi-layerspace grid pavilion‘Man the Producer’, atExpo ’67, Montreal,Canada. (PhotographKamlesh Parikh,ArchitecturalAssociation PhotoLibrary)
connected by a space grid bridge to an adjacent small-er structure of similar form (both were octahedra withthe longer axis vertical and truncated at the base).11
The Pyramid and Volcano (also known as the Gyrotron),in Figure 1.12, are shown in plan and section in Figure1.13 (Architects: Sean Kenny, George Djurkovic;
Engineer: Boyd Auger). The contract to supply thespace grid was won by the Aluminium Company ofCanada Ltd (ALCAN) who have their head office inMontreal. Over 8500 aluminium tubes 4.9 m long,152 mm diameter and having four different wall thick-nesses were used in the structures. Cladding was
Early development of space grids 7
1.10(a) Truncation oftetrahedron to formgeometry of the grid(b) nesting oftruncated tetrahedrato form parallelsurfaces and (c)configuration of floorgrids for the pavilions‘Man the Explorer’and ‘Man theProducer’, at Expo’67, Montreal, Canada(Drawing: JohnChilton)
1.11Elevation of typicalwall construction forthe pavilions ‘Man theExplorer’ and ‘Manthe Producer’, atExpo ’67, Montreal,Canada (Drawing:John Chilton)
8 Space Grid Structures
1.12Pyramid and Volcano (Gyrotron) multi-layer aluminium space trusses at Expo’67, Montreal, Canada (PhotographE.H. Robinson, ArchitecturalAssociation Photo Library)
1.13Plan and section ofthe Pyramid andVolcano (Gyrotron)multi-layer aluminiumspace trusses atExpo ’67, Montreal,Canada (Drawing:John Chilton)
applied to the internal surface thus fully exposing theexternal space grid.
At around the same time, the wider use of electroniccomputers and the development of programs to enablespace grid structures to be analysed more accuratelyincreased confidence in their use for larger and longerspan structures. It is interesting to note that, due to theinefficiency of the structural analysis computer softwareexisting at the time, a completely new program capableof dealing with large structural configurations was writ-ten in order to analyse the multi-layer grid of the Pyramidand Volcano described above.
During the late 1960s and early 1970s many of thepioneering space grid systems were superseded by sec-ond generation systems. British Steel Corporation (TubesDivision), now British Steel Tubes & Pipes, developedthe Nodus system with a small range of sophisticatedstandard node joints, designed to suit their tubular sec-tion products, and produced in different sizes with vary-ing load capacities. All of the standard joints were test-ed to failure in a special rig, at their research centre inCorby, to prove their effectiveness, and a full size 30.5 mby 30.5 m, 1.52 m deep space grid (Figure 1.14) wasalso built and tested. This structure was dismantled aftertesting and re-erected for use as the Space StructuresResearch Laboratory at the University of Surrey, inGuildford, UK (Figure 1.15).
For the Olympiad held in Mexico City in 1968, thearchitects Felix Candela, Antoni Peyri and Castenada
Tamborrel designed a Sports Palace covered by a dim-pled copper-clad dome. The supporting structure was aseries of orthogonal intersecting trussed arches thatformed a double-curved, double-layer space grid of132 m span.12
Expo ’70 in Osaka, Japan also featured several spacegrid structures. Significantly, the centrepiece was thehuge 291.6 m by 108 m space truss, supported on onlysix columns at a height of 30 m above the ground, whichcovered the Festival Plaza (shown later in Figure 5.1).The design and erection of this space grid, designed byarchitect Kenzo Tange and engineer Yoshikatsu Tsuboi,is described in more detail in Chapter 5. Pods contain-ing exhibits, including a capsule house designed by KishoKurokawa,13 were suspended within the 7.6 m deep roofstructure. Several of the pavilions were designed byMetabolist architects and incorporated space grids, forexample, the Expo Tower by Kiyonori Kikutake and theToshiba IHI and Takara Beautilion also by Kurokawa.13
A total of 1444 tetrahedral modular units were used inthe Toshiba IHI pavilion (Figure 1.16) and only four typesof module of different strength were incorporated in thestructure. The Takara Beautilion (Figure 1.17) was con-structed using a space frame with a cubic multi-layergrid, assembled from rigid jointed modules that were bolt-ed together at the mid-length of each member. Eachmodule was fabricated from twelve tubes (100 mm indiameter) bent through right angles and connected bygusset plates and circular flange plates to form six arms
Early development of space grids 9
1.14Prototype Nodusspace truss, Corby(Photograph courtesyBritish Steel Tubes &Pipes)
of equal length, each consisting of four tubes. Around200 modules were used, each with overall dimensions3.3 m by 3.3 m. Assembly was accomplished in only afew days. Prefabricated stainless steel capsules con-taining exhibits were inserted within the repetitive grid.As a result of the prefabrication of space grid modulesand capsules, the whole of this pavilion was erected inone week.
Notable examples of long-span space grids con-structed in 1970 and 1973 were the British Airways main-tenance hangars (formerly owned by BOAC) at HeathrowAirport, London, designed by Z. S. Makowski andAssociates.14 The hangar roofs were diagonal double-layer grids 3.66 m deep and provided a column-free cov-ered area 67 m by 138 m in plan. In this case, the spacegrids were not constructed from a proprietary system butwere manufactured from tubular steel prefabricated ele-ments joined on site with bolted grid connectors.
In the 1980s the use of continuous cold-formed steelsections for the top and bottom chord members of ‘node-less’ space trusses led to the development of cheaper,lightweight systems, such as Harley, which originated inAustralia, that can compete against well-established por-tal frame construction for medium span buildings. In thistype of space grid, which is described in more detail inChapter 3, the continuous chords in the two orthogonaldirections are of ‘C’ section bolted back-to-back at thenodes.
In the 1980s and early 1990s the CUBIC Space Frame,SPACEgrid and Conder Harley space grid systemsemerged in the UK being respectively a modular spaceframe, a development of the UNIBAT space truss sys-tem and a modified version of the Australian Harleyspace truss system.
10 Space Grid Structures
1.15Prototype Nodus space truss re-erected as the Space StructuresResearch Laboratory, University of Surrey, Guildford, UK(Photograph courtesy British Steel Tubes & Pipes)
1.16Toshiba IHI pavilion, Expo ’70, Osaka,Japan composed of tetrahedral spacegrid modules. Architect: Kisho Kurokawa(Photograph Dennis Crompton,Architectural Association Photo Library)
Although by no means an exhaustive review of thehistorical development of space grid structures, thischapter has served to introduce the work of some of theengineers and architects who have influenced theadvancement of this efficient, usually modular, structur-al form. Several of the systems mentioned above aredescribed in more detail in Chapter 3 together with more
recent developments. The story continues in Chapter 5where a series of studies of interesting projects, com-pleted over the last thirty years, are presented, com-mencing with the space grid of the Festival Plaza at Expo’70.
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7 Wachsmann, K. (1961). The Turning Point ofBuilding. Reinhold.
8 Du Château, S. (1995). Space structure – structurespace. In Lightweight Structures in Civil Engineering(J. B. Obrebski, ed.) pp. 756–66, magat®, MagdalenaBurska, Warsaw.
9 Makowski, Z. S. (1975). Space structures ofStéphane du Château. Building Specification, 6 (5),31–40.
10 Fentiman, H. G. (1966). Developments in Canada inthe fabrication and construction of three-dimension-al structures using the Triodetic system. In SpaceStructures (R. M. Davies, ed.), pp. 1073–82,Blackwell Scientific.
11 Auger, B., Solomon, E. W. and Alcock, D. G. (1966).An aluminium space frame construction. InInternational Conference on Space Structures,Department of Civil Engineering, University ofSurrey, Paper J2.
12 Gordon, B. F. (1983). Olympic Architecture: buildingfor the Summer Games. Wiley.
13 Kurokawa, K. (1977). Metabolism in Architecture.Studio Vista.
14 Makowski, Z. S. (ed.) (1981). Analysis, Design andConstruction of Double Layer Grids. Applied SciencePublishers.
Early development of space grids 11
1.17Takara Beautilion, Expo ’70, Osaka, Japan, assembled from sixbranched, rigid-jointed modules to form a cubic space grid.Architect: Kisho Kurokawa (Photograph Richard Ronald,Architectural Association Photo Library)
There is often a tendency for architects, and possiblymore so engineers, to think in terms of planar structuressuch as beams, trusses and portal frames when con-sidering methods of spanning space. However, in manycases there are advantages to be gained from thinkingin three dimensions and adopting spatial structures formedium to long spans. This is particularly true whereheavy point loads or moving loads are to be supported.
Of course, all structures are three-dimensional in thesense that they have length, depth and thickness.However, planar beams and trusses are predominantlytwo-dimensional in their structural action, as they effec-tively resist loads applied only in one direction betweentheir supports (usually in the vertical plane).Nevertheless, even for these simple structures it isunwise to neglect their stability in three-dimensions. Forexample, beams and trusses, in bending, are madedeeper with increasing span and this, in turn, increasesthe tendency for the compression zone to buckle side-ways, perpendicular to the vertical plane. To counteractthis tendency, lateral bracing of the compression zonemust be provided. With a system of multiple parallelbeams with bracing systems at right angles to the span,it may become economical to take advantage of the ben-efits of three-dimensional structural action describedbelow. Because of the planar nature of individual beamsor trusses, they must be designed to resist the full mag-nitude of any point or moving load applied to them.However, with some modification of the lateral bracingsystem provided to maintain stability of typical beamsand trusses, it may be employed to distribute loadsbetween adjacent beams. This forms a three-dimensionalstructure where loads are rapidly distributed throughoutthe whole system. Every member usually contributessome resistance to the applied load unless the load islocated at or very near a support.
Why two-way spanning structures?
To demonstrate the principle and benefit of using a two-way spanning structure we can consider a familiar exam-ple in the home, the woven canvas webbing often usedfor seats of stools or to support chair cushions. If web-bing strips are used only in one direction, a load applied
to one strip will cause it to sag and transfer load to onlytwo sides of the supporting frame. However, if the web-bing strips are interwoven in two orthogonal directionsthe loaded strip is partly supported by all of the others.This reduces the sag of the loaded strip and distributesthe applied load more evenly to all sides of the frame.In the second case, each strip does not have to be capa-ble of carrying the full applied load on its own and alighter structure can be used for the supporting frame.Another advantage is that, if one of the webbing stripsbreaks, the seat as a whole will still support loads.
Similar benefits may accrue from the use of two-wayspanning structures in architecture and engineering. Forexample, a load applied to a simple one-way spanningbeam or plane truss, must be transmitted through thestructure directly to its supports (Figures 2.1(a) and2.1(b)). If, however, a grid of connected intersectingbeams or trusses is formed in the horizontal plane, avertical load applied to any one beam or truss will bedistributed, in part, to all the other elements in the gridand thus to all of the supports. Figure 2.1(c) shows thisfor a small grid of intersecting trusses. Although, in thesecases, the structural action differs from that describedabove for the woven webbing (bending and shear for thebeams, axial forces for the trusses and pure tension forthe webbing), an analogous, more efficient, load-sharingsystem has been produced. A configuration of inter-secting beams is usually described as a single-layer gridand a very common example of its use in buildings isthe coffered reinforced concrete slab where the orthog-onal ribs produced by the coffering effectively form a gridof intersecting beams supporting a thin floor slab.
When the span of the structure exceeds about 10 m,the use of beam elements in a single layer grid becomesless economical and open web trusses or Vierendeelgirders may be substituted for the solid beams. The struc-ture then effectively consists of two parallel horizontalgrids of ‘chord’ elements connected with a pattern of ver-tical and/or inclined ‘web’ elements between the twoplane grids. This three-dimensional structure is general-ly described as a double-layer or space grid, and is alsocommonly known as a space frame or space trussdepending on the type of bracing between the two lay-ers and the method of connecting the members. Double-layer grids are one of the most efficient and lightweight
2 Space grid geometry – thinking in threedimensions
structural systems due to their ability to share the taskof load carrying through the whole structure; see Figures2.2(a) and 2.2(b).
The term ‘space frame’ is often used loosely by bothengineers and architects, to describe many differenttypes of double-layer grid even though they may carryloads by quite different structural actions. The principaldifference is between:
Space grid geometry – thinking in three dimensions 13
2.1(a)A point load supported by a simply supported beam (Drawing byGraeme Barker © John Chilton)
2.1(b)A point load supported by a simply supported truss (Drawing byGraeme Barker © John Chilton)
2.1(c)A point load supported by a small space grid of intersectingtrusses (Drawing by Graeme Barker © John Chilton)
2.2(a)Deflection of a system of individual trusses (Drawing by GraemeBarker © John Chilton)
2.2(b)Deflection of a two-way spanning double-layer grid of intersectingtrusses demonstrating the load distribution advantage of the latter(Drawing by Graeme Barker © John Chilton)
1 double-layer grids with inclined web elements, suchas the grid shown in Figure 2.3(a), and
2 double-layer grids generally with no inclined web ele-ments, such as the grid with only horizontal chordsand vertical web elements shown in Figure 2.3(b).
The former (1) rely primarily on truss action achievedthrough full triangulation of the structure, which is com-monly composed of nominally ‘pin-ended’ bars or mem-bers connected between ‘node’ joints. In this type ofstructure, which should be more correctly called a spacetruss, if the loads are applied directly to the node joints,the bars within the space grid carry predominantly eitheraxial tension or compression forces. However, somebending is always present due to the self-weight of thebars spanning between the nodes, and secondary bend-ing effects may be introduced depending on the rigidi-ty and form of the connection between the bars andnodes.
Frames, in the more specific engineering sense, aregenerally not triangulated, have some or all joints fullyrigid, and resist the applied loads by a combination ofbending, shear and axial forces in all elements, evenwhen loads are only applied at the joints. The intersectingelements in the latter type of double-layer grid (2) areframes, in the same specific sense, as they also containfully rigid joints and rely on frame action to resist theapplied loads. They are genuine space frames and areusually either constructed from prefabricated, three-dimensional modules or they may be fabricated in situby welding individual elements together. Modular sys-tems have rigid joints within the components which arethen connected by site bolting (e.g the CUBIC SpaceFrame described in Chapter 3 or the multi-layer frameof the Takara Beautilion referred to in Chapter 1).Systems fabricated by welding on site usually form athree-dimensional, completely rigid-jointed structure.
To be able to distinguish between space trusses and‘true’ space frames is arguably not as important for anarchitect as it is for an engineer, although there are sit-uations when an understanding of the difference may beof benefit (e.g. from an aesthetic point of view given themore open nature of the ‘true’ space frame, which hasno diagonal members). In common usage the term‘space frame’ is often applied to all space grids, includ-ing most proprietary modular systems that are actuallyspace trusses. Even the proprietary name and/or thetechnical literature issued by manufacturers may refer tospace truss systems as space frames. However, the usehere of the broader term ‘space grid’, when speakinggenerally, will allow the distinction between space truss-es and ‘true’ space frames to be made when discussingaspects limited to just one of these structural types.
The decision whether to use a three-dimensional spacegrid or a one-way spanning structure is often influencedby the plan form of the building and the location of thesupporting structure. For instance, it may only be possi-ble to provide support along two opposing sides of a rec-tangular building, in which case a one-way spanning pri-mary structure will almost certainly be more economical,especially if the applied loads are uniformly distributedover the plan area of the roof or floor. However, whensupports can be provided along all sides of a square orrectangular plan, a two-way spanning grid may be con-sidered and it is then more difficult to decide which typeof structure is more appropriate. One consideration influ-encing the choice will be the degree of load distributionexpected in the three-dimensional structure. This dependson several factors, in particular the ratio of the spans ineach direction of the two-way grid – the span aspect ratio.
14 Space Grid Structures
2.3(a)Basic double-layer grid of intersecting trusses (Drawing by GraemeBarker © John Chilton)
2.3(b)Basic double-layer grid of intersecting Vierendeel girders (Drawingby Graeme Barker © John Chilton)
The influence of the span aspect ratio on load distri-bution within a two-way spanning structure may be illus-trated simply by considering a point load, W, applied atthe intersection of two orthogonal beams of span L1 andL2. If these beams are connected at their midpoints theywill form a very simple single-layer beam grid. Initially,it is assumed that both beams have the same materialand cross-sectional properties (i.e. the modulus of elas-ticity or Young’s Modulus (E) and the second momentof area (I) are the same for both). The relationshipbetween the span aspect ratio (L2/L1) and the loads car-ried by each beam W1 and W2 can easily be found bya series of calculations for different ratios of beam span.The equations are given in Appendix 1 and the rela-tionship is shown in Figure 2.4 where L2 is the longerspan and L1 the shorter span.
It can be noted from Figure 2.4 that, with I2/I1 = 1, thebeam with the longer span carries the least load, theshorter span carries the greater proportion of the load Wand that (as would be expected) equal load is carried byeach beam when they are both the same length. It canalso be seen that when the ratio of the two spans (L2/L1)exceeds 2.0 the load is primarily carried by the shorterbeam (89 per cent of the applied load when the aspectratio equals 2.0). This simple example demonstrates thatthe benefit of two-way spanning grids is greatest, if thestructure can be broken down into approximately squarebays in plan and that this benefit reduces rapidly as theratio between the two spans increases. Of course, in largespace grid structures, a double-layer grid is more usualand there are many more intersecting members but thebasic principle of using aspect ratios close to 1.0 stillapplies if an economical solution is to be obtained. If theaspect ratio is much greater than 1.0 the possibility ofdividing the longer span by introducing intermediatecolumns should be considered. Where a clear span isabsolutely essential, additional lines of support, in theform of stiff edge or intermediate beams on grid linesbetween columns, may be used to break the structureinto approximately square bays. This can be achievedwithin the depth of the space grid itself, by locally usingstiffer members along lines between opposing perimetercolumns. It can also be accomplished by locally increas-ing the depth of the space grid at appropriate intervals.
A property of all structures, including three-dimensionalgrids, is that applied load is attracted towards the stiffestparts. Therefore, it is possible to modify the proportionof the load carried by elements in the two directions ofa typical space grid by altering the stiffness of elementsappropriately. For example, in the simple two-beam sys-tem described above, it is possible to increase the stiff-ness of the longer beam to balance the load distributionbetween the two beams when they have different spans.This could be achieved by increasing the depth of thelonger beam and thus the magnitude of its second
moment of area I. Figure 2.4 also shows how the pro-portion of total load, W, carried by the longer beam variesfor different aspect ratios and for different beam stiff-ness. Although expensive, in full-scale space grids withrectangular bays, a similar modification of member prop-erties can be employed to modify the load distributioncharacteristics, for instance, by increasing the size ofchord members in the long span direction.
Space truss stability
The stability of rigid jointed space frames depends onthe bending resistance of the joints for its structuralintegrity. However, space truss structures depend ontheir geometrical configuration to ensure stability. To forma stable pin-jointed truss structure composed of nodesinterconnected by axially loaded bars only, a fully trian-gulated structure must be formed. In a three-dimensionalpin-jointed space truss structure, it is a necessary con-dition for stability, (variously known as Maxwell’sEquation or Foppl’s Principle), that,
n = 3j – 6, where n = number of bars in thestructurej = number of joints in thestructure6 is the minimum number ofsupport reactions.
There are many double-layer space truss geometries thatcomply with this condition. Some common ones aredescribed later in this chapter. From this equation, it also
Space grid geometry – thinking in three dimensions 15
2.4Relationship between span aspect ratio and proportion of total loadcarried by the longer span beam, L2, of the simple two-beamintersecting grid with ratio I2/I1 equal to 1, 2, 3 and 5 (Graph: JohnChilton)
follows that a structure that is not fully triangulated canbe made stable if suitable and sufficient additional exter-nal supports are provided.
Alternatively, the stability of common space gridgeometries can be related to the stability of simple poly-hedra. Therefore, we shall briefly look at the behaviourof these forms.
Stable polyhedral forms
Polyhedral forms are bodies in three-dimensional space.From well before the time of the ancient Greek civilization,mathematicians have studied and ascribed special prop-erties to them. The most basic of these forms are termedthe regular or Platonic polyhedra (Figure 2.5) and consistof the tetrahedron, cube (or hexahedron), octahedron,
dodecahedron and icosahedron. Each of these is com-posed of similar faces of regular polygons (i.e. the sidesof each face are the same length and each polyhedronhas faces of only one polygonal shape). In the study ofspace grids we are primarily concerned with bar and nodestructures. However, to understand the stability of three-dimensional structures in general, it is advantageous tostudy the behaviour of simple, regular, polyhedral shapes(composed as either bar and node or plate structures)when loads are applied to their vertices (or nodes).
Bar and node structures
The tetrahedron is the minimum stable, three-dimension-al, pin-jointed bar and node structure. It has four joints ornodes connected by six bars or members. Provided that
16 Space Grid Structures
2.5Platonic polyhedra as bar and node or pure plate structures (a) tetrahedron, (b) cube or hexahedron, (c) octahedron, (d) dodecahedron and(e) icosahedron. (Diagram courtesy: Ture Wester)
Plate structures – stable: Y movable: �
Lattice structures – stable: � movable: Y
the necessary support conditions can be satisfied, thisstructure complies with the equation above and is a sta-ble form which generates only axial forces in the bars whenloads are applied at the nodes (i.e. j = 4, n = 6 and 3j –6 = (3 � 4) – 6 = 6 ). The cube or hexahedron has eightjoints and twelve bars and provided that only the minimumof six support reactions are present, we find that n = 12but 3j – 6 = (3 � 8) – 6 = 18. Thus the pin-jointed cubestructure is unstable unless additional bars are insertedbetween the nodes or further support reactions are intro-duced. In the case of the octahedron n = 12, j = 6 and 3j– 6 = (3 � 6) – 6 = 12 and it is a stable pin-jointed barstructure. Following similar reasoning, it may be demon-strated that the pin-jointed dodecahedron is unstable as abar structure but that the icosahedron is stable. Therefore,as they are composed of bars and nodes, most double-layer space truss geometries are based on the stable poly-hedral forms (usually tetrahedral and octahedral or half-octahedral modules linked together).
Polyhedra as plate structures
Forming the same polyhedra from flat plate surfaces ratherthan from individual bars connected by pinned joints, andagain applying loads at the vertices, the tetrahedron, cubeand the dodecahedron are found to be stable structureswhilst the octahedron and icosahedron are not. The solePlatonic polyhedron that is stable both as a bar and nodestructure and as a plate structure is the tetrahedron. Ifone tries to demonstrate the plate behaviour using cardmodels it is necessary to cut off all the vertices to pre-vent the edges of the plates from acting like bars betweennodes. Once this is done the instability of the octahedronand the icosahedron can easily be seen.1
Combined bar and plate structures
Research has been carried out, in particular by Ture Westerat the Royal Academy of Fine Arts, in Copenhagen, intothe stability and structural duality of polyhedra composedexclusively of bars connected at nodes or of plates con-nected at their edges.1 His work has demonstrated thatthe two structural actions may be combined to form sta-ble space grids composed of bar elements and plate ele-ments. The ability to combine the two types of structuremight be exploited in metal space trusses combined withstructural plate elements of glass or plastic.
Advantages of using space grids
Some of the benefits to be gained from the use of spacegrid structures have already been outlined. These, and
other advantages, illustrated with appropriate built exam-ples, are described below.
As described above, the prime advantage of space gridstructures is that generally all elements contribute to theload carrying capacity. Planar beams or trusses must becapable, individually, of carrying any possible concen-trated or heavy moving loads (e.g. overhead cranes).However, in space grids such concentrated loads aredistributed more evenly throughout the structure and toall the supports. This can also reduce the cost of thesupporting structures as maximum column and founda-tion loads may be less. Maximum deflections are reducedcompared to plane structures of equivalent span, depthand applied loading, assuming that the structural ele-ments are of similar size. Alternatively, a lighter or shal-lower three-dimensional structure may be used to carrythe same loads, resulting in maximum deflections nogreater than those of a planar structure.
Installation of services
In space grids, the reasonably open nature of the struc-ture between the two plane grids allows easy installa-tion of mechanical and electrical services and air-han-dling ducts within the structural depth. Their fixing issimplified as there is a regular system of supports avail-able, thus greatly reducing or even eliminating the needfor secondary steelwork. If heavy equipment is to beinstalled within a space grid, the loads should ideally besupported at node joints. This is particularly necessaryin space trusses in order to minimize bending momentsin the chords. Otherwise, due account must be taken ofsuch loading in the initial design of the nominally axial-ly loaded members.
A good example of the load distribution properties ofa space grid, as well as the freedom to install plant andmachinery within the roof depth, being exploited to thefull, is in a food-processing factory in Nottingham,England, which was constructed with a CUBIC SpaceFrame roof. It was expected that, at different times dur-ing the life of the building, various areas of the factoryfloor would be used as refrigerated stores. To aid thisflexibility, 100 mm thick insulated panels were fixed tothe whole of the lower layer of the space grid roof andthe 75 m by 75 m structure (with just three internal sup-ports) was designed to take point loads totalling approx-imately 600 tonnes. This permitted almost total adapt-ability of the refrigeration plant configuration within the3 m deep roof space over the production and storageareas (Figure 2.6).
Space grid geometry – thinking in three dimensions 17
Space grids are highly redundant structures, whichmeans that, in general, failure of one or a limited num-ber of elements – for instance, the buckling of a com-pression member under excessive loading – does notnecessarily lead to overall collapse of the structure.There have, however, been exceptions to this; notably,the collapse of the space truss roof of the Hartford CivicCentre, Coliseum, in January 1978.2,3 This roof collapsedunder snow and ice loading early in the morning of 18January 1978, only a few hours after it had been occu-pied by a crowd of 5500 spectators at a basketball match.The subsequent investigations concluded that a fold linehad developed in the roof in a north–south direction(roughly perpendicular to direction of the longer roofspan) due to progressive buckling failure of the topchords of the truss. The failure occurred with a snowload of 78 to 88 kg/m2 (16 to 18 lb/ft2). It was conclud-ed that the space truss failed ‘at about one-half the totalload which would have caused first yielding in the weak-est member’ (see Ref. 3, p. 636).
In space trusses supported at the bottom nodes thereare usually four diagonal web members converging oneach support and these are in compression. Failure ofonly one of these due to accidental damage or bucklingunder excessive compression owing to an unforeseenload can lead to the partial or total collapse of the wholestructure, as the load originally carried by the failed mem-
ber transfers to the remaining three and in turn causestheir failure. The redundancy of space grid structuresalso assists with their resistance to damage from fire,explosion or seismic activity. In the case of fire or explo-sion there may be localized damage of the space grid,which allows the heat and smoke (in fire) or the force ofthe blast (in explosion) to escape. Unless critical ele-ments (e.g. highly stressed compression chords, or webmembers adjacent to individual column supports as pre-viously mentioned) are removed or weakened, total col-lapse is unlikely. The behaviour of space grids in fireand earthquake is discussed in more detail in the fol-lowing chapter.
Space grids are highly modular structures assembledfrom components that are almost exclusively factory fab-ricated. The components therefore, are usually producedwith high dimensional accuracy, with a high quality ofsurface finish and they are generally easily transportable,requiring little further work except assembly on site.Because of their modular nature, space grids may beextended without difficulty and even taken down andreassembled elsewhere. The Mero space grid stand forthe Edinburgh Tattoo (Figure 2.7) is an example of aspace truss that has been taken down and re-erectedannually, since 1973.
18 Space Grid Structures
2.6Equipment in the roofspace of the CUBICSpace Frame,Northern Foods,Nottingham(Photograph courtesyDavid HaguePhotography Ltd)
Sadly, some architects seem to exhibit a resistance tothe use of standard modular grid components. Perhapsthey feel that their creativity is somehow restrained.However, just as an amazing diversity of masonry archi-tecture has been produced using the standard modularcomponent of the brick, so, with imagination, the stan-dard components of a space grid system may be com-bined to generate exciting architectural forms. Someexamples are shown in Chapter 5.
Freedom of choice of support locations
Great choice in the location of supports is offered by spacegrid structures. Within reason, space grids can be sup-ported at any node of the grid and at practically any loca-tion in plan. This gives the architect considerable freedomin space planning beneath the grid. For instance, columnscan be concealed on the lines of internal partitions.However, as discussed previously, approximately squarestructural bays are preferable as they lead to a more effi-cient use of material. The appropriate location of grid sup-port and the effect that this can have on the structural effi-ciency is considered in more detail later in this chapter.
For ease of construction, most space grids have a reg-ular pattern that may be exploited architecturally to some
effect. Particularly striking effects can be achieved if thecolour chosen for the structural members contrasts withthe colour of the decking, or with the sky in the case ofunclad grids or fully glazed applications. The white dou-ble-layer space grid of the simple glass-covered entrancecanopy at the Georgia Dome, Atlanta, USA, shown inFigure 2.8 contrasts beautifully with the blue of the cloud-less sky. In fact, the colour chosen for a grid, as well asthe grid pattern itself, can influence considerably the per-ceived weight of the exposed structure. The effect maybe even more important than the actual member sizesor density of the grid. For instance, with appropriate light-ing, a white space grid set against a white metal linertray will not be particularly noticeable but the same gridset against a deep blue sky will be quite dramatic.
Ease of erection
A further advantage of the use of space grids is the effi-ciency of erection for large-span roof structures and espe-cially on sites with limited access. In the former case, thewhole roof can be assembled safely at or near groundlevel, complete with decking and services, and thenjacked into its final position. In the latter case, the smallcomponents of a space grid can be assembled at almostany location using only manual labour and simple light-weight tools, even inside existing buildings. An exampleof the advantage of ease of erection of the small com-
Space grid geometry – thinking in three dimensions 19
2.7The Mero stand forthe Edinburgh Tattoohas been taken downand re-erected atEdinburgh Castle,annually, since 1973(Photograph: JohnChilton)
ponents of a space grid, was the very first commercialuse of the CUBIC Space Frame in the Waverley Building,Nottingham Trent University, UK. Here an existing roofof a Victorian building was to be replaced in order to pro-vide a rehearsal theatre. Alternative schemes using stan-dard planar trusses and the CUBIC Space Frame weredrawn up. However, the tender for the space frame includ-ed a full-scale load test to prove the adequacy of the newsystem. Despite this additional expense, the space framesolution was cheaper overall as the modules could bemanually handled into the building and raised using sim-ple lifting gear, whilst the planar trusses required a large(and expensive) mobile crane to lift them into positionover the front of the building. Space grid erection meth-ods are considered in more detail in Chapter 4.
There are also some disadvantages in the use of spacegrids that must be offset against the considerable num-ber of advantages described above.
Of the disadvantages associated with space grid con-struction, perhaps the main one is the cost, which cansometimes be high when compared with alternative struc-tural systems such as portal frames. This disparity in costis particularly evident when space grids are used for rel-atively short spans, although the definition of a short spanis very dependent on the system under consideration.However, spans of less than 20 to 30 m can probably beconsidered short, for most space grids. Often a directcomparison of like with like is not made. For instance,increased frame-spacing in a portal framed structure willusually require additional or heavier purlins to support theroof decking and secondary steelwork may be necessaryto carry services and equipment, neither of which maybe needed if a space grid were used instead.
Although the regular geometry of space grids is gener-ally cited as one of their appealing features, to some eyesthey can appear very ‘busy’. In real buildings they arerarely seen in plan or in true elevation (as they general-ly appear on the architect’s drawings) but more typicallythey are viewed from quite close up and in perspective.Consequently, the regular nature of the geometry is lostand at some viewing angles, the ‘lightweight’ structurecan appear to be very dense indeed. The upper and lowergrid size, the grid depth, as well as the grid configura-tion, can have a considerable influence on the perceiveddensity of the double-layer structure. These factors arediscussed in more detail later in this chapter.
Again, this is a topic that also appears under the list ofadvantages. However, another common criticism ofspace grids is that the number and complexity of jointscan lead to longer erection times on site. The erectiontime obviously depends on the system being used for aparticular application as well as other factors such asthe chosen grid module. Designing the grid to containthe most practical minimum number of nodes is goodpractice as they are usually the most expensive com-ponents. This leads to economy of material costs andfaster erection times.
Space grids are mainly used in roof construction where,depending on the materials involved, nominal or no fire
20 Space Grid Structures
2.8Glass-covered canopy, Georgia Dome, Atlanta, USA (Photograph:John Chilton)
resistance is normally required. However, when they areused to support floors, some form of protection is usu-ally demanded to provide the necessary fire resistance,if they are exposed. This protection is difficult to achieveeconomically due to the high number and relatively largesurface area of the space grid elements, but intumes-cent coatings can be applied. The effect of fire on spacegrids is considered in more detail in Chapter 4.
There are many possible ways of dividing a flat planeusing a grid of lines connecting points in a regular orirregular pattern but this may produce considerable vari-ation in the length of the lines and the angles betweenthem. In modular structural systems such as single ordouble-layer grids it is normally considered advanta-geous if, in any particular structure, the number of dif-ferent member lengths can be limited and connectionangles at the joints standardized. However, with moderncomputer controlled cutting, drilling and machining equip-ment, it is now almost as simple to produce members
with many different lengths and nodes with many differ-ent connection angles without excessive cost penalty.Until recently, therefore, regular patterns were usuallyadopted for both the upper and lower layers of spacegrids. This approach can be rather restrictive as thereare only three regular polygons (i.e. polygons with allsides of equal length) that can be used exclusively tocompletely fill a plane. These are the equilateral trian-gle, square and hexagon. The regular plane tessellationsare shown in Figure 2.9(a)–(d) and these form the mostcommon chord configurations.
Using square configurations the grid lines can be par-allel to the edges of the grid (Figure 2.9(a)) or set onthe diagonal, usually at 45° to the edges (Figure 2.9(b)).Both of these are described as two-way grids as theyhave members orientated in only two directions.However, plane grids of triangles and hexagons producethree-way grids with members orientated in three direc-tions (Figure 2.9(c) and (d)). More complex grid geome-tries may be produced by combining the regular poly-gons or by using them in combination with otherpolygonal shapes (e.g. triangles and squares, trianglesand hexagons, squares and octagons).
Space grid geometry – thinking in three dimensions 21
2.9Tessellations of a flat plane with regular (a) squares, (b) rotated squares, (c) triangles and (d) hexagons (Drawing by Graeme Barker ©John Chilton)
Double-layer space grid structures, where two planegrids are separated by web members, do not necessar-ily have to have the same pattern or orientation in theupper and lower grids. In practice, for reasons of costand facility of connection of web members, the numberof common configurations is usually quite limited.
In the description of the more common forms of dou-ble-layer grid configurations that follows, the referenceto square grids also encompasses rectangular grids withdifferent spacing in each direction, as well as the pos-sibility of rhombic grids:
1 Square on square: where the upper chord grid isdirectly above the lower chord grid and the web mem-bers connect the layers in the vertical plane betweenthe upper and lower grids. When viewed in plan onlythe top square grid is seen (see Figure 2.10).
2 Square on square offset: where the top chord gridis offset, usually by half a grid square in both direc-tions, relative to the lower chord grid. In this config-uration the web members connect the intersectionpoints in the upper grid with the adjacent intersec-tions in the lower grid and a continuum of tetrahe-dral and half-octahedral cells is generated (seeFigure 2.11). This is the most commonly used con-figuration.
3 Square on diagonal square: where the lower chordgrid is set at 45° to, and is usually at a greater spac-ing than, the top chord grid. Again the web mem-bers connect the intersection points on the top andbottom grids (see Figure 2.12). A further alternativeversion of this grid configuration is diagonal onsquare where the upper grid is at 45° to the lines ofsupport and the lower grid is parallel to the supports.
22 Space Grid Structures
2.10Square on square grid configuration (Drawing by Graeme Barker ©John Chilton)
2.12Square on diagonal square grid configuration (Drawing by GraemeBarker © John Chilton)
2.11Square on square offset grid configuration (Drawing by GraemeBarker © John Chilton)
2.13Triangle on triangle offset grid configuration (Drawing by GraemeBarker © John Chilton)
4 Triangle on triangle offset: where both chord gridsare triangular but the intersections in the lower gridoccur below the centres of alternate triangles in theupper grid. In this case also, the web members con-nect the intersection points on the top grid with theadjacent intersections in the lower grid (see Figure2.13).
5 Triangle on hexagon: where the upper (denser) gridis triangular and the lower (more open) grid is hexag-onal due to removal of some lower chord and webelements from the triangle on triangle grid describedin 4 above (see Figure 2.14).
More open grid geometries are often possible in thelower layer of a double-layer grid because the membersare normally in tension (i.e. not subject to member buck-ling). The lower (tension) chords may, therefore, be
longer than the upper (compression) members eventhough the forces within them may be greater. In mod-ular space grid systems, for the same reason, completemodules can sometimes be omitted in a regular patternto produce a more open geometry and thus to reducethe self-weight of the structure. Figure 2.15 shows a gridwhere pyramidal modules have been removed on achequer-board pattern. This may be compared with thefull grid of Figure 2.11. An open grid with a non-regulartessellation is shown in Figure 2.16. Such economiesare not always feasible and before removing modules orreducing the density of the lower chord grid, the effectof the disposition of grid supports and the degree of loadreversal that may occur due to wind action should beassessed. Space grid roofs are usually flat or of low pitchand the action of a wind passing over the building caus-es negative pressure or suction over the whole roof area.
Space grid geometry – thinking in three dimensions 23
2.14Triangle on hexagon grid configuration (Drawing by Graeme Barker© John Chilton)
2.16Non-regular grid for upper and lower chords (Drawing by GraemeBarker © John Chilton)
2.15Sparse modular grid with modules omitted on a chequer-boardpattern to reduce its self-weight (Drawing by Graeme Barker ©John Chilton)
2.17Visual effect of the variation in grid spacing node density and webinclination – typical space grid (Drawing by Graeme Barker © JohnChilton)
When there are also large openings in the building (e.g.aircraft hangar doors) large internal pressures may alsobe generated by a strong wind blowing directly into theopening. The combined external suction and internalpressure act in the same direction, opposing and some-times exceeding the gravity loads on the roof. When thegravity loads are exceeded, the net loading on the roofis upwards, reversing the forces generated in the spacegrid by loads such as self-weight and snow. Thus mem-bers usually in tension may have to resist compressionunder wind action and this may be the critical designload for the chords of the lower grid.
Choice of grid configuration and the depth betweenthe chord layers will affect the economy of the spacegrid. For space trusses and frames constructed from pre-fabricated modules there is often less freedom to varythe grid geometry without cost penalty as modules willusually be produced only in a limited number of stan-dard sizes and depths. For bar- and node-type spacetrusses, the member lengths can be varied at will andthere is usually a range of node sizes and strengths tochoose from. Hence, the geometrical possibilities arealmost limitless. However, the node joints are normallythe most expensive components, therefore, the morenodes that there are in a given plan area the higher thematerial cost is likely to be. Also, with more nodes in thestructure, erection times are increased and, thus, over-all construction costs will be higher. Increasing the upperand lower grid spacing reduces the number of joints fora given plan area but there may be disadvantages. Forexample, in space trusses with a larger upper and lower
grid spacing, the depth between the two grid layers mayhave to be increased to accommodate the inclined webmembers at an appropriate angle – usually between 30°and 70° to the horizontal chords – and individual mem-bers will inevitably be longer. When the longer membersare subject to compressive forces, they may need to belarger in cross-section or wall thickness to avoid buck-ling if they are laterally unrestrained. Consequently, thespace truss may become heavier and more costly.
The visual effect of these variations can be seen inFigures 2.17 to 2.20 which illustrate structures of thesame span but with different grid densities and depth. Agrid of typical proportion is shown in Figure 2.17 and agrid of similar density but reduced depth is shown inFigure 2.18. The latter appears more open but chord andweb elements would need to be bigger because of thereduced structural depth. Figures 2.19 and 2.20 showthe same span with a grid spacing half that of Figures2.17 and 2.18 and different depths. The structures seemmuch denser and the number of joints and members hasincreased dramatically.
Defining the grid
The behaviour of space grid structures is analogous tothat of flat plates and before the widespread availabilityof fast digital computing and suitable three-dimensionalstructural analysis software, the forces within space gridswere determined using approximate hand calculationbased on plate theory. Computer technology has movedquickly during the 1980s and 1990s: processing speed
24 Space Grid Structures
2.18Visual effect of the variation in grid spacing node density and webinclination – shallow space grid with web members at an inefficientangle (Drawing by Graeme Barker © John Chilton)
2.19Visual effect of the variation in grid spacing node density and webinclination – shallow space grid with high density of nodes andmembers (Drawing by Graeme Barker © John Chilton)
has increased dramatically and memory and storagecapacities have expanded rapidly whilst their cost hasdecreased. Consequently, it is now possible to analysemany space grids, modelled as individual bar and nodestructures, on a desktop (or even notebook) computerin a few hours or even minutes depending on the sizeand complexity of the configuration and loading. To carryout the analysis it is necessary to define the structureunambiguously by specifying the positions of the nodes(for instance by using Cartesian coordinates relative tothree mutually perpendicular axes). Also the location, ori-entation and physical properties of each member, thetype of connection between bars and nodes (‘pinned’,fully rigid or semi-rigid joints) and the position and degreeof restraint for each support must be stipulated.Subsequently, a series of load cases can be defined forthe grid, including its self-weight, imposed loads such ascladding and installed services, the loads imposed in usesuch as floor loads, snow loads, wind loads and theeffect of temperature changes. In fact, defining the dis-position of the separate parts of a space grid – its con-figuration – is often the most time-consuming aspect ofperforming an analysis. However, space grid manufac-turers usually have pre-processing computer programs,particular to their product, to automatically generate nodecoordinates, member lists and the description of whichmembers are connected to which nodes, for simple grids.
Once a numerical description of the configuration of aspace grid structure has been established, further pro-cessing can be used to create more complex structuralforms. Configuration processing, as this is called, may
use additional computer programs developed by manu-facturers specifically for their products, or may use pro-grams such as Formian, based on Formex algebradeveloped by Professor H. Nooshin at the University ofSurrey, Guildford, UK.4 Further advances in the gener-ation of data to define grid configurations have evolvedfrom the exchange of data between computer-aideddesign (CAD) software, used for engineering and archi-tectural drawings, and structural analysis software.
As the majority of space grids are constructed as flat (ornear flat) planes, it is sometimes assumed that they mayonly be used in such circumstances. However, spacegrids are not limited to planar surfaces and more com-plex geometries such as barrel vaults, domes, hyperbolicparaboloids or even free-form surfaces may be gener-ated. These are usually formed from two parallel single-or double-curved surfaces, which define the upper andlower chord layers, separated by a constant dimension.If required, the two curved surfaces can be different, sothat the distance between the upper and lower chordlayers varies across the space grid. Figures 2.21 showsa space grid barrel vault and Figure 2.22 (a) and (b)show the plan and three-dimensional view of the spacegrid roof of the Anoeta Stadium, San Sebastián, Spain.Some built examples are described in Chapter 5 (forexample, the Sant Jordi Sports Palace, Palafolls SportsHall and Bentall Centre).
