Wind Drift Design of Steel Framed Buildings: An Analytical Study and a Survey of the Practice Daniel Christopher Berding Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Finley A. Charney W. Samuel Easterling ____________________ ____________________ Thomas M. Murray ____________________ June 29, 2006 Blacksburg, Virginia Keywords: structural steel, structural analysis, serviceability, wind, drift Copyright 2006, Daniel Christopher Berding Wind Drift Design of Steel Framed Buildings: An Analytical Study and a Survey of the Practice Daniel Christopher Berding Abstract The design of steel framed buildings must take into consideration the lateral drift of the structure due to wind loading and any serviceability issues that may arise from this lateral movement. This thesis focuses on one of these issues, damage to nonstructural components. Although there are no specific requirements in the United States governing the effects of wind drift, it is an important issue which may significantly impact the buildings structural performance and economy. Furthermore, because these serviceability issues are not codified, there is a wide variation among design firms in how they are dealt with, leading to a greater economic disparity. This thesis begins with a comprehensive review of the literature that covers all pertinent aspects of wind drift in steel framed buildings. Next an analytical study of the variations in modeling parameters is performed to demonstrate how simple assumptions can affect the overall buildings stiffness and lateral displacements. A study is then carried out to illustrate the different sources of elastic deformation in a variety of laterally loaded steel frames. The different modeling variables demonstrate how deformation sources vary with bay width, the number of bays and the number of stories, providing a useful set of comparisons. To ascertain how serviceability issues are dealt with from firm to firm, a survey of the practice is developed to update the one conducted in 1988 (ASCE). In effect, the thesis is presented with the intention of suggesting and establishing a comprehensive, performance based approach to the wind drift design of steel framed buildings. Acknowledgements The completion of this thesis and the attainment of my Masters Degree would not have been possible without the support and guidance from family, friends and the faculty of Virginia Tech. I would like to thank my Committee Chairman Dr. Finley A. Charney for providing assistance and guidance throughout my studies. The work I have done is largely a result of his previous and ongoing research. For the knowledge and insight that I have gained from working with him I am grateful. I would also like to thank Dr. Samuel Easterling and Dr. Thomas Murray for serving on my committee and enhancing my overall educational experience at Virginia Tech. "I get by with a little help from my friends." - John Lennon Without the support of family and friends none of this would have been achievable. I thank everyone who has been with me through this journey: my parents, siblings, my close friends. Special thanks goes out to Laurie Mazursky with whom I have shared countless hours throughout our undergraduate studies together at Vanderbilt University and graduate studies at Virginia Tech. “Don't let schooling interfere with your education. “ - Mark Twain ii i Table of Contents Abstract...............................................................................................................................ii Acknowledgements............................................................................................................iii Table of Contents...............................................................................................................iv List of Figures...................................................................................................................vii List of Tables.....................................................................................................................ix Chapter 1: Introduction...................................................................................................1 1.1 Philosophy of Design for Drift...........................................................................1 1.2 A Brief History of Wind and Structures.............................................................2 1.3 Project Scope......................................................................................................5 REFERENCES...............................................................................................................8 Chapter 2: Literature Review..........................................................................................9 2.1 Introduction.........................................................................................................9 2.2 Drift Limits and Damageability..........................................................................9 2.2.1 Definition of Damageability.......................................................................9 2.2.2 Drift and Damage Limits..........................................................................15 2.2.3 Codification of Serviceability Limit States...............................................17 2.3 Modeling and Analysis for Drift Design..........................................................18 2.3.1 Sources of Deformation............................................................................20 2.3.2 Modeling the Beam-Column Joint Region...............................................24 2.3.3 Connection Flexibility..............................................................................29 2.3.4 Composite Action.....................................................................................31 2.3.4.1 Floor Diaphragms.................................................................................33 2.3.5 Nonstructural Components.......................................................................35 2.3.5.1 Nonstructural Walls............................................................................36 2.3.5.2 Cladding..............................................................................................38 2.3.6 Foundation Stiffness Flexibility................................................................39 2.3.7 Second Order (P-Delta) Effects................................................................40 2.3.8 Structural Optimization....................................................................................42 2.4 Wind Loads.......................................................................................................43 2.4.1 Factors Affecting Design Wind Loads.....................................................44 2.4.1.1 