Design of Tall Buildings

Structural Analysis and Design of Tall Buildings Steel and Composite Construction Bungale S. Taranath Ph.D., RE., S.E. York INTERNATIONAL CODE COUNCll? CRC Press is an imprint of the Taylor & frauds Group, an informs business

Contents List of Figures List of Tables Foreword ICC Foreword Preface Acknowledgments Special Acknowledgment Author XX1 xxxix xli xliii xlv xlix li liii Chapter 1 Lateral Load Resisting Systems for Steel Buildings 1 Preview 1 1.1 Rigid Frames 2 1.1.1 Frames with Partially Rigid Connections 6 1.1.2 Review of Connection Behavior 6 1.1.2.1 Connection Classification 7 1.1.2.2 Connection Strength 7 1.1.2.3 Connection Ductility 7 1.1.2.4 Structural Analysis and Design 8 1.1.3 Beam Line Concept 10 1.2 Frames with Fully Restrained Connections 11 1.2.1 Special Moment Frame, Historic Perspective 13 1.2.1.1 Deflection Characteristics 14 1.2.2 Cantilever Bending Component 15 1.2.3 Shear Racking Component 15 1.2.4 Methods of Analysis 16 1.2.5 Drift Calculations 16 1.2.6 Truss Moment Frames 17 1.3 Concentric Braced Frames 17 1.3.1 Behavior 17 1.3.2 Types of Concentric Braces 19 1.4 Eccentric Braced Frames 21 1.4.1 Behavior 21 1.4.2 Deflection Characteristics 22 1.4.3 Seismic Design Considerations 23 1.4.3.1 Link Beam Design 24 1.4.3.2 Link-to-Column Connections 25 1.4.3.3 Diagonal Brace and Beam outside oflinks 25 1.4.3.4 Link Stiffness 26 1.4.3.5 Columns 26 1.4.3.6 Schematic Details 27 1.5 Buckling-Restrained Brace Frame 27 1.6 Steel Plate Shear Wall 31 1.6.1 Low-Seismic Design 32 1.6.2 High-Seismic Design 32 1.6.2.1 Behavior 33 1.6.2.2 AISC 341-05 Requirements for Special Plate Shear Walls...33

1.6.2.3 Modeling for Analysis 33 1.6.2.4 Capacity Design Methods 34 1.7 Staggered Truss 35 1.7.1 Behavior 37 1.7.2 Design Considerations 38 1.7.2.1 Floor Systems 38 1.7.2.2 Columns 38 1.7.2.3 Trusses 39 1.7.3 Seismic Design of Staggered Truss System 39 1.7.3.1 Response of Staggered Truss System to Seismic Loads 39 1.8 Interacting System of Braced and Rigid Frames 40 1.8.1 Behavior 43 1.9 Core and Outrigger Systems 44 1.9.1 Behavior 46 1.9.1.1 Outrigger Located at Top 48 1.9.1.2 Outrigger Located at Three-Quarter Height from Bottom 49 1.9.1.3 Outrigger at Mid-Height 51 1.9.1.4 Outriggers at Quarter-Height from Bottom 51 1.9.2 Optimum Location of a Single Outrigger 53 1.9.2.1 Analysis Outline 53 1.9.2.2 Detail Analysis 55 1.9.2.3 Computer Analysis 55 1.9.2.4 Conclusions 58 1.9.3 Optimum Locations of Two Outriggers 58 1.9.3.1 Recommendations for Optimum Locations 61 1.9.4 Vulnerability of Core and Outrigger System to Progressive Collapse 62 1.9.5 Offset Outriggers 63 1.9.6 Example Projects 64 1.10 Frame Tube Systems 66 1.10.1 Behavior 67 1.10.2 Shear Lag 69 1.11 Irregular Tube 71 1.12 Trussed Tube 72 1.13 Bundled Tube 74 1.13.1 Behavior 74 1.14 Ultimate High-Efficiency Systems for Ultra Tall Buildings 75 Chapter 2 Lateral Load-Resisting Systems for Composite Buildings 79 Preview 79 2.1 Composite Members 79 2.1.1 Composite Slabs 80 2.1.2 Composite Girders 81 2.1.3 Composite Columns 81 2.1.4 Composite Diagonals 82 2.1.5 Composite Shear Walls 83 2.2 Composite Subsystems 87 2.2.1 Composite Moment Frames 87 2.2.1.1 Ordinary Moment Frames 89 2.2.1.2 Special Moment Frames 89