Space grid geometry – thinking in three dimensions 25
2.20Visual effect of the variation in grid spacing node density and webinclination – deep space grid with close grid spacing, high densityof nodes and members (Drawing by Graeme Barker © JohnChilton)
2.21Double-layer barrel vault space grid (Drawing by Graeme Barker ©John Chilton)
The choice of the most advantageous support locationsfor the space grid will, of course, depend on the planform of the structure and architectural considerations.Nevertheless, the positions chosen may have a signifi-cant influence on the structural efficiency. Depending onthe grid configuration, it is possible to support either topor bottom node joints. In the former case, the web mem-bers immediately adjacent to the supports will usually bein tension and in the later case in compression. For agrid supported at the lower nodes in only a few loca-
tions, it may result that the web members around eachsupport are the most critical of the whole structure andfailure of one compression diagonal may result in pro-gressive collapse of the whole structure. For this rea-son, the potential for collapse of the grid can be reducedif it is supported at the upper nodes, maintaining themost heavily loaded diagonals in tension, although thesupporting columns, being longer, then themselvesbecome more vulnerable to buckling failure.
Some alternative support positions for a uniformlyloaded, square plan, square on square offset grid roofstructure, supported at the upper node joints, are shownin Figures 2.23 to 2.26. Intuitively, it can be appreciat-ed that the provision of supports at each node along thefull perimeter (Figure 2.23), is likely to be a more effi-cient arrangement for the space grid, than having sup-ports only at the corner nodes (Figure 2.24). With fulledge support, the applied loads have a shorter load pathto the ground although, because of the greater numberof columns, additional foundation costs may be incurred.For similar space grids subject to the same loading, themaximum member forces are lowest in the fully edge-supported case and the maximum vertical deflections arealso much smaller. However, slightly modifying the cor-ner-supported condition, with the introduction of one ormore intermediate supports along each edge (Figure2.25) will greatly improve the space grid performance atlittle extra cost for columns and foundations. With thissupport configuration an efficient space grid structure isachieved, whilst keeping the number of columns to asensible minimum.
Single columns located at the middle of each side(Figure 2.26) may also produce an efficient support sys-tem. In this case, the corners of the space grid are can-tilevered and counterbalance the central area; thus thevertical deflections and the member forces at the centreare reduced. Most of the bottom chord members will bein compression and most of the top chords in tension.
26 Space Grid Structures
2.22 (a)Plan of wave form space grid roof, Anoeta Stadium, San Sebastián,Spain (Courtesy Orona S. Coop., San Sebastián).
2.22 (b)Three-dimensionalview of waveform spacegrid roof,AnoetaStadium, SanSebastián,Spain(CourtesyOrona S.Coop., SanSebastián)
Maximum vertical deflections and chord forces can bereduced still further, in most of the above cases, if thesupports are located slightly inward from the edges ofthe space grid so that a short cantilever is producedaround the whole structure. Although this may introducecolumns into the main volume of the building, it can beadvantageous architecturally, giving the opportunity todefine circulation spaces around the periphery behindfully glazed, column-free elevations or a canopy toprovide shelter or shading around the full building perime-ter if desired. With some space truss systems the abilityto cantilever is limited as they are not usually designedto accept large compressive forces in the lower grid (forexample, the Space Deck pyramidal modules are gen-erally connected in the lower grid by slender rods thathave a relatively low compression resistance). Thesecantilevered support configurations should, therefore, beused with care. With excessive length of cantilever, thelimiting vertical deflections at the perimeter, under vari-ations in load, may become the critical design case.
In most books and product literature about space grids,it is usual to show supports on a uniform grid and,because of this, it is commonly assumed that space gridsmust be supported in such a regular manner. None theless, as long as sufficient supports are provided, it is
possible to place them under any node within the grid(see Figure 2.27). For an irregular plan form, the cost ofthe structure will only be increased marginally if supportsare not on a rigidly defined grid pattern.
Up to this point it has been assumed that the grid is sup-ported at discrete nodes along its edges or at individualinternal columns. However, an alternative method ofreducing both maximum vertical deflections and mem-ber forces in the space grid is to use ‘tree’ supportsinstead of individual columns. This is commonly achievedby providing a square-based inverted pyramid of‘branches’ at each support location. These may be com-posed of space truss members using the standard jointsor specially fabricated elements. As the grid is support-ed on several nodes at each column location, the forcesin the adjacent web bracing members are less than theywould have been with the grid supported on simplecolumns. Effectively, the span of the space grid isreduced. Tree supports can also be used to architecturaleffect (Figure 2.28) as they replicate the flow of forcesfrom the space grid into the supporting columns. With
Space grid geometry – thinking in three dimensions 27
2.23Square on square offset grid with full edge node support (Drawingby Graeme Barker © John Chilton)
2.25Square on square offset grid with corner and intermediate edgenode support (Drawing by Graeme Barker © John Chilton)
2.24Square on square offset grid with corner support only (Drawing byGraeme Barker © John Chilton)
2.26Square on square offset grid with mid-side support only (Drawingby Graeme Barker © John Chilton)
multi-span space grids, the economy derived from usingtree form columns is increased.
From the outside of a building having a space grid roof,it is often only the eave profile that gives any clue as tothe form of the structure within. There are three com-mon edge profiles that derive from the inherent geometryof space grids. Two alternatives result from the geometryof square on square offset space trusses. In one case,the top chord grid extends beyond the bottom chord gridand the web bracing between the two plane grids gen-erates an inclined cornice edge profile (Figure 2.29). Onthe other hand, if the lower grid extends beyond theupper grid, the bracing forms a mansard edge (Figure2.30). Other space grids such as systems of intersect-ing planar trusses and the CUBIC Space Frame lend
themselves to the use of vertical edge profiles (Figure2.31). A vertical edge can also be achieved with stan-dard space trusses by using a half-bay at the edges.The architect is not limited to these profiles as specialedge details (Figure 2.32) can be manufactured to orderand fixed to the standard space grid nodes or modules.
Multi-layer space grids
Where a flat double-layer space truss is spanning a con-siderable distance (over, say, 100 m) and/or the appliedloads are particularly heavy, it becomes necessary togreatly increase the depth between the upper and lowergrids, to limit the maximum deflection or resist high bend-ing moments. As the grid depth is increased, either theangle of the diagonal bracing becomes more verticaland/or the grid spacing of the two horizontal layers mustalso be increased. Eventually the depth and grid spacing
28 Space Grid Structures
2.27Square on square offset grid of variable plan form supported oncolumns at irregular centres (Drawing by Graeme Barker © JohnChilton)
2.29Cornice edge profile (Drawing by Graeme Barker © John Chilton)
2.30Mansard edge profile (Drawing by Graeme Barker © John Chilton)
2.28Tree supports mimicking the flow of forces to the column base(Drawing by Graeme Barker © John Chilton)
may be enlarged to such an extent that the compres-sion members (the top chords and many web bracingelements) become excessively long. Long, highly loadedcompression elements tend to be large in diameter withthick walls. Thus they are heavy and uneconomical, con-trary to the philosophy of lightness and economy of mate-rials behind the use of space grids. In such situations itis possible to introduce an intermediate horizontal gridbetween the normal upper and lower chord layers. Thisadditional layer allows the grid spacing of both outer lay-ers to be reduced. Consequently, the length of the topcompression chord members and the unrestrained lengthof the web compression members are reduced, with anappropriate reduction in member cross-section. A furtherbenefit is that the horizontal grid layers can each havedifferent configurations so that the most efficient chordlayout may be selected.
The intermediate layer is usually at or near the mid-depth of the grid, and in this location it is only lightlystressed (by analogy with the material at the mid-depthor neutral axis of a solid beam) and can therefore becomposed of lightweight elements and/or use a sparsegrid configuration. Although the additional layer increas-es the number of bars and nodes in the space trussstructure, it allows lighter compression members to beused. The extra cost of the additional lightly stressedbars and nodes is presumed to be less than the cost ofthe materials saved from the other components.
Multi-layer grids may also be used when only moder-ate distances are to be spanned by lightweight spacetruss systems that use cold-formed steel sections of lim-ited strength in compression. In this case, there are oftenstandard member lengths and longer span structures are
produced by assembling three (or more) layers from theregular kit of parts. A quite recent example of a deepthree-layer Mero space truss, the roof of the NationalIndoor Arena for Sport, constructed in 1990, inBirmingham, UK, is described in detail in Chapter 5.
Over the years, there has been much interest amongarchitects in the exploitation of multi-layer grids in theurban environment. Proposals have been made for theconstruction of gigantic space truss mega-cities in whichthe interstices of the multi-layer grid are inhabited by thecitizens of the twenty-first century and beyond. These con-cepts have yet to be realized, despite the current avail-ability of the necessary technology that has to some extentalready been proven in the harsh environment of deep-sea oil rig construction. Inhabited space grids on both thesmall and large scale are reviewed in Chapter 7.
1 Wester, T. (1983). Structural Order in Space: ThePlate-Lattice Dualism. Royal Academy of Fine Arts,School of Architecture, Copenhagen.
2 Smith, E. A. and Epstein, H. I. (1980). HartfordColiseum roof collapse: structural collapse sequenceand lessons learned. Civil Engineering – ASCE, April,pp. 59–62.
3 Thornton, C. H. and Lew, P. I. (1984). Investigationof the causes of Hartford Coliseum collapse. In ThirdInternational Conference on Space Structures (H.Nooshin, ed.) pp. 636–41, Elsevier.
4 Nooshin, H. and Disney, P. L. (1997). Formian 2.Multi-Science.
Space grid geometry – thinking in three dimensions 29
2.32Special edge profile (Drawing by Graeme Barker © John Chilton)
2.31Square edge profile (Drawing by Graeme Barker © John Chilton)
In this chapter, the materials that are used for space gridconstruction are briefly reviewed, various space gridtypes are categorized and representative commercialsystems are described for each category. As this bookis intended to present a general overview of space gridstructures and is not meant to be a design manual,detailed material specifications are not included. To cat-egorize the bar and node type space grids that form themajority of available systems, they are grouped accord-ing to the type of node joint that is used.
Materials for space grids
Most space grid systems for building structures are man-ufactured from steel, although aluminium has been usedfairly extensively and timber, concrete and reinforcedplastics have also been used. More exotically, experi-mental structures using bamboo poles1 have been inves-tigated and glass has also been incorporated into spacetrusses but only in sculptural objects.
High yield and mild steel tubes and sections, elementscold-formed from steel strip and castings from spheroidalgraphite iron are used. These are usually galvanizedand/or painted (known as the duplex system if both areused). Alternatively, aluminium alloy nodes and mem-bers may be employed. Although the typical density ofaluminium alloy (around 2700 kg/m3) is only approxi-mately one third that of steel (7865 kg/m3), it also has alower modulus of elasticity, or Young’s Modulus (Ealuminium
= 70 000 N/mm2 whilst Esteel = 205 000 N/mm2). The mod-ulus of elasticity of the components of a structure gov-ern its overall deflection. Therefore, because of the rel-ative moduli of elasticity, for an aluminium alloy spacegrid of approximately equivalent load capacity to a steelspace grid with equal span and imposed loading, theresulting aluminium structure may be lighter, unlessdeflections are critical. In which case, additional mater-ial may be required to keep deflections within accept-able limits. As the material cost for aluminium alloy isgreater than that of steel the choice of material willdepend very much on individual circumstances. Thecoefficients of thermal expansion for steel and alumini-um are 0.000012 /°C and 0.000024 /°C respectively, thusaluminium structures require more allowance to be madefor thermal movements caused by normal ambient tem-perature changes (see Chapter 4). Greater care is
required to weld aluminium than steel and as many spacegrid systems involve at least some welding in their man-ufacture, steel is the most commonly used material forthe members. Many systems use cast steel for end con-nectors and node joints.
Timber is also used in space trusses in the form ofroundwood poles, solid sawn timber and in the refinedform of glued laminated timber. As with most timber struc-tures, one of the principal design considerations is thetransfer of forces (particularly tensile forces) betweenmembers at the joints. Because of the high axial forcesexperienced by space grid members, individual mem-bers usually have metal inserts introduced at the endsso that the forces can be transferred over a greater lengthof the member. These metal inserts are connected tometal nodes (as in the Mero Holz system) or directly toeach other (as in systems designed by Pieter Huybersat TU Delft, described in detail in Chapter 5).
Concrete space grids, although much heavier (bothvisually and in actual weight) can become an economicproposition in countries where steel is relatively scarceand expensive and labour is cheap. This is often thecase in developing nations. For example, large reinforcedconcrete space truss pavilions were built for a perma-nent trade fair site at New Delhi, India, in 1982 wherefive pyramidal pavilions were constructed from in situreinforced concrete using multi-layer grids of octahedraland tetrahedral geometry.2,3
Some experimental space grid structures have beenmade using reinforced plastics, the most common beingglass reinforced polyester (GRP). However, the use ofthese materials is still in its infancy. Although having amore favourable strength to weight ratio than many tra-ditional structural materials, reinforced polymers displaycharacteristics such as higher coefficient of thermalexpansion, higher modulus of elasticity, deterioration withexposure to ultraviolet light and creep due to the vis-coelastic nature of the polymers used to bond the fibresthat can detract from their utility for many structures.
Space grid systems
Literally hundreds of different space grid systems havebeen developed since they were first introduced com-mercially over fifty years ago. Throughout the world newsystems are brought on to the market almost every year.
3 Materials and systems
Of these, some are used only once or last for only a fewprojects before their demise. Practically all are spacetrusses with diagonal web bracing between the chordlayers.
Commercial space grid systems can generally be divid-ed into three types: those that are assembled from dis-crete members running between node joints (oftenreferred to as ‘piece-small’ systems), those that areassembled using continuous chords and those that areassembled from factory prefabricated modules. In thefollowing sections, examples taken from some of themany systems currently available commercially are usedto illustrate the variety of products at the disposal of thedesigner. Some manufacturers market more than onesystem, in which case the most commonly used of theirsystems is described in the appropriate category.Addresses of a selection of space grid manufacturers,including those mentioned in this chapter, are given inAppendix 2.
The ‘piece-small’ systems primarily differ in the jointingmethod. Most use circular or square hollow tube mem-bers because of their better performance in resisting theforces present in space trusses (normally pure axial ten-sion or compression, with only secondary bendingeffects). Tubular members are also considered to havea superior aesthetic appearance. To architects this isespecially important, as space grids are normally leftexposed to view so that the building’s users can appre-ciate the pattern of the regular grid geometry. The maindifference between tubular members in the alternativesystems is the detailing of their ends for connection tothe nodes. In most types there is some addition to thebasic tubular member. For instance, in the Mero KK sys-tem in the form of a cone, in the Nodus system as solidribbed castings or in the KT Space Truss as capping andjointing plates. These additions are welded to the endsof the pre-cut tubular members. In other systems the tubeitself is modified at the ends, usually by flattening with aplain or crimped profile (e.g. Triodetic). There are somelightweight systems such as Unistrut/Moduspan that usecold-formed channel section members that are bent toshape and have bolt holes punched at the ends.
The distinguishing features of the ‘piece-small’ sys-tems are the shape of the nodes and method of mem-ber connection at those nodes. The tremendous varietyof node jointing systems (e.g. ‘ball’ joints, hollow spheres,profiled plates, etc.), illustrates the difficulty of achievinga simple, aesthetically pleasing joint. Joop Gerrits of TUDelft has carried out a detailed study of the morpholo-gy of the available node jointing systems in which heclassified them by node type.4 The categorization of var-
ious ‘piece-small’ space truss systems used here isbased on his proposals with, where necessary, furthersubdivision of the categories. These are as follows:
1 Spherical nodes:(a) solid(b) hollow.
2 Cylindrical.3 Prismatic.4 Plates.5 ‘Nodeless’.
Nodes based on a sphere are probably the most aes-thetically pleasing. Depending on the form of connectionof the adjacent members, they can provide a very clearand uncluttered appearance to the space grid. The class,which is taken to include ‘pure’ and faceted spheres, canbe further divided into solid and hollow types.
Materials and systems 31
3.1Typical node of tubular bamboo stem as studied by Dr MaxMengeringhausen (Photograph: John Chilton)
Solid spherical nodes
Solid cast steel spheres are drilled with threaded holesat the appropriate angle for connection of the adjacentmembers and are machined to provide appropriate bear-ing surfaces. The attachment of each member is usual-ly achieved with a single bolt on its central axis. In somesystems the ends of the members come into direct con-tact with the nodes, whilst in others the axial forces aretransmitted solely through the connecting bolts. The rep-resentative systems described in this section are (MeroKK, Germany, and Orona SEO, Spain).
The Mero KK space truss system, the first commercial-ly available, is still considered to be one of the most ele-gant solutions for the construction of space grid struc-tures. The elegance and simplicity of the Mero system
means that it is not only used in buildings but also forshop displays and exhibition stands using lightweightmaterials. Circular tube members are connected to cast‘ball’ joints at the nodes by a single concealed bolt foreach tube. The concept developed from studies of nat-ural structures, carried out in the 1930s, by the system’soriginator, Dr Max Mengeringhausen. His investigationof slender but strong natural structures such as wheatstalks and bamboo stems (Figure 3.1) revealed how theyderive their strength from the use of tubular cross-sec-tions stabilized by nodes at regular intervals along theirlength. The name Mero, by which the system is now wellknown, derives from an abbreviation of the original nameMengeringhausen Rohrbauweise.
Initially conceived as a system based on a fixedmodule, the Mero space truss had a universal node con-nector and a series of standard length members, startingat 1 m and progressing with a factor of √2 between
32 Space Grid Structures
3.2(a)Comparison of amodular structuralsystem and growth innature: Meromembers with afactor of √2 betweensequential sizesradiating from acentral node(Drawing: JohnChilton)
3.2(b)Comparison of amodular structuralsystem and growth innature: sectionthrough a Nautilusshell (Photograph:John Chilton)
sequential sizes (i.e 1.0, 1.41, 2.0, 2.82 m ... etc.). Thegrowth of member lengths drawn radiating from a cen-tral node creates a spiral form (Figure 3.2(a)) that, asMengeringhausen pointed out, echoes the spiral growthof the Nautilus shell (Figure 3.2(b)). However, there arenow several different types of node connector availablefrom Mero for a range of applications, in single and dou-ble-layer space grids and members are fabricated to anyrequired length. The original ‘ball’ joint, now known asthe KK system, is a hot-forged solid steel sphere fin-ished with 18 threaded holes and machined bearing sur-
faces at angles of 45°, 60° and 90° relative to each other(see Figure 3.3). Standard nodes are produced in bulkin a range of sizes suitable for the transmission of mem-ber forces of different magnitude. Stock nodes, with fewerholes, are also produced for common applications suchas standard support nodes.
With modern computer numerically controlled preci-sion drilling techniques, holes may now be drilled atalmost any required angle rather than only at the stan-dard angles, although there is a minimum angle of 35°specified between adjacent holes. This ability to drill and
Materials and systems 33
3.3Standard Mero KKnode with 18threaded holes andmachined bearingsurfaces at angles of45°, 60° and 90°relative to each other(Photograph: GlynHalls)
3.4Mero standardmember tapered conesections welded toeach end (completewith connection boltand sleeve)(Photograph: JohnChilton)
tap threaded holes at non-standard angles gives thedesigner much greater flexibility in selecting the geom-etry of the space grid.
Standard members are circular hollow steel (or alu-minium) tubes that have tapered cone sections weld-ed to each end (see Figure 3.4). Integral with eachcone there is a connection bolt and a sleeve with slot-ted hole and pin to allow the bolt to be rotated and toindicate when it has been fully tightened. For corrosionprotection the tubes are galvanized inside and out, andfinishes include a polyester powder-coated or two-parturethane wet process. The Mero Holz system uses lam-inated timber members that have short tubular steelinserts at the ends for connection to the nodes (seeFigure 3.5).
The size of the connecting bolt between tubes andnodes depends on the forces to be transmitted. Tensionforces have to be transmitted from the member end coneto the bolt by the internal bearing surface of the cone,then through the bolt in tension to the threads in thenode. Compression forces, however, are transmittedthrough the sleeve surrounding the connecting bolt bydirect contact of machined bearing faces and the bolteffectively only locates the member in the correct posi-tion on the node. The form of the spherical joint is suchthat the line of action of all member forces intersect atthe centre of the node so there are no eccentricities toinduce bending in the tubes that carry primarily axial ten-sion and compression forces. Manufacturer’s tables areavailable to show the relationship between node, tubeand connecting bolt capacities.
Generally Mero space trusses are supported using avariation of the standard node connector, depending onthe type of restraint required. Figure 4.3, in the follow-ing chapter, shows one of the sliding bearings support-
ing the Mero space truss roof at the National IndoorArena for Sport, Birmingham, UK.
As one would expect for a system has been in usefor over fifty years, there are, worldwide, thousands ofexamples of Mero space grids, both large and small.Nowadays, there are alternative node joints and mem-ber cross-sections to suit various applications such asdirect glazing of single-layer dome grids. However,single-layer grids, and therefore many of these new appli-cations, are beyond the scope of this study which isprimarily concerned with double or multi-layer grids. Oneof the most dramatic uses of the Mero system is for thegrandstand roofs at the stadium in Split (see the planand section shown in Figure 3.6). Constructed in 1978,in former Yugoslavia (now Croatia), these roofs are seg-ments of a 452 m diameter cylinder inclined at 11.2° tothe horizontal. The free edge spans 215 m with an arclength of 220 m (Figure 3.7). Together the two areas ofspace grid cover approximately 13 600 m2 with a dou-ble-layer square on square offset system, having griddimensions of 3.0 � 3.0 m, a structural depth of 2.3 mand a maximum cantilever of 45 m from the ellipticalperimeter of the stadium. The two areas of roof are sym-metrical only about the long axis of the stadium; thusthere are 12 832 members of 1143 different types and3460 nodes of 1678 types (839 configurations mirroredbecause of the symmetry). Translucent polycarbonatebarrel-vaulted ribs run parallel to the top chords of thespace grid from the perimeter to the free edge, with sec-ondary framing supported only at the nodes.
There are now worldwide many space truss systemsbased on the concept of cast ball joints and tubular mem-bers. For instance, the ‘TM Truss’ produced by TaiyoKogyo Co. in Japan, and ‘ABBA Space’ produced byABBA Space Structures in South Africa. The variation is
34 Space Grid Structures
3.5Mero Holz metalinsert to the ends oflaminated timbermembers (Redrawnfrom Mero technicalliterature: JohnChilton)
Materials and systems 35
3.6Plan and section ofthe Mero grandstandroofs at the stadiumin Split, in formerYugoslavia (nowCroatia). These roofsare segments of a452 m diametercylinder inclined at11.2° to the horizontal(Courtesy Mero)
3.7Mero grandstandroofs at the stadiumin Split, Croatia with afree edge spanning215 m with an arclength of 220 m(Photograph courtesyR. E. McConnel)
mainly in the method of connection between the tubeends and the ball joints, although some systems are veryclose to the original Mero system.
The Orona SEO space grid manufactured by Orona S.Coop., San Sebastián, Spain, is a ball and tube systemthat was introduced in the 1980s and used for the roofof the Sant Jordi Sports Palace, constructed in Barcelonafor the 1992 Olympics.
In the SEO system, the solid forged spherical joint hasa number of threaded holes, drilled according to the nodelocation within the grid and the geometry of the con-necting members. The number and position of the holesis limited only by the interference of adjacent connect-ed bars. Truncated conical end pieces are welded to thenormally cold-formed, longitudinally welded, steel tubemembers. The cones hold the connecting bolt which hasa hexagonal shank for the section near to the head anda normal plain/threaded section for the rest of the boltshank (see the typical section shown in Figure 3.8). Acapping sleeve, that maintains the correct distancebetween the end of the member and the node, surroundsthe hexagonal and the plain shank section of the bolt.The inner profile of the sleeve follows that of the boltand the outer profile also has hexagonal and plain sec-tions. To tighten the bolt, the hexagonal part of the sleeveis rotated so that the threaded length of the bolt entersthe node. This connection system allows any bar to beremoved easily from a completed grid at any time. Byunscrewing the sleeves at both ends of a member, thebolts retract inside the tube sufficiently to enable itsremoval and replacement. Thus damaged bars can berestored or it may be possible to increase the load capac-ity of a grid by upgrading the most critically loaded ele-ments.
During manufacture, the tubular members are assem-bled complete with end cones, bolts and sleeves, on anadjustable bed, ready for welding. The overall length ofthe component is fixed on this bed by the correct posi-
tioning of the end bolts so that tolerances in the indi-vidual member parts do not lead to accumulated errors.Following welding the length of each bar has a toleranceof ± 0.5 mm. The threaded holes in the spherical nodesare drilled and machined by a purpose-designed robotthat can be programmed manually, but is generally con-trolled by numerical data produced by post-processingof the structural analysis. A list of materials, node sizesand hole geometry, bars sizes and lengths is presentedin a form that can be read by the numerical control (NC)machines.
Normally an electrostatic polyester powder-coating fin-ish is applied to the tubes with a minimum thickness of70 microns. This is oven cured at 210 °C for twenty min-utes. A minimum surface treatment of degreasing andphosphating is applied prior to the application of the coat-ing. Further pre-treatments such as mechanical brush-ing, shot-blasting and galvanizing may also be applied,depending on the degree of oxidation of the surface andthe corrosion protection specified. The polyester finishhas good impact and scratch resistance and producesa lacquer-like surface. For the small diameter spheresthe same process as that used on the tubes can beapplied, however, with large diameters the greater thick-ness of the node material creates problems. Therefore,the larger nodes are shot-blasted, primed and then fin-ished with a two-coat epoxy or chlorinated rubber paint.
Hollow spherical nodes
Hollow spherical nodes are of two general types. Someare cast hollow as almost complete spheres and theseare subsequently pierced by drilled or punched holes inpredetermined locations (e.g. Spherobat, France; NSTruss, Japan; Tuball, Netherlands; Orbik, UK). Othersare composed of two pressed steel approximate hemi-spheres with or without an intermediate central disc (e.g.SDC, France; Oktaplatte, Germany; Vestrut, Italy; Nodus,UK). In the former type, connecting bolts are introducedthrough an access hole and screwed from inside thesphere into the adjacent members. Subsequently the
36 Space Grid Structures
3.8Section through atypical Orona SEOspace grid joint(Courtesy Orona S.Coop., San Sebastián,Spain)
access hole may be closed with a cap. In the latter case,there are various means of connection of the members.For example, Vestrut uses two near hemispherical partsand intermediate plates to clamp solid ‘T’-shaped con-nectors that are welded to the ends of the members.
The Nodus system, a ‘piece-small’ space truss, wasdeveloped during the late 1960s by the Tubes Divisionof the British Steel Corporation and introduced com-mercially in the early 1970s. Since 1985, Nodus hasbeen owned by Space Decks Ltd of Chard.
During development of the system, a series of stan-dard joints were evolved. Samples of each size and typeof joint were tested to failure, in purpose-designed test-ing rigs, at the British Steel Research Centre in Corby.Two series of tests were undertaken, the joints beingmodified after the first series in order to improve theirperformance. The second series confirmed the improve-ment and allowed strength design charts to be compiled.Following the laboratory tests a complete 30.5 by 30.5 mspace grid 1.52 m deep was fabricated and assembledby an independent company to ascertain the ease ofconstruction. A test load of 1.8 kN/m2 (equivalent to thedesign dead load plus 1.5 times the design imposedload) was applied to the structure for twenty-four hours,in accordance with the then current British Standard forsteel structures, BS 449. The residual strains measuredafter the test were well within the limits specified in thestandard.
The Nodus joint (Figure 3.9) uses a relatively complexassembly of parts. Special cast steel end connectors arebutt-welded to the chord and web bracing members infabrication jigs, to ensure dimensional accuracy of thespace truss components. The node itself is composedof two half-casings (one plain and one with lugs forattachment of the web bracing, Figure 3.10) and a spac-ing piece. Those are joined using a single high-strengthfriction grip bolt, nut and washer. As the bolt is tightenedthe ribbed end connectors of the chord members areclamped between the two half-casings. Web membersare joined by steel pins through the forked end connec-tors of the bracing to the lugs on the node casing.Standard edge joints are also produced. Two configura-tions of lug are available, one for connection of the brac-ing members on the same grid lines as the chords andthe other with the bracings oriented at 45° to the chordgrid. The plain casing has a hexagonal recess to receivethe bolt head so that it does not protrude above the levelof the top chord members, thus enabling decking to befixed directly to the chords where square hollow sectionsare used. Therefore, there can be a saving as secondarypurlins may not then be required. A result of the jointconfiguration is that chord members can be considered
continuous for local bending due to the decking loads.This reduces the magnitude of design bending momentsin the chords, but they must still be designed for thecombined effect of local bending and axial forces.
Four standard joints (reference 24, 30, 35 and 45) usehalf-casings of different size related to the chord sectiondimensions. The smallest joint (reference 24) is used forcircular hollow section (CHS) chords 60.3 mm in diam-eter and rectangular hollow section (RHS) chords 60 by60 mm, whilst the largest joints (reference 45) accom-modate circular sections of 114.3 mm diameter and rec-tangular sections 120 by 120 mm. Circular CHS in sec-tion bracing members have a minimum size of 42.4 mmfor all joints, whilst for rectangular bracings the minimumsize is 40 by 40 mm (except for joint type 45 where theminimum is 50 by 50 mm). The maximum sizes of brac-ing members that can be accommodated respectively bythe standard joints are 60.3, 60.3, 76.1 and 88.9 mmdiameter for CHS and 50, 60, 80 and 90 mm for RHS.
Pinned connection of the bracing members permitsvariation of the space frame depth limited only by therequirements of structural efficiency or interferencebetween members at the joint. A consequence of thegeometry of the joint is that the centrelines of bracing
Materials and systems 37
3.9The Nodus node joint developed by British Steel Tubes Division,now British Steel Tubes & Pipes (Courtesy Space Decks Ltd)
members and chords do not intersect at one single pointwithin the node thus generating small secondary bend-ing moments within the grid. The smaller the anglebetween the diagonal bracings and the plane of thechords, the greater is the eccentricity of the two inter-section points. Consequently, the secondary momentsare greater and the grid becomes less efficient.
Because the joints are only produced with two lug ori-entations, the possible grid configurations are limited tovariations of the square on square, square on squareoffset, or square on diagonal square layouts. Within thislimitation it is still possible to generate slightly cambered,barrel-vaulted and domed structures using the standardjoint. The use of Nodus in the National Exhibition Centrein Birmingham, UK, and the atrium roof and entrancecanopy of Terminal 2 at Manchester Airport, UK, aredescribed in detail in Chapter 5.
The most well known solid cylindrical node is that of theTriodetic system. This consists of an extruded alumini-um section with longitudinal slots into which the crimpedends of the hollow tubular bars are slotted. Clampingretains the bars in position between two end plates heldby a single bolt passing through the centre of the node.A similar type of node made from steel has been usedby Triodetic.
The Triodetic system of space grid construction is alsoa ‘piece-small’ system but uses a totally different con-cept for the connection of the individual members at thenodes. Developed during the 1950s by Fentiman Bros.of Ottawa, Canada, it was introduced commercially in1960. Recognizing that the key problem in space gridsis the efficient and simple connection of many elementsat the nodes, experimental assemblies and nodes wereproduced based initially on the ‘dovetail’ joint used intimber construction. However, the eventual solution camefrom H. G. Fentiman’s5 observation of the effectivenessof the gripping jaws in tensile testing machines. He rea-soned that, by providing matching indentations in thetubes of the space grid and in the node components, anefficient joint would result. The flattening (or coining) ofthe tubes does not remove any material and thus main-tains the strength of the cross-section.
This is one of the few systems that predominantly usesaluminium as the material for the bars and nodes, andwas developed at a time when there were restrictionson the use of steel in Canada. Circular drawn or seam-welded tube members have their ends crimped with acorrugated profile at the appropriate angle for connec-tion to the node and, at the same time, the membersare cut to the correct length with a tolerance of± 0.13 mm. Nodes (or hubs) are extruded in generallycylindrical sections with longitudinal profiled slots ready
38 Space Grid Structures
3.10Typical node castingsfor standard Nodusjoints (Photograph:John Chilton)
to receive the crimped ends of the members (see Figure3.11). Once all the members have been slid into placein the slots of the node, a bolt is passed through a cen-tral longitudinal hole and is tightened to hold retainingplates at each end of the cylinder. This is a very simplemethod of assembly but requires high precision in themanufacture of the nodes and members. At the time ofthe initial development of the system, the tolerances inthe standard aluminium extrusion processes did not pro-duce hubs of the necessary precision and improvedmethods of extrusion die production had to be estab-lished.
Although the system was originally developed with alu-minium tubes and hubs, in subsequent developmentsteel tubes have been used in combination with alu-minium hubs. With correct selection of materials andsuitable paint finishes it is possible to combine alumini-um and steel without encountering the usual problemsof electrolytic action between the two metals.
Flat or pressed plates are frequently used as the nodeconnectors in lightweight systems composed of cold-rolled steel channels (e.g. the original Unistrut, nowcalled Moduspan, USA). They are also used as con-
nectors in the timber roundwood pole space grids devel-oped by Pieter Huybers at TU Delft, in the Netherlandsdescribed in Chapter 5.
Moduspan (formerly Unistrut)
Moduspan market a variety of ‘piece-small’ space trusssystems, of which System I is the current version of thesystem originally invented and patented by Charles W.Attwood. In the basic system, five standard components,as shown in Figure 3.12, are assembled by simplebolting. There are two types of node connector bothpress-formed from 6 mm thick hot-rolled steel plate andhaving punched shear lugs and bolt holes for connec-tion of the members. The ‘in-strut’ connector, used in thetop layer of the grid, has lugs located on the inner facesof its diagonal planes while the ‘out-strut’ connector, usedin the bottom layer, has lugs located on the outer facesof its diagonal planes. Members having standard mod-ular lengths of 1.22 m and 1.52 m connect the nodesand the same members are used for the chords anddiagonals. These members are roll-formed 12 gauge(0.27 mm) thick hot-rolled steel in a lipped channel sec-tion, typically 41.3 mm wide by 41.3 or 61.9 mm deep,with holes punched near the ends for bolting to the nodesand to provide the necessary shear connection. The lasttwo standard components are a high-strength steel bolt
Materials and systems 39
3.11Triodetic nodes (orhubs) are extruded ingenerally cylindricalsections withlongitudinal profiledslots ready to receivethe crimped ends ofthe members(Photograph courtesyGlyn Halls)
(which has a shoulder to act as a shear lug) and a steelnut with counter-bored hole (to receive the shoulder ofthe bolt).
In addition to these five basic components, there arereinforcing struts to increase the capacity of the stan-dard members in highly loaded locations (such as adja-cent to columns), bearing seatings to transfer the loadfrom the space grid to the supporting structure, half con-nectors to accommodate abutment against a wall or the
use of a vertical fascia, etc. An example of the use ofModuspan for an entrance canopy at the Georgia Dome,Atlanta, is shown in Figure 3.13.
Because the special separate node components usual-ly represent a considerable proportion of the cost of a
40 Space Grid Structures
3.12Typical Moduspan(Unistrut) nodeshowing the cold-formed membersbolted to the nodeplate (Photograph:John Chilton)
3.13Entrance canopy,Georgia Dome,Atlanta, USA, usingModuspan(Photograph: JohnChilton)
space grid, some systems eliminate these completely,relying instead on direct connection between the endsof the grid members. Although this saves in overall cost,it tends to limit the possible configurations of the grid asthe end connections of members are often designed toaccommodate standard angles between the parts.
The Octet Truss developed by Buckminster Fuller,used extruded members with an X cross-section and withthe ends cut at the angles appropriate for tetrahedraland octahedral geometry (70.53° and 109.47° respec-tively). In the Multi-hinge system developed in the USAby Peter Pearce, fin plates with pre-drilled bolt holes arewelded to tubular members for assembly in predeter-mined configurations. An example of the use of the sys-tem is for Biosphere 2, in Arizona, USA, which isdescribed in Chapter 5.
Continuous chord systems
Systems with continuous chords could be considered asa halfway stage between the ‘piece-small’ and modulartypes as, although they are assembled from relativelysmall pieces, they generally have no special node com-ponent. The Unibat and SPACEgrid systems describedbelow, to some extent use continuous chords for the bot-tom layer of the grid. However, there are other systemsthat use both top and bottom chords that are continu-ous through the node joints. Although this can some-times lead to eccentricity of member forces at the joints,that in turn produce secondary bending in the members,
there are also benefits: there are no expensive nodes,fewer components are necessary and chords can bejoined by simple splices at positions between the chordintersections.
The Harley system was introduced into Europe by ConderGroup plc in 1989. It was manufactured under licencefrom the patent holders in Australia where it has beenavailable since 1980. After preliminary trials and the con-struction of a test structure, it was estimated that the sys-tem was highly competitive against more traditional por-tal frame construction for industrial and storage buildings.The series 80 Conder Harley space truss system is suit-able for structures with plan areas of 250 m2 upwards.
There are fundamental differences between this andthe other space truss systems described above. Thechord members are made from cold rolled steel contin-uously formed and cut to lengths up to 12.5 m. Therefore,in general, the chord members pass through the inter-sections with the diagonals rather than being broken bya separate nodal connector. To achieve this, the chordsin orthogonal directions are placed in slightly differenthorizontal planes. For instance, ‘C’ section chords canbe set back-to-back, thereby avoiding direct intersectionof the members. Web bracing members are circular tubesections. At each end they are crimped, bent to therequired bracing angle and drilled for bolting to the chordintersection. A typical joint layout is shown in Figure 3.14.
Materials and systems 41
3.14A typical Harley Type80 node joint(Photograph: JohnChilton)
As the centroids of the chord sections do not passdirectly through the centre of the node, neither do themember axial forces. There is, therefore, an eccentrici-ty inherent in the Harley Series 80 connection that gen-erates bending moments in the grid elements. These aredealt with by local reinforcement at the joints.
Manufacture from cold-formed strip allows productionof elements ranging in thickness from 1.5 to 8 mm in awide variety of chord profiles. Chords are cut to lengthand precision drilled for bolting at the predeterminedintersection points with a tolerance of (± 0.5 mm). TypicalUK grid dimensions are around 3 m in plan. For long-span applications, the Harley system is adaptable foruse in multi-layer grids or, alternatively, the basic mem-ber section sizes can be increased and a greater gridspacing adopted.
Mai Sky System
The patented Mai Sky System resulted from a desire toproduce an economical method of space grid construc-tion. Top grid geometry is square or rectangular with anoffset bottom layer. Chord members in one direction arecontinuous and have angled fin plates, with pre-drilledbolt holes, shop-welded to them at intervals appropriatefor the grid geometry. In the orthogonal direction thechords are discontinuous and have profiled end/fin plateswelded to them. These match those of the continuouschords. Diagonal bracing members have simple end finplates. Generally, square or circular hollow tubular sec-tions are used for all members. Figure 3.15 shows thetypical Mai Sky System joint.
Assembly of the system is by site bolting and is usu-ally carried out at ground level. The continuous chordsof the bottom layer are laid out and automatically spacedby connection of the discontinuous chords sections inthe orthogonal direction. At the same time as the chordsare bolted together, the diagonals are fixed between theangled plates. A similar process is used for the assem-bly of the top layer of the grid.
A continuous edge beam is normally used to supportthe grids at the top layer nodes. This is in turn support-ed on columns at intervals suitable to limit deflection ofthe grid supports. The roof decking and preliminary ser-vice installation can be carried out before the grid is lift-ed into position by crane.
Catrus is described as ‘a low-cost answer to the prob-lems of traditionally expensive structural systems’.6
Developed by Dr Ahmed El-Sheikh, of DundeeUniversity, in Scotland, and recently introduced in the
UK, it is now licensed to Technitube, in South Yorkshire.Primary considerations in the development of the trusssystem were low-cost, reliability and construction bene-fits. Research by Dr El-Sheikh showed that there wasonly limited use of space trusses mainly due to cost of‘node connectors to provide the concentric member con-nections’.7 Usually, such systems are sophisticated,expensive and cost more than simple beams or frames,even though the latter might require the use of morematerial. Space trusses are also vulnerable to ‘brittle’behaviour (i.e. they can in some cases collapse with lit-tle or no warning due to the failure of one or two mem-bers) and they also require good dimensional tolerances.However, they do benefit from lightness, high stiffness,ease of manufacture and ease of assembly. It is esti-mated that Catrus offers more strength and ductility thanmany other space truss systems. The eccentricitiesinherent in the node connections provide ductile failuremodes for the grid elements, which provide a betterreserve of strength after the initial buckling of a mem-ber and increased warning of failure.
42 Space Grid Structures
3.15Typical Mai Sky System joint (Courtesy Mai Sky Inc.)
The system uses rectangular hollow section (RHS)top chords, tubular diagonals (with flattened and bentends) and flat steel strip lower chords. Both the upperand lower chords run continuously across the node jointswhich are assembled using simple bolted connections(obviating the need for a special node joint). The RHStop chords are drilled on the centreline of the cross-sec-tion and, as can be seen in Figure 3.16, the connect-ing bolt passes vertically through the two chord mem-bers and the flattened and drilled ends of the four webbracing members. Chord members are produced inlengths to suit the particular grid dimensions of the spacetruss and they are spliced at suitable locations, usual-ly midway between the nodes. This maintains membercontinuity and stability, and simplifies joint details. Thesplices in the top (compression) chords use a shortlength of a larger-section RHS (with the top faceremoved to form a U section), which is then bolted to
both chord sections. Bottom chord splices can be madein three forms; by clamping the two chord sectionsbetween two short jointing plates; by a simple lappedsplice (with no additional cover plates) or, at the bottomnodes; by using a flat jointing plate. In proving tests dur-ing development of the system, splices with just twobolts were found to be as effective as those with fourbolts and the members to be almost as efficient as anunspliced chord. Introduction of the splices produced anobserved reduction in strength of 2 per cent and in stiff-ness of 12 per cent compared to fully continuous mem-bers.
There is more variation in the form of the modular unitsthat distinguish different prefabricated types. The square-based pyramid is the most common modular unit and isused to construct space trusses, however, other modu-lar systems, may, once assembled, form rigid-jointedspace frames. Modular systems may also use angle,channel, Universal Beam, or Universal Column sectionsfor the bars or members, as these are often cheaperthan hollow sections. Such sections can be connectedby simple bolting and welding.
Some space grid systems take advantage of the ben-efits of prefabrication to produce larger-scale modulesthat can be simply bolted together on site. This reducesthe amount of site assembly, speeding the erectionprocess. Depending on the shape of the module, theremay be an increase in transportation cost as some mod-ules can be stacked and nested easily (e.g. the square-based pyramids or half-octahedra of Space Deck, asshown in Figure 3.20) whilst others (e.g. CUBIC SpaceFrame modules, shown in Figure 3.28) require morespace.
Typically, the Unibat, Space Deck, ABBA Dekspaceand Mero DE systems use pyramidal modules, usuallyconsisting of angle or channel sections welded togetherto form a square base frame for the pyramid. Tubularweb elements are then welded to each corner of theframe on the diagonal and are also welded to a centralboss or connector. Straight bars or tubes are then usedto join the pyramid bosses to form the bottom chords ofa three-dimensional grid.
