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Structure and Architecture This Page Intentionally Left Blank  Structure and Architecture Angus J. Macdonald Department of Architecture, University of Edinburgh Second edition...

Structure and Architecture This Page Intentionally Left Blank  Structure and Architecture Angus J. Macdonald Department of Architecture, University of Edinburgh Second edition Architectural Press OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Structure and Architecture Architectural Press An imprint of Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published 1994 Reprinted 1995, 1996, 1997 Second 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 addressed to the publishers British Library Cataloguing in Publication Data Macdonald, Angus J. Structure and architecture. – 2nd ed. 1. Structural design. 2. Architectural design I. Title 721 ISBN 0 7506 4793 0 Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress Printed and bound in Great Britain Composition by Scribe Design, Gillingham, Kent  Contents Preface vii 6.3 Reading a building as a structural object 67 Acknowledgements ix 6.4 Conclusion 71 Introduction xi 7 Structure and architecture 73 1 The relationship of structure to building 1 7.1 Introduction 73 7.2 The types of relationship between 2 Structural requirements 9 structure and architecture 73 2.1 Introduction 9 7.3 The relationship between architects 2.2 Equilibrium 9 and engineers 114 2.3 Geometric stability 9 2.4 Strength and rigidity 15 Selected bibliography 124 2.5 Conclusion 21 Appendix 1: Simple two-dimensional force 3 Structural materials 22 systems and static equilibrium 128 3.1 Introduction 22 A1.1 Introduction 128 3.2 Masonry 22 A1.2 Force vectors and resultants 128 3.3 Timber 25 A1.3 Resolution of a force into 3.4 Steel 30 components 129 3.5 Concrete 35 A1.4 Moments of forces 129 A1.5 Static equilibrium and the equations 4 The relationship between structural form of equilibrium 129 and structural efficiency 37 A1.6 The ‘free-body-diagram’ 132 4.1 Introduction 37 A1.7 The ‘imaginary cut’ technique 132 4.2 The effect of form on internal force type 37 4.3 The concept of ‘improved’ shapes in Appendix 2: Stress and strain 134 cross-section and longitudinal A2.1 Introduction 134 profile 40 A2.2 Calculation of axial stress 135 4.4 Classification of structural elements 45 A2.3 Calculation of bending stress 135 A2.4 Strain 138 5 Complete structural arrangements 47 5.1 Introduction 47 Appendix 3: The concept of statical 5.2 Post-and-beam structures 48 determinacy 140 5.3 Semi-form-active structures 55 A3.1 Introduction 140 5.4 Form-active structures 57 A3.2 The characteristics of statically 5.5 Conclusion 59 determinate and statically indeterminate structures 140 6 The critical appraisal of structures 60 A3.3 Design considerations in relation to 6.1 Introduction 60 statical determinacy 146 6.2 Complexity and efficiency in structural design 60 Index 149 This Page Intentionally Left Blank  Preface to the second edition The major theme of this book is the have had on architectural style and form. The relationship between structural design and penultimate chapter, on structural criticism, architectural design. The various aspects of has also been extensively rewritten. It is hoped this are brought together in the last chapter that the ideas explored in both of these which has been expanded in this second chapters will contribute to the better edition, partly in response to comments from understanding of the essential and readers of the first edition, partly because my undervalued contribution of structural own ideas have changed and developed, and engineering to the Western architectural partly as a consequence of discussion of the tradition and to present-day practice. issues with colleagues in architecture and structural engineering. I have also added a Angus J. Macdonald section on the types of relationship which have Department of Architecture, existed between architects, builders and University of Edinburgh engineers, and on the influence which these December 2000 vii This Page Intentionally Left Blank  Acknowledgements Angus Macdonald would like to thank all in their captions. Thanks are due to all those those, too numerous to mention, who have who supplied illustrations and especially to assisted in the making of this book. Special Pat Hunt, Tony Hunt, the late Alastair Hunter, thanks are due to Stephen Gibson for his Jill Hunter and the staff of the picture libraries carefully crafted line drawings, Hilary Norman of Ove Arup & Partners, Anthony Hunt for her intelligent design, Thérèse Duriez for Associates, the British Cement Association, the picture research and the staff of Architectural Architectural Association, the British Press (and previously Butterworth-Heinemann) Architecture Library and the Courtauld for their hard work and patience in initiating, Institute. editing and producing the book, particularly Thanks are also due most particularly to Neil Warnock-Smith, Diane Chandler, Angela my wife Pat, for her continued Leopard, Siân Cryer and Sue Hamilton. encouragement and for her expert scrutiny of Illustrations other than those commissioned the typescript. specially for the book are individually credited ix This Page Intentionally Left Blank  Introduction It has long been recognised that an preserve its physical integrity and survive in appreciation of the role of structure is the world as a physical object. The part of the essential to the understanding of architecture. building which satisfies the need for ‘firmness’ It was Vitruvius, writing at the time of the is the structure. Structure is fundamental: founding of the Roman Empire, who identified without structure there is no building and the three basic components of architecture as therefore no ‘commodity’. Without well- firmitas, utilitas and venustas and Sir Henry designed structure there can be no ‘delight’. Wooton, in the seventeenth century1, who To appreciate fully the qualities of a work of translated these as ‘firmness’, ‘commodity’ and architecture the critic or observer should ‘delight’. Subsequent theorists have proposed therefore know something of its structural different systems by which buildings may be make-up. This requires an intuitive ability to analysed, their qualities discussed and their read a building as a structural object, a skill meanings understood but the Vitruvian which depends on a knowledge of the breakdown nevertheless still provides a valid functional requirements of structure and an basis for the examination and criticism of a ability to distinguish between the structural building. and the non-structural parts of the building. ‘Commodity’, which is perhaps the most The first of these attributes can only be obvious of the Vitruvian qualities to acquired by systematic study of those branches appreciate, refers to the practical functioning of mechanical science which are concerned of the building; the requirement that the set of with statics, equilibrium and the properties of spaces which is provided is actually useful and materials. The second depends on a knowledge serves the purpose for which the building was of buildings and how they are constructed. intended. ‘Delight’ is the term for the effect of These topics are reviewed briefly in the the building on the aesthetic sensibilities of preliminary chapters of this book. those who come into contact with it. It may The form of a structural armature is arise from one or more of a number of factors. inevitably very closely related to that of the The symbolic meanings of the chosen forms, building which it supports, and the act of the aesthetic qualities of the shapes, textures designing a building – of determining its and