2.2.2 Composite Braced Frames 91 2.2.3 Composite Eccentrically Braced Frames 93 2.2.4 Composite Construction 94 2.2.5 Temporary Bracing 95 2.3 Composite Building Systems 96 2.3.1 Reinforced Concrete Core with Steel Surround 96 2.3.2 Shear Wall-Frame Interacting Systems 98 2.3.3 Composite Tube Systems 99 2.3.4 Vertically Mixed Systems 100 2.3.5 Mega Frames with Super Columns 102 2.3.6 High-Efficiency Structure: Structural Concept 102 2.4 Seismic Design of Composite Buildings 104 Chapter 3 Gravity Systems for Steel Buildings 105 Preview 105 3.1 General Considerations 105 3.1.1 Steel and Cast Iron: Historical Perspective 105 3.1.1.1 Chronology of Steel Buildings 106 3.1.1.2 1920 through 1950 107 3.1.1.3 1950 through 1970 108 3.1.1.4 1970 to Present 108 3.1.2 Gravity Loads 109 3.1.3 Design Load Combinations 110 3.1.4 Required Strength 110 3.1.5 Limit States 110 3.1.6 Design for Strength Using Load and Resistance Factor Design Ill 3.1.7 Serviceability Concerns Ill 3.1.8 Deflections 112 3.2 Design of Members Subject to Compression 113 3.2.1 Buckling of Columns, Fundamentals 113 3.2.1.1 Euler's Formula 114 3.2.1.2 Energy Method of Calculating Critical Loads 116 3.2.2 Behavior of Compression Members 117 3.2.2.1 Element Instability 119 3.2.3 Limits on Slenderness Ratio, KL/r 119 3.2.4 Column Curves: Compressive Strength of Members without Slender Elements 119 3.2.5 Columns with Slender Unstiffened Elements: Yield Stress Reduction Factor, Q 121 3.2.6 Design Examples: Compression Members 122 3.2.6.1 Wide Flange Column, Design Example 124 3.2.6.2 HSS Column, Design Example 124 3.3 Design of Members Subject to Bending 128 3.3.1 Compact, Noncompact, and Slender Sections 130 3.3.2 Flexural Design of Doubly Symmetric Compact I-Shaped Members and Channels Bent about Their Major Axis 130 3.3.3 Design Examples, Members Subject to Bending and Shear 133 3.3.3.1 General Comments 133 3.3.3.2 Simple-Span Beam, Braced Top Flange 135 3.3.3.3 Simple-Span Beam, Unbraced Top Flange 137

3.4 Tension Members 139 3.4.1 Design Examples 140 3.4.1.1 Plate in Tension, Bolted Connection 140 3.4.1.2 Plate in Tension, Welded Connection 142 3.4.1.3 Double-Angle Hanger 143 3.4.1.4 Bottom Chord of a Long-Span Truss 144 3.4.1.5 Pin-Connected Tension Member 146 3.4.1.6 Eyebar Tension Member 147 3.5 Design for Shear, Additional Comments 149 3.5.1 Transverse Stiffeners 151 3.5.2 Tension Field Action 152 3.6 Design of Members for Combined Forces and Torsion (in Other Words, Members Subjected to Torture) 152 3.7 Design for Stability 154 3.7.1 Behavior of Beam Columns 154 3.7.2 Buckling of Columns 158 3.7.3 Second-Order Effects 158 3.7.4 Deformation of the Structure 159 3.7.5 Residual Stresses 159 3.7.6 Notional Load 160 3.7.7 Geometric Imperfections 161 3.7.8 Leaning Columns 162 3.8 AISC 360-10 Stability Provisions 162 3.8.1 Second-Order Analysis 162 3.8.2 Reduced Stiffness in the Analysis 163 3.8.3 Application of Notional Loads 163 3.8.4 Member Strength Checks 163 3.8.5 Step-by-Step Procedure for Direct Analysis Method 164 3.9 Understanding How Commercial Software Works 164 Chapter 4 Gravity Systems for Composite Buildings 167 Preview 167 4.1 Composite Metal Deck 168 4.1.1 SDI Specifications 169 4.2 Composite Beams 170 4.2.1 AISC Design Criteria: Composite Beams with Metal Deck and Concrete Topping 174 4.2.1.1 AISC Requirements, General Comments 176 4.2.1.2 Effective Width 178 4.2.1.3 Positive Flexural Strength 179 4.2.1.4 Negative Flexural Strength 179 4.2.1.5 Shear Connectors 180 4.2.1.6 Deflection Considerations 181 4.2.1.7 Design Outline for Composite Beam 183 4.3 Composite Joists and Trusses 186 4.3.1 Composite Joists 186 4.3.2 Composite Trusses 186 4.4 Other Types of Composite Floor Construction 189 4.5 Continuous Composite Beams 190 4.6 Nonprismatic Composite Beams and Girders 191

