7020s Load Path

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LOADS AND LOAD PATHS IN BUILDINGS: Principles of Structural Design

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Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xix Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxiii Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxv Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxvii CHAPTER 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

1.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.2 Types of Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 1.3 Types of Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3.1 General Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3.2 Classification Based on Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3.3 Classification by Construction Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3.4 Classification by Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 1.3.5 Classification for Analytical Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 1.3.6 Classification for Design Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 1.3.7 Classification for Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 1.3.8 Classification by Use Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 1.3.9 Classification Based on Occupancy Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 1.3.10 Classification Based on the Load Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 1.4 Building Systems and Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 1.4.1 Roofs and Floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 1.4.2 Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 1.4.3 Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 1.4.4 Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 1.4.5 Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 1.4.6 Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 1.4.7 Thin Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 1.4.8 Folded Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 1.4.9 Curved Space Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 ix

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x LOADS AND LOAD PATHS IN BUILDINGS 1.4.10 Arches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 1.4.11 Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 1.4.12 Membranes, Tents, and Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36 1.5 Structural Idealization for Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 1.5.1 Idealization of Members and Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 1.5.2 Global Idealization of Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 1.6 Structural Design Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 1.6.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 1.6.2 Design Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 1.6.2.1 Design Methods Based on Elastic Behavior . . . . . . . . . . . . . . . . . . . . .46 1.6.2.2 Design Methods Based on Inelastic Behavior . . . . . . . . . . . . . . . . . . . .47 1.6.2.3 Differences Between Various Design Methods . . . . . . . . . . . . . . . . . . .49 1.7 Building Codes, Standards, and Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 1.7.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 1.7.2 Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 1.7.3 Model Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 1.7.4 Standards and Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 1.8 Computational Accuracy in Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 1.9 Units Used in Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 CHAPTER 2

Types of Loads and Load Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 2.2 Classification of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 2.2.1 Classification based on Directionality: Gravity and Lateral Loads . . . . . . . . . . . .64 2.2.2 Classification According to Structural Response . . . . . . . . . . . . . . . . . . . . . . . . .70 2.2.2.1 Dynamic Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 2.2.2.2 Resonant Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 2.2.2.3 Vibration Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 2.2.2.4 Impact Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 2.2.2.5 Blast Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 2.2.2.6 Sonic Booms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82 2.2.2.7 Collision Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 2.2.3 Classification by Applied Mechanics Approach: Body and Surface Forces . . . . .85 2.2.4 Classification by Nature of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89 2.2.4.1 Snow Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89 2.2.4.2 Rain or Water Loads and Ponding Loads . . . . . . . . . . . . . . . . . . . . . . .90 2.2.4.3 Ice Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90 2.2.4.4 Moving Loads and Pedestrian Loads . . . . . . . . . . . . . . . . . . . . . . . . . . .90 2.2.5 Classification by Type of Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 2.2.5.1 Settlement of Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 2.2.5.2 Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96 2.2.6 Classification According to Variability in Time . . . . . . . . . . . . . . . . . . . . . . . . . .97 2.2.7 Classification of Load Based on Statistical Methods Used to Establish Design Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97

