(Architecture Ebook) Structure and Architecture 7

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Transcript of (Architecture Ebook) Structure and Architecture 7

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Structure and Architecture

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Structure and ArchitectureAngus J. Macdonald

Department of Architecture, University of Edinburgh

Second edition

Architectural PressOXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI

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Structure and Architecture

Architectural PressAn imprint of Butterworth-HeinemannLinacre 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 1994Reprinted 1995, 1996, 1997Second edition 2001

© Reed Educational and Professional Publishing Ltd 1994, 2001

All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright 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 0LP. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressedto the publishers

British Library Cataloguing in Publication DataMacdonald, Angus J.

Structure and architecture. – 2nd ed.1. Structural design. 2. Architectural designI. Title721

ISBN 0 7506 4793 0

Library of Congress Cataloguing in Publication DataA catalogue record for this book is available from the Library of Congress

Printed and bound in Great BritainComposition by Scribe Design, Gillingham, Kent

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Preface vii

Acknowledgements ix

Introduction xi

1 The relationship of structure to building 1

2 Structural requirements 92.1 Introduction 92.2 Equilibrium 92.3 Geometric stability 92.4 Strength and rigidity 152.5 Conclusion 21

3 Structural materials 223.1 Introduction 223.2 Masonry 223.3 Timber 253.4 Steel 303.5 Concrete 35

4 The relationship between structural formand structural efficiency 374.1 Introduction 374.2 The effect of form on internal

force type 374.3 The concept of ‘improved’ shapes in

cross-section and longitudinal profile 40

4.4 Classification of structural elements 45

5 Complete structural arrangements 475.1 Introduction 475.2 Post-and-beam structures 485.3 Semi-form-active structures 555.4 Form-active structures 575.5 Conclusion 59

6 The critical appraisal of structures 606.1 Introduction 606.2 Complexity and efficiency in structural

design 60

6.3 Reading a building as a structural object 67

6.4 Conclusion 71

7 Structure and architecture 737.1 Introduction 737.2 The types of relationship between

structure and architecture 737.3 The relationship between architects

and engineers 114

Selected bibliography 124

Appendix 1: Simple two-dimensional forcesystems and static equilibrium 128

A1.1 Introduction 128A1.2 Force vectors and resultants 128A1.3 Resolution of a force into

components 129A1.4 Moments of forces 129A1.5 Static equilibrium and the equations

of equilibrium 129A1.6 The ‘free-body-diagram’ 132A1.7 The ‘imaginary cut’ technique 132

Appendix 2: Stress and strain 134A2.1 Introduction 134A2.2 Calculation of axial stress 135A2.3 Calculation of bending stress 135A2.4 Strain 138

Appendix 3: The concept of staticaldeterminacy 140

A3.1 Introduction 140A3.2 The characteristics of statically

determinate and statically indeterminate structures 140

A3.3 Design considerations in relation to statical determinacy 146

Index 149

Contents

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The major theme of this book is therelationship between structural design andarchitectural design. The various aspects ofthis are brought together in the last chapterwhich has been expanded in this secondedition, partly in response to comments fromreaders of the first edition, partly because myown ideas have changed and developed, andpartly as a consequence of discussion of theissues with colleagues in architecture andstructural engineering. I have also added asection on the types of relationship which haveexisted between architects, builders andengineers, and on the influence which these

have had on architectural style and form. Thepenultimate chapter, on structural criticism,has also been extensively rewritten. It is hopedthat the ideas explored in both of thesechapters will contribute to the betterunderstanding of the essential andundervalued contribution of structuralengineering to the Western architecturaltradition and to present-day practice.

Angus J. MacdonaldDepartment of Architecture,

University of EdinburghDecember 2000

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Preface to the second edition

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Angus Macdonald would like to thank allthose, too numerous to mention, who haveassisted in the making of this book. Specialthanks are due to Stephen Gibson for hiscarefully crafted line drawings, Hilary Normanfor her intelligent design, Thérèse Duriez forpicture research and the staff of ArchitecturalPress (and previously Butterworth-Heinemann)for their hard work and patience in initiating,editing and producing the book, particularlyNeil Warnock-Smith, Diane Chandler, AngelaLeopard, Siân Cryer and Sue Hamilton.

Illustrations other than those commissionedspecially for the book are individually credited

in their captions. Thanks are due to all thosewho supplied illustrations and especially toPat Hunt, Tony Hunt, the late Alastair Hunter,Jill Hunter and the staff of the picture librariesof Ove Arup & Partners, Anthony HuntAssociates, the British Cement Association, theArchitectural Association, the BritishArchitecture Library and the CourtauldInstitute.

Thanks are also due most particularly tomy wife Pat, for her continuedencouragement and for her expert scrutiny ofthe typescript.

ix

Acknowledgements

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It has long been recognised that anappreciation of the role of structure isessential to the understanding of architecture.It was Vitruvius, writing at the time of thefounding of the Roman Empire, who identifiedthe three basic components of architecture asfirmitas, utilitas and venustas and Sir HenryWooton, in the seventeenth century1, whotranslated these as ‘firmness’, ‘commodity’ and‘delight’. Subsequent theorists have proposeddifferent systems by which buildings may beanalysed, their qualities discussed and theirmeanings understood but the Vitruvianbreakdown nevertheless still provides a validbasis for the examination and criticism of abuilding.

‘Commodity’, which is perhaps the mostobvious of the Vitruvian qualities toappreciate, refers to the practical functioningof the building; the requirement that the set ofspaces which is provided is actually useful andserves the purpose for which the building wasintended. ‘Delight’ is the term for the effect ofthe building on the aesthetic sensibilities ofthose who come into contact with it. It mayarise from one or more of a number of factors.The symbolic meanings of the chosen forms,the aesthetic qualities of the shapes, texturesand colours, the elegance with which thevarious practical and programmatic problemsposed by the building have been solved, andthe ways in which links have been madebetween the different aspects of the design areall possible generators of ‘delight’.

‘Firmness’ is the most basic quality. It isconcerned with the ability of the building to

preserve its physical integrity and survive inthe world as a physical object. The part of thebuilding which satisfies the need for ‘firmness’is the structure. Structure is fundamental:without structure there is no building andtherefore no ‘commodity’. Without well-designed structure there can be no ‘delight’.

To appreciate fully the qualities of a work ofarchitecture the critic or observer shouldtherefore know something of its structuralmake-up. This requires an intuitive ability toread a building as a structural object, a skillwhich depends on a knowledge of thefunctional requirements of structure and anability to distinguish between the structuraland the non-structural parts of the building.The first of these attributes can only beacquired by systematic study of those branchesof mechanical science which are concernedwith statics, equilibrium and the properties ofmaterials. The second depends on a knowledgeof buildings and how they are constructed.These topics are reviewed briefly in thepreliminary chapters of this book.

The form of a structural armature isinevitably very closely related to that of thebuilding which it supports, and the act ofdesigning a building – of determining itsoverall form – is therefore also an act ofstructural design. The relationship betweenstructural design and architectural design cantake many forms however. At one extreme it ispossible for an architect virtually to ignorestructural considerations while inventing theform of a building and to conceal entirely thestructural elements in the completed versionof the building. The Statue of Liberty (Fig. ii) atthe entrance to New York harbour, which, giventhat it contains an internal circulation system xi

Introduction

1 Wooton, H., The Elements of Architecture, 1624.

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of stairs and elevators, can be considered to bea building, is an example of this type. Thebuildings of early twentieth-centuryexpressionism, such as the Einstein Tower atPotsdam by Mendelsohn (Fig. iii) and somerecent buildings based on the ideas ofDeconstruction (see Figs 1.11 and 7.41 to 7.44)might be cited as further examples.

All of these buildings contain a structure,but the technical requirements of the structurehave not significantly influenced the formwhich has been adopted and the structuralelements themselves are not importantcontributors to the aesthetics of thearchitecture. At the other extreme it is possibleto produce a building which consists of little

other than structure. The Olympic Stadium inMunich (Fig. i), by the architects Behnisch andPartners with Frei Otto, is an example of this.Between these extremes many differentapproaches to the relationship betweenstructure and architecture are possible. In the‘high tech’ architecture of the 1980s (Fig. iv), forexample, the structural elements discipline theplan and general arrangement of the buildingand form an important part of the visualvocabulary. In the early Modern buildings ofGropius, Mies van der Rohe, Le Corbusier (seeFig. 7.34) and others, the forms which wereadopted were greatly influenced by the types ofgeometry which were suitable for steel andreinforced concrete structural frameworks.

Introduction

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Fig. i OlympicStadium, Munich,Germany, 1968–72;Behnisch & Partner,architects, with FreiOtto. In both the canopyand the raked seatingmost of what is seen isstructural. (Photo: A.Macdonald)

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The relationship between structure andarchitecture can therefore take many forms andit is the purpose of this book to explore theseagainst a background of information concerningthe technical properties and requirements ofstructures. The author hopes that it will befound useful by architectural critics andhistorians as well as students and practitionersof the professions concerned with building.

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Introduction

Fig. iv InmosMicroprocessor Factory,Newport, South Wales,1982; Richard RogersPartnership, architects;Anthony HuntAssociates, structuralengineers. The generalarrangement andappearance of thisbuilding were stronglyinfluenced by therequirements of theexposed structure. Theform of the latter wasdetermined by space-planning requirements.(Photo: Anthony HuntAssociates)

Fig. ii The thin external surface of theStatue of Liberty in New York Harbour, USA,is supported by a triangulated structuralframework. The influence of structuralconsiderations on the final version of theform was minimal.

Fig. iii Sketches byMendelsohn of theEinstein Tower,Potsdam, Germany,1917. Structuralrequirements had littleinfluence on the externalform of this building,although they did affectthe internal planning.Surprisingly, it wasconstructed inloadbearing masonry.

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The simplest way of describing the function ofan architectural structure is to say that it is thepart of a building which resists the loads thatare imposed on it. A building may be regardedas simply an envelope which encloses andsubdivides space in order to create a protectedenvironment. The surfaces which form theenvelope, that is the walls, the floors and theroof of the building, are subjected to varioustypes of loading: external surfaces are exposedto the climatic loads of snow, wind and rain;floors are subjected to the gravitational loadsof the occupants and their effects; and most ofthe surfaces also have to carry their ownweight (Fig. 1.1). All of these loads tend todistort the building envelope and to cause it to

collapse; it is to prevent this from happeningthat a structure is provided. The function of astructure may be summed up, therefore, asbeing to supply the strength and rigidity whichare required to prevent a building fromcollapsing. More precisely, it is the part of abuilding which conducts the loads which areimposed on it from the points where they ariseto the ground underneath the building, wherethey can ultimately be resisted.

The location of the structure within abuilding is not always obvious because thestructure can be integrated with the non-structural parts in various ways. Sometimes, asin the simple example of an igloo (Fig. 1.2), inwhich ice blocks form a self-supportingprotective dome, the structure and the spaceenclosing elements are one and the samething. Sometimes the structural and space-enclosing elements are entirely separate. Avery simple example is the tepee (Fig. 1.3), inwhich the protecting envelope is a skin offabric or hide which has insufficient rigidity toform an enclosure by itself and which issupported on a framework of timber poles.Complete separation of structure and envelopeoccurs here: the envelope is entirely non-structural and the poles have a purelystructural function.

The CNIT exhibition Hall in Paris (Fig. 1.4) isa sophisticated version of the igloo; thereinforced concrete shell which forms the mainelement of this enclosure is self-supportingand, therefore, structural. Separation of skinand structure occurs in the transparent walls,however, where the glass envelope issupported on a structure of mullions. Thechapel by Le Corbusier at Ronchamp (see Fig.7.40) is a similar example. The highly 1

Chapter 1

The relationship ofstructure to building

Fig. 1.1 Loads on the building envelope. Gravitationalloads due to snow and to the occupation of the buildingcause roof and floor structures to bend and inducecompressive internal forces in walls. Wind causes pressureand suction loads to act on all external surfaces.

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sculptured walls and roof of this building aremade from a combination of masonry andreinforced concrete and are self-supporting.They are at the same time the elements whichdefine the enclosure and the structuralelements which give it the ability to maintainits form and resist load. The very large icehockey arena at Yale by Saarinen (see Fig. 7.18)is yet another similar example. Here thebuilding envelope consists of a network ofsteel cables which are suspended betweenthree reinforced concrete arches, one in thevertical plane forming the spine of the buildingand two side arches almost in the horizontalplane. The composition of this building ismore complex than in the previous casesbecause the suspended envelope can bebroken down into the cable network, which hasa purely structural function, and a non-structural cladding system. It might also beargued that the arches have a purely structuralfunction and do not contribute directly to theenclosure of space.

The steel-frame warehouse by FosterAssociates at Thamesmead, UK (Fig. 1.5), isalmost a direct equivalent of the tepee. Theelements which form it are either purelystructural or entirely non-structural because

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Fig. 1.2 The igloo is a self-supporting compressive envelope.

Fig. 1.3 In the tepee a non-structural skin is supportedon a structural framework of timber poles.

Fig. 1.4 Exhibition Hall of the CNIT, Paris, France; Nicolas Esquillan, architect. The principal element is a self-supporting reinforced concrete shell.

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the corrugated sheet metal skin is entirelysupported by the steel frame, which has apurely structural function. A similar breakdownmay be seen in later buildings by the samearchitects, such as the Sainsbury Centre for theVisual Arts at Norwich and the warehouse andshowroom for the Renault car company atSwindon (see Fig. 3.19).

In most buildings the relationship betweenthe envelope and the structure is morecomplicated than in the above examples, andfrequently this is because the interior of thebuilding is subdivided to a greater extent byinternal walls and floors. For instance, inFoster Associates’ building for Willis, Faberand Dumas, Ipswich, UK (Figs 1.6 and 7.37), 3

The relationship of structure to building

Fig. 1.5 Modern art glass warehouse, Thamesmead, UK, 1973; Foster Associates, architects; Anthony Hunt Associates,structural engineers. A non-structural skin of profiled metal sheeting is supported on a steel framework, which has apurely structural function. (Photo: Andrew Mead)

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the reinforced concrete structure of floor slabsand columns may be thought of as having adual function. The columns are purelystructural, although they do punctuate theinterior spaces and are space-dividingelements, to some extent. The floors are bothstructural and space-dividing elements. Here,however, the situation is complicated by thefact that the structural floor slabs are toppedby non-structural floor finishing materials andhave ceilings suspended underneath them. Thefloor finishes and ceilings could be regarded asthe true space-defining elements and the slabitself as having a purely structural function.The glass walls of the building are entirelynon-structural and have a space-enclosingfunction only. The more recent Carré d’Artbuilding in Nîmes (Fig. 1.7), also by FosterAssociates, has a similar disposition of parts.As at Willis, Faber and Dumas a multi-storeyreinforced concrete structure supports anexternal non-loadbearing skin.

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Fig. 1.6 Willis, Faber and Dumas Office, Ipswich, UK,1974; Foster Associates, architects; Anthony HuntAssociates, structural engineers. The basic structure ofthis building is a series of reinforced concrete cofferedslab floors supported on a grid of columns. The externalwalls are of glass and are non-structural. In the finishedbuilding the floor slabs are visible only at the perimeter.Elsewhere they are concealed by floor finishes and a falseceiling.

Fig. 1.7 Carré d’Art, Nîmes, France, 1993; FosterAssociates, architects. A superb example of late twentieth-century Modernism. It has a reinforced concrete framestructure which supports a non-loadbearing external skinof glass. (Photo: James H. Morris)

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The Antigone building at Montpellier byRicardo Bofill (Fig. 1.8) is also supported by amulti-storey reinforced concrete framework.The facade here consists of a mixture of in situand pre-cast concrete elements, and this, likethe glass walls of the Willis, Faber and Dumasbuilding, relies on a structural framework ofcolumns and floor slabs for support. Althoughthis building appears to be much more solidthan those with fully glazed external walls itwas constructed in a similar way. The UlmExhibition and Assembly Building by RichardMeier (Fig. 1.9) is also supported by areinforced concrete structure. Here thestructural continuity (see Appendix 3) and

mouldability which concrete offers wereexploited to create a complex juxtaposition ofsolid and void. The building is of the samebasic type as those by Foster and Bofillhowever; a structural framework of reinforcedconcrete supports cladding elements which arenon-structural.

In the Centre Pompidou in Paris by Pianoand Rogers, a multi-storey steel framework isused to support reinforced concrete floors andnon-loadbearing glass walls. The breakdown of 5

The relationship of structure to building

Fig. 1.8 Antigone, Montpellier, France, 1983; RicardoBofill, architect. This building is supported by a reinforcedconcrete framework. The exterior walls are a combinationof in situ and pre-cast concrete. They carry their own weightbut rely on the interior framework for lateral support.(Photo: A. Macdonald)

Fig. 1.9 Ulm Exhibition and Assembly Building,Germany, 1986–93: Richard Meier & Partners, architects.The mouldability of concrete and the structural continuitywhich is a feature of this material are exploited here toproduce a complex juxtaposition of solid and void. (Photo: E. & F. McLachlan)

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parts is straightforward (Fig. 1.10): identicalplane-frames, consisting of long steel columnswhich rise through the entire height of thebuilding supporting triangulated girders ateach floor level, are placed parallel to eachother to form a rectangular plan. The concretefloors span between the triangulated girders.Additional small cast-steel girders projectbeyond the line of columns (Fig. 7.7) and areused to support stairs, escalators and servicing

components positioned along the sides of thebuilding outside the glass wall, which isattached to the frame near the columns. Asystem of cross-bracing on the sides of theframework prevents it from collapsing throughinstability.

The controlled disorder of the rooftop officeextension in Vienna by Coop Himmelblau (Fig.1.11) is in some respects a complete contrastto the controlled order of the CentrePompidou. Architecturally it is quite different,expressing chaos rather than order, butstructurally it is similar as the light externalenvelope is supported on a skeletal metalframework.

The house with masonry walls and timberfloor and roof structures is a traditional form ofbuilding in most parts of the world. It is found inmany forms, from the historic grand houses ofthe European landed aristocracy (Fig. 1.12) tomodern homes in the UK (Figs 1.13 and 1.14).Even the simplest versions of this form ofmasonry and timber building (Fig. 1.13) are fairlycomplex assemblies of elements. Initial

Structure and Architecture

Fig. 1.10 Centre Pompidou, Paris, France, 1977; Piano &Rogers, architects; Ove Arup & Partners, structuralengineers. The separation of structural and enclosingfunctions into distinct elements is obvious here. (Photo: A.Macdonald)

Fig. 1.11 Rooftop office in Vienna, Austria, 1988; CoopHimmelblau, architects. The forms chosen here have nostructural logic and were determined with almost noconsideration for technical requirements. This approachdesign is quite feasible in the present day so long as thebuilding is not too large.6

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7

The relationship of structure to building

Fig. 1.12 Château de Chambord, France, 1519–47. One of the grandest domestic buildings in Europe, the Château deChambord has a loadbearing masonry structure. Most of the walls are structural; the floors are either of timber or vaultedmasonry and the roof structure is of timber. (Photo: P. & A. Macdonald)

Fig. 1.13 Traditional construction in theUK, in its twentieth-century form, withloadbearing masonry walls and timberfloor and roof structures. All structuralelements are enclosed in non-structuralfinishing materials.

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consideration could result in a straightforwardbreakdown of parts with the masonry walls andtimber floors being regarded as having bothstructural and space-dividing functions and theroof as consisting of a combination of the purelysupportive trusses, which are the structuralelements, and the purely protective, non-structural skin. Closer examination would revealthat most of the major elements can in fact besubdivided into parts which are either purelystructural or entirely non-structural. The floors,for example, normally consist of an inner core oftimber joists and floor boarding, which are thestructural elements, enclosed by ceiling and floorfinishes. The latter are the non-structuralelements which are seen to divide the space. Asimilar breakdown is possible for the walls and infact very little of what is visible in the traditionalhouse is structural, as most of the structuralelements are covered by non-structural finishes.

To sum up, these few examples of verydifferent building types demonstrate that allbuildings contain a structure, the function ofwhich is to support the building envelope byconducting the forces which are applied to itfrom the points where they arise in thebuilding to the ground below it where theyare ultimately resisted. Sometimes thestructure is indistinguishable from theenclosing and space-dividing buildingenvelope, sometimes it is entirely separatefrom it; most often there is a mixture ofelements with structural, non-structural andcombined functions. In all cases the form ofthe structure is very closely related to that ofthe building taken as a whole and theelegance with which the structure fulfils itsfunction is something which affects thequality of the architecture.

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Fig. 1.14 Local authority housing, Haddington, Scotland,1974; J. A. W. Grant, architects. These buildings haveloadbearing masonry walls and timber floor and roofstructures. (Photo: Alastair Hunter)

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2.1 Introduction

To perform its function of supporting abuilding in response to whatever loads may beapplied to it, a structure must possess fourproperties: it must be capable of achieving astate of equilibrium, it must be stable, it musthave adequate strength and it must haveadequate rigidity. The meanings of these termsare explained in this chapter. The influence ofstructural requirements on the forms which areadopted for structures is also discussed. Thetreatment is presented in a non-mathematicalway and the definitions which are given are notthose of the theoretical physicist; they aresimply statements which are sufficientlyprecise to allow the significance of theconcepts to structural design to beappreciated.

2.2 Equilibrium

Structures must be capable of achieving astate of equilibrium under the action ofapplied load. This requires that the internalconfiguration of the structure together withthe means by which it is connected to itsfoundations must be such that all appliedloads are balanced exactly by reactionsgenerated at its foundations. Thewheelbarrow provides a simple demonstrationof the principles involved. When thewheelbarrow is at rest it is in a state of staticequilibrium. The gravitational forcesgenerated by its self weight and that of itscontents act vertically downwards and areexactly balanced by reacting forces acting atthe wheel and other supports. When a

horizontal force is applied to the wheelbarrowby its operator it moves horizontally and isnot therefore in a state of static equilibrium.This occurs because the interface between thewheelbarrow and the ground is incapable ofgenerating horizontal reacting forces. Thewheelbarrow is both a structure and amachine: it is a structure under the action ofgravitational load and a machine under theaction of horizontal load.

Despite the famous statement by onecelebrated commentator, buildings are notmachines1. Architectural structures must,therefore, be capable of achieving equilibriumunder all directions of load.

2.3 Geometric stability

Geometric stability is the property whichpreserves the geometry of a structure andallows its elements to act together to resistload. The distinction between stability andequilibrium is illustrated by the frameworkshown in Fig. 2.1 which is capable of achievinga state of equilibrium under the action ofgravitational load. The equilibrium is notstable, however, because the frame willcollapse if disturbed laterally2.

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Chapter 2

Structural requirements

1 ‘A house is a machine for living.’ Le Corbusier.2 Stability can also be distinguished from strength or

rigidity, because even if the elements of a structurehave sufficient strength and rigidity to sustain theloads which are imposed on them, it is still possiblefor the system as a whole to fail due to its beinggeometrically unstable as is demonstrated in Fig. 2.1.

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This simple arrangement demonstratesthat the critical factor, so far as the stabilityof any system is concerned, is the effect on itof a small disturbance. In the context ofstructures this is shown very simply in Fig. 2.2by the comparison of tensile and compressiveelements. If the alignment of either of these isdisturbed, the tensile element is pulled backinto line following the removal of thedisturbing agency but the compressiveelement, once its initially perfect alignmenthas been altered, progresses to an entirelynew position. The fundamental issue ofstability is demonstrated here, which is thatstable systems revert to their original statefollowing a slight disturbance whereas unstablesystems progress to an entirely new state.

The parts of structures which tend to beunstable are the ones in which compressiveforces act and these parts must therefore begiven special attention when the geometricstability of an arrangement is beingconsidered. The columns in a simplerectangular framework are examples of this(Fig. 2.1). The three-dimensional bridgestructure of Fig. 2.3 illustrates anotherpotentially unstable system. Compressionoccurs in the horizontal elements in the upperparts of this frame when the weight of anobject crossing the bridge is carried. Thearrangement would fail by instability when thisload was applied due to inadequate restraintof these compression parts. The compressiveinternal forces, which would inevitably occur

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Fig. 2.1 A rectangular frame with four hinges is capableof achieving a state of equilibrium but is unstable becauseany slight lateral disturbance to the columns will induce itto collapse. The frame on the right here is stabilised by thediagonal element which makes no direct contribution tothe resistance of the gravitational load.

Fig. 2.2 The tensileelement on the left here isstable because the loadspull it back into linefollowing a disturbance. Thecompressive element onthe right is fundamentallyunstable.

Original alignment Fig. 2.3 The horizontalelements in the tops ofthe bridge girders aresubjected tocompressive internalforce when the load isapplied. The system isunstable and anyeccentricity which ispresent initially causesan instability-typefailure to develop.

CompressionTension

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with some degree of eccentricity, would pushthe upper elements out of alignment andcause the whole structure to collapse.

The geometric instability of thearrangements in Figures 2.1 and 2.3 wouldhave been obvious if their response tohorizontal load had been considered (Fig. 2.4).This demonstrates one of the fundamentalrequirements for the geometric stability of anyarrangement of elements, which is that it mustbe capable of resisting loads from orthogonaldirections (two orthogonal directions for planearrangements and three for three-dimensionalarrangements). This is another way of sayingthat an arrangement must be capable ofachieving a state of equilibrium in response toforces from three orthogonal directions. Thestability or otherwise of a proposedarrangement can therefore be judged byconsidering the effect on it of sets of mutuallyperpendicular trial forces: if the arrangement iscapable of resisting all of these then it isstable, regardless of the loading pattern whichwill actually be applied to it in service.

Conversely, if an arrangement is not capable ofresisting load from three orthogonal directionsthen it will be unstable in service even thoughthe load which it is designed to resist will beapplied from only one direction.

It frequently occurs in architectural designthat a geometry which is potentially unstablemust be adopted in order that otherarchitectural requirements can be satisfied. Forexample, one of the most convenient structuralgeometries for buildings, that of therectangular frame, is unstable in its simplesthinge-jointed form, as has already been shown.Stability can be achieved with this geometry bythe use of rigid joints, by the insertion of adiagonal element or by the use of a rigiddiaphragm which fills up the interior of theframe (Fig. 2.5). Each of these hasdisadvantages. Rigid joints are the mostconvenient from a space-planning point ofview but are problematic structurally becausethey can render the structure staticallyindeterminate (see Appendix 3). Diagonalelements and diaphragms block the frameworkand can complicate space planning. In multi-panel arrangements, however, it is possible toproduce stability without blocking every panel.The row of frames in Fig. 2.6, for example, isstabilised by the insertion of a single diagonal.

11

Structural requirements

Fig. 2.4 Conditions for stability of frameworks. (a) Thetwo-dimensional system is stable if it is capable ofachieving equilibrium in response to forces from twomutually perpendicular directions. (b) The three-dimensional system is stable if it is capable of resistingforces from three directions. Note that in the caseillustrated the resistance of transverse horizontal load isachieved by the insertion of rigid joints in the end bays.

(a) (b)

Fig. 2.5 A rectangular frame can be stabilised by theinsertion of (a) a diagonal element or (b) a rigiddiaphragm, or (c) by the provision of rigid joints. A singlerigid joint is in fact sufficient to provide stability.

Fig. 2.6 A row of rectangular frames is stable if one panelonly is braced by any of the three methods shown in Fig. 2.5.

(a) (b) (c)

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Where frames are parallel to each other thethree-dimensional arrangement is stable if afew panels in each of the two principaldirections are stabilised in the vertical planeand the remaining frames are connected tothese by diagonal elements or diaphragms inthe horizontal plane (Fig. 2.7). A three-dimensional frame can therefore be stabilisedby the use of diagonal elements or diaphragmsin a limited number of panels in the verticaland horizontal planes. In multi-storeyarrangements these systems must be providedat every storey level.

None of the components which are addedto stabilise the geometry of the rectangularframe in Fig. 2.7 makes a direct contribution tothe resistance of gravitational load (i.e. thecarrying of weight, either of the structure itselfor of the elements and objects which itsupports). Such elements are called bracing

elements. Arrangements which do not requirebracing elements, either because they arefundamentally stable or because stability isprovided by rigid joints, are said to be self-bracing.

Most structures contain bracing elementswhose presence frequently affects both theinitial planning and the final appearance of thebuilding which it supports. The issue ofstability, and in particular the design ofbracing systems, is therefore something whichaffects the architecture of buildings.

Where a structure is subjected to loads fromdifferent directions, the elements which areused solely for bracing when the principal loadis applied frequently play a direct role inresisting secondary load. The diagonalelements in the frame of Fig. 2.7, for example,would be directly involved in the resistance ofany horizontal load which was applied, such asmight occur due to the action of wind. Becausereal structures are usually subjected to loadsfrom different directions, it is very rare forelements to be used solely for bracing.

The nature of the internal force in bracingcomponents depends on the direction in whichthe instability which they prevent occurs. InFig. 2.8, for example, the diagonal element willbe placed in tension if the frame sways to theright and in compression if it sways to the left.Because the direction of sway due to instabilitycannot be predicted when the structure isbeing designed, the single bracing elementwould have to be made strong enough to carryeither tension or compression. The resistanceof compression requires a much larger size ofcross-section than that of tension, however,especially if the element is long3, and this is acritical factor in determining its size. It isnormally more economical to insert bothdiagonal elements into a rectangular frame

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12

Fig. 2.7 Theseframes containthe minimumnumber ofbraced panelsrequired forstability.

3 This is because compression elements can suffer fromthe buckling phenomenon. The basic principles of thisare explained in elementary texts on structures such asEngel, H., Structural Principles, Prentice-Hall, EnglewoodCliffs, NJ, 1984. See also Macdonald, Angus J., StructuralDesign for Architecture, Architectural Press, Oxford, 1997,Appendix 2.

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(cross-bracing) than a single element and todesign both of them as tension-only elements.When the panel sways due to instability theelement which is placed in compression simplybuckles slightly and the whole of the restraintis provided by the tension diagonal.

It is common practice to provide morebracing elements than the minimum numberrequired so as to improve the resistance ofthree-dimensional frameworks to horizontalload. The framework in Fig. 2.7, for example,although theoretically stable, would sufferconsiderable distortion in response to ahorizontal load applied parallel to the long sideof the frame at the opposite end from thevertical-plane bracing. A load applied parallel tothe long side at this end of the frame would alsocause a certain amount of distress as somemovement of joints would inevitably occur in thetransmission of it to the vertical-plane bracing atthe other end. In practice the performance of theframe is more satisfactory if vertical-planebracing is provided at both ends (Fig. 2.9). Thisgives more restraint than is necessary forstability and makes the structure staticallyindeterminate (see Appendix 3), but results inthe horizontal loads being resisted close to thepoints where they are applied to the structure.

Another practical consideration in relationto the bracing of three-dimensional rectangularframes is the length of the diagonal elementswhich are provided. These sag in response totheir own weight and it is thereforeadvantageous to make them as short aspossible. For this reason bracing elements arefrequently restricted to a part of the panel inwhich they are located. The frame shown inFig. 2.10 contains this refinement.

Figures 2.11 and 2.12 show typical bracingsystems for multi-storey frameworks. Anothercommon arrangement, in which floor slabs actas diaphragm-type bracing in the horizontalplane in conjunction with vertical-planebracing of the diagonal type, is shown in Fig.2.13. When the rigid-joint method is used it is 13

Structural requirements

Fig. 2.8 Cross-bracing is used so that sway caused byinstability is always resisted by a diagonal element actingin tension. The compressive diagonal buckles slightly andcarries no load.

Fig. 2.9 In practical bracing schemes more elementsthan are strictly necessary to ensure stability are providedto improve the performance of frameworks in resistinghorizontal load. Frame (a) is stable but will sufferdistortion in response to horizontal load on the side walls.Its performance is enhanced if a diagonal element isprovided in both end walls (b). The lowest framework (c)contains the minimum number of elements required toresist effectively horizontal load from the two principalhorizontal directions. Note that the vertical-plane bracingelements are distributed around the structure in asymmetrical configuration.

(a)

(b)

(c)

Fig. 2.10 In practice, bracing elements are frequentlyconfined to a part of each panel only.

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normal practice to stabilise all panelsindividually by making all joints rigid. Thiseliminates the need for horizontal-planebracing altogether, although the floorsnormally act to distribute through thestructure any unevenness in the application ofhorizontal load. The rigid-joint method is thenormal method which is adopted forreinforced concrete frames, in whichcontinuity through junctions betweenelements can easily be achieved; diaphragmbracing is also used, however, in both verticaland horizontal planes in certain types ofreinforced concrete frame.

Loadbearing wall structures are those inwhich the external walls and internal partitionsserve as vertical structural elements. They arenormally constructed of masonry, reinforced

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14

Fig. 2.13 Concrete floor slabs are normally used ashorizontal-plane bracing of the diaphragm type which actsin conjunction with diagonal bracing in the vertical planes.

Fig. 2.12 These drawings of floor grid patterns for steelframeworks show typical locations for vertical-plane bracing.

Fig. 2.11 A typical bracing scheme for a multi-storeyframework. Vertical-plane bracing is provided in a limitednumber of bays and positioned symmetrically on plan. Allother bays are linked to this by diagonal bracing in thehorizontal plane at every storey level.

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concrete or timber, but combinations of thesematerials are also used. In all cases the jointsbetween walls and floors are normallyincapable of resisting bending action (in otherwords they behave as hinges) and the resultinglack of continuity means that rigid-frameaction cannot develop. Diaphragm bracing,provided by the walls themselves, is used tostabilise these structures.

A wall panel has high rotational stability inits own plane but is unstable in the out-of-plane direction (Fig. 2.14); vertical panelsmust, therefore, be grouped in pairs at right

angles to each other so that they providemutual support. For this to be effective thestructural connection which is provided in thevertical joint between panels must be capableof resisting shear4. Because loadbearing wallstructures are normally used for multi-cellularbuildings, the provision of an adequatenumber of vertical-plane bracing diaphragms

in two orthogonal directions is normallystraightforward (Fig. 2.15). It is unusualtherefore for bracing requirements to have asignificant effect on the internal planning ofthis type of building.

The need to ensure that a structuralframework is adequately braced is a factor thatcan affect the internal planning of buildings.The basic requirement is that some form ofbracing must be provided in three orthogonalplanes. If diagonal or diaphragm bracing isused in the vertical planes this must beaccommodated within the plan. Becausevertical-plane bracing is most effective when itis arranged symmetrically, either in internalcores or around the perimeter of the building,this can affect the space planning especially intall buildings where the effects of wind loadingare significant.

2.4 Strength and rigidity

2.4.1 IntroductionThe application of load to a structuregenerates internal forces in the elements andexternal reacting forces at the foundations (Fig.2.16) and the elements and foundations must 15

Structural requirements

4 See Engel, H., Structural Principles, Prentice-Hall,Englewood Cliffs, NJ, 1984 for an explanation of shear.

Fig. 2.14 Walls areunstable in the out-of-plane directionand must be groupedinto orthogonalarrangements forstability.

Fig. 2.15 Loadbearing masonry buildings are normallymulti-cellular structures which contain walls running intwo orthogonal directions. The arrangement is inherentlystable.

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have sufficient strength and rigidity to resistthese. They must not rupture when the peakload is applied; neither must the deflectionwhich results from the peak load be excessive.

The requirement for adequate strength issatisfied by ensuring that the levels of stresswhich occur in the various elements of astructure, when the peak loads are applied, arewithin acceptable limits. This is chiefly amatter of providing elements with cross-sections of adequate size, given the strength ofthe constituent material. The determination ofthe sizes required is carried out by structuralcalculations. The provision of adequate rigidityis similarly dealt with.

Structural calculations allow the strengthand rigidity of structures to be controlledprecisely. They are preceded by an assessmentof the load which a structure will be requiredto carry. The calculations can be considered tobe divisible into two parts and to consist firstlyof the structural analysis, which is theevaluation of the internal forces which occur inthe elements of the structure, and secondly,the element-sizing calculations which arecarried out to ensure that they will havesufficient strength and rigidity to resist theinternal forces which the loads will cause. Inmany cases, and always for statically

indeterminate structures (see Appendix 3), thetwo sets of calculations are carried outtogether, but it is possible to think of them asseparate operations and they are describedseparately here.

2.4.2 The assessment of loadThe assessment of the loads which will act ona structure involves the prediction of all thedifferent circumstances which will cause loadto be applied to a building in its lifetime (Fig.2.17) and the estimation of the greatest

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Fig. 2.16 The structural elements of a building conductthe loads to the foundations. They are subjected tointernal forces that generate stresses the magnitudes ofwhich depend on the intensities of the internal forces andthe sizes of the elements. The structure will collapse if thestress levels exceed the strength of the material.

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magnitudes of these loads. The maximum loadcould occur when the building was full ofpeople, when particularly heavy items ofequipment were installed, when it was exposedto the force of exceptionally high winds or as aresult of many other eventualities. Thedesigner must anticipate all of thesepossibilities and also investigate all likelycombinations of them.

The evaluation of load is a complex process,but guidance is normally available to thedesigner of a structure from loadingstandards5. These are documents in which dataand wisdom gained from experience arepresented systematically in a form whichallows the information to be applied in design.

2.4.3 The analysis calculationsThe purpose of structural analysis is todetermine the magnitudes of all of the forces,internal and external, which occur on and in a

structure when the most unfavourable loadconditions occur. To understand the variousprocesses of structural analysis it is necessaryto have a knowledge of the constituents ofstructural force systems and an appreciation ofconcepts, such as equilibrium, which are usedto derive relationships between them. Thesetopics are discussed in Appendix 1.

In the analysis of a structure the externalreactions which act at the foundations and theinternal forces in the elements are calculatedfrom the loads. This is a process in which thestructure is reduced to its most basic abstractform and considered separately from the restof the building which it will support.

An indication of the sequence of operationswhich are carried out in the analysis of asimple structure is given in Fig. 2.18. After apreliminary analysis has been carried out toevaluate the external reactions, the structure issubdivided into its main elements by making‘imaginary cuts’ (see Appendix 1.7) through thejunctions between them. This creates a set of‘free-body-diagrams’ (Appendix 1.6) in whichthe forces that act between the elements are 17

Structural requirements

5 In the UK the relevant standard is BS 6399, DesignLoading for Buildings, British Standards Institution, 1984.

Fig. 2.17 The prediction of the maximum load which will occur is one of the most problematic aspects of structuralcalculations. Loading standards are provided to assist with this but assessment of load is nevertheless one of the mostimprecise parts of the structural calculation process.

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exposed. Following the evaluation of theseinter-element forces the individual elementsare analysed separately for their internal forcesby further applications of the ‘imaginary cut’technique. In this way all of the internal forcesin the structure are determined.

In large, complex, statically indeterminatestructures the magnitudes of the internalforces are affected by the sizes and shapes ofthe element cross-sections and the propertiesof the constituent materials, as well as by themagnitudes of the loads and the overall

geometry of the structure. The reason for thisis explained in Appendix 3. In thesecircumstances the analysis and element-sizingcalculations are carried out together in a trialand error process which is only feasible in thecontext of computer-aided design.

The different types of internal force whichcan occur in a structural element are shown inFig. 2.19. As these have a very significantinfluence on the sizes and shapes which arespecified for elements they will be describedbriefly here.