colours, the elegance with which the overall form – is therefore also an act of various practical and programmatic problems structural design. The relationship between posed by the building have been solved, and structural design and architectural design can the ways in which links have been made take many forms however. At one extreme it is between the different aspects of the design are possible for an architect virtually to ignore all possible generators of ‘delight’. structural considerations while inventing the ‘Firmness’ is the most basic quality. It is form of a building and to conceal entirely the concerned with the ability of the building to structural elements in the completed version of the building. The Statue of Liberty (Fig. ii) at the entrance to New York harbour, which, given 1 Wooton, H., The Elements of Architecture, 1624. that it contains an internal circulation system xi Introduction of stairs and elevators, can be considered to be other than structure. The Olympic Stadium in a building, is an example of this type. The Munich (Fig. i), by the architects Behnisch and buildings of early twentieth-century Partners with Frei Otto, is an example of this. expressionism, such as the Einstein Tower at Between these extremes many different Potsdam by Mendelsohn (Fig. iii) and some approaches to the relationship between recent buildings based on the ideas of structure and architecture are possible. In the Deconstruction (see Figs 1.11 and 7.41 to 7.44) ‘high tech’ architecture of the 1980s (Fig. iv), for might be cited as further examples. example, the structural elements discipline the All of these buildings contain a structure, plan and general arrangement of the building but the technical requirements of the structure and form an important part of the visual have not significantly influenced the form vocabulary. In the early Modern buildings of which has been adopted and the structural Gropius, Mies van der Rohe, Le Corbusier (see elements themselves are not important Fig. 7.34) and others, the forms which were contributors to the aesthetics of the adopted were greatly influenced by the types of architecture. At the other extreme it is possible geometry which were suitable for steel and to produce a building which consists of little reinforced concrete structural frameworks. Fig. i Olympic Stadium, Munich, Germany, 1968–72; Behnisch & Partner, architects, with Frei Otto. In both the canopy and the raked seating most of what is seen is structural. (Photo: A. Macdonald) xii  Introduction Fig. iii Sketches by Mendelsohn of the Einstein Tower, Potsdam, Germany, 1917. Structural requirements had little influence on the external form of this building, although they did affect the internal planning. Surprisingly, it was constructed in loadbearing masonry. The relationship between structure and architecture can therefore take many forms and it is the purpose of this book to explore these against a background of information concerning the technical properties and requirements of Fig. ii The thin external surface of the structures. The author hopes that it will be Statue of Liberty in New York Harbour, USA, found useful by architectural critics and is supported by a triangulated structural framework. The influence of structural historians as well as students and practitioners considerations on the final version of the of the professions concerned with building. form was minimal. Fig. iv Inmos Microprocessor Factory, Newport, South Wales, 1982; Richard Rogers Partnership, architects; Anthony Hunt Associates, structural engineers. The general arrangement and appearance of this building were strongly influenced by the requirements of the exposed structure. The form of the latter was determined by space- planning requirements. (Photo: Anthony Hunt Associates) xiii This Page Intentionally Left Blank  Chapter 1 The relationship of structure to building The simplest way of describing the function of collapse; it is to prevent this from happening an architectural structure is to say that it is the that a structure is provided. The function of a part of a building which resists the loads that structure may be summed up, therefore, as are imposed on it. A building may be regarded being to supply the strength and rigidity which as simply an envelope which encloses and are required to prevent a building from subdivides space in order to create a protected collapsing. More precisely, it is the part of a environment. The surfaces which form the building which conducts the loads which are envelope, that is the walls, the floors and the imposed on it from the points where they arise roof of the building, are subjected to various to the ground underneath the building, where types of loading: external surfaces are exposed they can ultimately be resisted. to the climatic loads of snow, wind and rain; The location of the structure within a floors are subjected to the gravitational loads building is not always obvious because the of the occupants and their effects; and most of structure can be integrated with the non- the surfaces also have to carry their own structural parts in various ways. Sometimes, as weight (Fig. 1.1). All of these loads tend to in the simple example of an igloo (Fig. 1.2), in distort the building envelope and to cause it to which ice blocks form a self-supporting protective dome, the structure and the space enclosing elements are one and the same thing. Sometimes the structural and space- enclosing elements are entirely separate. A very simple example is the tepee (Fig. 1.3), in which the protecting envelope is a skin of fabric or hide which has insufficient rigidity to form an enclosure by itself and which is supported on a framework of timber poles. Complete separation of structure and envelope occurs here: the envelope is entirely non- structural and the poles have a purely structural function. The CNIT exhibition Hall in Paris (Fig. 1.4) is a sophisticated version of the igloo; the reinforced concrete shell which forms the main element of this enclosure is self-supporting and, therefore, structural. Separation of skin and structure occurs in the transparent walls, Fig. 1.1 Loads on the building envelope. Gravitational however, where the glass envelope is loads due to snow and to the occupation of the building cause roof and floor structures to bend and induce supported on a structure of mullions. The compressive internal forces in walls. Wind causes pressure chapel by Le Corbusier at Ronchamp (see Fig. and suction loads to act on all external surfaces. 7.40) is a similar example. The highly 1 Structure and Architecture sculptured walls and roof of this building are made from a combination of masonry and reinforced concrete and are self-supporting. They are at the same time the elements which define the enclosure and the structural elements which give it the ability to maintain its form and resist load. The very large ice hockey arena at Yale by Saarinen (see Fig. 7.18) is yet another similar example. Here the building envelope consists of a network of steel cables which are suspended between Fig. 1.2 The igloo is a self-supporting compressive envelope. three reinforced concrete arches, one in the vertical plane forming the spine of the building and two side arches almost in the horizontal plane. The composition of this building is more complex than in the previous cases because the suspended envelope can be broken down into the cable network, which has a purely structural function, and a non- structural cladding system. It might also be argued that the arches have a purely structural function and do not contribute directly to the enclosure of space. The steel-frame warehouse by Foster Associates at Thamesmead, UK (Fig. 1.5), is almost a direct equivalent of the tepee. The Fig. 1.3 In the tepee a non-structural skin is supported elements which form it are either purely on a structural framework of timber poles. structural or entirely non-structural because Fig. 1.4 Exhibition Hall of the CNIT, Paris, France; Nicolas Esquillan, architect. The principal element is a self- 2 supporting reinforced concrete shell.  