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Contents

2.3

2.4 2.5

2.6

xi

2.2.8 Construction Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98 2.2.9 Miscellaneous Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102 2.2.10 Some Important Precautions for Design and Construction . . . . . . . . . . . . . . . . .102 2.2.11 Summary of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104 Concurrent Action of Several Loads—Load Combinations . . . . . . . . . . . . . . . . . . . . . .105 2.3.1 Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105 2.3.2 Code Requirements for Loads and Load Combinations . . . . . . . . . . . . . . . . . . .106 2.3.3 Load Combinations for LRFD or Strength Design . . . . . . . . . . . . . . . . . . . . . . .107 2.3.3.1 Basic Load Combinations (2000 IBC) . . . . . . . . . . . . . . . . . . . . . . . . .108 2.3.3.2 Load Combinations for Concrete Structures . . . . . . . . . . . . . . . . . . . .112 2.3.3.3 Load Combination Equations in ASCE 7-98 . . . . . . . . . . . . . . . . . . . .113 2.3.3.4 LRFD Load Combinations Equations in 97 UBC . . . . . . . . . . . . . . . .114 2.3.4 Load Combinations for Allowable Stress or Service Load Design . . . . . . . . . . .116 2.3.4.1 Basic Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116 2.3.4.2 Alternate Basic Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . .120 2.3.4.3 Other Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121 2.3.4.4 Special Seismic Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . .121 2.3.5 Loads Not included in Code-Load Combinations— Abnormal or Extraordinary Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122 2.3.6 Other Load Combination Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123 2.3.7 Loading for Maximum Load Effects in Continuous Structures . . . . . . . . . . . . . .124 2.3.8 Load Combinations: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127 Building Components: Terminology and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . .127 The Load Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133 2.5.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133 2.5.2 Importance of Identification of Correct Load Path— The Hyatt Regency Hotel, Kansas City, Missouri, Disaster . . . . . . . . . . . . . . . .137 2.5.3 Load Paths in a Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144 2.5.4 Load Path for Gravity Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145 2.5.4.1 Load Path in Conventional Buildings (Beams-and-Column Frames) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145 2.5.4.2 Load Path in Nonconventional Buildings . . . . . . . . . . . . . . . . . . . . . .150 2.5.5 Load Path for Lateral Loads: The Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150 2.5.6 Types of Lateral Force Resisting Systems (LFRS) . . . . . . . . . . . . . . . . . . . . . . .153 2.5.7 Horizontal Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153 2.5.8 Vertical Elements of LFRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157 2.5.8.1 Classification of Vertical LFRS Based on Structural Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157 2.5.9 Lateral Force Resisting Systems for Tall Buildings . . . . . . . . . . . . . . . . . . . . . .169 Load Carried by Structural Members: The Influence Area, Tributary Area, and Effective Area Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172 2.6.1 Tributary Areas for Beams, Girders, and Columns . . . . . . . . . . . . . . . . . . . . . . .174 2.6.2 Tributary Areas for Walls, Pitched Roofs, and Roof Trusses . . . . . . . . . . . . . . .183 2.6.3 Summary of Load Paths and Tributary Areas . . . . . . . . . . . . . . . . . . . . . . . . . .188

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xii LOADS AND LOAD PATHS IN BUILDINGS 2.7 Building Failure Modes Due to Lateral Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188 2.8 Multiprotection Design of Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191 CHAPTER 3

Gravity Loads—Their Load Paths and Distribution . . . . . . . . . . . . . . . . . . . .199

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .199 3.2 Dead Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .199 3.2.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .199 3.2.2 Determination of Dead Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200 3.2.3 Variations in Calculation of Dead Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203 3.2.4 Consequences of Dead Load Underestimation . . . . . . . . . . . . . . . . . . . . . . . . . .203 3.3 Live loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205 3.3.1 Nature of Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205 3.3.2 Magnitude of Floor Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205 3.3.3 Partition Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206 3.3.4 Live Load for Parking Structures, and Truck and Bus Garages . . . . . . . . . . . . .213 3.3.5 Live Load Surveys and Statistical Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . .216 3.3.6 Reduction in Floor Live Load: The Concept and Methods . . . . . . . . . . . . . . . . .218 3.3.7 IBC and UBC Floor Live Load Reduction Methods . . . . . . . . . . . . . . . . . . . . . .220 3.3.8 Special Considerations for Live Load Reduction for Floor Members . . . . . . . . .224 3.3.9 A Comparison of Live Load Reduction Methods . . . . . . . . . . . . . . . . . . . . . . . .225 3.3.10 Loads on Girders Supporting Closely-Spaced Floor Beams . . . . . . . . . . . . . . . .227 3.3.11 Critical Distribution of Floor Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227 3.3.12 Examples: Floor Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228 3.4 Roof Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245 3.4.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245 3.4.2 IBC Provisions for Roof Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .247 3.4.3 UBC Provisions for Roof Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248 3.4.4 Critical Distribution of Roof Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248 3.4.5 Live Loads on Special Purpose Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .249 3.4.6 Examples: Roof Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .249 3.5 Gravity Loads on Columns of Multistory Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . .253 3.6 Roof Drainage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283 3.6.1 The Ponding Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283 3.6.2 Design Rain Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283 3.7 Moving and Vibratory Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284 3.7.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284 3.7.2 Impact Forces Due to Elevators and Machinery . . . . . . . . . . . . . . . . . . . . . . . . .285 3.7.3 Crane Live Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285 3.8 Loads for Heliports and Helistops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286 3.9 Gravity Loads and Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .287 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .292