In Fig. 2.19 an element is cut through at aparticular cross-section. In Fig. 2.19(a) theforces which are external to one of the

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Fig. 2.18 In structural analysis the complete structure isbroken down into two-dimensional components and theinternal forces in these are subsequently calculated. Thediagram shows the pattern forces which result fromgravitational load on the roof of a small building. Similarbreakdowns are carried out for the other forms of load anda complete picture is built up of the internal forces whichwill occur in each element during the life of the structure.

Uniformly distributed

Fig. 2.19 The investigation of internal forces in a simplebeam using the device of the ‘imaginary cut’. The cutproduces a free-body-diagram from which the nature of theinternal forces at a single cross-section can be deduced.The internal forces at other cross-sections can bedetermined from similar diagrams produced by cuts madein appropriate places. (a) Not in equilibrium. (b) Positionalequilibrium but not in rotational equilibrium. (c)Positional and rotational equilibrium. The shear force onthe cross-section 1.5 m from the left-hand support is15 kN; the bending moment on this cross-section is22.5 kNm.

(a)

(b)

(c)

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resulting sub-elements are marked. If thesewere indeed the only forces which acted on thesub-element it would not be in a state ofequilibrium. For equilibrium the forces mustbalance and this is clearly not the case here;an additional vertical force is required forequilibrium. As no other external forces arepresent on this part of the element the extraforce must act on the cross-section where thecut occurred. Although this force is external tothe sub-element it is an internal force so far asthe complete element is concerned and iscalled the ‘shear force’. Its magnitude at thecross-section where the cut was made issimply the difference between the externalforces which occur to one side of the cross-section, i.e. to the left of the cut.

Once the shear force is added to thediagram the question of the equilibrium ofthe sub-element can once more beexamined. In fact it is still not in a state ofequilibrium because the set of forces nowacting will produce a turning effect on thesub-element which will cause it to rotate in aclockwise sense. For equilibrium an anti-clockwise moment is required and as beforethis must act on the cross-section at the cutbecause no other external forces are present.The moment which acts at the cut and whichis required to establish rotationalequilibrium is called the bending moment atthe cross-section of the cut. Its magnitude isobtained from the moment equation ofequilibrium for the free-body-diagram. Oncethis is added to the diagram the system is ina state of static equilibrium, because all theconditions for equilibrium are now satisfied(see Appendix 1).

Shear force and bending moment are forceswhich occur inside structural elements andthey can be defined as follows. The shear forceat any location is the amount by which theexternal forces acting on the element, to oneside of that location, do not balance when theyare resolved perpendicular to the axis of theelement. The bending moment at a location inan element is the amount by which themoments of the external forces acting to oneside of the location, about any point in their

plane, do not balance. Shear force and bendingmoment occur in structural elements which arebent by the action of the applied load. Beamsand slabs are examples of such elements.

One other type of internal force can act onthe cross-section of an element, namely axialthrust (Fig. 2.20). This is defined as the amountby which the external forces acting on theelement to one side of a particular location donot balance when they are resolved parallel tothe direction of the element. Axial thrust canbe either tensile or compressive.

In the general case each cross-section of astructural element is acted upon by all threeinternal forces, namely shear force, bendingmoment and axial thrust. In the element-sizingpart of the calculations, cross-section sizes aredetermined that ensure the levels of stresswhich these produce are not excessive. Theefficiency with which these internal forces canbe resisted depends on the shape of the cross-section (see Section 4.2). 19

Structural requirements

Fig. 2.20 The ‘imaginary cut’ is a device for exposinginternal forces and rendering them susceptible toequilibrium analysis. In the simple beam shown here shearforce and bending moment are the only internal forcesrequired to produce equilibrium in the element isolated bythe cut. These are therefore the only internal forces whichact on the cross-section at which the cut was made. In thecase of the portal frame, axial thrust is also required at thecross-section exposed by the cut.

(a) (b)

(c) (d)

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The magnitudes of the internal forces instructural elements are rarely constant alongtheir lengths, but the internal forces at anycross-section can always be found by makingan ‘imaginary cut’ at that point and solving thefree-body-diagram which this creates.Repeated applications of the ‘imaginary cut’technique at different cross-sections (Fig.2.21), allows the full pattern of internal forcesto be evaluated. In present-day practice thesecalculations are processed by computer andthe results presented graphically in the form ofbending moment, shear force and axial thrustdiagrams for each structural element.

The shapes of bending moment, shear forceand axial thrust diagrams are of greatsignificance for the eventual shapes ofstructural elements because they indicate thelocations of the parts where greatest strengthwill be required. Bending moment is normallylarge in the vicinity of mid-span and near rigidjoints. Shear force is highest near supportjoints. Axial thrust is usually constant alongthe length of structural elements.

2.4.4 Element-sizing calculationsThe size of cross-section which is provided fora structural element must be such as to give itadequate strength and adequate rigidity. Inother words, the size of the cross-section mustallow the internal forces determined in theanalysis to be carried without overloading thestructural material and without the occurrenceof excessive deflection. The calculations whichare carried out to achieve this involve the useof the concepts of stress and strain (seeAppendix 2).

In the sizing calculations each element isconsidered individually and the area of cross-section determined which will maintain thestress at an acceptable level in response to thepeak internal forces. The detailed aspects ofthe calculations depend on the type of internalforce and, therefore, the stress involved and onthe properties of the structural material.

As with most types of design the evolutionof the final form and dimensions of a structureis, to some extent, a cyclic process. If theelement-sizing procedures yield cross-sectionswhich are considered to be excessively large orunsuitable in some other way, modification ofthe overall form of the structure will beundertaken so as to redistribute the internalforces. Then, the whole cycle of analysis andelement-sizing calculations must be repeated.

If a structure has a geometry which is stableand the cross-sections of the elements aresufficiently large to ensure that it has adequatestrength it will not collapse under the action ofthe loads which are applied to it. It willtherefore be safe, but this does not necessarilymean that its performance will be satisfactory(Fig. 2.22). It may suffer a large amount of

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Fig. 2.21 The magnitudes of internal forces normally varyalong the length of a structural element. Repeated use ofthe ‘imaginary cut’ technique yields the pattern of internalforces in this simple beam.

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deflection under the action of the load and anydeformation which is large enough to causedamage to brittle building components, suchas glass windows, or to cause alarm to thebuilding’s occupants or even simply to causeunsightly distortion of the building’s form is atype of structural failure.

The deflection which occurs in response to agiven application of load to a structuredepends on the sizes of the cross-sections ofthe elements6 and can be calculated onceelement dimensions have been determined. Ifthe sizes which have been specified to provideadequate strength will result in excessivedeflection they are increased by a suitableamount. Where this occurs it is the rigidityrequirement which is critical and whichdetermines the sizes of the structuralelements. Rigidity is therefore a phenomenonwhich is not directly related to strength; it is a

separate issue and is considered separately inthe design of structures.

2.5 Conclusion

In this chapter the factors which affect the basicrequirements of structures have been reviewed.The achievement of stable equilibrium hasbeen shown to be dependent largely on thegeometric configuration of the structure and istherefore a consideration which affects thedetermination of its form. A stable form canalmost always be made adequately strong andrigid, but the form chosen does affect theefficiency with which this can be accomplished.So far as the provision of adequate strength isconcerned the task of the structural designer isstraightforward, at least in principle. He or shemust determine by analysis of the structure thetypes and magnitudes of the internal forceswhich will occur in all of the elements when themaximum load is applied. Cross-section shapesand sizes must then be selected such that thestress levels are maintained within acceptablelimits. Once the cross-sections have beendetermined in this way the structure will beadequately strong. The amount of deflectionwhich will occur under the maximum load canthen be calculated. If this is excessive theelement sizes are increased to bring thedeflection within acceptable limits. Thedetailed procedures which are adopted forelement sizing depend on the types of internalforce which occur in each part of the structureand on the properties of the structuralmaterials.

21

Structural requirements

6 The deflection of a structure is also dependent on theproperties of the structural material and on the overallconfiguration of the structure.

Fig. 2.22 A structure with adequate strength will notcollapse, but excessive flexibility can render it unfit for itspurpose.

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3.1 Introduction

The shapes which are adopted for structuralelements are affected, to a large extent, by thenature of the materials from which they aremade. The physical properties of materialsdetermine the types of internal force whichthey can carry and, therefore, the types ofelement for which they are suitable.Unreinforced masonry, for example, may onlybe used in situations where compressive stressis present. Reinforced concrete performs wellwhen loaded in compression or bending, butnot particularly well in axial tension.

The processes by which materials aremanufactured and then fashioned intostructural elements also play a role indetermining the shapes of elements for whichthey are suitable. These aspects of theinfluence of material properties on structuralgeometry are now discussed in relation to thefour principal structural materials of masonry,timber, steel and reinforced concrete.

3.2 Masonry

Masonry is a composite material in whichindividual stones, bricks or blocks are beddedin mortar to form columns, walls, arches orvaults (Fig. 3.1). The range of different types ofmasonry is large due to the variety of types ofconstituent. Bricks may be of fired clay, bakedearth, concrete, or a range of similar materials,and blocks, which are simply very large bricks,can be similarly composed. Stone too is notone but a very wide range of materials, fromthe relatively soft sedimentary rocks such aslimestone to the very hard granites and other

igneous rocks. These ‘solid’ units can be usedin conjunction with a variety of differentmortars to produce a range of masonry types.All have certain properties in common andtherefore produce similar types of structuralelement. Other materials such as dried mud,pisé or even unreinforced concrete have similarproperties and can be used to make similartypes of element.

The physical properties which thesematerials have in common are moderatecompressive strength, minimal tensile strengthand relatively high density. The very low tensilestrength restricts the use of masonry toelements in which the principal internal forceis compressive, i.e. columns, walls andcompressive form-active types (see Section4.2) such as arches, vaults and domes.

In post-and-beam forms of structure (seeSection 5.2) it is normal for only the verticalelements to be of masonry. Notable exceptionsare the Greek temples (see Fig. 7.1), but inthese the spans of such horizontal elements asare made in stone are kept short bysubdivision of the interior space by rows ofcolumns or walls. Even so, most of theelements which span horizontally are in fact oftimber and only the most obvious, those in theexterior walls, are of stone. Where largehorizontal spans are constructed in masonrycompressive form-active shapes must beadopted (Fig. 3.1).

Where significant bending moment occurs inmasonry elements, for example as aconsequence of side thrusts on walls fromrafters or vaulted roof structures or from out-of-plane wind pressure on external walls, the levelof tensile bending stress is kept low by makingthe second moment of area (see Appendix 2) of22

Chapter 3

Structural materials

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the cross-section large. This can give rise tovery thick walls and columns and, therefore, toexcessively large volumes of masonry unlesssome form of ‘improved’ cross-section (seeSection 4.3) is used. Traditional versions of thisare buttressed walls. Those of medieval Gothiccathedrals or the voided and sculptured wallswhich support the large vaulted enclosures ofRoman antiquity (see Figs 7.30 to 7.32) areamong the most spectacular examples. In all ofthese the volume of masonry is small in

relation to the total effective thickness of thewall concerned. The fin and diaphragm walls ofrecent tall single-storey masonry buildings (Fig.3.2) are twentieth-century equivalents. In themodern buildings the bending moments whichoccur in the walls are caused principally bywind loading and not by the lateral thrustsfrom roof structures. Even where ‘improved’cross-sections are adopted the volume ofmaterial in a masonry structure is usually largeand produces walls and vaults which act as 23

Structural materials

Fig. 3.1 Chartres Cathedral,France, twelfth and thirteenthcenturies. The Gothic churchincorporates most of the variousforms for which masonry issuitable. Columns, walls andcompressive form-active archesand vaults are all visible here.(Photo: Courtauld Institute)

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effective thermal, acoustic and weathertightbarriers.

The fact that masonry structures are composedof very small basic units makes their constructionrelatively straightforward. Subject to the structuralconstraints outlined above, complex geometriescan be produced relatively easily, without theneed for sophisticated plant or techniques andvery large structures can be built by these simplemeans (Fig. 3.3). The only significantconstructional drawback of masonry is thathorizontal-span structures such as arches andvaults require temporary support until complete.

Other attributes of masonry-type materials arethat they are durable, and can be left exposed inboth the interiors and exteriors of buildings. Theyare also, in most locations, available locally insome form and do not therefore require to betransported over long distances. In other words,masonry is an environmentally friendly materialthe use of which must be expected to increase inthe future.

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Fig. 3.2 Where masonry will be subjected to significantbending moment, as in the case of external walls exposedto wind loading, the overall thickness must be largeenough to ensure that the tensile bending stress is notgreater than the compressive stress caused by thegravitational load. The wall need not be solid, however,and a selection of techniques for achieving thicknessefficiently is shown here.

(a)

(b) (c)

Fig. 3.3 Town Walls, Igerman, Iran. This late mediaevalbrickwork structure demonstrates one of the advantages ofmasonry, which is that very large constructions withcomplex geometries can be achieved by relatively simplebuilding processes.

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3.3 Timber

Timber has been used as a structural materialfrom earliest times. It possesses both tensileand compressive strength and, in the structuralrole is therefore suitable for elements whichcarry axial compression, axial tension andbending-type loads. Its most widespreadapplication in architecture has been inbuildings of domestic scale in which it hasbeen used to make complete structuralframeworks, and for the floors and roofs inloadbearing masonry structures. Rafters, floorbeams, skeleton frames, trusses, built-upbeams of various kinds, arches, shells andfolded forms have all been constructed intimber (Figs 3.4, 3.6, 3.9 and 3.10).

The fact of timber having been a livingorganism is responsible for the nature of itsphysical properties. The parts of the tree whichare used for structural timber – the heartwoodand sapwood of the trunk – have a structuralfunction in the living tree and therefore have,in common with most organisms, very goodstructural properties. The material iscomposed of long fibrous cells aligned parallelto the original tree trunk and therefore to thegrain which results from the annual rings. Thematerial of the cell walls gives timber itsstrength and the fact that its constituentelements are of low atomic weight isresponsible for its low density. The lightness inweight of timber is also due to its cellularinternal structure which produces elementcross-sections which are permanently‘improved’ (see Section 4.3).

Parallel to the grain, the strength isapproximately equal in tension and compressionso that planks aligned with the grain can beused for elements which carry axialcompression, axial tension or bending-typeloads as noted above. Perpendicular to the grainit is much less strong because the fibres areeasily crushed or pulled apart when subjected tocompression or tension in this direction.

This weakness perpendicular to the graincauses timber to have low shear strength whensubjected to bending-type loads and alsomakes it intolerant of the stress concentrations

such as occur in the vicinity of mechanicalfasteners such as bolts and screws. This can bemitigated by the use of timber connectors,which are devices designed to increase thearea of contact through which load istransmitted in a joint. Many different designsof timber connector are currently available(Fig. 3.5) but, despite their development, thedifficulty of making satisfactory structuralconnections with mechanical fasteners is afactor which limits the load carrying capacity oftimber elements, especially tensile elements.

The development in the twentieth century ofstructural glues for timber has to some extentsolved the problem of stress concentration atjoints, but timber which is to be glued must bevery carefully prepared if the joint is to developits full potential strength and the curing of theglue must be carried out under controlledconditions of temperature and relativehumidity1. This is impractical on building sites

25

Structural materials

Fig. 3.4 Methodist church, Haverhill, Suffolk, UK; J. W.Alderton, architect. A series of laminated timber portalframes is used here to provide a vault-like interior. Timberis also used for secondary structural elements and interiorlining. (Photo: S. Baynton)

1 A good explanation of the factors which affect thegluing of timber can be found in Gordon, J. E., The NewScience of Strong Materials, Penguin, London, 1968.

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and has to be regarded as a pre-fabricatingtechnique.

Timber suffers from a phenomenon knownas ‘moisture movement’. This arises becausethe precise dimensions of any piece of timberare dependent on its moisture content (theratio of the weight of water which it contains toits dry weight, expressed as a percentage). Thisis affected by the relative humidity of theenvironment and as the latter is subject tocontinuous change, the moisture content andtherefore the dimensions of timber alsofluctuate continuously. Timber shrinksfollowing a reduction in moisture content dueto decreasing relative humidity and swells ifthe moisture content increases. So far as thestructural use of timber is concerned, one ofthe most serious consequences of this is thatjoints made with mechanical fasteners tend towork loose.

The greatest change to the moisture contentof a specimen of timber occurs following thefelling of a tree after which it undergoes areduction from a value of around 150 per centin the living tree to between 10 and 20 percent, which is the normal range for moisturecontent of timber in a structure. This initialdrying out causes a large amount of shrinkageand must be carried out in controlled

conditions if damage to the timber is to beavoided. The controlled drying out of timber isknown as seasoning. It is a process in whichthe timber must be physically restrained toprevent the introduction of permanent twistsand other distortions caused by the differentialshrinkage which inevitably occurs, on atemporary basis, due to unevenness in thedrying out. The amount of differentialshrinkage must be kept to a minimum and thisfavours the cutting of the timber into plankswith small cross-sections, because the greatestvariation in moisture content occurs betweentimber at the core of a plank and that at thesurface where evaporation of moisture takesplace.

Timber elements can be either of sawntimber, which is simply timber cut directlyfrom a tree with little further processing otherthan shaping and smoothing, or manufacturedproducts, to which further processing has beenapplied. Important examples of the latter arelaminated timber and plywood.

The forms in which sawn timber is availableare, to a large extent, a consequence of thearboreal origins of the material. It isconvenient to cut planks from tree trunks bysawing parallel to the trunk direction and thisproduces straight, parallel-sided elements with

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Fig. 3.5 Timberconnectors are used toreduce the concentrationof stress in boltedconnections. A selectionof different types isshown here.

(a) (b) (c)

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rectangular cross-sections. Basic sawn-timbercomponents are relatively small (maximumlength around 6 m and maximum cross-sectionaround 75 mm � 250 mm) due partly to theobvious fact that the maximum sizes of cross-section and length are governed by the size ofthe original tree, but also to the desirability ofhaving small cross-sections for the seasoningprocess. They can be combined to form larger,composite elements such as trusses withnailed, screwed or bolted connections. Thescale of structural assemblies is usuallymodest, however, due to both the small sizesof the constituent planks and to the difficulty(already discussed) of making good structuralconnections with mechanical fasteners.

Timber is used in loadbearing-wallstructures both as the horizontal elements inmasonry buildings (see Fig. 1.13) and in all-timber configurations in which vertical timberelements are spaced close together to formwall panels (Fig. 3.6). The use of timber inskeleton frame structures (beams and columnsas opposed to closely spaced joists and wallpanels) is less common because theconcentration of internal forces which occursin these normally requires that a strongermaterial such as steel be adopted. In all casesspans are relatively small, typically 5 m forfloor structures of closely spaced joists ofrectangular cross-section, and 20 m for roofstructures with triangulated elements. All-timber structures rarely have more than two orthree storeys.

Timber products are manufactured by gluingsmall timber elements together in conditionsof close quality control. They are intended toexploit the advantages of timber while at thesame time minimising the effects of itsprincipal disadvantages, which are variability,dimensional instability, restrictions in the sizesof individual components and anisotropicbehaviour. Examples of timber products arelaminated timber, composite boards such asplywood, and combinations of sawn timberand composite board (Fig. 3.7).

Laminated timber (Fig. 3.7c) is a product inwhich elements with large rectangular cross-sections are built up by gluing together smaller

solid timber elements of rectangular cross-section. The obvious advantage of the processis that it allows the manufacture of solidelements with much larger cross-sections thanare possible in sawn timber. Very longelements are also possible because theconstituent boards are jointed end-to-end bymeans of finger joints (Fig. 3.8). The laminatingprocess also allows the construction ofelements which are tapered or have curved 27

Structural materials

Fig. 3.6 The all-timber house is a loadbearing wall form ofconstruction in which all of the structural elements in the walls, floorsand roof are of timber. An internal wall of closely spaced sawn-timberelements is here shown supporting the upper floor of a two-storeybuilding. Note temporary bracing which is necessary for stability untilcross-walls are inserted. (Photo: A. Macdonald)

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profiles. Arches (Figs 3.9 and 3.10) and portalframe elements (Fig. 3.4) are examples of this.

The general quality and strength oflaminated timber is higher than that of sawntimber for two principal reasons. Firstly, theuse of basic components which have smallcross-sections allows more effective seasoning,with fewer seasoning defects than can beachieved with large sawn-timber elements.Secondly, the use of the finger joint, whichcauses a minimal reduction in strength in theconstituent boards, allows any major defectswhich are present in these to be cut out. Theprincipal use of laminated timber is as anextension to the range of sawn-timberelements and it is employed in similarstructural configurations – for example asclosely spaced joists – and allows larger spansto be achieved. The higher strength oflaminated timber elements also allows it to beused effectively in skeleton frame construction.

Composite boards are manufacturedproducts composed of wood and glue. Thereare various types of these including plywood,blockboard and particle board, all of which areavailable in the form of thin sheets. The levelof glue impregnation is high and this impartsgood dimensional stability and reduces the

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Fig. 3.7 The I-beamwith the plywood web(b) and the laminatedbeam (c) are examplesof manufactured timberproducts. Thesenormally have bettertechnical propertiesthan plain sawn timberelements such as thatshown in (a). The highlevels of glueimpregnation inmanufactured beamsreduce dimensionalinstability, and majordefects, such as knots,are removed fromconstituent sub-elements.

Fig. 3.8 ‘Finger’ joints allow the constituent boards oflaminated timber elements to be produced in long lengths.They also make possible the cutting out of defects such asknots. (Photo: TRADA)

(a)

(b)

(c)

Fig. 3.9 Sports Dome, Perth, Scotland, UK. Laminatedtimber built-up sections can be produced in a variety ofconfigurations in addition to straight beams. Here a seriesof arch elements is used to produce the framework of adome.

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extent to which anisotropic behaviour occurs.Most composite boards also have highresistance to splitting at areas of stressconcentration around nails and screws.

Composite boards are used as secondarycomponents such as gusset plates in built-uptimber structures. Another common use is asthe web elements in composite beams of I- orrectangular-box section in which the flangesare sawn timber (Figs 3.11 and 3.12). 29

Structural materials

Fig. 3.10 David LloydTennis Centre, London,UK. The primarystructural elements arelaminated timber archeswhich span 35 m.(Photo: TRADA)

Fig. 3.11 Built-up-beams with I-shaped cross-sectionsconsisting of sawn timber flanges connected by aplywood web. The latter is corrugated which allows thenecessary compressive stability to be achieved with avery thin cross-section. (Photo: Finnish PlywoodInternational)

Fig. 3.12 Sports Stadium at Lähderanta, Sweden. Theprimary structural elements are plywood timber archeswith rectangular box cross-sections. (Photo: FinnishPlywood International)

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To sum up, timber is a material which offersthe designers of buildings a combination ofproperties that allow the creation oflightweight structures which are simple toconstruct. However, its relatively low strength,the small sizes of the basic components andthe difficulties associated with achieving goodstructural joints tend to limit the size ofstructure which is possible, and the majority oftimber structures are small in scale with shortspans and a small number of storeys.Currently, its most common application inarchitecture is in domestic building where it isused as a primary structural material either toform the entire structure of a building, as intimber wall-panel construction, or as thehorizontal elements in loadbearing masonrystructures.

3.4 Steel

The use of steel as a primary structuralmaterial dates from the late nineteenth centurywhen cheap methods for manufacturing it on alarge scale were developed. It is a material thathas good structural properties. It has highstrength and equal strength in tension andcompression and is therefore suitable for thefull range of structural elements and will resistaxial tension, axial compression and bending-type load with almost equal facility. Its densityis high, but the ratio of strength to weight isalso high so that steel components are notexcessively heavy in relation to their loadcarrying capacity, so long as structural formsare used which ensure that the material isused efficiently. Therefore, where bendingloads are carried it is essential that ‘improved’

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Fig. 3.13 Hopkins House, London, UK; Michael Hopkins, architect; Anthony Hunt Associates, structural engineers. Thefloor structure here consists of profiled steel sheeting which will support a timber deck. A more common configuration isfor the profiled steel deck to act compositely with an in situ concrete slab for which it serves as permanent formwork.(Photo: Pat Hunt)

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cross-sections (see Section 4.3) andlongitudinal profiles are adopted.

The high strength and high density of steelfavours its use in skeleton frame typestructures in which the volume of the structureis low in relation to the total volume of thebuilding which is supported, but a limitedrange of slab-type formats is also used. Anexample of a structural slab-type element isthe profiled floor deck in which a profiled steeldeck is used in conjunction with concrete, orexceptionally timber (Fig. 3.13), to form acomposite structure. These have ‘improved’corrugated cross-sections to ensure thatadequate levels of efficiency are achieved. Deckunits consisting of flat steel plate areuncommon.

The shapes of steel elements are greatlyinfluenced by the process which is used toform them. Most are shaped either by hot-rolling or by cold-forming. Hot-rolling is aprimary shaping process in which massive red-hot billets of steel are rolled between severalsets of profiled rollers. The cross-section of theoriginal billet, which is normally cast fromfreshly manufactured steel and is usuallyaround 0.5 m � 0.5 m square, is reduced bythe rolling process to much smallerdimensions and to a particular precise shape(Fig. 3.14). The range of cross-section shapeswhich are produced is very large and eachrequires its own set of finishing rollers.Elements that are intended for structural usehave shapes in which the second moment ofarea (see Appendix 2.3) is high in relation tothe total area (Fig. 3.15). I- and H- shapes ofcross-section are common for the largeelements which form the beams and columnsof structural frameworks. Channel and angleshapes are suitable for smaller elements suchas secondary cladding supports and sub-elements in triangulated frameworks. Square,circular and rectangular hollow sections areproduced in a wide range of sizes as are flatplates and solid bars of various thicknesses.Details of the dimensions and geometricproperties of all the standard sections arelisted in tables of section properties producedby steelwork manufacturers.

Structural materials

Fig. 3.14 The heaviest steel sections are produced by ahot-rolling process in which billets of steel are shaped byprofiled rollers. This results in elements which are straight,parallel sided and of constant cross-section. Thesefeatures must be taken into account by the designer whensteel is used in building and the resulting restrictions inform accepted. (Photo: British Steel)

Fig. 3.15 Hot-rolled steel elements. 31

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The other method by which large quantitiesof steel components are manufactured is cold-forming. In this process thin, flat sheets ofsteel, which have been produced by the hot-rolling process, are folded or bent in the coldstate to form structural cross-sections (Fig.3.16). The elements which result have similarcharacteristics to hot-rolled sections, in thatthey are parallel sided with constant cross-sections, but the thickness of the metal ismuch less so that they are both much lighterand, of course, have lower load carryingcapacities. The process allows morecomplicated shapes of cross-section to beachieved, however. Another difference fromhot-rolling is that the manufacturingequipment for cold-forming is much simplerand can be used to produce tailor-made cross-sections for specific applications. Due to theirlower carrying capacities cold-formed sectionsare used principally for secondary elements inroof structures, such as purlins, and forcladding support systems. Their potential forfuture development is enormous.

Structural steel components can also beproduced by casting, in which case verycomplex tailor-made shapes are possible. Thetechnique is problematic when used forstructural components, however, due to thedifficulty of ensuring that the castings are

sound and of consistent quality throughout. Inthe early years of ferrous metal structures inthe nineteenth century, when casting waswidely used, many structural failures occurred– most notably that of the Tay Railway Bridgein Scotland in 1879. The technique was rarelyused for most of the twentieth century buttechnical advances made possible its re-introduction. Prominent recent examples arethe ‘gerberettes’ at the Centre Pompidou, Paris(Figs 3.17 & 7.7) and the joints in the steelworkof the train shed at Waterloo Station, London(Fig. 7.17).

Most of the structural steelwork used inbuilding consists of elements of the hot-rolledtype and this has important consequences forthe layout and overall form of the structures.An obvious consequence of the rolling processis that the constituent elements are prismatic:they are parallel-sided with constant cross-sections and they are straight – this tends toimpose a regular, straight-sided format on thestructure (see Figs iv, 1.10 and 7.26). In recentyears, however, methods have been developedfor bending hot-rolled structural steelelements into curved profiles and this hasextended the range of forms for which steelcan be used. The manufacturing process does,however, still impose quite severe restrictionson the overall shape of structure for whichsteel can be used.

The manufacturing process also affects thelevel of efficiency which can be achieved insteel structures, for several reasons. Firstly, itis not normally possible to produce specifictailor-made cross-sections for particularapplications because special rollingequipment would be required to producethem and the capital cost of this wouldnormally be well beyond the budget of anindividual project. Standard sections mustnormally be adopted in the interests ofeconomy, and efficiency is compromised as aresult. An alternative is the use of tailor-madeelements built up by welding togetherstandard components, such as I-sections builtup from flat plate. This involves highermanufacturing costs than the use of standardrolled sections.

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Fig. 3.16 Cold-formed sections areformed from thinsteel sheet. A greatervariety of cross-section shapes ispossible than with thehot-rolling process.

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A second disadvantage of using an ‘off-the-peg’ item is that the standard section has aconstant cross-section and therefore constantstrength along its length. Most structuralelements are subjected to internal forces whichvary from cross-section to cross-section andtherefore have a requirement for varyingstrength along their length. It is, of course,possible to vary the size of cross-section whichis provided to a limited extent. The depth of anI-section element, for example, can be variedby cutting one or both flanges from the web,cutting the web to a tapered profile and thenwelding the flanges back on again. The sametype of tapered I-beam can also be producedby welding together three separate flat platesto form an I-shaped cross-section, as describedabove.

Because steel structures are pre-fabricated, the design of the joints betweenthe elements is an important aspect of theoverall design which affects both thestructural performance and the appearance ofthe frame. Joints are made either by boltingor by welding (Fig. 3.18). Bolted joints areless effective for the transmission of loadbecause bolt holes reduce the effective sizesof element cross-sections and give rise tostress concentrations. Bolted connections

can also be unsightly unless carefullydetailed. Welded joints are neater andtransmit load more effectively, but thewelding process is a highly skilled operationand requires that the components concernedbe very carefully prepared and preciselyaligned prior to the joint being made. Forthese reasons welding on building sites isnormally avoided and steel structures arenormally pre-fabricated by welding andbolted together on site. The need totransport elements to the site restricts boththe size and shape of individual components.

33

Structural materials

Fig. 3.17 The so-called ‘gerberettes’ at the Centre Pompidou in Paris,France, are cast steel components. No other process could haveproduced elements of this size and shape in steel. (Photo: A. Macdonald)

(a) (b)

Fig. 3.18 Joints in steelwork are normally made by acombination of bolting and welding. The welding is usuallycarried out in the fabricating workshop and the site joint ismade by bolting.

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Steel is manufactured in conditions of veryhigh quality control and therefore hasdependable properties which allow the use oflow factors of safety in structural design. This,together with its high strength, results inslender elements of lightweight appearance.The basic shapes of both hot- and cold-formedcomponents are controlled within smalltolerances and the metal lends itself to veryfine machining and welding with the result thatjoints of neat appearance can be made. Theoverall visual effect is of a structure which hasbeen made with great precision (Fig. 3.19).

Two problems associated with steel are itspoor performance in fire, due to the loss ofmechanical properties at relatively low

temperatures, and its high chemical instability,which makes it susceptible to corrosion. Bothof these have been overcome to some extentby the development of fireproof and corrosionprotection materials, especially paints, but theexposure of steel structures, either internally,where fire must be considered, or externally,where durability is an issue, is alwaysproblematic.

To sum up, steel is a very strong materialwith dependable properties. It is usedprincipally in skeleton frame types of structurein which the components are hot-rolled. Itallows the production of structures of a light,slender appearance and a feeling of neatnessand high precision. It is also capable of

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Fig. 3.19 Renault Sales Headquarters, Swindon, UK, 1983; Foster Associates, architects; Ove Arup & Partners, structuralengineers. Joints in steelwork can be detailed to look very neat and to convey a feeling of great precision. (Photo: AlastairHunter)

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producing very long span structures, andstructures of great height. The manufacturingprocess imposes certain restrictions on theforms of steel frames. Regular overall shapesproduced from straight, parallel-sidedelements are the most favoured.

3.5 Concrete

Concrete, which is a composite of stonefragments (aggregate) and cement binder, may beregarded as a kind of artificial masonry because ithas similar properties to stone and brick (highdensity, moderate compressive strength, minimaltensile strength). It is made by mixing togetherdry cement and aggregate in suitable proportionsand then adding water, which causes the cementto hydrolyse and subsequently the whole mixtureto set and harden to form a substance with stone-like qualities.

Plain, unreinforced concrete has similarproperties to masonry and so the constraintson its use are the same as those which applyto masonry, and which were outlined inSection 3.2. The most spectacular plainconcrete structures are also the earliest – themassive vaulted buildings of Roman antiquity(see Figs 7.30 to 7.32).

Concrete has one considerable advantageover stone, which is that it is available in semi-liquid form during the building process andthis has three important consequences. Firstly,it means that other materials can beincorporated into it easily to augment itsproperties. The most important of these is steelin the form of thin reinforcing bars which givethe resulting composite material (reinforcedconcrete) (Fig. 3.20) tensile and thereforebending strength as well as compressivestrength. Secondly, the availability of concretein liquid form allows it to be cast into a widevariety of shapes. Thirdly, the casting processallows very effective connections to be providedbetween elements and the resulting structuralcontinuity greatly enhances the efficiency of thestructure (see Appendix 3).

Reinforced concrete possesses tensile aswell as compressive strength and is therefore

suitable for all types of structural elementincluding those which carry bending-typeloads. It is also a reasonably strong material.Concrete can therefore be used in structuralconfigurations such as the skeleton frame forwhich a strong material is required and theresulting elements are reasonably slender. Itcan also be used to make long-span structuresand high, multi-storey structures.

Although concrete can be moulded intocomplicated shapes, relatively simple shapesare normally favoured for reasons of economyin construction (Fig. 3.21). The majority of

35

Structural materials

Fig. 3.20 In reinforced concrete, steel reinforcing bars arepositioned in locations where tensile stress occurs.

Fig. 3.21 Despite the mouldability of the material,reinforced concrete structures normally have a relativelysimple form so as to economise on construction costs. Atypical arrangement for a multi-storey framework is shown.

(a) (b)

(c) (d)

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reinforced concrete structures are thereforepost-and-beam arrangements (see Section 5.2)of straight beams and columns, with simplesolid rectangular or circular cross-sections,supporting plane slabs of constant thickness.The formwork in which such structures are castis simple to make and assemble and thereforeinexpensive, and can be re-used repeatedly inthe same building. These non-form-activearrangements (see Section 4.2) are relativelyinefficient but are satisfactory where the spansare short (up to 6 m). Where longer spans arerequired more efficient ‘improved’ types ofcross-section (see Section 4.3) and profile areadopted. The range of possibilities is large dueto the mouldability of the material. Commonlyused examples are coffered slabs and taperedbeam profiles.

The mouldability of concrete also makespossible the use of complex shapes and theinherent properties of the material are suchthat practically any shape is possible.Reinforced concrete has therefore been usedfor a very wide range of structural geometries.Examples of structures in which this has beenexploited are the Willis, Faber and Dumasbuilding (see Fig. 7.37), where the mouldabilityof concrete and the level of structuralcontinuity which it makes possible were usedto produce a multi-storey structure ofirregularly curved plan with floors which

cantilevered beyond the perimeter columns,and the Lloyd’s Building, in London (Fig. 7.9),in which an exposed concrete frame was givengreat prominence and detailed to express thestructural nature of its function. The buildingsof Richard Meier (see Fig. 1.9) and PeterEisenman (see Fig. 5.18) are also examples ofstructures in which the innate properties ofreinforced concrete have been well exploited.

Sometimes the geometries which areadopted for concrete structures are selected fortheir high efficiency. Form-active shells forwhich reinforced concrete is ideally suited areexamples of this (see Fig. 1.4). The efficiency ofthese is very high and spans of 100 m andmore have been achieved with shells a fewtens of millimetres in thickness. In other casesthe high levels of structural continuity havemade possible the creation of sculpturedbuilding forms which, though they may beexpressive of architectural meanings, are notparticularly sensible from a structural point ofview. A well-known example of this is the roofof the chapel at Ronchamp (see Fig. 7.40) byLe Corbusier, in which a highly individual andinefficient structural form is executed inreinforced concrete. Another example is theVitra Design Museum by Frank Gehry (see Fig.7.41). It would have been impossible to makethese forms in any other structural material.

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4.1 Introduction

This chapter is concerned with the relationshipbetween structural form and structuralperformance. In particular, the effect ofstructural geometry on the efficiency1 withwhich particular levels of strength and rigiditycan be achieved is explored.

The shapes of structural elements,especially the shapes of their longitudinalaxes in relation to the pattern of appliedload, determine the types of internal forcewhich occur within them and influence themagnitudes of these forces. These twofactors – the type and the magnitude of theinternal force created by a given applicationof load – have a marked effect on the levelof structural efficiency which can beachieved because they determine theamount of material which must be providedto give the elements adequate strength andrigidity.

A classification system for structuralelements is proposed here based on therelationship between form and efficiency. Itspurpose is to aid the understanding of the roleof structural elements in determining theperformance of complete structures. Ittherefore provides a basis for the reading of abuilding as a structural object.

4.2 The effect of form on internalforce type

Elements in architectural structures aresubjected principally either to axial internalforce or to bending-type internal force. Theymay also be subjected to a combination ofthese. The distinction between axial andbending is an important one, so far as efficiencyis concerned, because axial internal force can beresisted more efficiently than bending-typeinternal force. The principal reason for this isthat the distribution of stress which occurswithin the cross-sections of axially loadedelements is more or less constant, and thisuniform level of stress allows all of the materialin the element to be stressed to its limit. A sizeof cross-section is selected which ensures thatthe level of stress is as high as the materialconcerned can safely withstand and an efficientuse of material therefore results because all ofthe material present provides full value for itsweight. With bending stress, which varies inintensity in all cross-sections (Fig. 4.1) from aminimum at the neutral axis to a maximum atthe extreme fibres (see Appendix 2), only thematerial at the extreme fibres can be stressed toits limit. Most of the material present isunderstressed and therefore inefficiently used.

The type of internal force which occurs in anelement depends on the relationship betweenthe direction of its principal axis (itslongitudinal axis) and the direction of the loadwhich is applied to it (Fig. 4.2). If an element isstraight, axial internal force occurs if the load isapplied parallel to the longitudinal axis of theelement. Bending-type internal force occurs if itis applied at right angles to the longitudinal 37

Chapter 4

The relationshipbetween structural formand structural efficiency

1 Structural efficiency is considered here in terms of theweight of material which has to be provided to carry agiven amount of load. The efficiency of an element isregarded as high if the ratio of its strength to its weightis high.

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axis. If the load is applied obliquely, acombination of axial and bending stress occurs.The axial-only and bending-only cases are infact special cases of the more generalcombined case, but they are nevertheless themost commonly found types of loadingarrangement in architectural structures.

If an element is not straight, it will almostinevitably be subjected to a combination ofaxial and bending internal forces when a loadis applied, but there are important exceptionsto this as is illustrated in Fig. 4.3. Here, thestructural element consists of a flexible cable,supported at its ends, and from which variousloads are suspended. Because the cable has norigidity it is incapable of carrying any othertype of internal force but axial tension; it istherefore forced by the loads into a shapewhich allows it to resist the loads with aninternal force which is pure axial tension. Theshape traced by the longitudinal axis is uniqueto the load pattern and is called the ‘form-active’2 shape for that load.

