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Structural Engineering for Architects: A Handbook Published in 2013 by Laurence King Publishing Ltd 361–373 City Road London EC1V 1LR Tel +44 (0)20 7841 6900 Fax +44 (0)20 7841 6910 E enquiries@laurenceking.com www.laurenceking.com Design copyright © 2013 Laurence King Publishing Limited Text © 2013 Pete Silver, Will McLean, and Peter Evans Pete Silver, Will McLean, and Peter Evans have asserted their right under the Copyright, Designs and Patents Act 1988, to be identified as the Authors of this work. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without prior permission in writing from the publisher. A catalog record for this book is available from the British Library ISBN 978 178067 055 3 Designed by Hamish Muir US consultant: Christopher D. Rockey, SE, AIA, Assistant Professor, College of Architecture, Illinois Institute of Technology Printed in China Structural Engineering for Architects: A Handbook Pete Silver Will McLean Peter Evans Laurence King Publishing Contents Introduction 06 1 Structures in nature 08 4 Case studies 110 1.1 Tree 10 4.1 Introduction 112 1.2 Spiderweb 12 1.3 Eggshell 14 4.2 1850–1949 1.4 Soap bubbles 16 4.2.1 Viollet-le-Duc’s innovative 114 1.5 Human body 18 engineering approaches 4.2.2 St. Pancras Railway Station Shed 116 4.2.3 Eiffel Tower 118 2 Theory 22 4.2.4 Forth Rail Bridge 120 2.1 General theory of structures 24 4.2.5 All-Russia Exhibition 1896 122 2.1.1 Introduction 24 4.2.6 Tetrahedral Tower 124 2.1.2 External loads 25 4.2.7 Magazzini Generali Warehouse 126 2.1.3 Internal forces 25 4.2.8 Zarzuela Hippodrome 128 Axial 26 Shear 26 4.3 1950–1999 Bending 27 4.3.1 Crown Hall, Illinois Institute 130 Torsion 27 of Technology (IIT) Static equilibrium 28 4.3.2 Los Manantiales Restaurant 132 Simple analysis 30 4.3.3 Concrete Shell Structures, 134 Common beam formulae 36 England 2.1.4 Material properties 40 4.3.4 Geodesic Domes 136 Stress 40 4.3.5 Palazzo del Lavoro 140 Strain 44 (Palace of Labor) Steel properties 47 4.3.6 Concrete Shell Structures, 144 Concrete properties 48 Switzerland Timber properties 49 4.3.7 Jefferson National Expansion 150 2.1.5 Sectional properties 50 Monument (“Gateway Arch”) Bending 50 4.3.8 Maxi/Mini/Midi Systems 152 Axial compression 52 4.3.9 Tensegrity Structures 156 Deflection 55 4.3.10 Munich Olympic Stadium Roof 158 2.1.6 Fitness for purpose 56 4.3.11 Bini Domes—inflatable formwork 162 Vertical deflection 56 4.3.12 Niterói Contemporary Art Museum 164 Lateral deflection 57 4.3.13 Structural Glass 166 Vibration 57 2.1.7 Structures 58 4.4 2000–2010 Categories of structure 58 4.4.1 Ontario College of Art and Design 172 Stability 63 expansion, featuring the Towers 71 Sharp Centre for Design 4.4.2 Atlas Building 176 2.2 Structural systems 73 4.4.3 “Het Gebouw” (The Building) 178 2.2.1 Introduction 73 4.4.4 Hemeroscopium House 182 2.2.2 Material assessments 74 4.4.5 Kanagawa Institute of Technology 186 2.2.3 Structural components 77 (KAIT) Workshop/ Table Beam systems 78 4.4.6 Meads Reach Footbridge 190 Concrete slab systems 84 4.4.7 Pompidou-Metz 194 4.4.8 Burj Khalifa 198 3 Structural prototypes 86 3.1 Form finding 88 Further reading and 202 3.2 Load testing 92 resources 3.3 Visualizing forces 104 Index 204 Picture credits and acknowledgments 208 Introduction “At the age of 17 I was told that I This book is one of those love letters could never be an architect, as I would that one receives and only has to never fully comprehend building decide if one wants to respond. How structures. So that is how I came to much I wish I had come across this study architecture, with a chip on my book in my youth—it would have shoulder. I religiously attended all the saved so much effort spent reading so lectures on structural engineering, many boring ones. indeed any engineering, and found out that it was surprisingly easy to You can take it or leave it, but since it understand and, even better, that it is now available no one can now say was fun. Subsequently I fell in love that ‘you will never understand with the engineering science, not that structure.’ Take my word, this book I have ever fully comprehended it will give another dimension to your but—who cares? You don’t need to understanding of the planet we live on ‘understand’ love after all…. and above all…it’s fun!” Eva Jiricna June 2011 The aim of this book is to enable students of requirements of calculation) transcend the architecture to develop an intuitive purely technical aspect and, intentionally or understanding of structural engineering so not, contribute to artistic creation.”1 In these that, in the long term, they are able to statements Morandi is no more siding with conduct productive dialogs with structural the gifted “calculator” than with the engineers. It is also hoped that the book will flamboyant designer—he is merely on the serve as a valuable reference and sourcebook side of interesting work, which may appear for both architecture and engineering. unnervingly simple or unexpectedly expressive. In Giorgio Boaga’s book The Concrete Architecture of Riccardo Morandi, published In his 1956 book Structures, Pier Luigi Nervi in 1965, the Italian engineer Morandi explains his use of isostatic ribs, which discusses the perceived difficulty of the followed the stress patterns that had been architect–engineer relationship, but refuses made visible by new photoelastic imagery to take sides in this unhelpful argument. techniques. More recently, the detailed More importantly, he describes how “...it is arithmetic and algebraic calculations of Finite always possible, within certain limits, to Element Analysis (FEA) have been made solve a problem—functionally, structurally, visible through computer graphical output— and economically—in several equally valid an incredibly powerful tool for the more ways” and that “...the loving care given to the intuitively minded. A step further than this is formal details (quite independently of the structural engineer Timothy Lucas’s putative 6 explorations of a digital physical feedback The book is divided into four parts: system, which would enable the engineer to physically differentiate and explore the Part 1—Structures in nature describes some structural forces through an augmented common structural forms found in nature. physical model. Throughout the history of technology, physical testing has been and Part 2—Theory outlines a general theory of continues to be a vital component in the structures and structural systems that are development of technology and design commonly applied to the built environment. engineering strategies. Similarly, the field of biomimetics is surely only an academic Part 3—Structural prototypes introduces formalization of a timeless process, where methods for developing and testing we learn from the rapid prototyping of nature structural forms, including both “hands-on” and the previous unclaimed or forgotten modelmaking and full-scale prototypes, as inventions of man to develop new design, well as analytical computer modeling. engineering, material, and operational strategies. Part 4—Case studies presents a selection of key figures involved in the evolution of structural engineering and built form, from the mid-nineteenth century to the present. 1 Boaga, G., and Boni, B., The Concrete Architecture of Riccardo Morandi, London: Alex Tiranti, 1965, p. 10 7 1 Structures in nature 8 9 1 Structures in 1.1 nature Tree More than 80,000 species of tree, ranging from arctic willows a few inches high to giant redwoods that can grow to over 300 feet tall, cover 30 percent of the Earth’s dry land. Structure Trees come in various shapes and sizes, but all A tree trunk grows by adding a layer of new wood in possess the same basic structure. They have a central the cambium every year. Each layer of new wood column, the trunk, which supports a framework of added to a tree forms a visible ring that varies in limbs, branches, and twigs. This framework is called structure according to the seasons. A ring composed the crown, and it is estimated that there are a finite of a light part (spring growth) and a dark part (late number of branching systems for all tree species summer/fall growth) represents one year’s growth. (around 30). Branches and twigs in turn have an Timber used in construction is chosen on the basis of outside covering layer of leaves. A tree is anchored in having an even balance of stresses within the plank. If the ground using a network of roots, which spread a tree has grown on the side of a hill, it will grow and grow thicker in proportion to the growth of the stronger on one side and the stresses will be locked in tree above the ground. to create a harder “red” wood that will eventually cause a plank to warp—by twisting or bowing. All parts of the framework of a tree—trunk, branches, and twigs—are structural cantilevers with flexible connections at the junctions. All have the property of Wind resistance elastic behavior. Trees are generally able to withstand high winds Hardwood and softwood: these terms refer to the through their ability to bend, though some species types of tree from which the wood comes. Hardwood are more resilient than others. Wind energy is comes from deciduous forests; softwood from absorbed gradually, starting with the rapid oscillation coniferous forests. Although hardwoods are generally of the twigs, followed by the slower movement of the of a higher density and hardness than softwoods, branches, and finally through the gently swaying some (e.g. balsa) are softer. limbs and trunk. The greater surface area of a tree in leaf makes it more susceptible to failing under wind load. Growth Much of the energy produced by the leaves of a tree has to be diverted to make unproductive tissue (such as the woody trunk, branches, and roots) as the tree grows. The overwhelming portion of all trees (up to 99 percent) is made up of nonliving tissue, and all growth of new tissue takes place at only a few points on the tree: just inside the bark and at the tips of the twigs and roots. Between the outer (cambial) layer and the bark there is an ongoing process of creating sieve tubes, which transport food from the leaves to the roots. All wood is formed by the inner cambium and all food-conveying cells are formed by the outer cambium. 10 1 1 The basic structure of a tree a 2 b Section through a tree trunk a outer bark b inner bark c heartwood d cambium e sapwood c e d 2 11 1 Structures in 1.2 nature Spiderweb Material properties Web design and production Spider silk is also known as gossamer and is Spiders span gaps between objects by letting out a composed of complex protein molecules. Chains of fine adhesive thread to drift on the breeze across a these molecules, with varying properties, are woven gap. When it sticks to a suitable surface at the far end, together to form a material that has an enormous the spider will carefully walk along it and strengthen it capacity for absorbing energy. The silk of the Nephila with a second thread. This process is repeated until spider is the strongest natural fiber known to man. the thread is strong enough to support the rest of the web. The spider will then make Y-shaped netting by A general trend in spider-silk structure is a sequence adding more radials, while making sure that the of amino acids that self-assemble into a (beta) sheet distance between each radial is small enough to conformation. These sheets stack to form crystals, cross. This means that the number of radials in a web whereas the other parts of the structure form is related directly to the size of the spider and the amorphous areas. It is the interplay between the hard overall size of the web. Working from the inside out, crystalline segments and the elastic amorphous the spider will then produce a temporary spiral of regions that gives spider silk its extraordinary nonsticky, widely spaced threads to enable it to move properties. This high toughness is due to the breaking around its own web during construction. Then, of hydrogen bonds in these regions. The tensile beginning from the outside in, the spider will replace strength of spider silk is greater than the same weight this spiral with another, more closely spaced one of of steel; the thread of the orb-web spider can be adhesive threads. stretched 30–40 percent before it breaks. Impact resistance Silk production The properties of spider silk allow it to be strong in Spiders produce silken thread using glands located at tension, but also permit elastic deformation. When the tip of their abdomen. They use different gland completed, the entire spiderweb is under tension; types to produce different silks; some spiders are however, the elastic nature of the fibers enables it to capable of producing up to eight different silks during absorb the impact of a fast-flying insect. On impact a their lifetime. local oscillation will occur, and the faster the oscillation the greater the resistance. This ability to store energy, and the fact that most of the energy is dissipated as the fiber deforms, allows spiders to intercept and catch their prey, by absorbing these creatures’ kinetic energy. 12 1 1 2 The spider’s silk-spinning glands 2 Sequence of web building 3 A giant spiderweb 4 The successful completion of an arrested landing on the flight deck of an aircraft carrier. The “checkmates” to which the aircraft becomes attached perform a similar kind of impact resistance to that of a spiderweb. 3 4 13 1 Structures in 1.3 nature Eggshell The structure of an eggshell varies widely among species but it is essentially a matrix lined with mineral crystals, usually a compound such as calcium carbonate. It is not made of cells, and harder eggs are more mineralized than softer ones. Bird’s eggs—material properties Strength and shape Birds are known for their hard-shelled eggs. The The structure of a bird’s eggshell is strong in eggshell comprises approximately 95 percent calcium compression and weak in tension. As weight is placed carbonate crystals, which are stabilized by an organic on top of it, the outer portion of the shell will be (protein) matrix. Without the protein, the crystal subject to compression, while the inner wall will structure would be too brittle to keep its form. experience tension. The shell will thus resist the load of the mother hen. Young chicks are not strong, but by Shell thickness is the main factor that determines exerting point-load forces on the inside of the shell strength. The organic matrix has calcium-binding they are able to break out unaided (the chick has an properties and its organization during shell formation egg-tooth, which it uses to start a hole). influences the strength of the shell: its material must be deposited so that the size and organization of the It is the arch/dome shape of the eggshell that helps it crystalline (calcium carbonate) components are ideal, resist tension. thus leading to a strong shell. The majority of the shell is composed of long columns of calcium carbonate. The strength of the dome structure of an eggshell is dependent on its precise geometry—in particular, the The standard bird eggshell is a porous structure, radius of curvature. Pointed arches require less tensile covered on its outer surface with a cuticle (called the reinforcement than a simple, semicircular arch. This bloom on a chicken egg), which helps the egg retain means that a highly vaulted dome (low radius of its water and keep out bacteria. curvature) is stronger than a flatter dome (high radius of curvature). That is why it is easy to break an egg by In an average laying hen, the process of shell squeezing it from the sides but not by squeezing it formation takes around 20 hours. from its ends; staff members at the Ontario Science Centre in Toronto were successful in supporting a 200-pound person on an unbroken egg. 14 1 3 2 z x 1 4 5 A chicken egg 2 Generated eggshell mesh using shell-type elements 3 A microscopic view of the lattice structure of an eggshell 4 A low-tensile, compressive arch will resist larger forces when pointed 5 The stone and steel arches of the Pavilion of the Future, built by Peter Rice for the 1992 Seville Expo, express their resistance to forces by separating the tensile and compressive elements 15 1 Structures in 1.4 nature Soap bubbles Surface tension Merging A soap bubble exists because the surface layer of a When two soap bubbles merge, they will adopt the liquid has a certain surface tension that causes the shape with the smallest possible surface area. With layer to behave elastically. A bubble made with a pure bubbles of similar size, their common wall will be flat. liquid alone, however, is not stable, and a dissolved Smaller bubbles, having a higher internal pressure, surfactant such as soap is needed to stabilize it; soap will penetrate into larger ones while maintaining their acts to decrease the water’s surface tension, which original size. has the effect of stabilizing the bubble (via an action known as the Marangoni effect): as the soap film Where three or more bubbles meet, they organize stretches, the surface concentration of soap themselves so that only three bubble walls meet decreases, which in turn causes the surface tension to along a line. Since the surface tension is the same in increase. Soap, therefore, selectively strengthens the each of the three surfaces, the three angles between weakest parts of the bubble and tends to keep it from them must be equal to 120 degrees. This is the most stretching further. efficient choice, and is also the reason that cells of a beehive have the same 120-degree angle and form hexagons. Two merged soap bubbles provide the Shape optimum way of enclosing two given volumes of air of different size with the least surface area. This has The spherical shape of a soap bubble is also caused been termed “the double bubble theorem.” by surface tension. The tension causes the bubble to form a sphere, as this form has the smallest possible surface area for a given volume. A soap bubble, owing to the difference in outside and inside pressure, is a surface of constant mean curvature. 16 1 2 1 Merged soap bubbles 2 The double bubble theorem applied to the design of the biodomes at the Eden Project in Cornwall, UK, by Nicholas Grimshaw and Partners 17 1 Structures in 1.5 nature Human body Human skeleton Muscles—bodily movement The human skeleton has 206 bones that form a rigid The skeleton not only provides the frame that holds framework to which the softer tissues and organs of our bodies in shape, it also works in conjunction with the body are attached. Vital organs are protected by the body’s 650 muscles to allow movement to occur. the skeletal system. Bodily movement is thus carried out by the interaction of the muscular and skeletal systems. The human skeleton is divided into two distinct parts. Muscles are connected to bones by tendons, and The axial skeleton consists of bones that form the axis bones are connected to each other by ligaments. of the body—neck and backbone (vertebral column)— Bones meet one another with a joint; for example, the and support and protect the organs of the head (skull) elbow and knee form hinged joints, while the hip is a and trunk (sternum and rib cage). The appendicular ball-and-socket type of joint. The vertebrae that go to skeleton is composed of the bones that make up the make the spinal column are connected with an elastic shoulders, arms, and hands—the upper extremities— tissue known as cartilage. and those that make up the pelvis, legs, and feet—the lower extremities. Muscles that cause movement of a joint are connected to two different bones, and contract to pull them together. For example, a contraction of the Bones—material properties biceps and a relaxation of the triceps produces a bend at the elbow. The contraction of the triceps and Most bones are composed of both dense and spongy relaxation of the biceps produces a straightening of tissue. Compact bone is dense and hard, and forms the arm. the protective exterior portion of all bones. Spongy bone is found inside the compact bone, and is very porous (full of tiny holes). Bone tissue is composed of Tensegrity several types of cells embedded in a web of inorganic salts (mostly calcium and phosphorus) to give the It has been said that the human body, when taken as bone strength, and fibers to give the bone flexibility. a whole, is a tensegrity structure. In a tensegrity The hollow nature of bone structure may be structure, the compression elements do not touch compared with the relatively high resistance to each other insomuch as they are held in space by bending of hollow tubes as against that of solid rods. separate tension elements (strings, wires, or cables). The cell biologist and founding director of the Wyss Institute at Harvard, Don E. Ingber, has made the connection between the tensegrity structures of Kenneth Snelson (see page 156) and living cells, and asserts that “an astoundingly wide variety of natural systems, including carbon atoms, water molecules, proteins, viruses, cells, tissues, and even humans and other living creatures are constructed using a common form of architecture known as tensegrity.”1 1 Ingber, Donald, E., “The Architecture of Life” in Scientific American, pp. 48–57, January 1998 18 1 Ballet pose Walking is actually “falling with style.” If you try to walk very slowly, you will start to fall. Try leaning forward from the hips. At some point, your center of gravity goes “outside of you,” and one leg moves forward to form a triangle that keeps you from toppling over—keeps you stable. Carry on bending, and you will reach the point when the only way to maintain your center of gravity is to extend your other leg behind you. This is a process known as “cantilevering.” With built structures, a cantilever describes an element that projects laterally from the vertical. It relies on counterbalance for its stability and on triangulation to resist the bending moments and shear forces of the (canti-) lever arms. 2 Gymnastics rings The stressing of the human body as it strives to maintain a double cantilever 1 2 19 1 1.5 Structures in Human body nature 3 3 Tower of people A Spanish tradition (torres humanas), whose intention is self-evident. A number of strategies may be employed, but in all cases a decent foundation for the tower is critical. As with a tree, there is a uniform root structure that is acting to buttress the “column.” Every participant wears a wide belt to reinforce the connection between the spinal column and the pelvis, and hence protect the kidneys from undue pressure. 4 4 People circle A circle of people sitting on each others’ laps creates a type of tensegrity structure, by which they are all supported without the need for any furniture. 20 5 5 Flying buttress The structural principle of the human tower is also expressed in the flying buttresses traditionally used to brace low-tensile masonry structures. 6 T T C T T C C 6 Forth Rail Bridge T = Tension The designers of the Forth C = Compression Rail Bridge used their own R = Reaction bodies to demonstrate how the span of the bridge uses R1 R2 the cantilever principle. Replicated here, the bodies of the two men at ground level are acting as columns (in compression), and their arms are being pulled (in tension). The sticks are in compression and are transferring the load back to the chairs. 21 2 Theory 22 23 2 Theory 2.1 General theory of structures 2.1.1 Introduction In structural engineering terms, a and all must be sufficiently stable to building can be considered as a series resist any imposed lateral forces and of individual interconnected hence avoid “falling over.” Stability and components whose function is to the various load-transfer mechanisms transfer externally applied loads different building types employ to through a structural system into the achieve stability are explained in this building’s foundations. chapter using the building classifications developed by Heinrich This chapter examines the types of Engel. loads that can be applied to structures and the forces that develop within A brief glossary of the terms used in structural components to resist these this section is as follows: externally applied loads. Force—A measure of the interaction Structural engineering uses the between two bodies. Measured in principles of static equilibrium to pounds (lb) or kilopounds (kip), where analyze load distribution. In this chapter 1,000 lb = 1 kip. the basic concepts of static equilibrium are examined and explained using Load—A force acting on a structural simple models, while some common element. Measured in pounds (lb) or mathematical formulae are provided for kilopounds (kip), where 1,000 lb = 1 kip. common beam arrangements. Mass—A measure of the amount of To determine whether a structural material in an object. Measured in component is capable of resisting the pounds (lb). loads applied to it, two major factors have to be considered: the component’s Sigma (∑)—Mathematical term size, and the material from which it is meaning “the sum of.” For example: made. Further sections of this chapter ∑F = F1 + F2 + F3 examine both the geometric and material properties of structural Weight—A measure of the amount of components and their implications on gravitational force acting on an object. structural performance. Measured in pound mass (lb mass). While a building’s components must be designed to ensure that they are The mass of an object can be converted capable of withstanding the load into weight using the equation; applied without collapsing, they must also be designed to ensure they can Force = mass x g perform their desired purpose without wobbling, deflecting, or vibrating to where g is acceleration due to gravity = such an extent as to disturb the 32.2 ft/s2 building’s occupants or cause damage to fittings and fixtures. These criteria are often called “in service” or “serviceability” states and are explained in the section in this chapter entitled “Fitness for purpose.” Individual components are combined to form structures that vary from thin concrete shells to steel-trussed bridges to igloos to multistory high-rise towers, 24 2.1.2 External loads When external, dead, live, or wind loads Axially—These loads act in the direction are applied to a building they induce parallel to the length of a member and internal forces within the structural typically induce either internal elements that are transmitted into and compressive or tensile forces within it. resisted by the foundations. Perpendicularly—Perpendicular (or Newton’s third law of motion states shearing) loads act perpendicularly to that forces occur in pairs with each the direction of the length of a member. force of the pair being equal in This type of load can induce shear, magnitude and opposite in direction to bending, and torsional forces within a the other. Hence, for a building to be member depending on the geometry of stable every external load or force that the member and point of application of is applied to it has to be resisted by an the load. equal and opposite force at the supports. This state is called static Each of the five internal forces induced equilibrium. by externally applied loads—tension, compression, shear, bending, and External loads can be applied to a torsion—are explained in the following structural member in two fundamentally section. different ways: 25 2 2.1 Theory General theory of structures 2.1.3 Internal forces The process of structural analysis and and torsion) to which each member is design involves determining the subjected to ensure each member is magnitude of the various internal forces capable of resisting those forces. (compression, tension, shear, bending, Axial External compressive Axial loads act in the direction parallel to the length of structural systems that are under compressive loads point load applied to a member. They can either act to resist compressive are termed struts or, if they are vertical, columns. column loads, which try to shorten a member or resist tensile Members under tensile loads are termed ties. External tensile point loads, which try to lengthen the member. Members in load applied to a tie member Externally applied point load, W Externally applied point load, W Column (or strut) Tie in tension in compression Reaction at base, R Reaction at base, R Σ Vertical loads = 0 Σ Vertical loads = 0 therefore W = R therefore W = R Shear External point load Internal shear forces act perpendicularly to the structural member via either point loads, such as a applied to beam direction of the length of a member and are induced person standing on a beam, or distributed loads, such by externally applied shear loads. For the purposes of as the weight of a floor supported by a beam. analysis, shear loads are considered to be applied to a Externally applied point load, W External reaction at External reaction at support, R1 support, R2 L/2 L/2 Σ Vertical loads = 0 therefore W = R1+ R2 26 Bending External point load Bending, also termed flexure, occurs when a load is sum of the internal forces multiplied by the distance applied to beam applied perpendicularly to the longitudinal axis of a from the neutral axis is called the bending moment. developing bending member. This load induces internal forces that act Moments normally occur simultaneously with shear moment parallel to the length of a member. The magnitude of forces and are measured in kip feet (k-ft). A simple these internal forces varies proportionally across the example of a bending load moment can be depth of the member from compression at one face to demonstrated via a vertical shear load applied to the tension at the other. At a point between the end of a cantilevering beam. In this situation the compression and tension faces the internal force is bending moment can be calculated as the applied zero. This is termed the neutral axis. The algebraic shear load multiplied by the length of the cantilever. Externally applied point load, W External reaction at External reaction at support, R1 support, R2 L/2 L/2 Torsion External point load If the point of application of a load is “eccentric” from where the outer fibers experience the highest forces. applied to cantilevering the longitudinal axis of the member, a twisting The magnitude of torsion is a product of the applied beam developing torsion moment will be developed. This in turn induces load and distance from the point of application to the at support torsional forces within the member to resist the longitudinal axis of the member. Torsion is measured twisting action. Torsional forces are distributed across in kip feet (k-ft). the cross-section of a member in a circular manner Externally applied point load, W R e Eccentricity, e Σ Vertical loads = 0 therefore W = R Torsion developed at support, T = Wxe Also, new bending moment developed at support, M = WxL 27 2 2.1 2.1.3 Theory General theory of structures Internal forces Static equilibrium As stated, the applied loads on any structure must be And the clockwise bending moment around the same resisted by equal and opposite forces to achieve static point: equilibrium and thus adhere to Newton’s third law of motion. This concept can be demonstrated with a Mclock = W2 x L1 simple seesaw (see illustrations below). If the seesaw is balanced i.e. it is in static equilibrium, For the seesaw to be in equilibrium both of the then: following conditions need to be met: Mcounterclock = Mclock i) The sum of the applied vertical loads are resisted by equal and opposite reaction forces. W1 x L1 = W2 x L1 Hence W1 + W2 = R If these conditions are not achieved the seesaw will “fail” by falling to the ground. Further examples of ii) The sum of the moments around any arbitrary balanced systems are ilustrated on the opposite page. point is zero. The support reactions to a beam with a single point ΣM = 0 load can be calculated using the concepts of static equilibrium by considering a beam with a single point For a seesaw to be in static equilibrium the applied load to be an inverted seesaw (i.e. the applied load on vertical forces must be equal to the vertical reaction the beam is the support reaction to the seesaw and force: the beam support reactions are the seesaw applied loads). The support reactions generated from a point Hence, W1 + W 2 = R load of any magnitude placed on the beam can be calculated as indicated on the loaded beam opposite. Also the sum of the applied bending moments around any point must be zero. Hence considering the The concept of static equilibrium is fundamental to counterclockwise bending moment developed around the analysis of structural systems. The following the pivot point; section contains an example of an analysis technique called the “Method of Sections.” This indicates how Mcounterclock = W1 x L1 the concepts of static equilibrium can be used to calculate the forces in the internal members of a loaded truss. W1 W2 W1 L1 R L1 L1 R i) System in static equilibrium: W1 + W2 = R ii) Counterclockwise moment around pivot point, Mcounterclock = W1 x L1 W2 R L1 iii) Clockwise moment around pivot point, Mclock = W2 x L1 28 Counterclockwise moment around pivot point, Mcounterclock = W1 x L1 W1 W1 Clockwise moment around pivot point, Mclock = W2 x L1 If W1 = W2 it implies, Mcounterclock = Mclock Therefore, ΣM = 0 System is in static equilibrium L1 L1 Seesaw example 1 Counterclockwise moment around pivot point, Mcounterclock = W1 x L2 W1 W2 Clockwise moment around pivot point, Mclock = W3 x L1 If W1 = 2 x W3 and L1 = 2 x L2 Substituting W3 and L1 in clockwise moment gives: Mclock = (W1/2) x 2L2 W1 x L2 = Mcounterclock it implies, Mcounterclock = Mclock L2 L1 Therefore, ΣM = 0 System is in static equilibrium Seesaw example 2 Σ vertical forces = 0 C so RA + RB - 15 kips = 0 15 kips Rearranging; RB = 15 kips - RA & Σ moments around a point = 0 As Σ moments around any point are zero, it can be shown that taking the moments around the position of the point load, point C; RA x 20' = RB x 10' Substituting RB for RA gives; RA x 20' = (15 kips - RA) x 10' 20' 10' 20' RA = 150 k-ft - 10' RA 30' RA = 150 k-ft RA = 5 kips RB = 10 kips C RA = 5 kips Therefore if; RB = 15 kips - RA then RB = 10 kips Beam example 29 2 2.1 2.1.3 Theory General theory of structures Internal forces Simple analysis The axial force, shear force, bending moment, and The point along a fixed beam at which sagging torsion developed in a member under various loading moment turns to hogging moment (i.e. the point at scenarios can be calculated with simple formulae. which the moment is zero) is known as a point of These member actions are often displayed graphically contraflexure. Internal shearing forces are transferred using force diagrams. Common member loading through the fixed connection and into the columns as scenarios with the associated formulae and force axial loads in a similar manner to pinned connections. diagrams are indicated on pages 36–39. In addition, an example of the “Method of Sections” technique for Fixed connections reduce the midspan bending determining the forces within the members of a truss moment and deflection of a beam significantly in is included on pages 34–35 as this explains some comparison to pinned connections, enabling the use useful concepts of analysis and static equilibrium. of smaller beams. This is demonstrated in the photographs on page 32 of a simple model of To analyze a beam accurately the support conditions identical beams with identical loads at midspan, one must be modeled appropriately. The formulae on the with pinned and one with fixed supports. The bottom following pages use the concepts of “pinned” and photograph clearly shows the points of contraflexure “fixed” support conditions. “Pinned” supports act like that develop on the fixed model beam and the hinges and provide no resistance to rotation, whereas reduced midspan deflection. The formulae on the “fixed” supports are rigid and provide full resistance following pages indicate that the moment at the to rotation. A beam with pinned supports at both ends midspan of a fixed beam under a central point load is is termed “simply supported.” A beam with fixed half that of the same beam with pinned connections, supports at both ends is termed “fully fixed.” and that the deflection will be four times smaller. Considering the pinned support conditions in the Another significant advantage of frames with fixed context of the loaded frame indicated in the diagram connections is their ability to resist lateral loads shown opposite bottom, it can be seen that the without collapsing, as pinned frames would. This is loaded beam cannot transfer any moment into the examined in section on rigid framed structures. supporting columns. When load is applied to the beam the bottom face at midspan will experience Pinned connections are simpler to construct and less tension while the top face will be in compression. expensive than fixed connections because they are This is termed a “sagging” moment. The shear force not required to resist any transferred moment and applied to the beam is resisted by internal shear allow smaller, more slender columns to be utilized. forces within it, which are transferred through the pinned connection into the column as axial forces. The concept of fixed and pinned supports is theoretical—in practice, very few connections behave Considering the fixed support conditions in the as either purely pinned or rigidly fixed. These context of the loaded frame indicated in the diagram concepts are useful at the preliminary design stages opposite bottom, it can be seen that no rotation to quickly assess beam and column sizes and a between the column and beam can occur because as building’s resistance to lateral forces. the beam deflects under load the column will also be forced to deflect. This alters the deflected shape of the Beyond the preliminary design stages connections fixed frame in comparison to the pinned frame. As are either designed as pinned, and the connection with the pinned frame under load, a sagging moment details are developed to accommodate a degree of is developed at the midspan of the fixed frame. Unlike rotation, or the moment transfer between the beam the pinned frame, with the fixed frame moments also and column is calculated subject to the relative develop at the supports whereby the forces are stiffness of the members, and the connection is reversed, with tension developing in the upper designed to be capable of transferring this moment. section of the beam and compression in the lower The latter is known as a moment connection. section. This is termed a “hogging” moment. 30 Beam with simply supported end conditions Simple support allows rotation to occur Beam with fully fixed end conditions Fixed support resists rotation Simple frames with pinned and moment connection Pinned beam under Fixed beam under Fixed beam under vertical loading vertical loading lateral loading 31 2 2.1 2.1.3 Theory General theory of structures Internal forces Simple analysis Model of beam under load with pinned and fixed support conditions Simple models using wood beams loaded at midspan to demonstrate the implications of “pinned” and “fixed” ended beam support conditions on deflection Beam ends left free to rotate to replicate Point load P applied at “pinned” end condition allowing rotation midspan of beam to occur at each support P Beam with identical Length L Deflection at properties to the midspan due to fixed ended model point load “Pinned beam” Beam ends clamped to Point load P applied at replicate “fixed” end midspan of beam condition, not allowing rotation to occur at each Point of P Point of support contraflexure contraflexure Beam with identical Length L Deflection at properties to the midspan due to pinned ended model point load significantly less than the pinned “Fixed beam” example 32 Examples of pinned and moment connections in various materials Steel beams Steel columns Timber beams Reinforced concrete beams Typical pinned connections Typical fixed connections 33 2 2.1 2.1.3 Theory General theory of structures Internal forces Simple analysis Method of sections Glossary Fv = vertical loads Rv = vertical reaction M = bending moment FAB = Axial force in truss members The following four concepts can be used to calculate iv) Components of force: the forces in the members of a truss using the method of sections. A force can be described as two separate component forces acting at right angles to one another. Concepts Fx = F cos 30 θ i) Moment = Force x perpendicular distance Fy = F sin 30 θ from point of reference FV = VERTICAL COMPONENT OF ii) In a static system the sum of applied vertical forces equals the sum of the vertical reactions: ∑Fv = ∑R E, F CAN BE WRITTEN AS A RC F FV FO TRIANGLE OF FORCES FORCE iii) In a static system the bending moments θ θ around any point are zero: ∑M = 0 FH = HORIZONTAL COMPONENT FH OF FORCE Truss with central point load 20 kips B D F H K M P 10' A N C E G J L RA RN 10' 10' 10' 10' 10' 10' The following example shows how the Method of Sections uses the four concepts described above to calculate the forces within the vertical and diagonal members of this loaded truss. 