The Geometry of Equilibrium
James Clerk Maxwell and 21st-Century Structural Mechanics
Published on 22. May 2025
Book
Hardback
322 pages
978-1-009-39761-2 (ISBN)
Description
James Clerk Maxwell is one of the giants of scientific thought, and whilst his groundbreaking contributions to electromagnetism and statistical physics are well known, his profound insights into the theory of structures are appreciated less widely. Maxwell's approach was deeply geometrical, and this richly illustrated book reveals his astute perception of the remarkable dualities that exist between the form of a structure and the forces it can carry, with understandings that will surprise contemporary readers. Early chapters introduce the background in which Maxwell was working, followed by contributions by leading researchers describing the latest applications of these ideas. Subsequent chapters introduce the many subtopics that this work embraces. The book ends with Maxwell's original papers on structural mechanics, each annotated to highlight and explain the ideas therein. This is a wonderful resource for mathematicians, scientists, engineers, and designers to enter this rich and underexplored aspect of the genius of Maxwell.
Reviews / Votes
'Remarkable homage to the amazing creativity of James Clerk Maxwell. Three portraits accompanied Einstein from Germany into Princeton: Newton, Faraday, and Maxwell. But when asked if he stood on the shoulders of Newton, he replied 'No, on the shoulders of Maxwell'. Much has been written about Maxwell's creativity rooted in physical analogy. This is an erudite example of consequences of Maxwell's geometric thinking.' Julio M. Ottino, R.R. McCormick Institute and Walter P. Murphy Professor, Engineering and Applied Science, Northwestern University and author of The Nexus: The New Convergence or Art, Technology, and Science 'Engineers are largely ignorant of Maxwell's geometric methods applied to structural theory, and geometers are equally unaware of the application of their discipline to the design of structures. This book is an exciting attempt to remedy this and will interest engineers and mathematicians for its elegance and practical application.' Chris J. K. Williams, Chalmers University of Technology 'This rediscovery of James Clerk Maxwell by renowned expert opens a world of graphic statics, shell design and lightweight building for structural engineers. Maxwell's achievements turn out to be very modern because they help minimise the use of resources and, therefore, can lead to truly sustainable structures. What makes this book special is that the original papers of Maxwell are included and made readable through detailed explanations. A great effort by the authors for the benefit of the reader.' Mike Schlaich, Technische Universitaet BerlinMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 260 mm
Width: 208 mm
Thickness: 22 mm
Weight
920 gr
ISBN-13
978-1-009-39761-2 (9781009397612)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
William F. Baker is Consulting Partner at Skidmore, Owings and Merrill. He was the Structural Engineer for the world's tallest man-made structure (the Burj Khalifa in Dubai). He has received awards including the ASCE Outstanding Projects and Leaders Lifetime Award for Design and the Gold Medal of the Institution of Structural Engineers. He holds honorary doctorates from University of Stuttgart, Heriot-Watt University, Illinois Institute of Technology and University of Missouri. Allan McRobie is Professor of Structural Engineering at the University of Cambridge. He previously authored 'The Seduction of Curves' (2017) on the mathematics of curved geometry.
Content
List of Contributors; Preface; Editorial note; Part I. Maxwell and Structural Mechanics: 1. James Clerk Maxwell and structural mechanics William Baker and John Ochsendorf; 2. The importance of Maxwell's writings for 21st-century structural mechanics William Baker, Petia Tzokova, Juney Lee and Allan McRobie; 3. Geometric rigidity theory Robert Connelly, Simon Guest, Bernd Schulze and Walter Whiteley; 4. Maxwell's relevance to modern research in materials Heinrich Jaeger, Sidney Nagel and Vincenzo Vitelli; 5. Isotropic and architectural geometry Cameron Millar and Helmut Pottmann; 6. A brief introduction to mid-19th-century projective geometry and topology Marina Konstantatou and William Baker; Part II. Concepts from Maxwell's Articles on Structural Mechanics: 7. Plane reciprocal diagrams Corentin Fivet, Allan McRobie and William Baker; 8. Rules on counting, mechanisms and states of self-stress Allan McRobie and Marina Konstantatou; 9. The unit load method and the Maxwell reciprocal theorem Petia Tzokova, William Baker and Allan McRobie; 10. Maxwell's load path theorem William Baker and Petia Tzokova; 11. Projections of polyhedra Marina Konstantatou, William Baker and Allan McRobie; 12. Legendre transforms and polarities Allan McRobie and Marina Konstantatou; 13. Rankine reciprocal diagrams in three dimensions Masoud Akbarzadeh, Tom Van Mele, Juney Lee, Marton Hablicsek and Philippe Block; 14. Vector-based form and force diagrams in three dimensions Pierluigi D'Acunto and Patrick Ole Ohlbrock; 15. The two methods of representing stress in a three-dimensional body Toby Mitchell; 16. On the equilibrium of stress in a solid body Alessandro Beghini and Toby Mitchell; Part III. Annotated Original Articles by Maxwell on Structural Mechanics: note about this re-edition of Maxwell's papers; 1864a. On reciprocal figures and diagrams of forces; 1864b. On the calculation of the equilibrium and stiffness of; 1867. On the application of the theory of reciprocal polar figures to the construction of diagrams of forces; 1868. On reciprocal diagrams in space, and their relation to Airy's function of stress; 1870a. On reciprocal figures, frames, and diagrams of forces; 1870b. Communication: On reciprocal figures, frames, and diagrams of forces; 1876. On Bow's method of drawing diagrams in graphical statics, with illustrations from Peaucellier's linkage; References; Index.