Prestressed concrete : a fundamental approach / Edward G. Nawy.

CONTENIDO
1 BASIC CONCEPTS 1
1.1 Introduction 1
1.1.1 Comparison with Reinforced Concrete 2
1.1.2 Economics of Prestressed Concrete 4
1.2 Historical Development of Prestressing 5
1.3 Basic Concepts of Prestressing 8
1.3.1 Introduction 8
1.3.2 Basic Concept Method 10
1.3.3 C-Line Method 13
1.3.4 Load-Balancing Method 16
1.4 Computation of Fiber Stresses in a Prestressed Beam by the Basic Method 19
1.5 C-Line Computation of Fiber Stresses 22
1.6 Load-Balancing Computation of Fiber Stresses 23
1.7 SI Working Stress Concepts 24
2 MATERIALS AND SYSTEMS FOR PRESTRESSING 29
2.1 Concrete 29
2.1.1 Introduction 29
2.1.2 Parameters Affecting the Quality of Concrete 29
2.1.3 Properties of Hardened Concrete 29
2.2 Stress-Strain Curve of Concrete 34
2.3 Modulus of Elasticity and Change in Compressive Strength with Time 34
2.4 Creep 41
2.4.1 Effects of Creep 44
2.4.2 Rheologial Models 44
2.5 Shrinkage 46
2.6 Nonprestressing Reinforcement 49
2.7 Prestressing Reinforcement 53
2.7.1 Types of Reinforcement 53
2.7.2 Stress-Relieved Wires and Strands 53
2.7.3 High-Tensile-Strength Prestressing Bars 55
2.7.4 Steel Relaxation 56
2.7.5 Corrosion and Deterioration of Strands 57
2.8 ACI Maximum Permissible Stresses in Concrete and Reinforcement 58
2.8.1 Concrete Stresses in Flexure 58
2.8.2 Prestressing Steel Stresses 58
2.9 AASHTO Maximum Permissible Stresses in Concrete and Reinforcement 59
2.9.1 Concrete Stress es before Creep and Shrinkage Losses 59
2.9.2 Concrete Stresses at Service Load after Losses 59
2.9.3 Prestressing Steel Stresses 60
2.9.4 Relative Humidity Values 60
2.10 Prestressing Systems and Anchorages 61
2.10.1 Pretensioning 61
2.10.2 Post-Tensioning 64
2.10.3 Jacking System 64
2.10.4 Grouting of Post-Tensioned Tendons 66
2.11 Circular Prestressing 68
2.12 Ten Principles 68
3 PARTIAL LOSS OF PRESTRESS 72
3.1 Introduction 72
3.2 Elastic Shortening of Concrete (ES) 75
3.2.1 Pretensioned Elements 75
3.2.2 Post-tensioned Elements 77
3.3 Steel Stress Relaxation (R) 78
3.3.1 Relaxation Loss Computation 79
3.3.2 ACI-ASCE Method of Accounting for Relaxation Loss 80
3.4 Creep Loss (CR) 81
3.4.1 Computation of Creep Loss 82
3.5 Shrinkage Loss (SH) 83
3.5.1 Computation of Shrinkage Loss 84
3.6 Losses Due to Friction (F) 85
3.6.1 Curvature Effect 85
3.6.2 Wobble Effect 87
3.6.3 Computation of Friction Loss 88
3.7 Anchorage-Seating Losses (A) 89
3.7.1 Computation of Anchorage-Seating Loss 89
3.8 Change of Prestress Due to Bending of Member 90
3.9 Step-by-Step Computation of AII Time-Dependent Losses in a Pre-Tension Beam 93
3.10 Step-by-Step Computation of AII Time-Dependent Losses in a Post-Tension Beam 97
3.11 Lump-Sum Computation of Time-Dependent Losses in Prestress 100
3.12 SI Prestress Loss Expressions 101
4 FLEXURAL DESIGN OF PRESTRESSED CONCRETE ELEMENTS 107
4.1 Introduction 107
4.2 Selection of Geometrical Properties of Section Components 110
4.2.1 General Guidelines 110
4.2.2 Minimum Section Modulus 110
4.3 Service-Load Design Examples 115
4.3.1 Variable Tendon Eccentricity 115
4.3.2 Variable Tendon Eccentricity with No Height Limitation 122
4.3.3 Constant Tendon Eccentricity 126
4.4 Proper Selection of Beam Sections and Properties 129
4.4.1 General Guidelines 129
4.4.2 Gross Area, the Transformed Section, and the Presence of Ducts 130