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 a purely structural function. (Photo: Andrew Mead) the corrugated sheet metal skin is entirely In most buildings the relationship between supported by the steel frame, which has a the envelope and the structure is more purely structural function. A similar breakdown complicated than in the above examples, and may be seen in later buildings by the same frequently this is because the interior of the architects, such as the Sainsbury Centre for the building is subdivided to a greater extent by Visual Arts at Norwich and the warehouse and internal walls and floors. For instance, in showroom for the Renault car company at Foster Associates’ building for Willis, Faber Swindon (see Fig. 3.19). and Dumas, Ipswich, UK (Figs 1.6 and 7.37), 3 Structure and Architecture the reinforced concrete structure of floor slabs and columns may be thought of as having a dual function. The columns are purely structural, although they do punctuate the interior spaces and are space-dividing elements, to some extent. The floors are both structural and space-dividing elements. Here, however, the situation is complicated by the fact that the structural floor slabs are topped by non-structural floor finishing materials and have ceilings suspended underneath them. The floor finishes and ceilings could be regarded as the true space-defining elements and the slab itself as having a purely structural function. The glass walls of the building are entirely non-structural and have a space-enclosing function only. The more recent Carré d’Art building in Nîmes (Fig. 1.7), also by Foster Associates, has a similar disposition of parts. As at Willis, Faber and Dumas a multi-storey reinforced concrete structure supports an external non-loadbearing skin. Fig. 1.6 Willis, Faber and Dumas Office, Ipswich, UK, 1974; Foster Associates, architects; Anthony Hunt Associates, structural engineers. The basic structure of this building is a series of reinforced concrete coffered slab floors supported on a grid of columns. The external walls are of glass and are non-structural. In the finished building the floor slabs are visible only at the perimeter. Elsewhere they are concealed by floor finishes and a false ceiling. Fig. 1.7 Carré d’Art, Nîmes, France, 1993; Foster Associates, architects. A superb example of late twentieth- century Modernism. It has a reinforced concrete frame structure which supports a non-loadbearing external skin 4 of glass. (Photo: James H. Morris)  The relationship of structure to building The Antigone building at Montpellier by Ricardo Bofill (Fig. 1.8) is also supported by a multi-storey reinforced concrete framework. The facade here consists of a mixture of in situ and pre-cast concrete elements, and this, like the glass walls of the Willis, Faber and Dumas building, relies on a structural framework of columns and floor slabs for support. Although this building appears to be much more solid than those with fully glazed external walls it was constructed in a similar way. The Ulm Exhibition and Assembly Building by Richard Meier (Fig. 1.9) is also supported by a reinforced concrete structure. Here the structural continuity (see Appendix 3) and Fig. 1.9 Ulm Exhibition and Assembly Building, Germany, 1986–93: Richard Meier & Partners, architects. The mouldability of concrete and the structural continuity which is a feature of this material are exploited here to produce a complex juxtaposition of solid and void. (Photo: E. & F. McLachlan) mouldability which concrete offers were exploited to create a complex juxtaposition of solid and void. The building is of the same basic type as those by Foster and Bofill however; a structural framework of reinforced concrete supports cladding elements which are Fig. 1.8 Antigone, Montpellier, France, 1983; Ricardo non-structural. Bofill, architect. This building is supported by a reinforced In the Centre Pompidou in Paris by Piano concrete framework. The exterior walls are a combination of in situ and pre-cast concrete. They carry their own weight and Rogers, a multi-storey steel framework is but rely on the interior framework for lateral support. used to support reinforced concrete floors and (Photo: A. Macdonald) non-loadbearing glass walls. The breakdown of 5 Structure and Architecture Fig. 1.10 Centre Pompidou, Paris, France, 1977; Piano & Rogers, architects; Ove Arup & Partners, structural engineers. The separation of structural and enclosing functions into distinct elements is obvious here. (Photo: A. Macdonald) components positioned along the sides of the building outside the glass wall, which is attached to the frame near the columns. A system of cross-bracing on the sides of the framework prevents it from collapsing through instability. The controlled disorder of the rooftop office extension in Vienna by Coop Himmelblau (Fig. 1.11) is in some respects a complete contrast to the controlled order of the Centre Pompidou. Architecturally it is quite different, expressing chaos rather than order, but structurally it is similar as the light external envelope is supported on a skeletal metal framework. The house with masonry walls and timber floor and roof structures is a traditional form of building in most parts of the world. It is found in many forms, from the historic grand houses of the European landed aristocracy (Fig. 1.12) to modern homes in the UK (Figs 1.13 and 1.14). Even the simplest versions of this form of masonry and timber building (Fig. 1.13) are fairly complex assemblies of elements. Initial parts is straightforward (Fig. 1.10): identical plane-frames, consisting of long steel columns which rise through the entire height of the building supporting triangulated girders at each floor level, are placed parallel to each other to form a rectangular plan. The concrete floors span between the triangulated girders. Additional small cast-steel girders project beyond the line of columns (Fig. 7.7) and are used to support stairs, escalators and servicing Fig. 1.11 Rooftop office in Vienna, Austria, 1988; Coop Himmelblau, architects. The forms chosen here have no structural logic and were determined with almost no consideration for technical requirements. This approach design is quite feasible in the present day so long as the 6 building is not too large.  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 de Chambord has a loadbearing masonry structure. Most of the walls are structural; the floors are either of timber or vaulted masonry and the roof structure is of timber. (Photo: P. & A. Macdonald) Fig. 1.13 Traditional construction in the UK, in its twentieth-century form, with loadbearing masonry walls and timber floor and roof structures. All structural elements are enclosed in non-structural finishing materials. 