As is seen in Fig. 4.3 the shape which thecable adopts is dependent on the pattern ofload which is applied; the form-active shape isstraight-sided when the loads are concentratedat individual points and curved if the load isdistributed along it. If a cable is allowed simplyto sag under its own weight, which is adistributed load acting along its entire length, itadopts a curve known as a ‘catenary’ (Fig. 4.3).

An interesting feature of the form-activeshape for any load pattern is that if a rigidelement is constructed whose longitudinal axisis the mirror image of the form-active shapetaken up by the cable, then it too will besubjected exclusively to axial internal forceswhen the same load is applied, despite the factthat, being rigid, it could also carry a bending-type internal force. In the mirror-image form allthe axial internal forces are compressive (Fig.4.4).

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Fig. 4.1 (a) Elements which carry purely axial load aresubjected to axial stress whose intensity is constantacross all cross-sectional planes. (b) Pure bending-typeload (i.e. load which is normal to the axis of the element)causes bending stress to occur on all cross-sectionalplanes. The magnitude of this varies within each cross-section from a maximum compressive stress at oneextremity to a maximum tensile stress at the other.

Fig. 4.2 Basic relationships between loads and structural elements.(a) Load coincident with principal axis; axial internal force. (b) Loadperpendicular to the principal axis; bending-type internal force. (c)Load inclined to the principal axis; combined axial and bending-typeinternal force.

2 ‘Form-active’ is a term applied by Engel in his bookStructure Systems, 1967, to a structural element in whichthe shape of the longitudinal axis, in relation to thepattern of applied load, is such that the internal forceis axial.

Fig. 4.3 Tensile form-active shapes. Because it has norigidity a cable must take up a shape – the form-activeshape – which allows it to resist the load with a purelytensile internal force. Different load arrangements producedifferent form-active shapes.

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The cable structure and its rigid ‘mirrorimage’ counterpart are simple examples of awhole class of structural elements which carryaxial internal forces because their longitudinalaxes conform to the form-active shapes for theloads which are applied to them. These arecalled ‘form-active’ elements.

If, in a real structure, a flexible materialsuch as steel wire or cable is used to make anelement, it will automatically take up the form-active shape when load is applied. Flexiblematerial is in fact incapable of becominganything other than a form-active element. Ifthe material is rigid, however, and a form-active element is required, then it must bemade to conform to the form-active shape forthe load which is to be applied to it or, in thecase of a compressive element, to the mirrorimage of the form-active shape. If not, theinternal force will not be pure axial force andsome bending will occur.

Figure 4.5 shows a mixture of form-activeand non-form-active shapes. Two load patterns

are illustrated: a uniformly distributed loadacross the whole of the element and twoconcentrated loads applied at equal distancesacross them. For each load, elements (a) carrypure bending-type internal forces; no axialforce can occur in these because there is nocomponent of either load which is parallel tothe axis of the element. The elements in (b)have shapes which conform exactly to theform-active shapes of the loads. They aretherefore form-active elements which carryaxial internal forces only; in both cases theforces are compressive. The elements (c) donot conform to the form-active shapes for theloads and will not therefore carry pure axialinternal force. Neither will they be subjected topure bending; they will carry a combination ofbending and axial internal force.

So far as the shape of their longitudinalaxes are concerned, structural elements canthus be classified into three categories: form-active elements, non-form-active elementsand semi-form-active elements. Form-activeelements are those which conform to theform-active shape of the load pattern which isapplied to them and they contain axialinternal forces only. Non-form-activeelements are those whose longitudinal axisdoes not conform to the form-active shape ofthe loads and is such that no axialcomponent of internal force occurs. Thesecontain bending-type internal force only.Semi-form-active elements are elementswhose shapes are such that they contain acombination of bending and axial internalforces.

It is important to note that structuralelements can only be form-active in thecontext of a particular load pattern. There areno shapes which are form-active per se. Thecranked beam shape in Fig. 4.5, for example, isa fully form-active element when subjected tothe two concentrated loads, but a semi-form-active element when subjected to theuniformly distributed load.

Form-active shapes are potentially the mostefficient types of structural element and non-form-active shapes the least efficient. Theefficiency of semi-form-active elements 39

The relationship between structural form and structural efficiency

Fig. 4.4 Compressive form-active shapes.

Fig. 4.5 Examples of the relationship between elementshape, load pattern and element type. The latter isdetermined by the relationship between the shape of theelement and the form-active shape for the load patternwhich it carries. (a) Non-form-active (bending stress only).(b) Form-active (axial stress only). (c) Semi-form-active(combined bending and axial stress).

(a) (b) (c)

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depends on the extent to which they aredifferent from the form-active shape.

4.3 The concept of ‘improved’shapes in cross-section andlongitudinal profile

It will be remembered from the beginning ofSection 4.2 that the main reason for the lowefficiency of elements in which bending-typeinternal forces occur is the uneven distributionof stress which exists within every cross-section. This causes the material in the centreof the cross-section, adjacent to the neutralaxis (see Appendix 2), to be under-stressedand therefore inefficiently used. The efficiencyof an element can be improved if some of theunder-stressed material is removed and this

can be achieved by a judicious choice ofgeometry in both cross-section andlongitudinal profile.

Compare the cross-sections of Fig. 4.6 withthe diagram of bending stress distribution.Most of the material in the solid rectangularcross-section is under-stressed; the load isactually carried principally by the material inthe high stress regions of the cross-sectionwhich occur at its top and bottom extremities(the extreme fibres). In the I- and box-shapedcross-sections most of the under-stressedmaterial is eliminated; the strength ofelements which are given these cross-sectionsis almost as great as that of an element with asolid rectangular cross-section of the sameoverall dimensions; they contain significantlyless material and are therefore lighter andmore efficient.

A similar situation exists with slab-typeelements. Solid slabs are much less efficient intheir use of material than those in whichmaterial is removed from the interior, as canbe demonstrated by carrying out a simpleexperiment with card (Fig. 4.7). A flat piece ofthin card has a very low bending strength. Ifthe card is arranged into a folded or corrugatedgeometry the bending strength is greatlyincreased. The card with the folded orcorrugated cross-section has a strength whichis equivalent to that of a solid card with thesame total depth; it is, however, much lighterand therefore more efficient.

In general, cross-sections in which materialis located away from the centre are moreefficient in carrying bending-type loads thansolid cross-sections. Solid cross-sections are,of course, much simpler to make and for thisreason have an important place in the field ofarchitectural structures, but they are poorperformers compared to the I- or box-shapedcross-section so far as structural efficiency isconcerned. In the classification which will beproposed here, these two categories of cross-section are referred to as ‘simple solid’ and‘improved’ cross-sections.

The shape of an element in longitudinalprofile can be manipulated in a similar way toits cross-section to improve its performance in

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Fig. 4.6 The effect of cross-section shape on theefficiency of elements which carry bending-type loads. (a)In an element with a rectangular cross-section, highbending stress occurs at the extreme fibres only. Most ofthe material carries a low stress and is thereforeinefficiently used. (b) In ‘improved’ cross-sectionsefficiency is increased by elimination of most of theunderstressed material adjacent to the centre of the cross-section.

(a)

(b)

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resisting bending-type loads. The adjustmentcan take the form of alteration to the overallshape of the profile or to its internalgeometry.

To improve efficiency the overall shape isadjusted by varying the depth of the element:this is the dimension on which bendingstrength principally depends (see Appendix 2).If the depth is varied according to the intensityof bending (specifically to the magnitude ofthe bending moment) then a more efficient useof material is achieved than if a constant depthof cross-section is used. Figure 4.8 shows twobeam profiles which have been improved inthis way. They are deep at the locations where

the bending moment is high and shallowwhere it is low.

The internal geometry of the longitudinalprofile can also be improved by altering it toremove under-stressed material from theinterior of the element. Examples of elementsin which this has been done are shown in Fig.4.9. As in the case of cross-sectional shape theinternal geometry of the longitudinal profile ofan element will be referred to here as ‘simplesolid’ or ‘improved’.

One type of ‘improved’ profile which is ofgreat importance in architectural as well as allother types of structure is the triangulatedprofile (i.e. the profile which consists entirelyof triangles) (Fig. 4.10). If an element of thistype has loads applied to it at the vertices ofthe triangles only, then the individual sub-elements which form the triangles are

The relationship between structural form and structural efficiency

Fig. 4.7 The effect of cross-sectional shape on theefficiency with which bending-type load is resisted. (a)Thin card which has an inefficient rectangular cross-section. (b) Thin card folded to give an efficient ‘improved’cross-section. (c) Thick card with inefficient rectangularcross-section and having equivalent strength and stiffnessto the folded thin card.

(a)

(b)

(c)

Fig. 4.8 The efficiency of a non-form-active element can beimproved if its longitudinal profile is adjusted to conform tothe bending moment diagram so that high strength isprovided only where the internal force is high.

41

Fig. 4.9 The efficiency of non-form-active elements canbe improved by selecting a shape in longitudinal profile inwhich material is removed from the understressed centreof the element.

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subjected to axial internal forces only3 (Figs4.11 and 4.12). This applies no matter what therelationship is between the pattern of loadsand the longitudinal axis of the element, takenas a whole.

By eliminating bending stress from non-form-active elements the triangulated internalgeometry allows a high degree of structuralefficiency to be achieved. The advantage of thetriangulated element over the other class ofelement for which this is true – the form-activeelement – is that no special overall form is

required to produce the axial-stress-onlycondition. All that is required is that theinternal geometry be fully triangulated and theexternal load applied only at the joints.Triangulated elements do not, however,achieve quite such a high degree of structuralefficiency as form-active structures due to therelatively high level of internal force whichoccurs.

Certain bending-type elements with‘improved’ cross-sections are referred to as‘stressed skin’, ‘monocoque’ or ‘semi-monocoque’ elements to distinguish themfrom skeletal elements which consist of aframework of structural sub-elements coveredby non-structural skin. The distinction isperhaps best seen in the field of aeronauticalengineering by comparison of the structure ofa fabric-covered ‘stick-and-string’ biplane withthat of an all-metal aircraft (Fig. 4.13). In eachcase the fuselage is a structure which carriesbending as well as other types of internalforce, notably torsion. Aircraft structures must,of course, have a very high ratio of strength toweight. Form-active or semi-form-activearrangements are impractical, however,

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3 This property is a consequence of a characteristicunique to the triangle among geometric figures, whichis that its geometry can only be changed if the lengthof one or more of its sides is altered. (The geometry ofany other polygon can be changed by altering theangles between the sides and maintaining the sides ata constant length – Fig. 4.11.) The resistance which isgenerated by a triangulated structure to a potentialalteration in geometry (which is what occurs when aload is applied) takes the form of a resistance tochange in length of the sides of the triangles. Thisresults in the sub-elements which form the sides of thetriangles being placed into either axial tension or axialcompression. The axial-stress-only state thereforeoccurs no matter what the overall form of the element,provided that its internal geometry is fully triangulatedwith straight-sided triangles and the load is appliedonly to the joints between the sub-elements. If a loadis applied directly to one of the constituent sub-elements and not at a joint, as in Fig. 4.12, thenbending will occur in that sub-element.

Fig. 4.10 A solid beam is less strong and rigid than atriangulated structure of equivalent weight.

Fig. 4.12 The axial-internal-force-only condition does notoccur if load is applied to a triangulated structure otherthan at its joints.

Fig. 4.11 An alteration of the geometry of a triangle canonly occur if the length of one of the sides changes.Application of load to a triangle, which tends to distort itsgeometry, is therefore resisted by axial internal forces inthe elements.

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because the overall shapes of aircraft aredetermined from aerodynamic rather thanstructural considerations. The structures aretherefore non-form-active and must have‘improved’ internal structures so as to meetthe required levels of efficiency.

In the case of the early biplane fuselage thefabric skin had virtually no structural functionand the loads were carried entirely by theframework of timber and wire which, being

fully triangulated, was an efficient type ofstructure with a high ratio of strength toweight. Its disadvantage was that its potentialstrength was limited firstly by the relativeweakness of timber, and secondly by thedifficulty of making efficient joints between thetimber compressive elements and the wiretensile elements. As the size and speed ofaircraft increased and stronger aircraftstructures were required, the change to an all-metal structure became inevitable. The fabricskin was replaced by sheeting of aluminiumalloy and the internal structure of timber andwire by ribs and longitudinal stringers also ofaluminium alloy. In this more sophisticatedtype of aircraft structure, which is called asemi-monocoque structure, the metal skinacted with the ribs and stringers to form acomposite structure called a ‘stressed-skinsemi-monocoque’. Monocoque construction isthe term used where the element consists onlyof the stressed skin. 43

The relationship between structural form and structural efficiency

Fig. 4.13 The overall shapes of aircraft are determinedmainly from non-structural considerations, principallyaerodynamic performance requirements. The supportingstructures are therefore non-form-active, but the very highpriority which must be given to saving of weight results inthe adoption of configurations in which many‘improvements’ are incorporated. (a) The fuselage andwings of the ‘stick-and-string’ biplane have triangulatedstructures of timber and wire. The fabric covering has aminimal structural function. (b) The wings and fuselage ofthe all-metal aircraft are hollow box-beams in which theskin plays an essential structural role.

(a)

(b)

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In the semi-monocoque fuselage of an all-metal aircraft (Fig. 4.14), which is anon-form-active structural element with an‘improved’ cross-section, a very thin stressedskin is used which must be strengthened atregular intervals by ribs and stringers toprevent local buckling from occurring. Thetechnique of improvement may be seen to beoperating at several levels. The fuselage, takenas a whole, is a non-form-active element withan ‘improved’ hollow-tube cross-section.Further ‘improvement’ occurs in the tube walls,which have a complex cross-section consistingof the stressed skin acting in conjunction withthe strengthening ribs and stringers. Thesestrengthening sub-elements are in turn‘improved’ by having cross-sections of complexshape and circular holes cut in their webs.

The all-metal aircraft structure is therefore acomplicated assembly of sub-elements towhich the technique of ‘improvement’ hasbeen applied at several levels. The complexityresults in a structure which is efficient butwhich is very costly to produce. This is justified

in the interests of saving weight. Everykilonewton saved contributes to theperformance of the aircraft so weight saving isallocated a very high priority in the design.

A similar application of the features whichsave weight can be seen in the field of vehicledesign, especially railway carriages and motorcars. The structure of the modern railwaycarriage consists of a metal tube which formsits skin, spanning as a beam between thebogies on which it is mounted. It is a non-form-active ‘improved’ box beam. The structureof a motor car is similar: the steel car bodyacts as a beam to carry the weight of theengine, occupants, etc. between the roadwheels (Fig. 4.15). As in the case of theaeroplane the overall forms of rail and roadvehicles are determined largely from non-structural considerations, but the need to saveweight is given a high priority in the design.Again the use of ‘improved’ non-form-activemonocoque and semi-monocoque structuresconstitutes a sensible response to thetechnical problems posed.

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Fig. 4.14 The fuselage of the all-metal aircraft is a non-form-active structure which is ‘improved’ at various levels.The fuselage, taken as a whole, is a hollow box-beam.‘Improvements’ of several types are incorporated into thesub-elements which support the structural skin.

(a)

(b)

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The use of such elaborate forms of‘improvement’ as the monocoque or semi-monocoque stressed skin can rarely bejustified on technical grounds in architecturalstructures because the saving of weight is nota sufficiently high priority to justify theexpense of this complex type of structure. Inthe case of buildings, inefficient high-massstructures can actually be advantageous. Theyadd thermal mass and their weight counteractswind uplift.

The uses of the devices and configurationswhich produce efficient and thereforelightweight structures – the complex cross-section, the circular ‘lightening’ hole,triangulation of elements and profiling toconform to bending moment diagrams – arenot always appropriate from the technicalviewpoint in the context of architecture wherethey are justified technically only in situationsin which an efficient, lightweight structure isrequired (see Chapter 6). They can, however,have another architectural function which is toform a visual vocabulary of structure.

The use of the devices associated withstructural efficiency for stylistic purposes isdiscussed in Chapter 7. It might be observedhere that where this occurs they are often usedin situations which are inappropriatestructurally. The devices of ‘improvement’which were devised in the context ofaeronautical and vehicle engineering havebecome, in the hands of modern architects,

especially those of ‘high-tech’ architects, avisual version of the dead metaphor.

4.4 Classification of structuralelements

The principles outlined in the precedingsections, concerned with the various deviceswhich can be used to improve the efficiencyof structures, can form the basis of aclassification system for structural elements.This is illustrated in Table 4.1. The primarycategorisation is between form-active, semi-form-active and non-form-active elementsbecause this is the most important factor indetermining the level of efficiency which canbe achieved. Elements are further classifiedaccording to the degree of ‘improvement’which is present in their cross-sections andlongitudinal profiles. The number ofcombinations and permutations is very largeand a selection only of possibilities isillustrated in Table 4.1 to show the generalprinciples involved. The least efficientshapes (non-form-active elements withsimple shapes in both cross-section andlongitudinal profile) are placed at the top ofthe table and the degree of efficiency presentincreases towards the bottom of the table,where the most efficient shapes – tensileform-active elements – are placed. Adistinction is made between line elements, 45

The relationship between structural form and structural efficiency

Fig. 4.15 The metal body of a motor car is an ‘improved’non-form-active beam which spans between the road wheels.

(a)

(b)

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such as beams, in which one dimension issignificantly larger than the other two, andsurface elements, such as slabs, in whichone dimension is significantly smaller thanthe other two.

This system links the form, and thereforethe appearance, of a structure with itstechnical performance and provides a basis forreading a building, or indeed any artefact, as astructural object. This is an importantconsideration for anyone involved with eitherthe design of buildings or with their criticalappraisal.

The system is based on the idea ofefficiency: structural elements are classifiedaccording to the level of efficiency which theymake possible in the resistance of load whichis, of course, their principal function. The mainobjective of structural design, however, is theachievement of an appropriate level ofefficiency rather than the maximum possiblelevel of efficiency. The factors which determinethe level of efficiency which is appropriate arediscussed in Chapter 6. The discussion ofwhether or not an appropriate level ofefficiency has been achieved cannot take place,however, in the absence of a means of judgingefficiency. The system proposed here providesthat means.

An aspect of the relationship betweenstructure and architecture which has beentouched on in this chapter is the possibilitythat the features associated with structuralefficiency can be used as the basis of a visualvocabulary which conveys architecturalmeaning – the message being technicalprogress and excellence. This issue isdiscussed in Section 7.2.2.

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Table 4.1H

IGH

ST

RU

CT

UR

AL

EFFIC

IEN

CY

LO

W

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5.1 Introduction

Most structures are assemblies of largenumbers of elements and the performance ofthe complete structure depends principally onthe types of element which it contains and onthe ways in which these are connectedtogether. The classification of elements wasconsidered in Chapter 4, where the principalinfluence on element type was shown to be theshape of the element in relation to the patternof the applied load. In the context ofarchitecture, where gravitational loads arenormally paramount, there are three basicarrangements: post-and-beam, form-active andsemi-form-active (Fig. 5.1). Post-and-beamstructures are assemblies of vertical andhorizontal elements (the latter being non-form-active); fully form-active structures are

complete structures whose geometriesconform to the form-active shape for theprincipal load which is applied; arrangementswhich do not fall into either of these categoriesare semi-form-active.

The nature of the joints between elements(be they form-active, semi-form-active or non-form-active) significantly affects theperformance of structures and by this criterionthey are said to be either ‘discontinuous’ or‘continuous’ depending on how the elementsare connected. Discontinuous structurescontain only sufficient constraints to renderthem stable; they are assemblies of elementsconnected together by hinge-type joints1 andmost of them are also statically determinate(see Appendix 3). Typical examples are showndiagrammatically in Fig. 5.2. Continuousstructures, the majority of which are alsostatically indeterminate (see Appendix 3),contain more than the minimum number ofconstraints required for stability. They usuallyhave very few hinge-type joints and many havenone at all (Fig. 5.3). Most structuralgeometries can be made either continuous ordiscontinuous depending on the nature of theconnections between the elements.

The principal merit of the discontinuousstructure is that it is simple, both to designand to construct. Other advantages are that itsbehaviour in response to differentialsettlement of the foundations and to changesin the lengths of elements, such as occur

47

Chapter 5

Complete structuralarrangements

1 A hinge joint is not literally a hinge; it is simply a jointwhich is incapable of preventing elements fromrotating relative to each other; most junctions betweenelements fall into this category.

Fig. 5.1 The three categories of basic geometry. (a) Post-and-beam. (b) Semi-form-active. (c) Form-active.

(a)

(b)

(c)

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when they expand or contract due tovariations in temperature, does not give riseto additional stress. The discontinuousstructure adjusts its geometry in thesecircumstances to accommodate the movementwithout any internal force being introducedinto the elements. A disadvantage of thediscontinuous structure is that, for a givenapplication of load, it contains larger internalforces than a continuous structure with thesame basic geometry; larger elements arerequired to achieve the same load carryingcapacity and it is therefore less efficient. Afurther disadvantage is that it must normallybe given a more regular geometry than anequivalent continuous structure in order thatit can be geometrically stable. This restrictsthe freedom of the designer in the selection ofthe form which is adopted and obviouslyaffects the shape of the building which can besupported. The regular geometry of typicalsteel frameworks, many of which arediscontinuous (see Figs 2.11 and 5.16)illustrate this. The discontinuous structure istherefore a rather basic structural arrangementwhich is not very efficient but which is simpleand therefore economical to design andconstruct.

The behaviour of continuous structures isaltogether more complex than that ofdiscontinuous forms. They are more difficultboth to design and to construct (see Appendix3) and they are also unable to accommodatemovements such as thermal expansion andfoundation settlement without the creation ofinternal forces which are additional to thosecaused by the loads. They are neverthelesspotentially more efficient than discontinuousstructures and have a greater degree ofgeometric stability. These properties allow thedesigner greater freedom to manipulate theoverall form of the structure and therefore ofthe building which it supports. Figures 1.9 and7.37 show buildings with continuous structureswhich illustrate this point.

5.2 Post-and-beam structures

Post-and-beam structures are eitherloadbearing wall structures or frame structures.Both are commonly used structural forms andwithin each type a fairly wide variety ofdifferent structural arrangements, of both thecontinuous and the discontinuous types, arepossible. A large range of spans is alsopossible depending on the types of elementwhich are used.

The loadbearing wall structure is a post-and-beam arrangement in which a series ofhorizontal elements is supported on verticalwalls (Fig. 5.4). If, as is usually the case, thejoints between the elements are of the hingetype, the horizontal elements are subjected topure bending-type internal forces and thevertical elements to pure axial compressiveinternal forces when gravitational loads areapplied. The basic form is unstable butstability is provided by bracing walls, and theplans of these buildings therefore consist oftwo sets of walls: loadbearing walls andbracing walls (Fig. 5.5). The loadbearing walls,which carry the weights of the floors and roof,are usually positioned more or less parallel toone another at approximately equally spacedand as close together as space-planningrequirements will allow in order to minimise

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Fig. 5.2 Discontinuous structures. The multi-storey framehas insufficient constraints for stability and would requirethe addition of a bracing system. The three-hinge portalframe and three-hinge arch are self-bracing, staticallydeterminate structures.

Fig. 5.3 Continuous structures. All are self-bracing andstatically indeterminate.

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the spans. The bracing walls are normally runin a perpendicular direction and the interiorsof the buildings are therefore multi-cellularand rectilinear in plan. Irregular plan forms arepossible, however. In multi-storey versions theplan must be more or less the same at everylevel so as to maintain vertical continuity ofthe loadbearing walls.

Loadbearing wall structures are used for awide range of building types and sizes ofbuilding (Figs 5.6, 1.13 and 7.36). The smallestare domestic types of one or two storeys inwhich the floors and roofs are normally oftimber and the walls of either timber ormasonry. In all-timber construction (see Fig.3.6), the walls are composed of closely spacedcolumns tied together at the base and head ofthe walls to form panels, and the floors aresimilarly constructed. Where the walls are ofmasonry, the floors can be of timber orreinforced concrete. The latter are heavier butthey have the advantage of being able to spanin two directions simultaneously. This allowsthe adoption of more irregular arrangements ofsupporting walls and generally increasesplanning freedom (Fig. 5.7). Reinforcedconcrete floors are also capable of larger spansthan are timber floors; they provide buildingswhich are stronger and more stable and havethe added advantage of providing a fireproofstructure.

Although beams and slabs with simple,solid cross-sections are normally used for thefloor elements of loadbearing-wall buildings,because the spans are usually short (seeSection 6.2), axially stressed elements in theform of triangulated trusses are frequentlyused to form the horizontal elements in theroof structures. The most commonly usedlightweight roof elements are timber trusses(Fig. 5.8) and lightweight steel lattice girders.

The discontinuous loadbearing wallconfiguration is a very basic form of structurein which the most elementary types of bending(i.e. non-form-active) elements, with simple,solid cross-sections, are employed. Theirefficiency is low and a further disadvantage isthat the requirements of the structure imposefairly severe restrictions on the freedom of thedesigner to plan the form of the building – theprimary constraints being the need to adopt amulti-cellular interior in which none of thespaces is very large and, in multi-storeybuildings, a plan which is more or less thesame at every level. The structures arestraightforward and economical to construct,however. 49

Complete structural arrangements

Fig. 5.4 In the cross-section of a post-and-beamloadbearing masonry structure the reinforced concretefloors at the first- and second-storey levels span one waybetween the outer walls and central spine walls. Timbertrussed rafters carry the roof and span across the wholebuilding between the outer walls.

Fig. 5.5 Typical plan of a multi-storey loadbearing wallstructure. The floor structure spans one way betweenparallel structural walls. Selected walls in the orthogonaldirection act as bracing elements.

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Where greater freedom to plan the interiorof a building is required or where large interiorspaces are desirable, it is usually necessary toadopt some type of frame structure. This canallow the total elimination of structural walls,

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Fig. 5.6 Corinthian Court, Abingdon, UK; the Baron Willmore Partnership, architects; Glanville and Associates,structural engineers. The vertical structure of this three-storey office building, which measures 55 m by 20 m on plan andhas few internal walls, is of loadbearing masonry. The floors are of reinforced concrete.

Fig. 5.7 In these arrangements the floor structures aretwo-way spanning reinforced concrete slabs. This allowsmore freedom in the positioning of loadbearing walls thanis possible with one-way spanning timber or pre-castconcrete floors.

Fig. 5.8 Typical arrangement of elements in traditionalloadbearing masonry structure.

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and large interior spaces can be achieved aswell as significant variations in floor plansbetween different levels in multi-storeybuildings.

The principal characteristic of the frame isthat it is a skeletal structure consisting ofbeams supported by columns, with some formof slab floor and roof (Fig. 5.9). The walls areusually non-structural (some may be used asvertical-plane bracing) and are supportedentirely by the beam-column system. The totalvolume which is occupied by the structure isless than with loadbearing walls, andindividual elements therefore carry largerareas of floor or roof and are subjected togreater amounts of internal force. Strongmaterials such as steel and reinforcedconcrete must normally be used. Skeletonframes of timber, which is a relatively weakmaterial, must be of short span (max 5 m) iffloor loading is carried. Larger spans arepossible with single-storey timber structures,especially if efficient types of element such astriangulated trusses are used, but themaximum spans are always smaller than thoseof equivalent steel structures.

The most basic types of frame are arrangedas a series of identical ‘plane-frames’ of

rectangular geometry2, positioned parallel toone another to form rectangular or squarecolumn grids; the resulting buildings haveforms which are predominantly rectilinear inboth plan and cross-section (Fig. 5.9). Acommon variation of the above is obtained iftriangulated elements are used for thehorizontal parts of the structure (Fig. 5.10).Typical beam-column arrangements for singleand multi-storey frames are shown in Figs 5.11to 5.13; note that systems of primary andsecondary beams are used for both floor androof structures. These allow a reasonably evendistribution of internal force to be achievedbetween the various elements within aparticular floor or roof structure. In Fig. 5.12,for example, the primary beam AB supports alarger area of floor than the secondary beamCD, and therefore carries more load. Themagnitudes of the internal forces in each aresimilar, however, because the span of AB isshorter3.

51

Complete structural arrangements

Fig. 5.9 A typical multi-storey frame structure inwhich a skeleton of steelbeams and columnssupports a floor ofreinforced concrete slabs.Walls are non-structural andcan be positioned to suitspace-planningrequirements.

2 A plane-frame is simply a frame with all elements in asingle plane.

3 The critical internal force is bending moment, themagnitude of which depends on the span (see Section2.3.3).

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Structure and Architecture

Fig. 5.10 In this steel frame, efficienttriangulated elements carry the roofload. Floor loads are supported on lessefficient solid-web beams with I-shaped‘improved’ cross-sections.

Fig. 5.12 Typical floor layouts for multi-storey steel frames.

Fig. 5.11 A typical arrangementof primary and secondary beamsin a single-storey steel frame. Allbeams have ‘improved’triangulated profiles.

52

Fig. 5.13 ‘Improved’ elements are used for all beams andcolumns in steel frames. In this case I-section beams are used forthe floor structure and more efficient triangulated elements in theroof. The greater complexity and higher efficiency of the latter arejustified by the lighter roof loading (see Section 6.2). (Photo: PatHunt)

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Skeleton frames can be of either thediscontinuous or the continuous type. Steeland timber frames are normally discontinuousand reinforced concrete frames are normallycontinuous. In fully discontinuous frames allthe joints between beams and columns are ofthe hinge type (Fig. 5.14). This renders thebasic form unstable and reduces its efficiencyby isolating elements from each other andpreventing the transfer of bending momentbetween them (Fig. 5.15 – see also Appendix3). Stability is provided in the discontinuousframe by a separate bracing system, which cantake a number of forms (see Figs 2.10 to 2.13).The need both to ensure stability and toprovide adequate support for all areas of floorwith hinge-joined elements normally requiresthat discontinuous frames be given regulargeometries (Fig. 5.16).

If the connections in a frame are rigid, acontinuous structure normally results which isboth self-bracing and highly staticallyindeterminate (see Appendix 3). Continuousframes are therefore generally more elegantthan their discontinuous equivalents; elementsare lighter, spans longer and the absence ofvertical-plane bracing allows more openinteriors to be achieved. These advantages,together with the general planning freedom

53

Complete structural arrangements

Fig. 5.14 A typical arrangement for a discontinuousmulti-storey frame. All beam end connections are of thehinge type as are the column joints, which occur atalternate storey levels. The arrangement is highly unstableand requires a separate bracing system to resist horizontalload.

Fig. 5.16 Single-storey steel framework. Although someof the structural connections here are rigid, the majority ofthe horizontal elements have hinge joints. The regularity ofthe arrangement and the presence of a triangulatedbracing girder in the horizontal plane (top left) are typicalof a discontinuous framework. (Photo: Photo-Mayo Ltd)

Fig. 5.15 Preliminaryanalysis of adiscontinuous frame.Under gravitationalload the horizontalelements carry purebending and thevertical elements axialcompression. Sharingor shedding ofbending momentbetween elements isnot possible throughhinge joints.

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Structure and Architecture

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Fig. 5.17 Florey Building,Oxford, UK, 1971; JamesStirling, architect. The FloreyBuilding, with its crescent-shaped plan, complexcross-section and glazed wall,illustrates how the geometricfreedom made possible by acontinuous frame of in situconcrete can be exploited.(Photo: P. Macdonald)

Fig. 5.18 Miller House, Connecticut,USA, 1970; Peter Eisenman, architect.Eisenman is one of a number of Americanarchitects, including Richard Meier (seeFig. 1.9), who have exploited theopportunities made possible by thecontinuous framework. This type ofgeometry, with its intersecting grids andcontrasts of solid and void is only possiblewith a continuous structure.

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which a high degree of structural continuityallows, means that more complex geometriesthan are possible with discontinuous structurescan be adopted (Figs 5.17, 5.18 and 1.9).

Due to the ease with which continuity canbe achieved and to the absence of the ‘lack-of-fit’ problem (see Appendix 3), in situ reinforcedconcrete is a particularly suitable material forcontinuous frames. The degree of continuitywhich is possible even allows the beams in aframe to be eliminated and a two-wayspanning slab to be supported directly oncolumns to form what is called a ‘flat-slab’structure (Figs 5.19 and 7.33). This is bothhighly efficient in its use of material and fairlysimple to construct. The Willis, Faber andDumas building (Figs 1.6, 5.19 and 7.37) has atype of flat-slab structure and this buildingdemonstrates many of the advantages ofcontinuous structures; the geometric freedomwhich structural continuity allows isparticularly well illustrated.

5.3 Semi-form-active structures

Semi-form-active structures have formswhose geometry is neither post-and-beam

nor form-active. The elements thereforecontain the full range of internal force types(i.e. axial thrust, bending moment and shearforce). The magnitudes of the bendingmoments, which are of course the mostdifficult of the internal forces to resistefficiently, depend on the extent to which theshape is different from the form-active shapefor the loads. The bending moments aresignificantly smaller, however, than thosewhich occur in post-and-beam structures ofequivalent span.

Semi-form-active structures are usuallyadopted as support systems for buildings forone of two reasons. They may be chosenbecause it is necessary to achieve greaterefficiency than a post-and-beam structurewould allow, because a long span is involvedor because the applied load is light (seeSection 6.2). Alternatively, a semi-form-activestructure may be adopted because the shapeof the building which is to be supported issuch that neither a very simple post-and-beamstructure nor a highly efficient fully form-activestructure can be accommodated within it.

Figure 5.20 shows a typical example of atype of semi-form-active frame structure whichis frequently adopted to achieve long spans inconjunction with light loads. It can be 55

Complete structural arrangements

Fig. 5.19 Willis, Faber and Dumasoffice, Ipswich, UK, 1974; FosterAssociates, architects; Anthony HuntAssociates, structural engineers. Thecoffered floor slab is a flat-slab structurewith an ‘improved’ cross-section. (Photo:Pat Hunt)

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constructed in steel, reinforced concrete ortimber (Fig. 5.21). A variety of profiles andcross-sections are used for the frame elements,ranging from solid elements with rectangularcross-sections in the cases of reinforcedconcrete and laminated timber, to ‘improved’elements in the case of steel. As with other

types of frame, the range of spans which canbe achieved is large. In its most common form,this type of structure consists of a series ofidentical plane rigid frames arranged parallelto one another to form a rectangular plan (Fig.5.22).

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Fig. 5.20 The ubiquitous portal frame is a semi-form-active structure. The main elements in this example have‘improved’ I-shaped cross-sections. (Photo: Conder)

Fig. 5.21 The efficiency of the semi-form-active portalframe is affected by the shapes of cross-section andlongitudinal profile which are used. Variation of the depthof the cross-section and the use of I- or box-sections arecommon forms of ‘improvement’. The structure type ishighly versatile and is used over a wide range of spans.

Fig. 5.22 A typicalarrangement ofsemi-form-activeportal framesforming thestructure of a single-storey building.

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5.4 Form-active structures

Fully form-active structures are normally usedonly in circumstances where a specialstructural requirement to achieve a highdegree of structural efficiency exists, eitherbecause the span involved is very large orbecause a structure of exceptionally lightweight is required. They have geometries whichare more complicated than post-and-beam orsemi-form-active types and they producebuildings which have distinctive shapes (Figsiii and 5.23 to 5.25).

Included in this group are compressiveshells, tensile cable networks and air-supported tensile-membrane structures. Inalmost all cases more than one type ofelement is required, especially in tensilesystems which must normally havecompressive as well as tensile parts, and form-active shapes are frequently chosen for thecompressive elements as well as for the tensile

elements (see Fig. 7.18). In the case of largebuilding envelopes, the loads which areapplied are predominantly of the distributedrather than the concentrated type and theform-active geometry is therefore curved (seeChapter 4). Although a certain amount ofvariety of shape is possible with this type ofstructure, depending on the conditions ofsupport which are provided, the distinctivedoubly-curved geometry of the form-activeelement is something which must be acceptedby a designer who contemplates using thistype of arrangement.

Form-active structures are almost invariablystatically indeterminate and this, together withthe fact that they are difficult to construct,makes them very expensive in the present age,despite the fact that they make an efficient useof structural material. The level of complexitywhich is involved in their design andconstruction can be appreciated by consideringjust a few of the special design problems which

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Complete structural arrangements

Fig. 5.23 Grandstand at Lord’s Cricket Ground, London, UK, 1987; Michael Hopkins & Partners, architects; Ove Arup &Partners, structural engineers. The canopies which form the roof of this building are form-active tensile membranes.

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they create. The tensile envelopes, forexample, always assume the form-active shapefor the load which acts on them no matterwhat their initial geometry may have been.This is a consequence of their complete lack of

rigidity and it means that considerable caremust be taken in their manufacture to ensurethat the tailoring of the membrane or networkis correct. If this is not done and a membranewith a non-form-active geometry is produced,

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Fig. 5.24 Barton Malow Silverdome. A very large span isachieved here with a cable-reinforced air-supportedmembrane, which is a tensile form-active structure.

Fig. 5.25 Brynmawr Rubber Factory, Brynmawr, UK, 1952;Architects Co-Partnership, architects; Ove Arup & Partners,structural engineers. The principal enclosing elements hereare compressive form-active, elliptical paraboloid shellroofs. (Photo: Architectural Review)

(a)

(b)

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initially it will nevertheless be forced into theform-active shape when the load is applied,causing folds and wrinkles to develop whichare both unsightly and result in concentrationsof stress. Many other technical difficulties,associated with the attachment of themembranes to their supports and with theirbehaviour in response to dynamic loads, alsoarise in connection with the design of tensileform-active structures.

In the case of the compressive version ofthe form-active structure, the penalty which isincurred if it is not given the true form-activeshape for the load is that bending stressoccurs in the membrane. If this happensunintentionally there is a risk of strengthfailure, and it is therefore desirable that theexact geometry of the true form-active shapeshould be determined during the designprocess and that the structure be made toconform to it. Two problems arise, however.Firstly, the geometry of the form-active shapeis very complex and is difficult to determineaccurately, and thus difficult to reproduceexactly in a real structure. In particular, theradius of curvature of the surface is notconstant and this makes both the analysis ofthe structure and its construction difficult.Secondly, real structures are always subjectedto a variety of different forms of loading, whichmeans that the required form-active shapechanges as loads change. This does notpresent an insuperable problem in the case oftensile form-active-structures because, beingflexible, these can simply adjust their geometryto take up the different shapes which arerequired. So long as the change in load is nottoo extreme, the necessary adjustment can beaccommodated without the risk of seriouswrinkles developing. Compressive forms mustbe rigid, however, and so only one geometry ispossible. Therefore some bending stress willinevitably arise in a compressive form-activestructure due to changes which occur to the

loading. Thus these structures must be giventhe strength to resist bending stress and theymust be made thicker than would be necessaryif only direct stress was present.

The fact that bending stress can never betotally eliminated from compressive form-active structures means that they are inevitablyless efficient than their tensile equivalents. Italso means that the adoption of a true form-active shape, with all the complications whichthis involves, such as varying radii of curvature,is rarely considered to be justified. Acompromise is frequently made in which adoubly-curved shape, which is close to theform-active shape but which has a muchsimpler geometry, is adopted. These morepractical shapes achieve greater simplicityeither by having a constant radius of curvature,as in a spherical dome, or by beingtranslational forms, which can be generated bysimple curves such as parabolas or ellipses.The hyperbolic paraboloid and the ellipticalparaboloid (Fig. 5.25) are examples of thelatter. These shapes are simpler to analyse andto construct than true form-active shapes andby adopting them the designer elects to paythe penalty of lower efficiency to achieverelative ease of design and construction.

