Ductile Design ofinsaat.eskisehir.edu.tr/kivanct/İNŞ632/icerik/ductile...Dr. Uang has authored...

Ductile Design of Steel Structures

00_Bruneau_FM_pi-xxii.indd 1 6/13/11 3:01:10 PM

About the AuthorsMichel Bruneau, Ph.D., P.Eng., is Professor in the Department of Civil, Structural, and Environmental Engineering at the State University of New York at Buffalo, and an ASCE Fellow. He is a member of various AISC and CSA committees developing seis-mic design specifications for bridges and buildings. Dr. Bruneau has conducted extensive research on the evaluation and retrofit of existing steel structures sub-jected to large destructive forces. He has authored more than 400 technical publications and has received many awards for his work.

Chia-Ming Uang, Ph.D., is Professor in the Depart-ment of Structural Engineering at the University of California, San Diego. A member of the AISC’s Com-mittee on Specification and Committee on Research, he received the AISC Special Achievement Award in 2007. Dr. Uang has authored numerous articles on seismic behavior and design of steel structures.

Rafael Sabelli, S.E., is a Principal and Director of Seis-mic Design at Walter P. Moore and Associates, Inc., and was President of the Structural Engineers Association of California from 2009 to 2010. He is a member of the AISC Task Committee on the Seismic Provisions for Structural Steel Buildings and the ASCE 7 Seismic Sub-committee. Mr. Sabelli is the coauthor of AISC Design Guide 20: Steel Plate Shear Walls as well as of numerous research papers on conventional and buckling-restrained braced frames.


Ductile Design of Steel Structures

Michel Bruneau, Ph.D., P.Eng.

Chia-Ming Uang, Ph.D.

Rafael Sabelli, S.E.

Second Edition

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v

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Structural Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Common Properties of Steel Materials . . . . 8

2.2.1 Engineering Stress-Strain Curve . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Effect of Temperature on Stress-Strain Curve . . . . . . . . . . . . . 10

2.2.3 Effect of Temperature on Ductility and Notch-Toughness . . . . . . . . . . 15

2.2.4 Strain Rate Effect on Tensile and Yield Strengths . . . . . . . . . . . . . . . . 22

2.2.5 Probable Yield Strength . . . . . . . . . 222.3 Plasticity, Hysteresis, Bauschinger Effects . . . . 292.4 Metallurgical Process of Yielding,

Slip Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.5 Brittleness in Welded Sections . . . . . . . . . . . . 35

2.5.1 Metallurgical Transformations During Welding, Heat-Affected Zone, Preheating . . . . . . . . . . . . . . . 35

2.5.2 Hydrogen Embrittlement . . . . . . . 372.5.3 Carbon Equivalent . . . . . . . . . . . . . 402.5.4 Flame Cutting . . . . . . . . . . . . . . . . . 412.5.5 Weld Restraints . . . . . . . . . . . . . . . . 412.5.6 Lamellar Tearing . . . . . . . . . . . . . . . 442.5.7 Thick Steel Sections . . . . . . . . . . . . . 472.5.8 Fracture Mechanics . . . . . . . . . . . . . 492.5.9 Partial Penetration Welds . . . . . . . 50

2.5.10 K-Area Fractures . . . . . . . . . . . . . . . 502.5.11 Strain Aging . . . . . . . . . . . . . . . . . . . 542.5.12 Stress Corrosion . . . . . . . . . . . . . . . 552.5.13 Corrosion Fatigue . . . . . . . . . . . . . . 572.5.14 Ductility of Corroded Steel . . . . . . 60

2.6 Low-Cycle versus High-Cycle Fatigue . . . . 622.6.1 High-Cycle Fatigue . . . . . . . . . . . . . 622.6.2 Low-Cycle Fatigue . . . . . . . . . . . . . 62


vi C o n t e n t s C o n t e n t s vii

2.7 Material Models . . . . . . . . . . . . . . . . . . . . . . . 702.7.1 Rigid Plastic Model . . . . . . . . . . . . . 702.7.2 Elasto-Plastic Models . . . . . . . . . . . 702.7.3 Power, Ramberg-Osgood, and

Menegotto-Pinto Functions . . . . . . 722.7.4 Smooth Hysteretic Models . . . . . . 80

2.8 Advantages of Plastic Material Behavior . . . 942.9 Self-Study Problems . . . . . . . . . . . . . . . . . . . . 100

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3 Plastic Behavior at the Cross-Section Level . . . . . . 1113.1 Pure Flexural Yielding . . . . . . . . . . . . . . . . . . 111

3.1.1 Doubly Symmetric Sections . . . . . 1123.1.2 Sections Having a Single Axis of

Symmetry . . . . . . . . . . . . . . . . . . . . . 1173.1.3 Impact of Some Factors on Inelastic