4.4.4 Advantages of Curved or Harped Tendons 132
4.4.5 Limiting-Eccentricity Envelopes 132
4.4.6 Prestressing Tendon Envelopes 137
4.4.7 Reduction of Prestress Force Near Supports 139
4.5 End Blocks at Support Anchorage Zones 141
4.5.1 Stress Distribution 141
4.5.2 Development and Transfer Length in Pretensioned Members 142
4.5.3 Design of Reinforcement 146
4.5.4 Design of End Anchorage for Post-Tensioned Beams 148
4.5.5 Design of End Anchorage for Pretensioned Beams 151
4.6 Flexural Design of Composite Beams 152
4.6.1 Unshored Slab Case 153
4.6.2 Fully Shored Case 154
4.6.3 Effective Flange Width 155
4.7 Summary of Step-by-Step Trial-and-Adjustment Procedure for the Service-Load Design of Prestressed Members 156
4.8 Design of Composite Post-Tensioned Prestressed Simply Supported Section 162
4.9 Ultimate-Strength Flexural Design 171
4.9.1 Cracking-Load Moment 171
4.9.2 Partial Prestressing 172
4.9.3 Cracking Moment Evaluation 173
4.10 Load and Strength Factors 174
4.10.1 Reliability and Structural Safety of Concrete Components 174
4.10.2 ACI Load Factors and Safety Margins 179
4.10.3 Design Strength vs. Nominal Strength: Strength Reduction Factor fi 180
4.10.4 AASHTO Strength Reduction Factors 181
4.10.5 ANSI Alternative Load and Strength Reduction Factors 181
4.11 Limit State in Flexure at Ultimate Load in Bonded Members: Decompression to Ultimate Load 182
4.11.1 Introduction 182
4.11.2 The Equivalent Rectangular Block and Nominal Moment Strength 185
4.12 Preliminary Ultimate-Load Design 196
4.13 Summary Step-by-Step Procedure for Limit at Failure Design of the Prestressed Members 197
4.14 Ultimate Strength Design of Prestressed Simply Supported Beam by Strain Compatibility 199
4.15 Strength Design of Bonded Prestressed Simply Supported Beam Using Approximate Procedures 205
4.16 Use of the ANSI Load and Strength Reduction Factors in Example 4.10 209
4.17 SI Flexural Design Expressions 210
5 SHEAR AND TORSIONAL STRENGTH DESIGN 217
5.1 Introduction 217
5.2 Behavior of Homogeneous Beams in Shear 218
5.3 Behavior of Concrete Beams as Nonhomogeneous Sections 222
5.4 Concrete Beams without Diagonal Tension Reinforcement 222
5.4.1 Modes of Failure of Beams without Diagonal Tension Reinforcement 223
5.4.2 Flexural Failure (F) 223
5.4.3 Diagonal Tension Failure (Flexural Shear, FS) 225
5.4.4 Shear Compression Failure (Web Shear, WS) 226
5.5 Shear and Principal Stresses in Prestressed Beams 227
5.5.1 Flexure-Shear Strength (Vci) 228
5.5.2 Web-Shear Strength (Vcw) 231
5.5.3 Controlling Values of Vci and Vcw for the Determination of Web Concrete Strength Vc 233
5.6 Web-Shear Reinforcement 233
5.6.1 Web Steel Planar Truss Analogy 233
5.6.2 Web Steel Resistance 236
5.6.3 Limitation on Size and Spacing of Stirrups 237
5.7 Horizontal Shear Strength in Composite Construction 238
5.7.1 Service-Load Level 238
5.7.2 Ultimate-Load Level 239
5.7.3 Design of Composite-Action Dowel Reinforcement 241
5.8 Web Reinforcement Design Procedure for Shear 242
5.9 Principal Tensile Stresses in Flanged Sections and Design of Dowel-Action Vertical Steel in Composite Sections 245
5.10 Dowel Steel Design for Composite Action 247
5.11 Dowel Reinforcement Design for Composite Action in an Inverted T-Beam 248
5.12 Shear Strength and Web-Shear Steel Design in a Prestressed Beam 250
5.13 Web-Shear Steel Design by Detailed Procedures 253
