Matrix analysis of structural dynamics : applications and earthquake engineering

목차 (Table of Contents)

• CONTENTS
• Preface = ⅲ
• 1 Characteristics of Free and Forced Vibrations of Elementary Systems
• 1.1 Introduction = 1
• 1.2 Free Undamped Vibration = 1
• 1.2.1 Motion Equation and Solution = 1
• 1.2.2 Initial Conditions, Phase Angle and Natural Frequency = 3
• 1.2.3 Periodic and Harmonic Motion = 6
• 1.3 Free Damped Vibration = 7
• 1.3.1 Motion Equation and Viscous Damping = 7
• 1.3.2 Critical Damping, Overdamping and Underdamping = 9
• 1.3.3 Logarithmic Decrement and Evaluation of Viscous Damping Coefficient = 11
• 1.4 Forced Undamped Vibration = 14
• 1.4.1 Harmonic Forces = 14
• 1.4.2 Steady-State Vibration and Resonance = 15
• 1.4.3 Impulses and Shock Spectra = 19
• 1.4.4 General Loading - Step Forcing Function Method vs Duhamel's Integral = 24
• 1.5 Forced Damped Vibration = 29
• 1.5.1 Harmonic Forces = 29
• 1.5.2 Steady-State Vibration for Damped Vibration, Resonant and Peak Amplitude = 30
• 1.5.3 General Loading - Step-Forcing Function Method vs. Duhamel's Integral = 32
• 1.5.4 Transmissibility and Response to Foundation Motion = 36
• 1.6 Evaluation of Damping = 42
• 1.6.1 Equivalent Damping Coefficient Method = 42
• 1.6.2 Amplitude Method and Bandwidth Method = 43
• 1.7 Overview = 45
• Bibliography = 45
• 2 Elgensolution Techniques and Undamped Response Analysis of Multiple-Degree-of-Freedom Systems = 47
• PART A FUNDAMENTALS = 47
• 2.1 Introduction = 47
• 2.1.1 Characteristics of the Spring-Mass Model = 47
• 2.1.2 Advantages of the Lumped Mass Model = 48
• 2.2 Characteristics of Free Vibration of Two-Degree-of-Freedom Systems = 49
• 2.2.1 Motion Equations, Natural and Normal Modes = 49
• 2.2.2 Harmonic and Periodic Motion = 52
• 2.3 Dynamic Matrix Equation = 54
• 2.4 Orthogonality of Normal Modes = 55
• 2.5 Modal Matrix for Undamped Vibration = 56
• 2.5.1 Modal Matrices and Characteristics = 56
• 2.5.2 Response to Initial Disturbances, Dynamic Forces and Seismic Excitation = 58
• 2.5.3 Effect of Individual Modes on Response = 64
• 2.5.4 Response to Foundation Movement = 67
• 2.6 Eigensolution for Symmetric Matrix = 72
• 2.6.1 Iteration Method for Fundamental and Higher Modes = 72
• 2.6.2 Proof of Iterative Solution = 77
• 2.6.3 Extraction Technique for Natural Frequencies = 80
• 2.6.4 Choleski's Decomposition Method = 81
• 2.6.5 Generalized Jacobi Method = 87
• 2.6.6 Sturm Sequence Method = 95
• PART B ADVANCED TOPICS = 98
• 2.7 Eigensolution Technique for Unsymmetric Matrix = 98
• 2.7.1 Classification of Cases = 99
• 2.7.2 Iteration Method = 100
• 2.8 Response Analysis for Zero and Repeating Eigenvalues = 105
• 2.8.1 Zero and Repeating Eigenvalue Cases = 105
• 2.8.2 Orthogonality Properties = 105
• 2.8.3 Response Analysis = 109
• Bibliography = 114
• 3 Eigensolution Methods and Response Analysis for Proportional ani Nonproportional Damping = 117
• PART A FUNDAMENTALS = 117
• 3.1 Introduction = 117
• 3.2 Response Analysis for Proportional Damping = 117
• 3.2.1 Based on a Modal Matrix = 117
• 3.2.2 Proportional Damping = 120
