Introduction to Dynamics of Structures and Earthquake Engineering

ISBN-13: 9783319725406 / Angielski / Twarda / 2018 / 598 str.

Gian Paolo Cimellaro;Sebastiano Marasco

Opis

This work is an elementary but comprehensive textbook which provides the latest updates in the fields of Earthquake Engineering, Dynamics of Structures, Seismology and Seismic Design, introducing relevant new topics to the fields such as the Neodeterministic method.

Spis treści

Part I Dynamics of Structures

1 Introduction 

1.1 Idealization of the structures

1.2 Degrees of freedom 

1.3 Stiffness 

1.4 Mass 

1.5 Damping 

1.6 Equations of motion 

1.6.1 Free vibrations 

1.6.2 External excitations 

2 SDOF Systems 

2.1 Linear SDOF Systems

2.1.1 Free vibrations 

2.2 Response to harmonic excitations 

2.2.1 Undamped systems

2.2.2 Viscously damped systems 

2.3 Response to an impulsive excitation 

2.4 Response to a periodic excitation 

2.5 Earthquake response

2.6 Transmissibility function 

2.7 Nonlinear system response 

3 Methods of solution of the equation of motion 

3.1 Analytical methods

3.2 Duhamel’s integral 

3.3 Fourier series

3.4 Numerical methods

3.4.1 Explicit methods 

3.4.2 Implicit methods 

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xiv Contents

3.4.3 Comparison between the different numerical methods

3.4.4 Numerical methods for nonlinear problems 

4 MDOF systems

4.1 Discretization 

4.2 Shear Type and Bending Type Frames

4.3 Mass, Stiffness and Damping Matrix 

4.3.1 Bending Type Frames

4.3.2 Shear Type Frames

4.4 Reduction of DOFs 

4.5 Modal Analysis 

4.5.1 Vibrational Modes Response

4.5.2 Modal Expansion Of Displacements 

4.5.3 Energetic Considerations

4.6 Free Vibrations 

4.6.1 Undamped Systems 

4.6.2 Damped Systems 

4.7 Response to Harmonic Excitation

4.7.1 Undamped Systems

4.7.2 Viscously Damped Systems 

4.8 Earthquake response 

4.8.1 Numerical example

4.9 3D MDOF multistory buildings 

5 Energy dissipation 

5.1 Damping energy

5.2 Plastic energy

6 Damping on structures 

7 Distributed mass and elasticity systems

7.1 Vibrational Modes Analysis 

7.2 Vibrational Modes Analysis of Forced Systems

8 Generalized SDOF systems 

8.1 Lagrangian approach

8.2 Approximated solution

8.2.1 Example 1: system with distributed mass and elasticity

8.2.2 Example 2: system with distributed elasticity and lumped

mass 

8.2.3 Example 3: general systems 

Part II Introduction to Earthquake Engineering

Contents xv

9 Seismology and Earthquakes 

9.1 Basic concepts of seismology

9.1.1 Earthquake Genesis 

9.1.2 Seismological Parameters 

9.1.3 Waves Propagation 

9.1.4 Attenuation Relationship

9.2 Ground motion parameters 

9.2.1 Peak Parameters 

9.2.2 Frequency and energetic content 

9.2.3 Duration

9.2.4 Other parameters 

10 Major seismic events that occurred in Italy and in the world 

10.1 Introduction

10.2 Earthquakes occurred in Italy in the past 150 years

10.3 Earthquakes occurred in the World from 1960 to the present day

11 Seismic Hazard Analysis

11.1 Deterministic Seismic Hazard Analysis (DSHA) 

11.2 Probabilistic Seismic Hazard Analysis (PSHA)

12 Earthquake prediction

12.1 General aspects 

12.2 Prediction methods

12.2.1 Animal behavior 

12.2.2 Changes in VP/VS

12.2.3 Radon emission 

12.2.4 Electromagnetic variations

12.2.5 Precursory seismicity patterns 

12.3 Earthquake prediction and time-dependent seismic hazard scenarios

12.3.1 Algorithms for intermediate-term middle range earthquake

prediction

12.3.2 Neo-deterministic time-dependent seismic hazard

scenarios for the Italian territory 

12.4 Notable predictions 

12.4.1 Haicheng (China, 1975) 

12.4.2 Parkfield (USA, 1985-1993) 

12.4.3 Loma Prieta (USA, 1989)

12.4.4 L’Aquila (Italy, 2009) 

13 Seismic Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

13.1 Brief History of Italian Seismic Standards . . . . . . . . . . . . . . . . . . . . . . 285

13.2 Elastic Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

13.3 Uniform Hazard Spectrum (UHS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

13.4 Design Response Spectrum (DS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

13.4.1 Design Response spectrum according to NTC08 and EC8 . . 292

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13.4.2 Conditional Mean Spectrum (CMS) . . . . . . . . . . . . . . . . . . . . . 300