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Contents

CHAPTER 4

xiii

Snow, Ice, and Temperature-Induced Loads . . . . . . . . . . . . . . . . . . . . . . . . .295

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .295 4.2 Snow Load vs Roof Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298 4.3 Magnitude of Snow Load: ASCE 7-98 Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298 4.3.1 Ground Snow Load Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298 4.3.2 Design Snow Load on Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302 4.3.2.1 Flat-Roof Snow Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .304 4.3.2.2 Minimum Values of pf for Low-Slope Roofs . . . . . . . . . . . . . . . . . . . .304 4.3.2.3 Sloped-Roof Snow Loads, ps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .305 4.3.2.4 Roof Slope Factor for Curved Roofs . . . . . . . . . . . . . . . . . . . . . . . . . .305 4.3.2.5 Roof Slope Factor for Multiple Folded Plate, Saw-Tooth, and Barrel Vault Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .305 4.4 Partial Snow Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .306 4.5 Unbalanced Snow Load (ASCE 7-98) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309 4.5.1 Hip and Gable Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309 4.5.2 Curved Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310 4.5.3 Multiple Folded Plate, Saw-Tooth, and Barrel Vault Roofs . . . . . . . . . . . . . . . .310 4.5.4 Dome Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310 4.6 Drifts on Lower Roofs: Aerodynamic Shade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311 4.6.1 Snowdrift Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311 4.6.2 Determination of Loads Due to Snowdrift on Lower Roofs . . . . . . . . . . . . . . . .313 4.6.3 Determination of Snowdrift Due to Adjacent Structures and Terrain . . . . . . . . .318 4.6.4 Determination of Snowdrift Due to Roof Projections . . . . . . . . . . . . . . . . . . . . .318 4.7 Sliding Snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319 4.8 Rain on Snow Surcharge Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319 4.9 Snow Load Provisions in the 97 UBC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319 4.9.1 Design Snow load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319 4.9.2 Determination of Snow Load according to 97 UBC Appendix Chapter 16 Division I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320 4.9.3 Reduction in Ground Snow Load Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . .324 4.10 Load Factor for Snow Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .325 4.11 Load Path for Snow Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326 4.12 Unbalanced Snow Load (97 UBC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .328 4.12.1 Gable Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .328 4.12.2 Curved Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .334 4.13 Drift Loads on Lower Roofs, Decks, and Roof Projections . . . . . . . . . . . . . . . . . . . . . .334 4.13.1 Drift Loads for Lower Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .334 4.13.2 Snowdrift Loads on Roof of an Adjacent Lower Structure . . . . . . . . . . . . . . . . .338 4.13.3 Snow Load Due to Sliding Snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .338 4.13.4 Snow Drift on Roof Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .338 4.13.5 Intersection Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .338 4.13.6 Special Eave Requirements for Snow Load . . . . . . . . . . . . . . . . . . . . . . . . . . . .339

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xiv LOADS AND LOAD PATHS IN BUILDINGS 4.14 Ponding Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 4.14.1 Ponding Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 4.14.2 Ponding Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342 4.15 Ice Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342 4.15.1 Ice-Forming Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342 4.15.2 Ice Accretions and Their Effects on Structures . . . . . . . . . . . . . . . . . . . . . . . . .343 4.15.3 Design Ice Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .344 4.16 Temperature-Induced Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .345 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .352 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .354 CHAPTER 5