4.7 Moment-Connected Composite Haunch Girders 192 4.8 Composite Stub Girders 193 4.8.1 Behavior and Analysis 195 4.8.2 Stub Girder Design Example 197 4.8.3 Moment-Connected Stub Girder 200 4.8.4 Strengthening of Stub Girder 200 4.9 Composite Columns 201 4.9.1 Behavior 201 4.9.2 AISC Design Criteria, Encased Composite Columns 202 4.9.2.1 Limitations 202 4.9.2.2 Compressive Strength 203 4.9.2.3 Tensile Strength 204 4.9.2.4 Shear Strength 204 4.9.2.5 Load Transfer 204 4.9.2.6 Detailing Requirements 204 4.9.2.7 Strength of Stud Shear Connectors 205 4.9.3 AISC Design Criteria for Filled Composite Columns 205 4.9.3.1 Limitations 205 4.9.3.2 Compressive Strength 205 4.9.3.3 Tensile Strength 206 4.9.3.4 Shear Strength 206 4.9.3.5 Load Transfer 206 4.9.4 Summary of Composite Design Column 206 4.9.4.1 Nominal Strength of Composite Sections 206 4.9.4.2 Encased Composite Columns 207 4.9.4.3 Filled Composite Columns 208 4.9.5 Combined Axial Force and Flexure 209 Chapter 5 Wind Loads 211 Preview 211 5.1 Design Considerations 211 5.2 Variation of Wind Velocity with Height (Velocity Profile) 212 5.3 Probabilistic Approach 213 5.4 Vortex Shedding 215 5.5 ASCE 7-05 Wind Load Provisions 218 5.5.1 Analytical Procedure: Method 2, Overview 221 5.5.2 Analytical Method: Step-by-Step Procedure 224 5.5.3 Wind Speed-Up over Hills and Escarpments: Kzt Factor 227 5.5.4 Gust Effect Factor 227 5.5.4.1 Gust Effect Factor G for Rigid Structure: Simplified Method 228 5.5.4.2 Gust Effect Factor G for Rigid Structure: Improved Method 228 5.5.4.3 Gust Effect Factor Gf for Flexible or Dynamically Sensitive Buildings 230 5.5.5 Along-Wind Displacement and Acceleration 233 5.5.6 Summary of ASCE 7-05 Wind Provisions 234 5.6 Wind-Tunnel Tests 234 5.6.1 Types of Wind-Tunnel Tests 235 5.6.2 Option for Wind-Tunnel Testing 238

5.6.3 Lower Limits on Wind-Tunnel Test Results 238 5.6.3.1 Lower Limit on Pressures for Main Wind-Force Resisting System 238 5.6.3.2 Lower Limit on Pressures for Components and Cladding 238 5.7 Building Drift 238 5.8 Human Response to Wind-Induced Building Motions 239 5.9 Structural Properties Required for Wind-Tunnel Data Analysis 240 5.9.1 Natural Frequencies 240 5.9.2 Mode Shapes 240 5.9.3 Mass Distribution 240 5.9.4 Damping Ratio 241 5.9.5 Miscellaneous Information 241 5.10 Period Determination for Wind Design 241 5.11 ASCE 7-10 Wind Load Provisions 243 5.11.1 New Wind Speed Maps 243 5.11.2 Return of Exposure D 244 5.11.3 Wind-Borne Debris 244 Chapter 6 Seismic Design 245 Preview 245 6.1 Structural Dynamics 246 6.1.1 Dynamic Loads 247 6.1.1.1 Concept of Dynamic Load Factor 247 6.1.1.2 Difference between Static and Dynamic Analysis 250 6.1.1.3 Dynamic Effects due to Wind Gusts 253 6.1.2 Characteristics of a Dynamic Problem 254 6.1.3 Multiple Strategy of Seismic Design 255 6.1.3.1 Example of Portal Frame Subject to Ground Motions 256 6.1.4 Concept of Dynamic Equilibrium 258 6.1.5 Free Vibrations 259 6.1.6 Earthquake Excitation 260 6.1.6.1 Single-Degree-of-Freedom Systems 261 6.1.6.2 Numerical Integration, Design Example 261 6.1.6.3 Numerical Integration: A Summary 264 6.1.6.4 Summary of Structural Dynamics 266 6.1.7 Response Spectrum Method 268 6.1.7.1 Earthquake Response Spectrum 272 6.1.7.2 Deformation Response Spectrum 273 6.1.7.3 Pseudo-Velocity Response Spectrum 275 6.1.7.4 Pseudo-Acceleration Response Spectrum 275 6.1.7.5 Tripartite Response Spectrum: Combined Displacement-Velocity-Acceleration Spectrum 276 6.1.7.6 Characteristics of Response Spectrum 279 6.1.7.7 Difference between Design and Actual Response Spectra 281 6.1.7.8 Summary of Response Spectrum Analysis 282 6.1.8 Hysteresis Loop 283