5.5 Conclusion

In this chapter the three basic types ofstructural arrangement have been describedand a small selection of each has beenillustrated. A great number of variations ispossible within each type, depending on thenature of the elements of which they arecomposed. An ability to place a structurewithin the appropriate category forms a usefulbasis for assessing its performance and theappropriateness of its selection for a particularapplication.

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6.1 Introduction

It is said, albeit usually by critics, that creativeactivity is enriched by criticism. The world ofstructural engineering, in which a very largenumber of artefacts are created continuously,is, however, curiously devoid of a climate ofcriticism, and few engineering structuresreceive anything like the critical attentionwhich is accorded to even the most modest ofbuildings. There is therefore no tradition ofcriticism in structural engineering comparableto that which exists in architecture and theother arts1.

Design has been described as a problem-solving activity, an iterative process in whichself-criticism by the designer forms anessential part. It is with this type of criticism,rather than the journalistic type alluded toabove, that this chapter is principallyconcerned. It is not proposed, therefore, todeal comprehensively here with the subject ofstructural criticism but simply to identify thetechnical factors by which the merits ofstructures may be assessed.

Engineering is principally concerned witheconomy of means – a structure may beconsidered to have been well engineered if itfulfils its function with a minimum input ofmaterials and other resources. This does not

mean that the most efficient2 structure, whichproduces the required load-carrying capacitywith a minimum weight of material, isnecessarily the best; several other technicalfactors, including the complexity of theconstruction process and the subsequentdurability of the structure, will affect thejudgement of whether or not a structure issatisfactory. Frequently, the technicalrequirements conflict with one another. Forexample, as was seen in Chapter 4, efficientforms are invariably complex and thereforedifficult to design, construct and maintain.

This dichotomy between efficiency andsimplicity of form is a fundamental aspect ofstructural design. The final geometry which isadopted is always a compromise betweenthese two properties, and the elegance withwhich this compromise is achieved is one ofthe principal criteria of good structural design.In the context of architecture it affects therelationship between the appearance and theperformance of a structure. The factors onwhich the nature of the best compromisedepends are reviewed here.

6.2 Complexity and efficiency instructural design

A fundamental engineering requirement is thateconomy of means should be achieved. The

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The critical appraisal ofstructures

1 The controversy over whether or not structuralengineering is an art will not be entered into here. Thisis discussed at length in Billington, D. P., The Tower andthe Bridge, MIT Press, Cambridge, MA, 1983 and Holgate,A., The Art in Structural Design, Clarendon Press, Oxford,1986. See also Addis, W. B., The Art of the StructuralEngineer, Artemis, London, 1994.

2 As in Chapter 4, structural efficiency is considered herein terms of the weight of material which has to beprovided to carry a given amount of load. The efficiencyof a structure is regarded as high if the ratio of itsstrength to its weight is high.

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overall level of resources committed to aproject should be as small as possible. Asensible balance should be struck between thecomplexity required for high structuralefficiency (see Chapter 4) and the ease ofdesign, construction and maintenance whichthe adoption of a simple arrangement allows.It is the nature of this compromise which mustbe assessed by the critic who wishes to judgethe merits of a structure.

The aspects of structure on which efficiencydepends, where efficiency is judged primarilyin terms of the weight of material which mustbe provided to give a particular load-carryingcapacity, were outlined in Chapter 4. It wasshown that the volume and therefore theweight of material required for a structure isdependent principally on its overall form inrelation to the pattern of applied load and onthe shapes of the structural elements in bothcross-section and longitudinal profile. A basicclassification system based on the concepts ofform-active shape and ‘simple’ and ‘improved’cross-sections and longitudinal profiles wasdescribed; this allows judgements to be madeconcerning the level of efficiency which is likelyto be achieved with a particular structuralarrangement. Form-active shapes such astensile cables and compressive vaults wereseen to be potentially the most efficient, andnon-form-active beams the least efficient.

A property of structures which wasdemonstrated by this ordering of elements isthat the higher the efficiency the more complexthe form3. This is generally the case even whenrelatively minor measures are taken to improvestructural efficiency, such as the use of I-shaped or box-shaped cross-sections forbeams instead of solid rectangles, or atriangulated internal geometry instead of asolid web for a girder.

The complicated geometry which must beadopted to obtain high efficiency affects theease with which a structure can be constructedand its constituent components manufactured,and its subsequent durability. For example, atriangulated framework is both more difficultto construct and more difficult to maintainsubsequently than is a solid-web beam. Thedesigner of a structure must therefore balancethese considerations against the natural desireto minimise the amount of material involved.The level of efficiency which has been achievedshould be appropriate for the individualcircumstances of the structure.

It is not possible to specify precisely thelevel of efficiency which should be achieved ina particular structure, such is the complexityof the interrelationships between the variousfactors involved. It is possible, however, toidentify two main influences on this desirablelevel, namely the size of the span which astructure must achieve and the intensity ofthe external load which it will carry. Thelonger the span, the greater is the need forhigh efficiency; the higher the level of loadwhich is carried, the lower can the efficiencybe. These two influences are in fact differentaspects of the same phenomenon, namely arequirement to maintain the ratio of self-weight to external load at a more or lessconstant level. Implicit in this statement isthe idea that, in order to achieve the ideal ofmaximum economy of means, the level ofcomplexity of a structure should be theminimum consistent with achieving areasonable level of efficiency.

The effect on efficiency of increasing span isdemonstrated in the very simple example of abeam of rectangular cross-section carrying auniformly distributed load (Fig. 6.1). In thefigure, two beams of different spans are shown,each carrying the same intensity of load. Theone with the longer span must have a greaterdepth so as to have adequate strength. Theself-weight of each beam is directlyproportional to its depth and so the ratio ofload carried to self-weight per unit length ofbeam (the structural efficiency) is lessfavourable for the larger span. 61

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3 The concept of the optimum structure provides furtherevidence that complexity is necessary to achieve highlevels of efficiency – see Cox, H. L., The Design ofStructures of Least Weight, Pergamon, London, 1965 andMajid, K. I., Optimum Design of Structures, Newnes-Butterworth, London, 1974.

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Another way of demonstrating the sameeffect would be to use a beam element with aparticular cross-section across a range ofspans. The strength of the beam – its momentof resistance (see Appendix 2.3) – would beconstant. At small spans the maximumbending moment generated by the self-weightwould be low and the beam might have areasonable capacity to carry additional load.As the span was increased the bendingmoment generated by the self-weight wouldincrease and an ever greater proportion of thestrength available would have to be devoted tocarrying the self-weight. Eventually a spanwould be reached in which all of the strengthavailable was required to support only the self-weight. The structural efficiency of the beam(its capacity to carry external load divided byits weight) would steadily diminish as the spanincreased.

Thus, in the case of a horizontal span, whichis the most common type of structure found inarchitecture, the efficiency of an element witha particular shape of cross-section decreasesas the span increases. To maintain a constantlevel of efficiency over a range of spans,different shapes of cross-section have to beused. More efficient shapes have to be used asthe span is increased if a constant level of loadto self-weight (efficiency) is to be maintained.

The general principle involved here is thatthe larger the span, the greater the number of‘improvements’ required to maintain aconstant level of efficiency. The principle maybe extended to the overall form of a structureand indeed to the full range of factors whichaffect efficiency. Thus, to maintain a constantlevel of efficiency over a wide range of span,

simple non-form-active structures might beappropriate for short spans. As the span isincreased, elements with progressively more ofthe features associated with efficiency arerequired to maintain a constant level ofefficiency. At intermediate spans semi-form-active types are required, again progressingthrough the range of possibilities for‘improvement’. For the very largest spans,form-active structures have to be specified.

The relationship between structuralefficiency and intensity of applied load, whichis the other significant factor affecting‘economy of means’, can also be fairly easilydemonstrated. Taking again the simpleexample of a beam with a rectangular cross-section, the weight of this increases in directproportion with its depth while its strengthincreases with the square of its depth (seeAppendix 2.3). Thus, if the external load isincreased by a factor of two the doubling instrength which is required to carry this can beachieved by an increase in the depth which isless than twofold (in fact, by a factor of 1.4).The increase in the weight of the beam istherefore also less than twofold and the overallefficiency of the element carrying the doubleload is greater. Thus, for a given span andshape of cross-section, the efficiency of theelement increases as the intensity of loadincreases and larger cross-sections must bespecified. Conversely, if a particular level ofefficiency is required, this can be achieved withless efficient shapes of cross-section whenheavier loads are carried (the relationshipbetween efficiency and shape of cross-sectionis discussed in Section 4.3 and in Appendix2.3).

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Fig. 6.1 The weight of a beam isproportional to its depth, which mustincrease as span increases. Thus, the ratioof self-weight to imposed load carriedbecomes less favourable as span isincreased.

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An examination of extant structuresdemonstrates that the majority are in factdesigned in accordance with an awareness ofthe relationship between span, load andefficiency described above. Although it isalways possible to find exceptions, it isnevertheless generally true that structures ofshort span are mainly produced inconfigurations which are inefficient, i.e. post-and-beam non-form-active arrangements with‘simple’ shapes in cross-section andlongitudinal profile. As spans increase theincidence of features which produce increasedefficiency is greater and structures with verylong spans are always constructed in efficientformats. This is very obvious in bridgeengineering, as is illustrated in Fig. 6.2, andcan be demonstrated to be broadly true ofbuilding structures.

The most obvious demonstration of theinfluence of load intensity on the type ofelement which is employed is found in multi-storey frameworks. The principal loads on thehorizontal structural elements of these aregravitational loads and, of these, floor loadsare of much higher intensity than roof loads(from two to ten times as much). In multi-storey frameworks it is very common fordifferent structural configurations to be usedfor floor and roof structures, with roofstructures being given more of the featureswhich are associated with greater structuralefficiency, even though the spans are the same(see Fig. 5.13).

From all of the foregoing it is possible topicture a fairly tidy taxonomy of structures inwhich the type of structure which would bemost suitable for a particular applicationwould range from the simplest post-and-beamnon-form-active types for very short spans,through a series of ‘improved’ non-form-activeor semi-form-active types in the medium spanrange, to form-active structures for the longestspans. Because the underlying requirement ofstructural design is to produce a ratio of loadto self-weight which is approximately constant,the precise levels of span at which transitionsfrom less to more efficient types of elementwould be appropriate would be affected by the

load intensity: the higher the load carried, thelonger would be the span at which the changeto a more efficient type would be justified. Thetechnical factor which determines the preciselevel of span for which a particular structuralconfiguration is most appropriate is thefundamental engineering requirement thateconomy of means should be achieved.

One indicator of the extent to which thecorrect balance between complexity (andtherefore efficiency) and simplicity has beenachieved is cost. Although monetary cost isnot strictly a technical aspect of theperformance of a structure it does give anindication of the level of resources of all kindswhich will have been involved in its realisation.Cost is therefore a measure of the level ofeconomy of means which has been achievedand is frequently crucial in determining the 63

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Fig. 6.2 The four bridges illustrated here demonstratethe tendency for structural complexity to increase withspan due to the need for greater efficiency. (a) LuzancyBridge; span 55 m, post-and-beam. (b) SalginatobelBridge; span 90 m, compressive-form-active arch with solidcross-section. (c) Bayonne Bridge, span 504 m,compressive form-active arch with ‘improved’ triangulatedlongitudinal profile. (d) Severn Bridge, span 990 m, tensileform-active.

(a) (b)

(c)

(d)

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balance of efficiency and complexity which isappropriate in a particular case.

Cost is, of course, an artificial yardstickwhich is affected by the ways in which a societychooses to order its priorities. These are likely,increasingly, to be related to the realities ofshortages of materials and energy, and to theneed to reduce levels of industrial pollution.Cost, which, in the economic context of themodern world of the twentieth century, waslargely unrelated to these aspects of realityand which was eschewed by critics ofarchitecture as a measure of the worth of abuilding, may, in the twenty-first centurybecome an important consideration in theassessment of the appropriateness of astructure.

As with other aspects of design the issueswhich affect cost are related in complicatedways. For example, in considering cost inrelation to structural design, the designer musttake into account not only the cost of thestructure itself but also the effect of theselection of a particular structure type on otherbuilding costs. If, for example, it provedpossible to reduce the cost of a multi-storeystructure by slightly increasing the structuraldepth of each floor, this saving might becounteracted by an increase in the cost of thecladding and other building components. If astructure type were selected which, althoughmore expensive than an alternative, allowedthe building to be erected more quickly (e.g. asteel rather than a reinforced concrete frame),the increase in the cost of the structure mightbe more than offset by the savings involved inhaving the building completed more quickly.The issue of cost, in relation to structuraldesign, must therefore involve a considerationof other issues besides those which are solelyconcerned with the structure. Such factors areespecially important when the cost of thestructure itself may form a relatively smallproportion of the total cost of the building. Inspite of these reservations, it is neverthelesspossible to make certain general observationsconcerning the issue of purely structural costs.

Cost, and in particular the relationshipbetween labour costs and material costs in the

economy within which the structure isconstructed, strongly influences the ratio ofload carried to self-weight which is appropriatewithin a particular economic regime. This is amajor factor in determining the spans at whichthe transition from less to more structurallyefficient forms are made.

This can be illustrated by considering therelationship between material and labour costsfor a particular structure. Consider, forexample, the problem of a single-storeybuilding of moderate span – an example mightbe the Renault Centre (Fig. 3.19). It may beassumed that a steel framework is a sensibleform of structure to support such an enclosurebut the range of structural possibilitiesavailable to the designer is very large. Simplepost-and-beam forms with parallel-sidedbeams would be the least structurally efficientoption. Semi-form-active portal frameworkswith triangulated elements would be moreefficient. A cable supported structure or tentwould give the greatest efficiency in the use ofmaterial. The higher the efficiency, the greaterthe complexity and therefore the higher wouldbe the design and construction costs.

The relationship between material andlabour costs of all kinds is representeddiagramatically in Fig. 6.3. The optimum levelof efficiency corresponds with the minimumpoint in the curve indicating the total costs;this will correspond to a particular type ofstructure. Figure 6.3 also illustrates the effectof a variation in labour cost. The effect of anincrease in labour costs, relative to materialcosts, is to reduce the level of efficiency atwhich the optimum level of economy of meansoccurs. This effect accounts for variations inpatterns of building in different parts of theworld. The higher the cost of materials inrelation to labour, the greater is the incentiveto achieve high efficiency and the smaller isthe span at which the transition from less tomore efficient and therefore more complexconfigurations is justified.

Extreme examples of this are found in tribalsocieties in which the economic conditions aresuch that very complex structural forms areused for structures of relatively short span. The

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Bedouin tent, the igloo (Fig. 1.2) and the yurt(Fig. 6.4), all of which are form-activestructures, may represent the very manyexamples which might be cited. The availabilityof ample reserves of labour to build andmaintain complex structures and the fact thatthey are the most effective ways of usinglocally available materials are responsible forthis use of a wide range of different forms forshort spans, all of them very efficient.

The situation in the industrialised societiesof the developed world is that labour isexpensive in relation to material. This favoursthe use of forms which are structurallyinefficient but which are straightforward tobuild. The majority of the structures found inthe developed world are inefficient post-and-beam types, an excellent example of theprofligacy with material of the industrialisedculture.

It is possible to suggest that for a particularspan and load requirement and within aparticular set of economic circumstances therewill be a limited number of appropriate structure 65

The critical appraisal of structures

Cos

t

Structuralefficiency

Efficiency level forlowest cost structure

Efficiency level for lowest coststructure when design andconstruction costs are higher

Higher designand constructioncosts

Design andconstructioncosts

Totalcost

Total cost whendesign and constructioncost is higher

Material costs

Fig. 6.3 The relationshipbetween structural efficiencyand structural costs for astructure with a particular spanand load condition are shownhere diagramatically. Thequantity and therefore cost ofmaterial decreases as moreefficient types of structure areused. The latter have morecomplex forms, however, sothe cost of construction anddesign increases withincreased structural efficiency.The curve showing total costhas a minimum point whichgives the level of efficiencywhich is most cost-effective forthat particular structure. Iflabour costs increase inrelation to material costs, thelocation of the minimum in thetotal cost curve is displaced tothe left indicating that astructural form of lowerefficiency will now be the mostcost-effective.

Fig. 6.4 The yurt is the traditional house of the nomadicpeoples of Asia. It consists of a highly sophisticatedarrangement of self-bracing semi-form-active timberstructural elements which support a non-structural feltskin. It is light and its domed shape, which combinesmaximum internal volume with minimum surface area, isideal for heat conservation and also minimises windresistance. When judged by purely technical criteria thisbuilding-type will stand comparison with many of thoseproduced by the so-called technological societies of thelate twentieth century.

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types. These will range from the simplest post-and-beam non-form-active types for the shortestspans, to form-active shells and cable structuresfor the largest spans. The majority of buildingsconform to this pattern but there are exceptions.Some of these could be regarded as simply ill-considered designs. Others can be justified byspecial circumstances.

For example, if there is a significantrequirement for a lightweight structure, thiswould justify the use of a more efficientstructural form than might otherwise beconsidered appropriate for the span. Perhapsthe most extreme example of this is thebackpacker’s tent, an extremely short-spanbuilding for which a tensile form-activestructure (the most sophisticated and mostefficient type of structure) is used. Therequirement for minimum weight is, of course,the justification in this case. Other examplesare buildings which are temporary or whichmust be transported, such as those which aredesigned to house travelling exhibitions (seeFig. 7.24) or travelling theatres.

Another reason for adopting a structure typewhich might otherwise be considered

inappropriate for the span or load involvedmight be that the building had to be builtquickly. Where speed of erection is given thehighest priority, a lightweight steel frameworkmight be a sensible choice even though otherconsiderations such as the shortness of thespan might not justify this. The use oflightweight steel framing for short-spanbuildings such as houses, of which theHopkins House (Fig. 6.5) is a special case, is anexample of this.

Sometimes, where the structure is part ofthe aesthetic programme of the building, astructure type is selected for its visual featuresrather than from a consideration of purelytechnical issues. Many of the structures whichare found in so-called ‘high-tech’ architecturefall into this category. It is always possible tofind examples of buildings in which a clientwas prepared to pay excessively and thereforecommit excessive resources in terms of eithermaterials or labour, in order to have aspectacular structure which would beunjustified on purely technical grounds.

A technical issue which has not so far beenconsidered, but which should form part of any

Structure and Architecture

Fig. 6.5 Hopkins House,London, UK, 1977;Michael Hopkins,architect; Anthony HuntAssociates, structuralengineers. The very shortspans involved here wouldnot normally justify theuse of complextriangulated elements forthe horizontal structure.Ease and speed oferection were the maintechnical reasons for theirselection. The visualexcitement which theyproduce was,nevertheless, the principalreason for their adoption.(Photo: Anthony HuntAssociates)

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thorough assessment of a structure, is itsdurability. Both the durability properties of theindividual constituent materials and thedurability implications of combinations ofmaterials must be considered. In some cases,where a structure will be subjected to aparticularly hostile environment, the questionof durability will be given a high priority at thedesign stage and will affect both the choice ofmaterial and the choice of form. More often,choices will be dictated by other criteria – suchas span and load – and the question then tobe answered is whether the material has beenused sensibly. If, for example, the materialselected is steel, which, in its unprotectedstate is one of the least corrosion-resistantmaterials, the problem of durability should berecognised. This would mitigate against usingsteel exposed on the exterior of a building,especially in humid climates.

The structure should be capable of fulfillingthe function for which it is designedthroughout the intended life of the building,without requiring that an unreasonableamount of maintenance be carried out on it.This raises the question of what is reasonablein this context, which brings us back to thequestion of economy of means and relativecosts. So far as durability is concerned, abalance must be struck between initial costand subsequent maintenance and repair costs.No definite best solution to this can bespecified, but an assessment of theimplications for durability must form part ofany serious assessment of the merits of astructure.

6.3 Reading a building as astructural object

The idea that structural criticism should be anaspect of the standard critical appraisal of awork of architecture requires an ability, on thepart of the critic, to read a building as astructural object. The classification systemproposed in Chapter 4 provides a basis forthis. The system is based on a categorisationof elements according to structural efficiency.

As has been discussed in Section 6.2, themeasure of a good structure is not that thehighest level of structural efficiency has beenachieved, but that an appropriate level has beenachieved. The judgement of the latter can onlybe made from a position of knowledgeconcerning the factors which affect efficiency. Afew examples are now considered todemonstrate the use of the system for theappraisal of structures.

The Forth Railway Bridge4 (Fig. 6.6) is aspectacular example of a work of more or less‘pure’ engineering which makes anappropriate beginning. Although the generalarrangement of the bridge may seem verycomplex, it may be seen to be fairlystraightforward if visualised in accordancewith the concepts of ‘form-action’ and‘improvement’. The principal elements of thisstructure are paired, balanced cantilevers.This configuration was adopted so that thebridge could be constructed without the useof temporary supports. The structure wasself-supporting throughout the entireconstruction process. The cantilevers arelinked by short suspended spans, a cleverarrangement which allows the advantages ofstructural continuity to be achieved in adiscontinuous structure5.

The arrangement was therefore non-form-active and potentially inefficient. Given thespans involved, extensive measures werejustified to achieve an acceptable level ofefficiency. These took several forms: the profileof the main structure was made to conform tothe bending-moment diagram resulting fromthe principal load condition (a uniformlydistributed gravitational load across the wholestructure) and the internal geometry of thisprofile was fully triangulated. The rail trackswere carried on an internal viaduct – itself a

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4 See Macdonald, Angus J. and Boyd Whyte, I., The ForthBridge, Axel Menges, Stuttgart, 1997 for a morecomplete description of the structure and discussion ofits cultural significance.

5 See Section 5.1 and Appendix 3 for an explanation ofthe terms continuous and discontinuous structures.

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Structure and Architecture

Fig. 6.6 Basic structuralarrangement of the Forth RailwayBridge, Firth of Forth, UK. Thisstructure is a post-and-beamframework but, as with the RenaultHeadquarters (Figs 3.19 & 6.8), it hasbeen ‘improved’ at various levels.There is more justification for thecomplexity in this case due to thelarge span involved. (Photo: A. & P.Macdonald)

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non-form-active structure ‘improved’ bytriangulation – which was connected to themain structure only at the nodes of thetriangles. Thus, the principal sub-elements ofthe structure carried either direct tension ordirect compression. The individual sub-elements were given ‘improved’ cross-sections.The main compression sub-elements, forexample, are hollow tubes, most of them witha cross-section which is circular, which is themost efficient shape for resisting axialcompression. Thus, the structure of the ForthRailway Bridge has a basic form which ispotentially rather inefficient but which was‘improved’ in a number of ways.

The most common structural arrangementin the world of architecture is the post-and-beam form in which horizontal elements aresupported on vertical columns or walls. In themost basic version of this, the horizontalelements are non-form-active, under the actionof gravitational load, and the vertical elementsare axially loaded and may therefore beregarded as form-active. Countless versions ofthis arrangement have been used through thecenturies, and it is significant that the greatestvariations are to be seen in the non-form-active horizontal elements where theadvantages to be gained from the‘improvement’ of cross-sections andlongitudinal profiles are greatest.

The temples of Greek antiquity, of which theParthenon in Athens (see Fig. 7.1) is thesupreme example, are a very basic version ofthe post-and-beam arrangement. The level ofefficiency achieved here is low, and this is duepartly to the presence of non-form-activeelements and partly to the methods used todetermine the sizes and proportions of theelements. The priorities of the designers werenot those of the present-day engineer, and theidea of achieving efficiency in a materialisticsense was probably the last consideration inthe minds of Ictinus and his collaboratorswhen the dimensions of the Parthenon weredetermined. The building is perhaps the bestillustration of the fact that the achievement ofstructural efficiency is not a necessaryrequirement for great architecture.

In the twentieth century, by contrast,efficiency in the use of material was given ahigh priority partly in a genuine attempt toeconomise on material in order to save cost,but also as a consequence of the prevalence ofthe belief in the modernist ideal of ‘rational’design. The overall geometry of the inefficientnon-form-active post-and-beam form is soconvenient, however, that it has neverthelesscontinued to be the most widely used type ofarchitectural structure. It was normal in themodern period, however, for at least thehorizontal elements to have some form of‘improvement’ built into them. This wasespecially true of steel frameworks in which thebeams and columns invariably had ‘improved’I-shaped cross-sections and much use wasmade of the technique of internal triangulation.

In the Centre Pompidou, in Paris (Figs 6.7and 1.10), the basic arrangement of the

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Fig. 6.7 Load, bending moment and structural diagramsfor one of the principal elements in the floor structure ofthe Centre Pompidou, Paris, France. This is a non-form-active beam but the relatively long span involved justifiedthe incorporation of ‘improvements’. Height restrictionsprevented the matching of the longitudinal profile to thebending moment diagram, except in the cantilevered‘gerberette brackets’ at the extremities of the structure.Triangulation was the only form of ‘improvement’ whichwas feasible here for the main element (see also Figs 1.10,3.17, 7.7 and 7.8).

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structure is such that all of the horizontalelements are straight, non-form-active beamsand this configuration is therefore potentiallyvery inefficient. The triangulation of the maingirders and the use of ‘improved’ shapes incross-section and longitudinal profile of thecantilevered gerberettes (see Fig. 3.17)compensates for the potential inefficiency ofthe form, however, and the overall level ofefficiency which was achieved may be judgedto be moderate.

The framework of the Renault Building atSwindon, UK (see Fig. 3.19), may also beregarded as a post-and-beam frame as thebasic form of the structure is rectilinear (Fig.6.8). The beam-to-column junctions are rigid,however, and provide a degree of structuralcontinuity, so that both horizontal and verticalelements are subjected to a combination ofaxial and bending-type internal force under theaction of gravitational loads. The latter aretherefore semi-form-active. Because the basicshape of the structure is markedly differentfrom the form-active shape6, the magnitudes ofthe bending moments are high and thestructure is therefore potentially ratherinefficient. The longitudinal profiles of thehorizontal elements have, however, been‘improved’ in a number of ways. The overalldepth is varied in accordance with the bending-moment diagram and the profile itself issubdivided into a combination of a bar elementand an I-section element, the relative positionsof which are adjusted so that the bar elementforms the tensile component in the combinedcross-section and the I-section the compressiveelement7. The circular cross-section of the baris a sensible shape to carry the tensile load,while the I-section of the compressive part is asuitable choice in view of the need to resist

compressive instability, which is a bendingphenomenon. The cutting of circular holes fromits web (see Fig. 3.19) is another form of‘improvement’. A similar breakdown of thecross-section occurs in the vertical elements,but in these the compressive components arecircular hollow sections instead of I-sections.This is again sensible because thesecomponents are subjected to a greater amountof compression than their counterparts in thehorizontal elements, and the circle is an idealshape of cross-section with which to resistcompression. The choice of basic form, that ofa semi-form-active rectilinear framework, ispotentially only moderately efficient but, as inthe case of the Centre Pompidou, a number ofmeasures have been adopted to compensate

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6 The load pattern on the primary structure is a series ofclosely-spaced concentrated loads. The form-activeshape for this is similar to a catenary.

7 The bar element is sometimes above the I-section andsometimes below, depending upon the sense of thebending moment and therefore upon whether the topor the bottom of the combined section is in tension.

Fig. 6.8 Load, bending moment and structural diagramsof the Renault Headquarters building, Swindon, UK. Thebasic form of this structure is a post-and-beam non-form-active frame. ‘Improvements’ have been introduced atseveral levels: the overall profile of the structure has beenmade to conform to the bending moment diagram forgravitational load, the structure has been triangulatedinternally and some of the sub-elements have been further‘improved’ by having I-shaped cross-sections and circularholes cut in their webs (see also Figs 3.19).

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for this. The question of whether an appropriateoverall level of efficiency has been achieved inthis case is discussed in Section 7.2.2.

‘Improvements’ to element cross-sectionsare seen less often in buildings with reinforcedconcrete structures because concrete is bothlighter and cheaper than steel, so there is notthe same incentive to achieve even themoderate levels of structural efficiency of steelframeworks. Coffered slabs are used in theWillis, Faber and Dumas building (see Figs 1.6and 5.19), however, and are examples of‘improved’ non-form-active elements in a post-and-beam, reinforced concrete arrangement.Versions of this type of ‘improvement’ areincorporated into most reinforced concretestructures if the span is greater than 6 m.

These few examples of structuralclassification serve to illustrate the usefulnessof the system described in Section 4.4 as ameans of assessing the level of efficiencyachieved in a structure. It should never beassumed, however, when judging theappropriateness of a structural design for aparticular application, that the most efficientstructure is necessarily the best. Even in thecase of a ‘purely’ engineering structure, such asa bridge, other factors such as the level ofcomplexity of the construction process or theimplications of the form for long-termdurability have to be considered and there aremany situations in which a simple beam with arectangular cross-section – perhaps the leastefficient of structural forms – constitutes thebest technical solution to a structural supportproblem. The question to be decided when atechnical judgement is made about a structureis not so much one of whether the maximumpossible level of efficiency has been achievedas of whether an appropriate level has beenachieved.

6.4 Conclusion

Any formulation of the criteria by which themerits of a structure could be judged isinevitably controversial. Most people would,however, feel able to agree with the statement

that the principal objective of engineeringdesign is to provide an object which willfunction satisfactorily with maximum economyof means. This is summed up in the oldengineering adage that ‘an engineer issomeone who can do for £1 what any fool cando for £3’.

The assessment of whether or not areasonable level of economy of means hasbeen achieved involves the examination of anumber of different aspects of the design of anartefact. It is principally a matter of beingsatisfied that a reasonable balance has beenachieved between the quantity of materialused, the complexity of the design andconstruction processes, and the subsequentdurability and dependability of the artefact. Inthe context of structural engineering, theachievement of economy of means is notsimply a matter of minimising the amount ofmaterial which is required for a structure, butrather of making the best possible use of allthe material, effort and energy which areinvolved in its production. Because thesefactors are interrelated in complicated ways,the overall judgement required is notstraightforward.

One measure of the extent to whicheconomy of means has been achieved is cost,since the cost of the structure in monetaryterms is related to the total input of resourcesto the structure. Cost is, of course, almostentirely an artificial yardstick dependent on thecurrent market prices of labour, energy andmaterials. It is always related to a particulareconomic culture, but also to the resources,both human and environmental, which asociety has at its disposal. All of theseconsiderations are subject to change overtime.

It is possible to argue that from a purelyengineering point of view the structure whichis cheapest constitutes the best solution to theproblem of supporting an enclosure. In mostcultures the majority of ‘ordinary’ buildings arein fact constructed in such a way as tominimise cost. The judgement of whether ornot a particular structure constitutes goodengineering could therefore be made by 71

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comparing it to the mainstream ofcontemporary practice. If it is broadly similarto the majority of comparable structures it isprobably well engineered.

By this criterion the standard andubiquitous portal-frame shed, which is usedto house supermarkets and warehousesthroughout the industrialised world, wouldqualify as good engineering and the so-called ‘high-tech’ supersheds whichappeared in the architectural journals in the1980s would not, and would at best beregarded as expensive toys. It is necessary tobear in mind that what is being discussedhere is engineering and not architecturealthough, in the context of the need toevolve forms of building which meet therequirements of sustainability, thesedisciplines may have to become more closelyrelated in the future. If there were morecontact between these two extremes ofbuilding strategy, this might benefit both thevisual and the engineering environments.

It must always be borne in mind thatengineering is not about image making. It isabout the provision of artefacts which are useful.If the problem to be solved is very difficulttechnically – e.g. a very long span building, avehicle which must move with great speed or flythrough the air, or a structure which supportslife in an inhospitable environment – then theobject which is created is likely to be spectacularin some way and, if a building structure, may bevisually exciting. If the problem is not technicallydifficult – e.g. a building of modest span – thenthe best engineering solution will also bemodest although it may nevertheless be subtle;if it is well designed and elegant from anengineering point of view it will be exciting tothose who appreciate engineering design.Twentieth-century modernists who believed thatthe ‘celebration’ of the ‘excitement’ oftechnology was a necessary part of allarchitectural expression applied different criteriato the assessment of structure.

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7.1 Introduction

Two related but distinct issues are discussed inthis chapter. These are the relationshipbetween structure and architecture and therelationship between structural engineers andarchitects. Each of these may take more thanone form, and the type which is in play at anytime influences the effect which structure hason architecture. These are issues which shedan interesting sidelight on the history ofarchitecture.

Structure and architecture may be related ina wide variety of ways ranging between theextremes of complete domination of thearchitecture by the structure to total disregardof structural requirements in the determinationof both the form of a building and of itsaesthetic treatment. This infinite number ofpossibilities is discussed here under six broadheadings:

• ornamentation of structure• structure as ornament• structure as architecture• structure as form generator• structure accepted• structure ignored.

As in the case of the relationship betweenstructure and architecture, the relationshipbetween architects and structural engineersmay take a number of forms. This may rangefrom, at one extreme, a situation in which theform of a building is determined solely by thearchitect with the engineer being concernedonly with making it stand up, to, at the otherextreme, the engineer acting as architect anddetermining the form of the building and all

other architectural aspects of the design. Mid-way between these extremes is the situation inwhich architect and engineer collaborate fullyover the form of a building and evolve thedesign jointly. As will be seen, the type ofrelationship which is adopted has a significanteffect on the nature of the resultingarchitecture.

7.2 The types of relationshipbetween structure and architecture

7.2.1 Ornamentation of structureThere have been a number of periods in thehistory of Western architecture in which theformal logic of a favoured structural systemhas been allowed to influence, if not totallydetermine, the overall form of the buildingsinto which the age has poured itsarchitectural creativity. In the periods inwhich this mood has prevailed, the forms thathave been adopted have been logicalconsequences of the structural armatures ofbuildings. The category ornamentation ofstructure, in which the building consists oflittle more than a visible structural armatureadjusted in fairly minor ways for visualreasons, has been one version of this.

Perhaps the most celebrated building in theWestern architectural tradition in whichstructure dictated form was the Parthenon inAthens (Fig. 7.1). The architecture of theParthenon is tectonic: structural requirementsdictated the form and, although the purpose ofthe building was not to celebrate structuraltechnology, its formal logic was celebrated aspart of the visual expression. The Doric Order,which reached its greatest degree of 73

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refinement in this building, was a system ofornamentation evolved from the post-and-beam structural arrangement.

There was, of course, much more to thearchitecture of the Greek temple thanornamentation of a constructional system. Thearchetypal form of the buildings and thevocabulary and grammar of the ornamentationhave had a host of symbolic meaningsattributed to them by later commentators1. Noattempt was made, however, by the builders ofthe Greek temples, either to disguise thestructure or to adopt forms other than thosewhich could be fashioned in a logical andstraightforward manner from the availablematerials. In these buildings the structure and

the architectural expression co-exist in perfectharmony.

The same may be said of the major buildingsof the mediaeval Gothic period (see Fig. 3.1),which are also examples of the relationshipbetween structure and architecture that may bedescribed as ornamentation of structure. Like theGreek temples the largest of the Gothic buildingswere constructed almost entirely in masonry, butunlike the Greek temples they had spaciousinteriors which involved large horizontal roofspans. These could only be achieved in masonryby the use of compressive form-active vaults. Theinteriors were also lofty, which meant that thevaulted ceilings imposed horizontal thrust on thetops of high flanking walls and subjected them tobending moment as well as to axial internal force.The walls of these Gothic structures weretherefore semi-form-active elements (see Section4.2) carrying a combination of compressive-axial

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Fig. 7.1 The Parthenon, Athens, 5th century BC. Structure and architecture perfectly united.

1 For example, Scully, V., The Earth, the Temple and the Gods,Yale University Press, New Haven, 1979.

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and bending-type internal force. The archetypicalGothic arrangement of buttresses, flyingbuttresses and finials is a spectacular example ofa semi-form-active structure with ‘improved’cross-section and profile. Virtually everythingwhich is visible is structural and entirely justifiedon technical grounds. All elements were adjustedso as to be visually satisfactory: the ‘cabling’ ofcolumns, the provision of capitals on columnsand of string courses in walls and several othertypes of ornament were not essential structurally.

The strategy of ornamentation of structure,which was so successfully used in Greekantiquity and in the Gothic period, virtuallydisappeared from Western architecture at thetime of the Italian Renaissance. There wereseveral causes of this (see Section 7.3), one ofwhich was that the structural armatures ofbuildings were increasingly concealed behindforms of ornamentation which were notdirectly related to structural function. Forexample, the pilasters and half columns ofPalladio’s Palazzo Valmarana (Fig. 7.2) andmany other buildings of the period were notpositioned at locations which wereparticularly significant structurally. Theyformed part of a loadbearing wall in which allparts contributed equally to the load carryingfunction. Such disconnection of ornamentfrom structural function led to the structuraland aesthetic agendas drifting apart and hada profound effect on the type of relationshipwhich developed between architects andthose who were responsible for the technicalaspects of the design of buildings (seeSection 7.3).

It was not until the twentieth century, whenarchitects once again became interested intectonics (i.e. the making of architecture out ofthose fundamental parts of a buildingresponsible for holding it up) and in theaesthetic possibilities of the new structuraltechnologies of steel and reinforced concrete,that the ornamental use of exposed structurere-appeared in the architectural mainstream ofWestern architecture. It made its tentative firstappearance in the works of early Modernistssuch as Auguste Perret and Peter Behrens (Fig.7.3) and was also seen in the architecture of

Ludwig Mies van der Rohe. The structure ofthe Farnsworth House, for example, is exposedand forms a significant visual element. It wasalso adjusted slightly for visual reasons and inthat sense is an example of ornamentation ofstructure. Other more recent examples of suchvisual adjustments occurred in British HighTech. The exposed-steel structure of the

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Fig. 7.2 The Palazzo Valmarana, Vicenza, by AndreaPalladio. The pilasters on this façade have their origins ina structural function but here form the outer skin of astructural wall. The architectural interest of the buildingdoes not lie in its structural make-up, however.

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Reliance Controls building at Swindon, UK(Fig. 7.4), for example, by Team 4 and TonyHunt, is a fairly straightforward technicalresponse to the problems posed by theprogrammatic requirements of the buildingand stands up well to technical criticism2. It isnevertheless an example of ornamentation ofstructure rather than a work of pureengineering because it was adjusted in minorways to improve its appearance. The H-sectionUniversal Column3 which was selected for its

very slender purlins, for example, was lessefficient as a bending element than the I-section Universal Beam would have been. Itwas used because it was considered that thetapered flanges of the Universal Beam wereless satisfactory visually than the parallel-sided flanges of the Universal Column in thisstrictly rectilinear building.

The train shed of the International RailTerminal at Waterloo station in London (Fig.7.17) is another example. The overallconfiguration of the steel structure, whichforms the principal architectural element ofthis building, was determined from technicalconsiderations. The visual aspects of thedesign were carefully controlled, however, andthe design evolved through very closecollaboration between the teams of architectsand engineers from the offices of Nicholas

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Fig. 7.3 AEG Turbine Hall, Berlin, 1908; Peter Behrens, architect. Glass and structure alternate on the side walls of thisbuilding and the rhythm of the steel structure forms a significant component of the visual vocabulary. Unlike in manylater buildings of the Modern Movement the structure was used ‘honestly’; it was not modified significantly for purelyvisual effect. With the exception of the hinges at the bases of the columns it was also protected within the externalweathertight skin of the building. (Photo: A. Macdonald)

2 See Macdonald, Angus J., Anthony Hunt, ThomasTelford, London, 2000.

3 The Universal Column and Universal Beam are thenames of standard ranges of cross-sections for hot-rolled steel elements which are produced by the Britishsteel industry.