Wind-Induced Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .357

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .357 5.2 Wind Effects on Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .358 5.2.1 Wind Damage to Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .358 5.2.2 Damage Due to Hurricanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .362 5.2.3 Damage Due to Tornadoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .364 5.2.4 Wind-Related Serviceability Criteria for Tall Buildings . . . . . . . . . . . . . . . . . . .369 5.2.5 Wind Speeds and Pedestrian Comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .369 5.3 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .371 5.4 The Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .376 5.5 The Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .377 5.6 Wind Action in Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .378 5.7 Measurement of Wind Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .379 5.8 Variation in Wind Velocity with Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .385 5.9 Engineering Description of Wind Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .389 5.9.1 Wind Speed Defined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .389 5.9.2 Basic or Design Wind Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .390 5.9.3 Averaging Time and Wind Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .391 5.9.4 Relationship Between the Hourly Mean Speed and the 3-Second Gust Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .396 5.10 Wind Loading Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .399 5.10.1 Basic Wind Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .399 5.10.2 Wind-Induced Pressure on Buildings and Other Structures . . . . . . . . . . . . . . . .399 5.10.3 Exposure Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .407 5.10.3.1 ASCE 7-98 Exposure Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . .407 5.10.3.2 97 UBC Exposure Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .408 5.10.4 Effect of Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .412 5.10.5 Wind-Structure Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .412 5.11 Wind Loads and Structural Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .420 5.11.1 General Design Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .420 5.11.2 Design for Combined Loading Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421

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5.12 Calculation of Wind Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421 5.12.1 ASCE 7 Classification of Buildings and Other Structures . . . . . . . . . . . . . . . . .421 5.12.2 ASCE 7-98 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422 5.12.3 Effective Wind Area Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .426 5.12.4 The UBC Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .459 5.13 Wind Pressure Calculations by the UBC Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .468 5.13.1 Step-by-Step Procedure for Wind Pressure Calculations . . . . . . . . . . . . . . . . . .468 5.13.2 Discussion of Cq Coefficients (Shape Factor) . . . . . . . . . . . . . . . . . . . . . . . . . .469 5.13.3 Wind Loads on Primary Frames and Systems . . . . . . . . . . . . . . . . . . . . . . . . . .474 5.14 Diaphragm Loads Due to Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477 5.14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477 5.14.2 Analysis of Flexible Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477 5.14.3 Tributary Wall Height for Loads on Horizontal Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .480 5.14.4 Diaphragm Forces in Transverse and Longitudinal Directions . . . . . . . . . . . . . .480 5.15 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .481 5.16 Wind Pressures on Nonbuilding Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .507 5.17 Dynamic Effects of Wind on Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .510 5.18 Wind Tunnel Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .511 5.18.1 Purpose of Wind Tunnel Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .511 5.18.2 Types of Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .511 5.18.3 Model Test Results and Their Application to Prototypes . . . . . . . . . . . . . . . . . .513 5.18.4 Types of Model Tests for Buildings and Other Structures . . . . . . . . . . . . . . . . .514 5.19 Wind Pressures for Tornado Resistant Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .515 5.19.1 Design Wind Speeds for Tornadoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .515 5.19.2 Wind Loads Due to Tornadic Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .515 5.20 Bracing of Structures to Resist Wind Loads During Erection and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .520 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .521 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .522 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530 CHAPTER 6

Earthquake-Induced Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .535

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .535 6.2 The Earthquake Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .537 6.2.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .537 6.2.2 Effects of Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .542 6.2.2.1 Primary Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .542 6.2.2.2 Secondary Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .543 6.3 Causes of Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .544 6.3.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .544

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LOADS AND LOAD PATHS IN BUILDINGS