34 Step 1 From Concept ii) ΣW = ΣR Hence: 20 kips = RA + RN (Equation 1) From Concept iii) ΣM = 0 taking moments around support RA RN x 60' = 20k x 30' substituting into equation 1 gives RN = 10 kips RA = 20 - RN RA = 10 kips Step 2 20 kips Consider the truss is cut as shown left. The forces in the individual members of the truss FHK have to be replicated to B D F H K M P maintain static equilibrium. Initially assume the forces act in 10' FGK the directions indicated A N (tension). Note that C E G FGJ J L forces that pass through the joints produce 0 moment at these points as the perpendicular RA distance from line of force to point of 10' 10' 10' 10' reference is 0. Take moment around point G (Concept iii) (FHK x 10') + (RA x 30') = 0 Substituting in RA from Step 1 gives FHK = - 3 RA FHK = - 3 x 10k FHK = 30k The negative indicates that the direction of force is in the opposite direction than originally assumed, hence the force required to maintain static equilibrium in the cut truss model is compressive. Considering moments about point K (Concept iii) substituting RA gives: (20k x 10') + (FGJ x 10') – (RA x 40')= 0 FGJ x 10' = (10k x 40') – (20k x 10') FGJ = 200 k-ft/10' For the final unknown FGK consider vertical FGJ = 20k equilibrium of the cut truss. If ∑Fv = ∑Rv then the vertical component of FGK plus the other vertical loads and reactions must equal zero. Where: Vertical component of FGK = FGK sin θ (Equation 2) e opposite us sin θ = (length of the opposite leg of the triangle) = 1 en ot (length of the hypotenuse of the triangle) √2 p hy Therefore rewriting Equation 2 gives Vertical component of FGK = FGK (1/√2) Hence considering vertical forces and reactions: 20 - (1/√2) FGK – 10 = 0 FGK = 14.14k The positive value indicates that the force FGK is acting in the direction assumed on the cut truss diagram and is tensile. This process can be repeated at adjacent nodes to calculate all the internal member forces of the truss. 35 2 2.1 2.1.3 Theory General theory of structures Internal forces Common beam formulae Simply supported beam formulae for common load cases W = point load (kip) R = Reaction forces I = Second moment of area E = Young’s modulus ω = uniformly distributed L = Length (ft) (see section (see section load (kip/ft) Simply supported beam with central point load Simply supported beam with uniformly distributed load W ω R1 R2 R1 R2 L L Reactions: R1 = R2 = W/2 Reactions: R1 = R2 = ωL/2 Bending moment diagrams Mmax = W x L/4 Mmax = ω x L2/8 0 0 0 0 Shear force diagrams V1 max = W/2 V1 max = ω L/2 0 0 0 0 V2 max = W/2 V2 max = ωL/2 Deflection calculations 0 0 0 0 deflection max = WL3/48EI deflection max = 5ωL4/384EI 36 Fully fixed beam formulae for common load cases W = point load (kip) R = Reaction forces I = Second moment of area E = Young’s modulus ω = uniformly distributed L = Length (ft) (see section (see section load (kip/ft) Fully fixed beam with central point load Fully fixed beam with uniformly distributed load W ω kN/m R1 R2 R1 R2 L L Reactions: R1 = R2 = W/2 Reactions: R1 = R2 = ωL/2 Bending moment diagrams Mmax = W x L/8 Mmax = ω x L2/24 0 0 0 0 M = W x L/8 M M = ω L2/12 Shear force diagrams V1 max = W/2 V1 max = ω L/2 0 0 0 0 V2 max = W/2 V2 max = ωL/2 Deflection calculations 0 0 0 0 deflection max = WL3/192EI deflection max = ωL4/384EI 37 2 2.1 2.1.3 Theory General theory of structures Internal forces Common beam formulae Cantilevering beam with eccentric load W = point load (kip) R = reaction forces L2 = Length of cantilever T = torsion L1 = span of fixed ended V = shear force beam (ft) M = bending moment M1 T1 R1 W L 1 L2 T1 M1 Reactions: R1 = R2 = W/2 R2 Bending moment diagram L 1 /2 M su pp = M W L ms = 1 /8 W W kN L1 L1 / 8 L 1 /2 L2 M 2= W L 2 M su pp = W L 1 /8 V Shear force diagram su pp =W /2 L 1 /2 W L 1 /2 L2 V 2= W V su pp = W /2 Torsion diagram T su pp = W L 1 /2 L 1 /2 W L 1 /2 L2 T su pp = W L 1 /2 38 Uniformly loaded horizontal cable formulae w = uniformly distributed h = cable sag H = horizontal component s = sag ratio load (kip/ft) T = tension in cable of cable tension L = span V = vertical component of cable tension w T T H H h V L V Horizontal force H = wL2 / 8h Vertical force V = wL / 2 Sag ratio s = h/L Tension in cable T= wL2 wL 2 √(( 8h + 2 )) 39 2 2.1 Theory General theory of structures 2.1.4 Material properties A structural component’s ability to The two most fundamental material resist applied loads is based on two very properties that determine a material’s basic criteria: what it is made of structural characteristics are its stress (material properties), and how big it is and strain capacities. Stress is a (sectional properties). measure of the force per unit cross- section of material. Strain is a ratio This section examines material of the “change in dimension” to properties; section 2.1.5 examines “original dimension” of a material sectional properties. when it is loaded. Stress External loads applied to a structural element induce Shear loads develop shear stresses on the cross- internal forces within it. Stress is a measure of the section of the loaded member in the direction parallel intensity of these internal forces, and is expressed as with the direction of load. The distribution of shear force per unit area. This is normally written as pounds stress is termed the shear flow. This varies, the per square inch (lb/in2 or psi) or kips per square inch maximum occurring at the midpoint and reducing to (kips/in2 or ksi). zero at the extreme fibers. The maximum shear stress in a rectangular section is: As the load applied to an element increases, the τmax = 1.5W/A internal forces and therefore the internal stresses experienced by that element increase until eventually Where W = applied shear load the material reaches a limit beyond which it will fail. and A = cross-sectional area of member The limiting stress can be determined in two different ways: Typically, the average stress over the member i) “Yield stress” (or ‘proof stress’)—this is the cross-section is taken as simply: stress limit beyond which the material no longer behaves “elastically” (see section τaverage = W/A ii) “Ultimate stress”—this is the stress beyond which the material will fail by being either crushed or Shear forces also simultaneously induce stresses pulled apart. parallel with the longitudinal axis of the member called “complementary” shear stresses. These can be The process of designing a material that will not explained by considering a small length of a beam exceed its yield stress capacity is termed elastic under shear load as illustrated on the opposite page. design because the material will behave in In order for the small length of beam to maintain accordance with elastic principles in all load static equilibrium there must be an additional pair of conditions. Materials classed as ductile, such as mild equal and opposite forces acting at right angles to the steel, can be designed to exceed their maximum yield main shear forces in the beam. In some materials, stress using plastic design theory, which allows including timber, these complementary shear stresses greater loads to be supported than elastic design. These concepts are developed further in the bending can be more critical than the main shear stresses. stress section and in section Bending forces, as with axial forces, induce direct There are two types of stress that can be induced in a stresses within an element. Unlike axial force-induced structural element: “direct stress” and “shear stress.” stresses, the magnitude and the direction of direct Direct stresses are developed when an element is stresses due to bending vary across the cross-section subjected to an applied force parallel to its of a member. The extreme fibers of an element under longitudinal axis. Shear stresses are developed when bending experience the highest tension and an element is subjected to an applied force compression stresses simultaneously. In between the perpendicular to its longitudinal axis. extreme fibers the stress levels reduce to a point where stress is zero. This point is known as the neutral Axial loads act parallel to the length of a member and axis. In accordance with elastic theory, bending stress hence induce direct stresses, whereby the magnitude in a beam is calculated by dividing the applied of stress is calculated as the force applied divided by bending moment by the “section modulus” of the the cross-sectional area perpendicular to the direction beam. This is a sectional property explained in section of load. 40 Elements under axial stress External compressive point load applied to Externally applied point load, Externally applied point load, Stress, σ = P/A column P P where P = applied axial force External tensile point (in pounds or kips) load applied to column and A = cross-sectional area of the element Column (or strut) in compression Reaction at base, R Reaction at base, R Shear stress in beam under bending External point load applied to beam Externally applied point load, W Average vertical shear stress on cross- section perpendicular to longitudinal axis: Shear stress, τvert = W/A W = applied shear force (N) A = cross-sectional area (mm2) Complementary shear stress on cross- section parallel to longitudinal axis: Shear stress, τhoriz = WA'y/bI W = Applied shear force External reaction at External reaction at A' = Sectional area of section support, R1 support, R2 considered τ horiz y = Distance from centroid of area A' τ vert τ vert to elastic neutral axis Considering elemental section and b = Width of element considered taking moments around corner point. I = Second moment of area of whole y in order to achieve static equilibrium. section (see section Neutral axis τ horiz Horizontal complementary shear stresses are developed to resist moments generated by vertical shear stresses. Bending stress in beam under bending Beam under bending showing compression/ tension and neutral axis A Externally applied point load, W Bending stress, σ = M/S Where: M = bending moment S = section modulus (see section A Max. compressive stress at midspan Compression Zone (midspan) Neutral axis Tension Zone (midspan) Max. tensile stress at midspan A-A Stress distribution 41 2 2.1 2.1.4 Theory General theory of structures Material properties Stress Torsional forces induce shear stresses in the plane The polar second moment of area of a rectangular perpendicular to the longitudinal axis of a member. section is more complicated and beyond the scope of These shear stresses act in a circular nature and their this book; however, the stress in a rectangular section magnitude varies linearly across the cross-section is often approximate to: from zero at the center to a maximum at the outer face. Due to the radial nature of torsional stresses, the τsolid rectangle = 2T/hmin2(hmax –hmin/3) “shear flow” is highly dependent on the shape of the section under stress. Solid circular sections and where hmax and hmin represent the breadth and width hollow sections have a closed circular route that of the rectangular cross-section. stress can follow and hence these shapes are able to The values of the direct yield stress capacity, σ, and resist torsional loads more efficiently than “open” the shear yield stress capacity, τ, are generally not the sections (such as steel I beams). The torsional stress is same for a given material. For example, for mild steel: calculated using the polar second moment of area, which for a solid circular section is: Normal tensile yield stress σ = 40 ksi Polar second Jsolid circle = π D4/32 Normal compressive yield stress σ = 40 ksi moment of area Shear yield stress τ = 24 ksi Torsional stress τsolid circle = Tr/J Different materials can withstand differing maximum Where T = torsion shear and direct stress values, making some more D = diameter of shaft suited to structural applications than others. A list of and r = distance from center to various common materials with their associated point considered stress capacities is provided in the table on page 46. For τmax ,r = radius of section Element under torsion Eccentric external point load inducing torsional stress in beam Approximate shear stress due to torsion in solid rectangular section: Applied point load, W τ = 2 x T / hmin2 (hmax-hmin/3) Where h = dimensions of rectangular cross-section (ft) T = applied torsion = We (k-ft) Shear stress due to torsion in solid circular shaft: τ = Tr/(π D4/32) e Where T = applied torsion = We (k-ft) Eccentricity, e D = diameter of shaft (ft) r = distance from center of shaft to point of measurement (ft) 42 Metals and concrete are “isotropic” materials, While both concrete and mild steel are isotropic meaning that they have identical material properties materials they differ from one another in that the in all directions. Hence a cube of concrete or metal tensile and compressive strength of mild steel is will support the same compressive load regardless of identical. Concrete, however, has a high compressive which face of the cube the load is applied to. The capacity but negligible tensile strength in all axes, same is true for tensile and shear loads. Timber and primarily owing to the microscopic cracks that carbon fiber are orthotropic materials, meaning that develop in it during curing. Bending moments their material properties vary in different axes. For develop simultaneous compressive and tensile example, a cube of timber will compress more easily stresses in a structural member, and hence a concrete when the load is applied perpendicularly to the grain element would fail under very small loads due to its than if it is applied parallel to it. In addition, the shear poor tensile capacity. To counter this, concrete is stress capacity of timber parallel to the direction of its reinforced with longitudinal steel reinforcing bars in grain is significantly less than the shear strength areas that are subject to tensile forces. perpendicular to it. Because of this the complementary shear stresses described previously are often the critical shear design criteria of a timber beam under vertical load as opposed to the main shear stresses, which act in the direction of the applied load. Hence, when designing in orthotropic materials the orientation of the material laminations has to be considered at the design stage. Reinforced concrete beam section b Strain in concrete Zone of cross-section 0.8 x Fc = Compressive force in x in compression concrete Neutral axis Zone of cross-section in tension As Fst = Tensile force in steel Strain in steel Cross-section of reinforced concrete Strain Stress block and forces beam under bending 43 2 2.1 2.1.4 Theory General theory of structures Material properties Strain When a sample of material is placed under load it will material is behaving “plastically” and is represented undergo some deformation. This deformation will be by the plastic range indicated on the graph opposite. either via elongation, compression, or shearing depending on how the load is applied. Strain is a As load, and therefore stress, is increased measurement of the ratio of the extent of deformation incrementally the material will eventually reach its under load against the original dimension of a sample ultimate stress capacity, at which point it will break. of material. There are several different types of strain including linear, volumetric, and shear. Linear strain is Both mild steel grade A615 and aluminum 6061-T6 the ratio of the elongation under axial load against the have very similar stress capacities of around 40 kips original length. This is written as: per square inch, meaning that they will be able to support very similar loads prior to reaching their yield Strain, ε=δ/l strengths. Aluminum 6061-T6, however, has a Young’s modulus of 10,000 kips per square inch, which is where δ = deformation, and approximately three times smaller than that of mild l = original length steel at 29,000 kips per square inch; hence an aluminum beam will deflect three times more than an When they are loaded, most materials exhibit identical-sized mild-steel beam under the same loads. “elastic” behavior in accordance with Hooke’s Law. As In this example the steel beam can be said to have a load is applied materials deform and when the load is “flexural stiffness” three times greater than an removed they return to their original dimensions. aluminum beam as the geometrical properties I and L Plotting the strain against the stress in a material as it are constant. is loaded produces the graph illustrated on the opposite page. This example is based on a mild steel The extent of deformation that a material is able to sample. The straight line area indicates the linearly undergo before failure occurs determines whether it elastic region. In this area the material adheres to is classified as “brittle” or “ductile.” Materials that fail Hooke’s Law and returns to its original size as load is before strain reaches 5 percent are classified as brittle. released. The ratio of stress divided by strain in this These include concrete, timber, glass, and ceramics. region is a constant value known as the elastic Brittle materials tend to fail suddenly and without modulus. For tensile forces that induce tensile warning. Materials such as mild steel and aluminum stresses and strains, this is more commonly known as are classified as ductile, as they can exhibit a Young’s modulus. Other elastic moduli include the significant degree of deformation prior to failure. This shear modulus, volumetric modulus, and Poisson’s can often be seen as a change to the cross-section of ratio, all of which are briefly explained in the an element in tension, or high deflection of beams in diagrams opposite. bending. Young’s modulus, E = linear stress/linear strain Other properties that affect the performance of the =σ/ε most common structural materials are included in the following section. This value, combined with other sectional properties, is used to calculate the “stiffness” of structural members using the formula: Stiffness K = EI/L Where I = second moment of area (see section L = length of member The stiffness of a member or system of members is used when calculating the deflections of structural members and to determine the amount of load that is resisted by each of the members in a system where the stiffer elements will attract the greater loads. As the load applied to a sample of material is increased it will eventually reach its elastic limit beyond which it will not return to the exact dimensions upon release of the load. At this point the 44 Types of strain L = original dimension δ = deformation W = force Tensile strain Shear strain Volumetric strain W δ W δy W Ly L W W L δ Lz Lx δz δx Tensile strain, εL = δ/L Shear strain, εs = δ/L Volumetric strain, εv = δx/Lx + δy/Ly + δz/Lz Tensile stress, σ = W / A Shear stress, τ = W / A Volumetric modulus, or bulk modulus: Tensile modulus, or Young’s modulus: Shear modulus, or modulus of rigidity: K = dp / (dV/V) E=σ/ε G=τ/ε where: dp = differential change in pressure on object dV = differential change in volume of an object V = initial volume of object Poisson’s ratio W Poisson’s ratio, v = transverse strain / longitudinal strain v = (3K – 2G)/(6K + 2G) δy δz E = 2G( 1 +v) δx E = 3K(1 – 2v) L Stress/strain graph Ultimate strength Elastic limit Rupture stress Stress Elastic range Plastic range Strain 45 2 2.1 2.1.4 Theory General theory of structures Material properties Strain Young’s modulus The yield and ultimate Material Yield stress (k/in2) Ultimate stress (k/in2) Young’s modulus (k/in2) stress limits for some typical materials, together with their Mild steel 36 58 29,000 associated Young’s (ASTM A-36) moduli High-strength steel 50 65 29,000 (ASTM A992) Aluminum 35 38 10,000 6061-T6 Iron 35 38 10,000 Titanium 33 54 17,000 Tungsten 80 90 59,000 Concrete N/A 6 (compressive) 4,400 (f' = 6 ksi) Human hair N/A 55 560 Glass N/A 5 10,000 Carbon fiber N/A 700 (tensile) 42,000 (Cytec Thornel T-650/42 12KL) Bone N/A 20 (tensile) 2,500 (femur) 30 (compression) Natural rubber N/A 4 (tensile) 1,500 Graphene N/A 19,000 145,000 Douglas fir N/A 7 1,600 (softwood) 46 Steel properties Grade Fatigue Structural steel is graded to identify its yield stress Under cyclic loading and unloading, metal structures characteristic. The most common grades for steel can develop microscopic cracks at the surface owing sections in the US are A36 or A992, which represent a to “fatigue.” If left to develop, fatigue cracking can yield stress capacity of 36 ksi and 50 ksi respectively. lead to the sudden catastrophic failure of a member. Higher-strength steels contain higher levels of carbon. Structures subject to cyclic loading—such as road While increasing the carbon levels adds strength, it bridges, certain industrial buildings, gymnasiums, also increases brittleness and makes steel less easy to and dance floors—must be designed against fatigue weld. More brittle steel has a greater susceptibility to failure. This is done by estimating the number of brittle fracture in cold conditions, and hence steel loading cycles over the lifetime of the structure and must be specified not only based on its yield stress using experimental data to reduce the design stress characteristics but also the climate conditions to of the steel. which it will be exposed. Brittleness can be assessed by measuring the resistance of steel to impact. A common test to assess impact resistance is the Charpy v-notch test, which involves using a pendulum to strike a sample of material and calculating the energy absorbed in the sample by measuring how far the pendulum swings back after striking the sample. 47 2 2.1 2.1.4 Theory General theory of structures Material properties Concrete properties Grade controlled in several ways. These include reducing the Concrete is graded in terms of its compressive size of the concrete pour, protecting curing concrete strength and the exposure conditions that it will be from drying out by covering it with wet cloth, or subject to. The actual design-mix proportions, reducing the volume of water in the concrete mix by including the percentage of cement, will then be using chemical additives called plasticizers. designed specifically to meet these requirements. In reinforced concrete the cover of the concrete to the Creep steel reinforcing bars is also an important parameter. Creep is a phenomenon whereby a solid material The “cover” must be sufficient to ensure the steel under constant load gradually deforms. As concrete reinforcement is not exposed to any chemicals or beams are loaded they are subject to creep, which water in the environment that could cause it to rust. results in a gradual increase in deflection over time. As steel rusts it expands. This causes the concrete to The degree of creep is subject to many criteria spall, which in turn leads to greater damage including the concrete mix design and the relative occurring. Minimum depths of cover are provided in humidity during curing and in-use conditions. In the various concrete codes; they generally range from certain circumstances long-term creep deflections can 3 ⁄4" to 3" depending on the severity of the exposure be up to twice the short-term dead load deflections. conditions. The implications of creep can be particularly significant for concrete beams spanning over glass Shrinkage façades or non-loadbearing partitions. In these Concrete can shrink in several different ways after it is situations as the deflection of the concrete beam poured, owing to the loss of moisture and subsequent increases the non-loadbearing elements can be change in volume. These ways include drying subjected to load that they are not designed to shrinkage, plastic shrinkage, “autogenous” shrinkage, support, causing damage to occur. The effects of and “carbonation” shrinkage. All types of shrinkage creep are allowed for in the design process by form cracks, which can affect the durability and reducing the Young’s modulus of the concrete by up appearance of the material. Shrinkage can be to two-thirds at the design stage. 48 Timber properties Orthotropic area at, say, a knot. Engineered products also are Timber is an orthotropic material, and has varying more dimensionally stable as the thin veneers can be structural properties in different directions. This is dried effectively during the fabrication process, thus particularly relevant in shear design of timber beams alleviating the issue of drying out while in use. as the shear capacity parallel to the grain is significantly lower than the shear capacity Creep perpendicular to the grain; hence, when a beam is As with concrete, timber is subject to creep; the strain loaded in direction perpendicular to the grain it will can increase by 60 percent over ten years under generally fail in shear due to the complementary permanent load. This is often allowed for in the design shear stress (see section as opposed to the by the use of load duration factors, with higher normal shear stress. factors being applied to loads applied for longer periods. Natural material Timber being a naturally occurring material means Service class that it contains imperfections and irregularities such Timber exhibits different properties when wet, and as knots and can develop splits, known as shakes, as therefore the design must recognize the likelihood of it dries out. In addition timber is a hygroscopic the timber becoming wet and amend the material material meaning that it will give up moisture as it properties accordingly. dries out or take up moisture from the atmosphere depending on the relative humidity of its surroundings. Timber is unique among structural materials in these respects. Engineered timber products, such as glulam, Laminated Veneer Lumber (LVL), and Cross Laminated Timber (CLT) are manufactured from thin layers of timber glued together. This ensures enhanced mechanical properties in comparison to standard timber, as any imperfections are distributed across the length of the member as opposed to being concentrated in one 49 2 2.1 2.1.5 Theory General theory of structures Sectional properties 2.1.5 Sectional properties The dimensions of a structural They are not intended to give detailed element’s cross-section significantly guidance on the design of structural affect the ability of that member to elements, as that is beyond the scope of resist applied loads. this book, but rather to provide a conceptual understanding of how The following sections explain the cross-sectional geometry can impact relationship between geometrical the behavior of structural elements. sectional properties and the axial and bending stress capacities of an element. Bending A simply supported beam with a vertical load placed Written alternatively: at midspan will develop a bending moment. The upper fibers of the beam at midspan will experience a σ=My/I compressive stress while the lower fibers will experience a tensile stress. The stress across the This is commonly rewritten as: cross-section of the beam between these extreme fibers will vary as described in section At a σ = M / Sel particular position on the cross-section the stress will be zero. This is known as the neutral axis. where S is called the “elastic section modulus.” Intuition dictates that a ruler orientated as shown in the Hence, looking back at the intuitive example of the photograph opposite left will be “harder,” i.e. require a plastic ruler it can be seen that with a rule with greater load in order to bend than the ruler orientated cross-sectional dimensions of 11⁄2" x 1⁄8" thick, the as shown in the photograph on the right. associated elastic section moduli in the two different rectilinear orientations are as indicated opposite. This apparent increased strength of the ruler in the photograph on the left is due to a geometric property Many building design codes are written using plastic, called the “second moment of area” or “moment of as opposed to elastic, design theory. Elastic design inertia.” If a cross-section is divided into a series of limits the maximum stress within a section to the smaller areas and each of these areas is multiplied by elastic yield or proof stress. A beam designed in the square of the distance from their centroid to the accordance with elastic theory will reach its maximum neutral axis, the summation of these quantities for the bending capacity when the extreme fibers on its whole cross-sectional area is the second moment of upper and lower faces reach their elastic stress limit, area. For a rectangular section, this is calculated as: as indicated in the stress distribution diagrams opposite. The elastic section modulus explained Second moment of area, I = BD3 / 12 above is valid when this triangular stress distribution exists. where B = width of section, and D = depth of section Plastic design allows for some plastic deformation of the extreme fibers of a beam in, for example, bending Bending theory relates second moment of area, to occur when they reach the elastic stress limit, thus bending moment, and stress in the equation: distributing stress to the lower fibers, which can then also be designed to develop full elastic stress M/I=σ/y capacity. A stress block indicating a section that has developed full plastic capacity is indicated opposite. where M= bending moment, I= second moment of area, The elastic section modulus, S, can be replaced with σ= bending stress, and the plastic section modulus, Z, in the equations above y= distance to neutral axis to calculate the maximum plastic moment capacity of a section. The plastic section modulus of a rectangular beam is: Z = BD2/4 50 A rule orientated in two directions Cross-section of rule considered in two different orientations 1 ⁄8" y 11⁄2" y ⁄8" x 1 11⁄2" x Cross-sections of rule with section moduli Elastic section modulus about the x–x axis: Elastic section modulus about the y–y axis Elastic section modulus about the x–x axis: Elastic section modulus about the y–y axis: Sx = BD2/6 Sy = BD2/6 Where B = 0.125" Where B = 1.5" D = 1.50" D = 0.125" Hence Hence Sx = 0.125" x 1.50"2/6 Sy = (0.125"2 x 1.50")/6 = 0.0469 in3 = 0.00391 in3 When D = 1.50" the elastic section modulus of the section is 12 times higher than when the section is rotated through 90°. Providing the compression flange of the section is restrained this equates to the deeper section being capable of supporting over 11 times more load when orientated with a greater depth. Stress distributions across cross-section of beam in bending σmax σmax σmax Neutral axis σmax σmax σmax Elastic stress distribution Partial plastic stress distribution Full plastic stress distribution 51 2 2.1 2.1.5 Theory General theory of structures Sectional properties Axial compression Members under axial compressive load can fail in two and the deflected shape of the axially loaded column fundamentally different mechanisms: will change. The length over which buckling occurs in a pin-ended column is half of the length over which i) Compressive failure buckling can occur in a fully fixed column. A column ii) Buckling with one end fixed and one end free to rotate and move (a cantilever) will have an effective buckling Compressive failure is a function of the cross- length of twice a pinned column. These and other end sectional area of the section and the strength of the restraint conditions together with the associated material. Quite simply: if the load applied is too great column effective lengths are demonstrated for the column to withstand, it will crush the member. graphically on page 54. Equations developed by Euler describe the critical loads columns can withstand Hence, capacity of strut owing to pure compressive prior to buckling. These are: load is as follows: critical buckling load, Pcomp = π2 EI Pcomp= A σcompcap Le2 critical buckling stress, θ where Pcomp = crushing capacity of the strut under pure compressive ( ) = E πr Le load where Pcomp = compressive load in column A = area of section E = Young’s modulus σcompcap = compressive stress capacity Le = effective length of column material r = radius of gyration (see below) The “radius of gyration” is a geometrical property, Compressive failure generally governs the design of where: “short” columns. Longer, more slender, columns, however, are prone to fail via the second mechanism, r = √(I/A) buckling, which occurs before they reach their ultimate compressive capacity. where I = second moment of area (as explained in section When a long slender column is placed under an increasing axial load, that column will be seen to start A = Cross-sectional area to bow or buckle at a certain load magnitude. This can be demonstrated simply with a 12-inch plastic ruler as Slenderness is defined as: it is loaded carefully by hand. λ = Le/r If the load is increased further, the column will eventually fail in buckling rather than crushing. where Le = the effective length of the Buckling, unlike compressive failure, is a function of column both the height and the sectional properties of a r = least radius of gyration member. As can be seen from the equations above the buckling As the slenderness of a column increases the criteria capacity of a column is inversely proportional to the governing its axial strength alters from a stress- effective length of the column squared. Therefore, governed crushing capacity to a geometry-governed doubling the effective length will reduce the buckling buckling capacity once the slenderness exceeds a capacity by a factor of 22 = 4. In the case of a non- certain limit. The graph below indicates this symmetrical column section, the second moment of relationship. area will be different depending on which axis is being considered. As shown in the example of the While the height of a column is simply the distance 12-inch ruler, slender columns always fail in buckling from the base to the top, the “effective height” is the around their weakest axis and hence the slenderness extent of the column that is subjected to buckling and must always be calculated on the basis of the minor, is determined by the restraint conditions at either or smaller, axis. For this reason, typical column end. Pinned supports at the top and bottom provide sections such as wide flanges (W-shapes) tend to be no restraint to rotation, and therefore the deflected relatively symmetrical in comparison to, for example, shape of the column will be a single curve as it is universal steel beams, which have large disparities loaded axially, as indicated in the photograph of a between their slenderness ratios in the x and y axes rule opposite. When the top and bottom supports are (see diagrams on page 54). fixed, however, no rotation can occur at these points 52 A 12-inch rule under load by hand Axial load applied to a plastic rule Rule begins to buckle around weaker axis Column compression and buckling Compressive capacity 100 Zone governed by Euler buckling Zone governed by compressive capacity Strength (σ) Region indicating member compressive capacity 0 0 50 100 150 200 250 300 Slenderness (λ) 53 2 2.1 2.1.5 Theory General theory of structures Sectional properties Axial compression Effective lengths of columns with differing end restraints Lo = Actual length LE = Effective length Free Free LE=2.0Lo Roller Pinned Fixed Pinned LE=2.0Lo LE=1.0Lo LE=0.7Lo LE=0.5Lo LE=1.0Lo Pinned Fixed Pinned Fixed Fixed Fixed Standard universal beam and column sections Typical beam shape Typical column shape 81⁄8" 205⁄8" 8" 8" Section size: W8 x 31 (31 lb/ft) Section size: W21 x 48 (48 lb/ft) Second moment of area, Ix Second moment of area, Ix and associated radius of gyration, rx, in x axis: and associated radius of gyration, rx, in x axis: Ix = 110 in4 Ix = 959 in4 rx = 3.47 in4 rx = 8.24 in4 Second moment of area, Iy Second moment of area, Iy and associated radius of gyration, ry, in y axis: and associated radius of gyration, ry, in y axis: Iy = 37.1 in4 Iy = 38.7 in4 ry = 2.02 in4 ry = 1.66 in4 Hence for this column section the ratio of the slenderness around the Hence for this beam section the ratio of the slenderness around the stronger x-axis against the weaker y-axis is 3.47/2.02 = 1.72 stronger x-axis against the weaker y-axis is 8.24/1.66 = 4.96 54 Deflection While “bending moment” is a term for the internal While it does not relate to section properties, it is force that is developed in a member under load, worth noting that for a uniformly loaded element the “deflection” describes the extent to which a beam is deflection is also related to the length of an element displaced when loaded. to the power 4. Hence doubling the length of, for example, a 26 foot-long beam to 52 feet without The formulae for calculating the deflection of beams changing its section properties will result in an under common loading and support conditions are increase in deflection of 2 to the power 4, or 16 times indicated on the diagrams in section 2.1.3. the original deflection. Increasing the span of a 15-foot beam to 20 feet without changing any of the The second moment of area of a beam significantly section properties will result in the deflection impacts the degree a beam will deflect, as can be increasing by over 3 times. seen from the equation below for a simply supported beam supporting a uniformly distributed load. Deflection, δ = 5ωL4/(384EI) where ω = applied load per foot L = length of element E = Young’s modulus of material I = second moment of area of rectangular cross-section (= bd3/12) As explained in section, the second moment of area of a rectangular section is directly related to the cube of the depth of the section. Therefore the deflection of a beam under uniformly distributed load is inversely related to the cube of the depth of the member. So increasing the depth of a member by a factor of 2 reduces the deflection of the system by 2 to the power 3, which is 8 times. 55 2 2.1 Theory General theory of structures 2.1.6 Fitness for purpose So far, the performance of a structure “serviceability” limit states, and has been examined in relation to how generally relate to the movement of the well it could resist applied loads structure under various loads. without elements failing in terms of stress limits. This section examines another set of criteria that a structure has to meet to ensure that the building can serve the purposes for which it has been designed. These criteria are the Vertical deflection A beam can be designed to be perfectly capable of The allowable deflection criteria vary slightly between resisting the stresses induced by an applied vertical materials and codes of practice, but in general the design load, and therefore not pose any risk of governing deflection criteria for beams and slabs are causing a structural collapse, and yet still fail the approximately as shown below: serviceability deflection criteria, and hence be unsuitable. Beam Allowable dead + imposed = L/240 deflection load Excessive vertical deflection of beams and slabs can cause the following problems: and Allowable live load deflection = L/360 • Perceived movement by building users, causing or Allowable live load deflection = L/500 discomfort; for beams carrying brittle finishes (such as brick) • Damage of finishes, such as ceilings and services, which may be supported by the deflecting Cantilever Allowable dead + live load = L/120 structural members; deflection • Damage to the building cladding; and Allowable live load deflection = L/180 • Visually perceptible sagging of structural where L = length of beam elements, causing concern/alarm. In certain circumstances an increased deflection The extent to which a structure can deflect vertically criteria is required. For example, in commercial without exceeding any of the serviceability conditions buildings the cladding is often made from large is a function of the length of the span and the glazed units that are susceptible to damage owing to deflection under live load. Deflection under self the “racking” effect if the supporting beam deflects weight is not relevant to the first three items in the list significantly. To reduce this risk, edge members as this deflection would have already occurred prior supporting large glazed cladding elements are often to the application of the cladding, the services, and designed to meet L/1,000 or 1⁄2", whichever is the the live loads, and hence would not be additional to lesser of the two. any discomfort or damage that could occur. In order to limit the possibility of visual sagging, long-span beams can be fabricated with an upward curve that offsets some of the dead load deflection. This is called pre-cambering. Beams are often pre-cambered in the opposite direction to the deflection in order to cancel out the majority of the dead load deflection, thus reducing the overall perceived critical deflection. 