7 Structure and Architecture consideration could result in a straightforward To sum up, these few examples of very breakdown of parts with the masonry walls and different building types demonstrate that all timber floors being regarded as having both buildings contain a structure, the function of structural and space-dividing functions and the which is to support the building envelope by roof as consisting of a combination of the purely conducting the forces which are applied to it supportive trusses, which are the structural from the points where they arise in the elements, and the purely protective, non- building to the ground below it where they structural skin. Closer examination would reveal are ultimately resisted. Sometimes the that most of the major elements can in fact be structure is indistinguishable from the subdivided into parts which are either purely enclosing and space-dividing building structural or entirely non-structural. The floors, envelope, sometimes it is entirely separate for example, normally consist of an inner core of from it; most often there is a mixture of timber joists and floor boarding, which are the elements with structural, non-structural and structural elements, enclosed by ceiling and floor combined functions. In all cases the form of finishes. The latter are the non-structural the structure is very closely related to that of elements which are seen to divide the space. A the building taken as a whole and the similar breakdown is possible for the walls and in elegance with which the structure fulfils its fact very little of what is visible in the traditional function is something which affects the house is structural, as most of the structural quality of the architecture. elements are covered by non-structural finishes. Fig. 1.14 Local authority housing, Haddington, Scotland, 1974; J. A. W. Grant, architects. These buildings have loadbearing masonry walls and timber floor and roof structures. (Photo: Alastair Hunter) 8  Chapter 2 Structural requirements 2.1 Introduction horizontal force is applied to the wheelbarrow by its operator it moves horizontally and is To perform its function of supporting a not therefore in a state of static equilibrium. building in response to whatever loads may be This occurs because the interface between the applied to it, a structure must possess four wheelbarrow and the ground is incapable of properties: it must be capable of achieving a generating horizontal reacting forces. The state of equilibrium, it must be stable, it must wheelbarrow is both a structure and a have adequate strength and it must have machine: it is a structure under the action of adequate rigidity. The meanings of these terms gravitational load and a machine under the are explained in this chapter. The influence of action of horizontal load. structural requirements on the forms which are Despite the famous statement by one adopted for structures is also discussed. The celebrated commentator, buildings are not treatment is presented in a non-mathematical machines1. Architectural structures must, way and the definitions which are given are not therefore, be capable of achieving equilibrium those of the theoretical physicist; they are under all directions of load. simply statements which are sufficiently precise to allow the significance of the concepts to structural design to be 2.3 Geometric stability appreciated. Geometric stability is the property which preserves the geometry of a structure and 2.2 Equilibrium allows its elements to act together to resist load. The distinction between stability and Structures must be capable of achieving a equilibrium is illustrated by the framework state of equilibrium under the action of shown in Fig. 2.1 which is capable of achieving applied load. This requires that the internal a state of equilibrium under the action of configuration of the structure together with gravitational load. The equilibrium is not the means by which it is connected to its stable, however, because the frame will foundations must be such that all applied collapse if disturbed laterally2. loads are balanced exactly by reactions generated at its foundations. The wheelbarrow provides a simple demonstration of the principles involved. When the 1 ‘A house is a machine for living.’ Le Corbusier. wheelbarrow is at rest it is in a state of static 2 Stability can also be distinguished from strength or equilibrium. The gravitational forces rigidity, because even if the elements of a structure have sufficient strength and rigidity to sustain the generated by its self weight and that of its loads which are imposed on them, it is still possible contents act vertically downwards and are for the system as a whole to fail due to its being exactly balanced by reacting forces acting at geometrically unstable as is demonstrated in the wheel and other supports. When a Fig. 2.1. 9 Structure and Architecture Fig. 2.1 A rectangular frame with four hinges is capable of achieving a state of equilibrium but is unstable because any slight lateral disturbance to the columns will induce it to collapse. The frame on the right here is stabilised by the diagonal element which makes no direct contribution to the resistance of the gravitational load. This simple arrangement demonstrates The parts of structures which tend to be that the critical factor, so far as the stability unstable are the ones in which compressive of any system is concerned, is the effect on it forces act and these parts must therefore be of a small disturbance. In the context of given special attention when the geometric structures this is shown very simply in Fig. 2.2 stability of an arrangement is being by the comparison of tensile and compressive considered. The columns in a simple elements. If the alignment of either of these is rectangular framework are examples of this disturbed, the tensile element is pulled back (Fig. 2.1). The three-dimensional bridge into line following the removal of the structure of Fig. 2.3 illustrates another disturbing agency but the compressive potentially unstable system. Compression element, once its initially perfect alignment occurs in the horizontal elements in the upper has been altered, progresses to an entirely parts of this frame when the weight of an new position. The fundamental issue of object crossing the bridge is carried. The stability is demonstrated here, which is that arrangement would fail by instability when this stable systems revert to their original state load was applied due to inadequate restraint following a slight disturbance whereas unstable of these compression parts. The compressive systems progress to an entirely new state. internal forces, which would inevitably occur Original alignment Fig. 2.2 The tensile Fig. 2.3 The horizontal element on the left here is elements in the tops of stable because the loads the bridge girders are pull it back into line subjected to following a disturbance. The compressive internal compressive element on force when the load is the right is fundamentally applied. The system is unstable. unstable and any eccentricity which is present initially causes an instability-type failure to develop. Compression 10 Tension  Structural requirements with some degree of eccentricity, would push Conversely, if an arrangement is not capable of the upper elements out of alignment and resisting load from three orthogonal directions cause the whole structure to collapse. then it will be unstable in service even though The geometric instability of the the load which it is designed to resist will be arrangements in Figures 2.1 and 2.3 would applied from only one direction. have been obvious if their response to It frequently occurs in architectural design horizontal load had been considered (Fig. 2.4). that a geometry which is potentially unstable This demonstrates one of the fundamental must be adopted in order that other requirements for the geometric stability of any architectural requirements can be satisfied. For arrangement of elements, which is that it must example, one of the most convenient structural be capable of resisting loads from orthogonal geometries for buildings, that of the directions (two orthogonal directions for plane rectangular frame, is unstable in its simplest arrangements and three for three-dimensional