6.3.2 6.3.3

6.4

6.5

6.6 6.7

6.8

The Structure of Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .545 Theories of Earthquake Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .545 6.3.3.1 Dilational Source Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .545 6.3.3.2 Elastic Rebound Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .547 Earthquake Faults, Seismic Energy, and Ground Motion . . . . . . . . . . . . . . . . . . . . . . . .552 6.4.1 Types of Earthquake Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .552 6.4.2 Types of Seismic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .554 6.4.2.1 Body Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .555 6.4.2.2 Surface Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .556 6.4.3 Classification of Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .557 6.4.4 Characteristics of Seismic Ground Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .557 Measurement of Earthquake Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .557 6.5.1 Intensity Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .558 6.5.2 Magnitude Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .560 6.5.2.1 The Richter Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .560 6.5.2.2 Surface Wave, Body Wave, and Moment Magnitude . . . . . . . . . . . . .562 6.5.3 Qualitative Description of Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .566 6.5.4 Instrumentation for Earthquake Measurements . . . . . . . . . . . . . . . . . . . . . . . . .566 Effects of Seismic Vibrations on Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .567 Determination of Seismic Forces on a Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .573 6.7.1 Nature of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .573 6.7.2 Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .573 6.7.3 Methods of Determining Earthquake-Induced Forces . . . . . . . . . . . . . . . . . . . . .574 6.7.3.1 Applicability of Equivalent Static Force Procedure . . . . . . . . . . . . . . .574 6.7.3.2 Applicability of Dynamic Analysis Procedures . . . . . . . . . . . . . . . . . .576 6.7.3.3 Lateral Force Resisting Systems and Paths for Seismic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .577 The Equivalent Static Force Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .577 6.8.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .577 6.8.2 Seismic Zones: Regional Seismicity and Seismic Risk . . . . . . . . . . . . . . . . . . . .578 6.8.3 Geotechnical Considerations: Soil Profile Types . . . . . . . . . . . . . . . . . . . . . . . .579 6.8.4 Ground Response Coefficients Ca and Cv . . . . . . . . . . . . . . . . . . . . . . . . . . . . .581 6.8.5 Fundamental Period of the Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .582 6.8.6 Design Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .594 6.8.7 Seismic Sources and Near-Source Factors Na and Nv . . . . . . . . . . . . . . . . . . . . .599 6.8.8 Occupancy Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .602 6.8.9 Occupancy Importance Factor, I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .603 6.8.10 Structure Response Modification Coefficient R . . . . . . . . . . . . . . . . . . . . . . . . .604 6.8.11 Lateral Force Resisting Systems in Buildings . . . . . . . . . . . . . . . . . . . . . . . . . .605 6.8.12 Overstrength Factor o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .607 6.8.13 Reliability/Redundancy Factor  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .609 6.8.14 Drift Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .612 6.8.15 Seismic Load Provisions of the 97 UBC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .617

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Contents

6.9 6.10

6.11 6.12 6.13 6.14 6.15

6.16

6.17

6.18 6.19

6.20

xvii

6.8.16 Minimum Earthquake Loads for Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .618 6.8.17 Design Base Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .618 6.8.18 Seismic Response Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .620 Simplified Static Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .622 Distribution of Base Shear over the Height of a Building . . . . . . . . . . . . . . . . . . . . . . . .627 6.10.1 Story Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .627 6.10.2 Overturning Moments (OTM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .633 Vertical Component of Earthquake Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .634 Horizontal Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .635 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .636 Transfer of Seismic Forces from Vertical LFRS to Ground—The Load Path . . . . . . . . .659 System Response Modification Factor (R) for Bearing Wall and Dual Systems . . . . . . .660 6.15.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .660 6.15.2 R-Values for Combinations of Structural Systems . . . . . . . . . . . . . . . . . . . . . . .662 6.15.3 R-Values for Undefined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .665 Irregular Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .667 6.16.1 Building Irregularities and their Significance to Performance under Loads . . . .667 6.16.2 Vertical Irregularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .669 6.16.3 Plan Irregularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .670 Seismic Loads on Elements of Structures, Nonstructural Components, and Equipment Supported by Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .675 6.17.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .675 6.17.2 Determination of Out-of-Plane Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .677 6.17.2.1 Magnitude of Fp-Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .677 6.17.2.2 Anchorage of Elements and Components to Structure . . . . . . . . . . . . .684 Performance-Based Design Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .696 Dynamic Analysis Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .702 6.19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .702 6.19.2 Need for Dynamic Analysis of a Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . .702 6.19.3 Rationale for Mathematical Model of a Building for Dynamic Analysis . . . . . .704 6.19.4 Principles of Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .707 6.19.5 Analysis of Single Degree of Freedom Systems . . . . . . . . . . . . . . . . . . . . . . . . .707 6.19.5.1 Undamped Free Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .707 6.19.5.2 Damped Free Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .713 6.19.5.3 Undamped Force Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .725 Methods of Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .730 6.20.1 Response Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .730 6.20.1.1 Response Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .730 6.20.1.2 Accelerograms and Construction of Response Spectra . . . . . . . . . . . .739 6.20.1.3 Response History: Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . .741 6.20.1.4 Response Spectrum Characteristics and Tripartite Response Spectra . .750