6.2 Seismic Design Considerations 286 6.2.1 Seismic Response of Buildings 288 6.2.1.1 Building Motions and Deflections 289 6.2.1.2 Building Drift and Separation 290 6.2.1.3 Adjacent Buildings 290 6.2.2 Continuous Load Path 290 6.2.3 Building Configuration 291 6.2.4 Influence of Soil 293 6.2.5 Ductility 295 6.2.6 Redundancy 296 6.2.7 Damping 296 6.2.8 Diaphragms 299 6.2.9 Response of Elements Attached to Buildings 301 6.3 ASCE 7-05 Seismic Design Criteria and Requirements: Overview 303 6.3.1 Seismic Ground Motion Values, Ss and S{ 304 6.3.2 Site Coefficients Fa and Fv 305 6.3.3 Site Class SA, SB, Sc, SD, SE, and SF 306 6.3.4 Response Spectrum for the Determination of Design Base Shear 306 6.3.5 Site-Specific Ground Motion Analysis 309 6.3.6 Importance Factor IE 312 6.3.7 Occupancy Categories 312 6.3.7.1 Protected Access for Occupancy Category IV 312 6.3.8 Seismic Design Category 315 6.3.9 Design Requirements for SDC A Buildings 316 6.3.9.1 Lateral Forces 318 6.3.10 Geologic Hazards and Geotechnical Investigation 319 6.3.10.1 Seismic Design Basis 320 6.3.10.2 Structural System Selection 321 6.3.11 Building Irregularities 322 6.3.11.1 Plan (Horizontal) Irregularity 322 6.3.11.2 Vertical Irregularity 324 6.3.12 Redundancy Reliability Factor, p 327 6.3.13 Seismic Load Combinations 330 6.3.13.1 Vertical Seismic Load, 0.025DS 331 6.3.13.2 Overstrength Factor Q.0 331 6.3.14 Elements Supporting Discontinuous Walls or Frames 332 6.3.15 Direction of Loading 332 6.3.16 Period Determination 332 6.3.17 Inherent and Accidental Torsion 334 6.3.18 Overturning 335 6.3.19 PA Effects 335 6.3.20 Drift Determination 335 6.3.21 Deformation Compatibility 338 6.3.22 Seismic Response Modification Coefficient, R 339 6.3.23 Seismic Force Distribution for the Design of Lateral-Load-Resisting System 339 6.3.24 Seismic Loads due to Vertical Ground Motions 340 6.3.25 Seismic Force for the Design of Diaphragms 340 6.3.25.1 Distribution of Seismic Forces for Diaphragm Design... 342

