Earthquake Resistant Buildings

M.Y.H. Bangash

Earthquake ResistantBuildings

Dynamic Analyses, NumericalComputations, Codified Methods, CaseStudies and Examples

1 3

M.Y.H. BangashConsulting Engineer in AdvancedStructural Analysis

London, UK

ISBN 978-3-540-93817-0 e-ISBN 978-3-540-93818-7DOI 10.1007/978-3-540-93818-7Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2010920825

This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplicationof this publication or parts thereof is permitted only under the provisions of theGermanCopyright Lawof September 9, 1965, in its current version, and permission for use must always be obtained fromSpringer. Violations are liable to prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.

Cover design: deblik, Berlin

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

# 2011 M.Y.H. Bangash; London, UKPublished by: Springer-Verlag Berlin Heidelberg 2011

Preface

This book provides a general introduction to the topic of three-dimensional

analysis and design of buildings for resistance to the effects of earthquakes. It is

intended for a general readership, especially persons with an interest in the

design and construction of buildings under servere loadings.A major part of design for earthquake resistance involves the building

structure, which has a primary role in preventing serious damage or structural

collapse. Much of the material in this book examines building structures and,

specifically, their resistance to vertical and lateral forces or in combinations.

However, due to recent discovery of the vertical component of acceleration of

greater magnitude in the kobes’ earthquake the original concept of ‘‘lateral

force only’’ has changed. This book does advocate the contribution of this

disastrous component in the global analytical investigation.When the earthquake strikes, it shakes the whole building and its contents.

Full analysis for design layout and type of earthquakes, therefore, must include

considerations for the complete building construction, the building contents

and the building occupants.The work of designing for earthquake effects is formed by a steady stream of

studies, research, new technologies and the cumulative knowledge gained from

forensic studies of earthquake-damaged buildings. Design and construction

practices, regulating codes and professional standards continuously upgraded

due to the flow of this cumulative knowledge. Hence, any book on this subject

must regularly be updated. Since the effects are not the same, the earthquake

forces are always problematic.Over the years, earthquake has been the cause of great disasters in the form

of destruction of property and injury and loss of life to the population. The

unpredictability and sudden occurrence of earthquakes make them somewhat

mysterious, both to the general public and to professional building designers.

Until quite recently, design for earthquakes – if consciously considered at all –

was done with simplistic methods and a small database. Extensive study and

research and a great international effort and cooperation have vastly improved

design theories and procedures. Accordingly, most buildings in earthquake-

prone areas today are designed in considerable detail for seismic resistance.

v

Despite the best efforts of scientists and designers, most truly effective designmethods are those reinforced by experience. This experience, unfortunately,grown by leaps when a major earthquake occurs and strongly affects regions ofconsiderable development – notably urban areas. Observation of damagedbuildings by experts in forensic engineering adds immeasurably to our knowl-edge base. While extensive research studies are ongoing in many testing labora-tories, the biggest laboratory remains the real world and real earthquakes.

Design decisions that affect the seismic response of buildings range frombroad to highly specific ones.While much of this design workmay be performedby structural engineers, many decisions aremade by, or are strongly affected by,others. Building codes and industry standards establish restrictions on the useof procedures for analysis of structural behaviour and for the selection ofmaterials and basic systems for construction. Decisions about site development,building placement on sites, building forms and dimensions and the selection ofmaterials and details for construction are often made by so many others too.

On this respect it was necessary that the reader should look into codes ofpractice in certain countries prone to major earthquakes. Some codes includingthe Eurocode-8 are given together with numerical and analytical methods forcomparative studies. This approach enhances the design quality and createsconfidence in the designer on his/her work.

While ultimate collapse of the Building structure is a principal concern, thebuilding’s performance during an earthquake must be considered in many otherways as well. If the structure remains intact, but structural part of the buildingsustains critical damage, occupants are traumatized or injured, and it is infeasibleto restore the building for continued use; the design work may not be viewed assuccess.However, the necessity sometimes governs. Some countriesmay not havesophisticated tools and resources. Others must assist to provide them.

The work in this book is mostly analytical and hence should be accessible tothe broad range of people in the building design and construction fields. Thiscalls for some compromise since all are trained highly in some areas and less – ornot at all – in others. The readers should have general knowledge of buildingcodes, current construction technology, principal problems of planning build-ings and at least an introduction to design of simple structures for earthquake-prone buildings. Most of all, readers need some real motivation for learningabout making buildings safer during earthquakes. Many design examples andcase studies are included to make the book fully attractive to all and sundry.

Readers less prepared may wish to strengthen their backgrounds in order toget the most from the work in this book. The author gives a vast bibliography atthe end of this book and a list of references after each chapter so that the readercan carryout an in-depth study on a specific area missed out in detail. Thereader hopefully will understand the need for grappling with this complexsubject.

This book addresses the perplexing problem of how to maintain operabilityof equipment after a major earthquake. The programme is often more compli-cated than simple anchorage. Some critical types of equipment, for example,

vi Preface

are likely to fail operationally (false signalling of switches, etc.) even if adequatebase anchorage has been provided. It is the goal of this book to point out to thereader with a plan whereby equipment must be classified and subsequentlyqualified for the postulated seismic environment in a manner that best suitsthe individual piece of equipment. In some cases this qualification and analysiscan be accomplished only by sophisticated seismic testing programme, while atthe other end of the spectrum, equipment sometimes may be qualified simply byadequate architectural detailing. All too often, professional design teams andowners rely on an electric plug and gravity to keep a critical piece of equipmentin place during an earthquake and functional afterwards. Obviously, this is lessthan desirable situation. One part of the suggestion is devoted to the qualifica-tion procedures which include

� Testing� Analyses� Designer’s judgement� Prior experience� Design earthquakes� Seismic categories for equipment� Design specification procedures

The reader can easily be advised to refer to relevant codes such as Eurocode 8and its supplements and parts. This book does not go into details regarding theabove procedures but only concentrates on the analytical/design methodology.