56 Lateral deflection As with vertical deflection, the lateral deflection limits for most structures are determined to limit any perceived lateral movement and therefore discomfort to building users and limit damage to building elements. The maximum allowable deflection limit is related to the height of the building, and is often taken as: height/500. Vibration As well as in the case of deflection, a floor can also be neighbors, the calculations have to be repeated a deemed to fail serviceability requirements if it is number of times to take account of the effect of the subject to excessive vibrations. Vibrations can be neighboring elements. This leads to a more accurate caused by a single impulse force, such as the approximation of the behavior. Further executions of dropping of equipment, or, for example, an industrial the calculations will increase the accuracy of the process. analysis until a point when there is almost no difference between each subsequent repetition of the Essentially, vibration occurs when the floor structure calculations. In FEA these calculations can be run oscillates. The amplitude and frequency of each many times, enabling very accurate models of oscillation will determine how perceptible the components to be developed. Breaking the elements vibration is to the building user. Amplitude and down into even smaller pieces further increases the frequency are functions of the span and stiffness of accuracy of the FEA, but requires a greater number of the floorplate, its self weight, the intrinsic damping calculations to be undertaken and therefore greater within the floor, and the force that is causing the computing power. vibration to occur. The assessment of a floor’s vibration characteristics requires detailed calculations The actual movement of a floor when subject to and is often undertaken using Finite Element software vibration is usually well within the allowable for all but the simplest of structures. Finite Element deflection criteria; however, the perception to a Analysis (FEA) is a method that can be used to create building user can be of much greater discomfort. The a mathematical model of a structure. The technique acceptable levels of vibration vary significantly subdivides structural components into small pieces, between building usages, from industrial facilities at or elements, and sets up mathematical equations that one end to laboratories and hospital surgeries at the model the behavior of and interaction between these other. A range of acceptable vibration criteria is elements, and thus the structure as a whole. These available in design guides, advising on the maximum equations are then solved simultaneously in order to accelerations of the floor for different end-user find an approximate solution; that is, to predict how conditions. the structure will behave as it is put under load. As the behavior of each element affects and is affected by its FEA computer analysis of floor vibration 57 2 2.1 Theory General theory of structures 2.1.7 Structures Categories of structure The previous sections have examined the loads In reality, the practical requirements of achieving the applied to structural components, and how the required building function, form, and aesthetic while material and sectional properties of those supporting irregular loading conditions often components contribute to their structural capabilities. determine that structural components will have to be designed to act in more than one mechanism of load This section considers structures as whole entities of transfer at any one time. For example, a floorplate interconnected components and examines how they may be designed to support vertical loads via a can be categorized and stabilized. section active mechanism and simultaneously distribute lateral load to structural cores via a surface Heinrich Engel developed a system of categorization active mechanism. Similarly, arches and trusses are for structures, which was first published in 1965. He commonly required to support irregular loads that separated structural types into four categories: induce bending stresses in their components, thus reducing their structural effectiveness. In effect, most • Form active buildings are designed to compromise to some extent • Vector active between pure structural efficiency and practical • Surface active requirements. • Section active These categories form a useful system for examining the primary structural drivers for the vast majority of structural forms. Engel’s categories provide designers with a useful framework within which structural forms can be grouped. Once the mechanism of load transfer in a building is identified, a designer can determine what parameters will and will not affect the structural efficiency of that building, and develop a design accordingly. 58 Form active “Form active” structures rely on a series of flexible, chain, with the exception that whereas the chain’s non-rigid components to achieve a stable form under components are in pure tension an arch’s components loading. The most simplistic and easily apparent of are in pure compression. these forms is a chain or rope bridge, which will deflect in order to reflect the position of any load In a perfectly efficient form active structure, the placed upon it. Other, more three-dimensional components are subjected to pure axial stresses examples include tensile fabric and gridshell (either compression or tension) only. If a point load is structures, which when placed under tension also applied to the surface of a flexible form active create stable forms that can be manipulated using structure, deformations will occur. Even rigid arches double curves to create more interesting and more will develop bending under point loads (unless the stable arrangements. load is applied vertically at the crown of the arch), which significantly reduces their structural efficiency. Pneumatic structures are further examples of structures whose form is directly related to the (hydrostatic) forces applied to them. More common but less obvious examples of form active structures include arches. An arch can be considered to act in a similar manner to a loaded 1 2 1 The Olympiahalle, Olympic Park, Munich, Germany, 1972, a tensile fabric structure (see pages 158–61) 2 The Savill Building, a gridshell structure visitor center at Windsor Great Park, UK, Glen Howells Architects, Büro Happold and Robert Haskins Waters Engineers, 2006 3 Arch at Gaudí’s Casa Milà 3 4 4 Arch of the Winter Garden, Sheffield, UK, Pringle Richards Sharratt Architects and Buro Happold 5 Traditional stone arch of a Roman aqueduct, Segovia, Spain 6 Catenary arch of a suspension bridge in British Columbia, Canada 5 6 59 2 2.1 2.1.7 Theory General theory of structures Structures Categories of structure Vector active “Vector active” structural forms transfer load via a The efficiency of a vector active structure is series of interlinked rigid components, which are dependent on the individual members working in small in comparison to the length of the overall axial tension and compression only, rather than in structure and therefore not capable of developing bending. To achieve this the loads must be applied at significant bending or shear forces. The distribution of or through the points where the members connect— the externally applied force back to the points of known as the nodes. In reality it is often impossible to support is subject to the directional and geometrical avoid some bending moment occurring in some relationship between the components—hence the members of a truss due to accidental loading term “vector active.” A simple two-dimensional truss scenarios or, in the case of bridges, due to the load of is the most common example of a vector active traffic on the bottom chord. Therefore, individual structure. More complex examples include components of vector active structures are often spaceframes and spherical or hemispherical designed with some additional sectional capacity to dome structures. avoid instabilities developing. 1 1 Cape Fear Memorial Truss Bridge, Wilmington, USA 2 Lamella Dome of the Palazzetto Dello Sport, Rome, Italy, Pier Luigi Nervi 3 Lamella Dome at Materials Park, South Russell, Ohio, USA, John Terrence Kelly 4 Detail of a spaceframe structure 2 4 3 60 Surface active “Surface active” structures include concrete or generate local bending stresses. Openings within a masonry domes, cellular buildings, and concrete stressed surface, or other discontinuities, also reduce shells. These are characterized by rigid surfaces that the structural efficiency of the system. are capable of developing axial (compression and tension) and shear stresses. As with form active When a surface active structure is designed purely to structures, any applied forces are redirected via the respond to the forces applied to it, it can be an form or shape of the structures and therefore shape is extremely efficient form. For example, the reinforced- intrinsically linked to structural performance. concrete roof to Smithfield Market in London forms an elliptical paraboloid that covers a column-free area The efficiency of a surface active structure is of 225 x 125 feet and measures just 3 inches thick with dependent on the form of the surface in relation to a rise of nearly 30 feet. the forces applied to it. For example, the efficiency of a dome is driven by its height in relation to its span. In many buildings the floor structure is designed as a A perfectly hemispherical dome is the most horizontal surface active structural element, known as structurally efficient form in terms of material used a diaphragm. This is used to transfer lateral loads into and volume encapsulated. the vertically stiff elements of the building, such as shear walls or lift cores. This is expanded on in Again, as with form active structures, surface active section structures are poor at supporting point loads that 1 2 3 1 2, 3 Concrete Shell Aquarium, Interior and exterior views of City of Arts and Sciences, the reinforced-concrete roof Valencia, Spain, Santiago at Smithfield Market, London Calatrava and Félix Candela 61 2 2.1 2.1.7 Theory General theory of structures Structures Categories of structure Section active “Section active” structures are the most versatile and designed to resist bending, shear, and torsion forces most common form of structure in Engel’s system. as well as axial tension and compression. Section active structures rely on the sectional properties of individual rigid components, such as The structural efficiency of a section active structure beams and columns, to support applied loads. All is dependent on the cross-sectional properties of the buildings that are constructed from beams, slabs, and individual components and their unrestrained length columns—from agricultural sheds to high-rise and height. commercial buildings—can be described as section active. In contrast to form and vector active systems, the components of a section active system are 1 1 Standard concrete structural frame 2 Standard steel structural frame 3 Standard timber structural frame 2 3 62 Stability Any building, regardless of its particular load transfer cladding, such as large glazed panels or brickwork, mechanism, can be subjected to lateral forces. These are more susceptible to damage and hence are often are generated from wind, seismic, and/or “out of limited to overall height divided by 500. This is tolerance” forces developed due to a lack of verticality primarily to avoid damage occurring to the cladding in columns or the actual geometry of the building elements rather than to avoid discomfort to the itself. In all cases the structure must be designed to be building’s users, which will normally be negligible at capable of transferring these lateral forces into the such a level of deflection. foundations. This must be done without overstressing any structural elements and without the building There are several fundamentally different methods by undergoing significant lateral deflections. which a structure can be stabilized. The most common of these are explained in the following sections. The extent to which a structure can be allowed to deflect under lateral loads is dependent on the use of the building and the material from which it is constructed. Typically, buildings are designed with an allowable lateral deflection limit of height/300 under the most onerous loading conditions such as a 1-in-50-year wind scenario. Buildings with brittle Tolerance of wind and seismic loads 1 Lateral wind load i Initial profile of structure inducing lateral ii Deflected profile of deflection of structure structure 2 Seismic ground movement inducing lateral deflection of structure 3 Geometry of structure induces lateral deflection of structure i ii i i ii ii 1 2 3 63 2 2.1 2.1.7 Theory General theory of structures Structures Stability Rigid framed structures Rigid framed structures are constructed from a series to be able to transfer the applied loads into the of columns and beams that form a frame onto which foundations. Any discontinuities caused by the building’s cladding and floorplates are attached. requirements such as double-height floors or locally They are typically constructed from steel, reinforced removed columns will generate weak points and concrete, or timber. therefore necessitate larger, stiffer structural members in these locations to avoid exceeding the In rigid frames the resistance to horizontal loads is allowable deflection criteria. provided by a number of “stiff frames” located throughout the structure. In each of these stiff frames Lateral loads, particularly wind, can be applied in all the connection between the beam and the column is directions and so a rigid framed structure must be designed to be capable of transferring both the designed with frames orientated at right angles to bending moment and the shear force that are one another to resist all possible loading scenarios. developed by the applied horizontal forces (see diagram below). Since this stiff moment connection The floor slabs that span between each frame in a will not rotate, the frame will remain rigid under rigid framed structure (and most other stabilizing lateral load. The only lateral deflection that can occur systems) are often designed to act as diaphragms and will be due to the deflection of the vertical columns, distribute the lateral loads into each frame. In many which are designed to limit this deflection to within cases the horizontal depth of the slab provides a acceptable parameters. If the connections between sufficiently stiff element to ensure that it will not the beams and columns of a frame are designed with “rack” when lateral loads are applied. Even a timber pinned connections rather than moment connections, floor can be considered to be a stiff diaphragm when the frame would have no capacity to resist lateral detailed correctly. The location of large openings in loads and would form a mechanism that is by the floorplate must be carefully considered to ensure definition unstable. the diaphragm is not compromised. The rigid frames within a multistory building have to extend throughout the height of the building in order Rigid frame under vertical and lateral loads Vertical loads = ωvert Moment connections do not allow rotation to occur to joints Lateral loads = ωlat H L Shear reaction = magnitude of applied lateral load (ωlat x H) V1 V2 Frame reactions Vertical reaction due to vertical load = magnitude of applied vertical load (ωvert x L) RV1 RV1 Vertical reactions due to lateral loads result in tensile and compressive forces of equal magnitude but opposite directions where: Rlat = ωlat x H2/(2 x L) -RLAT RLAT Pinned frame under lateral loads forming mechanism Pinned connections allow rotation to occur and hence cannot resist lateral loads Lateral load 64 Rigid frames under lateral loads Regular rigid frame under lateral load Rigid frame with increased floor span at 3rd floor level Deflected shape Deflected shape Lateral load Lateral load Weak spot due to increased span of frame Rigid frame with double-height floor under lateral load Deflected shape Lateral load Weak spot due to double- height floor Floor slab acting as diaphragm Rigid frame with stiff floor plate under lateral load Rigid frame with floor plate containing significant openings under lateral load Deep floorplate provides stiff Large openings in slab reduce Deflected shape diaphragm ensuring the slab Deflected shape lateral stiffness of floorplate remains rectangular under lateral causing slab to “rack” under load lateral loads Rigid frames located evenly along length of structure Rigid frame Rigid frame Rigid frame Rigid frame Rigid frame Rigid frame producing uniform lateral deflection under lateral loads Lateral load Lateral load 65 2 2.1 2.1.7 Theory General theory of structures Structures Stability Braced framed structures Braced framed structures, like rigid framed examples, Designing a braced structure can have the following are fabricated from a series of beams and columns implications in comparison to a rigid structure: linked together via a floorplate acting as a diaphragm. Unlike in rigid framed construction, in braced frames • Reduced cost of beam/column connections the beam-to-column connection is designed as a • Reduced size and weight of beams and columns pinned connection, and thus is not capable of since they do not have to resist lateral forces resisting applied lateral loads. Instead stability is • Reduced complexity of beam/column connections provided via other elements such as shear walls, make fabrication easier cores, or braced frames located strategically throughout the plan of the building. These stiff The floorplans of rigid frame buildings, however, are elements—as is the case for the frames in a rigid not limited by the need for cores or shear walls and framed structure—must continue for the full height of can therefore accommodate more open-plan the building. arrangements than braced structures. Ideally the location of the stiff cores, bracing, or shear Such factors as the total height of a building, the walls in a braced structure will be distributed evenly height between each floor of a multistory building, on plan. This will result in an even deflection of the and the span between the columns all have a building under lateral load. If the shear wall and cores significant effect on frame stiffness. As frame stiffness are distributed non-symmetrically the structure can reduces, column and beam sizes must increase to be subject to twisting under lateral loads. meet the deflection requirements. These factors significantly influence the efficiency of braced and rigid frames and can determine which is the most suitable option. Rigid frame under Braced frame with cross Braced frame with shear lateral load bracing under lateral wall under lateral load load Lateral Load Bending moment due to Bending moment due to Bending moment due to lateral loads induces vertical lateral loads induces vertical lateral loads induces a tensile and compressive tensile and compressive bending moment at the base forces at the bases of the forces at the base of the of the shear wall, adjacent rigid frames cross-braced wall, adjacent columns support vertical columns support vertical loads only loads only 66 Plan of braced structure i Center of gravity of the iii Shear walls v Extent of deflection under with symmetrical building iv Edge of building lateral loads stabilizing elements ii Structural cores v iii i ii ii iv Applied lateral load Plan of braced structure i Center of gravity of the iii Shear walls v Extent of deflection under with nonsymmetrical building iv Edge of building lateral loads stabilizing elements. ii Structural cores Nonsymmetrical arrangement of cores causes twisting of building under lateral loads v iii ii i ii iv Applied lateral load Concrete diaphragm with a structural core: The Shard under construction, London, Renzo Piano Building Workshop 67 2 2.1 2.1.7 Theory General theory of structures Structures Stability Cellular structures Buildings fabricated from a series of solid walls and The floorplates and walls also have to be designed to floorplates can be described as cellular structures. The be capable of resisting the vertical loads applied by most common example of this form of construction is the building’s self weight and its occupants. As a typical masonry house with brick- and blockwork mentioned previously, this is an example where a cavity walls and a timber joist floorplate with timber structural element is designed with two distinct load floorboards. Other examples of common cellular transfer mechanisms: surface active to transfer the structures include in situ timber studwork structures, horizontal loads and section active to support the and precast concrete and prefabricated steel vertical loads. buildings. In summary, for cellular systems to be effective the The stability of a cellular structure is provided by the following conditions have to be achieved: walls, which act as surface active stiff panels that transfer the horizontal loads to the foundation level. i) Structural wall panels are vertically continuous Walls are significantly stiffer in their longitudinal axis through the height of the building, thus providing a than their transverse axis because stiffness is related direct stress path for loads to the foundations and to the cube of the depth of a member (see section avoiding transfer structures. So the walls in a cellular structure must be ii) The floorplate must be capable of acting as a distributed in both perpendicular directions to ensure diaphragm. Timber joists in particular require blocking the structure is capable of resisting the horizontal and to be positively fixed to the floorboards. wind loads that can be applied in all directions. iii) Holes in the floor should be located to allow sufficient connectivity between the floorplate and the As with framed buildings, the floorplates in a cellular stabilizing walls. structure have to act as diaphragms to transfer lateral iv) The floorplate must be positively connected to loads into the stiff walls oriented parallel to the the stabilizing walls to enable the shear forces to be direction of the applied load. Large openings for adequately transferred. staircases have to be located carefully to ensure that the floorplate remains stiff enough to distribute the forces effectively and to avoid distortion of the building under lateral load. Typical cellular building plan—colored walls indicate the elements providing effective lateral restraint under each lateral load condition Lateral load Lateral load 68 Structures inherently resistant to lateral forces Certain structures are inherently stable owing to their any additional stabilizing elements. The stability form. These include many form and surface active system of domes and tension fabric structures are examples such as domes, shells, gridshells, cable net, examined on the following sketches. and tension fabric structures. All of these can be designed to resist lateral forces without the need for Tension fabric structure T = tension Dome structure C = compression Fabric is stretched over steel Vertical load induces a horizontal frame in a double-curved, thrust through the arched three-dimensional form, which structure. Magnitude of T induces tensile forces in the horizontal thrust is dependent on fabric and compressive forces in the weight and profile of the T the frame. dome. T C C C C Force diagram under self weight Force diagram under self weight only only Under lateral load the tension in Lateral force induces increased the fabric in one direction vertical and horizontal reactions increases as the lateral forces are on the leeward face of the dome transferred through it into the and reduced vertical and Lateral load T supporting steel frames. horizontal reactions on this windward face. T T C C C C Force diagram under self weight Force diagram under self weight and lateral loads and lateral load 69 2 2.1 2.1.7 Theory General theory of structures Structures Stability Structures such as igloos 1, 1 airship hangars 2, and tensile fabric structures, for example London’s Millennium Dome 3, can resist lateral forces without any additional stabilizers 2 3 70 Towers As buildings extend in height, structural stability Interior structures are so called because their stability becomes increasingly difficult to achieve owing to the system is essentially located within the interior of the relative reduction in the height-to-width ratio. When a building via cores or shear walls. Exterior structures, structure approaches 30 stories or, say, 400 feet high, on the other hand, use the perimeter skin of the alternative, more complex stability systems are building to form a stiff tube to provide stability. needed to provide resistance to lateral forces. These different systems can be separated into two Examples of each of the subgroups of these distinct groups: typologies, together with the ranges over which they are efficient, are provided in the following tables. • Interior structures • Exterior structures Towers—interior structures Frame Frame Approx. Example type description efficient building number of stories Rigid or braced Structural cores, shear walls, >30 One Canada Square, frame or rigid beam-to-column London connections provide lateral 50 stories stability 770ft high Outrigger Cores provide stability, with >100 Taipei 101, Taiwan construction additional stiffness afforded 101 stories via “belt trusses” spaced at 1,670ft high regular story intervals, which are linked to outrigger columns; this arrangement increases the lever arm over which the lateral loads are distributed 71 2 2.1 2.1.7 Theory General theory of structures Structures Towers Towers—exterior structures Frame Frame Approx. Example type description efficient building number of stories Framed tube A series of closely spaced 100+ Aon Center, Chicago perimeter columns are 83 stories connected to the floor via 1,135ft high fixed connections, which allows them to act as a single large external core. This has a greater width than an internal core, making it more efficient. Braced tube A similar system to the 100+ John Hancock Center, framed tube, but the stiff Chicago outer core is formed via 100 stories a braced truss rather than 1,130ft high closely spaced columns Bundled tube A series of framed tubes 100+ Willis (formerly bundled together to utilize Sears) Tower, Chicago the increased strength of 108 stories several tubes structurally 1,450ft high linked. As the building height increases, some tubes are terminated Diagrid Uses a “diagrid” rather than <100 Swiss Re Tower, London a braced truss to form the 41 stories stiff perimeter tube 595ft high 72 2.2 Structural systems 2.2.1 Introduction This section examines the most common structural-frame materials used in building construction: steel, reinforced concrete, and timber. Section 2.2.2 discusses the attributes of each material against a series of criteria that help determine the suitability of each structural material in specific building types. Section 2.2.3 then provides general data for structural components including rules of thumb and economical span ranges. 73 2 2.2 Theory Structural systems 2.2.2 Structural material assessments Structural steel construction assessment Common usage All sectors, particularly high-rise Structural performance The inherent strength of steel determines that it is capable of spanning relatively long distances efficiently. This enables buildings to have larger grids with fewer columns Weight In general steel-framed buildings weigh less than concrete-framed ones, and therefore exert smaller loads onto their foundation system Deflection Deflection, as opposed to stress failure, is often a critical design criterion for steel beams—particularly long-span beams. This can be limited by pre-cambering up to two-thirds of the dead load applied to a steel beam Vibration As steel frames are often lightweight and relatively long-span, they can be susceptible to adverse in-use vibrations. This must be identified and designed out—by reducing spans, increasing permanent dead loads, or stiffening the system Fire protection Steel has virtually no inherent fire resistance and normally requires additional measures, such as sprayed or painted coatings applied directly to its surface or boarding with fire-resistant material, to achieve the necessary fire protection Program Steel frames can be erected very quickly in comparison to concrete frames, reducing construction programs. However, the use of following trades such as cladding and fire protection can offset this program advantage Sustainability The environmental performance of a steel-framed building in comparison to a concrete-framed building is subject to many variables, and should be examined on a case- by-case basis Cost The cost of a steel frame is generally driven by the weight of the steel used Flexibility Steel frames can be relatively easily strengthened or adapted post-construction 74 Reinforced concrete construction assessment Common usage All sectors Structural performance Reinforced concrete can be designed to span long or short distances depending on the depth and volume of reinforcement used. Post-tensioning of the concrete can be used to further increase the distances that can be efficiently spanned Weight In general, concrete-framed buildings weigh more than steel-framed buildings and therefore exert larger loads onto their foundation system Deflection The deflection of concrete elements is normally governed by the depth of the beam in relation to its span. Cambering of the formwork can be used to reduce the dead-weight deflections Vibration The heavy nature of long-span concrete frames reduces the risk of problems due to vibration; however, this must still be examined at design stage Fire protection Concrete has excellent inherent fire protection, achieved via the “cover” it affords to the reinforcing bars. Cover can be increased to achieve higher protection as required Program In situ concrete frames take longer to the requirement for following trades for construct than steel frames. Precast frames suspended ceilings and some cladding can be constructed in a similar timescale as that for steel frames. Overall building programs can be reduced if exposed concrete finishes are used, as this can negate Sustainability The environmental performance of a environmental strategy of a building; concrete-framed building in comparison to a however, the cooling/heating design strategy steel-framed building is subject to many must be developed to utilize this to achieve variables, and should be examined on a case- the maximum benefit by-case basis. The inherent thermal mass of a concrete frame can be used in the Cost The cost of a concrete frame is generally driven by the concrete volume, the mix design, the reinforcement volume, and the formwork type Flexibility In situ concrete is “poured” and can construction redesign is reliant on the therefore be formed into any shape more existence and accuracy of record drawings or easily than other materials. Existing concrete intrusive examination. Post-tensioned frames, in general terms, are more difficult to concrete is complicated further owing to the adapt than steel frames as the reinforcement requirement to avoid damage occurring to is not visible and hence any post- the post-tensioned tendons 75 2 2.2 2.2.2 Theory Structural systems Structural material assessments Timber construction assessment Common usage Residential, education. Typically low-rise (up to 5 stories) Structural performance Timber frames generally are designed to performance of timber. The grade of timber span shorter distances than concrete or steel. has a large bearing on its ability to resist load Glue-laminated timber and Laminated Veneer Lumber (LVL) are products that have been manufactured to increase the structural Weight The lightweight nature of timber makes it an excellent material for long-span lightly loaded roof structures or pedestrian bridges Deflection As with other materials, deflection is related to section depth Vibration As timber is primarily used to span shorter distances than other structural materials, vibration is often not a critical design driver Fire protection Requires significant fire protection Program Prefabricated timber frames with pre-applied insulation can facilitate a very rapid construction program Sustainability Arguably the only truly renewable construction material, if sourced responsibly. Overall environmental performance of the structure is still subject to many factors and should be examined on a case-by-case basis Cost Generally low-cost material, but the selection of connections (mechanical) can have a significant effect on cost Flexibility Highly flexible and adaptable 76 2.2.3 Structural components As with any “rule of thumb” system, the information provided in this section is of a general nature and is sufficiently accurate to provide a basic feel of the section sizes and depths required at the early design stage, but should always be proved via detailed calculations as the design progresses. The information in this section is divided into coverage of the structural elements—including beams, slabs, and columns—and then subdivided according to the various materials commonly used to form these elements. 77 2 2.2 2.2.3 Theory Structural systems Structural components Beam systems Properties of steel beams The aspect ratio between primary the performance of the beams. The and secondary beams can rules of thumb in this table assume significantly affect the load a system that an aspect ratio of approximately can support, and hence will impact 1:3 is achieved. Beam type Comments Typical Typical span span/depth range ratio Standard 1 Commonly used with precast Secondary 15:1 rolled wide concrete, concrete-infilled metal beams flange decking, and timber joist floors 30–50ft (W-shape) 2 Services pass either below or beam above structural beam Primary section 3 Shelf angles can be used with beams precast planks to reduce structural 20–30ft depth of floor Standard 1 Commonly used with precast Secondary 15:1 steel beam concrete, concrete-infilled metal beams with decking, and timber joist floors 30–50ft precast 2 Services pass either below or slab and above structural beam Primary structural 3 Shelf angles can be used with beams toppings precast planks to reduce structural 20–30ft depth of floor Standard 1 Commonly used with precast Secondary 15:1 steel beam concrete, concrete-infilled metal beams with decking, and timber joist floors 30–50ft precast 2 Services pass either below or slab on above structural beam Primary rolled steel 3 Shelf angles can be used with beams angles precast planks to reduce structural 20–30ft depth of floor Castellated 1 Commonly used in floor through the octagonal openings 45–60ft 18:1 rolled steel construction with precast or 4 At supports and points of high beam concrete-infilled metal decking point-loading, the octagonal holes 2 Castellations are formed by are often infilled with steel plate to profile-cutting the web of standard increase shear strength rolled sections such that when the 5 Holes measured typically 0.6 x D upper section is lifted and moved in width and are at 0.75 x D centers, laterally an octagon is formed in the where D is the depth of the web between the upper and lower castellated beam sections. The web is then re-welded, creating a deeper section 3 Services can be designed to pass Composite 1 Commonly used with precast Secondary 20:1 rolled steel concrete planks or concrete-infilled beams steel-beam beam with metal decking 30–60ft depth only concrete 2 Shear studs welded to the top slab on flange of the steel provide a shear Primary metal key between steel and concrete— beams decking allowing the concrete and steel to act 20–40ft compositely with the concrete slab, effectively forming a wide top flange to the steel beam 78 Properties of steel beams The aspect ratio between primary the performance of the beams. The and secondary beams can rules of thumb in this table assume significantly affect the load a system that an aspect ratio of approximately can support, and hence will impact 1:3 is achieved. Beam type Comments Typical Typical span span/depth range ratio Asymmet- 1 Commonly used with precast 15–30ft 25:1 rical steel concrete planks or concrete-infilled steel beam beam metal decking depth only (ASB) 2 The wider bottom flange allows the slab (precast or metal decking) to be constructed within the depth of the steel beam, thus reducing the overall construction depth 3 ASB sections are generally more expensive than standard rolled sections, but can provide significant floor-depth savings Composite 1 Used when standard rolled beams the fabricated beam to reduce weight 35–60ft 22:1 fabricated are inappropriate owing to and allow services to pass through steel beam steel beam insufficient strength, stiffness, or the beam, thus reducing overall only with limited construction depth construction depth concrete 2 Fabricated via steel plates welded slab on together metal 3 Used particularly to achieve long decking spans with shallow construction depths 4 Typically used with precast planks or concrete-infilled metal decking 5 Cellular holes are often cut into Steel truss 1 Used for long-span roofs and Bowstring arch truss 50–300ft 10:1 more heavily loaded floor structures Brown truss can vary 2 Can be designed as composite or Lenticular truss considerably noncomposite Burr arch truss 3 All truss connections are pinned Cantilevered truss 4 There are many different forms of Fink truss truss that have been designed all Howe truss over the world, particularly in bridge King post truss construction. These include: Queen post truss Allan truss K truss Bailey bridge truss Lattice truss Bollman truss Warren girder truss Vierendeel 1 A truss with no internal diagonal 50–150ft 10:1 truss elements, in which all of the connections are fixed-moment connections 2 Less structurally efficient than standard trusses with diagonal members, but the omission of diagonal members allows clear path for services and/or building users to pass Trussed 1 Commonly used as long-span roof From 80ft 5:1 steel arch structures, such as train stations or upward bridges 2 Arches rely on lateral restraints to St. Pancras resist spreading forces generated Station, within the arch structure. This can be London, achieved via a lateral restraint at the spans 240ft. support or by tying the base of the Trussed-arch arch together with a tension member bridges span known as a bowstring in excess of 1,600ft 79 2 2.2 2.2.3 Theory Structural systems Structural components Beam systems Properties of steel beams The aspect ratio between primary the performance of the beams. The and secondary beams can rules of thumb in this table assume significantly affect the load a system that an aspect ratio of approximately can support, and hence will impact 1:3 is achieved. Beam type Comments Typical Typical span span/depth range ratio Tied steel 1 Commonly used as long-span roof From 75ft 5:1 arch structures, such as train stations or upward Sydney bridges Harbour 2 Arches rely on lateral restraints to Bridge resist spreading forces generated within the arch structure. This can be achieved via a lateral restraint at the support or by tying the base of the arch together with a tension member known as a bowstring Steel space 1 Typically used for long-span 5–200ft 22:1 frame lightweight roof structures with but can go Montreal limited points of support up to 500ft Expo Dome 2 Frames span in multiple directions as opposed to unidirectional truss structures, making spaceframes extremely efficient 2 All connections are pinned Steel 1 Typically used for long-span Up to 275ft 22:1 domes lightweight roof structures in stadia (geodesic) or theater spaces Eden Project 2 Structurally similar to spaceframes but curved in two directions. Several different variations of dome have been developed, including the Schwedler, lamella, lattice, and geodesic types 3 All connections are pinned Steel 1 Typically used for long-span Up to 275ft 22:1 domes lightweight roof structures in stadia (lamella) or theater spaces Louisiana 2 Structurally similar to Superdome spaceframes but curved in two directions. Several different variations of dome have been developed, including the Schwedler, lamella, lattice, and geodesic types 3 All connections are pinned Steel 1 Typically used for long-span 65–200ft N/A portal single-story structures, such as Spans frames warehouses or agricultural buildings, driven by where haunches have little impact on haunch size ceilings or services coordination 2 Portal frames account for approximately 50 percent of structural-steel usage 80 Properties of concrete beams Beam type Comments Typical Typical span span/depth range ratio Reinforced 1 Commonly used with in situ beams are continuous or simply 20–35ft Continuous concrete concrete slabs. See section supported. (See section “Rigid beam beam for details of possible concrete slab Frames” for a description of a 26:1 arrangements continuous or moment connection.) 