SapRefer3.vp CSi Refer

• Table of Contents
  • Chapter I Introduction 1
    • Analysis Features 2
    • Structural Analysis and Design 3
    • About This Manual 3
    • Topics 3
    • Typographical Conventions 4
      • Bold for Definitions 4
      • Bold for Variable Data 4
      • Italics for Mathematical Variables 4
      • Italics for Emphasis 5
      • Capitalized Names 5
    • Bibliographic References 5
  • Chapter II Objects and Elements 7
    • Objects 7
    • Objects and Elements 8
    • Groups 9
  • Chapter III Coordinate Systems 11
    • Overview 12
    • Global Coordinate System 12
    • Upward and Horizontal Directions 13
    • Defining Coordinate Systems 13
      • Vector Cross Product 13
      • Defining the Three Axes Using Two Vectors 14
    • Local Coordinate Systems 14
    • Alternate Coordinate Systems 16
    • Cylindrical and Spherical Coordinates 17
  • Chapter IV Joints and Degrees of Freedom 21
    • Overview 22
    • Modeling Considerations 23
    • Local Coordinate System 24
    • Advanced Local Coordinate System 24
      • Reference Vectors 25
      • Defining the Axis Reference Vector 26
      • Defining the Plane Reference Vector 26
      • Determining the Local Axes from the Reference Vectors 27
      • Joint Coordinate Angles 28
    • Degrees of Freedom 30
      • Available and Unavailable Degrees of Freedom 31
      • Restrained Degrees of Freedom 32
      • Constrained Degrees of Freedom 32
      • Mixing Restraints and Constraints Not Recommended 32
      • Active Degrees of Freedom 33
      • Null Degrees of Freedom 34
    • Restraint Supports 34
    • Spring Supports 36
    • Nonlinear Supports 37
    • Distributed Supports 38
    • Joint Reactions 39
    • Base Reactions 39
    • Masses 40
    • Force Load 42
    • Ground Displacement Load 42
      • Restraint Displacements 43
      • Spring Displacements 44
      • Link/Support Displacements 45
    • Generalized Displacements 45
    • Degree of Freedom Output 46
    • Assembled Joint Mass Output 47
    • Displacement Output 47
    • Force Output 48
    • Element Joint Force Output 48
  • Chapter V Constraints and Welds 49
    • Overview 50
    • Body Constraint 51
      • Joint Connectivity 51
      • Local Coordinate System 51
      • Constraint Equations 51
    • Plane Definition 52
    • Diaphragm Constraint 53
      • Joint Connectivity 53
      • Local Coordinate System 53
      • Constraint Equations 54
    • Plate Constraint 55
      • Joint Connectivity 55
      • Local Coordinate System 55
      • Constraint Equations 55
    • Axis Definition 56
    • Rod Constraint 56
      • Joint Connectivity 57
      • Local Coordinate System 57
      • Constraint Equations 57
    • Beam Constraint 58
      • Joint Connectivity 58
      • Local Coordinate System 59
      • Constraint Equations 59
    • Equal Constraint 59
      • Joint Connectivity 60
      • Local Coordinate System 60
      • Selected Degrees of Freedom 60
      • Constraint Equations 60
    • Local Constraint 61
      • Joint Connectivity 61
      • No Local Coordinate System 62
      • Selected Degrees of Freedom 62
      • Constraint Equations 62
    • Welds 65
    • Automatic Master Joints 66
      • Stiffness, Mass, and Loads 66
      • Local Coordinate Systems 67
    • Constraint Output 67
  • Chapter VI Material Properties 69
    • Overview 70
    • Local Coordinate System 70
    • Stresses and Strains 71
    • Isotropic Materials 73
    • Uniaxial Materials 74
    • Orthotropic Materials 75
    • Anisotropic Materials 75
    • Temperature-Dependent Properties 76
    • Element Material Temperature 77
    • Mass Density 77
    • Weight Density 78
    • Material Damping 78
      • Modal Damping 79
      • Viscous Proportional Damping 80
      • Hysteretic Proportional Damping 80
    • Nonlinear Material Behavior 80
      • Tension and Compression 81
      • Shear 81
      • Hysteresis 82
      • Application 83
      • Friction and Dilitational Angles 84
    • Hysteresis Models 85
      • Backbone Curve (Action vs. Deformation) 86
      • Cyclic Behavior 86
      • Elastic Hysteresis Model 88
