Geotechnical, Geological and Earthquake Engineering


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Geotechnical, Geological and Earthquake Engineering
Volume 45
Series Editor Atilla Ansal, School of Engineering, Özyegˇin University, Istanbul, Turkey
Editorial Advisory Board Julian Bommer, Imperial College London, U.K. Jonathan D. Bray, University of California, Berkeley, U.S.A. Kyriazis Pitilakis, Aristotle University of Thessaloniki, Greece Susumu Yasuda, Tokyo Denki University, Japan

More information about this series at http://www.springer.com/series/6011

Gian Paolo Cimellaro • Sebastiano Marasco
Introduction to Dynamics of Structures and Earthquake Engineering
123

Gian Paolo Cimellaro Department of Structural, Geotechnical and Building Engineering (DISEG) Politecnico di Torino Torino, Italy

Sebastiano Marasco Department of Structural, Geotechnical and Building Engineering (DISEG) Politecnico di Torino Torino, Italy

Additional material to this book can be downloaded from http://extras.springer.com.

ISSN 1573-6059

ISSN 1872-4671 (electronic)

Geotechnical, Geological and Earthquake Engineering

ISBN 978-3-319-72540-6

ISBN 978-3-319-72541-3 (eBook)

https://doi.org/10.1007/978-3-319-72541-3

Library of Congress Control Number: 2017963746

© Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved 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, express 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.

Printed on acid-free paper

This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

I would like to dedicate this book to my grandfather, master of life and culture.

Foreword

It is a great pleasure to present Introduction to Dynamics of Structures and Earthquake Engineering by Gian Paolo Cimellaro and Sebastiano Marasco. The book locates itself between elementary books and books for advanced graduate studies. The book is divided into three parts: “Part I – Dynamics of Structures” introduces the main concepts of dynamics of structures. “Part II – Introduction to Earthquake Engineering” introduces the basic concepts of seismology, seismic hazard analysis, and different analysis methods. “Part III – Seismic Design of Buildings” describes how to model structures in seismic zones and the basic concepts of capacity design as well as new innovative techniques for the design of new and retrofit of existing buildings. The typical coverage of “Dynamics of Structures” starts properly with an introduction of the fundamental concepts of structural dynamics, with emphasis on the application of energy methods, analysis on the frequency domain, and signal processing, which are essentials necessary for the study of earthquake engineering. Part II introduces the main concepts of seismology, and probabilistic seismic hazard analysis, and provides a chapter dedicated to earthquake prediction methods. Part III introduces the basic concepts of capacity design within the context of Italian seismic design standards and highlights new and innovative techniques to improve structural performance, such as base isolation, tuned mass dampers, and supplemental viscous dampers. An entire chapter is also dedicated to the modeling of infill walls and the seismic behavior of masonry structures. The book presents also illustrative examples that help in understanding the subject and the link between theory and finite element programs, such as SAP2000. The information presented in this book can be used not only by students but also by those engineers engaged in the seismic design and retrofit of buildings who want to improve their understanding on the subject.

Berkeley, USA September 2017

Prof. Stephen Mahin

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Preface
The aim of this new book is to provide an elementary, but comprehensive, textbook which can be adopted for the courses of earthquake engineering at both the School of Engineering and the School of Architecture of the Politecnico di Torino, providing in an easy and accessible way the latest updates in the field. No previous knowledge of structural dynamics is assumed, making this book suitable for the reader that is learning the subject for the first time. However, the following background is required: • Static analysis of structures including statistically indeterminate structures and
matrix formulation • Rigid body dynamics • Mathematics: linear algebra and ordinary and partial differential equation
With respect to other classical books on dynamics of structures, this book emphasizes the application of energy methods and the analysis in the frequency domain with the corresponding visualization in the Gauss-Argant plan. Emphasis is also given to the applications of numerical methods for the solution of the equation of motion and to the ground motion selection to be used in time history analysis of structures which are more frequently used in current practice due to the increasing computational power of computers in the last decade.
The book is organized in three main parts: I. “Dynamics of Structures” II. “Introduction to Earthquake Engineering” III. “Seismic Design of Buildings”
Part I introduces the main concepts of dynamics of structures. Part II introduces the basic concepts of seismology, the seismic hazard analysis, and the different analysis methods. Part III describes how to model structures in a seismic zone and the basic concepts of capacity design (Chap. 15) as well as the new innovative techniques for the retrofit of new and existing buildings, such as passive energy dissipating systems (Chap. 17), tuned mass dampers (Chap. 18), and base isolation (Chap. 19). Chapter 20 focuses on the seismic behavior of masonry structures,
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Preface

while Chap. 21 provides a brief introduction to a structural analysis program called SAP2000. An appendix has also been included with some basic concepts of probability.
Several figures have been carefully designed and executed to be pedagogically effective. Many of them involve the use of computer simulations. Most of the references have been omitted in the book to avoid distracting the reader; however, a selected list of publications has been added at the end of each book chapter for further reading.

Torino, Italy July, 2017

Gian Paolo Cimellaro

Acknowledgments
This book has been written during a year of sabbatical leave that I spent at the University of California, Berkeley. It is the result of the research experience with my students and of the years that I have taught in the course of seismic engineering at the Politecnico di Torino. I am grateful to several present and former students who helped in the revision of the book such as my current Ph.D. student, Sebastiano Marasco, who is the coauthor of this book and is one of the developers of the computer software OpenSignal which is included in the book. He has also generated most of the numerical results which appear in the figures. Bridget Bassi, a student from MIT who was a visiting scholar at the Politecnico di Torino, helped with the revision of the English language of the script. Students Alessandro Cardoni, Ali Zamani Noori, Omar Kammouh, Glen Dervishaj, Erfan Sheikhi, Gerardo Leo, Marzia Bianco, Tommaso Romanazzi, Chiara Lesbo, and Sumaia Shek Yussuf Abdirashid assisted in editing and preparing the LaTeX document of the book.
I also wish to express my deepest appreciation to Prof. Andrei M. Reinhorn, Prof. T.T. Soong, and Prof. Steve Mahin for the influence they have had and still have on my professional growth.
We did our best to avoid any errors or misprints in this first edition of the book. Nevertheless, we would like to invite instructors, students, and professional engineers to contact me ([email protected]) if you identified any errors or if you have suggestions for improvements or need clarifications.
Gian Paolo Cimellaro
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Contents
Part I Dynamics of Structures 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Idealization of the Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6.1 Free Vibrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6.2 External Excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 SDOF Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1 Linear SDOF Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Free Vibrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Response to Harmonic Excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.1 Undamped Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.2 Viscously Damped Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Response to an Impulsive Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4 Response to a Periodic Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5 Earthquake Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6 Transmissibility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.7 Nonlinear System Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3 Methods of Solution of the Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.1 Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2 Duhamel’s Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
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