Flexural Behavior . . . . . . . . . . . . . . 1203.1.4 Behavior During Cyclic Loading . . . 127

3.2 Combined Flexural and Axial Loading . . . . 1293.2.1 Rectangular Cross-Section . . . . . . . 1323.2.2 Wide-Flange Sections: Strong-Axis

Bending . . . . . . . . . . . . . . . . . . . . . . 1323.2.3 Wide-Flange Sections: Weak-Axis

Bending . . . . . . . . . . . . . . . . . . . . . . 1363.2.4 Moment-Curvature Relationships 137

3.3 Combined Flexural and Shear Loading . . . . 1373.4 Combined Flexural, Axial, and

Shear Loading . . . . . . . . . . . . . . . . . . . . . . . . . 1423.5 Pure Plastic Torsion: Sand-Heap Analogy . . . . 145

3.5.1 Review of Important Elastic Analysis Results . . . . . . . . . . . . . . . 145

3.5.2 Sand-Heap Analogy . . . . . . . . . . . . 1463.6 Combined Flexure and Torsion . . . . . . . . . . . 1483.7 Biaxial Flexure . . . . . . . . . . . . . . . . . . . . . . . . . 150

3.7.1 General Principles . . . . . . . . . . . . . . 1503.7.2 Fiber Models . . . . . . . . . . . . . . . . . . 158

3.8 Composite Sections . . . . . . . . . . . . . . . . . . . . . 1603.9 Self-Study Problems . . . . . . . . . . . . . . . . . . . . 163

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

4 Concepts of Plastic Analysis . . . . . . . . . . . . . . . . . . . 1754.1 Introduction to Simple Plastic Analysis . . . . 1754.2 Simple Plastic Analysis Methods . . . . . . . . . 178

4.2.1 Event-to-Event Calculation (Step-by-Step Method) . . . . . . . . . . 178


vi C o n t e n t s C o n t e n t s vii

4.2.2 Equilibrium Method (Statical Method) . . . . . . . . . . . . . . . 181

4.2.3 Kinematic Method (Virtual-Work Method) . . . . . . . . . 186

4.3 Theorems of Simple Plastic Analysis . . . . . . 1914.3.1 Upper Bound Theorem . . . . . . . . . 1924.3.2 Lower Bound Theorem . . . . . . . . . 1924.3.3 Uniqueness Theorem . . . . . . . . . . . 192

4.4 Application of the Kinematic Method . . . . . 1934.4.1 Basic Mechanism Types . . . . . . . . . 1934.4.2 Combined Mechanism . . . . . . . . . . 1954.4.3 Mechanism Analysis by

Center of Rotation . . . . . . . . . . . . . . 2024.4.4 Distributed Loads . . . . . . . . . . . . . . 207

4.5 Shakedown Theorem (Deflection Stability) . . . . . . . . . . . . . . . . . . . . 215

4.6 Yield Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2224.6.1 General Framework . . . . . . . . . . . . 2224.6.2 Strength of Connections . . . . . . . . . 2294.6.3 Plastic Mechanisms of

Local Buckling . . . . . . . . . . . . . . . . . . 2354.7 Self-Study Problems . . . . . . . . . . . . . . . . . . . . 238

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

5 Systematic Methods of Plastic Analysis . . . . . . . . . 2495.1 Number of Basic Mechanisms . . . . . . . . . . . . 2495.2 Direct Combination of Mechanisms . . . . . . . 253

5.2.1 Example: One-Bay, One-Story Frame . . . . . . . . . . . . . . . . . . . . . . . . . . 253

5.2.2 Example: Two-Story Frame with Overhanging Bay . . . . . . . . . . . . . . 256

5.3 Method of Inequalities . . . . . . . . . . . . . . . . . . 2595.4 Self-Study Problems . . . . . . . . . . . . . . . . . . . . 266

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

6 Applications of Plastic Analysis . . . . . . . . . . . . . . . . 2736.1 Moment Redistribution Design Methods . . . 274

6.1.1 Statical Method of Design . . . . . . . 2746.1.2 Autostress Design Method . . . . . . 276

6.2 Capacity Design . . . . . . . . . . . . . . . . . . . . . . . 2796.2.1 Concepts . . . . . . . . . . . . . . . . . . . . . . 2796.2.2 Shear Failure Protection . . . . . . . . . 2816.2.3 Protection Against Column

Hinging . . . . . . . . . . . . . . . . . . . . . . . 284


viii C o n t e n t s C o n t e n t s ix

6.3 Push-Over Analysis . . . . . . . . . . . . . . . . . . . . 2856.3.1 Monotonic Push-Over Analysis . . . 2876.3.2 Cyclic Push-Over Analysis . . . . . . 294