The discussion of these topics leaves the designer with a complete course ofaction for qualifying all types of equipments, such as seismic devices to controlthe building structures during earthquakes. The author for this reason gives acomprehensive chapter on the subject.

One major measure to mitigate the earthquake hazards is to design and buildstructures through better engineering practices, so that these structures possessadequate earthquake-resistant capacity. Considerable research efforts havebeen carried out in the USA, Japan, China and other countries in the last fewdecades to advance earthquake engineering knowledge and design methods.This book summarizes the state-of-the-art knowledge and worldwide experi-ences, particularly those from China and the USA, and presents them system-atically in one volume for possible use by engineers, researchers, students, andother professionals in the field of earthquake engineering. Considering theactive research and rapid technological advances which have taken place inthis field, there has been a surprising shortage of suitable textbooks for seniorlevel or graduate level students. This book also attempts to help fill such a gap.

The book consists of 10 major parts: engineering seismology and earth-quake-resistant analyses and design. Special attention is placed on bridgingthe gap between these disciplines. For the convenience of the reader, funda-mentals of seismology, earthquake engineering and random processes, which,can be useful tools to describe the three-dimensional ground motions are givento assess the structural or soil response to them. Vast chapters are included.

Preface vii

This is followed by describing earthquake intensity, ground motions and itsdamaging effects. In the ensuing chapters concerning the earthquake-resistantdesign, both fundamental theories and new research problems and designstandards are introduced. In this book stochastic methods are introducedbecause of their potential to offer a new dimension in earthquake engineeringapplications. These two areas have been subjected to intensive research in recentyears and there is a potential in them to provide solutions to some specialproblems which might not be amenable to conventional approaches. Appen-dices are given for supporting analyses. Computer subroutines, which can beused with any known packages to suit the reader.

Although this book may appear to present a daunting amount of material, itis, nevertheless, just a toe in the door of the vast library of knowledge that exists.Readers may use this book to gain general awareness of the field or to launch amuch more exhaustive programme of study.

On design sides, many codified methods have been briefly mentioned. TheEurocode EC-8 and the American codes with examples have been highlighted.

The book will serve as a useful text for teachers preparing design syllabi forundergraduate and postgraduate courses. Each major section contains a fullexplanation which allows the book to be used by students and practicingengineers, particularly those facing formidable task of having to design/detailcomplicated building structures with unusual boundary conditions. Contrac-tors will also find this book useful in the preparation of construction drawings,and manufacturers will be interested in the guidance even in the text recordingcodified and newly developed methods and the manufacture of earthquakeresistant devices.

London, UK M.Y.H. Bangash

viii Preface

Acknowledgments

The author is indebted to many individuals, institutions, organizations and

research establishments mentioned in the text for helpful discussions and for

providing useful practical data and research materials.The author owes a special debt of gratitude to his family who, for the third

time, provided unwavering support.The author also acknowledges the following private communications:

Aerospace Daily (Aviation and Aerospace Research), 1156 15th Street NW,Washington, 20005, USA.

Azad Kashmir, Disaster Management Centre. Reports Jan. 2008–2009.Afghan Agency Press, 33 Oxford Street, London, UK.Agusta SpA, 21017 Cascina Costa di Samarate (VA), Italy.Ailsa Perth Shipbuilders Limited, Harbour Road, Troon, Ayrshire KA10

6DN, Scotland.Airbus Industrie, 1 Rond Point Maurice Bellonte, 31707 Blagnac Cedex,

France.Allison Gas Turbine, General Motors Corporation, Indianapolis, Indiana

46 206–0420, USA.AMX International, Aldwych House, Aldwych, London, WC2B 4JP, UK.Arizona State University, Tempe AZ, USA.AzadKashmir office for EarthquakeManagement Pakistan, 2009. Pakistan,

(Pukhtoon Khawa) N.W.F.P. Pakistan, Peshawar, Earthquake Division,2009, Pakistan

Bogazici, University, Turkey.Bremer Vulkan AG, Lindenstrasse 110, PO Box 750261, D-2820 Bremen 70,

Germany.British Library, Kingcross, London, UK.Catic, 5 Liang Guo Chang Road, East City District (PO Box 1671), Beijing,

China.Chantiers de l’Atlantique, Alsthom-30, Avenue Kleber, 75116 Paris, France.Chemical and Engineering News, 1155 16th Street NW, Washington DC

20036, USA.Chinese State Arsenals, 7A Yeutan Nanjie, Beijing, China.

ix

Conorzio Smin, 52, Villa Panama 00198, Rome, Italy.CITEFA, Zufratequ y Varela, 1603 Villa Martelli, Provincia de Buenos

Aires, Argentina.Daily Muslim, Abpara, Islamabad, Pakistan.Daily Telegraph, Peterborough Court, South Quay Plaza, Marshwall,

London E14, UK.Dassault-Breguet, 33 Rue de Professeur Victor Pauchet, 92420, Vaucresson,

France.Defense Nationale, 1 Place Joffre, 75700, Paris, France.Der Spiegel, 2000 Hamburg 11, Germany.Department of Engineering Sciences, University of California, San Diego,

CA, USA.Earthquake Hazard Prevention Institute, Wasada University, Shinju Ko-Ku,

Tokyo, JapanEarthquake Research Institute, University of Tokyo, JapanEvening Standard, Evening Standard Limited, 118 Fleet Street, London

EC4P 4DD, UK.Financial Times, Bracken House, 10 Cannon Street, London EC4P 4BY.Fokker, Corporate Centre, PO Box 12222, 1100 AE Amsterdam Zuidoost,

The Netherlands.Fukuyama University, Gakuen-Cho, Fukuyama, Hiroshima, JapanGeneral Dynamic Corporation, Pierre Laclede Centre, St Louis, Missouri

63105, USA (2003–2009).General Electric, Neumann Way, Evendale, Ohio 45215, USA.Graduate School of Engineering, Kyoto University, Kyoto, JapanGuardian, Guardian Newspapers Limited, 119 Farringdon Road, Londo

EC1R 3ER, UK.Hawker Siddeley Canada Limited, PO Box 6001, Toronto AMF, Ontario

L5P 1B3, Canada.Hindustan Aeronautics Limited, Indian Express Building, PO Box 5150,

Bangalore 560 017, India (Dr Ambedkar Veedhil).Howaldtswerke DeutscheWerft, PO Box 146309, D-2300Kiel 14, Germany.Imperial College Earthquake Engineering Centre, London, U.K. The Indian

institute of Technology, Bombay, India (2009).Independent, 40 City Road, London EC1Y 2DB, UK. (2007–2009)Information Aeronautiques et Spatiales, 6 Rue Galilee, 75116, Paris, France.Information Resources Annual, 4 Boulevard de 1’Empereur, B-1000, Brus-

sels, Belgium.Institute Fur Ange Nandte Mechanik, Techniche Universitat Braunschweig.