      • Kinematic Hysteresis Model 88
      • Degrading Hysteresis Model 89
      • Takeda Hysteresis Model 93
      • Pivot Hysteresis Model 94
      • Concrete Hysteresis Model 95
      • BRB Hardening Hysteresis Model 97
      • Isotropic Hysteresis Model 99
    • Modified Darwin-Pecknold Concrete Model 100
    • Time-dependent Properties 101
      • Properties 101
      • Time-Integration Control 102
    • Design-Type 102
  • Chapter VII The Frame Element 105
    • Overview 106
    • Joint Connectivity 107
      • Insertion Points 107
    • Degrees of Freedom 108
    • Local Coordinate System 108
      • Longitudinal Axis 1 109
      • Default Orientation 109
      • Coordinate Angle 110
    • Advanced Local Coordinate System 110
      • Reference Vector 112
      • Determining Transverse Axes 2 and 3 113
    • Section Properties 114
      • Local Coordinate System 115
      • Material Properties 115
      • Geometric Properties and Section Stiffnesses 116
      • Shape Type 116
      • Automatic Section Property Calculation 118
      • Section Property Database Files 118
      • Section-Designer Sections 118
      • Additional Mass and Weight 120
      • Non-prismatic Sections 120
    • Property Modifiers 123
      • Named Property Sets 124
    • Insertion Points 125
      • Local Axes 126
    • End Offsets 127
      • Clear Length 129
      • Rigid-end Factor 129
      • Effect upon Non-prismatic Elements 130
      • Effect upon Internal Force Output 130
      • Effect upon End Releases 130
    • End Releases 131
      • Unstable End Releases 132
      • Effect of End Offsets 132
      • Named Property Sets 132
    • Nonlinear Properties 133
      • Tension/Compression Limits 133
      • Plastic Hinge 134
    • Mass 134
    • Self-Weight Load 134
    • Gravity Load 135
    • Concentrated Span Load 135
    • Distributed Span Load 137
      • Loaded Length 137
      • Load Intensity 137
      • Projected Loads 137
    • Temperature Load 140
    • Strain Load 141
    • Deformation Load 141
    • Target-Force Load 142
    • Internal Force Output 142
      • Effect of End Offsets 144
    • Stress Output 144
  • Chapter VIII Hinge Properties 147
    • Overview 147
    • Hinge Properties 149
      • Hinge Length 150
      • Plastic Deformation Curve 150
      • Scaling the Curve 151
      • Strength Loss 152
      • Types of P-M2-M3 Hinges 153
      • Isotropic P-M2-M3 Hinge 153
      • Parametric P-M2-M3 Hinge 156
      • Fiber P-M2-M3 Hinge 156
      • Hysteresis Models 157
    • Automatic, User-Defined, and Generated Properties 158
    • Automatic Hinge Properties 159
    • Analysis Modeling 161
    • Computational Considerations 162
    • Analysis Results 163
  • Chapter IX The Cable Element 165
    • Overview 166
    • Joint Connectivity 167
    • Undeformed Length 167
    • Shape Calculator 168
      • Cable vs. Frame Elements 169
      • Number of Segments 170
    • Degrees of Freedom 170
    • Local Coordinate System 170
    • Section Properties 171
      • Material Properties 171
      • Geometric Properties and Section Stiffnesses 172
    • Mass 172
    • Self-Weight Load 172
    • Gravity Load 173
    • Distributed Span Load 173
    • Temperature Load 174
    • Strain and Deformation Load 174
    • Target-Force Load 174
    • Nonlinear Analysis 175
    • Element Output 175
  • Chapter X The Shell Element 177
    • Overview 178
      • Homogeneous 179
      • Layered 179
    • Joint Connectivity 180
      • Shape Guidelines 180
    • Edge Constraints 183
    • Degrees of Freedom 184
    • Local Coordinate System 185
      • Normal Axis 3 186
      • Default Orientation 186
      • Element Coordinate Angle 186
    • Advanced Local Coordinate System 186
      • Reference Vector 188
      • Determining Tangential Axes 1 and 2 189
    • Section Properties 190
      • Area Section Type 190
      • Shell Section Type 190
      • Homogeneous Section Properties 191
      • Layered Section Property 193
    • Property Modifiers 201
      • Named Property Sets 202
    • Joint Offsets and Thickness Overwrites 203
      • Joint Offsets 203
