Unified Theory of Concrete Structures

UNIFIED THEORY\nOF CONCRETE\nSTRUCTURES......Page 4
Contents......Page 8
About the Authors......Page 14
Preface......Page 18
Instructors’ Guide......Page 20
1.1 Overview......Page 22
1.2.1 Structural Analysis......Page 23
1.2.2 Main Regions vs Local Regions......Page 24
1.2.3 Member and Joint Design......Page 26
1.3.1 Principles and Applications of the Six Models......Page 27
1.3.2 Historical Development of Theories for Reinforced Concrete......Page 28
1.4.1 General Description......Page 34
1.4.2 Struts-and-ties Model for Beams......Page 35
1.4.3 Struts-and-ties Model for Knee Joints......Page 36
1.4.4 Comments......Page 41
2.1.1 Equilibrium in Bending......Page 44
2.1.2 Equilibrium in Element Shear......Page 45
2.1.3 Equilibrium in Beam Shear......Page 54
2.1.4 Equilibrium in Torsion......Page 55
2.1.5 Summary of Basic Equilibrium Equations......Page 57
2.2.1 Shear–Bending Interaction......Page 59
2.2.2 Torsion–Bending Interaction......Page 62
2.2.3 Shear–Torsion–Bending Interaction......Page 65
2.3 ACI Shear and Torsion Provisions......Page 72
2.3.1 Torsional Steel Design......Page 73
2.3.2 Shear Steel Design......Page 76
2.3.3 Maximum Shear and Torsional Strengths......Page 77
2.3.4 Other Design Considerations......Page 79
2.3.5 Design Example......Page 81
2.4 Comments on the Equilibrium (Plasticity) Truss Model......Page 88
3.1.1 Bernoulli Compatibility Truss Model......Page 92
3.1.2 Transformed Area for Reinforcing Bars......Page 98
3.1.3 Bending Rigidities of Cracked Sections......Page 99
3.1.4 Bending Rigidities of Uncracked Sections......Page 103
3.1.5 Bending Deflections of Reinforced Concrete Members......Page 105
3.2.1 Bernoulli Compatibility Truss Model......Page 109
3.2.2 Singly Reinforced Rectangular Beams......Page 114
3.2.3 Doubly Reinforced Rectangular Beams......Page 122
3.2.4 Flanged Beams......Page 126
3.2.5 Moment–Curvature (M–φ) Relationships......Page 129
3.3.1 Plastic Centroid and Eccentric Loading......Page 133
3.3.2 Balanced Condition......Page 136
3.3.3 Tension Failure......Page 137
3.3.4 Compression Failure......Page 139
3.3.5 Bending–Axial Load Interaction......Page 142
3.3.6 Moment–Axial Load–Curvature (M-N- φ) Relationship......Page 143
4.1.1 Stress Transformation......Page 146
4.1.2 Mohr Stress Circle......Page 148
4.1.3 Principal Stresses......Page 152
4.2.1 Strain Transformation......Page 153
4.2.2 Geometric Relationships......Page 155
4.2.3 Mohr Strain Circle......Page 157
4.2.4 Principle Strains......Page 158
4.3.1 Stress Condition and Crack Pattern in RC 2-D Elements......Page 159
4.3.2 Fixed Angle Theory......Page 161
4.3.3 Rotating Angle Theory......Page 163
4.3.4 ‘Contribution of Concrete’ (Vc)......Page 164
4.3.5 Mohr Stress Circles for RC Shear Elements......Page 166
5.1.1 Transformation Type of Equilibrium Equations......Page 170
5.1.2 First Type of Equilibrium Equations......Page 171
5.1.3 Second Type of Equilibrium Equations......Page 173
5.1.4 Equilibrium Equations in Terms of Double Angle......Page 174
5.1.5 Example Problem 5.1 Using Equilibrium (Plasticity) Truss Model......Page 175
5.2.1 Transformation Type of Compatibility Equations......Page 179
5.2.2 First Type of Compatibility Equations......Page 180
5.2.3 Second Type of Compatibility Equations......Page 181
5.2.4 Crack Control......Page 182
5.3.1 Basic Principles of MCTM......Page 186
5.3.2 Summary of Equations......Page 187
5.3.3 Solution Algorithm......Page 188
5.3.4 Example Problem 5.2 using MCTM......Page 189
5.3.5 Allowable Stress Design of RC 2-D Elements......Page 193
5.4.1 Basic Principles of RA-STM......Page 194
5.4.2 Summary of Equations......Page 195
5.4.3 Solution Algorithm......Page 199
5.4.4 Example Problem 5.3 for Sequential Loading......Page 202
5.4.5 2-D Elements under Proportional Loading......Page 209
5.4.6 Example Problem 5.4 for Proportional Loading......Page 215
5.4.7 Failure Modes of RC 2-D Elements......Page 223
5.5 Concluding Remarks......Page 230
6.1.1 Basic Principles of SMM......Page 232