Mean Recurrence Interval...................................................................44 2.4.1.2 Wind Velocity.....................................................................................48 2.4.1.3 Topography and Roughness of the Surrounding Terrain....................49 2.4.1.4 Wind Directionality............................................................................49 2.4.1.5 The Buildings Dynamic Characteristics.............................................50 2.4.1.6 Building Shape....................................................................................50 2.4.1.7 Shielding (Interference) Effects..........................................................50 2.4.2 Code Determined Wind Loads..................................................................51 2.4.3 Code Comparisons....................................................................................52 2.4.4 Wind Tunnel Testing................................................................................53 2.4.4.1 Rigid Pressure Model............................................................................55 2.4.4.2 Rigid High Frequency Force Balance Models......................................55 2.4.4.3 Aeroelastic Models...............................................................................56 iv 2.4.5 Database Assisted Design.........................................................................56 2.4.6 Computational Fluid Dynamics................................................................57 2.5 Building Response............................................................................................58 2.5.1 Methods of Measuring Response..............................................................59 2.5.1.1 Real Time Kinematic Global Positioning System (GPS).....................59 2.5.2 Boundary Layer Wind Tunnel vs. Full Scale Comparisons.....................59 2.5.2.1 High-rise Buildings...............................................................................61 2.5.2.2 Low-rise Buildings................................................................................65 2.6 Summary...........................................................................................................66 REFERENCES.............................................................................................................69 Chapter 3: Test Building Modeling and Analysis........................................................79 3.1 Overview...........................................................................................................79 3.2 Test Building: Structural System......................................................................79 3.2.1 Computer Software...................................................................................80 3.3 Lateral Loads....................................................................................................80 3.3.1 Wind Loads: Strength Design...................................................................81 3.3.2 Wind Loads: Serviceability Design..........................................................84 3.3.3 Loading Combinations..............................................................................86 3.4 Analytical Building Models..............................................................................87 3.4.1 Sources of Deformation............................................................................87 3.4.1.1 Displacement Participation Factors.......................................................90 3.4.2 P-Delta Effects..........................................................................................92 3.4.3 Beam Column Joint Modeling..................................................................94 3.4.4 Slab-Girder Interaction.............................................................................97 3.4.5 Live Loads for Analysis..........................................................................101 3.4.6 Nonstructural Components.....................................................................104 3.4.7 Recommended Model.............................................................................109 3.5 Summary and Conclusion...............................................................................113 REFERENCES...........................................................................................................116 Chapter 4: Sources of Deformation: An Analytical Study........................................117 4.1 Introduction.....................................................................................................117 4.2 Overview.........................................................................................................117 4.3 Method of Analysis.........................................................................................118 4.3.1 3-Story Frame Example..........................................................................124 4.3.2 Computer Software.................................................................................127 4.4 Description of Analysis...................................................................................127 4.5 Results of the Analysis....................................................................................128 4.5.1 Axial and Flexural Deformations............................................................130 4.5.2 Shear Deformations................................................................................130 4.5.3 Joint Deformations..................................................................................135 4.5.4 Member Contributions............................................................................136 4.6 Summary.........................................................................................................137 REFERENCES...........................................................................................................139 Chapter 5: Conclussions...............................................................................................140 5.1 Conclusions and Recommendations...............................................................140 5.1.1 Definition of Damage.............................................................................140 v 5.1.2 Basic Modeling and Analysis.................................................................141 5.1.3 Wind Loads.............................................................................................144 5.1.4 Building Response..................................................................................145 5.1.5 Wind Drift Design Survey......................................................................146 5.2 Final