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Grimshaw and Partners and Anthony HuntAssociates so that it performed wellaesthetically as well as technically.

These few examples serve to illustrate thatthroughout the entire span of the history ofWestern architecture from the temples of Greekantiquity to late-twentieth-century structuressuch as the Waterloo Terminal, buildings havebeen created in which architecture has beenmade from exposed structure. The architects ofsuch buildings have paid due regard to therequirements of the structural technology andhave reflected this in the basic forms of thebuildings. The architecture has therefore beenaffected in a quite fundamental way by thestructural technology involved. At the sametime the architects have not allowedtechnological considerations to inhibit theirarchitectural imagination. The results have

been well-resolved buildings which performwell when judged by either technical or non-technical criteria.

7.2.2 Structure as ornament

‘The engineer’s aesthetic4 and architecture –two things that march together and followone from the other.’5

The relationship between structure andarchitecture categorised here as structure asornament involves the manipulation ofstructural elements by criteria which are

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Fig. 7.4 Reliance Controls building, Swindon, UK, 1966; Team 4, architects; Tony Hunt, structural engineer. The exposedstructure of the Reliance Controls building formed an important part of the visual vocabulary. It was modified in minorways to improve its appearance. (Photo: Anthony Hunt Associates)

4 Author’s italics.5 Le Corbusier, Towards a New Architecture, Architectural

Press, London, 1927.

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principally visual and it is a relationship whichhas been largely a twentieth-centuryphenomenon. As in the category ornamentationof structure the structure is given visualprominence but unlike in ornamentation ofstructure, the design process is driven by visualrather than by technical considerations. As aconsequence the performance of thesestructures is often less than ideal when judgedby technical criteria. This is the feature whichdistinguishes structure as ornament fromornamentation of structure.

Three versions of structure as ornament maybe distinguished. In the first of these,structure is used symbolically. In this scenariothe devices which are associated withstructural efficiency (see Chapter 4), which aremostly borrowed from the aerospace industryand from science fiction, are used as a visualvocabulary which is intended to convey theidea of progress and of a future dominated bytechnology. The images associated withadvanced technology are manipulated freely toproduce an architecture which celebratestechnology. Often, the context is inappropriateand the resulting structures perform badly in atechnical sense.

In the second version, spectacular exposedstructure may be devised in response toartificially created circumstances. In this type ofbuilding, the forms of the exposed structureare justified technically, but only as thesolutions to unnecessary technical problemsthat have been created by the designers of thebuilding.

A third category of structure as ornamentinvolves the adoption of an approach in whichstructure is expressed so as to produce areadable building in which technology iscelebrated, but in which a visual agenda is pursuedwhich is incompatible with structural logic. The lack ofthe overt use of images associated withadvanced technology distinguishes this fromthe first category.

Where structure is used symbolically, avisual vocabulary which has its origins in thedesign of lightweight structural elements – forexample the I-shaped cross-section, thetriangulated girder, the circular hole cut in the

web, etc. (see Chapter 4) – is usedarchitecturally to symbolise technicalexcellence and to celebrate state-of-the-arttechnology. Much, though by no means all, ofthe architecture of British High Tech falls intothis category. The entrance canopy of theLloyds headquarters building in London is anexample (Fig. 7.5). The curved steel elementswhich form the structure of this canopy, withtheir circular ‘lightening’ holes (holes cut outto lighten the element – see Section 4.3) arereminiscent of the principal fuselage elementsin aircraft structures (Fig. 4.14). Thecomplexity of the arrangement is fully justifiedin the aeronautical context where saving ofweight is critical. The use of lightweightstructures in the canopy at Lloyds merelyincreases the probability that it will be blownaway by the wind. Its use here is entirelysymbolic.

The Renault Headquarters building inSwindon, UK, by Foster Associates and OveArup and Partners is another example of thisapproach (see Figs 3.19 and 6.8). The structureof this building is spectacular and a keycomponent of the building’s image, which isintended to convey the idea of a company witha serious commitment to ‘quality design’6 andan established position at the cutting edge oftechnology. The building is undoubtedlyelegant and it received much critical acclaimwhen it was completed; these designobjectives were therefore achieved. BernardHanon, President-Directeur General, RégieNationale des Usines Renault, on his first visitfelt moved to declare: ‘It’s a cathedral.’7.

The structure of the Renault building doesnot, however, stand up well to technicalcriticism. It consists of a steel-framesupporting a non-structural envelope. Thebasic form of the structure is of multi-bayportal frames running in two principaldirections. These have many of the featuresassociated with structural efficiency: the

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6 Lambot, I. (Ed.), Norman Foster: Foster Associates: Buildingsand Projects, Vol. 2, Watermark, Hong Kong, 1989.

7 Ibid.

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longitudinal profile of each frame is matchedto the bending-moment diagram for theprincipal load; the structure is trussed (i.e.separate compression and tensile elements areprovided); the compressive elements, whichmust have some resistance to bending, havefurther improvements in the form of I-shapedcross-sections and circular holes cut into thewebs. Although these features improve theefficiency of the structure, most of them arenot justified given the relatively short spansinvolved (see Chapter 6). The structure isunnecessarily complicated and there is nodoubt that a conventional portal-framearrangement (a primary/secondary structuralsystem with the portals serving as the primarystructure, as in the earlier building by FosterAssociates at Thamesmead, London (see Fig.1.5)), would have provided a more economicalstructure for this building. Such a solution wasrejected at the outset of the project by theclient on the grounds that it would not haveprovided an appropriate image for thecompany8. The decision to use the moreexpensive, more spectacular structure wastherefore taken on stylistic grounds.

The structure possesses a number of otherfeatures which may be criticised from a technicalpoint of view. One of these is the placing of asignificant part of it outside the weathertightenvelope, which has serious implications fordurability and maintenance. The configuration ofthe main structural elements is also far fromideal. The truss arrangement cannot toleratereversal of load because this would place thevery slender tension elements into compression.As designed, the structure is capable of resistingonly downward-acting gravitational loads andnot uplift. Reversal of load may tend to occur inflat-roofed buildings, however, due to the highsuction forces which wind can generate.Thickening of the tensile elements to give themthe capability to resist compression wasconsidered by the architect to be unacceptablevisually9 and so this problem was solved by

specifying heavier roof cladding than originallyintended (or indeed required) so that no reversalof load would occur. Thus the whole structurewas subjected, on a permanent basis, to a largergravitational load than was strictly necessary. Afurther observation which might be maderegarding the structure of this building is thatthe imagery employed is not particularly ‘cuttingedge’, much of it having been evolved in the 79

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Fig. 7.5 Entrance canopy, Lloyds headquarters building,London, UK, 1986; Richard Rogers and Partners, architects;Ove Arup & Partners, structural engineers. The curved steelribs with circular ‘lightening’ holes are reminiscent ofstructures found in the aerospace industry. (Photo: ColinMcWilliam)

8 Ibid.9 See Lambot, ibid.

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earliest days of iron and steel frame design inthe nineteenth century.

The sources of the visual vocabulary ofstructural technology used in the symbolicversion of structure as ornament are various and,for the most part, not architectural. In somecases the source has been science fiction. Moreusually, images were employed which wereperceived to represent very advancedtechnology, the most fruitful source for thelatter being aeronautical engineering where thesaving of weight is of paramount importance,and particularly the element with complex‘improved’ cross-section and circular ‘lightening’holes. Forms and element types which areassociated with high structural efficiency – seeChapter 4 – are therefore employed.

One of the problems facing the designers ofaircraft or vehicle structures is that the overallform is dictated by non-structuralconsiderations. The adoption of structurallyefficient form-active shapes is not possible andhigh efficiency has to be achieved byemploying the techniques of ‘improvement’.The whole vocabulary of techniques of‘improvement’ – stressed-skin monocoque andsemi-monocoque ‘improved’ beams, internaltriangulation, sub-elements with I-shapedcross-sections, tapered profiles and circular‘lightening’ holes – is exploited in these fieldsto achieve acceptable levels of efficiency (seeFigs 4.13 to 4.15). It is principally thisvocabulary which has been adopted byarchitects seeking to make a symbolic use ofstructure and which has often been applied insituations where the span or loading would notjustify the use of complicated structures of thistype on technical grounds alone.

The dichotomy between the appearance andthe reality of technical excellence is nowheremore apparent than in the works of the architectsof the ‘Future Systems’ group (Fig. 7.6):

‘Future Systems believes that borrowingtechnology developed from structuresdesigned to travel across land(automotive), or through water (marine),air (aviation) or vacuum (space) can helpto give energy to the spirit of architecture

by introducing a new generation ofbuildings which are efficient, elegant,versatile and exciting. This approach toshaping the future of architecture is basedon the celebration of technology, not theconcealment of it.’10

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10 Jan Kaplicky and David Nixon of Future Systems quotedin the final chapter of Wilkinson, C., Supersheds,Butterworth Architecture, Oxford, 1991. Later in thesame statement Kaplicky and Nixon declare, of thetechnology of vehicle and aerospace engineering, ‘It istechnology which is capable of yielding an architectureof sleek surfaces and slender forms – an architecture ofefficiency and elegance, and even excitement.’ It isclear from this quotation that it is the appearancerather than the technical reality which is attractive toKaplicky and Nixon.

Fig. 7.6 Green Building (project), 1990: Future Systems,architects. Technology transfer or technical image-making?Many technical criticisms could be made of this design.The elevation of the building above ground level isperhaps the most obvious as this requires that anelaborate structural system be adopted including floorstructures of steel-plate box-girders similar to those whichare used in long-span bridge construction. There is notechnical justification for their use here where a moreenvironmentally friendly structural system, such asreinforced concrete slabs supported on a conventionalcolumn grid, would have been a more convincing choice.This would not have been so exciting visually, but it wouldhave been more convincing in the context of the idea of asustainable architecture.

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The quotation reveals a degree of naivetyconcerning the nature of technology. Itcontains the assumption that dissimilartechnologies have basic similarities whichproduce similar solutions to quite differenttypes of problem.

The ‘borrowing of technology’ referred to inthe quotation above from Future Systems isproblematic. Another name for this is‘technology transfer’, a phenomenon in whichadvanced technology which has beendeveloped in one field is adapted and modifiedfor another. Technology transfer is a conceptwhich is of very limited validity becausecomponents and systems which are developedfor advanced technical applications, such asoccur in the aerospace industry, are designedto meet very specific combinations ofrequirements. Unless very similarcombinations occur in the field to which thetechnology is transferred it is unlikely that theresults will be satisfactory from a technologicalpoint of view. Such transfer is therefore alsomisleading symbolically on any level but themost simplistic.

The claims which are made for technologytransfer are largely spurious if judged bytechnical criteria concerned with function andefficiency. The reality of technology transfer toarchitecture is normally that it is the imageand appearance which is the attractive elementrather than the technology as such.

It is frequently stated by the protagonists ofthis kind of architecture11 that, because itappears to be advanced technically, it willprovide the solutions to the architecturalproblems posed by the worsening globalenvironmental situation. This is perhaps theirmost fallacious claim. The environmentalproblems caused by shortages of materials andenergy and by increasing levels of pollution arereal technical problems which require genuinetechnical solutions. Both the practice and theideology of the symbolic use of structure are

fundamentally incompatible with therequirements of a sustainable architecture. Themethodology of the symbolic use of structure,which is to a large extent a matter of borrowingimages and forms from other technical areaswithout seriously appraising their technicalsuitability, is incapable of addressing realtechnical problems of the type which are posedby the need for sustainability. The ideology isthat of Modernism which is committed to thebelief in technical progress and the continualdestruction and renewal of the builtenvironment12. This is a high-energy-consumption scenario which is not ecologicallysound.

The benefits of new technological solutionswould have to be much greater than at presentfor this approach to be useful. The forms of afuture sustainable architecture are more likely tobe evolved from the combination of innovativeenvironmental technology with traditionalbuilding forms, which are environmentallyfriendly because they are adapted to localclimatic conditions and are constructed indurable, locally available materials, than bytransferring technology from the extremelyenvironmentally unfriendly aerospace industry.

The second category of structure as ornamentinvolves an unnecessary structural problem,created either intentionally or unintentionally,which generates the need for a spectacularresponse. A good example of this is found inthe structure of the Centre Pompidou andconcerns the way in which the floor girders areconnected to the columns (Figs 7.7 and 6.7).

The rectangular cross-section of thisbuilding has three zones at every level (Fig.7.8). There is a central main space which isflanked by two peripheral zones: on one side ofthe building the peripheral zone is used for acirculation system of corridors and escalators;on the other it contains services. The architectschose to use the glass wall which formed thebuilding’s envelope to delineate these zones

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11 Chief amongst these is Richard Rogers and thearguments are set out in Rogers, Architecture, A ModernView, Thames and Hudson, London, 1991.

12 This is very well articulated by Charles Jencks in ‘TheNew Moderns’, AD Profile – New Architecture: The NewModerns and The Super Moderns, 1990.

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and placed the services and circulation zonesoutside the envelope. The distinction ismirrored in the structural arrangement: themain structural frames, which consist oftriangulated girders spanning the central space,are linked to the perimeter columns throughcantilever brackets, named ‘gerberettes’ afterthe nineteenth-century bridge engineer

Heinrich Gerber, which are associated with theperipheral zones. The joints between thebrackets and the main frames coincide with thebuilding’s glass wall and the spatial andstructural zonings are therefore identical.

The elaborate gerberette brackets, which aremajor visual elements on the exterior of thebuilding, pivot around the hinges connecting

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Fig. 7.7 Gerberette brackets, Centre Pompidou, Paris,France, 1978; Piano and Rogers, architects; Ove Arup &Partners, structural engineers. The floor girders are attachedto the inner ends of these brackets, which pivot on hingepins through the columns. The weights of the floors arecounterbalanced by tie forces applied at the outer ends ofthe brackets. The arrangement sends 25% more force intothe columns than would occur if the floor beams wereattached to them directly. (Photo: A. Macdonald)

Fig. 7.8 Cross-section, Centre Pompidou, Paris, France, 1978; Piano and Rogers, architects; Ove Arup & Partners, structuralengineers. The building is subdivided into three principal zones at every level and the spatial and structural arrangementscorrespond. The main interior spaces occupy a central zone associated with the main floor girders. The gerberette bracketsdefine peripheral zones on either side of the building which are associated with circulation and services.

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them to the columns (Fig. 7.7). The weights ofthe floors, which are supported on the inner endsof the brackets, are counterbalanced bydownward-acting reactions at the outer endsprovided by vertical tie rods linking them withthe foundations. This arrangement sends 25%more force into the columns at each level than isrequired to support the floors. The idea ofconnecting the floor girders to the columnsthrough these cantilevered brackets does nottherefore make a great deal of engineering sense.

Apart from the unnecessary overloading ofthe columns, the brackets themselves aresubjected to high levels of bending-type internalforce and their design presented an interesting,if unnecessary, challenge to the engineers. Therequired solution to this was to give the bracketsa highly complex geometry which reflected theirstructural function. The level of complexity couldonly be achieved by casting of the metal, and theidea of fabricating the brackets from cast steel, atechnique which was virtually unknown inarchitecture at the time, was both courageousand innovative. It allowed forms to be usedwhich were both expressive of the structuralfunction of the brackets and which made a moreefficient use of material than would haveoccurred had they been made from standardI-sections. According to Richard Rogers: ‘Wewere repeating the gerberette brackets over 200times and it was cheaper to use less steel than itwas to use an I-beam. That’s the argument onthat I would have thought’13.

Another advantage of casting was that itintroduced an element of hand crafting into thesteelwork. This was something of apreoccupation of Peter Rice, the principalstructural engineer on the project who, insomething of the tradition of the much earlierBritish Arts and Crafts Movement, believed thatmuch of the inhumanity of Modern architecturestemmed from the fact that it was composedentirely of machine-made components.

There were therefore several agendasinvolved, most of them concerned with visualrather than structural considerations, and

there is no doubt that the presence of theseunusual components on the exterior of thebuilding contributes greatly to its aestheticsuccess. Thus, the ingenious solution of anunnecessarily-created technical problem foundarchitectural expression. This is the essence ofthis version of structure as ornament. Its greatestexponent has perhaps been the Spanisharchitect/engineer Santiago Calatrava.

A third kind of architecture which involvesstructure of questionable technical validityoccurs in the context of a visual agenda that isincompatible with structural requirements. TheLloyds headquarters building (Fig. 7.9) in 83

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13 Interview with the author, February 2000.

Fig. 7.9 Lloyds headquarters building, London, UK, 1986;Richard Rogers and Partners, architects; Ove Arup &Partners, structural engineers. The building has arectangular plan and six projecting service towers.

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London, by the same designers who producedthe Centre Pompidou (Richard Rogers andPartners as architects and Ove Arup andPartners as structural engineers), is a goodexample of this.

Lloyds is a multi-storey office building witha rectangular plan (Fig. 7.10). The building hasa central atrium through most levels, whichconverts the floor plan into a rectangulardoughnut, and, as at the Centre Pompidou,services which are external to the building’senvelope. At Lloyds these are placed in aseries of towers which disguise therectilinearity of the building. There are alsoexternal ducts which grip the building like thetentacles of an octopus (Fig. 7.11). Thestructural armature is a reinforced concretebeam-and-column framework which supportsthe rectangular core of the building. This formsa prominent element of the visual vocabularybut is problematic technically.

The columns are located outside theperimeter of the floor structures which theysupport and this has the effect of increasingthe eccentricity with which load is applied tothe columns – a highly undesirableconsequence structurally. This solution wasadopted to make the structure ‘readable’ (acontinuing concern of Richard Rogers) byarticulating the different parts as separateidentifiable elements. It resulted in the floors

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Fig. 7.10 Plan, Lloyds headquartersbuilding, London, UK, 1986; RichardRogers and Partners, architects; Ove Arup& Partners, structural engineers. Thebuilding has a rectangular plan with acentral atrium. The structure is areinforced concrete beam-column framecarrying a one-way-spanning floor.

Fig. 7.11 Lloyds headquarters building, London, UK,1986; Richard Rogers and Partners, architects; Ove Arup &Partners, structural engineers. The service towers whichproject from the rectangular plan are one of the mostdistinctive features of the building.

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being connected to the columns throughelaborate pre-cast concrete brackets (Fig. 7.12).In this respect the Lloyds building is similar tothe Centre Pompidou. An architectural idea,‘readability’, created a problem which requireda structural response. The pre-cast columnjunctions were less spectacular than thegerberettes of the Centre Pompidou, but hadan equivalent function, both technically andvisually.

There are, however, important differencesbetween Pompidou and Lloyds which placethem in slightly different categories so far asthe relationship between structure andarchitecture is concerned. At Lloyds, the logicof readability was abandoned in the treatmentof the underside of the exposed reinforcedconcrete floors. These take the shape of arectangular doughnut in plan due to thepresence of the central atrium. Structurally,they consist of primary beams, spanningbetween columns at the perimeter and withinthe atrium, which support a ribbed one-way-spanning floor system. For purely visualreasons the presence of the primary beamswas suppressed and they were concealed bythe square grid of the floor structure. Theimpression thus given is that the floors are atwo-way-spanning system supported directlyon the columns without primary beams. Greatingenuity was required on the part of thestructural engineering team to produce astructure which had a satisfactory technicalperformance while at the same time appearingto be that which it was not.

This task was not made easier by anothervisual requirement, namely that the ribs of thefloor structure should appear to be parallel-sided rather than tapered. A small amount oftaper was in fact essential to allow theformwork to be extracted, but to make the ribsappear to be parallel-sided the taper wasupwards rather than downwards. This meantthat the formwork had to be taken out fromabove which eliminated the possibility ofcontinuity between the ribs and the floor slabwhich they support. The benefits of compositeaction between the ribs and the floor slab,which normally greatly increases the efficiency

of reinforced concrete floors, were thusforegone. The design of this structure wastherefore driven almost entirely by visualconsiderations and a heavy penalty was paid interms of structural efficiency. 85

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Fig. 7.12 Atrium, Lloyds headquarters building, London,UK, 1986; Richard Rogers and Partners, architects; OveArup & Partners, structural engineers. The columns are setoutside the perimeter of the floor decks and connected tothem through visually prominent pre-cast concretebrackets. The arrangement allows the structure to be easily‘read’ but is far from ideal structurally. It introducesbending into the columns, which causes highconcentrations of stress at the junctions.

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The conclusion which may be drawn fromthe above examples of structure as ornament isthat in many buildings with exposed structuresthe structure is technically flawed despiteappearing visually interesting. This does notmean that the architects and engineers whodesigned these buildings were incompetent orthat the buildings themselves are examples ofbad architecture. It does mean, however, thatin much architecture in which exposedstructure is used to convey the idea oftechnical excellence (most of High-Techarchitecture falls into this category), the formsand visual devices which have been employedare not themselves examples of technologywhich is appropriate to the function involved.It will remain to be seen whether thesebuildings stand the test of time, eitherphysically or intellectually: the ultimate fate ofmany of them, despite their enjoyablequalities, may be that of the discarded toy.

7.2.3 Structure as architecture

7.2.3.1 IntroductionThere have always been buildings whichconsisted of structure and only structure. Theigloo and the tepee (see Figs 1.2 and 1.3) areexamples and such buildings have, of course,existed throughout history and much of humanpre-history. In the world of architectural historyand criticism they are considered to be‘vernacular’ rather than ‘architecture’.Occasionally, they have found their way intothe architectural discourse and where this hasoccurred it has often been due to the very largescale of the particular example. Examples arethe Crystal Palace (Fig. 7.25) in the nineteenthcentury and the CNIT building (see Fig. 1.4) inthe twentieth. These were buildings in whichthe limits of what was technically feasible wereapproached and in which no compromise withstructural requirements was possible. This is athird type of relationship between structureand architecture which might be referred to asstructure without ornament, but perhaps evenmore accurately as structure as architecture.

The limits of what is possible structurallyare reached in the obvious cases of very long

spans and tall buildings. Other cases are thosein which extreme lightness is desirable, forexample because the building is required to beportable, or where some other technical issueis so important that it dictates the designprogramme.

7.2.3.2 The very long spanIt is necessary to begin a discussion on long-span structures by asking the question: whenis a span a long span? The answer offered herewill be: when, as a consequence of the size ofthe span, technical considerations are placedso high on the list of architectural prioritiesthat they significantly affect the aesthetictreatment of the building. As has already beendiscussed in Chapter 6, the technical problemposed by the long span is that of maintaining areasonable balance between the load carriedand the self-weight of the structure. The formsof longest-span structures are therefore thoseof the most efficient structure types, namelythe form-active types such as the compressivevault and the tensile membrane, and the non-or semi-form-active types into whichsignificant ‘improvements’ have beenincorporated.

In the pre-industrial age the structural formwhich was used for the widest spans was themasonry vault or the dome. The only otherstructural material available in the pre-industrial age was timber. Due to the smallsize of individual timbers, any large woodenstructure involved the joining together of manyelements, and making joints in timber whichhad satisfactory structural performance wasdifficult. In the absence of a satisfactoryjointing technology, large-scale structures intimber were not feasible in the pre-Modernworld. Also, the understanding of how toproduce efficient fully-triangulated trusses didnot occur until the nineteenth century.

The development of reinforced concrete inthe late nineteenth century allowed theextension of the maximum span which waspossible with the compressive form-active typeof structure. Reinforced concrete has a numberof advantages over masonry, the principal onebeing its capability to resist tension as well as

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compression and its consequent ability toresist bending. The vault and the dome are, ofcourse, compressive form-active structures, butthis does not mean that they are neversubjected to bending moment because theform-active shape is only valid for a specificload pattern. Structures which supportbuildings are subjected to variations in theload pattern, with the result that compressiveform-active structures will in somecircumstances become semi-form-active andbe required to resist bending. If the structuralmaterial has little tensile strength, as is thecase with masonry, its cross-section must besufficiently thick to prevent the tensile bendingstress from exceeding the compressive axialstress which is also present. Masonry vaultsand domes must therefore be fairly thick andthis compromises their efficiency. Anadditional complication with the use of thedome is that tensile stresses can develop inthe circumferential direction near the base ofthe structure with the result that cracksdevelop. Most masonry domes are in factreinforced to a limited extent with metal –usually in the form of iron bars – to counteractthis tendency.

Because reinforced concrete can resist bothtensile and bending stress, compressive form-active structures in this material can be madevery much thinner than those in masonry. Thisallows greater efficiency, and therefore greaterspans, to be achieved because the principalload on a dome or vault is the weight of thestructure itself.

Another advantage of reinforced concrete isthat it makes easier the adoption of ‘improved’cross-sections. This technique has been usedwith masonry domes, however, the twin skinsof Brunelleschi’s dome for Florence Cathedral(Fig. 7.13)14 being an example, but the

mouldability of reinforced concrete greatlyextended this potential for increasing theefficiency with which a dome or vault can resistbending moment caused by semi-form-activeload patterns.

Among the earliest examples of the use ofreinforced concrete for vaulting on a largescale are the airship hangars for Orly Airport in 87

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14 The twin skin arrangement may not have been adoptedfor structural reasons. An interesting speculation iswhether Brunelleschi, who was a brilliant technologist,may have had an intuitive understanding of theimproved structural performance which results from atwo-skin arrangement.

Fig. 7.13 Dome of the cathedral, Florence, Italy, 1420–36;Brunelleschi. The dome of the cathedral at Florence is asemi-form-active structure. The brickwork masonryenvelope has an ‘improved’ cross-section and consists ofinner and outer skins linked by diaphragms. An ingeniouspattern of brickwork bonding was adopted to ensuresatisfactory composite action. Given the span involved,and certain other constraints such as that the dome had tosit on an octagonal drum, it is difficult to imagine anyother form which would have been feasible structurally.This memorable work of architecture is therefore anexample of genuine ‘high tech’. The overall form wasdetermined from structural considerations and notcompromised for visual effect. (Drawing: R. J. Mainstone)

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Paris by Eugène Freyssinet (Fig. 7.14). Acorrugated cross-section was used in thesebuildings to improve the bending resistance ofthe vaults. Other masters of this type of

structure in the twentieth century were PierLuigi Nervi, Eduardo Torroja and FélixCandela. Nervi’s structures (Fig. 7.15) areespecially interesting because he developed asystem of construction which involved the useof pre-cast permanent formwork in ferro-cement, a type of concrete made from very fineaggregate and which could be moulded intoextremely slender and delicate shapes. Theelimination of much of the temporaryformwork and the ease with which the ferro-cement could be moulded into ‘improved’cross-sections of complex geometry, allowedlong-span structures of great sophistication tobe built relatively economically. The finaldome or vault consisted of a compositestructure of in-situ concrete and ferro-cementformwork.

Other notable examples of twentieth-century compressive form-active structures arethe CNIT building in Paris by Nicolas Esquillan(see Fig. 1.4) and the roof of the SmithfieldPoultry Market in London by R. S. Jenkins ofOve Arup and Partners (Fig. 7.16).

Compressive form-active structures are alsoproduced in metal, usually in the form oflattice arches or vaults, to achieve very longspans. Some of the most spectacular of theseare also among the earliest, the train shed atSt Pancras Station in London (1868) byWilliam Barlow and R. M. Ordish (span 73 m)(Fig. 7.51) and the structure of the Galerie desMachines for the Paris Exhibition of 1889, byContamin and Dutert (span 114 m) beingnotable examples. The subject has been wellreviewed by Wilkinson15. This traditioncontinues in the present day and notablerecent examples are the International RailTerminal at Waterloo Station, London, byNicholas Grimshaw & Partners with YRMAnthony Hunt Associates (Fig. 7.17) and thedesign for the Kansai Airport building forOsaka, Japan by Renzo Piano with Ove Arupand Partners.

Cable-network structures are another groupwhose appearance is distinctive because

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Fig. 7.14 Airship Hangars, Orly Airport, France, 1921;Eugène Freyssinet, structural engineer. The skin of thiscompressive form-active vault has a corrugated cross-section which allows efficient resistance to secondarybending moment. The form adopted was fully justifiedgiven the span involved and was almost entirelydetermined from structural considerations.

Fig. 7.15 Palazzetto dello Sport, Rome, Italy, 1960; PierLuigi Nervi, architect/engineer. This is another example ofa building with a form determined solely from structuralrequirements. The compressive form-active dome is acomposite of in situ and pre-cast reinforced concrete andhas an ‘improved’ corrugated cross-section. (Photo: BritishCement Association)

15 Op. cit.

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Fig. 7.16 Smithfield Poultry Market,London, UK; Ove Arup & Partners,structural engineers. The architecture hereis dominated by the semi-form-active shellstructure which forms the roof of thebuilding. Its adoption was justified by thespan of around 60 m. The ellipticalparaboloid shape was selected rather thana fully form-active geometry because itcould be easily described mathematically,which simplified both the design and theconstruction. (Photo: John Maltby Ltd)

Fig. 7.17 International Rail Terminal, Waterloo Station, London, UK, 1992; Nicholas Grimshaw & Partners, architects;YRM Anthony Hunt Associates, structural engineers. This building is part of a continuing tradition of long-span structuresfor railway stations. The design contains a number of innovatory features, most notably the use of tapering steel sub-elements. (Photo: J. Reid and J. Peck)

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technical considerations have been allocated avery high priority, due to the need to achieve along span or a very lightweight structure. Theyare tensile form-active structures in which avery high level of efficiency is achieved. Theirprincipal application has been as the roofstructures for large single-volume buildingssuch as sports arenas. The ice hockey arena atYale by Eero Saarinen (Fig. 7.18) and the cable-network structures of Frei Otto (see Fig. i) aretypical examples.

In these buildings the roof envelope is ananticlastic double-curved surface16: twoopposite curvatures exist at every location. Thesurface is formed by two sets of cables, oneconforming to each of the constituentdirections of curvature, an arrangement whichallows the cables to be pre-stressed against

each other. The opposing directions ofcurvature give the structure the ability totolerate reversals of load (necessary to resistwind loading without gross distortion inshape) and the pre-stressing enablesminimisation of the movement which occursunder variations in load (necessary to preventdamage to the roof cladding).

In the 1990s, a new generation of mast-supported synclastic cable networks wasdeveloped. The principal advantage of theseover the earlier anticlastic forms was that, dueto the greater simplicity of the form, themanufacture of the cladding was made easier.

The Millennium Dome in London (Fig. 7.19),which is not of course a dome in the structuralsense, is perhaps the best known of these. Inthis building a dome-shaped cable network issupported on a ring of 24 masts. The overalldiameter of the building is 358 m but themaximum span is approximately 225 m, whichis the diameter of the ring described by the 24masts. The size of the span makes the use of acomplex form-active structure entirely justified.The cable network to which the cladding isattached consists of a series of radial cables, inpairs, which span 25 m between nodessupported by hanger cables connecting themto the tops of the masts. The nodes are alsoconnected by circumferential cables whichprovide stability. The downward curving radialcables are pre-stressed against the hangercables and this makes them almost straightand converts the surface of the dome into aseries of facetted panels. It is thischaracteristic which simplifies the fabricationof the cladding. In fact, being tensile form-active elements, the radial cables are slightlycurved, and this curvature had to be allowedfor in the design of the cladding, but theoverall geometry is nevertheless considerablyless complex than an anticlastic surface. Thecladding fabric of the Millennium Dome isPTFE-coated glass fibre.

The few examples of cable networksillustrated here demonstrate that, althoughthis type of structure is truly form-active with ashape which is dependent on the pattern ofapplied load, the designer can exert

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16 The terms anticlastic and synclastic describe differentfamilies of curved surface. An anticlastic surface isdescribed by two sets of curves acting in oppositedirections. The canopy of the Olympic stadium atMunich (Fig. i) is an example. Synclastic surfaces arealso doubly curved but with the describing curvesacting in the same direction. The shell roof of theSmithfield Poultry market (Fig. 7.16) is an example ofthis type.

Fig. 7.18 David S. Ingalls ice hockey rink, Yale, USA,1959; Eero Saarinen, architect; Fred Severud, structuralengineer. A combination of compressive form-active archesand a tensile form-active cable network was used in thislong-span building. The architecture is totally dominatedby the structural form.

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considerable influence on the overall formthrough the choice of support conditions andsurface type. The cable network can besupported either on a configuration of semi-form-active arches or on a series of masts; itcan also be either synclastic or anticlastic andthe configurations which are adopted for theseinfluence the overall appearance of thebuilding.

Judged by the criteria outlined in Section6.3, most of the form-active vaulted and cablestructures are not without technicalshortcomings. They are difficult to design andbuild and, due to their low mass, provide poorthermal barriers. In addition, the durability ofthese structures, especially the cable networks,is lower than that of most conventionalbuilding envelopes. Acceptance of thesedeficiencies is justified, however, in theinterests of achieving the high levels ofstructural efficiency required to produce large

spans. In the cases described here thecompromise which has been reached issatisfactory, given the spans involved and theuses for which the buildings were designed.

All of the long-span buildings consideredhere may therefore be regarded as true ‘high-tech’ architecture. They are state-of-the-artexamples of structural technology employed toachieve some of the largest span enclosures inexistence. The technology employed wasnecessary to achieve the spans involved andthe resulting forms have been given minimalstylistic treatment.

7.2.3.3 Very tall buildingsIn the search for the truly high-tech building,which is another way of thinking of thecategory structure as architecture, the skyscraper isworthy of careful consideration. From astructural point of view two problems areposed by the very high building: one is the 91

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Fig. 7.19 Millennium Dome, London, UK, 1999; Richard Rogers and Partners, architects; Buro Happold, structuralengineers. This is mast-supported, dome-shaped cable network with a diameter of 358 m. The use of a tensile form-activestructure is fully justified for structures of this size.

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provision of adequate vertical support and theother is the difficulty of resisting high lateralloading, including the dynamic effect of wind.So far as vertical support is concerned, thestrength required of the columns or walls isgreatest at the base of the building, where theneed for an excessively large volume ofstructure is a potential problem. In the daysbefore the introduction of iron and steel thiswas a genuine difficulty which placed a limiton the possible height of structures. Theproblem was solved by the introduction ofsteel framing. Columns are loaded axially, andso long as the storey height is low enough tomaintain the slenderness ratio17 at areasonably low level and thus inhibit buckling,the strength of the material is such thatexcessive volume of structure does not occurwithin the maximum practical height limitsimposed by other, non-structural constraints.

The need to increase the level of verticalsupport towards the base of a tall building hasrarely been expressed architecturally. In manyskyscrapers the apparent size of the verticalstructure – the columns and walls – is identicalthroughout the entire height of the building.There have, of course, been many technicalinnovations in connection with aspects of thesupport of gravitational load in high buildings.In particular, as was pointed out byBillington18, changes in the relationshipbetween the vertical and horizontal structuralelements have led to the creation of largercolumn-free spaces in the interiors. Theseinnovations have, however, found very limitedarchitectural expression.

The need to accommodate wind loadingas opposed to gravitational loads has had agreater effect on the aesthetics of very tallbuildings. As with vertical support elements,in the majority of skyscrapers the architecthas been able to choose not to express the

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17 See Macdonald, Angus J., Structural Design for Architecture,Architectural Press, Oxford, 1997, Appendix 2, for anexplanation of slenderness ratio.

18 Billington, D. P., The Tower and the Bridge, Basic Books,New York, 1983.

Fig. 7.20 World Trade Centre, New York, USA, 1973;Minoru Yamasaki, architect; Skilling, Helle, Christiansen &Robertson, structural engineers. The closely-spacedcolumns on the exteriors of these buildings are structuraland form a ‘framed-tube’ which provides efficient resistanceto lateral load. In response to lateral load the building actsas a vertical cantilever with a hollow box cross-section. Thisis an example of a structural system, not compromised forvisual reasons, exerting a major influence on theappearance of the building. (Photo: R. J. Mainstone)

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bracing structure so that, although many ofthese buildings are innovative in a structuralsense, this is not visually obvious. The verytallest buildings, however, have beendesigned to behave as single verticalcantilevers with the structure concentratedon the exterior; in these cases theexpression of the structural action wasunavoidable.

The framed- and trussed-tubeconfigurations19 (Figs 7.20 and 7.21) areexamples of structural arrangements whichallow tall buildings to behave as vertical

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19 See Schueller, W., High Rise Building Structures, JohnWiley, London, 1977, for an explanation of bracingsystems for very tall buildings.

Fig. 7.21 John Hancock Building, Chicago,USA, 1969; Skidmore, Owings and Merrill,architects and structural engineers. Thetrussed-tube structure here forms a majorcomponent of the visual vocabulary. (Photo:Chris Smallwood)

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cantilevers in response to wind loads. In bothcases the building is treated as a hollow tube,a non-form-active element with an ‘improved’cross-section, in its resistance to lateralloading. The tube is formed by concentratingthe vertical structure at the perimeter of theplan. The floors span from this to a centralservices core which provides vertical supportbut does not normally contribute to theresistance of wind load.

Such buildings are usually given a squareplan. With the wind blowing parallel to one ofthe faces, the columns on the windward andleeward walls act as tensile and compressionflanges respectively of the cantilever cross-section, while the two remaining external wallsform a shear link between these. In the case ofthe framed tube, of which the World TradeCentre buildings in New York by MinoruYamasaki (Fig. 7.20) are examples, the shear

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Fig. 7.22 Sears Tower,Chicago, USA, 1974;Skidmore, Owings andMerrill, architects andstructural engineers. Thisbuilding, which is currentlythe tallest in the world, issubdivided internally by acruciform arrangement of‘walls’ of closely spacedcolumns which enhance itsresistance to wind loading.This structural layout isexpressed in the exteriorform.

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connection is provided by rigid frame actionbetween the columns and the very short beamswhich link them. In trussed-tube structures,such as the John Hancock Building in Chicagoby Skidmore, Owings and Merrill (Fig. 7.21),the shear connection is provided by diagonalbracing elements. Because in each of thesecases the special structural configurationwhich was adopted to provide resistance tolateral load resulted in the structure beingconcentrated in the outer walls of the building,the structure contributed significantly to, andindeed determined, the visual expression ofthe architecture. Hal Iyengar, chief structuralengineer in the Chicago office of Skidmore,Owings and Merrill described the relationshipthus:

‘... the characteristics of the project createa unique structure and then the architectcapitalises on it. That’s exactly whathappened in the Hancock building.’20

A development of the cantilever tube idea isthe so-called ‘bundled-tube’ – a system inwhich the shear connection between thewindward and leeward walls is made byinternal walls as well as those on the sides ofthe building. This results in a square gridarrangement of closely spaced ‘walls’ ofcolumns. The Sears Tower in Chicago, also bySkidmore, Owings and Merrill (Fig. 7.22), hasthis type of structure which is expressedarchitecturally, in this case by varying theheights of each of the compartments createdby the structural grid. The structural system istherefore a significant contributor to theexternal appearance of this building.

Thus, among very high buildings someexamples of structure as architecture may befound. These are truly high tech in the sensethat, because the limits of technicalpossibility have been approached, structuralconsiderations have been given a high priority

in the design – to the extent that theappearance of the building has beensignificantly affected by them.