2 At initial design stages, beam Generally in multispan bays it is Simply- width can be assumed as: depth/2.5 likely that the beams will be supported 3 Beams can be designed as continuous, while in single-span beam rectangular (typically), or as flanged bays they are likely to be simply 20:1 beams if the slab on either side of supported the beam is continuous for the entire Cantilevered length of the beam beam 4 Services typically pass above or 7:1 below concrete beams 5 A differentiation is made for concrete structures as to whether the Post- 1 Post-tensioning is a specialized can span longer distances than 20–50ft 22:1 tensioned construction process involving a traditional reinforced-concrete reinforced- series of high-tensile steel tendons beams concrete being cast within a concrete beam 3 Slab depths are reduced, leading beam and then tensioned up as the to less material and therefore less concrete beam begins to cure. Owing load owing to self weight to a predetermined curve in the 4 Post-tensioned beams are usually tendons, this tensioning induces a used in conjunction with post- compression force into the soffit of tensioned concrete slabs, and with the beam and a tensile force on the wide beams measuring upper face. These pre-induced approximately: span/5 compressive and tensile stresses offset some of the stresses induced in the beam element as it is loaded 2 Post-tensioned concrete beams Precast 1 Shallow (6–9 inches deep) precast Precast 22:1 prestressed prestressed beams in conjunction prestressed Member reinforced- with infill blocks are often used in floor beams depth is concrete residential floor construction 12–20ft often beam 2 Full precast prestressed concrete influenced frames are typically used in Precast by detailing commercial developments where a prestressed fast construction program is required frames 3 Deep (30–78 inches deep) precast 15–35ft prestressed beams are typically used in bridge construction where a fast Precast construction program is required prestressed 4 Connections between precast bridge beams and supporting columns beams require careful detailing 35–175ft 81 2 2.2 2.2.3 Theory Structural systems Structural components Beam systems Properties of timber beams Beam type Comments Typical Typical span span/depth range ratio Standard 1 Typically used in residential and joists nominally measuring up to 12 10–20ft 20:1 sawn- light commercial developments inches deep by 4 inches wide Subject to timber 2 Strength subject to grade of wood species and beams 3 Require fire protection usually grade of provided via plasterboard ceilings timber, 4 When sourced correctly, is the width, and most sustainable of structural spacing of materials joists 5 Larger sections of up to 12 x 12 inches, known as timber beams, can be sourced. Range and span-to- depth ratios relate to typical timber Typical structural timber cuts from a tree cross-section 82 Properties of engineered timber products Engineered timber products include positions. This in turn increases the Glue-laminated beams (glulam), strength of the element. Laminated Veneer Lumber (LVL), and The fabrication process also Laminated Strand Lumber (LSL). reduces the tendency of the Each of these products is members to warp, twist, or bow. fabricated from layers of sawn Engineered timber products can timber, which are glued together to be fabricated to a range of section form the beam. This process sizes and lengths. increases the homogeneity of the final product as all the imperfections within sawn timber, such as knots, are distributed along the beam rather than being concentrated at particular Beam type Comments Typical Typical span span/depth range ratio Glulam 1 Typically used in lightweight Roof beams 20:1 beams timber roofs (often exposed) or light 20–65ft commercial structures for standard 2 Can be fabricated to significantly section sizes longer lengths than standard sawn-timber joists Can increase 3 Strength subject to grade of to 165ft with timber used and number of nonstandard laminations, and is advised by sizes specific manufacturer Floor beams 15–45ft for standard section sizes Laminated 1 Can be used as simple beams Similar to 20:1 Veneer similar to glulam glulam Lumber 2 Typically used in residential, (LVL) and educational, or light commercial Laminated structures Strand 3 Can be fabricated to significantly Lumber longer lengths than standard (LSL) sawn-timber joist 4 Strength subject to grade of timber used and number of laminations, and is advised by specific manufacturer 5 Ranges and span-to-depth ratios similar to glulam. Timber 1 Manufactured with either 10–20ft 20:1 I-sections sawn-timber or LVL flanges and a Subject to plywood or Oriented Strand Board grade of (OSB) web timber, 2 Typically used in residential or width, and light commercial structures spacing of 3 Can be fabricated to significantly joists longer lengths than standard sawn-timber joists 4 Strength subject to grade of timber used and number of laminations, and is advised by specific manufacturer 5 Ranges and span-to-depth ratios similar to sawn-timber beams 83 2 2.2 2.2.3 Theory Structural systems Structural components Concrete slab systems Properties of concrete slab systems Beam type Comments Typical Typical span span/depth range ratio Flat slab 1 Flat slabs contain no downstand quicker to construct than other forms 20–35ft Multispan beams, providing a continuous flat of concrete-slab construction slabs 26:1 soffit. They are used in many 4 The self weight of a flat slab can situations, particularly commercial be reduced by inserting void formers developments within the depth of the slab; these 2 Flat soffits provide easy have negligible impact on the integration of services, as there is no structural capacity of the element requirement to divert pipes and ductwork under downstand beams 3 Flat soffits require simple formwork and reinforcement detailing, making them easier and Beam and 1 Beam and slab is a traditional 15–35ft Multispan slab form of reinforced-concrete slab and slabs 28:1 (one-way incorporates either one- or two-way span) spanning slabs Single-span 2 The downstand beams reduce the slabs 24:1 deflection of the system in comparison to a flat-slab solution Beam and 1 More efficient than one-way 25–40ft Multispan slab spanning slabs for longer spans slabs 35:1 (two-way 2 Requires more formworks to span) construct downstand beams in both Single-span directions slabs 32:1 Waffle slab 1 “Waffles” create a lightweight higher than normal standard 20–35ft Multispan (a.k.a. reinforced-concrete slab solution 4 Waffle-form molds are typically slabs 22:1 coffered 2 Waffle slabs span in two more expensive than traditional slab; directions, therefore the ratio of the reinforced-concrete formwork, and Single-span integral) spans in the x and y directions the reinforcement is more slabs 21:1 affects the efficiency of the slab. A complicated to fix square bay generally provides the optimum efficiency 3 They can be left exposed as a final finish, thus omitting the need for additional suspended ceilings. This requires the concrete finish to be of a Ribbed 1 Lightweight long-span reinforced- 20–35ft Multispan slab concrete slab solution slabs 22:1 (integral) 2 They can be left exposed as a final finish, thus omitting the need for Single-span additional suspended ceilings. This slabs 20:1 requires the concrete finish to be of a higher than normal standard 3 Ribbed form molds are typically more expensive than traditional reinforced-concrete formwork, and the reinforcement is more complicated to fix 84 Properties of post-tensioned reinforced concrete slabs The primary conceptual design Post-tensioned slabs limit the aspects of post-tensioned concrete flexibility of being able to cut holes design are listed below: into a floor system post-construction, Post-tensioning is a specialized owing to the risk of cutting through construction process as described in the post-tensioning tendons. the post-tensioned reinforced concrete beams section previously. Post-tensioned concrete slabs can span longer distances than traditional reinforced-concrete slabs. Slab depths are reduced, leading to less material and therefore less load owing to self weight. Beam type Comments Typical Typical span span/depth range ratio Post- 1 Flat slabs contain no downstand quicker to construct than other forms 20–35ft Multispan tensioned beams, providing a continuous flat of concrete-slab construction slabs 22:1 flat slab soffit. They are used in many 4 The self weight of a flat slab can situations, particularly commercial be reduced by inserting void formers Single-span developments within the depth of the slab; these slabs 30:1 2 Flat soffits provide easy have negligible impact on the integration of services as there is no structural capacity of the element requirement to divert pipes and 5 Additional checks need to be made ductwork under downstand beams to ensure vibration limits are 3 Flat soffits require simple achieved formwork and reinforcement detailing, making them easier and Post- 1 Waffles create a lightweight higher than normal standard 25–45ft Multispan tensioned reinforced-concrete slab solution 4 Waffle-form molds are typically slabs 26:1 waffle slab 2 Waffle slabs span in two more expensive than traditional directions, therefore the ratio of the reinforced-concrete formwork, and spans in the x and y directions the reinforcement is more affects the efficiency of the slab. A complicated to fix square bay generally provides the optimum efficiency 3 They can be left exposed as a final finish, thus omitting the need for additional suspended ceilings. This requires the concrete finish to be of a Post- 1 Post-tensioned beam-and-slab 20–45ft Multispan tensioned systems commonly comprise a wide beam 22:1 beam and banded beam with a beam width slab approximately span/5. Multispan 2 The downstand beams reduce the slab 40:1 deflection of the system in comparison to a flat-slab solution Single-span beam 20:1 Single-span slab 35:1 85 3 Structural prototypes 86 87 3 Structural 3.1 prototypes Form finding During the twentieth century, architects advent of computer-aided design along and engineers both developed ways of with an increased knowledge of the designing complex structural forms by behavior of materials, a variety of experimenting with physical models and approaches to form finding can now be through borrowing from structures pursued using computer programs to found in nature. Finding and creating calculate optimum structural solutions new structural forms was accomplished for given geometric parameters. by extracting geometric information from physical models, in particular three-dimensional compressive surfaces—shells—or three-dimensional tensile surfaces—membranes. With the Suspension models Structural application A “catenary” curve is derived from hanging a chain or Designers such as Frei Otto and Heinz Isler have used a cable that, when supported at each end, is allowed form-finding structural prototypes as both design and to bend under its own weight. In the case of a engineering tools. In the case of Otto—and suspension bridge, the cables that are stretched specifically his work with soap films—these models between the masts form a catenary curve; however, were painstakingly photographed, logged, mapped, once the cables become loaded (by hanging a deck and drawn, generating profiles for latterly realized from vertical cables placed at regular intervals) the projects. Heinz Isler, whose interest was in optimally curve becomes almost parabolic. When a catenary engineered thin reinforced concrete shells, regularly curve is inverted, it forms a naturally stable arch. used physical scale models to generate surface Arches produced in this way are structurally efficient, geometries. These reverse-engineered plaster models because the thrust into the ground will always follow were very accurately measured on a custom rig, with the line of the arch. the subsequently plotted profiles used as the basis for his large-scale “catenary” shells. To generate compressive, shell-like structures, a net or fabric is suspended from a set of points and then Virtual form finding fixed in position by saturating it with plaster and/or glue. This is then flipped over (mirrored horizontally) Form-finding software is now widely available as a to create a thin shell-like form. Owing to their design and analysis tool and is no longer solely the structural efficiency, these forms may be described domain of the professional engineering office. as “minimal surfaces.” Form-finding software is based on principles such as the geometric optimization of the soap-film modeling Soap films techniques pioneered by Frei Otto. Typical form- finding software contains a range of procedural Soap bubbles (see section 1.4) are physical geometric transformations as well as ascribable illustrations of a minimal surface. A minimal surface properties for the constituent material construction is more properly described as a surface with equal and arrangement, which may include fabric type, steel pressure on the inside and the outside. A film cabling, and connectors. The virtual model can then obtained by dipping a wire frame contoured be subject to prestress and live load simulations. closed shape into a soapy solution will produce a While there is no question of the value of these minimal surface. excellent new tools, which allow for fast iterative modeling, there are still good arguments for physical prototyping. The physical scale model as an analog of the final physical construction has much to tell the designer, not least in relation to material behavior and project-specific constructional and assembly issues. 88 1 1 Hanging nets Antoni Gaudí’s models explored the design of vaulted compression structures using the same principle as the catenary curve, by hanging weights from flexible nets and then inverting the resultant forms 2 Suspension model Structural model made to establish the form of the arches for a new train station in Stuttgart, Germany, 2000, by Christoph Ingenhoven and Partner, Frei Otto, Büro Happold, and Leonhardt and Andrae 2 89 3 3.1 Structural Form finding prototypes 3 3 Control points Images created using form-finding software for the design of membrane structures. Control points (CP) are used to create space. The program operates in such a way that when a force is applied to one point the load of the force is distributed homogeneously so that the membrane is always under tension to produce a smooth transition between points. 4 4 Soap-film model Model by Frei Otto for the design of a membrane structure using soap film on a wire-bounded framework. This is both a minimal and an anticlastic surface, which can be graphically described as a “double-ruled” surface, i.e. one that can be described using a grid of straight lines. 90 5 5 Ice shells Heinz Isler designed a technique whereby fabric was draped over masts and then saturated with water. In freezing temperatures the membranes solidified and the masts could be removed, forming “ice shells.” Shown here is an image of ice shells constructed at Cornell University, Ithaca, NY, in 1999 by Dr. Mark Valenzuela and Dr. Sanjay Arwade, with the assistance of undergraduates from Dr. Valenzuela’s Modern Structures class. 6 6 Modeling techniques Structural models can employ a range of form- finding techniques according to the properties of the materials used, as shown in the examples here. All models by second-year undergraduate students at the School of Architecture, University of Westminster, London, 2007–9. Left to right, top to bottom: Gridshell vault, formed using (elastic) timber strips that are held in tension and fixed at the base of the model. Complex surface built up of laser-cut profiles in an interlocking grid Interlocking cardboard profiles used to model a formwork core Disposable sticks and elastic bands employed to model a collapsible tensegrity dome Paper ribbons folded and interlocked to generate a regular solid Hyperbolic parabolas (saddle shapes) generated by saturating a hung fabric with plaster 91 3 Structural 3.2 prototypes Load testing Load testing has always been a critical As can be seen from Robert Stevenson’s part of structural design development. work on the Bell Rock Lighthouse, there While the prediction of the behavior of is evidence that the use of prototype materials and construction elements models was paramount to the resolution may be calculated mathematically and of successful structural design to resist with computer models (such as Finite the enormous power of the sea. Element Analysis and Computational Similarly, monolithic, compressive Fluid Dynamics, see pages 106–9), much vaults and domes have, from Gothic can be learned by prototyping and times, required innovative construction observation. The first time it was techniques and materials that are still understood that reinforced concrete under constant development. This could flex and bend under load was on section is also illustrated by a set of the completion of Berthold Lubetkin’s practical, problem-solving exercises, Penguin Pool at London Zoo in the showing examples of a considerable 1930s. variety of resolutions. 1 1 The spiraling, reinforced- concrete ramp of Lubetkin’s Penguin Pool at London Zoo, under construction in 1933 92 2 Bell Rock Lighthouse The design of the Bell Rock was the culmination of knowledge gained from the construction of previous lighthouses (many of which 2 had failed) and from prototyping with scale models. John Smeaton had built the Eddystone Lighthouse in 1759, pioneering the use of stone. Not only were the stones “dovetailed” to interlock with each other, but they also employed wedges similar to the dowels in a “scarf” joint. The ideal profile to resist the enormous impact from wind and waves was found to be parabolic in shape; Robert Stevenson and John Rennie are known to have built scale models against which they would throw buckets of water. Left: Photograph of Bell Rock Lighthouse showing the parabolic curve at the base Below left: Section through the interlocking stone blocks at foundation level Below: Models of the construction details. Held at the Museum of Scotland, Edinburgh 93 3 3.2 Structural Load testing prototypes 3 3 Thin-shell monolithic Above: domes Inflatable formworks, Modern (lightweight) showing reinforcing materials technology linked to the use of air-supported Left: formworks has greatly Load testing a dome improved the efficiency and practicality of casting concrete domes (which are similar in shape and structure to an eggshell). Inspired by prototypes developed by Félix Candela, Pier Luigi Nervi, and Anton Tedesko among others, shown here is a project by Dr. Arnold Wilson at the Brigham Young University Laboratories, Idaho, USA, to load test a thin-shell concrete dome. Using air-supported form technology (made from nylon-reinforced vinyl, which is left in place as a watertight finish), the dome is formed using polyurethane foam and sprayed (reinforced) concrete. 94 4 4 Brick vaults Inspired by the work of Eladio Dieste and others, the Vault201 prototype vault was built by MIT architecture students at the Cooper- Hewitt National Design Museum, New York. The vault spans 16ft, is 11⁄2in thick, and uses 720 bricks. The curvature of the vault is composed of splines that vary in profile but are fixed in length in order to keep an equal coursing pattern and to save custom-cutting too many bricks. In the end, as a result of prototyping, a taxonomic system of three different brick modules was developed. To quote the students: “1) learn from building, 2) analyze and abstract as rules, and 3) re-embed into the design process.” (See http://vaulting. wordpress.com/ for a full account of this project.) 95 3 3.2 Structural Load testing prototypes The following illustrations are taken from first-year materials, and students learned how the act of undergraduate student projects conducted at the “making” can form an integral part of the design University of Westminster, London, UK, from 2009 to process. Objects were assessed according to 2011. Students were introduced to common structural efficiency (lightness), craftsmanship, construction materials, fabrication processes, and construction details, and the innovative use workshop practices and were then asked to design of materials. and build a 1:1 scale object in order to solve a specific structural problem. Prototyping took the form of sketching, modelmaking, and experimenting with 5 5 Supports for a sheet of glass In this project the students explored testing methods to support a human body 8in in the air on a 0.62 sq in, 0.25in-deep sheet of (untempered) glass. All examples shown employ elements that are primarily in compression. (See section Axial compression.) a b c a, b Multiple, point-loaded structure exploring iteration and scale c–e Stiffness achieved using corrugation and stability through the use of a circular plan f–h The arch and the cantilever principle combined d e f i, j Pointed arches used as colonnades k, l A pointed arch, perforated for lightness, acting as a portal frame g h i j k l 96 m Students testing their support structures m 97 3 3.2 Structural Load testing prototypes 6 6 Brick-supporting plinth e The brief was to design a This project explored the column that could support a possibility of cantilevering single Fletton brick at a the brick, while at the same height of 3 feet, without time employing a minimum bending, buckling, or number of primary elements. rotating. The load was By using two rods with the considered primarily to be capacity for elastic vertical, though the plinth deformation they could be should resist torsion (see “laminated” together to act section Stress: simultaneously in tension Element under torsion). and compression to form a Maximum footprint was set rigid structure at 10 x 10in. These efficient minimal structures were to f be designed to fail under the A single, tapering lever arm a b c load of two bricks. was stiffened using a series of ribs, which also acted to a stabilize the structure at This project set out to ground level. The vertical explore the structural cantilever was completed by potential of the double helix tensioning the lever arm by employing elements back to the base of the made from a stiff material structure with the capacity for elastic deformation—in this case, g–i bamboo. Torsive forces were This deployable solution applied in order to twist used a telescoping opposing elements in mechanism. A set of opposite directions; they cardboard cylinders was were then locked at either slotted so that they could be end so that the forces pegged at various heights canceled each other out. This produced an extremely rigid j structure with a high This project set out to leave d e f strength-to-weight ratio a clear space below the brick while also being deployable. b The solution involved using This project consisted of a three armatures that were mast that was made up of each centrally hinged. The multiple, folded (paper) desired height was achieved elements slotted around a by tensioning each of the cylindrical core. Rigidity was arms to its neighbor with the achieved through a system appropriate length of cable of bracing that would resist torsional movement by k tensioning lever arms at the The core of the mast top and base, using a consisted of cards that were network of triangulating stacked and slotted together wires vertically. Rigidity was achieved by tensioning the c top to the base A lightweight, compressive lattice consisting of three l g h i masts that were intertwined This simple column was for stability stabilized by tensioning cables to the base plate d A monolithic, planar structure whose form was derived by extruding from a simple plan. A series of ribs was connected (critically) at the point of rotation. To prevent the thin, planar ribs from buckling under load, they were individually laminated (using foamboard) j k l 98 m Supported by 200 helium balloons, the brick was held by a perforated, polystyrene beam in order to stabilize and spread the load m 99 3 3.2 Structural Load testing prototypes 7 16" 16" Load from apple must be transferred to ground within this space 16" 16" a 7 Cantilever support for an apple The following illustrations show the results of an exercise to explore solutions to cantilevering an apple 16in horizontally and 16in vertically from a 16 x 16in footprint. The load was considered primarily to be vertical, though the apple should remain stable in the horizontal plane. The diagrams describe the tensile (red) and compressive (black) elements at work in the structures. a Diagram explaining the general requirements for each structure b Photographs of four selected structures with diagrams describing the tensile (red) and compressive (black) elements c The students’ solutions to this structural problem were varied and inventive b 100 c 101 3 3.2 Structural Load testing prototypes 8 8 Glass “sandwich” panel spanning element This structural prototype developed by David Charlton at the University of Westminster, London, UK, creates a “sandwich” panel using traditional incandescent light bulbs close-packed in hexagonal plan formation and bonded to thin sheets of glass using structural silicone. The glass honeycomb-like core created from recycled light bulbs utilizes the relative longitudinal compressive strength of the bulb similar to that of an eggshell (see Section 1.3 Eggshell). The close packing of the bulbs resists the tendency of the bulbs to buckle (and fracture), providing lateral stability. This novel prototype reminds us of the usefulness of putting distance between the top and bottom chord of a beam, truss, or spaceframe, thus creating structural “depth” with which to “span.” This prototype also shows how, with thoughtful geometric configuration, compressive strength can be maintained with lightweight and even fragile materials maintaining impressive strength and reducing dead (static) loads. 102 9 9 Cable net structure model utilized all of the A cable net structure for a structural attributes of the DIY version of London’s O2 original, albeit simplified Arena (formerly the by using eight rather Millennium Dome) was than twelve uprights constructed by first-year (compression members) undergraduate students at for this mast-supported the University of Greenwich, cable net. London, UK. This 1/36 scale 103 3 Structural 3.3 prototypes Visualizing forces A key development in engineering With the development of Finite Element analysis has been the ability to visualize Analysis (FEA) and application of the forces within a “structural model.” In a Finite Element Method (FEM), graphical process developed at the beginning of computing allows the designer to model the twentieth century, photoelastic a two- or three-dimensional structural modeling allowed scale models system or connection and study the fabricated from transparent cast resin fourth dimensional effects of gravity, to have the internal structural forces static and live loads, and other applied made visible. Using two polarizing structural forces. The advent of lenses set each side of a scale model, inexpensive computing allows a fully light is passed through the rig, and integrated Building Information Model birefringence (double refraction) occurs (BIM) to be recast or reconfigured with in direct relation to localized stress information feedback from FEA analysis patterns. Whereas physical models and additional dynamic environmental may have been previously used to factors such as wind loads, modeled verify structural calculations, these with Computational Fluid Dynamic photoelastic structural “analogs” allow (CFD) software. the designer to simultaneously test and observe structural forces and structures in action. Photoelastic modeling Photoelastic modeling is an experimental method to Professor Robert Mark of Princeton University determine stress distribution in a material, and is brilliantly illustrates both the method and analytical often used for determining stress-concentration usefulness of the photoelastic technique in his book factors in complex geometrical shapes. The method is Experiments in Gothic Structure (MIT Press, based on the property of birefringence, which is Cambridge, MA, 1982), where a series of comparative exhibited by certain transparent materials. A ray of (sectional) models of some of the great Gothic light passing through a birefringent material cathedrals of Europe are photoelastically modeled experiences two refractive indices. Photoelastic and subjected to notional live (wind) loads. These live materials exhibit this property only on the application and responsive illustrations of stress patterns in a of stress, and the magnitude of the refractive indices given structure provide valuable indicative evidence at each point in the material is directly related to the of localized “hot spots” for study or amelioration. The state of stress at that point. A model made out of such correlating numerical and algebraic structural materials produces an optical pattern representing its calculations, however, must be separately computed. internal stress patterns. 104 1 2 3 4 1 2 3 4 Photoelastic model of Photoelastic model of Photograph showing how A live loading model of Bourges Cathedral choir. The Beauvais Cathedral choir. Professor Mark simulated Amiens Cathedral subjected photoelastic interference The photoelastic interference dead weight (static loading) to simulated lateral wind patterns are produced by patterns are produced by on a model of Beauvais loading. Vertical wires are simulated dead weight simulated wind loading. Cathedral using hanging attached to the model and (static loading). weights of differing masses, evenly weighted. attached to corresponding cross-sectional locations. 105 3 3.3 Structural Visualizing forces prototypes Finite Element Analysis (FEA) The first step in using Finite Element Analysis (FEA) is properties of the materials used, the software then constructing a finite element model of the structure to conducts a series of computational procedures to be analyzed. Two- or three-dimensional CAD models determine effects such as deformations, strains, and are imported into FEA software and a “meshing” stresses, which are caused by applied structural procedure is used to define and break the model up loads. The results can then be studied using into a geometric arrangement of small elements and visualization tools within the FEA environment to nodes. Nodes represent points at which features such view and to identify the implications of the analysis. as displacements are calculated. Elements are Numerical and graphical tools allow the precise bounded by sets of nodes and define the localized location of data such as stresses and deflections to mass and stiffness properties of the model. Elements be identified. are also defined by mesh numbers, which allow reference to be made to corresponding deflections or stresses at specific model locations. Knowing the 1 1 Two-dimensional Finite Element Analysis (FEA) In the FEA analysis of a simple structure, an arch (a) has a uniform load applied (b). Image c shows how the arch behaves or deforms under load, with sides pushed outward, and the apex lowered. In image d color coding is introduced, representing the internal stress pattern distribution within the arch structure. a b c d 106 2 2 Acrylic tower project The following images illustrate the Finite Element Analysis of a 30-foot-tall triangular prismatic tower. The lower 10 feet of the prism comprise a fabricated steel plinth with the remainder manufactured from solid optical-quality acrylic. The prism structure has been analyzed using a three-dimensional computer model and Finite Element Analysis. The structure was modeled using brick elements for the acrylic prism and steel plinth. Steel tensioning rods were used to a b clamp the acrylic blocks together and were modeled using line elements with temperature boundary conditions applied to produce the desired level of pre-tension. Three models were produced. The first model was to determine the post-tensioning forces and the “along” wind response of the structure; the second model was to determine the “across” (or cross-wind) wind response, and the third model was to determine the effects of temperature on the tension rods. The FEA images present contour plots illustrating the resultant deflections and stress c d distributions for the “along” wind condition together with the first mode “natural resonant” frequencies and resultant deflections. Left to right, top to bottom: a Post-tension induced stress in an acrylic prism around steel rod fixings b Wind load-induced acrylic stress c “Along” wind load, showing resultant displacement d Localized stress in the steel base plate caused by “along” wind load e Movement caused by “first mode,” or natural resonant lateral frequency f Movement caused by e f “first mode,” or natural resonant torsional frequency 107 3 3.3 Structural Visualizing forces prototypes Computational Fluid Dynamics (CFD) The Navier-Stokes equations, named after Claude- able to explore variations in design that can, for Louis Navier and George Gabriel Stokes, are a set of example, improve natural ventilation or minimize equations that describe the motion of fluid excessive downdrafts from tall buildings. Using substances such as liquids and gases. The equations inbuilt or referenced weather data, this analytical are a dynamical statement of the balance of forces computer software allows the user to model and acting at any given region of the fluid. The various overlay annual wind speed, frequency, and direction, numerical approaches to solving the Navier-Stokes directly on top of a design model, helping the equations are collectively called Computational Fluid designer develop strategies for natural ventilation, Dynamics, or CFD. When translated into a graphical wind shelter, and appropriate structural resistance. format, the motion of the fluids can be seen as particles moving through space. CFD can then be used to simulate wind dynamics—speed and direction—in and around buildings. The architect is 1 1 CFD flow vector analysis section CFD flow vector analysis showing air movement and velocity in a cross-sectional view of an urban block. 108 2 2 CFD flow vector analysis plan CFD flow vector analysis showing air movement and velocity at two heights above an urban block. Note the prevailing southwesterly wind flow and the turbulence and vortex shedding around the tall building at the center bottom of the images. 109 4 Case studies 110 111 4 4.1 Case studies Introduction In attempting to describe and explain environment, the principles of which we structures and structural principles the still struggle to fully understand, let case studies that seem the most useful alone wholeheartedly embrace. While are often highly individualized “one these individuals are now figures from offs,” exemplary artifacts of unique the last century, their experimental individuals whose work was formed as work can be usefully understood as a part of a larger philosophical approach presenting a beautiful diversity of to societal needs, both contemporary approach for new ways of making the and for the future. We see this approach, world. It is in this context that the albeit in vastly different ways and exhibition mounted at the Architecture means, in the work of structural Museum, Munich, in 2010, innovators such as Pier Luigi Nervi, “Wendepunkte im Bauen—Von der Richard Buckminster Fuller, and Konrad seriellen zur digitalen Architektur,” Wachsmann, to name but three. All of revisited Konrad Wachsmann’s seminal these structural artists produced book of 1961 The Turning Point of compelling and prototypical projects Building and staged a show of how the experimenting with new construction legacies of work by figures like processes, fabrication methods, new Wachsmann can be re-read, thoughtfully geometric configurations, and assimilated, and, with the addition of programmatic determinants. The work new digital fabrication tools, provide of these structural pioneers also tested the fuel for some new kinds of (or completely circumvented) the limits architecture and engineering that of contemporary engineering and usefully (and delightfully) serve society. architectural orthodoxy, presenting new If it is unclear whether the likes of models for the production of our built Nervi, Fuller, Wachsmann (and even Jean 112 Prouvé and Frei Otto) are engineers, as a direct translation or materialization architects, builders, or artists then that of the structure’s very own structural surely is the point. The relationship analysis) to Antón García-Abril’s between the perception of the architect whimsical structural experiment the and the engineer can and has been a Hemeroscopium House of 2008. problematic one, with mutual misunderstanding from the less The case studies are shown within the talented (or officious) of both arts. context of the general work and impact Unhelpful internecine squabbles about of their creators, and are presented which professional body lays claim to chronologically. With just over half of which talent is irrelevant, except to say the examples derived from the second that these professions were slow to half of the twentieth century, this claim any of the aforementioned section also includes significant individuals as one of their own, their structures from the latter half of the prodigious but aberrant talents nineteenth century and state-of-the-art dismissed or, worse, treated with projects from the beginning of the benign neglect by their “professions.” twenty-first. The case studies are simply intended as a collection of structural diagrams, self-illustrating structural and material investigations realized as architecture. These range from the highly unusual concrete truss roof at Chiasso by Robert Maillart from 1924 (which can be seen 113 4 Case studies 4.2 1850–1949 4.2.1 Viollet-le-Duc’s innovative engineering approaches Structural description Engineer Rib vaulting Eugène Viollet-le-Duc (1814–1879) 1 Viollet-le-Duc was responsible for a series of major restorations to medieval buildings, and produced two significant illustrated dictionaries of architecture. He was considered an artist, a scientist, an engineer, an archaeologist, and a scholar. Viollet restored Notre Dame Cathedral, Hôtel de Cluny, and other well-known medieval buildings in Paris as well as the cathedrals of Amiens, Saint-Denis, and Lausanne (for which he was awarded a medal by an international jury) and numerous city halls and chateaux. He considered that the restoration of Gothic architecture required a deep understanding of, and respect for, the structural engineering from which much of its beauty was derived, but was not afraid to reinterpret a brief. He wrote that restoration is a “means to reestablish (a building) to a finished state, which may in fact never have actually existed at any given time.”1 In several unrealized projects for new buildings, Viollet determined that it was appropriate to apply the construction and materials technology of the day (such as cast iron) to the structural logic and forms of the Gothic period. He also explored natural forms, such as leaves and animal skeletons, and used the wings of bats as an influence for the design of vaulted roofs. 