POLITECNICO DI TORINO
Fundamentals of Dynamic of Structures and Earthquake Engineering Gian Paolo Cimellaro - Sebastiano Marasco
Universitas Studiorum
© 2015, Universitas Studiorum S.r.l. - Casa Editrice via Sottoriva, 9 46100 Mantova (MN) P. IVA 02346110204 tel. 0376 1810639 http://www.universitas-studiorum.it Prima edizione 2015 Finito di stampare nel settembre 2015 ISBN 978-88-99459-10-9
Table of Contents PART 1 DYNAMICS OF STRUCTURES 1. INTRODUCTION 1.1. Idealization of the Structures 1.2. Degrees of Freedom 1.3. Stiffness 1.4. Inertia 1.5. Damping 1.6. Equations of Motion
9 11 12 14 16 17 20
2. SDOF SYSTEMS 2.1. Free Vibrations 2.2. Response to Harmonic Excitations 2.3. System Response to an Impulsive Excitation 2.4. System Response to a Periodic Excitation 2.5. Nonlinear System Response 2.6. Earthquake Response of Linear Systems 2.7. Transmission Force at the Base of Elastic Systems Subjected to an Harmonic Excitation
23 23 32 48 51 52 53 54
3. METHODS OF SOLUTION OF THE EQUATIONS OF MOTION 3.1. Analytical Method 3.2. Duhamel’s Integral 3.3. Fourier Series Solution 3.4. Numerical Methods
57 57 62 64 67
4. ENERGY DISSIPATION 4.1. Damping Energy 4.2. Plastic Energy
91 92 93
5. MDOF SYSTEMS 5.1. Discretization 5.2. Shear Type and Bending Type Frames 5.3. Mass, Stiffness and Damping Matrix 5.4. Reduction of DOFs 5.5. Modal Analysis for Free Vibration Response 5.6. Solution of Free Vibration for Undamped Elastic Systems 5.7. Solution of Free Vibration for Damped Elastic Systems 5.8. Response to Harmonic Excitation 5.9. Earthquake Elastic Response
99 99 99 100 110 112 121 127 132 141
6. 3D MDOF MULTISTORY BUILDINGS
150
7. DAMPING ON STRUCTURES
158
8. DISTRIBUTED MASS AND ELASTICITY SYSTEMS 8.1. Vibrational Modes Analysis 8.2. Vibrational Modes Analysis of Forced Systems
161 162 164
9. GENERALIZED SDOF SYSTEM 9.1. Lagrangian Approach 9.2. Approximated Solution of Generalized Systems
166 166 167
PART 2 INTRODUCTION TO EARTHQUAKE ENGINEERING 10. BASIC CONCEPTS OF SEISMOLOGY 10.1. Earthquake Genesis 10.2. Seismological Parameters 10.3. Waves Propagation 10.4. Attenuation Relationship
177 177 184 191 196
11. EARTHQUAKE PREDICTION 11.1. General Aspects 11.2. Prediction Methods 11.3. Earthquake Prediction and Time-Dependent Seismic Hazard Scenarios 11.4. Notable Predictions
198 198 199 203 206
12. GROUND MOTION PARAMETERS 12.1. Peak Parameters 12.2. Frequency and Energetic Content 12.3. Duration 12.4. Other Parameters
212 212 212 220 222
13. ELASTIC RESPONSE SPECTRA
223
14. SEISMIC HAZARD 14.1. Deterministic Approach (DSHA) 14.2. Probabilistic Approach (PSHA)
225 225 229
PART 3 SEISMIC DESIGN OF BUILDING 15. ITALIAN SEISMIC RULES 15.1. Brief History of Seismic Italian Standards 15.2. General Approach in NTC08 And EC8
235 235 236
16. SEISMIC INPUT 16.1. Response Spectra 16.2. Use of Acceleration Histories
240 240 249
17. METHODS OF ANALYSIS 17.1. Linear Dynamic Analysis 17.2. Linear Static Analysis 17.3. Nonlinear Dynamic Analysis 17.4. Nonlinear Static Analysis
257 259 259 261 262
PART 4 OPENSIGNAL 18. OPENSIGNAL 18.1. Brief State of Art and Introduction to the Software 18.2. System Architecture 18.3. Sources of Strong Motion Records 18.4. Signal Processing and Filtering 18.5. Response Spectra Analysis 18.6. Earthquake Records Selection Criteria 18.7. Soil Response Analysis 18.8. Case Study
269 269 270 271 271 272 275 277 280
PART 5 SHAKING TABLE 19. SHAKING TABLE 19.1. Historical Notes 19.2. Shaking Table in Italy 19.3. Shaking Table at the Politecnico di Torino 19.4. Modalities of Seismic Simulation 19.5. DOFs of a Shaking Table 19.6. Fields of Application of a Shaking Table
288 288 294 298 299 300 301
References
303
G.P. Cimellaro - S. Marasco
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Fundamentals of Dynamic of Structures and Earthquake Engineering Acknowledgment Acknowledgment This book was prepared during a year of sabbatical leave that I spent at the University of California at Berkeley. This book has been influenced by my own research experience in collaboration with my students and by the years I have Aknowledgment spent Instructor in the Course Seismic Engineering at the This as book was prepared during of a year of sabbatical leave thatPolitecnico I spent at di theTorino. University of California at Berkeley. This book has been influenced by my own research experience in collaboration with my students and by the years I have This book has been written during a year of sabbatical leave that I spent at the of California at Berkeley. It is I spent am grateful to several students Engineering present and at former who helped inUniversity the revision of this book. My current as Instructor in thepeople Courseand of Seismic the Politecnico di Torino. the result of the research experience withismy studentsinand the years I have taught Instructorsoftware in the Course of Seismic Ph.D. student, Sebastiano Marasco that co-author thisofbook and developed theascomputer OPENSIGNAL Engineering attotheseveral diand Torino. which is included inPolitecnico the book. He hasstudents also generated the numerical results which appear thebook. figures. I am grateful people presentmost and of former who helped in the revision of in this MyBridget current Bassi, MIT