7.2.3.4 The lightweight buildingThe situation in which saving in weight is anessential requirement is another scenariowhich causes technical considerations to beallocated a very high priority in the design of abuilding. This often comes about when thebuilding is required to be portable. Thebackpacker’s tent – an extreme example of theneed to minimise weight in a portablebuilding – has already been mentioned.Portability requires not only that the buildingbe light but also that it be demountable –another purely technical consideration. Insuch a case the resulting building form isdetermined almost entirely by technicalcriteria.

As has been repeatedly emphasised, themost efficient type of structure is the form-active one and the traditional solution to theproblem of portable buildings is, of course,the tent, which is a tensile form-activestructure. The tent also has the advantage ofbeing easy to demount and collapse into asmall volume, which compressive form-activestructures have not, due to the rigidity whichthey must possess in order to resistcompression. This solution has thereforebeen widely used for temporary or portablebuildings throughout history and is found in avery wide range of situations from theportable houses of nomadic peoples to thetemporary buildings of industrialisedsocieties, whether in the form of tents forrecreation or temporary buildings for otherpurposes. Figure 7.23 shows an example ofstate-of-the-art engineering used for abuilding to house a temporary exhibition –another example of truly high-techarchitecture.

Although the field of temporary buildingsremains dominated by the tent in all its forms,the compressive form-active structure has alsobeen used for such purposes. A late-twentieth-century example was the building designed byRenzo Piano for the travelling exhibition of 95

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20 Conversation with Janice Tuchman reported inThornton, C., Tomasetti, R., Tuchman, J. and Joseph, L.,Exposed Structure in Building Design, McGraw-Hill, NewYork, 1993.

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IBM Europe (Fig. 7.24). This consisted of asemi-form-active vault which was ‘improved’ bytriangulation. The sub-elements werelaminated beechwood struts and ties linked bypolycarbonate pyramids. These elements werebolted together using aluminium connectors.The structure combined lightness of weight,which was achieved through the use of low-density materials and an efficient structuralgeometry, with ease of assembly – the twoessential requirements of a portable building.No technical compromises were made forvisual or stylistic reasons.

7.2.3.5 Special requirementsOther forms of special requirement besides theneed for a lightweight structure can result instructural issues being accorded the highest

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Fig. 7.23 Tent structure for temporary exhibition building, Hyde Park, London, UK; Ove Arup & Partners, structuralengineers. Lightweight, portable buildings may be considered as examples of genuine ‘high-tech’ architecture in any agebecause the forms adopted are determined almost entirely from structural and constructional considerations.

Fig. 7.24 Building for IBM Europe travelling exhibition;Renzo Piano, architect/engineer; Ove Arup & Partners,structural engineers. This building consists of a semi-form-active compressive vault. The ‘improved’ cross-section ofthe membrane is achieved with a highly sophisticatedcombination of laminated timber and plastic – each is amaterial which offers high strength for its weight. Technicalconsiderations reign supreme here to produce a portable,lightweight building.

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priority in the design of a building to the pointat which they exert a dominating influence onits form. A classic example of this from thenineteenth century was the Crystal Palace inLondon (Fig. 7.25) which was built to housethe Great Exhibition of 1851.

The problem which Joseph Paxton, thedesigner of the Crystal Palace, was required tosolve was that of producing a building whichcould be manufactured and erected veryquickly (nine months elapsed between theoriginal sketch design and the completion ofthe building) and which could subsequentlybe dismantled and re-erected elsewhere.Given the immense size of the building,comparable with that of a Gothic cathedral,the technical problem was indeed formidable.Paxton’s solution was to build a glasshouse –a glass envelope supported by an exposedstructure of iron and timber. It is difficult to

imagine any other contemporary structuralsolution which could have met the designrequirements. Possibly a series of very largetents would have sufficed – there was inexistence at the time a fairly large canvas- andrope-making capability associated withshipbuilding and a tradition of large tentmanufacture. Tents would not, however, haveprovided the lofty interior which was desirableto display adequately the latest products ofindustry. The Crystal Palace not only solvedthe problem of the large and lofty enclosure; itwas itself a demonstration of the capabilitiesof the latest industrial processes andtechniques of mass production.

The technology used for the building wasdeveloped by the builders of glasshouses forhorticulture, of whom Paxton was perhaps themost innovative. It contained much that theenthusiast of structural engineering and 97

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Fig. 7.25 Crystal Palace, London, UK, 1851; Joseph Paxton, architect/engineer. The Crystal Palace was a truly high-techbuilding and an inspiration to generations of modern architects. Unlike many twentieth-century buildings to which thelabel High Tech has been applied, it was at the forefront of what was technically possible at the time. The major decisionsaffecting the form of the building were taken for technical reasons and were not compromised for visual or stylistic effect.The building has technical shortcomings, such as the poor durability of the many joints in the external skin, but in thecontext of a temporary building it was appropriate that these were given a low priority.

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industrial technology could enjoy. The post-and-beam structure was appropriate for thespans and loads involved. Form-active archeswere used as the horizontal elements in thepost-and-beam format to span the largecentral ‘nave’ and ‘transepts’, and non-form-active, straight girders with triangulated‘improved’ profiles formed the shorter spans ofthe flanking ‘aisles’. The glazing conformed toa ridge-and-furrow arrangement, which wasdesigned originally in connection withhorticultural glasshouses to improve thedaylight-penetration characteristics – itprovided some shade during the hours aroundmid-day when the sun was high in the sky butadmitted more light in the early morning andlate evening. Although this characteristic wasnot particularly important in the case of theCrystal Palace, the arrangement enhanced thestructural performance by giving the glasscladding a structurally ‘improved’, corrugatedcross-section. Many other examples of goodtechnology were features of the building – oneof which was that the secondary beamssupporting the glazing served also as rainwaterguttering to conduct the run-off to the columnswhose circular hollow cross-sections, as wellas having ideal structural shapes forcompression elements, allowed them to

function as drain pipes. Another example wasthat much of the structure was discontinuousand this, through the elimination of the ‘lack-of-fit’ problem (see Appendix 3), together withthe very large degree of component repetition,facilitated both the rapid manufacture of theelements by mass-production techniques andthe very fast assembly of the building on site.

The building was therefore at the forefrontof contemporary technology – a genuineexample of a high-tech building – and wasideally suited to its purpose, which was tohouse a temporary exhibition. The technicalshortcomings of the arrangement – the lack ofthermal insulation, the susceptibility to leaksat the many joints in the cladding and thequestionable long-term durability of thestructure and of the cladding joints – were notsignificant in this context, as they would havebeen in a permanent building.

Many twentieth-century Modern architectshave been inspired by the glass-clad frameworkof the Crystal Palace. As was the case with thelater examples of ‘technology transfer’ alreadymentioned, although with some notableexceptions such as the Patera Buildingdescribed below, it was the imagery ratherthan the technical reality which was attractiveto them.

Structure and Architecture

Fig. 7.26 Patera Building;Michael Hopkins, architect;Anthony Hunt Associates,structural engineers. Thebuilding consists of alightweight steel frameworkwhich supports an insulatedcladding system and fullyglazed end walls. Theprincipal structuralelements are external andthe purlins and claddingrails are located within thecladding zone to give a veryclean interior. (Photo:Anthony Hunt Associates)

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The Patera Building, by Michael Hopkinswith Tony Hunt as structural engineer (Fig7.26) has been directly compared to theCrystal Palace because its design was alsobased on the principle of pre-fabrication. Theproject was an attempt to address theproblem of the poor architectural quality ofmost industrial estates by producing abuilding system which would be economic,flexible and stylish and linking this to adevelopment company which would act as theco-ordinator of industrial estates. Thedevelopment company would acquire land,design a layout of building plots and installinfrastructure. Individual tenant clients wouldthen have buildings tailor-made to theirrequirements within a consistent style offeredby a building system. The buildings would, ineffect, be industrial apartments capable ofbeing adapted to different client requirementsand offered for rent for varying lengths oftenure to suit clients’ needs.

The principal hardware element in theconcept was a basic building shell which couldbe erected and fitted out quickly to meet theneeds of an individual tenant and then easilyadapted to suit the requirements ofsubsequent tenants. It was envisaged that thescale of the operation would allow thebuilding to be treated as an industrialproduct; it would be developed and tested inprototype form and subsequentlymanufactured in sufficient numbers to coverits development costs.

It was envisaged that the erection of thebuilding would occur in three phases. The first ofthese was the laying of a rectangular foundationand ground-floor slab in which services would beincorporated. This was the interface between thesuperstructure and the site and rendered thebuilding non-site-specific. The building could bebuilt anywhere that this standard rectangularslab could be laid. The second stage was theerection of the superstructure, a shell ofcladding, incorporating trunking for electricaland telephone services, supported on a steelframework. The third stage was the subdivisionand fitting out of the interior to meet specificclient requirements.

The structure of the building consisted of aseries of triangulated portal frameworks whichspanned 13.2 m across the building, linked byrectangular-hollow-section purlins andcladding rails spaced 1.2 m apart and spanning3.6 m between the main frames. The mainframeworks were ingeniously designed to meetexacting performance requirements whichcalled for a structure that would be of stylishappearance with, for ease of containerisation,no element longer than 6.75 m and, for ease ofconstruction, no element heavier than couldbe lifted by a fork-lift truck (Fig. 7.27). To meet 99

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Fig. 7.27 Patera Building; Michael Hopkins, architect;Anthony Hunt Associates, structural engineers. Technicalconsiderations, such as the need for containerisation andfor simple assembly with a fork-lift truck exerted a majorinfluence on the design. (Photo: Anthony Hunt Associates)

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these requirements a hybrid 2-hinge/3-hingeportal framework was chosen. The inherentefficiency of the semi-form-active arrangement,together with the full triangulation of theelements and the relatively small ratio of spanto depth that was adopted, allowed very

slender circular-hollow-section sub-elementsto be used. Each portal consisted of twohorizontal and two vertical sub-units whichwere pre-fabricated by welding. Cast-steeljointing components allowed the use of veryprecise pin-type site connections and these

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Fig. 7.28 PateraBuilding; MichaelHopkins, architect;Anthony HuntAssociates, structuralengineers. The ingenioususe of pin connectionsand cast nodes allowed afully rigid joint to bemade between theprincipal elements whichcould be easilyassembled. (Photo:Anthony HuntAssociates)

Fig. 7.29 PateraBuilding. The mid-spanjoint in the primarystructure has a three-hinge tension-only link.Under gravitational loadthe latter collapses andthe joint as a wholebehaves as a hinge.Under wind uplift thetension-only link comesinto play and theconnection becomesrigid. The devicemaintains the laterally-restrained lower boomsof the structure incompression under allconditions of load.(Photo: Anthony HuntAssociates)

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were cleverly arranged at the junction betweenthe horizontal and vertical elements to providea rigid connection there (Fig. 7.28).

The hybrid 2-hinge/3-hinge arrangementwas adopted to eliminate the need foradditional lateral bracing of the compressionside of the structure by ensuring that theinner booms of the main elements, whichwere restrained laterally by the cladding,remained in compression under all conditionsof loading. The key to this behaviour was aningenious 3-pin tension-only link between thetop elements of the portal at the central joint(Fig. 7.29). Under gravitational load, this wassubjected to compression and collapsed toproduce a hinge joint between the mainelements at the mid-span position whichensured that compression was concentratedin the inner booms of the frame. If loadreversal occurred due to wind uplift, reversalof stress within the structure did not occurbecause the tension-only link now becamepart of the structure and converted the mainframe to a 2-hinge arrangement due to themid-span joint between the horizontalelements becoming rigid. This meant that thelaterally-restrained inner boom remained incompression and that most of the outer boomcontinued to be subjected only to tension.The need for lateral restraint for the outerbooms was therefore eliminated under allconditions of load.

The Patera building is therefore an exampleof architecture resulting from a skilful technicalsolution to a set of very particularrequirements. In this respect it is similar to theCrystal Palace.

7.2.3.6 ConclusionIn most of the cases described in this sectionthe buildings have consisted of little otherthan a structure, the form of which wasdetermined by purely technical criteria. Theinherent architectural delight thereforeconsisted of an appreciation of ‘pure’ structuralform. These truly high-tech structure types,especially the long-span, form-activestructures, are considered by many to bebeautiful, highly satisfying built forms.

Billington21 goes so far as to argue that theymay be considered to be examples of an artform and this issue has been discussed morerecently by Holgate22. It is questionable,however, although it may not be important,whether a shape which has been evolved frompurely technical considerations can beconsidered to be a work of art, howeverbeautiful it may appear to those with thetechnical knowledge to appreciate it.

7.2.4 Structure as form generator/structureacceptedThe terms structure as form generator and structureaccepted are used here to describe a relationshipbetween structure and architecture in whichstructural requirements are allowed toinfluence strongly the forms of buildings eventhough the structure itself is not necessarilyexposed. In this type of relationship theconfiguration of elements which is mostsensible structurally is accepted and thearchitecture accommodated to it. The reasonwhy two cases are distinguished is that thecloseness of the link between the architecturaland the structural agendas is subject toconsiderable variation. Sometimes it is verypositive, with the form-generating possibilitiesof structure being used to contribute to anarchitectural style. Alternatively, even thoughthe overall form of a building may have beendetermined largely to satisfy structuralrequirements, the architectural interest may lieelsewhere.

The vaulted structures of Roman antiquityare an example of the first of thesepossibilities. The large interior spaces of thebasilicas and bath houses of Imperial Rome,which are one of the chief glories of thearchitecture of the period and which areamong the largest interiors in Westernarchitecture, were roofed by vaults and domes

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21 Billington, D. P., Robert Maillart, MIT Press, Cambridge,MA, 1989.

22 See Holgate, A., The Art in Structural Design, ClarendonPress, Oxford, 1986 and Holgate, A., Aesthetics of BuiltForm, Oxford University Press, Oxford, 1992.

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Structure and Architecture

Fig. 7.30 ThePantheon, Rome,2nd century AD.The hemisphericalconcrete dome issupported on acylindrical drumalso of concrete.Both have thickcross-sectionswhich have been‘improved’ by theuse of coffers orvoids of varioustypes and thesetechnical deviceshave beenincorporated intothe visual schemeof the interior.

Fig. 7.31 The Basilica ofConstantine, Rome, 4thcentury AD. The vaultedroof of the principalinternal volume issupported on very thickwalls from which largevoids with vaulted ceilingshave been extracted toreduce the volume ofstructural materialrequired. These have beenused to create variety inthe disposition of internalvolumes. As at thePantheon the technical andvisual programmes of thearchitecture have beenbrilliantly combined.

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of masonry or unreinforced concrete (Figs 7.30to 7.32). The absence at the period of a strongstructural material which could withstandtension dictated that compressive form-activestructures be adopted to achieve the largespans involved. Lofty interiors of impressivegrandeur were created by placing the vaultsand domes on top of high walls which weregiven great thickness so as to accommodatethe lateral thrusts produced at the wall-heads.

The Roman architects and engineers quicklyappreciated that the walls did not have to besolid and a system of voided walls was developedwhich allowed a large overall thickness to beachieved using a minimum volume of material.The coffering on the undersides of vaults anddomes was a similar device for reducing thevolume and therefore weight of material involved.The walls of the main spaces in these vaultedstructures are semi-form-active elements with‘improved’ cross-sections. They carry axial loaddue to the weights of the vaults which theysupport and bending moments caused by thelateral thrusts of the vaults.

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Fig. 7.32 Construction system of Roman vault. Thelargest interiors in Rome were constructed in unreinforcedconcrete which was placed in a thin skin of brickworkwhich acted as permanent formwork. The structuralarmature was then faced in marble to create a sumptuousinterior. Although structural requirements dictated theoverall form of the building, no part of the structure wasvisible.

(a)

(b)

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Both the voiding of the walls and thecoffering of the vaults were used by thearchitects of Imperial Rome to create adistinctive architecture of the interior. ThePantheon in Rome (Fig. 7.30) is one of thebest examples. In this building the pattern ofthe coffering on the underside of the domehelps to increase the apparent size of theinterior and the voids and recesses in thewalls of the drum which supports the domecreate an illusion of the walls dissolving sothat the dome appears to float above theground.

Such techniques were further developed inthe designs for bath houses and basilicas(Fig. 7.31). Interiors were created in whichthe possibilities offered by the structuralsystem were fully exploited to producespaces of great interest and variety. Thedevice of the transverse groined vault wasalso used in these buildings – againprincipally for a technical, though notstructural, reason. This was adopted in orderto create flat areas of wall at high level whichcould be pierced by clerestory windowsadmitting light into what would otherwisehave been dark interiors.

The vaulted structures of Imperial Romeare therefore buildings in which featureswhich were necessary for structural reasonswere incorporated into the aestheticprogramme of the architecture. This was notcelebration of technology but rather theimaginative exploitation of technicalnecessity.

Many twentieth-century architectsattempted to produce a modern architecture inwhich the same principles were followed. Oneof the most enthusiastic exponents of theacceptance of structure as a generator of formwas Le Corbusier, and the structuraltechnology which he favoured was that of thenon-form-active reinforced concrete flat slab,capable of spanning simultaneously in twodirections and of cantilevering beyondperimeter columns. The structural action waswell expressed in his famous drawing (Fig.7.33) and the architectural opportunities whichit made possible were summarised by Le

Corbusier in his ‘five points of a newarchitecture’23.

This approach was used by Le Corbusier inthe design of most of his buildings. Thearchetype is perhaps the Villa Savoye (Fig.7.34), a building of prime importance in thedevelopment of the visual vocabulary oftwentieth-century Modernism. As in Romanantiquity, the structure here is not so muchcelebrated as accepted and its associatedopportunities exploited. Later buildings by LeCorbusier, such as the Unité d’Habitation atMarseilles or the monastery of La Tourettenear Lyon, show a similar combination ofstructural and aesthetic programmes.

The ‘Modernistic’ (as opposed to Modern –see Huxtable24) skyscrapers which wereconstructed in the 1920s and 1930s in the USA,such as the Chrysler (Fig. 7.35) and EmpireState buildings, are further examples of theadoption but not expression of a newstructural technology – in this case that of themulti-storey steel frame. Although thearchitectural treatment of these buildings was

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23 Le Corbusier, Five Points Towards a New Architecture, Paris,1926.

24 Huxtable, A. L., The Tall Building Reconsidered: The Search fora Skyscraper Style, Pantheon Books, New York, 1984.

Fig. 7.33 The advantages of the structural continuityafforded by reinforced concrete are admirably summarisedin the structural armature of Le Corbusier’s Domino Houseof 1914. Thin two-way spanning slabs are supporteddirectly on a grid of columns. The stairs provide bracing inthe two principal directions.

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more conventional than those by Le Corbusier,making use of a pre-existing architecturalvocabulary, they were nevertheless novel formswhich owed their originality to the structuraltechnology upon which they depended.

Another example of an early-twentieth-century building in which an innovativestructure was employed, although notexpressed in an overt way, was the Highpoint 1building in London by Berthold Lubetkin andOve Arup (Fig. 7.36). Here the structure was a‘continuous’, post-and-beam arrangement ofreinforced concrete walls and slabs. There wereno beams and few columns and therein lay oneof its innovatory aspects. The system offeredgreat planning freedom: where openings wererequired, the walls above acted as beams. Thelevel of structural efficiency was modest butwas entirely appropriate for the spansinvolved, and other aspects of the structure,such as its durability, were also highlysatisfactory. The method of construction wasalso original. The structure was cast on site ona reusable, moveable system of woodenformwork – also designed by Arup – and thebuilding represented, therefore, an harmoniousfusion of new architectural ideas withstructural and constructional innovations. Thearchitectural language used was discreet,however, and made no grand statement ofthese innovative technical features.

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Fig. 7.35 ChryslerBuilding, New York,USA, 1930; William VanAllen, architect.Although the overallforms of Modernisticskyscrapers such as theChrysler Building aredetermined by the steelframe structure thevisual treatment is not.(Photo: Petra Hodgson)

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Fig. 7.34 Villa Savoye,Poissy, France, 1931;architect, Le Corbusier.The reinforced concretestructural armature ofthis building has, to alarge extent, determinedits overall form. Manyother factors connectedto Le Corbusier’s searchfor a visual vocabularyappropriate to the‘machine age’contributed to the finalappearance of thebuilding, however.(Photo: Andrew Gilmour)

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Fig. 7.36 Highpoint 1, London, UK, 1938; Berthold Lubetkin, architect; Ove Arup, structural engineer. The structure ofthis building is of reinforced concrete which lends itself to a rectilinear form. The visual treatment was as muchinfluenced by stylistic ideas of what was visually appropriate for a modern architecture as it was by technical factorsconnected with the structure. (Photo: A. F. Kersting)

(a) (b)

Fig. 7.37 Willis, Faber and Dumas Office, Ipswich, UK, 1974; Foster Associates, architects; Anthony Hunt Associates,structural engineers. This building may be considered to be a late Modern equivalent of the Villa Savoye (Fig. 7.34).The relationship between structure, space planning and visual treatment is similar in both buildings. (Photo: JohnDonat)

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A late-twentieth-century example of thepositive acceptance rather than the expressionof structural technology is found in the Willis,Faber and Dumas building in Ipswich, UK byFoster Associates (Fig. 7.37) with the structuralengineer Tony Hunt. The structure is of thesame basic type as that in Le Corbusier’sdrawing (Fig. 7.33) and its capabilities werefully exploited in the creation of the curvilinearplan, the provision of large wall-free spaces inthe interior and the cantilevering of the floorslabs beyond the perimeter columns. Thebuilding has a roof garden and free non-structural treatment of both elevation and planand it therefore conforms to the requirementsof Le Corbusier’s ‘five points’.

Another example by Foster and Hunt is thepilot head office for IBM UK at Cosham (Fig.7.38). This was intended to serve as atemporary UK main office for the IBM companyand was located on a site adjacent to one onwhich a permanent headquarters building forIBM UK was already under construction. Whenthe design was commissioned, IBM, incommon with many rapidly-expanding

companies at the time, was making significantuse of clusters of timber-framed portablebuildings and envisaged that this type ofaccommodation would be the most suitablefor the temporary head office. FosterAssociates were instructed to report on themost suitable of the proprietary systems thenavailable and to advise on the disposition ofthe buildings on the site. This possibility wasindeed considered, but the solution whichFoster recommended was that of a custom-designed building based on lightweightindustrialised components, and it was thisscheme that was finally executed.

Due to the need to compete with theportable building alternative on cost andspeed of erection, and due to the fact that theground conditions were poor because the sitewas a former land-fill rubbish tip, technicalconsiderations exerted a major influence onthe design. The design of the structure wasparticularly crucial to the success of theproject. Tony Hunt considered using long piles(40 ft) to reach firm strata, but this would havemeant reducing the number of separate

Structure and architecture

Fig. 7.38 IBM pilothead office, Cosham,UK, 1973; FosterAssociates, architects;Anthony HuntAssociates, structuralengineers. Intended astemporaryaccommodation, Fosterand Hunt provided astylish building for thesame cost and withinthe same time-scale asthose of a cluster oftemporary buildings,which is what the clientoriginally envisaged.The form adopted wasto a large extentdictated by structuralrequirements. (Photo:Anthony HuntAssociates)

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foundations to a minimum and the resultinglong-span structure would have been slow toerect and expensive to produce. The alternativewas to use a short-span structure inconjunction with a rigid raft foundation thatwould ‘float’ on the low-bearing-capacitysubstrata. A number of such systems wereconsidered. The favoured system wasconfigured with lightweight triangulatedgirders which created a combined structureand services zone at roof level which wascrucial to the provision of the requiredflexibility in the use of space (Fig. 7.39).

The IBM pilot head office was remarkablysuccessful in almost every respect. It providedthe client with a distinctive, stylish buildingwhich was enjoyable in use for all grades ofemployee, and which was undoubtedly apreferable solution to the client’s requirementsthan the assemblage of proprietary portablebuildings that they had originally envisaged. Ameasure of the success of the building wasthat, although it had been intended astemporary accommodation to last for a periodof three to four years, it was retained by thecompany, following the completion of the

permanent head office, and converted for useas an independent research unit.

The choice of the lightweight steelworksystem was crucial to the success of the IBMbuilding. It was a straightforward assemblageof proprietary Metsec components. This wasboth inexpensive and allowed the structure tobe rapidly erected on site using no plant largerthan a fork-lift truck. The resulting speed andeconomy was what made the buildingcompetitive with the alternatives. The structuredoes not form a significant visual element asmost of it is concealed behind finishingelements. It did, however, exert a majorinfluence on the final form of the building. Thisis therefore structure as form generator rather thanstructure as architecture.

The architectural interest in the IBMbuilding lies in the stylish way in which thevarious components, particularly the finishingcomponents such as the glass external wall,were detailed. Thus, although the need toproduce a light and economical structurewhich could be erected very quickly played asignificant role in determining the overall formof the building, the relationship between

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Fig. 7.39 IBM pilothead office, Cosham,UK, 1973; FosterAssociates, architects;Anthony HuntAssociates, structuralengineers. The structurewas a steel frameworkwith lightweighttriangulated beamelements. These createda combined structuraland services zone, atroof level which wasessential to achieve therequired flexibility inthe use of the interior.(Photo: Anthony HuntAssociates)

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structure and architecture is here much lessdeterministic than was the case with thevaulted buildings of Roman antiquity or theWillis, Faber and Dumas building, where thefinal form was expressive of the behaviour ofthe constituent structural materials.

In the IBM pilot head office building, therelationship between structure andarchitecture is less direct than in the otherbuildings described in this section and isperhaps significantly different to warrant adifferent terminology, namely structure accepted.In this kind of relationship, a form is adoptedwhich is sensible structurally but thearchitectural interest is not closely related tostructural function. This is a relationshipbetween structure and architecture which iscommonly found in contemporary architectureand innumerable other examples could becited. It has, in fact, been the dominantrelationship between structure andarchitecture since the time of the ItalianRenaissance (see Section 7.3).

7.2.5 Structure ignored in the form-makingprocess and not forming part of theaesthetic programmeSince the development of the structuraltechnologies of steel and reinforced concrete ithas been possible to design buildings, at leastto a preliminary stage of the process, withoutconsidering how they will be supported orconstructed. This is possible because thestrength properties of steel and reinforcedconcrete are such that practically any form canbe built, provided that it is not too large andthat finance is not a limiting consideration.This freedom represents a significant and oftenunacknowledged contribution which structuraltechnology has made to architecture, liberatingarchitects from the constraints imposed by theneed to support buildings with masonry andtimber.

For most of the period following theintroduction of steel and reinforced concreteinto building in the late nineteenth century, thedominant architecture in the industrialisedworld was that of International Modernism. Mostof the architects of this movement subscribed to

the doctrine of rationalism and held the viewthat buildings should be tectonic, i.e. theybelieved that the visual vocabulary shouldemerge from, or at least be directly related to,the structural armature of the building, whichshould be determined by rational means. Theconsequence of this was that the forms of mostbuildings were relatively straightforward from astructural point of view – based on the geometryof the post-and-beam framework.

An additional factor which favoured the useof simple forms was that the design andconstruction of very complex forms waslaborious and costly, thus inhibiting the fullexploitation of the potential offered by thesenew materials. There were of courseexceptions. Erich Mendelsohn’s Einstein Towerin Potsdam (see Fig. iii), Gerrit Rietveld’sSchroeder House in Utrecht and Le Corbusier’schapel at Ronchamp (Fig. 7.40) weresuccessfully realised despite having complexforms unrelated to structural function. Theirrelatively small scale meant that it was notdifficult in each case to produce a structuralarmature which would support the form, ratherin the manner of the armature of a sculpture.

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Fig. 7.40 Notre-Dame-du-Haut, Ronchamp, France, 1954;Le Corbusier, architect. Structural considerations haveplayed very little part in the determination of the form ofthis building. Its small scale together with the excellentstructural properties of reinforced concrete, which wasused for the roof, meant that it could be constructedwithout difficulty. (Photo: P. Macdonald)

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The introduction of the computer in the latetwentieth century, firstly as a tool for structuralanalysis and subsequently as a design aid,which allowed very complex forms to bedescribed and cutting and fabricatingprocesses to be controlled, gave architectsalmost unlimited freedom in the matter ofform. This was a major factor in theintroduction of the very complex geometrieswhich appeared in architecture towards theend of the twentieth century. A good example isFrank Gehry’s highly complex and spectacularGuggenheim Museum in Bilbao, Spain.

Wolf Prix, of Coop Himmelblau, was anotherlate-twentieth-century architects who fullyexploited this freedom:

‘... we want to keep the design momentfree of all material constraints ...’25

‘In the initial stages structural planning isnever an immediate priority ...’26

Great ingenuity was often required of theengineers who devised the structural solutionsfor buildings whose forms had been devised ina purely sculptural way. That of the chapel atRonchamp is remarkable due to the greatsimplicity of the structure which supports thefree-form roof. The walls of the building are ofself-supporting stone masonry rendered white.There is a gap between the tops of these andthe underside of the roof so as to admit asmall amount of light into the interior in agesture which is architecturally significant. Thewalls do not therefore carry the weight of theroof.

The upwardly curving, oversailing roof isformed by a thin shell of reinforced concretewhich conceals an integral and conventionalpost-and-beam reinforced concrete framework.Reinforced concrete columns of small cross-section are embedded in the masonry walls ina regular grid, and carry beams which span

across the building. These provide supportfrom above for the roof shell, which sweeps upat the edges of the building to conceal them.Thus, although the overall form of the buildingbears no relation to the manner in which itfunctions structurally, a satisfactory andrelatively simple structure was accommodatedwithin it.

In more recent times a similar approach tothat adopted by Le Corbusier at Ronchamp, atleast so far as the relationship of structure toarchitecture is concerned, is to be found in theworks of the architects of the Deconstructionschool. The structural organisation of buildingssuch as the rooftop office in Vienna by CoopHimmelblau (see Fig. 1.11) or the Vitra DesignMuseum in Basel by Frank Gehry (Fig. 7.41)were relatively straightforward. The same maybe said of Daniel Libeskind’s Jewish Museumin Berlin (Fig. 7.42). More complexarrangements were required to realise thecomplicated geometries of Libeskind’sextension to the Victoria and Albert Museumin London (Figs 7.43 and 7.44) and the newImperial War Museum in Manchester.

Two important considerations must betaken into account when form is devisedwithout recourse to structural requirements.Firstly, because the form will almost certainlybe non-form-active, bending-type internal forcewill have to be resisted. Secondly, themagnitudes of the internal forces which aregenerated are likely to be high in relation tothe load carried. The implications of both ofthese considerations are that structuralmaterial will be inefficiently used and that theelement sizes required to produce adequatestrength will be high. This is a scenario whichcan result in structures which are clumsy andungainly.

A scale effect also operates because thestrength of structural material remainsconstant even though the size of the structureincreases. As was discussed in Chapter 6, allstructural forms, whatever their shape, tend tobecome less efficient as spans increase. Themaximum span for a given form occurs whenthe strength of the material is fully occupied,supporting the self-weight of the structure. If

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25 Quotations from On the Edge, the contribution of WolfPrix of Coop Himmelblau to Noever, P. (Ed.), Architecturein Transition: Between Deconstruction and New Modernism,Prestel-Verlag, Munich, 1991.

26 Ibid.

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Fig. 7.41 VitraDesign Museum,Basel, Switzerland,1989; Frank Gehry,architect. From atechnical point ofview forms such asthis present achallenge. Theirconstruction ismade possible bythe excellentstructural propertiesof present-daymaterials such asreinforced concreteand steel. The scaleof such a projectmust be smallhowever. (Photo: E.& F. Mclachlan)

Fig. 7.42 JewishMuseum, Berlin,1999; DanielLibeskindArchitekturburo,architects. The useof a reinforcedconcrete structuralframework hasallowed both ahighly sculpturedoverall form to becreated and a highdegree of freedom tobe achieved in thetreatment of thenon-structuralcladding of theexterior.

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Fig. 7.43 Design for an extension to the Victoria and Albert Museum, London, UK, 1995–; Daniel LibeskindArchitekturburo, architects; Ove Arup & Partners, structural engineers. Structural considerations had little influence onthe original design for this building.

Fig. 7.44 Design for an extension to the Victoria and Albert Museum, London, UK, 1995–; Daniel LibeskindArchitekturburo, architects; Ove Arup & Partners, structural engineers. The cross-section reveals that the structure is afairly conventional post-and-beam framework. The relatively small scale of the project, the excellent properties of modernstructural materials and the judicious use of structural continuity allowed this complex form to be realised.

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the form adopted is fundamentally inefficient,because it has been designed withoutreference to structural requirements, themaximum possible span may be quite small.

The neglect of structural issues in thedetermination of the form of a building cantherefore be problematic if a large span isinvolved. The small scale of the buildingsalready mentioned meant that the internalforces were not so large that they could not beresisted without the use of excessively largecross-sections. Eero Saarinen’s terminal forTWA at Idlewild (now Kennedy) Airport, NewYork (Fig. 7.45) paid similar disregard tostructural logic. Although the roof of thisbuilding was a reinforced concrete shell it didnot have a form-active shape. The form wasdetermined from visual rather than fromstructural considerations and, because it waslarger than Ronchamp, difficulties occurredwith the structure. These were overcome bymodifying the original design to strengthen theshell in the locations of highest internal force.

Jorn Utzon’s Sydney Opera House isanother example of this type of building (Fig.7.46). In this case, the scale was such that itwas impossible to overcome theconsequences of the complete disregard ofstructural and constructional concerns in thedetermination of the form. In the resultingsaga, in which the form of the building had tobe radically altered for constructional reasons,the architect resigned and the client was facedwith a protracted construction period and withcosts which were an order of magnitudegreater than had originally been envisaged.Amid great political controversy, the buildingwas nevertheless completed and has becomea distinctive image which is synonymous withSydney, if not with Australia, rather as theEiffel Tower, Big Ben or the Statue of Libertyhave come to represent other famous citiesand their respective countries. Although theexpertise of Ove Arup and Partners in solvingthe structural and constructional problemsbrought about by Utzon’s inspired, iftechnically flawed, original design areundisputed, the question of whether the finalform of the Sydney Opera House is good

architecture remains open. This building mayserve as a warning to architects who choose todisregard the inconveniences of structuralrequirements when determining form. The 113

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Fig. 7.45 TWA Terminal, Idlewild (now Kennedy) Airport,New York, USA, 1962; Eero Saarinen, architect; Ammanand Whitney, structural engineers. The form here was farfrom ideal structurally and strengthening ribs of greatthickness were required at locations of high internal force.The structure was therefore inefficient but constructionwas possible due to the relatively modest spans involved.(Photo: R. J. Mainstone)

Fig. 7.46 Opera House, Sydney, Australia, 1957–65; JornUtzon, architect; Ove Arup & Partners, structural engineers.The upper drawing here shows the original competition-winning proposal for the building which proved impossibleto build. The final scheme, though technically ingenious, isconsidered by many to be much less satisfactory visually.The significant difference between this and the buildings inFigs 7.41 to 7.45 is one of scale.

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consequence may be that the final form willbe different from their original vision in wayswhich they may be unable to control. Theignoring of structural logic in the creation ofform is indeed possible but only in thecontext of short spans. The success of therecent buildings by Coop Himmelblau, Gehryand Libeskind has depended on thissituation.

In all of the buildings considered in thissection the structure is present in order to doits mundane job of supporting the buildingenvelope. In this kind of architecture structuralengineers act as facilitators – the people whomake the building stand up. It should not bethought, however, that the world of structureshas played no part in the evolution of the free-form architecture which became fashionable inthe late twentieth century. It was the structuraltechniques which were developed in thetwentieth century which made such anarchitecture possible, and which gavearchitects the freedom to exploit geometrieswhich in previous centuries would have beenimpossible to realise.

7.2.6 ConclusionThis section has reviewed the interactionbetween structure and architecture and hasshown that this can operate in a variety ofways. It is hoped that the several categorieswhich have been identified for thisrelationship, however artificial they may be,nevertheless contribute to the understandingof the processes and interactions whichconstitute architectural design.

Six broad categories were identified andthese may be considered to be grouped indifferent ways – something which shedsfurther light on the design process. Onegrouping would be to subdivide the varioustypes of relationship into two broadcategories – structure exposed and structure hiddenfrom view. There are three sub-categories of thestructure exposed relationship: ornamentation ofstructure, structure as ornament and structure asarchitecture. Structure hidden also contains twosub-categories: structure as form generator/structure accepted and structure ignored.

The original six categories may alternativelybe considered as grouped into two otheroverarching categories namely structure respected,in which forms are adopted which perform wellwhen judged by technical criteria, and structuredisrespected, in which little account is taken ofstructural requirements when the form isdetermined. The first of these would includeornamentation of structure, structure as architecture,structure as form generator and structure accepted.The second would include structure as ornamentand structure ignored.

This second way of regarding the variouspossible relationships between structure andarchitecture focuses attention on the types ofcollaboration which can exist betweenarchitects and engineers, a fascinating aspectof the history of architecture. If structure is tobe respected, engineers and architects mustcollaborate in a positive way over the design ofa building. The engineer is then a member ofthe team of designers which evolves the formof the building. Where the relationships fallinto the category of structure disrespected theengineer can be simply a technician – theperson who works out how to build a formwhich has been determined by someone else.

7.3 The relationship betweenarchitects and engineers

Collaboration has always been requiredbetween architects and those who have thetechnical expertise to realise buildings. Thenature of the relationship has taken manyforms, and the form in play at any time hasalways influenced the nature of the interfacebetween structure and architecture.

In Greek and Roman antiquity, therelationship between the equivalents ofarchitects and engineers must have been veryclose in order to achieve the creation ofbuildings in which the requirements ofstructure and architecture were reconciled in avery positive way. In this period the architectand engineer would, in many cases, have beenthe same individual – the master builder. This

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methodology brought into being some of thegreatest buildings of the European Classicaltradition, always in the context of structurerespected. Ornamentation of structure produced theGreek temples (Fig. 7.1) and the Romantriumphal arches. Structure as form generator wasthe relationship that existed in the creation ofthe great interiors of Imperial Rome such asthe Pantheon (Fig. 7.30) and the Basilica ofConstantine (Fig. 7.31). In each case therelationship between structure andarchitecture was positive; the architecture wasborn out of a need to satisfy structuralrequirements. It meant that those responsiblefor the technical make-up of buildings also

played a significant role in determining theirarchitectural qualities and interest.

This type of relationship between theequivalents of architects and engineers wasmaintained during the medieval period inwhich the Gothic buildings, which were aversion of ornamentation of structure, wereproduced but it almost disappeared at thetime of the Italian Renaissance.

Andrea Palladio, for example, who began hisworking life as a stone mason and who wasentirely confident in the technology at hisdisposal, designed buildings which werepractical and sensible from a structuralviewpoint (Fig. 7.47). They belonged in the 115

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Fig. 7.47 Villa Emo,Fanzolo, Italy, 1564;Andrea Palladio,architect. Structuralrequirements exerted astrong influence on theform of this masonry andtimber building but thearchitectural interest layelsewhere.

(a)

(b)

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category structure accepted rather than structure asform generator, however, because thearchitectural interest of his work lay in the ideaof the building as a microcosm and his use ofharmonic proportion, hierarchicalarrangements of space and innovative uses ofclassical forms of ornamentation. The meansby which the buildings were constructed wereof little relevance to this agenda.

In Western architecture most of thebuildings from the Italian Renaissance to theModern period fall into this category. It issignificant that throughout this period theprincipal structural materials were masonryand timber. These are problematic structurallyin various ways27 and forced architects to adopt

structural forms which were sensible from astructural point of view. The requirements ofstructure had therefore to be respected but, inthe majority of buildings, the architecturalinterest lay elsewhere. This meant thatstructural considerations fell out of anydiscussion of architecture.

