Shell Structures for Architecture

338 Pages·2014·36.57 MB·English

Shell Structures for Architecture

Bringing together experts from research and practice, Shell Structures for Architecture: Form Finding and
Optimization presents contemporary design methods for shell and gridshell structures, covering form-finding
and structural optimization techniques. It introduces architecture and engineering practitioners and students to
structural shells and provides computational techniques to develop complex curved structural surfaces, in the
form of mathematics, computer algorithms, and design case studies.

�� Part I introduces the topic of shells, tracing the ancient relationship between structural form and forces, the
basics of shell behaviour, and the evolution of form-finding and structural optimization techniques.
�� Part II familiarizes the reader with form-finding techniques to explore expressive structural geometries,
covering the force density method, thrust network analysis, dynamic relaxation and particle-spring systems.
�� Part III focuses on shell shape and topology optimization, and provides a deeper understanding of gradient-
based methods and meta-heuristic techniques.
�� Part IV contains precedent studies of realised shells and gridshells describing their innovative design and
construction methods.

Sigrid Adriaenssens is a structural engineer and Assistant Professor at the Department of Civil and
Environmental Engineering at Princeton University, USA, where she directs the Form Finding Lab. She holds
a PhD in lightweight structures from the University of Bath, adapting the method of dynamic relaxation to
strained gridshells. She worked as a project engineer for Jane Wernick Associates, London, and Ney + Partners,
Brussels, on projects such as the Dutch National Maritime Museum in Amsterdam. At Princeton, she co-curated
the exhibition ‘German Shells: Efficiency in Form’ which examined a number of landmark German shell projects.

Philippe Block is a structural engineer and architect and Assistant Professor at the Institute of Technology in
Architecture, ETH Zurich, Switzerland, where he directs the BLOCK Research Group, and is founding partner
of structural engineering consultancy Ochsendorf, DeJong & Block LLC. He studied at the VUB, Belgium,
and MIT, USA, where he obtained his PhD. He has received the Hangai Prize and Tsuboi Award from the
International Association of Shells and Spatial Structures (IASS) as well as the Edoardo Benvenuto Prize. He
developed thrust network analysis for the analysis of historic vaulted masonry and design of new funicular shells.

Diederik Veenendaal is a civil engineer and a research assistant at the BLOCK Research Group, ETH Zurich,
Switzerland. He received his Masters from TU Delft, Netherlands and started his career at Witteveen+Bos
engineering consultants, working on groundfreezing analysis for the downtown stations of the Amsterdam
North/South subway line and the structural design for the largest tensioned membrane roof in the Netherlands,
the ice skating arena De Scheg. His current research involves the comparison of existing form-finding methods
and development of new ones for flexibly formed shells and other structural systems.

Chris Williams is a structural engineer and a Senior Lecturer at the University of Bath, UK. He specializes
in computational geometry and structural mechanics, in particular for lightweight structures and tall buildings,
and his work has been applied by architects and engineers, including Foster + Partners, Rogers Stirk Harbour
+ Partners and Buro Happold. He worked at Ove Arup and Partners, where he was responsible for structural
analysis of the Mannheim Multihalle. Since then, he has worked on such projects as the British Museum Great
Court roof, Weald & Downland Museum gridshell, and the Savill Gardens gridshell.

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Shell Structures
for Architecture

Form Finding and Optimization

Edited by Sigrid Adriaenssens, Philippe Block,
Diederik Veenendaal and Chris Williams

First published 2014
by Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

and by Routledge
711 Third Avenue, New York, NY 10017

Routledge is an imprint of the Taylor & Francis Group, an informa business

© 2014 selection and editorial material, Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal and
Chris Williams; individual chapters, the contributors

The right of the editors to be identified as the authors of the editorial material, and of the authors for
their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright,
Designs and Patents Act 1988.

All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by
any electronic, mechanical, or other means, now known or hereafter invented, including photocopying
and recording, or in any information storage or retrieval system, without permission in writing from the
publishers.

Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.

Every effort has been made to contact and acknowledge copyright owners. If any material has been
included without permission, the publishers offer their apologies. The publishers would be pleased to
have any errors or omissions brought to their attention so that corrections may be published at later
printing.