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xviii LOADS AND LOAD PATHS IN BUILDINGS 6.20.1.5 Design Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .753 6.20.1.6 Site-Dependent Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . .758 6.20.1.7 Influence of Other Parameters on Response Spectra . . . . . . . . . . . . . .759 6.20.2 Time-History Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .761 6.20.3 Pushover Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .762 6.21 Nonbuilding Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .762 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .767 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .776 APPENDIX A

Statistics on Selected Tall Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .781

APPENDIX B

Design Tables and Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .787

APPENDIX C

Equations for the Pressure Coefficient (GCP) . . . . . . . . . . . . . . . . . . . . . . . .801

APPENDIX D

Seismic Zones of the World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .809

APPENDIX E

Values of Coefficient Ct and the Reduction Factor [0.2  (De/hn)2] . . . . . . .815

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .821 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .849 Permissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .859

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CHAPTER 3: Gravity Loads: Their Load Paths and Distribution

239

simple and straightforward. However, in multistory buildings, certain floor areas may often be set aside for elevator shafts—no floor beams or girders can be placed in these areas. Such a layout results in some floor members having to support loads from floor areas that are not symmetrical with floor members’ position in the floor plan. Calculations for tributary areas, live load reduction, and member loads in such cases call for special attention to member layout. Example 3.7 presents just such a case. Example 3.7 The floor framing plan of a school building is shown in Figure E3.7a. Assuming that the floor consists of a 4-in.-thick reinforced concrete slab, and the dead load due to mechanical and electrical utilities, etc., is 10 lb/ft2, and assuming that columns receive loads from one level only, calculate design loads on all beams, girders, and columns.

9 at 10 ft = 90 ft

20 ft

B1

B1

B1

B1 C1

G1

B1

B1

B1 C2

G2

B1 G3

Open

20 ft

B1

B1

B2

B3

B4

Open

10 ft

G4

B3

B2

15 ft

FIGURE E3.7A Floor framing plan.

Solution: Commentary: Attention should be paid to determining the load path for gravity loads on members positioned around the space for the elevator shafts. Note that B4-beam is supported on G4-girder, which in turn is supported on two B2-beams. Each B2-beam is supported on a column and a bearing wall. Dead load: Unit weight of reinforced concrete  150 lb/ft3 Load due to 4 in. slab  (4/12)(1 ft)(1 ft)(150)  50 lb/ft2 Mechanical and electrical utilities  10 lb/ft2 D  50  10  60 lb/ft2 Live load: Floor live load: Lo  40 lb/ft2 (Table B3, Appendix B) Tributary widths and areas for various beams and girders are shown in Figure E3.7b.

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CHAPTER 3: Gravity Loads: Their Load Paths and Distribution

1

2

3

4

5

10

11

12

12 at 16 ft = 192 ft

A1

A

A3

B

B2

4 at 25 ft = 100 ft

C

C1

D

E 16 ft typ.

Glazed wall panel

FIGURE E3.10B Floor framing plan for the example building.

1

2

3

4

5

10

11

12

12 at 16 f t = 192 ft A

A1

A3

B

B2

4 at 25 ft = 100 ft

t C

C1

D

E Glazed wall panel

FIGURE E3.10C Tributary areas for various typical columns.

16 ft typ.

255

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CHAPTER 5: Wind-Induced Loads

437

Equation 5.38 is valid for rigid structures. For flexible open buildings and other structures, the design wind force on open buildings and other structures is determined from Equation 5.39: F  qz Gf Cf Af

(5.39)

where the net force coefficient, Gf, is defined by Equation 5.22. Note that Equations 5.38 and 5.39 give values of the force due to wind rather than pressure due to wind as given by Equations 5.33–5.37. Application of above equations is illustrated by the following examples. Although the analytical procedure imposes none of the restrictions of the simplified procedure, it does have its limitations. Refer to ASCE 7-98 Commentary Sect. 6.5 for a discussion of this topic. Example 5.6 illustrates use of the analytical procedure for the building of Example 5.5. Examples 5.7 and 5.8 illustrate calculations for the gust effect factors G and Gf for the MWFRS of a regular and a flexible building, respectively. Example 5.6 Analytical Procedure A building of rectangular configuration measures 64 ft x 32 ft x 16 ft high (Figure E5.6a). It consists of concrete masonry block (CMU) walls on three sides and a steel structure in front with glass. The roof, which also acts as a diaphragm, is flat and consists of joists spanning 32 ft and spaced at 4 ft on center, with roof panels 2 ft wide and 16 ft long. The building is located in Exposure C terrain that has 3-second gust speed of 100 mph. Determine wind pressures for the main wind-force resisting system (MWFRS) and components and cladding (C&C). Solution: 1. Velocity pressure, q: The velocity pressure is determined from Equation 5.15 (ASCE 7-98, Equation 6-13): p  0.00256KzKztKdV2I

