# Introduction to Dynamics of Structures and Earthquake Engineering, 1st ed. 2018Geotechnical, Geological and Earthquake Engineering Series, Vol. 45

## Authors: Cimellaro Gian Paolo, Marasco Sebastiano

Language: Anglais

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Introduction to Dynamics of Structures and Earthquake Engineering
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Introduction to Dynamics of Structures and Earthquake Engineering
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• ## Comment

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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.

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
xiii
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
12.2.4 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
xvi Contents
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
Provides a comprehensive and up-to-date overview of the fields of Earthquake Engineering, Dynamics of Structures, Seismology and Seismic Design
Emphasizes the application of energy methods and the analysis in the frequency domain with corresponding visualization in the Gauss-Argant plan
Illustrates 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 - Provides 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 - Introduces new topics in the field such as the Neodeterministic method in simplified terms