6.1.2 Research in RC 2-D Elements......Page 234
6.1.3 Poisson Effect in Reinforced Concrete......Page 237
6.1.4 Hsu/Zhu Ratios ν12 and ν21......Page 240
6.1.5 Experimental Stress–Strain Curves......Page 246
6.1.6 Softened Stress–Strain Relationship of Concrete in Compression......Page 248
6.1.7 Softening Coefficient ζ......Page 249
6.1.8 Smeared Stress–Strain Relationship of Concrete in Tension......Page 253
6.1.9 Smeared Stress–Strain Relationship of Mild Steel Bars in Concrete......Page 257
6.1.10 Smeared Stress–Strain Relationship of Concrete in Shear......Page 266
6.1.11 Solution Algorithm......Page 267
6.1.12 Example Problem 6.1......Page 269
6.2.1 Basic Principles of FA-STM......Page 276
6.2.2 Solution Algorithm......Page 278
6.2.3 Example Problem 6.2......Page 280
6.3.1 Basic Principles of CSMM......Page 287
6.3.2 Cyclic Stress–Strain Curves of Concrete......Page 288
6.3.3 Cyclic Stress–Strain Curves of Mild Steel......Page 293
6.3.5 Solution Procedure......Page 295
6.3.6 Hysteretic Loops......Page 297
6.3.7 Mechanism of Pinching and Failure under Cyclic Shear......Page 302
6.3.8 Eight Demonstration Panels......Page 305
6.3.10 Shear Ductility......Page 309
6.3.11 Shear Energy Dissipation......Page 310
7.1.1 Equilibrium Equations......Page 316
7.1.2 Compatibility Equations......Page 318
7.1.3 Constitutive Relationships of Concrete......Page 323
7.1.4 Governing Equations for Torsion......Page 328
7.1.5 Method of Solution......Page 330
7.1.6 Example Problem 7.1......Page 335
7.2.1 Analogy between Torsion and Bending......Page 341
7.2.2 Various Definitions of Lever Arm Area, Ao......Page 343
7.2.3 Thickness td of Shear Flow Zone for Design......Page 344
7.2.4 Simplified Design Formula for td......Page 347
7.2.5 Compatibility Torsion in Spandrel Beams......Page 349
7.2.6 Minimum Longitudinal Torsional Steel......Page 358
7.2.7 Design Examples 7.2......Page 359
8.1.1 Beams Subjected to Midspan Concentrated Load......Page 364
8.1.2 Beams Subjected to Uniformly Distributed Load......Page 367
8.2.1 Analysis of Beams Subjected to Uniformly Distributed Load......Page 371
8.2.2 Stirrup Forces and Triangular Shear Diagram......Page 372
8.2.3 Longitudinal Web Steel Forces......Page 375
8.2.4 Steel Stresses along a Diagonal Crack......Page 376
8.3.1 Background Information......Page 377
8.3.2 Prestressed Concrete I-Beam Tests at University of Houston......Page 378
8.3.3 UH Shear Strength Equation......Page 385
8.3.4 Maximum Shear Strength......Page 389
8.3.5 Minimum Stirrup Requirement......Page 392
8.3.6 Comparisons of Shear Design Methods with Tests......Page 393
8.3.7 Shear Design Example......Page 396
8.3.8 Three Shear Design Examples......Page 400
9.1.1 Finite Element Analysis (FEA)......Page 402
9.1.2 OpenSees–an Object-oriented FEA Framework......Page 404
9.1.4 FEA Formulations of 1-D and 2-D Models......Page 405
9.2.1 Material Models in OpenSees......Page 406
9.2.2 Material Models Developed at UH......Page 409
9.3 1-D Fiber Model for Frames......Page 413
9.4.1 Coordinate Systems for Concrete Structures......Page 414
9.4.2 Implementation......Page 415
9.5.1 Single Degree of Freedom versus Multiple Degrees of Freedom......Page 417
9.5.2 A Three-degrees-of-freedom Building......Page 420
9.5.3 Damping......Page 421
9.6.1 Load Control Iteration Scheme......Page 423
9.6.3 Dynamic Analysis Iteration Scheme......Page 424
9.7 Nonlinear Finite Element Program SCS......Page 427
10.1 RC Panels Under Static Load......Page 432
10.2 Prestresed Concrete Beams Under Static Load......Page 434
10.3.1Framed Shear Wall Units at UH......Page 436
10.3.2 Low-rise Framed Shear Walls at NCREE......Page 440
10.3.3 Mid-rise Framed Shear Walls at NCREE......Page 441
10.4 Post-tensioned Precast Bridge Columns under Reversed Cyclic Load......Page 443
10.5 Framed Shear Walls under Shake Table Excitations......Page 446
10.6 A Seven-story Wall Building under Shake Table Excitations......Page 449
Appendix......Page 454
References......Page 502
Index......Page 510