Other systems may use flat truss modules of differentconfiguration that can be assembled in a variety of ways,depending on the system. For instance, it is possible toform a two-way square on square space grid from basicflat rectangular truss modules connected by plate nodesin the upper and lower grids. The CUBIC Space Framedescribed below uses modules with upper and lowerchord configurations, T- or L-shaped in plan.
Materials and systems 43
3.16The connecting bolt of the Catrus passes vertically through the twochord members, and the flattened and drilled ends of the four webbracing members. Top members are spliced using a tight fittingchannel piece cut from an RHS whilst bottom members have asimple lap splice. (Courtesy A. El-Sheikh)
Modular space trusses
Space Deck (Figure 3.17) is a modular system that wasdeveloped in the early 1950s by Denings of Chard,UK.There are thousands of examples of Space Deck struc-tures all over the world, as the modular system has beenavailable for almost fifty years in essentially the sameform, with only minor changes in materials and metrica-tion of module dimensions.
The system is based on pyramidal units that areassembled from a square frame of steel angles con-nected by circular steel tube bracing members to a cen-tral cast steel boss. All elements of the pyramids arewelded together in a fabrication jig to ensure consistentdimensional accuracy. The cast boss at the apex of thepyramids (Figure 3.18) has a threaded hole on each sidein one horizontal direction and a threaded stud protrud-ing from each side in the orthogonal direction. High-ten-sile steel rod tie bars are used to connect the bosses ofadjacent pyramids. In one direction of the lower grid thetie bars have threaded ends (one left-hand and one right-hand) which screw directly into the tapped holes in thepyramid bosses. Tapped hexagonal coupling pieces areused at the ends of tie bars in the other orthogonal direc-tion to screw on to the protruding studs of the bosses.
Standard modules are produced having grid dimensionsof 1200 � 1200 mm with depths of either 750 or 1200 mm,1500 � 1500 mm with depths of 1200 and 1500 mm and
also 2000 × 2000 mm with a depth of 2000 mm. Differentstrength modules are available within the same overalldimensions. The variation in strength is in the size of brac-ing members, the stronger sections being used mainly toaccommodate the high shear forces present in the spacetruss around column supports. By its nature, assembly ofa Space Deck grid produces a cornice edge profile (asthe standard modules are inverted pyramids). Therefore,in addition to the stock modules, standard half-modulesare available to give a mansard edge where required.Special pyramid modules with varying grid dimensions arealso available, made to order.
During manufacture of the modules the top frameangles are cut to the required length, mitred and havethe holes for connecting bolts punched into what will bethe downstand leg of the frame. Diagonals are also cutto length with ends at the appropriate angle for subse-quent welding to the top frames and forged steel boss.The cast bosses are drilled and machined. All compo-nents are then degreased and the angles and diagonalsare also shot-blasted prior to the application of a paintor lacquer finish. Angles are then welded in a jig to pro-duce square frames that can either be used for the stan-dard modules or infill (top chord) trays in sparse grids,where some of the pyramidal units are omitted (usuallyon a chequer-board pattern). Standard pyramid modulesare assembled from an angle tray, boss and four diag-onals, in a jig, to close dimensional and angular toler-ances, and welded together.
44 Space Grid Structures
3.17Space Deck modules and connecting bars (Courtesy Space DecksLtd)
3.18Cast boss at the apex of the Space Deck pyramids (Photograph:John Chilton)
To assemble the Space Deck, the upper frames of thepyramids are bolted together through the downstand legsof the angles. The cast steel bosses are then joined withthe tie bars. Because of the combination of opposingscrew threads at each end of the tie bars, rotation of thebar screws it simultaneously into the boss (or on to thestud) at each end. This allows the distance betweenlower node centres to be easily adjusted to produce asmall camber in one or both directions; thus a slightlydomed or barrel-vaulted surface may be generated. Thefinal grid has a square on square offset configuration.
Space Deck grids can be supported at either the topor bottom layer either on a regular pattern or at random.Typical span to depth ratios are around 25 to 30 for fulledge supported roofs, although these ratios must bereduced if the roof is only supported at the corners.Cladding may be fixed directly to the space truss mod-ules that provide convenient support at 1.2 m, 1.5 m or2.0 m centres across the whole upper layer of the grid.Normally, a Space Deck roof has a perimeter angle trim-ming member but in situations where the overall plandimensions of a building do not relate directly to the stan-dard module dimensions, perimeter channels up to
Materials and systems 45
3.20Efficient stacking of Space Deck modules (Photograph: JohnChilton)
3.19Typical edge and glazing fixing details for Space Deck modules(Courtesy Space Decks Ltd)
200 mm wide or perimeter trays up to 375 mm wide canbe added. Some typical edge and glazing fixing detailsare shown in Figure 3.19.
Transportation of the Space Deck space truss is veryeconomical as the standard lightweight modules are eas-ily stacked together (Figure 3.20) and the tie rods aresimply bundled together. Large areas of Space Deck canbe carried on one standard lorry trailer.
The advantage of a lightweight modular roofing systemsuch as Space Deck is demonstrated by the project shownin Figure 3.21 where a new roof was installed over anexisting 6400 m2 area for PSA Projects, Edinburgh.Construction of a new slightly pitched roof over the exist-ing flat roof of limited load capacity was a problem. Tocarry out such a project in only eight weeks, over such alarge area, where cranage was difficult and the work hadto be carried out whilst the building was still functioningas normal, demanded the use of a lightweight modularstructure where the standard components were readilyavailable. The space truss was able to accommodate tothe irregular column grid of the existing structure and towork within the remaining load capacity of the existingcolumns.
Unibat and SPACEgrid
One of the great innovators in the field of space gridstructures was architect/engineer Stéphane du Château.Following a system of gradual development and refine-ment, his Unibat system appeared in 1962. It also iscomprised of pyramidal modules with rigid frames form-ing the upper chord layer, but in this variation, high-ten-sile steel bolts are used to connect the upper frames ofthe modules through their corners only. This is a much
46 Space Grid Structures
3.21Space Deck used fora new roof installedover a 6400 m2 areaof existing roof forPSA Projects,Edinburgh(Photograph courtesySpace Decks Ltd)
3.22ABBA Cubicspace system used for a multi-layer grid at theHighgate Shopping Centre, Johannesburg, South Africa(Photograph courtesy ABBA Space Structures)
simpler and quicker method of assembly and conse-quently leads to economies in erection time and costs.
SPACEgrid is a space truss modular system that wasdeveloped by Ronald G. Taylor from the Unibat systemthat he originally developed together with S. du Château.To refer to SPACEgrid as a system is perhaps a mis-nomer as there is no standard module or joint, thesebeing considered unnecessary restrictions for both engi-neering and architectural design. It is based on the con-cept that the most economical grid should be selectedaccording to the plan dimensions and loading. Further,that the most economical member sections, hot-rolled orcold formed steel or alternatively aluminium, should bechosen depending on the member forces present.Finally, it is considered that the joints should be designedspecifically to suit the chosen grid layout and the sizeand section of the members that have been selected.
The most common grid used by SPACEgrid is thediagonal square on square using, as with Unibat, pyra-midal modules that are often connected by only a sin-gle bolt at the corners of the upper grid. Bottom chordsmay be individual bars between the lower nodes or, inpreference, continuous members. This reduces the prob-lems associated with connecting several elements in ten-sion at each node as, with continuous chords, the con-nections do not necessarily have to be designed for thefull force in the chord (only for the portion of the chordforce transferred to or from the diagonals at the node).
Since 1983 ABBA Space Structures of Jeppestown,South Africa, have developed several ‘substructure’ sys-
Materials and systems 47
3.23ABBA Cubicspace system with patented Octanode connection (Photograph courtesy ABBA Space Structures)
3.24ABBA Dekspace system used for a space truss barrel vault at theSouthgate Shopping Centre, Johannesburg, South Africa(Photograph courtesy ABBA Space Structures)
tems of space truss construction. The high cost of tra-ditional space grids of linear members connected by auniversal node encouraged A. H. Noble to search foreconomic alternatives.
Cubicspace was developed by ABBA in 1983 and con-sists of square and triangular sub-frames that areassembled to form square on diagonal grids. At theHighgate Shopping Centre, Johannesburg, South Africa,in 1985, the Cubicspace system was used to constructa multi-layer space grid (Figure 3.22) and in 1986 thesame system was used for a Geotechnic Centre built forGold Fields. Individual space grid units in the secondstructure were connected using the patented Octanode(Figure 3.23) which was originally conceived as an octag-onal cylinder with top and bottom plates. By splitting theoctagon in half it became possible to preassemble man-ageable sub-units on the ground, ready to be craned intoposition and connected into the structure later.
The Dekspace system, introduced in 1987, consists ofpyramidal units with angle top frames and tubular diag-onals, and was first used for a 32 m diameter barrel vaultat the Apostolic Faith Mission at Vereeniging. As in theoriginal Space Deck system, the pyramids are boltedtogether through the angle frames but in this case theyare connected by tubular members in the lower grid.Consisting of two separate barrel vaults, each terminat-ing with a semi-dome and separated by an office block,the structure is known locally as the ‘Hot-Dog’ Church.Assembled in two halves, the barrel vaults were hingedat the supports, swung into position and spliced in theair along their centreline, whilst the semi-dome sectionswere built in successive layers from the ground up.
A 67.5 m long, 15 m diameter barrel vault was alsoconstructed, using Dekspace, at the Southgate ShoppingCentre, Johannesburg (Figure 3.24). The space trussvault, constructed from around 2000 apparently identical
pyramids, is supported on walls also of space grid. Thewhole structure is supported on only four pairs of columnsand has a maximum clear span of 30 m along the axis
48 Space Grid Structures
3.25Detail of special ‘passthrough’ chords forthe Dekspace spacetruss barrel vault atthe SouthgateShopping Centre,Johannesburg, SouthAfrica (Photographcourtesy ABBA SpaceStructures)
3.26ABBA Spider Frame module and connection details (CourtesyABBA Space Structures)
of the vault. In order to keep the number of pyramids toa minimum, and to maintain the bottom chords parallelto the top chords, it was originally envisaged that thelower chords would form a cruciform. Problems of geom-etry at the junction between the barrel vault and the ver-tical walls meant that these crossed members did notintersect directly. The solution was to allow one bar topass through a hole in the other and this arrangement(Figure 3.25) was, in the end, adopted for the wholestructure. Cruciform units were, therefore, replaced bytwo straight tubular members.
Most recently, Spider Frame has been developed andused in a few small projects, e.g. a single beam 12 mlong and 1.2 m deep at the Johannesburg GermanSchool and an entrance canopy composed of four 14.9 mlong beams, 1.36 m deep connected side by side. Thislatter structure includes a 6.8 m cantilever and is cov-ered with Ferrari Architectural Fabric. Based on cubicscaffolding, the spider units have eight arms extendingfrom a tubular section node out to the vertices of a cube.The units are then joined end to end by connecting thearms and threading them on to longitudinal rods (Figure3.26). It is envisaged that the concept could easily beapplied to other close-packing solids.
Modular space frames
CUBIC Space Frame
Developed during the late 1970s by Leszek Kubik andhis son Leslie, the CUBIC Space Frame system is mar-keted by Kubik Enterprises. As this is a modular system
containing no triangulation, the applied loads are resist-ed by frame action and the chords and vertical mem-bers are subjected to bending moments and shearforces, in addition to axial forces. It is, therefore, a ‘true’space frame system.
The concept of the CUBIC Space Frame is based onthe method used by engineers in the past to calculate,by hand, the forces and moments in Vierendeel girders.These girders have top and bottom chords spaced apartand connected only by rigid-jointed, vertical webmembers. Therefore, as they have no diagonal webmembers, they have to rely on frame action for their sta-bility and strength. Approximately halfway between eachof the verticals in the Vierendeel girder, there is a pointof contraflexure (zero bending moment) in the top andbottom chord members. In the original hand calculationmethods for the analysis of Vierendeel girders, fully rota-tionally free ‘pinned’ joints (that have zero bending resis-tance) were assumed to exist at the middle of each bayof the girder in order to simplify the solution of memberactions. If a double-layer grid is formed from a networkof intersecting Vierendeel girders arranged in two orthog-onal directions and physical ‘pin’ joints (rather than theassumed pin joints) are inserted in the upper and lowerchords midway between each chord intersection, the gridcan be broken down into similar modules that are ‘X’,‘T’ or ‘L’ shaped in plan. These are the basic modulesof the CUBIC Space Frame system (see Figure 3.27).Although the modules ‘nest’ together quite well for trans-portation when they are relatively small (Figure 3.28),larger modules, such as those used in the roof structureof the FFV Aerotech Hangar at Stansted Airport, UK,with chord lengths of 3.5 m and 2 m in the two orthog-
Materials and systems 49
3.27Standard CUBICSpace Framemodules of ‘X’, ‘T’and ‘L’ shape in planshowing typical nodeand spliceconfiguration(Drawing: JohnChilton)
onal directions, 4 m deep and weighing up to one tonne,are not so easy to handle or transport.
No special components are required to manufacturethe CUBIC Space Frame modules as they are assem-bled from standard hot-rolled steel sections and plates
welded together in a fabrication jig using standard cut-ting, drilling and welding techniques. In both orthogonaldirections, the fully welded node joint, which is assumedto be rigid, is at the point of maximum bending in eachmodule and it must also transfer the chord axial forces
50 Space Grid Structures
3.28CUBIC Space Framemodules nested fortransportation(Photograph: JohnChilton)
3.29CUBIC Space Frameroof for Hall 3 at theInternationalConvention Centre inBirmingham, UK(Photograph: DouglasTurner ConventionCentre JV, R.M.Douglas and TurnerInternational)
across the intersection. Consequently failure of the nodecould jeopardize the integrity of the structure. Therefore,the quality of welding at the joint must be well monitoredby non-destructive means (e.g., by ultrasonic testing).Welding of the lap plates at the mid-chord splice jointsmust also be well controlled. Final assembly of theCUBIC Space Frame is by site bolting of the lap joint(usually with high-strength bolts) in the upper and lowerchords.
The CUBIC Space Frame system was first used forre-roofing a rehearsal theatre 12 m � 20 m at TrentPolytechnic (now Nottingham Trent University), UK, in1979. Because it was a previously untried system, a fullload test was carried out to the then current BritishStandard, BS 449, at the fabricator’s works before deliv-ery to site. It is interesting to note that the contract waswon because the modular space frame could be assem-bled in situ, without heavy cranage. The cost of liftingthe originally proposed planar roof trusses over thefaçade of the existing building was more than the addi-tional cost of the space frame, including the load test.Since then, the CUBIC Space Frame has been usedsuccessfully to roof several building types, including fac-tory units and supermarkets where the absence of brac-ing members has allowed installation of plant, servicesand even offices within the depth of the space frame(see Figure 2.6 in the previous chapter).
The largest space grid constructed to date using theCUBIC Space Frame is the roof of a FFV Aerotech main-tenance hangar for Boeing 747 aircraft at StanstedAirport, near London. The design, fabrication and erec-tion of this building, completed in 1988, are described indetail in Chapter 5. In 1990 the system was used in Hall3 at the International Convention Centre in Birmingham,UK (Figure 3.29). The exhibition hall, a non-regular octa-gon in plan and approximately 55 m in span, was cov-ered by a CUBIC Space Frame capable of carrying apoint load of 30 tonnes at any of the nodes. Because of
the prominent position of the roof structure, a very highquality of detailing was used throughout for the fabri-cated nodes and splices.
A modification of the CUBIC Space Frame has morerecently been developed for medium-span composite floorconstruction in office buildings. This system exploits thefacility of service installation within the structural depththat is unobstructed by diagonal bracing or beam webs.
1 Ghavrami, K. and Moreira, L. E. (1993). Double-layerbamboo space structures. In Space Structures 4 (G.A. R. Parke and C. M. Howard, eds), vol. 1, pp.573–81, Thomas Telford.
2 Anon (1982). Concrete Space. Architects Journal,175(7), 20–1.
3 Anon (1982). Concrete Space Frame for DelhiExhibition Halls. RIBA Journal, 89(7), 50–1.
4 Gerrits, J.M. (1998). An architectomic approach tochoosing a space frame system. In LightweightStructures in Architecture, Engineering and Con-struction (R. Hough and R. Melcher, eds), vol. 2, pp.992–999, LSAA, Australia.
5 ‘Impressed by the gripping strength of the jaws ofthe testing machine on test specimens, he reasonedthat similar indentations on a node or connector ofsimilar strength should provide reasonable efficien-cy’ Fentinan, H. G. (1966). Developments in Canadain the fabrication and construction of three-dimen-sional structures using the Triodetic system. In SpaceStructures (R. M. Davies, ed.), p. 1074, BlackwellScientific.
6 Purvis, G. (1995). Cover price. Building, Number7911, 260(40), p. 68.
Materials and systems 51
The factors that affect the design and construction ofspace grids, such as, element structural behaviour, spanto depth ratios, support details, dimensional accuracy,pre-camber, cladding and glazing, erection, behaviour infire and behaviour under seismic loading are consideredin this chapter.
Element structural behaviour
The two most important structural consideration in thedesign of space truss elements are the buckling of com-pression chords and web bracing members, and thedesign of joints to effectively and efficiently transmit axialforces between the bars and nodes whilst minimizing
secondary bending effects. A diagram showing the typ-ical buckling failure mode of a corner-supported spacetruss is shown in Figure 4.1(a). Overloading of one topchord member may cause it to buckle and the force thatit was previously transmitting is then transferred to theadjacent top chords. These, in turn, may fail due to theextra loading until a full or partial ‘hinge’ is formed acrossthe whole structure and it collapses. Excessive shearload around the supporting columns may in a similar wayinduce progressive buckling of the web diagonals in com-pression (see Figure 4.1(b)). Space frames (with rigidnode joints and no diagonal bracing elements) have tobe designed for the bending moments induced by theframe action. In the majority of space truss systems, theconnection of member to node is effected so that the
4 Design and construction
4.1Buckling of compression elements in a corner-supported space grid (a) mid-span top chords and (b) web members near supports(Drawing: John Chilton)
axial forces pass through the centre of the joint, in orderthat secondary bending does not occur due to eccen-tricity of the forces. However, in some systems such asHarley (see previous chapter) the cold-formed channelsection chord members in the two orthogonal directionsin each layer are connected back-to-back. The line ofaction of the member axial forces is therefore displacedslightly from the centroid of the joint and secondary bend-ing effects have to be taken into account in the analy-sis and design.
Span/depth ratios for various supportconditions
It is difficult to generalize about the most economicalspan/depth ratio for space grid structures, as it is influ-enced by the method of support, type of loading and, toa large extent, on the system being considered. It hasbeen suggested by Z. S. Makowski1 that span/depth ratiosmay vary from 20 to 40 depending on the rigidity of thesystem used. Higher span/depth ratios can be achievedif all (or most) of the perimeter nodes are supported.However, the ratio should be reduced to about 15 to 20when the grid is only supported at or near the corners.
An optimization study carried out by René Motro2 con-sidered a square grid 25.2 m � 25.2 m supported at3.6 m intervals along the full perimeter, with the objec-tive of minimizing the self-weight of the grid. Seven dif-ferent grid configurations were studied with span/depthratios ranging from 9 to 35. Although there was a dif-ference in self-weight of 35 per cent between differentconfigurations, the study concluded that the optimum grid
depth was approximately 1/15 of the clear span in allcases. However, it must be remembered that in termsof overall economy of the roof construction the minimumself-weight of the grid may not be of prime importance.For example, when there is a planning restriction on theoverall height of a building, minimum depth might be theoptimum solution.
Manufacturers usually supply tables of typicalspan/depth ratios, for their products, with different sup-port conditions and a range of representative loadings.Span tables produced by Space Deck Ltd indicate that,for typical roof loadings in the UK, span/depth ratios ofabout 30 are possible using their standard modules. Forexample, a Space Deck roof supported on all edges,with a total imposed, decking and services load of1.30 kN/m2 in addition to its own weight will span up to39 � 39 m with a module only 1200 mm deep.
Support details and thermal movement
Space grids usually form structurally rigid plates, there-fore it is important that any potential movements are suit-ably accommodated in the support details. As with themajority of structures, this is usually achieved by the pro-vision of an appropriate combination of fixed and slidingbearings. Sliding bearings usually incorporate polytetra-fluorethylene (PTFE) surfaces fixed to separate parts ofthe bearing assembly in such a way that they are freeto slide relative to each other. Guide plates at the sidesusually restrict the movement to one direction and lip-ping of the bearing plates ensures that the two parts ofthe bearing cannot normally be separated. The base of
Design and construction 53
4.2Alternative lateral restraint positions tocontrol the movement of a space gridsubject to lateral forces whilst permittingrestricted movements due to temperaturechanges (a) typical layout for a grid withlarge aspect ratio generating greaterlateral force due to wind in one direction(Drawing: John Chilton)
the bearing is bolted to the supporting structure and theupper part of the bearing is bolted to the space grid.Thus, the grid and its support are connected in such away that restricted relative movement can take place.
A major source of movement in metal structures ischange of ambient temperature and this is especiallytrue when very long clear spans are involved. The effectof expansion or contraction of the space grid dependsvery much on the way in which the structure is sup-ported, in particular, the position and direction of hori-zontal restraints at the bearings. Besides movement dueto changes in ambient temperature, the bearings mayalso have to transfer horizontal forces, due to wind loadsor seismic activity, between the space grid and its sup-ports. To hold the space grid structure against lateralloads a minimum of three lateral restraints is required.The position of these restraints will depend on the dis-tribution and rigidity of the supporting structure and thesupporting structure must in turn be designed to resistthe lateral forces. Figure 4.2 shows alternative ways ofrestraining a space grid against lateral force, whilst per-mitting restricted movements due to temperaturechanges. A typical bearing which allows movement inone direction whilst restraining movement in the orthog-onal direction, and supports the Mero space grid roof ofthe National Indoor Arena for Sport, in Birmingham, UK,is shown in Figure 4.3.
Alternatively, the space grid may be rigidly fixed interms of horizontal movement to some or all of its sup-
ports. In this case, both the space grid and the sub-structure must be designed to cater for the forces gen-erated by temperature change. This alternative solutionwas used for the Boeing 747 maintenance hangar atStansted Airport, UK, described in detail in Chapter 5,where the CUBIC Space Frame was rigidly fixed in posi-tion at the top of the four main corner columns, whichacted as vertical cantilevers when resisting lateralforces. Thermal expansion and contraction wasassumed to occur relative to a notional fixed point atthe centre of the roof structure, whilst the tops of thecolumns were considered to bend away from or towardsthis notional point as dictated by the change in roofdimensions. The three-dimensional trussed columns andtheir foundations were then designed to accommodatethe forces induced by the movements in columns around23 m high.
In three-dimensional space grid structures in general,and long-span structures in particular, dimensional accu-racy is of paramount importance, as small variations inelement dimensions may accumulate to produce grosserrors in the dimensions of the final structure. Asdescribed in more detail below, this property can beexploited to produce a small pre-camber of space gridsby controlled variation of element dimensions.
54 Space Grid Structures
4.3Sliding bearingsupporting oneperimeter node of theMero space grid roofat the National IndoorArena for Sport,Birmingham, UK(Photograph: JohnChilton)
During the manufacturing process, components aretypically cut to length to tolerances better than 0.5 to1 mm. Many systems have parts that are fabricated fromtubes and cast metal end connector components (e.gthe Nodus and Mero KK systems) and these elementsmust be welded together to form complete members inaccurately dimensioned jigs, to ensure that the overalllength is within the required tolerance. In systems thatuse nodes to connect the individual members, these mustbe made to the same or better accuracy, with holesdrilled in the correct position and at the correct angle,with bearing faces precisely machined. Other systemsdo not have separate nodes, for example, the Multi-hingesystem developed by Peter Pearce and used in the con-struction of Biosphere 2 (see the case study in Chapter5). In such ‘nodeless’ systems, the members areattached to each other directly at the ends and they haveto be precisely pre-drilled in the correct positions toreceive the connecting bolts. In the Triodetic system thetubular members are crimped at the correct angle andlocation, and simultaneously cut accurately to the cor-rect length at the same time.
Fully modular systems such as Space Deck, theCUBIC Space Frame, ABBA Dekspace and SPACEgridare also welded up from accurately cut components inprecisely dimensioned jigs. This ensures overall dimen-sional accuracy for the modules, in this case, in three
dimensions. Because of the necessity for three-dimen-sional jigs for these modules, it is preferable if one (orjust a few) standard modules, if possible, are used forany structure as this reduces the number of adjustmentsthat must be made to the jig, and hence the cost of fab-rication.
Most space grid applications are for roof structures.Therefore, it is necessary to provide adequate falls forrainwater run-off and an additional pre-camber may alsobe incorporated to counteract the predicted verticaldeflection of the structure under imposed loading. In themajority of systems it is possible to achieve any requiredcamber by varying the chord lengths very slightly. Forinstance, if the upper chord members in one direction ofa grid pattern are all longer than the lower chords in thesame direction, a barrel vault (or arch) of any requiredradius can be generated (Figure 4.4(a)). Similarly, anangular ridge can be formed by shortening (or by elim-inating totally) one of the lower chord members (Figure4.4(b)). A stepped arch as in Figure 4.4(c) can beachieved by reducing the length of lower chords at reg-ular intervals along the section and free-form curves mayalso be produced by suitable manipulation of top and
Design and construction 55
4.4Camber of space grids: (a) uniformcurved camber formed by slightlyshortening all of the lower chordmembers in one direction, (b) ridgecamber formed by shortening onelower chord member in one directionunder the ridge, (c) stepped curvedcamber formed by slightly shorteningthe lower chord members in onedirection at regular bay intervals and(d) freeform curve generated bysuitable manipulation of top andbottom chord lengths in onedirection (Drawing: John Chilton)
bottom chord lengths (Figure 4.4(d)). To achieve limiteddouble-curved surfaces in three dimensions, it is possi-ble to have lower chords shorter in both directions of asquare grid and this generates a domed structure (Figure4.5). However, only shallow domes can be achieved inthis manner as geometrically incompatible internal defor-mations are generated if this approach is taken too far.In a similar fashion, shortening lower chords in one direc-tion and upper chords in the other direction of a squaregrid produces a saddle-type surface (Figure 4.6). Asnoted above, from the construction point of view, it mustbe realized that very small variations in length may causelarge differences in geometry of the space grid.
Cladding and glazing
Depending on the space grid system used, cladding andglazing elements may be supported directly by the top(or occasionally the bottom) chord members. If this isthe case, the local bending and shear induced in thechords by dead and imposed loads on the cladding haveto be considered in determining the member sizes. Thismay increase the size or thickness of the chords, andhence the cost of the grid. However, there will also bea saving, as separate purlins and purlin supports will notthen normally be necessary. The alternative is to pro-vide suitable brackets, or stools, at the node joints forpurlin fixing, hence ensuring that the self-weight of theroof decking and the imposed loads are transmitted to
the space grid as point loads at the nodes. In this case,the self-weight of the chord members is generally smallin comparison to the loads applied by the cladding in theformer case; thus only limited bending is induced. Anassessment of the cost of providing and installing a sep-arate purlin system compared with the additional mate-rial costs associated with loads being applied directly tothe chords (where the chosen space grid system per-mits) should be carried out to determine the most eco-nomical solution.
If cladding or glazing is fixed directly to the chords,then appropriate drainage falls must be provided by cam-bering or inclining the structural grid, as described in theprevious section. But if separate purlins are used, therequired gradient can be achieved by varying the heightof the purlin fixing stools. However, this may not beacceptable for very long span structures, as the heightof the purlin stools becomes excessive near the centreof the span, and therefore, cambering may still be nec-essary.
Methods of erection
There are several methods of erection for space gridsand more than one may be used in the construction ofa single grid. To some extent the method chosen willdepend on the system being used but overall grid size,site access, and component size, will also be determin-ing factors. In some cases erection can constitute a sig-
56 Space Grid Structures
4.5Domed camberformed by slightlyshortening all of thelower chord members(i.e, in bothdirections) (Drawing:John Chilton)
4.6Saddle surfaceformed by slightlyshortening all of thelower chord membersin one direction andthe top chords in theother direction(Drawing: JohnChilton)
nificant proportion of the overall cost of a space grid,therefore, it is important that the most efficient proce-dure is selected for each situation. This is one of theareas in which modular space grids have an advantageover ‘piece-small’ bar and node systems, as each mod-ule is an assembly of several individual members, there-fore, the number of site connections is reduced.
The most commonly used techniques are:
1 Assembly of all the individual space grid elementsor modules on a temporary staging or scaffolding, intheir permanent position.
2 Assembly of space grid elements or modules in theair, by cantilevering from existing portions of the roof.Usually, individual or small subsets of members arelifted into position by crane.
3 Assembly of space grid elements or modules intolarger panels (usually on the ground or a floor slab)before lifting them by crane and connecting them inthe air to areas of the grid that have already beeninstalled.
4 Assembly of the whole grid on the ground before lift-ing it on to the permanent supports by crane in oneoperation.
5 Assembly of a part or the whole space grid on theground before jacking or winching it into its final posi-tion over temporary or permanent supports.
The area of the construction site available to the spaceframe subcontractor is often a deciding factor whenchoosing the erection technique. For instance, when anacceptably flat unobstructed area is available adjacentto (or even directly below) the final location of the spacegrid and there is good access for cranes, it is often mucheasier to completely assemble a small grid on the groundor floor slab and then lift it by crane into its final posi-tion (method 4). This is particularly suitable if the indi-vidual pieces or modules can be manoeuvred by hand,as cranage is only required for a few hours. Of course,it is essential that the lifting points on the space grid arecorrectly selected so that individual members are notover-stressed and the structure is not permanently dam-aged during the lifting process.
Where the area directly under the space grid is avail-able for assembly but access is difficult for mobile cranes,method 5 may be preferred. The overall size of the spacegrid or the location of the assembly area may limit craneaccess. An example of the use of this erection methodwas the space grid of the Exhibition Centre, AnhembiPark, Sao Paulo, Brazil. The complete 260 � 260 m,650 tonne, double-layer grid was lifted 14 m vertically,using this method. Twenty-five temporary supports wereused for the twenty-seven hour operation. When such alarge area of space grid is being raised in one opera-tion at multiple locations, it is essential to control very
accurately the rate of vertical movement at all of the lift-ing points so that within specific predetermined limits thegrid remains horizontal. Excessive relative differences inlevel of the lifting points on the space grid could induceforces in some elements of the structure that may exceedthe forces experienced by those members under normaldead and imposed loading. It is generally much easierto control and monitor hydraulic jacking devices thancranes, therefore, the progress of a large-scale liftingoperation is better accomplished using such equipment.In recent years, computer control has greatly increasedthe ease with which such manoeuvres can be carriedout.
In situations where it would be difficult to lift the wholespace grid as one piece, or where it is not possible toassemble the whole grid on the ground, due to lack ofspace, the preassembly of units into a manageable areaof space grid is a good compromise (method 3). Thistechnique was used for the erection of the Nodus spacegrid roof at Terminal 2, Manchester Airport, UK wherethe total 6000 m2 area was divided into eleven sections,up to 25 tonnes in weight, which were placed by a 500-tonne mobile crane (see detailed study in Chapter 5).
Assembly by the connection of individual componentsin the air (method 2) is more appropriate for heavier mod-ules (or members) particularly when the site may not beobstructed by erection of the grid at ground level. Toaccelerate the overall construction schedule on a veryrestricted site, this technique was used for the majorityof the erection of the CUBIC Space Frame hangar roofat Stansted Airport. Consequently, other constructionoperations could be carried out simultaneously under theroof grid.
Usually, method 1 is only used when no other meansare possible, as staging and scaffolding are expensive.However, it may be necessary to use temporary sup-porting structures under some areas of large grids toestablish a structurally stable section of space grid forsubsequent connection, in the air, of larger preassem-bled sections or modules.
An important advantage may be gained from assem-bling the grid at or slightly above ground level prior tolifting it to its final position (methods 4 and 5). It is mucheasier, cheaper and safer to install building servicesand/or roof decking when this can be carried out fromthe ground. Expensive temporary access scaffolding maybe dispensed with and installation can proceed at thesame time as space grid assembly. A further advantageis that protection from the weather is available as soonas the space grid is raised into its final position, allow-ing other construction operations to be undertaken in thedry (in wet climates) or in the shade (in hot climates).
For the 1992 Olympics in Barcelona, the roof of theSant Jordi Sports Palace was constructed with the Oronasystem. It was erected using the innovative ‘Pantadome’
Design and construction 57
method proposed by engineer Mamoru Kawaguchi. Asa variation of method 5, the ‘Pantadome’ method allowsspace grids having complex double curvature to beassembled near to the ground, following a different cross-section from that of the permanent structure, before beingjacked vertically at the appropriate locations to transformtheir shape to the final profile. This is an exciting devel-opment in erection techniques for space grid structuresas it permits more complex three-dimensional forms tobe constructed economically. In Chapter 5 the designand construction of the Sant Jordi Sports Palace isreported in detail, and in Chapter 6 the principle of the‘Pantadome’ system is described at length and furtherexamples of its use are given.
Fire resistance of space grids
Space grid structures are predominantly, but not exclu-sively, constructed using steel members and joints. Theincremental reduction in the strength of steel withincreasing temperature is a well-known phenomenonwhich, in the event of fire, can lead to catastrophic col-lapse of building structures unless suitable protectivemeasures are taken to prevent overheating of the steel-work. In common with all steel structures, therefore, theeffect of fire on space grids must be considered
In a typical building structure, most or all membersmay be considered critical for the adequate performanceof the whole (or part) of the structural framework gen-erally, therefore, most members must be suitably pro-tected. Space grids, however, are redundant structuresin which the failure of one (or even several) elementsdoes not necessarily result in distress or collapse of thestructure. In certain circumstances the failure of one ormore members, through loss of strength or plastic buck-ling, might possibly be accommodated by a redistribu-tion of forces within the space grid although, for instance,the failure of highly loaded elements near supports incorner-supported structures would be very likely toinduce general collapse. Although not provoked by fire,the collapse of the roof of the Hartford Coliseum in 1978,described in Chapter 2, demonstrated the possibility ofprogressive collapse of the whole of a space grid dueto failure of one element.
In most countries Standard Fire Models are used toassess the effect of fire in buildings. However, there aremany parameters that influence the severity of a fire with-in a building compartment and this, in turn, determinesthe effect of the fire on the structure. The most impor-tant parameters are:
1 Fire load and distribution within a compartment (orhow much material there is to burn, how well it burnsand where it is).
2 The thermal characteristics of the compartmentboundaries (how easy it is for the heat to escape).
3 The geometry of the compartment.4 The area, position and shape of openings in the
boundaries.5 The rate at which the flammable material in the com-
partment burns (influences the rate of increase oftemperature and possibly the duration of the fire).
6 Ventilation rate (vents hot gases but can also fanflames).
7 Heat transfer within the compartment.
Normally the Standard Fire Models are not particularlyrefined due to the number and variability of the para-meters to be considered, although currently there is atendency to move towards more detailed computer sim-ulation of real fires (Natural Fire Models). The tradition-al fire models tend to consider that the gas temperatureis the same in the whole compartment. This is an unre-alistic assumption in the large-volume enclosures forwhich space grid structures are frequently used. In suchlarge volumes it is unlikely that all of the enclosing struc-ture will be affected and even less likely that it will besubjected to a uniform temperature throughout. Also, thespace grid may be well above the fire and therefore sub-ject to a smaller rise in temperature. Space grid struc-tures are, therefore, considered to be more vulnerableto localized fires in critical areas where members arehighly loaded or where redistribution of member loadsafter, for instance, the buckling of a compression mem-ber could lead to progressive collapse.
A procedure for the fire analysis of space grids hasbeen described by Ane Yarza.3 First, it involves thedescription of a fire model to determine the gas tem-perature distribution within the compartment under con-sideration over time. Once this has been found, heattransfer between the gases and the surface of the struc-tural elements can be modelled together with heat con-duction within the members. With an appropriate math-ematical model of these processes, the rise intemperature and the consequent reduction in strength ofthe steel over a given time can be found. Within themembers the temperature depends on its shape factor(a function of its shape, the ratio of its surface area toits cross-section, etc.) and the degree of insulation pro-vided to the surface. The effect of the temperature riseis included in a structural model of the space grid whichdescribes the modified material properties, structuralbehaviour and stability of elements. Finally, a series ofstructural analyses are carried out (with increasing timeand temperature) using the modified properties to deter-mine the stability of the space grid as a whole at eachstage. After each step, if collapse does not occur, theprocedure is repeated for an incremental increase in timeand temperature. Using this procedure it is possible to
58 Space Grid Structures
predict the order of failure of members and the behav-iour of the structure over the duration of a fire. Dependingon the specified period of fire resistance, it may be nec-essary to upgrade member sizes or insulate the steel-work to provide the protection required. Using the NaturalFire Model it may be necessary to carry out several dis-crete analyses to consider the effect of fires centred indifferent parts of the compartment.
Corner-supported space grids are most vulnerable infire, due to the potentially catastrophic failure of the diag-onal web members immediately adjacent to the supportsor to bending failure due to the collapse of the chordmembers running perpendicular to a single sectionthroughout the structure (as shown previously in Figure4.1). Therefore, wherever possible, space trusses shouldbe provided with full or intermittent edge supports. Forimproved performance of corner-supported space truss-es critical members adjacent to the corners can be over-sized to reduce their working stresses (thus raising thetemperature required to cause their failure).
Where fire protection of space grids is required, theonly real practical (but expensive) solution for insulatingthe structure, whilst simultaneously preserving its aes-thetic qualities, is to use intumescent coatings. Protectionis afforded by the swelling and foaming of the coatingat about 150 °C to form an insulating layer around thesteel. It should be possible to coat only the critical mem-bers within a large space grid to reduce the cost of fireprotection.
As with the thermal movements associated with nor-mal changes in ambient temperature, it is desirable toprovide appropriate sliding bearings to absorb the expan-sion of the space grid in a fire. Otherwise, the expan-sion may induce potentially damaging high compressiveforces in the space grid due to the rigid restraint. In thecase of a small fire beneath a large grid, the space griditself will provide a relatively unyielding restraint aroundthe localized expansion zone. Thus members not direct-ly heated by the fire may experience increased stress-es.
Space grids in seismic zones
Space grid structures form structurally rigid plates butare generally constructed of steel or aluminium usingmany joints. The combination of this rigidity with theductility of the construction material and the energy-absorbing potential of the connections provides excel-lent resistance to seismic loading. However, there aresituations in which space grids may exhibit ‘brittle’ behav-iour where the failure of a few or even one critical ele-ment may lead to sudden collapse of the whole struc-ture. In seismic design it is essential to identify thepotential ‘brittle’ modes of failure and to provide ade-
quate resistance so that ductility is maintained. Thecommon use of tubular members in space grids is ben-eficial due to their superior behaviour under the cyclicloading of earthquakes.
Seismic loading results from motion of the groundduring an earthquake combined with the inertia of thestructure. Rather than a direct loading the structure isactually forced to deform and this deformation inducesinternal forces. However, for design purposes, the seis-mic action is normally represented by an analogous sys-tem of external forces applied to the space grid. It is apotentially intense loading with a generally low proba-bility of occurrence and its effect depends on factors thatare different for each earthquake (such as maximumground acceleration, frequency profile and duration).
Modern seismic design codes are based on a DesignResponse Spectrum together with the structure’s loca-tion, importance, vibration period and ductility. In certaincircumstances, and where the double-layer space gridhas normal dimensions, regular shape and geometry, astraightforward Equivalent Static Force Analysis can becarried out. A simple elastic analysis ignores other char-acteristics of space grids, such as their potential for largeinelastic deformation without collapse. Ductility of thestructure dissipates seismic energy and can be used toachieve a more economical solution. However, there isalways the possibility of ‘brittle’ behaviour, involving aprogressive collapse initiated by the redistribution of loadfrom buckled members overloaded in compression.
The behaviour of a space grid depends on the rigidi-ty of the supporting structure with which it inevitably inter-acts. When it is supported on slender columns, the spacegrid can be considered to be a rigid diaphragm con-necting the tops of flexible columns. Lateral restraint ofthe grid may be provided by the columns acting as ver-tical cantilevers or through diagonal bracing betweencolumns. Where bracing is used, care must be taken toensure that thermal expansion of the grid will not beunduly restricted. This is usually achieved by locatingbracing midway along each side of a rectangular plan.Horizontal seismic forces are transmitted to the columnsin proportion to their relative stiffness.
Alternatively, where a space grid is supported on a mas-sive substructure, such as the inclined seating of a stadi-um, the roof is relatively flexible in comparison with thesupports. It does not contribute to the general earthquakeresistance of the whole building, solely transmitting seis-mic forces to the substructure. Detailing of connectionsbetween the grid and the supports in this case influencesthe behaviour of the grid under seismic loading. Horizontalseismic forces must be transmitted whilst allowing freethermal expansion of the space grid. It is essential thatsufficient allowance is made at the sliding bearings for thedifferential horizontal movement of the substructure.Vertical support must be maintained to prevent the space
Design and construction 59
grid from slipping off the bearings during an earthquake.The connections must also be sufficiently strong that theresistance of the substructure to seismic action is mobi-lized before the connections fail. A redundant strength fac-tor of 1.2 to 1.5 is generally recommended.4
1 Makowski, Z. S. (ed.) (1981). Analysis, Design andConstruction of Double-Layer Grids. Applied Science.
2 Motro, R. (1994). Structure and space structures. In
Application of Structural Morphology to Architecture(R. Höller, J. Hennicke and F. Klenk, eds), p. 119,University of Stuttgart.
3 Yarza, A., Pavia, P. and Parke, G. A. R. (1993). Anintroduction to the fire analysis of double-layer grids.In Space Structures 4 (G. A. R. Parke and C. M.Howard, eds), vol. 1, pp. 683–92, Thomas Telford.
4 Karamanos, A. S. and Karamanos, S. A. (1993).Seismic design of double-layer space grids and theirsupports. In Space Structures 4 (G. A. R. Parke andC. M. Howard, eds), vol. 1, pp. 476–84, ThomasTelford.
60 Space Grid Structures
Perhaps the best way to illustrate the huge potential forthe use of space grid structures is to show the manyways in which they can be used to produce aestheticallypleasing and efficient buildings. To this end, this chap-ter contains a series of case studies, presented inchronological order, to show how the technology hasdeveloped over approximately the last quarter of thetwentieth century. The studies encompass different build-ing types and sizes, in a variety of geometrical forms,ranging from small canopies to a stadium spanning over200 m. Most of the examples feature one of the multi-tude of available proprietary space grid systems,although some purpose designed and fabricated gridsare also represented. Significant aspects of their fabri-cation, construction and erection are described.