Recommendations..................................................................................146 REFERENCES...........................................................................................................149 Appendix A: Wind Drift Survey..................................................................................150 A.1 Overview.........................................................................................................150 A.2 Methods and Procedure...................................................................................151 A.3 Preliminary Results.........................................................................................153 A.4 ASCE Wind Drift Survey...............................................................................155 Instructions..............................................................................................................156 PART 1: General Drift and Perception of Motion Issues.......................................158 PART 2: Structural Analysis of Ten Story Building..............................................179 ASCE/SEI Wind Drift Survey Glossary.................................................................192 Appendix B: Results from the Analytical Models in Chapter 3...............................195 B.1 Introduction.....................................................................................................195 B.2 Results from 3.4.1 (Sources of Deformation).................................................195 B.3 Results from 3.4.2 (P-Delta Effects)...............................................................196 B.4 Results from 3.4.3 (Beam Column Joint Modeling).......................................197 B.5 Results from 3.4.4 (Slab-Girder Interaction)..................................................198 B.6 Results from 3.4.5 (Reduced Live Loads)......................................................199 B.7 Results from 3.4.6 (Nonstructural Components)............................................200 B.8 Results from 3.4.7 (The Recommended Model).............................................201 v i List of Figures Figure 2.1: Drift Measurements........................................................................................10 Figure 2.2: Drift Damageable Zone..................................................................................11 Figure 2.3: Drift Indices and Drift Damage Indices.........................................................12 Figure 2.4: Shear Strain Contours.....................................................................................14 Figure 2.5: Shear Strain vs. Damage Intensity.................................................................16 Figure 2.6: Typical Interior Sub-assemblage....................................................................20 Figure 2.7: Joint Rigidity..................................................................................................25 Figure 2.8: Common Analytical Joint Models..................................................................25 Figure 2.9: Krawinkler Model..........................................................................................26 Figure 2.10: Scissors Model.............................................................................................28 Figure 2.11: Girder Moment Regions...............................................................................31 Figure 2.12: Relative Diaphragm Stiffness.......................................................................34 Figure 2.13: Factors for Reduced MRI’s..........................................................................46 Figure 2.14 Wind Tunnel vs. Code Derived Wind Loads................................................54 Figure 3.1: Lateral Flexibility in the N-S Direction with Respect to Included Sources of Deformation....................................................................................................89 Figure 3.2: Lateral Flexibility in the E-W Direction with Respect to Included Sources of Deformation....................................................................................................90 Figure 3.3: Lateral Flexibility in the N-S Direction with Respect to P-Delta Effects......92 Figure 3.4: Lateral Flexibility in the E-W Direction with Respect to P-Delta Effects.....93 Figure 3.5: Lateral Flexibility in the E-W Direction with Respect to Joint Modeling.....97 Figure 3.6: Typical Composite Section Cross-section......................................................99 Figure 3.7: Model 4A Moment Diagrams.......................................................................100 Figure 3.8: Lateral Flexibility in the E-W Direction with Respect to Composite Action...........................................................................................................101 Figure 3.9: Lateral Flexibility in the N-S Direction with Respect to Survey-based Live Loads................................................................................................103 Figure 3.10: Lateral Flexibility in the E-W Direction with Respect to Survey-based Live Loads................................................................................................103 Figure 3.11: Lateral Flexibility in the N-S Direction with Respect to Nonstructural Components....................................................................................................................105 Figure 3.12: Lateral Flexibility in the E-W Direction with Respect to Nonstructural Components....................................................................................................................106 Figure 3.13: DDI vs. Interstory Drift Indices.................................................................107 Figure 3.14: Interstory Drift in the N-S Direction..........................................................108 Figure 3.15: Interstory Drift in the E-W Direction.........................................................109 Figure 3.16: Lateral Flexibility in the N-S Direction with Respect to the Recommended Model.....................................................................................................110 Figure 3.17: Lateral Flexibility in the E-W Direction with Respect to the Recommended Model.................................................................................................... 