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Mitchell Gohnert - Shell Structures: Theory and Application

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Mitchell Gohnert Shell Structures: Theory and Application
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This text provides a complete and thorough derivation of the mathematical theory of shell structures. Many books on shells only give the key equations or snippets of theory, skipping all of the mathematical steps required to solve for the key equations. This is understandable, because of the mathematical complexity of shell structures. Thus, the reader must just accept the design equations blindly, without achieving a complete understanding of shell theory. This book, therefore, fills this gap by providing a complete picture of shell theory. Class tested over three university post-graduate courses and one public course on shell structures, the book is mathematically intensive, but it written in an accessible style ideal for students of engineering mechanics in civil and mechanical engineers concentrations, as well as practicing structural engineers looking for a reference on shells.

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Book cover of Shell Structures Mitchell Gohnert Shell Structures Theory - photo 1
Book cover of Shell Structures
Mitchell Gohnert
Shell Structures
Theory and Application
Logo of the publisher Mitchell Gohnert University of the Witwatersrand - photo 2
Logo of the publisher
Mitchell Gohnert
University of the Witwatersrand, Johannsesburg, South Africa
ISBN 978-3-030-84806-4 e-ISBN 978-3-030-84807-1
https://doi.org/10.1007/978-3-030-84807-1
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my wife and children, whom I adore.
Foreword
From our birth and through lifes expectations, we grow and develop into the person we become.

The path we follow through life, with its many turns, mountains to climb and crossroads to choose, eventually leads us to our place today, and our final destination. Professor Mitchell Gohnert, my former student at Brigham Young University, has experienced a lifelong desire to be a structural engineer, with a special interest in the design and application of shell structures. This book is the result of his lifelong quest. Just as we are influenced by the teaching and training of others, we also influence others by the teaching and training we give throughout our lives. Mitch has gained much from the many people he has been involved with, and conversely, he has influenced, assisted and guided many through his mentorship and his expertise in the field of shell structures. Good ideas, called inspiration by some, come to each of us during our life.

When acted upon with persistence and determination, these ideas result in great accomplishments that benefit others.

Arnold Wilson
Contents
The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
M. Gohnert Shell Structures https://doi.org/10.1007/978-3-030-84807-1_1
1. Introduction
Mitchell Gohnert
(1)
University of the Witwatersrand, Johannsesburg, South Africa
Abstract
Shells, and in particular domes, have a symbolic meaning in many of the worlds civilizations. Some of the most iconic structures incorporate domes as their architectural center piece. Interestingly, most of these structures are religious gathering places, shrines, or temples and are found in cathedrals, stupas, mausoleums, and mosques.

The symbolism of domes is of ancient origin and is associated with deity and the celestial expanse of the heavens. The home of the ancients appeared to be under a heavenly dome, and the circle of the dome, a never ending line, is a symbol of eternity. This symbolism continues to this day, but has evolved over the centuries to include other closely associated meanings. Alexander the Great, and early Persian rulers, adopted domes in their architecture to symbolize their divine authority and power (Smith, The dome: study in the history of ideas. Princeton University Press, New Jersey, 1950; Hiscock, The symbol at your door. s.l.:SP Birkhauser Verlag Basel, 2010).

This practice has endured to modern times, and domes are seen in some of the most famed architectures, such as the US Capitol Building, the Vatican, and many other religious and governmental buildings around the world. The intent is to portray strength, influence, legitimacy of power, and piety. For these reasons, religious and centers of government will always include domes in their architecture.

Keywords
Symbolism Pantheon Hagia Sophia Nature Biological structures Haiti National Palace Membrane stresses St. Peters cathedral Smithfield market Chicken egg Sagrada Familia Chain St. Pauls cathedral
Shells, and in particular domes, have a symbolic meaning in many of the worlds civilizations.

Some of the most iconic structures incorporate domes as their architectural center piece. Interestingly, most of these structures are religious gathering places, shrines, or temples and are found in cathedrals, stupas, mausoleums, and mosques. The symbolism of domes is of ancient origin and is associated with deity and the celestial expanse of the heavens. The home of the ancients appeared to be under a heavenly dome, and the circle of the dome, a never ending line, is a symbol of eternity. This symbolism continues to this day, but has evolved over the centuries to include other closely associated meanings. Alexander the Great, and early Persian rulers, adopted domes in their architecture to symbolize their divine authority and power (Smith ).

This practice has endured to modern times, and domes are seen in some of the most famed architectures, such as the US Capitol Building, the Vatican, and many other religious and governmental buildings around the world. The intent is to portray strength, influence, legitimacy of power, and piety. For these reasons, religious and centers of government will always include domes in their architecture.

The endurance of this symbolism is fitting and appropriate, considering the seemingly mystical strength and the eternal nature of these structures. If we go back in history more than a thousand years, remnants of antiquity usually amount to nothing more than a pile of rubble, with the exception of a few columns standing here and there. However, of the structures that have survived, the vast majority are domes and arches.

The Pantheon in Rome (126 AD) (Fig. ) are prime examples. Both of these structures were built in seismic active regions and have been subjected to several major earthquakes; yet they stand today and are in remarkably good condition.

Fig 11 Antoine Desgodetzs 1682 rendition of the Pantheon Claude-Antoine - photo 3
Fig. 1.1 Antoine Desgodetzs 1682 rendition of the Pantheon (Claude-Antoine Jombert)
Fig 12 Dome of Hagia Sophia Wikimedia Commons Robert Raderschatt Despite - photo 4
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