hinge-jointed form, as has already been shown. arrangements). This is another way of saying Stability can be achieved with this geometry by that an arrangement must be capable of the use of rigid joints, by the insertion of a achieving a state of equilibrium in response to diagonal element or by the use of a rigid forces from three orthogonal directions. The diaphragm which fills up the interior of the stability or otherwise of a proposed frame (Fig. 2.5). Each of these has arrangement can therefore be judged by disadvantages. Rigid joints are the most considering the effect on it of sets of mutually convenient from a space-planning point of perpendicular trial forces: if the arrangement is view but are problematic structurally because capable of resisting all of these then it is they can render the structure statically stable, regardless of the loading pattern which indeterminate (see Appendix 3). Diagonal will actually be applied to it in service. elements and diaphragms block the framework and can complicate space planning. In multi- panel arrangements, however, it is possible to (a) (b) produce stability without blocking every panel. The row of frames in Fig. 2.6, for example, is stabilised by the insertion of a single diagonal. (a) (b) (c) Fig. 2.5 A rectangular frame can be stabilised by the insertion of (a) a diagonal element or (b) a rigid diaphragm, or (c) by the provision of rigid joints. A single rigid joint is in fact sufficient to provide stability. Fig. 2.4 Conditions for stability of frameworks. (a) The two-dimensional system is stable if it is capable of achieving equilibrium in response to forces from two mutually perpendicular directions. (b) The three- dimensional system is stable if it is capable of resisting forces from three directions. Note that in the case illustrated the resistance of transverse horizontal load is Fig. 2.6 A row of rectangular frames is stable if one panel achieved by the insertion of rigid joints in the end bays. only is braced by any of the three methods shown in Fig. 2.5. 11 Structure and Architecture Fig. 2.7 These elements. Arrangements which do not require frames contain bracing elements, either because they are the minimum number of fundamentally stable or because stability is braced panels provided by rigid joints, are said to be self- required for bracing. stability. Most structures contain bracing elements whose presence frequently affects both the initial planning and the final appearance of the building which it supports. The issue of stability, and in particular the design of bracing systems, is therefore something which affects the architecture of buildings. Where a structure is subjected to loads from different directions, the elements which are used solely for bracing when the principal load is applied frequently play a direct role in resisting secondary load. The diagonal elements in the frame of Fig. 2.7, for example, would be directly involved in the resistance of any horizontal load which was applied, such as might occur due to the action of wind. Because real structures are usually subjected to loads from different directions, it is very rare for elements to be used solely for bracing. The nature of the internal force in bracing components depends on the direction in which the instability which they prevent occurs. In Fig. 2.8, for example, the diagonal element will be placed in tension if the frame sways to the Where frames are parallel to each other the right and in compression if it sways to the left. three-dimensional arrangement is stable if a Because the direction of sway due to instability few panels in each of the two principal cannot be predicted when the structure is directions are stabilised in the vertical plane being designed, the single bracing element and the remaining frames are connected to would have to be made strong enough to carry these by diagonal elements or diaphragms in either tension or compression. The resistance the horizontal plane (Fig. 2.7). A three- of compression requires a much larger size of dimensional frame can therefore be stabilised cross-section than that of tension, however, by the use of diagonal elements or diaphragms especially if the element is long3, and this is a in a limited number of panels in the vertical critical factor in determining its size. It is and horizontal planes. In multi-storey normally more economical to insert both arrangements these systems must be provided diagonal elements into a rectangular frame at every storey level. None of the components which are added to stabilise the geometry of the rectangular 3 This is because compression elements can suffer from frame in Fig. 2.7 makes a direct contribution to the buckling phenomenon. The basic principles of this the resistance of gravitational load (i.e. the are explained in elementary texts on structures such as Engel, H., Structural Principles, Prentice-Hall, Englewood carrying of weight, either of the structure itself Cliffs, NJ, 1984. See also Macdonald, Angus J., Structural or of the elements and objects which it Design for Architecture, Architectural Press, Oxford, 1997, 12 supports). Such elements are called bracing Appendix 2.  Structural requirements (cross-bracing) than a single element and to (a) design both of them as tension-only elements. When the panel sways due to instability the element which is placed in compression simply buckles slightly and the whole of the restraint is provided by the tension diagonal. (b) Fig. 2.8 Cross-bracing is used so that sway caused by instability is always resisted by a diagonal element acting (c) in tension. The compressive diagonal buckles slightly and carries no load. It is common practice to provide more bracing elements than the minimum number Fig. 2.9 In practical bracing schemes more elements required so as to improve the resistance of than are strictly necessary to ensure stability are provided three-dimensional frameworks to horizontal to improve the performance of frameworks in resisting horizontal load. Frame (a) is stable but will suffer load. The framework in Fig. 2.7, for example, distortion in response to horizontal load on the side walls. although theoretically stable, would suffer Its performance is enhanced if a diagonal element is considerable distortion in response to a provided in both end walls (b). The lowest framework (c) horizontal load applied parallel to the long side contains the minimum number of elements required to of the frame at the opposite end from the resist effectively horizontal load from the two principal horizontal directions. Note that the vertical-plane bracing vertical-plane bracing. A load applied parallel to elements are distributed around the structure in a the long side at this end of the frame would also symmetrical configuration. cause a certain amount of distress as some movement of joints would inevitably occur in the transmission of it to the vertical-plane bracing at the other end. In practice the performance of the frame is more satisfactory if vertical-plane bracing is provided at both ends (Fig. 2.9). This gives more restraint than is necessary for stability and makes the structure statically indeterminate (see Appendix 3), but results in the horizontal loads being resisted close to the points where they are applied to the structure. Fig. 2.10 In practice, bracing elements are frequently Another practical consideration in relation confined to a part of each panel only. to the bracing of three-dimensional rectangular frames is the length of the diagonal elements which are provided. These sag in response to Figures 2.11 and 2.12 show typical bracing their own weight and it is therefore systems for multi-storey frameworks. Another advantageous to make them as short as common arrangement, in which floor slabs act possible. For this reason bracing elements are as diaphragm-type bracing in the horizontal frequently restricted to a part of the panel in plane in conjunction with vertical-plane which they are located. The frame shown in bracing of the diagonal type, is shown in Fig. Fig. 2.10 contains this refinement. 