• 3.3 Evaluation of Damping Coefficients and Factors = 121
• 3.3.1 Two Modes Required = 121
• 3.3.2 All Modes Required = 125
• 3.3.3 Damping Factors from Damping Coefficients = 125
• 3.4 Determination of Proportional and Nonproportional Damping = 126
• PART B ADVANCED TOPICS = 128
• 3.5 Characteristics of Complex Eigenvalues for Nonproportional Damping = 128
• 3.6 Iteration Method for Fundamental and Higher Modes of Complex Eigenvalues = 137
• 3.6.1 Fundamental Mode = 137
• 3.6.2 Orthogonality Condition and Iteration for Higher Modes = 139
• 3.6.3 Step-by-Step Procedures = 139
• 3.7 Response Analysis with Complex Eigenvalues = 149
• 3.8 Relationship Between Undamped, Proportional Damping, and Nonproportional Damping = 156
• Bibliography = 159
• 4. Dynamic Stiffness and Energy Methods for Distributed Mass Systems = 161
• 4.1 Introduction = 161
• 4.2 Derivation of Bernoulli-Euler Equation = 161
• 4.3 Derivation of Dynamic Stiffness Coefficients = 166
• 4.4 Characteristics of Dynamic Stiffness Coefficients = 168
• 4.4.1 Numerals and Curves for Coefficients = 168
• 4.4.2 Rayleigh's Dynamic Reciprocal Principle = 171
• 4.4.3 M$$\ddot u$$ller-Breslau's Principle = 173
• 4.5 Dynamic Stiffness, Load, and Mass Matrices = 175
• 4.5.1 Degree-of-Freedom of Plane Structural Systems = 175
• 4.5.2 Equilibrium Matrices = 176
• 4.5.3 Compatibility Matrices = 177
• 4.5.4 Dynamic Stiffness Matrix = 178
• 4.5.5 Dynamic Load Matrix = 179
• 4.5.6 System Matrix Equation = 180
• 4.6 Derivation of Dynamic Fixed-end Moments and Fixed-end Shears = 180
• 4.6.1 Differential Equations = 181
• 4.6.2 Uniform Load = 182
• 4.6.3 Triangular Load = 183
• 4.6.4 Concentrated Load between Nodes = 185
• 4.6.5 Foundation Movement = 186
• 4.7 Numerical Technique for Eigensolutions = 186
• 4.8 Steady-State Response Analysis = 198
• 4.9 Response for General Forcing Functions with and without Damping = 203
• 4.9.1 Kinetic and Strain Energy = 203
• 4.9.2 Orthogonality Condition = 204
• 4.9.3 Dissipated Energy and Work = 205
• 4.9.4 Response Equations = 206
• Bibliography = 212
• 5 Dynamic Stiffness Method for Coupling Vibration, Elastic Media and P-Δ Effect = 213
• PART A FUNDAMENTALS = 213
• 5.1 Introduction = 213
• 5.2 Longitudinal Vibration and Stiffness Coefficients = 213
• 5.3 Longitudinal Vibration and Stiffness Coefficients with Elastic Media = 214
• 5.4 Dynamic Analysis of Trusses and Elastic Frames = 216
• 5.4.1 Dynamic Stiffness Coefficients of Pin-connected Member = 216
• 5.4.2 Dynamic Stiffness Matrix of Trusses = 218
• 5.4.3 Dynamic Stiffness Matrix of Elastic Frames = 221
• 5.4.4 Coupling of Longitudinal and Flexural Vibration = 224
• 5.5 Torsional Vibration and Stiffness Coefficients = 229
• 5.6 Dynamic Stiffness Matrix of Grid Systems = 230
• 5.7 Coupling of Torsional and Flexural Vibration = 233
• PART B ADVANCED TOPICS = 237
• 5.8 Bernoulli-Euler Equation with Elastic Media = 237
• 5.9 Bernoulli-Euler Equation with Elastic Media and P-Δ Effect = 238
• 5.10 Timoshenko Equation(Bending and Shear Deformation and Rotatory Inertia) = 240
• 5.10.1 Differential Equations = 240
• 5.10.2 Stiffness Coefficients = 243