British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication Data
Shell structures for architecture : form finding and optimization / [compiled by] Sigrid Adriaenssens,
Philippe Block, Diederik Veenendaal, and Chris Williams.
pages cm
Includes bibliographical references and index.
1. Shells (Engineering) 2. Structural optimization. 3. Architecture. 4. Shapes. I. Adriaenssens, Sigrid,
1973- II. Block, Philippe. III. Veenendaal, Diederik. IV. Williams, Chris (Chris J. K.)
TA660.S5S484 2014
624.1'7762--dc23
2013028638

ISBN: 978-0-415-84059-0 (hbk)
ISBN: 978-0-415-84060-6 (pbk)
ISBN: 978-1-315-84927-0 (ebk)

Typeset in Adobe Caslon by Fakenham Prepress Solutions, Fakenham, Norfolk NR21 8NN

Illustrations edited by Madeleine Kindermann and Diederik Veenendaal.

The editor(s), author(s) and publisher of this book have used their best efforts in preparing the material in this book. These efforts include
the development, research, and testing of the theories and computer methods to determine their effectiveness. The editor(s), author(s) and
publisher make no warranty of any kind, expressed or implied, with regard to these methods explained, or the documentation contained
in this book. The editor(s), author(s) and publisher shall not be liable in any event for any damages, including incidental or consequential
damages, lost profits, or otherwise in connection with or arising out of the furnishing, performance, or use of any text and the methods
explained in this book.

Contents

Acknowledgements
vii

Forewords

On architects and engineers
viii
Jörg Schlaich

Sharing the same spirit
xii
Shigeru Ban

Introduction
1

Part I Shells for architecture
5

1 Exploring shell forms
7
John Ochsendorf and Philippe Block

2 Shaping forces
15
Laurent Ney and Sigrid Adriaenssens

3 What is a shell?
21
Chris Williams

4 Physical modelling and form finding
33
Bill Addis

5 Computational form finding and optimization
45
Kai-Uwe Bletzinger and Ekkehard Ramm

Part II Form finding
57

6 Force density method: design of a timber shell
59
Klaus Linkwitz

7 Thrust network analysis: design of a cut-stone masonry vault
71
Philippe Block, Lorenz Lachauer and Matthias Rippmann

8 Dynamic relaxation: design of a strained timber gridshell
89
Sigrid Adriaenssens, Mike Barnes, Richard Harris and Chris Williams

9 Particle-spring systems: design of a cantilevering concrete shell
103
Shajay Bhooshan, Diederik Veenendaal and Philippe Block

10 Comparison of form-finding methods
115
Diederik Veenendaal and Philippe Block

11 Steering of form
131
Axel Kilian

VI CONTENTS

Part III Structural optimization
141

12 Nonlinear force density method: constraints on force and geometry
143
Klaus Linkwitz and Diederik Veenendaal

13 Best-fit thrust network analysis: rationalization of freeform meshes
157
Tom Van Mele, Daniele Panozzo, Olga Sorkine-Hornung and Philippe Block

14 Discrete topology optimization: connectivity for gridshells
171
James N. Richardson, Sigrid Adriaenssens, Rajan Filomeno Coelho and Philippe Bouillard

15 Multi-criteria gridshell optimization: structural lattices on freeform surfaces
181
Peter Winslow

16 Eigenshells: structural patterns on modal forms
195
Panagiotis Michalatos and Sawako Kaijima

17 Homogenization method: distribution of material densities
211
Irmgard Lochner-Aldinger and Axel Schumacher

18 Computational morphogenesis: design of freeform surfaces
225
Alberto Pugnale, Tomás Méndez Echenagucia and Mario Sassone

Part IV Precedents
237

19 The Multihalle and the British Museum: a comparison of two gridshells
239
Chris Williams

20 Félix Candela and Heinz Isler: a comparison of two structural artists
247
Maria E. Moreyra Garlock and David P. Billington

21 Structural design of free-curved RC shells: an overview of built works
259
Mutsuro Sasaki

Conclusion

The congeniality of architecture and engineering – the future potential and relevance of shell
structures in architecture
271
Patrik Schumacher

Appendices

Appendix A: The finite element method in a nutshell
274
Chris Williams

Appendix B: Differential geometry and shell theory
281
Chris Williams

Appendix C: Genetic algorithms for structural design
290
Rajan Filomeno Coelho, Tomás Méndez Echenagucia, Alberto Pugnale and James N. Richardson

Appendix D: Subdivision surfaces
295
Paul Shepherd

Bibliography
299
List of contributors
304
List of credits
309
List of projects
311
Index