2.13. When the rigid-joint method is used it is 13 Structure and Architecture Fig. 2.11 A typical bracing scheme for a multi-storey framework. Vertical-plane bracing is provided in a limited number of bays and positioned symmetrically on plan. All other bays are linked to this by diagonal bracing in the horizontal plane at every storey level. normal practice to stabilise all panels individually by making all joints rigid. This eliminates the need for horizontal-plane bracing altogether, although the floors normally act to distribute through the structure any unevenness in the application of horizontal load. The rigid-joint method is the normal method which is adopted for reinforced concrete frames, in which continuity through junctions between elements can easily be achieved; diaphragm bracing is also used, however, in both vertical and horizontal planes in certain types of reinforced concrete frame. Loadbearing wall structures are those in which the external walls and internal partitions serve as vertical structural elements. They are normally constructed of masonry, reinforced Fig. 2.12 These drawings of floor grid patterns for steel frameworks show typical locations for vertical-plane bracing. Fig. 2.13 Concrete floor slabs are normally used as horizontal-plane bracing of the diaphragm type which acts 14 in conjunction with diagonal bracing in the vertical planes.  Structural requirements concrete or timber, but combinations of these materials are also used. In all cases the joints between walls and floors are normally incapable of resisting bending action (in other words they behave as hinges) and the resulting lack of continuity means that rigid-frame action cannot develop. Diaphragm bracing, provided by the walls themselves, is used to stabilise these structures. A wall panel has high rotational stability in its own plane but is unstable in the out-of- plane direction (Fig. 2.14); vertical panels must, therefore, be grouped in pairs at right Fig. 2.15 Loadbearing masonry buildings are normally multi-cellular structures which contain walls running in two orthogonal directions. The arrangement is inherently stable. in two orthogonal directions is normally straightforward (Fig. 2.15). It is unusual therefore for bracing requirements to have a significant effect on the internal planning of this type of building. The need to ensure that a structural framework is adequately braced is a factor that Fig. 2.14 Walls are can affect the internal planning of buildings. unstable in the The basic requirement is that some form of out-of-plane direction bracing must be provided in three orthogonal and must be grouped into orthogonal planes. If diagonal or diaphragm bracing is arrangements for used in the vertical planes this must be stability. accommodated within the plan. Because vertical-plane bracing is most effective when it is arranged symmetrically, either in internal cores or around the perimeter of the building, angles to each other so that they provide this can affect the space planning especially in mutual support. For this to be effective the tall buildings where the effects of wind loading structural connection which is provided in the are significant. vertical joint between panels must be capable of resisting shear4. Because loadbearing wall structures are normally used for multi-cellular 2.4 Strength and rigidity buildings, the provision of an adequate number of vertical-plane bracing diaphragms 2.4.1 Introduction The application of load to a structure generates internal forces in the elements and 4 See Engel, H., Structural Principles, Prentice-Hall, external reacting forces at the foundations (Fig. Englewood Cliffs, NJ, 1984 for an explanation of shear. 2.16) and the elements and foundations must 15 Structure and Architecture Fig. 2.16 The structural elements of a building conduct the loads to the foundations. They are subjected to internal forces that generate stresses the magnitudes of which depend on the intensities of the internal forces and the sizes of the elements. The structure will collapse if the stress levels exceed the strength of the material. have sufficient strength and rigidity to resist these. They must not rupture when the peak load is applied; neither must the deflection which results from the peak load be excessive. The requirement for adequate strength is satisfied by ensuring that the levels of stress which occur in the various elements of a structure, when the peak loads are applied, are within acceptable limits. This is chiefly a matter of providing elements with cross- sections of adequate size, given the strength of the constituent material. The determination of the sizes required is carried out by structural calculations. The provision of adequate rigidity is similarly dealt with. Structural calculations allow the strength and rigidity of structures to be controlled precisely. They are preceded by an assessment indeterminate structures (see Appendix 3), the of the load which a structure will be required two sets of calculations are carried out to carry. The calculations can be considered to together, but it is possible to think of them as be divisible into two parts and to consist firstly separate operations and they are described of the structural analysis, which is the separately here. evaluation of the internal forces which occur in the elements of the structure, and secondly, 2.4.2 The assessment of load the element-sizing calculations which are The assessment of the loads which will act on carried out to ensure that they will have a structure involves the prediction of all the sufficient strength and rigidity to resist the different circumstances which will cause load internal forces which the loads will cause. In to be applied to a building in its lifetime (Fig. 16 many cases, and always for statically 2.17) and the estimation of the greatest  Structural requirements Fig. 2.17 The prediction of the maximum load which will occur is one of the most problematic aspects of structural calculations. Loading standards are provided to assist with this but assessment of load is nevertheless one of the most imprecise parts of the structural calculation process. magnitudes of these loads. The maximum load structure when the most unfavourable load could occur when the building was full of conditions occur. To understand the various people, when particularly heavy items of processes of structural analysis it is necessary equipment were installed, when it was exposed to have a knowledge of the constituents of to the force of exceptionally high winds or as a structural force systems and an appreciation of result of many other eventualities. The concepts, such as equilibrium, which are used designer must anticipate all of these to derive relationships between them. These possibilities and also investigate all likely topics are discussed in Appendix 1. combinations of them. In the analysis of a structure the external The evaluation of load is a complex process, reactions which act at the foundations and the but guidance is normally available to the internal forces in the elements are calculated designer of a structure from loading from the loads. This is a process in which the standards5. These are documents in which data structure is reduced to its most basic abstract and wisdom gained from experience are form and considered separately from the rest presented