Space frame for the ‘Symbol Zone’, Expo’70, Osaka, Japan
The World Exposition in Osaka, in 1970, had as its theme‘Progress and Harmony for Humanity’ and at its centrethe Festival Square, masterminded by Kenzo Tange,1
was to symbolize the expression of ‘... a festival wherehuman beings can meet, shake hands, accord mindsand exchange wisdoms’. A huge, translucent, space
truss roof 291.6 m by 108 m, supported on only six lat-tice columns at a height of 30 m above the ground, cov-ered the Festival Square and dominated the site (Figure5.1). Based on a 10.8 m by 10.8 m square on squareoffset grid 7.637 m deep, the roof spanned 75.6 mbetween column centres across its width, with cantileversof 16.2 m at each side. In the longitudinal direction, therewere two 108 m spans and 37.8 m cantilevers at eachend. As can be seen in the plan and east elevation ofthe pavilion shown in Figure 5.2, one main span of thespace grid was pierced by a circular opening approxi-mately 54 m in diameter to allow the symbolic HeliosTower or Tower of the Sun, rising from the Concourseof Humanity, to soar above the roof (see centre of Figure5.1). The depth of the space truss was sufficient to allowexhibition spaces to be located within the roof structure.
This was space truss construction on a huge scaleand the length of the compression members required theuse of large-diameter steel tubes, 500 mm for chordsand 350 mm for diagonals. The tubes, of similar exter-nal dimension, varied in thickness from 7.9 to 30 mm,depending on the forces to be resisted, and were weld-ed to conical cast steel end pieces. These were thenconnected by 70 to 188 mm diameter high-tensile steelbolts to giant hollow cast steel spherical nodes 800 to1000 mm in diameter (see Figures 5.3 and 5.4 ). The
5 Case studies
5.1Aerial view of thespace truss 291.6 m� 108 m for the‘Symbol Zone’,Festival Plaza Expo’70, Osaka, Japan(Photograph courtesyMamoru Kawaguchi)
aesthetic of the roof structure was continued in the sup-porting columns which were constructed from similar ele-ments, surrounding a central 1.8 m diameter tubular post.A total of 2272 tube members were used, connected at639 nodes.2
It is interesting to note the philosophy that was adopt-ed for this structure in terms of accuracy of fabrication.For space grids it is essential that the position of thenodes conforms with the proposed geometry. This is usu-ally achieved by fabricating individual members andnodes to a high degree of accuracy, so that when theyare assembled accumulated errors or tolerances do notaffect the overall geometry, but this is expensive. Thealternative solution, adopted here, was to fabricate theelements of the space grid to less rigorous dimensionalaccuracies and to accurately fix the position of the nodes
in space whilst allowing for small adjustments of mem-ber lengths in the connection details. Such a solution isnot reasonable when there is a large number of nodesor when the grid is assembled in the air. However, inthis case, where there are widely spaced nodes andassembly was at ground level it was a feasible and effi-cient solution. Here the adjustment in member length (upto ± 25 mm) was achieved using several steel shims (seeFigure 5.4) inserted between the ends of the membercones and the spherical node. Angular discrepancieswere catered for by the use of spherical contact facesbetween the fixing bolts and the inside of the node cast-ing and by oversizing bolt holes by 12 mm to permitsome degree of rotation. The bolts were introduced intothe casting through an access hole that was later sealedby a cover plate.
62 Space Grid Structures
5.2Plan and east elevation of the space truss for the ‘Symbol Zone’, Festival Plaza Expo ’70, Osaka, Japan (Courtesy Mamoru Kawaguchi)
Case studies 63
5.3Typical ball joint ofspace truss for the‘Symbol Zone’,Festival Plaza Expo’70, Osaka, Japan(Photograph courtesyMamoru Kawaguchi)
5.4Diagram of typicalball joint, space trussfor the ‘Symbol Zone’,Festival Plaza Expo’70, Osaka, Japan,showing method ofconnection with largehigh-strength boltsand shims toaccommodateadjustments of themember length(Courtesy MamoruKawaguchi)
Assembly of the space grid was carried out on theground around the 1803 mm diameter central posts ofthe permanent columns. Subsequently, the roof was lift-ed in 80 mm steps, at the average rate of 2 m per day,using climbing pneumatic jacks of 450-tonne capacity.As the roof was lifted, erection of the outer frameworkof the columns was commenced and temporary strutswere set in place at the base to provide rigidity againstlateral seismic and wind forces, as can be seen in theerection sequence shown in Figure 5.5. When the liftingoperation was completed, the load was transferred fromthe jacks to the permanent column structure by installa-tion of the capital joints and removal of the temporarystruts at the base. Lateral restraint was then providedby rigid frame action between the columns and roof struc-ture, with ‘pinned’ column bases, thus reversing the pre-vious temporary condition. To avoid ‘locking-in’ forcesdue to temperature differences during this transfer, it wascarried out during one night.
An innovative solution, at the time, was the translucentroof which was made from inflated pillows introduced intoeach square of the top layer grid of the space truss. Twohundred and forty-three polyester film membrane cush-ions 9.9 m � 9.9 m were made from 1.1 m wide strips
250 microns thick. The upper skin was formed from sixlayers and the lower from five layers of polyester, witheach layer running perpendicularly to those adjacent.Inflation was with dry air normally at 50 mm water pres-sure, or 100 mm in strong wind conditions. A special ultra-violet-resistant film was used for the outer layers of eachpillow.3 The use of inflated pillows within roof structuresis currently finding favour with the use of highly translu-cent ethyltetrafluorethylene (ETFE) membranes.
Completed: 1969Architects: Kenzo Tange
Space frame and theme space architects: TomooFukuda and Koji Kamiya
Engineer: Yoshikatsu Tsuboi
Nusatsum House, Bella Coola Valley,British Columbia, Canada
The dwelling house is a building type where, in indus-trialized nations, there is little variation from the rigidadherence to cellular construction using orthogonal, load-bearing wall planes. This domination of the right anglewas challenged by Randall G. Satterwhite in his design
64 Space Grid Structures
5.5Lifting sequence, forthe space truss of the‘Symbol Zone’,Festival Plaza Expo’70, Osaka, Japan(Courtesy MamoruKawaguchi)
for Nusatsum House, Bella Coola Valley, BritishColumbia, constructed in 1978. Tetrahedral and octa-hedral geometry was used in the design of a multi-layerspace truss which initially splays outwards above thebase before tapering inwards again towards the peakedroof. In fact, the steep-sided load-bearing three-dimen-sional structure, clad in timber shingles, is nearly all roof.The cladding colour and general form of the house makeit highly reminiscent of the surrounding mountain peaksas can be seen in Figure 5.6.
Within the building, space truss nodes occur in horizontalplanes at ten different levels. Nodes and bars are omittedfrom the multi-layer grid, as required, to form a series ofinterlinked irregular polyhedral cells, the living spaces,inside the space truss (see Figure 5.7). The layout of thetriangulated grids at each horizontal level and a three-dimensional view of the structural configuration are shownin Figure 5.8. Architect, Randall Satterwhite, has com-mented that, rather than constructing the space truss tothe pre-defined floor configurations with bars and nodesomitted, it might have been simpler to assemble the fulldense grid and then subsequently to remove the unwant-ed structure, at each level, to form the required voids.
The space truss structure was composed of squaresection members, with a distance of approximately 1.5 mbetween node centres. Horizontal grid layers were thusspaced at approximately 1.06 m centres. The jointingsystem, illustrated in Figure 5.9, used prefabricated steelplate connectors with single bolts through the notchedends of the timber members.
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5.6Nusatsum House,constructed in 1978showing an uncannyresemblance to thesurrounding mountainpeaks (Photographcourtesy R. G.Satterwhite)
5.7Nusatsum House, internal view of irregular polyhedral living space(Photograph courtesy R. G. Satterwhite)
Noting the problems encountered in constructing thishouse, the architect Randall Satterwhite, proposed mod-ifications to the system4 as follows:
1 A revised jointing system that leaves flush surfacesfor cladding, using a stronger member/node con-nector with improved geometric flexibility.
2 Improved provision for movement of the timber struc-ture.
3 Increased member lengths to produce heights suit-able for habitable spaces between the horizontalgrids.
4 Computerized check on topography and memberforces.
66 Space Grid Structures
5.8Nusatsum House,scale model of themulti-layer space grid(Photograph courtesyR. G. Satterwhite)
5.9Nusatsum House,space truss node joint(Photograph courtesyR. G. Satterwhite)
5 Prefabrication of wall and floor components usingpanels that can be joined at the angles that occurbetween planes in the truss (180°,125°, 54°, 70° and109°).
6 A change to circular member cross-section.
A second research structure was later designed using3.0 m long roundwood poles, 150 mm in diameter, con-nected at one-piece aluminium nodes cast from 356 T6alloy.
Nusatsum House and the modified system demon-strate that it is possible to design and construct innova-tive housing forms using the efficient structural geome-try of space trusses and the environmentally friendlymaterial, timber. In particular, the second research struc-ture used roundwood poles (usually considered low-grade timber suitable only for items such as fence posts)for the main elements. Problems of acceptance occur,however, due to the general public’s reluctance toaccommodate to a planning grid based on the triangleand polygonal living spaces with inclined wall planes.Inhabitable space grids (large and small) are discussedin more detail in Chapter 7.
The Crystal Cathedral, Garden GroveCommunity Church, California, USA
Space grid structures are primarily used for supportinghorizontal and inclined roofs or, less commonly, floors.However, they are equally adaptable for use as verticalwalls. Although not common, there are some interestingexamples of buildings where almost all of the structureabove ground is a space grid. The Crystal Cathedral,Garden Grove Community Church, in California is onesuch; a building almost totally enclosed in a fully glazedspace structure (Figure 5.10). In fact the structure is nota true double-layer space grid as the inner chords runin only one direction, strictly making it a series of linkedplanar truss frames spanning in one direction. The archi-tects dictated that there should be no transverse innerchords to interrupt the visual flow of the structure.Nevertheless, the building is included here as it is gen-erally assumed to be a space grid or space frame struc-ture (and could easily have been) and because the closeconnection of the frames does allow loads to be sharedbetween them to some extent.
To those brought up in the European tradition of mag-nificent Gothic cathedrals constructed in masonry, theconcept of a church or cathedral comprising a spacestructure fully clad in silver-coated reflective glass isanathema. However, the masons constructing the greatcathedrals of medieval Europe were using their struc-tural skills to admit ever more light to the interior. TheReverend Dr Robert Schuller, who commissioned the
building, had previously preached for many years in theopen and would ideally have liked a building without roofor walls. With the benefits of modern materials and tech-nology the architects and engineers achieved the nextbest thing – what has been described in an article by R.E. Fischer in the Architectural Record 5 as ‘a glass tentof meaningful and breathtaking scale’ (p. 78).
With a modified diamond plan, the cathedral has majorand minor axes 126.5 m and 63.1 m long respectively(see Figure 5.11) and rises to 39 m above floor level.The space trusses are fabricated from tubular steel mem-bers, generally of 50.8, 63.5 and 76.2 mm diameter.Diagonals are mostly connected by welding or bolting togusset plates welded to the chords that run parallel tothe shorter axis of the diamond, as can be seen in theforeground of Figure 5.12. At the corners of the trussframes (the wall to roof junction) cast nodes are used toaccommodate the high stresses and complex memberconfigurations. Vertical as well as horizontal seismicforces, in accordance with the 1976 Uniform Building
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5.10Exterior view of the Crystal Cathedral, Garden Grove CommunityChurch, California (Photograph courtesy N. M. T. Jackson)
Code, were considered owing to the slenderness of theroof in comparison with the much stiffer wall construc-tion.
To minimize the visual intrusion of framing in the cur-tain wall glazing, the panes are flush-glazed using a low-modulus silicone sealant. Fixing to the space truss struc-ture is by clips that allow six-way adjustment. Asilver-coloured coating suppresses the heat of the solarradiation and the glazing admits just 8 per cent of inci-dent light.
This is an example in which the use of a ‘true’, two-way spanning, space truss was rejected for architectur-al reasons, to maintain the visual flow of the structure.This tends to reinforce one of the common argumentsagainst space grids in general, and space trusses in par-ticular, that the clarity of the geometry displayed in plansand elevations is lost in the building as constructed. Inthe Crystal Cathedral, the purity of the efficient structur-al form was sacrificed to lighten the structure visually.Even then, the impression from within the space grid isof a dense white filigree overlying the transparent enve-lope.
Completed: 1979/80Owner: Garden Grove Community Church, CaliforniaArchitect: Johnson/Burgee Architects (Philip Johnson
and John Burgee)Engineer: Severud-Perrone-Szegezdy-Sturm
Structural steel fabricator: Pittsburgh-Des Moines SteelCo.
68 Space Grid Structures
5.11Interior view along the 126.5 m long major axis of the CrystalCathedral, Garden Grove, California (Photograph courtesy N. M. T.Jackson)
5.12Typical nodeconnections in theCrystal Cathedral,Garden Grove,California (Photographcourtesy N. M. T.Jackson)
The National Exhibition Centre andBirmingham International Arena,Birmingham, UK
Phase 1 of the National Exhibition Centre on the outskirtsof Birmingham represents one of the most extensive usesof the Nodus system developed by British Steel, Tubes
Division (now British Steel Tubes & Pipes). Constructedin the late 1970s, the exhibition halls are on a regular30 m by 30 m column grid, which ideally lends itself tothe modular nature of the Nodus space grid. Roof areasare supported by ninety-three identical square on squareoffset assemblies of Nodus space truss, each 27.9 m by27.9 m (Figure 5.13). The repetitive nature of the standard
Case studies 69
5.13National ExhibitionCentre Birmingham,UK, standardstructural bay(Photograph courtesyBritish Steel, Tubes &Pipes)
5.14National ExhibitionCentre, Birmingham,UK, completedexhibition hall(Photograph courtesyBritish Steel, Tubes &Pipes)
structural bay allowed efficient design and fabrication ofthe space grid. The completed exhibition area is shownin Figure 5.14.
Hall 7 of the National Exhibition Centre, (Figure 5.15)also known as The Birmingham International Arena, pro-vides a column free area of 108 � 90 m and is used for
concerts as well as exhibitions. The building received aStructural Steel Design Award in 1981.6
A system of eight 32 m high Vierendeel masts (eachcomprising four 450 mm � 250 mm RHS columns) and273 mm diameter CHS ties support the intersectionpoints of a planar grid of square hollow section box-
70 Space Grid Structures
5.15The BirminghamInternational Arena(Photograph courtesyBritish Steel, Tubes &Pipes)
5.16The BirminghamInternational Arenashowing system ofVierendeel masts andCHS ties supportingthe planar beam grid.Note the raisedsection of roof at thecentre with clerestoryglazing around(Photograph courtesyBritish Steel, Tubes &Pipes)
trussed beams. The main trusses span at approximate-ly the third points of each side and divide the plan intonine bays that are infilled with Nodus space trusses, sim-ilar to those used in the other exhibition halls. The spacegrid of the central zone is slightly raised to provideclerestory glazing to admit daylight when required. Eacharea of Nodus space truss was assembled on the ground,(including lighting, services and sprinklers) before beinglifted and installed in the primary grid, as can be seenin Figure 5.16.
Owner: The National Exhibition Centre LtdArchitect: Edward D. Mills & Partners
Engineer: Ove Arup & PartnersSteelwork contractor: Redpath Engineering Ltd
Main contractor: R. M. DouglasSpace frame fabricators (Nodus): Pipework
Engineering Developments and Tubeworkers Ltd
Meishusama Hall, Shiga Sacred Garden,Shigaraki, Shiga, Japan
Completed in 1983, the Meishusama Hall of the ShigaSacred Garden (Figure 5.17) is an example of the useof both a planar single-layer grid and curved double-layerspace grids. This monumental building is a contempo-rary interpretation of the Japanese temple, which retainsthe traditional curved roof form whilst using the moderntechnology of steel structure and space grids to create
a vast enclosure of great presence, elegance and beau-ty in the mountain landscape. The hall, which is on animposing podium approximately 150 m by 75 m, rectan-gular in plan (Figure 5.18) is located near to Kyoto inJapan and was constructed as a place of assembly andworship for Shinji-Shumei-kai.7
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5.17Meishusama Hall,Shiga Sacred Garden,Shigaraki, Shiga,Japan (Photographcourtesy MamoruKawaguchi)
5.18Plan of the Meishusama Hall, Shiga Sacred Garden, Shigaraki,Shiga, Japan
Four huge corner ‘tusks’, supported on massive con-crete bases, rise above the reinforced concrete podium.The tusks, fabricated in sections from steel plates 23 to32 mm in thickness, joined on site by high-strength bolts,support a rectangular steel box girder frame 49.4 m by21.6 m. This in turn, is spanned by a planar diagonalgrid roof. On each of the four sides of the hall, a curveddouble-layer space truss hangs in a shallow catenarycurve. The space grids span 18.3 m horizontally betweenthe high-level rectangular frame and girders at theperimeter walls, and have a vertical drop of around 34 m.Grid dimensions are 2.88 m by 2.88 m for both the topand bottom layers of the space truss, which is 1 m deepand constructed from 216.3 mm diameter steel tubechord members.
Together, these structural elements enclose the vastimposing space of the hall, 58.2 m wide, 86 m long, soar-ing 43 m above the podium and having a seating capac-ity of 5670. Externally, the enclosing catenary space gridsare clad in 0.55 mm thick copper sheets supported ona 5 mm thick plywood deck. Beneath this, board insula-tion sits between timber rafters that are bolted to ribbedprecast concrete panels (900 mm � 2.88 m � 60 mm
thick) fixed to the space grid. On the inside (Figure 5.19)there is a smooth, apparently jointless, pastel finish toreflect the light entering around the fully glazed perime-ter walls, from the skylights and from glazed slots adja-cent to each corner tusk.
Completed: 1983Architect: Minoru Yamasaki & Associates
Engineer: Yoshikatsu TsuboiContractor: Shimizu Construction Co.
Jacob K. Javits Center, New York, USA
The Jacob K. Javits, New York Exhibition and ConventionCenter (Figure 5.20), built in the early 1980s, is thebiggest single area of space grid in the world.8 Practicallythe whole envelope of the enormous building is con-structed from space trusses on a standard grid moduleof 3.05 m. The gigantic pavilion, reminiscent of theCrystal Palace built in London in 1851, is sandwichedbetween Eleventh and Twelfth Avenues and Thirty-Fourth and Thirty-Ninth Streets in Manhattan, overlook-ing the Hudson River. The space grid has a plan area
72 Space Grid Structures
5.19Interior of Meishusama Hall, Shiga Sacred Garden, Shigaraki,Shiga, Japan (Photograph courtesy Mamoru Kawaguchi)
5.20The Jacob K. Javits, New York Exhibition and Convention Center(Photograph courtesy Alastair Gardner)
of over 53 000 m2, stretching over 300 m by 165 m witha maximum width of 220 m in the section through theentrance hall, where it rises to a maximum height of 47 mabove the floor. The architectural decision to clad thespace grid mainly in semi-reflective glass, means thatthe giant structure all but disappears during the day asit reflects the sky, whilst at night the regular geometryof the delicate space grid web is revealed by the inter-nal lighting.
A square 27 m � 27 m structural bay (Figure 5.21) isadopted for the Javits Center.9 This is directly related tothe normal stand size and layout for trade exhibitions.The structural bay dimensions, in turn, generate the 3 m� 3 m grid spacing of the space truss. At 1.5 m deep,the double-layer grid has a span/depth ratio of 18. Thiswas adopted for reasons of geometry and aesthetics, tomaintain the 45° inclination of the diagonals when viewedin section and to ease the transition from horizontal tovertical at the vertical corners of the walls. The
span/depth ratio appears to be rather conservative butthis can be explained by the presence of heavy loadsfrom ventilation equipment which, in some cases, canbe up to 30 000 kg in one bay. To emphasize the wayin which roof loads are channelled to the foundations,the space grid is supported on ‘tree’-type columns, the‘trunks’ consisting of four separate 400 mm diametertubes. Fire resistance is provided by columns filled withreinforced concrete. Along the perimeter of each squarebay an additional lower chord, connected by diagonalweb bracing, is provided to form a diamond shaped truss3 m deep overall. Each bay of the grid is therefore sup-ported on all edges by an integral downstand beam whichproduces a partial triple layer grid.
In the patented PG System space grid, there are steeltubes running between hollow truncated sphericalnodes, linked by a system of tension rods that passthrough the centre of the tubes (see Figure 5.22).Individual tubes range from 75 mm to 215 mm in diam-eter, with the larger diameters being tapered at the endsto avoid contact with neighbouring tubes at the joints.
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5.21Typical bay of the space truss, Jacob K. Javits, New YorkConvention Center (Photograph courtesy Alastair Gardner)
5.22Tension rod/tubular member detail, Jacob K. Javits, New YorkConvention Center (Courtesy Matthys Levy, Weidlinger Associates)
The tubes are considered to carry any compressivemember forces whilst the 75 000 high-tensile steel rods,located inside the tubes, carry any tensile memberforces. Rods range from 13 mm to 83 mm in diameter,and the hollow nodes have diameters of 215 mm to240 mm with several different wall thicknesses.Assembly of the system induces a small pre-stress inthe space grid. The upper chord tubes in the roof havea small ‘T’ section welded to the top to allow profiledsteel decking to be fixed directly to the space grid with-out using secondary purlins (Figure 5.23).
To accommodate the thermal movement of theimmense structure, the space truss is divided into sev-eral large areas bounded by diamond trusses with pairedchords, so that each area acts as an independentstructure. Expansion joints are provided in the claddingenvelope and bearings of three types (fixed in position,sliding in one direction and free to slide in any horizon-tal direction, as appropriate) are installed at the top of
the branched columns. Generally, the areas betweenexpansion joints are fixed at the centre, thus minimizingthe restraint to thermal movement and, consequently,the forces induced in the space grid by temperaturechanges. Almost exclusively the walls are not used tosupport the roof, which is supported by the internalcolumns. Predominantly the walls reaching down to theground are restrained laterally at their bases but are freeto move vertically.
A common problem with large flat roofs is that of dis-posal of rainwater. Usually, this is dealt with in spacegrid structures by providing a camber using slightly dif-ferent member lengths for upper and lower chords.However, in the Javits Center the difficulty was over-come in a different manner. A minimum deflection wasspecified for the roof bays (as well as the more usualmaximum deflection limit) and rainwater is assumed topond at the low points where it is collected and dis-charged to the drainage system. This obviates the needfor roof camber but might lead to problems if the drainagesystem is not adequately maintained. Although theglazed envelope of the building is 0.38 m from the outerlayer of the space truss, panels were generally on the
74 Space Grid Structures
5.23Decking support detail, New York Convention Center (CourtesyMatthys Levy, Weidlinger Associates)
5.24Special glazing panels at angles, corners and the mansard roof(Photograph courtesy Alastair Gardner)
same 3 m by 3 m grid but subdivided into 1.5 m by 1.5 msegments for reasons of economy and aesthetics. Thismeans that special panels had to be used for re-entrantangles, corners and the mansard edge of the roof (Figure5.24).
The Javits Center demonstrates the use of a propri-etary space grid system to enclose a huge light and airyvolume (Figure 5.25), creating this architectural spacefrom a simple square on square offset structural config-uration.
Owner: Convention Center Development Corp.Architect: Pei, Cobb Freed
Engineer: Weidlinger Associates, Salmon AssociatesSpace frame: PG System (PG Structures Inc.)
Oguni Dome, Oguni-machi, KumamotoPrefecture, Japan
Timber space grid structures are rare in comparison withtheir steel or aluminium counterparts. However, in Japan,there is a tradition of building large-scale structures, suchas temples, castles and pagodas, from timber, and theOguni Dome in the Kumamoto Prefecture of Kyushu fol-lows this tradition. Located in the south island of Japan,this large gymnasium, built in 1988, is a fine example ofthe use of timber in a modern double-curved, double-layer space truss roof (Figure 5.26). Preservative-treat-ed cedar, sugi in Japanese, is used throughout the roofwhich covers approximately 2835 m2 with an organicdomed form, clad in stainless steel. Plan dimensions are
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5.25Interior of New York Convention Center (Photograph courtesyAlastair Gardner)
5.26Interior view of theOguni Dome, KumamotoPrefecture, Kyushu,Japan – a timberdouble-layer grid(Photograph courtesyYoh Architects)
76 Space Grid Structures
5.27(a)North elevation, OguniDome (Courtesy YohArchitects)
5.27(b)Cross-section, OguniDome (Courtesy YohArchitects)
5.28Three-dimensionalcomputer model ofdomed space grid,Oguni Dome(Courtesy YohArchitects)
63 m by 47 m with a grid depth of only 2 m (a span todepth ratio of 23.5). Additional structural rigidity is derivedfrom the three-dimensional curved form of the roof, seenin the elevations and sections Figures 5.27(a) and5.27(b) and the three-dimensional view of Figure 5.28.This form allows a more slender space grid to be used.
The details of the space grid system used for thedomed roof of the gymnasium were refined through aseries of buildings by the same architect, Shoei Yoh.10,11
A standard steel space grid system, TM truss, was adapt-ed for use with timber members. As seen in Figure 5.29,solid cedar members, up to 110 by 150 mm, are usedfor the top chords and up to 110 by 170 mm for the bot-tom chords, with web bracing of 90 by 125 mm. At eachend of the timber members there is a steel connectorcomposed of a 42.7 mm diameter sleeve and bolt whichis welded to an end cap and plate insert. These are fixedto the timber using two 16 mm bolts and pressure grout-ing with epoxy resin. The members are then ready forconnection to the standard TM truss nodes, see Figures5.29 and 5.30. A secondary system of purlins and rafterssupports the stainless steel covered, insulated plywoodroof deck and precast ceiling panels.
An important consideration in the use of timber for thespace truss is its performance in case of fire. Timberburns or chars at a predictable rate and usually mem-bers can be oversized so that structural integrity is main-tained for a prescribed period. In the Oguni Dome thespace grid was raised, as can be seen in the detailedsection Figure 5.31, to a minimum height of 6.2 m above
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5.29Solid cedar membersof the Oguni Dome(Courtesy YohArchitects)
5.30Oguni Dome, steel connector inserts for timber members forconnection to standard TM truss ball nodes (Courtesy YohArchitects)
the gymnasium floor, to provide adequate distancebetween the structure and any possible fire at floor level.Some automatic sprinklers were also installed.
Considering the simplicity, elegance and aestheticappeal of this space grid dome made from a warm nat-ural, renewable structural material, it is perhaps surpris-ing that more roofs of a similar nature are not con-structed. Maybe this has something to do with a certainresistance, in many countries, to using timber for long-span structures as designers feel uncomfortable with itsless predictable material properties.
Architects: Yoh Design OfficeEngineers: Gengo Matsui and Atelier Furai
Contractor: Hashimoto Construction Co. Ltd
FFV Aerotech Hangar, Stansted Airport, UK
The FFV Aerotech Maintenance Hangar at StanstedAirport in the UK (Figure 5.32) is notable in that it is dia-mond shaped in plan and it is also the longest spanningCUBIC Space Frame to have been constructed to date.12
Formed from two isosceles triangles with side lengths of98 m, placed side by side, the long axis of the diamondis 170 m and the short axis is 98 m. With two door open-ings 72 m wide and 21 m high set in adjacent sides onthe long axis of the hangar, it accommodates two Boeing747-400 series aircraft (as shown in Figure 5.33). Thespace frame is supported on four major columns at thecorners of the diamond, two 5.9 m deep lattice girdersover the door openings and secondary columns atapproximately 6.1 m centres around the remainder of theperimeter. Wind forces are predominantly transmitted tothe ground by the four corner columns, which act as
78 Space Grid Structures
5.31Detailed section of perimeter wall and space grid, Oguni Dome(Courtesy Yoh Architects)
5.32FFV AerotechMaintenance Hangarat Stansted Airport,UK (Photograph: JohnChilton)
vertical cantilevers for this loading, whilst the remainingcolumns mainly resist vertical loads.
During the early development of the CUBIC SpaceFrame, there was some scepticism from engineers expe-rienced in the design of space grids as to the economyof a true space-frame structure, that relies heavily onbending resistance to carry load, when compared to moreconventional systems where the loads are resisted pri-marily by truss action (members in axial tension andcompression only). However, the CUBIC Space Frameroof for the Stansted hangar was chosen on grounds ofreduced cost over an alternative solution using a grid ofdeep lattice trusses infilled with space truss panels.Although the structural efficiency of the space frame maybe lower (i.e the ratio of the live load carried by the struc-ture when compared to its dead load) so that the struc-ture is heavier than an equivalent space truss, the useof simple, cheap, fabrication techniques in its manufac-ture can make the system cost-effective.
An orthogonal double-layer grid, with an overall depthof 4.0 m, was used, with upper and lower chords run-ning parallel to the principal axes of the diamond form(i.e. at an angle of 30° or 60° to the sides of the hangar).The main axes were divided into 48 equal bays in eachdirection, to give space grid modules approximately3.5 m by 2.0 m (Figures 5.34(a) and (b)). In total, 1201modules were used, the majority being ‘X’ shaped inplan, whilst the edge modules were generally ‘L’ shaped
in plan. All modules were fabricated in purpose-madejigs from standard Universal Beam and Column sectionsof seven different sizes, all nominally 200 or 400 mmdeep, and the seven different size vertical web elementswere all square or rectangular hollow sections varyingfrom 200 by 200 mm to 300 by 300 mm. The resultingmodules weighed between 0.5 and 1.0 tonnes. Rigidmoment connections between the chords and verticalswere reinforced with collar or flange plates and the endsof the tubular vertical posts were also capped with platesfully welded to the chord members. Connection betweenthe modules used high-tensile steel, bolted, lap jointswith plates welded to the webs at the ends of the chords.The maximum number of 24 mm diameter bolts in a lapwas twenty, reducing to a minimum of two in the mostlightly loaded lap joints. For rainwater run-off, the roofstructure was cambered in both directions by shorteningthe chord module lengths in the lower grid.
Several methods of assembly were used at differentstages of construction. Initially a temporary scaffoldingtower was erected at the middle of the hangar. Threesections of space frame, with a total length equal to theshort 98 m axis of the hangar and three modules in width,were then assembled on the ground. Using two mobilecranes the first section of space frame was then liftedand connected to one permanent column, whilst the otherend was held in the air by one crane. The other cranethen lifted the second preassembled section which wasthen bolted to the first section, using the standard chordlap joints, and rested on the temporary tower support.Subsequently, the remaining section of space frame waslifted and connected between the second section andthe other permanent column. This formed a space gridbridge across the minor axis of the hangar so that erec-tion could proceed on both sides if required. Moduleswere erected, individually or in small groups, on bothsides of the bridge until it was seven modules wide, atwhich point the temporary tower was removed. Erectionthen proceeded on both sides of the bridge towards theacute corners of the diamond plan. During assembly ofthe grid some lack of fit problems were encountered dueto the deformation of the grid under its own weight butthese were overcome by use of purpose-designedframes and jacking devices to stress the new line of roofmodules. Figure 5.35 shows the part-assembled gridunder construction.
Compared to the original roof design, the CUBICSpace Frame saved approximately 2 m in the overallheight of the hangar, reducing it to a little over 27 m. Forthe nearby Terminal Building, under construction at thesame time, there had been a planning restriction that theheight should not exceed that of the tallest tree on thesite (approximately 15 m above ground level). A similarrestriction would have been unreasonable for a hangardesigned to house aircraft that themselves are around
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5.33Sketch plan of hangar FFV Aerotech Maintenance Hangar atStansted Airport (Drawing: Carlos Márquez)
80 Space Grid Structures
5.34(a)Plan of FFV AerotechMaintenance Hangarat Stansted Airport(Drawing: CarlosMárquez)
5.34(b)Section of FFVAerotech MaintenanceHangar at StanstedAirport (Drawing:Carlos Márquez)
20 m above ground at their highest point, however, keep-ing the overall height to a minimum was a major archi-tectural design consideration.
In recognition of the innovative design of the hangarand its use of the CUBIC Space Frame, the project washonoured with the Supreme Award of the BritishConstruction Industry Awards 1989 and also gained aSteel Design Award in 1990.
Completed: 1988Architect: Faulks, Perry, Culley and Rech
Engineer: Sir Frederick Snow and Partners and BurksGreen and Partners (hangar steelwork and CUBIC
Space Frame)Consultant: M. Leszek Kubik
Main contractor: Costain Construction LtdSteelwork and space frame fabricator: A. R. Hunt
Erector: Butler & George
Sant Jordi Sports Palace, Barcelona, Spain
One of the most frequent criticisms that is levelled atspace grids, is that they are suitable for flat roofs cov-ering rectilinear floor plans but that they become uneco-nomic when used for more complicated roof forms orbuilding plans. This argument is powerfully and elegantlyrefuted by the Palau Sant Jordi, or Sant Jordi SportsPalace, in Barcelona (Figure 5.36). Following an inter-national design competition held in 1983, Arata Isozaki
(architect) and Mamoru Kawaguchi (engineer) were com-missioned to design the 15 000-seat Sports Palace whichwas to be constructed as the main indoor arena for the1992 Barcelona Olympiad. Conceptually, the designerswanted to capture the technology of the age and for thisreason chose a ‘mass-produced’ system but in the mod-ern sense where robotics, CAD, computer-aided manu-facture (CAM) and NC techniques allow ‘mass-produc-tion’ of small quantities with many variants. Hence, a‘mass-produced’ space truss was adopted but for a rea-sonably complex form that required the modern tech-nology for its economic fabrication and erection.13,14
All four sides of the stadium are curved in plan andthe cross-section is arched along both major axes (seeFigures 5.37 and 5.38(a) and (b)). There is a centralzone that is built to a slightly different curvature and alsotapers slightly in the direction of the long axis of thearena. This area is surrounded by a continuous skylightand is also perforated with smaller domed skylights ona pattern conforming to the space grid upper chord con-figuration. In contrast to the profiled-metal decking thatis more commonly used to clad space grids, the roof isfinished with two alternative materials – black ceramictiles and zinc metal sheeting.15 The impression generat-ed is that of a protective shell, shielding the athletes andspectators from the heat of the Barcelona summer sun.
The space grid roof has maximum plan dimensions of128 by 106 m within which the central zone, of differentcurvature, is approximately 80 by 60 metres. In both the
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5.35Part assembled roofgrid of FFV AerotechMaintenance Hangarat Stansted Airport(Photograph courtesyL. A. Kubik)
82 Space Grid Structures
5.36Sant Jordi SportsPalace, Barcelona,Spain (Photograph:John Chilton)
5.37Plan of the roofstructure, Sant JordiSports Palace(Courtesy MamoruKawaguchi)
central and perimeter sections of the roof the space trusshas a depth of only 2.50 metres (1/42 of the shorter spanof the arena). However, the domed nature of the roof (seeelevations in Figures 5.38(a) and (b)) clearly offers thedevelopment of significant arch (membrane) action so thatnormal flat roof span/depth ratios are not really applica-ble. From the top of the column supports to the high pointof the roof the maximum rise is 21 m with a maximumfinal height above the arena floor of approximately 45 m.
The roof structure was assembled from 9190 mem-bers mainly ranging from 76 mm to 267 mm in diame-ter, although some 406 mm and 508 mm tubes wereused at the periphery. Members are connected using2403 cast steel spherical nodes varying from 100 to250 mm in diameter. The whole space grid roof struc-ture stands on just sixty perimeter tubular steel columns508 mm or 609.6 mm in diameter, depending on theirlocation. The SEO system space truss (described inChapter 3) was manufactured by Orona using steel
tubes, fabricated to an accuracy of 0.3 mm in their length,and ‘ball type’ forged node joints drilled, using comput-erized numerical control (CNC) drilling equipment, toreceive the connecting bolts. Modern computer-con-trolled cutting and drilling techniques allowed practicalfabrication of dissimilar elements making the generationof the dome form more economic.
Notable though the form may be, perhaps the mostinnovative aspect of the space grid roof is its method oferection, which was developed by the Japanese engi-neer Mamoru Kawaguchi and is known as the‘Pantadome’ System. This technique, first used for theerection of the roof of the World Memorial Hall in Kobe,Japan, is described in detail in Chapter 6. It involves theassembly of the space grid in a partially folded form thatis subsequently unfolded into the final shape. Here, thisallowed efficient erection of the central portion of thiscomplex roof at low level near the arena floor before itwas raised to its final location.
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5.38(a)North elevation of theSant Jordi SportsPalace (CourtesyMamoru Kawaguchi)
5.38(b)West elevation andlongitudinal section ofthe Sant Jordi SportsPalace (CourtesyMamoru Kawaguchi)
84 Space Grid Structures
5.39Erection sequence ofSant Jordi SportsPalace using the‘Pantadome’ system(1) erection of centraldome, (2)erection/connection ofside frames, placedby Orona, andconstruction of liftingtowers and secondarystructure, (3) partiallift, (4) completed lift,(5) jacking towersremoved (CourtesyMamoru Kawaguchi)
The erection sequence shown in Figure 5.39, com-menced with the assembly of the centre portion of theroof on temporary supports, approximately 6 m abovethe floor of the arena, and directly beneath its final loca-tion in plan. Sixteen perimeter sections of space framewere then constructed and connected, by hinged joints,both to the perimeter columns and to the central roofsection. The perimeter columns were also hinged at theirbases (tangentially to the curve connecting the bases).It is interesting to note that the hinges were on the cen-tral axis of the 609.6 mm columns but offset towards theperimeter of the arena on the 508 mm columns. The con-sequent eccentricity of the vertical roof load aided thestability of the mechanism, as it ‘encouraged’ the hingesto fold in only one way (with the roof to the inside of thecolumns). At the corners of the arena, wide gaps wereleft between the perimeter space grid sections. Narrowergaps were left between the space grid sections alongthe arena sides. The plan view of the roof (Figure 5.40)shows the disposition of the space grid segments beforelifting and small circles indicate the positions of liftingtowers. At this stage, the whole structure was mechan-ically very flexible.
By a careful computer-controlled jacking operation,the central roof section was moved vertically to its finalposition between 22 November and 3 December 1988.Twelve jacking towers were used, with a tetrahedralframe at the top of each, to spread the jacking forceinto two nodes of the lower layer roof grid and to guar-antee full horizontal articulation. The jacking process
caused the perimeter space grid sections to be raisedfrom their initial orientation, pointing down into the bowlof the arena, to their final position pointing upwards tosupport the central dome section. During this operationthe tops of the perimeter columns were first forced out-wards, to allow the perimeter space grid sections tochange their alignment, before returning to the verticalwhen the central roof section achieved its final posi-tion. Subsequently, additional space grid members wereinserted into the gaps between the perimeter sectionsto complete the three-dimensional dome form and lockthe mechanism. The jacking towers were then removedleaving the floor of the arena free. Maximum verticaldisplacement of the roof during removal of the jackingforce and props was 140 mm, in close agreement withthe computer analysis of the roof. A secondary struc-ture, 60 � 22 m in plan and weighing 83 tonnes, whichcarries electronic scoreboards, video screens andsound equipment, is suspended at the centre of thearena from the domed space truss. This assembly waserected on the floor of the arena beneath the spacetruss dome and lifted to its final position during thesame operation, being raised from the arena floor onthe second day of the lift. Four stages of the actualerection process are shown in the sequence of pho-tographs in Figure 5.41.
On the principal hinge lines, those connecting the cen-tral dome to the side grids, and at the four corners ofthe arena, the roof has glazed strips that leave a per-manent reminder of the method of erection.
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5.40Plan layout of roof segments and location of jacking towers indicated by the small circles (Courtesy Mamoru Kawaguchi)
To accommodate thermal expansion and contractionof the large roof structure without inducing stresses inthe space truss, all of the perimeter columns are hingedat both top and bottom to allow free movement in adirection perpendicular to the roof perimeter. To resistlateral forces on the roof such as wind forces, pairs ofadjacent columns are linked at the top to form rigid por-tal frames (twenty-two in total: fourteen longitudinally and
eight transversely). Due to the method of support on alimited number of columns, to the spectator inside theSant Jordi Sports Palace, the space truss roof appearsto float above the mass of the concrete stands.
There are several advantages to this system of con-struction and erection. First, the assembly of the com-plex roof form is accomplished at a convenient levelabove the ground, where exposure to strong winds is
86 Space Grid Structures
5.41Aerial views of rooflifting sequence(Photograph courtesyMamoru Kawaguchi)
reduced and the dangers associated with working atheight are minimized. Second, it is possible to partiallycomplete the roof covering and install services withoutusing expensive secondary access structures. The samemethod of erection was also previously used for theNational Indoor Stadium in Singapore, where MamoruKawaguchi worked with the architect Kenzo Tange. Ithas been used subsequently for the Kadoma Sports Hall
and a stepped-surfaced dome with a 116 m diameter cir-cular plan, the Sun-Dome, Sabae, in Fukui Prefecture,Japan. Detailed studies of these further examples arepresented in Chapter 6.
Completed: 1990Architect: Arata Isozaki
Engineer: Mamoru KawaguchiSpace frame: Orona SEO system
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Biosphere 2, Sonoran Desert, Arizona, USA
Biosphere 2 was an exciting experiment in controlling thenatural environment within an airtight envelope and it wasfitting that such a project was housed within a giant space
grid.16 Constructed in 1990 in the harsh environment ofthe Arizona desert, near Tucson, the complex comprisedfive major pavilions; the Wilderness Biome; the IntensiveAgriculture Biome; the Habitat and two Lung Domes (socalled because the membranes within them controlled the
88 Space Grid Structures
5.42Biosphere 2,Wilderness Biome,55 m span steppedpyramid (Photographcourtesy PeterTrebilcock)
5.43Biosphere 2, IntensiveAgriculture Biomewith the Lung Domein the background(Photograph courtesyPeter Trebilcock)
variations in internal pressure in the Biomes, due tochanges in ambient temperature). The Wilderness Biomewas constructed from 40 000 members forming twostepped pyramids linked by a galleria stepped in section.Overall the building is 168 m long and spans up to 55 min the largest pyramid (Figure 5.42). The structure is total-ly glazed, as is the 15 000 member multi-vaulted struc-ture of the Intensive Agriculture Biome, seen in Figure5.43. A mixture of steel and glass cladding was used onthe space grid shell structure of the Habitat and almostexclusively steel cladding on the 55 m diameter LungDomes, seen in the background of Figure 5.43.
The space grid adopted for this project is a ‘nodeless’form, the Multi-hinge System developed by Peter Pearce(Figure 5.44). It was used in a double-layer for the twoBiomes and in a single layer for the Habitat and Lung
Domes. Instead of a separate node, each tubular mem-ber is closed by welded end caps and has pre-drilled finplates welded on to the tube in predetermined positionsadjacent to the ends.17 Assembly of the grid is achievedby bolting the members together directly, by means ofthe fins, in predetermined configurations. Transfer offorces within the joints is solely by shear resistance ofthe connecting bolts. A benefit of this method of ‘node-less’ connection is the stiffness of the joint whichimproves the overall performance of the space truss.