Two aspects of post-medieval architecturecontributed to this. Firstly, a subtle changeoccurred in the nature of the relationshipbetween structure and architecture becausethe structural armatures of buildings wereincreasingly concealed behind forms ofornamentation which were not directly relatedto structural function. The villa illustrated inFig. 7.47 is an example by Palladio. His designfor the Palazzo Valmarana in Vicenza (Fig. 7.2)is another. The Corinthian Order pilasterswhich were incorporated into the façade of thisbuilding formed the thin outer skin of a solidwall. The wall was the structural element and

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27 See Macdonald, A. J., Structural Design for Architecture,Architectural Press, Oxford, 1997, Chapters 5 and 6 fora discussion of these issues.

Fig. 7.48 St Paul’s Cathedral, London, UK, 17th century; Sir Christopher Wren, architect. In treatment of both the domeand the exterior wall the structural arrangement is not reflected in the visual programme.

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the pilasters had a symbolic rather than astructural role. The reduction of elements withstructural origins to components in a visualvocabulary, which was typical of thearchitecture of the period, caused thestructural and aesthetic agendas to drift apart.This in turn had a profound effect on the typeof relationship which developed betweenarchitects and those who were responsible forthe technical aspects of the design of abuilding.

The second change that occurred from theItalian Renaissance onwards was that mostbuildings were structurally unambitious. Atechnology of masonry walls and timber floor

and roof structures existed whose capabilitieswere well understood and which presentedlittle challenge to builders. There were obviousexceptions, Brunelleschi’s dome in Florencebeing an excellent example (Fig. 7.13), but inthe majority of buildings there was no sense ofexcitement in relation to the structural make-up. The forms adopted were sensible from astructural point of view, but there were nofurther structural ambitions. Even with largebuildings such as St Paul’s Cathedral inLondon (Figs 7.48 to 7.50) in which seriousstructural challenges had to be met, thestructure made no obvious contribution to thearchitecture. 117

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Fig. 7.49 St Paul’s Cathedral, London, UK, 17th century;Sir Christopher Wren, architect. The cross-section of thebuilding reveals that the structural arrangement isconventional with a high central nave and flying buttressescarrying the side thrusts created by the masonry vault. Thestructural action is concealed behind the external wall, theupper half of which is a non-structural screen.

Fig. 7.50 St Paul’s Cathedral, London, UK, 17th century;Sir Christopher Wren, architect. The dome is in three parts.The innermost part is a self-supporting masonryhemisphere. The outer skin is mounted on a timberframework supported by a cone of structural brickwork.

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For example, the stone external walls of thisbuilding form a wallpaper-like screen, wrappedaround the core of the building, which bearslittle relation to its structural make-up. Thecross-section of the building is similar to thatof a medieval Gothic church and consists of ahigh vaulted central nave flanked by loweraisles and with flying buttresses providinglateral support for the vault (Fig. 7.49). None ofthis is visible, or suggested, on the exterior.

The uncoupling of the structural from thevisual agenda at St Paul’s also occurred in thedesign of the dome, where Wren did notrequire that the interior and exterior profilesbear any relation to each other. The dome wasconstructed in three layers (Fig. 7.50). The partwhich is visible in the interior is a self-supporting structure – a semi-form-active

hemisphere in masonry. On the exterior, theprofile of the dome is completely disconnectedfrom the way in which it operates structurally.The structure is a cone of brickwork which isentirely hidden from view and which supportsdirectly the stone cupola at the apex of thedome. The external profile of the dome is alightweight skin supported on a timberformwork built out from the structural core. Thebrick cone conforms to the form-active shapefor the principal load which it carries – that ofthe weight of the cupola – but its shape bearsno relation to the form of the dome which isseen on either the interior or the exterior of thebuilding. The architecture of the exterior of St Paul’s, including that of the external wall andof the dome, is therefore unrelated visually tothe structure which supports it.

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Fig. 7.51 Train shed, St Pancras Station, London, UK, 1865; W. H. Barlow and R. M. Ordish, engineers. The architecturalqualities of the large iron-and-glass interiors of the nineteenth century went largely unrecognised at the time.118

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The distance between the architectural andstructural agendas was perhaps generally at itsgreatest towards the end of the nineteenthcentury and is exemplified by buildings such asSt Pancras Station in London (1865). Here, oneof the largest iron and glass vaults of thecentury, by W. H. Barlow and R. M. Ordish (Fig.7.51), a spectacular example of what could beachieved with the new technology of structuraliron, was concealed behind the bulk of GilbertScott’s Midland Hotel in the High Victorian

Gothic style (Fig. 7.52). The two parts of thebuilding were each fine examples of their type,but they inhabited different worlds. Thearchitectural qualities of the train shed wentunrecognised: it was considered as simply avulgar product of industry, necessary but notbeautiful, and the citizens of London wereprotected from the sight of it by a fine essay inRuskinian northern-Italian Gothic.

The visual disconnection of architecturefrom structure which is seen at St Paul’s

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Fig. 7.52 Midland Hotel,at St Pancras Station,London, UK, 1871; G.Gilbert Scott, architect. Theform of the train shed didnot influence thearchitectural agenda at StPancras.

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Cathedral and St Pancras Station illustrateswell the approach which was adopted byWestern architects from the ItalianRenaissance onwards. Architects were stillinterested in structure, but only as a means ofrealising built form which was generated fromideas which were remote from technicalconsiderations. This approach to architecturewas made easier following the development ofthe structural technologies of steel andreinforced concrete in the late nineteenthcentury and it was used in much of the Modernarchitecture of the twentieth century. Steel andreinforced concrete had much better structuralproperties than timber or masonry andreleased architects from the need to payattention to structural requirements, at least incases where the limits of what was technicallyfeasible were not being approached. This madepossible, in the twentieth century, a new kindof relationship between structure andarchitecture – structure ignored.

A consequence of the distancing of theaesthetic from the technical agenda, themaking of a distinction between architectureand building, was that architects no longerevolved the forms of buildings in a trulycollaborative partnership with those who wereresponsible for the technical aspects of design.The latter became technicians, responsible forensuring that the technical performance of abuilding would be satisfactory but notcontributing creatively to its form orappearance.

Several of the prominent early Modernarchitects were, however, interested intectonics, the architectural expression of thefundamental elements of buildings that areresponsible for holding them up. This causedmore collaborative relationships betweenarchitects and engineers to develop. The statusquo was nevertheless maintained concerningthe relationships between architects andengineers, and the design of a building wasstill very much dominated by the architect asthe leader of the group of professionals whocollaborated over its production. Modernismespoused rationalism but carried with it muchof the baggage of nineteenth-century

Romanticism. One particularly strong aspect ofthis situation was the idea of the architect as aheroic figure – in the parlance of architecturalcriticism, the ‘Modern Master’. Thus, althougharchitecture became ever more dependentupon new structural technologies in thetwentieth century and therefore upon the skilland expertise of engineers, most architectscontinued to behave, as they had done sincethe Italian Renaissance, as the masters of thedesign process and to treat the other designersinvolved as mere technicians. This view wasendorsed by most of the critics and historiansof Modernism who paid little regard to thetechnology which underpinned the Modernaesthetic and gave scant acknowledgement tothe engineers who developed it. The names ofthe engineers of the classic buildings of earlyModernism by architects such as WalterGropius, Ludwig Mies van der Rohe and LeCorbusier are rarely mentioned.

The subservient position of engineers inrelation to the conceptual stages ofarchitectural design was maintained throughthe Modern period and has continued into thepresent day, where it may be observed to bestill operating in some of the most prestigiousarchitectural projects. The extremely complexforms devised by architects such as FrankGehry (Fig. 7.41), Zaha Hadid or DanielLibeskind (Figs 7.43 and 7.44), for example,provide serious challenges to engineers, butthe engineers are not involved in the initialdetermination of the form.

A new type of relationship betweenarchitects and engineers, in which very positivecollaborations occurred with engineersinfluencing the design of buildings from thevery earliest stages, did, however, develop inthe twentieth century. The catalyst which madethis possible was the re-introduction oftectonics into the architectural discourse. Thisdrew attention to the visual qualities of theemerging structural technologies of ferrousmetal and reinforced concrete. It resulted inthe re-examination, from an architectural pointof view, of much nineteenth-century buildingthat had escaped the notice of a contemporaryarchitectural culture which had been

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preoccupied with revivals and ‘battles ofstyles’. Buildings such as the Crystal Palaceand the long-span train sheds of the mid-nineteenth century were seen by some earlyModernists to have interesting architecturalqualities. Buildings created by twentieth-century equivalents of the railway engineerswere also considered to be worthy of attentionand were given space in the architecturalmedia. Thus, aircraft hangars (surely thetwentieth-century equivalent of the train shed)by engineers such as Eugène Freyssinet (Fig.7.14) and Pier Luigi Nervi, were praised fortheir architectural qualities and this led to theconcept of the architect/engineer. Theemergence of the architect/engineers (EduardoTorroja, Ricardo Morandi, Owen Williams, and,in more recent times, Félix Candela andSantiago Calatrava are further examples) was asignificant event in twentieth-centuryarchitecture. All these individuals have enjoyedthe same kind of status as the leadingarchitects of their day.

The gap which had long existed betweenarchitects and engineers was not closed bythese engineers operating as architects ratherthan with architects. They have continued anestablished way of working in which thearchitect behaved very much as the leader ofthe design team, with structural engineers andother technical specialists playing a secondaryrole and making little direct and positivecontribution to the visual aspects of a design.It must be said that many engineers are veryhappy to work in this way and to leave thearchitectural aspects of a design to architectsand, in appropriate circumstances, a goodbuilding may be the result.

In the late twentieth century, however, adifferent way of working also becameestablished: certain groups of architects andengineers evolved highly collaborativerelationships, working in design teams ofarchitects, structural engineers, servicesengineers and quantity surveyors, in whichbuildings were evolved through a discursiveprocess. In this very close type of workingrelationship, all of the professionals involvedcontributed to the evolution of a design which

emerged as a truly joint effort. It was thismethod of working which made possible thestyle known as High Tech in which structureand services components formed majoraspects of the visual vocabulary of buildings.

The collaborations between architects,such as Norman Foster, Nicholas Grimshaw,Michael Hopkins and Richard Rogers withengineers such as Ted Happold, Tony Huntand Peter Rice, have been particularlyeffective. The working methodology involvedregular discursive meetings of the designteams in which all aspects of the design werediscussed. The closeness of thecollaborations was such that often, inretrospect, it was not possible to attributemany aspects of the final design to anyparticular individual28.

It was in this spirit that the best twentieth-century examples of ornamentation of structurewere produced (for example Reliance Controls(Fig. 7.4) and the Waterloo Terminal (Fig.7.17)). The genre has continued into the twenty-first century with buildings such as theNational Botanical Garden of Wales (Fig. 7.53)by Foster and Partners with Anthony HuntAssociates, and the Eden Project (Fig. 7.54) byNicholas Grimshaw and Partners with AnthonyHunt Associates. In the latter cases (and this isalso true of the earlier Waterloo building), acomplexity of form has been accomplishedwhich depends on the use of state-of-the-arttechniques of computer-aided design. Thistype of architecture is a strand of Modernismwhich has retained its vitality through theperiod in the late twentieth century in whichPostmodernism and Deconstruction have beenfashionable (both of these being examples ofstyles in which much less creativerelationships between structure andarchitecture have occurred29).

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28 The design team methodology was especially favouredby Tony Hunt who carried out work with all of theleading High-Tech architects; see Macdonald A. J.,Anthony Hunt, Thomas Telford, London, 2000.

29 Most Postmodern architecture falls into the categorystructure accepted while Deconstruction is mainly structureignored.

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The buildings in which the design-teammethodology was used are generally regardedas belonging to the High-Tech school. Thesituation is, however, more complex, as morethan one version of the relationship betweenstructure and architecture is discernible inHigh Tech. Many of the High-Tech buildingshave in fact been designed by traditionalmethods, with the architect attendingprincipally to visual and stylistic issues and theengineer confining his or her actions mainly tothe technical details of the structure. As hasbeen shown, the design of buildings such asthe Centre Pompidou was driven principally byvisual agendas in which the architects must beregarded as having operated very much as theleaders of the design teams.

Where truly collaborative relationshipshave occurred, however, the kind ofrelationship between architectural andstructural thinking which existed in antiquityand the Gothic period has been re-captured.In historic architecture, this existed in theform of the ‘master builder’. The present-daydesign team, operating in a truly collaborativeway and using state-of-the-art techniques ofcomputer-aided design, as with Grimshaw andHunt at Waterloo, is the modern equivalent ofthe master builder.

Three types of relationship betweenarchitects and engineers are currently in play.

In the overwhelming majority of Modernbuildings, the relationship between architectsand engineers which prevails is that whichbecame established from the ItalianRenaissance, namely a situation in which thearchitect determines the form of a building andsets the visual agenda, and the engineer actsprincipally as the technician who ensures thatit performs adequately in a technical sense.This type of relationship between architectsand engineers predominates in all of the sub-styles of Modernism including Postmodernismand Deconstruction.

A second type of relationship occurs wherethe architect and the engineer are the sameperson. Several prominent figures haveoperated in this way from the twentiethcentury onwards, including August Perret andRobert Maillart at the beginning of the century,Pier Luigi Nervi, Eduardo Torroja, OwenWilliams and Félix Candela in the mid-twentieth century and Santiago Calatrava atthe end of the twentieth century and in thepresent day. All of these architect/engineershave produced buildings in which thestrategies involved have been those of structureas architecture, structure as form generator orornamentation of structure. Their most memorablebuildings have been long-span enclosures inthe language of the form-active vault or tensilestructure. The aesthetic agenda has been

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Fig. 7.53 National Botanical Garden of Wales, 1999;Foster and Partners, architects, Anthony HuntAssociates, structural engineers. This innovative single-layer dome is a toroidal form executed inone-way-spanning tubular steel arches, of varying span,with orthogonal linking elements. Built form of thiscomplexity in steelwork was not possible before the ageof computer-aided design.

Fig. 7.54 The Eden Project, Cornwall, UK, 1999; NicholasGrimshaw and Partners, architects; Anthony HuntAssociates, structural engineers. The complexity of formmade possible by computer-aided design has brought intobeing a new generation of metal and glass structure.

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relatively simple – the appreciation of abuilding as a work of technology.

A third type of relationship betweenarchitects and engineers, that of a trulycollaborative partnership, re-emerged towardsthe end of the twentieth century. This hasinvolved engineers and architects co-operatingfully over the design of a building in a waywhich had not occurred since their equivalentscreated the cathedrals of medieval Gothic. Thebest of the buildings of High Tech have beendesigned in this way.

In the present day, this third category ofrelationship is producing a new kind ofarchitecture of great geometric complexity.The train shed at Waterloo Station by Huntand Grimshaw (Fig. 7.17) is an early example.This building may appear to be simply atwentieth-century version of the nineteenth-century iron-and-glass railway station, withrecent technical innovations such as weldablecast-steel joints. It may also appear to be HighTech. In fact, the steelwork possesses a levelof complexity which could not have beenaccomplished before the age of computer-

aided design and which is suggestive of thecomplexity of a living organism, one of theappropriate metaphors for the philosophies ofthe emerging organicist paradigm. Although,therefore, this building may be seen as adevelopment of the High Tech style, it issignificantly distinct to merit a different name,perhaps ‘organi-tech’. The same could be saidof the dome at the National Botanical Gardenof Wales (Fig. 7.53) by Foster and Partnerswith Anthony Hunt Associates, and of theEden Project (Fig. 7.54) by Nicholas Grimshawand Partners, also with Anthony HuntAssociates.

The realisation of the complex organic or‘land-form’30 shapes of these buildings givesappropriate visual expression to thesophistication of contemporary technology.They also provide ‘intimations’ in severalsenses of what might be involved in a ‘re-constructive’ post-modern architecturalpractice31 even while they remain linked to theModernist agenda concerned with thecelebration of technological progress.

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30 This term was used by Charles Jencks in an article inJencks, C. (Ed.), New Science = New Architecture?, AcademyEditions, London, 1997, in which he discussed the non-linear architecture of architects such as Eisenman,Gehry, Koolhaus and Miralles.

31 See Gablik, S., The Re-enchantment of Art, Thames andHudson, New York, 1991.

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Addis, W., The Art of the Structural Engineer,Artemis, London, 1994.

Ambrose, J., Building Structures, John Wiley, NewYork, 1988.

Amery, C., Architecture, Industry and Innovation: TheEarly Work of Nicholas Grimshaw and Partners,Phaidon, London, 1995.

Baird, J. A. and Ozelton, E. C., Timber Designer’sManual, 2nd edition, Crosby Lockwood Staples,London, 1984.

Balcombe, G., Mitchell’s History of Building,London, Batsford, 1985.

Benjamin, B. S., Structures for Architects, 2ndedition, Van Nostrand Reinhold, New York,1984.

Benjamin, J. R., Statically Indeterminate Structures,McGraw-Hill, New York, 1959.

Billington, D. P., Robert Maillart, MIT Press,Cambridge, MA, 1989.

Billington, D. P., The Tower and the Bridge, BasicBooks, New York, 1983.

Blanc, A., McEvoy, M. and Plank, R., Architectureand Construction in Steel, E. & F. N. Spon,London, 1993.

Blaser, W. (Ed.), Santiago Calatrava – Engineering Architecture, Borkhauser Verlag,Basel, 1989.

Boaga, G. and Boni, B., The Concrete Architecture ofRiccardo Morandi, Tiranti, London, 1965.

Breyer, D. E. and Ark, J. A., Design of WoodStructures, McGraw-Hill, New York, 1980.

Broadbent, G., Deconstruction: A Student Guide,Academy, London, 1991.

Brookes, A. and Grech, C., Connections: Studies inBuilding Assembly, Butterworth-Heinemann,Oxford, 1992.

Burchell, J. and Sunter, F. W., Design and Build inTimber Frame, Longman, London, 1987.

Ching, F. D. K., Building Construction Illustrated,Van Nostrand Reinhold, New York, 1975.

Coates, R. C., Coutie, M. G. and Kong, F. K.,Structural Analysis, 3rd edition, Van NostrandReinhold, Wokingham, 1988.

Conrads, U. (Ed.), Programmes and Manifestos onTwentieth Century Architecture, Lund Humphries,London, 1970.

Corbusier, Le, Five Points Towards a NewArchitecture, Paris, 1926.

Corbusier, Le, Towards a New Architecture,Architectural Press, London, 1927.

Cowan, H. J., Architectural Structures, Elsevier,New York, 1971.

Cowan, H. J. and Wilson, F., Structural Systems,Van Nostrand Reinhold, New York, 1981.

Cox, H. L., The Design of Structures of Least Weight,Pergamon, London, 1965.

Curtis, W. J. R., Modern Architecture Since 1900,Phaidon, London, 1982.

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Chapter 1

Selected bibliography

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Davies, C., High Tech Architecture, Thames &Hudson, London, 1988.

De Compoli, G., Statics of Structural Components,John Wiley, New York, 1983.

Denyer, S., African Traditional Architecture,Heinemann, London, 1978.

Dowling, P. J., Knowles, P. and Owens, G. W.,Structural Steel Design, Butterworths, London,1988.

Drew, P., Frei Otto, Granada Publishing,London, 1976.

Elliott, C. D., Technics and Architecture: TheDevelopment of Materials and Systems for Buildings,MIT Press, London, 1992.

Engel, H., Structure Systems, Deutsche Verlags-Anstalt, Stuttgart, 1967.

Engel, H., Structural Principles, Prentice-Hall,Englewood Cliffs, NJ, 1984.

Everett, A., Materials, Mitchell’s Building Series,Batsford, London, 1986.

Fraser, D. J., Conceptual Designs and PreliminaryAnalysis of Structures, Pitman Marshfield, MA, 1981.

Gablik, S., Has Modernism Failed?, Thames &Hudson, London, 1984.

Gablik, S., The Re-enchantment of Art, Thames andHudson, New York, 1991.

Gheorghiu, A. and Dragomit, V., The Geometry ofStructural Forms, Applied Science Publishers,London, 1978.

Glancey, J., New British Architecture, Thames &Hudson, London, 1990.

Gordon, J. E., Structures, Pelican, London, 1978.

Gordon, J. E., The New Science of Strong Materials,Pelican, London, 1968.

Gorst, T., The Buildings Around Us, E. & F. N.Spon, London, 1995.

Gössel, P. and Leuthäuser, G., Architecture in theTwentieth Century, Benedikt Taschen, Cologne,1991.Groak, S., The Idea of Building, E. & F. N. Spon,London, 1992.

Hammond, R., The Forth Bridge and its Builders,Eyre & Spottiswood, London, 1964.

Hart, F., Henn, W. and Sontag, H., Multi StoreyBuildings in Steel, Crosby Lockwood Staples,London, 1976.

Heinle, E. and Leonhardt, F., Towers: A HistoricalSurvey, Butterworth Architecture, London, 1988.

Herzog, T., Pneumatic Structures, CrosbyLockwood Staples, London, 1976.

Holgate, A., The Art in Structural Design,Clarendon Press, Oxford, 1986.

Holgate, A., Aesthetics of Built Form, OxfordUniversity Press, Oxford, 1992.

Horvath, K. A., The Selection of Load-bearingStructures for Buildings, Elsevier, London, 1986.

Howard, H. S., Structure: An Architect’s Approach,McGraw-Hill, New York, 1966.

Hunt, A., Tony Hunt’s Structures Notebook,Architectural Press, Oxford, 1997.

Hunt, A., Tony Hunt’s Sketchbook, ArchitecturalPress, Oxford, 1999.

Huxtable, A. L., The Tall Building Reconsidered: TheSearch for a Skyscraper Style, Pantheon Books,New York, 1984.

Jan van Pelt, R. and Westfall, C., ArchitecturalPrinciples in the Age of Historicism, Yale UniversityPress, New Haven, 1991.

Jencks, C., The Language of Post-modern Architecture,3rd edition, Academy, London, 1981.

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Jencks, C., Modern Movements in Architecture,Penguin Books, Harmondsworth, 1985.

Joedicke, J., Shell Architecture, Karl Kramer Verlag,Stuttgart, 1963.

Kong, F. K. and Evans, R. H., Reinforced andPrestressed Concrete, 2nd edition, Van NostrandReinhold, New York, 1981.

Lambot, I. (Ed.), Norman Foster: Foster Associates:Buildings and Projects, Vols 1–4, Watermark, HongKong, 1989–90.

Lin, T. Y. and Stotesbury, S. D., StructuralConcepts and Systems for Architects and Engineers,John Wiley, New York, 1981.

Macdonald, A. J., Wind Loading on Buildings,Applied Science Publishers, London, 1975.

Macdonald, A. J., Structural Design for Architecture,Architectural Press, Oxford, 1997.

Macdonald, A. J. and Boyd Whyte, I., The ForthBridge, Axel Menges, Stuttgart, 1997.

Macdonald, A. J., Anthony Hunt, Thomas Telford,London, 2000.

Mainstone, R., Developments in Structural Form,Allen Lane, Harmondsworth, 1975.

Mainstone, R., ‘Brunelleschi’s Dome’, TheArchitectural Review, CLXII (967) 156–166, Sept.1977.

Majid, K. I., Optimum Design of Structures,Newnes-Butterworths, London, 1974.

Makowski, Z. S., Steel Space Structures, MichaelJoseph, London, 1965.

Marder, T. (Ed.), The Critical Edge: Controversy inRecent American Architecture, MIT Press,Cambridge, MA, 1985.

Mark, R., Light, Wind and Structure, MIT Press,Cambridge, MA, 1990.

Mettem, C. J., Structural Timber Design andTechnology, Longman, London, 1986.

Morgan, W., The Elements of Structure, 2nd edition(revised I. G. Buckle), Longman, London, 1978.

Morgan, W. and Williams, D. T., StructuralMechanics, 5th edition (revised F. Durka),Longman, London, 1996.

Morris, A., Precast Concrete in Architecture, GeorgeGodwin, London, 1978.

Nervi, P. L., Structures, McGraw-Hill, New York,1956.

Nervi, P. L., Aesthetics and Technology in Building,Harvard University Press, Cambridge, MA, 1956.

Neville, A. R., Properties of Concrete, 3rd edition,Longman, London, 1986.

Noever, P. (Ed.), Architecture in Transition: BetweenDeconstruction and New Modernism, Prestel-Verlag,Munich, 1991.

Orton, A., The Way We Build Now, E. & F. N.Spon, London, 1988.

Otto, F., Tensile Structures, MIT Press, Cambridge,MA, 1973.

Papadakis, E., Engineering and Architecture,Architectural Design Profile No. 70, Academy,London, 1987.

Pawley, M., Theory and Design in the SecondMachine Age, Basil Blackwell, Oxford, 1990.

Piano, R., Projects and Buildings 1964–1983,Architectural Press, London, 1984.

Rice, P., An Engineer Imagines, Ellipsis, London,1994.

Robbin, T., Engineering a New Architecture, YaleUniversity Press, New Haven, 1996.

Salvadori, M., Why Buildings Stand Up, W. W.Norton, London, 1980.

Schodek, D. L., Structures, Prentice-Hall,Englewood Cliffs, NJ, 1980.

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Schueller, W., High-rise Building Structures, JohnWiley, London, 1977.

Scully, V., The Earth, the Temple and the Gods, YaleUniversity Press, New Haven, 1979.

Siegel, K., Structure and Form in ModernArchitecture, Reinhold, New York, 1962.

Strike, J., Construction Into Design, ButterworthArchitecture, Oxford, 1991.

Sunley, J. and Bedding, B. (Ed.), Timber inConstruction, Batsford, London, 1985.

Szabo, J. and Koller, L., Structural Design of CableSuspended Roofs, John Wiley, London, 1984.

Thornton, C., Tomasetti, R., Tuchman, J. andJoseph, L., Exposed Structure in Building Design,McGraw-Hill, New York, 1993.

Timoshenko, S. P. and Gere, J. H., Mechanics ofMaterials (SI Edition), Van Nostrand Reinhold,London, 1973.

Timoshenko, S. P. and Young, D. G., Theory ofStructures, 2nd edition, McGraw-Hill, New York,1965.

Torroja, E., Philosophy of Structures, University ofCalifornia Press, Berkeley, 1958.

Torroja, E., The Structures of Eduardo Torroja, F. W.Dodge, New York, 1958.

Venturi, R., Complexity and Contradiction in Architecture,Museum of Modern Art, New York, 1966.

Walker, D. (Ed.), The Great Engineers: The Art ofBritish Engineers 1937–1987, Academy Editions,London, 1987.

Watkin, D., A History of Western Architecture, Barrie& Jenkins, London, 1986.

Werner Rosenthal, H., Structural Decisions,Chapman and Hall, London, 1962.

West, H. H., Analysis of Structures, John Wiley,New York, 1980.

Wilkinson, C., Supersheds: The Architecture of Long-span Large-volume Buildings, ButterworthArchitecture, Oxford, 1991.

Williams, D. T., Morgan, W. and Durka, F.,Structural Mechanics, Pitman, London, 1980.

White, R. N., Gergely, P. and Sexsmith, R. G.,Structural Engineering, Vol. 1, John Wiley, NewYork, 1976.

Windsor, A., Peter Behrens, Architectural Press,London, 1981.

Zalewski, W. and Allen, E., Shaping Structures,John Wiley, New York, 1998.

Zukowski, J. (Ed.), Mies Reconsidered: His Career,Legacy, and Disciples, Art Institute of Chicago,Chicago, 1986.

127

Selected bibliography

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A1.1 Introduction

Structures are devices for conducting forcesfrom the points where they originate inbuildings to foundations where they areultimately resisted. They contain force systemswhich are in a state of static equilibrium. Anappreciation of the concepts of force,equilibrium and the elementary properties offorce systems is therefore fundamental to theunderstanding of structures.

A1.2 Force vectors and resultants

Force is a vector quantity which means thatboth its magnitude and its direction must bespecified in order to describe it fully. It can berepresented graphically by a line, called avector, which is drawn parallel to its directionand whose length is proportional to its

magnitude (Fig. A1.1). When two or more non-parallel forces act together, their combinedeffect is equivalent to that of a single forcewhich is called the resultant of the originalforces. The magnitude and direction of theresultant can be found graphically by vectoraddition in a ‘triangle of forces’ or a ‘polygonof forces’ (Fig. A1.2). In this type of additionthe resultant is always represented, in bothmagnitude and direction, by the line which isrequired to close the ‘triangle of forces’ or‘polygon of forces’.

128

Appendix 1

Simple two-dimensionalforce systems and staticequilibrium

Fig. A1.1 Force is a vector quantity and can berepresented by a line whose length is proportional to itsdirection and whose direction is parallel to its direction.

Fig. A1.2 Vector addition: thetriangle and polygon of forces. (a) Abody acted upon by two forces. (b)Vector addition produces a triangle offorces which yields the resultant. (c)The resultant has the same effect onthe body as the original forces, and istherefore exactly equivalent to them.(d) A body acted upon by three forces.(e) Vector addition produces apolygon of forces which yields theresultant. (f) The resultant has thesame effect on the body as theoriginal group of forces.

(a) (b) (c)

(d) (e) (f)

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A1.3 Resolution of a force intocomponents

Single forces can be subdivided into parts byreversing the process described above andconsidering them to be the resultant of two ormore components (Fig. A1.3). The technique iscalled the resolution of the force into itscomponents and it is useful because it allowsforce systems to be simplified into two sets offorces acting in orthogonal directions (i.e. twoperpendicular directions). It also allows theaddition of forces to be carried outalgebraically rather than graphically. Theresultant of the set of forces in Fig. A1.2, forexample, is easily calculated if each of theforces is first resolved into its horizontal andvertical components (Fig. A1.4).

A1.4 Moments of forces

Forces exert a turning effect, called a moment,about points which are not on their line ofaction. The magnitude of this is equal to theproduct of the magnitude of the force and theperpendicular distance between its line ofaction and the point about which the turningeffect occurs (Fig. A1.5).

A1.5 Static equilibrium and theequations of equilibrium

Structures are rigid bodies which are actedupon by external forces called loads. Theirresponse to these depends on thecharacteristics of the force system. If thestructure is acted upon by no force it may be

129

Appendix 1: Simple two-dimensional force systems and static equilibrium

Fig. A1.3 Resolution of aforce into components. (a) Asingle force. (b) A triangle offorces used to determine thevertical and horizontalcomponents of the single force:v = F sin �; h = F cos �. (c) Thevertical and horizontalcomponents are exactlyequivalent to the original force.

Fig. A1.4 Use of resolution offorces into components todetermine the resultant of a setof forces. (a) Three concurrentforces. (b) Resolution of theforces into vertical andhorizontal components. (c)Determination of the resultantby vector addition of thecomponents.

Fig. A1.5 The moment of aforce about a point is simply ameasure of the turning effectwhich it exerts about that point.

(a)

(a) (b) (c)

(b) (c)

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regarded as being in a state of rest. If it isacted upon by a single force, or by a group offorces which has a resultant, it moves, (moreprecisely it accelerates) under their action (Fig.A1.6). The direction of the movement is the

same as that of the line of action of the singleforce or resultant and the rate of accelerationis dependent on the relationship between themass of the structure and the magnitude of theforce. If the structure is acted upon by a groupof forces which has no resultant, that is agroup of forces whose ‘triangle of forces’ or‘polygon of forces’ is a closed figure, it mayremain at rest and a state of static equilibriumis said to exist. This is the condition which isrequired of the force systems which act on realstructures although, as will be seen below, theneed for the force system to have no resultant

is a necessary but not a sufficient condition forequilibrium.

The loads which act on real structures rarelyconstitute an equilibrium set by themselvesbut equilibrium is established by reactingforces which act between the structures andtheir foundations. These reacting forces are infact generated by the loads which tend tomove the structure against the resisting effectof the supports. The relationship which existsbetween the loading forces which act on astructure and the reacting forces which theseproduce at its foundations is demonstratedhere in a very simple example, which isillustrated in Fig. A1.7.

The example is concerned with theequilibrium or otherwise of a rigid body whichis situated on a frictionless surface (a block ofwood on a sheet of ice might be a practicalexample of this). In Fig. A1.7(a), a force (load)is applied to the body and, because the body isresting on a frictionless surface and noopposing force is possible, it moves inresponse to the force. In Fig. A1.7(b) the bodyencounters resistance in the form of animmovable object and as it is pushed againstthe object a reaction is generated whose

Structure and Architecture

Fig. A1.6 If a body is acted upon by aforce it will accelerate along the line ofaction of the force. The magnitude of theacceleration depends on the relationshipbetween the mass of the body and themagnitude of the force (Newton’s SecondLaw of Motion).

130

Fig. A1.7 Reacting forces are passive as they occur onlyas a result of other forces acting on objects. They aregenerated at locations where resistance is offered to themovement of the object. Equilibrium will occur only if thedisposition of resistance points is such that the actingforces together with the reactions form a closed forcepolygon and exert no net turning effect on the object. Thelatter condition is satisfied if the sum of the moments ofthe forces about any point in their plane is zero. (a) A bodyaccelerating under the action of a force. (b) Accelerationstopped and equilibrium established due to the presenceof an immovable object on the line of action of the force.This generates a reaction which is equal and opposite tothe acting force. Note the very simple ‘polygon’ of forceswhich the vector addition of the acting force and reactionproduces. (c) Equilibrium is not established if theimmovable object does not lie on the line of action of theforce F, even though the polygon of forces produces noresultant. The latter means that translational motion willnot occur but rotation is still possible. (d) A secondimmovable object restores equilibrium by producing asecond reacting force. Note that the magnitude anddirection of the original reaction are now different but theforce polygon is still a closed figure with no resultant.

(a) (b)

(c) (d)

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magnitude increases as the pressure on theobject increases until it is equal to that of theacting force. The reaction then balances thesystem and equilibrium is established.

In this case, because the object providing theresistance happened to lie on the line of actionof the acting force, one source of resistance onlywas required to bring about equilibrium. If theobject had not been in the line of action of theforce as in Fig. A1.7(c), the reaction wouldtogether still have been developed, but theresultant and the reaction would have produceda turning effect which would have rotated thebody. A second resisting object would then havebeen required to produce a second reaction toestablish equilibrium (Fig. A1.7(d)). Theexistence of the new reaction would cause themagnitude of the original reaction to change,but the total force system would neverthelesscontinue to have no resultant, as can be seenfrom the force polygon, and would therefore becapable of reaching equilibrium. Because, inthis case, the forces produce no net turningeffect on the body, as well as no net force, astate of equilibrium would exist.

The simple system shown in Fig. A1.7demonstrates a number of features which arepossessed by the force systems which act onarchitectural structures (Fig. A1.8). The first isthe function of the foundations of a structurewhich is to allow the development of suchreacting forces as are necessary to balance theacting forces (i.e. the loads). Every structuremust be supported by a foundation systemwhich is capable of producing a sufficientnumber of reactions to balance the loadingforces. The precise nature of the reactionswhich are developed depends on thecharacteristics of the loading system and onthe types of supports which are provided; thereactions change if the loads acting on thestructure change. If the structure is to be inequilibrium under all possible combinations ofload, it must be supported by a foundationsystem which will allow the necessaryreactions to be developed at the supportsunder all the load conditions.

The second feature which is demonstratedby the simple system in Fig. A1.7 is the set of

conditions which must be satisfied by a forcesystem if it is to be in a state of staticequilibrium. In fact there are just twoconditions; the force system must have noresultant in any direction and the forces mustexert no net turning effect on the structure.The first of these is satisfied if the componentsof the forces balance (sum to zero) when theyare resolved in any two directions and thesecond is satisfied if the sum of the momentsof the forces about any point in their plane iszero. It is normal to check for the equilibriumof a force system algebraically by resolving theforces into two orthogonal directions (usuallythe vertical and horizontal directions) and theconditions for equilibrium in a two-dimensional system can therefore besummarised by the following three equations:

The sum of the vertical components of all ofthe forces = 0

• Fv = 0

The sum of the horizontal components of allof the forces = 0

• Fh = 0

The sum of the moments of all of the forces= 0

• M = 0 131

Appendix 1: Simple two-dimensional force systems and static equilibrium

Fig. A1.8 Loads andreactions on anarchitectural structure.

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The two conditions for static equilibrium in aco-planar force system are the physical basis ofall elementary structural calculations and thethree equations of equilibrium which arederived from them are the fundamentalrelationships on which all of the elementarymethods of structural analysis are based.

A1.6 The ‘free-body-diagram’

In the analysis of structures, the equationswhich summarise the conditions forequilibrium are used in conjunction with theconcept of the ‘free-body-diagram’ to calculatethe magnitudes of the forces which are presentin structures. A ‘free-body-diagram’ is simply adiagram of a rigid object, the ‘free body’, onwhich all the forces which act on the body aremarked. The ‘free body’ might be a wholestructure or part of a structure and if, as itmust be, it is in a state of equilibrium, theforces which act on it must satisfy theconditions for equilibrium. The equations ofequilibrium can therefore be written for theforces which are present in the diagram andcan be solved for any of the forces whosemagnitudes are not known. For example, thethree equations of equilibrium for the structureillustrated in Fig. A1.9 are:

Vertical equilibrium:R1 + R2 = 10 + 10 + 5 (1)

Horizontal equilibrium:R3 – 20 = 0 (2)

Rotational equilibrium (taking momentsabout the left support):

10�2 + 10�4 + 5�6 – 20�1 – R2�8 = 0(3)

The solutions to these are:

from equation (3), R2 = 8.75 kN

from equation (2), R3 = 20 kN

from equation (1), by substituting for R2,R1 = 16.25 kN

A1.7 The ‘imaginary cut’ technique

The ‘imaginary cut’ is a device for exposinginternal forces as forces which are external to afree body which is part of the structure. Thisrenders them accessible for analysis. In itssimplest form this technique consists ofimagining that the structural element is cutthrough at the point where the internal forcesare to be determined and that one of theresulting two parts of it is removed. If this weredone to a real structure the remaining partwould, of course, collapse, but in thistechnique it is imagined that such forces as arenecessary to maintain the remaining part inequilibrium in its original position, are appliedto the face of the cut (Fig. A1.10). It is reasoned

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Fig. A1.9 Free-body-diagram of a roof truss.

Fig. A1.10 The investigation of internal forces in asimple beam using the device of the ‘imaginary cut’. Thecut produces a free-body-diagram from which the nature ofthe internal forces at a single cross-section can bededuced. The internal forces at other cross-sections can bedetermined from similar diagrams produced by cuts madein appropriate places.

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that these forces must be exactly equivalent tothe internal forces which acted on that cross-section in the structure before the cut wasmade and the device of the imaginary cuttherefore makes the internal forces accessiblefor equilibrium analysis by exposing them asforces which are external to a part of thestructure. They then appear in the ‘free-body-diagram’ (see Section A1.6) of that part of thestructure and can be calculated from theequations of equilibrium.

In the analysis of large structuralarrangements the device of the ‘imaginary cut’is used in several stages. The structure is firstsubdivided into individual elements (beams,columns, etc.) for which free-body-diagramsare drawn and the forces which pass betweenthe elements are calculated from these. Eachelement is then further sub-divided by‘imaginary cuts’ so that the internal forces ateach cross-section can be determined. Theprocedure is summarised in Fig. 2.18.