317

Acknowledgements

The editors would like to express their gratitude to the
following people and institutions. Without their help
it would not have been possible to realize this book in
its current form.
First of all, we are grateful to our independent
reviewers, Jack Bakker, Daniel Piker and Samar Malek,
for their helpful comments during the final revisions
of the manuscript. Specific parts of the book were also
proofread, for which we would like to acknowledge
Hannah Bands, Victor Charpentier, Allison Halpern,
Matthew Horner, Alex Jordan, Lorenz Lachauer, Luca
Nagy, Renato Perucchio, Daniel Reynolds, Landolf
Rhode-Barbarigos, Edward Segal, Matthew Streeter,
Peter Szerzo and Mariam Wahed.
Copyright permissions for specific figures were
obtained with the help of Gianni Birindelli, Claudia
Ernst, Ines Groschupp, Lothar Gründig, Helmut
Hornik, Toni Kotnik, Gabriela Metzger, Matthias
Rippmann and Hans-Jörg Schek. We thank Rafael
Astudillo Pastor, René Motro, Sergio Pellegrino
and John Abel of the International Association of
Shell and Spatial Structures (IASS) for granting
copyright permission for the use of several publica-
tions (Bletzinger, 2011; Ramm, 2004), which were
partially reproduced in Chapter 5.
Several people assisted in the editorial process,
whom we would like to thank: Masoud Akbarzadeh for
his help in draughting the first manuscript; Madeleine
Kindermann, Lucas Uhlmann and Ramon Weber
for creating and adapting illustrations; Yuki Otsubo,
Ryuichi Watanabe and Meghan Krupka for translating
the chapter submitted by Mutsuro Sasaki; Shajay
Bhooshan, Yoshiyuki Hiraiwa, Monika Jocher, Guy
Nordenson, Junko Sakuta and Katrien Vandermarliere
for supporting our correspondence and communi-
cation with particular authors; and Astrid Smitham for
providing editorial assistance during the first months

of the book project. We wish to acknowledge the
supportive team at Routledge Architecture, Taylor &
Francis: Francesca Ford, commissioning editor; Laura
Williamson and Emma Gadsden, senior editorial
assistants for architecture books; Alanna Donaldson,
senior production editor; Janice Baiton, copy-editor;
and Christine James, proofreader.
The matter of whether or not Antoni Gaudí used
hanging models to design the Sagrada Família was
settled with the help of Rainer Graefe, Santiago
Huerta and Joseph Tomlow, who independently
confirmed that this hypothesis is unsubstantiated and
unlikely.
We are especially indebted to the authors for
their excellent contributions, and their patience
during the editorial process: Bill Addis, Shigeru
Ban, Mike Barnes, Shajay Bhooshan, David P.
Billington, Kai-Uwe Bletzinger, Philippe Bouillard,
Rajan Filomeno Coelho, Maria E. Moreyra Garlock,
Richard Harris, Sawako Kaijima, Axel Kilian, Lorenz
Lachauer,
Klaus
Linkwitz,
Irmgard
Lochner-
Aldinger, Tomás Méndez Echenagucia, Panagiotis
Michalatos, Laurent Ney, John Ochsendorf, Daniele
Panozzo, Alberto Pugnale, Ekkehard Ramm, James
N. Richardson, Matthias Rippmann, Mutsuro Sasaki,
Mario Sassone, Jörg Schlaich, Axel Schumacher,
Patrik Schumacher, Paul Shepherd, Olga Sorkine-
Hornung, Tom Van Mele and Peter Winslow. We
would also thank their respective companies and
institutions for allowing them the time to contribute
to our publication and providing environments in
which they were able to develop their invaluable
knowledge and expertise.
Finally, we would like to thank our friends and
families for supporting us during the writing and
editing of this book, and in particular Felix, Hannah,
Julia, Madeleine, Paul, Pieter and Regine.

FOREWORD
On architects and engineers

Jörg Schlaich

There is still a widespread misunderstanding concerning
the role of architects and structural engineers: it is
said that architects are the designers of a building
from concept to detail, whereas the engineers (only)
care for its stability. In fact, it is its function which
clearly attributes a building to either an architect or
an engineer only, or to both: to an architect only if
it is multifunctional in a social context – typically a
family house where no engineer is needed – and to an
engineer only if it serves a singular structural purpose
– typically built infrastructure such as a bridge where
no architect is needed. A high-rise building typically
needs both, an architect and an engineer.
The more the form of a building or structure
develops from its flow of forces, the more it is under
the responsibility of the engineer.
Especially due to the fact that most infrastructure,
such as towers, power plants, long-span roofs and
bridges, is large and long-lasting, a responsible
engineer will seek the advice of an architect or a
landscape designer when deciding on the material or
the scale of their bridge or sports hall in an urban or
natural environment.