5.14 Design of Web Reinforcement for a PCI Standard Single Composite T -Beam 256
5.15 Brackets and Corbels 260
5.15.1 Shear Friction Hypothesis for Shear Transfer in Corbels 261
5.15.2 Horizontal External Force Effect 263
5.15.3 Sequence of Corbel Design Steps 266
5.15.4 Design of a Bracket or Corbel 251
5.15.5 SI Expressions for Shear in Prestressed Concrete Beams 270
5.15.6 SI Shear Design of Prestressed Beams 271
5.16 Torsional Behavior and Strength 275
5.16.1 Introduction 275
5.16.2 Pure Torsion in Plain Concrete Elements 277
5.17 Torsion in Reinforced and Prestressed Concrete Elements 283
5.17.1 Skew-Bending Theory 284
5.17.2 Space Truss Analogy Theory 286
5.17.3 Compression Field Theory 287
5.17.4 Plasticity Equilibrium Truss Theory 292
5.17.5 Design of Prestressed Concrete Beams Subjected to Combined Torsion, Shear and Bending in Accordance with the ACI 318-95 Code 298
5.18 Design Procedure for Combined Torsion and Shear 304
5.19 Flowchart for Design of Prestressed Concrete Beams in Combined Torsion and Shear 308
5.20 Design of Web Reinforcement for Combined Torsion and Shear in Prestressed Beams 308
5.21 SI Combined Torsion and Shear Design of Prestressed Beam 317
6 INDETERMINATE PRESTRESSED CONCRETE STRUCTURES 325
6.1 Introduction 325
6.2 Disadvantages of Continuity in Prestressing 326
6.3 Tendon Layout for Continuous Beams 326
6.4 Elastic Analysis for Prestress Continuity 329
6.4.1 Introduction 329
6.4.2 Support Displacement Method 329
6.4.3 Equivalent Load Method 333
6.5 Examples Involving Continuity 334
6.5.1 Effect of Continuity on Transformation of C-Line for Draped Tendons 334
6.5.2 Effect of Continuity on Transformation of C-Line for Harped Tendons 338
6.6 Linear Transformation and Concordance of Tendons 341
6.6.1 Verification of Tendon Linear Transformation Theorem 341
6.6.2 Concordance Hypotheses 344
6.7 Ultimate Strength and Limit State at Failure of Continuous Beams 347
6.8 Tendon Profile Envelope and Modifications 349
6.9 Tendon and C-Line Location in Continuous Beams 350
6.10 Tendon Transformation to Utilize Advantages of Continuity 360
6.11 Design for Continuity Using Nonprestressed Steel at Support 365
6.12 Indeterminate Frames and Portals 368
6.12.1 General Properties 368
6.12.2 Forces and Moments in Portal Frames 369
6.12.3 Application to Prestressed Concrete Frames 374
6.12.4 Design of Prestressed Concrete Bonded Frame 390
6.13 Limit Design (Analysis) of Indeterminate Beams and Frames 390
6.13.1 Method of Imposed Rotations 391
6.13.2 Determination of Plastic Hinge Rotations in Continuous Beams 394
6.13.3 Rotational Capacity of Plastic Hinges 398
6.13.4 Calculation of Available Rotational Capacity 400
6.13.5 Check for Plastic Rotation Serviceability 401
6.13.6 Transverse Confining Reinforcement for Seismic Design 402
6.13.7 Selection of Confining Reinforcement 405
7 CAMBER, DEFLECTION, AND CRACK CONTROL 409
7.1 Introduction 409
7.2 Basic Assumptions in Deflection Calculations 410
7.3 Short-Term (Instantaneous) Deflection of Uncracked and Cracked Members 410
7.3.1 Load-Deflection Relationship 410
7.3.2 Uncracked Sections 414
7.3.3 Cracked Sections 420
7.4 Short-Term Deflection at Service Load 425
7.5 Short-Term Deflection of Cracked Prestressed Beam 432
7.6 Construction of Moment-Curvature Diagram 433
7.7 Long-Term Effects on Deflection and Camber 439
7.7.1 PCI Multipliers Method 439