• 5.10.3 Fixed-end Forces for Steady-State Vibration = 246
• 5.10.4 Response Analysis for General Forcing Functions = 247
• 5.10.5 Effect of Various Parameters on Frequencies = 252
• 5.11 Timoshenko Equation with Elastic Media and P-Δ Effect = 252
• 5.11.1 Differential Equations = 253
• 5.11.2 Stiffness Coefficients = 255
• 5.11.3 Fixed-end Forces = 256
• 5.11.4 Case Studies of the Effect of Various Parameters on Frequencies = 257
• Bibliography = 258
• 6 Consistent Mass Method for Frames and Finite Elements = 261
• PART A FUNDAMENTALS = 261
• 6.1 Introduction = 261
• 6.2 Energy Method for Motion Equation = 262
• 6.2.1 Rigid Frames = 263
• 6.2.2 Elastic Frames = 265
• 6.3 Stiffness, Mass and Generalized Force Matrices for Frame Members = 265
• 6.3.1 Two-Force Member = 265
• 6.3.2 Torsional Member = 268
• 6.3.3 Flexural Member = 270
• 6.4 Eigenvalue Comparisons Among Lumped Mass, Dynamic Stiffness and Consistent Mass Methods = 283
• PART B ADVANCED TOPICS = 285
• 6.5 Stiffness, Mass and Generalized Force Matrices for Finite Elements = 285
• 6.5.1 Finite Element Formulation - Generalized Coordinates = 286
• 6.5.2 Finite Element Formulation - Natural Coordinates = 291
• 6.6 Motion Equation with P-Δ Effect = 303
• 6.6.1 Potential Energy and Motion Equation = 303
• 6.6.2 Geometric Matrix with Rotation and Deflection = 305
• 6.6.3 Geometric Matrix(String Stiffness) with Deflection = 305
• 6.7 Timoshenko Prismatic Member with P-Δ Effect = 306
• 6.7.1 Displacement and Shape Functions = 306
• 6.7.2 Stiffness Matrix = 308
• 6.7.3 Mass Matrix = 309
• 6.7.4 Generalized Force Matrix = 312
• 6.7.5 Geometric Matrix = 312
• 6.8 Timoshenko Tapered Member with P-Δ Effect = 314
• 6.8.1 Stiffness Matrix = 314
• 6.8.2 Mass Matrix = 315
• 6.8.3 Generalized Force Matrix = 317
• 6.8.4 Geometric Matrix = 317
• 6.9 Comments on Lumped Mass, Consistent Mass, and Dynamic Stiffness Models = 318
• Bibliography = 319
• 7 Numerical Integration Methods and Seismic Response Spectra for Single- and Multi-Component Seismic Input = 321
• PART A FUNDAMENTALS = 321
• 7.1 Introduction = 321
• 7.2 Earthquakes and Their Effects on Structures = 321
• 7.2.1 Earthquake Characteristics = 321
• 7.2.2 Intensity, Magnitude, and Acceleration of Earthquakes = 322
• 7.2.3 Relationship Between Seismic Zone, Acceleration, Magnitude, and Intensity = 326
• 7.2.4 Earthquake Principal Components = 327
• 7.3 Numerical Integration and Stability = 329
• 7.3.1 Newmark Integration Method = 329
• 7.3.2 Wilson-θ Method = 332
• 7.3.3 General Numerical Integration Related to Newmark and Wilson-θ Methods = 334
• 7.3.4 Runge-Kutta Fourth-Order Method = 338
• 7.3.5 Numerical Stability and Error of Newmark and Wilson-θ Methods = 350
• 7.3.6 Numerical Stability of Runge-Kutta Fourth-Order Method = 358
• 7.4 Seismic Response Spectra for Analysis and Design = 361
• 7.4.1 Response Spectra, Pseudo-Spectra and Principal-Component Spectra = 362
• 7.4.2 Housner's Average Design Spectra = 369
• 7.4.3 Newmark Elastic Design Spectra = 371
• 7.4.4 Newmark Inelastic Design Spectra = 372
• 7.4.5 Site-Dependent Spectra and UBC-94Design Spectra = 378