It is only culture that can convert our built
environment into civilization.

Shells play a special, singular role for engineers. Their
shape directly derives from their flow of forces, and
defines their load-bearing behaviour and lightness,
saving material by creating local employment, their
social aspect. This is especially true for thin concrete
shells with their characteristic curvatures: single
curvature (cylindrical and conical), synclastic (dome-
like), anticlastic (saddle-like) or free (experimental).

If well formed, there are no bending but membrane
forces only (axial compression and tension) in a
shell, permitting its thickness to be around 80mm
for reinforced or prestressed concrete, even down
to 12mm for fibre reinforced concrete (Fig. 0.1).
Though these concrete shells initially do not leave
much space for an architect (or even for the fantasy
of an engineer), it is fortunately not unusual that the
two collaborate fruitfully or that an engineer himself
has the courage and imagination to go beyond strict
logic.
So Pier Luigi Nervi’s Palazzetto dello Sport in Rome
would have fulfilled its purpose at considerably lower
cost with a tensile ring on vertical supports instead of
the inclined Y-shaped columns as built, but it would
have looked like a boring and ugly tank (Fig. 0.2). Only
a creative engineer could have made such a proposal
as built!
In case of the large hypar roof for the Hamburg
Alster-Schwimmhalle, the architect insisted that the
edge beams should be free cantilevering beyond the
facade. This caused vivid discussions, because according
to the classical shell literature a hypar shell cannot
transfer shear forces from edge beams but needs direct
support as evident from the wonderful Candela shells
(Fig. 0.3).
But the architect insisted and thus made us find a
revolutionary though very simple solution by super-
imposing the classical saddle surface for the surface
loads with the straight line generators’ surface for
edge loads (Fig. 0.4). The result was a perfect structure
thanks to the insisting architect.
During the last decades concrete shells lost more
ground to: 1) cable nets; 2) textile membranes; and
3) steel grids. In terms of their load bearing, these

FOREWORD: ON ARCHITECTS AND ENGINEERS IX

Figure 0.1 Bundesgartenschau Pavilion, with a 12mm fibre
reinforced concrete shell, Stuttgart, 1977

Figure 0.2 Palazzetto dello Sport by Pier Luigi Nervi, Rome,
1958

Figure 0.3 Hypar shell with direct edge beam supports for the
Church of San José Obrero by Félix Candela, Monterey, 1959

can also be considered as shells. Let us discuss one
example for each of them.

Cable nets

In 1967, the international competition for the sport
fields of the 1972 Olympic Games in Munich was won
by architects Behnisch+Partners from Stuttgart, even
though they hardly fulfilled the requirements. In fact,

they instead brought in an idea which was absolutely
convincing, to bring together under one continuous and
floating roof all sports facilities: the stadium, the sport
hall, the swimming hall, and all transitions connecting
them (Fig. 0.5). This is exactly what we engineers
expect from our architect if structure plays a significant
role: an idea, a concept, a proposal, but leaving the
structural solution to us. Together with Frei Otto and
Fritz Auer from Behnisch+Partners, we developed a

X JÖRG SCHLAICH

prestressed cable-net structure with 75cm quadran-
gular mesh-width, adaptable to any shape, subdivided
by edge cables, supported by masts, held down by
anchors and, finally, covered with Plexiglas. This huge
but nevertheless light and floating roof has been very
well accepted and is still very popular, thanks to an ideal
cooperation between architects and engineers, each of
them playing their role in a useful manner.

Steel gridshells

The courtyard of the Museum of Hamburg History,
L-shaped in plan, was to be covered with a glass roof,
as light and transparent as possible. The architect
Volkwin Marg expressed with his sketch his wishes,
his ideas which stimulated our adequate structural
solution: a quadrangular mesh or grid, 1.2/1.2m from
60mm × 40mm steel members, diagonally stiffened by
thin, prestressed cables (Fig. 0.6). By change of angles,
the grid can easily adapt to a smooth doubly curved
transition between the two cylindrical shells, which
themselves are stiffened by radial spokes (Fig. 0.6).
Thus, the fear of the client that his historic building
would suffer from the roof could be relieved.