1 Viollet-le-Duc, E., The Foundations of Architecture: Selections from the Dictionnaire raisonné, New York: George Braziller, 1990, p. 170 114 2 1, 2 Compositions in masonry and iron. From E. Viollet-le- Duc, Entretiens sur l’Architecture, Paris, 1863 115 4 4.2 Case studies 1850–1949 4.2.2 St. Pancras Railway Station Shed Structural description Location Plan dimensions Engineers Wrought-iron barrel vault London, England 690ft long x William Henry Barlow roof with cast-iron columns 240ft arch span wide (1812–1902) and Rowland Completion date Mason Ordish 1869 Height 100ft Contractor The Butterley Company 1 1 The initial plan of the station was laid out by won by George Gilbert Scott with a brick St. Pancras Station, the meeting of the styles: William Henry Barlow. Barlow modified the Gothic Revival building. section original plans by raising the station 20 feet With a covered area of 183,000 square feet, on 720 iron columns, thus providing a usable William Barlow’s train shed is still considered undercroft space and also allowing the to be one of the largest enclosed spaces in approach tracks to cross the Regent’s Canal the world. on a bridge rather than a tunnel. A space for a hotel fronting the shed was included in the plan, and the competition for its design was 116 2 2 3 Station under construction 3 St. Pancras Station, interior view 117 4 4.2 Case studies 1850–1949 4.2.3 Eiffel Tower Structural description Location Height Engineers Contractor Steel pylon or lattice tower Paris, France 1,060ft Gustave Eiffel (1832–1922), Gustave Eiffel (Eiffel & Cie) Maurice Koechlin, and Emile Completion date Plan dimensions Nouguier Architect 1889 410ft x 410ft Stephen Sauvestre For the Universal Exhibition of 1889, a date hurricanes, which could threaten the stability that marked the centenary of the French of the edifice.”2 Revolution, the French Journal Officiel The greatest difficulty in erecting the tower launched a major competition to “study the was the connection of the four main pillars at possibility of erecting an iron tower on the the first-floor level. The pillars sprang at a Champ-de-Mars. The tower would have a precise angle from bases that were 260 feet square base, 410 feet on each side, and 985 apart to connect with the second floor at a feet high.” The proposal by entrepreneur height of 165 feet. Gustave Eiffel, engineers Maurice Koechlin All of the construction elements were and Emile Nouguier, and architect Stephen fabricated in Eiffel’s factory located on the Sauvestre was chosen. In 1884, Gustave Eiffel outskirts of Paris. Each of the 18,038 sections had registered a patent “for a new used to construct the tower was traced out to configuration allowing the construction of an accuracy of a tenth of a millimeter, and metal supports and pylons capable of they were then put together using temporary exceeding a height of 985 feet.”1 The bolts to form prefabricated sections of company was aiming to achieve the iconic around 16 feet in length. height of 1,000 feet (more precisely, 304.8 On site, the bolts were replaced one by one meters). For the competition, Stephen with a total of 2,500,000 thermally assembled Sauvestre was employed to transform what rivets, which contracted during cooling to was essentially a large pylon into a ensure a very tight fit. decorative, functional structure. He proposed The pillars rest on concrete foundations stone pedestals to dress the legs, installed several feet below ground level on monumental arches to link the columns and top of a layer of compacted gravel. Each the first level, large glass-walled halls on corner edge rests on its own supporting each level, and a bulb-shaped design for block, applying to it a pressure of 6,000 to the top. 8,000 pounds per square foot, and each block The curvature of the uprights was designed is joined to the others by underground walls. to offer the most efficient wind resistance In all, the construction weighs 11,100 tons. possible, as Eiffel explained: “Now to what Between 150 and 300 workers were on site at phenomenon did I have to give primary any one time. concern in designing the Tower? It was wind resistance. Well then! I hold that the 1, 2 Eiffel, G., Excerpt from an interview in the French curvature of the monument’s four outer newspaper Le Temps, February 14, 1887 edges, which is as mathematical calculation dictated it should be ... will give a great impression of strength and beauty, for it will reveal to the eyes of the observer the boldness of the design as a whole. Likewise the many empty spaces built into the very elements of construction will clearly display the constant concern not to submit any unnecessary surfaces to the violent action of 118 1 1 Sketch describing Eiffel’s construction principle P P 2 Detail photograph of the Eiffel Tower showing the P rivets 3 Overall view of the tower P 3 M N P 0 0 2 119 4 4.2 Case studies 1850–1949 4.2.4 Forth Rail Bridge Structural description Location Length Engineers Contractor Cantilever truss bridge Queensferry, near 11⁄2 miles Benjamin Baker (1840–1907), Sir William Arrol & Co. Edinburgh, Scotland Allan Stewart, and John Fowler Completion date 1890 1 The Forth Rail Bridge, connecting Edinburgh of 480 feet at each end. Each of the main with Fife, is the longest cantilever bridge in spans is made up of two cantilevering arms the world for rail transport, and the world’s that support a 350-foot central truss. second longest such structure after the Connecting each end of the bridge to the river Quebec Bridge. It was designed by Benjamin banks is a series of 165-foot span trusses. Baker, Allan Stewart, and John Fowler, who The cantilever arms spring from three also oversaw the building work. The bridge 330-foot-tall towers, which are built around was built by Glasgow-based company Sir four primary columns that each rest on a William Arrol & Co. between 1883 and 1890, separate foundation. The southern group of and was the first in Britain to be constructed foundations had to be constructed as using steel alone; up to this time, the caissons under compressed air to a depth of strength and quality of steel yields could not 90 feet. While the two cantilevering arms that be predicted. spring from each of the towers The design concept for the bridge was counterbalance each other, the shoreward illustrated by Baker in his “human cantilever” ends carry weights of about 1,100 tons to model (see section 1.5). The bridge comprises counterbalance half the weight of the two main spans of 1,710 feet with two spans suspended spans and live load. 120 1 View of the Forth Rail Bridge under construction 2 The Forth Rail Bridge today 2 The use of cantilevers in bridge nomination as a UNESCO World Heritage construction was not a new idea, but Baker’s site. During construction, over 450 workers design included calculations for incidence of were injured and 98 lost their lives. erection stresses, provisions for reducing future maintenance costs, calculations for wind pressures (evidenced by the Tay Bridge disaster), and the effect of temperature variation on the structure. A recent materials analysis of the bridge, ca. 2002, found that the steel in it—estimated to weigh between 60,000 and 75,000 tons—is still in good condition. The weight limit for any train on the bridge is 1,570 tons, meaning that any current UK locomotive can use the bridge. Up to 200 trains per day crossed the bridge in 2006. The bridge is being considered for 121 4 4.2 Case studies 1850–1949 4.2.5 All-Russia Exhibition 1896 Structural description Location Engineer Hyperboloid tower; Nizhny Novgorod, Russia Vladimir Shukhov steel, tensile enclosure; (1853–1939) double-curvature steel gridshell His “gittermasts,” attenuated hyperbolic paraboloids, were true minimum weight forms.1 Matthew Wells The All-Russia Industrial and Art Exhibition of and construction of hyperboloids of 1896 was held in Nizhny Novgorod on the left revolution and hyperbolic paraboloids. bank of the Oka River. The event was the Hyperbolic structures have a negative biggest pre-revolution exhibition in the Gaussian curvature, meaning that they curve Russian Empire, and was organized with inward rather than outward. As doubly ruled money allotted by Czar Nicholas II. The surfaces, they can be made with a lattice of All-Russia Industrial Conference was held straight beams so remain relatively concurrently with the exhibition, which straightforward to build. Inspired by showcased the best of Russian industrial observing the action of a woven basket developments from the latter part of the holding up a heavy weight, Shukhov solved nineteenth century. the problem of designing lightweight, For the exhibition, the engineer and efficient water towers by employing a scientist Vladimir Shukhov pioneered the use hyberbolic, steel, lattice shell. Owing to its of steel in a number of radical building types, lattice structure, the tower also experiences including the world’s first hyperboloid tower; minimum wind load. the world’s first steel, tensile enclosure; and Shukhov called it azhurnaia bashnia (“lace the first double-curvature steel gridshell. tower”/”lattice tower”). The system was In the 1880s, Shukhov had begun designing patented in 1899, and over the next 20 years roof systems that minimized the use of he designed and built nearly 200 of these materials, time, and labor. Probably based on towers, no two exactly alike, with heights Pafnuty Chebyshev’s work on the theory of ranging between 40 and 225 feet. best approximations of functions, Shukhov invented a new system that was innovative 1 Wells, M., Engineers: A History of Engineering and Structural Design, Oxford: Routledge, 2010, p. 130 both structurally and spatially; he derived a family of equations to enable the calculation 122 1 1 2 4 The world’s first double- The world’s first steel, tensile Drawing of the “gittermast” curvature (diagonally enclosure—the Elliptical framed) steel gridshell, Pavilion of the All-Russia 5 shown during construction. Exhibition, during Interior view of the mast The roofs of these pavilions construction in 1895 looking up were formed entirely of a lattice of straight angle iron 3 6 and flat iron bars The Hyperboloid Water Tower View of the completed mast —the world’s first steel, lattice, shell structure, completed in 1896 2 6 3 4 5 123 4 4.2 Case studies 1850–1949 4.2.6 Tetrahedral Tower Structural description Location Height Designer Engineer Octet truss spaceframe Beinn Bhreagh, 82ft Dr. Alexander Graham Bell Frederick Baldwin tower Nova Scotia, Canada (1847–1922) Plan dimensions Completion date Triangle with 6ft sides 1907 Alexander Graham Bell discovered the octet Bell appreciated that the kite structure truss while conducting research on flying might be applicable to ground-based, machines. lightweight metal frames, and his Bell wanted to develop a kite that would be experiments with tetrahedral cells large enough to carry a man. In the same way culminated in the construction of an that, in the second half of the century, the observation tower at Beinn Bhreagh, his geodesic dome would solve Buckminster summer estate near Baddeck, Nova Scotia. Fuller’s problem of enclosing the maximum Bell assigned the engineer Frederick amount of space with the lightest structure, Baldwin the job of building the tower, each the tetrahedron enabled Bell to increase the “cell” of which was composed of six 4-foot- size of a kite without increasing its weight. long pieces of 5⁄8-inch diameter ordinary His first innovation was to remove a face galvanized iron pipe and four connecting from the standard box kite, producing a nuts. Each cell could support 4,000 pounds triangular section—lighter, more rigid, and without stress. On completion in September less prone to torsion under wind load. He 1907, the tower stood nearly 82 feet high. went on to combine several small triangular The octet truss is now a common, standard kites, thus increasing the surface area with component, used in many construction little increase in weight, until eventually applications and seen every day in cranes settling on the tetrahedron, one of nature’s throughout the world. most stable structures. Dr. Bell said of his own, inventive ability to apply discoveries made in one field to another: “We are all too much inclined, I think, to walk through life with our eyes shut. There are things all round us and right at our very feet that we have never seen, because we have never really looked.”1 1 Carson, M. K., Alexander Graham Bell: Giving Voice to the World, New York: Sterling, 2007, p. 118 124 1 1 Bell’s design for a multicelled, tetrahedral kite 2 Observation tower at Beinn Bhreagh, constructed using unskilled labor and sited deliberately so as to be subjected to high wind loads 2 125 4 4.2 Case studies 1850–1949 4.2.7 Magazzini Generali Warehouse Structural description Location Plan dimensions Engineer Reinforced-concrete, gabled, Chiasso, Switzerland 110ft wide x 80ft long Robert Maillart (1872–1940) constant-force truss- supported roof Completion date 1924 1 The truss takes up a plantlike form, with the connecting elements between the reminiscent of certain structural top and bottom chord placed vertically, forms of the “art nouveau” period similar to a Vierendeel truss. In addition, the such as in ... the buildings of the six trusses are also longitudinally connected Catalan, Antoni Gaudí.1 by four linear elements to prevent buckling. Max Bill The most formally complex elements of the structure are the 12 column supports, which Built at the beginning of the twentieth bifurcate at the top with the major structural century, this remarkable structure is still in support pulled in on each side to pick up the use as a bonded warehouse for temporary truss, and with a smaller arm extending to storage of goods in transit at the Swiss/Italian the edge of the gable. These geometrically industrial border town of Chiasso. It is an complex columns (T-shaped in section) are excellent example of a self-illustrating additionally shaped to reflect specific structural idea realized in in situ reinforced structural and functional requirements, concrete. The most visually striking elements including an enlarged, protected base for this are the concrete trusses, which are cast in storage depot and a longitudinal arched conjunction with the gabled roof slab. The diaphragm wall where the column meets the thin roof slab acts to reinforce the truss, providing structural stiffening and an compressive top chord of trusses that are even load distribution. supported by split “treelike” columns with In a paper for the Society for the History of cantilevered arms. The resultant form, given Technology, authors Mark, Chiu, and Abel2 the dimensional constraints and a gabled undertook a structural analysis of this unique cross-section for snow load, is an almost building. Using numerical and photoelastic perfectly built diagram of evenly distributed methods, they confirmed that its sculpted internal forces. form is in fact more structurally expedient The structure consists of six reinforced than is suggested by its carefully crafted concrete trusses creating a clear span appearance, wherein, as Max Bill stated in between structural supports of 80 feet. An his monograph on Maillart, “The form additional covering 13 feet either side is follows the flow of forces.” The results of their created by a cantilevered edge, creating an analysis showed “almost uniform force overall covered width of 120 feet. The unique levels” in the upper and lower truss chords, design means that all chords in the trusses showing that the form is derived from, or at are of the same cross-sectional dimension least closely replicates, the moment diagram. 126 5 A 2 B C D Analysis also showed that the monolithic 3 1 Cross-section drawing of construction, working in conjunction with the Maillart’s unique roof design geometry of the cross-section and the 2 designed connections, allows the roof to Main view of Chiasso “shed” function as a type of “stressed skin” interior structure. In conclusion, the analysis clearly 3 confirms that the structural logic is successful Detail of cast column and an even distribution of internal forces is support at the roof edge achieved alongside specific programmatic 4 and site requirements, specifically its Detail of column and industrial use and issues of snow loads. hanging truss connection Maillart’s work with concrete was influential 5 on the work of architects and engineers like Diagram of the structural logic and development of the Pier Luigi Nervi, who includes the Chiasso 4 roof form: warehouse and shed in his book Structures, A shows a simply supported in the chapter “Understanding Structures beam B shows the bending Intuitively.” The adjacent warehouse is also moment of that beam structurally interesting as an early example C shows the reversal of that moment diagram of flat-slab construction, wherein Maillart D is a diagram of Maillart’s replaced beams in the structure with ultimate structural resolution specially designed columns and column of the Chiasso “shed” capitals designed to provide the necessary structural stiffness and axial support. 1 Bill, M., Robert Maillart: Bridges and Constructions, London: Pall Mall Press, 1969, p. 171 2 Mark, R., Chiu, J. K., and Abel, J. F., “Stress Analysis of Historic Structures: Maillart’s Warehouse at Chiasso” in Technology and Culture, Vol. 15, No. 1 (Jan. 1974), pp. 49–63 127 4 4.2 Case studies 1850–1949 4.2.8 Zarzuela Hippodrome Structural description Location Engineer Doubly curved reinforced Madrid, Spain Eduardo Torroja (1899–1961) concrete shell structures Completion date 1935 Eduardo Torroja, the Spanish engineer, was Torroja is quoted as saying: “…far more born in 1899 into a family of mathematicians, than the technical results, I value the engineers, and physicists. He was the experience in its human, social, and founder of the International Association for professional dimension … to create Shell Structures (IASS) and, at its peak in the organizations where the different 1930s, Eduardo Torroja’s Engineering Bureau professions, the upper and lower echelons, was producing many innovative designs and could work together in perfect harmony; experimental construction techniques, where everyone has grown accustomed to including early developments in prestressing living a life on the highest rung of humanity, concrete. where courtesy, mutual respect, and support, In 1959, at a time when shell structures and maximum personal dignity reign.”1 were frequently used all over the world to roof buildings such as sports and exhibition 1 Schaeffer, R. E., Eduardo Torroja: Works and halls, industrial plants, silos, and cooling Projects; book reviewed by Pilar Chías Navarro and Tomás Abad Balboa in Journal of the International towers, Torroja organized and convened an Association for Shell and Spatial Structures (IASS), International Colloquium in Madrid. During Vol. 47, No. 3, December, 2006, p. 152 this colloquium, Torroja proposed the founding of the IASS. 128 1 2 3 1 Section through the roof 2 Aerial view showing the double-curved roof under construction 3 The roof of the grandstand at the Zarzuela racecourse cantilevers some 42ft 129 4 Case studies 4.3 1950–1999 4.3.1 Crown Hall, Illinois Institute of Technology (IIT) Structural description Location Plan dimensions Architect Steel portal frame with Chicago, USA 220ft long x 120ft wide Ludwig Mies van der Rohe cantilevered ends (1886–1969) Completion date Height 1956 271⁄2ft 1 2 Where technology attains its true fulfilment, it transcends into architecture.1 Ludwig Mies van der Rohe One of Mies van der Rohe’s most celebrated acoustic ceiling. Two stairs to the lower works, Crown Hall remains an elegant and floor—leading to additional lecture, teaching, concisely engineered structure well over 50 and library spaces—punctuate the largely years after its completion. Built as part of a unobstructed ground-floor level. The main 120-acre campus entirely designed by Mies floor also contains low, freestanding oak-clad in the Bronzeville neighborhood of Chicago, partitions and two nonstructural, slim service Crown Hall remains the centerpiece of this risers, which are the only floor-to-ceiling remarkable architectural park, which is still elements. the main IIT campus out of five that the While there are no gratuitous structural institute has in the city. Crown Hall was gymnastics, Mies cleverly reverses a typical designed to house the faculty of architecture beam-and-roof arrangement and sets the and town planning (a very deliberate, four main structural beams at 60-foot centers proximate relationship), and Mies had a across the outside of the roof, supported by particular interest in this project as he eight external columns, forming welded directed the architecture program at IIT from portal frames made from hot-rolled steel 1938 until 1958. The building is arranged over sections. This structural arrangement two levels and uses a planning module of 10 maintains a perfectly clear space and smooth feet. To enter, you ascend 6 feet on travertine uninterrupted soffit. The nature of the stone steps and enter the clear-span space of fabricated steel construction also creates the main “studio” floor, a single-volume usefully rigid connections and obviates the space 220 feet long, 120 feet wide, and 18 need for any visible cross-bracing. The roof feet between terrazzo floor and white-painted projects 20 feet beyond the main steel frames 130 4 5 3 1 at each end, enhancing the effect of its still an exemplary model of well-worked Main entrance to Crown Hall, with two of the four underside as a kind of floating plane. This structural logic, elegant material fabricated plated beams steel-framed prism is glazed on all sides with composition, and forthright utility. Mies had sandblasted (translucent) glazing to the lower also used the “exterior structure” logic found 2 Rear entrance to Crown Hall panels. The building was renovated in 2005 at Crown Hall in his National Theater, by Kreuck & Sexton Architects, who Mannheim competition entry of 1953, 3 Axonometric illustration undertook a thorough and fastidious job that although for this much larger structure, 525 showing the structural involved an entire reglazing, sandblasting the feet long and 262 feet wide, he had proposed assembly steelwork and repainting in an appropriate to replace the solid steel of the plate girders 4 “Mies Black” that did not contain lead and with an open steel lattice truss. Mies Detail of column support and will not fade in sunlight. executed many projects in Chicago, but plate-steel support beam, which incorporates an access The steelwork for Crown Hall is a mixture alongside his Lakeshore Drive apartments, ladder of square-section of standard hot-rolled column and angle the newly restored Crown Hall remains one steel welded to the column flanges sections, and specially fabricated steel of his most potent and enduring works. components. Eight larger columns at 60-foot 5 centers support the four custom-fabricated 1 Blaser, W., Mies van der Rohe, London: Thames and Corner detail, showing Hudson, 1972, p. 80 sandblasted glass at lower plate girders, which are 6 feet high. level Intermediate, smaller H-section columns are located at 10-foot centers and delineate the glazing regime. With all structural elements visible and clearly expressed, and featuring impeccable detailed design, Crown Hall is 131 4 4.3 Case studies 1950–1999 4.3.2 Los Manantiales Restaurant Structural description Location Engineer Architects Reinforced-concrete Xochimilco, Mexico City, Félix Candela (1910–1997) Fernando Alvarez Ordóñez, hyperbolic shell Mexico Joaquin Alvarez Ordóñez Completion date 1958 It may be said there are two basic criteria for a proper shell: the shell must be stable and of a shape which permits an easy way to work. It should be as symmetrical as possible because this simplifies its behavior. Either interior groins (as in the restaurant in Xochimilco) or exterior edges should be able to send loads to points of support, or else there should be a continuous support along certain edges.1 Félix Candela Candela collaborated with Colin Faber on the Hyperbolic parabolas may also be general form of the restaurant. The form of understood as ruled surfaces. That is to say, the shell is a “groined” vault, made up from their three-dimensional geometry can be four intersecting hyperbolic parabolas with generated by series of straight lines. The form curved edges free of any edge stiffeners so boards for construction followed the path of as to reveal the thinness of the shell. The these straight-line generators. Once the groins are the valleys in the shell, formed at reinforcing steel mesh had been laid on the convergence of the intersecting them, the concrete was poured by hand, one hyperbolic parabolas. bucket at a time. Candela stiffened the groins using V-section beams. These V-beams are reinforced with 1 Faber, C., Candela: The Shell Builder, New York: steel, while the rest of the shell has only Reinhold Publishing Corp., 1963, p. 199 nominal reinforcing to resist local cracking. For the foundations, Candela anchored the V-beams into footings shaped like inverted umbrellas to keep the shell from sinking into the soft soil. The footings were then linked with steel tie bars to resist lateral thrusts from the shell. 132 1 1 3 Plan The buildling during construction 2 Section and elevation 4–6 The building today 2 3 5 4 6 133 4 4.3 Case studies 1950–1999 4.3.3 Concrete Shell Structures, England Structural description Location Architect Concrete shell structures Markham Moor and Ermine, Sam Scorer (1923–2003) Lincolnshire, England Completion dates 1959/1963 Sam Scorer was a prolific architect, and in the emphasis very strongly being one of a addition to his pioneering work on shell “tent of meeting.” The font is at the lowest structures he carried out much building- point of the church and the altar, also conservation work including major designed by Scorer, at the highest—all restoration on Lincoln Cathedral in the UK. presided over by a fine stained-glass window He was chairman of his local planning designed by Keith New, who also designed committee, produced Architecture East windows in the rebuilt Coventry Cathedral. Midlands magazine in the mid-1960s, and The pouring of the 3-inch-thick concrete was a Fellow of the Royal Society of Arts. roof at St. John’s had to be done in one As a talented painter in his own right, and continuous operation, in very frosty in giving vent to his artistic frustrations, conditions. Although kerosene burners were Scorer came up with radical designs for employed to prevent freezing, hairline cracks hyperbolic-paraboloid (doubly curved) appeared on drying, requiring additional roofs—most notably in a Lincoln church and support for the concrete tie beam beneath what is now a roadside restaurant on the A1 the floor, for which more concrete was added at Markham Moor. to the two pools of water (that reflect the The last-named was originally designed as significance of baptism) at either end of it. a canopy over a gas station, extending at one The outer surface of the roof was covered in end from a long, low building housing an fiberboard and super-purity aluminum (since office and kiosk over a row of pumps. A few re-clad in a proprietary membrane in the late years after its construction in the late 1950s, a 1990s, after damage). The formwork of the restaurant was built underneath the flying roof had such a fine appearance that it was roof. Early in the new millennium it was retained, producing a fine ceiling comprising threatened with demolition to make way for a a mass of timber slats. The church was slip road, but a campaign in 2005 granted it a completed in 1962 and was listed in 1995. reprieve. Unlike the restaurant, the interior of St. John’s Church fully benefits from having such a majestic roof—its saucer shape effectively eliminating the need for columns, allowing a large interior space unencumbered by structure. From the outset, Scorer was interested in how theology related to the building, what the church stood for, how it worked, and how it related to the community, 134 1 5 1 2 6 Gas station canopy, Markham Moor 2–4 St. John’s Church 5 Diagram of the hyperbolic- paraboloid roof structure 6 Copy of one of Sam Scorer’s sketches for the church bell tower 7–8 St. John’s Church 3 7 4 8 135 4 4.3 Case studies 1950–1999 4.3.4 Geodesic Domes Structural description System designer Geodesic dome structures Richard Buckminster Fuller (1895–1983) …world engineering not only was surprised by the geodesic behavior but clearly stated that it was unable to explain or predict the unprecedented performance per pound efficacy of the geodesic structures by any of the academically known principles of analysis.1 Richard Buckminster Fuller When discussing the work of Richard artifact) in themselves, they are also closely Buckminster Fuller (also referred to as related to Fuller’s social and technological “Bucky”), it is difficult to do so without mapping of the world, with the mathematics mentioning his larger theoretical and of geodesy crucial to establishing networks philosophical project for what he called of food distribution, energy systems, “Spaceship Earth.” This project, which lasted freshwater supply, and shelter. As his long- the duration of his professional life, time collaborator Shoji Sadao recently noted, encompassed a highly tuned, environmental, “For Bucky, the problem of transferring the “humane” consciousness and interests that planet’s spherical form on to a two- were to include energy, transportation, and dimensional piece of paper had not been servicing systems with special attention resolved satisfactorily.”2 given to that most fundamental of human The geodesic dome patented by Fuller in needs, shelter. As an ex-US Navy man, Fuller 1954 is known to be the most structurally recognized the logistical and operational efficient of the domes derived from the excellence of this highly resourced icosahedron (a 20-sided polyhedron). In the organization, if not its sociopolitical raison patent application, Fuller described it as a d’être. Buckminster Fuller declared that the spherical mast, which evenly distributes designer must concern himself with tension and compression throughout the “Livingry” not weaponry, and so began his structure. The form combines the structural lifelong experiment “of what one man can advantages of the sphere (which encloses the do,” which was to embrace art, architecture, most space within the least surface, and is engineering, and poetry. As well as being a strongest against internal pressure) with highly skilled and articulate strategist, Fuller those of the tetrahedron (which encloses the also interested himself in what he described least space with the most surface and has the as the artifacts of his ideas, which in greatest stiffness against external pressure). themselves are highly original. These A geodesic structure distributes loads evenly inventions include several patented structural across its surface and, as with a spaceframe, systems, most notably the geodesic dome, is efficient to construct, as it is composed which latterly became synonymous with entirely of small elements. The geodesic Fuller. It is worth noting that while geodesic dome is the product of a geometry based on geometry and geodesic domes are an end (or the shortest line between two points on a 136 Figure 1 from Fuller’s US Patent 3,197,927, in which he describes different geodesic structural configurations based on the “great circle” subdivision of a sphere mathematically defined surface; it takes its connection details. Domes were fabricated name from the science of geodesy— from a wide range of materials, which measuring the size and shape of the Earth. It included cardboard, plywood sheets, sheet consists of a grid of polygons that is the steel, and fiber-reinforced plastics. Four key result of the geodesic lines intersecting. The domes and dome types are described number of times that you subdivide one of overleaf. They utilize different materials and the triangular icosahedra faces is described fabrication processes but are all derived from as the “frequency”; the higher the frequency, Fuller’s geodesic geometry. the more triangles there are, and the stronger the dome will be. The scalability of the 1 Krausse, J., and Lichtenstein, C., Your Private Sky: geodesic dome is interesting, with Fuller R. Buckminster Fuller, Zürich, Lars Müller Publishers, 2001, p. 229 pointing out that “… every time a geodesic 2 Sadao, S., A Brief History of Geodesic Domes, dome’s diameter is doubled, it has eight Buckminster Fuller 1895–1983, Madrid: AV times as many contained molecules of Monographs 143, 2010, p. 87 atmosphere but only four times as much 3 Fuller, R. B., Critical Path, New York: St. Martin’s enclosing shell…”3 This realization led to Press, 1981, p. 209 Fuller’s proposal in 1950 to enclose the whole of midtown Manhattan in a 2-mile-diameter geodesic dome, whose enclosure would have weighed significantly less than the volume of air contained within and whose structure would be largely rendered invisible because of physical proximity and our relative visual acuity. Fuller and his consultancy companies, Synergetics and Geodesics Inc., produced many structural types of geodesic enclosure, working in collaboration with other architects and engineers. Fuller also licensed his technology, which comprised the patented geometric configuration and various 137 4 4.3 4.2.4 Case studies 1950–1999 Geodesic Domes The Climatron, St. Louis, Missouri, 1960 Architect Plan dimensions Murphy and Mackey 175ft diameter Architects Height 70ft This climate-controlled enclosure has recently carried through interconnected aluminum rods. The celebrated its 50-year anniversary as a tropical and structure is held aloft on a series of structural-steel subtropical greenhouse at the Missouri Botanical articulated columns. The Climatron was originally clad Garden. The clients had wanted a large space without in acrylic plexiglas panels, which were replaced with any internal walls or supports, which led them to glass and an additional support frame in the 1990 Fuller’s new technology. The structure is a quarter- refurbishment. sphere dome fabricated from tubular aluminum sections, acting in compression, which are bolted to cast connector joints (or nodes) with tensile forces 1 1 2 Recent photograph of the restored Climatron dome 2 Detail of the Climatron’s aluminum structural frame. Note the reciprocating tension rods Wood River Dome, Wood River, Illinois, 1960 Architect Plan dimensions R. Buckminster Fuller 385ft diameter with Synergetics Inc (James Fitzgibbon and Height Pete Barnwell) 120ft This dome is the less-celebrated near relation of The welded sheet-steel skin, which acts in tension as well Union Tank Car Building in Baton Rouge, Louisiana, as providing the environmental envelope. The Wood which was demolished in 2008. When the Baton River dome was built from the top down, with the Rouge dome was constructed in 1958, it was the structure gradually raised pneumatically with a huge world’s largest clear span—a record that it held for 11 air-inflated fabric bag. The building remains in use for years. The Wood River dome is an almost identical the servicing of railcars. construction, albeit with a less elaborate interior. Both structures are geodesic exoskeletons of welded tubular steel, fixed to a folded 7⁄64-inch (12-gauge) 3 3 4 Recent picture of the Wood River dome 4 Detail of the Wood River dome showing the sheet-steel structural skin and tubular-steel exoskeleton 138 Geodestic (Fly’s Eye) Dome, Snowmass, Colorado, 1965 Architect Plan dimensions R. Buckminster Fuller 26ft diameter Height 20ft In 1965, Fuller was granted a patent on his Monohex- properties of Glass Reinforced Plastic (GRP) to create Geodestic structures, which he also called the Fly’s an additional upstand around the openings. This Eye Dome. While still based on his geodesic compound (or double) curvature creates a very strong geometry, he utilized the configuration of pentagons construction component. and hexagons that we recognize as a simple football. Fuller then created holes (the “eyes”) in the pentagons and hexagons, leaving a triangular-shaped component to connect them. Combined with this geometric development, Fuller also used the plastic 5 5 A 26-foot diameter Fly’s Eye Dome, made from 50 GRP panels, which are bolted together using 2,000 stainless-steel bolts The USA Pavilion, Montreal, Canada, 1967 Architect Plan dimensions R. Buckminster Fuller, 250ft diameter Shoji Sadao Height 200ft The pavilion was constructed for the Montreal Expo exists as an ecological museum overlooking the city of 1967, and consisted of a three-quarter sphere, of Montreal. Interestingly, if you look for the equator geodesic, double-layered, tubular-steel space grid. (or the horizontal half-point) of the dome you will Fuller’s geodesic dome was originally weathered see that the horizontals below (toward the ground) using 1,900 molded acrylic panels, which are parallel and of decreasing circumference, incorporated six triangular sun blinds within each whereas the structural geometry above the equator six-sided panel, and were automatically opened or is purely geodesic. closed in response to the movement of the sun in relation to the structure. This remarkable structure still 6 6 7 Recent composite photograph of the Montreal dome 7 Detail of the Montreal dome showing welded-steel tubular framework 139 4 4.3 Case studies 1950–1999 4.3.5 Palazzo del Lavoro (Palace of Labor) Structural description Location Floor area Architects Contractor Reinforced-concrete and Turin, Italy 485,000ft2 (270,000ft2 on the Pier Luigi Nervi (1891–1979) Nervi & Bartoli steel cantilevered canopies ground floor) and Antonio Nervi Completion date 1961 Height of canopies 65ft Pier Luigi Nervi was one of the great prefabricated off-site as a series of 20 tapered architect/engineer/builders of the latter part steel fins radially arrayed around a central of the twentieth century. He worked as a hub, which is bolted to the concrete column structural engineer and designer on some head. A gap of 61⁄2 feet is left between each remarkable collaborations, such as Giò structural canopy and a glazed element Ponti’s Pirelli Tower (Turin 1955–6) and with introduced in order to provide rooflights— Marcel Breuer on the UNESCO Headquarters with the external glazed envelope created by (Paris, 1955–8). It is, however, his single- “Jean Prouvé type” folded-steel mullions, authored works or collaborations with his which are held on hinged connections to son Antonio that remain his most distinct allow for thermal expansion. In addition to contributions to the field of architecture and the main internal exhibition floor, a construction. The Palazzo del Lavoro is one mezzanine level wraps around three sides, such project; it is particularly notable for the independently supported by a separate speed of its construction, which provided column grid and with an in situ cast slab 485,000 square feet of exhibition space in featuring Nervi’s innovative “isostatic” rib little over 11 months. The unusual structural geometries. design, comprising 16 independent column/ Nervi, writing in his book Structures, canopies, was employed in order that explains that his employee, Aldo Arcangeli, finishing work could run concurrently with had suggested that the ribs of a concrete slab structural work—a criterion that would have should follow the lines of a structure’s proved problematic with a single roof principal bending moments. These isostatic structure. lines were made visible in the technology, Each roof structure, or “mushroom” relatively new for the period, of photoelastic canopy, measures 130 feet square and 65 feet modeling, wherein the stress patterns of a high. The mushroom support columns are clear substrate are made visible through cast in six vertical sections, with the steel polarized light. By constructing a scale model formwork for each section subdivided into of a structure in a clear epoxy, Nervi began to four reusable molds that were bolted create a new development of the surface together. The casting of each column lasted geometry and structural behavior of a ten days. The horizontal joint lines are clearly concrete floor slab. He first employed this detailed as a recessed shadow gap. The new technique in the Gatti Wool Mill in Rome geometric form of each column transforms (1951), where 16 curved ribs connect back to from a 16-foot-wide cruciform at the base, to each column head in a repeated pattern, a circular profile at the top, with an 8-foot which is beautifully reproduced using diameter. The surface finish of the columns is reusable ferrocement formwork—another further articulated by the close vertical board technological development pioneered by markings of the inside of the formwork mold. Nervi. However, structural engineer Matthew Originally the mushroom canopy structures Wells, writing in Engineers: A History of were conceived in concrete, but for speed of Engineering and Structural Design, is broadly construction the canopy elements were dismissive of these “isostatic” lines as 140 1 1 meaningless and paradoxical, in that by distribution of tensile steel reinforcement. Reflected ceiling plan, showing the isostatic rib reflecting structural action in built form you The fabrication process of Nervi’s layout prototyped at the thus affect the structural action that you had ferrocement also meant that expensive and Gatti Wool Mill, Rome (1951) originally modeled. Given Nervi’s role as a complex timber formwork could be largely designer these observations seem petty, as dispensed with, as the fine steel meshes, structural optimization was perhaps only one densely layered into a fibrous matrix, could of many factors influencing the conception, hold their shape while a cement mortar is engineering and construction of his work. It hand-applied with trowels. Ferrocement was is worth noting that Nervi was a builder as used for the highly detailed, reusable well as an architect and engineer, and that it “isostatic” formwork molds and in its own seems unlikely that without his direct right as a thin, cementitious panel. Notable involvement—and that of his builder cousin, ferrocement projects include the prototype John Bartoli—he would have been able to Nervi- and Bartoli-designed storage building, produce such structurally and architecturally Magliana (Rome, 1945), fabricated in ambitious forms. undulating panels of 1.2-inch-thick Pier Luigi Nervi also made a considerable ferrocement; and the La Giuseppa motorboat, contribution to the construction industry constructed in 1972 and still seaworthy through new production processes, including almost 40 years later. Nervi and Bartoli’s prefabrication and material innovations such skilled workforce was also used in the as ferrocement, which was developed and prefabrication of building components. Using patented by Nervi and Bartoli as a new the processes and techniques of the terrazzo construction material. Ferrocement consisted and concrete industries, which worked in of the use of a strong cementitious mortar both prefabrication and in situ cases, Nervi mix, built up over densely packed fine was able to control quality, program, and metal-mesh reinforcement. Originally cost. Interestingly, in the Palazzetto dello pioneering it for shipbuilding in the 1940s, Sport (Rome, 1957) he employed a Nervi was determined to develop a combination of precast trapezoidal concrete reinforced-concrete technology that could panels (variously sized, with protruding steel dispense with labor-intensive timber reinforcement) with in situ concrete ribs cast formwork for complex geometric forms and between them, forming downstand beams to that simultaneously optimized the structural ensure a structurally integral whole. performance of the material, creating what Claudio Greco calls “a more homogenous 1 Greco, C., “The ‘Ferro-Cemento’ of Pier Luigi Nervi, and efficient composite.”1 Working in The New Material and the First Experimental Building” in Spatial Structures: Heritage, Present and conjunction with Professor Oberti at the Future, proceedings of the IASS International Politecnico of Milan, Nervi’s tests on the symposium 1995, June 5–9, 1995, Milan: S.G.E. ferrocement revealed a considerable Publishers, 1995, pp. 309–316 improvement of the tensile strength of the material in comparison with ordinary reinforced concrete and its relatively crude 141 4 4.3 4.3.5 Case studies 1950–1999 Palazzo del Lavoro (Palace of Labor) 3 2 4 142 5 2 Recent interior view of the Palazzo del Lavoro, showing the independent “mushroom” canopies 3 Detail of column form and the transition from a cruciform base to a circular column head 4 Elevation of one of the 16 “mushroom” canopies 5 Detail of column head and radial steel fins 6 Detail of canopy soffit 6 143 4 4.3 Case studies 1950–1999 4.3.6 Concrete Shell Structures, Switzerland Structural description Location Completion date System designer