• 7.4.6 Various Definitions of Ductility = 380
• PART B ADVANCED TOPICS = 383
• 7.5 Torsional Response Spectra = 383
• 7.5.1 Ground Rotational Records Generation = 383
• 7.5.2 Construction of Torsional Response Spectra = 389
• 7.6 Response Spectra Analysis of a Multiple d.o.f. Systems = 390
• 7.6.1 SRSS Modal Combination Method = 393
• 7.6.2 CQC Modal Combination Method = 394
• 7.6.3 Structural Response Due to Multiple-Component Seismic Input = 397
• 7.7 Maximum(Worst-Case) Response Analysis for Six Seismic Components = 399
• 7.7.1 Based on SRSS Method = 400
• 7.7.2 Based on CQC Method = 404
• 7.8 Composite Translational Spectrum and Torsional Spectrum = 410
• 7.8.1 Construction of the Composite Response Spectrum = 411
• 7.8.2 Composite Spectral Modal Analysis = 412
• 7.9 Overview = 414
• Bibliography = 414
• 8 Formulation and Response Analysis of Three-Dimensional Building Systems with Walls and Bracings = 417
• PART A FUNDAMENTALS = 417
• 8.1 Introduction = 417
• 8.2 Joints, Members, Coordinate Systems, and Degree of Freedom(d.o.f.) = 417
• 8.3 Coordinate Transformation Between JCS and GCS : Methods 1 and 2 = 418
• 8.4 Force Transformation Between Slave Joint and Master Joint = 424
• 8.5 System d.o.f. as Related to Coordinate and Force Transformation = 426
• 8.6 Beam-Columns = 429
• 8.6.1 Coordinate Transformation Between ECS and JCS or GCS : Methods 1 and 2 = 429
• 8.6.2 Beam-Column Stiffness in the ECS = 431
• 8.6.3 Beam-Column Stiffness in the JCS or GCS Based on Method 1 = 434
• 8.6.4 Beam-Column Geometric Matrix(String Stiffness) in ECS and JCS or GCS Based on Method 1 = 438
• 8.7 Shear Walls = 439
• 8.7.1 Shear-Wall ECS and GCS Relationship Based on Method 1 = 439
• 8.7.2 Shear-Wall Stiffness in the ECS = 441
• 8.7.3 Shear-Wall Stiffness in the JCS or GCS Based on Method 1 = 447
• 8.7.4 Shear-Wall Geometric Matrix(String Stiffness) in the JCS or GCS Based on Method 1 = 455
• 8.8 Bracing Elements = 455
• 8.8.1 Bracing-Element ECS and GCS Relationship Based on Method 1 = 455
• 8.8.2 Bracing-Element Stiffness in ECS = 457
• 8.8.3 Bracing-Element Stiffness in the JCS or GCS Based on Method 1 = 457
• 8.9 Structural Characteristics of 3-D Building Systems = 462
• 8.10 Rigid Zone Between Member End and Joint Center = 462
• 8.11 Building-Structure-Element Stiffness with Rigid Zone = 464
• 8.11.1 Beam-Column Stiffness in ECS Based on Method 2 = 464
• 8.11.2 Beam-Column Stiffness in GCS Based on Method 2 = 466
• 8.11.3 Beam-Column Geometric Matrix(String Stiffness) in JCS or GCS Based on Method 2 = 473
• 8.11.4 Beam Stiffness in the GCS Based on Method 2 = 475
• 8.11.5 Bracing-Element Stiffness in the JCS or GCS Based on Method 2 = 479
• 8.11.6 Shear-Wall Stiffness in the JCS or GCS Based on Method 2 = 482
• 8.11.7 Shear-Wall Geometric Matrix(String Stiffness) in the JCS or GCS Based on Method 2 = 487
• PART B ADVANCED TOPICS = 490
• 8.12 Assembly of Structural Global Stiffness Matrix = 490
• 8.12.1 General System Assembly(GSA) = 490
• 8.12.2 Floor-by-Floor Assembly(FFA) = 498
• 8.13 Mass Matrix Assembly = 504
• 8.14 Loading Matrix Assembly = 508
