Three dimensional static and dynamic analysis of structures: A physical approach with emphasis on earthquake engineering

Title Page......Page 1
Copyright......Page 2
Structural Engineering is.........Page 3
Preface to Third Edition......Page 4
Personal Remarks......Page 5
Contents......Page 7
ANISOTROPIC MATERIALS......Page 19
USE OF MATERIAL PROPERTIES WITHIN COMPUTER PROGRAMS......Page 22
ISOTROPIC MATERIALS......Page 23
PLANE STRAIN ISOTROPIC MATERIALS......Page 24
PLANE STRESS ISOTROPIC MATERIALS......Page 25
PROPERTIES OF FLUID-LIKE MATERIALS......Page 26
SHEAR AND COMPRESSION WAVE VELOCITIES......Page 27
AXISYMMETRIC MATERIAL PROPERTIES......Page 28
FORCE-DEFORMATION RELATIONSHIPS......Page 29
REFERENCES......Page 30
INTRODUCTION......Page 31
STRESS RESULTANTS - FORCES AND MOMENTS......Page 32
COMPATIBILITY REQUIREMENTS......Page 33
DEFINITION OF ROTATION......Page 34
EQUATIONS AT MATERIAL INTERFACES......Page 35
STATICALLY DETERMINATE STRUCTURES......Page 37
DISPLACEMENT TRANSFORMATION MATRIX......Page 39
SOLUTION OF STATICALLY DETERMINATE SYSTEM......Page 41
GENERAL SOLUTION OF STRUCTURAL SYSTEMS......Page 42
SUMMARY......Page 43
REFERENCES......Page 44
INTRODUCTION......Page 45
VIRTUAL AND REAL WORK......Page 46
POTENTIAL ENERGY AND KINETIC ENERGY......Page 48
STRAIN ENERGY......Page 50
EXTERNAL WORK......Page 51
STATIONARY ENERGY PRINCIPLE......Page 53
THE FORCE METHOD......Page 54
LAGRANGE’S EQUATION OF MOTION......Page 56
CONSERVATION OF MOMENTUM......Page 57
SUMMARY......Page 59
REFERENCES......Page 60
INTRODUCTION......Page 61
ANALYSIS OF AN AXIAL ELEMENT......Page 62
TWO-DIMENSIONAL FRAME ELEMENT......Page 64
THREE-DIMENSIONAL FRAME ELEMENT......Page 68
MEMBER END-RELEASES......Page 72
SUMMARY......Page 73
INTRODUCTION......Page 74
A SIMPLE ONE-DIMENSIONAL EXAMPLE......Page 75
ONE-DIMENSIONAL INTEGRATION FORMULAS......Page 77
TWO-DIMENSIONAL SHAPE FUNCTIONS......Page 79
NUMERICAL INTEGRATION IN TWO DIMENSIONS......Page 83
THREE-DIMENSIONAL SHAPE FUNCTIONS......Page 85
TRIANGULAR AND TETRAHEDRAL ELEMENTS......Page 87
SUMMARY......Page 88
REFERENCES......Page 89
INTRODUCTION......Page 90
ELEMENTS WITH SHEAR LOCKING......Page 91
ADDITION OF INCOMPATIBLE MODES......Page 92
FORMATION OF ELEMENT STIFFNESS MATRIX......Page 93
INCOMPATIBLE TWO-DIMENSIONAL ELEMENTS......Page 94
EXAMPLE USING INCOMPATIBLE DISPLACEMENTS......Page 95
THREE-DIMENSIONAL INCOMPATIBLE ELEMENTS......Page 96
SUMMARY......Page 97
REFERENCES......Page 98
INTRODUCTION......Page 99
DISPLACEMENT BOUNDARY CONDITIONS......Page 100
NUMERICAL PROBLEMS IN STRUCTURAL ANALYSIS......Page 101
GENERAL THEORY ASSOCIATED WITH CONSTRAINTS......Page 102
FLOOR DIAPHRAGM CONSTRAINTS......Page 104
RIGID CONSTRAINTS......Page 109
USE OF CONSTRAINTS IN BEAM-SHELL ANALYSIS......Page 110
USE OF CONSTRAINTS IN SHEAR WALL ANALYSIS......Page 111
USE OF CONSTRAINTS FOR MESH TRANSITIONS......Page 112