Contractor Reinforced concrete shells Wyss Garden Center/ 1962/1968/1982 Heinz Isler (1926–2009) Willi Bösiger AG Deitingen Süd Service Station/Brühl Sports Center Solothurn, Switzerland Over a period of more than 40 years, Swiss- with plaster and then accurately measuring born engineer Heinz Isler created a unique the curvature of the surface, with his own body of work. His material was reinforced measuring jig, a calibrated pointed steel rod concrete, with which he created a built relocatable and capable of measuring to encyclopedia of thin concrete-shell within a thousandth of an inch in the x, y, and structures, through a process of intuitive z dimensions. When challenged about the form finding coupled with modelmaking, consistency of this empirical approach to prototyping, and analytical tools of his own structural development and testing, Isler devising. His work is primarily located in described how the measured data would be Switzerland, but the quality of the projects plotted as a series of two-dimensional curved and his unique working methods have profiles, with any inaccurate measurements extended his influence much farther afield. clearly showing. During structural modeling What is striking when visiting Isler’s Swiss of the square-plan bubble shells, Isler was projects is how well maintained they are— surprised to find that the static load of the with the exception of the service-station roof structures was not evenly distributed to the at Deitingen, which is structurally intact but four edges of the shell, but that 90 percent of with which its international oil company the total load was distributed to the four tenant’s corporate identity does not chime. corners. This discovery has subsequently His factory buildings and sports and garden seen the bubble shells employed for literally centers are clearly coveted by their hundreds of mostly industrial projects for enlightened owners, who recognize their large factory, warehouse, and transport interesting fusion of structural and material purposes. The shells typically range from 50- efficiency with a highly expressive form. As to 300-foot spans, feature a circular opening self-illustrating structural concepts, these at their apex for daylighting and ventilation, delicately frozen membranes absolutely and are clad with a fiber-reinforced plastic confirm the structural integrity of specific dome, also developed by Isler. In profile, geometric forms, material properties, gravity, these structures feature an edge beam that and scale. doubles as a gutter and has a span-to-depth Isler’s concrete roof shells can be crudely ratio of 1:25; the circular openings are divided into three main types: bubble shells, reinforced by an upstand approximately 10 freeform shells, and inverted membrane inches deep, although the main structural shells. Bubble shells were one of his first real shell is only 3 to 4 inches thick. structural innovations in the development of The other key Isler shell type that utilizes large-span shells. Inspired by the geometry form-finding techniques is the inverted of a pillow, Isler developed a test rig where membrane shell, where a hanging he could inflate a rubber membrane to form membrane or flexible grid is hung from four a double-curved synclastic “pillow” shape in corners, loaded and subjected to gravity. The pure tension, which logic suggested would resultant tensile form is then made rigid and form a compression shell if inverted. Isler’s turned upside down to form a self-supporting testing included coating the inflated structure compressive structure. Isler used many 144 1 1 modeling techniques to create these forms, between supports and to direct rainwater to A cross-section of the inverted membrane shell of including fabric saturated in wet plaster or the corners. The external surface of the Wyss Deitingen Süd Service resin that was then allowed to dry before shell was, and is, painted, whereas most of Station inverting the surface to create a prototype Isler’s shells are not. This was primarily an structure. Isler also discovered other useful aesthetic decision, but also a recognition that structural devices in the form-finding this type of shell is not a purely compressive process—and that by hanging a fabric structure and that where areas of tension membrane from four points set in from the occur local cracking might appear, making corners, the free-hanging edge material the structure susceptible to rainwater. The forms a beam or arch structure when building is almost 50 years old, and although rigidized and inverted. A key example of the the glazing system has been refurbished the inverted membrane shell technique is the shell remains in excellent condition. iconic Deitingen Süd Service Station project, The importance of continual modeling and where two identical triangular (in plan) testing was key to the success of Isler’s three-point-supported shells, each 85 feet projects, as was a highly skilled construction wide, span 105 feet with a pure compressive team. The fabrication of a concrete shell steel-reinforced concrete shell of only 31⁄2 requires a large amount of timber formwork inches thickness. The relationship between and attendant carpentry—a fact of which Isler the support points of such structures is was well aware. In order to mitigate waste, important to note, and to avoid hugely costly he began to utilize woodwool panels as a slab foundations the support points are permanent formwork and interior finish, literally connected with prestressed tension which was both thermally and acoustically ties. beneficial. He also designed reusable glued The third key type of Heinz Isler shell laminated (glulam) timber formwork for structure comprises what he calls freeform products such as the bubble shells. shells. These are not derived from the form One of the key features of Isler’s work is finding of inflation or hanging-gravity that the process of design, engineering, and catenary models—or by mathematics, such construction of these shell structures is all as the “anticlastic,” or saddle-shaped, form of under his close control, and that only the a hyperbolic paraboloid—but through a process of modelmaking and prototyping graphic process of carefully interfaced radii (sometimes at full scale) would have allowed and compound curves. The garden center the construction of these unique projects. pavilion at Wyss is an early example of such a Surely the most elegant illustration of his structure, from 1962. With a span of 80 feet, a ideas, and certainly the most ephemeral, are shell only 23⁄4 inches thick is created, which the ice forms he constructed by hanging has four support points. The original curtain- fabric, which he then saturated with water wall glazing for these buildings was hung before the Swiss winter completed the from a series of slender prestressed process, forming delicate ice shells. mullions. The free edges of the shell are turned up, to form a kind of stiffened arch 145 4 4.3 4.3.6 Case studies 1950–1999 Concrete Shell Structures, Switzerland 2 3 4 Wyss Garden Center shell, Detail of Wyss shell, showing Corner support detail, almost 50 years after its the cantilevered “folded” shaped to funnel rainwater construction edges that protrude at the central span by 111⁄2 feet 2 3 4 146 5 6 5 Panoramic view of Deitingen Süd Service Station, showing both shells 6 Roadside shell at Deitingen Süd 147 4 4.3 4.3.6 Case studies 1950–1999 Concrete Shell Structures, Switzerland 7 8 7 Solothurn Tennis Center, showing one bay of the repeated “hanging membrane” type shell 8 Corner detail of Brühl Sports Center, Solothurn 148 9 9 Connection detail between two shells at Brühl Sports Center, Solothurn 10 Interior of Brühl Sports Center, Solothurn, with central openable rooflight 10 149 4 4.3 Case studies 1950–1999 4.3.7 Jefferson National Expansion Monument (“Gateway Arch”) Structural description Location Plan dimensions Architect Engineer Weighted stressed-skin St. Louis, Missouri, USA 630ft between legs at Eero Saarinen (1910–1961) Hannskarl Bandel catenary arch ground level (Eero Saarinen and (Severud-Perrone-Sturm- Completion date Associates) Bandel) 1965 Height 630ft Fabrication and construction Pittsburgh-Des Moines Steel Company Although the first Jefferson structural type. The structure consists of a Memorial design of 1948 was of double skin of steel held together with partly subjective inspiration, it was internal ribs, which forms a type of stressed also a stroke of rational structural skin or semi-monocoque structure and functionalism: a catenary arch which, dispenses with any separate structural geometrically, was as predictable frame—so this is not a steel-clad structural as a circle.1 framework; here, the cladding is also the Allan Temko structure. The outer skin was fabricated in 1 ⁄4-inch cutlery-grade type 304 stainless-steel Upon his victory in the international design sheet and the inner skin is 3⁄8-inch carbon-steel competition in 1947, the winning notification sheet. The two arch legs were constructed letter was famously sent not to Eero Saarinen simultaneously from 142 prefabricated but his father, the other “E” Saarinen: highly sections. On-site cranes of up to 72 feet in acclaimed architect, Eliel. Once this mix-up height lifted these segments, after which was resolved, Eero set about assembling a operation specially designed climbing cranes, team to design and engineer this monument mounted to the back of the arch legs, would to the westward expansion of the United lift each segment into place. Each section was States. The structural engineering consultancy welded together, with no little skill involved in of Severud-Perrone-Sturm-Bandel was such long, fully welded seams, which cause chosen, and a principal of this office, Dr. local distortion owing to heat. As the Hannskarl Bandel, began to work together construction proceeded, the cantilever of each with Saarinen to develop the project. Bandel leg steadily increased, and at 530 feet high a is credited with helping Saarinen achieve the 255-foot stabilizing truss was raised using the desired geometry of the arch. In a brilliant climbing cranes and fixed until the arch was account of the engineering and construction complete. The final two “keystone” segments process, a former colleague of Bandel’s, Nils were designed to be fixed into place very D. Olssen,2 explains how Saarinen’s desire to early in the morning when the temperature of utilize a hanging-chain “catenary” curve was the structure was stable. However, when transformed when Bandel modeled a news of this momentous occasion got out, catenary curve from differently sized and the mayor requested a daylight operation so weighted links, which altered the profile to that it could be recorded for posterity. When Saarinen’s desired shape. This early modeling sun hit the structure, differential movement in seems to have proved extremely useful in the legs prevented the final connection—a developing an equilateral triangular, prismatic dilemma that was only solved by the cross-section of tapering size, with a flat edge attendance of the local fire service, who to the back of each leg. At ground level, the cooled the back of the arches with sprayed legs stand 630 feet apart, which matches the water that caused each leg to slowly rise to arch’s visible (above-ground) height. The the correct position. arch’s external cross-section varies from 54 Interestingly, the void between the inner feet at the base to 17 feet at the apex. As a and outer steel skins of the arch was filled structural work, the monument is not only with concrete up to a height of 300 feet and challenging in its geometry but also in its reinforced with steel tendons; above this material construction, assembly, and level, steel stiffeners were employed. This 150 1 concrete mass is used to prevent sway and ensure that the thrust line is straight down into the 60-foot-deep foundations, rather than forcing the legs outward. The concrete also helps to resist buckling, a technique that was utilized in the very slender, rakishly angled columns of Will Alsop’s Peckham Library 21 (London, 2000), which were pumped with St. Louis Arch photographed concrete after they were positioned. In at night pictures, the Jefferson Memorial is an 2 impressive piece of processed steel. However, View of the stainless-steel what may not be immediately obvious is that arch from ground level, which shows the tapering this is a visitor “experience” and, in the best triangular cross-section. tradition of such edifices—including Eiffel’s Note the panel lines, eponymous tower, the Statue of Liberty indicating the sheet-steel construction (Eiffel-engineered), and London’s Great Fire “Monument”—this is a building for 3 An illustration from ascending. In what Bandel told Olssen was CADenary tool v2, a virtual the real engineering triumph of this project, catenary modeling program not-quite-vertical transportational devices that has been developed by Dr. Axel Kilian take you up to a prismatic interior of seemingly doll’s-house proportions, from the windows of which you can view eastward to the mighty Mississippi River and westward to St. Louis and beyond. From ground level, you would be hard-pressed to even see these 3 lookout windows. A unique tram system, devised by lift specialist Dick Bowser and comprising five-person pressed-steel capsules on a “paternoster” type loop, takes you from the underground museum (buried in the slab) to the summit. The arch legs also contain a service lift and emergency-escape stairs. 1 Temko, A., Eero Saarinen, New York: George Braziller Inc., 1962, p. 42 2 Olssen, N. D., “Jefferson National Expansion Memorial (The Saint Louis Arch)” in Spans (The Quarterly Newsletter of Inspired Bridge Technologies), third edition, July 2003, pp. 1–3 151 4 4.3 Case studies 1950–1999 4.3.8 Maxi/Mini/Midi Systems Structural description Location Plan dimensions Architect and system Steel column-and-truss Switzerland Various designer structures Fritz Haller (b. 1924) Completion date Various (1962–2000) The Swiss autodidact architect Fritz Haller opaque, glazed, fixed, and openable— has produced three notable steel completes the building envelope. The column construction systems, but curiously is still configuration is of particular structural better known for the system furniture he interest, as lateral stability is cleverly designed for USM. These structural systems, absorbed in moment connections and some dating back to the early 1960s, have carefully disaggregated columns, which can proved highly effective as flexible and incorporate vertical servicing where required, adaptable “open” systems, and are also while visually the effect is curiously more quietly structurally innovative. transparent than might be expected. The Haller’s three distinct steel building column size in the Maxi system is consistent systems are: the Maxi system, for single- from edge to internal supports (despite story large-span structures; the Midi, for different loading conditions) in order to multistory, medium-span, and densely maintain maximum flexibility for future serviced structures; and his Mini system for expansion or reconfiguration of these one- or two-story small-span structures. The primarily industrial buildings. USM factory in Münsingen utilizes the Maxi Haller’s second system was the Mini system, but the whole facility has been an system (1968), which has been utilized for ongoing project between USM and Haller, private residences, small school classes, and which has seen seven phases of construction pavilions. Designed for one- and two-story and expansion between 1962 and 2000. The structures with spans of 20–24 feet, this Maxi system (1963) is the most universal and system uses a mixture of components deliberately open-ended: based upon a including steel Square Hollow Sections (SHS) 47-foot grid, columns are fabricated from and custom-folded plate-steel elements. four outward-facing rolled-steel-angle Parallels could be made with the work of sections connected at a distance by steel Jean Prouvé, whom Haller knew, particularly flats. Large open trusses, also fabricated in the use of break-press formed from standard steel-angle sections, sit within components, which were relatively the open cruciform column heads to lightweight in relation to the hot-rolled complete the structure. The system is sections of the Maxi system and were designed to be reconfigurable and easily specifically designed for ease of assembly, demountable, and a concise palette of structural performance and utility. The roofing finishes and cladding systems— folded-steel column/mullions (designed to 152 1 1 resist shear stresses) work in both the linear services distribution and maintenance, Extract from a patent drawing of a variation of the condition of a supporting wall and the corner supports and locations for multiple and easily Midi system, 1977 condition, cleverly turning a corner by virtue adapted internal partitioning, and simple of their unique profile. Beams are formed connections for external envelope and from thin folded plate steel and castellated cladding systems. With legislative and for reduced weight and service runs; the regulatory changes in thermal-performance beams also incorporate additional triangular- requirements, both the Maxi and the Mini shaped “tabs” folded from the flange, to system have thermal-bridge issues that support or fix a soffit or ceiling surface to. would require design changes. However, the The Midi system (1976) is arguably the most Midi system is still being used for new sophisticated of Haller’s architectural projects in spite of Haller’s retiring from “products,” and combines the use of folded- practice, with new schemes coordinated by plate and pressed-metal components and the 2bm architekten. utility of regular hot-rolled steel sections. Interestingly, you will not enjoy any Designed with a planning module of 8 feet, fetishized, large-scale cross-bracing in a this is the most open system and can be used Haller project, as lateral stability is cleverly for structures of several stories. Grid absorbed in moment connections and the configurations of 311⁄2 x 311⁄2 feet, 47 x 311⁄2 carefully disaggregated columns and beams. feet, and 24 x 24 feet, or a mix of these, are The lack of visible cross-bracing allows the possible, with columns relocatable anywhere structural system to remain sufficiently on that grid. A doubling up of the top and “open” as to allow major modification, bottom chords and vertical bracing forms a extension, or replacement without difficulty unique truss design. The truss is then owing to lack of structural interdependencies. stiffened with a specially fabricated folded- and-pressed steel component, which connects all four steel-angle truss chords, thus creating a strong lateral connection that also acts to resist torsional forces. The Midi system has been used for schools, offices, and other commercial buildings and represents a higher order of geometric and dimensional coordination, providing for 153 4 4.3 4.3.8 Case studies 1950–1999 Maxi/Mini/Midi Systems 2 3 4 2 USM factory: interior of factory showing administrative offices, Münsingen, Switzerland 3 Detail of Maxi system column at building edge, USM factory, Münsingen, Switzerland 4 SBB circular accommodation buildings, utilizing a radial version of the Midi system, Löwenburg, Murten, Switzerland, 1982 5 Temporary school classroom using the Mini system, Solothurn, Switzerland 6 Private residence using the Mini system, 1967, Solothurn, Switzerland 154 5 6 155 4 4.3 Case studies 1950–1999 4.3.9 Tensegrity Structures Structural description Location Height Artist Tubular aluminum and steel Kröller-Müller Museum, 100ft Kenneth Snelson (b. 1927) cable tensegrity tower Otterlo, Netherlands structure Plan dimensions Completion date 20ft x 20ft 1969 The ancient invention of weaving discontinuity of tensile and compressive reveals in a direct way the basic and forces creates tremendous structural integrity universal properties of natural with an even more remarkable material structure such as modularity, left and efficiency, most certainly doing more with right helical symmetry, and less and presenting a very useful model of elementary structural geometry … what Snelson calls “forces made visible.”3 Weaving and tensegrity share the Within the worlds of architecture and same grounding principle of construction, examples of tensegrity alternating helical directions; of left to structures are thus far relatively limited in right; of bypasses clockwise and number; although the deployment of counterclockwise.1 tensegrity for the Kurilpa Bridge in Brisbane, Kenneth Snelson Australia is impressive, that example may not be the most elegant exemplar of the Over the summers of 1948 and 1949, Kenneth structural efficiencies integral to tensegrity. Snelson was a student at the unique Kenneth Snelson has worked as a fine artist educational experiment that was Black since the 1950s and is, through his sculptural Mountain College, North Carolina, USA, commissions and maquettes, the preeminent where staff included composer John Cage, communicator of the potential of the dancer and choreographer Merce tensegrity structure in all of its forms and Cunningham, painter Willem de Kooning, and configurations and at a number of different (most importantly for Snelson) polymath scales. Notable works include Easy Landing Richard Buckminster Fuller, for whom (Baltimore, MD, 1977), which is a horizontal Snelson began to make models for use in sculpture supported at three points and Fuller’s lectures. During his time as a student, cantilevered at each end; his Needle Tower Snelson developed and formalized the sculptures I and II (Washington and Otterlo, structural innovation of the tensegrity 1968 and 1971), which are tapering columns structure, or as Snelson prefers “continuous made up of 24 progressively smaller (three tension, discontinuous compression compressive element) modules; and his structures,”2 whereby the compression Rainbow Arch sculpture (private collection, elements of a given structure do not touch 2001), which creates a semicircular arch using each other, insomuch as they are held in similar three-component modules. In his space by separate tension elements (strings, Needle Tower II, Snelson uses a repeated wires, or cables). There was subsequently geometric configuration of 24 four-strut much disagreement about the intellectual tensegrities, but with each module ownership of this engineering discovery, but decreasingly scaled. The effect is to make the both Fuller and Snelson registered patents in tower look even taller than its considerable relation to tensegrity structures, with Fuller height of 100 feet. The modules at the top of coining the word “tensegrity,” formed from the tower more closely resemble Snelson’s tension and integrity, as one of his composite smaller-scale structural sculptures, whereas designed nouns. “Tensegrity” was included in the base module uses building-construction The Oxford English Dictionary in 1985. sized elements, none of which appear to have The structural interest in tensegrities is suffered any kind of weathering or fatigue more than a vernacular curiosity, as the since their installation over 40 years ago. 156 1 2 3 1 Needle Tower II, Kröller- Müller Museum, 1969 2 Needle Tower II during annual cleaning, 2011 3 Two configurations of a simple three-strut tensegrity structure, where the compressive struts (and thus the forces) are both connected and held apart with tensile wires If Snelson has extended structural cells, and asserts: “An astoundingly wide possibilities through sculpture, then Fuller’s variety of natural systems, including carbon thought experiment about the potential for atoms, water molecules, proteins, viruses, such structures is equally inspiring. Musing cells, tissues, and even humans and other on the structural qualities of the rim-and- living creatures are constructed using a spoke bicycle wheel, it seemed to Fuller that common form of architecture known as this was perhaps the most ubiquitous tensegrity.”6 Ingber summarizes the instance of “tensional integrity where tension operational characteristics of tensegrities was primary and comprehensive and thus: “Tensegrity structures are mechanically compression secondary and local.”4 Fuller stable not because of the strength of saw the possibility of applying the tensegrity individual members, but because of the way principle at various scales, and posits the idea the entire structure distributes and balances of replacing the wheel’s compressive struts, mechanical stresses.”7 And so, although this or members, with miniature tensegrity structural principle is a rarely deployed structures, and the struts within the miniature commodity in the construction industry, its tensegrity masts replaced by even smaller inherent strength and potential lightness offer tensegrity masts, and so on until you reach huge possibilities in the fields of structural molecular-sized manipulations. “At this stage engineering, architecture, and beyond. of local miniaturization the inherent discontinuous-compression, tensional 1 http://www.kennethsnelson.net/icons/struc.htm integrity of the non-solid atomic structures (accessed 20.9.12) 2 Heartney, E., Kenneth Snelson: Forces Made Visible, themselves would coincide with the overall Lennox, MA: Hard Press Editions, 2009, p. 22 structuring principle of the whole series of 3 Op. cit., p. 9 masts-within-masts complex, thus 4,5 Krausse J., and Lichtenstein C., Your Private Sky: eliminating any further requirements of the R. Buckminster Fuller, Zürich, Lars Müller Publishers, now utterly obsolete conception of ‘solid’ 2001, p. 232 6,7 Ingber, D. E., “The Architecture of Life” in anything.”5 The cell biologist and founding Scientific American, January 1998, pp. 48–57 director of the Wyss Institute, Don E. Ingber, has made the connection between the tensegrity structures of Snelson and living 157 4 4.3 Case studies 1950–1999 4.3.10 Munich Olympic Stadium Roof Structural description Location Roof area Architect Engineers Mast-supported cable net Munich, Germany 371,000ft2 Günter Behnisch (1922–2010) Fritz Leonhardt, Jörg with Frei Otto (b. 1925) Schlaich, and Heinz Isler Completion date Height of tallest mast 1972 260ft Frei Otto not only considers the value is not dependent on the temporary nature of his membrane durability of a structure, nor on the structures desirable, but admits that amount of preciousness of its his objections to making architecture material. On the other hand, stem from his reluctance to fill the temporariness does not mean Earth’s surface with lasting buildings. improvisation, as is evident from the He hesitates to pursue a project unless amount of research invested in each he is certain that its realization will be lightweight structure.1 temporary enough not to be in man’s Ludwig Gläser way. This endorsement of obsolescence contradicts the traditional view of architecture as a fulfilment of man’s need for monuments. Yet, as vernacular buildings of all periods prove, artistic Given the above, it seems contradictory that spectators at the rear of the west stand, and this most celebrated work of Frei Otto no they support, or “pick up,” the skin of the roof longer belongs to the category of temporary at two points with suspended cables. The or ephemeral structures, having been front edge of the roof is held taut by a designated as national protected monument continuous edge cable, pulled across the in 2000. It may also be worth noting that Otto structure and anchored to the north and was not even involved in Günter Behnisch’s south of the stadium. The technical winning competition entry of 1967, although challenges of an innovative project like this its design and technology were clearly were numerous—not least coping with the influenced by Rolf Gutbrod and Otto’s massive tensile forces required to act on the recently completed German Pavilion at the cable net, keeping it in place. The two biggest Montreal Expo in April 1967. When the tensile loads at the front edge, with pulls of technical feasibility of the competition winner up to 11,200 kip, were resisted by inclined- was subsequently called into question, Frei slot and gravity-anchor foundations, which Otto was contacted by Behnisch, and, formed massive buried concrete diaphragm working with his Institute of Lightweight walls using opposing geometry and mass to Structures (IL) in Stuttgart, Otto developed resist the tensile forces. Elsewhere in the the final form for the stadium roof. stadium, ground anchors were used to resist This colossal roof structure consists of nine tensile forces, a technology untried in interconnected “anticlastic” (or saddle- Germany at that time. The cable-net surfaces shaped), curved cable nets, which are themselves were formed by a rectangular supported by welded tubular-steel masts up grid of paired cables, of either 7⁄16 inch or to 260 feet long and with a 11,200 kip load 5 ⁄8 inch diameter. The grid dimension was capacity. The masts, which puncture the roof 30 inches; however, Otto was not happy with membrane, are positioned behind the this, arguing that a 20-inch grid would be 158 1 1 considerably safer during construction. The model these hitherto unimaginable Diagram of two bays of the Munich Olympic stadium cables are fixed together at intersections with structures. In particular, Otto developed soap- roof showing how the aluminum clamps, which allow them to bubble modeling, wherein the fine meniscus anticlastic roof surface is of a soap film finds its form within a rotate in relation to each other when pulled created with a mast- supported cable net pulled into the final configuration. The edge cables geometrically delineated frame. This type of down to ground at the back and main support lines are all in 31⁄8-inch- prototyping was born out of Otto’s close with the free edge supported by a longitudinal tensile diameter steel cable, with the front edge observation of nature and natural processes cable consisting of a bundle of these elements in a way that pre-dates the development of clamped together in cast-steel “arms.” The biomimetic engineering, whereby engineers cable net was eventually clad in 310 foot x 10 define solutions through the study of natural foot x 3⁄16-inch-thick clear acrylic panels fixed processes (human, animal, and organic). by flexible neoprene connectors at the Otto’s experimental work, carried out with cable-intersection nodes, with the joints students of the IL in Stuttgart, are particularly between the panels sealed by a neoprene well documented in the IL Documents, a strip clamped to the panel edges. The series of books published between 1969 and weathering strips are, curiously, one of the 1995, which investigate specific material, most visible delineations of the structural structural, and geometric properties. This form, although they are nonstructural. The substantial body of research is unique in that original design had investigated cladding the the ambitions of the work are neither cable net in a PVC membrane, timber exclusively engineering nor design, but a sheathing, or even thin precast concrete synthesis of the two. panels. Otto has subsequently constructed The Munich Olympic Stadium remains a cable-net structures that are entirely clad in remarkable achievement, which must have glass. seemed startling 40 years ago. Frei Otto Frei Otto had first developed cable-net remains one of the very few figures whose structures in the early 1960s, when his work interest in structural innovation and with fabric structures began to become experimentation outweighs his ambitions as dimensionally limited by the tensile strength a builder. In a lecture at the Architectural of a given substrate. By disaggregating the Association in the late 1990s, Otto explained tensile forces into a low-resolution weave of to a questioner that, owing to the nature of fewer but stronger fibers (typically steel his constructions—which might be a tent or cabling), Otto could achieve considerably an inflatable—he was never entirely sure of larger structures, which were first seriously the location or number of Frei Otto buildings prototyped at the Montreal Expo in 1967. The in existence on the planet at any given cable net forms a structural grid, which is moment. then clad—in the case of Montreal, largely in fabric. Cable nets are certainly not the only 1 Gläser, L., The Work of Frei Otto, New York: MoMA, structural innovation of Frei Otto, who 1972, p. 10 pioneered the use of tensile fabric structures and developed a formidable array of pneumatic and branching structures. What is particularly impressive about his work are the form-finding techniques he developed to 159 4 4.3 4.3.10 Case studies 1950–1999 Munich Olympic Stadium Roof 2 32 Munich Olympic Stadium: view of main stand 3 Detail of tubular-steel compression mast at the rear of the stadium 4 Roof covering to the rear of the main stadium 5 Detail of cable-net and polycarbonate panel connection 6 The cable-supported roof incorporates floodlight rigs. Tours of the stadium include a walk on the roof edge 7 The tensile roof-edge element comprises a cluster of ten separate woven-steel cables 4 160 5 6 7 161 4 4.3 Case studies 1950–1999 4.3.11 Bini Domes—inflatable formwork Structural description Location Height System designer Architects Reinforced-concrete dome, Killarney Heights, New 18ft Dr. Dante Bini (b. 1932) NSW Department of Public utilizing inflatable South Wales, Australia Works with Dr. Dante Bini formwork Plan dimensions Completion date 60ft diameter Engineers 1973 Taylor, Thompson, and Whitting Consulting Engineers with Dr. Dante Bini For over 45 years, Italian-born architect Dr. could evolve and how a lightweight and Dante N. Bini has dedicated his professional low-cost resource such as air could be life to the development of what he calls utilized in the construction industry. Concrete “automated construction technologies.” In shell structures like Isler’s and Félix Candela’s 1965, in Bologna, Italy, he successfully are structurally efficient and enclose huge constructed a 40-foot-diameter, 20-foot-high volumes with a small amount of material, but hemispherical concrete shell structure in the fabrication of formwork required a large three hours, using the unique pneumatic on-site semi-skilled workforce. Bini’s formwork of a giant balloon. This first inflatable formwork, or “Pneumoform,” prototype did, however, have some teething eradicates the need for such a large site team problems, particularly the uneven and allows for more high-speed construction. distribution of the wet concrete caused by an The sequence of fabrication first involves unpredictable (asymmetric) inflation. the construction of a ring beam and ground- Improvements were made, and in 1967 at floor slab. The ring beam cleverly contains a Columbia University, New York, Bini “cast in” egg-shaped void, which will contain demonstrated in two hours the construction a separate inflatable tube to hold the main of another large-scale “Binishell.” For this membrane in place during inflation as well as first US prototype, Bini utilized a complex air inlets and outlets. The internal web of helical “springs” with steel “pneumoform” of nylon-reinforced neoprene reinforcement bars threaded through their is then laid over the slab and secured at the middle, which allowed for a geometrically edge; on top of it, a complex network of criss- controlled inflation and thus a uniform crossing helical springs is stretched across concrete distribution across the shell the diameter of the circular ground slab. The structure. For this demonstration and springs have no specific structural function subsequent Binishell structures, an additional but control the even distribution of steel external membrane was also used, which reinforcement bars, which are threaded allowed for the subsequent vibration and through the springs, and also maintain an compaction of the concrete, post-inflation. even concrete thickness by holding the mix in Over 1,500 Binishells were constructed place. Once the reinforcement is in place, the throughout the world between 1970 and concrete is poured. A regular concrete mix is 1990, with diameters of between 40 and 120 used with small amounts of retarders and feet and with a varying elliptical section. plasticizers added to extend the workability Less interested in the experimental form of the mix for two to three hours. After the finding of Swiss engineer Heinz Isler’s pour, an outer membrane of PVC is laid over elegant European shells, Bini was concerned the wet concrete, which will help to control with how the construction process itself evaporation during the setting process and 162 1 1–4 Construction of Killarney Heights Public School Binishell, New South Wales, Australia, 1973 5 Completed building 2 allow for vibration of the concrete. The inflation procedure then begins, using low-pressure blowers, and takes about one hour; pressure is regulated by controlling the outlet to maintain an even “lift.” When the shell is fully inflated, the concrete is vibrated using rolling carts hung from cables at the top of the structure. The internal air pressure is maintained for between one and three 3 days depending on the diameter. For a 120-foot-diameter dome, the thickness of the completed shell is 5 inches at the base and 3 inches at the crown. Critical to the success of this innovative construction technique and structural type was the system design and fast construction program. Bini designed the 60-foot-diameter dome for Killarney Heights Public School, New South Wales, to be erected (with foundations already in place) in 12 days. On the tenth day the concrete-covered 4 membrane was inflated and subsequently vibrated free of air pockets with the innovative guided vehicles (described above). By day 12, the reinforced concrete shell was sufficiently stable to begin to cut openings for entrances, windows, and ventilation. 5 163 4 4.3 Case studies 1950–1999 4.3.12 Niterói Contemporary Art Museum Structural description Location Plan dimensions Architect Engineer Cylindrical cantilever Niterói, Rio de Janeiro, Brazil 165ft diameter at roof level Oscar Niemeyer (1907–2012) Bruno Contarini Completion date Height 1996 521⁄2ft 1 Oscar Niemeyer was in his eighties when he Each sheet of the seventy 3⁄4-inch-thick designed the Niterói Contemporary Art triplex glass plates is 16 feet high and 6 feet Museum along with his long-time wide. Framed by steel bars and with an collaborating engineer, Bruno Contarini. inclination of 40 degrees to the horizontal The building consists of three floors built plane, they can sustain a load equivalent to into a cupola that cantilevers from a 20 people. cylindrical base. The base springs from a The structure was designed to withstand a reflecting pool, and the cupola is accessed by weight equivalent of 80 pounds per foot, and a snaking ramp. The building is constructed winds of up to 125 miles per hour. It from reinforced concrete and employs three consumed 113 million cubic feet of concrete. circular floorplates ranging from 115 to 130 feet in diameter and supported by a central cylinder 30 feet in diameter. The floorplates employ prestressed girders resting on 16-inch-diameter columns. 164 2 3 4 1 3 Niterói Contemporary Art Detail of the central cylinder Museum base and reflecting pool 2 4 Cross-section through the Interior view looking out to museum Guanabara Bay 165 4 4.3 Case studies 1950–1999 4.3.13 Structural Glass Structural description Locations Engineer Loadbearing glass Various Tim Macfarlane (b. 1954) structures Completion dates 1990–1997 Glass is no longer an ornamental item … but has emerged into a structural element.1 Fazlur Khan In the early 1990s, there was a quiet wonderful diversity of reinforced-concrete revolution in the way that glass was use as architects and engineers began to test employed in architecture as a structural the limits of this new material at the material. This increased experimentation in beginning of the twentieth century. From the application of glass was not limited to the Maillart, to Luigi Nervi, to Félix Candela (to thin sheath of the building skin—framed in name but three), these “structural artists” timber, steel, or aluminum—but increasingly were not reading rule books but writing extended to frameless glazing and, them, each in his own highly individualized ultimately, to structural glazing with no way and for differing programmatic support at all other than crafted laminations instances. After this flowering of diverse and of glass itself and the magic of structural intriguing engineering approaches, silicone. At the forefront of these new Macfarlane suggests that a kind of Fordism approaches to the art, architecture, and took over and industrial efficiency tended to specifically the engineering of these normalize and limit possibilities. With experimental and innovative projects was the industry less likely to be “light on its feet” structural engineer Tim Macfarlane of and more likely to play an increasingly Dewhurst Macfarlane Consulting Engineers. protectionist game, the possibilities were Through a series of small but iconic limited through a codification of structural projects in close collaboration with architects properties linked to relative economic such as Rick Mather, Eva Jiricna, and success and known methods of construction. Ohlhausen DuBois Architects, Macfarlane The reliance on a mathematical model to helped to change the way in which glass was create a design is only one approach, and classified as a construction material and Macfarlane states: “Maths has never led me redefined the engineering potential of this to a solution, but has helped to determine wondrous substrate. He likens this process to how to represent the solution.”2 Macfarlane “making rules up as you go along” insomuch also adds that the full extent or knowledge of as the structural properties and material- a material and its properties are virtually performance expectations were not unfathomable, and therefore structural comprehensively codified as part of the possibilities and strategies should not be structural investigations. Macfarlane also limited by our own experience. draws parallels with the proliferation and Macfarlane categorizes a brief history of his 166 1 1 own work, and the technological The Klein Residence, Santa Fe, New Mexico, by development of structural glass, with a series Ohlhausen DuBois of projects, prototypes, and material tests Architects, uses glass as a that are detailed overleaf. These range from primary loadbearing element (for description see overleaf) simple, lateral innovations in fabrication or assembly to completely new methods of construction using glass. Macfarlane cites the advent of the consulting engineer, formalized between 1907 and 1915, as an important evolutionary stage in the proliferation of structural possibilities. These possibilities are, by definition, only limited by our knowledge of material properties, fabrication, and assembly techniques, as well as other instruments of structural advantage such as geometry. However, Macfarlane thinks that it is only through the full exploration of these fields that architects and engineers can challenge the intellectual-property-protected “products” of patented systems of construction and better answer the detailed programmatic requirements of any given job with hitherto unimagined structural and engineering solutions. 