133

Appendix 1: Simple two-dimensional force systems and static equilibrium

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A2.1 Introduction

Stress and strain are important concepts in theconsideration of both strength and rigidity.They are inevitable and inseparableconsequences of the action of load on astructural material. Stress may be thought ofas the agency which resists load; strain is themeasure of the deformation which occurs whenstress is generated.

The stress in a structural element is theinternal force divided by the area of the cross-section on which it acts. Stress is thereforeinternal force per unit area of cross-section;conversely internal force can be regarded asthe accumulated effect of stress.

The strength of a material is measured interms of the maximum stress which it canwithstand – its failure stress. The strength of astructural element is the maximum internalforce which it can withstand. This depends onboth the strength of the constituent materialand the size and shape of its cross-section. Theultimate strength of the element is reachedwhen the stress level exceeds the failure stressof the material.

Several different types of stress can occur ina structural element depending on thedirection of the load which is applied inrelation to its principal dimension. If the loadis coincident with the principal axis of theelement it causes axial internal force andproduces axial stress (Fig. A2.1). A load iscalled a bending-type load if its direction isperpendicular to the principal axis of theelement (Fig. A2.2); this produces the internalforces of bending moment and shear forcewhich cause a combination of bending stressand shear stress respectively to act on thecross-sectional planes of the element.

The dimensional change which occurs to aspecimen of material as a result of theapplication of load is expressed in terms of thedimensionless quantity strain. This is definedas the change in a specified dimension dividedby the original value of that dimension. The134

Appendix 2

Stress and strain

Fig. A2.1 Axial load occurs where the line of action ofthe applied force is coincident with the axis of thestructural element. This causes axial stress.

Fig. A2.2 Bending-type load occurs where the line ofaction of the applied force is perpendicular to the axis ofthe element. This causes bending and shear stress to occuron the cross-sectional planes.

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precise nature of strain depends on the type ofstress with which it occurs. Axial stressproduces axial strain, which occurs in adirection parallel to the principal dimension ofthe element and is defined as the ratio of thechange in length which occurs, to the originallength of the element (Fig. A2.3). Shear strain,to give another example, is defined in terms ofthe amount of angular distortion which occurs(Fig. A2.4).

Stress and strain are the quantities by whichthe mechanical behaviour of materials inresponse to load is judged. For a given loadtheir magnitudes depend on the sizes of thestructural elements concerned and they aretherefore key quantities in the determinationof element sizes. The size of cross-sectionmust be such that the stress which resultsfrom the internal forces caused by the loads isless than the failure or yield stress of thematerial by an adequate margin. The rigidity isadequate if the deflection of the structuretaken as a whole is not excessive.

A2.2 Calculation of axial stress

The axial stress in an element is uniformlydistributed across the cross-section (Fig. A2.5)and is calculated from the following equation:

f = P/A

where: f = axial stressP = axial thrustA = area of cross-section.

Axial stress can be tensile or compressive. Ifthe size of cross-section does not vary alongthe length of an element the magnitude of theaxial stress is the same at all locations.

A2.3 Calculation of bending stress

Bending stress occurs in an element if theexternal loads cause bending moment to acton its cross-sections. The magnitude of thebending stress varies within each cross-sectionfrom maximum stresses in tension andcompression in the extreme fibres on oppositesides of the cross-section, to a minimum stressin the centre (at the centroid) where the stresschanges from compression to tension (Fig.A2.6). It may also vary between cross-sectionsdue to variation in the bending moment alongthe element.

The magnitude of bending stress at anypoint in an element depends on four factors,namely the bending moment at the cross- 135

Appendix 2: Stress and strain

Fig. A2.3 Axial strain.

Fig. A2.4 Shear strain.

Fig. A2.5 Tensile stress onthe cross-section of anelement subjected to axialtension. The intensity of thisis normally assumed to beconstant across the cross-section.

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section in which the point is situated, the sizeof the cross-section, the shape of the cross-section and the location of the point within thecross-section. The relationship between theseparameters is

f = My/I

where: f = bending stress at a distance yfrom the neutral axis of thecross-section (the axisthrough the centroid)

M = bending moment at the cross-section

I = the second moment of area ofthe cross-section about theaxis through its centroid; thisdepends on both the size andthe shape of the cross-section.

This relationship allows the bending stress atany level in any element cross-section to becalculated from the bending moment at that

cross-section. It is equivalent to the axialstress formula f = P/A.

The equation stated above is called theelastic bending formula. It is only valid in theelastic range (see Section A2.4). It is one of themost important relationships in the theory ofstructures and it is used in a variety of forms,in the design calculations of structuralelements which are subjected to bending-typeloads. A number of points may be noted inconnection with this equation:

1 The property of a beam cross-section onwhich the relationship between bendingmoment and bending stress depends is itssecond moment of area (I) about theparticular axis through its centroid which isnormal to the plane in which the bendingloads lie. This axis is the neutral axis of thebeam.

I is a property of the shape of the cross-section. Its definition is

I = ≡y2dA

For those who are not mathematicallyminded Fig. A2.7 may make the meaning ofthe term more clear. The second moment ofarea of a cross-section about the axisthrough its centroid can be evaluated bybreaking up the total area into small parts.

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Fig. A2.6 Distribution of bending stress on a cross-section of an element carrying a bending-type load. (a)Deflected shape. Compressive stress occurs on the insideof the curve (upper half of the cross-section) and tensilestress on the outside of the curve. (b) Cut-away diagram.Shear force and shear stress are not shown.

(a)

(b)

Fig. A2.7 A short length of beam with a cross-section ofindeterminate shape is shown here. The contributionwhich the shaded strip of cross-section makes to theresistance of bending is proportional to ∂I = y2∂A. Theability of the whole cross-section to resist bending is thesum of the contributions of the elemental areas of thecross-section:

I = �y2∂AIf ∂A is small this becomes:

I = ≡y2∂A.

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The second moment of area of any partabout the centroidal axis is simply the areaof the part multiplied by the square of itsdistance from the axis. The second momentof area of the whole cross-section is thesum of all of the small second moments ofarea of the parts.

The reason why this rather strangequantity I, which is concerned with thedistribution of the area of the cross-sectionwith respect to its centroidal axis,determines the bending resistance of thebeam is that the size of the contributionwhich each piece of material within thecross-section makes to the total bendingresistance depends on its remoteness fromthe neutral axis (more precisely on thesquare of its distance from the neutral axis).

The bending strength of a cross-sectiontherefore depends on the extent to whichthe material in it is dispersed away from theneutral axis and I is the measure of this. Fig.A2.8 shows three beam cross-sections, all ofthe same total area. (a) is stronger inbending with respect to the X–X axis than(b), which is stronger than (c), despite thefact that the total cross-sectional area ofeach is the same; this is because (a) has thelargest I about the X–X axis, (b) the nextlargest and (c) the smallest.

The efficiency of a beam in resisting abending-type load depends on therelationship between the second moment ofarea of its cross-section and its total area ofcross-section. I determines the bendingstrength and A the weight (i.e. the totalamount of material present).

2 The elastic bending formula is used tocalculate the bending stress at any fibre adistance y from the neural axis of a beamcross-section. The maximum stresses occurat the extreme fibres, where the values of yare greatest, and, for the purpose ofcalculating extreme fibre stresses, theequation is frequently written in the form,

fmax = M/Z

where: Z = I/ymax

Z is called the modulus of the cross-section.(It is often referred to as the ‘sectionmodulus’; sometimes the term ‘elasticmodulus’ is used and this is unfortunatebecause it leads to confusion with the term‘modulus of elasticity’ – see Section A2.4.)

If the cross-section of an element is notsymmetrical about the axis through itscentroid the maximum stresses in tensionand compression are different. Where thisoccurs two section moduli are quoted for thecross-section, one for each value of ymax.)

3 In the form M = fI/y or M = fZ the elasticbending formula can be used, inconjunction with a relevant allowable stressvalue, to calculate the maximum value ofbending moment which a beam cross-section can resist. This is called the‘moment of resistance’ of the cross-section.

4 In the form

Zreq = Mmax/fmax

where: Zreq = modulus of cross-sectionrequired for adequatestrength

Mmax = bending moment caused bymaximum load

fmax = maximum allowable stress

the formula can be used to determine thesize of cross-section required for a particular 137

Appendix 2: Stress and strain

Fig. A2.8 All of these beam cross-sections have the samearea of 5000 mm2 but (a) has the greatest bending strengthabout the X–X axis because it has the largest Ix–x.

(a) (b) (c)

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beam. This is an essential stage in element-sizing calculations.

A2.4 Strain

To understand the causes of strain it isnecessary to appreciate how structural materialresponds when load is applied to it. Itsbehaviour is in fact similar to that of a spring(Fig. A2.9).

In the unloaded state it is at rest; it has aparticular length and occupies a particularvolume. If a compressive load is applied, as inFig. A2.9, there is at first nothing to resist it;the material in the immediate locality of theload simply deforms under its action and theends of the element move closer together. Thishas the effect of generating internal force inthe material which resists the load andattempts to return the element to its originallength. The magnitude of the resisting forceincreases as the deformation increases and themovement ceases when sufficient deformationhas occurred to generate enough internal forceto resist totally the applied load. Equilibriumis then established with the element carryingthe load, but only after it has suffered a certainamount of deformation.

The important point here is that theresistance of load can occur only ifdeformation of material also occurs; astructure can therefore be regarded assomething which is animate and which moveseither when a load is applied to it or if the loadchanges. The need to prevent the movement

from being excessive is a consideration whichinfluences structural design.

The relationship between stress and strainis one of the fundamental properties of amaterial. Figure A2.10 shows graphs of axialstress plotted against axial strain for steel andconcrete. In both cases the graph is a straightline in the initial stages of loading, the so-called ‘elastic’ range, and a curve in the higherloading range, which is called the ‘inelastic’ or‘plastic’ range. In the elastic range the stress isdirectly proportional to the strain and the ratioof stress to strain, which is the gradient of thegraph, is constant and is called the ‘modulusof elasticity’ of the material (E).

In the inelastic range the amount ofdeformation which occurs for a given increasein load is greater than in the elastic range. Afurther difference between the two ranges isthat if the load is released after the inelasticrange has been entered the specimen does notreturn to its original length: a permanent

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Fig. A2.9 Deformation following the application of load.The behaviour of a block of material is similar to that of aspring.

Fig. A2.10 Typical graphs of stress against strain for steeland concrete. (a) Steel. (b) Concrete.

(a)

(b)

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deformation occurs and the material is said tohave ‘yielded’. In the case of steel thetransition between elastic and inelasticbehaviour occurs at a well-defined level ofstress, called the yield stress. Concreteproduces a more gradual transition. If aspecimen of either material is subjected to aload which increases indefinitely a failurestress is eventually reached; the magnitude ofthis is usually significantly greater than theyield stress.

The modulus of elasticity is one of thefundamental properties of a material. If it ishigh, a small amount of deformation only isrequired to produce a given amount of stressand therefore to resist a given amount of load.Such materials feel hard to the touch; steeland stone are examples. Where the modulus of

elasticity of a material is low the amount ofdeformation which occurs before a load isresisted is high; this gives the material, rubberfor example, a soft feel.

A further point in connection with stressand strain is that the load/deflection graphs forcomplete structures are similar to thestress/strain graphs for the materials fromwhich they are made. When the stress in thematerial in a complete structure is within theelastic range, the load/deflection graph for thestructure as a whole is a straight line and thebehaviour of the structure is said to be linear.If the material in the structure is stressed inthe inelastic range the load/deflectionrelationship for the whole structure will not bea straight line and the structure is said toexhibit non-linear behaviour.

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Appendix 2: Stress and strain

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A3.1 Introduction

It has been shown that the conditions forequilibrium of a set of coplanar forces can besummarised in the three equations ofequilibrium (see Appendix 1). These equationscan be solved as a simultaneous set for theforces in a force system which are unknown aswas shown in connection with Fig. A1.9.

A structure which can be fully solved fromthe equations of equilibrium in this way is saidto be statically determinate. The structure inFig. A3.1, which has four external reactions,cannot be solved by this method because thenumber of unknown reactions is greater than

the number of equations which can be derivedby considering the equilibrium of the externalforce system. The structure in Fig. A3.2 is alsoinsoluble by equilibrium due to the fact thatthe number of internal forces which it containsis greater than the number of independentequations which can be derived by consideringonly the equilibrium of all possible ‘free-body-diagrams’. These structures are said to bestatically indeterminate.

Structures can therefore be subdivided intotwo categories, those which are staticallydeterminate and those which are staticallyindeterminate. The two types behave insignificantly different ways in response to loadand the decision as to which should beadopted in a particular situation is animportant aspect of structural design. Moststructural geometries can be produced ineither form and the designer of a structuremust take a conscious decision as to whichtype is appropriate. The choice affects thedetailed geometry of the structure and caninfluence the selection of the structuralmaterial.

A3.2 The characteristics of staticallydeterminate and staticallyindeterminate structures

A3.2.1 Internal forcesIn Fig. A3.3 two independent staticallydeterminate structures, ABC and ADC, areshown. They happen to share the samesupports, A and C, but in every other respectthey are independent. If horizontal loads of Pand 2P are applied to joints B and D,respectively, the structures will resist these;

Appendix 3

The concept of staticaldeterminacy

Fig. A3.1 The framework (a) is statically determinate.Framework (b) is statically indeterminate because the fourexternal reactions cannot be solved from the threeequations of equilibrium which can be derived.

140

Fig. A3.2 Although the externalforce system of this structure isstatically determinate theframework is staticallyindeterminate because itcontains more elements than arerequired for internal stability. Itwill not be possible to solve thestructure for all of the internalforces by considering staticequilibrium only.

(a) (b)

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internal forces and reactions will be developed,all of which can be calculated from theequations of equilibrium, and the elementswill undergo axial strain, the magnitudes ofwhich will depend on the elasticity of thematerial and the sizes of the element cross-sections. Both joints B and D will suffer lateraldeflections but these will not affect theinternal forces in the elements, which will besolely dependent on the external loads and onthe geometries of the arrangement (to a firstapproximation).

If a fifth element is added, which connectsjoints B and D, the system becomes staticallyindeterminate. The two joints are nowconstrained to deflect by the same amountunder all load conditions and if the two loadsare applied as before the extent of theresulting elongation or contraction of theelements will not be the same as occurredwhen the joints B and D were free to deflectindependently. This means that the joint whichpreviously deflected less will be pulled orpushed further than before and the reverse willoccur to the other joint. A transfer of load willtherefore occur along the element BD and thiswill alter the pattern of internal forces in thewhole frame. The amount of load transfer, andtherefore of change to the internal forcesystem, will depend on the difference betweenthe deflections which occurred to the twojoints in the statically determinate forms. Thisis determined by the rigidity of the elements,so the distribution of internal forces in the

statically indeterminate structure is thereforedependent on the properties of the elementsas well as on the overall geometry of the frameand the magnitudes of the external loads. Theelement properties must therefore be takeninto account in the analysis of this structure.This is generally true of staticallyindeterminate structures and is one of theimportant differences between staticallydeterminate and statically indeterminatestructures.

The fact that element properties have to beconsidered in the analysis of staticallyindeterminate structures makes their analysismuch more complicated than that ofequivalent statically determinate structures; inparticular, it requires that the rigidity of theelements be taken into account. As this canonly be done once the element dimensionshave been decided and a material selected, itmeans that the design calculations forstatically indeterminate structures must becarried out on a trial and error basis. A set ofelement sizes must be selected initially toallow the analysis to be carried out. Once theinternal forces have been calculated thesuitability of the trial sizes can be assessed bycalculating the stress which will occur in them.The element sizes must normally be altered tosuit the particular internal forces which occurand this causes a change in the pattern of theinternal forces. A further analysis is thenrequired to calculate the new internal forces,followed by a further revision of the element 141

Appendix 3: The concept of statical determinacy

Fig. A3.3 The pattern of internal forces in a staticallyindeterminate structure depends on the properties of theelements as well as on the overall geometry of thearrangement. (a) ABC and ADC are independent staticallydeterminate structures. (b) The two structures are free todeflect independently in response to load. (c) Thepresence of element BD renders the arrangement statically

indeterminate. Joints B and D must undergo the samedeflection; internal force, dependent on the relativemagnitudes of S1 and S2, occurs in BD and this alters thewhole pattern of internal forces. The final distribution ofinternal force depends on the elasticity of the elements aswell as the overall geometry of the structure.

(a) (b) (c)

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dimensions. The sequence must be continueduntil satisfactory element sizes are obtained.Cycles of calculations of this type are routinein computer-aided design.

By comparison, the calculations forstatically determinate structures are muchmore straightforward. The internal forces in theelements depend solely on the external loadsand on the overall geometry of the structure.They can therefore be calculated before anydecision on element dimensions or a structuralmaterial has been taken. Once the internalforces are known, a material can be chosen andappropriate element dimensions selected.These will not affect the pattern of the internalforces and so a single sequence of calculationsis sufficient to complete the design.

A3.2.2 Efficiency in the use of materialThe efficiency with which structural material isused is normally greater with staticallyindeterminate structures because the presenceof a larger number of constraints allows a moredirect transmission of loads to the foundationsand a more even sharing of load by all of theelements. The benefits of staticalindeterminacy in this respect are most easily

seen in relation to structures with rigid joints,in which the resulting structural continuitycauses smaller bending moments to occurthan are present in equivalent staticallydeterminate structures under the same loadconditions. As before the differences betweenthe two types of structure can be appreciatedby studying very simple examples.

The simply supported beam (Fig. A3.4),whose supports offer no restraint againstrotation of the beam ends, is a staticallydeterminate structure. The deflected shape ofthis, in response to a uniformly distributedload, is a sagging curve in which, as in allstructures which are subjected to bending, theintensity of the curvature at every cross-sectionis directly proportional to the magnitude of thebending moment at that cross-section. Thecurvature is greatest at mid-span anddecreases to zero at the supports where thebeam ends tilt but remain straight.

A beam whose ends are restrained againstrotation is a statically indeterminate structure(Fig. A3.5). The fixed-end supports are eachcapable of producing three external reactionsand the total of six reactions makes thesolution of the external force system

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Fig. A3.4 Load,deflection and bendingmoment diagrams for astatically determinatesimply supportedbeam.

Fig. A3.5 Load, deflection and bending momentdiagrams for a statically indeterminate beam subjected tothe same load pattern as in Fig. A3.4. The effect of therestraint at the supports, which are the cause of thestatical indeterminacy, is to reduce the value of themaximum bending moment.

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impossible from the three equations ofequilibrium which can be derived. Anotherconsequence of the end fixities, and of themoment reactions which result from them, isthat the ends of the beam remain horizontalwhen a load is applied. The mid-span portionstill adopts a sagging curve, but the amount ofsag is less than in the simply supported case,because a reversal in the direction of thecurvature occurs at each end. The effect is seenin the bending moment diagram, in whichregions of negative bending moment occur tocorrespond with the hogging curvature at thebeam ends. The reduction in the sag at mid-span is associated with a smaller positivebending moment than occurs in the simplysupported beam.

The total depth of the bending momentdiagram is the same for both beams, but theeffect of the end fixity is to reduce themaximum positive bending moment at mid-span from wL/8, for the simply supportedbeam, to wL/24 for the beam with fixed ends,where w is the total load carried and L is thespan. The overall maximum bending momentin the fixed-ended beam is in fact a negativevalue of –wL/12, which occurs at its ends. Theeffect of fixing the ends of the beam and ofmaking it statically indeterminate is thereforeto reduce the maximum value of the bendingmoment from wL/8 at mid-span to –wL/12 atthe supports.

As the bending stress in a beam iseverywhere directly proportional to thebending moment, assuming that the cross-section is constant along its length, thehighest stresses in the fixed-ended beam occurat the ends of the span and are less, by a factorof 2/3, than the highest stress in the equivalentsimply supported beam, which occurs at mid-span. The fixed-ended beam is therefore ableto carry a load which is 1.5 times greater thanthe load on an equivalent simply supportedbeam before it is stressed to the same extent;it is therefore 1.5 times as strong. Conversely,a fixed-ended beam which is 2/3 the size of anequivalent simply supported beam can carrythe same load with equal safety. The adoptionof the statically indeterminate form therefore

allows a more efficient use to be made of thestructural material. As with most gains, there isa cost, which in this case arises from thedifficulty of providing fixed-ended supportconditions.

In more complicated structures, where manyelements are present, the benefits of end fixityare achieved by making the joints betweenthem rigid. Such structures are calledcontinuous structures and they are normallystatically indeterminate. In the beam which iscontinuous over a number of supports (Fig.A3.6), the continuity between adjacent spansproduces a deflected form which is a singlecontinuous curve. The hogging at the supportscorresponds to areas of negative bendingmoment and reduces the magnitude of the

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Appendix 3: The concept of statical determinacy

Fig. A3.6 A beam which is continuous over a number ofsupports is a statically indeterminate structure. Themagnitudes of the bending moments in each span arelower than if hinge joints were provided at each support(the statically determinate form).

Fig. A3.7 A frame with rigid beam-to-column joints is staticallyindeterminate. The bending moment inthe beam is less than it would be ifhinge connections were provided, butat a cost of introducing bendingmoment into the columns.

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positive bending moments in the mid-spanpositions. The effect of the hogging is thereforesimilar to that which is produced by themoment reactions which occur in the fixed-ended beam of Fig. A3.5. The same effect isseen in the rigid frame (Fig. A3.7) in which therigid beam-to-column joints allow the columnsto restrain the ends of the single beam whichis present.

A3.2.3 The ‘lack-of-fit’ problemWith the possible exception of in situ reinforcedconcrete structures, most structures areprefabricated to some extent so that theirconstruction on site is a process of assembly.As prefabricated components can never beproduced with precisely the correctdimensions, the question of ‘lack-of-fit’ and ofthe tolerance which must be allowed for this isa necessary consideration in structural design.It can affect the decision on whether to use astatically determinate or indeterminate form,because the tolerance of statically determinatestructures to ‘lack-of-fit’ is much greater thanthat of statically indeterminate structures. Asin the case of other properties the reason forthis can be seen from an examination of thebehaviour of a small framework (Fig. A3.8).

The arrangement in Fig. A3.8(a) is staticallydeterminate while that in Fig. A3.8(b) is anequivalent statically indeterminate form. It willbe assumed that the frames are assembledfrom straight elements, that the structural

material is steel and that the hinge-type jointsare made by bolting. The elements would befabricated in a steel fabrication workshop andall bolt holes would be pre-drilled. However, itwould be impossible to cut the elements toexactly the correct length, or to drill the boltholes in exactly the correct positions; therewould always be some small error no matterhow much care was taken in the fabricationprocess.

The initial stages of the assembly would bethe same for both forms and might consist ofbolting the beams to the tops of the twocolumns. The resulting arrangements wouldstill be mechanisms at this stage and anydiscrepancies which existed between thelength of the next element to be inserted, thatis the first diagonal element, and the length ofthe space into which it must fit, could beeliminated by swaying the assembly until thedistance between the joints was exactly thesame as the length of the element. Theinsertion of the first diagonal element wouldcomplete the assembly of the staticallydeterminate form. To complete the staticallyindeterminate form the second diagonal mustbe added. If any discrepancy exists betweenthe length of this and the distance between thejoints to which it must be attached, thedistance cannot now be adjusted easily bymoving the partly assembled frame because itis now a structure and will resist any forcewhich is applied to it in an attempt to alter itsshape. A significant force would therefore haveto be applied to distort the frame before thefinal element could be inserted. This wouldproduce stress in the elements, which wouldtend to restore the frame to its original shapewhen the force was released after the insertionof the final element. The presence of thesecond diagonal element in the frame wouldprevent it from returning to its original shape,

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Fig. A3.8 The ‘lack-of-fit’ problem. (a) Staticallydeterminate frame. (b) Statically indeterminate form. (c)The arrangement is unstable until the first diagonalelement is inserted. There is no lack-of-fit problem inassembling the statically determinate frame. (d) After thefirst diagonal is in place the arrangement has a stablegeometry. There is therefore a potential lack-of-fit problemin inserting the last element in the statically indeterminateversion of the frame.

(a) (b) (c) (d)

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however, and the result would be that all ofthe elements in the frame would finally carry apermanent stress as a result of the ‘lack-of-fit’.This would be additional to any stress whichthey had to carry as a result of the applicationof the frame’s legitimate load.

The performance in respect of ‘lack-of-fit’ isan important difference between staticallydeterminate and statically indeterminatestructures. Statically determinate structurescan be assembled fairly easily despite the factthat it is impossible to fabricate structuralcomponents with absolute accuracy as anydiscrepancy which exists between the actualdimensions of components and their intendeddimensions can normally be accommodatedduring the construction process. This does, ofcourse, result in a final structural geometrywhich is slightly different from the shape whichwas planned, but the level of accuracy reachedin the fabrication is normally such that anydiscrepancy is undetectable to the naked eyedespite being significant from the point of viewof the introduction of ‘lack-of-fit’ stresses.

In the case of statically indeterminatestructures even small discrepancies in thedimensions can lead to difficulties in assemblyand the problem becomes more acute as thedegree of indeterminacy is increased. It hastwo aspects: firstly, there is the difficulty ofactually constructing the structure if theelements do not fit perfectly; and secondly,there is the possibility that ‘lack-of-fit’ stressesmay be developed, which will reduce itscarrying capacity. The problem is dealt with byminimising the amount of ‘lack-of-fit’ whichoccurs and also by devising means of‘adjusting’ the lengths of the elements duringconstruction (for example by use of packingplates). Both of these require that highstandards are achieved in the detailed designof the structures, in the manufacture of itscomponents and also in the setting out of thestructure on site. A consequence of the ‘lack-of-fit’ problem, therefore, is that both thedesign and the construction of staticallyindeterminate structures are more difficult andtherefore more expensive than those ofequivalent statically determinate structures.

A3.2.4 Thermal expansion and ‘temperature’stressesIt was seen in Section A3.2.3 that in the case ofstatically indeterminate structures stresses canbe introduced into the elements if they do notfit perfectly when the structure is assembled.Even if perfect fit were to be achieved initially,however, any subsequent alteration to thedimensions of elements due to thermalexpansion or contraction would lead to thecreation of stress. Such stress is known as‘temperature’ stress. It does not occur instatically determinate structures, in whichsmall changes in dimensions due to thermalexpansion are accommodated by minoradjustments to the structure’s shape withoutthe introduction of stress.

Thermal expansion must be considered inthe design of most statically indeterminatestructures and the elements made strongenough to resist the resulting additional stresswhich will occur. This depends on the range oftemperature to which the structure will beexposed and on the coefficient of thermalexpansion of the material. It is a factor whichobviously reduces the load carrying capacityand therefore efficiency of staticallyindeterminate structures.

A3.2.5 The effect of differential settlementof foundationsJust as a statically determinate structure canadjust its geometry in response to minorchanges in the dimensions of elements

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Appendix 3: The concept of statical determinacy

Fig. A3.9 The effect of differential settlement ondeterminate and indeterminate structures. (a) Thestatically determinate three-hinge frame can adjust itsgeometry to accommodate foundation movement withoutthe introduction of bending in the elements. (b) Bendingof elements and the introduction of stress is an inevitableconsequence of foundation movement in the two-hingeframe which is statically indeterminate.

(a) (b)

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without the introduction of internal force andtherefore stress, it can also accommodatedifferential settlement of its foundations (Fig.A3.9). Determinate structures can in facttolerate fairly large foundation movementswithout distress to the structure. Staticallyindeterminate forms, on the other hand,cannot make this kind of adjustment withoutstress being introduced into the material, andit is therefore important that significantdifferential settlement of foundations beavoided in their case. The issue can affect thechoice of structure type for a particularbuilding. If, for example, a building is to beerected on a site where the ground conditionsare problematic, such as might occur in anarea liable to mining subsidence, the choicemight be between a statically determinatestructure on individual foundations whichwould be capable of accommodatingmovement or an indeterminate structure ondeep piled or a raft foundation. The latterwould probably be a considerably moreexpensive solution.

A3.2.6 The effect of the state of determinacyon the freedom of the designer tomanipulate the formBecause statically indeterminate structurescontain more constraints than are required forstability, more than one path will normally existby which a load can be conducted through thestructure to the foundations. In other words,the task of conducting a load through thestructure from the point at which it is appliedto the foundations is shared between thevarious structural elements. This does notoccur with statically determinate structures inwhich there is normally only one route bywhich a load can pass through the structure.

A consequence of the redundancy which ispresent in statically indeterminate forms isthat elements can be removed withoutcompromising the viability of the structure (theremaining elements then carry higher internalforces). This property of staticallyindeterminate structures gives the designermuch more freedom to manipulate the form atthe design stage than is available with a

statically determinate structure. In the case ofa statically indeterminate two-way spanningreinforced concrete slab, for example, thedesigner has the freedom to incorporate voidsin the floor slabs, cantilever the floors beyondthe perimeter columns, and generally to adoptirregularity in the form which would not bepossible with a statically determinate steelframe. The fact that statically indeterminatestructures are self-bracing is another factorwhich increases the freedom available to thedesigner of the structure.

A3.3 Design considerations inrelation to statical determinacy

Most structural geometries can be produced ineither a statically determinate or a staticallyindeterminate form depending on how theconstituent elements are connected together.The question of which should be adopted in aparticular case is one of the fundamentalissues of the design process and the decisionis influenced by the factors which have beenconsidered above. The main advantage ofstatically indeterminate structures is that theyallow a more efficient use of material thanequivalent statically determinate forms. It istherefore possible to achieve longer spans andcarry heavier loads than with staticallydeterminate equivalents. The principaldisadvantage of statically indeterminatestructures are that they are more complex todesign and more difficult to construct thanstatically determinate equivalents; thesefactors usually make them more expensivedespite their greater efficiency. Otherdisadvantages are the possibilities of ‘lack-of-fit’ and ‘temperature’ stresses and the greatersusceptibility of statically indeterminatestructures to damage as a result of differentialsettlement of foundations. These variousfactors are weighed against each other by thedesigner of a structure who must decide whichtype is more suitable in an individual case.

The decision as to which material should beused for a structure is often related to thedecision on determinacy. Reinforced concrete

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is ideal for statically indeterminate structuresdue to the ease with which continuity can beachieved without the disadvantage of the ‘lack-of-fit’ problem and also to its low coefficient ofthermal expansion, which results intemperature stresses being low. Mostreinforced concrete structures are thereforedesigned to be statically indeterminate.

The use of steel for statically indeterminatestructures, on the other hand, can beproblematical due to the ‘lack-of-fit’ problemand to the relatively high coefficient of thermalexpansion of the material. Steel thereforetends to be used for statically determinatestructures rather than for staticallyindeterminate structures unless the particularadvantages of indeterminacy are specificallyrequired in conjunction with the use of steel.Steel and timber are in fact particularlysuitable for statically determinate structuresdue to the ease with which hinge-type jointscan be produced in these materials.

Usually the circumstances of a particularbuilding will dictate the choice of structure

type and material. If a building is of small ormoderately large size with no very large spansthen the simplicity of the staticallydeterminate form will normally favour its use.If very high structural efficiency is required toachieve long spans or simply to provide anelegant structural form then this might favourthe use of statical indeterminacy inconjunction with a strong material such assteel. The resulting structure would beexpensive, however. Where relatively highefficiency is required to carry very heavy loadsthen a statically indeterminate structure inreinforced concrete might be the best choice. Ifa structure is to be placed on a site on whichdifferential settlement is likely to occur, theuse of a statically determinate form inconjunction with a suitable material such astimber or steel would probably be appropriate.The decision on the type of structure istherefore taken in conjunction with thedecision on structural material, and both aredependent on the individual circumstances ofthe building concerned.

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AEG Turbine Hall, Berlin,Germany, 76

Airship Hangars, Orly, France,88

Architects Co-Partnership, 58Arup, O., 105Alderton, I.W., 25Analysis, structural, 17, 20Antigone building,

Montpellier, France, 5Axial thrust, 19

Barlow, W.H., 88, 118Basilica of Constantine,

Rome, Italy, 102, 115Behnisch, G., xiiBehrens, P., 75, 76Bending moment, 18–20, 41Bofill, R., 5Bracing, 11–15Brunelleschi, P., 88, 117Brynmawr Rubber Factory,

Brynmawr, UK, 58

Calatrava, S., 83, 121Candela, F., 88, 121Carré d’Art, Nîmes, France, 4Centre Pompidou, Paris,

France, 5, 6, 32, 33, 69–7-,81–3, 84–5

Chartres Cathedral, France, 23

Château de Chambord,France, 7

Chrysler Building, New York,USA, 104–5

CNIT exhibition hall, Paris, 1,2, 86, 88

Concrete, 35

Continuous structure, 47–8,53, 54 140–7

Coop Himmelblau, 6, 110, 113Corbusier, Le, xii, 1, 9, 36, 77,

104, 110, 120Cost, 63–5Crystal Palace, London, UK,

86, 97, 121

Deconstruction, xiiDeutsches Museum, Berlin,

Germany, 110–11Determinate structure, 140–7Differential settlement, 145–6Discontinuous structure, 47–8,

53, 140–7Dome, 87

Eden Project, Cornwall, UK,121–2, 123

Efficiency, 37–46, 60–7, 142–4Einstein Tower, Potsdam, xii,

xiiiEisenman, P., 36, 54Elastic bending formula,

136–8Element sizing, 20–1Emo, Villa, Fanzolo, Italy, 115Empire State Building, New

York, USA, 104Engel, H., 12, 38Equilibrium, 9, 129–32Esquillan, N., 2, 88Exhibition and Assembly

Building, Ulm, Germany, 5Extreme fibre stress, 37–8

Farnsworth House, Illinois,USA, 75

Ferro-cement, 88Flat slab structure, 35, 55Florence Cathedral, 88, 117Florey building, Oxford, UK, 54Force:

internal, 16, 37moment of, 129resolution of, 129vector, 128

Form active structure, 36,38–40, 46, 47, 57–9, 61

Forth Railway Bridge, UK,67–9

Foster Associates, 2–5, 34, 55,78, 106–7

Free-body diagram, 17–20, 132Freyssinet, E., 88, 121Future Systems, 80–1

Galérie des Machines, Paris,France, 88

Gehry, F., 36, 111, 113, 120Gerber, H., 82Gerberette brackets, 32–3, 70,

82–3Grant, J.A.W., 8Grimshaw, N., 77, 88, 121, 123Gropius, W., xii

Hadid, Z., 120Hancock Building, Chicago,

USA, 93, 95Happold, Buro, 91Happold, E., 121Highpoint, London, UK, 105–6High Tech, xii, 72, 75, 78, 86,

121, 122Hopkins House, 30, 66, 99–101Hopkins, M., 30, 57, 66, 121 149

Index

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Hunt, A., xiii, 3, 4, 30, 34, 55,76, 77, 98, 101, 106–7,121, 123

IBM Europe travellingexhibition building, 96

IBM Pilot Head Office,Cosham, UK, 107–9

Ictinus, 69Igerman, Iran, 24Igloo, 1, 2Imaginary cut, 17, 20, 132–3Imperial War Museum,

Manchester, UK, 110Improved cross-section, 40–6,

55Improved profile, 41–6Indeterminate structure, 53,

140–7Ingalls Ice Hockey Stadium,

Yale, USA, 2, 90INMOS Microprocessing

factory, Newport, UK, xiiiIyengar, H., 95

Jenkins, R., 88

Kansai Airport, Osaaka, Japan,88

Kaplicky, J., 80

‘Lack of fit’ problem, 55, 144–5Libeskind, D., 110–1, 113, 120Lloyds Headquarters Building,

London, UK, 36, 78, 79,83–5

Loadbearing wall structure,15, 48–51

Loading, 1, 16–17Lord’s Cricket Ground,

London, UK, 57Lubetkin, B., 105

Masonry, 22–4Meier, R., 5, 36, 54Mendelsohn, E., xiiMidland Hotel, London, UK,

119Mies van der Rohe, L., xii, 120

Millennium Dome, London,UK, 90–1

Miller House, Connecticut,USA, 54

Modern Art Glass warehouse,Thamesmead, UK, 2, 3, 79

Modulus of elasticity, 138Moment of resistance, 137Monocoque structure, 42Morandi, R., 121

National Botanic Garden ofWales, UK, 121–2

Nervi, P., 88, 121Nixon, D., 80Notre-Dame-du-Haut,

Ronchamp, France, 1, 36,109, 110, 113

Olympic Stadium, Munich,Germany, xii

Ordish, R., 88, 118–19Otto, F., xii, 90Ove Arup and Partners, 6, 57,

58, 78, 82, 84, 88, 96, 113

Palladio, A., 75, 115Palazzetto dello Sport, Rome,

Italy, 88Pantheon, Rome, Italy, 102, 115Parthenon, Athens, Greece,

69, 73–4Patera building, 98–101Paxton, J., 97Perret, A., 75Piano, R., 5, 6, 82, 88, 96Polygon of forces, 128, 130Pompidou Centre, Paris,

France, see CentrePomprdou, Paris, France

Post-and-beam structure, 47,48–55, 69

Prix, W., 110

Reliance Controls building,Swindon, UK, 76, 77

Renault Headquartersbuilding, Swindon, UK,34, 70, 78

Rice, P., 83, 121Rigidity, 21Rogers, R., xiii, 5, 6, 81, 82, 83,

91, 121

Saarinen, E., 2, 90, 113Sainsbury Centre for the

Visual Arts, Norwich, UK,3

Savoye, Villa, Poissy, France,105

Scott, G.G., 119Sears Tower, Chicago, USA,

94, 95Second moment of area,

137–8Section modulus, 137Semi-form-active structure,

39, 46, 47, 55–6, 62Semi-monocoque structure,

43–5, 80Severud, F., 90Shear force, 18–20Sydney Opera House, Sydney,

Australia, 113Skeleton-frame structure, 51–5Skidmore, Owings and Merrill,

93, 94, 95Smithfield Poultry Market,

London, UK, 88–9St Pancras Station, London,

UK, 88, 118–9St Paul’s Cathedral, London,

UK, 116–7Stability, 9–15Statue of Liberty, New York,

USA, xiiiSteel, 30–5Stirling, J., 54Strain, 138–9Strength, 15–6Stress:

axial, 37–8, 135bending, 37–8, 135–8

Stressed skin structure, 42–5,80

Tay Railway Bridge, UK, 32Team 4, 77Technology transfer, 81

Index

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Temperature stress, 145–6Tepee, 1, 2Thermal expansion, 145Timber, 25–30Torroja, E., 88, 121Triangle of forces, 128, 130Triangulated structure, 42, 61TWA Terminal, New York, USA,

113

Unité d’Habitation, Marseilles,France, 104

Utzon, J., 113

Valmarana, Palazzo, Vicenza,Italy, 75, 116

Vault, 88, 103Victoria and Albert Museum,

London, UK, 110, 112Vitra Design Museum, Basel,

Switzerland, 36, 111Vitruvius, xi

Waterloo International RailTerminal, London, UK,76, 77, 88–9, 123

Williams, O., 121

Willis, Faber and DumasBuilding, Ipswich, UK, 3,4, 5, 36, 55, 71, 106–7, 109

Wooton, H., xiWorld Trade Centre, New York,

USA, 92, 94Wren, C., 116–17

Yamasaki, M., 92, 94Yield stress, 138–9YRM Anthony Hunt

Associates, 88Yurt, 65

151

Index

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