      • Effect of Joint Offsets on the Local Axes 204
      • Thickness Overwrites 205
    • Mass 206
    • Self-Weight Load 206
    • Gravity Load 207
    • Uniform Load 207
    • Surface Pressure Load 208
    • Temperature Load 209
    • Strain Load 210
    • Internal Force and Stress Output 210
  • Chapter XI The Plane Element 215
    • Overview 216
    • Joint Connectivity 217
    • Degrees of Freedom 217
    • Local Coordinate System 217
    • Stresses and Strains 217
    • Section Properties 218
      • Section Type 218
      • Material Properties 219
      • Material Angle 219
      • Thickness 219
      • Incompatible Bending Modes 220
    • Mass 220
    • Self-Weight Load 221
    • Gravity Load 221
    • Surface Pressure Load 222
    • Pore Pressure Load 222
    • Temperature Load 223
    • Stress Output 223
  • Chapter XII The Asolid Element 225
    • Overview 226
    • Joint Connectivity 226
    • Degrees of Freedom 227
    • Local Coordinate System 227
    • Stresses and Strains 228
    • Section Properties 228
      • Section Type 228
      • Material Properties 229
      • Material Angle 229
      • Axis of Symmetry 230
      • Arc and Thickness 231
      • Incompatible Bending Modes 232
    • Mass 232
    • Self-Weight Load 232
    • Gravity Load 233
    • Surface Pressure Load 233
    • Pore Pressure Load 234
    • Temperature Load 234
    • Rotate Load 234
    • Stress Output 235
  • Chapter XIII The Solid Element 237
    • Overview 238
    • Joint Connectivity 238
      • Degenerate Solids 239
    • Degrees of Freedom 240
    • Local Coordinate System 240
    • Advanced Local Coordinate System 240
      • Reference Vectors 241
      • Defining the Axis Reference Vector 241
      • Defining the Plane Reference Vector 242
      • Determining the Local Axes from the Reference Vectors 243
      • Element Coordinate Angles 243
    • Stresses and Strains 246
    • Solid Properties 246
      • Material Properties 246
      • Material Angles 246
      • Incompatible Bending Modes 247
    • Mass 248
    • Self-Weight Load 248
    • Gravity Load 249
    • Surface Pressure Load 249
    • Pore Pressure Load 249
    • Temperature Load 250
    • Stress Output 250
  • Chapter XIV The Link/Support Element—Basic 251
    • Overview 252
    • Joint Connectivity 253
      • Conversion from One-Joint Objects to Two-Joint Elements 253
    • Zero-Length Elements 253
    • Degrees of Freedom 254
    • Local Coordinate System 254
      • Longitudinal Axis 1 255
      • Default Orientation 255
      • Coordinate Angle 256
    • Advanced Local Coordinate System 256
      • Axis Reference Vector 257
      • Plane Reference Vector 258
      • Determining Transverse Axes 2 and 3 259
    • Internal Deformations 260
    • Link/Support Properties 263
      • Local Coordinate System 264
      • Internal Spring Hinges 264
      • Spring Force-Deformation Relationships 266
      • Element Internal Forces 267
      • Uncoupled Linear Force-Deformation Relationships 267
      • Types of Linear/Nonlinear Properties 269
    • Coupled Linear Property 270
    • Fixed Degrees of Freedom 270
    • Mass 271
    • Self-Weight Load 272
    • Gravity Load 272
    • Internal Force and Deformation Output 273
  • Chapter XV The Link/Support Element—Advanced 275
    • Overview 276
    • Nonlinear Link/Support Properties 276
    • Linear Effective Stiffness 277
      • Special Considerations for Modal Analyses 277
    • Linear Effective Damping 278
    • Exponential Maxwell Damper Property 279
    • Bilinear Maxwell Damper Property 281
    • Friction-Spring Damper Property 282
    • Gap Property 286
    • Hook Property 286
    • Wen Plasticity Property 287
    • Multi-Linear Elastic Property 289
    • Multi-Linear Plastic Property 289
    • Hysteretic (Rubber) Isolator Property 291
    • Friction-Pendulum Isolator Property 292
      • Axial Behavior 293
      • Shear Behavior 294
      • Linear Behavior 297
    • Double-Acting Friction-Pendulum Isolator Property 297
      • Axial Behavior 297
      • Shear Behavior 298
      • Linear Behavior 299