1 Khan, Y. S., Engineering Architecture: The Visions of Fazlur R. Khan, New York: Norton, 2004, p. 79 2 Interview with Tim Macfarlane by Will McLean, 3 May 2012 167 4 4.3 4.3.13 Case studies 1950–1999 Structural Glass Joseph store Structural description Location Architect Engineers Tensile steel rods and London, England Eva Jiricna (b. 1939) Dewhurst Macfarlane structural glass frame Completion date 1990 2 A seemingly small but important innovation 2 Joseph store staircase with allowed this intricate and elegant staircase to have layered glass stair treads and its trademark transparent stair treads. In each case, stainless-steel rods Macfarlane layered together, but did not laminate, a 3⁄4-inch sheet of sandblasted annealed glass and a 5 ⁄8-inch-thick piece of acrylic. The glass provided stiffness and a hardwearing top, the acrylic a safety factor. Klein Residence Structural description Location Architects Engineers Glass as primary Santa Fe, New Mexico Ohlhausen DuBois Architects Dewhurst Macfarlane loadbearing element Completion date 2007 The Klein Residence represents an audacious sheets are slightly shorter so that all load travels approach to structural glass. Its use for the house’s through the central sheet. The structural glass wall was glass lookout pavilion is both “double-take” inducing engineered with a safety factor of three and designed and a thoroughly worked engineering solution. The to have a maximum deflection of L/100, which is 13⁄8 aim was to create a living room with uninterrupted inches over the 111⁄2-foot height. To avoid any visible views toward the mountains without any visible framing at the head and sill of the glass, a special steel structural impediment. The result is a space where the channel was fabricated and recessed into the floor and two glazed sides of the living room meet in the soffit. The success of the engineering concept depends northwest corner with the steel structure of the roof on an even distribution of the static load throughout supported by the glass alone. The architect Mark the seven panels; this became one of the main DuBois has stated that “the architectural space formed challenges for the design and engineering team. The by the loadbearing glass wall is visually remarkable solution was to make the steel channel adjustable, and psychologically very intriguing.”1 After initially using threaded rods at the top and bottom of the glass exploring the option of an all-glass corner column panels. Stacks of spring washers were used at the roof (L-shaped or cruciform in plan), the design team connection to further ensure equitable support along proceeded with the concept of an all-glass multipanel the length of the wall and redistribute that load in the bearing wall. The wall, 111⁄2 feet high by 28 feet long, case of a panel failure. If previous developments of comprises seven equally sized panels and makes up structural glass have produced remarkable “all glass” the west wall of the room. The adjacent north wall structures, then the Klein Residence shows how glass (also fully glazed) is visually identical, but non- can be utilized as a structural support system for other loadbearing. Each structural glass panel is fabricated (non-glass) elements. from three sheets of fully tempered (toughened) glass laminated with PVB film. The central sheet is 3⁄4 inch 1 http://www.boishaus.com/glass_performance_days_2007.pdf (accessed 20.9.12) thick, with 1⁄4-inch sheets each side. The two outside 168 All-glass Extension Structural description Location Architect Structural engineers Laminated all-glass beam London, England Rick Mather Dewhurst Macfarlane and column structure Completion date 1992 3 This extension to a private residence, although 3 All-glass extension showing relatively modest in scale, has had an enormous laminated glass beams and impact on the perception and expectations of glass columns technology in architecture. This is a lean-to structure, in which the columns and beams comprise laminations of three 1⁄2-inch-thick sheets of annealed glass bonded together with clear resin. The beams are cut to a curved profile, and are 11 inches deep at their midpoints, and 8 inches deep at the column connection, which is a mortise-and-tenon joint (see Broadfield House, below). The columns, which are 8 inches deep, are similar laminations to the beams, and this layering provides an inbuilt safety factor. The structure is clad in double-glazed units that uniquely feature glass-edge spacers for increased transparency, and the roof panels are coated with a conductive layer that can be used as a heating element. Broadfield House Glass Museum Structural description Location Architect Engineers Laminated all-glass beam Dudley, England Design Antenna Dewhurst Macfarlane and column structure with all-glass box beam Completion date 1994 4 This all-glass structure was built as an extension to 4 All-glass extension showing Broadfield House Glass Museum in Dudley. The glass mortise-and-tenon joint technology is similar to that used in Macfarlane’s between column and beam earlier All-glass Extension with Rick Mather, but this project is significantly larger, with the structure measuring 36 feet long x 19 feet wide x 111⁄2 feet high. The glass columns and beams are 11⁄4 inches thick, and made from three layers of 3⁄8-inch annealed glass bonded with a resin laminate. The beams and columns are connected at the top edge by a mortise- and-tenon joint, with the center layer of three laminations protruding from the column and the central layer of the beam cut back accordingly. The columns are at 42-inch centers and are 8 inches deep, with the beams 12 inches deep. The double-glazed cladding panels of the front face and roof are bonded to columns and beams with structural silicone. Another intriguing feature of this project is the 7-foot-wide opening created for glass doors, which is achieved using an all-glass box beam or lintel—surely another structural first. 169 4 4.3 4.3.13 Case studies 1950–1999 Structural Glass Station Entrance Canopy Structural description Location Designers and engineers Cantilevered glass beams in Yurakucho, Tokyo, Japan Dewhurst Macfarlane four offset sections Completion date 1997 5 On the plaza of Rafael Viñoly’s Tokyo International 5 Yurakucho Station canopy Forum, Tim Macfarlane was invited to submit a design model for a canopy to Yurakucho underground station. What 6 he designed, engineered, and ultimately built was an Detail of Yurakucho Station unprecedented 35-foot-long x 16-foot-wide canopy showing overlapping cantilevered canopy, fabricated entirely from glass. glass beam connections The glass roof is supported by three glass composite beams, which each consist of four groupings of glass blades that taper from the cantilever connection to the unsupported edge. The glass-beam components consist of two 3⁄4-inch-thick glass sheets, laminated together, which are bolted at the midpoint and at the end of the next offset group of glass “blades.” The number of laminated, layered glass components is four at the steel cantilever connection and reduces to 6 a single glass component (of two laminated layers) at the canopy top edge. The mechanical connections between the components are made with 2-inch-diameter high- strength stainless-steel pins, with specially designed bezels fitted to the holes for a more even load distribution. What made this project technically feasible was a combination of the physical testing carried out with glass fabricators Firman Glass and City University, and Finite Element Analysis. Although the results of this glass testing had been successful, the clients decided to also use acrylic as beam components as an additional safety factor; these elements are only visible through their different edge color, which is much lighter than that of glass. The outer canopy skin is made from a lamination of two 3 ⁄4-inch glass sheets, with joints bonded and sealed with structural silicone. 170 Apple Stores Structural description Locations Architects Laminated glass panels and Various Bohlin Cywinski Jackson all-glass reciprocal beam system Completion date Designers and engineers 2006 Dewhurst Macfarlane 7 Dewhurst Macfarlane’s work for Apple includes a 7 Apple Store all-glass stair, number of technical innovations. The trademark Chicago, 2010 all-glass stair treads are three-ply glass laminates 8 bonded together with SentryGlas®, an extremely All-glass stair detail showing strong ionoplast interlayer. Cleverly, a stainless steel bolted stair treads, Apple bracket is laminated into the central section, which Store, Chicago, 2010 can then be bolt-connected to the all-glass balustrade. 9 For the Fifth Avenue Apple Cube, the process of Glass cube, Apple Store, laminating, or embedding, stainless steel fixings Fifth Avenue, New York, 2006 within the layered glass components was repeated, but to reduce the number and complexity of junctions 10–11 Details showing the in the roof a reciprocal framed structure was used. reciprocating stainless steel The reciprocal frame concept can be described as connections, Apple Store, building big spans with short lengths. This method of Fifth Avenue, New York making short lengths go a long way (or span farther than their length) was an expedient solution arrived at by medieval builders. The ease of construction, or certainly the omission of complex four-way connections, was a factor in the use of a reciprocal beam arrangement for the Fifth Avenue glass cube. A reciprocal arrangement of laminated glass beams in the 32 foot x 32 foot roof utilizes stainless steel joist hangars at the midpoint of the cross beams, creating a planar reciprocal arrangement that is both structurally and constructionally efficient. 8 9 10 11 171 4 Case studies 4.4 2000–2010 4.4.1 Ontario College of Art and Design expansion, featuring the Sharp Centre for Design Structural description Location Plan dimensions Height of tapered Architects Steel-truss box Toronto, Ontario, Canada Steel-truss “box” 280ft long columns William Alsop (b. 1947) with x 100ft wide x 33ft high 85ft Young + Wright Architects Completion date 2004 Floor area Engineers 90,400ft2 Carruthers & Wallace Ltd 1 1 Ontario College of Art and Design (OCAD), Sharp Centre for Visual Art: view looking south toward the CN Tower 2 View looking north When British architect William Alsop was and the roof. The engineers worked closely invited to design an extension for the Ontario with the architects in positioning and College of Art and Design (OCAD), he orientating the 98-foot-long legs in a spurned the adjacent site set aside for the seemingly random arrangement that also scheme and instead elevated this new makes structural sense. The triangle is a department in a pixelated aluminum-clad famously efficient and, more importantly, steel box eight stories above the existing structurally stable shape, and the leg pairs structures, propped on pencil-thin canted were thus designed as a series of triangular legs. supports. Another consideration was creating The starting point for the structural stable elements at ground level to support engineers was to create a “tabletop”: a stiff, these legs. The leg-support structures, which inhabitable structure supported on legs. The extend from the ground level down into the stiffness is afforded by two-level structural- underlying rock, comprise concrete caissons steel trusses that span in an east–west (piles) that range from 3 feet to 61⁄2 feet in direction and are shaped by large diagonal diameter, and extend a distance of up to 60 members running through them, which are feet into the rock. The caissons are configured designed to allow for the passage of both in a triangular pattern (for each pair of people and services. Between these large columns) and interconnected at grade level two-story-height assemblies run longitudinal to form a three-dimensional frame. Another structures that link the horizontal trusses very important structural consideration is the together and provide the perimeter box of design of the tabletop to resist lateral loads, the “table.” To make this box sufficiently stiff, which come from two sources in downtown the structure is braced horizontally at the Toronto: wind loads and earthquakes. These levels of the main and intermediate floors lateral loadings are resisted in two ways: one 172 2 is the orientation of the triangular leg a wall thickness of 1 inch. The computer elements, which are most effective at structural model used to evaluate static and resisting lateral loads in the transverse live loads estimated a maximum horizontal direction; the other is the large, stiff, displacement of 5⁄16 inches at the southeastern cantilevered, concrete stair-core element corner of the “tabletop.” The structural design positioned at the northern end of the also includes redundancy, to provide building, which resists most of the lateral alternative load paths in the event of the loads in the longitudinal direction. catastrophic failure of a leg support. The tabletop is supported by six pairs of legs; the architect wanted what he called “cigar legs,” which were created by using a large steel Circular Hollow Section (CHS) with specially rolled fabricated-steel conical components welded to each end. These leg elements worked well structurally but were large and heavy items, which carried logistical implications. To avoid unnecessary transportation costs and complex site operations, the steelwork was designed and fabricated in pieces that could be trial- preassembled in a workshop and then subsequently reassembled on site. The hollow structural-steel “cigar legs” are 89 feet in length and 36 inches in diameter, with 173 4 4.4 4.4.1 Case studies 2000–2010 Ontario College of Art and Design expansion, featuring the Sharp Centre for Design 3 4 3 Long section, showing how the concrete core provides a vertical link and lateral stability to the elevated “tabletop” extension 4 Cross-section, showing the extent of the cantilevered frame 174 5 6 7 5 6 7 Structural diagram, Structural diagram, Structural diagram, illustrating bending-moment illustrating wind load in illustrating wind deflection effects and dead (static) load east–west direction of steel structure at level five 8 Steel-frame construction built around the concrete lift/ stair core, with 8 out of the 12 final columns in place 9 Placement of the final two pairs of leg supports. Note the blue-painted steel-leg armatures used to hold the legs in the correct position during construction 10 Detail of double-leg connections to the underside of the steel “tabletop” structure, with stiffening plates welded to the web of the universal beam 11 View of 95-foot-long steel legs at the fabrication shop, showing the specially rolled, tapered, welded end sections 12 Details of the steel-leg base connection 8 9 10 11 12 175 4 4.4 Case studies 2000–2010 4.4.2 Atlas Building Structural description Location Plan dimensions Architects Engineer Reinforced precast concrete Wageningen, Netherlands 145ft long x 145ft wide Rafael Viñoly (b. 1944) Pieters Bouwtechniek B.V. exoskeleton with steel box (Rafael Viñoly Architects) beams Completion date Height with Van den Oever, Zaaijer 2005 85ft & Partners Architecten The idea of an exoskeleton, and that the are held in place with steel dowels and structural function of a building could be chemical fixant. At each floor level, 2-inch- purposely made visible, is not a new one; the diameter steel tension rods are cast into the Atlas Building is an excellent recent example precast units. The former resist any of this genre, which notably includes Piano problematic shear loads caused by thermal and Rogers’ Centre Pompidou and the more expansion of individual units. integrated diagrid of Norman Foster’s Swiss The high-quality precast finish of the Re “Gherkin” building. This new seven-story double-diamond external framework office and laboratory for Wageningen components was achieved with reusable University is part of the university’s move to steel formwork and self-compacting a new campus in De Born, north of concrete. Titanium dioxide, an ingredient Wageningen. The outer frame is constructed more commonly utilized in house paint and from large double-diamond precast concrete toothpaste, was used as an admixture to help elements measuring 24 feet long and 12 feet whiten the concrete and inhibit mold growth. high, with the reinforced concrete elements Recent trials in the Dutch city of Hengelo measuring 153⁄4 inches wide and tapering to have also seen titanium dioxide being 15 inches at the front edge. Cast into the experimentally used as photocatalytic center of each of the precast components is a coating on concrete, which in sunlight will steel plate, which picks up one of the metabolize harmful nitrogen oxides specially fabricated steel box beams, and contained in vehicle exhausts into more spans across to an internal column to the benign nitrates. The building façades are edge of the atrium. The connections with virtually identical except for cutaway sections steel beams and the precast concrete at ground level on two sides for access doors exoskeleton are carefully controlled with and the main entrance, which is a two-story slotted-hole and pin connections, ensuring hexagonal void punched through the that only vertical load (and no lateral latticework of the north façade. A 295-foot- differential movement) is transferred to the long steel entrance bridge leads you into frame; two internal concrete cores are the building. designed to resist lateral loading. The plan of the building is that of a “square donut,” and the structural arrangement is such that there are no columns in the open floor space. The precast concrete units are fixed together using a simple keyed joint, and 176 1 2 3 1 2 3 South-facing façade of the Façade detail Corner detail, showing the Atlas Building, with concrete steel “internal beam” exoskeleton wrapped around connection and the and supporting the building horizontal steel tension rods 177 4 4.4 Case studies 2000–2010 4.4.3 “Het Gebouw” (The Building) Structural description Location Plan dimensions Architects Engineers Double (balanced) Leidsche Rijn, Utrecht, 90ft long x 13ft wide (each Stanley Brouwn (b. 1935) Pieters Bouwtechniek B.V. cantilevered steel tube Netherlands block) and Bertus Mulder (b. 1929) Completion date Height 2006 25ft This temporary exhibition space is a hot-rolled steel sections, with bracing collaboration between the Dutch conceptual provided by diagonal steel rods. Where the artist Stanley Brouwn and architect Bertus two blocks meet, the steel sections are Mulder, known for his restoration of the considerably enlarged and moment Rietveld-Schröder House and recent connections provided with stiffened corner reconstruction of the Rietveld Pavilion at the plates. The structure is built using primarily Kröller-Müller Museum. “Het Gebouw” (The bolted connections and was originally Building) plays a neat structural game with a designed to be demounted and relocated. square-section prismatic slab perched at a Het Gebouw sits on the edge of Leidsche 90-degree rotation atop its close relation, Rijn, the site of a new residential creating a balanced cantilever 38 feet long at development for 80,000 people west of its greatest extent. Stanley Brouwn is one of Utrecht, and the pavilion is adjacent to a Holland’s most celebrated artists, and is best large geodesic dome constructed from known for his conceptual artworks in relation cardboard tubes and designed by Japanese to walking and feet. In a notable series of architect Shigeru Ban. “Het Gebouw” and works from 1960 to 1964, entitled this way Ban’s “Paper Dome” were both built as brouwn, the artist stopped passers-by and cultural buildings, with Het Gebouw hosting asked them to draw directions from a to b. In regular art exhibitions and the Paper Dome 1960, Brouwn also documented all the shoe operating as a community theater. These stores in Amsterdam and began to make a projects, commissioned by Bureau Beyond, series of measured walks. Interestingly, he were to act as magnets and a focus for future measured these walks in the Stanley Brouwn developments—once again extending the Foot (SB foot), which was based on the built-environment frontier, and reminding us length of his own foot. One SB foot measures why the Netherlands is one of Europe’s most 10 inches, and the design of the Het Gebouw densely populated countries. Het Gebouw pavilion is based upon this module. The was originally commissioned for five years, length of each block is 90 feet and the cross- but the building’s success as what architect section of each block measures 13 feet x Bertus Mulder describes as “An autonomous 13 feet. The building is subdivided into a work of art,” and increasingly as a local 5 SB-foot grid, which is clearly visible and landmark, has persuaded the municipal helps to organize the building components. authorities to retain the structure. However, The structural challenge was to create a rigid owing to major construction work in the upper level with two identical cantilevers of vicinity the local ground level is being raised 38 feet. The structure is fabricated from small by 31⁄2 feet and as a consequence Het 178 1 Gebouw will also be raised; Bertus Mulder 1 Artist Stanley Brouwn’s original model explained that the building will not have to be disassembled, but can be lifted as a single entity and refixed to a modified and elevated foundation. Two sections in each block of the building are glazed both sides with an entrance door centrally located in one of the glazed panels, all coordinated with Brouwn’s dimensional system. The gallery curator explained that during a recent exhibition-opening party, a large crowd of children and parents had caused noticeable movement in the cantilevered ends: a not unpleasant but slightly unnerving experience. In actuality, Mulder explained, 200 people in one end of this small building would still not be cause for (structural) concern, but it is difficult to see how they would all fit in. As well as an enigmatic work of art and architecture, Het Gebouw is an excellent structural model that illustrates the performative possibilities of simple materials cleverly arranged. 179 4 4.4 4.4.3 Case studies 2000–2010 “Het Gebouw” (The Building) 2 3 180 4 2, 3 Het Gebouw and the delicate structural balancing act 4 Beneath one of the gravity-defying cantilevers 5 The steel skeletal framework. Note the diagonal tensile- steel rods in the walls of the upper structure and the heavier, steel SHS elements used in the central (connecting) section 5 181 4 4.4 Case studies 2000–2010 4.4.4 Hemeroscopium House Structural description Location Floor area Architects Technical architect Helical cantilever Las Rozas, Madrid, Spain 4,300ft2 Antón García-Abril (b. 1969), Javier Cuesta Elena Pérez, Débora Mesa, Completion date Height Marina Otero, Ricardo Sanz, Contractor 2008 30ft and Jorge Consuegra, Materia Inorgánica Ensamble Studio 1 1 As a structural diagram, a construction one year, but the structural frames took a Eastern elevation of the Hemeroscopium House, sequence, and as a set of constructional mere seven days to assemble. The structure showing granite elements, the Hemeroscopium House is an for the house consists of seven key elements, counterweight exceedingly elegant pedagogic tool. which are stacked up using a helicoidal Components include a warren truss, a arrangement. The first element is the stable Vierendeel truss, and three forms and sizes of and heaviest “mother beam,” which is 72 feet prefabricated reinforced-concrete beams. long and 83⁄4 feet high and weighs a not This project for a private residence northwest inconsiderable 65 tons. This concrete I-beam of Madrid also employs a 22-ton rough-hewn is prefabricated off-site and uses specially granite boulder as a kind of anchor and designed pre-tensioned steel reinforcement counterweight balanced atop the structure, to achieve its desired strength. The second without which we are assured there would be element is an inverted U-shaped beam of 72 no structure at all. In a recent lecture in feet, which picks up another massive London, architect Antón García-Abril concrete I-beam at its cantilevered end and explained that it is the “gravitational traces also, at its midpoint, a U-shaped concrete that make the space.”1 The complex beam that has reinforced glazed ends, is engineering and design for the project took filled with water, and acts as an elevated, 182 linear swimming pool. That this 69-foot-long structure in its entirety are, however, pool contains 28 tons of water only seeks to explicitly illustrated. There has been no reinforce the complex network of structural attempt to hide or obfuscate structural interdependencies. As the low-slung actions, with this single house able to structural helicoids rise, a transparency of tell a number of stories, both structural beam elements is introduced using steel to and spatial. create the fifth and sixth spanning elements—a steel Vierendeel and warren 1 García-Abril, A., “Stones and Beams,” lecture given truss, respectively—and the seventh and final at the Architectural Association School of Architecture, March 2, 2011 beam is another concrete I-beam, upon the end of which sits the granite counterweight drilled through and bolted to the beam. This counterweight allows the last beam, which is balanced atop the water-filled beam, to cantilever at its other end and support the steel warren truss. These complex structural relationships between the elements and the 183 4 4.4 4.4.4 Case studies 2000–2010 Hemeroscopium House 2 3 184 2 4 South elevation, with cantilevered linear pool 3 Fabrication drawing of concrete beam no.3, showing the distribution of steel reinforcement 4 Axonometric drawing showing structural logic and sequential assembly 185 4 4.4 Case studies 2000–2010 4.4.5 Kanagawa Institute of Technology (KAIT) Workshop/ Table Structural description Location Floor area Architect Engineers Post-tensioned, structurally Kanagawa, Japan 21,400ft2 Junya Ishigami (b. 1974) Konishi Structural Engineers optimized steel frame (Junya Ishigami + Completion date Height Associates) Contractor 2008 161⁄2ft Kajima Corporation Software Tomonaga Tokuyama Though not immediately obvious to the eye, there are two different types of columns in the structure, the verticals (those bearing vertical forces), and the horizontals (those bearing (or resisting) horizontal forces). I wanted to make the columns as slender as possible, and assigning the forces was more effective than trying to make every column bear both. I didn’t want just any sort of slender columns.1 Junya Ishigami Junya Ishigami is a young architect who does with strips of rooflights. not seem to be afraid of producing wonderful Although this project is visually stunning, pieces of architecture and design while in that a lightness and transparency is simultaneously employing the creative maintained with numerous yet startlingly potential of engineering properties and slender columns, this is only half of the story. dynamics. If Ishigami’s Table project of 2005 The engineering of this structure is an is both engineering set piece and conjuring extremely precise and yet unorthodox mix of act—which, based on our engineering parametrically defined precision and a preconceptions, appears to defy gravity— radically innovative hierarchy of structural then his workshop for the Kanagawa Institute “action designation.” Ishigami creates two of Technology (KAIT) is a complete work of “classes” of column, ostensibly for two architecture and engineering. different functions: one set of columns to Commissioned as part of the university’s carry the load of the I-beam roof grid and one redevelopment of its campus, this set to resist lateral movement, which the 21,500-square-foot single-story structure was architect calls the vertical and horizontal designed as an open-access studio facility, columns. Where Ishigami has been extremely available for students to undertake project skillful is in creating a lightweight forest of work in a range of different media. The columns where the specific structural architect conceived of the building as a stroll function of any given one cannot be through the woods that cleverly delineates identified. The supports are all differently the one-room environment into ambiguous sized and vary from column no. 240 (a domains through column densities and compact 31⁄8 x 21⁄4-inch solid steel section) to disposition “in a way that gives no hint that column no. 277 (61⁄4 x 5⁄8-inch steel flat), with any rules or plan for their placement exist.”2 all of them specifically orientated at angles The plan of the building is a slightly skewed down to a tolerance of one decimal place. The square; a single roof plane is held aloft by construction of KAIT was critical in 305 columns, each unique in its cross-section maintaining Ishigami’s aim of creating an sizing and orientation. The building is glazed even treatment of all column connections. on all sides, and the deep plan lit throughout The columns are erected using two different 186 processes according to their type. For the ambitions of a design project. His Table verticals, the bases are joined to independent project, which has been exhibited in Basel, foundations, with steel I-beams placed across London, Tokyo, and Venice, is worth the top ends. Pin joints are used to attach the mentioning in relation to the general themes verticals to the beams. The detail of these of this book for its structural audacity and pins is ultimately concealed in order to match creative “reverse engineering.” A table the welded detail of the horizontals’ top ends. surface (31 feet long x 81⁄2 feet wide x 31⁄2 feet In order to keep the horizontals (the lateral- high) of 1⁄8-inch-thick steel is held by four legs, resisting columns) slender and prevent their one located at each corner. That the table can own weight acting on them as a vertical support its own material weight over this force, they were suspended from the roof span is seemingly impossible; that it can beams. After the verticals were joined to the support everyday objects such as fruit bowls beams, the horizontals were inserted with a and vases seems illusory at the very least. crane from above the beams and fixed. The What Ishigami has done has pre-rolled the horizontals are not intended to bear snow top of the table, like the spring of a clockwork loads and other vertical forces, so the initial mechanism, and the tabletop is only bought design was to keep their connection with the level when unrolled and carefully loaded with floor vertically loose to avoid potential precisely placed and weighted objects. The buckling from snow load. The problem with table is so delicately balanced and making loose holes and inserting the structurally optimized as to slowly ripple to horizontals into them was that you would the touch. As is shown by the KAIT project, make visible details that didn’t match the Junya Ishigami’s innovations are both corresponding details of the verticals at the structurally inventive and polemically rich floor–column connection. This outcome was and provide clues to hitherto unimagined unacceptable to Ishigami, so he used another design solutions for a new generation of approach: before fixing the horizontals to the architects and engineers. beams the roof was preemptively loaded with weights equal to the snow load, and 1, 2 Ishigami, J., Project information provided by the then the columns were fixed. When the office of Junya Ishigami & Associates, 2011 temporary loading is removed, the horizontals (lateral-load columns) are put into tension, thus preventing bending if the structure is snow loaded. The process maintains the required ambiguity of structural function that Ishigami required while creating a new structural type—or at least a new structural approach, achieved through very detailed analysis using software developed by his firm. Junya Ishigami belongs to a long line of designers for whom the structural strategy, logic, and material use of any given design are codependent with the programmatic 187 4 4.4 4.4.5 Case studies 2000–2010 Kanagawa Institute of Technology (KAIT) Workshop/ Table 3 1 Plan drawing, showing the unusual layout of the 305 columns, which are indicated by dots 2 1 < Diagram showing the                                               <  < < < roof-beam structure and the two designated “classes” of < < < < < column < < < < < 3 < KAIT under construction, < 4 < < showing the separate < < < column-cluster foundations  < < < < 4 < < < View of roof structure during < < construction, with red prime-painted steel sections < < < < < to left of picture temporarily < < in place to replicate snow < < < loading < < < < < 5 < < Section drawing through the                                 edge of the KAIT building ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; 2 5 188 6 6 8 11 Exterior view of completed Architect’s drawing of the Factory photograph showing building Table project, with locations the steel tabletop being of table objects and their rolled (prestressed) 7 weight Interior view of finished 12 project before occupation 9 The “gravity-defying” Finite Element Analysis finished, fully laden Table (FEA) diagram of the tabletop 10 Elevation drawing of the Table in its “deployed” and “undeployed” (rolled-up) state 7 8 9 10 2 r=9312 r= 931 0 R=9 R=9 0 r= 5031 r= 5031 r= 4 11 73 73 4 11 r= 03 r= 17 r=17 03 r= 11 1 39 39 r=1 1100 r= 932 r= 932 r= 85 5 85 r= 5 9500 11 12 189 4 4.4 Case studies 2000–2010 4.4.6 Meads Reach Footbridge Structural description Location Length Architect Artist Portal-frame profile with a Bristol, England 180ft Niall McLaughlin (b. 1962) Martin Richman stainless-steel stressed skin Completion date Engineer 2008 Timothy Lucas (Price & Myers) The art of structure is how and where to put the holes.1 Robert Le Ricolais The brief from the client for an “invisible” bridge’s spanning capacity, with the walkway for pedestrians and cyclists over underside of the structure providing lateral Bristol’s floating harbor was developed by stiffness. The “walkable” deck of the bridge is architect Niall McLaughlin, engineers Price & the only element that is not welded, and it is Myers (Geometrics Group), and the light formed from a series of removable textured artist Martin Richman. The ambition of and perforated stainless-steel panels. These “invisibility” led the design team to look at a panels allow access to the lighting battens perforated surface that would not have to be fixed inside the bridge. The bottom edge lit at night but could be a source of profile of the bridge is formed from a solid illumination itself, emitting light through a stainless-steel rod, which helps to resist distribution of holes. tensile forces. The structural form of the bridge is that of a The perforations that cover the bridge are four-legged portal frame with flexible, pinned interesting in a number of ways; primarily base connections at each end. The span is employed so as to allow the bridge to achieved by using the torsion-box principle luminesce in darkness, putting holes in a of a plane wing, creating a stressed-skin bridge is also structurally intriguing. structure made entirely from grade 2205 Although there is a risk that you structurally stainless steel. The bridge is formed from a weaken the bridge, you are also removing series of perforated stainless-steel ribs, material and thus lightening the static “dead” connected to a thin-plate perforated load, which is structurally beneficial. The size stainless-steel spine element; the ribs are of the perforations varies from a diameter of also connected by intermediate longitudinal 3 ⁄8 inch to a maximum of 15⁄8 inch. The holes sheet steel struts and internal cross-bracing are positioned at regular centers, with their elements inside the deck. This relatively diameter locally determined from a Finite lightweight framework is then wrapped in Element Analysis (FEA) of a stressed-skin 1 ⁄4-inch stainless-steel perforated sheets, unpunctured model. The engineers managed which are welded to the subframe assembly to link their structural data map to a (this is a fully welded structure). The depth of spreadsheet, which produced a series of the balustrades is effectively forming the numerical maps with varying perforation 190 1 Elevation of “portal” bridge. The portal design creates rigid connections at the haunches of the bridge, while the pinned base connections allow for the thermal expansion and live loading of the structure 1 2 Exploded view, showing construction elements diameters detailed. This information could be 2 sent direct to the CNC plasma cutters that were cutting the steel sheets for the bridge. In areas of high stress distribution, such as the haunches of the “portal” bridge legs, the holes decrease in size, and sometimes there are no holes at all. Niall McLaughlin has said, “the pattern of holes becomes a stress map of the work the bridge has to do to cross the river.”2 In all, there are 55,000 perforations. The bridge was preassembled in sections, which were welded together on a vacant plot adjacent to the final location, and the 83-ton bridge was lifted whole by a mobile crane into its final position. The bridge links the harbor to the city center, and has received awards from both the Royal Institute of British Architects (RIBA) and the Institution of Structural Engineers. 