An essential part of the Biosphere 2 project was themaintenance of an environment separate from that ofBiosphere 1 (i.e. Earth itself). Therefore, it was of para-mount importance that there was, as near as possible,an airtight seal between the structure and glazing orcladding panels. Pearce Systems developed an airtightversion of their Integral Glazing System using materialscompatible with those of the space grid, steel glazingframes with glass bonded to them in the factory, with sil-icone structural sealants. Pre-glazed frames weremechanically fixed to the space truss and a siliconecaulking was applied between adjoining units. The struc-tural geometry was designed to reduce movements dueto thermal effects to a minimum and the use of steelglazing frames practically eliminated any differential ther-mal movement between the primary structure and itscladding. Therefore, no expansion joints were needed inthe structure and the small movements between the glaz-ing panels and the space truss could be accommodat-ed easily by the sealant. However, as Biosphere 2 isdesigned for a life of over 100 years, there is the pos-sibility that the sealing compounds may deteriorate withtime and affect the airtightness.
In the Biosphere 2 project the flexibility in use of spacegrid structures is abundantly demonstrated as the PearceMulti-hinge System is used for a wide range of structuralforms and for both single- and double-layer space grids.
Architects: Margaret Augustine, Phil Hawes, John Allen
Space frame contractor: Pearce Systems International, USA
National Indoor Arena for Sport,Birmingham, UK
The Birmingham National Indoor Arena for Sport (NIAS)18
is of similar size to the Sant Jordi Sports Palace inBarcelona (described above) and was built, under adesign and build contract, at about the same time.However, the configuration chosen for its space grid roofand the method of erection were completely different.Although the Birmingham Arena, seen under construc-tion in Figure 5.45, has the familiar stadium plan form
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5.44Multi-hinge System ‘nodeless’ joint (Photograph courtesy PeterTrebilcock)
of a quadrilateral with curved sides, the space grid roofin this case is a three-layer space truss with horizontalsoffit, inclined top chords and mansard edges, con-structed using the Mero KK system (described in Chapter3). As the geometrical form (a flat plate rather than thedomed profile of the Sant Jordi Sports Palace) is not asstructurally efficient, the 128 m by 90 m space truss is10 m deep at the centre, reducing to approximately 8 mdeep at the top of the mansard edges (see the plan inFigure 5.46 and section in Figure 5.47). The span todepth ratio is, therefore, approximately 9:1 in this case.
With this depth of space grid it becomes more eco-nomical to use a triple-layer system, as this reduces thelength of compression members (e.g. top chord and webbracing elements) which have to be designed to resistbuckling under axial compressive forces, where thelength of the member has a considerable influence onits load carrying capacity. Consequently, by the adop-tion of a triple-layer grid, the cross-sectional dimensions,and therefore the weight, of the compression membersis reduced. This more than compensates for the increasein weight due to the additional horizontal middle grid layerand extra node joints. On the other hand, it adds to thenumber of node joints required and increases the com-plexity of the roof structure, thus tending to extend thetime and cost of erection. In the Birmingham NIAS roof,the middle-layer nodes are situated 4.0 m above thelower layer at the perimeter and 4.7 m at the centre ofthe span.
The roof uses 4934 tubular members varying from76.1 mm diameter with 2.9 mm wall thickness up to219.1 mm diameter, 22.2 mm thick. Over half the mem-bers are 127 mm diameter or bigger. Diameters of theMero KK nodes range from 110 mm to 350 mm withthose of 155 and 228 mm diameter being the most com-mon sizes. Self-weight of the space truss is 0.42 kN/m2
which is approximately 20 per cent of the total designdead and imposed load for the roof.19 The grid is sup-ported at thirty-six nodes on sliding bearings that permitthermal movement to take place radially from the cen-tre of the roof (see above, Figure 4.3).
One of the advantages of space grid construction isthat large structures can be assembled from smallelements on site with limited disruption to other site activ-ities. At the Birmingham Arena the site had very restrict-ed access, with a main railway line running through itscentre and a canal to one side. In fact, the arena hadto be built straddling the railway line, which was enclosedin a new tunnel. Multistorey car parks on each side ofthe tunnel completed the podium on which the stadiumwas built. Initially, the 145 m long tunnel was construct-ed by the main contractor to cover and protect the railwayand provide a working platform at what would eventual-ly become the arena floor level. At each side of thistunnel, the reinforced concrete framed car parks wereerected and above these, the raked seating for the spec-tators. A concrete ring beam support for the space gridwas cast in situ to the rear of the seating. Ring beam
90 Space Grid Structures
5.45Birmingham NationalIndoor Arena forSport (NIAS) underconstruction(Photograph courtesyMero UK)
Case studies 91
5.46Plan of the space grid layout for the roof of the Birmingham National Indoor Arena for Sport (Courtesy Mero UK)
5.47Cross-section of the Birmingham National Indoor Arena for Sport (Courtesy Mero UK)
construction progressed from one end of the arena, thusallowing erection of the space frame to commence beforethe concrete substructure was complete. Installation ofcladding and services then followed closely behind theerection of the space grid.
Two distinct methods of assembly were used for thespace grid. The first section of roof to be installed wasabove the raked seating at one end of the arena and,to establish a structurally stable section of space grid,temporary falsework was constructed from standardMero parts to provide a working platform and to sustainthe grid until it became self-supporting. Subsequently,small ‘spiders’ of a few tubular members connected toone node were assembled at arena level (Figure 5.48)and lifted into position, using a gantry crane runningalong the top of the railway tunnel. The ‘spider’ sectionswere then connected, in the air, to the previously erect-ed section of space grid (Figure 5.49).
As construction progressed along the principal axis ofthe arena, temporary props were installed at predeter-mined levels and locations to limit the deformation of theincomplete space grid under the dead loads. Once theroof structure was completed the temporary props wereremoved in order to fully transfer loads to the permanentsupports and allow the roof to take up its naturaldeformed shape. During the process of load transfer, themeasured vertical deflection at the centre of the roof(131 mm) was about 10 mm less than that predicted bythe computer analysis of the structure.
92 Space Grid Structures
5.48Assembly at arena level of a ‘spider’ of several space gridmembers connected to a single node, NIAS, Birmingham(Photograph: John Chilton)
5.49Connection of ‘spider’to previously erectedsection of space grid(Photograph: JohnChilton)
The space grid roof of the Birmingham Arena is cov-ered with a perforated steel deck supported on cold-formed steel purlins attached to the space truss by brack-ets screwed into the Mero KK ball joints in the top layer.Above the decking there are acoustic insulation and afurther 130 mm of mineral wool thermal insulation sep-arated by a vapour check membrane. A site heat-weld-ed Trocal membrane, fixed mechanically through theinsulation to the metal deck, provides the weatherproofenvelope.
It was simple to install access ways and apparatusthroughout the roof structure due to the regular supportsprovided by the grid chords. Given the building’s use,an allowance of 0.72 kN/m2 was included for roof ser-vice loading, plus 700 m of walkways with a load of1.35 kN/m2. At its centre, the space truss carries a largesuspended electronic scoreboard and a large quantity oflighting, sound and ventilation equipment. The completeroof, including the built-up roofing system and all walk-way gantries, was programmed to be completed in twen-ty-nine weeks. This tight schedule was achieved with twodays to spare.
Completed: 1990Architect: Hellmuth Obata Kassabaum (HOK)/
Percy Thomas PartnershipSpace frame contractor: Mero UK
Main contractor: Laing Midlands
Lan Chile, Maintenance Hangar,Aeropuerto Comodoro Arturo MerinoBenítez, Santiago, Chile
Aeropuerto Comodoro Arturo Merino Benítez, Santiago,is the main international airport for Chile, which has oneof the fastest growing economies in Latin America. Tocater for the increased number of national and interna-tional flights generated by the high level of economic activ-ity, a maintenance hangar was constructed for Lan Chile,one of the national airlines.20 As well as being used tomaintain its own fleet, the facilities are also available toother carriers. The hangar (Figure 5.50) which is 5300 m2
in area can accommodate simultaneously one Boeing B-747 and two B-737s. It also houses a mezzanine floor forstores, offices and specialist workshops. A steel structurewas chosen because of the necessity for a long clear spanto provide a flexible space and because it was predictedthat the poor ground conditions would lead to differentialsettlement incompatible with other types of structure.Chile, being at the rim of the Pacific tectonic plate, is azone of relatively high seismic activity. The well-knownresistance of space grids to seismic loading pointedtowards the adoption of this type of high-strength, light-weight steel structure for the large clear span.
The 75 m � 75 m hangar roof has four main trussedsteel corner columns, ‘L’ shaped in plan, with columnsof square hollow section 400 mm � 400 mm wall thick-ness 12.5 mm. These are designed to resist the lateral
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5.50Lan Chile hangar,Aeropuerto ComodoroArturo Merino Benítez,Santiago, Chile(Photograph: JohnChilton)
wind and seismic forces. Smaller intermediate columnscarry only vertical load. Perimeter beams link the cornercolumns. The space grid is composed of eighty-onesquare inverted pyramidal modules set on a chequeredpattern grid (i.e. as can be seen in Figure 5.51, alter-nate squares in the diagonal grid do not contain diago-nal bracing members). Top chords of the grid run at anangle of 45° to the sides of the hangar whilst the bot-tom chords, which connect the vertices of the pyramids,run parallel to the sides at 7.5 m centres, thus forminga rotated square on square offset space truss. Each pyra-mid module is 5.3 m by 5.3 m (or 7.5 m by 7.5 m on thediagonal) and 3.87 m deep. They were fabricated on sitein two purpose-made jigs to maintain the precise dimen-sional accuracy required. Although the space grid weighsonly 20 kg/m2 on average, it is able to sustain a con-centrated load of 10 tonnes at any of its nodes, to allowfor the installation of an overhead crane in future. Thisdemonstrates one of the advantages of space grids, theirability to easily accommodate point loads at almost anylocation.
With a simple square roof supported on cornercolumns, it would have been relatively straightforward toassemble the space grid on the floor of the hangar andthen to lift it to its final location by jacking using the per-
manent columns. However, the construction programmedid not permit this and, in fact, the modules were assem-bled in the air, each being supported temporarily on aprop so that the correct unloaded roof profile wasobtained.
To reduce the possibility of condensation on the steel-work, the aluminium-clad roof has mineral wool insula-tion. Roof drainage is into gutters running parallel to thedoor opening, at 15 m centres. Secondary steelwork sup-ported on stools at the upper nodes support a purlin sys-tem to carry the roof decking. Overall, the building is anexcellent example of the use of space grid structures toobtain large clear span volumes of great flexibility in usingtechnology easily exploitable in developing countries.
Year: 1988–91Architects: Cayo César Riquelme V., Rodrigo
Riquelme A., Rafael Videla B., Arquitectos AsociadosStructural engineers: Fluor Daniel Chile S.A., Pablo
Weithhofer, Reinaldo González (Chile), Ronald Taylor (England)
Project director engineer: Carlos Jouanne B.Contractors: Tecsa, Socometal, Construtora B.D.S.,
Vapor Indutrial S.A., Emanor, Ingevec
Palafolls Sports Hall, Spain
Situated between the city of Barcelona and Spain’s CostaBrava, Palafolls is a small town where a sports hall, con-structed in 1991, has a space grid roof of striking form.This roof structure is an example that contradicts thecommonly held perception that space grids are appro-priate only for planar roofs of simple rectangular planform. Its shape was derived from a simple scale work-ing model (Figure 5.52) proposed by the project’s archi-tect Arata Isozaki, who also designed the Sant JordiSports Palace for the 1992 Olympics in Barcelona. Infact, the roof in Palafolls bears some resemblance toIsozaki’s original proposal for the larger Barcelona roof.
The scheme as a whole is based on a 70 m diametercircular plan. Half of this is an open-air sports facility,whilst the remainder is a multi-use pavilion, semicircularin plan, covered by a double-layer, three-way space truss.To provide good natural illumination within the hall, thenorth elevation, which bisects the grand plan, comprisesa vertical glazed façade incorporating deep triangulation(see Figure 5.53) down to a row of vertical columns. Thisdramatic aspect supports one edge of the space truss,whilst the remainder is supported at regular intervalsalong the circular perimeter (see Figure 5.54). Althoughsymmetrical about an axis perpendicular to the glazedfaçade, the roof is an intricate three-dimensionally curvedsurface that is divided into three principal zones. Thecomplexity is compounded by the introduction of a verti-
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5.51Plan of space grid roof, Lan Chile hangar, Aeropuerto ComodoroArturo Merino Benítez, Santiago, Chile (Drawing: John Chilton)
ROOF PLANLAN CHILE HANGAR SANTIAGO
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5.52Concept model,Palafolls Sports Hall,near Barcelona(Photograph courtesyJ. Martínez-Calzón)
5.53Deep truss supports,Palafolls Sports Hall,near Barcelona(Photograph courtesyJ. Martínez-Calzón)
5.54Junction between thetoroidal andspheroidal roof zonesalso showing theperimeter columnsupports, PalafollsSports Hall, nearBarcelona(Photograph courtesyJ. Martínez-Calzón)
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5.55Detailed roofgeometry, PalafollsSports Hall, nearBarcelona (CourtesyJ. Martínez-Calzón)
cal orange segment main rooflight window near the cen-tre and two ‘eyebrow’ windows at the perimeter, to admitnatural daylight to the areas remote from the north ele-vation. At the centre, covering the main sports hall area,there is a spheroidal dome area, external radius 24.35 m,bordered on two sides by the vertical faces of the façadeand the main roof window parallel to it. The centre ofrotation of this dome is offset from the centre of the over-all circular plan. At a lower level a toroidal area, 24.75 mradius in plan and 12.74 m radius in section, surrounds
the central dome and covers the ancillary accommoda-tion. A pseudo-conical area forms a transition betweenthese two main parts, a small conical area joins the baseof the roof window to the outer toroidal zone and twofolds in the perimeter of the toroid form the secondarywindows. The complex curved roof geometry is shown indetail in the part-plan and sections of Figure 5.55 andthe three-dimensional view of Figure 5.56.
Both the upper and lower surfaces of the double-layergrid were generated from a triangular mesh. To achieve
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5.56Three-dimensionalview of the outer layerof the roof grid,Palafolls Sports Hall,near Barcelona(Courtesy J. Martínez-Calzón)
5.57ORTZ joint detail, Palafolls Sports Hall, near Barcelona (Courtesy J. Martínez-Calzón)
a smooth surface and accommodate the defined roofgeometry, with its rapid variation in shape, a relativelyfine grid was required for the upper and lower layers. Inturn, this necessitated a small distance between the topand bottom grids (only 1.125 m). For a roof of this sizethe grid, therefore, required an abnormally large numberof spherical nodes joints (1691 in the top layer and 1607in the bottom layer) and a total of 14 429 members.21,22
Construction of the roof used the ORTZ space trusssystem (Figure 5.57) formed from spherical nodes andtubular bars. The CAD-CAM computerized design andmanufacturing system employed by LANIK S.A. of SanSebastián, Spain, ensured that site assembly wasstraightforward. Tubular steel bars varying between 40.2and 115.7 mm in diameter were used to connect thespherical nodes of between 60 and 210 mm in diame-ter. In total the space truss weighs 64 tonnes, around33 kg/m2 overall, of which approximately 17 per centresults from the weight of the nodes. Erection was facil-itated by using vertical props (Figure 5.58) at predeter-mined nodes to receive previously assembled roof seg-ments. On completion of the space truss structure, loadwas transferred to the permanent supports by graduallylowering the props using the threaded spindles at theirbases. During this procedure, the noted maximum ver-tical deflection at symmetrical points on the structureagreed closely with the predicted value of 21 mm.
Internally, the roof is lined with timber decking whichis fixed to timber purlins spanning between the nodes ofthe space grid. As can be seen in Figure 5.59, the white
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5.58Erection of pre-assembled roof sections, showing temporarypropping of the space grid, Palafolls Sports Hall, near Barcelona(Photograph courtesy J. Martínez-Calzón)
5.59Interior view of theroof after cladding,Palafolls Sports Hall,near Barcelona(Photograph courtesyJ. Martínez-Calzón)
dense, wave-form grid contrasts with the warm shadesof timber roof lining, whilst the segment window intro-duces diffused light to the centre of the sports hall.23
Externally, the roof is covered with standing seam metaldecking (Figure 5.60).
Completed: November 1991Client: Ayuntamiento de Palafolls (Barcelona)
Architect: Arata IsozakiStructural engineer: Professor Dr J. Martínez-Calzón,
Estudio de Ingenieria, MadridContractor: LANIK S.A., Chofre 11 – 1, 20001 San
Space grids at Expo ’92, Seville, Spain
Although it is often thought that space grids were struc-tures of the 1970s and 1980s and that architects nowprefer to use individual ‘one-off’ solutions for their steelbuildings rather than industrialized modular systems,there were many examples to be seen at Expo ’92 heldin Seville, Spain.24,25 Space grids were, in fact, to beseen everywhere as over 50 000 m2 of the site was cov-ered by these structures planted with flowers and smallshrubs in order to provide shading. The system devel-oped by Félix Escrig and J. Valcarcel was based on the
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5.60Exterior view of theroof after cladding,Palafolls Sports Hall,near Barcelona(Photograph courtesyJ. Martínez-Calzón)
5.61(a)Concept sketch, Expo ’92, Seville (Courtesy Félix Escrig)
5.61(b)Computer model for shading structures, Expo ’92, Seville (CourtesyFélix Escrig)
concept shown in Figure 5.61(a) realized in the struc-ture shown in Figure 5.61(b). The grid, approximately1.0 m deep and 1.5 m wide, had the web elements madefrom a continuous length of steel tube bent to the cor-rect profile.
In the Pavilion of Extremadura, a glass floor with largecentral opening was supported by a space grid (Figure5.62) assembled from the modules shown in Figure 5.63connected by ties in the bottom layer. This structure wasassembled in the air, with no temporary support, by grad-ually adding modules from the perimeter towards thecentre (Figure 5.64).
Architecturally, the ONCE (Organización Nacional deCiegos de España) pavilion at Expo ’92 (Figure 5.65)had a simple rectangular plan form based on the com-bination of two cuboids. Main lateral and vertical sup-ports for the pavilion were provided by eight, full-height,diagonal reinforced concrete walls clad in stone (one ateach corner of the two cuboids). Figure 5.66 shows theplan of the pavilion.
In this pavilion constructed for the Spanish NationalOrganisation for the Blind, the contrast between dark-ness and light, opacity and transparency, was empha-sized by the insertion of six large, fully glazed curtainwalls between these solid walls in order to admit natur-al light. The glazed walls were supported by double-layergrids assembled from Orona space trusses used verti-cally instead of the more usual horizontal orientation.The six space truss panels totalling 2533 m2 consist ofthree walls of 436 m2, one wall of 389 m2 and two walls
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5.62Floor grid layout forthe Pavilion ofExtremadura, Expo’92, Seville (CourtesyFélix Escrig)
5.63Individual module and method of assembly for floor construction ofthe Pavilion of Extremadura, Expo ’92, Seville (Courtesy FélixEscrig)
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5.64Pavilion ofExtremadura floor gridduring erection(Photograph courtesyFélix Escrig)
5.65ONCE Pavilion Expo’92, Seville(Photograph courtesyORONA S. Coop.Ltda.)
of 418 m2, all of square on square offset configuration.Module size was standardized at 1.51 by 1.54 m with agrid depth of 1.3 m for the upper 15.4 m of the wallsreducing to 0.5 m for 5.4 m at the base, as can be seenin the wall elevation and section shown in Figure 5.67.The main supports for the space grids, which have main-
ly to resist lateral wind forces, were located at the roofand down the two abutting concrete side walls.
To moderate the hot summer climate of Seville, therewas a ventilated space between the two layers of glaz-ing that were fixed to the opposite faces of the spacetruss (Figure 5.68). The single-glazed outer skin of grey
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5.66Plan of ONCE PavilionExpo ’92, Seville,showing layout ofsolid diagonal wallsand vertical spacegrids (CourtesyORONA S. Coop.Ltda.)
5.67Elevation and section of typical verticalspace grid wall panel for ONCE PavilionExpo ’92, Seville (Courtesy ORONA S.Coop. Ltda.)
reflective glass was designed to reject a high proportionof the solar radiation and the double-glazed inner skinformed the weatherproof building envelope. Special fix-ings (Figures 5.69(a) and (b)) designed and fabricatedby Orona were used to secure the glazing panels to thestandard spherical nodes of the space trusses.
Client: ONCEArchitect: M & B Arquitectos, S.A. (Gilbert Barbany
and Sebastián Mateu)Contractor: Construcción y Gestión de Servicios S.A.
Space frame contractor: Orona S. Coop. Ltda., SanSebastián, Spain
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5.68ONCE Pavilion Expo’92, Seville, lower wallconstruction(Photograph: JohnChilton)
5.69(a)Details of special glazing fixings, for the ONCE Pavilion interior(Courtesy Orona S. Coop. Ltda.)
5.69(b)Details of special glazing fixings, for the ONCE Pavilion exterior
(Courtesy Orona S. Coop. Ltda.)
United Nations Pavilion
One of the more striking structures at the Expo was thesculptural half-dome, double-layer space grid of the UnitedNations Pavilion. The white finish of the tubular metal struc-ture contrasted magnificently with the deep blue of theSeville sky (Figure 5.70) and the massing of the pavilion.
Slightly more than a quarter segment of a sphere, thestructure had an outer radius of 18 m, an overall height of22 m and a grid thickness of 1 m. The total developed sur-face of 1244 m2 was supported at thirteen points (at alter-nate perimeter nodes) around the semicircular base, radius17.55 m (see Figure 5.71). Design loadings included thegrid self-weight of 10 kg/m2, point loads of 38 kg/node atthe joints supporting ornamental features and an allowanceof ± 30 °C for change of ambient temperature.
Architects: José Ramón Rodriguez Gautier, JavierMorales and Luis Uruñuela (Expo ’92)
Space frame contractor: Orona S. Coop. Ltda., SanSebastián, Spain
Markethall, Eagle Centre, Derby, UK
As part of the refurbishment programme of the EagleCentre Market in Derby, UK (Figure 5.72), a ConderHarley System 80, space grid roof of about 9000 m2 waserected in ten weeks from October 1991 to January1992.26,27 The original market, constructed in the 1970s,had hexagonal stalls on a honeycomb grid but was con-sidered below standard for modern fire regulations dueto the distances to fire exits and their poor visibility. Therewas also limited provision for the evacuation of smokein the event of a fire. Alternative solutions within the sev-eral design constraints were sought by Derby CityCouncil. These included that the new roof and marketstructures had to be within the load capacity of the exist-ing market floor and substructure and that the amenitiesand access to the adjacent Derby Playhouse and base-ment car park had to be maintained during construction.
Fire escape routes were improved and the visibilityproblem overcome by changing to a rectangular grid lay-out for the stalls. To combat the smoke evacuation prob-lem the roof was raised over the whole market and addi-tional ventilation provided. The Conder Harley System80 space truss, which employs cold-rolled steel mem-bers, was selected for the roof as it provided a light-weight structure that could be easily installed within thesite access constraints. Along two sides the roof abutsthe main structure of the Eagle Centre, whilst on theother sides a proprietary glazed curtain wall systemadmits light into Markethall.
Existing columns were on a 8.1 m by 7.5 m grid butthese dimensions were doubled for the new column grid
used to support the rectangle on rectangle offset spacetruss. Tubular steel four-branched ‘trees’ were providedon a regular 16.2 m by 15 m grid at approximately 6 mabove the market floor. Despite being supported on alter-nate columns of the original grid, the roof load per foun-dation pile was still within the original capacity. As theexact perimeter of the new space grid roof was difficult toascertain before demolition of the old structure, the edgeswere cantilevered close to the sides and over existingbuildings and then a weather-tight infill was provided later.
Cold-rolled ‘C’ section steel profiles were used for theupper and lower chords which were continuous acrossseveral bays of the 2.7 × 2.5 m grid. Diagonal web brac-ing was of lightweight steel tubes crimped and bent atthe required angle for bolting. The chords were splicedbetween nodes to simplify the connection of the bracing
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5.70Quarter sphere space grid for the United Nations Pavilion, Expo’92, Seville (Photograph: John Chilton)
at the chord intersections. A typical chord splice is shownin Figure 5.73. Given the access problems at the site,the small, lightweight components of the Conder HarleySystem 80 made delivery, handling and erection of theroof structure much easier.
Three alternative methods of erection were used forthis project. Parts of the space grid were erected overareas where public access had to be maintained (e.g.the Derby Playhouse entrance) and these were assem-bled on temporary scaffolding. Other sectors at theperimeter were assembled in small sections and liftedinto place by mobile crane. However, the majority of thespace grid, in areas of up to 1000 m2, was preassem-bled on the existing concrete slab of the market floorand raised into its final position by a proprietary hydrauliclifting process over a system of temporary columns(Figure 5.74). Rooflights were installed on top of thespace truss before it was lifted.
Although this may be considered a rather mundaneand simple project from the architectural point of view,the new Eagle Centre Markethall roof demonstrates thesuitability of space grid structures for refurbishment pro-jects, especially where lightness is paramount (as in thiscase where the new structure had to be carried by theexisting foundation piles).
Owner: CIN PropertiesArchitect: Building Design Partnership and
Progressive Design AssociatesEngineer: Kenchington Ford plc
General and space frame contractor: Conder Projects
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5.72Eagle Centre Market, Derby, UK (Photograph: John Chilton)
5.71Plan, section and three-dimensional view ofquarter sphere space grid,United Nations Pavilion,Expo ’92, Seville (CourtesyOrona S. Coop. Ltda.)
Barrel Vault Atrium, The Bentall Centre,Kingston upon Thames, UK
The fully glazed atrium roof at The Bentall Centre,Kingston upon Thames (Figure 5.75) is a relatively smallspan, space truss, barrel vault that stretches for 120 mand reaches 31 m above the floor of the shopping mall.Within this length, the barrel vault incorporates a 15.4 mspan semicircular three-pinned arch section, a similarsmaller arch supported on vertical space grid walls3.75 m high and 10.01 m between bearings, and an apsein the form of a quarter sphere.28,29 Figure 5.76 (a) showsthe part roof plan and side elevation and Figure 5.76 (b)shows the junction between the barrel vaults of differentradius. The main vaults are constructed from a modifiedversion of the standard Space Deck welded pyramidalmodular system. In order to incorporate a fibre optic lightfor decorative illumination at night, a variation of the stan-dard module was developed with a flat circular boss(120 mm diameter, 50 mm thick and with a central hole)at the vertex of the inverted pyramids.
Twenty-four modules, each 495 mm deep overall, formthe 15.4 m span barrel vault. These are not square, being937.5 mm wide along the axis of the vault and formingchords of 1010 mm around the arch. To accommodatethe 7.5° angle between each module, the steel anglesof the upper grid frame parallel to the main axis of thevault, use specially produced sections with an angle of93.75° between the legs. In the smaller vault the samenumber of modules, of the same 495 mm depth, wereused around the curve of the vault, thus maintaining thesame angle between modules. Here, the modules were625 mm along the main roof axis and 698 mm around
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5.73Eagle Centre Market,Conder Harley,System 80 chordsplice with reinforcingsection bolted insidethe channel section(Photograph: JohnChilton)
5.74Eagle Centre Market, preassembled grid ready for lifting overtemporary columns. A further area of space grid assembledpreviously on temporary scaffolding can be seen in thebackground (Photograph: John Chilton)
the arch; 625 mm by 625 mm in the vertical walls. Figure5.77 shows the cross-section through the 10.1 m barrelvault and Figure 5.78 shows support, glazing fixing andcoffered panel fixing details.
It is generally necessary to consider the potential ther-mal movement of space grids, and this structure was noexception. Due to its overall length, expansion joints hadto be incorporated along the barrel vault by breakingdown the structure into smaller lengths and leaving agap between these bays. The possibility of differentialmovement between the buildings supporting the barrelvault also had to be considered. Following computer
analysis of alternative structural mechanisms it wasdecided to construct the barrel vault as a three-pinnedarch (with pin joints at the supports and crown as seenin the section in Figure 5.77) to minimize adverse effectson the glazing and cladding panels. The predicted max-imum temperature for the roof structure was 50 °C andthe adoption of the three-pinned arch avoided the gen-eration of excessive forces due to thermal expansion thatcould have otherwise occurred in this case.
Erection of the space grid was expedited by the con-struction of a temporary working platform, made from stan-dard Space Deck modules, positioned just below the
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5.75Barrel-vault atrium at The BentallCentre, Kingston upon Thames(Photograph courtesy SpaceDecks Ltd)
springing point of the vaults and spanning the width of theatrium. This solution allowed other work to proceed beneaththe temporary deck and was cheaper than erecting scaf-folding from the atrium floor level. To erect the barrel vaults,half-arch sections were assembled on the working plat-form. Then, following the erection procedure shown inFigure 5.79, one half section was positioned and held inplace by tower crane, whilst the other half was lifted intoposition and joined to it at the ridge to form the stablethree-pinned arch. The new bay was then connected tothe adjacent completed space truss. Tower crane liftingcapacity dictated the size of the preassembled sections.
Overall, the space grid provided a lightweight modu-
lar solution to the architectural problem of controlling theillumination within the extensive atrium of the BentallCentre. Perforated metal coffered ceiling panels,designed to curtail direct sunlight by 50 per cent, aresupported easily on the regular grid, and the bosses ofthe inner nodes house the fibre optic lighting that pro-duces a star-spangled array against the dark night sky.Primary and secondary structures are combined to pro-duce an efficient system.
Client: Norwich UnionArchitect and engineer: Building Design Partnership
Main contractor: MowlemSpace frame contractor: Space Decks Ltd
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5.76(a) Part roof plan andside elevation of theatrium roof, BentallCentre, Kingstonupon Thames(courtesy Space Decks Ltd). (b) TheBentall Centre,Kingston uponThames, three-dimensional view ofjunction between 15.4and 10.l m barrelvaults (CourtesySpace Decks Ltd)
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5.77The Bentall Centre, Kingston upon Thames, cross-section through 10.1 m span three-pinned barrel-vault (Courtesy Space Decks Ltd)
5.78The Bentall Centre, Kingston upon Thames, construction details for supports, glazing fixingand coffered panel fixing (Courtesy Space Decks Ltd)
Terminal 2, Manchester Airport, UK
Pressure on the existing terminal facilities at ManchesterAirport, UK, required a new terminal building, which wasopened in 1993.30 The new facility incorporates 6000 m2
of space grid roof. Powder polyester-coated Nodusspace truss, is used to form three glazed atria and anentrance concourse 115 m long. This comprises approx-imately 180 tonnes of steel, in excess of 2500 jointsand 10 000 tubular members. The square on square off-
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5.80Aerial view of Nodusspace grid roof underconstruction, Terminal2, Manchester Airport,UK (Photographcourtesy SpaceDecks Ltd)
5.79The Bentall Centre, Kingston upon Thames, diagram of erection procedure; (a) half-arches assembled on temporary Space Deck workingplatform (b) one half lifted on to permanent support and held up by tower crane and (c) second half lifted placed and connected to formfull arch (Courtesy Space Decks Ltd)
set grid includes inclined and flat planar sections on atotal of sixteen levels, as can be seen in the aerial viewof the space grid under construction (Figure 5.80). Insuch a visually prominent situation, the space gridrequires a high level of consistent detailing. Therefore,throughout the space truss, hot-finished British Steel60.3 mm diameter circular hollow section top and bot-tom chords and 48.3 mm diameter bracing members areused. For economy, the tube wall thicknesses are var-
ied depending on the member forces but the size of theNodus joints is standardized to maintain a consistentaesthetic.
The three atria are perimeter-supported every two gridbays along their length, whilst the entrance concourseis generally supported every two bays at the rear and atthree bay intervals at the front, where there is also a4.8 m, two bay, cantilevered section (as shown in theroof plan and section in Figures 5.81 and 5.82).
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5.81Roof plan, Terminal 2,Manchester Airport,UK (Courtesy SpaceDecks Ltd)
5.82Roof section, Terminal 2 , Manchester Airport, UK (Courtesy Space Decks Ltd)
Assembly of the space truss was carried out on theground away from the terminal building to avoid inter-ference with other construction work. After assembly, theroof was lifted in eleven separate sections by a 500 tonnemobile crane (Figure 5.83). The heaviest roof assemblyweighed 25 tonnes and the longest reach required toplace a space truss section was over 75 metres.
A separate entrance canopy was also constructedusing 30 tonnes of Nodus space truss. The double-layergrids of the canopy provide a homogeneous structuraltheme although space grids are not usually consideredeconomical when used to span primarily in one direc-tion, as a beam, as they do here. In this roof structure,supported on ten tubular lattice columns, there were 885joints. Some cantilevered sections of the canopy weresuspended from tubular ties/struts attached to masts.The canopy was covered with single-skin profiled metaldecking on the horizontal surfaces and tinted laminatedglass on the inclined faces of the mansard edges.
Overall, the Manchester Airport Terminal 2 projectdemonstrates the versatility of the Nodus space trusswhich allows coherent structural detailing throughout theexposed and glazed sections of the roof despite the manydifferent forms.
Client: Manchester International Airport PLCProject Management: T2 Project Management Team,Manchester Airport Directorate of Development andPlanning. City Architect, City Engineer, Audit Team,
Taylor Woodrow Construction
Management contractor: AMEC Projects LtdDesign co-ordinator, architect and interior designer:
Scott, Brownrigg & TurnerStructural engineer: Scott, Wilson Kirkpatrick
Steelwork contractor: William Hare LtdSteelwork contractor (space frame): Space Decks Ltd
Fantasy Island, Pyramid, Skegness, UK
This project illustrates the use of lightweight sections (theSpace Decks Ltd Multiframe System) to form a largepyramidal structure, but perhaps the most interestingaspect of this project is that the whole space grid wasassembled in an adjacent car park before being liftedand transported 100 m to its final location.
The pyramid 50 m by 50 m in plan and 20 m high (seethe plan and elevation in Figure 5.84) was assembledfrom four similar triangular segments of rectangle on rec-tangle space grid, having a 2.94 m by 3.84 m module,1.9 m deep. To erect the structure several cranes wererequired. Initially, one segment was lifted on to tempo-rary supports and the apex of the triangle was held aloft,to maintain the segment in its correct inclined position.A second segment was then lifted and connected to itstemporary supports on the opposite side of the squarebased pyramid and to the first segment at the apex.
Thus a stable ‘A’ frame (Figure 5.85) was created towhich the remaining two segments were then fixed. Once
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5.83Lifting a pre-assembled section ofNodus space grid atTerminal 2,Manchester Airport(Photograph courtesySpace Decks Ltd)
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5.84Plan and elevation, pyramidal Multiframe space grid for Fantasy Island, Skegness, UK (Courtesy Space Decks Ltd)
5.85Part erected pyramidin the car parkadjacent to its finallocation; twosegments are alreadyconnected to form astable ‘A’ frame(Courtesy SpaceDecks Ltd)
PLAN ON SEGMENTS
SKEGNESS PYRAMIDMULTIFRAME SCHEME
the complete pyramid had been assembled, it was lift-ed at its apex by a single large mobile crane and swunginto its final position (Figure 5.86). The strength and light-ness of the Multiframe grid enabled this delicate liftingoperation to be accomplished without difficulty.
Client: Blue Anchor Leisure LtdArchitect: IDS Studios
Engineer and space frame contractor: Space DecksLtd
Roundwood timber space trusses
Timber is a material that is not commonly used for theconstruction of space grid structures. However, someexamples have been constructed using what is rarelyconsidered a suitable material for long-span buildings,roundwood poles. In well-managed timber plantationstrees are initially planted close together to encouragethem to grow fast and straight. As their size increasesit is necessary to thin out the plantation to provide morelight and nutrition to each tree. During this thinningprocess many trees between 150 and 200 mm in diam-eter are felled, a size too small to be of much practicaluse as structural sawn timber. However, after debark-ing, suitably straight specimens can be used structural-ly, as roundwood poles, and these are eminently suit-able for use in cheap timber space truss structures.
The fibres in the section of a tree trunk run only approx-imately longitudinally. Thus, when the cross-section issawn into smaller rectangular sections, the strength ofthe timber is reduced as some of the fibres are now nolonger continuous along the piece of wood. Typically, thebasic permissible stresses in bending, tension and com-pression of sawn structural timber are respectively aboutone-third, one-quarter and two-thirds of those of rounddebarked timber. Machine-rounded timber is slightlyweaker than debarked timber. Equally important, muchof the original cross-section is simply cut off and wast-ed. By trimming four sides of a circular trunk to form asquare section the usable cross-sectional area isreduced by 36 per cent, the elastic section modulus(directly related to the bending resistance of the beam)is reduced by 40 per cent and the second moment ofarea (related to buckling of struts under axial compres-sion and deflection of beams) by 57 per cent (Figure5.87). The members in space trusses carry mainly axialforces and the solid circular cross-section of the round-wood poles is ideal for resisting axial compression (justas circular tubes of steel and aluminium are used inmetal space trusses). As with all timber structures themain problem to be overcome is the design of a strongconnection between the individual elements, particularlyin tension, and this is further exacerbated when the sec-tions are circular. The difficulty of joining timber is espe-cially pertinent to space trusses where there will typically
114 Space Grid Structures
5.86Complete 50 m by50 m pyramid beinglifted into its finallocation by a singlelarge mobile crane(Courtesy SpaceDecks Ltd)
be eight members radiating from a node in a square onsquare offset grid. Metal connectors of some form aretherefore necessary.
The basic material for the members – roundwood poles– is relatively cheap. Therefore, it is logical to derive ajointing system that is also cheap and simple. Dr PieterHuybers at the Technical University in Delft, theNetherlands, has developed a simple wire lacing method(using an appropriate lacing tool) for clamping galvanizedsteel connector plates in the pre-slotted ends of round-wood poles (Figure 5.88). The procedure for installationof connector plates is as follows. After cutting the slotand drilling transverse holes, the pre-drilled, plate con-nector is inserted. Then tubular liners are installed in theholes and the wire lacing is passed through. The lacingtool is then used to tension the wire to a preset value;the ends of the wires are trimmed and hammered intothe face of the timber.
Several different plate connectors have been devel-oped, some of which require a separate node and oth-ers that can be connected together directly (nodelessconstruction). Experimental and agricultural space gridprojects have been constructed from roundwood polesin the Netherlands and in the UK.31 For example, a smallsingle-layer, lattice dome exhibition pavilion 5.8 m diam-eter and 5.5 m high was built in 1984 and reconstruct-ed in Delft in 1987. An equipment storage shed, 16.2 mby 10.8 m, constructed at Lelystad, in the Netherlands(Figure 5.89) had a space truss roof made of 100 mmdiameter larch poles, supported on eleven timbercolumns. The four by six bay square on square offsetgrid was built in 1986 using the galvanized steel 6 mmthick circular node and 6 � 90 � 260 mm connectorplates shown in Figure 5.90. For durability, the timberwas impregnated with CCA (copper cyanide arsenic)preservative. In the UK, also in 1986, an 8.1 m � 18.9 mprototype agricultural building was constructed atBridget’s Farm, near Winchester (a Ministry of Agricultureexperimental farm). Supported on twelve columns, theroundwood timber space truss was 1.9 m deep and com-prised of 168 roundwood members of 100 mm diameterand 2.5 m in length. All members were prepared off siteand only bolted connections were necessary to assem-ble the grid before it was lifted by crane on to the 200 mmdiameter timber columns. More recently, in 1995, anobservation tower 27 m in height was erected, atApeldoorn in the Netherlands, using roundwood polesup to 200 mm in diameter.
The tower (Figure 5.91) can be considered a verticalset of rectangular on rectangular offset grids (Figure5.92) in which the connecting nodes (Figure 5.93) areassembled from four identical components fabricatedfrom standard steel angle. Once assembled the nodesallow up to eighteen bars to be connected, dependingon the configuration.
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5.87Reduction in section of a piece of timber from roundwood tosquare. (This reduces the area by 36 per cent, the elastic sectionmodulus by 40 per cent and the second moment of area by 57 percent) (Drawing: John Chilton)
5.88Lacing tool being used to secure a metal connector plate into aroundwood pole (Photograph courtesy Pieter Huybers)
116 Space Grid Structures
5.89Equipment storage shed, 16.2 m by 10.8 m, constructed at Lelystad, in the Netherlands (Photograph courtesy Pieter Huybers)
5.90Galvanized steel6 mm thick circularnode and 6 � 90 �260 mm connectorplates used atLelystad, in theNetherlands(Photograph courtesyPieter Huybers)
The projects described above, although generallysmall in nature, demonstrate that efficient three-dimen-sional structures can be constructed from what is oftenconsidered to be, at best, low-grade timber and in manycases material only fit for being reduced to wood chipsor pulp. There is, of course, no reason why this form ofconstruction should not be used for more prestigiousarchitectural projects, for instance, visitor centres, muse-ums or low-energy designs. As the material is cheap andplentifully available in countries with forests, and theassembly technique is relatively simple, roundwood polespace grids have high potential for exploitation in theconstruction of factory, storage and agricultural buildingsin developing countries.
Architect: Pieter HuybersEngineer: Pieter Huybers/De Bondt
Construction: Mulder b.v., Apeldoorn
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5.91Roundwood pole tower at Apeldoorn, the Netherlands, assembledfrom timber components 120 to 200 mm diameter (Photographcourtesy Pieter Huybers)
5.92Three-dimensional view of the structure for the roundwood poletower at Apeldoorn, the Netherlands (Courtesy Pieter Huybers/H.Hendriks, De Bondt)
Atlanta Pavilion (unbuilt project)
As noted in the previous example, timber is used infre-quently for space grids and in turn space grids are rarelyused to support roofs having irregular geometry.However, timber was the material chosen for the pro-posed Atlanta Pavilion, which was to be built to housefacilities for visitors to that city during the Olympic Gamesheld there in July 1996. The pavilion would have includ-ed an exciting free-form, space grid with apparently ran-dom, roof geometry.
The original project brief given to the Atlanta-basedarchitects, Scogin Elam and Bray by the Committee forthe Olympic Development Atlanta (CODA), called for aticket booth, a cafeteria and an audio visual experience– The Atlanta Experience – to provide information aboutthe city and its environs. To generate a striking land-mark for the prominent air-rights site, situated above thePeachtree MARTA station in central Atlanta, the archi-tects proposed a large free-form shading canopy risingto approximately 33 m at its highest point.
The client, CODA, invited Ove Arup and PartnersInternational Ltd to collaborate with the architects toinvestigate how the project might be accomplished.Timber products are manufactured by the owners of theair rights, Georgia Pacific, who have offices in a high-rise building adjacent to the site. This, together with theproposed short life for the building (two to three years)and restrictions on the load (an additional 250 lb/ft2 or1050 kg/m2) that could be imposed on the existing con-
crete roof structure, suggested timber as the main mate-rial for the exhibition space, access ramps and roofcanopy.
Initially, the free-form roof was rationalized in such away that the random appearance could be maintainedwhilst the geometry could be defined and communicat-ed to the contractor to permit economic construction.After measurement of the architects’ model, a comput-er model (shown in elevation in Figure 5.94 (a)) wasgenerated based on 2.4 m � 2.4 m (8 ft � 8 ft) grid,viewed in plan (see Figure 5.94(b)).