student that has been and at the Politecnico di in Torino as visiting scholar helped withasthe revision the IPh.D. am grateful toSebastiano several present former students who in the revisionand of she the book such myOPENSIGNAL currentofPh.D. student, Marasco that is co-author thishelped book and developed the computer software English which islanguage. included inMarasco the book.that Heishas also generated most of numericalthe results whichsoftware appear in the figures. Bridget student, Sebastiano co-author in this book andthe developed computer OPENSIGNAL which Bassi, MIT in student that He has has beenalso at the Politecnico as visiting scholar andappear she helped the revision of the is included the book. generated mostdiofTorino the numerical results which in thewith figures. Bridget Bassi, I English also wish to express my deep appreciation to Prof. Andrei M. Reinhorn, Prof. T.T. Soong, Prof. Steve Mahin and Prof. language. MIT student that has been at the Politecnico di Torino as visiting scholar and she helped with the revision of the English Alessandro De Stefano for the influence they have had and still have on my professional growth. language. I also wish to express my deep appreciation to Prof. Andrei M. Reinhorn, Prof. T.T. Soong, Prof. Steve Mahin I also wish to express my deep appreciation to Prof. Andrei M. Reinhorn, Prof. T.T. Soong, Prof. Steve Mahin and Prof. and Prof.the Alessandro Defor Stefano for the they have hadhave and on still have on my professional growth. By being the By being firstStefano edition of theinfluence book, weinfluence did our remove errors and misprints, however instructors, Alessandro De the they havebest hadtoand still my professional growth.I encourage first edition the book, we did ourtobest to to remove errors and misprints, however if I encourage instructors, and students and of professional engineers write me (gianpaolo.cimellaro@polito.it) you identify errors or students if you have professional engineers to write tobook, me (gianpaolo.cimellaro@polito.it) if you errors or if you have suggestions for suggestions for improvements and clarifications. By being the first edition of the we did our best to remove errors andidentify misprints, however I encourage instructors, improvements and clarifications. students and professional engineers to write to me (gianpaolo.cimellaro@polito.it) if you identify errors or if you have suggestions for improvements and clarifications. Gian Paolo Cimellaro Gian Paolo Cimellaro Why a new book? The reason this new book is to provide an elementary but comprehensive textbook which can be adopted in the Why a newofbook? course of Earthquake Engineering in both the School of Engineering and Architecture of the Politecnico di Torino, providing theoflatest in the in a an simple way. No knowledge of structural dynamics is assumed The reason this updates new book is tofield, provide elementary butprevious comprehensive textbook which can be adopted in the making book suitable for the reader learning the subject for the firstand time. However the following background is course this of Earthquake Engineering in both the School of Engineering Architecture of the Politecnico di Torino, required: providing the latest updates in the field, in a simple way. No previous knowledge of structural dynamics is assumed making this book suitable for the reader 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 Static analysis of structures, including statistically indeterminate structures and matrix formulation Mathematics: linear algebra, ordinary and partial differential equations Rigid body dynamics With respect to other classical books inordinary Dynamic Structures, the current book Mathematics: linear algebra, andofpartial differential equations emphasizes the application of energy methods and the analyses in the frequency domain with the correspoding visualization in the Gauss-Argant Plan. Emphasis is also to the applications of numerical methods (section 3.4) book for theemphasizes solution ofthe the application equation ofof motions With respect to given other classical books in Dynamic of Structures, the current energy and to the and ground selection 4) to be used inwith timethe history analysis of structtures which more frequently methods the motion analyses in the (Part frequency domain correspoding visualization in the are Gauss-Argant Plan. used in current practice due to the increasing computational power of computers in the last decade. Emphasis is also given to the applications of numerical methods (section 3.4) for the solution of the equation of motions and to the ground motion selection (Part 4) to be used in time history analysis of structtures which are more frequently Most of current the references havetobeen omitted in the book topower avoid ofdistricting reader; however a selected list of used in practice due the increasing computational computersthe in the last decade. references has been added at the end of the book for further reading. Most of the references have been omitted in the book to avoid districting the reader; however a selected list of references has been added at the end of the book for further reading.
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