6.4 Seismic Design Using Plastic Analysis . . . . 2956.5 Global versus Local Ductility Demands . . . 296

6.5.1 Displacement Ductility versus Curvature Ductility . . . . . . . . . . . . . 296

6.5.2 Ductility of Yielding Link for Structural Element in Series . . . . . 300

6.6 Displacement Compatibility of Nonductile Systems . . . . . . . . . . . . . . . . . . . . 302

6.7 Self-Study Problems . . . . . . . . . . . . . . . . . . . . 303References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

7 Building Code Seismic Design Philosophy . . . . . . 3097.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3097.2 Need for Ductility in Seismic Design . . . . . . 309

7.2.1 Elastic Response and Response Spectrum . . . . . . . . . . . . . . . . . . . . . 310

7.2.2 Inelastic Response and Ductility Reduction . . . . . . . . . . . . . . . . . . . . . 312

7.3 Collapse Mechanism versus Yield Mechanism . . . . . . . . . . . . . . . . . . . . . . . 315

7.4 Design Earthquake . . . . . . . . . . . . . . . . . . . . . 3167.5 Equivalent Lateral Force Procedure . . . . . . . 3187.6 Physical Meaning of Seismic

Performance Factors . . . . . . . . . . . . . . . . . . . . 3207.7 Capacity Design . . . . . . . . . . . . . . . . . . . . . . . 322

7.7.1 Global-Level Approach . . . . . . . . . 3237.7.2 Local-Level Approach . . . . . . . . . . 324

7.8 Performance-Based Seismic Design Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

7.8.1 Seismic Performance Objective . . . 3277.8.2 USA: ASCE 7 . . . . . . . . . . . . . . . . . . 3287.8.3 Canada: NBCC . . . . . . . . . . . . . . . . 3297.8.4 Japan: BSL . . . . . . . . . . . . . . . . . . . . 3317.8.5 Seismic Design of Tall Buildings . . . 3337.8.6 Next-Generation Performance-Based

Seismic Design . . . . . . . . . . . . . . . . . 3357.9 Historical Perspective of Seismic Codes . . . 336

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

8 Design of Ductile Moment-Resisting Frames . . . . 3458.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

8.1.1 Historical Developments . . . . . . . . 346


viii C o n t e n t s C o n t e n t s ix

8.1.2 General Behavior and Plastic Mechanism . . . . . . . . . . . . . 347

8.1.3 Design Philosophy . . . . . . . . . . . . . 3478.2 Basic Response of Ductile Moment-Resisting

Frames to Lateral Loads . . . . . . . . . . . . . . . . . 3488.2.1 Internal Forces During Seismic

Response . . . . . . . . . . . . . . . . . . . . . . 3488.2.2 Plastic Rotation Demands . . . . . . . 3508.2.3 Lateral Bracing and

Local Buckling . . . . . . . . . . . . . . . . . 3518.3 Ductile Moment-Frame Column Design . . . 352

8.3.1 Axial Forces in Columns . . . . . . . . 3528.3.2 Considerations for

Column Splices . . . . . . . . . . . . . . . . 3528.3.3 Strong-Column/Weak-Beam

Philosophy . . . . . . . . . . . . . . . . . . . . 3538.3.4 Effect of Axial Forces on

Column Ductility . . . . . . . . . . . . . . 3578.4 Panel Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

8.4.1 Flange Distortion and Column Web Yielding/Crippling Prevention . . . 358

8.4.2 Forces on Panel Zones . . . . . . . . . . 3628.4.3 Behavior of Panel Zones . . . . . . . . 3648.4.4 Modeling of Panel Zone Behavior . . . 3708.4.5 Design of Panel Zone . . . . . . . . . . . 374

8.5 Beam-to-Column Connections . . . . . . . . . . . 3778.5.1 Knowledge and Practice Prior

to the 1994 Northridge Earthquake . . . . . . . . . . . . . . . . . . . . 377

8.5.2 Damage During the Northridge Earthquake . . . . . . . . . . . . . . . . . . . . 389

8.5.3 Causes for Failures . . . . . . . . . . . . . 4018.5.4 Reexamination of Pre-Northridge

Practice . . . . . . . . . . . . . . . . . . . . . . . 4108.5.5 Post-Northridge Beam-to-Column

Connections Design Strategies for New Buildings—Initial Concepts . . . 412

8.5.6 Post-Northridge Beam-to-Column Prequalified Connections . . . . . . . . 432

8.5.7 International Relevance . . . . . . . . . 4388.5.8 Semi-Rigid (Partially Restrained)

Bolted Connections . . . . . . . . . . . . . 4468.6 Design of a Ductile Moment Frame . . . . . . . 450

8.6.1 General Connection Design Issues 450


x C o n t e n t s C o n t e n t s xi

8.6.2 Welding and Quality Control Issues . . . . . . . . . . . . . . . . . . . . . . . . . 451

8.6.3 Generic Design Procedure . . . . . . . 4528.7 P-D Stability of Moment Resisting

Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4588.7.1 Fundamental Concept and