Individual nodes were displaced vertically until the sur-face obtained approximated to that of the physical model.Thus, each square in plan was covered by a warpedsurface. To produce a surface that could be clad usingflat panels, each quadrilateral was divided into two tri-angular facets that could be supported by the timberspace grid (Figure 5.95).
Three options were considered for the structure tosupport the roof surface: two alternative space grids,one with 2.4 m � 1.2 m (8 ft � 4 ft) triangular uppergrid and the other with an 2.4 m � 2.4 m (8 ft � 8 ft)square upper grid, and a tree-like structure on a 3.05 m� 3.05 m (10 ft � 10 ft) grid. Models were constructedby the architects to assess the structural alternativesfrom the aesthetic viewpoint and the 2.4 m by 2.4 m(8 ft by 8 ft) square grid was subsequently selected.The space grid and enclosure model are shown inFigure 5.96.
Because of the irregular geometry of the space grid,steel spherical nodes were considered most appropriateto connect the glulam timber members in a manner sim-ilar to the Mero Holz system described in Chapter 3.Supports for the grid were arranged in an apparently ran-dom pattern with inclined columns of glulam timber upto 30.5 m (100 ft) in length. This configuration of cruci-form glulam columns, fabricated from two square sec-tions fixed to a rectangular section, one on each side,provided overall lateral stability to the canopy when linkedto the bending stiff space grid. Sizes for the sphericalnodes and the minimum angle that could be accommo-dated between the grid members were determined byIngenieurbüro Peter Bertsche in Germany.
Client: Committee for the Olympic Development AtlantaArchitect: Scogin Elam and Bray, Atlanta
Engineer: Ove Arup and Partners/Ingenieurbüro Bertsche
Milan Fair, New Exhibition Facilities, Milan,Italy
The new buildings for the Milan Fair, situated in a restrict-ed location near the centre of the city and adjacent to a
118 Space Grid Structures
5.93Typical node for tower at Apeldoorn, the Netherlands (a)unassembled and (b) assembled (Courtesy Pieter Huybers/H.Hendriks, de Bondt)
Case studies 119
5.94(a)Elevation of therationalized computermodel of the AtlantaPavilion (CourtesyScogin Elam andBray)
5.94(b)Plan of therationalized computermodel of the AtlantaPavilion. (CourtesyScogin Elam andBray)
principal road, feature three large pavilions accommo-dating two-storey exhibition areas and roof-top parkingfacilities (Figures 5.97). The pavilions, which cover anarea approximately 650 � 100 m, incorporate many pre-fabricated elements, primarily precast concrete compo-nents, for speed of erection. However, the upper exhi-bition floor is of particular interest in this study as it
features a deep, double-layer composite space trussstructure.32,33
The exhibition floor is suspended 15 m above groundlevel in square bays corner-supported by columns on a20 m by 20 m grid. A live load of 15 kN/m2 was speci-fied for the exhibition area floor. When this heavy load-ing was considered together with the regular square plan
120 Space Grid Structures
5.95Cladding model forthe Atlanta Pavilionshowing the divisionof warped squareplanes into triangularcladding sections(Courtesy ScoginElam and Bray)
5.96Space grid andenclosure modeldemonstrating thegeometricalcomplexity of thestructure (CourtesyScogin Elam andBray)
Case studies 121
5.97Milan Fair Exhibition Facilities floor plan and elevations of a typical pavilion (Courtesy G. C. Giuliani, Redesco srl.)
bays, the access required for mechanical and electricalservices and adequate fire separation of the upper andlower exhibition areas, the adoption of a deep two-wayspanning floor structure with concrete deck was deemedappropriate.
The solution employed utilizes upper and lower con-crete decks separated by steel space truss diagonalsto form a composite space grid structure 2.74 m deepoverall. Figure 5.98 shows the plan and section of atypical floor bay, with the top left quadrant of the planillustrating the waffle pattern of the lower concrete slaband the top right quadrant representing the dispositionof the precast waffles and the corner bracing struts. Thelower left and right quadrants depict the position andorientation of the cast nodes in the lower and upper lay-ers respectively and the layout of the steel ‘web’ mem-bers. Lower deck concrete slabs were post-tensioned,cast in situ, waffle type. Generally only 60 mm thick, theslab had 0.3 m deep by 0.55 m wide ribs housing thepre-stressing cables on a 2.5 m by 2.5 m grid and duc-tile cast iron nodes embedded in the concrete at each
rib intersection. Between the upper and lower concreteslabs, each 20 m by 20 m floor bay contained internalhalf-octahedral/tetrahedral tubular steel bracing on a2.5 m by 2.5 m grid and tetrahedral edge assemblieson a 1.25 m by 2.5 m grid. Grid depth between the upperand lower layers was 2.35 m. After installation of thereinforcement, pre-stressing cables and the steel trusscomponents the lower deck concrete was cast onreusable metal formwork. Upper slabs were also castin-situ, on permanent waffle-shaped precast concreteformwork only 50 mm thick. The permanent formworkwas supported from the upper cast nodes again on a2.5 m by 2.5 m grid. A three-dimensional view of a fullfloor bay is shown in Figure 5.99 and detailed views ofthe steel and prestressing components (before con-creting) and the completed column/deck junction areshown in Figure 5.100. At the corners, additional steelbracing struts and cast iron elements link the adjacentfloor nodes to bearings set in recesses in the precastconcrete columns. These elements articulate so thatthey do not interfere with the raising of the floor between
122 Space Grid Structures
5.98Plan and section of typical floor bay, MilanFair Exhibition Facilities (Courtesy G. C.Giuliani, Redesco srl.)
the precast columns but can be subsequently deployedto provide support from the columns. The assembly pro-cedure for the composite space truss structure is shownin Figure 5.101 and can be summarized in the follow-ing phases:
1 Preparation of the 20 � 20 m steel movable form-work between the four columns; preassembly ofspace truss segments complete with nodes attached.
2 Placing of preassembled space truss segments onformwork; placing of preassembled steel bar rein-forcement and pre-stressing cables.
3 Concreting, curing and pre-stressing of the lowerslab; installation of ducts, wiring equipment, etc.
4 Placing of precast waffles and reinforcement forupper slab.
5 Concreting of the upper slab.6 Hoisting of the complete orthotropic slab using
hydraulic jacks.7 Final positioning, extension of retractable corner ele-
ments inside column recesses; connection tocolumns.
Phases 1 to 5 were carried out at ground level beforeraising each 480 tonne floor bay to its final location 15 min the air. The placing of precast waffles on top of thepreassembled space truss units (phase 4), is shown inFigure 5.102.
Case studies 123
5.99Three-dimensional view of typical floor bay 20 m by 20 m seen from below, Milan Fair Exhibition Facilities (Courtesy G. C. Giuliani, Redescosrl.)
5.100Detailed views of steel components and the completed floorassembly at the corners. Note the pre-stressing tendons passingthrough the cast nodes (Courtesy G. C. Giuliani, Redesco srl.)
An important feature of the floor construction is thecast node joints which act as shear connectors betweenthe concrete slabs and the steel bracing. Of the three
solutions considered for these joints, (fabrication fromwelded plates and machined billets, casting in steel orductile cast iron) the latter was selected due to its econ-omy and the possibility of monitoring defects using non-destructive ultrasonic testing. All of the cast nodes havea portion embedded in the concrete slab and lugs ori-entated to connect the steel tube diagonals. In the bot-tom layer the embedded cast section has holes to allowthe pre-stressing tendons to pass through the castingand in the upper layer the embedded section is a moretraditional shear stud. Different pin diameters for con-nection to the tubular diagonals and the different thick-nesses required to cater for the design forces, resultedin twenty-eight types of node casting. Dimensions for thecast nodes were accurately controlled and the use ofautomated drilling and machining ensured that the holesto receive pins were correctly located relative to the cen-tre of the joint with a tolerance of ± 0.5 mm. Fabricationdetails for a typical lower-layer node, where provision ismade for the passing of pre-stressing strands and for atypical upper-layer node, with shear connection and sup-ports for the precast floor formwork, are shown in Figure5.103. Typical finished top-node castings are shown inFigure 5.104.
Steel tube sizes for the bracing members variedaccording to the forces to be resisted. Diameters rangedfrom 75 to 270 mm but those over 140 mm were onlyrequired near the corners to transfer the load to the bear-ings. With variations of section size and lug connectorplate size, thirty different member-types were producedusing automated CAM technology to ensure that therequired tolerance for the distance between pin con-nector holes was achieved.
124 Space Grid Structures
5.101Phases for assembly and erection of a floor bay, Milan FairExhibition Facilities: (1) preparation of the movable steel formworkand preassembly of space truss elements; (2) placing of spacetruss, reinforcing bars and pre-stressing cables; (3) concreting oflower slab, installation of services; (4) placing of precast wafflesand reinforcement of upper deck; (5 and 6) concreting of upperslab and lifting of completed floor section; (7) extension ofretractable corners and connection to columns (Courtesy G. C.Giuliani, Redesco srl.)
5.102Phase 4 of assembly/erection of the floor bay, Milan Fair ExhibitionFacilities, the precast waffles being installed prior to concreting ofthe upper floor (Courtesy G. C. Giuliani, Redesco srl.)
(5) and (6)
(1) and (2)
Case studies 125
5.103Fabrication details fortypical lower layercast node and typicalupper layer castnode, Milan FairExhibition Facilities(Courtesy G. C.Giuliani, Redesco srl.)
This floor structure demonstrates the adaptability ofspace grids from their more common role as lightweightsupports for long-span roofs to more heavily loadedapplications. It shows how well tried technologies andmaterials can be used in combination to their best advan-tage, in an innovative way, to achieve an economicalsolution for long-span floors.
Client: Ente Autonomo Fiera MilanoContract period: September 1994 – November 1996Structural consultants: dr. eng. Gian Carlo Giuliani,
dr. eng. Mauro Eugenio GiulianiStructural design: Redesco srl, Milan, Italy
Construction: Itaca Joint Venture (CMC/Recchi/G.Maltauro/E. Frabboni/CGC/Italtel Telesis/Kone)
Stadium Australia, Sydney, Australia
At the time of writing, December 1998, Stadium Australia(Figure 5.105) is currently under construction34 in prepa-ration for the Olympic Games to be held in Sydney inthe year 2000. The vast stadium, of 110 000 seatedcapacity for the duration of the Games, will eventuallyhold 80 000 spectators (after the removal of temporarystands at each end of the arena). Sight distances to thefield of play dictate the form of the stadium which isapproximately circular in plan around the rectangular
playing field with covered seating along the longer sidesof the arena.
The solution adopted for the roof over this seating isa diagrid steel space truss supported at the outer perime-ter on the raked stand and at the other edge by a deeparch truss spanning 285.6 m (Figure 5.106). The spacegrid supports secondary members that, in turn, supportthe twin-wall polycarbonate sheet glazing. To minimizethe overall height of the stadium the roof diagrid formspart of a hyperbolic paraboloid surface, arching alongthe major axis of the stadium and sagging along theminor axis. Placing the arch above the roof surfaceimproves its structural efficiency and also maintainsunobstructed views for the spectators high in the stands.The chords of the double-layer grid are set on the diag-onal (i.e. at an angle of 45° to the stadium axis) in orderto generate the double-curved surface using straightlines. A 10 m � 10 m grid (Figure 5.107) was adopted.This has a depth that varies from a maximum of 4 mdown to zero at the perimeter, in line with the three-dimensional bending moment envelope for the surface.To accommodate differences in geometry between thepositions of the diagrid perimeter nodes and the supportbeams of the raked seating, the two were linked by aprismatic truss (Figure 5.108).
In its eventual form the stadium will have additionalareas of roof over the end stands. These will also uti-lize a 10 m � 10 m grid and taper towards the edges
126 Space Grid Structures
5.104Typical upper layercast nodes awaitinginstallation, Milan FairExhibition Facilities.Examples of thetubular steel webelements can be seenin the foreground(Photograph: JohnChilton)
from a maximum depth of 6 m at the centre. Before theseend roof sections are installed the membrane actionassociated with the saddle surface is unable to develop.In the permanent roof configuration, the perimeter pris-
matic beam is extended to form a complete undulatingring and the infill diagrids allow some significant mem-brane action to occur. Thus the structural efficiency ofthe infill sections is enhanced.
Case studies 127
5.105Stadium Australia,Sydney, underconstruction inpreparation for theOlympic Games inthe year 2000(Photograph: JohnChilton)
5.106The 285.6 m spanarch supporting thefront edge of thehyperbolic paraboloidspace grid roofsurface of StadiumAustralia. Thecurvature of the roofgrid can clearly beseen (Photograph:John Chilton)
Anticipating future developments, the design of the roofand arch supports allows for the addition of a fullyretractable infill roof weighing up to 6000 tonnes. Aninteresting feature of the space grid roof is that (at thesuggestion of the fabricator, National Engineering) theelements are connected by vertical axis pins that passthrough horizontal connector plates (Figure 5.109). In thetop layer the chords follow straight lines but in the bot-
tom layer the variations in chord direction are achievedby a fold in the node plates.
Although it was originally proposed to erect the dia-grid by connection of individual inverted pyramids, in theair, the eventual erection process commenced with theproduction, on the ground, of assemblies up to 90 m inlength. These were then craned into position, connect-ed at each end to the arch and perimeter truss respec-
128 Space Grid Structures
5.107Roof plan of 10 m � 10 m diagrid,Stadium Australia (CourtesyMODUS Consulting)
5.108Perimeter roof trussbetween the diagridand the rakedseating. Installationof the twin-wallpolycarbonate roofpanels is in progress(Photograph: JohnChilton)
tively, before being gradually lowered and connected tothe adjacent grid elements.
Despite its enormous span of almost 300 m, at aweight of 88 kg/m2 the roof steelwork of StadiumAustralia demonstrates the economy and efficiency ofspace grids. In this project the provision for the lateraddition of a retractable roof appropriately leads us intothe following chapter where such structures are dis-cussed along with foldable and deployable space grids.
Client: Olympic Coordination AuthorityArchitect: Bligh Lobb Sports Architects (Sydney)
Contractor: Multiplex Constructions (NSW) Pty LimitedEngineer: MODUS Consulting
1 Tange, K. (1970). Kenzo Tange 1946–69,Architecture and Urban Design (Udo Kultermann,ed.) p. 284, Pall Mall Press, London. © Verlag fürArchitektur Artemis Zürich, Switzerland.
2 Tsuboi, Y. and Kawaguchi, M. (1972). The space
frame for the Symbol Zone of Expo 70. InProceedings 1971 IASS Pacific Symposium Part IIon Tension Structures and Space Frames, Tokyoand Kyoto, pp. 893–904, Architectural Institute ofJapan.
3 Kawaguchi, M. (1992). On a few topics of membranestructures. In Innovative Large Span Structures (N.K. Srivastava, A. N. Sherbourne and J. Roorda, eds)vol. 1, pp. 28–48, The Canadian Society for CivilEngineering.
4 Satterwhite, R. G. (1984). Space frames as houses.In Proceedings of the Third International Conferenceon Space Frames (H. Nooshin, ed.) pp. 1031–4,Elsevier.
5 Fischer, R. E. (1980). The Crystal Cathedral: embod-iment of light and nature. Architectural Record,November, 168 (7), 77–85.
6 Anon (1981). Structural Steel Design Award 1981.Acier-Stahl-Steel, 4, p. 149.
7 Yamasaki, M. (1983) Shinji Shumei-kai Temple.Japan Architect, September 1983 (8309) 58 (317)22–29.
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5.109Typical roof nodes of the diagonal of Stadium Australia showing theuse of horizontal plates and vertical pin connectors (CourtesyMODUS Consulting)
8 Anon (1980). A vast space frame wraps New York’sConvention Center like a taut fabric. ArchitecturalRecord, Mid-August 168 (3), 47–57.
9 Levy, M. (1997). Tetrahedral purity: the Javits Center.In Beyond the Cube (J.-F. Gabriel, ed.) pp. 189–209,Wiley.
10 Yoh, S. (1989). Oguni Dome. The Japan Architect,February 382, 35–41.
11 Sakamoto, I. (1992). Wooden spatial structures inJapan. Bulletin of IASS, 33 (109), 111–13.
12 Kubik, L. A. and Chilton, J. C. (1991). Design andconstruction of the CUBIC Space Frame roof,Maintenance Hangar, Stansted Airport. In SpatialStructures at the Turn of the Century, (T. Wester, S.J. Medwadowski, and I. Mogensen, eds) vol. 1, pp.135–42, Kunstakademiets Forlag Arkitektskolen.
13 Reina, P. (1990). Barcelona builds for the Olympicsand beyond. Engineering News Record, 15 February,34–6.
14 Kawaguchi, M. and Abe, M. (1992). Design and con-struction of Sant Jordi Sports Palace, a venue forBarcelona Olympics. Bulletin of the InternationalAssociation for Shell and Spatial Structures, 33(109), 69–88.
15 Delgado, R. (1990). Palau D’Sports Sant Jordi,Editorial Trazos SA de Arquitectura y Construccion,(in Spanish).
16 Allen, J. (1991). Biosphere 2 – The HumanExperiment (Anthony Blake, ed.). Penguin Books.
17 Pearce, P. J. (1993). From snow crystals to spaceenclosure systems: implementing the future of archi-tecture. In Space Structures 4 (G. A. R. Parke andC. M. Howard, eds) vol. 2, pp. 2063–73, ThomasTelford.
18 Doyle, N. (1990). World class Birmingham. NewBuilder, 59 November, 20–1.
19 Roche, J. J. and Elliott, A. W. (1991). The Merospace frame roof to Birmingham’s National IndoorArena for Sport. Steel Construction Today, 5 (2)March, 64–7.
20 Anon (1992). Obras Relevantes en Acero 1962–1992. Compañia Siderurgica Huachipato S.A.,Empresa CAP, pp. 81–4 (in Spanish).
21 Martínez-Calzón, J. (1995). Palafolls Sports Hall : asingular roof. In Spatial Structures: Heritage, Present
and Future (G. C. Giuliani, ed.) vol. 1, pp. 629–38,IASS International Symposium.
22 Martínez-Calzón, J. (1995). Palafolls Sports Hall: asingular roof. IASS Bulletin, 36 (3), 157–66.
23 Arata Isozaki and Associates (1995). Multi-sportspavilion in Palafolls, Barcelona. ON Diseño, 179,68–85.
24 Rispa, R., Alonso de los Rios, C. and Aguaza, M.-J. (eds) (1992). Expo ’92 Sevilla, Arquitectura yDiseño. Electa, pp. 290–1.
25 La Arquitectura de la Expo ’92. ON Diseño, 224–8.26 Codd, B. and White, S. H. (1992). Eagle Centre
Market refurbishment, Derby. The StructuralEngineer, 70 (5), March, 77–80.
27 Codd, B. (1991). Conder introduces Harley spaceframe to Europe. Steel Construction Today, 5 (2),March, 77–80.
28 Baird, S. C., James, N. L. and Shotton, J. E. (1993).Space deck barrel vault to the Bentall Centre,Kingston upon Thames. In Space Structures 4 (G.A. R. Parke and C. M. Howard, eds) vol. 2, pp.1392–9, Thomas Telford.
29 Peachey, D. H. and Dyer, D. J. (1994). Design andconstruction of the new Bentall Centre, Kingston-upon-Thames, Surrey. Proceedings of the Institutionof Civil Engineers, Structures and Buildings, 104,November, 369–76.
30 British Steel (Tubes and Pipes) (1994). Case Study8, Manchester Airport Building, 12 August, pp. 34–36.
31 Huybers, P. (1990). Thin poles of roundwood forstructural engineering applications in building.Structural Engineering Review, 2, 169–82.
32 Guiliani, M. E. (1995). Innovative composite spatialstructures for the New Milano Fair Exhibition facili-ties. In Spatial Structures: Heritage, Present andFuture (G. C. Giuliani, ed.) vol. 1, pp. 451–66, IASSInternational Symposium.
33 Giuliani, M. E. (1995). Innovative composite spatialstructures for the New Milano Fair Exhibition facili-ties. IASS Bulletin, 36 (3), 167–82.
34 Morley, S. and Whatmore, J. (1998). StadiumAustralia. In Lightweight Structures in Architecture,Engineering and Construction (R. Hough and R.Melchers, eds) pp. 41–8, LSAA.
130 Space Grid Structures
Deployable and foldable space grids
One area in which space grids are set to advance in thefuture is the field of deployable and foldable structures.The property of deployability in a space grid structuremay be used just once or many times. For example, thedeployability may be used to facilitate the erection of apermanent building or support structure. An obviousapplication is in outer space where large structures arerequired to support equipment such as arrays of photo-voltaic panels. These space grids can be assembled incompact form, transported into outer space and thendeployed in a ‘one-off’ operation. Alternatively, tempo-rary transportable buildings can benefit from the use ofrapidly deployable structures. In this case, the space gridis deployed each time the building is erected, later beingcollapsed down to a more compact form before beingmoved to store or another location. The process can berepeated any number of times.
Emilio Pérez Piñero
The concept of deployable structures is not new. Amonghis many studies of structures, the great Renaissancethinker and artist, Leonardo da Vinci (1452–1519)sketched a simple planar deployable mechanism inVolume 1 of his Codex Madrid.1 We are also familiarwith common deployable structures such as the foldinglattices used for lift doors. Three-dimensional structuresof this type were first developed by Spanish engineerEmilio Pérez Piñero (Figure 6.1), who was born in 1936and died tragically in a car accident in 1972.2 In the early1960s he designed and patented reticulated foldablespace grids. In such structures the basic folding unit ismade of two members connected together at or neartheir mid-length to produce a ‘scissor’ mechanism (Figure6.2(a)). The ends of the members of several scissormechanisms may then be connected together in a pre-defined way, in order to form an expanding truss-like
6 Deployable, foldable and retractablespace grids
6.1Emilio Pérez Piñero seen with one ofhis experimental folding space grids(Photograph courtesy FundaciónPiñero)
arrangement, as seen in Figure 6.2(b). A series of theseplanar assemblies may be connected by similar scissormechanisms running transversely, so forming a foldingthree-dimensional grid (Figure 6.2(c)). To limit the exten-sion of the planar assemblies, some form of restraint,such as flexible or folding ties, may be inserted betweenadjacent member ends. To lock the mechanism fully theflexible ties may be replaced by bars. A similar processcan be used to stabilize a three-dimensional deployablegrid.
Pérez Piñero proposed single and double-layer domedand planar grids for mobile theatres, pavilions and exhi-
bition buildings. For example, in 1964 an 8000 m2 exhi-bition pavilion, composed of many 12 � 9 m deployablespace grid modules weighing only 500 kg each, waserected in Madrid for the summer. Folded for transporteach module was only 0.8 � 0.7 m in plan (see Figures6.3). Module deployment was carried out on the ground,using sets of wheels (Figure 6.4), then the foldable struc-ture was made stable by introducing additional barsbefore the profiled metal roofing panels were fixed(Figure 6.5). Taken down in only seven days, the wholepavilion was subsequently moved to San Sebastián andlater to Barcelona.
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6.2Deployable structures: (a) basic ‘scissor’ mechanism, (b) ‘scissor’ truss-like assembly and (c) three-dimensional folding barrel vault grid(Drawing: John Chilton)
(a) (b) (c)
6.3Travelling exhibitionpavilion of 8000 m2
with foldable spacegrid roof designed byEmilio Pérez Piñero –folded state(Photograph courtesyFundación Piñero)
The long section and plan of a similar demountabletheatre project of 1971 is shown in Figures 6.6(a) and6.6(b). Here the folding space grid is primarily support-ed at four locations each with four struts guyed to main-tain lateral stability of the structure.
Pérez Piñero also worked with Salvador Dalí on a pro-ject to develop a foldable sculpture that was coveredwith eighty-four glass panes and had geometry basedon the hypercube. Figure 6.7 shows Pérez Piñero pre-senting his third scale model of the structure to Dalí, in
its completely folded state and Figure 6.8 shows theunfolded structure against the background of the EiffelTower in Paris. Félix Escrig has commented2 that thiswas the first example of a foldable space grid (see Figure6.9) in which the covering was attached to the structureduring deployment, all previous examples having had thecladding fixed once they were fully open.
The work of Pérez Piñero was sadly curtailed due tohis untimely death. However, in later years his ideaswere taken up and further developed by (among others)
Deployable, foldable and retractable space grids 133
6.4Foldable travelling exhibition pavilion during deployment(Photograph courtesy Fundación Piñero)
6.5Foldable travelling exhibition pavilion – deployed state with some ofthe roof plates installed (Photograph courtesy Fundación Piñero)
6.6 (a)Long section through the demountable theatre, designed by Emilio Pérez Piñero 1971, showing the folding roof in its open position and thesystem of supports (Courtesy Fundación Piñero)
134 Space Grid Structures
6.6 (b)Plan of the demountable theatre, designed by Emilio Pérez Piñero 1971, showing the folding roof in its open position and the system ofsupports (Courtesy Fundación Piñero)
6.7Third scale model of folding sculpture(in fully folded state) being shown byEmilio Pérez Piñero to Salvador Dalí athis home in Cadaqués, Spain(Photograph courtesy FundaciónPiñero)
Ziegler, Calatrava, Valcárcel, Escrig and Hernandez.Examples of the work of some of these are describedlater in this chapter. The easy acceptance of foldablegrids is demonstrated by the ubiquitous cylindricallycurved foldable display panels developed by Ziegler andused at exhibitions worldwide.
Venezuela Pavilion, Expo ’92, Seville,Spain
One of the grounds often stated for not using space gridsis cost of erection. In recent times, the use of foldableor deployable structures has been explored as a meansof countering this argument. A remarkable example ofthis is the Venezuela Pavilion constructed for Expo ’92in Seville, Spain, (see Figure 6.10). Due to the high costof construction in Spain it was proposed to manufacturethe pavilion in Venezuela and transport it to Seville.3,4,5
Further, as it was to be a temporary building that wouldbe transported back to Venezuela after the Exposition,a deployable space grid was an attractive alternative.The concept was also considered to accord well with thetheme of the Exposition, ‘The Era of the Discoveries’.
Deployable, foldable and retractable space grids 135
6.9Detail drawing of the foldingstructure with folding glasscovering plates that remainattached to it duringdeployment (CourtesyFundación Piñero)
6.8Glass-covered folding sculpture by Emilio Pérez Piñero andSalvador Dalí (in unfolded state) against the background of theEiffel Tower in Paris (Photograph courtesy Fundación Piñero)
Essentially a large audiovisual display room, the pavil-ion was conceived with a basic triangular cross-sectionthat would permit the use of simple foldable planar spacetrusses. The longer of the two inclined planes of the sec-tion was divided into spans of 13 and 18 m by an inter-mediate support while the other plane (a slightly inclined,
136 Space Grid Structures
6.10Venezuela Pavilion atExpo ’92, Seville(Photograph: JohnChilton)
6.11(a) Section through a typical hinged node for the deployable spacegrid, (b) deployment sequence for the space grid of the VenezuelaPavilion at Expo ‘92, Seville. The grid changes from the tightlyfolded to fully open and restrained state from left to right (CourtesyC. H. Hernandez, and W. Zalewski; drawing: John Chilton)
almost vertical, wall) was 18 m high. Although predom-inantly spanning in one direction, the addition of trans-verse elements between the unfolded trusses ensuredload distribution in three dimensions.
Aluminium alloy 6261 (with a density of 2.71 kg/m3)was selected for the structure to reduce the weight tobe transported and handled. The aluminium industriesof Venezuela combined to produce the material, therequired moulds for extrusions, and to fabricate and paintthe foldable space truss. To enable deployment, thespace truss contains hinged nodes (Figure 6.11(a)) thatpermit a ‘concertina’-type folding in one plane so thatthe trusses, initially parallel in the folded state, finallysplay at 90° to each other in the unfolded state. The
hinges are locked after full deployment by ‘staples’ thatalso carry the cladding that is suspended from the lowerchords of the space truss. In the main spanning direc-tion the twin tubular upper and lower chord members arecontinuous, with the hinged nodes fixed to them at 2 mintervals. Diagonal bracing in the folded trusses and thetransverse members used to fix the space grid afterdeployment are tubes with flattened ends to facilitatebolting to the nodes. Figure 6.11(b) shows in section thesequence of deployment from the fully folded state,through unfolding to the fully deployed state with stabi-lizing bars inserted.
Two separate sections of deployable space grid werepreassembled. One section of twenty-two trusses 13 m
Deployable, foldable and retractable space grids 137
6.12Deployment of theVenezuela Pavilionspace grid(expanding from thecentre) whilstsuspended from astiff lifting beam(Courtesy C. H.Hernandez, and W.Zalewski; drawing:John Chilton)
long and a second section that was made from two inde-pendent sets each of twenty-two trusses, 18 m long. Oneend of each of the two parts of this second, 18 m long,section were joined together by hinges to form a closedpackage for transportation. This package (including thepacking material) weighed only 8000 kg and had over-all dimensions of 18.8 m � 3 m � 2.8 m.
On site, each 2.8 m wide bundle was hung like a cur-tain from the centre of a special truss lifting beam, pro-vided at the bottom chord with a rail and a set of bogiesjoined together by a steel cable. To deploy each spacegrid, the folded bundle was pulled out symmetrically from
the centre until it reached its full 22 m width, as shownin Figure 6.12. Temporary measures were taken to pre-vent re-folding then transverse elements were added tostabilize the structure and form a two-way grid. Finally,the unfolded grids were placed in their permanent posi-tions in the building. The shorter section spanningbetween the ground and the intermediate support pro-vided by the projection area and the doubled sectionopening out to be fixed at two supports leaving the hingeline at the apex of the pavilion section (see Figure 6.13).
Sandwich cladding panels were composed of a lightgrey glass reinforced polyester (GRP) exterior surface
138 Space Grid Structures
6.13Unfolding of the fully deployed space grid of the Venezuela Pavilion at Expo ’92, Seville. A short section spans from the ground to anintermediate support and the doubled section opens out leaving the hinge line at the apex of the pavilion (Courtesy C. H. Hernandez andW. Zalewski; drawing: John Chilton)
and dark-grey coated galvanized steel interior filled withrigid polyurethane foam insulation. The panels were fixedto secondary tubular elements suspended by adjustablebolts from the underside of the grid nodes. Joints betweenpanels were weather-proofed with silicone sealant.
This simple but elegant Pavilion demonstrated thepotential for deployable building structures in architectureas the 6475 piece, 1242 m2, space grid was fabricatedin Venezuela, over 5000 miles (8000 km), from the Expo’92 site. It was transported to Seville in compact form,and then unfolded and erected in just thirteen hours(including the installation of the members needed to makethe grid rigid). By using continuous members in one direc-tion, the number of grid components was smaller andassembly was therefore quicker. Fabrication took placein controlled conditions in a workshop but the size of gridwas restricted by transportation and crane capacity.Nevertheless, the wider use of rapidly erected, deploy-able space grids is an exciting prospect for the future.
The ‘Pantadome’ erection system
Space grids are frequently used for long-span roof struc-tures for sports stadiums or aircraft hangars, for exam-ple, and in these situations the method of erection maysignificantly affect the cost of construction. Considerablesavings in time and cost can be made, if the roof canbe erected with the minimum of interference with the restof the construction process and as near to the groundas possible, to reduce cranage costs. For this reason,planar space grids are often erected on temporary sup-ports a few metres above the ground at a level conve-nient for the installation of services and roof cladding,prior to hoisting or jacking into the final position. Thisworks well for flat space grids but, when there is signif-icant three-dimensional curvature in the roof, this methodis more difficult to employ. R. Buckminster Fuller triedalternative methods of erection to facilitate the con-struction of his geodesic domes. For instance, in 1957,in Honolulu, he used a system suspending the partiallycompleted dome with wire ropes from a central tower.6,7
As concentric rings of structure were added at theperimeter the dome was raised further up the tower.Construction work was therefore always near to groundlevel. Two years later he constructed a 117 m dome at
Deployable, foldable and retractable space grids 139
6.14(a)Plans and cross-sections of the ‘Pantadome’ system for domes withthree hinge lines (where bars are temporarily removed on hingeline No.2 to allow deployment and replaced later to stabilize themechanism) (Courtesy Mamoru Kawaguchi)
6.14(b)Plans and cross-sections of the ‘Pantadome’ system for doubly-folded domes with five hinge lines (in this case bars aretemporarily removed on hinge lines No.2 and No.4, to allowdeployment, and replaced later to stabilize the mechanism.)(Courtesy Mamoru Kawaguchi)
Wood River, USA, where part was lifted using air pres-sure on a balloon-like envelope.
A recent innovation in this area is the ‘Pantadome’system developed by the Japanese engineer, MamoruKawaguchi.8 The principle of this system depends on thefact that a structure having four or more hinged joints in
one plane is a mechanism and can be moved freely.Most people are familiar with the hinged mechanisms,or pantographs, that are used to maintain electrical con-tact between the electric motors of railway locomotivesand the overhead cables that provide the power to drivethem or as a device for copying drawings either direct-
140 Space Grid Structures
6.15Model showing theerection procedure forthe ‘Pantadome’system for a single-layer grid dome withthree hinge linesshowing (a) thecentral dome at ornear ground level withan intermediate ringof structure foldeddown to connect thedome and supports,(b) the dome partiallylifted (note that thehinge points at thetop of the supportingtriangles have movedoutwards to allow thecentral area to passthrough), (c) the fullydeployed mechanismand (d) the fullystable structure afterinsertion of additionalbars between theintermediate hingepoints (Photographscourtesy MamoruKawaguchi)(a)
ly or with a change of scale. Similarly, we are familiarwith the flexibility of hinged mechanisms (in the engi-neering sense) in general. Mamoru Kawaguchi hasadapted this flexibility to allow efficient erection of non-planar roof forms.
Complex building cross-sections to be constructed
using space grids may be subdivided into sections thatcan be hinged to each other and to the supports at theperimeter. With an appropriate selection of the hingelocations, it may be possible to ‘fold’ the cross-sectionso that, in its folded form, the majority of the roof con-tour is near to the ground. Subsequently the space grid
Deployable, foldable and retractable space grids 141
may be unfolded into the desired profile and ‘locked’ intoposition, so that it is no longer a mechanism. The basicprinciple of the ‘Pantadome’ system is shown in Figures6.14(a) and 6.14(b) for domes with a three-hinged or afive-hinged mechanism respectively. In order to stabilizethe dome after lifting, additional bars must be introducedalong hinge line No.2 in Figure 6.14(a) or along hingelines No.2 and No.4 in Figure 6.14(b). Figure 6.15(a) to(d) shows photographs of a model demonstrating theprocedure for the erection of a single layer grid domewith three hinge lines. Detailed studies of the use of the‘Pantadome’ system for the erection of roof structures of
different configuration show the flexibility of the method.The Sant Jordi Sport Palace, Barcelona, Spain, con-structed as the arena for the 1992 Olympic Games wasdescribed in detail in Chapter 5 and other roofs aredescribed below.
World Memorial Hall, Kobe, Japan
The first realization of the ‘Pantadome’ system8 was forthe World Memorial Hall in Kobe, Japan, which was com-pleted in 1984 ready for the Universiade held there in
142 Space Grid Structures
6.16World Memorial Hallin Kobe, Japan(Photograph courtesyMamoru Kawaguchi)
6.17Interior of the WorldMemorial Hall inKobe, Japan(Photograph courtesyMamoru Kawaguchi)
1985 (see Figure 6.16 and 6.17) and subsequently asan all-purpose hall. Particular design requirements werethat it should house a 160 m running track, seat 10 000spectators and that there should be at least 24 m head-room internally to accommodate large yachts in exhibi-tions. The final solution was a building approximately 70� 110 m with 34 m radius quarter spheres at each endconnected by a 40.8 m long cylindrical vault. Centred1 m above ground level the semicircular vault rises toalmost 40 m.
Rigid frames were used to accommodate a large num-ber of window openings in the lower part of the sidewalls, however, a 1.5 m deep space truss formed therest of the building envelope. On a standard 2.5 � 2.5 mgrid the space truss used more than 12 000 steel tubu-lar members (respectively, 101.6 mm diameter for thechords and 76.3 mm diameter for the web members). Allmembers were welded to the spherical nodes (216.3 mmand 267.4 mm in diameter) which were formed frompressed steel plates with welded diaphragms.
The erection procedure for the Kobe World MemorialHall is shown in section in Figure 6.18. There was onehinge line at the base of the enclosure, a second at theinterface between the rigid frames and the space trussand a third within the space truss itself. During assem-bly there were eighteen temporary supports 6.5 m highlocated under the hinge line in the space truss. Thesesupports were subsequently used in the lifting operation.Some members were omitted from the structure at thisstage to permit the mechanism to form and to allow itto move freely whilst the dome was being raised.Although there were several possible methods for liftingthe assembled grid, the well tried ‘push-up’ system waspreferred by the contractor Takenaka Komuten Co. Ltd.Parallel 50 tonne jacks at each temporary support wereused to push up posts that were extendible at the baseas lifting progressed. Temporary ties connected thehinges at the tops of the posts (under the central cylin-drical vault) to take the horizontal thrust and maintainstability. Initially, the tops of the rigid side frames movedoutwards as the space truss thrust upwards betweenthem, subsequently they moved inwards to form part ofdome cross-section as it reached its full height. After lift-ing, additional members were added to complete thedome, clamping the mechanism, and the props and tieswere removed. The change in shape experienced by theroof structure during lifting can be seen in Figures 6.19(a) and (b). During this process the ‘push-up’ points wereraised by over 20 m and the structure almost tripled inheight.
To prevent permanent damage due to over-stressingof the roof during the lifting operation, the process wascarefully monitored and controlled. For the lifting frames,measurements were taken of horizontal and vertical dis-placement, loading and pressure of hydraulic units and,
for the roof structure, stresses were monitored usingstrain gauges at 281 positions and deflections by meansof automatic levelling at 33 locations.
In a preliminary report on the effects of the catastrophic‘Great Hanshin-Awaji’ earthquake, magnitude 7.2 on theRichter scale, which struck the city of Kobe on 17 January1995, it was reported that ‘no major structural damagewas found’ in the space grid structure of the dome.9 Theperformance of the dome, which was constructed on
Deployable, foldable and retractable space grids 143
6.18Sections showing three stages of erection for the World MemorialHall, Kobe (top) before lifting, (middle) during lifting and (bottom)final position (Courtesy Mamoru Kawaguchi)
made ground, under the severe accelerations imposedby the earthquake demonstrates the suitability of spacegrids for structures in seismic zones.
Engineer: Mamoru KawaguchiContractor: Takenaka Komuten Co. Ltd
Indoor Stadium, Singapore
The Singapore Indoor Stadium (Figure 6.20) completedin 1989, is a building of totally different form for whichthe same Pantadome system of erection was used.Reminiscent of the traditional roof form of an oriental
144 Space Grid Structures
6.19(a)Raising of WorldMemorial Hall inKobe, Japan, roof infolded position(Photograph courtesyMamoru Kawaguchi)
6.19(b)Raising of WorldMemorial Hall inKobe, Japan, roof infinal position(Photograph courtesyMamoru Kawaguchi)
temple or pagoda the 14 000 m2 roof is a diamond shapewith maximum dimensions 219 m � 126 m. The com-pleted multipurpose stadium houses almost 12 000 spec-tators around a playing area 65 � 45 m and accommo-dates ‘either two basketball, five volleyball, four indoortennis or 12 badminton courts’.10,11
The space grid structure is a combination of two major‘keel’ trusses, spanning along the main axes of the dia-mond plan, and four double-layer curved space trusses,each part of a 65 m radius cylinder. Connecting the endsof the fully welded keel trusses there is a tension ringto resist their outward thrust. Sixty-four columns alongthe perimeter and two pairs of internal columns, set121 m apart under the keel trusses running on the longerroof axis, provide permanent support for the structure.Nippon Steel Corporation’s NS truss system was usedon a 3.0 � 3.0 m grid, 2.5 m deep, for the space trusssurfaces between the keel trusses. A total of 7700 tubu-lar steel members 76.2 mm to 457.2 mm diameter wereused in the space truss with nodes between 150 and490 mm diameter.
At first glance, the form of this roof appears to be morecomplex than that of the Kobe Memorial Hall; howeverit was divided into only seven separate sections for con-struction, five of which were to be moved using thePantadome System. Two sections of roof in the acuteangles of the diamond shape were constructed by con-ventional methods. A central ‘hat’ section bounded byfour hinge lines parallel to the sides of the building
(essentially a small version of the whole roof structure)was constructed on temporary supports and scaffolding9 m above the arena floor. Four curved roof sectionswere constructed close to the profile of the arena stands,each connected at one end to a hinge line of the cen-tral hat section and at the other to hinge lines at the topof the perimeter columns. There was also a third hingeline at the base of the perimeter columns. Between theseassembled sections, four small areas of roof were left tobe filled in after the roof had been raised 20 m, over oneweek at the end of February 1989, to its final positionusing a push-up system similar to that used at Kobe.Different stages of the erection process are shown dia-grammatically in Figure 6.21.
A maximum allowance of 20 mm differential heightbetween push-up points was considered in the structur-al analysis of the simulated erection sequence. Followingcomputer analysis, it was found that horizontal tie barsbetween lifting points were not required in this instance
Deployable, foldable and retractable space grids 145
6.20The Singapore Indoor Stadium (Photograph courtesy MamoruKawaguchi)
6.21Computer-generated, three-dimensional view of the assembly, liftingand final phases of erection for the space grid roof, SingaporeIndoor Stadium (Courtesy Mamoru Kawaguchi)
to maintain stability. Reasons given for adopting thismethod of erection for the roof project were the improvedsafety of working at lower level, better quality control,the reduced construction period and a reduction of theneed for scaffolding.
Architect: Kenzo Tange Associates, and RSPArchitects, Planners and Engineers
Engineers : Mamoru Kawaguchi & Engineers (roofstructure), Takumi Orimoto Structural Engineers &
Associates, RSP Architects, Planners and EngineersContractors: Ssangyong-Guan Ho Construction J/V,
and Nippon Steel Corporation
Sun-Dome, Sabae, Fukui Prefecture, Japan
In 1995, the ‘Pantadome’ system was used for the erec-tion of the 116 m diameter Sun-Dome at Sabae, FukuiPrefecture, in Japan.12 Designed for use as the mainvenue for the 1995 World Gymnastics Championships,the multi-use arena has fully retractable seating for 6000and can also be used for exhibitions, fairs, concerts andother sporting events.
Because of the heavy snowfalls experienced in theregion, the final roof surface of the space grid is steppedto control the possibility of snow sliding in avalanchesfrom the spherical dome (see the aerial photograph,Figure 6.22). In fact, the roof was designed to retain allof the snow that falls on it, with a consequent designsnow load of 600 kg/m2. To cater for this high loading,
the double-layer space grid was designed with the inten-tion of carrying the load in the most efficient manner.Consequently, the highest compression forces are in thebottom layer of the space truss, whilst the role of theupper layer and web bracing is primarily to precludebuckling of the lower chords. Special cast steel jointswere developed to ensure high efficiency force trans-mission in the lower layer of the grid.