13.5 Use of Acceleration time histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

13.5.1 Ground Motion Selection and Modification . . . . . . . . . . . . . . 304

13.5.2 Available Databases for Signal Processing and Ground

Motion Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

14 Opensignal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

14.1 State of Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

14.2 Structure of the software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

14.3 Strong Motion Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

14.4 Signal Processing and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

14.4.1 Response Spectra Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

14.5 Seismic Records Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

14.6 Approximated Site Response Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 318

14.7 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

15 Methods of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

15.1 Linear Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

15.2 Linear Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

15.3 Nonlinear Static Analysis - Pushover . . . . . . . . . . . . . . . . . . . . . . . . . . 334

15.3.1 Capacity spectrum analysis method . . . . . . . . . . . . . . . . . . . . . 339

15.3.2 N2 method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

15.4 Direct displacement-based seismic design procedure . . . . . . . . . . . . . 343

15.5 Nonlinear Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

Part III Seismic Design of Buildings

16 Brief introduction to SAP2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

16.1.1 Files Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

16.1.2 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

16.1.3 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350

16.1.4 Materials and Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

16.1.5 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

16.1.6 Restrains and Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

16.2 Analysis Methods in SAP2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

16.2.1 Linear Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

16.2.2 Linear Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

17 Modeling of Structures in Seismic Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

17.2 Shear-type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

17.3 Bending-Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

17.4 Seismic Isolated Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

17.4.1 Seismic Isolated Structures in SAP2000 . . . . . . . . . . . . . . . . . 363

17.5 Shear walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

Contents xvii

17.5.1 Shear Walls in SAP2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

18 Seismic modeling of infill walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

<18.2 Influential Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

18.2.1 Strength of the Masonry Infill . . . . . . . . . . . . . . . . . . . . . . . . . . 371

18.2.2 Characteristics of the Reinforced Concrete Frame . . . . . . . . . 372

18.2.3 Relative Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

18.2.4 Gaps between Infills and Surrounding Frame . . . . . . . . . . . . . 372

18.2.5 Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

18.3 Mechanisms of failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

18.3.1 Failure modes of infills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

18.3.2 Failure modes of surrounding reinforced concrete frames . . . 377

18.4 Existing Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

18.4.1 Stiffness methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

18.4.2 Strength methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

18.5 Mechanisms of crisis in plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

18.5.1 Breakage caused by combined compressive and bending

stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

18.5.2 Breakage of the wall caused by shear with diagonal . . . . . . . 394

18.5.3 Breakage of the wall caused by shear with diagonal . . . . . . . 395

18.6 Mechanisms of crisis out of plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

18.6.1 Simple overturning on a one-story monolithic wall . . . . . . . . 396

18.6.2 Simple overturning on a one-story double courtain wall . . . . 398

18.6.3 Composite overturning of a diagonal wedge . . . . . . . . . . . . . . 398

18.6.4 Composite Overturning mechanism of the cantonal . . . . . . . . 400

18.6.5 Vertical flexure on a one-story monolithic wall . . . . . . . . . . . . 402

18.6.6 Vertical Flexure on a one-story double courtain wall . . . . . . . 404

18.6.7 Horizontal Flexure on a non-confined monolithic wall . . . . . 405

18.6.8 Horizontal Flexure on a confined monolithic wall . . . . . . . . . 408

19 Capacity Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

19.1 Design of beams for bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

19.2 Design of beams for shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

19.3 Design of columns in bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

19.4 Design of columns in shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

19.5 Beam-column joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

20 Passive energy dissipating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

20.1 Balance equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

20.2 Types of Passive Energy Dissipating System . . . . . . . . . . . . . . . . . . . . 423

20.2.1 Displacement-activated dampers . . . . . . . . . . . . . . . . . . . . . . . 423

20.2.2 Viscous and viscoelastic dampers . . . . . . . . . . . . . . . . . . . . . . . 436

20.3 Mechanical model of dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

20.4 Characteristics of the braces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

xviii Contents

20.5 Seismic behavior of a passive brace . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

20.6 Seismic Design of damping systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

20.7 Geometric amplification of dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

21 Tuned-Mass Dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

21.1 Undamped TMD under harmonic loading . . . . . . . . . . . . . . . . . . . . . . 449

21.2 Undamped TMD under harmonic base motion . . . . . . . . . . . . . . . . . . 453

21.3 Damped TMD under harmonic loading . . . . . . . . . . . . . . . . . . . . . . . . 455

21.4 Active TMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

21.5 Analysis of a multi-degree of freedom structures . . . . . . . . . . . . . . . . 46021.6 Design considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