LAGRANGE MULTIPLIERS AND PENALTY FUNCTIONS......Page 114
SUMMARY......Page 115
INTRODUCTION......Page 116
THE QUADRILATERAL ELEMENT......Page 118
STRAIN-DISPLACEMENT EQUATIONS......Page 122
THE QUADRILATERAL ELEMENT STIFFNESS......Page 123
SATISFYING THE PATCH TEST......Page 124
OTHER PLATE BENDING ELEMENTS......Page 125
NUMERICAL EXAMPLES......Page 126
One Element Beam......Page 127
Point Load On Simply Supported Square Plate......Page 128
Uniform Load On Simply Supported Square Plate......Page 129
Evaluation of Triangular Plate Bending Elements......Page 130
Use of Plate Element to Model Torsion in Beams......Page 131
REFERENCES......Page 132
INTRODUCTION......Page 133
BASIC ASSUMPTIONS......Page 134
DISPLACEMENT APPROXIMATION......Page 135
INTRODUCTION OF NODE ROTATION......Page 136
STRAIN-DISPLACEMENT EQUATIONS......Page 137
TRANSFORM RELATIVE TO ABSOLUTE ROTATIONS......Page 138
NUMERICAL EXAMPLE......Page 140
SUMMARY......Page 141
REFERENCES......Page 142
INTRODUCTION......Page 143
A SIMPLE QUADRILATERAL SHELL ELEMENT......Page 144
MODELING CURVED SHELLS WITH FLAT ELEMENTS......Page 145
TRIANGULAR SHELL ELEMENTS......Page 146
ANALYSIS OF THE SCORDELIS-LO BARREL VAULT......Page 147
HEMISPHERICAL SHELL EXAMPLE......Page 149
REFERENCES......Page 150
DEFINITION OF GEOMETRIC STIFFNESS......Page 151
APPROXIMATE BUCKLING ANALYSIS......Page 153
P-DELTA ANALYSIS OF BUILDINGS......Page 155
EQUATIONS FOR THREE-DIMENSIONAL BUILDINGS......Page 158
THE MAGNITUDE OF P-DELTA EFFECTS......Page 159
P-DELTA ANALYSIS WITHOUT COMPUTER PROGRAM MODIFICATION......Page 160
GENERAL FORMULATION OF GEOMETRY STIFFNESS......Page 161
SUMMARY......Page 163
REFERENCES......Page 164
INTRODUCTION......Page 165
DYNAMIC EQUILIBRIUM......Page 166
STEP-BY-STEP SOLUTION METHOD......Page 168
RESPONSE SPECTRA ANALYSIS......Page 169
SOLUTION IN THE FREQUENCY DOMAIN......Page 170
UNDAMPED HARMONIC RESPONSE......Page 171
UNDAMPED FREE VIBRATIONS......Page 172
SUMMARY......Page 173
REFERENCES......Page 174
EQUATIONS TO BE SOLVED......Page 175
TRANSFORMATION TO MODAL EQUATIONS......Page 176
RESPONSE DUE TO INITIAL CONDITIONS ONLY......Page 177
GENERAL SOLUTION DUE TO ARBITRARY LOADING......Page 179
SOLUTION FOR PERIODIC LOADING......Page 184
PARTICIPATING MASS RATIOS......Page 185
STATIC LOAD PARTICIPATION RATIOS......Page 187
DYNAMIC LOAD PARTICIPATION RATIOS......Page 188
SUMMARY......Page 190
INTRODUCTION......Page 191
DETERMINATE SEARCH METHOD......Page 192
INVERSE ITERATION......Page 193
GRAM-SCHMIDT ORTHOGONALIZATION......Page 194
BLOCK SUBSPACE ITERATION......Page 195
SOLUTION OF SINGULAR SYSTEMS......Page 196
GENERATION OF LOAD-DEPENDENT RITZ VECTORS......Page 197
A PHYSICAL EXPLANATION OF THE LDR ALGORITHM......Page 199
COMPARISON OF SOLUTIONS USING EIGEN AND RITZ VECTORS......Page 201
CORRECTION FOR HIGHER MODE TRUNCATION......Page 203
VERTICAL DIRECTION SEISMIC RESPONSE......Page 205
SUMMARY......Page 208