Initially, the roof grid was folded to form a 40 m diam-eter central dome, constructed on the arena floor, encom-passed by sixteen radial segments of the lower dome,each supported on four perimeter columns. As in previ-ous Pantadome applications, small slots of incompletestructure were left between each dome segment to befilled in after the lifting operation. Hinged connectionswere provided at the perimeter of the central raised domeand at the top and bottom of each perimeter column. Toraise the roof structure, it was pushed up vertically ateight points around the perimeter of the central dome.Final locking of the structural mechanism was achievedby introducing the missing space truss members betweenthe radial segments. A series of sections through thedome at various stages of the lifting process are shownin Figure 6.23. As can be seen from these, the shortsupporting perimeter columns are inclined at more than50° to the vertical during deployment whilst returning tothe vertical position in the final phase.
Architect: Professor S. Okazaki, Fukui UniversityEngineer: Mamoru Kawaguchi & Engineers
146 Space Grid Structures
6.22Aerial view of theSun-Dome, Sabae,Fukui Prefecture,Japan. The steppedprofile adopted toprevent snow fromslipping from the roofmay clearly be seen(Photograph courtesyMamoru Kawaguchi)
Deployable, foldable and retractable space grids 147
6.23Sections showing thelifting sequence forthe Sun-Dome, Sabae(Courtesy MamoruKawaguchi)
Namihaya Dome, Kadoma Sports Centre,Mitsushima, Kadoma-City, Osaka Prefecture, Japan
Completed in March 1996, the Kadoma Sports Centre,Osaka, Japan (Figure 6.24), is a complex comprising a6000-seat main arena with two swimming pools (a rac-ing pool 50 � 25.5 m and a diving pool 25 � 25 m) andtwo ancillary facilities, a smaller arena and another pool(Figure 6.25). Of prime interest in this study of spacegrids, is the main arena, which has an oval planenveloped by an oval double-layer space truss structure,the Namihaya Dome, 110 m � 127 m and rising to42.65 m (Figure 6.26). However, the major architecturalfeature of the spectacular shallow-domed roof is the 5°inclination of its equator. The overall effect of the build-ing’s form is that of a gigantic discus half buried in theground, as can be seen in Figure 6.24.
As the roof was to be raised using the PantadomeSystem.8,12 the inclination introduced additional erectionproblems. The detailed longitudinal section illustrating thelifting sequence (Figure 6.27), shows that the posts usedto push-up the roof are themselves inclined at 5° to thevertical. This section also shows the disposition of thehinges in the space truss, in both top and bottom chords.The central section of the dome comprised a completeoval panel 66 m by 86 m whilst the middle and lower sec-tions were each divided radially into fourteen segments.
A special lifting system was devised for this struc-ture so that the roof could be raised from its positionnear arena level to almost its full height in just one day.The partially lifted roof structure of the sports hall isshown in Figure 6.28, where it can be seen that someof the cladding has already been installed. Distinctareas of space grid are clearly visible, separated byzones that will be infilled after the structure has beenfully lifted and the dome has achieved its prescribedgeometry. The posts used to lift the roof can be seencontrasted against the underside of the central roof sec-tion.
Because of its inclined equator, the roof was analysedclosely by computer at nine different steps in thePantadome process. Following this analysis, it was dis-covered that some member stresses and dome defor-mations might be very large during the final stages ofthe push-up although they were within acceptable limitsuntil then. The major lift, of just over 28 m, was achievedusing temporary posts, hydraulic jacks and steel cables,and accomplished in just one day. It left the central sec-tion of the dome 0.6 m below its final location as therewere fears that the dome could become unstable at thatstage. As the roof was raised, forces in the posts grad-ually decreased as the roof load was transferred to theperimeter supports. However, the majority of load trans-fer took place during the last small push-up steps, which
148 Space Grid Structures
6.24Namihaya Dome,Kadoma SportsCentre – exterior viewclearly showing the 5°inclination of the roofstructure (Photographcourtesy MamoruKawaguchi)
took place over three months. During this slow raisingthrough the last 0.6 m, a total of 1296 members wereintroduced into the slots between the segments of the
middle and lower sections of the dome, according to astrict order of placement to maintain the stability of thestructure.
Deployable, foldable and retractable space grids 149
6.25Namihaya Dome, Kadoma Sports Centre – floor plan and elevation (Courtesy Mamoru Kawaguchi)
150 Space Grid Structures
6.26Namihaya Dome, Kadoma Sports Centre – longitudinal and transverse sections showing the complex geometry of the double curved spacegrid (Courtesy Mamoru Kawaguchi)
6.27Namihaya Dome, Kadoma Sports Centre – section showing folding and lifting arrangements with hinge lines in the top and bottom chordlayers (Courtesy Mamoru Kawaguchi)
The successful conclusion of this project demonstrat-ed the adaptability of the Pantadome system of erectionto a complex structural form, an inclined oval space griddome. At the same time, it showed that extreme caremust be taken to ensure the stability of the structure atall times during the push-up process.
Client: Osaka PrefectureArchitects: Showa Sekkei Co. Ltd
Engineer: Mamoru Kawaguchi & Engineers (roofstructure)
Main contractor: Takenaka Corporation
During 1997 the same system of erection was used forthe Nara Convention Hall where the walls of the long,narrow lenticular plan building were hinged at their base,at the top and at a point a little above their mid-height.12
This structure was raised between 1 and 6 December1997. The wide variety of large scale projects so far com-pleted using the ‘Pantadome’ System have demonstrat-ed its eminent suitability for efficient and speedy con-struction of space grids of complex form. It will mostcertainly be widely used for similar projects in the future.
Folding roof for swimming pool, SanPablo, Seville, Spain
Following the early work of Pérez Piñero, Félix Escrig andhis colleagues at the School of Architecture in Seville have
experimented with lightweight folding grid structures.13,14,15
A recent example was used for the cover of an Olympic-sized swimming pool in San Pablo, Seville, where curvedgrids of this form were used to suspend a membrane coverover the pool. Delivered to site as a tight bundle of con-nected tubular members, the expanding grid was placedin the bottom of the empty pool and partially deployed toallow attachment of the membrane to the lower nodes.Then the whole roof structure was lifted by crane from asingle point at the centre of the grid, and stretched outover the empty pool, deploying the membrane at the sametime. Subsequently, diagonals were added between theupper nodes to convert the mechanism into a stable form.The sequence of unfolding is shown in Figures 6.29. Atypical central node detail is shown in Figure 6.30 wherethe method of connection of individual members around acentral spindle can be seen as well as the method of sus-pending the membrane inside the folding grid.
The completed roofs provide a lightweight anddemountable cover for the pool, offering enclosure fromthe elements in winter and an appealing glowing struc-tural form at night (Figure 6.31).
Architects: Félix Escrig and José Sanchez.
Retractable roof structures
During the late 1980s and the 1990s it has becomeincreasingly popular to provide large sports stadiums with
Deployable, foldable and retractable space grids 151
6.28Lower structure of theKadoma SportsCentre showing theextent of pre-installation ofcladding and servicesbefore lifting and thezones that will beinfilled after lifting(Photograph courtesyKyo Takenouchi)
152 Space Grid Structures
6.29Swimming pool cover, San Pablo, Seville, Spain: the sequence ofunfolding the deployable roof grid (Courtesy Félix Escrig)
6.30Typical central node of the pool cover showing the method ofsuspending the membrane inside the folding grid (Courtesy FélixEscrig)
6.31Exterior night view ofthe deployable three-dimensional spacegrid pool cover, SanPablo, Seville, Spain(Photograph courtesyFélix Escrig)
a retractable roof, especially in countries where the cli-mate is such that adverse weather conditions may occurat almost any time of the year. Although such roofs areexpensive and in purely financial terms it is difficult tojustify their construction, municipal authorities are wellaware of the prestige that they give their city.
Skydome, Toronto, Canada
The roof of the Skydome, besides being one of the longestclear-span space grid structures in the world, is alsoretractable, leaving 91 per cent of the seating open tothe sky when fully open. This striking feature of theSkydome lends spectacle to the sporting events held with-in the arena, as well as permitting the facilities to be usedto their best advantage in all weathers, all year round.Completed in 1989, the circular bowl of the stadium isthe home of the Toronto Blue Jays baseball team. Bymoving some of the seating, the arena can also be adapt-ed for football. Near Lake Ontario and close to the cen-tre of the city, the Skydome is adjacent to the CN Tower,one of the tallest structures in the world. Thus two impos-ing architectural and engineering achievements standside by side. From the start, the Skydome was envis-aged as a symbol for the city of Toronto and the domi-nant roof form has been described by the architect RodRobbie as ‘an organic crustacean form with a clearly vis-ible orientation towards the south and the noon sun’.16
The retractable roof, which can be opened in 20 min-utes, is divided into four sections, one fixed and threemoving (see Figure 6.32 in the closed state). There aretwo sliding arch sections, of 208 m and 202 m spanrespectively, one moving inside the other, and oneretractable quarter dome sector, of 175 m maximumspan, that moves along a circular track. A further staticquarter dome forms the remaining section of the roof.The upper arch is 55 m wide, the lower 48 m wide whilstthe fixed and moving dome segments have maximumwidths of 44.4 and 48.4 m respectively. Although not builtfrom a modular space grid system, the structure is includ-ed here as the structural configuration used effectivelyforms a double-layer space grid. The arch sections aregenerated from a series of parallel planar arch trusses,generally at 7.0 m centres, with transverse trusses andbracing in the planes of the top and bottom chords.Similarly, a space grid structure is produced for each ofthe quarter domes by four main arch trusses, with radi-al rib trusses and diagonal bracing.
During the retraction process, first the smaller ‘inner’arch (segment B in Figure 6.33) moves along its 55 mtrack to rest over the fixed quarter dome (segment D),then the larger ‘outer’ arch (segment A) retracts 103 mto its final position over these two segments. Finally, themovable quarter dome (segment C) glides 309 m roundthe curved perimeter track and nests under segment Aand B and above segment D (see the open and closedpositions shown in Figure 6.33). The weights of the mov-
Deployable, foldable and retractable space grids 153
6.32Roof of the TorontoSkydome in theclosed position seenfrom the CN tower.The roof retracts fromleft to right as seenfrom this position(Photograph: JohnChilton)
154 Space Grid Structures
6.33Diagram of roofmovements duringretraction. SegmentsA, B and C retract topositions abovesegment D in theorder B, A, D(Drawing: JohnChilton)
able roof segments A, B and C are 2400, 2200 and 1800tonnes respectively.17,18
Architect: Roderick G. RobbieEngineer: Michael Allen, Adjeleian Allen Rubeli
LimitedSpace frame contractor: Dominion Bridge Co.
In this chapter we have seen some innovative ideas andmethods of using folding, deployable and retractablespace grids. Single-layer folding grids are also beingexplored by Chuck Hobermann in the USA. Given theversatility of folding grid structures there is great poten-tial for their extensive adoption for construction projectsin the future. There is considerable scope for their appli-cation for a wide variety of uses such as as an economicmethod of erection or as a means of providing easilyadaptable or demountable and reusable structures.
1 Pérez Valcárcel, J. and Escrig, F. (1994). Pioneeringin expandable structures: the Madrid 1 notebook byLeonardo da Vinci. Bulletin of the InternationalAssociation for Shell and Spatial Structures, 35/1(114), 33–45.
2 Escrig, F. (1993). Las Estructuras de Emilio PérezPiñero. In Arquitectura Transformable, (F. Escrig,ed.) p. 26 (in Spanish). Escuela Técnica Superior deArquitectura de Sevilla (ETSAS).
3 Hernandez, C. H. and Zalewski, W. (1993).Expandable structure for the Venezuelan Pavilion atExpo ’92. In Space Structures 4 (G. A. R. Parke andC. M. Howard, eds) vol. 2, pp. 1710–19, ThomasTelford.
4 Hernandez, C. H. (1991). Mobile and rapid assem-bly structure. Engineering (P. S. Bulson, ed.) vol. 8,pp. 237–48, Computational Mechanics Publications.
5 Loreto, A. (ed.) (1993). Pabellon de Venezuela Expo’92 Sevilla, Instituto de Desarrollo Experimental dela Construccion, Universidad Central de Venezuela.
6 R. Buckminster Fuller (1975). Synergetics. Mac-millan.
7 Ulm, R. C. and Heathcote, R. L. (1959). Dome builtfrom top down. Civil Engineering, December, 29 (12),872–5.
8 Kawaguchi, M. and Mitsumune, S. (1984). A domi-cal space frame foldable during erection.
International Conference on Space Structures, pp.982–87, University of Surrey, September.
9 Kato, S., Kawaguchi, K. and Saka, T. (1995). Pre-liminary report on Hanshin earthquake. In SpatialStructures: Heritage, Present and Future (G. C.Giuliani, ed.) vol. 2, pp. 1059–66, quote p. 1064, SGE.
10 Dorai, J. (1989). Indoor stadium will be ready aheadof time. The Straits Times, 1 March 1989, p. 39.
11 Abe, M., Aso, Y., Muto, Y., Kosaka, T., Harada, A.,Kimura, I. and Shirai, T. (1993). Design andConstruction of Singapore Indoor Stadium – anExample of Pantadome System. In Public AssemblyStructures from Antiquity to the Present, ProceedingsIASS Symposium, pp. 371–80, Mimar SinanUniversity.
12 Kawaguchi, M. and Abe, M. (1998). A structural sys-tem suitable for rational construction. In LightweightStructures in Architecture, Engineering andConstruction, (R. Hough and R. Melchers, eds) pp.85–94, LSAA.
13 Escrig, F., Valcárcel, J. P. and Sánchez, J. (1995).Deployable structures squared in plan design andconstruction. In Spatial Structures: Heritage, Presentand Future (G. C. Giuliani, ed.) vol.1, pp. 483–92,SGE.
14 Escrig, F. (1993). Geometría de las EstructurasDesplegables de Aspas. In ArquitecturaTransformable, (F. Escrig, ed.), p. 93 (in Spanish).Escuela Técnica Superior de Arquitectura de Sevilla(ETSAS).
15 Pérez Valcárcel, J. B. (1993). Cálculo de EstructurasDesplegables de Barras. In ArquitecturaTransformable, (F. Escrig, ed.), p. 125 (in Spanish).Escuela Técnica Superior de Arquitectura de Sevilla(ETSAS).
16 Robbie, R. G. (1992). The Architecture of the TorontoSkydome. In Innovative Large Span Structures (N.K. Srivastava, A. N. Sherbourne and J. Roorda, eds)vol. 1, pp. 52–61, The Canadian Society for CivilEngineering.
17 Allen, C. M. (1992). Toronto Skydome RoofStructure; Engineering Challenge. In InnovativeLarge Span Structures (N. K. Srivastava, A. N.Sherbourne and J. Roorda, eds) vol. 1, pp. 63–71,The Canadian Society for Civil Engineering.
18 Charalambu, H. (1992). Design of the roof movingsystem. In Innovative Large Span Structures (N. K.Srivastava, A. N. Sherbourne and J. Roorda, eds)vol. 1, pp. 82–93, The Canadian Society for CivilEngineering.
Deployable, foldable and retractable space grids 155
In the two preceding chapters we have seen the widevariety of uses to which space grid structures can beput. Their use in deployable, foldable and retractablestructures will no doubt continue to develop in subse-quent years. This chapter highlights some areas wherespace grid structures have been little used to date butwhere they might be exploited to a greater extent in thefuture.
Polyhedral space grid buildings
It is well accepted that buildings can be composed of acontinuum of polyhedral cells but it is unfortunate thatthe cell shape that usually springs to mind is based onthe rectilinear cuboid, with parallel planes of wall, floorand ceiling. This need not be the case, as there aremany more visually exciting combinations of polyhedralspaces that can form inhabitable buildings. Althoughpracticality may have some influence on the matter itappears to be prejudice and familiarity that lead us toadopt the common rectilinear building form. More ‘exot-ic’ spaces are usually reserved for buildings of specialsignificance, such as churches, assembly or sports hallsand theatres, rather than dwellings. With some excep-tions, space grids do not conform to rectilinear geome-try in three dimensions.
There have been many proposals for the use of spacegrids, both for individual dwellings and as multi-layergrids for complete urban environments. Many of theseideas have been based on the fascination that polyhe-dral geometry holds for many architects and engineers.Those who question the mundaneness of the dominantrectilinear box that composes most spaces within build-ings, have looked longingly at the possibilities of spacefilling packings of polyhedra of alternative form. InChapter 1, the inventor Alexander Graham Bell’s fasci-nation with the strength and lightness of tetrahedra wasnoted. He considered that the basic tetrahedral modulecould be used as a building block to construct largerstructures and built a house and a framework for a giantwindbreak from them.1
There are some existing buildings that have beenplanned on octahedral/tetrahedral geometry. For exam-ple, large reinforced concrete space truss pavilions werebuilt at a permanent trade fair site at New Delhi, India,
in 1982. Five pyramidal-form pavilions were constructedfrom in situ reinforced concrete using multi-layer grids ofthis type.2,3 Nusatsum House, described in some detailin Chapter 5, shows the use of habitable multi-layer gridson the small scale.
High-rise and megastructures
Although most space grids are fabricated from steel oraluminium, they are not solely restricted to metal as theconstruction material. Louis Kahn’s Yale Art Gallery, YaleUniversity, New Haven, Connecticut, USA, (1950–4) wasbuilt using tetrahedral space grid floors in reinforced con-crete, although the planning of the building did not real-ly reflect the reticulation of the structure. In the middleof the 1950s, Louis Kahn was influenced very much bythe ideas of Buckminster Fuller. At this time he collab-orated with Anne Griswold Tyng in the design of a 188 m(616 ft) high City Tower for Philadelphia (1952–7). Thiswork, commissioned by the Concrete Institute of Americato demonstrate the innovative use of the material, wasbased on tetrahedral geometry and stabilized by con-crete tetrahedral floors. I. M. Pei’s Bank of China, 1989,has an external bracing structure, on a large scale, thatencloses the high-rise building in a giant space grid.Michael Burt et al. have also proposed megacities oflarge space grids – Infinite Polyhedral Lattice (IPL) –constructed from elements made from small-spacegrids.4,5 This is much as the Eiffel Tower is constructedfrom lattice elements that are assembled to produce alarger lattice structure.
Over many years, J. François Gabriel has studied theuse of polyhedra in the design and construction of build-ings of all sizes. He has investigated, in particular, thearchitecture of high-rise buildings constructed using a six-directional, multi-layer, space-filling, space grids, com-posed of tetrahedra and octahedra.6 With this type ofspace-filling lattice it is possible to generate continuoushorizontal plane grids by orientating the octahedra in twoways (a) with their long axis set vertically and (b) with onetriangular face in the horizontal plane (see Figure 7.1(a)and (b)). The first of these produces a multi-layer versionof the common square-on-square offset two-way spacegrid, whilst the latter produces the less common triangle-on-triangle offset multi-layer three-way space grid.
7 Future developments
Future developments 157
7.1Octahedral-tetrahedral space filling lattices (a) two-way and (b) three-way (Drawing: John Chilton)
7.2Multi-layer three-way grid modified to create structure-free ‘Hexmod’ cells and unobstructed spaces for vertical circulation of lifts and serviceducts (Drawing: John Chilton, after J. François Gabriel)
158 Space Grid Structures
7.3‘Space town’ of 126 storeys proposed by J. François Gabriel usinga large-scale, three-way space grid (Courtesy J. François Gabriel)
7.4Axonometric view of one octahedral module of the megastructure.Each side is a space truss composed of eight octahedra linked byfourteen tetrahedra of side length 4 m (Courtesy J. FrançoisGabriel)
7.5Assembly of ‘Hexmod’ cells to form a megastructure withhexagonal accommodation (vertical walls and horizontal floors)dispersed through the multi-layer space grid (Courtesy J. FrançoisGabriel)
7.6Similar assembly of ‘Hexmod’ cells with the diagonals of the largeoctahedron removed to reveal the hexagonal shape of the corebuilding (Courtesy J. François Gabriel)
Architects are concerned with the division of spaceand the use to which it may be put. Within the space-filling three-way, multi-layer grid the integration of verti-cal circulation is a problem, therefore, J. François Gabrielhas proposed a modification of the basic grid, eliminat-ing some members whilst maintaining structural stabili-ty. This produces a spatial lattice in which a structure-free hexagonal cell or ‘Hexmod’ may be placedthroughout and unobstructed vertical circulation (for liftsand service ducts) is also possible (Figure 7.2).
To create a high-rise, megastructure or ‘space town’,Gabriel has suggested the construction of a large-scalemulti-layer, three-way grid in which a smaller-scale mod-ified three-way grid containing hexagonal rooms or
‘Hexmods’ are provided as living and/or office space.Figure 7.3 shows his proposed ‘space town’ of 126storeys in which only the octahedral sections of the macrogrid are inhabited. Each of the large octahedra (Figure7.4) is composed of twelve space trusses in turn con-sisting of eight octahedra linked by fourteen tetrahedrawith side lengths of 4 metres (giving a storey height of3.27 m). The large octahedron is subdivided with a small-er three-way grid of similar orientation containing the‘Hexmod’ rooms (Figure 7.5), which are not allowed toprotrude beyond the planes of the mega-octahedra. Ascan be seen in Figure 7.6 (where the six diagonal spacetruss members have been removed from the large octa-hedron) the basic building shape is also hexagonal. Due
Future developments 159
7.7Plan view of the threeidenticalmegastructure helicesused to form the‘space town’. Thelarge octahedra areenclosed in a glassenvelope andadditional spacetrusses hold thehelices together(Courtesy J. FrançoisGabriel)
to the geometry of the three-way grid, each hexagon (inboth the small and large grid) is displaced horizontallyrelative to the layer below. Therefore, the structure (againat both scales) consists of linked helical spirals.
A plan view of the proposed ‘space town’ composedof three identical helices and with the octahedra enclosedwithin a glass envelope is shown in Figure 7.7. The indi-vidual helices are held together by additional horizontalspace trusses. Gabriel has suggested that the hexago-nal void at the centre could house high-speed lifts stop-ping at every ninth storey. In the similar view of Figure7.8, some ‘Hexmods’ have been allowed to penetratethe enclosure of the large octahedron and horizontalaccess platforms have been added between adjacent
helices. These modifications are shown in detail in Figure7.9. The adoptions of such a structural system wouldrepresent quite a radical change in the thinking of mostarchitects and engineers as it would require the accep-tance of hexagonal spaces within a octahedral/tetrahe-dral space grid system. An alternative that uses the morecommon two-way space-filling system is describedbelow.
In Japan, the Shimizu Corporation has proposed thebuilding of a pyramidal ‘city-in-the-air’ (Figure 7.10) which
160 Space Grid Structures
7.8Similar view of the‘space town’ wheresome ‘Hexmods’ havebeen allowed topenetrate the glassenvelope of the largeoctahedra andhorizontal accessplatforms have beenadded to link thehelices (Courtesy J.François Gabriel)
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7.9Detail of the‘Hexmods’ penetratingthe enclosure of thelarge octahedra andthe access platform(Courtesy J. FrançoisGabriel)
7.10A pyramid ‘city-in-the-air’ concept namedTRY2004 proposedby the ShimizuCorporation, whichuses a multi-layer gridover 2000 m high(Courtesy ShimizuCorporation)
would, during working hours, contain around 1 millionpeople. The concept, named ‘TRY2004’, consists of asquare-based, pyramidal, multi-layer, space trussmegastructure, 2800 m by 2800 m at ground level andreaching 2004 m into the sky.7,8 The primary structure isbased on octahedral units each formed by joining two350 m by 350 m square-based pyramids, 250.5 m high,base to base. Combined together in layers, these formthe well-known geometry of the octet truss.
It is not proposed to clad the complete pyramid on theexternal faces to form one large enclosure. However, with-in the primary structure individually enclosed residential,office and commercial buildings up to 100 storeys highare to be suspended. Figure 7.11 shows the method ofsupport for a typical office building within the structure.A similar system of suspension is proposed for high-riseresidential units of pyramidal/octahedral form. The resi-dential units are to be concentrated at the lower levels
162 Space Grid Structures
7.11Method of suspension ofoffice blocks within theTRY2004 megacity spacegrid, i.e. vertically in theoctagons of the grid(Courtesy ShimizuCorporation)
7.12Typical 50 m diameternode within the megagridshowing the proposal fortransport interchangecontained within thenode (Courtesy ShimizuCorporation)
and at the perimeter of the pyramid, whilst office devel-opment is to be located at the core. Leisure and com-mercial facilities are planned for the high levels wherethey command the best views.
One important reason for adopting the pyramidalshape was the improved penetration of daylight into thespace grid. It was shown that annually the pyramidalform would collect 25 per cent more sunlight per unit ofsurface area and 81 per cent more sunlight per unit vol-ume than would a cubic form (45 per cent and 151 percent more respectively than would a more typical ‘sky-scraper’). The combination of the pyramidal form withthe fully triangulated three-dimensional grid system alsowould provide excellent resistance to lateral loads suchas wind and earthquakes.
Construction of such a multi-layer space grid wouldrequire tubular members and spherical nodes of hugeproportion. It is proposed that the horizontal elements ofthe grid be tubes 10 m in diameter, housing transporta-tion systems using linear induction motors. The diago-nal members 16 m in diameter would generally containservices and a continuously circulating cable-car systemof transport. Nodes 50 m in diameter would provide cir-culation between the horizontal and diagonal trans-portation systems and would also be used to collect sun-light for distribution by optical fibres. A typical node withthe connecting horizontal and diagonal members isshown in Figure 7.12. To reduce the weight of the struc-ture, it would be constructed using lightweight materialsreinforced with glass and carbon fibres.
Assembly would be facilitated by the use of stan-dardized components and robots to build segments thatwould be erected by ‘push-up’ methods. According tothe Shimizu Corporation, such a megacity could be con-structed for 88 trillion yen (1990 prices) and would requireapproximately seven years to complete. The conceptdemonstrates the eminent suitability of multi-layer spacetrusses for the construction of such large-scale projects,using tubular elements where the internal void may beused for transportation. Although this is still a dream (ofwhich the desirability of realization might be questionedin terms of environmental impact and social acceptabil-ity), it represents one possible future for the use of spacegrids.
The combination of space grids with decking in floor con-struction is not new. In recent years there has been con-siderable research into composite action between aspace grid and the concrete floor plate. In Chapter 5 thecomposite floor construction for the Milan Fair Complexwas described in detail. This was developed as a sys-tem for a specific problem but there is also potential for
the use of standard space grid components in compos-ite floor construction for multistorey buildings.
In typical modern composite floors, the overall con-struction depth often has to be increased to allow thepassage of ventilation ducts beneath the downstandbeams. The open nature of space grid structures allowsthe easy passage of services within the structural depththus reducing overall storey (floor to floor) heights with-in the building. Potentially, this could mean an extra floorfor a given building height proscribed by planning con-trols or the provision of the same floor space within aless tall structure. The former provides more lettablespace in the same volume with little increase in con-struction cost (one extra floor structure), whilst the latterproduces savings due to the reduced size of the build-ing envelope.
Considerable research has taken place over recentyears to develop a version of the CUBIC Space Frameas a standard system for composite floor construction.Also, the Catrus system described in Chapter 3 has twocomposite systems currently under development, one
Future developments 163
7.13Extended upper node connection bolt, shear connector for theCatrus acting compositely with a concrete deck. The flat deckingsheet is a permanent shutter for the slab concrete (Courtesy Al-Sheikh)
incorporating a concrete top slab and the other con-nected to a timber deck. For the composite concrete ver-sion, shear connection between the in situ slab and thespace truss is provided by an extended upper node con-nection bolt and top nut, as shown in Figure 7.13. Theuse of the normal connecting bolt with an additional nuteliminates the need for welding (required for standardshear studs in traditional composite steel/concrete floorconstruction). Flat steel sheet decking, clamped by thenode connecting bolts between the upper chords run-ning in the two orthogonal directions, is used to supportthe wet concrete. Profiled decking is not requiredbecause membrane action is mobilized to provide a veryeconomical solution.
When used with timber decking, a simple short con-necting piece made from 1.6 to 2.0 mm thick cold-formedsteel sheet is used. This has a single bolt hole at thecentre for connection to the space grid node and fourholes to permit the timber boarding to be attached.
Tensegrity and space grids
When using the combination of steel, or aluminium, andglass as structural materials, wherever possible archi-tects try to minimize the size of the metallic structurerequired to support the transparency of the glass. To thisend in the Musee des Beaux Arts, Montreal, Canada,Mero developed a system of glazing support using theirNK joint. The structural glazing bars were supported onflying stainless steel tubular struts suspended by a gridof tension bars and connected by the modified ball joint.Thus, using a modified version of the Mero system, verylight and airy glazed gallery spaces were produced (seeFigure 7.14). The adoption of standard space grid com-ponents achieved economy in construction whilst allow-ing the architect to exploit the transparency of glass asfreely as possible. Although related to tensegrity struc-tures (described below) this was really an example of atwo-way strutted beam or beam-string type structure.
Since their discovery and patenting in the early 1960sby Buckminster Fuller, Snelson and Emmerich, ‘tenseg-rity’ structures have fascinated architects and engineersalike, although there have been relatively few practicalapplications of the concept. (The term ‘tensegrity’ wascoined by Buckminster Fuller to describe the system oftensile integrity). There is not space here to go into detailabout geometry and behaviour of these structures wherecompression elements are usually held in place only byelements in direct tension. However, research is cur-rently being carried out by Motro and Hanaor, amongothers, to develop double-layer tensegrity grid systems(Figure 7.15) with a view to their possible use in roofstructures. Although these work in model form there areseveral technical and constructional problems to be over-
come before they can be used on the larger scale.However, one advantage of double-layer tensegrity gridsis that they are easy to collapse and could thereforepotentially be used for deployable grids.
Quasicrystal geometry: combining rodsand plates
According to some designers, a negative aspect of spacegrids is the inflexibility of the usual member configura-tion patterns, these being mainly based on combinationsof regular octahedral and tetrahedral forms. Recentlyhowever, the possibilities resulting from the use of alter-native standard unit cells to create three-dimensionalnon-repeating patterns has been explored. A very excit-ing means of generating such patterns has derived from
164 Space Grid Structures
7.14Tensile system supporting glazing at the Musee des Beaux Arts,Montreal, Canada (Courtesy Mero)
the study of forms in multidimensional mathematicalspace (i.e. having more than the three spatial dimen-sions of the real world). For example, a three-dimen-sional cube may be represented by a drawing on thetwo-dimensional surface of a piece of paper. The two-dimensional sketch of a cube is, in fact, the outline ofthe shadow cast by the cubic lattice. Similarly, objectsof higher mathematical dimension may also be repre-sented in lower dimensions (i.e. the ‘shadow’ of a four-dimensional object may exist in three-dimensionalspace). Exciting ideas for the use of geometries fromhigher dimensions have come from the studies carriedout by, amongst others, Steve Baer, Koji Miyazaki andHaresh Lalvani.
One field of multidimensional geometry has led to thediscovery of quasicrystals, crystal-like solid objects thatcan be packed together to form a continuous solid. Using
the basic quasicrystal geometry it is possible to constructtwo different solid or wireframe cells, each with six sim-ilar rhombic faces, one ‘fat’ cell and one ‘thin’ cell. Thestandard rhombic face is as shown in Figure 7.16(a) andthe six standard faces of the two cell types are assem-bled with different angles between the faces to producethe ‘thin’ and ‘fat’ versions. Figure 7.16(b) shows the ‘fat’cell and figure 7.16(c) the ‘thin’ cell. These individualcells can be combined to produce a continuum with theproperty that the edges or bars of the cells form non-repeating patterns in three dimensions. The orientationof the edges or members of the cells is such that theideal shape for the connecting nodes is a regular dodec-ahedron, with members perpendicular to its faces. Withinthe space grid, all bars have the same length betweennode centres and all connecting nodes have the sameorientation in three-dimensional space, this being a fur-ther property of quasicrystal geometry.
Artist Tony Robbin, who works in New York, has exper-imented with the use of quasicrystal geometry in his art9
and more recently in architecture. The fundamental prob-lem with the elements of quasicrystals as architecturalbuilding blocks is that the rhombic faces are unstable aspure bar and node structures (but then so are the squarefaces of the cube, a very common building form!). Ascommented by Erik Reitzel, a structural engineer whohas collaborated with Robbin, most engineers intuitivelywant to triangulate each rhombic face and the rhombo-hedral cells by introducing diagonal members to stabi-lize them.10 However, this disguises the quasicrystalgeometry and masks the fascinating patterns that canbe generated. One alternative is to brace the structureby using fully rigid node joints; it also is possible to stiff-en the rhombic faces by introducing structural plates (as,incidentally, is often done in cubic structures). To revealthe full splendour of the quasicrystal geometry, trans-parent plates of glass or polycarbonate sheet may beused.
A quasicrystal form was proposed for an extension tobe constructed at the Technical University at Lyngby, inDenmark. Originally COAST was to be a full-scale addi-tion to the outside of one of the existing buildings (Figure7.17). However, despite being championed by ErikReitzel, structural engineer for the project, in the end,due to cost restraints, only a sculptural form was built inthe atrium of the administration block. The sculpture wasassembled, by Tony Robbin and a team of students,over one month using over 10 000 individual parts (sim-ilar machined dodecahedral aluminium nodes and bars,all of equal length). As can be seen in Figure 7.18 all ofthe dodecahedral nodes in the sculptural space grid havethe same orientation, as noted earlier.
An interesting quality of quasicrystal geometry is that,although it consists of a non-repeating pattern, the shad-ows cast when light is passed through a structure with
Future developments 165
7.15Double-layer tensegrity grid where there is no direct contactbetween the compression elements (Photograph courtesy RenéMotro)
that geometry can form regular patterns. For instance,Figure 7.19 shows the shadows cast on the ground atdifferent times of the day by sunlight shining through aquasicrystal dome. The sculpture constructed at Lyngbyexploits this property and, in addition to the fascinatingform of the object itself, the shadows cast on the floorof the atrium mutate continuously during the day as theangle of the sunlight entering the roof changes. Becausethe quasicrystal geometry is not stable as a pure pin-jointed lattice structure, plates of coloured Plexiglasshave been introduced at various locations throughout thesculpture to ensure its stability. These multi-hued translu-cent panels add to the visual excitement of the sculp-tural form itself and also generate fascinating combina-tions of colours in the shadows projected on to the floorof the atrium below.
Exploration of this exciting new geometry for use instructures is still in its infancy. However, the sculpture atLyngby has demonstrated its potential for generatingdelightful architectural configurations. This stimulating con-struction contradicts at least two of the common criticismslevelled at space grids: the monotony of the repetitivegeometry and the difficulty of producing complex three-dimensional forms using a small set of standard elements.All of the nodes of the quasicrystal space grid are similardodecahedra that are orientated in the same way in spaceand all of the member lengths (between node centres)are the same. Consequently, all of the stiffening panelsare the same shape and size but vary in orientation. Trulythree-dimensional structural art is the outcome of this kit
of standard parts. It is possible to envisage roof structurescomposed of deep quasicrystal space grids partially sta-bilized by the double-glazing units that form the weather-proof envelope, whilst coloured panels at other positionsin the structure complete the stabilizing function, filter thesunlight and produce ever-changing combinations of lightand shadow. As with the pioneering sculpture at Lyngby,the challenge for the future will be to construct stable qua-sicrystal building structures whilst maintaining the trans-parency and filigree of the relatively open geometry.
What does the future hold?
In this and the previous chapter some recent develop-ments in space grid structures have been discussed.These examples demonstrate that space grids havecome of age and that from the regular modular systemsdeveloped around fifty years ago, diverse possibilities ofgeometry and deployability are now beginning to beexplored and exploited. Computer controlled cutting,machining and drilling of space grid components meansthat designers are no longer restricted to standardgeometries. Driven by the need for oil exploration andextraction in the oceans, oil-rigs up to around 1000 m inheight and utilizing large diameter tubular steel membershave been constructed. The technology and materialsdeveloped for these giant structures is now available tobe used in the construction of space grid, megastruc-tures. In office developments there is a continuing
166 Space Grid Structures
7.16Quasicrystal geometry(a) basic rhombicface, (b) the ‘thin’ and(c) the ‘fat’quasicrystal unit cellsshown as 3-dimensional cells andunfolded (Drawing:John Chilton)
Future developments 167
7.18The quasicrystalsculpture in theatrium at theTechnical University,Lyngby, Denmark(Photograph: JohnChilton)
7.17Original COAST quasicrystal building extension atthe Technical University, Lyngby, Denmark asproposed by Tony Robbin and Erik Reitzel(Courtesy Tony Robbin)
demand for ever-longer floor spans to provide columnfree workspaces. This demand could be satisfied by theuse of composite space grid floors. Lightness and trans-parency are fashionable qualities for architectural struc-tures and architects continue to seek innovative struc-tural solutions. In this area double-layer tensegrity gridsand quasicrystal grids are still in their infancy with many,perhaps as yet unthought of, grid forms to be discov-ered. Folding, deployable and retractable structures, too,have yet to realize their full potential.
Without a doubt the future of space grid structures isassured and still developing 100 years after AlexanderGraham Bell’s experiments to find a more efficient struc-ture for kites.
1 Bell, A. G. (1903). The tetrahedral principle in kite struc-ture. National Geographic, 14 (6), June, 231.
2 Anon (1982). Architects Journal, 17 February, p. 21.3 Anon (1982). RIBA Journal, July, pp. 50–1.
4 Shriftalig, D., Burt, M., Bogdanov, A., Mincovich, V. andTaran, D. (1992). I.P.L. megastructure. In InnovativeLarge Span Structures (N. K. Srivastava, A, N.Sherbourne and J. Roorda, eds) vol 1, pp. 616–26, CSCE.
5 Frances, M., Rosenhouse, G. and Burt, M. (1992).Highly regular multi-layered cylindrical shells of infinitepolyhedral lattice. In Innovative Large Span Structures(N. K. Srivastava, A, N. Sherbourne and J. Roorda,eds) vol. 1, pp. 542–51, CSCE.
6 Gabriel, J. F. (1997). Are space frames habitable. InBeyond the Cube (J. F. Gabriel, ed.) p. 439, John Wiley.
7 Sugizaki, K. (1992). Super high-rise mega-city concept‘Pyramid-TRY2004’. In Innovative Large SpanStructures (N. K. Srivastava, A. N. Sherbourne and J.Roorda, eds) vol. 1, pp. 164–74, CSCE.
8 Shimizu Corporation (1991). TRY 2004. Technical lit-erature, Shimizu Corporation.
9 Robbin, T. (1992). Fourfield: Computers, Art and the4th Dimension. Little, Brown and Co.
10 Reitzel, E. and Robbin, T. (1993). A quasicrystal forDenmark’s COAST. In Space Structures 4 (G. A. R.Parke and C. M. Howard, eds) vol. 2, pp. 1980–7,Thomas Telford.
168 Space Grid Structures
7.19Diagram showing the varying shadow pattern under a quasicrystal dome as the sun passes overhead (Courtesy Tony Robbin)
Appendix 1: two-way spanning structures
Considering a system of two beams of span L1 and L2
that intersect at right angles and are connected at theirmid-span, we can determine the amount of any loadapplied at the intersection point that will be carried byeach beam. The proportion of the applied load W car-ried by each will be W1 for beam 1 and W2 for beam 2,and the sum W1 + W2 will equal the total load W. Thevertical deflection of each beam, which depends on theload and span of each, can be calculated easily for thepoint of contact at mid-span. Knowing that the deflectionof both beams must be the same at the point where theyare connected, and given the span of each beam, it isthen possible to determine the proportion of load W car-ried by each.
Assuming that the beams have the same material andcross-sectional properties (i.e Young’s Modulus E andthe second moment of area I are the same for both), forbeam 1 the mid-span deflection �1 = W1L1
3/48EI and forbeam 2 the mid-span deflection �2 = W2L2
3/48EI. As thetwo beams are connected together at their midpoint, theirdeflections must be equal (�1 = �2). Therefore, as theterm 48EI is constant for both beams and can be can-celled from both equations,
W1L13 = W2L2
3 or W1 = W2L23/L1
3 (Equation 1)
From this equation and the fact that W1 + W2 = W, TableA.1 can be prepared to show the proportion of the totalload W carried by each of the two beams for differentspan ratios.
Span ratio 1.0 1.2 1.5 2.0 3.0(L2/L1)
Beam 1 (W1) 0.500W 0.633W 0.771W 0.889W 0.964WBeam 2 (W2) 0.500W 0.367W 0.229W 0.111W 0.036W
Note: E and I constant, L2 longer span and L1 shorter span.
Where the beams in the two directions have differentstiffness (i.e. the value of I is different for each), Equation1 above is modified by the ratio of the two values of Iand becomes:
W1 = (W2I1L23)/(I2L1
3) (Equation 2)
A graphical representation of these equations is givenas Figure 2.4 in Chapter 2 for ratios of I2/I1 of 1, 2, 3and 5.
Appendix 2: list of manufacturers
There are many space grid manufacturers throughoutthe world and it would be a considerable task to list themall. Therefore, only a limited list that includes the lastknown addresses of the manufacturers mentioned in thetext is given here.