(a)

Roof panels 2 x 16 ft CMU wall

Open web joist

16 ft

64 ft 32 ft

FIGURE E5.6A Building for Example 5.6.

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The internal pressure coefficient, 0.18 or 0.18, will be used as appropriate to give the most critical pressure. The wind pressures on joists are Zone 3: p  (18.7)[(2.8)  (0.18)]  55.7 lb/ft2 Zone 2: p  (18.7)[(1.8)  (0.18)]  37.0 lb/ft2 Zone 1: p  (18.7)[(1.0)  (0.18)]  22.1 lb/ft2 Zones 1, 2, and 3: p  (18.7)[(0.3)  (0.18)]  9.0 lb/ft2 The width a of zones 2 and 3 remains the same as before: a  3.2 ft Example 5.7 Calculation of the gust effect factor, G, for the building of Example 5.6. Determine the gust effect factor for the building of Example 5.6. Solution: For rigid structures, the gust effect factor, G, is given by Equation 5.18:  (1 + 1.7gQ Iz Q  G = 0.925   1 + 1.7gv Iz 

(a)

where I z  intensity of turbulence at height z and given by Equation 5.19:  Iz = c(33 / z )1/ 6

(b)

Q in Equation (a) is given by Equation 5.20: Q=

1  B + h 1 + 0.63   Lz 

0.63

Lz = l( z / 33)ε

(c)

(d)

Values of various quantities in Equation (d) are obtained from ASCE Table 6-4 for Exposure C, as follows: z  zmin  15 ft, l  500 ft, c  0.2. Thus, Lz = l( z / 33)ε = 500(15 / 33)1/ 5.0 = 427 ft Iz = c(33 / z )1/ 6 = 0.2(33 / 15)1/ 6 = 0.228

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654

LOADS AND LOAD PATHS IN BUILDINGS

Commentary: The increase in the base shear by 51.6% is the result of (a) change in the type of occupancy—from special occupancy (I  1.0) to essential facility (I  1.25)—and (b) change in the type of building system—from SMRF (R  8.5) to a steel EBF (R  7.0). Together, the two changes account for increase in the base shear by   (8.5)(1.25) − 1 = 1.518 − 1.0 = 0.518 or 51.8%    ( 7.0)(1.0) The change in base shear in this problem is not affected by the change in the fundamental period, T  0.66 sec for the steel SMRF versus 0.564 sec for the steel EBF. Example 6.13 Vertical shear distribution for a seven-story building Figure E6.13a shows the plan and elevation of a seven-story reinforced concrete office building located in Seismic Zone 4, approximately 3 miles from a Seismic Source Type A. The soil conditions for the building site are not yet known. The building has a complete vertical load resisting frame. The lateral seismic forces are resisted by special moment resisting concrete frames in the E-W direction and by concrete shear walls in the N-S direction. Calculate the Fx-forces at various levels of this building. Dead and live loads acting on the roof and floors of the building have been averaged/estimated on a per square foot area basis as follows: Roof loading: Roofing and insulation Ceiling Mechanical and electrical Miscellaneous Framing (including SMRF members) Partitions (for seismic load only) Shear walls (average weight) Live load (reducible)

psf 7.0 3.0 2.0 1.0 137.0 5.0 8.0 20.0

Floor loading: Floor finish Ceiling Mechanical and electrical Miscellaneous Framing (includes SMRF members)

psf 1.0 3.0 2.0 1.0 143.0

Partitions (for seismic only)

10.0

Shear walls (average weight)

16.0

Live load (reducible)

50.0

Curtain wall (average weight of wall per square foot of wall area)

15.0