REFERENCES......Page 209
INTRODUCTION......Page 210
DEFINITION OF A RESPONSE SPECTRUM......Page 211
TYPICAL RESPONSE SPECTRUM CURVES......Page 213
THE CQC METHOD OF MODAL COMBINATION......Page 217
NUMERICAL EXAMPLE OF MODAL COMBINATION......Page 218
DESIGN SPECTRA......Page 221
ORTHOGONAL EFFECTS IN SPECTRAL ANALYSIS......Page 222
Basic Equations for Calculation of Spectral Forces......Page 223
The General CQC3 Method......Page 225
Examples of Three-Dimensional Spectra Analyses......Page 226
Story Drift Calculations......Page 230
Design Checks for Steel and Concrete Beams......Page 231
SUMMARY......Page 232
REFERENCES......Page 233
INTRODUCTION......Page 234
SITE RESPONSE ANALYSIS......Page 235
KINEMATIC OR SOIL STRUCTURE INTERACTION......Page 236
RESPONSE DUE TO MULTI-SUPPORT INPUT MOTIONS......Page 239
ANALYSIS OF GRAVITY DAM AND FOUNDATION......Page 242
THE MASSLESS FOUNDATION APPROXIMATION......Page 244
APPROXIMATE RADIATION BOUNDARY CONDITIONS......Page 245
USE OF SPRINGS AT THE BASE OF A STRUCTURE......Page 247
SUMMARY......Page 248
REFERENCES......Page 249
INTRODUCTION......Page 250
THREE-DIMENSIONAL COMPUTER MODEL......Page 252
THREE-DIMENSIONAL MODE SHAPES AND FREQUENCIES......Page 253
THREE-DIMENSIONAL DYNAMIC ANALYSIS......Page 257
Dynamic Design Base Shear......Page 258
Directional and Orthogonal Effects......Page 259
Dynamic Displacements and Member Forces......Page 260
NUMERICAL EXAMPLE......Page 261
DYNAMIC ANALYSIS METHOD SUMMARY......Page 264
SUMMARY......Page 265
REFERENCES......Page 267
INTRODUCTION......Page 268
STRUCTURES WITH A LIMITED NUMBER OF NONLINEAR ELEMENTS......Page 269
FUNDAMENTAL EQUILIBRIUM EQUATIONS......Page 270
CALCULATION OF NONLINEAR FORCES......Page 271
TRANSFORMATION TO MODAL COORDINATES......Page 272
SOLUTION OF NONLINEAR MODAL EQUATIONS......Page 274
STATIC NONLINEAR ANALYSIS OF FRAME STRUCTURE......Page 276
DYNAMIC NONLINEAR ANALYSIS OF FRAME STRUCTURE......Page 279
SEISMIC ANALYSIS OF ELEVATED WATER TANK......Page 281
SUMMARY......Page 282
INTRODUCTION......Page 284
ENERGY DISSIPATION IN REAL STRUCTURES......Page 285
MODAL DAMPING VIOLATES DYNAMIC EQUILIBRIUM......Page 287
NUMERICAL EXAMPLE......Page 288
STIFFNESS AND MASS PROPORTIONAL DAMPING......Page 289
CALCULATION OF ORTHOGONAL DAMPING MATRICES......Page 290
NONLINEAR ENERGY DISSIPATION......Page 292
REFERENCES......Page 293
INTRODUCTION......Page 294
NEWMARK FAMILY OF METHODS......Page 295
STABILITY OF NEWMARK’S METHOD......Page 297
THE AVERAGE ACCELERATION METHOD......Page 298
WILSON’S 
 FACTOR......Page 299
THE USE OF STIFFNESS PROPORTIONAL DAMPING......Page 300
THE HILBER, HUGHES AND TAYLOR 
 METHOD......Page 301
NONLINEAR ANALYSIS......Page 302
REFERENCES......Page 303
INTRODUCTION......Page 305
GENERAL THREE-DIMENSIONAL TWO-NODE ELEMENT......Page 306
GENERAL PLASTICITY ELEMENT......Page 307
DIFFERENT POSITIVE AND NEGATIVE PROPERTIES......Page 309
THE BILINEAR TENSION-GAP-YIELD ELEMENT......Page 310