Figure 0.4 The cantilevering hypar of the Alster-
Schwimmhalle, Hamburg, 1967

Figure 0.5 The cable-net structure of the Munich Olympic
Roofs, 1972 (from left to right: Heinz Isler, Fritz Auer, Frei
Otto, Jörg Schlaich, Fritz Leonhardt, Rudolf Bergermann and
Knut Gabriel)

FOREWORD: ON ARCHITECTS AND ENGINEERS XI

Textile membranes

As we know from our clothes, we can produce doubly
curved surfaces from plane textile with the help of
a cutting pattern. If prestressed (by reducing the
cutting patterns), they behave under loads as an ideal
membrane shell and can even permit convertible roofs,

such as those for the Wolfgang Meyer Sports Centre
Hamburg-Stellingen (Fig. 0.7).
In a fruitful cooperation of architect and engineer
neither of them will impose their opinion because it
is only the result that counts! To build in untouched
nature can only be justified by creating a responsible
building culture.

Figure 0.6 Sketched and completed steel gridshell for the Museum of Hamburg History, 1989

Figure 0.7 Roof for the ice skating rink of the Wolfgang Meyer Sports Centre Hamburg-Stellingen, Hamburg, 1994

FOREWORD
Sharing the same spirit

Shigeru Ban

Shell structures are but one of many different, inter-
esting structural systems. If a gridshell structure
happens to be suitable for a project, I use it, but
otherwise I design another appropriate system.
An architect shouldn’t concentrate on one type of
structure, and should take notice of all possible struc-
tural systems. Without an understanding of structures,
we cannot design a building. If you would have some

preference, it would be very difficult to adjust to
different programmes.
Frei Otto is a notable exception. He has his own
specialities: cable-net structures, membrane struc-
tures and lightweight structures. He does not design
everything, yet he’s also an architect. When I got the
commission for the Japan Pavilion at the 2000 Expo
in Hannover (Fig. 0.8), I immediately contacted him,
and he agreed to collaborate with me. This had been
a dream ever since I was a student. He does not like
to make complicated connections, he always strives
for minimum effort, minimum labour, minimum

materials, and so on; ideals I really share with him.
Like me, Frei Otto is not a form-making architect,
meaning that we always design according to a combi-
nation of structural logics, architectural constraints
and the programmes contained within the structure.
That’s why our collaboration went very well. We share
the same spirit.
If I design just a shell, I always try to look for the
most appropriate, most structurally efficient shape
to reduce bending moments and the size of the

Figure 0.8 Japan Pavilion at Expo 2000, Hannover

Figure 0.9 Centre Pompidou, Metz, 2010

FOREWORD: SHARING THE SAME SPIRIT XIII

members. However, I might not always have total
freedom to design the most minimal shape for the
material, because the shape of the shell is also defined
by other constraints. For the Centre Pompidou in
Metz (Fig. 0.9), a museum, we needed to have large,
column-free spans for the galleries underneath. As a
result, it was designed as a large, suspended surface:
part of it is in tension, some part in compression. At
first sight, the Haesley Nine Bridges golf clubhouse
has a similar system (Fig. 0.10). But, because we could
have a repetition of the supports, it developed into a
set of compressive arches, creating the characteristic
quality of the internal space. So, the shapes came from
the programme.
The structural engineer Hermann Blumer worked
on both of these projects, and was a key contributor to
the design of the Centre Pompidou. After he joined
our team, he went back to my original design and

solved all the technical problems. Nowadays, for any
timber structure, in any country, I work with him. I
just send him the design and he solves all the technical
issues. He immediately understands what I want to
do: the collaboration between us is really perfect. I
choose particular engineers for particular projects. As
an engineering student, you have to develop your own
interests and understand your own abilities and limita-
tions. Study under the guidance of a good professor,
because an engineer always moves into a certain type
of structure as a speciality. This is not a bad thing,
but merely an observation. Some engineers are an
exception and are capable of designing anything, like
Jörg Schlaich, who is also good at shell structures. But,
as I said, to me it is important that we can share the
same spirit, the same priorities. Even if someone is a
genius engineer, if we cannot share the same priorities,
it doesn’t work out.

Figure 0.10 Haesley Nine Bridges golf clubhouse, Jeju Island, South Korea, 2010

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