• 8.14.1 Vertical Static or Harmonic Forces = 509
• 8.14.2 Lateral Wind Forces = 511
• 8.14.3 Lateral Dynamic Loads = 513
• 8.14.4 Seismic Excitations = 514
• 8.15 Analysis and Response Behavior of Sample Structural Systems = 516
• 8.16 Overview = 523
• Bibliography = 525
• 9 Various Hysteresis Models and Nonlinear Response Analysis = 527
• PART A FUNDAMENTALS = 527
• 9.1 Introduction = 527
• 9.1.1 Material Nonlinearity and Stress-Strain Models = 528
• 9.1.2 Bauschinger Effect on Moment-Curvature Relationship = 528
• 9.2 Elasto-Plastic Hysteresis Model = 529
• 9.2.1 Stiffness Matrix Formulation = 532
• 9.3 Bilinear Hysteresis Model = 534
• 9.3.1 Stiffness Matrix Formulation = 535
• 9.4 Convergence Techniques at Overshooting Regions = 538
• 9.4.1 State of Yield and Time-Increment Technique = 538
• 9.4.2 Unbalanced Force Technique = 539
• 9.4.3 Equilibrium and Compatibility Checks for Numerical Solutions = 552
• 9.5 Curvilinear Hysteresis Model = 555
• 9.5.1 Stiffness Matrix Formulation = 556
• 9.5.2 Stiffness Comparison Between Bilinear and Curvilinear Models = 560
• 9.6 Ramberg-Osgood Hysteresis Model = 562
• 9.6.1 Parameter Evaluations of Ramberg-Osgood Stress-Strain Curve = 562
• 9.6.2 Ramberg-Osgood Moment-Curvature Curves = 563
• 9.6.3 Stiffness Matrix Formulation for Skeleton Curve = 565
• 9.6.4 Stiffness Matrix Formulation for Branch Curve = 570
• PART B ADVANCED TOPICS = 579
• 9.7 Geometric Nonlinearity = 579
• 9.8 Interaction Effect on Beam Columns = 589
• 9.9 Elasto-Plastic Analysis of Consistent Mass Systems = 591
• 9.9.1 Stiffness Matrix Formulation = 591
• 9.9.2 Moments, Shears and Plastic Hinge Rotations = 595
• 9.10 Hysteresis Models of Steel Bracing, RC Beams, Columns and Shear Walls = 604
• 9.11 Overview = 604
• Bibliography = 605
• 10 Static and Dynamic Lateral-Force Procedures and Related Effects in Building Codes of UBC-94, UBC-97 and IBC-2000 = 607
• PART A FUNDAMENTALS = 607
• 10.1 Introduction = 607
• 10.2 Background of Lateral Force Procedures in Building Codes = 608
• 10.2.1 Effective Earthquake Force and Effective Mass = 608
• 10.2.2 Base Shear and Overturning Moment = 610
• 10.3 UBC-94and Design Parameters = 612
• 10.3.1 Criteria for Appropriate Lateral-Force Procedure = 612
• 10.3.2 Base Shear of Static Lateral-Force Procedure and Related Parameters = 612
• 10.3.3 Vertical Distribution of Lateral Force = 620
• 10.3.4 Story Shear and Overturning Moment = 620
• 10.3.5 Torsion and P-Δ Effect = 621
• 10.3.6 Story Drift Limitations = 623
• 10.3.7 $$3R_w$$／8 Factor = 623
• 10.4 UBC-97 and Design Parameters = 624
• 10.4.1 Criteria for Appropriate Lateral-Force Procedure = 624
• 10.4.2 Base Shear of Static Lateral-Force Procedure and Related Parameters = 624
• 10.4.3 $$R_w$$ and R Relationship vs Load Combination = 626
• 10.4.4 Load Combination for Strength Design and Allowable Stress Design = 627
• 10.4.5 Story Shear, Overturning Moment and Restoring Moment = 631
• 10.4.6 Story Drift, P-Δ Effect and Torsion = 632
• 10.4.7 Relationships Among $$3R_w$$／8, $$\Omega _0$$ and $$0.7R\Delta _s$$ = 632
• 10.5 IBC-2000 and Design Parameters = 633