NONLINEAR GAP-CRUSH ELEMENT......Page 311
VISCOUS DAMPING ELEMENTS......Page 312
THREE-DIMENSIONAL FRICTION-GAP ELEMENT......Page 314
SUMMARY......Page 316
INTRODUCTION......Page 317
EQUILIBRIUM EQUATIONS FOR DISPLACEMENT INPUT......Page 319
USE OF PSEUDO-STATIC DISPLACEMENTS......Page 321
SOLUTION OF DYNAMIC EQUILIBRIUM EQUATIONS......Page 322
Example Structure......Page 323
Effect of Time Step Size for Zero Damping......Page 325
Earthquake Analysis with Finite Damping......Page 328
The Effect of Mode Truncation......Page 331
USE OF LOAD DEPENDENT RITZ VECTORS......Page 333
SOLUTION USING STEP-BY-STEP INTEGRATION......Page 334
SUMMARY......Page 336
INTRODUCTION......Page 338
VECTOR CROSS PRODUCT......Page 339
VECTORS TO DEFINE A LOCAL REFERENCE SYSTEM......Page 341
FORTRAN SUBROUTINES FOR VECTOR OPERATIONS......Page 342
INTRODUCTION......Page 344
DEFINITION OF MATRIX NOTATION......Page 345
MATRIX TRANSPOSE AND SCALAR MULTIPLICATION......Page 347
PROGRAMMING MATRIX MULTIPLICATION......Page 349
SUMMARY......Page 350
INTRODUCTION......Page 352
NUMERICAL EXAMPLE......Page 353
THE GAUSS ELIMINATION ALGORITHM......Page 354
SOLUTION OF A GENERAL SET OF LINEAR EQUATIONS......Page 356
ALTERNATIVE TO PIVOTING......Page 357
MATRIX INVERSION......Page 359
PHYSICAL INTERPRETATION OF MATRIX INVERSION......Page 361
PARTIAL GAUSS ELIMINATION, STATIC CONDENSATION AND SUBSTRUCTURE ANALYSIS......Page 363
EQUATIONS STORED IN BANDED OR PROFILE FORM......Page 364
Triangularization or Factorization of the A Matrix......Page 367
Calculation of x by Backsubstitution......Page 369
DIAGONAL CANCELLATION AND NUMERICAL ACCURACY......Page 370
REFERENCES......Page 371
INTRODUCTION......Page 372
THE JACOBI METHOD......Page 373
CALCULATION OF 3D PRINCIPAL STRESSES......Page 375
SOLUTION OF THE GENERAL EIGENVALUE PROBLEM......Page 376
SUMMARY......Page 377
INTRODUCTION......Page 378
SUMMARY......Page 381
INTRODUCTION......Page 382
BASIC ASSUMPTIONS......Page 383
EFFECTIVE SHEAR AREA......Page 386
INTRODUCTION......Page 388
ONE-DIMENSIONAL GAUSS QUADRATURE......Page 389
NUMERICAL INTEGRATION IN TWO DIMENSIONS......Page 391
AN EIGHT-POINT TWO-DIMENSIONAL RULE......Page 392
AN EIGHT-POINT LOWER ORDER RULE......Page 393
A FIVE-POINT INTEGRATION RULE......Page 394
THREE-DIMENSIONAL INTEGRATION RULES......Page 395
SELECTIVE INTEGRATION......Page 397
SUMMARY......Page 398
DEFINITION OF ONE NUMERICAL OPERATION......Page 400
SPEED OF DIFFERENT COMPUTER SYSTEMS......Page 401
PAGING OPERATING SYSTEMS......Page 402
SUMMARY......Page 403
SIMPLE EXAMPLE......Page 404
GENERAL FORMULATION......Page 406
CALCULATION OF STRESSES WITHIN FINITE ELEMENTS......Page 407
INTRODUCTION......Page 410
GROUND ACCELERATION RECORDS......Page 411
CALCULATION OF ACCELERATION RECORD FROM DISPLACEMENT RECORD......Page 412
CREATING CONSISTENT ACCELERATION RECORD......Page 414
SUMMARY......Page 417
INDEX......Page 418