6.3.25.2 General Procedure for Diagram Design 342 6.3.25.3 Diaphragm Design Summary: Buildings Assigned to SDC C and Higher 343 6.3.26 Catalog of Seismic Design Requirements 345 6.3.26.1 Buildings in SDC A 345 6.3.26.2 SDC B Buildings 347 6.3.26.3 SDC C Buildings 348 6.3.26.4 SDC D Buildings 349 6.3.26.5 SDC E Buildings 351 6.3.26.6 SDC F Buildings 351 6.3.27 Analysis Procedures 351 Chapter 7 Seismic Provisions for Structural Steel Buildings, ANSI/AISC 341-10 355 Preview 355 7.1 AISC 341-10 Seismic Provisions, Overview 357 7.1.1 General Requirements 357 7.1.2 Member and Connection Design 358 7.1.3 Moment Frames 359 7.1.4 Stability of Beams and Columns 359 7.1.5 Intermediate Moment Frames 360 7.1.6 Special Truss Moment Frames 360 7.1.6.1 Special Concentric Braced Frames 360 7.1.7 Eccentrically Braced Frames 361 7.1.8 Buckling-Restrained Braced Frames 361 7.1.9 Special Plate Shear Walls 363 7.1.10 Composite Structural Steel and Reinforced Concrete Systems 363 7.2 AISC 341-10, Detailed Discussion 364 7.2.1 Moment Frame Systems 365 7.2.1.1 SMF Design 367 7.2.1.2 AISC Prequalified Connections 368 7.2.1.3 Ductile Behavior 368 7.2.1.4 Seismically Compact Sections 369 7.2.1.5 Demand Critical Welds 369 7.2.1.6 Protected Zones 369 7.2.1.7 Panel Zone of Beam-to-Column Connections 369 7.2.2 Moment Frame Systems 370 7.2.2.1 Ordinary Moment Frames 370 7.2.2.2 Intermediate Moment Frames 372 7.2.2.3 Special Moment Frames 373 7.2.2.4 Special Truss Moment Frames 377 7.2.3 Braced-Frame and Shear-Wall Systems 379 7.2.3.1 Ordinary Concentrically Braced Frames 380 7.2.3.2 Special Concentrically Braced Frames 380 7.2.3.3 Eccentrically Braced Frames 383 7.2.3.4 Buckling-Restrained Braced Frames 388 7.2.4 Special Plate Shear Walls 391 7.2.5 Composite Systems 395 7.2.5.1 Composite Ordinary Moment Frames 395 7.2.5.2 Composite Intermediate Moment Frames 395

7.2.5.3 Composite Special Moment Frames 397 7.2.5.4 Composite Partially Restrained Moment Frames 399 7.2.5.5 Composite Ordinary Braced Frames 399 7.2.5.6 Composite Special Concentrically Braced Frames 400 7.2.5.7 Composite Eccentrically Braced Frames 400 7.2.5.8 Composite Ordinary Reinforced Concrete Shear Walls with Steel Elements 401 7.2.5.9 Composite Special Reinforced Concrete Shear Walls with Steel Elements 403 7.2.5.10 Composite Steel Plate Shear Walls 404 7.3 Prequalified Seismic Moment Connection 406 7.4 List of Significant Technical Provisions of AISC 341-05/10 406 7.5 Additional Comments on Seismic Design of Steel Buildings 407 7.5.1 Concentric Braced Frames 407 Chapter 8 Seismic Rehabilitation of Existing Steel Buildings 411 Preview 411 8.1 Social Issues in Seism ic Rehabilitation 413 8.2 General Steps in Seismic Rehabilitation 413 8.2.1 Initial Considerations 414 8.2.2 Rehabilitation Objective 415 8.2.2.1 Performance Levels 415 8.2.2.2 Seismic Hazard 415 8.2.2.3 Selecting a Rehabilitation Objective 415 8.2.2.4 Rehabilitation Method 416 8.2.2.5 Rehabilitation Strategy 416 8.2.3 Analysis Procedures 416 8.2.4 Verification of Rehabilitation Design 417 8.2.5 Nonstructural Risk Mitigation 417 8.2.5.1 Disabled Access Improvements 417 8.2.5.2 Hazardous Material Removal 417 8.2.5.3 Design, Testing and Inspection, and Management Fees 417 8.2.5.4 Historic Preservation Costs 417 8.3 Seismic Rehabilitation of Existing Buildings ASCE/SEI Standard 41-06... 418 8.3.1 Overview of Performance Levels 425 8.3.2 Permitted Design Methods 427 8.3.3 Systematic Rehabilitation 428 8.3.3.1 Determination of Seismic Ground Motions 429 8.3.3.2 Determination of As-Built Conditions 429 8.3.3.3 Primary and Secondary Components 429 8.3.3.4 Setting Up Analytical Model and Determination of Design Forces 430 8.3.3.5 Combined Gravity and Seismic Demand 432 8.3.3.6 Component Capacities gce, (2<xand Design Actions 433 8.3.3.7 Capacity versus Demand Comparisons 434 8.3.3.8 Development of Seismic Strengthening Strategies 436 8.3.4 ASCE/SEI 41-06: Design Example 442 8.3.5 Summary 447