D-38106, Braunschweig, Germany (2009).Institutodi Energetica, Universita degdi studi Reggio Calibria, Reggio,

Calibria, ItalyInternational Aero-engines AG, 287Main Street, East Hartford, Connecticut

06108, USA.

x Acknowledgments

Israel Aircraft Industries Limited, Ben-Gurion International Airport, Israel70100.

IsraelMinistry of Defence, 8 David Elazar Street, Hakiryah 61909, Tel Aviv,Israel.

KAL (Korean Air), Aerospace Division, Marine Centre Building 18FL,118-2 Ga Namdaernun-Ro, Chung-ku, Seoul, South Korea.

Kangwon Industrial Company Limited, 6-2-KA Shinmoon-Ro, Chongro-ku,Seoul, South Korea.

Kawasaki Heavy Industries Limited, 1–18 Nakamachi-Dori, 2-Chome,Chuo-ku, Kobe, Japan.

Konoike Construction Co Limited, Osaka, JapanKorea Tacoma Marine Industries Limited, PO Box 339, Masan, Korea.Krauss-Maffei AG, Wehrtocknik GmbH Krauss-Maffei Strasse 2, 8000

Munich 50, Germany.Krupp Mak Maschinenbau GmbH, PO Box 9009, 2300 Kiel 17, Germany.Laboratory for Earthquake Engineering, National Technical University of

Athens, Athens, GreeceLimited, Quadrant House, The Quadrant, Sutton, Surrey SM2 5AS, UK.Lockheed Corporation, 4500 ParkGranada Boulevard, Calabasas, California

91399-0610, USA.Matra Defense, 37 Avenue Louis-Breguet BP1, 78146 Velizy-Villa Coublay

Cedex, France.Massachusetts Institute of Technology, USA (2003–2009).McDonnell Douglas Corporation, PO Box 516, St Louis, Missouri 63166,

USA.MitsubishiHeavy Industries Limited, 5-1Marunouchi, 2-Chome, Chiyoda-ku,

Tokyo 100, Japan.Muto Institute of Earthquake Engineering Tokyo, Japan (2001–2010).NASA, 600 Independence Avenue SW, Washington DC 20546, USA.Nederlandse Verenigde Scheepsbouw Bureaus, PO Box 16350, 2500 BJ, The

Hague, The Netherlands.Netherland Naval Industries Group, PO Box 16350, 2500 BJ, The Hague,

The Netherlands.New York Times, 229 West 43rd Street, New York, NY 10036, USA.Nuclear Engineering International, c/o Reed Business Publishing HouseObserver, Observer Limited, Chelsea Bridge House, Queenstown Road,

London SW8 4NN, UK.Offshore Engineer, Thomas Telford Limited, Thomas Telford House,

1 Heron Quay, London E14 9XF, UK.OTO Melara, Via Valdilocchi 15, 19100 La Spezia, Italy.Pakistan Aeronautical Complex, Kamra, District Attock, Punjab Province,

Pakistan.PlesseyMarine Limited,WilkinthroopHouse, Templecombe, Somerset BA8

ODH, UK.Princeton University U.S.A.

Acknowledgments xi

Promavia SA, Chaussee de Fleurs 181, 13-6200 Gosselies Aeroport,Belgium.

SAC (Shenyang Aircraft Company), PO Box 328, Shenyang, Liaoning,China. Short Brothers pic, PO Box 241, Airport Road, Belfast BT39DZ, Northern Ireland.

Seismological Society of America, U.S.A.Sikorsky, 6900 North Main Street, Stratford, Connecticut 06601-1381,

USA. Soloy Conversions Limited, 450 Pat Kennedy Way SW, Olympia,Washington 98502, USA.

Soltam Limited, PO Box 1371, Haifa, Israel.SRC Group of Companies, 63 Rue de Stalle, Brussels 1180, Belgium.State University of Newyork at Buffalo, U.S.A.Tamse, Avda, Rolon 1441/43, 2609 Boulgone sur Mer, Provincia de Buenos

Aires, Argentina.Technische Universitat Berlin, Sekr B7, D1000, Berlin 12, Germany.The American Society of Civil Engineers, U.S.A.The Institution of Civil Engineers, Great George Street, Westminster,

London SW1, UK.The Institution of Mechanical Engineers, 1 Bird Cage Walk, Westminster,

London SW1, UK.The National University of Athens, Greece.The World Conferences on Earthquake Engineering–Management

1960–2002. California Institute, California, U.S.A.Thomson-CSF, 122 Avenue du General Leclerc, 92105 Boulogne Billan-

court, France.Texas A&M university, U.S.A.Textron Lycoming, 550 Main Street, Stratford, Connecticut 06497, USA.Times Index,Research Publications, PO Box 45, Reading RGl 8HF, UK.Turbomeca, Bordes, 64320 Bizanos, France.Universita degdi studi di cantania, Italy.University of Perugia, Loc. Pentima Bassa, 21, Terni, ItalyUSSR Public Relations Offices, Ministry of Defence, Moscow, USSR.

xii Acknowledgments

Dedicated Acknowledgement

(a) Acknowledgement to Scholars in Earthquake Engineering. There are anumber of people who worked for life cannot be left alone. It is difficultto name all of them here. The authors heart goes out for them and theirwork. They richly deserve their place. The following are chosen for thededicated acknowledgement:

� Professor Thomas. A. Jaeger Bundesomstalt fur material prufung, Berlin,Germany

� Dr. Bruno A. Boley, Northwestern University, Illinois, U.S.A.� Dr. M. Watabe, Ibaraki, Japan� V.V. Bertera, University of California, U.S.A.� Professor H.B. Seed, Earthquake Engineering Center, University of

California, U.S.A.� Professor H. Shibata, University of Tokyo, Japan.� Professor J. Lysmer, Earthquake Engineering Center, University of

California, Berkeley, California U.S.A.� Professor R. Clough, University of California, U.S.A.� Professor H. Ambarasy, Impertial College, London, U.K.� Professor G.W. Housner, California Institute of Technology, U.S.A.� Dr. J. Blume, University of California, U.S.A.