    • Triple-Pendulum Isolator Property 299
      • Axial Behavior 299
      • Shear Behavior 300
      • Linear Behavior 304
    • Nonlinear Deformation Loads 304
    • Frequency-Dependent Link/Support Properties 306
  • Chapter XVI The Tendon Object 309
    • Overview 310
    • Geometry 310
    • Discretization 311
    • Tendons Modeled as Loads or Elements 311
    • Connectivity 311
    • Degrees of Freedom 312
    • Local Coordinate Systems 313
      • Base-line Local Coordinate System 313
      • Natural Local Coordinate System 313
    • Section Properties 314
      • Material Properties 314
      • Geometric Properties and Section Stiffnesses 314
    • Tension/Compression Limits 315
    • Mass 316
    • Prestress Load 316
    • Self-Weight Load 317
    • Gravity Load 318
    • Temperature Load 318
    • Strain Load 318
    • Deformation Load 319
    • Target-Force Load 319
    • Internal Force Output 320
  • Chapter XVII Load Patterns 321
    • Overview 322
    • Load Patterns, Load Cases, and Load Combinations 323
    • Defining Load Patterns 323
    • Coordinate Systems and Load Components 324
      • Effect upon Large-Displacements Analysis 324
    • Force Load 325
    • Ground Displacement Load 325
    • Self-Weight Load 325
    • Gravity Load 326
    • Concentrated Span Load 327
    • Distributed Span Load 327
    • Tendon Prestress Load 327
    • Uniform Load 328
    • Surface Pressure Load 328
    • Pore Pressure Load 328
    • Temperature Load 330
    • Strain Load 331
    • Deformation Load 331
    • Target-Force Load 331
    • Rotate Load 332
    • Joint Patterns 332
    • Mass Source 334
      • Mass from Specified Load Patterns 335
      • Negative Mass 336
      • Multiple Mass Sources 336
      • Automated Lateral Loads 338
    • Acceleration Loads 338
  • Chapter XVIII Load Cases 341
    • Overview 342
    • Load Cases 343
    • Types of Analysis 343
    • Sequence of Analysis 344
    • Running Load Cases 345
    • Linear and Nonlinear Load Cases 346
    • Linear Static Analysis 347
    • Multi-Step Static Analysis 348
    • Linear Buckling Analysis 349
    • Functions 350
    • Load Combinations (Combos) 351
      • Contributing Cases 351
      • Types of Combos 352
      • Examples 353
      • Correspondence 354
      • Additional Considerations 357
    • Global Energy Response 357
    • Equation Solvers 361
    • Environment Variables to Control Analysis 362
      • SAPFIRE_NUM_THREADS 362
      • SAPFIRE_FILESIZE_MB 363
    • Accessing the Assembled Stiffness and Mass Matrices 363
  • Chapter XIX Modal Analysis 365
    • Overview 365
    • Eigenvector Analysis 366
      • Number of Modes 367
      • Frequency Range 368
      • Automatic Shifting 369
      • Convergence Tolerance 369
      • Static-Correction Modes 370
    • Ritz-Vector Analysis 372
      • Number of Modes 373
      • Starting Load Vectors 373
      • Number of Generation Cycles 375
    • Modal Analysis Output 375
      • Periods and Frequencies 376
      • Participation Factors 376
      • Participating Mass Ratios 377
      • Static and Dynamic Load Participation Ratios 378
  • Chapter XX Response-Spectrum Analysis 383
    • Overview 383
    • Local Coordinate System 385
    • Response-Spectrum Function 385
      • Damping 386
    • Modal Damping 387
    • Modal Combination 388
      • Periodic and Rigid Response 388
      • CQC Method 390
      • GMC Method 390
      • SRSS Method 390
      • Absolute Sum Method 391
      • NRC Ten-Percent Method 391
      • NRC Double-Sum Method 391
    • Directional Combination 391
      • SRSS Method 391
      • CQC3 Method 392
      • Absolute Sum Method 393
    • Response-Spectrum Analysis Output 394
      • Damping and Accelerations 394
      • Modal Amplitudes 394
      • Base Reactions 395
  • Chapter XXI Linear Time-History Analysis 397
    • Overview 398
    • Loading 398
      • Defining the Spatial Load Vectors 399
      • Defining the Time Functions 400
    • Initial Conditions 402
    • Time Steps 402
    • Modal Time-History Analysis 403
      • Modal Damping 404
    • Direct-Integration Time-History Analysis 405