21.7 Application of TMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

21.8 Application of ATMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

22 Base Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

22.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

22.1.1 First isolator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

22.2 Theory of linear seismically isolation systems . . . . . . . . . . . . . . . . . . . 470

22.3 Seismic isolation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

22.3.1 High-damping rubber bearing . . . . . . . . . . . . . . . . . . . . . . . . . . 480

22.3.2 Low-damping natural and synthetic rubber bearing . . . . . . . . 483

22.3.3 Lead rubber bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

22.3.4 Friction pendulum system (FPS) . . . . . . . . . . . . . . . . . . . . . . . 486

22.3.5 Spring-type system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

22.3.6 Rocking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

22.4 Installation of isolated buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

22.4.1 Mid-story base isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

22.5 Designing a seismically isolated building . . . . . . . . . . . . . . . . . . . . . . . 491

22.5.1 Design guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

23 Masonry structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

23.2 Types of masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

23.3 Collapse mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

23.3.1 Out of plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510

23.3.2 In plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

23.4 Kinematic equilibrium method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

23.4.1 Example 1: simple overturning . . . . . . . . . . . . . . . . . . . . . . . . . 514

23.4.2 Example 2: design of a reinforcing tie system . . . . . . . . . . . . . 519

23.5 Retrofit interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

23.5.1 Traditional retrofit interventions . . . . . . . . . . . . . . . . . . . . . . . . 521

23.5.2 Modern retrofit interventions . . . . . . . . . . . . . . . . . . . . . . . . . . 521

23.5.3 Classification of interventions . . . . . . . . . . . . . . . . . . . . . . . . . . 522

Contents xix

A Fundamentals of Probability and Statistics . . . . . . . . . . . . . . . . . . . . . . . . 541

A.1 Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

A.2 The Venn diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

A.3 Mathematics of probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

A.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

A.5 The Theorem of Total Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

A.6 Probability Distribution of a Random Variable . . . . . . . . . . . . . . . . . . 544

A.7 Useful probability distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545

A.8 Multiple Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

A.9 The Conditional and Marginal Distributions . . . . . . . . . . . . . . . . . . . . 548

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

O autorze

Gian Paolo Cimellaro is currently Associate Professor at the Politecnico di Torino. He has been recently Visiting Professor at the University of California Berkeley (2014-2016). He obtained his M.S. (2005) and Ph.D. (2008) from the University at Buffalo (SUNY) in USA.  Graduated cum laude in Civil Engineering, University of Rome La Sapienza (2001). He is the Chair of the ASCE Committee on “Disaster Resilience of Structures, Infrastructures and Communities” in USA. In 2011, he has received the Fib Achievement Award for Young Engineers, sponsored by fib - the international federation for structural concrete. In 2015, he has received the Seed Grant Award from the Siebel Energy Institute of UC Berkeley. Prof. Cimellaro current research interests address earthquake engineering with emphasis to community resilience to natural disasters such as earthquakes. He has been awarded a grant of 1.3 M € by the European Research Council for the research project "IDEAL RESCUE: Integrated Design and control of sustainable communities During emergencies" ERC-2014-StG (2015-2019). This is the most prestigious prize assigned in Europe to researchers, performing high-risk and high-gain ground-breaking research.

Sebastiano Marasco is currently Ph.D. student at the Politecnico di Torino (Italy). He received his master degree in Civil Engineering from the Politecnico di Torino in 2014. His thesis focused on the signal processing of earthquake records and he has implemented a software called Opensignal for earthquake record processing and selection adopted in both practice and  academic field.  His expertise is in the advanced software programming, in the seismic design of reinforced concrete buildings and in the F.E.M. analysis. His research under the supervision of Professor Gian Paolo Cimellaro is focused on the assessment of resilience in a urban environment. This research is part of project IDEal reSCUE founded by the European Research Council. As a part of this research, he has collected the building’s data within a virtual city and developed an algorithm for estimating the capacity of each building under a seismic event.

Blurb

This work is an elementary but comprehensive textbook which provides the latest updates in the fields of Earthquake Engineering, Dynamics of Structures, Seismology and Seismic Design, introducing relevant new topics to the fields such as the Neodeterministic method. Its main purpose is to illustrate the application of energy methods and the analysis in the frequency domain with the corresponding visualization in the Gauss-Argant plan. However, 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. As supplementary materials, this book provides “OPENSIGNAL", a rare and unique software for ground motion selection and processing that can be used by professionals to select the correct earthquake records that would run in the nonlinear analysis. 

The book contains clear illustrations and figures to describe the subject in an intuitive way. It uses simple language and terminology and the math is limited only to cases where it is essential to understand the physical meaning of the system. 

Therefore, it is suitable also for those readers who approach these subjects for the first time and who only have a basic understanding of mathematics (linear algebra) and static analysis of structures.