7.7.2 Incremental Time-Steps Method 441
7.7.3 Approximate Time-Steps Method 444
7.7.4 Computer Methods for Deflection Evaluation 446
7.7.5 Deflection of Composite Beams 446
7.8 Permissible Limits of Calculated Deflection 446
7.9 Long-Term Camber and Deflection Calculation by the PCI Multipliers Method 450
7.10 Long-Term Camber and Deflection Calculation by the Incremental Time-Steps Method 451
7.11 Long-Term Camber and Deflection Calculation by the Approximate Time-Steps Method 464
7.12 Long-Term Deflection of Composite Double T Cracked Beam 468
7.13 Cracking Behavior and Crack Control in Prestressed Beams 474
7.13.1 Introduction 474
7.13.2 Mathematical Model Formulation for Serviceability Evaluation 475
7.13.3 Expressions for Pretensioned Beams 476
7.13.4 Expressions for Post-Tensioned Beams 477
7.13.5 Long-Term Effects on Crack Width Development 479
7.13.6 Tolerable Crack Widths 480
7.14 Crack Width and Spacing Evaluation in Pretensioned T-Beam Without Mild Steel 480
7.15 Crack Width and Spacing Evaluation in Pretensioned T-Beam Containing Nonprestressed Steel 481
7.16 Crack Width and Spacing Evaluation in Pretensioned I-Beam Containing Nonprestressed Mild Steel 482
7.17 Crack Width and Spacing Evaluation for Post-tensioned T-Beam Containing Nonprestressed 483
7.18 SI Deflection and Cracking Expressions 484
7.19 SI Deflection Control 485
7.20 SI Crack Control 490
8 PRESTRESSED COMPRESSION AND TENSION MEMBERS 459
8.1 Introduction 495
8.2 Prestressed Compression Members: Load-Moment Interaction in Columns and Piles 496
8.3 Strength Reduction Factor Fi 502
8.4 Operational Procedure for the Design of Nonslender Prestressed Compression Members 506
8.5 Construction of Nominal Load-Moment (Pn-Mn) and Design (Pu-Mu) Interaction Diagrams 508
8.6 Limit State at Buckling Failure of Slender (Long) Prestressed Columns 513
8.7 Moment Magnification Method-First Order Analysis 518
8.8 Second-Order Frame Analysis and P-Delta Effects 521
8.9 Operational Procedure and Flowchart for the Design of Slender Columns 523
8.10 Design of Slender (Long) Prestressed Column 523
8.11 Compression Members in Biaxial Bending 530
8.11.1 Exact Method of Analysis 530
8.11.2 Load Contour Method of Analysis 532
8.11.3 Step-by-Step Operational Procedure for the Design of Biaxially Loaded Columns 534
8.12 Practical Design Considerations 536
8.12.1 Longitudinal or Main Reinforcement 536
8.12.2 Lateral Reinforcement for Columns 536
8.13 Design of Spiral Lateral Reinforcement 539
8.14 Prestressed Tension Members 539
8.14.1 Service-Load Stresses 539
8.14.2 Deformation Behavior 542
8.14.3 Decompression and Cracking 542
8.14.4 Limit State at Failure and Safety Factors 543
8.15 Suggested Step-by-Step Procedure for the Design of Tension Members 543
8.16 Design of Linear Tension Members 545
9 TWO-WAY PRESTRESSED CONCRETE FLOOR SYSTEMS 550
9.1 Introduction: Review of Methods 550
9.1.1 The Semielastic ACI Code Approach 553
9.1.2 The Yield-Line Theory 553
9.1.3 The Limit Theory of Plates 553
9.1.4 The Strip Method 554
9.1.5 Summary 554
9.2 Flexural Behavior of Two-Way Slabs and Plates 554
9.2.1 Two-Way Action 554
9.2.2 Relative Stiffness Effects 555
9.3 Tbe Equivalent Frame Method 556
9.3.1 Introduction 556
9.3.2 Limitations of the Direct Design Method 557
9.3.3 Determination of the Statical Moment Mo 557
9.3.4 Equivalent Frame Analysis 560