• 10.5.1 Criteria for Appropriate Lateral-Force Procedure = 633
• 10.5.2 Base Shear of Equivalent Lateral-Force Procedure and Related Parameters = 633
• 10.5.3 Vertical Distribution of Lateral Force = 638
• 10.5.4 Horizontal Shear Distribution and Overturning Moment = 639
• 10.5.5 Deflection and Story Drift = 639
• 10.5.6 P-Δ Effect = 640
• 10.6 Summary Comparison of UBC-94, UBC-97 and IBC-2000 Lateral-Force Procedures = 641
• 10.7 Numerical Illustrations of Lateral-Force Procedure for UBC-94, UBC-97 and IBC-2000 = 648
• 10.8 Techniques for Calculating Rigidity Center = 672
• 10.8.1 Method A - Using individual Member Stiffness for Rigid-floor Shear Buildings = 672
• 10.8.2 Method B - Using Relative Rigidity of individual Bays for General Buildings = 673
• PART B ADVANCED TOPICS = 675
• 10.9 Dynamic Analysis Procedures of UBC-94, UBC-97 and IBC-2000 = 675
• 10.9.1 UBC-94 Dynamic Analysis Procedure = 675
• 10.9.2 UBC-97 Dynamic Analysis Procedure = 676
• 10.9.3 IBC-2000 Dynamic Analysis Procedure = 678
• 10.9.4 Regionalized Seismic Zone Maps and Design Response Spectra in UBC-97 and IBC-2000 = 682
• 10.10 Summary Comparison of UBC-94, UBC-97 and IBC-2000 Dynamic Analysis Procedures = 684
• 10.11 Numerical illustrations of Dynamic Analysis Procedures for UBC-94, UBC-97 and IBC-2000 = 688
• 10.12 Overview = 705
• Bibliography = 705
• Chapter 1 Problems = 707
• Chapter 2 Problems = 715
• Chapter 3 Problems = 721
• Chapter 4 Problems = 723
• Chapter 5 Problems = 727
• Chapter 6 Problems = 733
• Chapter 7 Problems = 741
• Chapter 8 Problems = 745
• Chapter 9 Problems = 753
• Chapter 10 Problems = 757
• Chapter 1 Solutions = 763
• Chapter 2 Solutions = 767
• Chapter 3 Solutions = 773
• Chapter 4 Solutions = 777
• Chapter 5 Solutions = 783
• Chapter 6 Solutions = 791
• Chapter 7 Solutions = 797
• Chapter 8 Solutions = 799
• Chapter 9 Solutions = 807
• Chapter 10 Solutions = 811
• Appendix A Lagrange's Equation = 817
• Appendix B Derivation of Ground Rotational Records = 823
• Appendix C Vector Analysis Fundamentals = 827
• Appendix D Transformation Matrix Between JCS and GCS = 831
• Appendix E Transformation Matrix Between ECS and GCS for Beam Column = 843
• Appendix F Transformation Matrix ［A'］ and Stiffness Matrix ［$$K_{eg}^i$$］ of Beam Column with Rigid Zone = 851
• Appendix G Computer Program for Newmark Method = 855
• Appendix H Computer Program for Wilson-θ Method = 863
• Appendix I Computer Program for CQC Method = 865
• Appendix J Jain-Goel-Hanson Steel-Bracing Hysteresis Model and Computer Program = 875
• Appendix K Takeda Model for RC Columns and Beams and Computer Program = 895
• Appendix L Cheng-Mertz Model for Bending Coupling with Shear and Axial Deformations of Low-Rise Shear Walls and Computer Program = 913
• BENDING : Low-Rise Shear Wall Cheng-Mertz Hysteresis Model = 913
• SHEAR : Low-Rise Shear Wall Cheng-Mertz Hysteresis Model = 932
• AXIAL : Low-Rise Shear Wall Cheng-Mertz Hysteresis Model = 952
• Appendix M Cheng-Lou Axial Hysteresis Model for RC Columns and Walls and Computer Program = 967
• Notation = 979
• Index = 989