(b) Acknowledgement Companies and Research Establishments in Earth-quake Engineering. Their help is enormous.

� Toda Construction Company Ltd, Tokyo, Japan� Tennessee Valley Authority, Tennessee, U.S.A.� Nuclear Regulatory Commission (NRG) Washingtons DC. U.S.A.� Lawrence Livermore Laboratory, Livermore, University of California,

U.S.A.� Saap 2000, University of California Computer Center, University of

California U.S.A.� The Architectural Institute of Japan, Tokyo, Japan

xiii

� Carnegie Institute of Washington, Washington D.C., U.S.A.� Institute de Ingeniera, UNAM, Mexico, U.S.A.� Ministry of Construction, Tokyo, Japan� Kyoto University Disaster Prevention Laboratory, Kyoto, Japan

xiv Dedicated Acknowledgement

Contents

1 Introduction to Earthquake with Explanatory Data . . . . . . . . . . . . . . . 11.1 Earthquake or Seismic Analysis and Design

Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Plate Tectonic and Inner Structure of Earth . . . . . . . . . . . . . . 11.3 Types of Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Seismograph And Seismicity . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Seismic Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Magnitude of the Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6.1 Seismic Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.7 The World Earthquake Countries and Codes of Practices . . . 111.8 Intensity Scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.8.1 Earthquake Intensity Scale . . . . . . . . . . . . . . . . . . . . . . 241.8.2 Intensity Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 251.8.3 Abnormal Intensity Region. . . . . . . . . . . . . . . . . . . . . . 311.8.4 Factors Controlling Intensity Distribution . . . . . . . . . . 31

1.9 Earthquake Intensity Attenuation . . . . . . . . . . . . . . . . . . . . . . 321.9.1 Epicentral Intensity and Magnitude . . . . . . . . . . . . . . . 32

1.10 Geotechnical Earthquake Engineering. . . . . . . . . . . . . . . . . . . 321.11 Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.11.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.11.2 Types of Damage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.12 Earthquake-Induced Settlement . . . . . . . . . . . . . . . . . . . . . . . . 341.13 Bearing Capacity Analyses for Earthquakes . . . . . . . . . . . . . . 351.14 Slope Stability Analysis for Earthquakes . . . . . . . . . . . . . . . . . 351.15 Energy Released in an Earthquake . . . . . . . . . . . . . . . . . . . . . 361.16 Earthquake Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371.17 Impedance Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401.18 Glossary of Earthquake/Seismology . . . . . . . . . . . . . . . . . . . . 411.19 Artificial Generation of Earthquake . . . . . . . . . . . . . . . . . . . . 451.20 Net Result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

xv

2 Existing Codes on Earthquake Design with and Without Seismic

Devices and Tabulated Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.1 Existing Codes on Earthquake Design. . . . . . . . . . . . . . . . . . . . 51

2.1.1 Algeria: RPA (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.1.2 Argentina : INPRES-CIRSOC 103 (1991) . . . . . . . . . . 532.1.3 Australia: AS11704 (1993). . . . . . . . . . . . . . . . . . . . . . . 572.1.4 China: TJ 11-78 and GBJ 11-89 . . . . . . . . . . . . . . . . . . 602.1.5 Europe: 1-1 (Oct 94); 1-2 (Oct 94); 1-3 (Feb 95);

Part 2 (Dec 94); Part 5 (Oct 94); Eurocode 8. . . . . . . . . 642.1.6 India and Pakistan: IS-1893 (1984) and PKS

395-Rev (1986). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.1.7 Iran: ICRD (1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772.1.8 Israel: IC-413 (1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.1.9 Italy: CNR-GNDT (1986) and Eurocode EC8

is Implemented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832.1.10 Japan: BLEO (1981) . . . . . . . . . . . . . . . . . . . . . . . . . . . 842.1.11 Mexico: UNAM (1983) M III (1988) . . . . . . . . . . . . . . 882.1.12 New Zealand: NZS 4203 (1992) and NZNSEE

(1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922.1.13 USA: UBC-91 (1991) and SEAOC (1990). . . . . . . . . . . 952.1.14 Codes Involving Seismic Devices and Isolation

Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

3 Basic Structural Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1433.1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1433.2 Structural Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

3.2.1 General Introduction to Basic Dynamics . . . . . . . . . . . . 1433.2.2 Single-Degree-of-Freedom Systems – Undamped

Free Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1443.2.3 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 1493.2.4 Multi-Degree-of-Freedom System. . . . . . . . . . . . . . . . . . 1523.2.5 Dynamic Response of Mode Superposition . . . . . . . . . . 159

3.3 Examples of Dynamic Analysis of Building Framesand Their Elements Under Various Loadingsand Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1623.3.1 Example 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1633.3.2 Example 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1653.3.3 Example 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1673.3.4 Example 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1693.3.5 Example 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1723.3.6 Example 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1793.3.7 Example 3.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1813.3.8 Example 3.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1823.3.9 Example 3.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

xvi Contents

3.3.10 Example 3.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1853.3.11 Example 3.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1903.3.12 Generalized Numerical Methods in Structural

Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

4 Earthquake Response Spectra With Coded Design Examples . . . . . . . 2074.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2074.2 Fourier Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.3 Combined Spectrum Sd-V-Sa . . . . . . . . . . . . . . . . . . . . . . . . . . . 2184.4 Construction of Response Spectrum . . . . . . . . . . . . . . . . . . . . . 2194.5 Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

4.5.1 Example 4.1 American Practice. . . . . . . . . . . . . . . . . . . . 2214.5.2 Example 4.2 American and Other Practices . . . . . . . . . . 2244.5.3 Example 4.3 Algeria and Argentina Practices . . . . . . . . . 2294.5.4 Example 4.4 American Practice. . . . . . . . . . . . . . . . . . . . 2364.5.5 Example 4.5 American Practice. . . . . . . . . . . . . . . . . . . . 2374.5.6 Example 4.6 American Practice. . . . . . . . . . . . . . . . . . . . 2424.5.7 Elastic Design Spectrum: Construction of Design

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2444.6 Earthquake Response of Inelastic Systems . . . . . . . . . . . . . . . . 252

4.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2524.6.2 De-amplification Factors . . . . . . . . . . . . . . . . . . . . . . . . 2544.6.3 Response Modification Factors . . . . . . . . . . . . . . . . . . . 2564.6.4 Energy Content and Spectra . . . . . . . . . . . . . . . . . . . . . . 2574.6.5 Example 4.7 American Practice. . . . . . . . . . . . . . . . . . . . 2594.6.6 Example 4.8 American Practice. . . . . . . . . . . . . . . . . . . . 2614.6.7 Example 4.9 European Practice. . . . . . . . . . . . . . . . . . . . 2714.6.8 Example 4.10 British Practice . . . . . . . . . . . . . . . . . . . . . 2814.6.9 Yield Strength and Deformation from the Response

Spectrum (American Practice). . . . . . . . . . . . . . . . . . . . . 2844.7 Equivalent Static Force Method Based on Eurocode-8. . . . . . . 286

4.7.1 General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2864.7.2 Evaluation of Lumped Masses to Various Floor

Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2864.7.3 Response Spectrum Method . . . . . . . . . . . . . . . . . . . . . . 2884.7.4 Example 4.12 Step-by-Step Design Analysis Based

on EC8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

5 Dynamic Finite Element Analysis of Structures . . . . . . . . . . . . . . . . . . 3055.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3055.2 Dynamic Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

5.2.1 Lumped Mass system . . . . . . . . . . . . . . . . . . . . . . . . . . . 3055.3 Solution of the Dynamic Equilibrium Equations . . . . . . . . . . . 306

5.3.1 Mode Superposition Method . . . . . . . . . . . . . . . . . . . . . 3075.4 Step-By-Step Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . 312

Contents xvii

5.4.1 Fundamental Equilibrium Equations . . . . . . . . . . . . . 3125.4.2 Supplementary Devices . . . . . . . . . . . . . . . . . . . . . . . . 313

5.5 Runge–Kutta Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3155.5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

5.6 Non-linear Response of Multi-Degrees-of-FreedomSystems: Incremental Method . . . . . . . . . . . . . . . . . . . . . . . . . 317

5.7 Summary of the Wilson-�Method. . . . . . . . . . . . . . . . . . . . . . 3205.8 Dynamic Finite Element Formulation with Base Isolation . . . 3225.9 Added Viscoelastic Dampers (VEDs) in Seismic Buildings . . . 323

5.9.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3235.9.2 Generalized Equation of Motion when Dampers

Are Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3245.9.3 System Dynamic Equation with Friction Dampers . . 324

5.10 Non-linear Control of Earthquake Buildings with Actuators . . 3275.10.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3275.10.2 Analysis Involving Actuators . . . . . . . . . . . . . . . . . . . 327

5.11 Spectrum Analysis with Finite Element . . . . . . . . . . . . . . . . . . 3325.11.1 Calculation by Quadratic Integration . . . . . . . . . . . . . 3345.11.2 Calculation by Cubic Integration . . . . . . . . . . . . . . . . 3345.11.3 Cubic Integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3345.11.4 Mode Frequency Analysis using Finite Element. . . . . 3355.11.5 Dynamic Analysis: Time-Domain Technique . . . . . . . 338

5.12 Sample Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3505.12.1 Plastic Potential of the Same Form as the Yield Surface. . . 3505.12.2 von Mises Yield Surface Associated with Isotropic

Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3515.12.3 Dynamic Local and Global Stability Analysis . . . . . . 360

5.13 Dynamic Analysis of Buildings in Three Dimensions . . . . . . . 3625.13.1 General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 3625.13.2 Finite Element Analysis of Framed Tubular

Buildings Under Static and Dynamic LoadInfluences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

5.14 Finite Element Modelling of Building Structures – Step byStep Formulations Incorporating All Previous Sections . . . . . 3655.14.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3655.14.2 Solid Isoparametric Element Representing Concrete . . 3665.14.3 The Shape Function . . . . . . . . . . . . . . . . . . . . . . . . . . 3685.14.4 Derivatives and the Jacobian Matrix . . . . . . . . . . . . . 3685.14.5 Determination of Strains . . . . . . . . . . . . . . . . . . . . . . . 3705.14.6 Determination of Stresses . . . . . . . . . . . . . . . . . . . . . . 3715.14.7 Load Vectors and Material Stiffness Matrix. . . . . . . . 3715.14.8 The Membrane Isoparametric Elements . . . . . . . . . . . 3755.14.9 Isoparametric Line Elements. . . . . . . . . . . . . . . . . . . . 3795.14.10 Element Types, Shape Functions, Derivatives,

Stiffness Matrices for Finite Element . . . . . . . . . . . . . 387

xviii Contents

5.15 Criteria for Convergence and Acceleration . . . . . . . . . . . . . . . 3935.15.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3985.15.2 Hallquist et al. Method . . . . . . . . . . . . . . . . . . . . . . . . 398

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

6 Geotechnical Earthquake Engineering and Soil–Structure

Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4056.1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4056.2 Concrete Structures – Seismic Criteria, Numerical

Modelling of Soil–Building Structure Interactionand Isolators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4066.2.1 Structural Design Requirements for Building

Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4066.2.2 Structure Framing Systems . . . . . . . . . . . . . . . . . . . . . 407

6.3 Combination of Load Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . 4136.4 Deflection and Drift Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4146.5 Equivalent Lateral Force Procedure . . . . . . . . . . . . . . . . . . . . . 415

6.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4156.5.2 Seismic Base Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4156.5.3 Period Determination . . . . . . . . . . . . . . . . . . . . . . . . . 4166.5.4 Vertical Distribution of Seismic Forces. . . . . . . . . . . . 417

6.6 Horizontal Shear Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 4186.6.1 Torsion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4186.6.2 Overturning (determined by all codes) . . . . . . . . . . . . 419

6.7 Drift Determination and P�� Effects. . . . . . . . . . . . . . . . . . . . 4196.7.1 Storey Drift Determination (determined by all codes) 4196.7.2 P�� Effects (determined according to all codes) . . . . 420

6.8 Modal Analysis Procedure: Codified Approach . . . . . . . . . . . . 4206.8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4206.8.2 Modal Base Shear as by Codified Methods . . . . . . . . 4216.8.3 Modal Forces, Deflection and Drifts . . . . . . . . . . . . . 4226.8.4 Soil–Concrete Structure Interaction Effects . . . . . . . . 423

6.9 Methods of Analysis Using Soil-Structure Interaction . . . . . . . 4266.9.1 General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 4266.9.2 Response-Spectrum Analysis. . . . . . . . . . . . . . . . . . . . 4266.9.3 Time-History Analysis. . . . . . . . . . . . . . . . . . . . . . . . . 4276.9.4 Characteristics of Interaction . . . . . . . . . . . . . . . . . . . 427

6.10 Site Response – A Critical Problem in Soil–StructureInteraction Analyses for Embedded Structures . . . . . . . . . . . . 4306.10.1 Vertical Earthquake Response and P�� Effect . . . . . 4306.10.2 P�� Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4306.10.3 Frequency Domain Analysis of an MDF System . . . . 4336.10.4 Some Non-linear Response Spectra . . . . . . . . . . . . . . 4346.10.5 Soil–Structure Interaction Numerical Technique . . . . 4356.10.6 Substructure Method in the Frequency Domain. . . . . 436

Contents xix

6.11 Mode Superposition Method – Numerical Modelling . . . . . . . 4386.12 Mass Moments of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

6.12.1 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4416.13 Modelling of Isolators with Soil–Structure Interaction . . . . . . 441

6.13.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4416.13.2 Isolation System Components . . . . . . . . . . . . . . . . . . . . 4436.13.3 Numerical Modelling of Equations of Motion

with Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4436.13.4 Displacement and Rotation of Isolation Buildings . . . . 444

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

7 Response of Controlled Buildings – Case Studies . . . . . . . . . . . . . . . . . 4557.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4557.2 Building With Controlled Devices . . . . . . . . . . . . . . . . . . . . . . . 457

7.2.1 Special Symbols with Controlled Devices . . . . . . . . . . . . 4597.2.2 Seismic Waveforms and Spectra . . . . . . . . . . . . . . . . . . . 4607.2.3 Maximum Acceleration and Magnification . . . . . . . . . . 4627.2.4 Three-Dimensional Simulation of the Seismic

Wave Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4627.3 Evaluation of Control Devices and the Response-Control

Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4627.3.1 Initial Statistical Investigation of Response-Controlled

Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4627.3.2 Permutations and Combinations. . . . . . . . . . . . . . . . . . . 469

7.4 Permutations and Combinations of Devices . . . . . . . . . . . . . . . 4727.5 Seismic Design of Tall Buildings in Japan – A

Comprehensive Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5237.5.1 General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5237.5.2 Resimulation Analysis of SMB Based on the Kobe

Earthquake Using Three-Dimensional Finite ElementAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

7.5.3 Data I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5297.5.4 Data II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

8 Seismic Criteria and Design Examples Based on American

Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5558.1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5558.2 Structural Design Requirements for Structures . . . . . . . . . . . . . 555

8.2.1 Introduction to the Design Basis. . . . . . . . . . . . . . . . . . . 5558.3 Drift Determination and P �� Effects. . . . . . . . . . . . . . . . . . . 556

8.3.1 Storey Drift Determination . . . . . . . . . . . . . . . . . . . . . . 5568.4 P �� Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5568.5 Modal Forces, Deflection and Drifts . . . . . . . . . . . . . . . . . . . . . 5578.6 Soil–Concrete Structure Interaction Effects. . . . . . . . . . . . . . . . 557

8.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

xx Contents

8.7 Equivalent Lateral Forces Procedure. . . . . . . . . . . . . . . . . . . . . 5578.7.1 Base Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5588.7.2 Effective Structural Period . . . . . . . . . . . . . . . . . . . . . . 559

9 Design of Structural Elements Based on Eurocode 8 . . . . . . . . . . . . . . 5659.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5659.2 Existing Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

9.2.1 Explanations Based on Clause 4.2.3 of EC8Regarding Structural Regularity. A Reference is Madeto Eurocode 8: Part 1 – Design of Structuresfor Earthquake Resistance . . . . . . . . . . . . . . . . . . . . . . . 567

9.2.2 Seismological Actions (Refer Clause 3.2 of EC8) . . . . . . 5679.3 Avoidance in the Design and Construction in Earthquake

Zones: Contributing Factors Responsible for CollapseConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

9.4 Superstructure and Structural Systems . . . . . . . . . . . . . . . . . . . 5699.4.1 Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5699.4.2 Structural Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

9.5 Response Spectra Based on EU Code 8 . . . . . . . . . . . . . . . . . . . 5729.5.1 The Behaviour Factor q. . . . . . . . . . . . . . . . . . . . . . . . . . 574

9.6 Seismic Design Philosophy of Building FramesUsing Eurocode 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5759.6.1 General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 575