Parameters . . . . . . . . . . . . . . . . . . . . 4598.7.2 Impact on Hysteretic Behavior . . . 4618.7.3 Design Requirements . . . . . . . . . . . 463

8.8 Design Example . . . . . . . . . . . . . . . . . . . . . . . . 4648.8.1 Building Description and

Loading . . . . . . . . . . . . . . . . . . . . . . . 4658.8.2 Global Requirements . . . . . . . . . . . 4658.8.3 Basis of Design . . . . . . . . . . . . . . . . 4668.8.4 Iterative Analysis and

Proportioning . . . . . . . . . . . . . . . . . 4678.8.5 Member Checks . . . . . . . . . . . . . . . . 4708.8.6 WUF-W Connection Design . . . . . 4728.8.7 Detailing . . . . . . . . . . . . . . . . . . . . . 4838.8.8 Bracing . . . . . . . . . . . . . . . . . . . . . . . 4838.8.9 Completion of Design . . . . . . . . . . 486


9 Design of Ductile Concentrically Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4999.1.1 Historical Developments . . . . . . . . 4999.1.2 General Behavior and Plastic

Mechanism . . . . . . . . . . . . . . . . . . . . 5029.1.3 Design Philosophy . . . . . . . . . . . . . 503

9.2 Hysteretic Behavior of Single Braces . . . . . . 5069.2.1 Brace Physical Inelastic Cyclic

Behavior . . . . . . . . . . . . . . . . . . . . . . 5069.2.2 Brace Slenderness . . . . . . . . . . . . . . 5089.2.3 Compression Strength Degradation

of Brace Under Repeated Loading . . . . . . . . . . . . . . . . . . . . . . . 516

9.2.4 Brace Compression Overstrength at First Buckling . . . . . . . . . . . . . . . 521

9.2.5 Evolution of Codified Strength and Slenderness Limits . . . . . . . . . . . . . 523

9.2.6 Local Buckling . . . . . . . . . . . . . . . . . 5239.2.7 Low-Cycle Fatigue Models . . . . . . 5299.2.8 Models of Single Brace Behavior . . . 535


x C o n t e n t s C o n t e n t s xi

9.3 Hysteretic Behavior and Design of Concentrically Braced Frames . . . . . . . . . . . 536

9.3.1 System Configuration and General Issues . . . . . . . . . . . . . . . . . 536

9.3.2 Brace Design . . . . . . . . . . . . . . . . . . 5429.3.3 Beam Design . . . . . . . . . . . . . . . . . . 5479.3.4 Column Design . . . . . . . . . . . . . . . . 5529.3.5 Connection Design . . . . . . . . . . . . . 5569.3.6 Other Issues . . . . . . . . . . . . . . . . . . . 560

9.4 Other Concentric Braced-Frame Systems . . . . 5649.4.1 Special Truss Moment Frames

(STMF) . . . . . . . . . . . . . . . . . . . . . . . 5649.4.2 Zipper Frames . . . . . . . . . . . . . . . . . 565


Loading . . . . . . . . . . . . . . . . . . . . . . . 5669.5.2 Global Requirements . . . . . . . . . . . 5679.5.3 Basis of Design . . . . . . . . . . . . . . . . 5689.5.4 Preliminary Brace Sizing . . . . . . . . 5709.5.5 Plastic Mechanism Analysis . . . . . 5709.5.6 Capacity Design of Beam . . . . . . . . 5719.5.7 Capacity Design of Column . . . . . 5739.5.8 Iterative Analysis and

Proportioning . . . . . . . . . . . . . . . . . 5759.5.9 Connection Design . . . . . . . . . . . . . 575

9.5.10 Completion of Design . . . . . . . . . . 5769.5.11 Additional Consideration: Gravity

Bias in Seismic Systems . . . . . . . . . 5769.6 Self-Study Problems . . . . . . . . . . . . . . . . . . . . 579

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

10 Design of Ductile Eccentrically Braced Frames . . . . 59110.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

10.1.1 Historical Development . . . . . . . . . 59110.1.2 General Behavior and Plastic

Mechanism . . . . . . . . . . . . . . . . . . . 59210.1.3 Design Philosophy . . . . . . . . . . . . . 593

10.2 Link Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 59410.2.1 Stiffened and Unstiffened Links . . . 59410.2.2 Critical Length for Shear

Yielding . . . . . . . . . . . . . . . . . . . . . . 59510.2.3 Classifications of Links and Link