systematically in a form which of the building which it will support. allows the information to be applied in design. An indication of the sequence of operations which are carried out in the analysis of a 2.4.3 The analysis calculations simple structure is given in Fig. 2.18. After a The purpose of structural analysis is to preliminary analysis has been carried out to determine the magnitudes of all of the forces, evaluate the external reactions, the structure is internal and external, which occur on and in a subdivided into its main elements by making ‘imaginary cuts’ (see Appendix 1.7) through the junctions between them. This creates a set of 5 In the UK the relevant standard is BS 6399, Design ‘free-body-diagrams’ (Appendix 1.6) in which Loading for Buildings, British Standards Institution, 1984. the forces that act between the elements are 17 Structure and Architecture Uniformly distributed geometry of the structure. The reason for this is explained in Appendix 3. In these circumstances the analysis and element-sizing calculations are carried out together in a trial and error process which is only feasible in the context of computer-aided design. The different types of internal force which can occur in a structural element are shown in Fig. 2.19. As these have a very significant influence on the sizes and shapes which are specified for elements they will be described briefly here. In Fig. 2.19 an element is cut through at a particular cross-section. In Fig. 2.19(a) the forces which are external to one of the (a) Fig. 2.18 In structural analysis the complete structure is broken down into two-dimensional components and the (b) internal forces in these are subsequently calculated. The diagram shows the pattern forces which result from gravitational load on the roof of a small building. Similar breakdowns are carried out for the other forms of load and a complete picture is built up of the internal forces which will occur in each element during the life of the structure. (c) exposed. Following the evaluation of these inter-element forces the individual elements are analysed separately for their internal forces Fig. 2.19 The investigation of internal forces in a simple beam using the device of the ‘imaginary cut’. The cut by further applications of the ‘imaginary cut’ produces a free-body-diagram from which the nature of the technique. In this way all of the internal forces internal forces at a single cross-section can be deduced. in the structure are determined. The internal forces at other cross-sections can be In large, complex, statically indeterminate determined from similar diagrams produced by cuts made structures the magnitudes of the internal in appropriate places. (a) Not in equilibrium. (b) Positional equilibrium but not in rotational equilibrium. (c) forces are affected by the sizes and shapes of Positional and rotational equilibrium. The shear force on the element cross-sections and the properties the cross-section 1.5 m from the left-hand support is of the constituent materials, as well as by the 15 kN; the bending moment on this cross-section is 18 magnitudes of the loads and the overall 22.5 kNm.  Structural requirements resulting sub-elements are marked. If these were indeed the only forces which acted on the sub-element it would not be in a state of equilibrium. For equilibrium the forces must balance and this is clearly not the case here; an additional vertical force is required for equilibrium. As no other external forces are present on this part of the element the extra (a) (b) force must act on the cross-section where the cut occurred. Although this force is external to the sub-element it is an internal force so far as the complete element is concerned and is called the ‘shear force’. Its magnitude at the cross-section where the cut was made is simply the difference between the external (c) (d) forces which occur to one side of the cross- section, i.e. to the left of the cut. Once the shear force is added to the Fig. 2.20 The ‘imaginary cut’ is a device for exposing diagram the question of the equilibrium of internal forces and rendering them susceptible to the sub-element can once more be equilibrium analysis. In the simple beam shown here shear examined. In fact it is still not in a state of force and bending moment are the only internal forces equilibrium because the set of forces now required to produce equilibrium in the element isolated by the cut. These are therefore the only internal forces which acting will produce a turning effect on the act on the cross-section at which the cut was made. In the sub-element which will cause it to rotate in a case of the portal frame, axial thrust is also required at the clockwise sense. For equilibrium an anti- cross-section exposed by the cut. clockwise moment is required and as before this must act on the cross-section at the cut because no other external forces are present. plane, do not balance. Shear force and bending The moment which acts at the cut and which moment occur in structural elements which are is required to establish rotational bent by the action of the applied load. Beams equilibrium is called the bending moment at and slabs are examples of such elements. the cross-section of the cut. Its magnitude is One other type of internal force can act on obtained from the moment equation of the cross-section of an element, namely axial equilibrium for the free-body-diagram. Once thrust (Fig. 2.20). This is defined as the amount this is added to the diagram the system is in by which the external forces acting on the a state of static equilibrium, because all the element to one side of a particular location do conditions for equilibrium are now satisfied not balance when they are resolved parallel to (see Appendix 1). the direction of the element. Axial thrust can Shear force and bending moment are forces be either tensile or compressive. which occur inside structural elements and In the general case each cross-section of a they can be defined as follows. The shear force structural element is acted upon by all three at any location is the amount by which the internal forces, namely shear force, bending external forces acting on the element, to one moment and axial thrust. In the element-sizing side of that location, do not balance when they part of the calculations, cross-section sizes are are resolved perpendicular to the axis of the determined that ensure the levels of stress element. The bending moment at a location in which these produce are not excessive. The an element is the amount by which the efficiency with which these internal forces can moments of the external forces acting to one be resisted depends on the shape of the cross- side of the location, about any point in their section (see Section 4.2). 19 Structure and Architecture The shapes of bending moment, shear force and axial thrust diagrams are of great significance for the eventual shapes of structural elements because they indicate the locations of the parts where greatest strength will be required. Bending moment is normally large in the vicinity of mid-span and near rigid joints. Shear force is highest near support joints. Axial thrust is usually constant along the length of structural elements. 