ABBA Space Structures ccPO Box 34409Jeppestown 2043South Africa
Kubik Enterprises Ltd17 Birchwood DriveRavensheadNottinghamshireNG 15 9EEUK
Mai Sky System Inc.228 East Avenue APO Box 1066SalinaKS 67402-1066USA
Mero (UK) plcUnit 4, Ancells CourtFleetHampshireGU13 8UYUK
Mero RaumstrukturGmbH & Co. WürzburgPO Box 61 69Steinachstrasse 5D-8700 WürzburgGermany
NS Space TrussNippon Steel Co. Ltd2-6-3 OtemachiChiyoda-kuTokyo 100Japan
Orona S. Coop. Ltda.Aptdo. Correos 131220080 San SebastiánSpain
Ramco-YKK (Singapore) Pte. Ltd9 Benoi CrescentJurongSingapore 2262
Space Decks LtdChardSomersetTA20 2AAUnited Kingdom
Tridim Lahaye s.a.6250 AiseauBelgium
Tianjin Space Frame Co.Department of Civil EngineeringTianjin UniversityTianjin (300072)People’s Republic of China
TM TrussTaiyo Kogyo Corporation3-22-1 HigashiyamaMeguro-kuTokyo 153Japan
Unibat International15 rue Hégésippe-Moreau75018 ParisFrance
UNISTRUTSpace Frame Systems, Inc.45081 Geddes Rd.CantonMI 48188USA
UskonSSI Group LimitedPO Box 2WhitchurchShropshireSY 13 1WLUK
VestrutCentro Acciai Spa70032 Bitonto (BA)s.s. 98 KM 78,900Italy
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ABBA Cubicspace, 46, 47, 3.22, 3.23ABBA Dekspace, 43, 47, 55, 3.24ABBA Space Structures, 34, 47, 48,
169ABBA Spider Frame, 48, 3.26Ability to cantilever, 27Access platform, 161, 7.9Accuracy of fabrication, 62Acoustic insulation, 93Adaptability, 17Additional bars or members, 142, 143Advantages of using space grids, 17Aeropuerto Comodoro Arturo Merino
Benítez, 93Aesthetics, 31, 73, 75, 78, 111, 118Affleck, Desbarats, Dimakopoulos,
Lebensold, Sise (CCWE)(architects), 5
Agriculture Biome, 88, 5.43Air-handling ducts, 17Alexander Graham Bell 1, 2, 156, 168,
1.1Allen, John (architect), 89Allen, Michael (engineer), 155Aluminium Company of Canada Ltd
(ALCAN), 7Aluminium, 4, 5, 8, 30, 34, 38, 47,
137, 156, 164, 1.7, 1.12, 1.13Ane Yarza (engineer), 58Anne Griswold Tyng (architect), 156Anoeta Stadium, San Sebastián,
Spain, 25, 26, 2.22(a), 2.22(b)Antoni Peyri (architect), 9Apeldoorm observation tower, 115,
117, 118, 5.91, 5.92, 5.93Apostolic Faith Mission, Vereeniging,
48Arata Isozaki (architect), 81, 87, 94, 99Aspect ratio, 14, 15, 2.4Assembly and erection, 124, 5.101,
5.102Assembly at arena level, 92, 5.48Assembly in the air, 94, 100Assembly on temporary scaffolding,
105Assembly, 57, 100, 112, 123, 145,
5.63, 6.21Atelier Furai, 78Atlanta Pavilion, 118–120, 5.94(a),
5.94(b), 5.95Atlanta, 40, 3.13
Atrium, 166, 167, 7.18Attwood, Charles W. (engineer), 39Auger, Boyd (engineer), 7Augustine, Margaret (architect), 89Automated drilling and machining, 124Ayuntamiento de Palafolls, 99
Baer, Steve, 165Ball joints, 31, 33, 63, 5.3, 5.4Bamboo, 30, 31, 32, 3.1Bank of China, 156Bar and node structures, 16, 24, 25,
30, 2.5Barbany, Gilbert (architect), 103Barrel vault, 25, 47, 48, 49, 55, 106,
107, 108, 109, 132, 3.24, 3.25,5.75, 5.76, 5.77, 6.2
Barrel-vaulted, 38, 45Beam-string type structure, 164Bearings, 74Beinn Bhreagh, 2Bell, Alexander Graham, 1, 2, 156,
168, 1.1Bending moments, 17, 28, 42, 52, 126Bentall Centre, 25, 108, 109, 5.76, 5.78Biomes, 89Biosphere 1, (Earth), 89Biosphere 2, Sonoran Desert, Arizona,
41, 55, 88, 89, 5.42, 5.43Birmingham National Indoor Arena for
Sport (NIAS), 89, 90, 91, 93, 5.45,5.46, 5.47
Bligh Lobb Sports Architecture, 129Boyd Auger (engineer), 7Bridget’s Farm, near Winchester, UK,
115British Airways maintenance hangars,
Heathrow Airport, UK, 10British Steel Corporation (Tubes
Division), 9, 37, 69, 3.9British Steel Corporation, 9, 37, 69, 3.9British Steel Tubes & Pipes, 9, 69Brittle behaviour, 59Buckling, 18, 24, 26, 42, 52, 58, 90,
146, 4.1Buckminster Fuller, Richard, 2, 3, 4, 6,
41, 139, 156, 164, 1.2, 1.3, 1.8Building Design Partnership
(architects/engineers), 105, 108Burks Green and Partners (engineers),
Burt, Michael, 156
Calatrava, Santiago(architect/engineer), 135
CAM, 81, 124Camber of space grids, 55, 4.4Camber, 38, 74Candela, Félix (architect), 9Cartesian coordinates, 25Cast boss, 44, 3.18Cast nodes, 123, 124, 125, 126,
5.100, 5.103, 5.104Cast steel joints, 146Castenada Tamborrel (architect), 9Castings, 30Catenary curve, 72Catrus, 42, 43, 163, 3.16Cayo César Riquelme V. (architect), 94Cedar, 75, 77, 5.29Central node, 152, 6.30Charles W. Attwood (engineer), 39Chequer-board pattern, 23, 44, 2.15Chlorinated rubber paint, 36Chord splice, 106, 5.73Chuck Hobermann (engineer), 155City Tower, Philadelphia, 156Cladding and glazing, 56Cladding model, 120, 5.95Cladding panels, 107Cladding, 45, 74, 89, 98, 133, 137,
138, 139, 148, 5.59COAST quasicrystal building extension,
Lyngby, Denmark, 165, 167, 7.17Coefficients of thermal expansion, 30Coffered panel fixing, 109, 5.78Coffered reinforced concrete slab, 12Coining, 4, 38Cold rolled steel continuously formed,
41Cold-formed members, 10, 29, 40,
104, 3.12Cold-formed steel sheet, 164Collapse, 18, 164Coloured panels, 166Coloured Plexiglass, 166Combined bar and plate structures, 17Commercial systems, 30Committee for the Olympic
Development Atlanta (CODA), 118Complex geometry, 25, 120, 150, 166,
Note: entries given in italic refer to figure numbers.
Composite space grid floorconstruction, 123, 163, 168
Computer analysis, 24, 25, 92, 145Computer controlled cutting, 21, 166Computer model, 76, 99, 5.28, 5.61(b)Computer numerically controlled
(CNC), 33, 57, 83Computer-aided design, 25Computer-aided manufacture (CAM),
81Computer-controlled jacking operation,
85Concept model, 95, 5.52Concept sketch, 99Concertina-type folding, 137Concourse of Humanity, Expo ’70,
Osaka, Japan, 61Concrete deck, 122, 163Concrete Institute of America, 156Concrete top slab, 163, 164, 7.13Concrete, 30, 72Conder Group plc, 41Conder Harley System, 10, 80, 104,
105, 106, 5.73Conder Projects, 105Configuration, 25Conical, 97Connected, in the air, 92Connector plates, 116, 5.90Construction details, 109, 5.78Constructional problems, 164Contamin and Dutert (engineers), 1Continuous chords, 10, 31, 41, 47Continuously circulating cable-car
system, 163Continuum, 165Contraction, 54, 86Convention Center Development Corp.
Jacob K. Javits Center, New York,75
Corby, 9, 37Corner and intermediate edge node
support, 27, 2.25Corner-supported space grid, 27, 52,
59, 2.24, 4.1Cornice edge, 28, 44, 2.29Corrosion, 34Cost of construction, 20, 139Covering plates, 135, 6.9Creep, 30Crimped ends, 38, 39, 3.11Cruciform glulam columns, 118Crystal Cathedral, Garden Grove,
Community Church, California, 67,68, 5.10, 5.11, 5.12
Crystal Palace, 1, 72Crystal-like solid objects, 165Cube, 16, 17, 2.5Cubic multi-layer space grid, 9, 11,
CUBIC Space Frame, 10, 14, 17, 18,20, 28, 43, 49, 50, 51, 54, 55, 57,78, 79, 81, 163, 2.6, 3.27, 3.28,3.29
Cubicspace (ABBA), 48Cuboid, 156Cylindrical nodes, 31, 38Cylindrical sections, 39, 3.11Cylindrical vault, 143
Dalí, Salvador, 133, 134, 135, 6.7, 6.8De Bondt, 117Decking, 74, 81, 93, 99, 112, 163Defining the grid, 24Deflection, 17, 26, 27, 28, 30, 55, 74,
92, 98, 143, 169Dekspace (ABBA), 48, 3.25Demountable theatre, 133, 134, 6.6(a),
6.6(b)Denings of Chard, 2, 44Density, 30Deployable pool cover, 152, 6.31Deployable space grid, 131, 136, 137,
164, 6.11Deployable structures, 131, 132, 139,
6.2Deployed mechanism, 140, 6.15Deployment, 137, 139, 6.12, 6.14(a),
6.14(b)Design of joints, 52Design Response Spectrum, 59Diagonal double-layer grids, 10Diagonal on square grid, 22Diagrid steel space truss, 126, 127,
128, 5.107, 5.108Differential movement, 59, 107Dimensional accuracy, 18, 44, 54, 55,
94Disadvantages, 20, 24Division of space, 159Djurkovic, George, 7Dodecahedral nodes, 165Dodecahedron, 16, 17, 2.5Domed camber, 56, 4.5Domed structures, 25, 38, 45, 56, 75,
76, 77, 83, 85, 139, 148, 6.14(a)Double curved space grids, 145, 150,
6.26Double layer grids, 6, 12, 13, 14, 17,
21, 22, 49, 57, 71, 72, 73, 75, 79,89, 94, 97, 100, 104, 126, 132,146, 148, 153, 1.8, 2.2(b), 2.3(a),2.3(b)
Double-glazing units, 166Double-layer barrel vault, 25, 2.21Double-layer composite space truss,
120Double-layer tensegrity grids, 164, 165,
168, 7.15Doubly-folded domes, 139, 6.14(b)
Ductility, 42, 59
Eagle Centre Market Derby, 104, 105,106, 5.72, 5.73, 5.74
Earthquakes, 18, 59, 60, 163Ease of erection, 19Eave profile, 28Eccentricity of member forces, 41Eccentricity, 42, 53Economy, 24, 28Edge and glazing fixing details, 45, 46,
3.19Edge profiles, 28Edinburgh Tattoo, 18, 19, 2.7Edward D. Mills & Partners
(architects), 71Eiffel Tower, 1, 156Electrical services, 17Electrostatic polyester powder-coating,
36El-Sheikh, Dr Ahmed, 42Emilio Pérez Piñero, 131, 132, 133,
134, 135, 151, 6.1, 6.3, 6.6(a),6.6(b), 6.7, 6.8
Emmerich, D.G. (engineer), 164End/fin plates, 42Energy-absorption, 59Epoxy resin, 77Equipment in roof space, 18, 2.6Equipment storage shed, Lelystad,
Netherlands, 115, 116, 5.89Equivalent Static Force Analysis, 59Erection, 20, 24, 43, 47, 57, 64, 84,
85, 101, 105, 107, 108, 110, 120,128, 131, 135, 140, 141, 142,143, 144, 145, 148, 151, 5.64,5.79, 6.15, 6.18, 6.21
Erik Reitzel, 165, 167, 7.17Escrig, Félix (architect), 99, 133, 135,
membranes, 64Exhibition Centre, Anhembi Park, Sao
Paulo, Brazil, 57Exhibition pavilion, 132Expanding grids, 151Expansion joints, 74, 89, 107Expansion, 54, 86Experimental folding space grids, 131,
6.1Explosion, 18Expo ’67, Montreal, Canada, 6, 7, 8,
1.9, 1.10, 1.11, 1.12, 1.13Expo ’70, Osaka, Japan, 9, 10, 11,
1.16, 1.17Expo ’92, Seville, Spain, 99, 100, 101,
102, 103, 104, 105, 136, 138,139, 5.61(b), 5.62, 5.63, 5.65,5.66, 5.67, 5.68, 5.70, 5.71, 6.10,6.11, 6.13
Expo Tower, Expo ’70, Osaka, Japan, 9Extended upper node connection bolt
(Catrus), 164Extruded tubular members, 4Extrusion, 39
Fabrication jigs, 44, 50Failure, 18Fantasy Island, pyramid, Skegness,
112, 113, 5.84Fat cell (quasicrystal), 165Faulks, Perry, Culley and Rech
(architects), 81Félix Candela (architect), 9Félix Escrig, 99, 133, 135, 151Fentiman, A. E., 38Fentiman Bros., Ottawa, 4, 5, 38, 1.7Festival Plaza Expo ’70, Osaka,
Japan, 9, 61, 63, 5.1, 5.3, 5.4FFV Aerotech Maintenance Hangar,
Stansted Airport, 49, 51, 78, 79,80, 81, 5.32, 5.33, 5.34(a),5.34(b), 5.35
Fibre optic lighting, 106, 108Fire analysis of space grids, 58Fire protection, 20Fire resistance, 58, 59, 73Fire, 18, 77, 104, 122Five-hinged mechanism, 139, 142,
6.14(b)Fixed and sliding bearings, 53Fixing details, 17, 107Flat circular boss, 106Flat plates, 24Flat steel sheet decking, 164Flexible or folding ties, 132Floor construction, 163Fluor Daniel Chile S.A. (engineers), 94Foldable display panels, 135Foldable space grids, 131, 132, 136,
150, 151, 6.27Folding glass structure, 135, 6.9Folding roof for swimming pool, San
Pablo, Seville, 151, 6.29, 6.30,6.31
Folding sculpture, 134, 135, 6.7, 6.8Folding, deployable and retractable
structures, 155, 168Foppl’s Principle, 15Ford Rotunda Building, Dearborn,
Michigan, 3, 1.3Formian and Formex algebra, 25Four-dimensional objects, 165Frame action, 14, 49Free-form curves, 55, 4.4Free-form surfaces, 25Fukuda Tomoo (architect), 64Full edge node support, 26, 27, 2.23Fully rigid node joints, 165Furai, Atelier, 78
Future developments, 156
Gabriel, J-François (architect), 156,158, 159, 160, 7.3
Galerie des Machines, Paris, 1 Galvanized steel connector, 115Garden Grove, Community Church,
California, 67, 68, 5.10, 5.11, 5.12Gengo Matsui (engineer), 78Geodesic domes, 3, 5, 6, 1.8Geometrical complexity, 120, 5.96Geometrics Inc., 4Geometry, 19, 20, 23, 24, 28, 34, 36,
37, 41, 49, 56, 62, 65, 67, 68, 73,96, 97, 98, 133, 148, 156, 162,164, 166, 5.55
George Djurkovic, 7Georgia Dome, 40, 3.13Georgia Pacific, 118Geotechnic Centre, South Africa, 48Gerrits, Joop (engineer), 31Gilbert Barbany (architect) and
Sebastián Mateu, 103Giuliani, Dr eng. Gian Carlo, 126Giuliani, Dr eng. Mauro Eugenio, 126Glass and glazing, 17, 30, 68, 71, 74,
94, 102, 103, 107, 126, 163, 164,165
Glass envelope, 159, 160, 7.7, 7.8Glass reinforced polyester (GRP), 30,
138Glass-covered canopy, 20, 2.8Glazing fixing, 103, 109, 5.69(a),
5.69(b), 5.78Glued laminated timber, 30, 118González, Reinaldo (engineer), 94Great Hanshin-Awaji earthquake,
Kobe, Japan, 143Grid configuration and geometry, 21,
23, 24, 31Grid densities, 24Grid modules, 10, 1.16Griswold Tyng, Anne (architect), 156Gyrotron, 7, 8, 1.12, 1.13
Habitable multi-layer grids, 156Habitat Biome, Biosphere 2, Sonoran
Desert, Arizona, 88, 89Half-octahedra, 17, 22, 43, 44, 122Hall 3, International Convention
Centre, Birmingham, UK, 50, 51,3.29
Hanaor, Ariel (engineer), 164Haresh Lalvani (architect), 165Harley (Series 80), 42Harley Type 80 node joint, 41, 3.14Harley, 10, 41, 53Hartford Civic Centre Coliseum, USA,
18, 58Hawes, Phil (architect), 89
Heavy equipment, 17Helices, 160, 7.8Helios Tower, Expo ’70, Osaka, Japan,
61Hellmuth Obata Kassabaum (HOK)
(architects), 93Hernandez, Henrique (architect), 135Hexagonal accommodation and
spaces, 158, 159, 160, 7.5, 7.6Hexmod cells, 157, 158, 159, 160,
161, 7.2, 7.5, 7.6, 7.8, 7.9Highgate Shopping Centre,
Johannesburg, South Africa 46,48, 3.22
High-rise residential units, 162Hinge lines, 145, 150, 6.27Hinged mechanisms, 140, 141Hinged nodes and joints, 137, 140Hobermann, Chuck (engineer), 155Hollow spherical nodes, 31, 36Horizontal access platforms, 160, 7.8Horizontal plates, 129, 5.109Hot-Dog Church, Apostolic Faith
Mission, Vereeniging, South Africa,48
Hubs, 38, 39, 3.11Hyperbolic paraboloid, 25, 126, 127,
Icosahedron, 16, 17, 2.5IDS Studios (architects), 114Inclined oval space grid, 148, 151Indoor Stadium, Singapore, 144Infinite Polyhedral Lattice (IPL), 156Inflated pillows, 64Ingenieurbüro Peter Bertsche, 118Insertion of additional bars, 140, 6.15Installation of services, 17, 139Insulated panels, 17Integral Glazing System, 89Integration of vertical circulation, 159Intensive Agriculture Biome,
Biosphere 2, Sonoran Desert,Arizona, 88, 89
Intermediate layers, 29Internal wind pressures, 24International Arena, Birmingham, 69,
70, 5.15, 5.16Intersecting trusses, 13, 14, 2.1(c),
2.2(b), 2.3(a)Intumescent coatings, 21, 59Inverted pyramids, 27, 106, 128Irregular geometry, 27, 118Isozaki, Arata (architect), 81, 87, 94,
Jacob K. Javits, New York Exhibitionand Convention Center, USA, 72,73, 74, 75, 5.20, 5.21, 5.22
Javier Morales (architect), 104Jigs, 55, 79Johannesburg German School, South
Africa, 49John Allen (architect), 89Johnson/Burgee Architects, 68Joop Gerrits (engineer), 31José Ramón Rodríguez Gautier
(architect), 104José Sánchez (architect), 151
Kadoma Sports Centre, 87, 148, 149,150, 151, 6.24, 6.25, 6.26, 6.27,6.28
Kahn, Louis (architect), 156Kamiya, Koji (architect), 64Kawaguchi, Mamoru, 58, 81, 83, 87,
140, 141, 144Kenchington Ford plc (engineers), 105Kenny, Sean, 7Kenzo Tange (architect), 9, 61, 64, 87,
146Kikutake, Kiyonori (architect), 9Kobe World Memorial Hall, Japan,
143, 145Koji Miyazaki, 165Konrad Wachsmann (engineer), 3,
1.4KT Space Truss, 31Kubik Enterprises Ltd, 49, 169Kubik, Leslie A. (engineer), 49Kubik, Leszek (engineer), 49, 81Kurokawa, Kisho (architect), 9, 10, 11,
Lacing tool, 115, 5.88Lack of fit, 79Lalvani, Haresh (architect), 165Laminated timber, 34, 3.5Lan Chile hangar, Aeropuerto
Comodoro Arturo Merino Benítez,93, 94, 5.50, 5.51
LANIK S.A., 98, 99Large openings, 24Lateral bracing, 12Lateral forces and loads , 53, 54, 86,
163, 4.2Lateral stability and restraints, 53, 54,
59, 64, 133, 4.2Lateral wind forces, 102Leisure and commercial facilities, 163Lelystad, Netherlands, 116, 5.89, 5.90Leonardo da Vinci, 131Leslie A. Kubik (engineer), 49Leszek Kubik (engineer), 49Lifting sequence, 147, 148, 6.23Lifting, 57, 64, 112, 114, 143, 145,
148, 151, 5.5, 5.83, 6.18, 6.21,6.28
Lifts and service ducts, 159
Lightweight materials, 163Lightweight systems, 39, 46Linked helical spirals, 160List of manufacturers, 169Load distribution, 12, 14, 15, 17Load reversal, 23Location of jacking towers, 85, 5.40Long-span floors, 126Louis Kahn (architect), 156Luis Uruñuela (architect), 104Lung Domes, Biosphere 2, Sonoran
Desert, Arizona, USA, 88, 89, 5.43
M & B Arquitectos, S.A. (architects),103
Machined dodecahedral aluminiumnodes and bars, 165
Machining and drilling, 166Mai Sky System Inc., 42, 169, 3.15Makowski, Z.S., 53Mamoru Kawaguchi & Engineers, 146,
151Mamoru Kawaguchi, 58, 81, 83, 87,
140, 141, 144Man the Explorer, Expo ’67, Montreal,
Canada, 5, 7, 1.10, 1.11Man the Producer, Expo ’67, Montreal,
Canada, 5, 6, 7, 1.9, 1.10, 1.11Manchester Airport Terminal 2, UK,
110, 112Mansard edges, 28, 44, 75, 90, 112,
2.30Margaret Augustine (architect), 89Markethall, Eagle Centre, Derby, UK,
104Martínez-Calzón, J. (engineer), 99Material cost, 30Mateu, Sebastián (architect), 103Matsui, Gengo (engineer), 78Maxwell’s Equation, 15Mechanical and electrical services,
122Mechanisms, 143, 151Megacity, 163Megagrid, 162, 7.12Mega-octahedra, 159Megastructure helices, 159, 7.7Mega-structures, 5, 158, 159, 166, 7.4,
7.5Meishusama Hall, Shiga Sacred
Garden, Shigaraki, Shiga, Japan,71, 72, 5.17, 5.18, 5.19
Member properties, 15Membrane action, 127, 164Mengeringhausen, Dr Max, 2, 31, 32,
33, 3.1Mero (UK) plc, 169Mero DE, 43Mero Holz, 30, 34, 118, 3.5
Mero KK, 31, 32, 33, 55, 90, 93, 3.3Mero Raumstruktur, 169MERO, 2, 18, 19, 32, 33, 34, 35, 36,
54, 164, 2.7, 3.2(a), 3.4, 3.6, 3.7,4.3
Metabolist architects, 9Metal connector plates, 115, 5.88Metal inserts, 30, 34, 3.5Method of suspending the membrane,
152, 6.30Method of suspension of office blocks,
162, 7.11Methods of erection, 56, 79, 87, 139,
146Mexico City, 9Michael Allen (engineer), Adjeleian
Allen Rubeli Limited, 155Michael Burt, 156Middle-layer nodes, 90Mid-side supports, 27, 2.26Milan Fair, New Exhibition Facilities,
Milan, Italy, 118, 121, 122, 123,124, 125, 126, 163, 5.97, 5.98,5.99, 5.101, 5.102, 5.103, 5.104
Minimum self-weight, 53Ministry of Public Building and Works,
2Minoru Yamasaki & Associates
(architect), 72Miyazaki, Koji, 165Models, 118, 134, 140, 6.7, 6.15Modified ball joint, 164Modular components, 18Modular systems, 5, 41, 43, 44, 47,
49Modules, 9, 100, 5.63Modulus of elasticity, 30MODUS Consulting, 129Moduspan, 39, 40, 3.12, 3.13Montreal Expo ’67, Canada, 5Morales, Javier (architect), 104Motro, Réne, 164Multidimensional geometry, 165Multidimensional mathematical space,
165Multiframe System, 112, 113, 114,
5.84Multi-hinge system, 41, 55, 89, 5.44Multi-layer space grid, 5, 6, 8, 14, 28,
29, 30, 34, 42, 46, 48, 65, 156,158, 161, 163, 163, 1.9, 1.12,1.13, 3.22, 7.5, 7.10
Multi-layer three-way grid, 156, 157,159, 7.2
Multi-span space grids, 28Multistorey buildings, 163Musee des Beaux Art, Montreal,
Canada, 164, 7.14Museum of Modern Art, New York,
Namihaya Dome, Kadoma SportsCentre, Japan, 148, 149, 150,6.24, 6.25, 6.26, 6.27
Nara Convention Hall, Japan, 151National Engineering, 128National Exhibition Centre,
Birmingham, UK, 38, 69, 70, 5.13,5.14
National Indoor Arena for Sport,Birmingham, UK, 29, 34, 54, 89,92, 4.3, 5.48
National Indoor Stadium, Singapore,87
Nautilus shell, 32, 33, 3.2(b)Nenk system, 2Netherlands Pavilion, Expo ’67,
Montreal, Canada, 4New Delhi, 156New York Convention Center, 72, 73,
74, 75, 5.20, 5.21, 5.22, 5.23,5.24, 5.25
Nippon Steel Corporation, 145, 146NK joint, 164Noble, A. H., 48Node castings, 38, 124, 3.10Node connections, 68, 5.12Node detail, 151Node joint(s), 9, 15, 66, 5.9Node jointing systems, 31Node plate(s), 40, 128, 3.12Node tower, 118, 5.93Node, 33, 3.3Node(s), 50 m diameter, 162, 163,
7.12Nodeless construction, 3, 31Nodeless joint(s), 89, 5.44Nodeless space trusses, 10Nodeless systems, 55Nodeless, 89, 115Nodus joint, 37, 38, 111, 3.9, 3.10Nodus, 9, 36, 37, 55, 57, 69, 71, 110,
112, 1.14, 5.80, 5.83Non-destructive ultrasonic testing, 124Non-regular grids, 23, 2.16Non-regular tessellation, 23Non-repeating patterns in three
dimensions, 165Nooshin, Professor H., 25NS Space Truss, 36, 145, 170Numerical control (NC), 36Nusatsum House, Bella Coola Valley,
British Colombia, Canada, 64, 65,66, 67, 156, 5.6, 5.7, 5.9
Octagons, 162, 7.11Octahedra, 158, 159, 160, 7.4, 7.7Octahedral modules, 158, 162, 7.4Octahedral, 17, 30, 41, 65, 159Octahedral/tetrahedral geometry, 156,
Octahedral/tetrahedral space gridsystem, 160
Octahedral-tetrahedral space fillinglattices, 157, 7.1
Octahedron, 16, 17, 158, 2.5, 7.6Octanode connection, 47, 48, 3.23Octet trusses, 3, 41, 162, 1.3Oguni Dome, Kumamoto Prefecture,
Kyushu, 75, 76, 77, 78, 5.26,5.27(a), 5.27(b), 5.28, 5.29, 5.30
Okazaki, Professor S., FukuiUniversity, 146
Oktaplatte, 36Olympic Games, 9, 118, 126, 127,
142, 5.105ONCE Pavilion, Expo ’92, Seville,
Spain, 100Operation, 57Optical fibres, 163Optimum grid depth, 53Orbik, 36Organización Nacional de Ciegos de
España (ONCE), 100, 101, 102,103, 5.65, 5.66, 5.67, 5.68,5.69(a), 5.69(b)
Orientation, 166Orona S. Coop. Ltda., 57, 83, 100,
103, 104, 170Orona SEO system, 32, 36, 83, 84,
87, 3.8, 5.39ORTZ joint, 97, 5.57ORTZ space truss system, 98Ove Arup & Partners, 71Ove Arup and Partners International
Pablo Weithhofer (engineer), 94Palafolls Sport Hall, 25, 94, 95, 96, 97,
98, 5.52, 5.53, 5.54, 5.55, 5.56,5.57, 5.58, 5.59
Palau Sant Jordi (see Sant JordiSports Palace)
Pantadome system, 57, 58, 83, 84,139, 140, 142, 144, 145, 146,148, 151, 5.39, 6.14(a), 6.14(b),6.15
Paraboloids, 25Pass through chords, 48, 49, 3.25Pavilion of Extremadura, Expo ’92,
Seville, Spain, 100, 101, 5.62,5.63, 5.64
Peachtree MARTA station, Atlanta,USA, 118
Pearce, Peter (engineer), 41, 55, 89Pearce Systems International, USA, 89Pei, Cobb Freed (architects), 75Pei, I.M., 156Penetration of daylight, 163Percy Thomas Partnership (architects),
Pérez Piñero, Emilio (engineer), 131,132, 133, 134, 135, 151, 6.1, 6.3,6.6(a), 6.6(b), 6.7, 6.8
Perforated steel deck, 93Perimeter-supported space grid, 111Permanent shutter, 163, 7.13Peyri, Antoni (architect), 9PG System, 73, 75Phil Hawes (architect), 89Piece small systems, 31, 37, 38, 39,
41, 57Pieter Huybers, 30, 39, 115, 117Pin-ended bars, 14Plant and machinery, 17Plate connectors, 65Plate structures, 16, 17, 31, 2.5Plate theory, 24Platonic polyhedra, 16, 17, 2.5Point loads, 17Polycarbonate sheet, 165Polyester film membrane cushions, 64Polyester powder-coating, 34Polygonal living spaces, 67Polyhedra as plate structures, 17Polyhedra, 16, 17Polyhedral geometry, 156Polyhedral living space, 65, 5.7Polyhedral space grid buildings, 156Polyhedral spaces, 16, 17, 65, 156Polytetrafluoroethylene (PTFE), 53Preassembled grid sections, 106, 108,
5.74Pre-assembly, 112, 5.83Pre-camber, 54, 55Pre-fabrication of modules, 10, 14, 24,
31, 43Pre-installation of cladding and
services, 151, 6.28Pressed plates, 39Pre-stressing tendons, 124Pre-stressing, 74, 122, 123, 124,
5.100, 5.101Profiled plates, 31, 42Profiled slots, 38, 39, 3.11Progressive collapse, 26, 58, 59Progressive Design Associates
(architects), 105Props, 98Protection, 34PSA Projects, Edinburgh, 46, 3.21Pseudo-conical geometry, 97Purlins and purlin supports, 56Purpose-made jigs, 94Push-up erection process, 143, 145,
148, 151, 163Pyramid and Volcano, Expo ’67,
Montreal, Canada, 7, 8, 9, 1.12,1.13
Pyramid, Fantasy Island, Skegness,UK, 112, 113, 114, 5.85, 5.86
Pyramidal ‘city-in-the-air’, TRY 2004,160, 161, 163, 7.10
Pyramidal modular systems, 106Pyramidal modules, 4, 5, 27, 43, 46,
47, 94, 1.5(b), 1.6Pyramidal units, 44, 48Pyramidal, multi-layer, space truss
megastructure, 162Pyramidal/octahedral, 162Pyramidal-form pavilions, 156Pyramitec, 4, 1.5(b)
Quarter dome, 153Quarter sphere space grid, 104, 105,
106, 5.70, 5.71Quasicrystal dome, 166, 168, 7.19Quasicrystal geometry, 164, 165, 166,
7.16Quasicrystal grids, 168Quasicrystal sculpture, 167, 7.18Quasicrystal unit cells, 166, 7.16Quasicrystals, 165
Rafael Videla B. (architect), 94Rainwater, 74, 79Ramco-YKK (Singapore) Pte. Ltd, 170Randall G. Satterwhite, 64, 65, 66Rationalized computer model, 119,
5.94(a), 5.94(b)Rectangle on rectangle offset space
grid, 104, 112Rectangular on rectangular offset,
115Redesco srl, Milan, Italy (engineers),
126Reduction in section, 115, 5.87Redundancy, 18Regular dodecahedron, 165Regular modular systems, 166Regular patterns, 166Reinaldo González (engineer), 94Reinforced concrete, 156Reinforced plastics, 30Reitzel, Erik, 165, 167, 7.17René Motro, 53Resistance to damage, 18Restraint, 132Retractable roof structures, 128, 129,
151Retraction, 153Rhombic faces, 165, 166, 7.16Richard Buckminster Fuller (engineer),
2, 3, 4, 6, 41, 139, 156, 164, 1.2,1.3, 1.8
Ridge camber, 55, 4.4Rigid polyurethane foam insulation, 139Rigid-jointed modules, 11, 1.17Robbie, Roderick G. (architect), 153,
155Robbin, Tony, 165, 167, 7.17
Robots, 163Robustness, 18Rodrigo Riquelme A. (architect), 94Rods and plates, 164Ronald G. Taylor (engineer), 47, 94Roof lifting sequence, Sant Jordi
Sports Palace, Barcelona, 86, 5.41Roof movements during retraction,
Toronto Skydome, 154, 6.33Roundwood pole tower, Apeldoorm,
Netherlands, 117, 5.91, 5.92Roundwood poles, 30, 67, 114, 115,
117, 5.87, 5.88Roundwood, timber space trusses, 114RSP Architects, Planners and
Sadao Inc., 4Saddle surface, 56, 127, 4.6Salmon Associates (engineers), 75Salvador Dalí, 133, 134, 135, 6.7, 6.8San Pablo, Seville, swimming pool
cover, 152, 6.29, 6.31Sánchez, José (architect), 151Sant Jordi Sports Palace, Barcelona,
Spain, 25, 36, 57, 58, 81, 82, 84,86, 89, 90, 94, 142, 5.36, 5.37,5.39
Satterwhite, Randall G., 64, 65, 66Schuller, Reverend Dr Robert, 67Scissor mechanism, 131, 132, 6.2Scogin Elam and Bray, Atlanta
(architects), 118Scott, Brownrigg & Turner (architects),
112Scott, Wilson Kirkpatrick (engineers),
112Sculptural space grid, 165, 166SDC system, 36Sean Kenny (architect), 7Secondary bending effects, 53Secondary purlins, 74Secondary steelwork, 17Seismic activity, 54, 93Seismic design, 59Seismic forces, 67, 94Seismic loading, 59, 93Seismic zones, 144Self-weight, 24Semi-circular three-pinned arch, 106Semi-dome, 48Semi-reflective glass, 73SEO system, Orona , 32, 36, 83, 84,
87, 3.8, 5.39Series 80 Conder Harley, 41Service ducts, 157, 7.2Service loading, 93Services, 87, 163Severud-Perrone-Szegezdy-Sturm
Shading structures, 99, 5.61(b)Shadow pattern, 165, 166, 168, 7.19Shear connector, Catrus, 163, 164,
7.13Shiga Sacred Garden, Shinji-Shumei-
kai, Japan, 71Shimizu Corporation, 160, 161, 163,
7.10Shoei Yoh (architect), 77Showa Sekkei Co. Ltd (architects), 151Silicone sealant, 139Simpson, Gumpertz and Heger Inc.,4Singapore Indoor Stadium, 144, 145,
6.20, 6.21Single-layer grid dome, 140, 142, 6.15Single-layer grid, 12, 89Sir Frederick Snow and Partners
(engineers), 81Skydome, Toronto, Canada, 153Sliding arch, 153Sliding bearings, 54, 59, 90, 4.3Snelson, K., 164Snow, 24, 25, 146, 6.22Solid hub joints, 5, 1.7Solid or wireframe cells, 165Solid sawn timber, 30Solid spherical nodes, 32Southgate Shopping Centre,
Johannesburg, South Africa, 47,48, 3.24, 3.25
Space Deck Ltd, Chard, UK, 37, 53,108, 112, 114, 170
Space Deck modules, 44, 45, 107,3.17, 3.19, 3.20
Space Deck, 2, 27, 43, 45, 44, 46, 48,55, 106, 110, 3.18, 3.21, 5.79
Space filling packings of polyhedra,156
Space grid and enclosure model, 120,5.96
Space grid modules, 79Space grid systems, 30, 31Space grids at Expo ’92, Seville, 99Space Structures Research Laboratory,
9, 10, 1.15Space town, 158, 159, 160, 7.3, 7.7,
7.8Space truss, 65Space-filling polyhedra, 5SPACEgrid, 10, 41, 46, 47, 55Span to depth ratios, 45, 53, 73, 90Spanish National Organisation for the
Blind (ONCE), 100Sparse modular grid, 23, 2.15Special edge details, 28, 29, 2.32Spherical nodes, 31, 73, 163Spherobat, 4, 36Spheroidal dome, 97Spheroidal graphite iron, 30Spider Frame, 49
Spiders, 92, 5.49Splices, 43, 105Square edge profile, 29, 2.31Square on diagonal square grids, 22,
38, 48, 2.12Square-based pyramids, 43, 162Square-on-square offset grids, 22, 26,
27, 28, 38, 45, 69, 75, 102, 110,111, 115, 156, 2.10, 2.11, 2.23,2.24, 2.25, 2.26, 2.27
Stability, 12, 15, 16, 43, 85, 143, 146,149, 151, 159
Stable quasicrystal building structures,166
Stacking modules, 45, 3.20Stadium Australia, Sydney, 126, 127,
128, 129, 5.105, 5.106, 5.107Stadium, Split, Croatia, 34, 35, 3.6, 3.7Stainless steel tubular struts, 164Standard Fire Models, 58Stansted Airport, UK, 78, 79, 80, 81,
5.32, 5.33, 5.34(a), 5.34(b), 5.35Steel Design Award, 81Steel inserts, 34Steel rod tie bars, 44Stéphane du Château
(architect/engineer), 4, 46, 47,1.5(a), 1.5(b)
Stepped curved camber, 55, 4.4Stepped profile, 146, 6.22Stepped pyramids, 89Steve Baer, 165Stiffening panels, 166Stiffness, 15Stresses, 143Structural analysis software, 25Structural analysis, 145Structural efficiency, 26, 79Structural glazing, 164Structural Steel Design Award, 70Sun-Dome, Sabae, Fukui Prefecture,
87, 146, 147, 6.22, 6.23Support locations, 19, 26Supreme Award of the British
Construction Industry Awards, 81Swimming pool cover, San Pablo,
Seville, Spain, 152, 6.29Symbol Zone Festival Plaza Expo ’70,
Osaka, Japan, 61, 62, 63, 64, 5.1,5.2, 5.3, 5.4, 5.5
Taiyo Kogyo Corporation 34, 170Takara Beautilion, 9, 11, 14, 1.17Takenaka Corporation, 151Takenaka Komuten Co. Ltd, 143, 144Takumi Orimoto Structural Engineers &
Associates, 146Tange, Kenzo (architect), 9, 61, 64,
87, 146Tapered cone sections, 33, 34, 3.4
Taylor, Ronald G. (engineer), 47, 94Technical University, Delft,
Netherlands, 115Technical University, Lyngby,
Denmark, 165, 167, 7.17, 7.18Technitube, 42Temperature changes, 25, 53, 54, 64,
74, 4.2Temporary building, 135Temporary props and supports, 92, 98,
105, 106, 112, 143, 148, 5.58,5.74
Temporary working platform, 92, 107Tensegrity (tensile integrity), 164Tensile system supporting glazing,
164, 7.14Terminal 2, Manchester Airport, UK,
38, 57, 11, 1110, 112, 5.80, 5.81,5.82, 5.83
Tessellations of a flat plane, 21, 2.9Tetrahedra, 17, 22, 30, 41, 65, 122,
156, 158, 159, 7.4Tetrahedral modular units, 9, 156Tetrahedral space grid floors, 156Tetrahedral space, 10, 1.16Tetrahedron, 16, 17, 2.5The Bentall Centre, Kingston upon
Thames, UK, 106, 107, 109, 110,5.75, 5.77, 5.79
The Era of the Discoveries, 135Thermal insulation, 93Thermal movements, 30, 59, 74, 89,
90, 107Thin and fat quasicrystals, 166, 7.16Thin quasicrystal cell, 165Three hinge lines, 139, 140, 142,
6.14(a), 6.15Three-dimensional curved surface, 94Three-dimensional modules, 14Three-dimensional non-repeating
patterns, 164Three-dimensional structural action, 12Three-dimensional structural art, 166Three-pinned arch, 107, 108, 142Three-way space grids, 21, 94, 157,
158, 160, 7.1, 7.3Three-way, multi-layer grid, 159Tianjin Space Frame Co., 170Tie bars, 45Timber deck, 164Timber double-layer grid, 75, 5.26Timber roundwood pole, 39Timber, 30, 65, 66, 67, 72, 75, 77, 78,
98, 99, 114, 115, 117, 118, 5.30,5.87, 5.91
TM Truss, 34, 77, 170, 5.30Tolerances, 36, 38, 39, 42, 55, 62,
124Tomoo, Fukuda (architect), 64Tony Robbin, 165, 167, 7.17
Toroidal and spheroidal roof zones, 95,97, 5.54
Toronto Skydome, 153, 6.32Toshiba IHI pavilion, Expo ’70, Osaka,
Japan, 9, 10, 1.16Tower of the Sun, Expo ’70, Osaka,
Japan, 61Translucent roof panels, 64, 166Transparency, 164, 165Transport interchange, 162, 7.12Transportable buildings, 131Transportation, 43, 46, 49, 135, 138,
139, 163Travelling exhibition pavilion, 132, 133,
6.3, 6.4, 6.5Tree supports, 27, 73, 104, 118Triangle on hexagon grids, 23, 2.14Triangle-on triangle offset grids, 22,
23, 156, 2.13Triangular cladding, 120, 5.95Triangular facets, 118Triangular mesh, 97Triangulation, 14, 15, 94, 163Tridim Lahaye s.a., 170Tridimatic, 4Tridirectionelle S.D.C., 4, 1.5(a)Triodetic, 4, 5, 31, 38, 39, 55, 1.7, 3.11Triple layer grid, 73, 90Trocal membrane, 93Truncated tetrahedra, 5, 7, 1.10TRY2004 megacity, 160, 161, 162,
7.10, 7.11Tuball, 36Ture Wester (engineer), 17Twin-wall polycarbonate roof panels,
126, 128, 5.108Two-way space filling system, 160Two-way space grid, 157, 7.1Two-way spanning grids, 12, 13, 14,
15, 21, 68 156, 169, 2.2(b)Typical floor bay, 122, 5.98Typical floor bay, 123, 5.99Typical hinged node, 136, 6.11
Unfolding fully deployed space grid,138, 6.13
Unfolding the deployable roof grid,152, 6.29
UNIBAT, 4, 5, 10, 41, 43, 46, 47, 170,1.6
Uniform Building Code, 67Uniform curved camber, 55, 4.4Unistrut/Moduspan, 31, 39, 40, 170, 3.12United Nations Pavilion, Expo ’92,
Seville, 104, 105, 5.70, 5.71University of Surrey, Guildford, UK, 9,
10, 25, 1.15Uruñuela, Luis (architect), 104US pavilion, Expo ’67, Montreal,
Canada, 4, 6, 1.8
Valcárcel, J. (engineer), 99, 135Variation in grid spacing, 23, 24, 25,
2.17, 2.18, 2.19, 2.20Venezuela Pavilion, Expo ’92, Seville,
135, 136, 137, 138, 6.10, 6.11,6.12, 6.13
Ventilation ducts, 163Vertical circulation of lifts, 157, 7.2Vertical edge profile, 28Vertical pin connectors, 128, 129,
5.109Vertical space grids, 102, 5.66, 5.67Vestrut, 36, 170Vierendeel girders, 12, 14, 49, 70,
Wachsmann, Konrad (engineer), 3, 1.4
Wall construction, 103, 5.68Warped surfaces, 118, 120, 5.95Wave-form grid, 99Waverley Building, Nottingham Trent
University, UK, 20 Weather-proof envelope, 166Weidlinger Associates (engineers), 75Weithhofer, Pablo (engineer), 94Wester, Ture (engineer), 17What does the future hold, 166Wilderness Biome, Biosphere 2,
Sonoran Desert, Arizona, 88, 89,5.42
Wind action and loads, 23, 25, 53, 54,64, 86, 163, 4.2
Working platforms, 108, 110, 5.79World Memorial Hall, Kobe, 83, 142,
143, 144, 6.16, 6.17, 6.18,6.19(a), 6.19(b)
Yale Art Gallery, Yale University, NewHaven, Connecticut, 156
Yarza, Ane (engineer), 58Yoh Design Office, 78Yoh, Shoei (architect), 77Yoshikatsu Tsuboi, 9, 64, 72Young’s Modulus, 30, 169
Z. S. Makowski and Associates, 10Ziegler, 135