Deformation Capacity . . . . . . . . . . 59710.2.4 Link Transverse Stiffener . . . . . . . . 59810.2.5 Effect of Axial Force . . . . . . . . . . . . 601


xii C o n t e n t s C o n t e n t s xiii

10.2.6 Effect of Concrete Slab . . . . . . . . . . 60210.2.7 Link Overstrength . . . . . . . . . . . . . 60210.2.8 Qualification Test and Loading

Protocol Effect . . . . . . . . . . . . . . . . . 60310.3 EBF Lateral Stiffness and Strength . . . . . . . . 604

10.3.1 Elastic Stiffness . . . . . . . . . . . . . . . . 60410.3.2 Link Required Rotation . . . . . . . . . 60410.3.3 Plastic Analysis and Ultimate

Frame Strength . . . . . . . . . . . . . . . . 60610.4 Ductility Design . . . . . . . . . . . . . . . . . . . . . . . . 609

10.4.1 Sizing of Links . . . . . . . . . . . . . . . . . 60910.4.2 Link Detailing . . . . . . . . . . . . . . . . . 60910.4.3 Lateral Bracing of Link . . . . . . . . . 614

10.5 Capacity Design of Other Structural Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

10.5.1 General . . . . . . . . . . . . . . . . . . . . . . . 61510.5.2 Internal Force Distribution . . . . . . 61610.5.3 Diagonal Braces . . . . . . . . . . . . . . . 61810.5.4 Beams Outside of Link . . . . . . . . . . 61910.5.5 Columns . . . . . . . . . . . . . . . . . . . . . . 62010.5.6 Connections . . . . . . . . . . . . . . . . . . . 620


Loading . . . . . . . . . . . . . . . . . . . . . . 62510.6.2 Global Requirements . . . . . . . . . . . 62610.6.3 Basis of Design . . . . . . . . . . . . . . . . 62710.6.4 Sizing of Links . . . . . . . . . . . . . . . . . 62810.6.5 Final Link Design Check . . . . . . . . 63810.6.6 Link Rotation . . . . . . . . . . . . . . . . . . 64010.6.7 Link Detailing . . . . . . . . . . . . . . . . . 64110.6.8 Completion of Design . . . . . . . . . . 642


11 Design of Ductile Buckling-Restrained Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 65111.2 Buckling-Restrained Braced Frames versus

Conventional Frames . . . . . . . . . . . . . . . . . . . 65111.3 Concept and Components of

Buckling-Restrained Brace . . . . . . . . . . . . . . . 65411.4 Development of BRBs . . . . . . . . . . . . . . . . . . . 65611.5 Nonductile Failure Modes . . . . . . . . . . . . . . . 661

11.5.1 Steel Casing . . . . . . . . . . . . . . . . . . . 66111.5.2 Brace Connection . . . . . . . . . . . . . . 662


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11.5.3 Frame Distortion Effect on Gusset Connection . . . . . . . . . . . . . 666

11.6 BRBF Configuration . . . . . . . . . . . . . . . . . . . . 66711.7 Design of Buckling-Restrained Braces . . . . . 669

11.7.1 Brace Design . . . . . . . . . . . . . . . . . . 66911.7.2 Elastic Modeling . . . . . . . . . . . . . . . 66911.7.3 Gravity Loads . . . . . . . . . . . . . . . . . 670

11.8 Capacity Design of BRBF . . . . . . . . . . . . . . . . 67111.8.1 AISC Testing Requirements . . . . . . 67211.8.2 Brace Casing . . . . . . . . . . . . . . . . . . 67311.8.3 Brace Connections . . . . . . . . . . . . . 67311.8.4 Beams and Columns . . . . . . . . . . . . 674

11.9 Nonlinear Modeling . . . . . . . . . . . . . . . . . . . . 67411.10 Design Example . . . . . . . . . . . . . . . . . . . . . . . . 675

11.10.1 Building Description and Loading . . . . . . . . . . . . . . . . . . . . . . . 675

11.10.2 Global Requirements . . . . . . . . . . . 67511.10.3 Basis of Design . . . . . . . . . . . . . . . . . 67511.10.4 Iterative Analysis and

Proportioning . . . . . . . . . . . . . . . . . 67811.10.5 Brace Validation and Testing . . . . . 68411.10.6 Completion of Design . . . . . . . . . . . 686

11.11 Self-Study Problem . . . . . . . . . . . . . . . . . . . . . 686References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687

12 Design of Ductile Steel Plate Shear Walls . . . . . . . 68912.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

12.1.1 General Concepts . . . . . . . . . . . . . . 68912.1.2 Historical Developments . . . . . . . . 69212.1.3 International Implementations . . . 699

12.2 Behavior of Steel Plate Shear Walls . . . . . . . 70312.2.1 General Behavior . . . . . . . . . . . . . . 70312.2.2 Plastic Mechanism . . . . . . . . . . . . . 70612.2.3 Design Philosophy and Hysteretic