9.3.5 Pattern Loading of Spans 563
9.4 Two-Directional Load Balancing 564
9.5 Flexural Strength of Prestressed Plates 569
9.5.1 Design Moments Mu 569
9.6 Bending of Prestressing Tendons and Limiting Concrete Stresses 570
9.6.1 Distribution of Prestressing Tendons 570
9.6.2 Limiting Concrete Tensile Stresses at Service Load (ft, psi) 572
9.7 Load-Balancing Design of a Single-Panel Two-Way Floor Slab 575
9.8 One-Way Slab Systems 581
9.9 Shear-Moment Transfer to Columns Supporting Flat Plates 581
9.9.1 Shear Strength 581
9.9.2 Shear-Moment Transfer 581
9.9.3 Deflection Requirements for Minimum Thickness-An Indirect Approach 584
9.10 Step-by-Step Trial-and-Adjustment Procedure for the Design of a Two-Way Prestressed Slab and Plate System 586
9.11 Design of Prestressed Post-Tensioned Flat-Plate Floor System 592
9.12 Direct Method of Deflection Evaluation 611
9.12.1 The Equivalent Frame Approach 611
9.12.2 Column and Middle Strip Deflections 613
9.13 Deflection Evaluation of Two-Way Prestressed Concrete Floor Slabs 614
9.14 Yield-Line Theory for Two-Way-Action Plates 618
9.14.1 Fundamental Concepts of Hinge-Field Failure Mechanisms in Flexure 619
9.14.2 Failure Mechanisms and Moment Capacities of Slabs of Various Shapes Subjected to Distributed or Concentrated Loads 624
9.15 Yield-Line Moment Strength of a Two-Way Prestressed Concrete Plate 631
10 CONNECTIONS FOR PRESTRESSED CONCRETE ELEMENTS 635
10.1 Introduction 635
10.2 Tolerances 636
10.3 Composite Members 636
10.4 Reinforced Concrete Bearing in Composite Members 637
10.4.1 Reinforced Bearing Design 641
10.5 Dapped-End Beam Connections 643
10.5.1 Determination of Reinforcement to Resist Failure 645
10.5.2 Dapped-End Beam Connection Design 648
10.6 Reinforced Concrete Brackets and Corbels 650
10.7 Concrete Beam Ledges 650
10.7.1 Design of Ledge Beam Connection 653
10.8 Selected Connection Details 655
11 PRESTRESSED CONCRETE CIRCULAR STORAGE TANKS AND STEEL ROOFS 664
11.1 Introduction 664
11.2 Design Principles and Procedures 665
11.2.1 Internal Loads 665
11.2.2 Restraining Moment Mo and Radial Shear Force Qo at Freely Sliding Wall Base Fuel to Liquid Pressure 667
11.2.3 General Equations of Forces and Displacements 672
11.2.4 Ring Shear Qo and Moment Mo, Gas Containment 676
11.3 Moment Mo and Ring Force Qo in Liquid-Retaining Tank 677
11.4 Ring Force Qy at Intermediate Heights of Wall 679
11.5 Cylindrical Steel Membrane Coefficients 680
11.6 Prestressing Effects on Wall Stresses for Fully Hinged, Partially Sliding and Hinged, Fully Fixed, and Partially Fixed Bases 698
11.6.1 Freely Sliding Wall Base 698
11.6.2 Hinged Wall Base 698
11.6.3 Partially Sliding and Hinged Wall Base 699
11.6.4 Fully Fixed Wall Base 701
11.6.5 Partially Fixed Wall Base 703
11.7 Recommended Practice for Situ-Cast and Precast Prestressed Concrete Circular Storage Tanks 709
11.7.1 Stresss 709
11.7.2 Required Strength Load Factors 709
11.7.3 Minimum Wall Design Requirements 711
11.8 Crack Control in Walls of Circular Prestressed Concrete Tanks 713
11.9 Tank Roof Design 713
11.9.1 Membrane Theory of Spherieal Domes 714
11.10 Prestressed Concrete Tanks with Circumferential Tendons 720
11.11 Step-by-Step Procedure for the Design of Circular Prestressed Concrete Tanks and Dome Roofs 721
11.12 Design of Circular Prestressed Concrete Water-Retaining Tank and Its Domed Roof 729