      • Time Integration Parameters 406
      • Damping 406
  • Chapter XXII Geometric Nonlinearity 409
    • Overview 409
    • Nonlinear Load Cases 411
    • The P-Delta Effect 413
      • P-Delta Forces in the Frame Element 415
      • P-Delta Forces in the Link/Support Element 418
      • Other Elements 419
    • Initial P-Delta Analysis 419
      • Building Structures 420
      • Cable Structures 422
      • Guyed Towers 422
    • Large Displacements 422
      • Applications 423
      • Initial Large-Displacement Analysis 423
  • Chapter XXIII Nonlinear Static Analysis 425
    • Overview 426
    • Nonlinearity 426
    • Important Considerations 427
    • Loading 428
    • Load Application Control 428
      • Load Control 429
      • Displacement Control 429
    • Initial Conditions 430
    • Output Steps 431
      • Saving Multiple Steps 431
    • Nonlinear Solution Control 433
      • Maximum Total Steps 434
      • Maximum Null (Zero) Steps 434
      • Event-to-Event Stepping Control 434
      • Nonlinear Iteration 435
      • Line Search Option 436
    • Static Pushover Analysis 437
    • Staged Construction 439
      • Stages 439
      • Changing Section Properties 442
      • Output Steps 442
      • Example 443
    • Target-Force Iteration 444
  • Chapter XXIV Nonlinear Time-History Analysis 447
    • Overview 448
    • Nonlinearity 448
    • Loading 449
    • Initial Conditions 449
    • Time Steps 450
    • Nonlinear Modal Time-History Analysis (FNA) 451
      • Initial Conditions 451
      • Link/Support Effective Stiffness 452
      • Mode Superposition 452
      • Modal Damping 454
      • Iterative Solution 455
      • Static Period 457
    • Nonlinear Direct-Integration Time-History Analysis 458
      • Time Integration Parameters 458
      • Nonlinearity 459
      • Initial Conditions 459
      • Damping 459
      • Nonlinear Solution Control 461
  • Chapter XXV Frequency-Domain Analyses 465
    • Overview 466
    • Harmonic Motion 466
    • Frequency Domain 467
    • Damping 468
      • Sources of Damping 468
    • Loading 469
      • Defining the Spatial Load Vectors 470
    • Frequency Steps 471
    • Steady-State Analysis 471
      • Example 472
    • Power-Spectral-Density Analysis 473
      • Example 474
  • Chapter XXVI Moving-Load Analysis 477
    • Overview for CSiBridge 478
    • Moving-Load Analysis in SAP2000 479
    • Bridge Modeler 480
    • Moving-Load Analysis Procedure 481
    • Lanes 482
      • Centerline and Direction 482
      • Eccentricity 482
      • Centrifugal Radius 483
      • Width 483
      • Interior and Exterior Edges 483
      • Discretization 484
    • Influence Lines and Surfaces 485
    • Vehicle Live Loads 487
      • Distribution of Loads 487
      • Axle Loads 487
      • Uniform Loads 487
      • Minimum Edge Distances 487
      • Directions of Loading 488
      • Restricting a Vehicle to the Lane Length 492
      • Application of Loads to the Influence Surface 492
      • Length Effects 494
      • Application of Loads in Multi-Step Analysis 495
    • General Vehicle 495
      • Specification 497
      • Moving the Vehicle 498
    • Vehicle Response Components 498
      • Superstructure (Span) Moment 498
      • Negative Superstructure (Span) Moment 499
      • Reactions at Interior Supports 500
    • Standard Vehicles 500
    • Vehicle Classes 508
    • Moving-Load Load Cases 509
      • Directions of Loading 510
      • Example 1 — AASHTO HS Loading 512
      • Example 2 — AASHTO HL Loading 513
      • Example 3 — Caltrans Permit Loading 514
      • Example 4 — Restricted Caltrans Permit Loading 516
      • Example 5 — Eurocode Characteristic Load Model 1 518
    • Moving Load Response Control 519
      • Bridge Response Groups 519
      • Correspondence 520
      • Influence Line Tolerance 520
      • Exact and Quick Response Calculation 521
    • Step-By-Step Analysis 521
      • Loading 522
      • Static Analysis 522
      • Time-History Analysis 523
      • Enveloping and Load Combinations 524
    • Computational Considerations 524
  • Chapter XXVII References 527