Energy Dissipation . . . . . . . . . . . . . 71012.3 Analysis and Modeling . . . . . . . . . . . . . . . . . 712

12.3.1 Strip Models . . . . . . . . . . . . . . . . . . 71212.3.2 Finite Element Models . . . . . . . . . . 71512.3.3 Demands on HBEs . . . . . . . . . . . . . 71512.3.4 Demands on VBEs . . . . . . . . . . . . . 728

12.4 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73612.4.1 Introduction . . . . . . . . . . . . . . . . . . . 73612.4.2 Web Plate Design . . . . . . . . . . . . . . 73712.4.3 HBE Design . . . . . . . . . . . . . . . . . . . 74112.4.4 VBE Design . . . . . . . . . . . . . . . . . . . 750


xiv C o n t e n t s C o n t e n t s xv

12.4.5 Distribution of Lateral Force Between Frame and Infill . . . . . . . 753

12.4.6 Connection Details . . . . . . . . . . . . . 75412.4.7 Design of Openings . . . . . . . . . . . . 756

12.5 Perforated Steel Plate Shear Walls . . . . . . . . 75812.5.1 Special Perforated Steel Plate

Shear Walls . . . . . . . . . . . . . . . . . . . 75812.5.2 Steel Plate Shear Walls with

Reinforced Corners Cutouts . . . . . 76312.6 Design Example . . . . . . . . . . . . . . . . . . . . . . . . 767

12.6.1 Building Description and Loading . . . . . . . . . . . . . . . . . . . . . . 767

12.6.2 Global Requirements . . . . . . . . . . . 76712.6.3 Basis of Design . . . . . . . . . . . . . . . . 76912.6.4 Web Design . . . . . . . . . . . . . . . . . . . 77012.6.5 HBE Design . . . . . . . . . . . . . . . . . . . 77212.6.6 VBE Design . . . . . . . . . . . . . . . . . . . 77612.6.7 Drift . . . . . . . . . . . . . . . . . . . . . . . . . 77812.6.8 HBE Connection Design . . . . . . . . 77912.6.9 Completion of Design . . . . . . . . . . 779


13 Other Ductile Steel Energy Dissipating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

13.1 Structural Fuse Concept . . . . . . . . . . . . . . . . . 78713.2 Energy Dissipation Through Steel

Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79013.2.1 Early Concepts . . . . . . . . . . . . . . . . 79013.2.2 Triangular Plates in Flexure . . . . . 79213.2.3 Tapered Shapes . . . . . . . . . . . . . . . . 80113.2.4 C-Shaped and E-Shaped Devices . 803

13.3 Energy Dissipation Through Friction . . . . . . 80613.4 Rocking Systems . . . . . . . . . . . . . . . . . . . . . . . 81813.5 Self-Centering Post-Tensioned Systems . . . . 82313.6 Alternative Metallic Materials: Lead,

Shape-Memory Alloys, and Others . . . . . . . 82613.7 Validation Quantification . . . . . . . . . . . . . . . . 827

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828

14 Stability and Rotation Capacity of Steel Beams . . . . 83714.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 83714.2 Plate Elastic and Postelastic Buckling

Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84014.3 General Description of Inelastic Beam

Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845


xiv C o n t e n t s C o n t e n t s xv

14.3.1 Beams with Uniform Bending Moment . . . . . . . . . . . . . . . . . . . . . . 845

14.3.2 Beams with Moment Gradient . . . 84614.3.3 Comparison of Beam Behavior

Under Uniform Moment and Moment Gradient . . . . . . . . . . . . . . 849

14.4 Inelastic Flange Local Buckling . . . . . . . . . . . 84914.4.1 Modeling Assumptions . . . . . . . . . 84914.4.2 Buckling of an Orthotropic

Plate . . . . . . . . . . . . . . . . . . . . . . . . . 85114.4.3 Torsional Buckling of a Restrained

Rectangular Plate . . . . . . . . . . . . . . 85314.5 Web Local Buckling . . . . . . . . . . . . . . . . . . . . 85914.6 Inelastic Lateral-Torsional Buckling . . . . . . . 862

14.6.1 General . . . . . . . . . . . . . . . . . . . . . . . 86214.6.2 Beam Under Uniform Moment . . . . 86314.6.3 Beam Under Moment Gradient . . . . 868

14.7 Code Comparisons . . . . . . . . . . . . . . . . . . . . . 87414.8 Interaction of Beam Buckling Modes . . . . . . 87714.9 Cyclic Beam Buckling Behavior . . . . . . . . . . 881

14.10 Self-Study Problem . . . . . . . . . . . . . . . . . . . . . 888References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 891


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xvii

Preface

The first edition of Ductile Design of Steel Structures, published in 1998, arrived at a time when the structural design practice was undergoing important changes. Most significantly, the impact

of the Northridge and Kobe earthquakes was still being felt in the engineering community, and substantial shifts in philosophy for the seismic design of steel structures were underway. This led to numer-ous and frequent changes to the relevant seismic design and detailing provisions for steel structures in many codes and design standards—all while the United States completed the process of unifying its three major regional model design codes into the International Building Code (first published in 2000, and eventually adopted by all states and most municipalities in the country), and while the American Institute of Steel Construction (AISC) unified its Load and Resistance Factor Design (LRFD) and Allowable Stress Design (ASD) requirements into a single specifications.