9.7 Load Combinations and Strength Verification . . . . . . . . . . . . . 5789.7.1 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5789.7.2 Capacity Design Effects: Method Stated

in the Eurocode-8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5789.7.3 Design Provisions for Earthquake Resistance

of Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5809.7.4 Second-Order Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5819.7.5 Resistance Verification of Concrete Sections . . . . . . . . . 581

9.8 Analysis and Design of a Steel Portal Frame under SeismicLoads. A Reference is Made to Fig. 9.6. . . . . . . . . . . . . . . . . . . 5969.8.1 Data on Loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5969.8.2 Bending Moments, Vertical and Horizontal

Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5979.8.3 Ultimate Design Moments and Shears (Moment-

Capacity Design) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597

10 Earthquake–Induced Collision, Pounding and Pushover

of Adjacent Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60110.1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60110.2 Analytical Formulation for the Pushover . . . . . . . . . . . . . . . . 60410.3 Linear Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

10.3.1 Post-contact Conditions . . . . . . . . . . . . . . . . . . . . . . . 609

Contents xxi

10.4 Calculation of Building Separation Distance . . . . . . . . . . . . . . 61210.4.1 Minimum Separation Distance Required

to Avoid Structural Pounding . . . . . . . . . . . . . . . . . . . 61210.5 Data for Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61410.6 Discussion on Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

Additional Extensive Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

Appendix A Subroutines for Program ISOPAR and Program F-Bang . . 645

Appendix B KOBE (Japan) Earthquake Versus Kashmir (Pakistan)

Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705

xxii Contents

Generalised Notation

In advanced analysis and numerical modelling certain welknown notations areused universaly. These together with the ones given in the text are to be adopted.Where ever additional notations are necessary, especially in the codes for thedesign of structural elements, they should be defined clearly in this area.

Based on specific analyses, the analyst has the options to substitute anynotations which are clearly defined in the analytical or computational work.

A Constant

A Projected area, hardening parameter

A0 Initial surface area

AST Surface area of the enclosure

AV Vent area�A Normalized vent area

a Radius of the gas sphere

a0 Loaded length, initial radius of gas sphere

B Burden

[B] Geometric compliance matrix

BG Blasting gelatine

b Spaces between charges

b1 Distance between two rows of charges

CD,Cd Drag coefficient or other coefficients

C0d Discharge coefficient

Cf Charge size factor, correction factor

Cl A coefficient which prevents moving rocks from an instant velocity

[Cin] Damping coefficient matrix

Cp Specific heat capacity at constant pressure

Cr Reflection coefficient

Cv Specific heat capacity at constant volume

ca; cl; c ; c� Coefficients for modes

xxiii

D Depth of floater, diameter[D] Material compliance matrixDa Maximum aggregate sizeDi Diameter of iceDp Penetration depth of an infinitely thick slabDIF Dynamic increase factord Depth, diameter

d0 Depth of bomb from ground surfaceE Young’s modulusEb Young’s modulus of the base material�Eer Maximum energy input occurring at resonanceEic Young’s modulus of iceEK Energy lossEna Energy at ambient conditionsEne Specific energy of explosivesER Energy releaseEt Tangent moduluse Base of natural logarithme Coefficient of restitution, efficiency factor

F Resisting force, reinforcement coefficientFad The added mass forceF1(t) ImpactF(t) Impulse/impactFs Average fragment size shape factorf Functionf Frequency (natural or fundamental), correction factorfa Static design stress of reinforcementfc Characteristic compressive stressf 0c Static ultimate compressive strength of concrete at 28 daysf *ci Coupling factorfd Transmission factorf 0dc Dynamic ultimate compressive strength of concretefds Dynamic design stress of reinforcementfdu Dynamic ultimate stress of reinforcementfdyn Dynamic yield stress of reinforcementf *TR Transitional factorfu Static ultimate stress of reinforcementfy Static yield stress of reinforcement

G Elastic shear modulusGa DecelerationGf Energy release rate

xxiv Generalised Notation

Gm, Gs Moduli of elasticity in shear and mass half spaceg Acceleration due to gravity

H HeightHs Significant wave heightHE High explosionHP Horsepowerh Height, depth, thickness

I Second moment of area, identification factor[I] Identity matrixI1 The first invariant of the stress tensorip Injection/extraction of the fissure

J1, J2, J3 First, second and third invariants of the stress deviator tensorJF, J Jacobian

K Vent coefficient, explosion rate constant, elastic bulk modulus[Kc] Element stiffness matrixKp Probability coefficientsKs Stiffness coefficient at impactKTOT Composite stiffness matrixKW Reduction coefficient of the chargeK� Correction factorKE Kinetic energykcr Size reduction factorkr Heat capacity ratiokt Torsional spring constant

L LengthL0 Wave numberLi Length of the weapon in contactln, loge Natural logarithmlx Projected distance in x direction

M Mach number[M] Mass matrixM 0 Coefficient for the first part of the equation for a forced vibration*MA Fragment distribution parameterMp Ultimate or plastic moment or mass of particlem Mass

N Nose-shaped factorNc Nitrocelluloid

Generalised Notation xxv

Nf Number of fragments

N 0Coefficient for the second part of the equation for a forcedvibration

NG Nitroglycerinen Attenuation coefficientPi Interior pressure incrementPm Peak pressurePu Ultimate capacityPE Potential energyPETN Pentaerythrite tetra-nitratep Explosion pressurepa Atmospheric pressurepd Drag loadpdf Peak diffraction pressurepgh Gaugehole pressure in rocks

ppa

Pressure due to gas explosion on the interface of the gases and themedium

pr Reflected pressurepro Reflected overpressurep 0s Standard overpressure for reference explosionpso OverpressurePstag Stagnation pressure

Qsp Explosive specific heat (TNT)qdo Dynamic pressure

RDistance of the charge weight gas constant, Reynolds number,Thickness ratio

R0 Radius of the shock front{R(t)} Residual load vectorRT Soil resistanceRvd Cavity radius for a spherical chargeRw, rs Radius of the cavity of the charger Radiusro; r ; r� Factors for translation, rocking and torsion

Si Slip at node iSij Deviatoric stressSL Loss factorS��(f) Spectral density of surface elevations –i!t or distance or wave steepness, width, slope of the semi-log