1 Quoted in Sandaker, B. N., On Span and Space: Exploring Structures in Architecture, Oxford: Routledge, 2008, p. 71 2 Spring, M., Meads Reach footbridge, Bristol, PropertyWeek.com, 23 July 2010 191 4 4.4 4.4.6 Case studies 2000–2010 Meads Reach Footbridge 3 3 Detail drawings: plan, elevation, and rib details 4 Visualization of stress distribution through Finite Element Analysis (FEA) 5 A sample of the spreadsheet used to generate the machine code for automated CNC laser cutting of the perforations 6 Developable surfaces: the °1/25 geometrically complex surfaces of the structure were carefully modeled to allow them to be developed from flat sheets, for ease of fabrication 85 Ø 85 Ø 7 3D model of stainless-steel component with variably sized hole cut-outs 8 85 Ø 3D model 4 5 6 7 8 192 9 11 10 9 Fabrication of bridge in stainless steel, showing ribs and spine elements 10 Lifting the bridge (whole) into position 11 The Meads Reach Footbridge is illuminated, so that the inner ribbed structure is revealed at night 12, 13 Detail of finished bridge 12 13 193 4 4.4 Case studies 2000–2010 4.4.7 Pompidou-Metz Structural description Location Plan dimensions Architects Production software Timber gridshell roof Metz, Lorraine, France Hexagonal roof 300ft Shigeru Ban (b. 1957), Design to Production structure wide—86,000ft2 Jean de Gastines, Philip Completion date Gumuchdjian Specialist timber 2010 Floor area fabricator 115,200ft2 Engineers Holzbau Amann Terrell Group Fabric membrane Contractor Taiyo Europe Demathieu & Bard I bought this hat 10 years ago in Paris, but it’s the same you see everywhere in Asia, usually worn by field workers. It has a bamboo structure, a layer of insulation, and oil paper as waterproofing. The building has the same fundamental elements, including the hexagonal weave pattern.1 Shigeru Ban Pompidou-Metz, a new outpost of the vertical circulation and access to the elevated eponymous Paris-based parent institution, is gallery elements, supports the prow of the an exhibition space for visual art with a timber roof “hat” with a tubular steel ring. restaurant, store, and auditorium. The three Similar rings are also used to form four main gallery spaces are 260-foot-long openings in the roof for the protruding rectangular tubes stacked on top of each galleries. Interestingly, assembly of the other with picture windows at each end. A timber gridshell was started from its highest 250-foot-high concrete-and-steel tower point, and by using scaffold support towers connects the gallery spaces, and the entire the timber framework was built outward from structure is wrapped in a fabric-clad this central tower to the edge beams. The hexagonal timber-gridshell structure. edge beams themselves are also glulam The roof of the new Pompidou-Metz was timber, but with a considerably deeper inspired in part by the woven canework of a section than that of the roof; they work as Chinese hat that architect Shigeru Ban found simple two-dimensional arch structures, in a Paris market. The roof, hexagonal in plan, minimizing the number of edge supports to is a giant, triaxial, woven, double-layered six: one for each apex of the hexagon. The timber gridshell with a three-way parallel edge supports are formed by pulling the grid of 91⁄2-foot modules. The structure gridshell down through the horizontal plane consists of 715 tons of glue-laminated timber to form six three-dimensional latticework elements, prefabricated in a German factory columns, set back from the edge of the and assembled on site. The majority of these structure. This complex timber gridshell elements are glulam planks 17 inches wide, spans up to 130 feet. 51⁄2 inches deep, and approximately 50 feet in Although hexagonal in plan this is not a length. The planks are overlaid in three symmetrical surface; the geometry of this directions and then a second layer of planks timber grid is pulled up and down through is added with timber blocks between, the horizontal plane, utilizing both synclastic increasing the depth and thus the structural and anticlastic curvature to provide stiffness. performance of the assemblage. A tubular The tighter radii of the lattice columns concrete-and-steel tower, which contains the provide excellent structural stiffness and 194 1 1 resistance to wind loads. The structure fabrication purposes it was decided to create View of a virtually complete Pompidou-Metz at night, underwent rigorous wind-tunnel testing at oversized, single, curved elements and with the timber gridshell Nantes’ CSTB (Centre Scientifique et machine the additional curvature. The clearly visible through the laminated timber elements are connected Technique du Bâtiment), as well as testing for PTFE fabric skin snow loadings and subsequent internal end to end using steel plates spliced into the climatic effects. head of each plank and then bolted. The original structural design of the project The timber structure is covered with a was undertaken by Cecil Balmond’s specialist waterproof membrane made from fiberglass engineering studio, Advanced Geometry and Teflon (PTFE or polytetrafluoroethylene). Unit, at Arup. This early design differed from The PTFE is cut from flat sheet and conventional gridshells in that it employed assembled into panels using pattern-cutting the use of reciprocal beams fabricated from software to precisely mimic the timber form. steel and timber, specifically designed to The membrane is then connected back to the simplify the connections by cojoining the structure using T-section steel elements. The woven node points in a structural “sandwich” fabric is held 12 inches away from the timber or lamination. The final realization of the structure, to allow for a smooth airflow and project used the more conventional gridshell prevent condensation. system of a double-layered three-way woven timber grid, comprising six layers of glulam 1 Lang Ho, C., “Interview: Shigeru Ban” in Modern timber planks at 16-inch offsets with steel Painters, May 28, 2010, p. 22 bolts connecting the node points. The use of glulam timber, however, made it possible to preform the planks with a specific radius: each was fabricated with a single custom curve along its length, and was then Computer Numerical Control (CNC) milled to introduce a secondary twist (or curvature). It would have been possible to laminate the timber planks in two directions, but for 195 4 4.4 4.4.7 Case studies 2000–2010 Pompidou-Metz 2 3 5 Diagram showing the double Double-curved glulam Computer model of the curvature of the timber timber planks being timber latticework, with all “planks.” The first curvature prepared at the factory in elements to scale is created by glue-laminating Germany. Each plank is single curved elements approximately 49 feet long 6 along the length of the Construction picture, with member, with additional 4 laminated-timber perimeter curvature (or twist) Detail of special turnbuckle edge beams clearly visible introduced by machining the tool, created to winch the and the tubular-steel timber element across the planks together on site framings fixed around the short section protruding galleries 2 5 3 6 4 196 7 9 10 11 Detail of computer model, Diagram showing the Looking from the top of one Interior photograph showing showing the tight geometry geometry and assembly of of the gallery tubes, we can the intersection of the of the lattice leg elements the three-way double- see the second layer of tubular-steel service tower layered timber lattice timber planks being laid over and the apex of the timber 8 structure the lattice, with spacing roof structure Detail of a timber lattice leg blocks shown support, showing the steel ring that holds down the PTFE fabric covering 7 9 8 10 11 197 4 4.4 Case studies 2000–2010 4.4.8 Burj Khalifa Structural description Location Floor area Architect and engineer Contractor Buttressed core tower Dubai, United Arab Emirates 3 million ft2 William F. Baker (b. 1953), Samsung/BeSix/Arabtec Skidmore Owings, and Completion date Height Merrill (Partner in Charge of Foundation contractor 2010 2,717ft Structural and Civil NASA Multiplex Engineering) While the world’s tallest building, and indeed achievement, is the increased structural the world’s tallest manmade structure, is stability that the tapering Y-shaped form located in the Middle East, the Burj Khalifa is affords, employing what William F. Baker very much a product of North American describes as a “buttressed core” structural engineering, and more specifically the system. The core, a hexagonal tube that high-rise progenitor of Chicago. The location contains all the vertical access, is buttressed of the tallest “skyscraper” has been a at 120-degree intervals by three tapering constantly changing competition that follows accommodation wings. Unusually for a economic migrations and has now found its building of this immense height, the external way to Dubai. Chicago-based Skidmore, form of the structure is asymmetric, which is Owings and Merrill’s role in the evolution of not a lightly used design conceit but the the high-rise is significant, with five out of result of extensive wind-tunnel testing and ten of the world’s tallest buildings being the numerous Computational Fluid Dynamic work of SOM. In this context, it is important (CFD) modelings of the tower, which to make reference to the remarkable confirmed that tapering the structure and contribution that SOM engineer Fazlur Khan offsetting stepped changes in building width made to development of new forms of would prevent the consolidation of organized high-rise structural thinking, such as the vortex shedding and substantially reduce the “trussed tube” of the John Hancock Center wind forces acting on the building. The and the “bundled tube” of the Sears Tower effects of the wind are also mitigated by the (now renamed the Willis Tower). The legacy of glazing mullions, or “fins,” which SOM have Khan’s quiet but significant innovations still likened to the dimples on a golf ball, “to resonates in the construction of tall buildings, create surface turbulence and reduce the where material and structural efficiencies are lateral drag forces on the building.”1 achieved through new geometric The building is constructed of reinforced configurations and radical rethinkings of concrete—a feat that would have been engineering orthodoxy. unimaginable in 1965, when Fazlur Khan had At 2,717 feet high, the Burj Khalifa sets a seemingly pushed the limit for high-rise new building-height record, which for reinforced-concrete design with the 37-story economic reasons alone is unlikely to be Brunswick Building in Chicago. New analysis surpassed any time soon. This predominantly techniques and the refinement of concrete residential block was conceived with a technology have made the Burj project Y-shaped plan, the utility of which delivers possible. The technical challenges, however, increased surface area (and thus vistas for its of pumping concrete to such heights over residents). More important, however, in what such long distances and in such extreme heat is undoubtedly a major engineering were considerable (UAE temperatures can 198 exceed 120˚F). Other technical challenges for utilizes a titanium mesh beneath the raft a building this large, and with such along with electricity to repel harmful significant static loads, are the time- chemicals. dependent changes of concrete shrinkage The construction sequencing of the tower and creep; over a 30-year period it is was also vital to the long-term durability of predicted that vertical shortening will reduce the structure, especially in light of the the overall height of the building by asymmetrically spiraling layout of the approximately 12 inches. This shrinkage and structural setbacks. The superstructure of the creep also creates changes in the structural tower uses a range of concrete mixes, from performance of reinforced concrete 12,000 psi to 9,000 psi cube strength insomuch as it alters the ratio of how much containing Portland cement and fly ash, and load is taken up by the concrete and how was constructed using a self-climbing (jump much by the internal steel reinforcing (rebar). form) system, and a mixture of specially It has been estimated that immediately after designed steel formwork for curved columns construction the concrete in the walls and and proprietary systems for the concrete floor at level 135 will support 85 percent of decks. the load, with the rebar supporting 15 The vast scale of this project is perhaps percent. It is predicted that after 30 years this best illustrated with climate data, which ratio will have changed to 70:30 percent, with shows that a ground temperature of 115˚F is the rebar taking twice the load it did when reduced to 100˚F on the 162nd floor at the top the structure was completed. of the tower; similarly, there is a 30 percent The building is supported on a solid reduction in humidity between the top and reinforced-concrete raft, 12 feet thick; the bottom of the building. material is a C50 Self Compacting Concrete (SCC). This concrete raft is supported by 194 1 Baker, W. F., Mazeika, A., and Pawlikowski, J., “The friction piles, each 5 feet in diameter and 140 Development of Burj Dubai and The New Beijing Poly Plaza” in Structures Congress 2009: Integrated feet long, and each designed for a load Design: Everything Matters, American Society of Civil capacity of 3,300 tons. The groundwater in Engineers, pp. 1–10 the site was found to contain high concentrations of chloride and sulfate, which could prove extremely corrosive to the foundations. Several strategies were employed to prevent this potentially harmful corrosion, such as a specially formulated concrete mix, various waterproofing technologies, and cathodic protection, which 199 4 4.4 4.4.8 Case studies 2000–2010 Burj Khalifa 1 2 1, 2 The completed Burj Khalifa, currently the world’s tallest building: note the asymmetrical setbacks designed to “confuse” the wind 200 4 3 3 4 5 Wind-tunnel testing of a Detail of the concrete 1:500 scale model of the structure with a four-story tower. The wind tunnel section of cladding in place. models contain pressure The fast-track nature of taps to collect wind data contemporary construction from different areas of the means that the structural building model build and finished cladding are programmed simultaneously to allow for internal fitout 5 The Burj Khalifa under construction with the tripartite plan of the buttressed core visible 201 Further reading and Ackermann, Kurt (et al), Building for Industry (Industriebau), resources Surrey: Watermark Publications, 1991 Adams, Jonathan, Columns: Detail in Building, London: Academy Editions, 1998 Addis, William, Creativity and Innovation: The Structural Engineer’s Contribution to Design, Oxford: Architectural Press, 2001 Anderson, Stanford (ed.). Eladio Dieste, Innovation in Structural Art, New York: Princeton Architectural Press, 2004 Bechthold, Martin, Innovative Surface Structures Technologies and Applications, Oxford: Taylor & Francis, 2008 Beukers, Adriaan, Lightness: the inevitable renaissance of minimum energy structures, Rotterdam: 010, 1998 Bill, Max, Robert Maillart: Bridges and Constructions, London: Pall Mall Press, 1969 Billington, David P., The Art of Structural Design: A Swiss Legacy, New Haven: Yale University Press, 2003 Blaser, Werner, Mies van der Rohe, London: Thames and Hudson, 1972 Blockley, D., The New Penguin Dictionary of Civil Engineering, London: Penguin, 2009 Boaga, Giorgio, and Boni, Benito, The Concrete Architecture of Riccardo Morandi, London: Alex Tiranti, 1965 Borrego, John, Space Grid Structures, Cambridge, MA: MIT Press, 1968 Burgess, S. C., and Pasini, D., “Analysis of the structural efficiency of trees” in Journal of Engineering Design, Vol. 15, No. 2, April 2004, pp.177–193, Oxford: Taylor & Francis, 2004 Carter, Peter, Mies van der Rohe at Work, London: Phaidon, 1999 Chanakya, Arya, Design of Structural Elements, Oxford: Taylor & Francis, 2009 Chilton, John, The Engineer’s Contribution to Contemporary Architecture: Heinz Isler, London: Thomas Telford, 2000 Cobb, Fiona, Structural Engineer’s Pocket Book, Oxford: Butterworth-Heinemann, 2008 Coucke, P., Jacobs, G., Sas, P., and De Baerdemaeker, J., Comparative Analysis of the Static and Dynamic Mechanical Eggshell Behaviour of a Chicken Egg, Department of Agro- engineering and Economics, International Conference on Noise and Vibration Engineering, ISMA 23, September 16–18 1998, pp.1497–1502, Department of Mechanical Engineering, KU Leuven, Belgium, downloadable as a PDF from www. isma-isaac.be/publications/isma23 Coutts, M. P., and Grace, J., Wind and Trees, Cambridge: Cambridge University Press, 1995 Denny, Mark, The Physical Properties of Spider’s Silk and their Role in the design of Orb-webs, Department of Zoology, Duke University, Durham, North Carolina, 1976, downloadable as a PDF from: jeb.biologists.org/ content/65/2/483.full.pdf Elliot, Cecil D., Technics and Architecture, Cambridge, MA: MIT Press, 1992 Engel, Heinrich; Structure Systems, New York: Van Nostrand Reinhold Company, 1981 Fisher, R. E., Architectural Engineering—New Structures, New York: McGraw-Hill, 1964 Fuller, R. B., Inventions: The Patented Works of R. Buckminster Fuller, New York: St. Martin’s Press, 1983 202 Gole, R. S., and Kumar, P., Spider’s silk: Investigation Nordenson, Guy (ed.), Seven Structural Engineers: The Félix of spinning process, web material and its properties, Candela Lectures, New York: Museum of Modern Art, 2008 Department of Biological Sciences and Bioengineering, Indian Institute of Technology Kanpur, Kanpur, 208016, Otto, Frei, Finding Form, Fellbach: Edition Axel Menges, 1995 downloadable as a PDF from: www.iitk.ac.in/bsbe/web%20 on%20asmi/spider.pdf Popovic Larsen, O., Reciprocal Frame Architecture, Oxford: Architectural Press, 2008 Goodchild, C. H., Economic Concrete Frame Elements: A Pre- Scheme Design Handbook for the Rapid Sizing and Selection Rice, P., An Engineer Imagines, London: Ellipsis, 1993 of Reinforced Concrete Frame Elements in Multi-Storey Buildings, Surrey: British Cement Association, 1997 Sandaker, B., The Structural Basis of Architecture, Oxford: Routledge, 2011 Gordon, J. E., Structures: Or Why Things Don’t Fall Down, London: Penguin, 1978 Scott, Fred, On Altering Architecture, Oxford: Routledge, 2007 Greco, Claudio, Pier Luigi Nervi, Lucerne: Quart Verlag, 2008 Steel Construction Institute, Steel Designers’ Manual, Chichester: Wiley-Blackwell, 2005 Heartney, E., Kenneth Snelson: Forces Made Visible, Stockbridge, MA: Hard Press Editions, 2009 Torroja, Eduardo, Philosophy of Structures, Los Angeles: University of California Press, 1958 Heyman, Jacques, Structural Analysis: A Historical Approach, Cambridge: Cambridge University Press, 1998 Twentieth-Century Engineering, exhibition catalog, New York: Museum of Modern Art, 1964 Hilson, Barry, Basic Structural Behaviour, London: Thomas Telford, 1993 Veltkamp, M., Free Form Structural Design: Schemes, Systems & Prototypes of Structures for Irregular Shaped Holgate, Alan, The Work of Jörg Schlaich and his Team, Buildings, Delft: Delft University Press, 2007 Stuttgart: Axel Menges, 1997 Wachsmann, K., The Turning Point of Building, New York: Hunt, Tony, Tony Hunt’s Structures Notebook, Oxford: Reinhold, 1961 Architectural Press, 1997 Wells, M., Engineers: A History of Engineering and Structural Ioannides, S. A., and Ruddy, J. L., Rules of Thumb for Steel Design, Oxford: Routledge, 2010 Design (paper presented at the North American Steel Conference), Chicago: Modern Steel Construction, February Useful websites: 2000, downloadable as a PDF from www.modernsteel.com/ http://en.structurae.de issue.php?date=February_2000 http://eng.archinform.net http://designexplorer.net/ Kappraff, J., Connections, New York: McGraw-Hill, 1991 http://www.tatasteelconstruction.com Khan, Y. S., Engineering Architecture, New York: Norton, 2004 (websites accessed 10.10.12) Krausse, J., Your Private Sky—Buckminster Fuller, Zürich: Lars Müller Publishers, 2001 LeDuff, P., and Jahchan, N., Eggshell Dome Discrepant Event, Teacher’s Guide SED 695B, 2005, http://www.csun. edu/~mk411573/discrepant/discrepant_event.html Macdonald, A. J., Structure & Architecture, Oxford: Architectural Press, 2001 Margolis, I., Architects + Engineers = Structure, London: John Wiley & Sons, 2002 Mark, R., Experiments in Gothic Structure, Cambridge, MA: MIT Press, 1989 Megson, T. H. G., Structural and Stress Analysis, Oxford: Elsevier, 2005 Millais, M., Building Structures, London: E & F Spon, 1997 Morgan, J., and Cannell, M. G. R., Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading, Tree Physiology 3, pp.365–374, Victoria, BC: Heron Publishing, 1987, downloadable as a PDF from: treephys.oxfordjournals.org/ content/3/4/365.full.pdf Mosley, B., Bungey, J., and Hulse, R., Reinforced Concrete Design, Basingstoke: Palgrave, 2007 Nerdinger, W., Frei Otto: Complete Works, Basel: Birkhauser, 2005 Nerdinger, W. (et al), Wendepunkte im Bauen Von der seriellen zur digitalen Architektur, Munich: Edition Detail, 2010 Nervi, Pier Luigi, Structures, New York: F. W. Dodge Corporation, 1956 203 Index airship hangars 70 columns 52, 126 Alsop, William: Ontario College of Art and Design extension, cylindrical 164–5 Page numbers in italics Toronto, Canada 172–5 defined 19 refer to picture captions aluminum 44, 46, 134, 138, 156, 172 deflection 56 Aon Center, Chicago, USA 72 frames 130, 150, 156, 173, 174 arches in load testing 96, 98, 100–1 bending stress capacity 58, 59 in nature 10, 19 catenary arches 59, 88, 150–1 shear loads and forces 19, 38 and compression 15, 59 stability 19, 98 pointed arches 14, 15, 96 Cape Fear Memorial Truss Bridge, Wilmington, USA 60 stability 79, 80 carbon fiber 43, 46 and tension 15 catenary curves 88, 89 Arwade, Dr. Sanjay 91 Charlton, David 102 Christoph Ingenhoven and Partner: train station, Stuttgart, Baker, Benjamin: Forth Rail Bridge, Queensferry, Scotland 21, Germany 89 120–1 columns Baker, William F. (Skidmore, Owings and Merrill) 198 buckling 52, 53 Baldwin, Frederick: Tetrahedral Tower, Nova Scotia, Canada cantilevers 52, 126 124–5 and compression 21, 26, 41, 52, 53 Ban, Shigeru 178 deflection 30, 52 Pompidou-Metz, Metz, Lorraine, France 194–7 height and width 52, 54 Barlow, William Henry: St. Pancras Railway Station shed, in nature 10, 20 London 79, 116–17 outrigger 71 Bartoli, John 141 standard sections 52, 54 beams 78–83 steel 33, 52, 152–5, 186–7, 188 bending moments 27, 28, 30, 36, 37, 38, 50, 127 support conditions 30, 33, 52, 54, 126, 186–7 bending stress capacity 40, 41, 43, 50–1 and truss systems 152–5 cantilevers 27, 38, 56, 79, 81, 170 Young’s modulus 52 common formulae 24, 36–9 see also frames; plinths and compression 30, 40, 41, 50, 81 compression/compressive elements concrete 33, 43, 48, 75, 78, 81, 182–5 and arches 15, 59 deflection 30, 32, 36–7, 44, 48, 55, 56, 74, 75 axial compression 52–4, 96 eccentric loads 27, 38, 40 and beams 30, 40, 41, 50, 81 fixed connections 30, 31, 32, 37, 52, 72, 79 and bending stress 40, 41, 43, 50 loading analysis 24, 30–9 and columns 21, 26, 41, 52, 53 moment connections 30, 31, 33, 64, 79, 81, 152, 153, 178 compressive capacity 42, 43, 48, 49 neutral axis 40, 41, 43, 50, 51 compressive failure 52 pinned connections 30, 31, 32, 33, 52, 64, 66, 79, 80 and external loads 21, 25, 26, 35, 44, 52–4, 69, 96, 102 “second moment of area” 36, 37, 41, 42, 44, 50, 52, 55 and frames 59, 60, 61, 62, 64, 66 section moduli 40, 41, 50, 51 and internal forces 25, 26, 27 shear loads and forces 26, 27, 30, 36–8, 40, 41 in nature 14, 15, 18 and slabs 78, 79, 81, 84, 85 neutral axis 27, 40, 41, 43, 50, 51 standard sections 52, 54, 78, 79, 82, 83 in tensegrity structures 18, 156, 157 static equilibrium 28, 29, 40, 41 and trusses 35 steel 33, 42, 44, 52, 74, 78–80, 176–7 Computational Fluid Dynamics (CFD) 104, 108–9, 198 support conditions 30–3, 36–7 concrete and tension 30, 40, 41, 44, 81 beam support conditions 33, 43 timber 33, 49, 82–3 beams 48, 78, 81 torsion 27, 38, 42 compressive capacity 43, 48 Young’s modulus 36, 37, 55 creep 48, 199 see also frames deflection 48 Behnisch, Günter: Munich Olympic Stadium Roof, Germany domes 61, 94 59, 158–61 failure 43 Bell, Alexander Graham: Tetrahedral Tower, Nova Scotia, frames 62, 74, 81 Canada 124–5 grade 48 Bell Rock Lighthouse 92, 93 properties 43, 48, 81 Bini, Dr. Dante: Bini Domes, New South Wales, Australia reinforcing 43 see also reinforced concrete 162–3 shell structures 61, 94, 134–5, 162 biomimetics 7, 159 shrinkage 48, 199 bone 12, 46 slabs 78, 79, 81, 84, 140 bridges 47, 59, 60, 81 standard concrete 62 cantilevered 21, 120–1 strain capacity 43, 46, 49 footbridges 190–3 stress capacity 43, 46 steel 79, 80, 120–1 sustainability 74 suspension 59, 88 tensile capacity 43 truss 21, 60, 79, 120–1 weight 74 Brouwn, Stanley: “Het Gebouw,” Leidsche Rijn, Utrecht, Young’s modulus 46, 48 Netherlands 178–81 construction programs 74, 75, 76 Büro Happold 59, 89 Contarini, Bruno 164 buttresses/buttressing 20, 21, 198–201 control points 90 Cross Laminated Timber (CLT) 49, 83 cables 39, 88, 103, 156–61 Calatrava, Santiago: Concrete Shell Aquarium, Valencia, dead loads 48, 56, 74, 190 Spain 61 deflection Candela, Félix 94, 162, 166 beams 30, 32, 36–7, 44, 48, 55, 56, 74, 75 Concrete Shell Aquarium, Valencia, Spain 61 calculations 36, 37, 55 Los Manantiales Restaurant, Mexico City, Mexico 132–3 cantilevers 56 canopies 134, 135, 140–3, 170 columns 30, 52 cantilevers 178–85 concrete 48, 75 beams 27, 38, 56, 79, 81, 170 defined 55 bending moments 19, 27, 38 and fitness for purpose 24, 56–7 bridges 21, 120–1 lateral 57, 63 canopies 129, 140–3, 170 slabs 56 204 steel 74 timber 76 ice shell, Cornell University, NY 91 vertical 56 igloos 70 diaphragms impact resistance 12, 13, 47, 93 floorplates 61, 64, 65, 66, 68 “in service” state see fitness for purpose walls 126, 158 Ingber, Don E. (Wyss Institute, Harvard) 18, 157 domes 14, 17, 60, 61, 69, 70 Integrated Building Information Model (BIM) 104 concrete 61, 94, 162–3 internal forces 26–39 geodesic 80, 124, 136–9 analyzing 24, 30–9 lamella 60, 80 bending moments 25, 27, 28, 30, 34, 36, 37, 38, 55 load testing 92, 94 common beam loading scenarios 36–9 steel 80 compression 25, 26, 27 deflection calculations 36, 37, 55 Eddystone Lighthouse 93 and external loads 25, 26–7, 40 eggshells 14, 15 method of sections technique 28, 30, 34–5 Eiffel, Gustave: Eiffel Tower, Paris, France 118–19 shear forces 25, 26, 27, 30, 36–8, 40, 60, 64, 68 elastic design theory 40, 50 and static equilibrium 25, 28–9, 40 elastic moduli 44, 50, 51 and stress 40 Engel, Heinrich 24, 58, 62 tension 25, 26, 158 Euler equations 52, 53 torsion 25, 26, 27, 38, 42, 98 external loads 25 International Association for Shell Structures (IASS) 128 axial 25, 26, 40, 44, 52–4, 96 iron 46, 116 and compression 21, 25, 26, 35, 44, 52–4, 69, 96, 102 Ishigami, Junya: Kanagawa Institue of Technology workshop/ and deformation 12, 44 table, Japan 186–9 distributed loads 26, 36–7, 39, 55, 71, 90, 144 Isler, Heinz 88, 91, 144–5, 158, 162 and internal forces 25, 26–7, 40 Brühl Sports Center, Solothurn, Switzerland 148–9 load testing 92–103 Deitingen Süd Service Station, Switzerland 144, 145, 147 load transfer mechanisms 21, 30, 58, 60, 61, 64, 68, 69, 176 Wyss Garden Center, Switzerland 145, 146 perpendicular loads 25 point loads 26–9, 30, 34, 36–8, 41–2, 59, 61, 78, 96 John Hancock Center, Chicago, USA 72, 198 shear loads 25, 26, 27, 30, 40, 43, 49, 176 and static equilibrium 24, 25, 28–9, 40 Kelly, John Terrence: Lamella Dome, Materials Park, South and tension 21, 25, 26, 30 Russell, Ohio, USA 60 Khan, Fazlur (Skidmore, Owings and Merrill) 198 Faber, Colin 132 Kilian, Dr. Axel 151 ferrocement 141 Koechlin, Maurice 118 financial issues 74, 75, 76 Kreuck & Sexton: Crown Hall, IIT, Chicago, USA 131 Finite Element Analysis (FEA) 6, 57, 104, 106–7, 170, 190, 192 Kröller-Müller Museum, Otterlo, Netherlands 156, 157 fire protection 74, 75, 76, 82 fitness for purpose 24, 56–7 Laminated Strand Lumber (LSL) 83 floorplates 57, 58, 61, 64, 65, 66, 68 Laminated Veneer Lumber (LVL) 49, 76, 83 floors and stability 57, 61, 64, 65 live loads 56, 88, 104, 105, 120, 173, 191 Fowler, John: Forth Rail Bridge, Queensferry, Scotland 21, loads 24 see also dead loads; external loads; live loads; 120–1 seismic loads; snow loads; wind loads frames Louisiana Superdome, USA 80 bending moments 64, 66 Lubetkin, Berthold: Penguin Pool, London Zoo, London 92 braced 66–7, 71, 72 Lucas, Timothy 6–7, 190 cantilevered 130, 150, 156, 173, 174 and compression 59, 60, 61, 62, 64, 66 Macfarlane, Tim 166–7 concrete 62, 64, 75, 81, 176–7 all-glass extension, London (Mather) 169 diagrids 72 Apple stores (Bohlin Cywinski Jackson) 171 fixed 30, 31 Broadfield House Glass Museum, Dudley, England (Design outrigger construction 71 Antenna) 169 pinned 30, 31 Joseph store, London (Jiricna) 168 portal 80, 96, 130–1, 190–3 Klein Residence, Santa Fe, New Mexico (Ohlhausen DuBois rigid 62, 64, 65, 66, 71 Architects) 167, 168 spaceframe structures 60, 80, 102, 124–5, 136, 139 Yurakucho Station canopy, Tokyo, Japan 170 stability 30, 63, 64–7, 71, 172–3, 176, 186, 190 Maillart, Robert 126, 166 steel 62, 64, 69, 74, 80, 130–1, 181, 186–9 Magazzini Generali Warehouse, Chiasso, Switzerland 113, timber 62, 76 126–7 and trusses 60, 71, 72, 80 Mark, Professor Robert 104, 105 tubular 72, 138, 139, 156–7, 178–81, 198–201 material properties 40 vibration 74, 75 brittleness 44, 47, 63 Fuller, Richard Buckminster 112, 124, 136–7, 156, 157 buckling 52, 53, 151 Geodestic (Fly’s Eye) Dome, Snowmass, Colorado, USA deformation 12, 44 139 ductility 40, 44 The USA Pavilion, Montreal Expo, Canada (1967) 80, 139 elasticity 10, 12, 16, 40, 44, 45, 49 Wood River Dome, Illinois, USA 138 isotropic materials 43 load resistance 24, 43 Garcia-Abril, Antón: Hemeroscopium House, Las Rozas, in nature 12, 14, 18 Madrid, Spain 113, 182–5 orthotropic materials 43, 49 Gaudí, Antoni 89 strain capacity 14, 40, 44–6 Casa Milà, Barcelona, Spain 59 stress capacity 12, 14, 40–3, 46 glass 46, 102, 166–71 and structural systems 74–6 Glen Howells Architects: The Savill Building, Windsor Great McLaughlin, Niall: Meads Reach Footbridge, Bristol, England Park, UK 59 190–3 glulam 49, 76, 83, 145, 194, 195, 196 “Method of Sections” technique 28, 30, 34–5 graphene 46 Mies van der Rohe, Ludwig: Crown Hall, IIT, Chicago, USA Grimshaw, Nicholas: Eden Project, Cornwall, UK 17, 80 130–1 Millennium Dome, London 70 Haller, Fritz: Maxi/Mini/Midi Systems 152–5 modeling techniques 91 the human body 18, 19–21 Computational Fluid Dynamics 108–9, 198 human hair 46 Finite Element Analysis 106–7 205 Integrated Building Information Model 104 Scorer, Sam: Concrete Shell Structures, Lincolnshire, England photoelastic modeling 6, 104, 105, 140 134–5 soap film 88, 90, 159 sectional properties 40, 44, 50 suspension models 88, 89 axial compression 52–4, 96 see also prototyping/prototypes bending stress 50–1 Morandi, Riccardo 6 section moduli 40, 41, 50, 51 Murphy and Mackey Architects: The Climatron, St. Louis, see also deflection Missouri, USA 138 seesaws 28, 29 seismic loads 63 nature serviceability state see fitness for purpose prototyping 7, 88, 124, 159 shell structures structures in 10–21, 88 concrete 61, 88, 94, 128–9, 132–5, 144–9, 162 Navier-Stokes equations 108 ice shells 91, 145 Nervi, Antonio: Palazzo del Lavoro, Turin, Italy 140, 142–3 see also eggshells Nervi, Pier Luigi 6, 94, 112, 127, 140–1, 166 Shukhov, Vladimir: All-Russia Exhibition (1896), Nizhny Lamella Dome, Palazzetto Dello Sport, Rome, Italy 60 Novgorod, Russia 122–3 Palazzo del Lavoro, Turin, Italy 140, 142–3 Sir William Arrol & Co. 120 neutral axis 27, 40, 41, 43, 50, 51 Skidmore, Owings and Merrill (SOM): Burj Khalifa, Dubai, Newton’s third law of motion 25, 28 United Arab Emirates 198–201 Niemeyer, Oscar: Niterói Contemporary Art Museum, Rio de slabs Janeiro, Brazil 164–5 and beams 78, 79, 81, 84, 85 Nouguier, Emile 118 concrete 78, 79, 81, 84–5, 126, 140 deflection 56 One Canada Square, London 71 floor slabs 64, 65, 140, 162 Oriented Strand Board (OSB) 83 waffle slabs 84, 85 Otto, Frei 88, 112, 158, 159 Smithfield Market, London 61 Munich Olympic Stadium Roof, Germany 59, 158–61 Snelson, Kenneth: tensegrity structures 18, 156–7 soap-film models 88, 90 snow loads 126, 187, 188, 195 train station, Stuttgart, Germany 89 soap bubbles 16, 17 software people circles 21 CADenary tool program 151 plastic 50, 52, 53, 137, 139, 144 Computational Fluid Dynamics 104, 108, 198 plastic design theory 40, 50 Finite Element Analysis 57, 106 plastic section modulus 50 form-finding 88, 90 plinths 98, 107 spiderwebs 12, 13 Poisson’s ratio 44, 45 static equilibrium 24, 25, 28–9, 30, 35, 40, 41 Pringle Richards Sharratt Architects: Winter Garden, Sheffield, steel UK 59 beams 33, 42, 44, 52, 74, 78–80, 176–7 prototyping/prototypes bridges 79, 80, 120–1 form finding 88–91 columns 33, 52, 152–5, 186–7, 188 load testing 92–103 compressive capacity 42, 43 nature 7, 88, 124, 159 deflection 74 visualizing forces 104–9 domes 80 Prouvé, Jean 112, 140 failure 44, 47, 74 pylons 118–19 fatigue 47 flexibility of use 74 reinforced concrete 48 frames 62, 64, 69, 74, 80, 130–1, 181, 186–9 beams 33, 43, 75, 81, 182–5 grade 44, 47 bending stress capacity 43, 92 gridshell structures 122–3 deflection 75 lattice 118–19, 122–3 domes 162–3 mild steel 40, 42, 43, 44, 46 flexibility of use 75 properties 47, 74, 78–80 frames 64, 75, 176–7 in reinforced concrete 43, 48 properties 43, 48, 75 roofs 79, 80, 140–3 roofs 61, 126–7, 140–3 sheet steel 137, 138, 150, 151, 190 shell structures 88, 128–9, 132–3, 144–9 skin 138, 150–1, 190–3 slabs 84, 85, 126 spaceframe structures 80, 139 structural assessment 75 stainless steel 139, 150, 168, 170, 171, 190–3 sustainability 75 standard steel 52, 62 tensile capacity 43 strain capacity 43, 44, 46 vibration 75 stress capacity 40, 42, 43, 44, 46, 48 weight 75 structural assessment 74 Renzo Piano Building Workshop: The Shard, London 67 sustainability 74, 75 Rice, Peter: Pavilion of the Future, Seville Expo (1992) 15 tensile capacity 43, 81 Richman, Martin 190 towers 118–19, 122–3 Robert Haskins Waters Engineers 59 trusses 79, 120–1, 152–5, 172–5, 182–5 Roman aqueduct, Segovia, Spain 59 vibration 74 roofs weight 74, 75 barrel vault 116–17 Young’s modulus 44, 46 concrete 61, 126–7, 140–3 Stevenson, Robert 92 isostatic ribs 6, 140–1 Stewart, Allan: Forth Rail Bridge, Queensferry, Scotland 21, rib vaulting 114–15 120–1 steel 79, 80, 140–3 strain 44–6 timber 76, 83 defined 40 truss-supported 79, 113, 126–7 and deformation 12, 44 see also canopies and failure 44 rubber (natural) 46 measuring 44, 45, 46 strain capacity 14, 40, 43, 44–6, 49 Saarinen, Eero: Jefferson National Expansion Monument stress ratio 44, 45 (“Gateway Arch”), St Louis, Missouri, USA 150–1 and tension 44, 45 Sadao, Shoji 136 types of 44, 45 The USA Pavilion, Montreal Expo, Canada (1967) 80, 139 stress 40–3 Sauvestre, Stephen 118 axial stress 40, 41, 59 206 bending stress 40, 41, 43, 49, 50–1, 58, 59, 60, 61 standard timber 49, 62 defined 40 strain capacity 46 direct stress 40, 42, 68 strength classes 49 and failure 40, 56, 74 stress capacity 10, 43, 46, 49 and material properties 12, 14, 40–3 structural assessment 76 in nature 10, 19 sustainability 76, 82 shear stress 40, 41, 42, 43, 45, 49, 61, 153 tensile capacity 49 strain ratio 44, 45 weight 76, 83 stress capacity 12, 14, 40–3, 46 Young’s modulus 46 torsional stress 42 see also glulam ultimate stress 40, 44, 46 titanium 46 yield (proof) stress 40, 42, 46, 47 Torroja, Eduardo: Zarzuela Hippodrome, Madrid, Spain 128–9 structures towers 71 bending moments 30, 43, 60, 140, 175 see also beams buttressing 20, 198–201 bending stress capacity 40, 41, 43, 50, 51, 58, 61, 92 exterior structures 71, 72 cable net structures 69, 103, 158–61 human 20, 21 categories 58–72 hyperboloid 122–3 cellular structures 61, 68 interior structures 71 concrete shell structures 61, 88, 94, 128–9, 132–5, 144–9, lattice 98, 118–19, 122–3 162 modeling 107 form active structures 59, 61, 62 spaceframe structures 124–5 glass structures 102, 166–71 stability 71, 98, 118, 198 gridshell structures 59, 69, 91, 122–3, 194–7 steel 118–19, 122–3 hyperbolic structures 91, 122–3, 132–3 structure 20, 21 load 24, 25 tubular frames 72, 156–7, 198–201 in nature 10–21, 88 see also pylons pneumatic structures 59, 138, 159, 162–3 trees 10, 11, 20, 126 see also timber section active structures 62 trusses spaceframe structures 60, 80, 102, 124–5, 136, 139 bending stress capacity 58, 60 spiral 12, 92, 199 in bridges 21, 60, 79, 120–1 spiral structures 12, 92, 199 and column systems 152–5 stability 19, 24, 57, 63–70, 96, 102, 152, 153 and compression 35 static equilibrium 24, 25, 28–9, 30, 35, 40, 41 and frames 60, 71, 72, 80 structural material assessments 74–6 method of sections technique 28, 30, 34–5 surface active structures 61 octet 124–5 tensile fabric structures 59, 69, 70, 138, 159 in roofs 79, 113, 126–7 vector active structures 60, 62 steel 79, 120–1, 152–5, 172–5, 182–5 see also arches; bridges; columns; domes; frames; shell and tension 35 structures; tensegrity structures; towers Vierendeel trusses 79, 126, 182, 183 struts 26, 41 warren 79, 182 suspension bridge, British Columbia, Canada 59 tungsten 46 sustainability issues 74, 75, 76, 82 Swiss Re Tower, London 72 University of Greenwich, London (student prototypes) 103 Sydney Harbour Bridge, Australia 80 University of Westminster, London (student prototypes) 91, 96–102 Taipei 101, Taiwan 71 Tedesko, Anton 94 Valenzuela, Dr. Mark 91 tensegrity structures 156–7 vaults compression/compressive elements 18, 156, 157 barrel vaulting 116–17 in nature 18, 20 brick 95 tension/tensile elements 18, 156 gridshell 91 tension/tensile elements load testing 92, 95 and arches 15 rib vaulting 114–15 and beams 30, 40, 41, 44, 81 see also domes and bending stress 40, 41, 43, 50 vibration 24, 57, 74, 75, 76 and external loads 21, 25, 26, 30 Viñoly, Rafael: Atlas Building, Wageningen, Netherlands and frames 59, 60, 61, 62, 64, 66 176–7 and internal forces 25, 26, 158 Viollet-le-Duc, Eugène 114–15 in nature 12, 14, 15, 16, 18 and strain 44, 45 Wachsmann, Konrad 112 surface tension 16 walls in tensegrity structures 18, 156, 157 as diaphragms 126, 158 tensile capacity 43, 49, 81 shear walls 66, 71 tensile fabric structures 59, 69, 70, 138, 159 for stability 68, 71 and trusses 35 Willis (formerly Sears) Tower, Chicago, USA 72, 198 timber Wilson, Dr. Arnold 94 beams 33, 49, 82–3 wind loads 63, 64, 68, 107, 108–9, 122, 124, 175 bending stress capacity 49 wind resistance 10, 93, 118, 121, 164, 194–5, 198 see also compressive capacity 43, 49 wind loads creep 49 deflection 76 Young’s modulus 36, 37, 44, 46, 55 elasticity 49 flexibility 76 frames 62, 76 grade 49 grain 43 gridshell structures 194–7 hardwood 10 imperfections 49 properties 43, 49, 76, 82–3 roofs 76, 83 serviceability 49 softwood 10, 46 207 Picture credits Pictures by Will McLean, Pete Silver, and Peter Evans, except 105 (1–4) Images courtesy of Prof. Robert Mark where indicated below: 108–9 Drawings by Akos Kovacs 13 (1) David Scarf/Science Photo Library 114–115 Private collection, London 13 (4) Carrier USS Abraham Lincoln (CVN72), U.S. Navy, 116 National Archives photo by Photographer’s Mate Airman Justin Blake 117 (2) National Railway Museum/Science and Society Picture 15 (2) Generated eggshell mesh using shell-type elements. Library (Based on a diagram from Comparative Analysis of the Static 117 (3) ©Toby/Fotolia and Dynamic Mechanical Eggshell Behaviour of a Chicken 119 (2) Popperfoto/Getty Images Egg by P. Coucke, G. Jacobs, and J. De Baerdemaeker, 119 (3) ©Paul M.R. Maeyaert Department of Agro-engineering and -economics, KU Leuven, 120 scotlandsimages.com/Crown Copyright 2008. The Belgium, and P. Sas, Department of Mechanical Engineering, National Archives of Scotland division PMA, KU Leuven, Belgium) 121 ©Louise McGilviray/Fotolia 15 (3) ©Dennis Kunkel Microscopy, Inc./Visuals Unlimited/ 123 (1–4) Wikimedia Commons Corbis Rights Managed 123 (5–6) Photographs by Vladimir Schukov 15 (4) ©Paul M.R. Maeyaert 125 (1) ©Bettmann/Corbis 15 (5) Courtesy MBM Arquitectes 125 (2) ©John Alexander Douglas Mucurdy/National 17 (2) Laurence King Publishing Geographic Society/Corbis 19 (1) ©Alexander Yakovlev/Fotolia 129 (2) Courtesy: CSIC IETcc 19 (2) ©Rick Rickman/NewSport/Corbis 129 (3) ©Bildarchiv Monheim GmbH/Alamy 20 (3) William Ruddock 133 (3) ©Cecil Handisyde-AA 20 (4) Image courtesy of Patrick Hughes, photography by 133 (4 & 6) Luis M. Castañeda John Timbers 133 (5) Jorge Ayala/www.ayarchitecture.com 59 (1) ©[apply pictures]/Alamy 135 (1–4 & 6–8) Courtesy of William Ruddock 59 (2) ©travelbild.com/Alamy 137 (1) US Patent 3,197,927 59 (3) ©Visions of America, LLC/Alamy 138 (3–4) Images courtesy of © Karl Hartig 59 (4) ©Tracey Whitefoot/Alamy 139 (5) Courtesy, The Estate of R. Buckminster Fuller 59 (5) ©Suzanne Bosman/Alamy 142–143 Images courtesy of Andrea Giodorno 59 (6) ©Jon Bower Canada/Alamy 151 (1) Daniel Schwen (Wikimedia Commons) 60 (1) ©Wiskerke/Alamy 151 (3) Image courtesy of Axel Kilian, Designexplorer 60 (2) ©VIEW Pictures Ltd/Alamy 153 (1) US Patent 4,059,937 60 (3) ©J.D. Fisher/Alamy 157 (1) © Kenneth Snelson 60 (4) ©Michael Snell/Alamy 163 (1–5) Images courtesy of Dante Bini, photography by Max 61 (1) ©imagebroker/Alamy Dupain 61 (2) ©VIEW Pictures Ltd/Alamy 164 ©Trajano Paiva/Alamy 61 (3) © Arcaid Images/Alamy 165 (3) ©Arcaid Images/Alamy 67 bottom right © PSL Images/Alamy 165 (4) ©MJ Photography/Alamy 70 (1) iStockphoto/Thinkstock 167 Frank Oudeman 70 (2) ©stockex/Alamy 168–171 (1–10) Images courtesy of Dewhurst Macfarlane 70 (3) Stockbyte/Thinkstock 172 Photograph by Richard Johnson, © Will Alsop, Alsop 71, 72 top, 72 top center iStockphoto/Thinkstock Architects, Archial Group 72 bottom center Comstock/Thinkstock 173 Photograph by Richard Johnson, © Will Alsop, Alsop 72 bottom Hemera/Thinkstock Architects, Archial Group 80 top iStockphoto/Thinkstock 174 © Will Alsop, Alsop Architects, Archial Group 80 center mambo6435/Shutterstock 175 (5–7) Images courtesy of Carruthers Wallace 80 center bottom ©David R. Frazier Photolibrary, Inc./Alamy 175 (8–12) © Will Alsop, Alsop Architects, Archial Group 80 bottom iStockphoto/Thinkstock 179–81 Images courtesy of Bertus Mulder 83 center ©Tim Cuff/Alamy 182–85 Images courtesy of Ensamble Studio 89 (1) photo courtesy of www.nooksncorners.com 188–89 Images courtesy of Junya Ishigami and Associates 89 (2) Holger Knauf—www.holgerknauf.de 191–93 Images courtesy of Price & Myers and M-Tec/WEC 90 (4) Courtesy Atelier Frei Otto Group 91 (5) Courtesy Heinz Isler 195 ©imagebroker/Alamy 92 RIBA (image no. 2845-23) 196 (3, 4 & 6) Images courtesy of Holzbau Amann 93 top ©Ian Cowe/Alamy 196 (5) Image courtesy of designtoproduction, Zürich 94 (3) Images courtesy of Dr. Arnold Wilson at the Brigham 197 (7) Image courtesy of designtoproduction, Zürich Young University Laboratories (TBC) 197 (8–11) Images courtesy of Holzbau Amann 95 (4) Images courtesy of MIT Masonry Research Group 200–201 © Skidmore, Owings & Merrill LLP (MRG): John Ochsendorf, Mallory Taub, Philippe Block, Lara Davis, Florence Guiraud Doughty, Scott Ferebee, Emily Lo, Sze Ngai Ting, Robin Willis, Masoud Akbarzadeh, Michael Cohen, Samantha Cohen, Samuel Kronick, and Fabiana Meacham Authors’ Jessica Brew acknowledgments Philip Cooper Liz Faber Samantha Hardingham Kate Heron Eva Jiricna Tim Macfarlane Bert and Freda McLean Robert Mark Bertus Mulder Christian Müller Nils D. Olssen William Ruddock Esther Silver 208