Chapter 9 Special Topics 449 Preview 449 9.1 Architectural Review of Tall Buildings 449 9.2 Evolution of High-Rise Architecture 451 9.3 Tall Buildings 452 9.3.1 World Trade Center Towers, New York 453 9.3.2 Empire State Building, New York 459 9.3.3 Bank One Center, Indianapolis, Indiana 460 9.3.4 MTA Headquarters, Los Angeles, California 460 9.3.5 AT&T Building, New York City, New York 462 9.3.6 Miglin-Beitler Tower, Chicago, Illinois 463 9.3.7 One Detroit Center, Detroit, Michigan 465 9.3.8 Jin Mao Tower, Shanghai, China 467 9.3.9 Petronas Towers, Malaysia 470 9.3.10 One-Ninety-One Peachtree, Atlanta, Georgia 472 9.3.11 Nations Bank Plaza, Atlanta, Georgia 472 9.3.12 U.S. Bank Tower First Interstate World Center, Library Square, Los Angeles, California 475 9.3.13 21st Century Tower, China 477 9.3.14 Torre Mayor Office Building, Mexico City 480 9.3.15 Fox Plaza, Los Angeles, California 482 9.3.16 Figueroa at Wilshire, Los Angeles, California 482 9.3.17 California Plaza, Los Angeles, California 483 9.3.18 Citicorp Tower, Los Angeles, California 487 9.3.19 Taipei Financial Center, Taiwan 490 9.3.20 Caja Madrid Tower, Spain 494 9.3.21 Federation Tower, Moscow, Russia Tower A 496 9.3.22 The New York Times Building, New York 496 9.3.23 Pacific First Center, Seattle, Washington 497 9.3.24 Gate Way Center 497 9.3.25 Two Union Square, Seattle, Washington 497 9.3.26 InterFirst Plaza, Dallas, Texas 498 9.3.27 Bank of China Tower, Hong Kong 499 9.3.28 Bank of Southwest Tower, Houston, Texas 500 9.3.29 First City Tower, Houston, Texas 502 9.3.30 America Tower, Houston, Texas 504 9.3.31 The Bow Tower, Calgary, Alberta, Canada 506 9.3.32 Shard Tower, London, United Kingdom 506 9.3.33 Hearst Tower, New York 507 9.3.34 Standard Oil of Indiana Building, Chicago, Illinois 507 9.3.35 The Renaissance Project, San Diego, California 510 9.3.36 Tokyo City Hall, Tower 1, Japan 514 9.3.37 Bell Atlantic Tower, Philadelphia, Pennsylvania 516 9.3.38 Norwest Center, Minneapolis, Minnesota 518 9.3.39 First Bank Place, Minneapolis, Minnesota 521 9.3.40 Allied Bank Tower, Dallas, Texas 521 9.3.41 Future of Tall Buildings 525 9.4 Building Motion Perception 526 9.5 Structural Damping 527

9.6 Performance-Based Design 528 9.6.1 Alternative Design Criteria: 2008 LATBSDC 529 9.6.2 Recommended Administrative Bulletin on the Seismic Design and Review of Tall Buildings Using Nonprescriptive Procedures AB-083 530 9.6.3 Pushover Analysis 530 9.6.4 Concluding Remarks 531 9.7 Preliminary Analysis Techniques 532 9.7.1 Portal Method 533 9.7.2 Cantilever Method 534 9.7.3 Design Examples: Portal and Cantilever Methods 536 9.7.4 Framed Tubes 538 9.7.5 Vierendeel Truss 540 9.7.6 Preliminary Wind Loads 544 9.7.7 Preliminary Seismic Loads 550 9.7.7.1 = Building Height, Hn 160 ft 558 9.7.7.2 Buildings Taller than 160ft 559 9.7.8 Differential Shortening of Columns 560 9.7.8.1 Simplified Method of Calculating Ar Axial Shortening of Columns 573 9.7.8.2 Derivation of Simplified Expression for Az 573 9.7.8.3 Column Length Corrections, Ac 579 9.7.8.4 Column Shortening Verification during Construction 582 9.7.9 Unit Weight of Structural Steel for Preliminary Estimate 582 9.7.9.1 Concept of Premium for Height 585 Chapter 10 Connection Details 589 Preview 589 References 621 Index 625