Although these whirlwind changes made the first edition a timely document in 1998, they also progressively left it in need of an update sooner than expected. Even though the fundamental principles and structural behaviors emphasized throughout the first edition of this book remained valid, design principles and examples were anchored in specifications that had changed in a number of subtle ways over time (more so than is typically the case from one code cycle to another). With publication of the AISC 2010 Seismic Provisions and of the 2009 CSA S16 Standard for the Design of Steel Structures, crystal-lizing the knowledge developed in the prior 15 years on this topic (and becoming more similar to each other in content and design philoso-phy), and with the evolution of code changes foreseen to return to a more regular pace—barring another major earthquake that would challenge design wisdom—publication of a revised second edition of Ductile Design of Steel Structures is again timely.

Two audiences were kept in mind when writing this book: prac-ticing engineers and graduate students. With respect to the first audi-ence, engineers are nowadays exposed to a wide range of professional development opportunities, and day courses on seismic design of steel structures are common. Similar information is also scattered


P r e f a c e xix

over the World Wide Web (albeit covering the same topic with vari-ous degrees of technical rigor, depending on the source). This widely available and accessible information has been helpful to dispel the erroneous belief that the ductile nature of structural steel directly translates into inherently ductile structures, but a first introduction to the topic of ductile design usually leaves the engineer with many questions on the origin of many design requirements and strategies to achieve ductile structural behavior. With respect to the second group, although seismic design is not part of most undergraduate civil engi-neering curricula, substantial opportunities exist for graduate learn-ing on this topic. Nowadays, most graduate structural engineering programs in North America offer a general seismic design course, often complemented by specialized courses on the design of ductile concrete and ductile steel structures, and textbooks that comprehen-sively cover design aspects related to this topic are needed.

In that perspective, the second edition of Ductile Design of Steel Structures is intended to serve both as a reference textbook on this topic and as a resource document providing breadth and depth in support of graduate and professional education opportunities. It aims to help senior undergraduate and graduate students, as well as professionals, design ductile steel structures in an informed manner. It summarizes the relevant existing information on this topic (often scattered in research reports, journal articles, and conference proceed-ings) into chapters on material, cross-section, component, and system response, providing useful guidance and design examples while pre-senting the concepts and key research results supporting the ratio-nale underlying many of the current design principles. It is written starting from the assumption that the reader has background knowl-edge of conventional (nonseismic) steel design.

The emphasis of this book is on earthquake-resistant design because providing ductile structures is crucial to ensure seismic sur-vival. However, there exist many other important applications of the principles and design approaches outlined in this textbook. For example, knowledge of how to design and detail steel structures to achieve ductile behavior is vital to ensure the satisfactory perfor-mance of structures exposed to other extreme events, such as blast forces, and to prevent their progressive collapse—two topics pushed to the forefront by the September 11, 2001 events. Other possible applications of ductile steel design include offshore structures sub-jected to extreme wave and ice loads, as well as bridges that can now be designed to carry normal traffic using an alternative bridge design procedure (the Autostress method) that relies heavily on ductile response and requires a good understanding of the shakedown the-ory. Likewise, for existing construction, plastic analysis can provide a much better estimate of a structure’s actual strength than procedures based on elastic analysis, which in turn can be used advantageously to minimize the extent of needed rehabilitations—an important

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P r e f a c e xix xviii P r e f a c e

advantage given that the rehabilitation of existing buildings is a growing market in North America, as part of the revitalization activi-ties taking place in many city centers of seismic and nonseismic regions (as a consequence of either commuters’ frustrations, the aging North American infrastructure, the projected North American popu-lation growth patterns, the goals of historical or heritage building preservation, and/or other societal trends). Thus, although the focus of this text is earthquake engineering, the information presented herein is broadly applicable to the ductile design of steel structures.

For its second edition, this book has been substantially expanded as follows:

• Threeentirelynewchaptershavebeenadded,torespectivelyaddress the design of buckling-restrained braced frames (Chapter 11) and steel plate shear walls (Chapter 12), and to review some hysteretic energy dissipating systems and design strategies that have been the subject of growing interest and proposed to achieve the objective of ductile design (Chapter 13). The latter chapter addresses struc-tural fuses, hysteretic energy dissipating devices, bime-tallic friction, rocking, and self-centering systems; it replaces the former Chapter 11 that only provided a cursory overview of passive energy dissipation.