2.4.4 Element-sizing calculations The size of cross-section which is provided for a structural element must be such as to give it adequate strength and adequate rigidity. In other words, the size of the cross-section must allow the internal forces determined in the analysis to be carried without overloading the structural material and without the occurrence of excessive deflection. The calculations which are carried out to achieve this involve the use of the concepts of stress and strain (see Appendix 2). In the sizing calculations each element is considered individually and the area of cross- section determined which will maintain the stress at an acceptable level in response to the peak internal forces. The detailed aspects of the calculations depend on the type of internal Fig. 2.21 The magnitudes of internal forces normally vary force and, therefore, the stress involved and on along the length of a structural element. Repeated use of the properties of the structural material. the ‘imaginary cut’ technique yields the pattern of internal As with most types of design the evolution forces in this simple beam. of the final form and dimensions of a structure is, to some extent, a cyclic process. If the element-sizing procedures yield cross-sections The magnitudes of the internal forces in which are considered to be excessively large or structural elements are rarely constant along unsuitable in some other way, modification of their lengths, but the internal forces at any the overall form of the structure will be cross-section can always be found by making undertaken so as to redistribute the internal an ‘imaginary cut’ at that point and solving the forces. Then, the whole cycle of analysis and free-body-diagram which this creates. element-sizing calculations must be repeated. Repeated applications of the ‘imaginary cut’ If a structure has a geometry which is stable technique at different cross-sections (Fig. and the cross-sections of the elements are 2.21), allows the full pattern of internal forces sufficiently large to ensure that it has adequate to be evaluated. In present-day practice these strength it will not collapse under the action of calculations are processed by computer and the loads which are applied to it. It will the results presented graphically in the form of therefore be safe, but this does not necessarily bending moment, shear force and axial thrust mean that its performance will be satisfactory 20 diagrams for each structural element. (Fig. 2.22). It may suffer a large amount of  Structural requirements separate issue and is considered separately in the design of structures. 2.5 Conclusion In this chapter the factors which affect the basic requirements of structures have been reviewed. The achievement of stable equilibrium has been shown to be dependent largely on the geometric configuration of the structure and is therefore a consideration which affects the Fig. 2.22 A structure with adequate strength will not determination of its form. A stable form can collapse, but excessive flexibility can render it unfit for its almost always be made adequately strong and purpose. rigid, but the form chosen does affect the efficiency with which this can be accomplished. So far as the provision of adequate strength is deflection under the action of the load and any concerned the task of the structural designer is deformation which is large enough to cause straightforward, at least in principle. He or she damage to brittle building components, such must determine by analysis of the structure the as glass windows, or to cause alarm to the types and magnitudes of the internal forces building’s occupants or even simply to cause which will occur in all of the elements when the unsightly distortion of the building’s form is a maximum load is applied. Cross-section shapes type of structural failure. and sizes must then be selected such that the The deflection which occurs in response to a stress levels are maintained within acceptable given application of load to a structure limits. Once the cross-sections have been depends on the sizes of the cross-sections of determined in this way the structure will be the elements6 and can be calculated once adequately strong. The amount of deflection element dimensions have been determined. If which will occur under the maximum load can the sizes which have been specified to provide then be calculated. If this is excessive the adequate strength will result in excessive element sizes are increased to bring the deflection they are increased by a suitable deflection within acceptable limits. The amount. Where this occurs it is the rigidity detailed procedures which are adopted for requirement which is critical and which element sizing depend on the types of internal determines the sizes of the structural force which occur in each part of the structure elements. Rigidity is therefore a phenomenon and on the properties of the structural which is not directly related to strength; it is a materials. 6 The deflection of a structure is also dependent on the properties of the structural material and on the overall configuration of the structure. 21  Chapter 3 Structural materials 3.1 Introduction igneous rocks. These ‘solid’ units can be used in conjunction with a variety of different The shapes which are adopted for structural mortars to produce a range of masonry types. elements are affected, to a large extent, by the All have certain properties in common and nature of the materials from which they are therefore produce similar types of structural made. The physical properties of materials element. Other materials such as dried mud, determine the types of internal force which pisé or even unreinforced concrete have similar they can carry and, therefore, the types of properties and can be used to make similar element for which they are suitable. types of element. Unreinforced masonry, for example, may only The physical properties which these be used in situations where compressive stress materials have in common are moderate is present. Reinforced concrete performs well compressive strength, minimal tensile strength when loaded in compression or bending, but and relatively high density. The very low tensile not particularly well in axial tension. strength restricts the use of masonry to The processes by which materials are elements in which the principal internal force manufactured and then fashioned into is compressive, i.e. columns, walls and structural elements also play a role in compressive form-active types (see Section determining the shapes of elements for which 4.2) such as arches, vaults and domes. they are suitable. These aspects of the In post-and-beam forms of structure (see influence of material properties on structural Section 5.2) it is normal for only the vertical geometry are now discussed in relation to the elements to be of masonry. Notable exceptions four principal structural materials of masonry, are the Greek temples (see Fig. 7.1), but in timber, steel and reinforced concrete. these the spans of such horizontal elements as are made in stone are kept short by subdivision of the interior space by rows of 3.2 Masonry columns or walls. Even so, most of the elements which span horizontally are in fact of Masonry is a composite material in which timber and only the most obvious, those in the individual stones, bricks or blocks are bedded exterior walls, are of stone. Where large in mortar to form columns, walls, arches or horizontal spans are constructed in masonry vaults (Fig. 3.1). The range of different types of compressive form-active shapes must be masonry is large due to the variety of types of adopted (Fig. 3.1). constituent. Bricks may be of fired clay, baked Where significant bending moment occurs in earth, concrete, or a range of similar materials, masonry elements, for example as a and blocks, which are simply very large bricks, consequence of side thrusts on walls from can be similarly composed. Stone too is not rafters or vaulted roof structures or from out-of- one but a very wide range of materials, from plane wind pressure on external walls, the level the relatively soft sedimentary rocks such as of tensile bending stress is kept low by making 22 limestone to t