T Temperature, period, restoring torqueTa Ambient temperatureTd Delayed time

xxvi Generalised Notation

T 0’i Ice sheet thicknessTps Post shock temperature[T 00] Transformation matrixTR Transmissibilityt TimetA Arrival timetav Average timetc Thickness of the metaltd Duration timetexp Expansion timeti Ice thicknesstp Thickness to prevent penetration, perforationtsc Scabbing thickness, scaling timetsp Spalling thickness

U Shock front velocityu Particle velocity

V Volume, velocityV0 Velocity factorVRn Velocity at the end of the nth layer�b Fragment velocity or normalized burning velocity�bt Velocity affected by temperature�c Ultimate shear stress permitted on an unreinforced web�con Initial velocity of concentrated charges�f Maximum post-failure fragment velocity�in, �0 Initial velocity�1 Limiting velocity�m Maximum mass velocity for explosion�p Perforation velocity�pz Propagation velocities of longitudinal waves�RZ Propagation velocities of Rayleigh waves�r Residual velocity of primary fragment after perforation or

pE/p

�s

Velocity of sound in air or striking velocity of primary fragmentor missile

�so Blast-generated velocity at initial conditions�su Velocity of the upper layer�sz Propagation velocities of transverse waves�szs Propagation velocity of the explosion� 0xs Initial velocity of shock waves in water�z Phase velocity�zp Velocity of the charge

Generalised Notation xxvii

W Charge weightW1/3, Y Weapon yieldWt Weight of the target materialwa Maximum weightwf Forcing frequencyX Amplitude of displacement_X Amplitude of velocity€X Amplitude of accelerationXf Fetch in metresX(x) Amplitude of the wave at a distance xX0 Amplitude of the wave at a source of explosionx Distance, displacement, dissipation factorx Relative distance_x Velocity in dynamic analysis€x0 Acceleration in dynamic analysis{x}* Displacement vectorxcr Crushed lengthxi Translationxn Amplitude after n cyclesxp Penetration depthxr Total length

Z Depth of the point on the structure

� Cone angle of ice, constant for the charge�a; �l; � Spring constants�B Factor for mode shapes�0 Angle of projection of a missile, constant�� Constant� Constant for the charge, angle of reflected shock�� Constant Damping factor, viscosity parameterf !f/! Particle displacements� Pile top displacementij Kronecker deltam,

0m,

00m Element displacement

st Static deflectiont Time increment� Strain_" Strain rate�d Delayed elastic strain� Surface profile� Deflection angle

xxviii Generalised Notation

�g Average crack propagation angle� A constant of proportionality f Jet fluid velocity� Poisson’s ratio�a Mass density of stone�w Mass density of water� Stress�c Crushing strength�cu Ultimate compressive stress�f Ice flexural strength(�nn)

c Interface normal stress(�nt)

c Interface shear stress�pi Peak stress�t Uniaxial tensile strength�o Crack shear strength� Phase difference Circumference of projectile! Circular frequencyl, m, n, p,

q, r, s, t Direction cosinesX,Y,Z;

x, y, z Cartesian coordinates(�, �, �) Local coordinates

Generalised Notation xxix

Conversion Tables

Weight

1 g = 0.0353 oz 1 oz = 28.35 g

1 kg = 2.205 lbs 1 lb = 0.4536 kg

1 kg = 0.197 cwt 1 cwt = 50.8 kg

1 tonne = 0.9842 long ton 1 long ton = 1.016 tonne

1 tonne = 1.1023 short ton 1 short ton = 0.907 tonne

1 tonne = 1000 kg 1 stone = 6.35 kg

Length

1 cm = 0.394 in 1 in = 2.54 cm = 25.4 mm

1m = 3.281 ft 1 ft = 0.3048m

1m = 1.094 yd 1 yd = 0.9144m

1 km = 0.621 mile 1 mile = 1.609 km

1 km = 0.54 nautical mile 1 nautical mile = 1.852 km

Area

1 cm2 = 0.155 in2 1 in2 = 6.4516 cm2

1 dm2 = 0.1076 ft2 1 ft2 = 9.29 dm2

1m2 = 1.196 yd2 1 yd2 = 0.8361m2

1 km2 = 0.386 sq mile 1 sq mile = 2.59 km2

1 ha = 2.47 acres 1 acre = 0.405 ha

Volume

1 cm3 = 0.061 in3 1 in3 = 16.387 cm3

1 dm3 = 0.0353 ft3 1 ft3 = 28.317 dm3

1m3 = 1.309 yd3 1 yd3 = 0.764m3

1m3 = 35.4 ft3 1 ft3 = 0.0283m3

1 litre = 0.220 Imp gallon 1 Imp gallon = 4.546 litres

1000 cm3 = 0.220 Imp gallon 1 US gallon = 3.782 litres

1 litre = 0.264 US gallon

xxxi

Density

1 kg/m3= 0.6242 lb/ft3 1 lb/ft3= 16.02 kg/m3

Force and pressure

1 ton = 9964 N1 lbf/ft = 14.59 N/m1 lbf/ft2 = 47.88 N/m2

1 lbf in = 0.113Nm1 psi = 1lbf/in2 = 6895 N/m2 = 6.895 kN/m2

1 kgf/cm2 = 98070 N/m2

1 bar = 14.5 psi = 105 N/m2

1 mbar = 0.0001 N/mm2

1 kip = 1000 lb

Temperature, energy, power

18C = 5/9(8F � 32) 1 J = 1 milli-Newton0 K = �273.168C 1 HP = 745.7 watts08R = �459.698F 1 W = 1 J/s

1 BTU = 1055 JNotation

lb = pound weight 8R = RankineLbf = pound force 8F = Fahrenheitin = inch oz = ouncecm = centimetre cwt = one hundred weightm = metre g = gramkm = kilometre kg = kilogramd = deci yd = yardft = foot HP = horsepowerha = hectare W = watts = second N = Newton8C = centigrade = Celsius J = JouleK = Kelvin

xxxii Conversion Tables