• Thepreviouschapteronbracedframeshasbeencompletelyrewritten, to eliminate obsolete and/or ambiguous informa-tion and, more importantly, to reflect the substantial changes and new developments that have taken place and have been implemented in the AISC and CSA design requirements since the last edition of this book. Concentrically braced frames and eccentrically braced frames are now each cov-ered in separate chapters. Each chapter provides thorough insights into the knowledge on those topics that has led to the current design provisions and corresponding capacity design procedures.

• Thechapteronmoment-resistingframeshasbeensubstan-tially expanded, to reflect the major changes and develop-ments in design requirements that have taken place since 1997.

• Chapter2hasbeenexpandedtoincludeadditionalinfor-mation and new knowledge on steel’s high-temperature properties, strain rate effects, k-area fractures, strain aging, and stress corrosion, as well as information on fatigue and ductility of corroded shapes, yielding mechanism, new steel grades, and low-cycle fatigue mod-eling. It also includes a new section on hysteretic models, which provides much needed information for the nonlinear


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inelastic analyses more frequently required by specific engineering projects nowadays.

• Chapter 3 (on cross-section properties) has been revised toaddress biaxial bending, introduce layer models (required for some nonlinear analyses), and add information on plastic strength of concrete-filled steel tube cross-sections.

• Chapter4 (onplasticanalysis)hasbeenexpandedto intro-duce yield line analysis, which is important for calculation of connections’ ultimate strength and resistance to out-of-plane loads (such as blast loads).

• Chapter 6 (on applications of plastic analysis) has beenexpanded to address global versus local ductility demand and some other important code-related issues.

• TobetterlinkwithChapters8to13,focusedonearthquakeengineering applications, Chapter 7 (formerly Chapter 9) has been entirely rewritten, focusing on the basic principles to relate seismic design forces and corresponding ductile demands in structures.

• NewdesignexamplesinChapters8to12havebeendevel-oped in compliance with the AISC Seismic Provisions (ANSI/AISC 341-10) and Load and Resistance Factor Design, and from a practicing engineering perspective. Note that the examples in the first edition of this book approached seismic design as a secondary design step called “ductile design” (coupled with “drift-control design” in the special case of moment-resisting frames), which consisted of a design iteration starting with the results from a first design step accomplished using conventional steel design principles in nonseismic appli-cations (called “strength design”). That two-step approach is still valid and the examples contained in the first edition remain instructive in many ways. However, the publication by the American Institute of Design Construction of design aids for seismic design has made seismic design more expe-ditious, eliminating the benefits of the two-step approach. Therefore, this second edition contains only new design examples consistent with this new context.

• Self-studyproblemshavebeenprovidedformostchapters;these could be assigned to students by instructors using this book as a textbook—note that all of the problems are for-mer assignment or exam questions I gave to students at the University at Buffalo or the University of Ottawa. Partial solu-tions to the problems will eventually be accessible to instruc-tors via a password-protected link posted on the website www.michelbruneau.com.


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• Chapter14istheonlychapterthatremainsunmodifiedsincethe first edition. While interesting research has been conducted since the mid-1990s on the topics covered in this chapter, it has not resulted in changes to the seismic design provisions at the time of this writing.

The authorship of this second edition reflects these numerous changes in scope, breath, and structure. I sincerely thank my co authors for helping to bring this project to fruition, namely Chia-Ming Uang (Professor, University of California, San Diego) for writing most of Chapters 7, 10, 11, and 14, and Rafael Sabelli (Structural Engineer, Walter P. Moore, Oakland, CA) for developing the design examples at the end of Chapters 8 to 12 and contributing parts of Chapter 11. The challenges of bringing to life a second edition that is twice the length of the first can be overwhelming, and their com-mitment and contributions are gratefully acknowledged.

From a graduate curriculum perspective, the resulting expanded textbook provides enough material to support two graduate courses: a first course on plastic analysis and design, using the material in Chapters 2 to 6, and a second course on the seismic design of steel structures based on Chapters 7 to 13. However, another effective approach is to use some aspects of all chapters as part of a single graduate course, covering only the essential aspects of Chapters 2 to 6 needed to understand the capacity design in support of the material presented in Chapters 7 to 12 (or 7 to 10 for shorter academic terms), leaving the rest of the material for future self-study in answer to project needs or for professional development purposes. Other combinations also are anticipated, reflecting the preferences and teaching styles of various instructors.

Finally, suggestions and general feedback on this book are always welcome (including e-mails confirming that there are people in this world reading book prefaces). A list of errors brought to the authors’ attention will be compiled into an errata list eventually posted on the website www.michelbruneau.com, until fixed by the publisher in subsequent printings.

Michel Bruneau, Ph.D., P.Eng.


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