111 Figure 3.18: Moment Frame and X-Braced Frame.........................................................112 Figure 4.1: Five Story Planar Truss................................................................................118 Figure 4.2: 3-Story Planar Frame....................................................................................122 Figure 4.3: Modified (a) and Traditional (b) Girder Shear and Moment Distributions..122 vi i Figure 4.4: Modified (a) and Traditional (b) Column Shear and Moment Distributions123 Figure 4.5: Results Grouped by Number of Stories........................................................131 Figure 4.6: Results Grouped by Deformation Source.....................................................133 Figure 4.7: Comparison of Joint Deformation Sources..................................................136 Figure 4.8: Comparison of Member Contributions.........................................................137 Figure A.1: Site Map and Aerial Photograph................................................................184 Figure A.2: Typical Floor Plan (Roof Plan is Similar)..................................................185 Figure A.3: Moment Frame............................................................................................186 Figure A.4: Braced Frame #1..........................................................................................187 Figure A.5: Braced Frame #2..........................................................................................188 Figure A.6: Typical Gravity Frame................................................................................189 Figure A.7: Typical Moment Frame Connections..........................................................190 Figure A.8: Typical Braced Frame Connections............................................................191 Figure A9. Various Simple Joint Models......................................................................194 Figure A10. Various Mechanical Joint Models.............................................................194 vi ii List of Tables Table 2.1: Drift Indices and Drift Damage Indices...........................................................13 Table 2.2: Damage Limits for Several Types of Partition Walls......................................16 Table 2.3: Suggested Lateral Deflection Limits given in the Eurocode...........................18 Table 2.4: Factors for Reduced MRI’s.............................................................................46 Table 3.1: 50 Year Wind Loads in the N-S Direction......................................................83 Table 3.2: 50 Year Wind Loads in the E-W Direction.....................................................84 Table 3.3: 10 Year Wind Loads in the N-S Direction......................................................86 Table 3.4: 10 Year Wind Loads in the E-W Direction.....................................................86 Table 3.5: Modeling Parameters.......................................................................................88 Table 3.6: DPF’s for the N-S (Braced Frame) Direction.................................................91 Table 3.7: DPF’s for the E-W (Moment Frame) Direction..............................................91 Table 3.8: Modeling Parameters.......................................................................................92 Table 3.9: Modeling Parameters.......................................................................................96 Table 3.10: Composite Moments of Inertia......................................................................99 Table 3.11: Modeling Parameters...................................................................................100 Table 3.12: Modeling Parameters...................................................................................102 Table 3.13: Modeling Parameters...................................................................................105 Table 3.14: DDI vs. Interstory Drift Indices...................................................................107 Table 3.15: Modeling Parameters...................................................................................109 Table 3.16: DDI vs. Interstory Drift Index for the Bays of Figure 3.19.........................112 Table 4.1: Virtual Work Calculations for the Truss of Figure 4.1..................................120 Table 4.2: Virtual Work Calculations for the Frame of Figure 4.2................................126 Table 4.3: Summary of the Models.................................................................................127 Table 4.4: Analysis Summary.........................................................................................129 Table 4.5: Effect of Joint Modeling on Total Roof Drift................................................135 Table 4.6: Member Contributions...................................................................................136 Table B.1: Lateral Displacements in the N-S Direction.................................................195 Table B.2: Lateral Displacements in the E-W Direction................................................195 Table B.3: Modal Periods and Shapes............................................................................196 Table B.4: Lateral Displacements in the N-S Direction.................................................196 Table B.5: Lateral Displacements in the E-W Direction................................................196 Table B.6: Modal Periods and Shapes............................................................................197 Table B.7: Lateral Displacements in the N-S Direction.................................................197 Table B.8: Lateral Displacements in the E-W Direction................................................197 Table B.9: Modal Periods and Shapes............................................................................198 Table B.10: Lateral Displacements in the N-S Direction...............................................198 Table B.11: Lateral Displacements in the E-W Direction..............................................198 Table B.12: Modal Periods and Shapes..........................................................................199 Table B.13: Lateral Displacements in the N-S Direction...............................................199 Table B.14: Lateral Displacements in the E-W Direction..............................................199 Table B.15: Modal Periods and Shapes..........................................................................200 Table B.16: Lateral Displacements in the N-S Direction...............................................200 Table B.17: Lateral Displacements in the E-W Direction..............................................200 ix Table B.18: Modal Periods and Shapes..........................................................................201 Table B.19: Lateral Displacements in the N-S Direction...............................................201 Table B.20: Lateral Displacements in the E-W Direction..............................................201 Table B.21: Modal Periods and Shapes..........................................................................202 x